Handbook of Macroeconomics, Part 3

INTRODUCTION

TO THE SERIES

The aim of the Handbooks in Economics series is to produce Handbooks for various branches of economics, each of which is a definitive source, reference, and teaching supplement for use by professional researchers and advanced graduate students. Each Handbook provides self-contained surveys of the current state of a branch of economics in the form of chapters prepared by leading specialists on various aspects of this branch of economics. These surveys summarize not only received results but also newer developments, from recent journal articles and discussion papers. Some original material is also included, but the main goal is to provide comprehensive and accessible surveys. The Handbooks are intended to provide not only useful reference volumes for professional collections but also possible supplementary readings for advanced courses for graduate students in economics. KENNETH J. ARROW and MICHAEL D. INTRILIGATOR

PUBLISHER'S

NOTE

For a complete overview of the Handbooks in Economics Series, please refer to the listing at the end of this volume.

CONTENTS OF THE HANDBOOK

VOLUME 1A PART 1 - E M P I R I C A L A N D H I S T O R I C A L P E R F O R M A N C E

Chapter 1 Business Cycle Fluctuations in US Macroeconomic Time Series JAMES H. STOCK and MARK W WATSON

Chapter 2 Monetary Policy Shocks: What Have we Learned and to What End? LAWRENCE J. CHRISTIANO, MARTIN EICHENBAUM and CHARLES L. EVANS

Chapter 3 Monetary Policy Regimes and Economic Performance: The Historical Record MICHAEL D. BORDO AND ANNA J. SCHWARTZ

Chapter 4 The New Empirics of Economic Growth STEVEN N. DURLAUF and DANNY T. QUAH PART 2 - M E T H O D S O F D Y N A M I C A N A L Y S I S

Chapter 5 Numerical Solution of Dynamic Economic Models MANUEL S. SANTOS

Chapter 6 Indeterminacy and Sunspots in Macroeconomics JESS BENHABIB and ROGER E.A. FARMER

Chapter 7 Learning Dynamics GEORGE W. EVANS and SEPPO HONKAPOHJA

Chapter 8 Micro Data and General Equilibrium Models MARTIN BROWNING, LARS PETER HANSEN and JAMES J. HECKMAN

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viii PART 3 - M O D E L S O F E C O N O M I C G R O W T H

Chapter 9 Neoclassical Growth Theory ROBERT M. SOLOW

Chapter 10 Explaining Cross-Country Income Differences ELLEN R. McGRATTAN and JAMES A. SCHMITZ, Jr.

VOLUME 1B PART 4 - C O N S U M P T I O N A N D I N V E S T M E N T

Chapter 11 Consumption ORAZIO R ATTANASIO

Chapter 12 Aggregate Investment RICARDO J. CABALLERO

Chapter 13 Inventories VALERIE A. RAMEY and KE;NNETH D. WEST PART 5 - M O D E L S O F E C O N O M I C F L U C T U A T I O N S

Chapter 14 Resuscitating Real Business Cycles ROBERT G. KING AND SERG10 T. REBELO

Chapter 15 Staggered Price and Wage Setting in Macroeconomics JOHN B. TAYLOR

Chapter 16 The Cyclical Behavior of Prices and Costs JULIO J. ROTEMBERG and MICHAEL WOODFORD

Chapter 17 Labor-Market Frictions and Employment Fluctuations ROBERT E. HALL

Chapter 18 Job Reallocation, Employmant Fluctuations and Unemployment DALE T. MORTENSEN and CHRISTOPHER A. PISSARIDES

Contents of the Handbook

Contents of the Handbook

VOLUME 1C PART 6 - F I N A N C I A L M A R K E T S A N D T H E M A C R O E C O N O M Y

Chapter 19 Asset Prices, Consumption, and the Business Cycle JOHN Y. CAMPBELL

Chapter 20 Human Behavior and the Efficiency of the Financial System ROBERT J. SHILLER

Chapter 21 The Financial Accelerator in a Quantitative Business Cycle Framework BEN S. BERNANKE, MARK GERTLER and SIMON G1LCHRIST PART 7 - M O N E T A R Y A N D F I S C A L P O L I C Y

Chapter 22 Political Economics and Macroeconomic Policy TORSTEN PERSSON and GUIDO TABELLINI

Chapter 23 Issues in the Design of Monetary Policy Rules BENNETT T. McCALLUM

Chapter 24 Inflation Stabilization and BOP Crises in Developing Countries GUILLERMO A. CALVO and CARLOS A. VI~GH

Chapter 25 Government Debt DOUGLAS W ELMENDORF AND N. GREGORY MANKIW

Chapter 26 Optimal Fiscal and Monetary Policy V.V CHARI and PATRICK J. KEHOE

ix

PREFACE TO THE HANDBOOK

Purpose The Handbook of Macroeconomics aims to provide a survey of the state of knowledge in the broad area that includes the theories and facts of economic growth and economic fluctuations, as well as the consequences of monetary and fiscal policies for general economic conditions.

Progress in Macroeconomics Macroeconomic issues are central concerns in economics. Hence it is surprising that (with the exception of the subset of these topics addressed in the Handbook of Monetary Economics) no review of this area has been undertaken in the Handbook of Economics series until now. Surprising or not, we find that now is an especially auspicious time to present such a review of the field. Macroeconomics underwent a revolution in the 1970's and 1980's, due to the introduction of the methods of rational expectations, dynamic optimization, and general equilibrium analysis into macroeconomic models, to the development of new theories of economic fluctuations, and to the introduction of sophisticated methods for the analysis of economic time series. These developments were both important and exciting. However, the rapid change in methods and theories led to considerable disagreement, especially in the 1980's, as to whether there was any core of common beliefs, even about the defining problems of the subject, that united macroeconomists any longer. The 1990's have also been exciting, but for a different reason. In our view, the modern methods of analysis have progressed to the point where they are now much better able to address practical or substantive macroeconomic questions - whether traditional, new, empirical, or policy-related. Indeed, we find that it is no longer necessary to choose between more powerful methods and practical policy concerns. We believe that both the progress and the focus on substantive problems has led to a situation in macroeconomics where the area of common ground is considerable, though we cannot yet announce a "new synthesis" that could be endorsed by most scholars working in the field. For this reason, we have organized this Handbook around substantive macroeconomic problems, and not around alternative methodological approaches or schools of thought.

xi

xii

Prefiwe

The extent to which the field has changed over the past decade is considerable, and we think that there is a great need for the survey of the current state ofmacroeconomics that we and the other contributors to this book have attempted here. We hope that the Handbook of Macroeconomics will be useful as a teaching supplement in graduate courses in the field, and also as a reference that will assist researchers in one area of macroeconomics to become better acquainted with developments in other branches of the field. Overview

The Handbook of" Macroeconomics includes 26 chapters, arranged into seven parts. Part 1 reviews evidence on the Empirical and Historical PerJbrmance of the aggregate economy, to provide factual background for tile modeling efforts and policy discussion of the remaining chapters. It includes evidence on the character of business fluctuations, on long-run economic growth and the persistence of crosscountry differences in income levels, and on economic performance under alternative policy regimes. Part 2 on Methods of Dynamic Analysis treats several technical issues that arise in the study of economic models which are dynamic and in which agents' expectations about the future are critical to equilibrium determination. These include methods for the calibration and computation of models with intertemporal equilibria, the analysis of the determinacy of equilibria, and the use of "learning" dynamics to consider the stability of such equilibria. These topics are important for economic theory in general, and some are also treated in the Handbook of Mathematical Economics, The Handbook of Econometrics, and the Handbook of Computational Economics, for example, from a somewhat different perspective. Here we emphasize results - such as the problems associated with the calibration of general equilibrium models using microeconomic studies - that have particular application to macroeconomic models. The Handbook then turns to a review of theoretical models of macroeconomic phenomena. Part 3 reviews Models" of Economic Growth, including both the determinants of long-run levels of income per capita and the sources of cross-country income differences. Both "neoclassical" and "endogenous" theories of growth are discussed. Part 4 treats models of Consumption and Investment demand, from the point of view of intertemporal optimization. Part 5 covers Models" of Economic Fluctuations. In the chapters in this part we see a common approach to model formulation and testing, emphasizing intertemporal optimization, quantitative general equilibrium modeling, and the systematic comparison of model predictions with economic time series. This common approach allows for consideration of a variety of views about the ultimate sources of economic fluctuations and of the efficiency of the market mechanisms that amplify and propagate them. Part 6 treats Financial Markets and the Macroeconomy. The chapters in this part consider the relation between financial market developments and aggregate economic

Preface

xiii

activity, both from the point of view of how business fluctuations affect financial markets, and how financial market disturbances affect overall economic activity. These chapters also delve into the question of whether financial market behavior can be understood in terms of the postulates of rational expectations and intertemporal optimization that are used so extensively in modern macroeconomics-an issue of fundamental importance to our subject that can be, and has been, subject to special scrutiny kn the area of financial economics because of the unusual quality of available data. Finally, Part 7 reviews a number of Monetary and Fiscal Policy issues. Here we consider both the positive theory (or political economics) of government policymaking and the normative theory. Both the nature of ideal (or second-best) outcomes according to economic theory and the choice of simple rules that may offer practical guidance for policymakers are discussed. Lessons from economic theory and from experience with alternative policy regimes are reviewed. None of the chapters in this part focus entirely on international, or open economy, macroeconomic policies, because many such issues are addressed in the Handbook of International Economics. Nevertheless, open-economy issues cannot be separated from closed-economy issues as the analysis of disinflation policies and currency crises in this part of the Handbook of Macroeconomics, or the analysis of policy regimes in the Part I of the Handbook of Macroeconomics make clear.

Acknowledgements Our use of the pronoun "we" in this preface should not, of course, be taken to suggest that much, if any, of the credit for what is useful in these volumes is due to the Handbook's editors. We wish to acknowledge the tremendous debt we owe to the authors of the chapters in this Handbook, who not only prepared the individual chapters, but also provided us with much useful advice about the organization of the overall project. We are grateful for their efforts and for their patience with our slow progress toward completion of the Handbook. We hope that they will find that the final product justifies their efforts. We also wish to thank the Federal Reserve Bank of New York, the Federal Reserve Bank of San Francisco, and the Center for Economic Policy Research at Stanford University for financial support for two conferences on "Recent Developments in Macroeconomics" at which drafts of the Handbook chapters were presented and discussed, and especially to Jack Beebe and Rick Mishkin who made these two useful conferences happen. The deadlines, feedback, and commentary at these conferences were essential to the successful completion of the Handbook. We also would like to thank Jean Koentop for managing the manuscript as it neared completion. Stanford, California Princeton, New Jersey

John B. Taylor Michael Woodford

Chapter 19

A S S E T PRICES, C O N S U M P T I O N , A N D THE BUSINESS CYCLE * JOHN Y. CAMPBELL Harvard University and NBER. Department of Economics, Littauer Center, Harvard University, Cambridge, MA 02138, USA

Contents Abstract Keywords 1. Introduction 2. International asset market data 3. The equity p r e m i u m puzzle 3.1. The stochastic discount factor 3.2. Consumption-based asset pricing with power utility 3.3. The riskfree rate puzzle 3.4. Bond returns and the equity premium and riskfrce rate puzzles 3.5. Separating risk aversion and intertemporal substitution 4. The d y n a m i c s o f asset returns and c o n s u m p t i o n 4.1. Time-variation in conditional expectations 4.2. A loglinear asset pricing framework 4.3. The stock market volatility puzzle 4.4. Implications for the equity premium puzzle 4.5. What does the stock market forecast? 4.6. Changing volatility in stock returns 4.7. What does the bond market forecast? 5. C y c l i c a l variation in the price o f risk 5.1. Habit formation 5.2. Models with heterogeneous agents

1232 1232 1233 1238 1245 1245 1249 1252 1255 1256 1260 1260 1264 1268 1272 1275 1277 1280 1284 1284 1290

* This chapter draws heavily on John Y. Campbell, "Consumption and the Stock Market: Interpreting International Experience", Swedish Economic Policy Review 3:251-299, Autumn 1996. I am grateful to the National Science Foundation for financial support, to Tim Chue, Vassil Konstantinov, and Luis Viceira for able research assistance, to Andrew Abel, Olivier Blanchard, Ricardo Caballero, Robert Shiller, Andrei Shleifer, John Taylor, and Michael Woodford for helpful comments, and to Barclays de Zoete Wedd Securities Limited, Morgan Stanley Capital International, David Barr, Bjorn Hansson, and Paul S6derlind for providing data. Handbook of Mactveconomics, Volume 1, Edited by J.B. lhylor and M. WoodJbrd © 1999 Elsevier Science B.V. All tqghts reserved 1231

1232 5.3. Irrational expectations 6. Some implications for macroeconomics References

J..Y Campbell 1293 1296 1298

Abstract This chapter reviews the behavior of financial asset prices in relation to consumption. The chapter lists some important stylized facts that characterize US data, and relates them to recent developments in equilibrium asset pricing theory. Data from other countries are examined to see which features of the US experience apply more generally. The chapter argues that to make sense of asset market behavior one needs a model in which the market price of risk is high, time-varying, and correlated with the state of the economy. Models that have this feature, including models with habitformation in utility, heterogeneous investors, and irrational expectations, are discussed. The main focus is on stock returns and short-term real interest rates, but bond returns are also considered.

Keywords JEL classification: G12

Ch. 19." Asset Prices, Consumption, and the Business Cycle

1233

1. Introduction

The behavior of aggregate stock prices is a subject of enduring fascination to investors, policymakers, and economists. In recent years stock markets have continued to show some familiar patterns, including high average returns and volatile and procyclical price movements. Economists have struggled to understand these patterns. If stock prices are determined by fundamentals, then what exactly are these fundamentals and what is the mechanism by which they move prices? Researchers, working primarily with US data, have documented a host of interesting stylized facts about the stock market and its relation to short-term interest rates and aggregate consumption: (1) The average real return on stock is high. In quarterly US data over the period 1947.2 to 1996.4, a standard data set that is used throughout this chapter, the average real stock return has been 7.6% at an annual rate. (Here and throughout the chapter, the word return is used to mean a log or continuously compounded return unless otherwise stated.) (2) The average riskless real interest rate is low. 3-month Treasury bills deliver a return that is riskless in nominal terms and close to riskless in real terms because there is only modest uncertainty about inflation at a 3-month horizon. In the postwar quarterly US data, the average real return on 3-month Treasury bills has been 0.8% per year. (3) Real stock returns are volatile, with an annualized standard deviation of 15.5% in the US data. (4) The real interest rate is much less volatile. The annualized standard deviation of the ex post real return on US Treasury bills is 1.8%, and much of this is due to short-run inflation risk. Less than half the variance of the real bill return is forecastable, so the standard deviation of the ex ante real interest rate is considerably smaller than 1.8%. (5) Real consumption growth is very smooth. The annualized standard deviation of the growth rate of seasonally adjusted real consumption of nondurables and services is 1.1% in the US data. (6) Real dividend growth is extremely volatile at short horizons because dividend data are not adjusted to remove seasonality in dividend payments. The annualized quarterly standard deviation of real dividend growth is 28.8% in the US data. At longer horizons, however, the volatility of dividend growth is intermediate between the volatility of stock returns and the volatility of consumption growth. At an annual frequency, for example, the volatility of real dividend growth is only 6% in the US data. (7) Quarterly real consumption growth and real dividend growth have a very weak correlation of 0.06 in the US data, but the correlation increases at lower frequencies to just over 0.25 at a 4-year horizon. (8) Real consumption growth and real stock returns have a quarterly correlation of 0.22 in the US data. The correlation increases to 0.33 at a 1-year horizon, and declines at longer horizons.

1234

J.Y. Campbell

(9)

Quarterly real dividend growth and real stock returns have a very weak correlation of 0.04 in the US data, but the correlation increases dramatically at lower frequencies to reach 0.51 at a 4-year horizon. (10) Real US consumption growth is not well forecast by its own history or by the stock market. The first-order autocorrelation of the quarterly growth rate of real nondurables and services consumption is a modest 0.2, and the log pricedividend ratio forecasts less than 5% of the variation of real consumption growth at horizons of 1 to 4 years. (11) Real US dividend growth has some short-run forecastability arising from the seasonality of dividend payments. But it is not well forecast by the stock market. The log price-dividend ratio forecasts no more than about 8% of the variation of real dividend growth at horizons of 1 to 4 years. (12) The real interest rate has some positive serial correlation; its first-order autocorrelation in postwar quarterly US data is 0.5. However the real interest rate is not well forecast by the stock market, since the log price-dividend ratio forecasts less than 1% of the variation of the real interest rate at horizons of 1 to 4 years. (13) Excess returns on US stock over Treasury bills are highly forecastable. The log price-dividend ratio forecasts 18% of the variance of the excess return at a 1-year horizon, 34% at a 2-year horizon, and 51% at a 4-year horizon. These facts raise two important questions for students of macroeconomics and finance: • Why is the average real stock return so high in relation to the average short-term real interest rate? • Why is the volatility of real stock returns so high in relation to the volatility of the short-term real interest rate? Mehra and Prescott (1985) call the first question the "equity premium puzzle". 1 Finance theory explains the expected excess return on any risky asset over the riskless interest rate as the quantity of risk times the price of risk. In a standard consumptionbased asset pricing model of the type studied by Hansen and Singleton (1983), the quantity of stock market risk is measured by the covariance of the excess stock return with consumption growth, while the price of risk is the coefficient of relative risk aversion of a representative investor. The high average stock return and low riskless interest rate (stylized facts 1 and 2) imply that the expected excess return on stock, the equity premium, is high. But the smoothness of consumption (stylized fact 5) makes the covariance of stock returns with consumption low; hence the equity premium can only be explained by a very high coefficient of risk aversion. Shiller (1982), Hansen and Jagannathan (1991), and Cochrane and Hansen (1992) have related the equity premium puzzle to the volatility of the stochastic discount factor, or equivalently the volatility of the intertemporal marginal rate of substitution of a representative investor. Expressed in these terms, the equity premium puzzle is

I For excellent recent surveys, see Cochrane and l-lansen (1992) or Kocherlakota(1996).

Ch. 19:

Asset Prices, Consumption, and the Business Cycle

1235

that an extremely volatile stochastic discount factor is required to match the ratio of the equity premium to the standard deviation of stock returns (the Sharpe ratio of the stock market). Some authors, such as Kandel and Stambaugh (1991), have responded to the equity premium puzzle by arguing that risk aversion is indeed much higher than traditionally thought. However this can lead to the "riskfree rate puzzle" of Weil (1989). If investors are very risk averse, then they have a strong desire to transfer wealth from periods with high consumption to periods with low consumption. Since consumption has tended to grow steadily over time, high risk aversion makes investors want to borrow to reduce the discrepancy between future consumption and present consumption. To reconcile this with the low real interest rate we observe, we must postulate that investors are extremely patient; their preferences give future consumption almost as much weight as current consumption, or even greater weight than current consumption. In other words they have a low or even negative rate of time preference. I will call the second question the "stock market volatility puzzle". To understand the puzzle, it is helpful to classify the possible sources of stock market volatility. Recall first that prices, dividends, and returns are not independent but are linked by an accounting identity. If an asset's price is high today, then either its dividend must be high tomorrow, or its return must be low between today and tomorrow, or its price must be even higher tomorrow. If one excludes the possibility that an asset price can grow explosively forever in a "rational bubble", then it follows that an asset with a high price today must have some combination of high dividends over tile indefinite future and low returns over the indefinite future. Investors must recognize this fact in forming their expectations, so when an asset price is high investors expect some combination of high future dividends and low future returns. Movements in prices must then be associated with some combination of changing expectations ("news") about future dividends and changing expectations about future returns; the latter can in turn be broken into news about future riskless real interest rates and news about future excess returns on stocks over short-term debt. Until the early 1980s, most financial economists believed that there was very little predictable variation in stock returns and that dividend news was by far the most important factor driving stock market fluctuations. LeRoy and Porter (1981) and Shiller (1981) challenged this orthodoxy by pointing out that plausible measures of expected future dividends are far less volatile than real stock prices. Their work is related to stylized facts 6, 9, and 11. Later in the 1980s Campbell and Shiller (1988), Fama and French (1988a,b, 1989), Poterba and Summers (1988) and others showed that real stock returns are highly forecastable at long horizons. The variables that predict returns are ratios of stock prices to scale factors such as dividends, earnings, moving averages of earnings, or the book value of equity. When stock prices are high relative to these scale factors, subsequent long-horizon real stock returns tend to be low. This predictable variation in stock returns is not matched by any equivalent variation in long-term real interest rates, which are comparatively stable and do not seem to move with the stock market.

1236

J.Y. Campbell

in the late 1970s, for example, real interest rates were unusually low yet stock prices were depressed, implying high forecast stock returns; the 1980s saw much higher real interest rates along with buoyant stock prices, implying low forecast stock returns. Thus excess returns on stock over Treasury bills are just as forecastable as real returns on stock. This work is related to stylized facts 12 and 13. Campbell (1991) uses this evidence to show that the great bulk of stock market volatility is associated with changing forecasts of excess stock returns. Changing forecasts of dividend growth and real interest rates are much less important empirically. The stock market volatility puzzle is closely related to the equity premium puzzle. A complete model of stock market behavior must explain both the average level of stock prices and their movements over time. One strand of work on the equity premium puzzle makes this explicit by studying not the consumption covariance of measured stock returns, but the consumption covariance of returns on hypothetical assets whose dividends are determined by consumption. The same model is used to generate both the volatility of stock prices and the implied equity premium. This was the approach of Mehra and Prescott (1985), and many subsequent authors have followed their lead. Unfortunately, it is not easy to construct a general equilibrium model that fits all the stylized facts given above. The standard model of Mehra and Prescott (1985) gets variation in stock price-dividend ratios only from predictable variation in consumption growth which moves the expected dividend growth rate and the riskless real interest rate. The model is not consistent with the empirical evidence for predictable variation in excess stock returns. Bond market data pose a further challenge to this standard model of stock returns. In the model, stocks behave very much like long-term real bonds; both assets are driven by long-term movements in the riskless real interest rate. Thus parameter values that produce a large equity premium tend also to produce a large term premium on real bonds. While there is no direct evidence on real bond premia, nominal bond premia have historically been much smaller than equity premia. Since the data suggest that predictable variation in excess returns is an important source of stock market volatility, researchers have begun to develop models in which the quantity of stock market risk or the price of risk change through time. ARCH models and other econometric methods show that the conditional variance of stock returns is highly variable. If this conditional variance is an adequate proxy for the quantity of stock market risk, then perhaps it can explain the predictability of excess stock returns. There are several problems with this approach. First, changes in conditional variance are most dramatic in daily or monthly data and are much weaker at lower frequencies. There is some business-cycle variation in volatility, but it does not seem strong enough to explain large movements in aggregate stock prices [Bollerslev, Chou and Kroner (1992), Schwert (1989)]. Second, forecasts of excess stock returns do not move proportionally with estimates of conditional variance [Harvey (1989, 1991), Chou, Engle and Kane (1992)]. Finally, one would like to derive stock market volatility endogenously within a model rather than treating it as an exogenous variable. There is little evidence of cyclical variation in consumption or dividend volatility that could explain the variation in stock market volatility.

Ch. 19:

Asset Prices, Consumption, and the Business Cycle

1237

A more promising possibility is that the price of risk varies over time. Time-variation in the price of risk arises naturally in a model with a representative agent whose utility displays habit-formation. Campbell and Cochrane (1999), building on the work of Abel (1990), Constantinides (1990), and others, have proposed a simple asset pricing model of this sort. Campbell and Cochrane suggest that assets are priced as if there were a representative agent whose utility is a power function of the difference between consumption and "habit", where habit is a slow-moving nonlinear average of past aggregate consumption. This utility fi.mction makes the agent more risk-averse in bad times, when consumption is low relative to its past history, than in good times, when consumption is high relative to its past history. Stock market volatility is explained by a small amount of underlying consumption (dividend) risk, amplified by variable risk aversion; the equity premium is explained by high stock market volatility, together with a high average level of risk aversion. Time-variation in the price of risk can also arise from the interaction of heterogeneous agents. Constantinides and Duffle (l 996) develop a simple framework with many agents who have identical utility functions but heterogeneous streams of labor income; they show how changes in the cross-sectional distribution of income can generate any desired behavior of the market price of risk. Grossman and Zhou (1996) and Wang (1996) move in a somewhat different direction by exploring the interactions of agents who have different levels of risk aversion. Some aspects of asset market behavior could also be explained by irrational expectations of investors. If investors are excessively pessimistic about economic growth, for example, they will overprice short-term bills and underprice stocks; this would help to explain the equity premium and riskfree rate puzzles. If investors overestimate the persistence of variations in economic growth, they will overprice stocks when growth has been high and underprice them when growth has been low, producing time-variation in the price of risk [Barsky and DeLong (1993)]. This chapter has three objectives. First, it tries to summarize recent work on stock price behavior, much of which is highly technical, in a way that is accessible to a broader professional audience. Second, the chapter summarizes stock market data from other countries and asks which of the US stylized facts hold true more generally. The recent theoretical literature is used to guide the exploration of the international data. Third, the chapter systematically compares stock market data with bond market data. This is an important discipline because some popular models of stock prices are difficult to reconcile with the behavior of bond prices. The organization of the chapter is as follows. Section 2 introduces the international data and reviews stylized facts 1-9 to see which of them apply outside the USA. (Additional details are given in a Data Appendix available on the author's web page or by request from the author.) Section 3 discusses the equity premium puzzle, taking the volatility of stock returns as given. Section 4 discusses the stock market volatility puzzle; this section also reviews stylized facts 10-13 in the international data. Sections 3 and 4 drive one towards the conclusion that the price of risk is both high and time-varying. It must be high to explain the equity premium puzzle, and it

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J. Y Campbell

must be time-varying to explain the predictable variation in stock returns that seems to be responsible for the volatility o f stock returns. Section 5 discusses models which produce this result, including models with habit-formation in utility, heterogeneous investors, and irrational expectations. Section 6 draws some implications for other topics in macroeconomics, including the modelling of investment, labor supply, and the welfare costs o f economic fluctuations.

2. International asset market data

The stylized facts described in the previous section apply to postwar quarterly US data. Most empirical work on stock prices uses this data set, or a longer annual US time series originally put together by Shiller (1981). But data on stock prices, interest rates, and consumption are also available for many other countries. In this chapter I use an updated version o f the international developed-country data set in Campbell (1996a). The data set includes Morgan Stanley Capital International (MSCI) stock market data covering the period since 1970. ! combine the MSCI data with macroeconomic data on consumption, short- and long-term interest rates, and the price level from the International Financial Statistics (IFS) of the International Monetary Fund. For some countries the IFS data are only available quarterly over a shorter sample period, so I use the longest available sample for each country. Sample start dates range from 1970.1 to 1982.2, and sample end dates range from 1995.1 to 1996.4. I work with data from 11 countries: Australia, Canada, France, Germany, Italy, Japan, the Netherlands, Sweden, Switzerland, the United Kingdom, and the United States 2. For some purposes it is useful to have data over a much longer span of calendar time. I have been able to obtain annual data for Sweden over the period 1920-1994 and the U K over the period 1919-1994 to complement the US annual data for the period 1891-1995. The Swedish data come from Frennberg and Hansson (1992) and Hassler, Lundvik, Persson and S6derlind (1994), while the UK data come from Barclays de Zoete Wedd Securities (1995) and The Economist (1987) 3. In working with international stock market data, it is important to keep in mind that different national stock markets are o f very different sizes, both absolutely and in

2 The first version of this paper, following Campbell (1996a), also presented data for Spain. However Spain, unlike the other countries in the sample, underwent a major political change to democratic government during the sample period, and both asset returns and inflation show dramatic shifts fi'om the 1970s to the 1980s. It seems more conservative to consider Spain as an emerging market and exclude it from the developed-countrydata set. 3 1 acknowledge the invaluable assistance of Bjorn Hansson and Paul S6derlind with the Swedish data, and David Barr with the UK data. Full details about the construction of the quarterly and annual data are given in a Data Appendix available on the attthor's web page or by request fi'om the author.

1239

Ch. 19." Asset Prices, Consumption, and the Business Cycle

Table 1 MSCI market capitalization, 1993a Country

V/ (Bill. of US$)

--

vl

(%)

GDPi

v,

- -

VusMxcl

(%)

-

vi -

(%)

~f';4 Vi

AUL

117.9

41.55

4.65

1.85

CAN

167.3

30.62

6.60

2.63

FR

272.5

22.49

10.75

4.29

GER

280.7

16.83

11.07

4.41

ITA

86.8

9.45

3.42

1.37

JAP

1651.9

39.74

65.16

25.98

NTH

136.7

45.91

5.39

2.15

SWD

62.9

36.22

2.48

0.99

SWT

205.6

87.46

8.12

3.23

758.4

79.52

29.91

11.93

USA

UK MSCI

2535.3

37.25

100.00

39.88

USA

CRSP

4875.6

71.64

192.30

a vi is the stock index market capitalization in billions of 1993 US dollars. All stock index data are

from Morgan Stanley Capital International(MSCI), except for USA-CRSP which is from the Center for Research in Security Prices. Vi/GDP i is the index market capitalization as a percentage of 1993 GDP, Vi/VtjsMscI is the index market capitalization as a percentage of the market capitalization of the US MSCI index, and V i / ( ~ i Vi) is the percentage share of the index market capitalization in the total market capitalization of all the MSCI indexes. Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; 1TA, Italy; JPN, Japan; NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America. proportion to national GDP's. Table 1 illustrates this by reporting several measures of stock market capitalization for the quarterly MSCI data. Column 1 gives the market capitalization for each country's MSCI index at the end of 1993, in billions of $US. Column 2 gives the market capitalization for each country as a fraction of its GDP. Column 3 gives the market capitalization for each country as a fraction of the US MSCI index capitalization. Column 4 gives the market capitalization for each country as a fraction of the value-weighted world MSCI index capitalization. Since the MSCI index for the United States is only a subset of the US market, the last row of the table gives the same statistics for the value-weighted index of New York Stock Exchange and American Stock Exchange stocks reported by the Center for Research in Security Prices (CRSP) at the University of Chicago. Table 1 shows that most countries' stock markets are dwarfed by the US market. Column 3, for example, shows that the Japanese MSCI index is worth only 65% of the US MSCI index, the U K MSCI index is worth only 30% of the US index, the French and German MSCI indexes are worth only 11% of the US index, and all

1240

J.Y. Campbell

other countries' indexes are worth less than 10% o f the US index. Column 4 shows that the U S A and Japan together account for 66% o f the world market capitalization, while the USA, Japan, the UK, France, and Germany together account for 86%. In interpreting these numbers one must keep in mind that the M S C I indexes do not cover the whole market in each country (the US M S C I index, for example, is worth about h a l f the US CRSP index), but they do give a guide to relative magnitudes across countries. Table 1 also shows that different countries' stock market values are very different as a fraction o f GDP. I f one thinks that total wealth-output ratios are likely to be fairly constant across countries, then this indicates that national stock markets are very different fractions o f total wealth in different countries. In highly capitalized countries such as the UK and Switzerland, the MSCI index accounts for about 80% o f GDP, whereas in Germany and Italy it accounts for less than 20% o f GDR The theoretical convention o f treating the stock market as a claim to total consumption, or as a proxy for the aggregate wealth o f an economy, makes much more sense in the highly capitalized countries 4. Table 2 reports summary statistics for international asset returns. For each country the table reports the mean, standard deviation, and first-order autocorrelation o f the real stock return and the real return on a short-term debt instrument 5. The first line o f Table 2 gives numbers for the standard postwar quarterly US data set summarized in the introduction. The next panel gives numbers for the 11-country quarterly MSCI data, and the bottom panel gives numbers for the long-term annual data sets. The table shows that the first four stylized facts given in the introduction are fairly robust across countries. (1) Stock markets have delivered average real returns o f 5% or better in almost every country and time period. The exceptions to this occur in short-term quarterly data, and are concentrated in markets that are particularly small relative to GDP (Italy), or that predominantly represent claims on natural resources (Australia and Canada). (2) Short-term debt has rarely delivered an average real return above 3%. The exceptions to this occur in two countries, Germany and the Netherlands, whose sample periods begin in the late 1970s and thus exclude much o f the surprise inflation o f the oil-shock period.

4 Stock ownership also tends to be much more concentrated in the countries with low capitalization. La Porta, Lopez-de-Silanes, Shleifer and Vishny (1997) have related these international patterns to differences in the protections afforded outside investors by different legal systems. 5 As explained in the Data Appendix, the best available short-term interest rate is sometimes a Treasury bill rate and sometimes another money market interest rate. Both means and standard deviations are given in almualized percentage points. To annualize the raw quarterly numbers, means are multiplied by 400 while standard deviations are multiplied by 200 (since standard deviations increase with the square root of the time interval in serially uncorrelated data).

Ch. 19." Asset Prices, Consumption, and the Business Cycle

1241

Table 2 International stock and bill returns a Country

Sample period

re

o(r~)

p(rc)

-~ rj

a(rf )

p(rj )

USA

1947.2-1996.4

7.569

15.453

0.104

0.794

1.761

0.501

AUL

1970.1 1996.3

2.633

23.459

0.008

1.820

2,604

0.636

CAN

1970.1-1996.3

4,518

16,721

0.119

2.738

1.932

0.674

FR

1973.2-1996.3

7.207

22.877

0,088

2.736

1.917

0.714

GER

1978.4-1996.3

8.135

20.326

0,066

3.338

1.161

0.322

ITA

1971.2-1995.3

0.514

27.244

0.071

2.064

2.957

0.681

JPN

1970.2--1996.3

5.831

21,881

0,017

1.538

2.347

0.493

NTH

1977.2-1996.2

12.721

15.719

0.027

3.705

1.542

SWD

1970.1-1995.1

7.948

23.867

0.053

1.520

2.966

SWT

1982.~1996,3

11.548

20.431

0.112

1.466

1.603

0.255

UK

1970.1-1996,3

7,236

21,555

0,103

1,081

3.067

0,474

USA

1970.1-1996.4

5.893

17.355

0.076

1.350

1,722

0.568

SWD

1920-1994

6.219

18.654

0.064

2.073

5.918

0,708

UK

1919-1994

7.314

22.675

-0.024

1.198

5.446

0.591

USA

1891 1995

6.697

18.634

0.025

1.955

8.919

0.338

-0.099 0.218

a ~ is the mean log real return on the stock market index, multiplied by 400 in quarterly data or 100 in annual data to express in annualized percentage points, tY(re) is the standard deviation of the log real return on the market index, multiplied by 200 in quarterly data or 100 in annual data to express in annualized percentage points, p(re) is the first-order autocorrelation of the log real return on the market index, rT, o(rf), and p(t).) are defined in the same way for the real return on a 3-month money market instrument. The money market instruments vary across countries and are described in detail in the Data Appendix. Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan; NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America.

(3) The annualized standard deviation o f stock returns ranges from 15% to 27%. It is striking that the market w i t h the highest volatility, Italy, is the smallest market relative to G D P and the one w i t h the lowest average return, (4) In quarterly data the annualized volatility o f real returns on short debt is around 3 % for the UK, Italy, and Sweden, around 2 . 5 % for Australia and Japan, and below 2 % for all other countries. Volatility is higher in l o n g - t e r m annual data because o f large swings in inflation in the interwar period, particularly in t 9 1 9 - 2 1 . M u c h o f the volatility in these real returns is probably due to unanticipated inflation and does not reflect volatility in the ex ante real interest rate.

1242

J Y. Campbell

These numbers show that high average stock returns, relative to the returns on shortterm debt, are not unique to the United States but characterize many other countries as well. Recently a number o f authors have suggested that average excess returns in the U S A may be overstated by sample selection or survivorship bias. i f economists study the U S A because it has had an unusually successful economy, then sample average US stock returns may overstate the true mean US stock return. Brown, Goetzmann and Ross (1995) present a formal model o f this effect. While survivorship bias m a y affect data from all the countries included in Table 2, it is reassuring that the stylized facts are so consistent across these countries 6. Table 3 turns to data on aggregate consumption and stock market dividends. The table is organized in the same way as Table 2. It illustrates the robustness o f two more o f the stylized facts given in the introduction. (5) In the postwar period the annualized standard deviation of real consumption growth is never above 3%. This is true even though data are used on total consumption, rather than nondurables and services consumption, for all countries other than the USA. Even in the longer annual data, which include the turbulent interwar period, consumption volatility slightly exceeds 3% only in the USA. (6) The volatility o f dividend growth is much greater than the volatility o f consumption growth, but generally less than the volatility o f stock returns. The exceptions to this occur in countries with highly seasonal dividend payments; these countries have large negative autocorrelations for quarterly dividend growth and much smaller volatility when dividend growth is measured over a full year rather than over a quarter. Table 4 reports the contemporaneous correlations among real consumption growth, real dividend growth, and stock returns. It turns out that these correlations are somewhat sensitive to the timing convention used for consumption. A timing convention is needed because the level o f consumption is a flow during a quarter rather than a point-in-time observation; that is, the consumption data are timeaveraged 7. If we think o f a given quarter's consumption data as measuring consumption at the beginning o f the quarter, then consumption growth for the quarter is next quarter's consumption divided by this quarter's consumption. If on the other hand

6 Goetzmalm and Jorion (1997) consider imernational stock-price data from earlier in the 20th Century and argue that the long-term average real growth rate of stock prices has been higher in the US than elsewhere. However they do not have data on dividend yields, which are an important component of total return and are likely to have been particularly important in Europe dtmng the troubled intei~ar period. 7 Tilne-averaging is one of a number of interrelated issues that arise in relating measured consumption data to the theoretical concept of consumption. Other issues include measurement error, seasonal adjustment, and the possibilitythat some goods classified as nondurable in the national income accounts are in fact durable. Grossman, Melino and Shiller (1987), Wheatley (1988), Miron (1986), and Heaton (1995) handle time-averaging, measurement error, seasonality, and dinability, respectively, in a much more careful way than is possible here, while Wilcox (1992) provides a detailed account of the sampling procedures used to constxuct US consumption data.

1243

Ch. 19." Asset Prices, Consumption, and the Business Cycle

Table 3 International consumption and dividends a Country

Sample period

Ac

o(Ac)

p(Ac)

Ad

~r(Ad)

p(Ad)

USA

1947.2-1996.4

1.921

1.085

0.221

2.225

28.794

-0.544

AUL

1970.1-1996.3

1.886

2.138

0.351

0.883

36.134

-0.451

CAN

1970.1 1996.3

1.853

2.083

0.113

-0.741

5.783

FR

1973.2 1996.3

1.600

2.121

--0.093

1.214

GER

1978.4 1996.3

1.592

2.478

-0.328

1.079

8.528

0.018

ITA

1971.2-1995.3

2.341

1.724

0.253

-4.919

19.635

0.294

JPN

1970.2-1996.3

3.384

2.347

-0.225

2.489

4.504

0.363

NTH

1977.2 1996.2

1.661

2.772

-0.265

4.007

4.958

0.277

SWD

1970.1-1995.1

0.705

1.920

0.305

1.861

13.595

0.335

SWT

1982.2-1996.3

0.376

2.246

-0.4t9

4.143

6.156

0.165

13.383

0.540 -0.159

UK

1970.1-1996.3

1.991

2.583

-0.017

0.681

7.125

0.335

USA

1970.1 1996.4

1.722

0.917

0.390

0.619

17.229

0.581 0.214

SWD

1920 1994

1.790

2.866

0.159

0.423

12.215

UK

1919-1994

1.443

2.898

0.281

1.844

7.966

USA

1891-1995

1.773

3.256

-0.117

1.485

14.207

0.225 -0.087

a Ac is the mean log real consumption growth rate, multiplied by 400 in quarterly data or 100 in annual data to express in annualized percentage points, cr(Ac) is the standard deviation of the log real consumption growth rate, multiplied by 200 in quarterly data or 100 in annual data to express in annualized percentage points, p(Ac) is the first-order autocorrelation of the log real consumption growth rate. Ad, a(Ad), and p(Ad) are defined in the same way for the real dividend growth rate. Consumption is nondurables and selwices consumption in the USA, and total consumption elsewhere. Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan; NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America. we think o f the c o n s u m p t i o n data as m e a s u r i n g c o n s u m p t i o n at the end o f the quarter, then c o n s u m p t i o n growth is this quarter's c o n s u m p t i o n divided by last quarter's consumption. Table 4 uses the former, " b e g i n n i n g - o f - q u a r t e r " timing convention because this p r o d u c e s a higher c o n t e m p o r a n e o u s correlation b e t w e e n c o n s u m p t i o n growth and stock returns. The t i m i n g convention has less effect on correlations w h e n the data are m e a s u r e d at l o n g e r horizons. Table 4 also shows h o w the correlations a m o n g real c o n s u m p t i o n growth, real dividend growth, and real stock returns v a r y w i t h the horizon. Each pairwise correlation a m o n g these series is calculated for h o r i z o n s o f 1, 4, 8, and 16 quarters in the quarterly data and for horizons o f 1, 2, 4, and 8 years in the l o n g - t e r m annual data. The table illustrates three m o r e stylized facts f r o m the introduction.

J.Y. Campbell

1244

%

I

I l l

II

II

[I

I I

I

', ~ '~ , .o ~" ~b o

m 0

I I

I I

II

I

I I

I

I

I

~

fa,

>~

I

N

0

~

;a4zaaza;a

d e m ~ : d ~ d ~ d o

NN~

~

a ca

Ch. 19: AssetPrices', Consumption, and the Business Cycle

1245

(7) Real consumption growth and dividend growth are generally weakly positively correlated in the quarterly data. In many countries the correlation increases strongly with the measurement horizon. However long-horizon correlations remain close to zero for Australia and Switzerland, and are substantially negative for Italy (with a very small stock market) and Japan (with anomalous dividend behavior). The correlations of consumption and dividend growth are positive and often quite large in the longer-term annual data sets. (8) The correlations between real consumption growth rates and stock returns are quite variable across countries. They tend to be somewhat higher in high-capitalization countries (with the notable exception of Switzerland), which is consistent with the view that stock returns proxy more accurately for wealth returns in these countries. Correlations typically increase with the measurement horizon out to 1 or 2 years, and are moderately positive in the longer-term annual data sets. (9) The correlations between real dividend growth rates and stock returns are small at a quarterly horizon but increase dramatically with the horizon. This pattern holds in every country. The correlations also increase strongly with the horizon in the longer-term annual data. After this preliminary look at the data, I now use some simple finance theory to interpret the stylized facts.

3. The equity premium puzzle 3.1. The stochastic discount factor To understand the equity premium puzzle, consider the intertemporal choice problem of an investor, indexed by k, who can trade freely in some asset i and can obtain a gross simple rate of return (1 +Ri, t+l) o n the asset held from time t to time t + 1. If the investor consumes Ck~ at time t and has time-separable utility with discount factor 6 and period utility U(Ckt), then her first-order condition is

g'((~t) = 6E~ [(1 +Ri, l+l)Ut(Ck,t+l)].

(1)

The left-hand side of Eqnation (1) is the marginal utility cost of consuming one real dollar less at time t; the right-hand side is the expected marginal utility benefit from investing the dollar in asset i at time t, selling it at time t + 1, and consuming the proceeds. The investor equates marginal cost and marginal benefit, so Equation (1) must describe the optimum. Dividing Equation (1) by U'(C~) yields

v'(G,,+,)]j

1 = Et (1 +Ri,,~,)6 ~

--E, [(1 +Ri,,+,)Ma,,+lJ,

(2)

where Mk,t.~l = 6U'(Ck, t+l)/U/(Ct) is the intertemporal marginal rate of substitution of the investor, also known as the stochastic discountjdctor. This way of writing the

1246

J..Y Campbell

model in discrete time is due originally to Grossman and Shiller (1981), while the continuous-time version of the model is due to Breeden (1979). Cochrane and Hansen (1992) and Hansen and Jagannathan (1991) have developed the implications of the discrete-time model in detail. The derivation just given for Equation (2) assumes the existence of an investor maximizing a time-separable utility function, but in fact the equation holds more generally. The existence of a positive stochastic discount factor is guaranteed by the absence of arbitrage in markets in which non-satiated investors can trade freely without transactions costs. In general there can be many such stochastic discount factors for example, different investors k whose marginal utilities follow different stochastic processes will have different M~, t+l - but each stochastic discount factor must satisfy Equation (2). It is common practice to drop the subscript k from this equation and simply write

1 = E, [(1 +&t+,lMi+~].

(3)

In complete markets the stochastic discount factor Mt+l is unique because investors can trade with one another to eliminate any idiosyncratic variation in their marginal utilities. To understand the implications of Equation (3) it is helpful to write the expectation of the product as the product of expectations plus the covariance,

E1[(1 +Ri,,~l)m~+l] = Et[(l + Ri,,+I)]E~[M,+I] + Covt[R~,l.~,M,+~].

(4)

Substituting into Equation (3) and rearranging gives 1 + E,[R~,,+I] -

1 - Covt[Ri, ¢+1,Mr+l] Et[Mt+l]

(5)

An asset with a high expected simple return must have a low covariance with the stochastic discount factor. Such an asset tends to have low retunas when investors have high marginal utility. It is risky in that it fails to deliver wealth precisely when wealth is most valuable to investors. Investors therefore demand a large risk premium to hold it. Equation (5) must hold for any asset, including a riskless asset whose gross simple return is 1 + Ry;t ~1. Since the simple riskless return has zero covariance with the stochastic discount factor (or any other random variable), it is just the reciprocal of the expectation of the stochastic discount factor: 1 1 +R/;,+t - Et[M,+I]"

(6)

This can be used to rewrite Equation (5) as 1 +Et[Ri,,+t] = (1 +RLt+I)(1 -Cov,[Ri,~+L,Mi+l]).

(7)

For simplicity I now follow Hansen and Singleton (1983) and assume that the joint conditional distribution of asset returns and the stochastic discount factor is lognormal

Ch. 19." Asset Prices, Consumption, and the Business Cycle

1247

and homoskedastic. While these assumptions are not literally realistic - stock returns in particular have fat-tailed distributions with variances that change over time - they do make it easier to discuss the main forces that should determine the equity premium. When a random variable X is conditionally lognormally distributed, it has the convenient property that log E t X

E~ l o g X + ½Vart logX,

(8)

where VartlogX = G [ ( l o g X - E t l o g X ) 2 ] . I f in addition X is conditionally homoskedastic, then Var, l o g X = E[(logX - E, l o g X ) 2] = Var(logX - Et logX). Thus with joint conditional lognormality and homoskedasticity of asset returns and consumption, I can take logs of Equation (3) and obtain 2 0 = Etri, t+l + Etmt+l + (1) [02 + O£, + 20,m].

(9)

Here rnt - log(Mr) and r , - - log(1 + Ri,), while 02 denotes the unconditional variance of log return innovations Var(r/, t+t - G r i , t+l), a 2 denotes the unconditional variance of innovations to the stochastic discount factor Var(mt~l Etmt+l), and G,, denotes the unconditional covariance of innovations Cov(ri, t+l - Elri, t v l , rntel - Etmt+l). Equation (9) has both time-series and cross-sectional implications. Consider first an asset with a riskless real return rt; ¢ ) 1. For this asset the return innovation variance c~2 and the covariance aim are both zero, so the riskless real interest rate obeys

rj;l+l = - E t m t + l

02

2

(10)

This equation is the log counterpart of Equation (6). Subtracting Equation (10) from Equation (9) yields an expression for the expected excess return on risky assets over the riskless rate:

o.2 Et[ri,/+1 - 9; tM] + ~ - - - o i ....

2

(ll)

The variance term on the left-hand side of Equation (11) is a Jensen's Inequality adjustment arising from the fact that we are describing expectations of log returns. This term would disappear if we rewrote the equation in terms of the log expectation of the ratio of gross simple returns: log G [(1 + Ri, t + I ) / ( 1 + Rf, ~+1)] = - a i m . The righthand side of Equation (11) says that the log risk premium is determined by the negative of the covariance of the asset with the stochastic discount factor. This equation is the log counterpart of Equation (7). The covariance O,m can be written as the product of the standard deviation of the asset return a,., the standard deviation of the stochastic discount factor (7,,,, and the

J Y. Campbell

1248

V~=7

>,~° ~

•~ ,.=

03 r.~

L) '~

:~

Z

q,

~

~P

•~ = o° f~

,.~

~'"

~o

~

II

rm ~ .

3

o,~o

2~=~


.~#

o

.-

o

o

&S .o~ <

Ch. 19: Asset Prices, Consumption, and the Business Cycle

1249

correlation between the asset return and the stochastic discount factor Pim. Since Pim ~ - 1 , - ~ m <, ~YiOrn. Substituting into Equation (11), Om >1

Et[ri, t+l - rl;t-, 1] + 0,2/2

(12)

This inequality was first derived by Shiller (1982); a multi-asset version was derived by Hansen and Jagannathan (1991) and developed further by Cochrane and Hansen (1992). The right-hand side of Equation (12) is the excess return on an asset, adjusted for Jensen's Inequality, divided by the standard deviation of the asset's return - a logarithmic Sharpe ratio for the asset. Equation (12) says that the standard deviation of the log stochastic discount factor must be greater than this Sharpe ratio for all assets i, that is, it must be greater than the maximum possible Sharpe ratio obtainable in asset markets. Table 5 uses Equation (12) to illustrate the equity premium puzzle. For each data set the first column of the table reports the average excess return on stock over shortterm debt, adjusted for Jensen's inequality by adding one-half the sample variance of the excess log return to get a sample estimate of the numerator in Equation (12). This adjusted average excess return is multiplied by 400 to express it in annualized percentage points. The second column of the table gives the aunualized standard deviation of the excess log stock return, a sample estimate of the denominator in Equation (12). This standard deviation was reported earlier in Table 2. The third column gives the ratio of the first two columns, multiplied by 100; this is a sample estimate of the lower bound on the standard deviation of the log stochastic discount factor, expressed in annualized percentage points. In the postwar US data the estimated lower bound is a standard deviation greater than 50% a year; in the other quarterly data sets it is below 10% for Italy, between 15% and 20% for Australia and Canada, and above 30% for all the other countries, in the long-run annual data sets the lower bound on the standard deviation exceeds 30% for all three countries. 3.2. Consumption-based asset p r i c i n g with p o w e r utility

To understand why these numbers are disturbing, I now follow Mehra and Prescott (1985) and other classic papers on the equity premium puzzle and assume that there is a representative agent who maximizes a time-separable power utility function defined over aggregate consumption G:

u(G)

C¢-Y-1

-

- - ,

1-7

(13)

where y is the coefficient of relative risk aversion. This utility function has several important properties. First, it is scale-invariant; with constant return distributions, risk premia do not change over time as aggregate wealth and the scale of the

1250

J g CampbeH

economy increase. Related to this, if different investors in the econonW have different wealth levels but the same power utility function, then they can be aggregated into a single representative investor with the same utility function as the individual investors. A possibly less desirable property of power utility is that the elasticity of intertemporal substitution, which I write as ~p, is the reciprocal of the coefficient of relative risk aversion y. Epstein and Zin (1989, 1991) and Weil (1989) have proposed a more general utility specification that preserves the scale-invariance of power utility but breaks the tight link between the coefficient of relative risk aversion and the elasticity of intertemporal substitution. I discuss this form of utility in section 3.4 below. Power utility implies that marginal utility UI(C,) = Ct r, and the stochastic discount factor Mt+l = CS(Ct+t/CI) -r. The assumption made previously that the stochastic discount factor is conditionally lognormal will be implied by the assumption that aggregate consumption is conditionally lognormal [Hansen and Singleton (1983)]. Making this assumption for expositional convenience, the log stochastic discount factor is mt+l = log(cS)- 7Ac,+1, where c, --- log(Q), and Equation (9) becomes 0 = Etri,,+l +log (5- yE, Act~l + (½) [a,.2+ y20~2-

2ro, c].

(14)

Here a 2 denotes Var(ct+l -Etct+l), the unconditional variance of log consumption innovations, and eric denotes Cov(ri, t + l - Etri, t Fl, ct+l - EtCt+l), the unconditional covariance of innovations. Equation (10) now becomes tj/;,+t =

log C5+

]/EtAct+l

~,2at2 2

(15)

This equation says that the riskless real rate is linear in expected consumption growth, with slope coefficient equal to the coefficient of relative risk aversion. The conditional variance of consumption growth has a negative effect on the riskless rate which can be interpreted as a precautionary savings effect. Equation (11) becomes Et[ri, t+~ --rj;t+l] + ~ - = 7oic.

(16)

The log risk premium on any asset is the coefficient of relative risk aversion times the covariance of the asset return with consumption growth. Intuitively, an asset with a high consumption covariance tends to have low returns when consumption is low, that is, when the marginal utility of consumption is high. Such an asset is risky and commands a large risk premium. Table 5 uses Equation (16) to illustrate the equity premium puzzle. As already discussed, the first column of the table reports a sample estimate of the left-hand

Ch. 19." Asset Prices, Consumption, and the Business Cycle

1251

side of Equation (16), multiplied by 400 to express it in annualized percentage points. The second column reports the annualized standard deviation of the excess log stock return (given earlier in Table 2), the fourth column reports the annualized standard deviation of consumption growth (given earlier in Table 3), the fifth column reports the correlation between the excess log stock return and consumption growth, and the sixth column gives the product of these three variables which is the annualized covariance a,~. between the log stock return and consumption growth. Finally, the table gives two columns with implied risk aversion coefficients. The column headed RRA(1) uses Equation (16) directly, dividing the adjusted average excess return by the estimated covariance to get estimated risk aversion 8. The column headed RRA(2) sets the correlation of stock returns and consumption growth equal to one before calculating risk aversion. While this is of course a counterfactual exercise, it is a valuable diagnostic because it indicates the extent to which the equity premium puzzle arises from the smoothness of consumption rather than the low correlation between consumption and stock returns. The correlation is hard to measure accurately because it is easily distorted by short-term measurement errors in consumption, and Table 4 indicates that the sample correlation is quite sensitive to the measurement horizon. By setting the correlation to one, the RRA(2) column indicates the extent to which the equity premium puzzle is robust to such issues. A correlation of one is also implicitly assumed in the volatility bound for the stochastic discount factor, Equation (12), and in many calibration exercises such as Mehra and Prescott (1985), Campbell and Cochrane (1999), or Abel (1999). Table 5 shows that the equity premium puzzle is a robust phenomenon in international data. The coefficients of relative risk aversion in the RRA(1) column are generally extremely large. They are usually many times greater than 10, the maximum level considered plausible by Mehra and Prescott (1985). In a few cases the risk aversion coefficients are negative because the estimated covariance of stock returns with consumption growth is negative, but in these cases the covariance is extremely close to zero. Even when one ignores the low correlation between stock returns and consumption growth and gives the model its best chance by setting the correlation to one, the RRA(2) column still has risk aversion coefficients above 10 in most cases. Thus the fact shown in Table 4, that for some countries the correlation of stock returns and consumption increases with the horizon, is unable by itself to resolve the equity premium puzzle. The risk aversion estimates in Table 5 are of course point estimates and are subject to sampling error. No standard errors are reported for these estimates. However authors such as Cecchetti, Lam and Mark (1993) and Kocherlakota (1996), studying the long-

8 The calculation is done correctly, in natural units, even though the table reports averageexcess returns and covafiances in percentage point units. Equivalently, the ratio of the quantities given in the table is multiplied by 100.

1252

J E Campbell

run annual US data, have found small enough standard errors that they can reject risk aversion coefficients below about 8 at conventional significance levels. O f course, the validity o f these tests depends on the characteristics o f the data set in which they are used. Rietz (1988) has argued that there may be a peso problem in these data. A peso problem arises when there is a small positive probability of an important event, and investors take this probability into account when setting market prices. If the event does not occur in a particular sample period, investors will appear irrational in the sample and economists will mis-estimate their preferences. While it may seem unlikely that this could be an important problem in 100 years of annual data, Rietz (1988) argues that an economic catastrophe that destroys almost all stock-market value can be extremely unlikely and yet have a major depressing effect on stock prices. One difficulty with this argument is that it requires not only a potential catastrophe, but one which affects stock market investors more seriously than investors in short-term debt instruments. Many countries that have experienced catastrophes, such as Russia or Germany, have seen very low returns on short-term government debt as well as on equity. A peso problem that affects both asset returns equally will affect estimates o f the average levels of returns but not estimates of the equity premium 9. The major example of a disaster for stockholders that did not negatively affect bondholders is the Great Depression of the early 1930s, but o f course this is included in the long-run annual data for Sweden, the UK, and the USA, all of which display an equity premium puzzle. Also, the consistency o f the results across countries requires investors in all countries to be concerned about catastrophes. I f the potential catastrophes are uncorrelated across countries, then it becomes less likely that the data set includes no catastrophes; thus the argument seems to require a potential international catastrophe that affects all countries simultaneously.

3.3. The riskf?ee rate puzzle One response to the equity premium puzzle is to consider larger values for the coefficient of relative risk aversion ~/. Kandel and Stambaugh (1991) have advocated

9 This point is relevant for the study of Goetzmann and Jorion (1997). These authors measure average growth rates &real stock prices, as a proxy for real stock returns, bnt they do not look at real returns on short-term debt. They find low real stock-price growth rates in many countries in the early 20th Century; in some cases these may have been accompanied by low returns to holders of short-term debt. Note also that stock-price growth rates are a poor proxy for total stock returns in periods where investors expect low growth rates, since dividend yields will tend to be higher in such periods.

Ch. 19:

Asset Prices, Consumption, and the Business Cycle

1253

this l°. However this leads to a second puzzle. Equation (15) implies that the unconditional mean riskless interest rate is

Er];t+l = - l o g 6 + g g -

y2~ 2 '

(17)

where g is the mean growth rate o f consumption. Since g is positive, as shown in Table 3, high values o f 7 imply high values o f 7g. Ignoring the term -y2o~2/2 for the moment, this can be reconciled with low average short-term real interest rates, shown in Table 2, only if the discount factor 6 is close to or even greater than one, corresponding to a low or even negative rate of time preference. This is the riskfree rate puzzle emphasized by Weil (1989). Intuitively, the riskfree rate puzzle is that if investors are risk-averse then with power utility they must also be extremely unwilling to substitute intertemporally. Given positive average consumption growth, a low riskless interest rate and a high rate of time preference, such investors would have a strong desire to borrow from the future to reduce their average consumption growth rate. A low riskless interest rate is possible in equilibrium only if investors have a low or negative rate o f time preference that reduces their desire to borrow 11 O f course, if the risk aversion coefficient g is high enough then the negative quadratic term -V2a~/2 in Equation (17) dominates the linear term and pushes the riskless interest rate down again. The quadratic term reflects precautionary savings; risk-averse agents with uncertain consumption streams have a precautionary desire to save, which can work against their desire to borrow. But a reasonable rate o f time preference is obtained only as a knife-edge case. Table 6 illustrates the riskfree rate puzzle in international data. The table first shows the average riskfree rate from Table 2 and the mean consumption growth rate and standard deviation o f consumption growth from Table 3. These moments and the risk aversion coefficients calculated in Table 5 are substituted into Equation (17), and the equation is solved for an implied time preference rate. The time preference rate is reported in percentage points per year; it can be interpreted as the riskless real interest rate that would prevail if consumption were known to be constant forever at its current level, with no growth and no volatility. Risk aversion coefficients in the RRA(2) range imply negative time preference rates in every country except Switzerland, whereas larger risk aversion coefficients in the RRA(I) range imply time preference rates that are often positive but always implausible and vary wildly across countries.

J0 One might think that introspection would be sufficient to rule out very large values of V, but Kandel and Stambaugh (1991) point out that introspection can deliver very different estimates of risk aversion depending on the size of the gamble considered. This suggests that introspection can be misleading or that some more general model of utility is needed. I~ As Abel (1999) and Kocherlakota (1996) point out, negative time preference is consistent with finite utility in a time-separable model provided that consumption is growing, and marginal utility shrinking, sufficiently rapidly. The question is whether negative thne preference is plausible.

J.Y. Campbell

1254 Table 6 The riskfree rate puzzle a Country

Sample period

r~

Ac

o(Ae)

RRA(1)

USA

1947.2-1996.3

0.794

1 . 9 0 8 1.084

246.556

112.474

47.600

-76.710

AUL

1970.1 1996.2

1.820

1 . 8 5 4 2.142

45.704

-34.995

7.107

-10.196

CAN

1970.1-1996.2

2.738

1 . 9 4 8 2.034

56.434

8.965

-13.066

FR GER

1973.~1996.2 1978.4-1996.2

2.736 3.338

1 . 5 8 1 2.130 1.576 2.495

<0 343.133

ITA

1971.2 1995.2

2.064

2.424

JPN NTH

1970.2-1996.2 1977.2-1996.1

1.538 3.705

3.416 2.353 1 . 4 6 6 2.654

SWD

1970.1 1994.4

1.520

0.750

1.917 >1000

SWT

1982.2-1996.2

1.466

0.414

2.261

UK USA

1970.1 1996.2 1970.1-1996.3

1.08i 1.350

2.025 2.589 1 . 7 1 0 0.919

SWD

1920 1993

2.073

1 . 7 4 8 2.862

65.642

63.778

11.091 -12.274

UK USA

1919-1993 1891-1994

1.198 1.955

1 . 3 5 8 2.820 1 . 7 4 2 3.257

39.914 20.861

10.364 11.305

14.174 10.366

1.684 >1000

TPR(1)

41.346 N/A >1000 >1000

14.634 -15.536 13.327 12.142 4.703

-9.021

13.440 23.970

-39.375 -11.201

>1000

20.705

-6.126

N/A

26.785

8.698

134.118 41.222 >1000 >1000 <0

RRA(2) TPR(2)

1 5 6 . 3 0 8 503.692 1 5 0 . 1 3 6 -160.275

14.858 -21.600 37.255 -56.505

-10.057 10.406

a ~: is the mean money market return from Table 2, in annualized percentage points. Ae and cr(Ae) are the mean and standard deviation of consmnption growth from Table 3, in annualized percentage points. RRA(1) and RRA(2) are the risk aversion coefficients from Table 5. TPR(1)= 7 - RRA(1)Ac + RRA(1)2g2(Ac)/200, and TPR(2) = ~ - RRA(2)Ac + RRA(2)2oZ(Ac)/200. From Equation (17), these time preference rates give the real interest rate, in annualized percentage points, that would prevail if consumption growth had zero mean and zero standard deviation and risk aversion were RRA(1) or RRA(2), respectively. Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan; NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America.

A n interesting issue is h o w m i s m e a s u r e m e n t o f average inflation m i g h t affect these calculations. There is a g r o w i n g consensus that in recent years conventional price indices have overstated true inflation by failing to fully capture the effects o f quality improvements, c o n s u m e r substitution to cheaper retail outlets, and price declines in n e w l y introduced goods. I f inflation is overstated by, say, 1%, the real interest rate is understated by 1%, w h i c h by itself m i g h t help to explain the riskfree rate puzzle. U n f o r t u n a t e l y the real growth rate o f c o n s u m p t i o n is also understated by 1%, w h i c h worsens the riskfree rate puzzle. W h e n y > 1, this second effect d o m i n a t e s and understated inflation m a k e s the riskfree rate p u z z l e even harder to explain.

Ch. 19." Asset Prices, Consumption, and the Business Cycle

1255

Table 7 International yield spreads and bond excess returns Country

Sample period

USA

1947.2-1996.4

AUL

1970.1-1996.3

a(s)

p(s)

er~

1.199

0.999

0.783

0.938

1.669

~

a

a(erb)

p(erb)

0.011

8.923

0.070

0.750

0.156

8.602

0.162

CAN

1970.1 1996.3

1.057

1.651

0.819

0.950

9.334

-0.009

FR GER

1973.2 1996.3 1978.4-1996.3

0.917 0.99l

1.547 1.502

0.733 0.869

1.440 0.899

8.158 7.434

0.298 0.117

ITA

197t.~1995.3

0.200

2.025

0.759

1.386

9.493

0.335

JPN NTH

1970.2-1996.3 1977.2-1996.2

0.593 1.212

1.488 1.789

0.843 0.574

1.687 1549

9.165 7.996

-0.058 0.032

SWD

1970.1-1995.1

0.930

2.046

0.724

0.212

7.575

0.244

SWT

1982.2 1996.3

0.471

1.655

0.755

1.071

6.572

0.268

UK USA

1970.1 1996.3 1970.1-1996.4

1.202 1.562

2.106 1.190

0.893 0.737

0.959 1.504

11.611 10.703

0.057 0.033

SWD UK

1920-1994 1919-1994

0.284 1.272

1.140 1.505

0.280 0.694

-0.075 0.318

6.974 8.812

0.185 -0.098

USA

1891 1995

0.720

1.550

0.592

0.172

6.499

0.153

a S is the mean of the log yield spread, the difference between the log yield on long-term bonds and the log 3-month money market return, expressed in annualized percentage points. ~7(s) is the standard deviation of the log yield spread and p(s) is its first-order autocorrelation, erh, a(ert,), and p(erb) are defined in the same way for the excess 3-month return on long-term bonds over money market instruments, where the bond return is calculated from the bond yield using the par-bond approximation given in Campbell, Lo and MacKinlay (1997), Chapter 10, equation (10.1.I9). Full details of this calculation are given in thc Data Appendix. Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan; NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America.

3.4. Bond returns and the equity premium and riskfree rate puzzles S o m e authors have argued that the riskfree interest rate is low because short-term g o v e r n m e n t debt is m o r e liquid than l o n g - t e r m financial assets. Short-term debt is " m o n e y l i k e " in that it facilitates transactions and can be traded at m i n i m a l cost. The liquidity advantage o f debt reduces its e q u i l i b r i u m return and increases the equity p r e m i u m [Bansal and C o l e m a n (1996), H e a t o n and Lucas (1996)]. The difficulty with this argument is that it implies that all l o n g - t e r m assets should have large excess returns over short-term debt. L o n g - t e r m g o v e r n m e n t bonds, for example, are not m o n e y l i k e and so the liquidity a r g u m e n t implies that they should offer a large t e r m p r e m i u m . But historically, the t e r m p r e m i u m has been m a n y times smaller than the equity p r e m i u m . This point is illustrated in Table 7, which reports two

1256

J g Campbell

alternative measures of the term premium. The first measure is the average log yield spread on long-term bonds over the short-term interest rate, while the second is the average quarterly excess log return on long bonds. In a long enough sample these two averages should coincide if there is no upward or downward drift in interest rates. The average yield spread is typically between 0.5% and 1.5%. A notable outlier is Italy, which has a negative average yield spread in this period. Average long bond returns are quite variable across countries, reflecting differences in inflationary experiences; however in no country does the average excess bond return exceed 1.7% per year. Thus both measures suggest that term premia are far smaller than equity premia. Table 8 develops this point further by repeating the calculations of Table 5, using bond returns rather than equity returns. The average excess log return on bonds over short debt, adjusted for Jensen's Inequality, is divided by the standard deviation of the excess bond return to calculate a bond Sharpe ratio which is a lower bound on the standard deviation of the stochastic discount factor. The Sharpe ratio for bonds is several times smaller than the Sharpe ratio for equities, indicating that term premia are small even after taking account of the lower volatility of bond returns. This finding is not consistent with a strong liquidity effect at the short end of the term structure, but it is consistent with a consumption-based asset pricing model if bond returns have a low correlation with consumption growth. Table 8 shows that sample consumption correlations often are lower for bonds, so that RRA(1) risk aversion estimates for bonds, which use these correlations, are often comparable to those for equities. A direct test of the liquidity story is to measure excess returns on stocks over long bonds, rather than over short debt. If the equity premium is due to a liquidity effect on short-term interest rates, then there should be no "equity-bond premium" puzzle. Table 9 carries out this exercise and finds that the equity-bond premium puzzle is just as severe as the standard equity premium puzzle 12.

3.5. Separating risk aversion and intertemporal substitution Epstein and Zin (1989, 1991) and Weil (1989) use the theoretical framework of Kreps and Porteus (1978) to develop a more flexible version of the basic power utility model. That model is restrictive in that it makes the elasticity of intertemporal substitution, % the reciprocal of the coefficient of relative risk aversion, 7. Yet it is not clear that these two concepts should be linked so tightly. Risk aversion describes the consumer's reluctance to substitute consumption across states of the world and is meaningful even

12 The excess return of equities over bonds must be measured with the appropriate correction for Jensen's Inequality. From Equation (16), the appropriate measure is the log excess return on equities over short-term debt, less the log excess return on bonds over short-term debt, plus one-halfthe variance of the log equity return, less one-half the variance of the log bond return.

1257

Ch, 19.• Asset Prices, Consumption, and the Business Cycle

~, ~

o

~,,

~

.

,

~

r¢3 t'4

V

V

,.n

~

~.

~

~.. V

•~

z

I

,.~

%

t-'q

~

t" ~

~

~

rz

t

0

t'-q

,,6 ~6 ,,6

•

"

~

~

~

~

~

~

~

~

~

~

~

r~

2

Z

JK Campbell

1258

¢S"~ ~

o O9 oo ~

V

V

~

~

<~

%

~o ~ ,

~

~~

~ .~q

L~ i ~~

_ ~ ~2

.

.

~

~

.

~

.

°<%

.

~

"~'" "~

J

~ ~.~

I!~ ~ -~

< ~.~

o

~

o

o

~

,~ ~.~

1259

Ch. 19: Asset Prices, Consumption, and the Business Cycle

in an atemporal setting, whereas the elasticity of intertemporal substitution describes the consumer's willingness to substitute consumption over time and is meaningful even in a deterministic setting. The Epstein-Zin--Weil model retains many of the attractive features of power utility but breaks the link between the parameters y and ~p. The Epstein-Zin-Weil objective function is defined recursively by 0

U,=

(1-6)C 7+6

G_.f\

,

(18)

where 0 = (1 - y ) / ( l - l/W). When y - I/W, 0 = 1 and Equation (18) becomes linear; it can then be solved forward to yield the familiar time-separable power utility model. The integemporal budget constraint for a represemative agent can be written as V/t+1 - (1 + Rw, t+l) (J4zt CI),

(19)

- -

where Wt+l is the representative agent's wealth, and (1 + Rw, t+l) is the gross simple return on the portfolio of all invested wealth 13. This form of the budget constraint is appropriate for a complete-markets model in which wealth includes human capital as well as financial assets. Epstein and Zin use dynamic programming arguments to show that Equations (18) and (19) together imply an Euler equation of the form

I=G

\CT-t /

(1 +Rw, t < )

(1 +R,,,+I)

1 .

(20)

If I assume that asset returns and consumption are homoskedastic and jointly lognormal, then this implies that the riskless real interest rate is rj;t+l = - l o g 6 +

0-1 2 0 E,[Act+l] + ~ 2 - - cG - ~ 2

2 o~.

(21)

The riskless interest rate is a constant, plus 1/~p times expected consumption growth. In the power utility model, 1/ip = y and 0 = 1, so Equation (21) reduces to Equation (15). The premium on risky assets, including the wealth portfolio itself, is 62 o,, E,[ri,,+l] - rj;,+l + " - 0 +(1 - O)oiw. 2 ~0

(22)

The risk premium on asset i is a weighted combination of asset i's covariance with consumption growth (divided by the elasticity of intertemporal substitution W) and

13 This is often called the "market" return and written Rm,t~ i, but l have already used m to denote the stochastic discount factor so I write R,,,t~l to avoid confusion.

J.Y. Campbell

1260

asset i's covariance with the return on wealth. The weights are 0 and 1 - 0 respectively. The Epstein-Zin-Weil model thus nests the consumption CAPM with power utility (0 = 1) and the traditional static CAPM (0 = 0). Equations (21) and (22) seem to indicate that Epstein-Zin-Weil utility might be helpful in resolving the equity premium and riskfree rate puzzles. First, in Equation (21) a high risk aversion coefficient does not necessarily imply a low average riskfree rate, because

Erj;t+l = - l o g 6 +

g +

0--1

2

~rw -

0

or2.

(23)

The average consumption growth rate is divided by ~p here, and in the Epstein-ZinWell framework ~p need not be small even if ~ is large. Second, Equation (22) suggests that it might not even be necessary to have a high risk aversion coefficient to explain the equity premium. I f 0 ~ 1, then the risk premium on an asset is determined in part by its covariance with the wealth portfolio, a/w. If the return on wealth is more volatile than consumption growth, as implied by the common use of a stock index return as a proxy for the return on wealth, then Oiw may be much larger than oic, and this may help to explain the equity premium. Unfortunately, there are serious difficulties with both these potential escape routes from the equity premium and riskfree rate puzzles. The difficulty with the first is that there is direct empirical evidence for a low elasticity of intertemporal substitution in consumption. The difficulty with the second is that consumption and wealth are linked through the intertemporal budget constraint; if consumption is smooth and wealth is volatile, this itself is a puzzle that must be explained, not an exogenous fact that can be used to resolve other puzzles. I now develop these points in detail by analyzing the dynamic behavior of stock returns and short-term interest rates in relation to consumption.

4. The dynamics of asset returns and consumption 4.1. Time-variation in conditional expectations

Equations (21) and (22) imply a tight link between rational expectations of asset returns and of consumption growth. Expected asset returns are perfectly correlated with expected consumption growth, with a standard deviation 1/~p times as large. Equivalently, the standard deviation of expected consumption growth is ~p times as large as the standard deviation of expected asset returns.

Ch. 19: Asset Prices', Consumption, and the Business Cycle

1261

This suggests a way to estimate % Hansen and Singleton (1983), followed by Campbell and Mankiw (1989), Hall (1988), and others, have proposed an instrumental variables (IV) regression approach. I f we define an error term t/i, t+l ~ ri, t+l

- -

Et[ri, t+l] - 7(Act+t - Et[ACt+l]),

then we can rewrite Equations (21) and (22) as a regression equation,

(24) In general the error term t/i,t+l will be correlated with realized consumption growth so OLS is not an appropriate estimation method. However t/i,t+l is uncorrelated with any variables in the information set at time t. Hence any lagged variables correlated with asset returns can be used as instruments in an IV regression to estimate 1/% Table 10 illustrates two-stage least squares estimation o f Equation (24). In each panel the first set o f results uses the short-term real interest rate, while the second set uses the real stock return. The instruments are the asset return, the consumption growth rate, and the log price-dividend ratio. The instruments are lagged twice to avoid difficulties caused by time-aggregation of the consumption data ]Campbell and Mankiw (1989, 1991), Wheatley (1988)]. For each asset and set o f instruments, the table first reports the R 2 statistics and significance levels for first-stage regressions o f the asset return and consumption growth rate onto the instruments. The table then shows the IV estimate of 1/~p with its standard error, and (in the column headed "Test (1)") the R 2 statistic for a regression of the residual on the instruments together with the associated significance level of a test o f the over-identifying restrictions o f the model. The quarterly results in Table 10 show that the short-term real interest rate is highly forecastable in every country except Germany. The real stock return is also forecastable in many countries, but there is weaker evidence for forecastability in consumption growth. In fact the R 2 statistic for forecasting consumption growth is lower than the R 2 statistic for stock returns in all but four of the quarterly data sets. The IV estimates of 1/~p are very imprecise; they are sometimes large and positive, often negative, but they are almost never significantly different from zero. The overidentifying restrictions of the model are often strongly rejected, particularly when the short-term interest rate is used in the model. Results are similar for the annual data sets in Table 10, except that twice-lagged instruments have almost no ability to forecast real interest rates or stock returns in the annual US data 14

14 Campbell, Lo and MacKinlay (1997), Table 8.2, shows much greater fbrecastability of returns using once-lagged instruments in a similar annual US data set. Even with twice-lagged hlstruments, US annual returns become forecastable once one increases the return horizon beyond one year, as shown in Table 12 below.

1262

J Y. Campbell

Table 10 Predictable variation in returns and consumption growth a Count~2¢

USA

AUL

CAN

FR

GER

ITA

JPN

NTH

SWD

Sample period

1947.~1996.3

1970.2 1996.2

1970.2 1996.2

1973.2-1996.2

1978.4-1996.2

1971.2-1995.2

1970.~1996.2

1977.2-1996.1

1970.2 1994.4

Asset

First-stage regressions

(1/~--~) (s.e.)

Test b (s.e.)

1

2

ri

Ac

rf

0.160 0.000

0.037 0.077

0.260 0.740

0.025 0.114

0.165 0.000

0.037 0.027

re

0.065 0.003

0.037 0.077

-8.187 7.069

0.021 0.028

0.035 0.033

0.025 0.090

rf

0.404 0.000

0.013 0.432

4.450 2.973

0.099 0.107

0.017 0.419

0,008 0,676

r,,

0.060 0.034

0.013 0.432

20.250 13.145

0.038 0.026

0.004 0.828

0.003 0.856

rf

0.292 0.000

0.048 0.042

-0.970 0.677

-0.174 0.177

0.142 0.001

0.041 0.123

r~

0.040 0.269

0.048 0,042

6.635 4.536

0.130 0.092

0.004 0.822

0.004 0.819

r!

0.519 0.000

0.010 0.751

-2.189 2.170

-0.051 0.133

0.073 0.037

0.009 0,667

r~

0.111 0.006

0.010 0.751

-27.662 29.994

-0.021 0.026

0.006 0,750

0.004 0.833

1)-

0.062 0.328

0.057 0.085

0.481 0.354

1.773 1.141

0.005 0.840

0.005 0.841

r~

0.046 0.050

0.057 0.085

-6.117 4.992

0.079 0.066

0.017 0.569

0.018 0.547

rj

0.405 0.000

0.010 0.877

-2.432 3.353

-0.019 0.113

0.171 0.000

0.010 0,624

re

0.048 0.278

0.010 0.877

19.919 26.244

0.016 0.034

0.013 0.540

0.007 0.734

rf

0.203 0.002

0.044 0.081

-0.446 0.464

-0.093 0.266

0.162 0.000

0.04 l 0.121

r~

0.115 0,001

0.044 0.081

11.028 5.458

0.047 0.027

0.026 0.260

0.019 0.376

rj

0.248 0.000

0.024 0.373

0,167 0.385

0.052 0.428

0.218 0,000

0.023 0.428

re

0.021 0.756

0.024 0.373

-4.532 6.571

-0.138 0.162

0.005 0,835

0,005 0.832

rj

0.262 0.000

0.005 0.806

-1.056 2,949

-0.007 0.085

0.197 0000

0.005 0,779

r~,

0.110 0.039

0.005 0.806

15.210 21.187

0.004 0.017

0.047 0.107

0.005 0.790

continued on next page

1263

Ch. 19." Asset Prices, Consumption, and the Business Cycle

Table 10, continued Country

SWT

UK

USA

SWD

UK

USA

Sample period

1982.2 1996.2

1970.~1996.2

1970.2-1996.3

1920-1993

1920-1993

1891-1994

Asset

First-stage regressions

(1/~-~) (s.e.)

~ (s.e.)

1

Test b 2

ri

Ac

rf

0.194 0.000

0.007 0.887

0.731 1.273

0.065 0.397

0.074 0.136

0.006 0.844

re

0.033 0.270

0.007 0.887

20.084 31.100

0.048 0.070

0.000 0.996

0.000 0.996

rf

0.306 0.000

0.057 0.042

1.992 0.988

0.260 0.136

0.047 0.090

0.028 0.238

re

0.097 0.094

0.057 0.042

-4.493 3.793

0.038 0.034

0.056 0.058

0.040 0.132

J)

0.307 0.000

0.071 0.015

1.573 0.704

0.t02 0.111

0.188 0.000

0.062 0.041

rC

0.069 0.095

0.071 0.015

4.977 7.677

0.016 0.023

0.069 0.029

0.071 0.025

rf

0.302 0.000

0.052 0.202

2.740 1.466

0.194 0.t61

0.037 0.266

0.023 0.437

r~

0.041 0.342

0.052 0.202

-1.537 3.349

0.043 0.082

0.034 0.304

0.041 0.236

r~/

0.265 0.000

0.061 0.140

2.499 1.509

0.197 0.123

0.056 0.139

0.033 0.314

r~,

0.147 0.096

0.061 0.140

5.861 4.569

0.037 0.021

0.115 0.017

0.055 0.144

~/

0.013 0.783

0.065 0.004

-0.293 0.892

-0.202 0.341

0.012 0.552

0.049 0.085

r,,

0.037 0.184

0.065 0.004

0.723 2.003

0.038 0.070

0.040 0.132

0.074 0.024

a This table reports two-stage least squares eshination results for Equations (24) and (25). The first set of results for each country uses the short-term real interest rate, while the second set uses the real stock return. The instruments are the asset return, the consumption growth rate, and the log price-dividend ratio, lagged twice. For each asset and set o f instruments, the first two colunms show the R 2 statistics, with significance levels below, lbr first-stage regressions o f the asset return and consumption growth rate onto the instruments. The third column shows the IV estimate of 1/~p from Equation (24) with its standard error below, and the fourth column shows the IV estimate of ~p from Equation (25) with its standard error below. The fifth column, headed "Test (1)", shows the R 2 statistic for a regression of the residual from Equation (24) on the instruments, with the associated significance level below of a test of the over-identifying restrictions of the model. The sixth column, headed "Test (2)" is the equivalent of the fifth column for Equation (25). Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan; NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America. b Tests: (1)ri,t~ j =t, ti-t-(1/~O)Act+t+rli,t+l; (2) Act+t - Ti + ~/)1~,1~1 +~z,t41.

J E Campbell

1264

Campbell and Mankiw (1989, 1991) have explored this regression in more detail, using both US and international data, and have found that predictable variation in consumption growth is often associated with predictable variation in income growth. This suggests that some consumers keep their consumption close to their income, either because they follow "rules of thumb", or because they are liquidity-constrained, or because they are "buffer-stock" savers [Deaton (1991), Carroll (1992)]. After controlling for the effect of predictable income growth, there is little remaining predictable variation in consumption growth to be explained by consumers' response to variation in real interest rates. One problem with IV estimation of Equation (24) is that the instruments are only very weakly correlated with the regressor because consumption growth is hard to forecast in this data set. Nelson and Startz (1990) have shown that in this situation asymptotic theory can be a poor guide to inference in finite samples; the asymptotic standard error of the coefficient tends to be too small and the overidentifying restrictions of the model may be rejected even when it is true. To circumvent this problem, one can reverse the regression (24) and estimate A c t + 1 = ~ -t- ~gri, t+ 1 + ~i,t+l.

(25)

If the orthogonality conditions hold, then the estimate of 'qJ in Equation (25) will asymptotically be the reciprocal of the estimate of 1/~p in Equation (24). In a finite sample, however, if ~p is small then IV estimates of Equation (25) will be better behaved than IV estimates of Equation (24). In Table 7 ~p is almost always estimated to be close to zero. The estimates are much more precise than those for 1/% The overidentifying restrictions of the model are sometimes rejected, but less often and less strongly than when Equation (24) is estimated. These results suggest that the elasticity of intertemporal substitution ~p is small, so that the generality of the Epstein-Zin-Weil model, which allows ~p to be large even if ~/is large, does not actually help one fit the data on consumption and asset returns 15.

4.2. A loglinear asset pricing J?amework in order to understand the second momems of stock returns, it is essential to have a framework relating movements in stock prices to movements in expected future dividends and discount rates. The present value model of stock prices is intractably nonlinear when expected stock returns are time-varying, and this has forced researchers to use one of several available simplifying assumptions. The most common approach is to assume a discrete-state Markov process either for dividend growth [Mehra and

15 Attanasio and Weber (1993) and Beaudry and van Wincoop (1996) have argued that this conclusion depends on the use of aggregate consumption data. They work with cohort-level and state-level data, respectively, and fred some evidence for a larger elasticity of intertemporal substitution.

Ch. 19: Asset Prices', Consumption, and the Business Cycle

1265

Prescott (1985)] or, following Hamilton (1989), for conditionally expected dividend growth [Abel (1994, 1999), Cecchetti, Lam and Mark (1990, 1993), Kandel and Stambaugh (1991)]. The Markov structure makes it possible to solve the present value model, but the derived expressions for returns tend to be extremely complicated and so these papers usually emphasize numerical results derived under specific numerical assumptions about parameter values 16. An alternative framework, which produces simpler closed-form expressions and hence is better suited for an overview of the literature, is the loglinear approximation to the exact present value model suggested by Campbell and Shiller (1988). Campbell and Shiller's loglinear relation between prices, dividends, and returns provides an accounting framework: High prices must eventually be followed by high future dividends or low future returns, and high prices must be associated with high expected future dividends or low expected future returns. Similarly, high returns must be associated with upward revisions in expected future dividends or downward revisions in expected future returns. The loglinear approximation starts with the definition of the log return on some asset i, ri, t+l ~ log(Pi, t+l + Di, t+l) - log(Pit). The timing convention here is that prices are measured at the end of each period so that they represent claims to next period's dividends. The log return is a nonlinear function of log prices Pit and pi, t+l and log dividends di, t+l, but it can be approximated around the mean log dividend-price ratio, (dit - P a ) , using a first-order Taylor expansion. The resulting approximation is ri, t+l ~ k +/)Pi, t tl +(1 -/))di, t + l - P i t ,

(26)

where/) and k are parameters of linearization defined b y / ) = 1/(1 + e x p ( ~ ) ) and k log(/)) - (1 - / ) ) l o g ( l / / ) - 1). When the dividend-price ratio is constant, then p P i / ( P i + Di), the ratio of the ex-dividend to the cum-dividend stock price. In the postwar quarterly US data shown in Table 3, the average price-dividend ratio has been 26.4 on an annual basis, implying that/) should be about 0.964 in annual data 17 The Taylor approximation (26) replaces the log of the sum of the stock price and the dividend in the exact relation with a weighted average of the log stock price and the log dividend. The log stock price gets a weight/) close to one, while the log dividend gets a weight 1 - p close to zero because the dividend is on average much smaller than the stock price, so a given percentage change in the dividend has a much smaller effect on the return than a given percentage change in the price. =

Ic, A partial exception to this statement is that Abel (1994) derives several analytical results for the first moments of retarns in a Markov model for expected dividend growth. 17 Strictly speaking both p and k should have asset subscripts i, but 1 omit these for simplicity. The asset pricing formulas later in this chapter assume that all assets have the samep, which simplifiessome expressions but does not change any of the qualitative conclusions.

1266

JE Campbe#

Equation (26) is a linear difference equation for the log stock price. Solving forward, imposing the terminal condition that limj~o~ PJPi, t+j = 0 , taking expectations, and subtracting the current dividend, one gets 0<3

pit-d#-

k 1 -p

kE~ Zp.i[Adi,~+l+j-ri,,+l+j].

(27)

.i=o

This equation says that the log price-dividend ratio is high when dividends are expected to grow rapidly, or when stock returns are expected to be low. The equation should be thought of as an accounting identity rather than a behavioral model; it has been obtained merely by approximating an identity, solving forward subject to a terminal condition, and taking expectations. Intuitively, if the stock price is high today, then from the definition of the return and the terminal condition that the stock price is non-explosive, there must either be high dividends or low stock returns in the future. hwestors must then expect some combination of high dividends and low stock returns if their expectations are to be consistent with the observed price. The terminal condition used to obtain Equation (27) is perhaps controversial. Models of "rational bubbles" do not impose this condition. Blanchard and Watson (1982) and Froot and Obstfeld (1991) have proposed simple, explicit models of explosive bubbles in asset prices. There are however several reasons to rule out such bubbles. The theoretical circumstances under which bubbles can exist are quite restrictive; Tirole (1985), for example, uses an overlapping generations framework and finds that bubbles can only exist if the economy is dynamically inefficient, a condition which seems unlikely on prior grounds and which is hard to reconcile with the empirical evidence of Abel, Mankiw, Summers and Zeckhauser (1989). Santos and Woodford (1997) also conclude that the conditions under which bubbles can exist are fragile. Empirically, bubbles imply explosive behavior of prices in relation to dividends and other measures of fundamentals; there is no evidence of this, although nonlinear bubble models are hard to reject using standard linear econometric methods is Equation (27) describes the log price-dividend ratio rather than the log price itself. This is a useful way to write the model because in many data sets dividends appear to follow a loglinear unit root process, so that log dividends and log prices are nonstationary. In this case changes in log dividends are stationary, so from Equation (27) the log price-dividend ratio is stationary provided that the expected stock return is stationary. Thus log stock prices and dividends are cointegrated, and the stationary linear combination of these variables involves no unknown parameters since it is just the log ratio. Table 11 reports some summary statistics for international stock prices in relation to dividends. The table gives the average price-dividend ratio, the standard deviation

t8 Campbell,Lo and MacKinlay (1997), Chapter 7, gives a somewhatmore detailedtextbook discussion of the literature on rational bubbles.

1267

Ch. 19." Asset Prices, Consumption, and the Business Cycle

Table 11 International stock prices and dividends a Country

Sample period

P/D

a(p-d)

ADF(1)

Ap

Ad

USA

1947.~1996.4

27.121

0.265

0.941

-1.752

3.547

2.225

1.688

AUL CAN FR GER ITA JPN NTH SP SWD SWT UK USA

1970.1 1996.3 1970.1-1996.3 1973.2-1996.3 1978.4-1996.3 1971.2-1995.3 1970.2-1996.3 1977.2 1996.2 1984.2 1996.2 1970.1-1995.1 1982.2-1996.3 1970.1 1996.3 1970.1 1996.4

25.919 30.108 22.718 27.787 41.345 91.251 21.139 22.509 35.021 47.320 18.434 27.882

0.267 0.221 0.541 0.300 0.318 0.642 0.272 0.319 0.439 0.217 0.280 0.235

0.856 0.902 0.971 0.922 0.882 0.964 0.932 0.823 0.941 0.814 0.913 0.904

3.273 -1.900 -1.3t0 -1.660 -3.743 -1.574 -0.727 -3.075 -1.632 -1.588 -1.657 -1.372

-1.410 0.754 1.358 4.186 2.172 4.192 7.540 6.843 4.922 9.291 1.464 2.034

0.883 -0.741 -1.214 1.079 4.919 2.489 4.007 -3.086 1.861 4.143 0.681 0.619

-2.477 1.200 2.538 3.853 3.531 6.974 3.637 10.078 3.499 6.074 0.579 1.582

SWD UK USA

1920-1994 1919 1994 1891-1995

26.706 20.806 22.733

0.333 0.238 0.279

0.746 0.514 0.778

0.768 4.093 -1.868

2.129 2.064 2.064

0.423 1.844 1.485

2.054 0.220 0.477

p(p

d)

Ap-d

a P/D is the mean price-dividend ratio, c~(p - d ) is the standard deviation of the log price-dividend ratio in natural units (not annualized percentage points), p(p - d) is the first-order autocorrelation of the log

price-dividend ratio. ADF(1) is the augmented Dickey-Fuller t-ratio for the lagged log price--dividend ratio when the change in the log price-dividend ratio is regressed on a constant, four lagged changes, and the lagged log price dividend ratio. Ap, Ad, and A p - d are the mean changes in log prices, log dividends, and the log price-dividend ratio respectively, in annualized percentage points. Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan; NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America.

of the log p r i c e - d i v i d e n d ratio in natural units, the first-order autocorrelation o f the log p r i c e - d i v i d e n d ratio, average growth rates o f prices, dividends, and the log p r i c e dividend ratio in percentage points per year, and a test statistic for the null hypothesis that the log p r i c e - d i v i d e n d ratio has a unit root. Following standard practice, the p r i c e dividend ratio is m e a s u r e d as the ratio o f the current stock price to the total o f dividends paid during the past year. Average p r i c e - d i v i d e n d ratios vary considerably across countries but generally lie b e t w e e n 20 and 30. The extreme outlier is Japan, w h i c h has a n average p r i c e - d i v i d e n d ratio o f 91. The volatility and first-order autocorrelation o f the log p r i c e - d i v i d e n d ratio are also unusually high for Japan, reflecting an u p w a r d trend in the Japanese log p r i c e -

J.Y. Campbell

1268

dividend ratio for much of the sample period which is also visible in the average growth rates of prices and dividends at the right of the table. Other countries in the quarterly data set, with the exception of France, have firstorder autocorrelation coefficients for the log price-dividend ratio of between 0.85 and 0.95. Unit root tests do not reject the unit root null hypothesis for most of these countries, but this may reflect low power of the tests in short data samples. Equation (27) implies that the log price-dividend ratio must be stationary if real dividend growth and stock returns are stationary, so this gives some reason to assume stationarity for the series. So far I have written asset prices as linear combinations of expected future dividends and returns. Following Campbell (1991), I can also write asset returns as linear combinations of revisions in expected future dividends and returns. Substituting Equation (27) into Equation (26), I obtain OO

ri, l+l - E t ri, t+l = (Et+l - E t ) ~ P J A ~ , t , 1 .i- o

OO

pJri, t +l+j.

i:j- (Et ~l - E t ) ~ j -

(28)

1

This equation says that unexpected stock returns must be associated with changes in expectations of future dividends or real returns. An increase in expected future dividends is associated with a capital gain today, while an increase in expected future returns is associated with a capital loss today. The reason is that with a given dividend stream, higher future returns can only be generated by future price appreciation from a lower current price.

4.3. The stock market oolatility puzzle I now use this accounting framework to illustrate the stock market volatility puzzle. The intertemporal budget constraint for a representative agent, Equation (19), implies that aggregate consumption is the dividend on the portfolio of all invested wealth, denoted by subscript w:

dwt = ct.

(29)

Many authors, including Grossman and Shiller (1981), Lucas (1978), and Mehra and Prescott (1985), have assumed that the aggregate stock market, denoted by subscript e for equity, is equivalent to the wealth portfolio and thus pays consumption as its dividend. Here I follow Campbell (1986) and Abel (1999) and make the slightly more general assumption that the dividend on equity equals aggregate consumption raised to a power )~. In logs, we have

det - ,~ct.

(30)

Abel (1999) shows that the coefficient )~ can be interpreted as a measure of leverage. When )~ > 1, dividends and stock returns are more volatile than the returns on the

Ch. 19." AssetPrices, Consumption, and the Business Cycle

1269

aggregate wealth portfolio. This framework has the additional advantage that a riskless real bond with infinite maturity - an inflation-indexed consol, denoted by subscript b can be priced merely by setting )~ = 0. The representative-agent asset pricing model with Epstein-Zin-Weil utility, conditional lognormality, and homoskedasticity [Equations (21) and (22)] implies that

Etre, t+l=~e+(@)EtAct+l,

(31)

where g~ is an asset-specific constant term. The expected log return on equity, like the expected log return on any other asset, is just a constant plus expected consumption growth divided by the elasticity of intertemporal substitution % Power utility is the special case where the coefficient of relative risk aversion y is the reciprocal of ~p so the effect of expected consumption growth on expected asset returns is proportional to y; but this is not true in general. Substituting Equations (30) and (31) into Equations (27) and (28), I find that

~-t-

(32)

)~-- ~)) Et ZpJmct+l±f, j=0

and

re, t+l -Et re, t+l = Z(Act+l -E/AG+I)+

Z-

(Et+l - E t )

Zp/Act+I+j.

(33)

j=[

Expected future consumption growth has offsetting effects on the log price-dividend ratio. It has a direct positive effect by increasing expected future dividends X-forone, but it has an indirect negative effect by increasing expected future real interest rates (1/~0)-for-one. The unexpected log return on the stock market is X times contemporaneous unexpected consumption growth (since contemporaneous consumption growth increases the contemporaneous dividend X-for-one), plus (3,- 1/~p) times the discounted sum of revisions in expected future consumption growth. For future reference I note that Equation (33) can be inverted to express consumption growth as a function of tile unexpected return on equity and revisions in expectations about future returns on equity. Rearranging Equation (33) and using Equation (31), ACt+l - Et Act+l =

(re, t ~q- Efre, t+l) +

-~P (Et~l-Et)ZpJr.,t+l+j. j=l

(34) An innovation in the equity return raises wealth by a factor (1/;~), and this raises consumption by the same factor. Increases in expected future equity returns have offsetting income and substitution effects on consumption; the positive income effect is (t/)~), and the negative substitution effect is - %

1270

1 Y. Campbell

These equations can be simplified if I assume that expected aggregate consumption growth, which I write as zt, follows an AR(1) process with mean g and positive persistence O: Act+l = zt + Cc, t+l,

(35)

zt+l = (1 - O)g + ~zt + ez, t+l.

(36)

This is a linear version o f the model used by Cecchetti, Lam and Mark (1990, 1993) and Kandel and Stambaugh (1991), in which expected consumption growth follows a persistent discrete-state Markov process. The contemporaneous shocks to realized consumption growth ~c,t+~ and expected future consumption growth c~,t+~ may be positively or negatively correlated. The correlation between these contemporaneous shocks controls the univariate autocovariances of consumption growth; the first-order autocovariance is ~bVar(zt)+ Cov(ez, t ~1, co, t+l), and higher-order autocovariances die out geometrically at rate ~b. Thus consumption growth inherits the positive serial correlation of the zt process unless the contemporaneous shocks are sufficiently negatively correlated. An important special case of the model sets Cz,t+l = ~ec, t+l to make consumption growth itself an AR(1) process; this is a linear version of the model of Mehra and Prescott (1985) 19 From Equation (21), the riskless interest rate is linear in expected consumption growth zs, so this model implies a homoskedastic AR(1) process for the riskless interest rate, with persistence 0. It is a discrete-time version of the Vasicek (1977) model o f the term structure o f interest rates. Campbell, Lo and MacKinlay (1997), Chapter 11, gives a detailed textbook exposition of this model following Backus (1993), Singleton (1990), and Sun (1992). Equations (35) and (36) allow me to rewrite Equations (32) and (33) as _Pc, - det

-

1-p

+

,~-

+

~

(37)

1-p~bJ '

and =

-

ez,~+l.

(38)

Equation (38) shows why it is difficult to match the volatility of stock returns within this standard framework. The most obvious way to generate volatile stock returns is

19 The empirical evidence on univariate serial correlation in consumption growth is mixed. Table 4 shows small negative autocorrelation in 8 out of 12 quarterly data sets, but only 1 out of 3 annual data sets. Measurement problems may bias these autocorrelations in either direction. Durability of consumption tends to bias autocorrelation downwards, but time-averaging and seasonal adjustment tend to bias it upwards. Empirical estimates of discrete-state Markov models by Cecchetti, Lain and Mark (1990, 1993), Kandel and Stambaugh (1991), and Mehra and Prescott (1985) find some evidence for modest but persistent predictable variation in consumption growth.

Ch. 19: Asset Prices', Consumption, and the Business Cycle

1271

to assume a large ,t, that is, a volatile dividend, increasing )~, however, has mixed effects; it increases the volatility of the first term in Equation (38) proportionally, but as long as '1 < 1/*p it diminishes the volatility of the second term because the dividend and real interest rate effects of expected consumption growth offset each other more exactly. The overall volatility of stock returns may actually fall, or grow only slowly, with '1 until the point is reached where '1 > 1/~p. The empirical evidence for small ~p presented in Table 10 suggests that very high ,t will be needed to generate volatile stock returns. A similar point has been made by Abel (1999), who emphasizes that predictable variation in expected consumption growth can dampen stock market volatility and exacerbate the equity premium puzzle. This model also tends to produce highly volatile returns on real (inflation-indexed) bonds. By setting '1 = 0 in Equations (37) and (38), the log yield and unexpected return on a real consol bond, denoted by a subscript b, are

Ybt = db~ Pbt -

kl, ~ 1- p

+

1 - p~ ] '

(39)

and

rb, t+l-Etrb, t + l - - - ( ; )

( 1 P _ ~ ) e z , t+l .

(40)

When ~p is small, even modest variation in zt will tend to produce large variation in the riskffee interest rate and in the yields and returns on long-term real bonds. The correlation of stock and real bond returns is positive if )~ < 1/% but turns negative if '1 is large enough so that ,~ > 1/~p. Of course, all these calculations are dependent on the assumption made at the beginning of this subsection, that the log dividend on stocks is a multiple )~ of log aggregate consumption. More general models, allowing separate variation in dividends and consumption, can in principle generate volatile stock returns without excessive variation in real interest rates. For example, we might modify Equation (30) to allow a second autonomous component of the dividend: det -'1c~ ~ at,

(41)

where Aat ~q has a similar structure to consumption growth, being forecast by an AR(1) state variable:

Aat~l - Yt + ~a,t+l,

(42)

Yt+l = (1 - 0)v + Oy, -~ ey,~+l.

(43)

This modification of the basic model would add a term v/(1 ---p) + (Yt v)/(1 -pO) to the formula for the log price-dividend ratio, Equation (37), and would add a term

JY. Campbell

1272

~a,t+l + p~y,t+l/(l - p O ) to the formula for the unexpected log stock return, (38). Cecchetti, Lain and Mark (1993) estimate a discrete-state Markov model allowing for this sort of separate variability in consumption and dividends. While such a model provides a more realistic description of dividends, it requires large predictable movements in dividends to explain stock market volatility. Unfortunately, as section 4.5 shows, there is little evidence for this.

4.4. Implications Jbr the equity premium puzzle I now return to the basic model in which the log dividend is a multiple of log aggregate consumption, and use the formulas derived in the previous subsection to gain a deeper understanding of the equity premium puzzle. The discussion of the puzzle in section 3 treated the covariance of stock returns with consumption as exogenous, but given a tight link between stock dividends and consumption the covariance can be derived from the stochastic properties of consumption itself. This is the approach of many papers including Abel (1994, 1999), Kandel and Stambaugh (1991), Mehra and Prescott (1985), and Rietz (1988). An advantage of this approach is that it clarifies the implications of Epstein-ZinWeil utility. The Epstein-Zin-Weil Euler equation is derived by imposing a budget constraint that links consumption and wealth, and it explains risk premia by the covariances of asset returns with both consumption growth and the return on the wealth portfolio. The stochastic properties of consumption, together with the budget constraint, can be used to substitute either consumption or wealth out of the EpsteinZin-Weil model. To understand this point, note that Equation (33) applies to the return on the wealth portfolio when ,~ = 1. Setting e = w and )~ = 1, Equation (33) becomes rw, t+~-Etrw, t+l

Act+l-EtAct~l +

1-

(Et+~-Et)ZpJAc~+l~/,

(44)

j=l

an equation derived by Restoy and Weil (1998) applying the approach of Campbell (1993). It follows that the covariance of any asset return with the wealth portfolio must satisfy

aiw- o~c+ ( 1 - ~ )

ai~,

(45)

where agz denotes the covariance of asset return i with revisions in expectations of future consumption growth: oc

aig =~ Coy (ri, t +~- E~ri, t +1, (Et+ l - Et) Z pJ Act+ l+j). j-1

The letter g is used here as a mnemonic for consumption growth.

(46)

Ch. 19." Asset Prices, Consumption, and the Business Cycle

1273

Substituting this expression into the formula for risk premia in the Epstein-Zin-Weil model, Equation (22), that formula simplifies to

Et[ri,t+l]-rj;t+l + ~- = ]/(Yic-~ Y-

Oig.

(47)

The risk premium on any asset is the coefficient of risk aversion 3/times the covariance of that asset with consumption growth, plus ( 7 - 1/~p) times the covariance of the asset with revisions in expected future consumption growth. The second term is zero if X = 1/% the power utility case, or if there are no revisions in expected future consumption growth 20. I now return to the assumption made in the previous subsection that expected consumption growth is an AR(1) process given by Equation (36). Under this assumption, (E,+I - Et) Z j=l

pJAct+L+j=

ez, t +1.

(48)

Equations (38), (47) and (48) imply that E,[r~,,t+l]-

rf, l+l + -~

y

(49) This expression nests many of the leading cases explored in the literature on the equity premium puzzle. To understand it, it is helpful to break the equity premium into two components, the premium on real consol bonds over the riskless interest rate, and the premium on equities over real consol bonds:

4 E,[rt,,,+ll-rt,t+l+T=7[-~ (1 P--@)

_}_(~/_~) [_@{1_~)20z21 " Et[re,,+l- r<,+I] + 022

(50)

~-Y'~Ia~2+(
(51) 20 Using a continuous-time model, Svensson (1989) also emphasizes that risk premia in the Epstein Zin Weil model are determined only by risk aversion when investment opportunities and expected consumption growth are constant.

1274

J. Z Campbell

Equations (50) and (51) add up to Equation (49). The first term in each of these expressions represents the premium under power utility, while the second term represents the effect on the premium of moving to Epstein-Zin utility and allowing the coefficient of risk aversion to differ from the reciprocal of the intertemporal elasticity of substitution. Given the evidence for small ~p presented in section 4.1, the key issue is whether Epstein-Zin utility allows y to be smaller than 1/lp and in this sense helps resolve the equity premium puzzle. Under power utility, the real bond premium in Equation (50) is determined by the covariance oc., of realized consumption growth and innovations to expected future consumption growth. If this covariance is positive, then an increase in consumption is associated with higher expected future consumption growth, higher real interest rates, and lower bond prices. Real bonds accordingly have hedge value and the real bond premium is negative. If oc~ is negative, then the real bond premium is positive 21. Under Epstein-Zin utility with g < 1/% assets that covary negatively with expected future consumption growth have higher risk premia. Since real bonds have this characteristic, Epstein-Zin utility with ]/ < 1/~p tends to produce large term premia. This runs counter to the empirical observation in Tables 7 and 8 that term premia are only modest; while the term premia measured in the tables are on nominal rather than real bonds, nominal term premia should if anything be larger than real term premia because they include a reward for bearing inflation risk which is unlikely to be negative. The premium on equities over real bonds is proportional to the coefficient )~ that governs the volatility of dividend growth. Under power utility the equity-bond premium is just risk aversion y times 7~times terms in G2 and ocz. Since both G.2 and G.z must be small to match the observed moments of consumption growth, it is hard to rationalize the large equity-bond premium shown in Table 9. Epstein-Zin utility with g < 1/~p adds a second term in oc~ and 62. Unfortunately the o~2 term is negative, which makes it even harder to rationalize the equity-bond premium. In conclusion, the consumption-based model with Epstein-Zin-Weil utility is no more successful than the consumption-based model with power utility in fitting equity and bond premia with a small coefficient of relative risk aversion. Given the time-series evidence for a small intertemporal elasticity of substitution % relative risk aversion y must be large - close to the reciprocal of ~p as implied by power utility - in order to produce the large equity premia and small bond premia that are measured in the data. Campbell (1993) uses these relations in a different way. Instead of substituting the wealth return out of the Epstein-Zin-Weil model, Campbell substitutes consumption

21 Calnpbetl(1986) developsthis intuition in a univariatemodel for consumptiongrowth.

Ch. 19." Asset Prices, Consumption, and the Business Cycle

1275

out of the model to get a discrete-time version of the intertemporal CAPM o f Merton (1973). Setting e = w and )~ = 1 in Equation (34), the innovation in consumption is O(3

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(53)

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The risk premium on any asset is the coefficient o f risk aversion y times the covariance of that asset with the return on the wealth portfolio, plus (y - 1) times the covariance of the asset with revisions in expected future returns on wealth. The second term is zero if y - 1; in this case it is well known that intertemporal asset demands are zero and asset pricing is myopic. Campbell (1996b) uses this formula to study US stock price data, assuming that the log return on wealth is a linear combination of the stock return and the return on human capital (proxied by innovations to labor income). He argues that mean-reversion in US stock prices implies a positive covariance O~w between US stock returns and the current return on wealth, but a negative covariance a~h between US stock returns and revisions in expected future returns on wealth. Equation (55) then implies that increases in y above one have only a damped effect on the equity premium, so high risk aversion is needed to explain the equity premium puzzle. This conclusion is reached without any reference to measured aggregate consumption data.

4.5. What does the stock market Jorecast? All the calculations in sections 4.3 and 4.4 rely heavily on the assumptions of the representative-agent model with power utility, lognormal distributions, constant variances, and a deterministic link between stock dividends and consumption. They

1276

J.Y. Campbell

leave open the possibility that the stock market volatility puzzle could be resolved by relaxing these assumptions, for example to allow independent variation in dividends in the manner discussed at the end of Section 4.3. A more direct way to understand the stock market volatility puzzle is to use the loglinear asset pricing framework to study the empirical relationships between log price-dividend ratios and future consumption or dividend growth rates, real interest rates, and excess stock returns. According to Equation (27), the log price-dividend ratio embodies rational forecasts of dividend growth rates and stock returns, which in turn are the sum of real interest rates and excess stock returns, discounted to an infinite horizon. One can compare the empirical importance of these different forecasts by regressing long-horizon consumption and dividend growth rates, real interest rates,and excess stock returns onto the log price dividend ratio. Table 12 (p. 1278) reports the results of this exercise. For comparative purposes real output growth, realized stock market volatility, and the excess bond return are also included as dependent variables. For each quarterly data set the dependent variables are computed in natural units over 4, 8, and 16 quarters (1, 2, and 4years) and regressed onto the log price-dividend ratio divided by its standard deviation. Thus the regression coefficient gives the effect of a one standard deviation change in the log price-dividend ratio on the cumulative growth rate or rate of return in natural units. The table reports the regression coefficient, heteroskedasticity- and autocorrelation-consistent t statistic, and R 2 statistic. In the benchmark postwar quarterly US data, the log price-dividend ratio has no clear ability to forecast consumption growth, output growth, dividend growth, or the real interest rate at any horizon. What it does forecast is the excess return on stocks, with t statistics that start above 4 and increase, and with R 2 statistics that start at 0.20 and increase to 0.55 at a 4-year horizon. In the introduction these results were summarized as stylized facts 10, 11, 12, and 13. Table 12 extends them to international data. (10) Regressions of consumption growth on the log price-dividend ratio give very mixed results across countries. There are statistically significant positive coefficients in Germany and the Netherlands, but statistically significant negative coefficients in Australia, Canada, Italy, Japan, and Switzerland. The other countries resemble the USA in that they have no statistically significant consumption growth forecasts. The regressions with output growth as the dependent variable show a similar pattern across countries. (11) Results are somewhat more promising for real dividend growth in many countries. Positive and statistically significant coefficients are fotmd in Canada, France, Germany, Italy, Japan, the Netherlands, Sweden, and the UK. It seems clear that changing forecasts of real dividend growth have some role to play in explaining stock market movements. (12) The short-term real interest rate does not seem to be a promising candidate for the driving force behind stock market fluctuations. One would expect to find high price-dividend ratios forecasting low real interest rates, but the regression

Ch. 19: Asset Prices, Consumption, and the Business Cycle

1277

coefficients are significantly positive in France, Italy, Japan, the Netherlands, Sweden, Switzerland, and the UK. This presumably reflects the fact that stock markets in most countries were depressed in the 1970s, when real interest rates were low, and buoyant during the 1980s, when real interest rates were high. (13) Finally, the log price-dividend ratio is a powerful forecaster of excess stock returns in almost every country. The regression coefficients are uniformly negative and statistically significant. In the long-term annual data for Sweden, the UK, and the USA, I use horizons of 1 year, 4 years, and 8 years. In the US data the log price-dividend ratio fails to forecast real dividend growth, suggesting that authors such as Barsky and DeLong (t993) overemphasize the role of dividend forecasts in interpreting long-run US experience. Consistent with the quarterly results, the log price-dividend ratio also fails to forecast consumption growth, output growth, or the real interest rate, but does forecast excess stock returns. The UK data are similar, although here the 8-year regression coefficients for consumption growth and dividend growth are even statistically significant with the wrong (negative) sign. The 8-year regression coefficient for the real interest rate is also significantly negative, consistent with the idea that the UK stock market is related to the real interest rate. But much the strongest relation is between the log pricedividend ratio and future excess returns on the UK stock market. The Swedish data are quite different; here the log price-dividend ratio forecasts short-run dividend growth positively but has no predictive power for consumption growth, output growth, the real interest rate, or the excess log stock return. The rightmost column of Table 12 considers one more dependent variable, the excess bond return. The predictive power of the stock market for excess stock returns does not generally carry over to excess bond returns; there are significant negative coefficients only in Australia and the UK (and in Germany and Switzerland at long horizons). Overall, these results suggest that a new model of stock market volatility is needed. The standard model of section 4.3 drives all stock market fluctuations from changing forecasts of long-run consumption growth, dividend growth, and real interest rates; forecasts of excess stock returns are constant. The data for many countries suggest instead that forecasts of consumption growth, dividend growth, and real interest rates are variable only in the short run, so that long-run forecasts of these variables are almost constant; stock market fluctuations seem to be driven largely by changing forecasts of excess stock returns.

4.6. Changing volatility in stock returns

One reason why excess stock returns might be predictable is that the risk of stock market investment, as measured for example by the volatility of stock returns, might vary over time. With a constant price of risk, shifts in the quantity of risk will lead to changes in the equity risk premium.

1278

J. Y Campbell

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There is a vast literature documenting the fact that stock market volatility does change with time. However, the variation in volatility is concentrated at high frequencies; it is most dramatic in daily or monthly data and is much less striking at lower frequencies. There is some business-cycle variation in volatility, but it does not seem strong enough to explain large movements in aggregate stock prices [Bollerslev, Chou and Kroner (1992), Schwert (1989)]. A second difficulty is that there is only weak evidence that periods of high stock market volatility coincide with periods of predictably high stock returns. Some papers do find a positive relationship between conditional first and second moments of returns [Bollerslev, Engle and Wooldridge (1988), French, Schwert and Stambaugh (1987), Harvey (1989)], but other papers find that when short-term nominal interest rates are high, the conditional volatility of stock returns is high while the conditional mean stock return is low [Campbell (1987), Glosten, Jagannathan and Runkle (1993)]. French, Schwert and Stambaugh (1987) emphasize that innovations in volatility are strongly negatively correlated with innovations in returns. This could be indirect evidence for a positive relationship between volatility and expected returns, but it could also indicate that negative shocks to stock prices raise volatility, perhaps by raising financial or operating leverage of companies [Black (1976)]. Some researchers have built models that allow for independent variation in the quantity and price of risk. Harvey (1989, 1991) uses "the Generalized Method of Moments to estimate such a system, and finds that the price of risk appears to vary countercyclically. Chou, Engle and Kane (1992) find similar results using a GARCH framework. Within the confines of this chapter it is not possible to do justice to the sophistication of the econometrics used in this literature. Instead i illustrate the empirical findings of the literature by constructing a crude measure of ex post volatility for excess stock returns - the average over 4, 8, or 16 quarters of the squared quarterly excess stock return - and regressing it onto the log price-dividend ratio. The results of this regression are reported in the sixth data column of Table 12. There are nmnerous significant coefficients in these regressions, but they are all positive, indicating that high price-dividend ratios predict high, not tow volatility in these data. These results reinforce the conclusion of the literature that the price of risk seems to vary over time in relation to the level of aggregate consumption. Section 5 discusses economic models that have this property. 4.7. What does the bond market forecast?

I conclude this section by briefly comparing the results of Table 12 with those that carl be obtained using bond market data. Table 13 repeats the regressions of Table 12 using the yield spread between long-term and short-term bonds as the regressor. Many authors have found that in US data, yield spreads have some ability to forecast excess bond returns [Campbell (1987), Campbell and Shiller (199l), Fama and Bliss (1987)].

Ch. 19:

Asset Prices', Consumption, and the Business Cycle

1281

This contradicts the expectations hypothesis of the term structure, the hypothesis that excess bond returns are unforecastable. Other authors have found that yield spreads are powerful forecasters of macroeconomic conditions, particularly output growth [Chen (1991), Estrella and Hardouvelis (1991)]. Fama and French (1989) have argued that both price-dividend ratios and yield spreads capture short-term cyclical conditions, although yield spreads are more highly correlated with conventional measures of the US business cycle. The results of Table 13 are strikingly different from those of Table 12. In the quarterly data, yield spreads forecast positive output growth in almost every country, and positive consumption growth in many countries. Outside the USA, there is also a strong tendency for yield spreads to forecast low real interest rates. Thus the findings of Chen (1991) and Estrella and Hardouvelis (1991) carry over to international data. Yield spreads are much less successful as forecasters of excess stock returns, stock market volatility, or even excess bond returns; the ability of the yield spread to forecast excess bond returns appears to be primarily a US rather than an international phenomenon 2~. Similar conclusions are reported by Hardouvelis (1994) and B ekaert, Hodrick and Marshall (1997). While these authors do report some evidence for predictability of excess bond returns in international data, the evidence is much weaker than in US data. These results are consistent with the view that there is some procyclical variation in tile short-term real interest rate which is not matched by the long-term real interest rate. Thus yield spreads tend to rise at business cycle troughs when real interest rates are predictably low and future output and consumption growth are predictably high. This interpretation is complicated by the fact that yields are measured on nominal bonds rather than real bonds. Inflationary expectations and monetary policy therefore have a large impact on yield spreads. The particular characteristics of US monetary policy may help to explain why previously reported US results do not carry over to other countries in Table 13. US monetary policy has tended to smooth real and nominal interest rates, which reduces the forecastability of real interest rates and increases the sensitivity of the yield spread to changes in bond-market risk premia. Mankiw and Miron (1986) have found that the yield spread was a better forecaster of US interest rates in the period before the founding of the Federal Reserve, while Kugler (1988) has found that the yield spread is a better forecaster of interest rates in Germany and Switzerland and has related this to the characteristics of German and Swiss monetary policy. The findings in Table 13 are consistent with this literature.

22 Results at a one-quarter horizon, not reported in the table, are qualitatively consistent with the longhorizon results.

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5. Cyclical variation in the price of risk In previous sections I have documented a challenging array of stylized facts and have discussed the problems they pose for standard asset pricing theory. Briefly, the equity premium puzzle suggests that risk aversion must be high on average to explain high average excess stock returns, while the stock market volatility puzzle suggests that risk aversion must vary over time to explain predictable variation in excess returns and the associated volatility of stock prices. This section describes some models that display these features.

5.1. Habit formation Constantinides (1990), Ryder and Heal (1973), and Sundaresan (1989) have argued for the importance of habit formation, a positive effect of today's consumption on tomorrow's marginal utility of consumption. Several modeling issues arise at the outset. Writing the period utility function as U(Ct,Xt), where Xt is the time-varying habit or subsistence level, the first issue is the functional form for U(.). Abel (1990, 1999) has proposed that U(.) should be a power function of the ratio CJX~, while Boldrin, Christiano and Fisher (1995), Campbell and Cochrane (1999), Constantinides (1990), and Sundaresan (1989) have used a power function of the difference Ct-Xt. The second issue is the effect of an agent's own decisions on future levels of habit. In standard "internal habit" models such as those in Constantinides (1990) and Sundaresan (1989), habit depends on an agent's own consumption and the agent takes account of this when choosing how much to consume. In "external habit" models such as those in Abel (1990, 1999) and Campbell and Cochrane (1999), habit depends on aggregate consumption which is unaffected by any one agent's decisions. Abel calls this "catching up with the Joneses". The third issue is the speed with which habit reacts to individual or aggregate consumption. Abel (1990, 1999), Durra and Singleton (1986), and Ferson and Constantinides (1991) make habit depend on one lag of consumption, whereas Boldrin, Christiano and Fisher (1995), Constantinides (1990), Sundaresan (1989), Campbell and Cochrane (1999), and Heaton (1995) assume that habit reacts only gradually to changes in consumption. The choice between ratio models and difference models of habit is important because ratio models have constant risk aversion whereas difference models have time-varying risk aversion. To see this, consider Abel's (1990, 1996) specification in which an agent's utility can be written as a power function of the ratio CSXt, C~

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Ch. 19: Asset Prices, Consumption, and the Business Cycle

1285

where Ct i is aggregate past consumption and the parameter t¢ governs the degree of time-nonseparability. Since there is a representative agent, in equilibrium aggregate consumption equals the agent's own consumption, so in equilibrium

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With this specification of utility, in equilibrium the first-order condition is 1 = OEt [(1 +Ri, t+I)(Ct/Ct_I)~V(Y-1)(CI_I/Ct)Y].

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Equation (60) says that the riskless real interest rate equals its value under power utility, less t c ( y - 1)Act. Holding consumption today and expected consumption tomorrow constant, an increase in consumption yesterday increases the marginal utility of consumption today. This makes the representative agent want to borrow from the future, driving up the real interest rate. Equation (61) describing the risk premium is exactly the same as Equation (16), the risk premium formula for the power utility model. The external habit simply adds a term to the Euler equation (59) which is known at time t, and this does not affect the risk premium. Abel (1990, 1999) nevertheless argues that catching up with the Joneses can help to explain the equity premium puzzle. This argument is based on two considerations. First, the average level of the riskless rate in Equation (60) is - l o g 6 - y2o~.2/2+ (y - tc(y - 1))g, where g is the average consumption growth rate. When risk aversion y is very large, a positive t¢ reduces the average riskless rate. Thus catching up with the Joneses enables one to increase risk aversion to solve the equity premium puzzle without encountering the riskless rate puzzle. Second, a positive t¢ is likely to make the riskless real interest rate more variable because of the term -tc(y-1)Ac, in Equation (60). If one solves for the stock returns implied by the assumption that stock dividends equal consumption, a more variable real interest rate increases the covariance of stock returns and consumption oic and drives up the equity premium. The second of these points can be regarded as a weakness rather than a strength of the model. The puzzle illustrated in Table 5 is that the ratio of the measured equity premium to the measured covariance oic is large; increasing the consumption covariance oic does not by itself help to explain the size of this ratio. Also, Table 2 shows that the real interest rate is fairly stable ex post, while Table 7 shows that at most half of its variance is forecastable. Thus the standard deviation of the expected

1286

J. Y C a m p b e l l

real interest rate is quite small, and this is not consistent with large values of t¢ and y in Equation (60). This difficulty with the riskless real interest rate is a fundamental problem for habit formation models. Time-nonseparable preferences make marginal utility volatile even when consumption is smooth, because consumers derive utility from consumption relative to its recent history rather than from the absolute level of consumption. But unless the consumption and habit processes take particular forms, time-nonseparability also creates large swings in expected marginal utility at successive dates, and this implies large movements in the real interest rate. I now present an alternative specification in which it is possible to solve this problem, and in which risk aversion varies over time. Campbell and Cochrane (1999) build a model with external habit formation in which a representative agent derives utility from the difference between consumption and a time-varying subsistence or habit level. They assume that log consumption follows a random walk. This fits the observation that most countries do not have highly predictable consumption or dividend growth rates (Tables 7 and 9). The consumption growth process is Act+l = g + ~c, t+l,

(62)

where co, t+1 is a normal homoskedastic innovation with variance ao2. This is just the ARMA(1,1) model (35) of the previous section, with constant expected consumption growth. The utility function of the representative agent takes the form oc

Et

[C

V ' 6J ~ t+j-

X~

1-y

j-0

,~ 1 .y

t+jj

-1

(63)

Here Xt is the level of habit, 6 is the subjective discount factor, and 7 is the utility curvature parameter. Utility depends on a power function of the difference between consumption and habit; it is only defined when consumption exceeds habit. It is convenient to capture the relation between consumption and habit by the surplus consumption ratio St, defined by St =-

G-X, C,

(64)

The surplus consumption ratio is the fraction of consumption that exceeds habit and is therefore available to generate utility in Equation (63). If habit Xt is held fixed as consumption Ct varies, the local coefficient of relative risk aversion is -Cute_ uc

7 St'

(65)

where uc and ucc are the first and second derivatives of utility with respect to consumption. Risk aversion rises as the surplus consumption ratio St declines, that

Ch. 19." Asset Prices, Consumption, and the Business Cycle

1287

is, as consumption approaches the habit level. Note that y, the curvature parameter in utility, is no longer the coefficient of relative risk aversion in this model. To complete the description of preferences, one must specify how the habit Xt evolves over time in response to aggregate consumption. Campbell and Cochrane suggest an AR(1) model for the log surplus consumption ratio, st -= log(St): s~+l = (1 - q0)~+ q)st + Z (st) ~c,t+l.

(66)

The parameter q0 governs the persistence of the log surplus consumption ratio, while the "sensitivity function" Z(st) controls the sensitivity of st~-i and thus of log habit xt+l to innovations in consumption growth ce, t+l. Equation (66) specifies that today's habit is a complex nonlinear function of current and past consumption. A linear approximation may help to understand it. If I substitute the definition st =- log(1 - exp(xt - ct)) into Equation (66) and linearize around the steady state, I find that Equation (66) is approximately a traditional habit-formation model in which log habit responds slowly and linearly to log consumption, CxD

xM ,-~ (1-q0)a+qvxt+(1

q))~cpJct=i.

q0)ct= a + ( l

(67)

j-0

The linear model (67) has two serious problems. First, when consumption follows an exogenous process such as Equation (62) there is nothing to stop consumption falling below habit, in which case utility is undefined. This problem does not arise when one specifies a process for st, since any real value for st corresponds to positive S~ and hence Ct > Xt. Second, the linear model typically implies a highly volatile riskless real interest rate. The process (66) with a non-constant sensitivity function Z(st) allows one to control or even eliminate variation in the riskless interest rate. To derive the real interest rate implied by this model, one first calculates the marginal utility of consumption as

d(Ct) = ( G - X , ) 7 = S r C r .

(68)

The gross simple risktess rate is then (i +RIll) = (0E, UU'(Q) t ( G ' l ) ~) ' = (OEt ( ~ t i J

7

,/(C'4~-Y)' \-GI. ' .

(69)

Taking logs, and using Equations (62) and (66), the log riskless real interest rate is 2

r/) 1 = - log(0) + yg - y(1 - cp)(s, - s) - -7~G'

-

2

[Z(s,) + 1]2 .

(70)

The first two terms on the right-hand side of Equation (70) are familiar from the power utility model (17), while the last two terms are new. The third term (linear in

1288

JY. Campbell

(st -~)) reflects intertemporal substitution. If the surplus consumption ratio is low, the marginal utility of consumption is high. However, the surplus consumption ratio is expected to revert to its mean, so marginal utility is expected to fall in the future. Therefore, the consumer would like to borrow and this drives up the equilibrium riskfree interest rate. Note that what determines intertemporal substitution is meanreversion in marginal utility, not mean-reversion in consumption itself. In this model consumption follows a random walk so there is no mean-reversion in consumption; but habit formation causes the consumer to adjust gradually to a new level of consunlption, creating mean-reversion in marginal utility. The fourth term (linear in D~(s~)+ l] 2) reflects precautionary savings. As uncertainty increases, consumers become more willing to save and this drives down the equilibrium riskless interest rate. Note that what determines precautionary savings is uncertainty about marginal utility, not uncertainty about consumption itself. In this model the consumption process is homoskedastic so there is no time-variation in uncertainty about consumption; but habit formation makes a given level of consumption uncertainty more serious for marginal utility ,when consumption is low relative to habit. Equation (70) can be made to match the observed stability of real interest rates in two ways. First, it is helpful if the habit persistence parameter q~ is close to one, since this limits the strength of the intertemporal substitution effect. Second, the precautionary savings effect offsets the intertemporal substitution effect if A(s~) declines with st. In fact, Campbell and Cochrane parametrize the ,~(st) function so that these two effects exactly offset each other everywhere, implying a constant riskless interest rate. With a constant riskless rate, real bonds of all maturities are also riskless and there are no real term premia. Thus in the Campbell-Cochrane model the equity premium is also an equity-bond premium. The sensitivity function ,~(st) is not fully determined by the requirement of a constant riskless interest rate. Campbell and Cochrane choose the function to satisfy three conditions: (1) The riskless real interest rate is constant. (2) Habit is predetermined at the steady state s~ = 3. (3) Habit is predetermined near the steady state, or, equivalently, positive shocks to consumption may increase habit but never reduce it. To understand conditions (2) and (3), recall that the traditional notion of habit makes it a predetermined variable. On the other hand habit cannot be predetermined everywhere, or a sufficiently low realization of consumption growth would leave consumption below habit. To make habit "as predetermined as possible", Campbell and Cochrane assume that habit is predetermined at and near the steady state. This also eliminates the counterintuitive possibility that positive shocks to consumption cause declines in habit. Using these three conditions, Campbell and Cochrane show that the steady-state surplus consumption ratio must be a function of the other parameters of the model, and that the sensitivity function )~(st) must take a particular form. Campbell and Cochrane pick parameters for the model by calibrating it to fit postwar quarterly US data. They choose the mean consumption growth rate g = 1.89% per year and the standard

Ch. 19:

Asset Prices, Consumption, and the Business Cycle

1289

deviation of consumption growth oc = 1.50% per year to match the moments of the US consumption data. Campbell and Cochrane follow Mehra and Prescott (1985) by assuming that the stock market pays a dividend equal to consumption. They also consider a more realistic model in which the dividend is a random walk whose innovations are correlated with consumption growth. They show that results in this model are very similar because the implied regression coefficient of dividend growth on consumption growth is close to one, which produces similar asset price behavior. They use numerical methods to find the price-dividend ratio for the stock market as a function of the state variable st. They set the persistence of the state variable, ~, equal to 0.87 per year to match the persistence of the log price-dividend ratio. They choose y = 2.00 to match the ratio of unconditional mean to unconditional standard deviation of return in US stock returns. These parameter values imply that at the steady state, the surplus consumption ratio = 0.057 so habit is about 94% of consumption. Finally, Campbell and Cochrane choose the discount factor 6 = 0.89 to give a riskless real interest rate of just under 1% per year. It is important to understand that with these parameter values the model uses high average risk aversion to fit the high unconditional equity premium. Steady-state risk aversion is y/S = 2.00/0.057 = 35. In this respect the model resembles a power utility model with a very high risk aversion coefficient. There are however two important differences between the model with habit formation and the power utility model with high risk aversion. First, the model with habit formation avoids the riskfree rate puzzle. Evaluating Equation (70) at the steadystate surplus consumption ratio and using the restrictions on the sensitivity function )~(&), the constant riskless interest rate in the Campbell-Cochrane model is

r/+j

- log(6) + y g -

~-.

(71)

In the power utility model the same large coefficient y would appear in the consumption growth term and the consumption volatility term [Equation (17)]; in the CampbellCochrane model the curvature parameter ]e appears in the consumption growth term, and this is much lower than the steady-state risk aversion coefficient y/5: which appears in the consumption volatility term. Thus a much lower value of the discount factor 6 is consistent with the average level of the risk free interest rate, and the model implies a less sensitive relationship between mean consumption growth and interest rates. Second, the model with habit formation has risk aversion that varies with the level of consumption, whereas a power utility model has constant risk aversion. The time.variation in risk aversion generates predictable movements in excess stock returns like those documented in Table 12, enabling the Campbell-Cochrane model to match the volatility of stock prices even with a smooth consumption series and a constant riskless interest rate.

1290

J Y. Campbell

5.2. Models' with heterogeneous agents All the models considered so far assume that assets can be priced as if there is a representative agent who consumes aggregate consumption. An alternative view is that aggregate consumption is not an adequate proxy for the consumption of stock market investors. One simple explanation for a discrepancy between these two measures of consumption is that there are two types of agents in the economy: constrained agents who are prevented from trading in asset markets and simply consume their labor income each period, and unconstrained agents. The consumption of the constrained agents is irrelevant to the determination of equilibrium asset prices, but it may be a large fraction of aggregate consumption. Campbell and Mankiw (1989) argue that predictable variation in consumption growth, correlated with predictable variation in income growth, suggests an important role for constrained agents, while Mankiw and Zeldes (1991) and Brav and Geczy (1996) use US panel data to show that the consumption of stockholders is more volatile and more highly correlated with the stock market than the consumption of non-stockholders. Such effects are likely to be even more important in countries with low stock market capitalization and concentrated equity ownership. The constrained agents in the above model do not directly influence asset prices, because they are assumed not to hold or trade financial assets. Another strand of the literature argues that there may be some investors who buy and sell stocks for exogenous, perhaps psychological reasons. These "noise traders" can influence stock prices because other investors, who are rational utility-maximizers, must be induced to accommodate their shifts in demand. If utility-maximizing investors are risk-averse, then they will only buy stocks from noise traders who wish to sell if stock prices fall and expected stock returns rise; conversely they will only sell stocks to noise traders who wish to buy if stock prices rise and expected stock returns fall. Campbell and Kyle (1993), Cutler, Poterba and Summers (1991), DeLong, Shleifer, Summers and Waldmalm (1990), and Shiller (1984) develop this model in some detail. The model implies that rational investors do. not hold the market portfolio - instead they shift in and out of the stock market in response to changing demand from noise traders - and do not consume aggregate consumption since some consumption is accounted for by noise traders. This makes the model hard to test without having detailed information on the investment strategies of different market participants 23. It is also possible that utility-maximizing stock market investors are heterogeneous in important ways. If investors are subject to large idiosyncratic risks in their labor income and can share these risks only indirectly by trading a few assets such as stocks

23 Recent work surveyed by Shiller (1999) attempts to place the behavior of noise traders on a firmer psychologicalfolmdation. Benartzi and Thaler (1995), fbr example, argue that psychologicalbiases make noise traders reluctant to hold stocks, and that this helps to explain the equity premium puzzle.

Ch. 19: Asset Prices, Consumption, and the Business Cycle

1291

and Treasury bills, their individual consumption paths may be much more volatile than aggregate consumption. Even if individual investors have the same power utility function, so that any individual's consumption growth rate raised to the power - y would be a valid stochastic discount factor, the aggregate consumption growth rate raised to the power - y may not be a valid stochastic discount factor. This problem is an example of Jensen's Inequality. Since marginal utility is nonlinear, the average of investors' marginal utilities of consumption is not generally the same as the marginal utility of average consumption. The problem disappears when investors' individual consumption streams are perfectly correlated with one another as they will be in a complete markets setting. Grossman and Shiller (1982) point out that it also disappears in a continuous-time model when the processes for individual consumption streams and asset prices are diffusions. Recently Constantinides and Duffle (1996) have provided a simple framework within which the effects of heterogeneity can be understood. Constantinides and Duffle postulate an economy in which individual investors k have different consumption levels Ckt. The cross-sectional distribution of individual consumption is lognormal, and the change from time t to time t + 1 in individual log consumption is cross-sectionally uncorrelated with the level of individual log consumption at time t. All investors have the same power utility function with time discount factor 6 and coefficient of relative risk aversion y, In this economy each investor's own intertemporal marginal rate of substitution is a valid stochastic discount factor. Hence the cross-sectional average of investors' intertemporal marginal rates of substitution is a valid stochastic discount factor. I write this as

M,+~ = 6E,\~ L \ ~ - k , )

/

'

(72)

where E[ denotes an expectation taken over the cross-sectional distribution at time t. That is, for any cross-sectionally random variable Xk~,

E:x,,

- lim

K 1 ~Xkt, k-I

the limit as the number of cross-sectional units increases of the cross-sectional sample average of Xkt 24. Note that E[Xkt will in general vary over time and need not be lognormally distributed conditional on past information.

24 Constantinides and Duffle (1996) present a more rigorous discussion.

J.Y. Campbell

1292

The assumption of cross-sectional lognormality means that the log stochastic discount factor, m[+1 = log(M~ 1), can be written as a function of the cross-sectional mean and variance of the change in log consumption: mr+ t

= - l o g ( b ) - yEt+jAck, t+1 +

Var~+lAck, t+l,

(73)

where Var[ is defined analogously to E[ as K

Var/Xl, = lim 1 K--,oo K

~(X~ lEt&,)2 ' k=l

and like E[ will in general vary over time. An economist who knows the underlying preference parameters of investors but does not understand the heterogeneity in this economy might attempt to construct a representative-agent stochastic discount factor, M/~, using aggregate consumption: /E/+l[G,t+l] )

r

-'uF+'l - b k

(74)

The log of this stochastic discount factor can also be related to the cross-sectional mean and variance of the change in log consumption: me+]=-log(b)-yEt+,Ack, t + l - (~)[Vart+lck, t+ 1 - Var/c?,l]

(7s) - - l o g ( O ) - y E 2 i . , A c k , , + , - (7)[Var,*~_iAc'k,,+,], where the second equality follows from the relation ck, tH ckf + Ack,t+l and the fact that Ack, t+l is cross-sectionally uncorrelated with ckt. The diflbrence between these two variables can now be written as m/~ 1 - m " lI~A = Y(Y2+ 1)Vart+lACk, . t kl.

(76)

The time series of this difference can have a nonzero mean, helping to explain the riskfree rate puzzle, and a nonzero variance, helping to explain the equity premium puzzle. If the cross-sectional variance of log consumption growth is negatively correlated with the level of aggregate consumption, so that idiosyncratic risk increases in economic downturns, then the true stochastic discount factor m[+1 will be more strongly countercyclical than the representative-agent stochastic discount factor constructed using the same preference parameters; this has the potential to explain the high price of risk without assuming that individual investors have high risk aversion. Mankiw (1986) makes a similar point in a two-period model.

Ch. 19: Asset Prices, Consumption, and the Business Cycle

1293

An important unresolved question is whether the heterogeneity we can measure has the characteristics that are needed to help resolve the asset pricing puzzles. In the Constantinides-Duffie model the heterogeneity must be large to have important effects on the stochastic discount factor; a cross-sectional standard deviation of log consumption growth of 20%, for example, is a cross-sectional variance of only 0.04, and it is variation in this number over time that is needed to explain the equity premium puzzle. Interestingly, the effect of heterogeneity is strongly increasing in risk aversion since Var~*+lAck,t+l is multiplied by y(g + 1)/2 in Equation (76). This suggests that heterogeneity may supplement high risk aversion but cannot altogether replace it as an explanation for the equity premium puzzle 25. It is also important to note that idiosyncratic shocks have large effects in the Constantinides-Duffie model because they are permanent. Heaton and Lucas (1996) calibrate individual income processes to micro data from the Panel Study of Income Dynamics (PSID). Because the PSID data show that idiosyncratic income variation is largely transitory, Heaton and Lucas find that investors can minimize its effects on their consumption by borrowing and lending. This prevents heterogeneity from having any large effects on aggregate asset prices. To get around this problem, several recent papers have combined heterogeneity with constraints on borrowing. Heaton and Lucas (1996) and Krusell and Smith (1997) find that borrowing constraints or large costs of trading equities are needed to explain the equity premium. Constantinides, Donaldson and Mehra (1998) focus on heterogeneity across generations; in a stylized three-period overlapping generations model they find that they can match the equity premium if they prevent young agents from borrowing to buy equities. All of these models assume that agents have identical preferences. But heterogeneity in preferences may also be important. Several authors have recently argued that trading between investors with different degrees of risk aversion or time preference, possibly in the presence of market frictions, can lead to time-variation in the market price of risk [Aiyagari and Gertler (1998), Grossman and Zhou (1996), Sandroni (1997), Wang (1996)]. This seems likely to be an active research area in the next few years. 5.3. Irrational expectations

So far I have maintained the assumption that investors have rational expectations and understand the time-series behavior of dividend and consumption growth. A number of papers have explored the consequences of relaxing this assumption. [See for example

25 Lettau (1997) reaches a similar conclusion by assuming that individuals consume their income, and calculating the risk-aversion coefficients needed to put model-based stochastic discount factors inside the Hansen-Jagannathan volatility bounds. This procedure is conservative in that individuals trading in financial markets are normally able to achieve some smoothing of consumption relative to income. Nevertheless Lettau finds that high individual risk aversion is still needed to satisfy the Hansen,~ Jagannathan bounds.

1294

JY

CampbeH

Barberis, Shleifer and Vishny (1998), Barsky and DeLong (1993), Cecchetti, Lam and Mark (1998), Chow (1989), or Hansen, Sargent and Tallarini (1997)] 26 In the absence of arbitrage, there exist positive state prices that can rationalize the prices of traded financial assets. These state prices equal subjective state probabilities multiplied by ratios of marginal utilities in different states. Thus given any model of utility, there exist subjective probabilities that produce the necessary state prices and in this sense explain the observed prices of traded financial assets. The interesting question is whether these subjective probabilities are sufficiently close to objective probabilities, and sufficiently related to known psychological biases in behavior, to be plausible. Many of the papers in this area work in partial equilibrium and assume that stocks are priced by discounting expected future dividends at a constant rate. This assumption makes it easy to derive any desired behavior of stock prices directly from assumptions on dividend expectations. Barsky and DeLong (1993), for example, assume that investors believe dividends to be generated by a doubly integrated process, so that the dividend growth rate has a unit root. These expectations imply that rapid dividend growth increases stock prices more than proportionally, so that the price-dividend ratio rises when dividends are growing strongly. If dividend growth is in fact stationary, then the high price-dividend ratio is typically followed by dividend disappointments, low stock returns, and reversion to the long-run mean pric~dividend ratio. Thus Barsky and DeLong's model can account for the volatility puzzle and the predictability of stock returns. In general equilibrium, dividends are linked to consumption so investors' irrational expectations about dividend growth should be linked to their irrational expectations about consumption growth, interest rates are not exogenous, but like stock prices, are determined by investors' expectations. Thus it is significantly harder to build a general equilibrium model with irrational expectations. To see how irrationality can affect asset prices, consider first a static model in which log consumption follows a random walk (q} = 0) with drift g. Investors understand that consumption is a random walk, but they expect it to grow at rate ~ instead of g. Equation (37) implies that the log price-dividend ratio is

P e t - d e t -- i - p +

(77)

~ --

Equation (21) implies that the riskless imerest rate is 0-1

rL ,+1 - - log 6 + ~ + ~ - -

26 There is also import.

2

0

2

ow - ~-~- o7,

(78)

Ch. 19: Asset Prices, Consumption, and the Business Cycle

1295

and the rationally expected equity premium is Et[r~,,+,l

4

- rf, t-t-1 -t- T

(79)

= ~I-~0"2 -I- ~L(M- D)"

The first term on the right-hand side of Equation (79) is the standard formula for the equity premium in a model with serially uncorrelated consumption growth. This is investors' irrational expectation o f the equity premium. The second term arises because dividend growth is systematically different from what investors expect. This model illustrates that irrational pessimism among investors @ < g) can lower the average riskfree rate and increase the equity premium. Thus pessimism has the same effects on asset prices as a low rate o f time preference and a high coefficient o f risk aversion, and it can help to explain both the riskfree rate puzzle and the equity premium puzzle 27. To explain the volatility puzzle, a more complicated model o f irrationality is needed. Suppose now that log consumption growth follows an AR(1) process, a special case of Equation (35), but that investors believe the persistence coefficient to be ~} when in fact it is q)28. In this case the riskfree interest rate is given by ^

(80)

r/;t+l = / ~ f + ~ ( A c t - g ) , while the rationally expected equity premium is

<

E,fr~,,~,I-,r~;,,,+T=~-(,}-O)

~

,~-

+,~ (A<-g),

(81)

where/~f and/J~ are constants. If 0 is larger than ~b, and if the term in square brackets in Equation (81) is positive, then the equity premium falls when consumption growth has been rapid, and rises when consumption growth has been weak. This model, which can be seen as a general equilibrium version of Barsky and DeLong (1993), fits the apparent cyclical variation in the market price of risk. One difficulty with this explanation for stock market behavior is that it has strong implications for bond market behavior. Consumption growth drives up the riskless

27 The effect of pessimism on the average price-dividend ratio is ambiguous, for the usual reason that lower riskfree rates and lower expected dividend growth have offsetting effects. Hansen, Sargent and Tallarini (1997) also emphasize that irrational pessimism can be observationally equivalent to lower time preference and higher risk aversion. 28 All alternative formulation would be to assume, following Equation (35), that log consumption growth is predicted by a state variable x~ that investors observe, but that investors misperceive tile persistence of this process to be ~ rather than ~. In this case investors correctly forecast consumption growth over the next period, but incorrectly forecast subsequent consumption growth. Their irrationality has no effect on the riskfiee interest rate but causes time-variation in equity and bond premia.

JY. Campbell

1296

interest rate and the real bond premium even while it drives down the equity premium. Barsky and DeLong (1993) work in partial equilibrium so they do not confront this problem. Cecchetti, Lain and Mark (1998) handle it by allowing the degree of investors' irrationality itself to be stochastic and time-varying 29. 6. Some implications tbr m a c r o e c o n o m i c s The research summarized in this chapter has important implications for various aspects of macroeconomics. I conclude by briefly discussing some of these. A first set of issues concerns the modelling of production, and hence of investment. This chapter has followed the bulk of the asset pricing literature by concentrating on the relation between asset prices and consumption, without asking how consumption is determined in relation to investment and production. Ultimately this is unsatisfactory, and authors such as Cochrane (1991, 1996) and Rouwenhorst (1995) have argued that asset pricing should place a renewed emphasis on the investment decisions of firms. Standard macroeconomic models with production, such as the canonical real business cycle model of Prescott (1986), imply that asset prices are extremely stable. The real interest rate equals the marginal product of capital, which is perturbed only by technology shocks and changes in the quantity of capital; when the model is calibrated to US data the standard deviation of the real interest rate is only a few basis points. The return on capital is equally stable because capital can costlessly be transformed into consumption goods, so its price is always fixed at one and uncertainty in the return comes only from uncertainty about dividends. If real business cycle models are to generate volatile asset returns, they must be modified to include adjustment costs in investment so that changes in the demand for capital cause changes in the value of installed capital, or Tobin's q, rather than changes in the quantity of capital. Baxter and Crucini (1993), Jermann (t998), and Christiano and Fisher (1995), among others, show how this can be done. The adjustment costs affect not only asset prices, but other aspects of the model; the response of investment to shocks falls, for example, so larger shocks are needed to explain the cyclical behavior of investment. The modelling of labor supply is an equally difficult problem. Any model in which workers choose their labor supply implies a first-order condition of the form

OU OC~G~-

OU ON,'

(82)

where Gt is the real wage and Nt is labor supply. A well-known difficulty in business cycle theory is that with a constant real wage, the marginal utility of consumption

29 The work of Rietz (1988) can be understood in a similar way.Rictz argues that investors are concerned about an unlikely but serious event that has not actually occurred. Given the data we have, investors appear to be irrational but in fact, with a long enough data sample, they will prove to be rational.

Ch. 19: Asset Prices, Consumption, and the Business Cycle

1297

OU/OCt will be perfectly correlated with the marginal disutility of work -OU/ON~. Since the marginal utility of consumption is declining in consumption while the marginal disutility of work is increasing in hours, this implies that consumption and hours worked will be negatively correlated. In the data, of course, consumption and hours worked are positively correlated since they are both procyclical. This problem can be resolved if the real wage is procyclical; then when consumption and hours increase in an expansion the decline in marginal utility of consumption is more than offset by an increase in the real wage. In a standard model with log utility of consumption only a 1% increase in the real wage is needed to offset the decline in marginal utility caused by a 1% increase in consumption. But preferences of the sort suggested by the asset pricing literature, with high risk aversion and low intertemporal elasticity of substitution, have rapidly declining marginal utility of consumption. These preferences imply that a much larger increase in the real wage will be needed to offset the effect on labor supply of a given increase in consumption. Boldrin, Christiano and Fisher (1995) and Lettau and Uhlig (1996) confront this problem; Boldrin, Christiano and Fisher try to resolve it by using a two-sector framework with limited mobility of labor between sectors. In their framework the first-order condition (82) does not hold contemporaneously, but only in expectation. Models with production also help one to move away from the common assumption that stock market dividends equal consumption or equivalently, that the aggregate stock market equals total national wealth. This assumption is clearly untrue even for the United States, and is even less appropriate for countries with smaller stock markets. While one can relax the assumption by writing down exogenous correlated timeseries processes for dividends and consumption in the manner of section 4.3, it will ultimately be more satisfactory to derive both dividends and consumption within a general equilibrium model. Another important set of issues concerns the links between different national economies and their financial markets. In this chapter I have treated each national stock market as a separate entity with its own pricing model. That is, I have assumed that national economies are entirely closed so that there is no integrated world capital market. This assumption may be appropriate for examining long-term historical data, but it seems questionable under modern conditions. There is much work to be done on the pricing of national stock markets in a model with a perfectly or partially integrated world capital market. Finally, the asset pricing literature is important in understanding the welfare costs of macroeconomic fluctuations. There has recently been a tendency for economists to downplay the importance of economic fluctuations in favor of an emphasis on long-term economic growth. But models of habit formation imply that consumers take fluctuations extremely seriously. Fluctuations have important negative effects on welfare because they move consumption in the short term, when agents have little time to adjust; reductions in long-term growth, on the other hand, allow agents' habit levels to adjust gradually.

1298

J. E Campbell

This conclusion is not an artifact o f a particular utility function and habit formation process. As A t k e s o n and Phelan (1994) emphasize, it m u s t result from any utility function that explains the level o f the equity p r e m i u m . The choice b e t w e e n risky stocks and stable m o n e y market instruments offers investors a tradeoff b e t w e e n the m e a n growth rate o f their wealth and the volatility o f this growth rate. The fact that so m u c h extra m e a n growth is available from volatile stock market investments implies that investors find volatility to be a serious threat to their welfare. E c o n o m i c policymakers should take this into account w h e n they face policy tradeoffs between e c o n o m i c growth and m a c r o e c o n o m i c stability.

References Abel, A.B. (1990), "Asset prices under habit formation and catching up with the Joneses", American Economic Review Papers and Proceedings 80:38 42. Abel, A.B. (1994), "Exact solutions for expected rates of return under Markov regime switching: implications for the equity premium puzzle", Journal of Money, Credit and Banking 26:345 361. Abel, A.B. (1999), "Risk premia and term premia in general equilibrium", Journal of Monetary Economics 43:3-33. Abel, A.B., N.G. Mankiw, L.H. Sumxners and R.J. Zeckhauser (1989), "Assessing dynamic efficiency: theory and evidence", Review of Economic Studies 56:1-20. Aiyagari, S.R., and M. Gertler (1998), "Overreaction of asset prices in general equilibrium", Working Paper No. 6747 (NBER). Atkeson, A., and C. Phelan (1994), "Reconsidering the costs of business cycles with incomplete markets", in: S. Fischer and J.J. Rotentherg, eds., NBER Macroeconomics Annual 1994 (MIT Press, Cambridge, MA) 187507. Attanasio, O.R, and G. Weber (1993), "Consumption growth, the interest rate, and aggregation", Review of Economic Studies 60:631-649. Backus, D. (1993), "Cox-Ingersoll Ross in discrete time", unpublished paper (New York University). Bansal, R., and W.J. Coleman II (1996), "A monetal7 explanation of the equity premium, tern1 premium, and risk-free rate puzzles", Journal of Political Economy 104:1135-1171. Barberis, N., A. Shleifer and R.W. Vishny (1998), "A model of investor sentiment", Journal of Financial Economics 49:307 343. Barclays de Zoete Wedd Securities (1995), The BZW Equity-Gilt Study: investment in the London Stock Market since 1918 (London). Barsky, R.B., and J.B. DeLong (1993), "Why does the stock market fluctuate?", Quarterly Jomnal of Economics 107:291-311. Baxter, M., and M.J. Crucini (t993), "Explaining saving investment correlations", American Economic Review 83:416-436. Beaudry, R, and E. van Wincoop (1996), "The intertemporal elasticity of substitution: an exploration using a US panel of state data", Economica 63:495 512. Bekaert, G., R.J. Hodrick and D.A. Marshall (1997), "'Peso problem' explanations for term structure anomalies", Working Paper No. 6147 (NBER). Benartzi, S., and R.H. Thaler (1995), "Myopic loss aversion and the equity premium puzzle", Quarterly Journal of Economics 110:73-92. Black, E (1976), "Studies of stock price volatility changes", Proceedings of the 1976 Meetings of the Business and Economic Statistics Section (American Statistical Association) 177--181.

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Blanchard, O.J., and M.W. Watson (1982), "Bubbles, rational expectations, and financial markets", in: E Wachtel, ed., Crises in the Economic and Financial Structure: Bubbles, Bursts, and Shocks (Lexington Publishers, Lexington, MA). Boldrin, M., L.J. Christiano and J. Fisher (1995), "Asset pricing lessons for modeling business cycles", Working Paper No. 5262 (NBER). Bollerslev, T., R. Engle and J. Wooldridge (1988), "A capital asset pricing model with time varying covariances", Journal of Political Economy 96:116 131. Bollerslev, T., R.Y. Chou and K.E Kroner (1992), "ARCH modeling in finance: a review of the theory and empirical evidence", Journal of Econometrics 52:5-59. Bray, A., and C.C. Geczy (1996), "An empirical resurrection of the simple consumption CAPM with power utility", unpublished paper (University of Chicago). Breeden, D. (1979), "An intertemporal asset pricing model with stochastic consumption and investment opportunities", Journal of Financial Economics 7:265-296. Brown, S., W. Goetzmann and S. Ross (1995), "Survival", Journal of Finance 50:853-873. Campbell, J.Y. (1986), "Bond and stock returns in a simple exchange model", Quarterly Journal of Economics 101:785-804. Campbell, J.Y. (1987), "Stock returns and the term structure", Journal of Financial Economics 18: 373~99. Campbell, J.Y. (1991 ), "A variance decomposition for stock returns", Economic Journal 101 : 157-179. Campbell, J.Y. (1993), "lntertemporal asset pricing without consumption data", American Economic Review 83:487-512. Campbell, J.Y. (1996a), "Consumption and the stock market: interpreting international experience", Swedish Economic Policy Review 3:251-299. Campbell, J.Y. (1996b), "Understanding risk and return", Journal of Political Economy 104:298-345. Campbell, J.Y., and J.H. Cochrane (1999), "By force of habit: a consumption-based explanation of aggregate stock market behavior", Journal of Political Economy 107:205-251. Campbell, J.Y., and A.S. Kyle (1993), "Smart money, noise trading, and stock price behavior", Review of Economic Studies 60:1-34. Campbell, J.Y., and N.G. Mankiw (1989), "Consumption, income, and interest rates: reinterpreting the time series evidence", in: O.J. Blanchard and S. Fischer, eds., National Bureau of Economic Research Macroeconomics Annual 4:185~ 16. Campbell, J.Y., and N.G. Mankiw (1991), "The response of consumption to income: a cross-cotmtry investigation", European Economic Review 35: 723-767. Campbell, J.Y., and R.J. Shiller (1988), "The dividend-price ratio and expectations of future dividends and discount factors", Review of Financial Studies 1:195-227. Campbell, J.Y., and R.J. Shiller (1991), "Yield spreads and interest rate movements: a bird's eye view", Review of Economic Studies 58:495 514. Campbell, J.Y., A.W. Lo and A.C. MacKinlay (1997), The Econometrics of Financial Markets (Princeton University Press, Princeton, NJ). Carroll, C.D. (1992), "The buffer-stock theory of saving: some macroeconornic evidence", Brookings Papers on Economic Activity t992(2):61-156. Cecchetti, S.G., E-S. Lain and N.C. Mark (1990), "Mean reversion in equilibrium asset prices", American Economic Review 80:3984 18. Cecchetti, S.G., E-S. Lain and N.C. Mark (1993), "The equity premium and the risk-fiee rate: matching the moments", Journal of Monetary Economics 31:2t~45. Cecchetti, S.G., R-S. Lain and N.C. Mark (1998), "Asset pricing with distorted beliefs: are equity returns too good to be true?", Working Paper No. 6354 (NBER). Chen, N. (1991), "Financial investment opportunities and the macroeconomy", Journal of Finance 46:52%554. Chou, R.Y., R.E Engle and A. Kane (1992), "Measuring risk aversion from excess returns on a stock index", Journal of Econometrics 52:201~24.

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Chow, G.C. (1989), "Rational versus adaptive expectations in present value models", Review of Economics and Statistics 71:376 384. Christiano, L.J., and J. Fisher (1995), "Tobin's q and asset returns: implications for business cycle analysis", Working Paper No. 5292 (NBER). Cochrane, J.H. (1991), "Production-based asset pricing and the link between stock returns and economic fluctuations", Journal of Finance 46:209-237. Cochrane, J.H. (1996), "A cross-sectional test of an investment-based asset pricing model", Journal of Political Economy 104:572~521. Cochrane, J.H., and L.R Hansen (1992), "Asset pricing lessons for macroeconomics", in: O.J. Blanchard and S. Fischer, eds., NBER Maeroeconomics Annual 1992 (The MIT Press, Cambridge). Constantinides, G.M. (1990), "Habit formation: a resolution of the equity premium puzzle", Journal of Political Economy 98:519-543. Constantinides, G.M., and D. Duffle (1996), "Asset pricing with heterogeneous consumers", Journal of Political Economy 104:219-240. Constantinides, G.M., J.B. Donaldson and R. Mehra (1998), "Junior can't borrow: a new perspective on tile equity premium puzzle", Working Paper No. 6617 (NBER). Cutler, D.M., J.M. Poterba and L.H. Summers (1991), "Speculative dynamics", Review of Economic Studies 58:529-546. Deaton, A.S. (1991), "Saving and liquidity constraints", Econometrica 59:1221-1248. DeLong, J.B., A. Shleifer, L.H. Summers and R.J. Waldmann (1990), "Noise trader risk in financial markets", Journal of Political Economy 98:703-738. Dunn, K.B., and K.J. Singleton (1986), "Modeling the term structure of interest rates under non-separable utility and durability of goods", Journal of Financial Economics 17:27-55. Epstein, L.G., and S.E. Zin (1989), "Substitution, risk aversion, and the temporal behavior of consumption and asset returns: a theoretical fiamework", Econometrica 57:937-968. Epstein, L.G., and S.E. Zin (1991), "Substitution, risk aversion, and the temporal behavior of consmnption and asset returns: an empirical investigation", Journal of Political Economy 99:263-286. Estrella, A., and G.A. Hardouvelis (1991), "The term structure as a predictor of real economic activity", Journal of Finance 46:555-576. Fama, E.E, and R. Bliss (1987), "The information in long-maturity forward rates", American Economic Review 77:68(~692. Fama, E.E, and K.R. French (1988a), "Permanent and temporary components of stock prices", Journal of Political Economy 96:246-273. Fama, E.E, and K.R. French (1988b), "Dividend yields and expected stock returns", Journal of Financial Economics 22:3 27. Fama, E.E, and K.R. French (1989), "Business conditions and expected returns on stocks and bonds", Journal of Financial Economics 25:23~49. Ferson, W.E., and G.M. Constantinides (1991), "Habit persistence and durability in aggregate consumption: empirical tests", Journal of Financial Economics 29:199-240. French, K., G.W. Schwert and R.E Stambaugh (1987), "Expected stock returns and volatility", Journal of Financial Economics 19:3-30. Frennberg, R, and B. Hansson (1992), "Computation of a monthly index for Swedish stock returns 1919-t989", Scandinavian Economic History Review 40:3-27. Froot, K., and M. Obstfeld (1991), "Intrinsic bubbles: the case of stock prices", American Economic Review 81:t189-1217. Glosten, L, R. Jagannathan and D. Runkle (1993), "On the relation between the expected value and the volatility of the nominal excess return on stocks", Journal of Finance 48:177%180I. Goetzmmur, W.N., and R Jorion (1997), "A century of global stock markets", Working Paper No. 5901 (NBER). Grossman, S.J., and R.J. Shiller (198l), "The determinants of the variability of stock market prices", American Economic Review 71:222 227.

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Grossman, S.J., and R.J. Shiller (1982), "Consumption correlatedness and risk measurement in economies with non-traded assets and heterogeneous information", Journal of Financial Economics 10:195-210. Grossman, S.J., and Z. Zhou (1996), "Equilibrium analysis of portfolio insurance", Journal of Finance 51:1379 1403. Grossman, S.J., A. Melino and R.J. Shiller (1987), "Estimating the continuous time consumption based asset pricing model", Journal of Business and Economic Statistics 5:315-328. Hall, R.E. (1988), "Intertemporal substitution in consumption", Journal of Political Economy 96:221~273. Hamilton, J.D. (1989), "A new approach to the analysis of nonstationary returns and the business cycle", Econometa%a 57:357-384. Hansen, L.P, and R. Jagannathan (1991), "Restrictions on intertemporal marginal rates of substitution implied by asset returns", Journal of Political Economy 99:225-262. Hansen, L.P., and K.J. Singleton (1983), "Stochastic consumption, risk aversion, and the temporal behavior of asset returns", Journal of Political Economy 91:249-268. Hansen, L.P, T.J. Sargent and T.D. Tallarini Jr (1997), "Robust permanent income and pricing", unpublished paper (University of Chicago and Carnegie Mellon University); Review of Economic Studies, fbrthcoming. Hardouvelis, G.A. (1994), "The term structure spread and future changes in long and short rates in the G7 countries: Is there a puzzle?", Journal of Monetary Economics 33:255283. Harvey, C.R. (1989), "Time-varying conditional covariances in tests of asset pricing models", Journal of Financial Economics 24:289-317. Harvey, C.R. (1991), "The world price of covariance risk", Journal of Finance 46:111-157. Hassler, J., E Lundvik, T. Persson and E S6derlind (1994), "The Swedish business cycle: stylized facts over 130 years", in: V. Bergstr/Sm and A. Vredin, eds., Measuring and Interpreting Business Cycles (Clarendon Press, Oxford). Heaton, J. (1995), "'An empirical investigation of asset pricing with temporally dependent preference specifications", Econometrica 63:681-717. Heaton, J., and D.J. Lucas (1996), "Evaluating the effects of incomplete markets on risk sharing and asset pricing", Journal of Political Economy 104:443-487. Jermann, U.J. (1998), "Asset pricing in production economies", Journal of Monetary Economics 41: 257-275. Kandel, S., and R.E Stambaugh (t991), "Asset returns and intertemporal preferences", Journal of Monetary Economics 27:39-71. Kocherlakota, N. (1996), "The equity premium: it's still a puzzle", Journal of Economic Literature 34:42~ 1. Kreps, D.M., and E.L. Porteus (1978), "Temporal resolution of uncertainty and dynamic choice theory", Econometriea 46:185-200. Kxusell, E, and A.A. Smith Jr (1997), "Income and wealth heterogeneity, portfolio choice, and equilibrium asset returns", Macroeconomic Dynamics 1:387-422. Kugler, E (1988), "An empirical note on the term structure and interest rate stabilization policies", Quarterly Journal of Economics 103:78%792. La Porta, R., E Lopez-de-Silanes, A. Shleifer and R.W. Vishny (1997), "Legal determinants of external finance", Journal of Finance 52:1131-1150. LeRoy, S.E, and R.D. Porter (1981), "The present value relation: tests based on variance bounds", Econometriea 49:555-577. Lettan, M. (1997), "Idiosyncratic risk and volatility bounds", unpublished paper (CentER, Tilburg University). Lettau, M., and H. Uhlig (1996), "Asset prices and business cycles: successes and pitfalls of the general equilibrium approach", unpublished paper (CentER, Tilburg University). Lucas Jr, R.E. (1978), "Asset prices in an exchange economy", Econometrica 46:1429-1446.

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Mankiw, N.G. (1986), "The equity premium and the concentration of aggregate shocks", Journal of Financial Economics 17:211-219. Mankiw, N.G., and J.A. Miron (1986), "The changing behavior of the term structure of interest rates", Quarterly Journal of Economics 101:211228. Mankiw, N.G., and S.E Zeldcs (1991), "The consumption of stockholders and non-stockholders", Journal of Financial Economics 29:97-112. Mehra, R., and E.C. Prescott (1985), "The equity premium puzzle", Journal of Monetary Economics 15:145-161. Merton, R. (1973), "An intertemporal capital asset pricing model", Econometa@a 41:867-887. Miron, J.A. (1986), "Seasonal fluctuations and the life cycle-permanent income hypothesis of consumption", Journal of Political Economy 94:1258 1279. Nelson, C.R., and R. Startz (1990), "The distribution of the instrumental variables estimator and its t-ratio when the instrument is a poor one", Journal of Business 63:S125-$140. Poterba, J.M., and L.H. Summers (1988), "Mean reversion in stock returns: evidence and implications", Journal of Financial Economics 22:27-60. Prescott, E.C. (1986), "Theory ahead of business cycle measurement", Carnegie-Rnchester Conference Series on Public Policy 25:11-66. Restoy, E, and E Weil (1998), "Approximate equilibrium asset prices", Working Paper No. 6611 (NBER). Rietz, 32 (1988), "The equity risk premium: a solution?", Journal of Monetary Economics 21:117-132. Rouwenhorst, K.G. (1995), "Asset pricing implications of equilibrium business cycle models", in: T.E Cooley, ed., Frontiers of Business Cycle Research (Princeton University Press, Princeton, NJ). Ryder Jr, H.E., and G.M. Heal (1973), "Optimum growth with intertemporally dependent preferences", Review of Economic Studies 40:1-33. Sandroni, A. (1997), "Asset prices, wealth distribution, and intertemporal preference shocks", unpublished paper (University of Pennsylvania). Santos, M.S., and M. Woodford (1997), "Rational asset pricing bubbles", Econometrica 65:19 57. Schwert, G.W. (1989), "Why does stock market volatility change over time?", Journal of Finance 44:1115 1153. Shiller, R.J. (i 981), "Do stock prices move too much to be justified by subsequent changes in dividends?", American Economic Review 71:421-436. Shiller, R.J. (1982), "Consumption, asset markets, and macroeconomic fluctuations", Carnegie Mellon Conference Series on Public Policy 17:203-238. Shiller, R.J. (1984), "Stock prices and social dynamics", Brookings Papers on Economic Activity 1984(2):457M98. Shiller, R.J. (1999), "Human behavior and the efficiency of the financial system", ch. 20, this Handbook. Singleton, K. (1990), "Specification and estimation ofintertemporal asset pricing models", in B. Friedman and E Hahn, eds., Handbook of Monetary Economics (North-Holland, Amsterdam). Sun, T. (I992), "Real and nominal interest rates: a discrete-time model and its continuous-time limit", Review of Financial Studies 5:581-611. Stmdaresan, S.M. (1989), "Intertemporally dependent preferences and the volatility of consumption and wealth", Review of Financial Studies 2:73 88. Svensson, L.E.O. (1989), "Portfolio choice with non-expected utility in continuous time", Economics Letters 30:313--317. The Economist (1987), One Hundred Years of Economic Statistics (The Economist, London). Tirole, J. (1985), "Asset bubbles and overlapping generations", Econometrica 53:1499-1527. Vasicek, O. (1977), "An equilibrium characterization of the term structure", Journal of Financial Economics 5:177-188. Wang, J. (1996), "The term structure of interest rates in a pure exchange economy with heterogeneous investors", Journal of Financial Economics 41:75 110. Weil, E (i989), "The equity premium puzzle and the risk-t?ec rate puzzle", Journal of Monetary Economics 24:401-421.

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Wheatley, S. (1988), "Some tests of the consumption-based asset pricing model", Journal of Monetary Economics 22:193~ 18. Wilcox, D. (1992), "The construction of US consumption data: some facts and their implications for empirical work", American Economic Review 82:922-941.

Chapter 20

HUMAN

BEHAVIOR

EFFICIENCY

AND

THE

OF THE FINANCIAL

SYSTEM*

ROBERT J. SHILLER Yale Unioersity

Contents

Abstract 1306 Keywords 1306 Introduction 1307 1. Prospect theory 1308 2. Regret and cognitive dissonance 1313 3. Anchoring 1314 4. Mental compartments 1317 Overconfidence, over- and under-reaction and the representativeness heuristic 1318 1324 6. The disjunction effect 1325 7. Gambling behavior and speculation 1325 8. The irrelevance o f history 1328 9. Magical thinking 1329 10. Quasi-magical thinking 1330 11. Attention anomalies and the availability heuristic 1331 12. Culture and social contagion 1332 13. A global culture 1333 14. Concluding remarks 1334 References .

* An earlier version was presented at a conference Recent Developments in Maclveconomics at the Federal Reselwe Bank of New York, February 27-28, 1997. The author is indebted to Ricky Lain for research assistance, and to Michael Krause, Virginia Shiller, Andrei Shleifer, David Wilcox, and the editors for helpful comments. This research was supported by the National Science Foundation. Handbook o f Macroeconomics, Volume 1, Edited by ~B. ~l~ylor and M. WoodJbrd © 1999 Elsevier Science B. l( All rights reserved

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Abstract

Recent literature in empirical finance is surveyed in its relation to underlying behavioral principles, principles which come primarily from psychology, sociology, and anthropology. The behavioral principles discussed are: prospect theory, regret and cognitive dissonance, anchoring, mental compartments, overconfidence, over- and under-reaction, representativeness heuristic, the disjunction effect, gambling behavior and speculation, perceived irrelevance of history, magical thinking, quasi-magical thinking, attention anomalies, the availability heuristic, culture and social contagion, and global culture.

Keywords efficient markets, random walk, excess volatility, anomalies in finance, stock market, prospect theory, regret and cognitive dissonance, anchoring, mental compartments, overconfidence, overreaction, underreaction, representativeness heuristic, the disjunction effect, gambling behavior and speculation, irrelevance of history, magical thinking, quasi-magical thinking, attention anomalies, the availability heuristic, culture and social contagion, global culture JEL classification: G10

Ch. 20." Human Behavior and the Efficiency of the Financial System

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Introduction

Theories of human behavior from psychology, sociology, and anthropology have helped motivate much recent empirical research on the behavior of financial markets. In this paper I will survey some of the most significant theories (for empirical finance) in these other social sciences and the empirical finance literature itself. Particular attention will be paid to the implications of these theories for the efficient markets hypothesis in finance. This is the hypothesis that financial prices efficiently incorporate all public information and that prices can be regarded as optimal estimates of true investment value at all times. The efficient markets hypothesis in turn is based on more primitive notions that people behave rationally, or accurately maximize expected utility, and are able to process all available information. The idea behind the term "efficient markets hypothesis", a term coined by Harry Roberts (1967) l, has a long history in financial research, a far longer history than the term itself has. The hypothesis (without the words efficient markets) was given a clear statement in Gibson (1889), and has apparently been widely known at least since then, if not long before. All this time there has also been tension over the hypothesis, a feeling among many that there is something egregiously wrong with it; for an early example, see Mackay (1841). In the past couple of decades the finance literature has amassed a substantial number of observations of apparent anomalies (from the standpoint of the efficient markets hypothesis) in financial markets. These anomalies suggest that the underlying principles of rational behavior underlying the efficient markets hypothesis are not entirely correct and that we need to look as well at other models of human behavior, as have been studied in the other social sciences. The organization of this paper is different from that of other accounts of the literature on behavioral finance [for example, De Bondt and Thaler (1996) or Fama (1997)]: this paper is organized around a list of theories from the other social sciences that are used by researchers in finance, rather than around a list of anomalies. I organized the paper this way because, in reality, most of the fundamental principles that we want to stress here really do seem to be imported from the other social sciences. No surprise here: researchers in these other social sciences have done most of the work over the last century on understanding less-than-perfectly-rational human behavior. Moreover, each anomaly in finance typically has more than one possible explanation in terms of these theories from the other social sciences. The anomalies are observed in complex real world settings, where many possible factors are at work, not in the experimental psychologist's laboratory. Each of their theories contributes a little to our understanding of the anomalies, and there is typically no way to quantify or prove the relevance of any one theory: It is better to set forth the theories from the other social sciences themselves, describing when possible the controlled experiments that demonstrate their validity, and give for each a few illustrations of applications in finance. I The Roberts (1967) paper has never been published; the fame of his paper apparently owes to the discussion of it in Fama (1970).

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Before beginning, it should be noted that theories of human behavior from these other social sciences often have underlying motivation that is different from that of economic theories. Their theories are often intended to be robust to application in a variety of everyday, unstructured experiences, while the economic theories are often intended to be robust in the different sense that, even if the problems the economic agents face become very clearly defined, their behavior will not change after they learn how to solve the problems. Many of the underlying behavioral principles from psychology and other social sciences that are discussed below are unstable and the hypothesized behavioral phenomena may disappear when the situation becomes better structured and people have had a lot of opportunity to learn about it. Indeed, there are papers in the psychology literature claiming that many of the cognitive biases in human judgment under uncertainty uncovered by experimental psychologists will disappear when the experiment is changed so that the probabilities and issues that the experiment raises are explained clearly enough to subjects [see, for example, Gigerenzer (1991)]. Experimental subjects can in many cases be convinced, if given proper instruction, that their initial behavior in the experimental situation was irrational, and they will then correct their ways. To economists, such evidence is taken to be more damning to the theories than it would be by the social scientists in these other disciplines. Apparently economists at large have not fully appreciated the extent to which enduring patterns can be found in this "unstable" human behavior. Some examples below will illustrate the application of theories from other social sciences to understanding anomalies in financial markets will illustrate. Each section below, until the conclusion, refers to a theory taken from the literature in psychology, sociology or anthropology. The only order of these sections is that I have placed first theories that seem to have the more concrete applications in finance, leaving some more impressionistic applications to the end. in the conclusion, I attempt to put these theories into perspective, and to recall that there are also important strengths in conventional economic theory and in the efficient markets hypothesis itself.

1. Prospect theory Prospect theory [Kahneman and Tversky (1979), Tversky and Kahneman (1992)j has probably had more impact than any other behavioral theory on economic research. Prospect theory is very influential despite the fact that it is still viewed by much of the economics profession at large as of far less importance than expected utility theory. Among economists, prospect theory has a distinct, though still prominent, second place to expected utility theory for most research. I should say something first about the expected utility theory that still retains the position of highest honor in the pantheon of economic tools, it has dominated much economic theory so long because the theory offers a parsimonious representation of truly rational behavior under uncertainty. The axioms [Savage (1954)] from which

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expected utility theory is derived are undeniably sensible representations of basic requirements of rationality. For many purposes, it serves well to base an economic theory on such assumptions of strictly rational behavior, especially if the assumptions of the model are based on simple, robust realities, if the model concerns wellconsidered decisions of informed people, and if the phenomenon to be explained is one of stable behavior over many repetitions, where learning about subtle issues has a good chance of occurring. Still, despite the obvious attractiveness of expected utility theory, it has long been known that the theory has systematically mispredicted human behavior, at least in certain circumstances. Allais (1953) reported examples showing that in choosing between certain lotteries, people systematically violate the theory. Kahneman and Tversky (1979) give the following experimental evidence to illustrate one of Allais' examples. When their subjects were asked to choose between a lottery offering a 25% chance of winning 3000 and a lottery offering a 20% chance of winning 4000, 65% of their subjects chose the latter, while when subjects were asked to choose between a 100% chance of winning 3000 and an 80% chance of winning 4000, 80% chose the former. Expected utility theory predicts that they should not choose differently in these two cases, since the second choice is the same as the first except that all probabilities are multiplied by the same constant. Their preference for the first choice in the lottery when it is certain in this example illustrates what is called the "certainty effect", a preference for certain outcomes. Prospect theory is a mathematically-formulated alternative to the theory of expected utility maximization, an alternative that is supposed to capture the results of such experimental research. (A prospect is the Kahneman-Tversky name for a lottery as in the Allais example above.) Prospect theory actually resembles expected utility theory in that individuals are represented as maximizing a weighted sum of "utilities", although the weights are not the same as probabilities and the "utilities" are determined by what they call a "value function" rather than a utility function. The weights are, according to Kalmeman and Tversky (1979) determined by a function of true probabilities which gives zero weight to extremely low probabilities and a weight of one to extremely high probabilities. That is, people behave as if they regard extremely improbable events as impossible and extremely probable events as certain. However, events that are just very improbable (not extremely improbable) are given too much weight; people behave as if they exaggerate the probability. Events that are very probable (not extremely probable) are given too little weight; people behave as if they underestimate the probability. What constitutes an extremely low (rather than very low) probability or an extremely high (rather than very high) probability is determined by individuals' subjective impression and prospect theory is not precise about this. Between the very low and very high probabilities, the weighting function (weights as a function of true probabilities) has a slope of less than one. This shape for the weighting function allows prospect theory to explain the Allais certainty effect noted just above. Since the 20% and 25% probabilities are in the range of the weighting function where its slope is less than one, the weights people attach to

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the two outcomes are more nearly equal than are the probabilities, and people tend just to choose the lottery that pays more if it wins. In contrast, in the second lottery choice the 80% probability is reduced by the weighting function while the 100% probability is not; the weights people attach to the two outcomes are more unequal than are the probabilities, and people tend just to choose the outcome that is certain. If we modify expected utility function only by substituting the Kahneman and Tversky weights for the probabilities in expected utility theory, we might help explain a number of puzzling phenomena in observed human behavior toward risk. For a familiar example, such a modification could explain the apparent public enthusiasm for highprize lotteries, even though the probability of winning is so low that expected payout of the lottery is not high. It could also explain such a phenomenon as the observed tendency for overpaying for airline flight insurance (life insurance policies that one purchases before an airline flight, that has coverage only during that flight), Eisner and Strotz (1961). The Kahneman-Tversky weighting function may explain observed overpricing of out-of-the-money and in-the-money options. Much empirical work on stock options pricing has uncovered a phenomenon called the "options smile" [see Mayhew (1995) for a review]. This means that both deep out-of-the-money and deep in-the-money options have relatively high prices, when compared with their theoretical prices using Black-Scholes formulae, while near-the-money options are more nearly correctly priced. Options theorists, accustomed to describing the implied volatility of the stock implicit in options prices, like to state this phenomenon not in terms of option prices but in terms of these implied volatilities. When the implied volatility for options of various strike prices at a point in time derived using the Black-Scholes (1973) formula are plotted, on the vertical axis, against the strike price on the horizontal axis, the curve often resembles a smile. The curve is higher both for low strike price (out-of-themoney) options and for high strike price (in-the-money) options than it is for middlerange strike prices. This options smile might possibly be explained in terms of the distortion in probabilities represented by the Kahneman-Tversky weighting function, since the theory would suggest that people act as if they overestimate the small probability that the price of the underlying crosses the strike price and underestimate the high probability that the price remains on the same side of the strike price. The Kahneman-Tversky weighting function might even explain the down-turned corners of the mouth that some smiles exhibit [see Fortune (1996)] if at these extremes the discontinuities at the extremes of the weighting fi.mction become relevant 2.

2 There are other potential explanations of the options smile in terms of nonnormality or jump processes for returns, and these have received the attention in the options literature. Such explanations might even provide a completerational basis for the smile, though it ishard to know for sure. Since the 1987 stock market crash, the options smile has usually appeared distorted into an options "leer", with the left side of the mouth higher (e.g., the deep out-of-the-moneyputs are especially overpriced), see Bates (1995), Jackwcrth and Rubinstein (1995) and Bates (1991). Public memories of the 1987 crash are apparently at work in producing this "leer"

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We now turn to the other foundation of prospect theory, the Kahneman and Tversky (1979) value function. The value function differs from the utility function in expected utility theory in a very critical respect: the function (of wealth or payout) has a kink in it at a point, the "reference point", the location of which is determined by the subjective impressions of the individual. The reference point is the individual's point of comparison, the "status quo" against which alternative scenarios are contrasted. Taking value as a function of wealth, the Kahneman-Tversky (1979) value function is upward sloping everywhere, but with an abrupt decline in slope at the reference point (today's wealth or whatever measure of wealth that is psychologically important to the subject). For wealth levels above the reference point, the value function is concave downward, just as are conventional utility functions. At the reference point, the value function may be regarded, from the fact that its slope changes abruptly there, as infinitely concave downward. For wealth levels below the reference point, Kahneman and Tversky found evidence that the value function is concave upward, not downward. People are risk lovers for losses, they asserted. Perhaps the most significant thing to notice about the Kahneman-Tversky value function is just the discontinuity in slope at the reference value, the abrupt downward change in slope as one moves upward past the reference value. Prospect theory does not nail down accurately what determines the location of the reference point, just as it does not nail down accurately, for the weighting function, what is the difference between very high probabilities and extremely high probabilities. The theory does not specify these matters because experimental evidence has not produced any systematic patterns of behavior that can be codified in a general theory. However, the reference point is thought to be determined by some point of comparison that the subject finds convenient, something readily visible or suggested by the wording of a question. This discontinuity means that, in making choices between risky outcomes, people will behave in a risk averse manner, no matter how small the amounts at stake are. This is a contrast to the prediction of expected utility theory with a utility function of wealth without kinks, for which, since the utility function is approximately linear for small wealth changes, people should behave as if they are risk neutral for small bets. That people would usually be risk neutral for small bets would be the prediction of expected utility theory even if the utility function has such a slope discontinuity, since the probability that wealth is currently at the kink is generally zero. With prospect theory, in contrast, the kink always moves with wealth to stay at the perceived current level of wealth (or the current point of reference); the kink is always relevant. Samuelson (1963) told a story which he perceived as demonstrating a violation of expected utility theory, and, although it came before Kahneman and Tversky's prospect theory, it illustrates the importance of the kink in the value function. Samuelson reported that he asked a lunch colleague whether he would accept a bet that paid him $200 with a probability of 0.5 and lost him $100 with a probability of 0.5. The colleague said he would not take the bet, but that he would take a hundred of them. With 100 such bets, his expected total winnings are $5000 and he has virtually no chance of losing any money. It seems intuitively compelling to many people that

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one would readily take the complete set o f bets, even if any element o f the set is unattractive. Samuelson proved that if his colleague would answer the same way at any wealth level, then he necessarily violates expected utility theory. Samuelson's colleague is not, however, in violation o f prospect theory. When viewing a single bet, the kink in the value function is the dominant consideration. If he were to judge 100 bets sequentially, the kink would always be relevant (the reference point would move with each successive bet) and he would reject all o f them. But if he were to judge 100 bets together, the collective outcomes would be far above today's value function kink, and the bet is, by prospect theory, clearly desirable. The failures to accept many such bets when one considers them individually has been called "myopic loss aversion" by Benartzi and Thaler (1995). They argue that, assuming estimated values for the magnitude of the kink in tbe Kahneman-Tversky value function, the "equity premium puzzle" of Mehra and Prescott (1985) can be resolved; see also Siegel and Thaler (1997). Today, the term "equity premium puzzle", coined by Mehra and Prescott (1985), is widely used to refer to the puzzlingly high historical average returns o f stocks relative to bonds 3. The equity premium is the difference between the historical average return in the stock market and the historical average return on investments in bonds or treasury bills. According to Siegel (1998), the equity premium of US stocks over shortterm government bonds has averaged 6.1% a year for the United States for 1926-1992, and so one naturally wonders why people invest at all in debt if it is so outperformed by stocks 4. Those who have tried to reconcile the equity premium with rational investor behavior commonly point out the higher risk that short-run stock market returns show: investors presumably are not fully enticed by the higher average returns o f stocks since stocks carry higher risk. But, such riskiness o f stocks is not a justification o f the equity premium, at least assuming that investors are mostly long term. Most investors ought to be investing over decades, since most o f us expect to live for many decades, and to spend the twilight o f their lives living off savings. Over long periods o f times, it has actually been long-term bonds (whose payout is fixed in nominal terms), not the stocks, that have been more risky in real terms, since the consumer price index has been, despite its low variability from month to month, very variable over long intervals o f time, see Siegel (1998). Moreover, stocks appear strictly to dominate bonds: there is

3 Mehra and Prescott did not discover the equity premium. Perhaps that honor should go to Smith (1925), although there must be even earlier antecedents in some forms. Mehra and Prescott's original contribution seems to have been, in the context of present-value investor intertemporal optimizing models, to stress that the amount of risk aversion that would justify the equity premium, given the observed correlation of stocks with consumption, would imply much higher riskless interest rates than we in fact see. 4 Siegel (1998, p. 20). However, Siegel notes that the US equity premium was only 1.9% per year 18161870 and 2.8% per year 1871-1925.

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no thirty-year period since 1861 in which a broad portfolio o f stocks was outperformed either by bonds or treasury bills 5. Benartzi and Thaler (1995) show that if people use a one-year horizon to evaluate investments in the stock market, then the high equity premium is explained by myopic loss aversion. Moreover, prospect theory does not suggest that in this case riskless real interest rates need be particularly high. Thus, if we accept prospect theory and that people frame stock market returns as short-term, the equity premium puzzle is solved. Benartzi and Thaler (1996) demonstrated experimentally that when subjects are asked to allocate their defined contribution pension plans between stocks and fixed incomes, their responses differed sharply depending on how historical returns were presented to them. If they were shown 30 one-year returns, their median allocation to stocks was 40%, but if they were shown 30-year returns their median allocation to stocks was 90%. Thaler, Tversky, Kahneman and Schwartz (1997) show further experiments confirming this response. Loss aversion has also been used to explain other macroeconomic phenomena~ savings behavior [Bowman, Minehart and Rabin (1993)] and job search behavior [Bryant (l 990)].

2. Regret and cognitive dissonance There is a human tendency to feel the pain of regret at having made errors, even small errors, not putting such errors into a larger perspective. One "kicks oneself" at having done something foolish. If one wishes to avoid the pain of regret, one may alter one's behavior in ways that would in some cases be irrational unless account is taken of the pain o f regret. The pain o f regret at having made errors is in some senses embodied in the Kahneman-Tversky notion o f a kink in the value function at the reference point. There are also other ways of representing how people behave who feel pain o f regret. Loomes and Sugden (1982) have suggested that people maximize the expected value of a "modified utility function" which is a function o f the utility they achieve from a choice as well as the utility they would have achieved from another choice that was considered. Bell (1982) proposed a similar analysis. Regret theory may apparently help explain the fact that investors defer selling stocks that have gone down in value and accelerate the selling o f stocks that have gone up in value, Shefrin and Statmau (1985). Regret theory may be interpreted as implying that

5 Siegel (1998). It should be noted that one must push the investor horizon up to a fairly high number, around 30 years, before one finds that historically stocks have always outperformed bonds since 1861; for ten-year periods of time one finds that bonds oRen outperform stocks. There are not many thirty-year periods in stock market history, so this information might be judged as insubstantial. Moreover, Siegel notes that even with a thirty-year period stocks did not always outperform bonds in the US before 1861.

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investors avoid selling stocks that have gone down in order not to finalize the error they make and not to feel the regret. They sell stocks that have gone up in order that they cannot regret failing to do so before the stock later fell, should it do so. That such behavior exists has been documented using volume of trade data by Ferris, Haugen and Makhija (1988) and Odean (1996). Cognitive dissonance is the mental conflict that people experience when they are presented with evidence that their beliefs or assumptions are wrong; as such, cognitive dissonance might be classified as a sort of pain of regret, regret over mistaken beliefs. As with regret theory, the theory of cognitive dissonance [Festinger (1957)] asserts that there is a tendency for people to take actions to reduce cognitive dissonance that would not normally be considered fully rational: the person may avoid the new information or develop contorted arguments to maintain the beliefs or assumptions. There is empirical support that people often make the errors represented by the theory of cognitive dissonance. For example, in a classic study, Erlich, Guttman, Schopenback and Mills (1957) showed that new car purchasers selectively avoid reading, after the purchase is completed, advertisements for car models that they did not choose, and are attracted to advertisements for the car they chose. McFadden (1974) modeled the effect of cognitive dissonance in terms of a probability of forgetting contrary evidence and showed how this probability will ultimately distort subjective probabilities. Goetzmann and Peles (1993) have argued that the same theory of cognitive dissonance could explain the observed phenomenon that money flows in more rapidly to mutual funds that have performed extremely well than flows out from mutual funds that have performed extremely poorly: investors in losing funds are unwilling to confront the evidence that they made a bad investment by selling their investments.

3. Anchoring It is well-known that when people are asked to make quantitative assessments their assessments are influenced by suggestions. An example of this is found in the results survey researchers obtain. These researchers often ask people about their incomes using questionnaires in which respondents are instructed to indicate which of a number of income brackets, shown as choices on the questionnaire, their incomes fall into. It has been shown that the answers people give are influenced by the brackets shown on the questionnaire. The tendency to be influenced by such suggestions is called "anchoring" by psychologists. In some cases, at least, anchoring may be rational behavior for respondents. They may rationally assume that the deviser of the questionnaire uses some information (in this case, about typical people's incomes) when devising the questionnaire. Not fully remembering their own income, they may rely on the information in the brackets to help them answer better. If the brackets do contain information, then it is rational for subjects to allow themselves to be influenced by the brackets.

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While anchoring undoubtedly has an information-response component in many circumstances, it has also been shown that anchoring behavior persists even when information is absent. In one experiment Tversky and Kahneman (1974), subjects were given simple questions whose answers were in percentages, e.g., the percentage of African nations in the United Nations. A wheel of fortune with numbers from 1 to 100 was spun before the subjects. Obviously, the number at which the wheel of fortune stopped had no relevance to the question just asked. Subjects were asked whether their answer was higher or lower than the wheel of fortune number, and then to give their own answer. Respondents' answers were strongly influenced by the "wheel of fortune." For example, the median estimates of the percentage of African countries in the United Nations were 25 and 45 for groups that received 10 and 65, respectively, as starting points (p. 184). Values in speculative markets, like the stock market, are inherently ambiguous. Who would know what the value of the Dow Jones Industrial Average should be? Is it really "worth" 6000 today? Or 5000 or 7000? or 2000 or 10000? There is no agreed~ upon economic theory that would answer these questions. In the absence of any better information, past prices (or asking prices or prices of similar objects or other simple comparisons) are likely to be important determinants of prices today. That anchoring affects valuations, even by experts, was demonstrated by Northcraft and Neale (1987) in the context of real estate valuation. All subjects were taken to a house for sale, asked to inspect the house for up to 20 minutes, and were given a ten-page packet of information about the house and about other houses in the area, giving square footage and characteristics of the properties, and prices of the other properties. The same packet was given to all subjects except that the asking price of the property under consideration and its implied price per square foot were changed between subjects. Subjects were asked for their own opinions of its appraisal value, appropriate listing price, purchase price, and the lowest offer the subject would accept for the house if the subject were the seller. The real estate agents who were given an asking price of $119900 had a mean predicted appraisal value of $114204, listing price of $1 l 7 745, purchase price of $111454 and a lowest acceptable offer of $11l 136, while the real estate agents who were given an asking price of $149900 had a mean appraisal value of $128 754, listing price of $130 981, predicted purchase price of $127318, and a lowest offer of $123818. The changed asking prices thus swayed their valuations by 11% to 14% of the value of the house. Similar results were found with amateur subjects. While this experiment does not rule out that the effect of the asking price was due to a rational response to the assumed information in the asking price, the effects of asking price are remarkably large, given that so much other information on the house was also given. Moreover, when subjects were asked aftelwards to list the items of information that weighed most heavily in their valuations, only 8% of the expert subjects and only 9% of the amateur subjects listed asking price of the property under consideration among the top three items. Note that the valuation problem presented to these subjects is far less difficult or ambiguous than the problem of determining the "correct" value for the stock market, since here they are implicitly

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being asked to assume that the comparable properties are correctly valued. [See also McFadden (1974) and Silberman and Klock (1989).] One might object that the notion that anchoring on past prices helps determine present prices in the stock market might be inconsistent with the low serial correlation of stock price changes, that is with the roughly random-walk behavior of daily or monthly stock prices that has been widely noted 6. This conclusion is not warranted however. Models of "smart money" (i.e., people who are unusually alert to profit opportunities in financial markets) seeking to exploit serial correlation in price, models which also include ordinary investors, are consistent with the implications that serial correlation is low and yet the anchoring remains important for the level of stock prices [see Shiller (1984, 1990)]. By extension from these experimental results, it is to be presumed that very many economic phenomena are influenced by anchoring. Gruen and Gizycki (1993) used it to explain the widely observed anomaly 7 that forward discounts do not properly explain subsequent exchange rate movements. The anchoring phenomenon would appear relevant to the "sticky prices" that are so talked about by macroeconomists. So long as past prices are taken as suggestions of new prices, the new prices will tend to be close to the past prices. The more ambiguous the value of a commodity, the more important a suggestion is likely to be, and the more important anchoring is likely to be for price determination. The anchoring phenomenon may help to explain certain international puzzles observed in financial markets. US investors who thought in the late 1980s that Japanese stock price-earnings ratios were outrageously high then may have been influenced by the readily-available anchor of (much lower) US price-earnings ratios. By the mid 1990s, many US investors felt that the Tokyo market is no longer overpriced [see Shiller, Kon-Ya and Tsutsui (1996)]. The price-earnings ratios remain much higher than in the US perhaps because of the anchor of the widely-publicized high Tokyo price-earnings ratios of the late 1980s. Anchoring may also be behind certain forms of money illusion. The term money illusion, introduced by Fisher (1928), refers to a human tendency to make inadequate allowance, in economic decisions, for the rate of inflation, and to confuse real and nominal quantities. Shafir, Diamond and Tversky (1997) have shown experimentally that people tend to give different answers to the same hypothetical decision problem depending on whether the problem was presented in a way that stressed nominal

6 The notion that speculative prices approximately describe "random walks" was tirst proposed by Bachelier (1900). It became widely associated with the efficientmarkets hypothesis, the hypothesis that market prices efficientlyincorporate all availablehlformation, with the work of Fama (1970). For further information on the literature on the random walk and efficient markets theory see also Cootner (1964), Malkiel (1981), and Fama (1991). 7 For a discussion of the anomaly, see Backus et al. (1995) and Froot and Thalcr (1990)

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quantities or in a way that stressed real quantities. The quantities that were shown in the question (whether nominal or real) may have functioned as anchors 8.

4. Mental compartments Related to the anchoring and framing phenomena is a human tendency to place particular events into mental compartments based on superficial attributes. Instead of looking at the big picture, as would be implied by expected utility theory, they look at individual small decisions separately. People may tend to place their investments into arbitrarily separate mental compartments, and react separately to the investments based on which compartment they are in. Shefrin and Statman (1994) have argued that individual investors think naturally in terms o f having a "safe" part of their portfolio that is protected from downside risk and a risky part that is designed for a chance o f getting rich. Shefrin and Thaler (1988) have argued that people put their sources of income into three categories, current wage and salary income, asset income, and future income, and spend differently out of the present values of these different incomes. For example, people are reluctant to spend out of future income even if it is certain to arrive. The tendency for people to allow themselves to be influenced by their own mental compartments might explain the observed tendency for stock prices to jump up when the stock is added to the Standard and Poor Stock Index [see Shleifer (1986)]. It might also help explain the widely noted "January effect" anomaly. This anomaly, that stock prices tend to go up in January, has been observed in as many as 15 different countries [Gultekin and Gultekin (1983)]. The anomaly cannot be explained in terms o f effects related to the tax year, since it persists also in Great Britain (whose tax year begins in April) and Australia (whose tax year begins in July), see Thaler (1987). If people view the year end as a time of reckoning and a new year as a new beginning, they may be inclined to behave differently at the turn o f the year, and this may explain the January effect. A tendency to separate out decisions into separate mental compartments may also be behind the observed tendency for hedgers to tend to hedge specific trades, rather than their overall profit situation. Ren6 Stulz (1996, p. 8), in summarizing the results of his research and that o f others on the practice o f risk management by firms, concludes that: It immediately follows from the modern theory of risk management that one should be concerned about factors that affect the present value of future cash flows. This is quite different from much of the current practice of risk management where one is concerned about hedging transaction risk or the risk of transactions expected to occur in the short rtm.

s There appears to be much more to money illusion than just anchoring; people associate nominal quantities with opinions about the economy, anticipated behavior of the government, fairness, and prestige, opinions that are not generally shared by economists, see Shiller (1997a,b).

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The Wharton/CIBC Wood Gundy 1995 Survey of Derivatives Usage by US Non-Financial Firms [Bodnar and Marston (1996)] studied 350 firms: 176 firms in the manufacturing sector, 77 firms in the primary products sector, and 97 firms in the service sector. When asked by the Wharton surveyors what was the most important objective of hedging strategy, 49% answered managing "volatility in cashflows", 42% answered managing "volatility in accounting earnings", and only 8% answered managing "the market value o f the firm" (1% answered "managing balance sheet accounts and ratios"). Fifty percent o f the respondents in the survey reported frequently hedging contractual commitments, but only 8% reported frequently hedging competitive/economic exposure. It is striking that only 8% reported that their most important objective is the market value of the firm, since maximizing the market value of the firm is, by much financial theory, the ultimate objective of the management of the firm. It is o f course hard to know just what people meant by their choices of answers, but there is indeed evidence that firms are driven in their hedging by the objective o f hedging specific near-term transactions, and neglect consideration o f future transactions or other potential factors that might also pose longer run risks to the firm. In the Wharton study, among respondents hedging foreign currency risks, 50% reported hedging anticipated transactions less than one year off, but only 11% reported frequently hedging transactions more than one year off. This discrepancy is striking, since most o f the value of the firm (and most o f the concerns it has about its market value) must come in future years, not the present year 9.

5. Overconfidence, over- and under-reaction and the representativeness heuristic People often tend to show, in experimental settings, excessive confidence about their own judgments. Lichtenstein, Fischhoff and Phillips (1977) asked subjects to answer simple factual questions (e.g., "Is Quito the capital o f Ecuador?") and then asked them to give the probability that their answer was right: subjects tended to overestimate the probability that they were right, in response to a wide variety of questions. Such studies have been criticized [see Gigerenzer (1991)] as merely reflecting nothing more than a difference between subjective and frequentist definitions o f

9 Recent surveys of hedging behavior of firms indicates that despite extensive development of derivative products, actual use of these products for hedging is far from optimal. Of the firms cited in the Wharton study, only 40.5% reported using derivatives at all. On the other hand, Dolde (1993) surveyed 244 Fortune 500 companies and concluded that over 85% used swaps, forwards, futures or options in managing financial risk. Nance et al. (1993) in a survey of 194 farms reported that 62% used hedging instruments in 1986. These studies concentrated on rather larger companies than did the Wharton study. Overall, these studies may be interpreted as revealing a suq~risingly low fraction of respondents who do any hedging, given that firms are composed of many people, any one of whom might be expected to initiate the use of derivatives at least tbr some limited purpose.

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probability, i.e., critics claimed that individuals were simply reporting a subjective degree of certainty, not the fraction times they are right in such circumstances. However, in reaction to such criticism, Fischhoff, Slovic and Lichtenstein (1977) repeated the experiments asking the subjects for probability odds that they are right and very clearly explaining what such odds mean, and even asking them to stake money on their answer. The overconfidence phenomenon persisted. Moreover, in cases where the subjects said they were certain they were right, they were in fact right only about 80% of the time: there is no interpretation o f subjective probability that could reconcile this result with correct judgments. A tendency towards overconfidence among ordinary investors seems apparent when one interviews them. One quickly hears what seem to be overconfident statements. But how can it be that people systematically are so overconfident? Why wouldn't people learn from life's experiences to correct their overconfidence? Obviously, people do learn substantially in circumstances when the consequences of their errors are repeatedly presented to them, and sometimes they even overreact and show too little confidence. But still there seems to be a common bias towards overconfidence. Overconfidence is apparently related to some deep-set psychological phenomena: Ross (1987) argues that much overconfidence is related to a broader difficulty with "situational construal", a difficulty in making adequate allowance for the uncertainty in one's own view o f the broad situation, a more global difficulty tied up with multiple mental processes. Overconfidence may also be traced to the "representativeness heuristic", Tversky and Kahneman (1974), a tendency for people to try to categorize events as typical or representative of a well-known class, and then, in making probability estimates, to overstress the importance o f such a categorization, disregarding evidence about the underlying probabilities 10. One consequence o f this heuristic is a tendency for people to see patterns in data that are truly random, to feel confident, for example, that a series which is in fact a random walk is not a random walk l l Overconfidence itself does not imply that people overreact (or underreact) to all news. In fact, evidence on the extent o f overreaction or underreaction of speculative asset prices to news has been mixed. There has indeed been evidence of overreaction. The first substantial statistical evidence for what might be called a general market overreaction can be found in the literature on excess volatility o f speculative asset prices, Shiller (1979, 1981a,b) and LeRoy and Porter (1981). We showed statistical evidence that speculative asset prices show persistent deviations from the long-term trend implied by the presentvalue efficient markets model, and then, over horizons o f many years, to return to this

l0 People tend to neglect "base rates", the unconditional probabilities or frequencies of events, see Meehl and Rosen (1955). tt Rabin (1998) characterizes this judgment error as a tendency to over-intbr the probability distribution from short sequences. Part of overconfidence may be nothing more than simple tbrgetting of contrary evidence; a tendency to forget is by its very nature not something that one can learn to prevent.

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trend. This pattern o f price behavior, it was argued, made aggregate stock prices much more volatile than would be implied by the efficient markets model. It appears as i f stock prices overreact to some news, or to their own past values, before investors come to their senses and correct the prices. Our arguments led to a spirited debate about the validity o f the efficient markets model in the finance literature, a literature that has too many facets to summarize here, except to say that it confirms there are many potential interpretations o f any statistical results based on limited data 12. M y own view o f the outcome o f this debate is that it is quite likely that speculative asset prices tend to be excessively volatile. Certainly, at the very least, one can say that no one has been able to put forth any evidence that there is not excess volatility in speculative asset prices. For an evaluation o f this literature, see Shiller (1989), Campbell and Shiller (1988, 1989), West (1988), and Campbell, Lo and MacKinlay (1997, ch. 7). Since then, papers by De Bondt and Thaler (1985), Fama and French (1988), Poterba and Summers (1988), and Cutler, Poterba and Summers (1991) have confirmed the excess volatility claims by showing that returns tend to be negatively autocorrelated over horizons o f three to five years, that an initial overreaction is gradually corrected. Moreover, Campbell and Shiller (1988, 1989) show that aggregate stock market dividend yields or earnings yields are positively correlated with subsequently observed returns over similar intervals; see also Dreman and Berry (1995)13. Campbell and Shiller (1998) connect this predictive power to the observed stationarity o f these ratios. Since the ratios have no substantial trend over a century and appear mean reverting over nmch shorter time intervals, the ratio must predict future changes in either the numerator (the dividend or earnings) or the denominator (the price); we showed that it has been unequivocally the denominator, the price, that has restored the ratios to their mean after they depart from it, and not the numerator. La Porta (1996) found that stocks for which analysts projected low earnings growth tended to show upward price j u m p s on earnings announcement dates, and stocks for which analysts projected high earnings growth tended to show downward price jumps on earnings announcement dates. He interprets this as consistent with a hypothesis that analysts (and the market) excessively extrapolated past earnings movements and only gradually correct their errors as earnings news comes in. The behavior o f initial p u n i c offerings around

t2 There has been some confusion about the sense in which the present=value efficient markets model puts restrictions on tile short-run (or high-frequency) movements in speculative asset prices. The issues are laid out in Shiller (1979), (appendix). Kleidon (1986) rediscovered the same ideas again but gave a markedly different interpretation of the implications for tests of market efficiency. 13 An extensive summary of the literature on serial correlation of US stock indcx returns is in Campbell et al. (1997). Chapter 2 documents the positive serial correlation of returns over short horizons but concludes that the evidence for negative serial correlation of returns over long horizons is weak. Chapter 7, however, shows evidence that long-horizon returns are negatively correlated with the price earnings ratio and price-dividend ratio. Recent critics of claims that long-horizon returns can be forecasted include Goctzmann and Jorion (1993), Nelson and Kim (1993) and Kirby (1997). In my view, they succeed in reducing the force of the evidence, but not the conclusion that long-horizon returns are quite probably forecastab/e.

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announcement dates appears also to indicate some overreaction and later rebound, see Ibbotson and Ritter (1988) and Ritter (1991). On the other hand, there has also been evidence o f what might be called underreaction. Most days when big news breaks have been days o f only modest stock market price movements, the big movements tending to come on days when there is little news, see Cutler, Poterba and Summers (1989). Cutler, Poterba and Summers (1991) also found that for a number o f indices o f returns on major categories o f speculative assets there has been a tendency for positive autocorrelation o f short-run returns over short horizons, less than a year; see also Jegadeesh and Titman (1993) and Chart, Jegadeesh and Lakonishok (1996)14. This positive serial correlation in return indices has been interpreted as implying an initial underreaction o f prices to news, to be made up gradually later. Bernard and Thomas (1992) found evidence o f underreaction of stock prices to changes, from the previous year, in company earnings: prices react with a lag to earnings news; see also Ball and Brown (1968)15. Irving Fisher (1930, ch. XXI, pp. 493-494) thought that, because o f human error, nominal interest rates tend to underreact to inflation, so that there is a tendency for low real interest rates in periods o f high inflation, and high real rates in periods o f low inflation. More recent data appear to confirm this behavior o f real interest rates, and data on inflationary expectations also bear out Fisher's interpretation that the phenomenon has to do with human error; see De Bondt and Bange (1992) and Shefrin (1997) tr. Does the fact that securities prices sometimes underreact pose any problems for the psychological theory that people tend to be overconfident? Some observers seem to think that it does. In fact, however, overconfidence and overreaction are quite different phenomena. People simply cannot overreact to everything: if they are overconfident they will make errors, but not in any specified direction in all circumstances. The concepts o f overreaction or underreaction, while they may be useful in certain contexts, are not likely to be good psychological foundations on which to organize a general theory o f economic behavior. The fact that both overreaction and underreaction are observed in financial markets has been interpreted b y Fama (1997) as evidence that the anomalies from the standpoint

14 Lo and MacKinlay (1988) and Lehmann (1990), however, find evidence of negative serial corrclation of individual weekly stock returns between successive weeks. As explained by Lo and MacKinlay (1990), weekly returns on portfolios of these same stocks still exhibit positive serial correlation from week to week because the cross-covariances between returns of individual stocks arc positive. They conclude that this pattern of cross-covariances is not what one would expect to find based on theories of investor inertia. Lehmann, however, has a different interpretation of the negative week-to-week serial correlation of individual weekly stock returns, that the negative serial correlation reflects nothing more than the behavior of market makers facing order imbalances and asymmetric information. ~5 Firms' management appear acutely aware that earnings growth has a psychological impact on prices, and so attempt to manage earnings accotmting to provide a steady growth path. Impressive evidence that they do so is found in Degeorge et al. (1999). 16 Modigliani and Cohn (1979) argue that public failure to understand the relation of interest rates to inflation has caused the stock market to overreact to nominal interest rate changes.

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of efficient markets theory are just "chance results", and that therefore the theory of market efficiency survives the challenge of its critics. He is right, of course, that both overreaction and underreaction together may sometimes seem a little puzzling. But one is not likely to want to dismiss these as "chance results" if one has an appreciation for the psychological theory that might well bear on these phenomena. In his survey of behavioral finance Fama (1997) makes no more than a couple of oblique references to any literature from the other social sciences. In fact, Fama states that the literature on testing market efficiency has no clearly stated alternative, "the alternative hypothesis is vague, market inefficiency" (p. 1). Of course, if one has little appreciation of these alternative theories then one might well conclude that the efficient markets theory, for all its weaknesses, is the best theory we have. Fama appears to believe that the principal alternative theory is just one of consistent overreaction or underreaction, and says that "since the anomalies literature has not settled on a testable alternative to market efficiency, to get the ball rolling, I assume that reasonable alternatives must predict either over-reaction or under-reaction" (p. 2). The psychological theories reviewed here cannot be reduced to such simple terms, contrary to Fama's expectations. Barberis, Shleifer and Vishny (1997) provide a psychological model, involving the representativeness heuristic as well as a principle of conservatism [Edwards (1968)], that offers a reconciliation of the overreaction and underreaction evidence from financial markets; see also Daniel, Hirshleifer and Subrahmanyam (1997) and Wang (1997). More work could be done in understanding when it is that people overreact in financial markets and when it is that they underreact. Understanding these overreaction and underreaction phenomena together appears to be a fertile field for research at the present time. There is neither reason to think that it is easy obtain such an understanding, nor reason to despair that it can ever be done. Overconfidence may have more clear implications for the volume of trade in financial markets than for any tendency to overreact. If we connect the phenomenon of overconfidence with the phenomenon of anchoring, we see the origins of differences of opinion among investors, and some of the source of the high volume of trade among investors. People may fail to appreciate the extent to which their own opinions are affected by anchoring to cues that randomly influenced them, and take action when there is little reason to do so. The extent of the volume of trade in financial markets has long appeared to be a puzzle. The annual turnover rate (shares sold divided by all shares outstanding) for New York Stock Exchange Stocks has averaged 18% a year from the 1950s through the 1970s and has been much higher in certain years. The turnover rate was 73% in 1987 and 67% in 1930. It does not appear to be possible to justify the number of trades in stocks and other speculative assets in terms of the normal life-cycle ins and outs of the market. Theorists have established a "nonspeculation theorem" that states that rational agents who differ from each other only in terms of information and who have no reason to trade in the absence of information will not trade [Milgrom and Stokey (1982), Geanakoplos (1992)].

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Apparently, many investors do feel that they do have speculative reasons to trade often, and apparently this must have to do with some tendency for each individual to have beliefs that he or she perceives as better than others' beliefs. It is as if most people think they are above average. Odean (1998), in analyzing individual customer accounts at a nationwide discount brokerage house, examined the profits that customers made on trades that were apparently not motivated by liquidity demands, tax loss selling, portfolio rebalancing, or a move to lower-risk securities. On the remaining trades, the returns on the stocks purchased was on average lower, not higher, than on those sold. This appears to be evidence of overconfidence among these investors. Within the week of the stock market crash of October 19, 1987 1 sent out questionnaires to 2000 wealthy individual investors and 1000 institutional investors, asking them to recall their thoughts and reasons for action on that day; see Shiller (1987b). There were 605 completed responses from individuals and 284 responses from institutions. One of the questions I asked was: "Did you think at any point on October 19, 1987 that you had a pretty good idea when a rebound was to occur?" Of individual investors, 29.2% said yes, of institutional investors, 28.0% said yes. These numbers seem to be surprisingly high: one wonders why people thought they knew what was going to happen in such an unusual situation. Among those who bought on that day, the numbers were even higher, 47.1% and 47.9% respectively. The next question on the questionnaire was "If yes, what made you think you knew when a rebound was to occur?" Here, there was a conspicuous absence of sensible answers; often the answers referred to "intuition" or "gut feeling." It would appear that the high volume of trade on the day of the stock market crash, as well as the occurrence, duration, and reversal of the crash was in part determined by overconfidence in such intuitive feelings 17 If people are not independent of each other in forming overconfident judgments about investments, and if these judgments change collectively through time, then these "noisy" judgments will tend to cause prices of speculative assets to deviate from their true investment value. Then a "contrarian" investment strategy, advocated by Graham and Dodd (1934) and Dreman (1977) among many others, a strategy of investing in assets that are currently out of favor by most investors, ought to be advantageous. Indeed, there is much evidence that such contrarian investment strategy does pay off, see for example, De Bondt and Thaler (1985), Fama and French (1988, 1992), Fama (1991), and Lakonishok, Shleifer and Vislmy (1994). That a simple contrarian strategy may be profitable may appear to some to be surprising: one might think that "smart money", by competing with each other to benefit from the profit opportunities, would ultimately have the effect of eliminating any such profit opportunities. But, there are

17 See also Case and Shiller (1988) ~br a similar analysis of recent real estate booms and busts. On the other hand, Garber (1990) analyzes some famous speculative bubbles, including the tulipomania in the 17th century, and concludesthat they may have been rational.

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reasons to doubt that such smart money will indeed have this effect; see Shiller (1984), DeLong et al. (1990a,b), and Shleifer and Vishny (1995)Is.

6. The disjunction effect The disjunction effect is a tendency for people to want to wait to make decisions until information is revealed, even if the information is not really important for the decision, and even if they would make the same decision regardless o f the information. The disjunction effect is a contradiction to the "sure-tbing principle" of rational behavior [Savage (1954)]. Experiments showing the disjunction effect were performed by Tversky and Shafir (1992). They asked their subjects whether they would take one o f the bets that Samuelson's lunch colleague, discussed above, had refused a coin toss in which one has equal chances to win $200 or lose $100. Those who took the one bet were then asked whether they wanted to take another such bet. If they were asked after the outcome o f the first bet was known, then it was found that a majority o f respondents took the second bet whether or not they had won the first. However, a majority would not take the bet if they had to make the decision before the outcome of the bet was known. This is a puzzling result: if one's decision is the same regardless of the outcome of the first bet, then it would seem that one would make the same decision before knowing the outcome. Tversky and Shafir gave their sense of the possible thought patterns that accompany such behavior: if the outcome o f the first bet is known and is good, then subjects think that they have nothing to lose in taking the second, and if the outcome is bad they want to try to recoup their losses. But if the outcome is not known, then they have no clear reason to accept the second bet. The disjunction effect might help explain changes in the volatility of speculative asset prices or changes in the volume o f trade of speculative asset prices at times when information is revealed. Thus, for example, the disjunction effect can in principle explain why there is sometimes low volatility and low volume of trade just before an important announcement is made, and higher volatility or volume of trade after the announcement is made. Shafir and Tversky (1992) give the example o f presidential elections, which sometimes induce stock market volatility when the election outcome is known even though many skeptics may doubt that the election outcome has any clear implications for market value.

18 Even public expectations of a stock market crash does not prevent the stock market fiom rising; there is evidence from options prices that the stock market crash of 1987 was in some sense expected before it happened; see Bates (1991, 1995). Lee et al. (1991) argue that investor expectations, or rather "sentiment" can be measured by closed-end mutual fund discounts, which vary through time.

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7. Gambling behavior and speculation A tendency to gamble, to play games that bring on unnecessary risks, has been found to pervade widely divergent human cultures around the world and appears to be indicative of a basic human trait, Bolen and Boyd (1968). Kallick et al. (1975) estimated that 61% of the adult population in the United States participated in some form of gambling or betting in 1974. They also estimated that 1.1% of men and 0.5% of women are "probably compulsive gamblers", while an additional 2.7% of men and 1% of women are "potential compulsive gamblers." These figures are not trivial, and it is important to keep in mind that compulsive gambling represents only an extreme form of the behavior that is more common. The tendency for people to gamble has provided a puzzle for the theory of human behavior under uncertainty, since it means that we must accommodate both riskavoiding behavior (as evidenced by people's willingness to purchase insurance) with an apparent risk-loving behavior. Friedman and Savage (1948) proposed that the co-existence of these behaviors might be explained by utility functions that become concave upward in extremely high range, but such an explanation has many problems. For one thing, people who gamble do not appear to be systematically risk seekers in any general sense, instead they are seeking specific forms of entertainment or arousal 19. Moreover, the gambling urge is compartmentalized in people's lives, it tends to take for each individual only certain forms: people specialize in certain games. The favored forms of gambling tend to be associated with a sort of ego involvement: people may feel that they are especially good at the games they favor or that they are especially lucky with these. The complexity of human behavior exemplified by the gambling phenomenon has to be taken into account in understanding the etiology of bubbles in speculative markets. Gamblers may have very rational expectations, at some level, for the likely outcome of their gambling, and yet have other feelings that drive their actual behavior. Economists tend to speak of quantitative "expectations" as if these were the only characterization of people's outlooks that mattered. It is my impression, from interviews and survey results, that the same people who are highly emotionally involved with the notion that the stock market will go up may give very sensible, unexciting forecasts of the market if asked to make quantitative forecasts. 8. The irrelevance of history One particular kind of overconfidence that appears to be common is a tendency to believe that history is irrelevant, not a guide to the future, and that the future must 19 According to the American Psychiatric Association's DSM-1V (1994), "Most individuals with Pathological Gambling say that they are seeking 'action' (an aroused, euphoric state) even more than money. Increasinglylarger bets, or greater risks, may be needed to continue to produce the desired level of excitement" (p. 616).

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be judged afresh now using intuitive weighing only of the special factors we see now. This kind of overconfidence discourages taking lessons from past statistics; indeed most financial market participants virtually never study historical data for correlations or other such statistics; they take their anchors instead from casual recent observations. Until academic researchers started collecting financial data, most was just thrown away as irrelevant. One reason that people may think that history is irrelevant is a human tendency toward historical determinism, a tendency to think that historical events should have been known in advance. According to historian Florovsky (1969, p. 364): in retrospect we seem to perceive the logic of events, which unfold themselves in a regular order, according to a recognizable pattern, with an alleged inner necessity, so that we get the impression that it really could not have happened otherwise. Fischhoff (1975) attempted to demonstrate this tendency towards historical determinism by presenting experimental subjects with incomplete historical stories, stories that are missing the final outcome o f the event. The stories were from historical periods remote enough in time that the subjects would almost certainly not know the actual outcome. Subjects were asked to assign probabilities to each of four different possible conclusions to the story (only one of which was the true outcome). There were two groups of subjects, one of which was told that one of the four outcomes had in fact happened. The probability given to the outcomes was on average 10% higher when people were told it was the actual outcome. Fischhoff's demonstration o f a behavior consistent with belief in historical determinism may not demonstrate the full magnitude of such behavior, because it does not capture the effects of social cognition o f past events, a cognition that may tend to remember historical facts that are viewed as causing subsequent historical events, or are comaected to them, and to forget historical facts that seem not to fit in with subsequent events. It will generally be impossible to demonstrate such phenomena of social cognition in short laboratory experiments. A human tendency to believe in historical determinism would tend to encourage people to assume that past exigencies (the stock market crash of 1929, the great depression, the world wars, and so on) were probably somewhat known in advance, or, at least, that before these events people had substantial reason to worry that they might happen. There may tend to be a feeling that there is nothing definite on the horizon now, as there presumably was before these past events 2o. It is in this human tendency toward believing history is irrelevant that the equity premium puzzle, discussed above, may have its most important explanation. People may tend just not to think that the past stock market return history itself gives any indication of the future, at least not until they perceive that authorities are in agreement that it does.

20 This ~belmg can of course be disrupted, if a sudden event calls to mind parallels to a past event, or if the social cognition memorializes and interprets a past event as likely to be repeated.

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According to the representativeness heuristic, discussed above, people may see past return history as relevant to the future only if they see the present circumstances as representative in some details o f widely remembered past periods. Thus, for example, the public appears to have made much, just before the stock market crash o f 1987, o f similarities in that period to the period just before the crash o f 1929. Newspapers, including the Wall S t r e e t J o u r n a l on the morning o f the stock market crash o f October 19, 1987, showed plots o f stock prices before October 1929 superimposed on a plot o f stock prices before October 1987, suggesting comparisons. In this way, historical events can be remembered and viewed as relevant, but this is not any systematic analysis o f past data. Lack o f learning from historical lessons regarding financial and economic uncertainties may explain why many investors show little real interest in diversification around the world and why most investors appear totally uninterested in the correlation o f their investments with their labor income, violating with their behavior one o f the most fundamental premises o f financial theory. Most people do not make true diversification around the world a high priority, and virtually no one is short the company that he or she works for, or is short the stock market in one's own country, as would be suggested by economic theory 21 . A prominent reason that most people appear apathetic about schemes to protect them from price level uncertainty in nominal contracts is that they just do not seem to think that past actual price level movements are any indicator o f future uncertainty. In a questionnaire I distributed [Shiller (1997a)] to a random sample from phone books in the U S A and Turkey, the following question was posed: We want to know how accurately you think that financial experts in America (Turkey) can predict the price level in 2006, ten years from now. Can you tell us, if these experts think that a "market basket" of goods and services that the typical person buys will cost $1,000 (100 million TL) in 2006, then you think it will probably actually cost: (Please fill in your lower and upper bounds on the price:) Between $ (TL) and $ (TL) The median ratio between high and low was 4/3 for US respondents and 3/2 for Turkish respondents. Only a few respondents wrote numbers implying double- or tripledigit ratios, even in Turkey. The ratios not far from one that most respondents revealed would seem to suggest excessive confidence in the predictability o f price levels. Note that in Turkey the CPI increased three-fold between 1964 and 1974, 31-fold between 1974 and 1984, and 128-fold between 1984 and 1994. But, Turkish respondents appear to connect the price level movements with prior political and social events that may be perceived as having largely predicted the price movements, events that are themselves

2~ Kusko et al. (1997) showed, using data on 10000 401k plan participants in a manufacturing firm, found that barely 20% of participants directed any of their own balances into an S&P index fund, while nearly 25% of participants directed all of their discretionary balances into a fund invested completely in the own company stock.

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not likely to be repeated in the same way. While these people have apparently learned to take certain steps to protect themselves from price level uncertainty (such as not investing in long-term nominal bonds), they do not appear to have a well-developed understanding of the potential uncertainty of the Turkish Lira that would allow them to deal systematically with such uncertainty. For example, they have shown relatively little interest in government indexed bonds.

9. Magical thinking B.E Skinner (1948) in what is now regarded as a classic experiment fed starved experimental pigeons small quantities of food at regular fifteen-second intervals with no dependence whatsoever on the bird's behavior. Even though the feeding was unaffected by their behavior, the birds began to behave as if they had a "superstition" that something in their behavior caused the feeding [see also McFadden (1974)]. Each pigeon apparently conditioned itself to exhibit a specific behavior to get the food, and because each bird exhibited its characteristic behavior so reliably, it was never deconditioned: One bird was conditioned to turn counter-clockwise in the cage, making two or three turns between reinforcements. Another repeatedly thrust its head into one of the upper corners of the cage. A third developed a " tossing" response, as if placing its head beneath an invisible bar and lifting it repeatedly ... Skinner (1948, p. 168)

Arbitrary behaviors that are so generated are referred to with the term "magical thinking" by psychologists. A wide variety of economic behaviors are likely to be generated in exactly the same way that the arbitrary behaviors of the pigeons are generated. Thus, for example, firms' investment or management decisions that happened to precede increases in sales or profits may tend to be repeated, and if this happens in a period of rising profits (as when the economy is recovering from a recession) the notion that these decisions were the cause of the sales or profit increase will be reinforced. Because firms are similar to each other and observe each other, the magical thinking may be social, rather than individual, and hence may have aggregate effects. Roll (1986), with his hubris hypothesis concerning corporate takeovers, aigued that managers of bidder firms may become overconfident of their own abilities to judge firms, because of their luck in their first takeovers. This overconfidence can cause them to overbid in subsequent takeover attempts. The tendency for speculative markets to respond to certain news variables may be generated analogously. The US stock market used often to be buoyed by positive news about the economy, but in recent years it appears to tend to be moved in the opposite direction by such news. This new "perverse" movement pattern for the stock market is sometimes justified in the media by a theory that the good news will cause the Federal Reserve to tighten monetary policy and that then the higher interest rates will lower the stock market. But the whole belief could be the result of a chain of events that was

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set off by some initial chance movements of the stock market. Because people believe these theories they may then behave so that the stock price does indeed behave as hypothesized, the initial correlations will persist later, and thereby reinforce the belief.

10. Quasi-magical thinking The term quasi-magical thinldng, as defined by Shafir and Tversky (1992), is used to describe situations in which people act as if they erroneously believe that their actions can influence an outcome (as with magical thinking) but in which they in fact do not believe this. It includes acting as if one thinks that one can take actions that will, in effect, undo what is obviously predetermined, or that one can change history. For example, Quattrone and Tversky (1984) divided subjects into a control and experimental group and then asked people in both groups to see how long they could bear to hold their hands in some ice water. In the experimental group, subjects were told that people with strong hearts were better able to endure the ice water. They found that those in the experimental group in fact held their hands in the ice water longer. If indeed, as appears to be the case, those in the experimental group held their hands in the ice water longer to prove that they had strong hearts, then this would be quasimagical, since no notion was involved that there was any causal link from holding hands in ice water to strengthening the heart. While this particular experimental outcome might also be explained as the result of a desire for self deception, Shafir and Tversky report as well as other experiments that suggest that people do behave as if they think they can change predetermined conditions. Shafir and Tversky (1992) show, with an experimental variant of Newcomb's Paradox, that people behave as if they can influence the amount of money already placed in a box. Quasi-magical thinking appears to operate more strongly when outcomes of future events, rather than historical events, are involved. Langer (1975) showed that people place larger bets if invited to bet before a coin is tossed than after (where the outcome has been concealed), as if they think that they can better influence a coin not yet tossed. It appears likely that such quasi-magical thinking explains certain economic phenomena that would be difficult to explain the basis of strictly rational behavior. Such thinking may explain why people vote, and why shareholders exercise their proxies. In most elections, people must know that the probability that they will decide the election must be astronomically small, and they would thus rationally decide not to vote. Quasi-magical thinking, thinking that in good societies people vote and so if I vote I can increase the likelihood that we have a good society or a good company, might explain such voting. The ability of labor union members or oligopolists to act in concert with their counterparts, despite an incentive to free-ride, or defect, may also be explained by quasi-magical thinking~

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The disposition effect [Shefrin and Statman (1985)] referred to above, the tendency for individuals to want to hold losers and sell winners might also be related to quasimagical thinking, if people feel at some level that holding on to losers can reverse the fact that they have already lost. Public demand for stocks at a time when they are apparently overvalued may be influenced by quasi-magical thinking, a notion that if I hold, then the stocks will continue to rise.

11. Attention anomalies and the availability heuristic William James (1890, p. 402) criticized earlier psychologists, who in their theories effectively assumed that the human mind takes account o f all sensory input, for taking no note of the phenomenon o f selective attention: But the moment one thinks of the matter, one sees how false a notion of experience that is which would make it tantamount to the mere presence to the senses of an outward order. Millions of items of the outward order are present to nay senses which never properly enter into my experience. Why? Because they have no interest for me. My experience is what 1 agree to attend to. Only those items which l notice shape my mind - without selective interest, experience is utter chaos. The same criticism might equally well be applied to expected utility maximization models in economics, for assuming that people attend to all facts that are necessary for maximization o f the assumed objective function [Berger (1994) elaborates on this point]. Attention is associated with language; the structure of our language invites attention to categories that are represented in the language. Taylor (1989) showed, for example, that certain concepts o f "the self" were apparently absent from languages in the time o f Augustine. The language shapes our attention to even the most inward o f phenomena. In economics, certain terms were apparently virtually absent from popular discourse fifty or more years ago: gross national product, the money supply, the consumer price index. Now, many economists are wont to model individual attention to these concepts as if they were part o f the external reality that is manifest to all normal minds. Attention may be capricious because it is affected by the "salience" o f the object; whether it is easily discerned or not [Taylor and Thompson (1982)] or by the "vividness" o f the presentation, whether the presentation has colorful details. Judgments may be affected, according to the "availability heuristic", that is, by the "ease with which instances or associations come to mind" [Tversky and Kahneman (1974)]. Investment fashions and fads, and the resulting volatility o f speculative asset prices, appear to be related to the capriciousness o f public attention [Shiller (1984, 1987a)]. Investor attention to categories o f investments (stocks versus bonds or real estate, investing abroad versus investing at home) seems to be affected by alternating waves o f public attention or inattention. Investor attention to the market at all seems to vary through time, and major crashes in financial markets appear to be phenomena

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of attention, in which an inordinate amount of public attention is suddenly focused on the markets 22 Economic theories that are most successful are those that take proper account of the limitations and capriciousness of attention. One reason that the hypothesis of no unexploited arbitrage opportunities (a hypothesis that has led to the Black-Scholes (1973) option pricing theory, the Ross (1976) arbitrage pricing theory, and other constructs of finance) has been so successful is that it does not rely on pervasive public attention. The essence of the no-arbitrage assumption, when it is used successfully to produce theories in finance, is that the arbitrage opportunities, were they to ever exist, would be exploited and eliminated even if only a tiny fraction of investors were paying attention to the opportunity.

12. Culture and social contagion The concept of culture, central to sociology and cultural anthropology ever since the work of Tylor (1871), Durkheim (1893) and Weber (1947), is related to the selective attention that the human mind exhibits. There is a social cognition, reenforced by conversation, ritual and symbols, that is unique to each interconnected group of people; to each nation, tribe, or social group. People tend not to remember well facts or ideas that are not given attention in the social cognition, even though a few people may be aware of such facts. If one speaks to groups of people about ideas that are foreign to their culture, one may find that someone in the group will know of the ideas, and yet the ideas have no currency in the group and hence have no influence on their behavior at large. The array of facts, suppositions, symbols, categories of thought that represent a culture have subtle and far-reaching affects on human behavior. For a classic example, Durkheim (1897), in a careful study of differing suicide rates across countries, found that there was no apparent explanation for these differing rates other than cultural differences. Cultural anthropologists have used methods of inferring elements of primitive culture by immersing themselves in the society, observing their everyday life, and talking and listening to them nonjudgmentally, letting them direct the conversation. From such learning, for example, Ltvy-Strauss (1966, pp. 9-10) wrote persuasively that the customs of primitive people that we may tend to view as inexplicably savage actually arise as a logical consequence of a belief system common to all who belong to the society, a belief system which we can grow to understand only with great difficulty:

22 There is evidence that the stock market crash of 1987 can be viewed in these terms, see Shiller (1989).

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The real question is not whether the touch of a woodpecker's beak does in fact cure toothache. It is rather whether there is a point of view from which a woodpecker's beak and a man's tooth can be seen as "going together" (the use of this congruity for therapeutic purposes being only one of its possible uses) and whether some initial order can be introduced into the universe by means of these groupings.... The thought we call primitive is founded on this demand for order. The same methods that cultural anthropologists use to study primitive peoples can also be used to study modern cultures. O ' B a r r and C o N e y (1992) studied pension fund managers using personal interviews and cultural anthropological methods. They concluded that each pension fund has its own culture, associated often with a colorful story o f the origin o f their own organization, akin to the creation myths o f primitive peoples. The culture o f the pension fund is a belief system about investing strategy and that culture actually drives investment decisions. Cultural factors were found to have great influence because o f a widespread desire to displace responsibility for decisions onto the organization, and because o f a desire to maintain personal relationships within the organization 23. Psychological research that delineates the factors that go into the formation o f culture has been undertaken under the rubric o f social psychology and attitude change, or under social cognition. There is indeed an enormous volume o f research in these areas. For surveys, one may refer to McGuire (1985) for attitude change or Levine and Resnick (1993) for social cognition. One difficulty that these researchers have encountered with experimental work is that o f disentangling the "rational" reasons for the imitation o f others with the purely psychological. Some recent economic literature has indeed shown the subtlety o f the informational influences on people's behavior (learning from each other), see Bannerjee (1992), Bikhchandani et al. (1992), Leahy (1994), and Shiller (1995).

13. A global culture We see many examples o f imitation across countries apparently widely separated by both physical and language barriers. Fashions o f dress, music, and youthful rebellion, are obvious examples. The convergence o f seemingly arbitrary fashions across nations is evidence that something more is at work in producing internationally-similar human behavior than just rational reactions to c o m m o n information sets relevant to economic fundamentals, see Featherstone (1990). A n d yet it will not be an easy matter for us to decide in what avenues global culture exerts its influence [Hannerz (1990), p. 237]: There is now a world culture, but we had better make sure that we understand what this means. it is marked by an organization of diversity rather than by a replication of uniformity. No total

23 The psychologist Janis (1972) has documented with case studies how social patterns ("groupthink") within decision making groups can cause even highly intelligent people to make disastrously wrong decisions.

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homogenizationof systems of meaning and expression has occurred, nor does it appear likely that there will be one any time soon. But the world has become one network of social relationships, and between its different regions there is a flow of meanings as well as of people and goods. Sociologists have made it their business to study patterns of influence within cultures, and we ought to be able to learn something about the nature of global culture from their endeavors. For example, one study of patterns of influence regarded as a classic among sociologists is the in-depth study of the town of Rovere by sociologist Robert Merton (1957). After extensive study of the nature of interpersonal influence, he sought meaningful ways to categorize people. He found that it was meaningful to divide people into two broad categories: locals (who follow local news and derive status by their connectedness with others) and cosmopolitans (who orient themselves instead to world news and derive status from without the community). He found that the influence of cosmopolitans on locals transcended both their numbers and their stock of useful information. We must bear this conclusion in mind when deciding how likely it is that incipient cultural trends are pervasive across many different nations. Reading such sociological studies inclines us to rather different interpretations of globally similar behaviors than might occur naturally to many traditional economists. Why did the real estate markets in many cities around the world rise together into the late 1980s and fall in the early 1990s? [See Goetzmarm and Wachter (1996) and Hendershott (1997).] Why have the stock markets of the world moved somewhat together? Why did the stock markets of the world show greater tendency to move together after the stock market crash of 1987? [See von Furstenberg and Jeon (1989) and King, Sentana and Wadhwani (1994).] If we recognize the global nature of culture, there is no reason to assume that these events have anything to do with genuine information about economic fundamentals.

14. Concluding remarks Since this paper was written in response to an invitation to summarize literature on behavioral theory in finance, it has focused exclusively on this topic, neglecting the bulk of finance literature. Because of its focus on anomalies and departures from conventional notions of rationality, I worry that the reader of this paper can get a mistaken impression about the place of behavioral theory in finance and of the importance of conventional theory. The lesson from the literature surveyed here, and the list of varied behavioral phenomena, is not that "anything can happen" in financial markets. Indeed, while the behavioral theories have much latitude for interpretation, when they are combined with observations about behavior in financial markets, they allow us to develop theories that do have some restrictive implications. Moreover, conventional efficient markets theory is not completely out the window. I could have, had that been the goal of this paper, found very many papers that suggest that markets are impressively efficient in certain respects.

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Financial anomalies that intuitive assessments of human nature might lead one to expect to find, or anomalies one hears casually about, often turn out to be tiny, ephemeral, or nonexistent. There is, for example, virtually no Friday the thirteenth effect [Chamberlain et al. (199 l), Dyl and Maberly (1988)]. Investors apparently aren't that foolish. Heeding the lessons of the behavioral research surveyed here is not going to be simple and easy for financial researchers. Doing research that is sensitive to lessons from behavioral research does not mean entirely abandoning research in the conventional expected utility framework. The expected utility framework can be a workhorse for some sensible research, if it is used appropriately. It can also be a starting point, a point of comparison from which to frame other theories. It is critically important for research to maintain an appropriate perspective about h u m a n behavior and an awareness of its complexity. When one does produce a model, in whatever tradition, one should do so with a sense of the limits of the model, the reasonableness of its approximations, and the sensibility of its proposed applications.

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Chapter 21

THE FINANCIAL ACCELERATOR IN A QUANTITATIVE BUSINESS CYCLE FRAMEWORK* BEN S. BERNANKE, MARK GERTLER and SIMON GILCHRIST Princeton University, New York University, and Boston Unicersity**

Contents Abstract Keywords 1. Introduction 2. The model: o v e r v i e w and basic assumptions 3. The d e m a n d for capital and the role o f net worth 3.1. Contract terms when there is no aggregate risk 3.2. Contract terms when there is aggregate risk 3.3. Net worth and the optimal choice of capital 4. General e q u i l i b r i u m 4.1. The entrepreneurial sector 4.2. The complete log-linearized model 4.2.1. Two extensions of the baseline model 4.2.1.1. Investment delays 4.2.1,2. Heterogeneous firms 5. M o d e l simulations 5.1. Model parametrization 5.2. Results 5.2.1. Response to a monetary policy shock 5.2.2. Shock to technology, demand, and wealth 5.2.3. Investment delays and heterogeneous firms 6. A h i g h l y selected r e v i e w o f the literature 7. D i r e c t i o n s for furore w o r k A p p e n d i x A. The o p t i m a l financial contract and the d e m a n d for capital A. 1. The partial equilibrium contracting problem A.2. The log-normal distribution A.3. Aggregate risk

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* Thanks to Michael Woodford, Don Morgan and John Taylor for helpful conanents, and to the NSF and C.M Starr Center for financial support. ** Each author is also affiliated with the National Bmeau of Economic Research. Handbook of Macroeconomics, Volume 1, Edited by J..B. laylor and M. WoodJb~d © 1999 Elsevier Science B.V. All rights reserved 1341

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Appendix B. Household, retail and government sectors B. 1. Households B.2. The retail sector and price setting B.3. Government sector

References

B.S. B e r n a n k e et al.

1387 1387 1388 1389 1390

Abstract This chapter develops a dynamic general equilibrium model that is intended to help clarify the role of credit market frictions in business fluctuations, from both a qualitative and a quantitative standpoint. The model is a synthesis of the leading approaches in the literature. In particular, the framework exhibits a "financial accelerator", in that endogenous developments in credit markets work to amplify and propagate shocks to the macroeconomy. In addition, we add several features to the model that are designed to enhance the empirical relevance. First, we incorporate money and price stickiness, which allows us to study how credit market frictions may influence the transmission of monetary policy. In addition, we allow for lags in investment which enables the model to generate both hump-shaped output dynamics and a lead-lag relation between asset prices and investment, as is consistent with the data. Finally, we allow for heterogeneity among firms to capture the fact that borrowers have differential access to capital markets. Under reasonable parametrizations of the model, the financial accelerator has a significant influence on business cycle dynamics.

Keywords financial accelerator, business fluctuations, monetary policy

JEL classification: E30, E44, E50

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1. Introduction

The canonical real business cycle model and the textbook Keynesian IS-LM model differ in many fundamental ways. However, these two standard frameworks for macroeconomic analysis do share one strong implication: Except for the term structure of real interest rates, which, together with expectations of future payouts, determines real asset prices, in these models conditions in financial and credit markets do not affect the real economy. In other words, these two mainstream approaches both adopt the assumptions underlying the Modigliani-Miller (1958) theorem, which implies that financial structure is both indeterminate and irrelevant to real economic outcomes. Of course, it can be argued that the standard assumption of financial-structure irrelevance is only a simplification, not to be taken literally, and not harmful if the "frictions" in financial and credit markets are sufficiently small. However, as Gertler (1988) discusses, there is a long-standing alternative tradition in macroeconomics, beginning with Fisher and Keynes if not earlier authors, that gives a more central role to credit-market conditions in the propagation of cyclical fluctuations. In this alternative view, deteriorating credit-market conditions - sharp increases in insolvencies and bankruptcies, rising real debt burdens, collapsing asset prices, and bank failures are not simply passive reflections of a declining real economy, but are in themselves a major factor depressing economic activity. For example, Fisher (1933) attributed the severity of the Great Depression in part to the heavy burden of debt and ensuing financial distress associated with the deflation of the early 1930s, a theme taken up half a century later by Bernanke (1983). More recently, distressed banking systems and adverse credit-market conditions have been cited as sources of serious macroeconomic contractions in Scandinavia, Latin America, Japan, and other East Asian countries. In the US context, both policy-makers and academics have put some of the blame for the slow recovery of the economy from the 1990-1991 recession on heavy corporate debt burdens and an undercapitalized banking system [see, e.g., Bernanke and Lown (1992)]. The feedbacks from credit markets to the real economy in these episodes may or may not be as strong as some have maintained; but it must be emphasized that the conventional macroeconomic paradigms, as usually presented, do not even give us ways of thinking about such effects. The principal objective of this chapter is to show that credit-market imperfections can be incorporated into standard macroeconomic models in a relatively straightforward yet rigorous way. Besides our desire to be able to evaluate the role of creditmarket factors in the most dramatic episodes, such as the Depression or the more recent crises (such as those in East Asia), there are two additional reasons for attempting to bring such effects into mainstream models of economic fluctuations. First, it appears that introducing credit-market frictions into the standard models can help improve their ability to explain even "garden-variety" cyclical fluctuations. In particular, in the context of standard dynamic macroeconomic models, we show in this chapter that credit-market frictions may significantly amplify both real and nominal shocks to the economy. This extra amplification is a step toward resolving the puzzle of how

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relatively small shocks (modest changes in real interest rates induced by monetary policy, for example, or the small average changes in firm costs induced by even a relatively large movement in oil prices) can nevertheless have large real effects. Introducing credit-market frictions has the added advantage of permitting the standard models to explain a broader class of important cyclical phenomena, such as changes in credit extension and the spreads between safe and risky interest rates. The second reason for incorporating credit-market effects into mainstream models is that modern empirical research on the determinants of aggregate demand and (to a lesser extent) of aggregate supply has often ascribed an important role to various credit-market frictions. Recent empirical work on consumption, for example, has emphasized the importance of limits on borrowing and the closely-related "buffer stock" behavior [Mariger (1987), Zeldes (1989), Jappelli (1990), Deaton (1991), Eberly (1994), Gourinchas and Parker (1995), Engelhardt (1996), Carroll (1997), Ludvigson (1997), Bacchetta and Gerlach (1997)]. In the investment literature, despite some recent rehabilitation of a role for neoclassical cost-of-capital effects [Cummins, Hassett and Hubbard (1994), Hassett and Hubbard (1996)], there remains considerable evidence for the view that cash flow, leverage, and other balance-sheet factors also have a major influence on investment spending [Fazzari, Hubbard and Petersen (1988), Hoshi, Kashyap and Scharfstein (1991), Whited (1992), Gross (1994), Gilchrist and Himmelberg (1995), Hubbard, Kashyap and Whited (1995)] 1. Similar conclusions are reached by recent studies of the determinants of inventories and of employment [Cantor (1990), Blinder and Maccini (1991), Kashyap, Lamont and Stein (1994), Sharpe (1994), Carpenter, Fazzari and Petersen (1994)]. Aggregate modeling, if it is to describe the dynamics of spending and production realistically, needs to take these empirical findings into account 2. How does one go about incorporating financial distress and similar concepts into macroeconomics? While it seems that there has always been an empirical case for including credit-market factors in the mainstream model, early writers found it difficult to bring such apparently diverse and chaotic phenomena into their formal analyses. As a result, advocacy of a role for these factors in aggregate dynamics fell for the most part to economists outside the US academic mainstream, such as Hyman Minsky, and to some forecasters and financial-market practitioners, such as Otto Eckstein and Allen Sinai (l 986), Albert Wojnilower (1980), and Henry Kaufma~ (1986). However, over the past twenty-five years, breakthroughs in the economics of incomplete and asymmetric information [beginning with Akerlof (1970)] and the extensive adoption of these ideas in corporate finance and other applied fields [e.g., Jensen and Meckling (1976)], have made possible more formal theoretical 1 A critique of the cash-flowliterature is given by Kaplan and Zingales (1997). See Chirinko (1993) for a broad survey of the empirical literature in inveslment. 2 Contemporarymacroeconometricforecasting models, such as the MPS model used by the Federal Reserve, typicallydo incorporatefactors such as borrowing constraints and cash-flow effects. See for example Braytonet al. (1997).

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analyses of credit-market imperfections. In particular, it is now well understood that asymmetries of infonnaIion play a key role in borrower-lender relationships; that lending institutions and financial contracts typically take the forms that they do in order to reduce the costs of gathering information and to mitigate principal-agent problems in credit markets; and that the common feature of most of the diverse problems that can occur in credit markets is a worsening of informational asymmetries and increases in the associated agency costs. Because credit-market crises (and less dramatic malfunctions) increase the real costs of extending credit and reduce the efficiency of the process of matching lenders and potential borrowers, these events may have widespread real effects. In short, when credit markets are characterized by asymmetric information and agency problems, the Modigliani-Miller irrelevance theorem no longer applies. Drawing on insights from the literature on asymmetric information and agency costs in lending relationships, in this chapter we develop a dynamic general equilibrium model that we hope will be useful for understanding the role of credit-market frictions in cyclical fluctuations. The model is a synthesis of several approaches already in the literature, and is partly intended as an expository device. But because it combines attractive features of several previous models, we think the framework presented here has something new to offer, hnportantly, we believe that the model is of some use in assessing the quantitative implications of credit-market frictions for macroeconomic analysis. In particular, our framework exhibits a "financial accelerator" [Bernanke, Gertler and Gilchrist (1996)], in that endogenous developments in credit markets work to propagate and amplify shocks to the macroeconomy. The key mechanism involves the link between "external finance premium" (the difference between the cost of funds raised externally and the opportunity cost of funds internal to the firm) and the net worth of potential borrowers (defined as the borrowers' liquid assets plus collateral value of illiquid assets less outstanding obligations). With credit-market frictions present, and with the total amount of financing required held constant, standard models of lending with asymmetric information imply that the external finance premium depends inversely on borrowers' net worth. This inverse relationship arises because, when borrowers have little wealth to contribute to project financing, the potential divergence of interests between the borrower and the suppliers of external funds is greater, implying increased agency costs; in equilibrium, lenders must be compensated ~br higher agency costs by a larger premium. To the extent that borrowers' net worth is procyclical (because of the procyclicality of profits and asset prices, for example), the external finance premium will be countercyclical, enhancing the swings in borrowing and thus in investment, spending, and production. We also add to the framework several features designed to enhance the empirical relevance. First, we incorporate price stickiness and money into the analysis, using modeling devices familiar from New Keynesian research, which allows us to study the effects of monetary policy in an economy with credit-market frictions. In addition, we allow for decision lags in investment, which enables the model to generate both

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hump-shaped output dynamics and a lead-lag relationship between asset prices and investment, as is consistent with the data. Finally, we allow for heterogeneity among firms to capture the real-world fact that borrowers have differential access to capital markets. All these improvements significantly enhance the value of the model for quantitative analysis, in our view. The rest of the chapter is organized as follows. Section 2 introduces the model analyzed in the present chapter. Section 3 considers the source of the financial accelerator: a credit-market friction which evolves from a particular form of asymmetric information between lenders and potential borrowers. It then performs a partial equilibrium analysis of the resulting terms of borrowing and of firms' demand for capital, and derives the link between net worth and the demand for capital that is the essence of the financial accelerator. Section 4 embeds the credit-market model in a Dynamic New Keynesian (DNK) model of the business cycle, using the device proposed by Calvo (1983) to incorporate price stickiness and a role for monetary policy; it also considers several extensions, such as allowing for lags in investment and for differential credit access across firms. Section 5 presents simulation results, drawing comparisons between the cases including and excluding the credit-market friction. Here we show that the financial accelerator works to amplify and propagate shocks to the economy in a quantitatively significant way. Section 6 then gives a brief and selective survey that describes how the framework present fits in the literature. Section 7 then describes several directions for future research. Two appendices contain additional discussion and analysis of the partial-equilibrium contracting problem and the dynamic general equilibrium model in which the contracting problem is embedded.

2. The model: overview and basic assumptions Our model is a variant of the Dynamic New Keynesian (DNK) framework, modified to allow for financial accelerator effects on investment. The baseline DNK model is essentially a stochastic growth model that incorporates money, monopolistic competition, and nominal price rigidities. We take this framework as the starting point for several reasons. First, this approach has become widely accepted in the literature 3 It has the qualitative empirical appeal of the IS-LM model, but is motivated from first principles. Second, it is possible to study monetary policy with this framework. For our purposes, this means that it is possible to illustrate how credit market imperfections influence the transmission of monetary policy, a theme emphasized in much of the recent literature 4. Finally, in the limiting case of perfect price flexibility, the cyclical properties of the model closely resemble those of a real business cycle framework. In

3 See Goodfriend and King (1997) for an exposition of the DNK approach. 4 For a review of the recent literature on the role of credit market fiqctions in the transmission of monetary policy, see Bernanke and Gertler (1995).

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this approximate sense, the DNK model nests the real business cycle paradigm as a special case. It thus has the virtue of versatility. Extending any type of contemporary business cycle model to incorporate financial accelerator effects is, however, not straightforward. There are two general problems: First, because we want lending and borrowing to occur among private agents in equilibrium, we cannot use the representative agent paradigm but must instead grapple with the complications introduced by heterogeneity among agents. Second, we would like the financial contracts that agents use in the model to be motivated as far as possible from first principles. Since financial contracts and institutions are endogenous, results that hinge on arbitrary restrictions on financial relationships may be suspect. Most of the nonstandard assumptions that we make in setting up our model are designed to facilitate aggregation (despite individual heterogeneity) and permit an endogenous financial structure, thus addressing these two key issues. The basic structure of our model is as follows: There are three types of agents, called households, entrepreneurs, and retailers. Households and entrepreneurs are distinct from one another in order to explicitly motivate lending and borrowing. Adding retailers permits us to incorporate inertia in price setting in a tractable way, as we discuss. In addition, our model includes a government, which conducts both fiscal and monetary policy. Households live forever; they work, consume, and save. They hold both real money balances and interest-bearing assets. We provide more details on household behavior below. For inducing the effect we refer to as the financial accelerator, entrepreneurs play the key role in our model. These individuals are assumed to be risk-neutral and have finite horizons: Specifically, we assume that each entrepreneur has a constant probability y of surviving to the next period (implying an expected lifetime of 1@)" The assumption of finite horizons for entrepreneurs is intended to capture the phenomenon of ongoing births and deaths of firms, as well as to preclude the possibility that the entrepreneurial sector will ultimately accumulate enough wealth to be fully self-financing. Having the survival probability be constant (independent of age) facilitates aggregation. We assume the birth rate of entrepreneurs to be such that the fraction of agents who are entrepreneurs is constant. In each period t entrepreneurs acquire physical capital. (Entrepreneurs who "die" in period t are not allowed to purchase capital, but instead simply consume their accumulated resources and depart from the scene.) Physical capital acquired in period t is used in combination with hired labor to produce output in period t + 1, by means of a constant-returns to scale technology. Acquisitions of capital are financed by entrepreneurial wealth, or "net worth", and borrowing. The net worth of entrepreneurs comes from two sources: profits (including capital gains) accumulated from previous capital investment and income from supplying labor (we assume that entrepreneurs supply one unit of labor inelastically to the general labor market). As stressed in the literature, entrepreneurs' net worth plays a critical role in the dynamics of the model. Net worth matters because a borrower's financial position

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is a key determinant of his cost of external finance. Higher levels of net worth allow for increased self-financing (equivalently, collateralized external finance), mitigating the agency problems associated with external finance and reducing the external finance premium faced by the entrepreneur in equilibrium. To endogenously motivate the existence of an external finance premium, we postulate a simple agency problem that introduces a conflict of interest between a borrower and his respective lenders. The financial contract is then designed to minimize the expected agency costs. For tractability we assume that there is enough anonymity in financial markets that only one-period contracts between borrowers and lenders are feasible [a similar assumption is made by Carlstrom and Fuerst (1997)]. Allowing for longer-term contracts would not affect our basic results 5. The tbrm of the agency problem we introduce, together with the assumption of constant returns to scale in production, is sufficient (as we shall see) to generate a linear relationship between the demand for capital goods and entrepreneurial net worth, which facilitates aggregation. One complication is that to introduce the nominal stickiness intrinsic to the DNK framework, at least some suppliers must be price setters, i.e., they must face downward-sloping demand curves. However, assuming that entrepreneurs are imperfect competitors complicates aggregation, since in that case the demand for capital by individual firms is no longer linear in net worth. We avoid this problem by distinguishing between entrepreneurs and other agents, called' retailers. Entrepreneurs produce wholesale goods in competitive markets, and then sell their output to retailers who are monopolistic competitors. Retailers do nothing other than buy goods from entrepreneurs, differentiate them (costlessly), then re-sell them to households. The monopoly power of retailers provides the source of nominal stickiness in the economy; otherwise, retailers play no role. We assume that profits from retail activity are rebated lump-sum to households. Having described the general setup of the model, we proceed in two steps. First, we derive the key microeconomic relationship of the model: the dependence of a firm's demand for capital on the potential borrower's net worth. To do so, we consider the firm's (entrepreneur's) partial equilibrium problem of jointly determining its demand for capital and terms of external finance in negotiation with a competitive lender (e.g., a financial intermediary). Second, we embed these relationships !n an othe1~ise conventional DNK model. Our objective is to show how fluctuations in borrowers' net worth can act to amplify and propagate exogenous shocks to the system. For most of the analysis we assume that there is a single type of firm; however, we eventually extend the model to allow for heterogeneous firms with differential access to credit.

So long as borrowers have finite horizons, net worth influences the terms of borrowing, even ai~er allowing for nmlti-period contracts. See, for example, Gertter (1992).

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3. The demand for capital and the role of net worth

We now study the capital investment decision at the firm level, taking as given the price of capital goods and the expected return to capital. In the subsequent section we endogenize capital prices and returns as part of a general equilibrium solution. At time t, the entrepreneur who manages firm j purchases capital for use at t + I. The quantity of capital purchased is denoted K/+I, with the subscript denoting the period in which the capital is actually used, and the superscript j denoting the firm. The price paid per unit of capital in period t is Qt. Capital is homogeneous, and so it does not matter whether the capital the entrepreneur purchases is newly produced within the period or is "old", depreciated capital. Having the entrepreneur purchase (or repurchase) his entire capital stock each period is a modeling device to ensure, realistically, that leverage restrictions or other financial constraints apply to the firm as a whole, not just to the marginal investment. The return to capital is sensitive to both aggregate and idiosyncratic risk. The ex post gross return on capital for firmj is t'~JPk * ' t + l , where coy is an idiosyncratic disturbance to firmj's return and Rk+l is the ex post aggregate return to capital (i.e., the gross return averaged across firms). The random variable (.0j is i.i.d, across time and across firms, with a continuous and once-differentiable c.d.f., F(~o), over a non-negative support, and E{{oJ} = 1. We impose the following restriction on the corresponding hazard rate h((o):

O(coh(o))) 0a)

> 0,

(3.1)

where h(co) _= ~dF(~o) F(o~" This regularity condition is a relatively weak restriction that is satisfied by most conventional distributions, including for example the log-normal. At the end of period t (going into period t + 1) entrepreneur j has available net worth, N/+ 1. To finance the difference between his expenditures on capital goods and his net worth he must borrow an amount BJ<, given by BtJl = Q, K ,+, j -N,+J 1.

(3.2)

The entrepreneur borrows from a financial intermediary that obtains its funds from households. The financial intermediary faces an opportunity cost of funds between t and t + 1 equal to the economy's riskless gross rate of return, Rt+l. The riskless rate is the relevant opportunity cost because in the equilibrium of our model, the intermediary holds a perfectly safe portfolio (it perfectly diversifies the idiosyncratic risk involved in lending). Because entrepreneurs are risk-neutral and households are risk-averse, the loan contract the intermediary signs has entrepreneurs absorb any aggregate risk, as we discuss below. To motivate a nontrivial role for financial structure, we follow a number of previous papers in assuming a "costly state verification" (CSV) problem of the type first

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analyzed by Townsend (1979), in which lenders must pay a fixed "auditing cost" in order to observe an individual borrower's realized return (the borrower observes the return for free). As Townsend showed, this assumption allows us to motivate why uncollateralized external finance may be more expensive than internal finance without imposing arbitrary restrictions on the contract structure. There are many other specifications of the incentive problem between the entrepreneur and outside lenders that can generate qualitatively similar results. The virtues of the Townsend formulation are its simplicity and descriptive realism. Following the CSV approach, we assume that the lender must pay a cost if he or she wishes to observe the borrower's realized return on capital. This auditing cost is interpretable as the cost of bankruptcy (including for example auditing, accounting, and legal costs, as well as losses associated with asset liquidation and interruption of business). The monitoring cost is assumed to equal a proportion/~ of the realized k .i I. gross payoff to the firm's capital, i.e., the monitoring cost equals /~ ~oi Rt+lQtKi+ Although one might expect that there would be economies of scale in monitoring, the proportionality assumption is very convenient in our context and does not seem too unreasonable. 3.1. Contract terms when there is no aggregate risk To describe the optimal contractual arrangement, it is useful to first work through the case where the aggregate return to capital Rt:'+l is known in advance. In this instance the only uncertainty about the project's return is idiosyncratic to the firm, as in the conventional version of the CSV problem. Absent any aggregate uncertainty, the optimal contract under costly state verification looks very much like standard risky debt (see Appendix A for a detailed analysis of the contracting problem): In particular, the entrepreneur chooses the value of firm capital, QtKi+J t, and the associated level of borrowing, B/+L, prior to the realization of the idiosyncratic shock. Given QtKi+l, / B[+I, and Rt+ k l, the optimal contract may be characterized by a gross non-default loan rate, Z/~I, and a threshold value of the idiosyncratic shock ~)i, call it ~sJ, such that for values of the idiosyncratic shock greater than or equal to ~J, the entrepreneur is able to repay the loan at the contractuai rate, Z j 1. That is, N./ is defined by ....j ~ - j ./ .J ~ R~+lQtKi~ 1 = Zt ~lBt ~1

(3.3)

When ~o/ ) c~-j, under the optimal contract the entrepreneur repays the lender the r j j j /~ j ,- j j promised amount Zi+lBt+ 1 and keeps the difference, equal to co Rt+l QtKi~. ~ - Zi +~B:, 1. If coy < N:, the entrepreneur cannot pay the contractual return and thus declares default, in this situation the lending intermediary pays the auditing cost and gets to keep what it finds. That is, the intermediary's net receipts are (1 -l~)v)R~+~ Q~K/+ 1. A defaulting entrepreneur receives nothing.

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The values o f NJ and Z/~ 1 under the optimal contract are determined by the requirement that the financial intermediary receive an expected return equal to the opportunity cost o f its funds. Because the loan risk in this case is perfectly diversifiable, the relevant opportunity cost to the intermediary is the riskless rate, Rt+l. Accordingly, the loan contract must satisfy P

[ 1 - F ( ~ S ) I Z• / + I B" / + ," + ( 1 - ~ t )

/~

~oJ

k j ' ~oRt+lQtKi+ 1 dF(~o)= R,+,S/+t,

(3.4)

where the left-hand side o f Equation (3.4) is the expected gross return on the loan to the entrepreneur and the right side is the intermediary's opportunity cost o f lending. Note that F ( ~ j) gives the probability o f default. Combining Equations (3.2) and (3.3) with Equation (3.4) yields the following expression for ~5i: p

[1 - F ( ~ J ) ] ~ j -+-(1-:-~) ./0

(o dF(co) R~+IQtK/+ , -- Rt+I(QtKJ1 - N,{ 1).

(3.5)

By using Equation (3.4) to eliminate Z~I, we are able to express the lender's expected return simply as a function of the cutoff value o f the firm's idiosyncratic productivity shock, k5s. There are two effects o f changing ~ J on the expected return, and they work in opposite directions. A rise in NJ increases the non-default payoff; on the other hand, it also raises the default probability, which lowers the expected payoff. The assumed restrictions on the hazard function given by Equation (3.1) imply that the expected return reaches a maximum at an unique interior value of N i : As NJ rises above this value the expected return declines due to the increased likelihood of default 6. For values of ~Os below the maxinmm, the function is increasing and concave 7. I f the lender's opportunity cost is so large that there does not exist a value of NJ that generates the required expected return, then the borrower is "rationed" from the market. Appendix A provides details. For simplicity, in what follows, we consider only equilibria without rationing, i.e., equilibria in which the equilibrium value of b5j always lies below the maximum feasible value a. Under the parametrizations we use later, this condition is in fact satisfied. r' Flb see that the maximmn must be in the interior of the support of co, note that as cO/ approaches its upper bound, the default probability converges to unity. Appendix A shows that the interior optimum is unique. 7 The change in the expected payoff fl'om a unit increase m cOJ is {[ 1 -F(cOJ)] -#cO/dF(cOJ)}R~+IQtKii 1 The first term in the expression in brackets reflects the rise in the non-default payoff. The second term reflects the rise in expected default costs. Note that we can rewrite this expression as {1 - ~SJh(USJ)}[1 - F(?O/)]RI+1QtK/+I, where h(a0 = VdF(co) - ~ is the hazard rate. Given Equation (3.i), the derivative of this expression is negative for values of COj below the maxinmm one feasible, implying that the expected payoff is concave in this range. 8 Note also that since we are restricting attention to non-rationing equilibria, the lender's expected return is always increasing in COJ.

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3.2. Contract terms when there is aggregate risk With aggregate uncertainty present, NJ will in general depend on the ex post realization of R)+~. Our assumption that the entrepreneur is risk-neutral leads to a simple contract structure, despite this complication. Because he cares only about the mean return on his wealth, the entrepreneur is willing to bear all the aggregate risk 9. Thus he is willing to guarantee the lender a return that is free o f any systematic risk, i.e., conditional on the ex post realization ofR~+l, the borrower offers a (state-contingent) non-default payment that guarantees the lender a return equal in expected value to the riskless rate. (Note that the only residual risk the lender bears arises from the idiosyncratic shock o)/+1, and is thus diversifiable.) Put differently, Equation (3.5) now implies a set of restrictions, k 1. The result is a schedule for 75j, contingent on the one for each realization o f Rt+ realized aggregate state. As we are restricting attention to non-rationing equilibria, we consider only parametrizations where there in fact exists a value o f N / for each aggregate state that satisfies Equation (3.5). Diversification by intermediaries implies that households earn the riskless rate on their saving. Descriptively, the existence o f aggregate uncertainty effectively ties the risky loan rate Z/+~to macroeconomic conditions. In particular, the loan rate adjusts countercyclically. For example, a realization o f R~k+l that is lower than expected raises

Zi/~ ; that is, to compensate for the increased default probability due to the low average return to capital, the non-default payment must rise. This in turn implies an increase in the cutoff value o f the idiosyncratic productivity shock, ~5j. Thus the model implies, reasonably, that default probabilities and default premia rise when the aggregate return to capital is lower than expected ~0

3.3. Net worth and the optimal choice o f capital

Thus far we have described how the state-contingent values of N / and ziJ~ are determined, given the ex post realization of R~/'+l and the ex ante choices of Q:K j i and B/~ I. We now turn to the entrepreneur's general problem o f determining his demand for capital.

9 The entrepreneur's value function can be shown to be linear in wealth because (i) his utility is linear in consumption and (ii) the project he is investing in exhibits constant returns to scale. [See, e.g., Bernanke and Gertler (1989, 1990).] 10 This kind of state-contingent financial arrangement is a bit stylized, but may be thought of as corresponding to the following scenario: Let the maturity of the debt be shorter than the maturity of the firm's project. The debt is then rolled over after the realization of the aggregate m~certainty. If there is bad aggregate news, then the new loan rate is higher than would be otherwise. To implement the sort of risk-sharing arrangement implied by the model, therefore, all that is necessary is that some component of the financing have a shorter maturity than that of the project.

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Given the state-contingent debt form of the optimal contract, the expected return to the entrepreneur may be expressed as E

{fi /

k

j

o)Rt+ 1QtKi+ 1 dF(co) - (1 - F ( ~ J ) ) N J R ~ I QtK/+ l

)

(3.6)

,

k where expectations are taken with respect to the random variable, Rt+l, and it is understood that ~ / may be made contingent on the realization of this variable. Combining this relation with Equation (3.5) allows us to simplify the entrepreneur's objective to maximization of

{ Jo

}

O9 )

L1 -

-U;+O,J

(3.7)

k k 1} is the ratio of the realized return to capital to the expected where U[a~I =_ Rt+j/E{Rt+ return. Given that the intermediary must receive a competitive return, the entrepreneur internalizes the expected default costs, as Equation (3.7) suggests. The formal investment and contracting problem then reduces to choosing K/+I and a schedule for N/ (as a function of the realized values of R)+I) to maximize Equation (3.7), subject to the set of state-contingent constraints implied by Equation (3.5). The distributions of the aggregate and idiosyncratic risks to the return to capital, the price of capital, and the quantity of net worth that the entrepreneur brings to the table are taken as given in the maximization. Let st ~ E{R~+I/Rt+I } be the expected discounted return to capital. For entrepreneurs to purchase capital in the competitive equilibrium it must be the case that st ~> 1. Given s: ~> 1, the first-order necessary conditions yield the following relation for optimal capital purchases (see Appendix A for details): QaK/~, = *p(st)N/+j,

with

W(1) == l, W:(') > O.

(3.8)

Equation (3.8) describes the critical link between capital expenditures by the firm and financial conditions, as measured by the wedge between the expected the return to capital and the safe rate, st, and by entrepreneurial net worth, Art/1 JL. Given the value o f K/+ l that satisfies Equation (3.8), the schedule for NJ is pinned down uniquely by the state-contingent constraint on the expected return to debt, defined by Equation (3.5). Equation (3.8) is a key relationship in the model: It shows that capital expenditures by each firm are proportional to the net worth of the owner/entrepreneur, with a proportionality factor that is increasing in the expected discounted return to capital, st. Everything else equal, a rise in the expected discounted return to capital reduces the expected default probability. As a consequence, the entrepreneur carl take on more

l J In the costly enforcememmodel of Kiyotakiand Moore (1997), ~p(.)- 1, implyingQ,K,. t - Ni+j .

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Demandf 0 ~ , i .

,,///,, .,.'"

E .2 o

c~

c5 --f

6

l

[

I

i

7

8

9

10

~ - - T - -

11

12

CapitalStock Fig. 1. Effect of an increase in net worth. debt and expand the size o f his firm. He is constrained from raising the size o f the firm indefinitely by the fact that expected default costs also rise as the ratio of borrowing to net worth increases. An equivalent way of expressing Equation (3.8) is

/ E{Rf,.l} = s[

Nj \ ~',+1. | R,~,,

\ o,K/+,]

s'(.) < 0.

(3.9)

For an entrepreneur who is not fully self-financed, in equilibrium the return to capital will be equated to the marginal cost of external finance. Thus Equation (3.9) expresses the equilibrium condition that the ratio s o f the cost of external finance to the safe rate - which we have called the discounted return to capital but may be equally well interpreted as the external finance premium - depends inversely on the share of the finn's capital investment that is financed by the entrepreneur's own net worth. Figure 1 illustrates this relationship using the actual contract calibrated for model analysis in the next section. Firm j ' s demand for capital is on the horizontal axis and the cost o f funds normalized by the safe rate of return is on the vertical axis. For capital stocks which can be financed entirely by the entrepreneur's net worth, in this case K < 4.6, the firm faces a cost of funds equal to the risk free rate. As capital acquisitions rise into the range where external finance is necessary, the costof-funds curve becomes upward sloping, reflecting the increase in expected default costs associated with the higher ratio o f debt to net worth. While the supply o f funds curve is -upward sloping, owing to constant returns to scale, the demand for capital is horizontal at an expected return 2 percentage points above the risk free rate.

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Point E, where the firm's marginal cost of funds equals the expected return to capital yields the optimal choice of the capital stock K = 9.2. For this contract, the leverage ratio is 50%. It is easy to illustrate how a shift in the firm's financial position affects its demand for capital. A 15% increase in net worth, Ni~ L, for example, causes the rightward shift in the cost-of-funds curve depicted by the hatched line in Figure 1. At the old level of capital demand, the premium for external finance declines: The rise in net worth relative to the capital stock reduces the expected default probability, everything else equal. As a consequence, the firm is able to expand capacity to point U . Similarly, a decline in net worth reduces the firm's effective demand for capital. In the next section we incorporate this firm-level relation into a general equilibrium framework. Before proceeding, however, we note that, in general, when the firm's demand for capital depends on its financial position, aggregation becomes difficult. The reason is that, in general, the total demand for capital will depend on the distribution of wealth across firms. Here, however, the assumption of constant returns to scale throughout induces a proportional relation between net worth and capital demand at the firm level; further, the factor of proportionality is independent of firm-specific factors. Thus it is straightforward to aggregate Equation (3.8) to derive a relationship between the total demand for capital and the total stock of entrepreneurial net worth.

4. General equilibrium We now embed the partial equilibrium contracting problem between the lender and the entrepreneur within a dynamic general equilibrium model. Among other things, this will permit us to endogenize the safe interest rate, the return to capital, and the relative price of capital, all of which were taken as given in the partial equilibrium. We proceed in several steps. First we characterize aggregate behavior for the entrepreneurial sector. From this exercise we obtain aggregate demand curves for labor and capital, given the real wage and the riskless interest rate. The market demand for capital is a key component of the model since it reflects the impact of financial market imperfections. We also derive how the aggregate stock of entrepreneurial net worth, an important state variable determining the demand for capital, evolves over time. We next place our "non-standard" entrepreneurial sector within a conventional Dynamic New Keynesian framework. To do so, we add to the model both households and retailers, the latter being included only in order to introduce price inertia in a t~cactable manner. We also add a government sector that conducts fiscal and monetary policies. Since much of the model is standard, we simply write the log-linearized framework used for computations and defer a more detailed derivation to Appendix B. Expressing the model in a log-linearized form makes the way in which the financial accelerator influences business cycle dynamics reasonably transparent.

B.X Bernanke et al.

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4.1. The entrepreneurial sector Recall that entrepreneurs purchase capital in each period for use in the subsequent period. Capital is used in combination with hired labor to produce (wholesale) output. We assume that production is constant returns to scale, which allows us to write the production function as an aggregate relationship. We specify the aggregate production function relevant to any given period t as

Yt = AtKaL]-a,

(4.1)

where Yt is aggregate output o f wholesale goods, Kt is the aggregate amount of capital purchased by entrepreneurs in period t - 1, L~ is labor input, and At is an exogenous technology parameter. Let It denote aggregate investment expenditures. The aggregate capital stock evolves according to

K,+I =

k,K, j K t + ( 1 - 6 ) K t ,

(4.2)

where /5 is the depreciation rate. We assume that there are increasing marginal adjustment costs in the production o f capital, which we capture by assuming that aggregate investment expenditures of L yield a gross output of new capital goods • (I~/Kt)Kt, where q~(.) is increasing and concave and q~(0) = 0. We include adjustment costs to permit a variable price o f capital. As in Kiyotaki and Moore (1997), the idea is to have asset price variability contribute to volatility in entrepreneurial net worth. In equilibrium, given the adjustment cost function, the price o f a unit o f capital in terms of the numeraire good, Qt, is given by 12

=

.

(4.3)

We normalize the adjustment cost function so that the price of capital goods is unity in the steady state. Assume that entrepreneurs sell their output to retailers. Let 1/X~ be the relative price o f wholesale goods. Equivalently, Xt is the gross markup of retail goods over wholesale

~2 1b implement investment expenditures in the decentralized equilibrium, think of there being competitive capital producing firms that purchase raw output as a materials input, I~ and combine it with rented capital, Kt to produce new capital goods via the production function q3(g~ I, )Kt. These capital goods are then sold at the price Qt. Since the capital-producing technology assumes constant returns to scale, these capital-producing firms earn zero profits in equilibrium. Equation (4.3) is derived from the first-order condition for investment for one of these firms.

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goods. Then the C o b b - D o u g l a s production technology implies that the rent paid to a unit o f capital in t + 1 (for production o f wholesale goods) is 13

1 aYl+l Xt+l Kt+l The expected gross return to holding a unit o f capital from t to t + 1 can be written k E{Rz+ 1} = E

1 aYt+l

x,2, x,+~ + Q t + l ( 1 - 6 ) Ot

} '

(4.4)

Substitution o f Equations (4.1) and (4.3) into Equation (4.4) yields a reasonably conventional demand curve for new capital. As usual, the return on capital depends inversely on the level o f investment, reflecting diminishing returns. The supply curve for investment finance is obtained by aggregating Equation (3.8) over firms, and inverting to obtain: l, I: Nt+l E{Rt+ I } = s

(4.5)

As in Equation (3.9), the function s(.) is the ratio o f the costs o f external and internal finance; it is decreasing in Nt+l/QtKt+l for Nt~l < QtKt+l. The unusual feature o f this supply curve, o f course, is the dependence o f the cost o f funds on the aggregate financial condition o f entrepreneurs, as measured by the ratio Nt+l/QtI(t+l. The dynamic behavior o f capital demand and the return to capital depend on the evolution o f entrepreneurial net worth, N:+l. N:+I reflects the equity stake that entrepreneurs have in their firms, and accordingly depends on firms' earnings net o f interest payments to lenders. As a technical matter, however, it is necessary to start entrepreneurs off with some net worth in order to allow them to begin operations. Following Bernanke and Gertler (1989) and Carlstrom and Fuerst (1997), we assume

t~ To be consistent with our assumption that adjustment costs are external to the firm, we assume that entrepreneurs sell their capital at the end of period t + 1 to the investment sector at price Q~+I. Thus capital is then used to produce new investment goods and resold at the price Q,j. The "rental rate" (Q, 1- Qt+l) reflects the influence of capital accumulation on adjustment costs. This rate is determhled by the zero-profit condition

Q,~2 /

1t \

It

Q,)=o.

In steady state q~( ~ ) = 6 and ~ ' ( U~ :t ) = 1, implying that Q = Q = 1. Around tile steady state, the diffbrence between Qt~l and Qt is second order. We therefore omit the rental term and express Equation (4.4) using Q:~ I rather than Qt+l-

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B.X Berv~anke et al.

that, in addition to operating firms, entrepreneurs supplement their income by working in the general labor market. Total labor input Lt is taken to be the following composite of household labor, HI, and "entrepreneurial labor", HI:

L, =Ht++(H/)t-+.

(4,6)

We assume further that entrepreneurs supply their labor inelastically, and we normalize total entrepreneurial labor to unity 14. In the calibrations below we keep the share of income going to entrepreneurial labor small (on the order of .01), so that this modification of the standard production function does not have significant direct effects on the results. Let Vt be entrepreneurial equity (i.e., wealth accumulated by entrepreneurs from operating firms), let W[ denote the entrepreneurial wage, and let ?st denote the state+ contingent value of ?5 set in period t. Then aggregate entrepreneurial net worth at the end of period t, N1+1, is given by

N++I = yVt + W[

(4.7)

with

gt=R)Qt 1Kt-(Rt

~fO°' ~R)Qt-IKtdF(o)~ ~~-t5 ] (Qt-IK" - ~Vt-1)' \ 4-

(4.8)

where g V~ is the equity held by entrepreneurs at t - 1 who are still in business at t. (Entrepreneurs who fail in t consume the residual equity (1 - 7)V, That is, C 7 = (1 - y)V,) Entrepreneurial equity equals gross earnings on holdings of equity from t - 1 to t less repayment of borrowings. The ratio of default costs to quantity borrowed,

# f~, (eRrk Qt jKt dF(co) Qt 1Kt

-- Nt-i

reflects the premium for external finance. Clearly, under any reasonable parametrization, entrepreneurial equity provides the main source of variation in Nt+l. Further, this equity may be highly sensitive to unexpected shifts in asset prices, especially if firms are leveraged. To illustrate, let U[k =- R) - E t j{R~} be the unexpected shift in the gross return to capital, and let

14 Note that entrepreneurs do not have to work only on their own projects (such an assumiption would violate aggregate returns to scale, given that individual projccts can be of different sizes).

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U/p =-- f o ' o)Q~_~Kt dF( co) - Et .i { ~ ' ~oQt 1Kt dF(~o)} be the unexpected shift in the conditional (on the aggregate state) default costs. We can express Vt as V, = [U~k(1-ttU/P)]Qt 1Kt+E, l{V~}.

(4.9)

Now consider the impact of a unexpected increase in the ex post return to capital. Differentiating Equation (4.9) yields an expression for the elasticity of entrepreneurial equity with respect to an unanticipated movement in the return to capital:

ovt/E, l{v,} _ Et I{R~}Qt-IKt /> 1. or;kin, 1{R? } E,, { )

(4.10)

According to Equation (4.10), an unexpected one percent change in the ex post return to capital leads to a percentage change in entrepreneurial equity equal to the ratio of gross holdings of capital to equity. To the extent that entrepreneurs are leveraged, this ratio exceeds unity, implying a magnification effect of unexpected asset returns on entrepreneurial equity. The key point here is that unexpected movements in asset prices, which are likely the largest source of unexpected movements in gross returns, can have a substantial effect on firms' financial positions. In the general equilibrium, further, there is a kind of multiplier effect, as we shall see. An unanticipated rise in asset prices raises net worth more than proportionately, which stimulates investment and, in turn, raises asset prices even further. And so on. This phenomenon will become evident in the model simulations. We next obtain demand curves for household and entrepreneurial labor, found by equating marginal product with the wage for each case:

(1 - a ) ~

= x, N,

(1 -a)(1 - ~ ) ~

(4.11)

= x, wf,

(4.12)

where W~ is the real wage for household labor and Wf is the real wage for entrepreneurial labor. Combining Equations (4.1), (4.7), (4.8), and (4.12) and imposing the condition that entrepreneurial labor is fixed at unity, yields a difference equation for Nt+l:

(4.13) + (1 - a)(1

O)AtK~H~ l-")o.

Equation (4.13) and the supply curve tbr investment funds, Equation (4.5), are the two basic ingredients of the financial accelerator. The latter equation describes how

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movements in net worth influence the cost of capital. The former characterizes the endogenous variation in net worth. Thus far we have determined wholesale output, investment and the evolution of capital, the price of capital, and the evolution of net worth, given the riskless real interest rate Rt+l, the household real wage Wt, and the relative price of wholesale goods I/X, To determine these prices and complete the model, we need to add the household, retail, and government sectors. 4.2. The complete log-linearized model

We now present the complete macroeconomic framework. Much of the derivation is standard and not central to the development of the financial accelerator. We therefore simply write the complete log-linearized model directly, and defer most of the details to Appendix B. As we have emphasized, the model is a DNK framework modified to allow for a financial accelerator. In the background, along with the entrepreneurs we have described are households and retailers. Households are infinitely-lived agents who consume, save, work, and hold monetary and nonmonetary assets. We assume that household utility is separable over time and over consumption, real money balances, and leisure. Momentary utility, further, is logarithmic in each of these arguments is. As is standard in the literature, to motivate sticky prices we modify the model to allow for monopolistic competition and (implicit) costs of adjusting nominal prices. It is inconvenient to assume that the entrepreneurs who purchase capital and produce output in this model are monopolistically competitive, since that assumption would complicate the analyses of the financial contract with lenders and of the evolution of net worth. To avoid this problem, we instead assume that the monopolistic competition occurs at the "retail" level. Specifically, we assume there exists a continuum of retailers (of measure one). Retailers buy output from entrepreneur-producers in a competitive market, then slightly differentiate the output they purchase (say, by painting it a unique color or adding a brand name) at no resource cost. Because the product is differentiated, each retailer has a bit of market power. Households and firms then purchase CES aggregates of these retail goods. It is these CES aggregates that are converted into consumption and investment goods, and whose price index defines the aggregate price level. Profits from retail activity are rebated lump-sum to households (i.e., households are the ultimate owners of retail outlets.) To introduce price inertia, we assume that a given retailer is free to change his price in a given period only with probability 1 - 0. The expected duration of any price change is 1@0- This device, following Calvo (1983), provides a simple way to incorporate staggered long-term nominal price setting. Because the probability of changing price is independent of history, the aggregation problem is greatly simplified. One extra

~5 In particular, householdatilityis givenby £ {~;~ 0[3~[ln(C~,k) + _~ln(Mt.JP, .-/~) + ~ In{1 l[,+i,)]}.

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twist, following Bernanke and Woodford (1997), is that firms setting prices at t are assumed to do so prior to the realization of any aggregate uncertainty at time t. Let lower case variables denote percent deviations from the steady state, and let ratios of capital letters without time subscript denotes the steady state value of the respective ratio. Further, let ~ denote a collection of terms of second-order importance in the equation for any variable z, and let e[ be an i.i.d, disturbance to the equation for variable z. Finally, let Gt denote government consumption, :rt =-p~ - p t - i the rate of inflation from t - 1 to t, and r'/+1 ==- r~+~ + E { p t + l - P t } be the nominal interest rate. It is then convenient to express the complete log-linearized model in terms of four blocks of equations: (1) aggregate demand; (2) aggregate supply; (3) evolution of the state variables; and (4) monetary policy rule and shock processes. Appendix B provides details. (1) Aggregate d e m a n d C

1

G

Ce

y~ = ]7c, + ~ i t + ~ g t + --c~'yt + "

+ q~,

(4.14)

ct = -rt+L + Et {ct+l },

(4.15)

c~ = nt,l + " " +0~:~,

(4.16)

Et{r~÷I}

-Fz+I

-"-u[¥1t+l

r ) + t - ( 1 -- e ) @ t kl -

(qt +kt÷l)],

kt--i Xt+l) @ eqt~ 1 q ,

qt = cp(it - kt).

(4.17) (4.18) (4.19)

(2) Aggregate Supply yt = a, + a k t + (1 - a ) g 2 h ,

(4.20)

Yt- ht-xt -ct

(4.21)

=

~-Iht,

YL) : E t l{l~(-Xt)+ ~2Tt+l }.

(4.22)

(3) Evolution of State Variables kt+l = 6it + (1 - 6 ) k ,

yRK

t,

(4.23)

(4.24)

B.X Bernanke et al.

1362 (4) M o n e t a r y Policy R u l e a n d S h o c k P r o c e s s e s

r, - p r t 1 + gac~ I + el",

17 I

t~

(4.25)

& = pggt-i + ~ ,

(4.26)

aL = p,,at-i + g/,

(4.27)

with

(;

log Iz

~ P

D

# j)

e)dF(~o)R~Qt_IK/DK

)l

,

?O

6o dF(~o)R/',

O~'e = log(1-Ce+l/Ni+~ ) i T c~T;/N ' q~t" =

(Ri'lR-

N 1)K (r~"+q~-i +kt)+

lp(Rk/R) ~'(Rk/R) ' 1),,'

N

[2)(Y/X)

Yt-x~,

1- b (1 - cs) + a Y / ( X K ) '

( ~ ( I / K ) 1)t q) ~ ((D(I/K)

(1 - a)(1 -

(1~_) K" ~

(1 -- 0/~).

Equation (4.14) is the log-lineafized version of the resource constraint. The primary determinants of the variation in aggregate expenditures Yt are household consumption ct, investment it, and government consumption gL. Of lesser importance is variation in entrepreneurial consumption c~ 16. Finally, variation in resources devoted monitoring cost, embedded in the term ~ , also matters in principle. Under reasonable parametrizations, however, this factor has no perceptible impact on dynamics. Household consumption is governed by the consumption Euler relation, given by Equation (4.15). The unit coefficient on the real interest rate (i.e., the intertemporal elasticity of substitution) reflects the assumption of logarithmic utility over con.sumption. By enforcing the standard consumption Euler equation, we are effectively assuming that financial market frictions do not impede household behavior. Numerous authors have argued, however, that credit constraints at the household level influence a non-trivial portion of aggregate consumption spending. An interesting extension of

16 Note that each variable in the log-lmearizedresource constraint is weighted by the variable's share of output in the steady state. Under any reasonableparametrizationof the model, c~ has a relativelylow weight.

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this model would be to incorporate household borrowing and associated frictions. With some slight modification, the financial accelerator would then also apply to household spending, strengthening the overall effect. Since entrepreneurial consumption is a (small) fixed fraction of aggregate net worth (recall that entrepreneurs who retire simply consume their assets), it simply varies proportionately with aggregate net worth, as Equation (4.16) indicates. Equations (4.17), (4.18), and (4.19) characterize investment demand. They are the log-linearized versions of Equations (4.5), (4.4) and (4.3), respectively. Equation (4.17), in particular, characterizes the influence of net worth on investment. In /, the absence of capital market frictions, this relation collapses to Et{rf+~ } -rt+l = 0: Investment is pushed to the point where the expected return on capital, Et{r~+ 1 }, equals the opportunity cost of funds rt+117. With capital market frictions present, however, the cost of external funds depends on entrepreneurs' percentage equity holding, i.e., net worth relative to the gross value of capital, nt~l - (qr + ktf-l). A rise in this ratio reduces the cost of external funds, implying that investment will rise. While Equation (4.17) embeds the financial accelerator, Equations (4.18) and (4.19) are conventional (loglinearized) relations for the marginal product of capital and the link between asset prices and investment. Equations (4.20), (4.21) and (4.22) constitute the aggregate supply block. Equation (4.20) is the linearized version of the production function (4.1), after incorporating the assumption that the supply of entrepreneurial labor is fixed. Equation (4.21) characterizes labor market equilibrium. The left side is the marginal product of labor weighted by the marginal utility of consumption 18. In equilibrium, it varies proportionately with the markup of retail goods over wholesale goods (i.e., the inverse of the relative price of wholesale goods.) Equation (4.22) characterizes price adjustment, as implied by the staggered price setting formulation of Calvo (1983) that we described earlier [along with the modification suggested by Bernanke and Woodford (1997)]. This equation has the flavor of a traditional Phillips curve, once it is recognized that the markup xt varies inversely with the state of demand. With nominal price rigidities, the retail firms that hold their prices fixed over the period respond to increased demand by selling more. To accommodate the rise in sales they increase their purchases of wholesale goods from entrepreneurs, which bids up the relative wholesale price and bids down the markup. it is tbr this reason that - x t provides a measure of demand when prices are sticky. In turn, the sensitivity of inflation to demand depends on the degree of price inertia: The slope coefficient t¢ can be shown to be decreasing in 0, the probability an individual price stays fixed from period to period. One difference between Equation (4.22) and 17 In the absence of capital market frictions, the first-ordercondition from the entrepreneur'spartial equilibrium capital choice decision yields E{R)+ I } = Rt+ L. In this instance if E{R~'4 l} > R , j, the entrepreneurwould buy an infinite amount of capital, and if E{R~+1} < R~+l,he wouldbuy none. When E{Rt+ I } - R ~ 1, he is indifferentabout the scale of operation of his firm. i~ Given logarithmicpreferences,the marginal utility of consumption is simply -%.

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a traditional expectations-augmented Phillips curve is that it involves expected future inflation as opposed to expected current inflation. This alteration reflects the forwardlooking nature of price setting 19 Equations (4.23) and (4.24) are transition equations for the two state variables, capital kt and net worth nt. The relation for capital, Equation (4.23), is standard, and is just the linearized version of Equation (4.2). The evolution of net worth depends primarily on the net return to entrepreneurs on their equity stake, given by the first term, and on the lagged value of net worth. Note again that a one percent rise in the return to capital relative to the riskless rate has a disproportionate impact on net worth due to the leverage effect described in the previous section. In particular, the impact of r) - r~ on nt+l is weighted by the coefficient y R K / N , which is the ratio of gross capital holdings to entrepreneurial net worth. How the financial accelerator augments the conventional D N K model should now be fairly transparent. Net worth affects investment through the arbitrage Equation (4.17). Equation (4.24) then characterizes the evolution of net worth. Thus, among other things, the financial accelerator adds another state variable to the model, enriching the dynamics. All the other equations of the model are conventional for the D N K framework [particularly King and Wohnan's (1996) version with adjustment costs of capital]. Equation (4.25) is the monetary policy rule 2°. Following conventional wisdom, we take the short-term nominal interest rate to be the instrument of monetary policy. We consider a simple rule, according to which the central bank adjusts the current nominal interest rate in response to the lagged inflation rate and the lagged interest rate. Rules o f this form do a reasonably good job of describing the variation of short term interest rates [see Clarida, Gali and Gertler (1997)]. We also considered variants that allow for responses to output as well as inflation, in the spirit of the Taylor (1993) rule. Obviously, the greater the extent to which monetary policy is able to stabilize output, the smaller is the role of the financial accelerator to amplify and propagate business cycles, as would be true for any kind o f propagation mechanism. With the financial accelerator mechanism present, however, smaller countercyclical movements in interest rates are required to dampen output fluctuations. Finally, Equations (4.26) and (4.27) impose that the exogenous disturbances to government spending and technology obey stationary autoregressive processes. We next consider two extensions of the model.

-~oc k t9 Iterating Equation (4.22) forward yields zct = ~,z¢=0/3 ~c(p,w ~ -Pt+k)- With forward-looking price setting, how fast prices adjust depends on the expected discounted stream of future demand. 2o The interest rate rule may be thought of as a money supply equation. The associated money demand equation is given by m, -Pt = ct - ( ~ ) r~l~. Note that under interest-rate targeting this relation simply determines the path of the nominal money stock. To implement its choice of the nominal interest rate~ the central bank adjusts the money stock to satisfy this equation.

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4.2.1. Two extensions o f the baseline model

Two modifications that we consider are: (1) allowing for delays in investment; and (2) allowing for firms with differential access to credit. The first modification permits the model to generate the kind of hump-shaped output dynamics that are observed in the data. The second is meant to increase descriptive realism. 4.2.1.1. Inoestment delays. Disturbances to the economy typically appear to generate a

delayed and hump-shaped response of output. A classic example is the output response to a monetary policy shock [see, e.g., Christiano, Eichenbaum and Evans (1996) and Bernanke and Mihov (1998)]. It takes roughly two quarters before an orthogonalized innovation in the federal funds rate, for example, generates a significant movement in output. The peak of the output response occurs well after the peak in the funds rate deviation. Rotemberg and Woodford (1997) address this issue by assuming that consumption expenditures are determined two periods in advance (in a model in which non-durable consumption is the only type of private expenditure). We take an approach that is similar in spirit, but instead assume that it is investment expenditures rather than consumption expenditures that are determined in advance. We focus on investment for two reasons. First, the idea that investment expenditures take time to plan is highly plausible, as recently documented by Christiano and Todd (1996). Second, movements in consumption lead movements in investment over the cycle, as emphasized by Bernanke and Gertler (1995) and Christiano and Todd (1996). For example, Bernanke and Gertler (1995) show that in response to a monetary policy shock household spending responds fairly quickly, well in advance of business capital expenditures. Modifying the model to allow for investment delays is straightforward. Suppose that investment expenditure are chosenj periods in advance. Then the first-order condition relating the price of capital to investment, Equation (4.3), is modified to I

1

(4.28) Note that the link between asset prices and investment now holds only in expectation. With the time4o-plan feature, shocks to the economy have an immediate effect on asset prices, but a delayed effect on investment and output 21. To incorporate the investment delay in the model, we simply replace Equation (4.19) with the following log-linearized version of Equation (4.28): Et{qt+j - q)(it+j - kt+j)} - 0.

In our simulations, we take j = 1.

21 Asset prices move inunediately since the return to capital depends on the expected capital gain.

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4.2.1.2. Heterogeneous firms. The baseline model assumes that all firms are alike ex ante, except for initial net worth. In practice, o f course, there is considerable heterogeneity among firms along many dimensions, in particular in access to credit [see, e.g., the discussion in Gertler and Gilchrist (1994)]. To see how heterogeneity affects the results, we add to our model the assumption that there are two types o f firms, those that have easy access to credit, ceteris paribus, and those that (for various informational or incentive reasons, for example) have less access to credit. To accommodate two different types o f firms, we assume that there are two types o f intermediate goods (one produced by each type o f firm) which are combined into a single wholesale good via a CES aggregator. Production of the intermediate good is given by

Yit =A itKaI-[~tH it it t i~(1 J a £2),

i = 1,2.

(4.29)

Aggregate wholesale output is composed o f sectoral output according to (4.30)

= [ . Y ~ + (1 - . ) Y 2 ] ('/"~

We also assume that capital is sector-specific, and that there are costs of adjusting the capital stock within each sector: (4.31)

Ki, t , 1 - Kit = ()(Ii#K.)K. - 6K..

Let ji denote the number of periods in advance that investment expenditures must be chosen in sector i (note that the lag may differ across sectors): Then the link between asset prices and investment in each sector is given by

Note that the price of capital may differ across sectors, but that arbitrage requires that each sector generate the same expected return to capital k Et{ IRkk1,t+l - R2,t+I] [3CI/Cg+I}

=0,

where

~1P5

x,,t+~ + Q,,,+I(I - ,5) /Q,~.

and

Pit p~=a\

(Y1L) p-1 r, j '

Pzt Py

(l_a)(Y2t)P \ r, j

I

are the relative (wholesale) prices of goods produced in sectors t and 2 respectively.

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As we discuss in the next section, it is easy to parametrize the model so that firms in each sector face differential costs o f credit. Further, as we illustrate below, the financial accelerator can still be quite potent, even if only a portion o f firms face significant capital market frictions. Indeed, there may spillover effects from constrained to nonconstrained firms. it is straightforward to log-linearize these equations and append them to the general model. Modified will be the aggregate supply block, to allow for the two types of intermediate output, and the law o f motion for capital, to allow for two distinct types of capital.

5. Model simulations

In this section we present the results of some quantitative experiments to illustrate how the financial accelerator influences business cycle dynamics within the DNK framework. Specifically, we consider how credit-market imperfections amplify and propagate various shocks to the economy. We also examine the effects of allowing for delays in investment and of allowing for some firms to have better access to credit market than others. 5.1. M o d e l parametrization

We choose fairly standard values for the taste and technology parameters. We set the quarterly discount factor fi to 0.99 (which also pins down the steady state quarterly riskless rate, R = [3-1). We fix the labor supply elasticity, t/, at 3.0, in keeping with much o f the literature 22. As is also within convention, the capital share, a, is 0.35, and the household labor share, (1 - a)(1 - g2), is 0.64. The share of income accruing to entrepreneurs' labor is accordingly equal to 0.01. The quarterly depreciation rate for capital, 6, is assigned the usual value of 0.025. We take the steadystate share o f government expenditures in total output, G / Y , to be 0.2, the approximate historical average. The serial correlation parameters for the technology and government expenditure shocks, pa and pg, are assumed to be 1.0 and 0.95, respectively. Finally, the elasticity o f the price of capital with respect to the investment capital ratio, q), is taken to be 0.25. There is no firm consensus in the literature about what this parameter value should be 23. Reasonable assumptions about adjustment costs suggest that the value should lie within a range from 0.0 to 0.50.

22 in particular, we fix average hours worked relative to total hours available at a value that, in conjunction with logarithmic preferences over leisure, generates the desired labor supply elasticity. 23 King and Wolman (1996) use a value of 2.0, based on estimates fi-om aggregate data by Chirinko (1993). Because this value implies implausibly high adjustment costs, we do not use it.

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The non-standard parameters of our model pertain to the interplay between real and financial factors within the entrepreneurial sector 24. Specifically, we choose parameters to imply the following three steady state outcomes: (1) a risk spread, R ~ - R , equal to two hundred basis points, approximately the historical average spread between the prime lending rate and the six-month Treasury bill rate; (2) an annualized business failure rate, F(N), of three percent, the approximate rate in the data; (3) a ratio of capital to net worth, ~, K of 2 (or equivalently, a leverage ratio of 0.5), the approximate value in the data. l b obtain these steady state values we choose the "death rate" of entrepreneurs, 1 - y, to be 0.0272 (quarterly), we take the idiosyncratic productivity variable, log(o)), to be log-normally distributed with variance equal to 0.28, and we set the fraction of realized payoffs lost in bankruptcy,/~, to 0.12. We note that our choice for/~ is within the reasonable set of estimates for bankruptcy costs 25. The final parameters to be selected are those related to the rate of price adjustment and to the policy rule. We let the probability a firm does not change its price within a given period, 0, equal to 0.75, implying that the average period between price adjustments is four quarters. In the policy rule, Equation (4.25), we set the autoregressive parameter, p, to 0.9 and the coefficient on inflation equal to 0.11 (implying a long-run rise in the nominal interest rate of one hundred and ten basis points in response to a permanent one hundred basis point increase in inflation.) These numbers are roughly in line with the evidence, allowing for the fact that there have been shifts in the actual feedback rule over time [see Clarida, Gali and Gertler (1997)]. 5.2. Results

In our experiments we consider four types of aggregate shocks: (1) a monetary policy shock, (2) a technology shock, (3) a government expenditure shock, and (4) a one° time, unanticipated transfer of wealth from households to entrepreneurs. We first study the response of the economy to these shocks in our model, excluding and including the financial accelerator. We then consider the implications of allowing for investment delays and heterogeneous firms. 5.2.1. Response to a monetary policy shock

The first experiment we consider is a monetary policy shock, specifically an unanticipated exogenous movement in the short-term interest rate. Analyzing the response of the model economy to a monetary policy disturbance provides a good way to evaluate our framework since a lengthy literature has produced a consensus of

24 Ore parameter choices here follow closely Fisher (1996) and Carlstrom and Fuerst (t997). 2s See the discussion of bankruptcy costs in Carlstrom and Fuerst (1997). They actually use a higher number than we do (0.20 versus 0.12).

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Fig. 2. Impulse response to a funds rate shock. opinion about how the economy responds to this kind o f shock 26. Figure 2 summarizes this evidence, and also presents some new evidence on the behavior of several rate spread variables that proxy for premium for external funds, a key element o f our model. The results in Figure 2 are based on a five-variable quarterly VAR that includes four "standard" macroeconomic variables - the log o f real GDR the log o f the GDP deflator, the log o f a commodity price index, the federal funds rate -- along with two rate spread variables. To identify the policy shock, we order the funds rate after the price and output variables, based on the view that monetary policy can respond contemporaneously to these variables but can affect them only with a lag. We order tile spread variable after the funds rate based on the assumption that innovations in these variables do not contain any marginal information that is useful for setting current monetary policy. The two rate spread variables we consider are the difference between the six-month commercial paper rate and the six-month T-bill rate and the difference between the prime lending rate and the six-month T-bill rate.

26 See, for example, Ctmstiano, Eichenbaum and Evans (t996), Bernanke m~d Gertler (1995), Bernal~e and Mihov (1998), and Leeper, Sims and Zha (1996).

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Figure 2 illustrates the impulse responses of several variables to a negative innovation in the federal funds rate. As is typically found in the literature, output declines after about two quarters, and the price level declines after about six quarters. The output decline, further, persists well after the funds rate reverts to trend. Finally, each of the spread variables rises fairly quickly, leading the downturn in output 27. Figure 3 reports the impact of the same experiment, but this time using the model economy. As in all the subsequent figures, the time units on the graphs are to be interpreted as quarters. In each picture the hatched line designates the "baseline" impulse response, generated by fixing the external finance premium at its steady state level instead of allowing it to respond to changes in the capital-net worth ratio. In other words, the baseline simulations are based on a model with the same steady state as the complete model with imperfect credit markets, but in which the additional dynamics associated with the financial accelerator have been "turned off". The solid line in each picture indicates the response observed in the complete model, with the financial accelerator included. The figure shows the impact of an unanticipated 25 basis point (on an annual basis) decline in the nominal interest rate. Although the addition of credit-market frictions does not substantially affect the behavior of the nominal rate of interest, it does lead to a stronger response of real variables. In particular, with the financial accelerator included, the initial response of output to a given monetary impulse is about 50% greater, and the effect on investment is nearly twice as great. Further, the persistence of the real effects is substantially greater in the presence of the credit-market factors, e.g., relative to trend, output and investment in the model with credit-market imperfections after four quarters are about where they are in baseline model after only two quarters. The impact of the financial accelerator is mirrored in the behavior of the external finance premium, which is passive in the baseline model (by assumption) but declines sharply in the complete model, slowly reverting to trend. The unanticipated decline in the funds rate stimulates the demand for capital, which in turn raises investment and the price of capital. The unanticipated increase in asset prices raises net worth, forcing down the external finance premium, which in turn further stimulates investment. A kind of multiplier effect arises, since the burst in investment raises asset prices and net worth, further pushing up investment. Entrepreneurial net worth reverts to trend as firms leave the market, but the effect is slow enough to make the external finance premium persist below trend. This persistence in net worth and the external finance premium provides the additional source of dynamics. It is interesting to observe that the response of the spread in the model economy matches the VAR evidence reasonably well.

27 It is worth noting that the impulse response of the prime-rate spread is twice as large as the impulse response of the commercial-paperspread. Since commercial paper issuers are high quality firms, this result is consistent with our model's implication that lower-quality borrowers experience larger spread movementsin response to business cycle shocks.

1371

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It is worth emphasizing that this experiment generates substantial output persistence without relying on an unusually high labor supply elasticity, as is required for the baseline model [see, e.g., the discussion in Chari, Kehoe and McGrattan (1996)]. The countercyclical movement in the premium for external funds (which is the essence of the financial accelerator) serves to flatten the marginal cost curve, as does making labor supply elastic in the baseline model. Overall, these results lend some supports to the claims of Bernanke and Gertler (1995), that credit-market effects can help explain both the strength of the economy's response to monetary policy and the tendency for policy effects to linger even after interest rates have returned to normal. The fact that the model economy replicates the VAR evidence reasonably well is particularly encouraging. The one major point of discrepancy is that the response of output to a monetary shock is delayed in the data, but occurs immediately in the model economy 28. We show shortly, however, that this problem can be fixed by allowing for investment delays.

2~ It is also true that the output response is large relative to the interest rate shock. This partly reflects the high degree of intertemporal substitution embedded in the household savings decision, It may also reflect unreasonably short investment delays.

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Figure 4 displays the effects on output of three alternative shocks: a technology shock, a demand shock (specifically a shock to government expenditures), and a redistribution of wealth between entrepreneurs and households. Once again, the hatched lines show impulse responses from the baseline model with the financial accelerator shut off, and the solid lines show the results from the full model. As the figure shows, the financial accelerator magnifies and propagates both the technology and demand shocks. Interestingly, the magnitude of the effects is about the same as for the monetary policy shock. Again, the central mechanism is the rise in asset prices associated with the investment boom, which raises net worth and thus reduces the external finance premium. The extra persistence comes about because net worth is slow to revert to trend. A positive shock to entrepreneurial wealth (more precisely, a redistribution fi:om households to entrepreneurs) has essentially no effect in the baseline model, but has both significant impact and propagation effects when credit-market frictions are present. The wealth shock portrayed is equal in magnitude to about 1% of the initial wealth of entrepreneurs and about 0.05% of the wealth of households. The transfer of wealth drives up the demand for investment goods, which raises the price of capital and thus entrepreneurs' wealth, initiating a positive feedback loop; thus, although the exogenous shock increases entrepreneurial net worth directly by only 1%, the total effect on entrepreneurs' wealth including the endogenous increase in asset prices exceeds 2%. Output rises by 1% at an annual rate, and substantial persistence is generated by the slow decay of entrepreneurial net worth. Thus the addition of credit-market effects raises the possibility that relatively small changes in entrepreneurial wealth could be an important source of cyclical fluctuations. This case is an interesting one, as it is reminiscent of(and motivated by) Fisher's (1933) "debt-deflation" argument, that redistributions between creditors and debtors arising from unanticipated price changes can have important real effects. Indeed, Fisher argued

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that this kind of mechanism accounted for the depth and protractedness of the Great Depression 29. The same kind of reasoning, further, helps explain why the recent spate of currency crises have had devastating real effects. To the extent loans from abroad are denominated in units of a foreign currency, an exchange rate collapse redistributes wealth from domestic borrowers to foreign lenders. 5.2.3. Investment delays and heterogeneous firms

We now suppose that investment expenditures must be planned one quarter in advance, as in Section 5.2, and consider the effect of a monetary shock. As Figure 5 illustrates, an expansionary monetary policy shock (again, an unanticipated 25 basis point decline in the funds rate) now generates a hump-shaped response of output, as in the data. This hump-shaped response is considerably more accentuated when the financial accelerator is allowed to operate. The initial response of output is still too strong, suggesting that it may be desirable to build in other types of lags. On the other hand, the persistence of the response of output is considerably greater than in the case without investment delays, and comes much closer to matching the data. Interestingly, there remains an immediate response of the external funds premium as the data suggest. The reason is that asset prices rise immediately, in anticipation of the investment boom. We next consider the model with heterogeneous firms. We choose parameters so that firms in sector 2 face a steady-state premium for external finance of 3% per year, while firms in sector l face a premium of only 1%. We set a = .5125 to generate an average steady-state premium of 2%. As a consequence of this assumption, roughly half of the economy's output is produced by credit-constrained firms, a breakdown which is in accord with the rough evidence summarized in Bernanke, Gertler and Gilctu'ist (1996). We set p = 0.9, implying that the goods produced in the two sectors are close substitutes. Assuming a high degree of substitutability biases the results against finding important aggregate effects of credit-market frictions in this setup; however, our results turned out to be not very sensitive to the choice o f p . With sector-specific adjustment costs, the effective marginal cost of adjusting the aggregate capital stock is dramatically increased owing to the additional curvature implied by the two sector model. To achieve the same degree of overall capital adjustment as in the one-sector model we lower the adjustment cost elasticity q) from 0.25 to 0.1. Finally, we allow for a one-period delay in the investment of sector-2 firms and a two period delay for sector-1 firms. This choice is based on the observation that credit-constrained firms tend to be smaller, and rims likely more flexible [see, e.g., Gertler and Gilchrist (1994)]. All other parameters are the same as in the baseline DNK model. Figure 6 shows the results of a shock to monetary policy in the model with heterogeneous firms. The top left panel shows the response of output (the solid line),

29 Bernanke and Gertler (1989, 1990) argue that the tinancial accelerator mechanismprovides a tormal rationale for Fisher's debt-deflationtheory of the Great Depression.

B.S. B e r n a n k e et al.

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relative to the baseline case with the financial accelerator shut off (the hatched line). In response to an unanticipated fall in the funds rate, output rises by approximately the same amount as it did in the aggregative New Keynesian model with investment delays, both for the baseline model without credit-market frictions and for the complete model with differential access of firms to credit. One interesting difference is that the differential investment delays across sectors smooth out the hump-shaped response of output, adding to the overall persistence of the output response. Thus, the effect of credit-market frictions on the propagation of shocks is roughly the same in the onesector and two-sector versions of the model. The two-sector model also has cross-sectional implications, of course. The top and bottom panels on the right side of Figure 6 show the sectoral responses of output and investment. The solid line corresponds to the sector facing the relatively higher cost of external finance and the dotted line corresponds to the other sector. We find that, in response to an expansionary monetary policy shock, investment by firms with relatively poor access to external credit markets rises by nearly three times as much as the investment of firms with better access to credit. This "excess sensitivity" of the more constrained firms is consistent with evidence reported by Gertler and Gilchrist (1994), Kashyap, Lamont and Stein (1994), Oliner and Rudebusch (1994), Morgan ( 1998), and

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Fig. 6. Monetaryshock multisectormodel with investmentdelays. All panels: time horizon in quarters. Aggregate output: models with and without financial accelerator; other panels: model with financial accelerator. others. Although investment differs sharply across firrns in the simulation, changes in output are similar for the two types of firms. Differing output effects could be produced, for example, by introducing inventories or inputs to production that must be financed by borrowing. Our finding that constrained firms' investment spending reacts more strongly to monetary policy contrasts with that of Fisher (1996), who obtains an ambiguous result. We suspect that the main source of the difference in predictions is that, in our setting, borrowers' net worth is endogenous and is a key channel through which monetary policy affects credit availability. In Fisher's model, in contrast, borrowers' equity positions are exogenously fixed and are unaffected by changes in policy.

6. A highly selected review of the literature The theoretical and empirical literatures on credit-market imperfections are immense, Until recently, the great bulk of this research has been partial equilibrium in nature, e.g., theoretical analyses of equilibria in credit markets with asymmetric information

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and agency costs, or empirical studies of the effects of credit-market imperfections on various types of spending, including consumption, housing, business investment, and inventory investlnent. Some leading recent examples of the latter category are cited in the introduction; see, e.g., Bernanke, Gertler and Gilchrist (1996) tbr additional references. Other surveys of these literatures which the reader may find useful include Gertler (1988), Gertler and Hubbard (1988), Jaffee and Stiglitz (1990), Bernanke (1993), Calomiris (1993), Gertler and Gilchrist (1993), Kashyap and Stein (1994), Oliner and Rudebusch (1994), Bernanke and Gertler (1995), and Hubbard (1995). To keep our survey of relevant literature brief, we limit consideration to the more recent work that, like the present research, studies the implications of credit-market frictions for macroeconomic dynamics. Even within this limited field our review must necessarily be selective; we focus on the work that bears the closest relationship to the model we have presented. In particular, we do not discuss the burgeoning related literature on the role of financial markets in economic growth [see, e.g., Levine (1997) for a survey of this topic] or in economic development [see, e.g., Townsend (1995)]. Nor do we consider research focusing on the role of banks in business cycles, primarily because there has been little work on the "bank lending channel" and related effects in an explicitly dynamic context 3o. We do believe however that the incorporation of a banking sector into our model would be a highly worthwhile exercise. Indeed, given that commercial banks borrow to order to fund investments in information-intensive, risky projects, and in this way bear resemblance to the entrepreneurs in our model, one could envision a relatively straightforward that allows for agency frictions int tile intermediary sector. On the theoretical side, the two principal antecedents of the approach used in the present chapter are Bernanke and Gertler (1989) and Kiyotaki and Moore (1997). Bernanke and Gertler (1989) analyze an overlapping-generations model in which borrowers/firms with fixed-size investment projects to finance face the "costly state verification" problem of Townsend (1979) and Gale and Hellwig (1985) 31. As we discussed in detail in the presentation of our model above, the optimal contract in this setting has the features of a standard debt contract. As we noted earlier, the principal virtue of this setup, other than simplicity, is that it motivates an inverse relationship between the potential borrower's wealth and the expected agency costs of the lenderborrower relationship (here, the agency costs are equated with monitoring/bankruptcy costs). In particular, a potential borrower with high net worth needs to rely relatively little on external finance; he thus faces at most a small risk of bankruptcy and a small

3o Interestingrecent exceptions are Gersbach (t997) and Krishnamurthy (t997). Holmstrom and Tirole (1997) analyzethe role of bank collateral and monitoring in a static context. Severalpapers have studied the role of banks in the context of "limited participation" models, see for example Fisher (1996) and Cooley and Quadrini (1997).] 31 Williamson (1987) also incorporates the costly state verification assanaption into a modified real business cycle naodel.

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premium on external finance. A borrower with less resources of his own to invest, in contrast, faces a high bankruptcy risk and a high external finance premium. In the Bernanke-Gertler model, shocks to the economy are amplified and propagated by their effects on borrowers' cash flows. For example, an adverse productivity shock lowers current cash flows, reducing the ability of firms to finance investment projects from retained earnings. This decline in net worth raises the average external finance premium and the cost of new investments. Declining investment lowers economic activity and cash flows in subsequent periods, amplifying and propagating the effects of the initial shock. Bernanke and Gertler show that this effect can generate serially correlated movements in aggregate output, even though the exogenous shocks to the system are i.i.d. They also show that in their model the dynamics of the cycle are nonlinear; in particular, the weaker the initial financial condition of borrowers, the more powerful is the propagation effect through cash flows. A number of subsequent papers have shown that this basic analysis can be extended and deepened without affecting the qualitative results: For example, Gertler (1992) considers the case of multi-period financial contracts. Aghion and Bolton (1997) give an extensive analysis of the shortrun and long-run dynamic behavior of a closely-related model. And Aghion, Banerjee and Piketty (1997) show how the dynamics of this sort of model are affected when interest rate movements are endogenous (Bernanke and Gertler assume that the real interest rate is fixed by the availability of an alternative technology.) The model that we presented utilizes a number of the features of the Bernanke-Gertler model, notably the overlapping-generations assumption for entrepreneurs and the costly state verification model of intermediation. As in Bernanke and Gertler (1989), our model here implies a central role for the endogenous evolution of borrowers' net worth in macroeconomic dynamics. Other authors have developed dynamic macroeconomic models in which cash flows play a critical role in the propagation mechanism. Notably, Greenwald and Stiglitz (1993) construct a model in which, as in Bernanke and Gertler (1989), firms have access only to debt financing (equity finance is ruled out by assumption). Because bankruptcy is costly, firms are reluctant to become highly levered; their initial equity or net worth thus effectively constrains the quantity of funds that they can raise in capital markets. Greenwald and Stiglitz assume that there is a one-period lag between the use of variable inputs and the production of output. A firm that suffers a decline in cash flow is able to finance fewer inputs and less production. Lower production implies lower profits, which propagates the effects of the initial fall in cash flow. The Greenwald-Stiglitz model thus illustrates that financial factors may affect the level of inputs, such as employment or inventories, as well as the level of capital investment (as in Bernanke-Gertler). The basic intuition concerning how credit-market imperfections propagate the cycle is similar in the two models, however. The net worth of borrowers changes not only in response to variations in cash flow, but also (and often, more dramatically) to changes in the valuation of the real and financial assets that they hold. Indeed, changes in asset values are taken by Fisher (1933) and other classical writers on the subject to be the principal means by which

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financial forces propagate an economic decline. This element was added to the formal literature by Kiyotaki and Moore (1997), who develop a dynamic equilibrium model in which endogenous fluctuations in the market prices o f an asset (land, in their example) are the main source o f changes in borrowers' net worth and hence in spending and production 32. Kiyotaki and Moore analyze a stylized example in which land serves both as a factor o f production and as a source o f collateral for loans to producers, in this economy, a temporary shock (to productivity, for example) lowers the value o f land and hence o f producers' collateral. This leads in turn to tightened borrowing constraints, less production and spending, and finally to still further reductions in land values, which propagates the shock further through time 33. We consider the asset-price channel to be an important one, and it plays an important role in generating the significant quantitative effects we obtained in our calibration exercises 34. Turning from theoretical to empirical research, we note that there are very few examples o f fully articulated macro models including capital-market imperfections that have been estimated by classical methods (the major exception being some large macroeconometric forecasting models, as noted in the introduction). The quantitative research most closely related to the present chapter uses the calibration technique. Our work here is particularly influenced by Carlstrom and Fuerst (1997), which in turn draws from analyses by Fisher (1996), Fuerst (1995) and Gertler (1995), as well as from the theoretical model o f Bernanke and Gertler (1989) discussed above. As we do in the model presented in this chapter, Carlstrom and Fuerst (1997) study the optimal lending contract between financial intermediaries and entrepreneurs when verifying the return to entrepreneurs' projects is costly for the lender. They then embed the resulting representation o f credit markets in an otherwise conventional real business cycle model. They find that the endogenous evolution o f net worth plays an important role in the simulated dynamic responses o f the model to various types o f shock.

32 Suarez and Sussman (1997) present a dynamic model in which asset price declines, induced by "fire sales" by bankrupt firms, contribute to cyclical fluctuations. 33 In the model we presented earlier, entrepreneurs do not obtain insurance against aggregate shocks because their indirect utility functions are linear in wealth (due to the assumptions of risk neutrality and constant returns to scale), while households are risk-averse. Krishnamurthy (1997) points out that in more general settings entrepreneurs are likely to want to obtain this kind of insurance, which raises the question of why the posited credit-market effects should be empirically relevant. Krishnamurthy's answer is that the ability of lenders or other insurers to insure against large aggregate shocks depends in turn on the insurers' own net worth, which may be reduced during a severe recession. He goes on to develop a model with implications similar to that of Kiyotaki and Moore (1997), except that it is the net worth of lenders or insurers, rather than that of borrowers, that plays the crucial role. See Kiyotaki and Moore (1998) tbr a related argument. 34 Another potentially interesting chatmel, emphasized by Kiyotaki and Moorc (1998), involves the interdependency that arises from credit chains, where firms are simultaneously lending and borrowing. These authors show that small shocks can induce a kind of domino effect, due to the chain, that leads to big effects on the economy.

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An interesting finding of their research is that the model with credit-market frictions generates a hump-shaped output response, consistent with most empirical findings. Our model presented above has many features in comrnon with that of Carlstrom and Fuerst (1997). Putting aside some technical details, there are however two major differences between the two models. First, we consider a sticky-price setting in the Dynamic New Keynesian tradition, while Carlstrom and Fuerst restrict themselves to a model with flexible prices. Thus we are able to examine the interaction of credit-market frictions with shocks to monetary policy, or to other nominal variables. The second difference is more subtle but is also important: Carlstrom and Fuerst assume that the agency problem applies only to producers of investment goods, who produce capital directly from the output good. The output good is produced, using both capital and labor, by separate firms who do not face agency problems in external finance. As a result of these assumptions, in the Carlstrom-Fuerst model, changes in net worth affect the economy primarily by affecting the supply price of capital (when net worth is low, less capital is produced at any given price). In our model, in contrast, the agency problem applies to producers of final output, who own the economy's durable capital stock. Since borrowers own the economy's capital stock, changes in the price of capital directly affect their net worth; that is, our model more directly incorporates the asset price effects stressed by Kiyotaki and Moore (1997). As a result, we find that creditmarket frictions amplify shocks to the economy to a greater degree than do Carlstrom and Fuerst. On the other hand, a clear virtue of Carlstrom-Fuerst model is that the credit-mechanism helps able to explain the real world auto-correlation properties of output.

7. Directions ti)r future work In subsequent research we hope to consider several extensions to the work so far: First, as noted above, we have not addressed the role of banks in cyclical fluctuations, despite considerable attention to banking in the previous theoretical and empirical literatures. There are several ways to incorporate a nontrivial role for banks into our framework; one possibility is to allow the financial intermediaries which lend to entrepreneurs to face financial frictions in raising funds themselves. In this case, the net worth of the banking sector, as well as the net worth of entrepreneurs, will matter for the models' dynamics. Second, an important institutional fact is that debt contracts in low-inflation countries are almost always set in nominal terms, rather than in real terms as in this chapter. It would be relatively easy to incorporate nominal contracting into this model, in order to evaluate whether the redistributions among debtors and creditors associated with unanticipated changes in the price level are of quantitative significance. Doing so would enable us to critically assess recent arguments that deflation may pose a serious threat to the US economy.

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Third, we have restricted the analysis to a closed economy. It would be interesting to extend the analysis to the open economy. By doing so it would be possible to analyze how a currency crisis may induce financial distress that is transmitted to the real sector 35. As we discussed in Section 5, to the extent an exchange rate collapse redistributes wealth from domestic borrowers to domestic lenders (owing to the fact that loans are denominated in units o f foreign currency), the model o f our chapter predicts a contraction in real activity. Finally, in this chapter we have restricted the credit-market frictions to the investment sector. It would be interesting to study how the results might be affected if these frictions affect other components o f spending, such as consumption, inventory investment, and housing.

Appendix A. The optimal financial contract and the demand for capital In this appendix we provide a detailed analysis of the partial equilibrium costly-stateverification problem discussed in Section 3. We start with the case of no aggregate risk and show that under the assumptions made in the text, the optimal contract provides a monotonically increasing relationship between the capital/wealth ratio and the premium on external funds: QK/N = ~(RX/R) with ~p/(.) > 0. We also establish that the default probability N is a strictly increasing function o f the premium RX/R, implying that the optimal contract guarantees an interior solution and therefore does not involve quantity rationing of credit. This appendix also provides functional forms for the contract structure. In particular, for the case o f the log-normal distribution we provide exact analytical expressions for the payoff functions to the lender and entrepreneur. In the final section of this appendix we extend the analysis to the case of aggregate risk and show that the previously established results continue to hold.

A. L The partial equilibrium contracting problem Let profits per unit of capital equal coRk, where co ~ [0, ec) is an idiosyncratic shock with E(co) = 1. We assume F(x) = Pr[co < x] is a continuous probability distribution with F(0) = 0. We denote b y f ( c o ) the pdf o f o . Given an initial level o f net worth N, and a price of capital Q, the entrepreneur borrows QK - N, to invest K units o f capital in the project. The total return on capital is thus o)RkQK. We assume co is unknown to both the entrepreneur and the lender prior to the investment decision. After the investment decision is made, the lender can only observe co by paying the monitoring cost l~coR~QK, where 0 < ¢~ < 1. Let the required return on lending equal R, with R < R K,

35 See Mishkin (1997) for a discussion of how the financial accelerator mechanism may be useful ~br understanding the recent currency crises in Mexico and Southeast Asia.

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The optimal contract specifies a cutoffvalue N such that i f co ~> N, the borrower pays the lender the fixed amount NR KQK and keeps the equity (co - - ~ ) R K QK. Alternatively; if co < N, the borrower receives nothing, while the lender monitors the borrower and receives (1 - IJ)coRK QK in residual claims net o f monitoring costs, in equilibrium, the lender earns an expected return equal to the safe rate R implying [NPr(co ~> N ) + (1 -/OE(colco < N) Pr(co < N)]RKQK = R ( Q K - N ) . Given constant returns to scale, the cutoff N determines the division o f expected gross profits RXQK between borrower and lender. We define F(~5) as the expected gross share o f profits going to the lender: F(~) =

f0

cof(co) d o + N

f(co) dco, ,]co

and note that F'(~) = 1-F(~),

F'(N)

-f(N),

implying that the gross payment to the lender is strictly concave in the cutoff value N. We similarly define g G ( N ) as the expected monitoring costs:

14G (~) ==-p

f0~ col(co) do,

and note that

~ c ' (~) -: p~f(~). The net share o f profits going to the lender is F(~0) - t~G(N), and the share going to the entrepreneur is 1 - F(N), where by definition F(o--) satisfies 0 < F ( N ) < 1. The assumptions made above imply: F(bS)-pG(~)>0

for

N C ( 0 , oo)

and lim F ( N ) - p G ( N ) = 0, ~ 0

lim F(cd) - #G(bS) = l - ~. 75 .---* o c

We therefore assume that Rk(1 - #) < R, otherwise the firm could obtain unbounded profits under monitoring that occurs with probability one s6.

36 The bound on F(~5) can be easily seen 17oii1the Ihct that both F(N) = E(~@~ < W)Pr(w < (~).-~ NPr(co ~>N) and 1 F(N) = (E(~o!(o >~~) -N)Pr(~o/> N) are positive. The limits on F(~5) -/~G(~]) can be seen by recognizing that G(?5) = E(co[~o < ~)Pr(m < N) so that lim~o~ G(N) = E(~o) = 1.

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Let h(N) = (f(~o)/(1 - F ( N ) ) , the hazard rate. We assume that Nh(N) is increasing in N 37. There are two immediate implications from this assumption regarding the shape of the net payoff to the lender. First, differentiating F(N) - #G(N), there exists an ~* such that

F'(~5)--t~G'(N) = (1 - F ( N ) ) ( 1 -/~Nh(N)) > 0

for

N < o) ,

implying that the net payoff to the lender reaches a global maximum at N*. The second implication of this assumption is that

F'(~)G"(~)-r"(~)6'(co)

- d(--d@T0°)))(1- F ( e ) ) ) 2 > 0

for all

These two implications are used to guarantee a non-rationing outcome. The optimal contracting problem with non-stochastic monitoring may now be written as

F (N) )Rk QK

max(1 K,~O

subject to [F(N) - pG(o)]RI'QK = R(QK - N). It is easiest to analyse this problem by first explicitly defining the premium on external funds s = Rk/R and then, owing to constant returns to scale, normalizing by wealth and using k = Q K / N the capital/wealth ratio as the choice variable 3s. Defining 2 as the Lagrange multiplier on the constraint that lenders earn their required rate of return

37 Any monotonically increasing transformation of the normal distribution satisfies this condition. To see this, define the inverse transformation z = z(?5), z'(N) > 0, with z ~ N(0, 1). The hazard rate for the standard normal satisfies h(z) = O(z)/(t - qS(z)), implying

(1

~o0(z(co)) ~(z(~)))

Difl'erentiating Nh(N) we obtain

d(o~h((o))

h(z(N)) + Oh'(z(N)) z'(N) > O,

dN where the inequality follows from the fact that the hazard rate for the standard normal is positive and strictly increasing. 3s It is worth noting that the basic contract structure as well as the non-rationing outcome extends in a straightforward manner to the case of non-constant returns to capital, as long as monitoring costs remain proportional to capital returns.

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in expectation, the first-order conditions for an interior solution to this problem may be written: : r ' ( ~ - ~ [ r ' ( @ - ~ G ' ( ~ ) ] = 0, k " [(1 - F(o~)) + ,~(F(o---)- # 6 ( 0 ) ] ;t" [ F ( N ) -

yG(N)lsk

- (k -

s - )~ = 0,

1) = 0.

Since F ( ~ k~G(N) is increasing on (0,N*) and decreasing on (N*, oo), the lender would never choose N > N*. We first consider the case 0 < co < N* which implies an interior solution 39. As we will show below, a sufficient condition to guarantee an interior solution is 1

s < F ( ~ * ) - ~tG(~*) - s * . We will argue below that s / > s* cannot be an equilibrium. A s s u m i n g an interior solution, the EO.C. with respect to the cutoff-(5 implies we can write the Lagrange multiplier )~ as a function o f N:

Z(~) =

r,(~

F'(~) ~G'(~)

Taking derivatives we obtain ~,(~)

-

~ [r'(~)a"(@ [r'(~

- F"(~)G'(@] -

~G'(~] 2

>0

for

~C(0,~*),

where the inequality follows directly from the assumption that ~ h ( ~ ) is increasing. Taking limits we obtain lim 2 ( ~ )

1,

~/--~0

lim )~(~o)= +oo. ?5 --~ i5"

Now define X(@ p(~5) =_ (1 - F(?~) + 3,(F(~) - / ~ G ( ~ ) ) ' then the EO.C. imply that the cutoff ~ satisfies s = p(N)

(A. 1)

so that p ( N ) is the wedge between the expected rate o f return on capital and the safe return demanded by lenders. Again, computing derivatives we obtain 2~ ( ) 1 - C(~) p'(?~-) = p ( ~ ' ~. . ( 1 - F ( ~ ) + J ~ ( F ( ~ ) - ~ G ( ~ ) )

> 0

for

N 5 (0, N~),

and taking limits: lim p ( ~ ) - - 1, ~-~0

lim p ( ~ ) = .,-.,~3"

1 1 ( F ( N * ) - # G ( N * ) ) ~ s* < -1--. / 2

Thus, for s < s*, these conditions guarantee a one-to-one mapping between the optimal cutoff N and the premium on external fhnds s. By inverting Equation (A.1) we may 39 Obviously, 65 = 0 cannot be a solution if s > 1.

B.X Bernanke et al.

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express this relationship as N = ~(s), where N~(s) > 0 for s E (1,s*). Equation (A.1) thus establishes the monotonically increasing relationship between default probabilities and the premium on external funds. Now define T ( ~ ) -- 1 +

x(r(~)

- ~G(~))

1 - r(~

Then, given a cutoff N C (0, ~*) the EO.C. imply a unique capital/wealth (and hence leverage) ratio: k

kv(~.

(A.2)

Computing derivatives we obtain

~'(~) r'(~) ~'(~): ~ (~(~)-- 1)+ q~(~5) > 0 1- r ( ~ )

for

co E (0, ~*),

and taking limits: lim ~ ( N ) = 1, ~--+0

lim

tp(N) = +oc.

o) ---~ a~*

Combining Equation (A. 1) with Equation (A.2) we may express the capital/wealth ratio as an increasing function of the premium on external funds: k - ~p(s),

(A.3)

with

'q/(s) > 0 tbr s c (I,s*). Since lim~o~o, q-t(~o) - +oc and lim~o--+~o*p(~5) - s*, as s approaches s* from below, the capital stock becomes unbounded. In equilibrium this will lower the excess return s. Now consider the possibility that the lender sets o) - co*. The lender would only do so if the excess return s is greater than s*. In this case, the lender receives an expected excess return equal to

(c(~*)

~G(~*)) sk k =

S

--

S*

S*

k >0.

Since the expected excess return is strictly positive for all k, the lender is willing to lend out an arbitrary large amount, and both the borrower and lender can obtain unbounded profits. Again, such actions would drive down the rate o f return on capital

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The Financial Accelerator in a Quantitative Business Cycle Framework

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in equilibrium, ensuring s < s* and guaranteeing an interior solution for the cutoff ~ (o, ~*). A.2. The l o g - n o r m a l d i s t r i b u t i o n

In this section, we provide analytical expressions for F(~--) and _F(N) - /~G(N), for the case where co is distributed log-normally 4°. Under the assumption that ln(co) ~ N(-½cr 2, cr2) we have E(co) = 1 and 1 -

E(co]co/> ~ ) -

4,(~ 1 -

-

a)

¢(z)

'

where @(.) is the c.d.f, of the standard normal and z is related to N through z - 0n(N) + 0.502)/o ". Using the fact that 1 - F ( N ) = (E(co]co ~> 05) - co) Pr(co ~> ~)), we obtain

r ( m ) - O(z

c0 + m[l - o(~)1

and r(co)-

~ G ( m ) = (l - ~ ) q , ( ~ -

,J) + co[1 - O(z)].

A.3. A g g r e g a t e r i s k

To accommodate the possibility o f aggregate risk, we modify the contracting framework in the following manner. Let profits per unit o f capital expenditures now equal rcoR k where co represents the idiosyncratic shock, r represents an aggregate shock to the profit rate, and E(co) = E ( r ) = 1. Since entrepreneurs are risk neutral, we assume that they bear all the aggregate risk associated with the contract. Again, letting Rk the ex ante premium on external funds, and k = Q K / N , capital per dollar of s = ~self-financing, the optimal contracting problem may be now be written: m a x E { ( 1 - F(zoD)risk ~ X [(F(N)

t~G(~5))risk - ( k - 1)1},

where ,l is the ex post value (after the realization of the aggregate shock r) of the Lagrange multiplier on the constraint that lenders earn their required return and E{ } refers to expectations taken over the distribution o f the aggregate shock ~. We wish to establish that with the addition of aggregate risk, the capital/wealth ratio k is a still an increasing function o f the ex ante premium on external funds. Define

40 Since the log-normal is a monotonic transformation of the normal, it satisfies the condition d(~h((~)))/d?~ > O.

B.S. Bernankeet al.

1386

F ( N ) -= I - F ( ~ ) + )~(F(co) - # G ( N ) ) . T h e first-order conditions for the contracting p r o b l e m m a y be written as

N - r ' ( N ) - z [ r ' ( ~ ) -- ~ c ' ( N ) ]

= 0,

k : E { F ( o ) ~s - ,t(N)} = 0, Z : (r(~

- ~G(~)

~s - (k - l) = 0.

A g a i n , under no rationing, the first-order condition with respect to ~) defines the f u n c t i o n 3,(N). This function is identical to )~(N) defined in the case o f no a g g r e g a t e risk. The constraint that lenders earn their required rate o f return defines an implicit function for the c u t o f f N = N(fi, s, k) 41 . C o m p u t i n g derivatives we obtain 0F

-(F(N)--- ~G(N))

Os

<0

(r,(~-

~a,(N))s

(r,(o)-

~a,(N))(~s)

and 0F

ok

1 --

>0.

To obtain a relationship o f the f o r m k = ~p(s), ~p'(s) > 0 we totally differentiate the first-order condition with respect to capital:

E ~D"(N)ds+~tsFt(N) Os-dS+o~dk

-)~'(~)

~-sdS+~dk

=0.

R e a r r a n g i n g gives

dk

E/(~sr'(N)--

OF + ~F(N)} X'(~o)) N

U s i n g the fact that F ' ( N ) --- ~ ' ( N ) ( F ( N ) - ~ O ( N ) )

41 As a technical matter, it is possible that the innovation in aggregate returns is sufficiently low that N(/~, s, k) > N*, in which case the lender would set N = N* and effectively absorb some of the aggregate risk. We rule out this possibility by assumption. An alternative interpretation is that we solve a contracting problem that is approximately correct and note that in our parametrized model aggregate shocks would have to be implausibly large before such distortions to the contract could be considered numerically relevant.

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we obtain = ~'(~)k

~,

implying that dk/ds simplifies to the expression d k _ E{fisF(~) - ~ ' ( ~ ) ~ ds

}

t -- OF

Since ON/Os < O, Oo)/Ok > 0, and U(N) > 0, the numerator and denominator of this expression are positive, thus establishing the positive relationship between the capital/wealth ratio k and the premium on external funds s. Appendix B. Household, retail and government sectors

We now describe the details of the household, retail, and govermnent sectors that, along with details of the entrepreneurial sector presented in Section 4, underlie the log-linearized macroeconomic framework. B.1. Households

Our household sector is reasonably conventional. There is a continuum of households of length unity. Each household works, consumes, holds money, and invests its savings in a financial intermediary that pays the riskless rate of return. Ct is household consumption, Mt/P~ is real money balances acquired at t and carried into t + 1, H/ is household labor supply, W~ is the real wage for household labor, Tt is lump sum taxes, Dt is deposits held at intermediaries (in real terms), and Ht is dividends received from ownership of retail firms. The household's objective is given by OG

max Et Z

[3k [ln(Ct+:~)+ ~ ln(Mt,/~/P~ k) + ~ ln( 1 Ht ~k)]-

(B. 1)

k-0

The individual household budget constraint is given by Ct = WtH: - Tt +17: + RtD~- Dt+l +

(M,-I - iV/:) P:

(B.2)

The household chooses C/, D~+I, Hi and Mt/Pr to maximize Equation (B. 1) subject to Equation (B.2). Solving the household's problem yields standard first-order conditions for consumption/saving, labor supply, and money holdings: 1

E f

1

B.S. Bernanke et al.

1388

W, 1

e

1

(B.4)

* Ct = b 1 - ~ '

Mt

-

~Ct ( R ; + I ~ I ) - I

Pt

\

,

(t3.5)

Rt+l

where R~ 1 is the gross nominal interest, i.e., n Pt~.l _ 1. it+ I -7_ Rt+ 1 Pt

Note that the first-order condition for M,/Pt implies that the demand for real money balances is positively related to consumption and inversely related to the net nominal interest rate. Finally, note that in equilibrium, household deposits at intermediaries equal total loanable funds supplied to entrepreneurs:

D l -- Bt. B.2. The retail sector and price setting

As is standard in the literature, to motivate sticky prices we modify the model to allow for monopolistic competition and (implicit) costs of adjusting nominal prices. As is discussed in the text, we assume that the monopolistic competition occurs at the "retail" level. Let Y,(z) be the quantity of output sold by retailer z, measured in units of wholesale goods, and let Pt(z) be the nominal price. Total final usable goods, Y{, are the following composite of individual retail goods:

=E/01 with e > 1. The corresponding price index is given by

Final output may then be either transformed into a single type of consumption good, invested, consumed by the government or used up in monitoring costs. In particular, the economy-wide resource constraint is given by

Y[=Ct+C[+L+Gt+/J

J0 ~odF(co)R~Q,~K~,

where C[ is enta'epreneurial consumption and # fo~)'o)dF(co)RfQ gate monitoring costs.

(B.8) 1I£t reflects aggre=

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Given the index (B.6) that aggregates individual retail goods into final goods, the demand curve facing each retailer is given by r,(z) =

(P,(z) /

yi

(B9)

The retailer then chooses the sale price Pt(z), taking as given the demand curve and the price of wholesale goods, P~. To introduce price inertia, we assume that the retailer is free to change its price in a given period only with probability 1 - 0, following Calvo (1983). Let P[ denote the price set by retailers who are able to change prices at t, and let Yt*(z) denote the demand given this price. Retailer z chooses his price to maximize expected discounted profits, given by

o~ r p . pw -[ /a t_ ~ t + k * /~=o Ol'Et-I [l,t,/, Pt+k Yt+lc(z)~ ,

(B.10)

where the discount rate A,/, = fiCJ(Ct~/,) is the household (i.e., shareholder) intertemporal marginal rate of substitution, which the retailer takes as given, and where P ~ =-- PriNt is the nominal price of wholesale goods. Differentiating the objective with respect to P[ implies that the optimally set price satisfies

~OkE,

1 At,k \Pt+k/

kp.k -

p~+~j

:0.

(B.11)

k=0

Roughly speaking, the retailer sets his price so that in expectation discounted marginal revenue equals discounted marginal cost, given the constraint that the nominal price is fixed in period k with probability Ok. Given that the fraction 0 of retailers do not change their price in period t, the aggregate price evolves according to

Pt = [OP~_~ + (10)(P;)(I-~)] ~/(t c),

(B.12)

where P[ satisfies Equation (B.11). By combining Equations (B.11) and (B.12), and then log-linearizing, it is possible to obtain the Phillips curve in the text, Equation (4.22).

B.3. Government sector We now close the model by specifying the government budget constraint. We assume that government expenditures are financed by lump-sum taxes and money creation as follows:

Gt-

M,-M,~ Pt

4 Tt.

The government adjusts the mix of financing between money creation and lnmp-sum taxes to support the interest rate rule given by Equation (4.25).

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This, in conjunction with the characterization in Section 5 o f the entrepreneurial sector and the m o n e t a r y policy rule and shock processes, completes the description o f the model.

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Greenwald, B., and J. Stiglitz (t993), "Financial market imperfections and business cycles", Quarterly Journal of Economics 108:77-114. Gross, D. (1994), "The investment and financing decisions of liquidity-constrained firms", unpublished paper (MIT). Hassett, K.A., and R.G. Hubbard (1996), "Tax policy and investment", Working Paper No. 5683 (NBER, July). Holmstrom, B., and J. Tirole (1997), "Financial intermediation, loanable funds, and the real sector", Quarterly Journal of Economics 1 t3:663-692. Hoshi, T., A.K. Kashyap and D. Scharfstein (1991), "Corporate structure, liquidity, and investment: evidence from Japanese industrial groups", Quarterly Journal of Economics 106:33-60. Hubbard, R.G. (1995), "Is there a "credit channel" for monetary policy?", Review 77 (Federal Reserve Bank of St. Louis, May/June) 63-77. Hubbard, R.G., A.K. Kashyap and T. Whited (1995), "Internal finance and firm invesmlent", Journal of Money, Credit and Banking 27:683 701. Jaffee, D.M., and J. Stiglitz (1990), "Credit rationing '°, in: B.M. Friedman and EH. Hahn, Handbook of Monetary Economics (North-Holland, Amsterdam). Jappelli, T. (1990), "Who is credit-constrained in the U.S. economy?", Quarterly Journal of Economics 105:219~34. Jensen, M., and W. Meckling (1976), "Theory of the firm: managerial behavior, agency costs, and capital structure", Journal of Financial Economics 3:305-360. Kaplan, S.N., and L. Zingales (1997), "Do investment-cash flow sensitivities provide useful measures of financing constraints?", Quarterly Journal of Economics 112:159~16. Kashyap, A.K., and J.C. Stein (1994), "Monetary policy and bank lending", in: N.G. Mankiw, ed., Monetary Policy (University of Chicago Press fbr NBER, Chicago, IL) 221-262. Kashyap, A.K., O.A. Lamont and J.C. Stein (1994), "Credit conditions and the cyclical behavior of inventories", Quarterly Journal of Economics 109:565 592. Kaufman, H. (1986), "Debt: the threat to economic and financial stability", in: Debt, Stability, and Public Policy (Federal Reserve Bank of Kansas City) 15-26. King, R.G., and A.L. Wolman (1996), "Inflation targeting in a St. Louis model of the 21st centtuy", Working Paper No. 5507 (NBER, March). Kiyotaki, N., and J. Moore (1997), "Credit cycles", Journal of Political Economy 105:211-248. Kiyotaki, N., and J. Moore (1998), "Credit chains", unpublished paper (London School of Economics). Krishnamurthy, A. (1997), "Collateral constraints and the credit channel", unpublished paper (MIT). Leeper, E.M., C.A. Sims and T. Zha (1996), "What does monetary policy do?", Brookings Papers on Economic Activity 1996(2): 1 63. Levine, R. (1997), "Financial development and economic growth: views and agenda", Journal of Economic Literature 35:688-726. Lndvigson, S. (1997), "Consumption and credit: a model of time-varying liquidity constraints", unpublished paper (Federal Reserve Bank of New York, October). Mariger, R.E (1987), "A life-cycle consumption model with liquidity constraints: theory and empirical results", Econometrica 55:533-558. Mishkin, F.S. (1997), "The causes and propagation of financial instability: lessons ~br policymakers", in: C. Hakkio, ed., Maintaining Financial Stability in a Global Economy (Federal Reserve Bank of Kansas City). Modigliani, E, and M. Miller (1958), "The cost of capital, corporation finance, and the theory of investment", American Economic Review 48:261-297. Morgan, D. (1998), "The lending view of monetary policy and bank loan commitments", Journal of Money, Credit and Banking 30:102-118. Oliner, S.D., and G.D. Rudebusch (1994), "Is there a broad credit channel for monetary policy'?", unpublished paper (Board of Governors of the Federal Reserve System).

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Rotemberg, J.J., and M. Woodford (1997), "An optimization-based econometric framework for the evaluation of monetary policy", NBER Macroeconomics Annual, 297-345. Sharpe, S. (1994), "Financial market imperfections, firm leverage, and the cyclicality of employment", American Economic Review 84:1060~1074. Suarez, J., and O. Sussman (1997), "A stylized model of financially-driven bushless cycles", unpublished paper (CEMFI and Ben-Gurion University, September). Taylor, J.B. (1993), "Discretion versus rules in practice", Carnegie-Rochester Conference Series on Public Policy 39:195-214. Townsend, R.M. (1979), "Optimal contracts and competitive markets with costly state verification", Journal of Economic Theory 21:265-293. Townsend, R.M. (1995), "Fhlancial systems in northern Thai villages", Quarterly Journal of Economics 110:1011-1046. Whited, T, (1992), "Debt, liquidity constraints, and corporate investment: evidence from panel data", Journal of Finance 47:1425-1460. Williamson, S. (1987), "Financial intermediation, business failures, and real business cycles", Journal of Political Economy 95:1196-1216. Wojnilower, A. (1980), "The central role of credit crunches in recent 151ancial history", Brookings Papers on Economic Activity 1980(2):277-326. Zeldes, S.E (1989), "Consumption and liquidity constraints: an empirical investigation", Journal of Political Economy 97:305-346.

Chapter 22

POLITICAL ECONOMICS AND MACROECONOMIC POLICY* TORSTEN PERSSON Institute for International Economic Studies, Stockholm University, S-106 91 Stockholm, Sweden. E-mail: [email protected]. GUIDO TABELLINI IGIER, Bocconi University, via Salasco 3/5, 20136 Milano, Italy. E-mail: [email protected]

Contents Abstract Keywords 1. I n t r o d u c t i o n

Part A. Monetary Policy 2. C r e d i b i l i t y o f m o n e t a r y p o l i c y 2.1. A simple positive model of monetary policy 2.2. Ex ante optimal monetary policy 2.3. Discretion and credibility 2.4. Reputation 2.5. Notes on the literature 3. Political cycles 3.1. Opportunistic governments 3.1.1. Moral hazard in monetary policy 3.1.2. The equilibrium 3.1.3. Adverse selection 3.2. Partisan governments 3.2.1. The model 3.2.2. Economic equilibrium 3.2.3. Political equilibrium 3.3. Notes on the literature

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* We are grateful to participants in the Handbook conference at the Federal Reserve Bank of New York, to our discussant Adam Posen and to Roel Beetsma, Jon Faust, Francesco Lippi, Ken Rogofl, Lars Svensson and Jolm Taylor for helpful comments. The research was supported by Harvard University, by a grant fi:om the Bank of Sweden Tercentenary Foundation and by a TMR Grant fi:om the Europema Commission. We are grateful to Christina Lrnnblad and Alessandra Startari for editorial assistance. Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor" and M. WoodJbrd © 1999 Elsevier Science B. I( All tights reserved 1397

1398 4. Institutions and incentives 4.1. Fixed exchange rates: simple rules and escape clauses 4.2. Central bank independence 4.3. Inflation targets and inflation contracts 4.4. Notes on the literature

Part B. Fiscal Policy 5. Credibility o f fiscal policy 5.1. The capital levy problem 5.1.1. The model 5.1.2. The e x a n w optimal policy 5.1.3. Equilibrium under discretion 5.1.4. Extensions 5.2. Multiple equilibria and confidence crises 5.3. Public debt management 5.4. Reputation and enforcement 5.5. Notes on the literature 6. Politics o f public debt 6.1. Political instability in a two-party system 6.1.1. Economic equilibrium 6.1.2. The political system 6.1.3. Equilibrium policy 6.1.4. Endogenous election outcomes 6.1.5. Discussion 6.2. Coalition governments 6.2.1. Equilibrium debt issue 6.2.2. A stronger budget process 6.3. Delayed stabilizations 6.4. Debt and intergenerationat politics 6.5. Notes on the literature

Part C. Politics and Growth 7. Fiscal policy and growth 7.1. Inequality and growth 7.2. Political instability and growth 7.3. Property rights and growth 7.4. Notes on the literature References

77. P e r s s o n a n d G. Tabellini

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Abstract

This chapter surveys the recent literature on the theory of macroeconomic policy. We study the effect of various incentive constraints on the policy making process, such as lack of credibility, political opportunism, political ideology, and divided government. The survey is organized in three parts. Part I deals with monetary policy in a simple Phillips curve model: it covers credibility issues, political business cycles, and optimal design of monetary institutions. Part II deals with fiscal policy in a dynamic general equilibrium set up: the main topics here are credibility of tax policy, and political determinants of budget deficits. Part II! studies economic growth in models with endogenous fiscal policy.

Keywords politics, monetary policy, fiscal policy, credibility, budget deficits J E L classification: E5, E6, H2, H3, O1

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1. Introduction

Traditional macroeconomic policy analysis asks the positive question of how the economy responds to alternative, but exogenous, policy actions or rules. Knowing these responses, the analyst can go on to the normative problem of policy advice. The best action or rule is selected, given a specific objective function. But as macroeconomists, we should also be able to shed light on a more ambitious set of questions. Why is it that we observe such different inflation rates across countries and time? Why did we not observe peace-time accumulations of government debt until the seventies, and why did they arise only in some countries? Why are growth rates so different in different parts of the world? To answer such questions, we need a positive theory, explaining why different countries choose different macroeconomic policies. Early steps towards such a theory were taken about twenty years ago; the credibility problem in macroeconomic policy was introduced by Kydland and Prescott (1977) and Calvo (1978), and the first models of electoral and partisan motivations in policymaking were suggested by Nordhaus (1975) and Hibbs (1977). The literature did not really take off until ten years later. But since then "political economy", or "political economics" as we prefer to call it, has been one of the most active fields in macroeconomics as well as in other branches of economics 1. With its emphasis on institutions as important determinants of policy, this literature has taken the normative analysis one step further, replacing the question: Which policies should be followed? with the question: What policymaking institutions produce better policy outcomes? In surveying this literature, we split the material into three parts: Part I deals with monetary policy, Part II with fiscal policy, and Part III with growth. Following the conventional approach in the literature, this division is based both on substance and on methodology. The monetary policy part relies on quadratic loss functions over macroeconomic outcomes and on models incorporating rational expectations, but assuming an ad hoc Phillips Curve. The fiscal policy and growth parts have better microfoundations: agents' preferences, technologies and endowments govern their economic and political interactions in simple, but complete, two-period general equilibrium models. Each part emphasizes the credibility and politics ofpolicymaking, and includes a normative evaluation of different institutions. The general approach of this line of research is to explain deviations in observed economic policies from a hypothetical social optimum by appealing to specific incentive constraints in the decision problem of optimizing policymakers. The positive analysis focuses on identifying the relevant incentive constraints, while the normative analysis focuses on institutional reforms which may relax them. Despite the separation into three parts, several common themes run throughout the chapter, reflecting similar incentive constraints. It is useful to summarize already here the nature of these incentive constraints, when they arise, and their positive and normative implications.

Many recent contributionshave been collectedin Persson and 'labellini (1994a).

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Desirable policies may suffer from lack o f credibility when policy decisions are taken sequentially over time (under "discretion") and the government lacks a nondistorting policy instrument, so that the socially optimal policy (the optimal policy in the absence of the incentive constraint) yields a second-best outcome. Lack of credibility has several positive implications, and arises both in monetary and in fiscal policy. When the government takes private expectations embodied in private economic decisions as given, it neglects the policy effects rumfing through expectation formation. This way, equilibrium average inflation or wealth taxes become too high. Moreover, in a Natural Rate world, monetary policy and inflation respond to all shocks, and not only to those over which the monetary authority has an information advantage, as the optimal policy should do. Losing control of private expectations also makes the governanen~ a prospective victim of confidence crises: runs on public debt, capital flight, or speculative attacks on the currency. All these events stem from the same fundamental problem: the government is forced to react to self-fulfilling private expectations. Finally, lack of credibility breaks a Modigliani-Miller theorem of government finance, in the same way as incentive constraints in the relationship between owners and managers break the Modigliani-Miller theorem of corporate finance. The composition of the outstanding public debt into nominal or real securities (i.e. indexed to the price level) affects the propensity of a govenmaent to rely on unexpected inflation as a source of government revenue. Similarly, the maturity composition o f government debt affects the likelihood of debt runs or the interest rate policies that future governments want to pursue. Thus, public debt management can relax future incentive constraints and thereby affect private sector expectations. Lack of credibility also has implications for institution design. First, it makes delegation to an independent policymaker desirable. Second, it makes it desirable to restrict the tasks of the policymaker. Rather than pursuing loosely defined social welfare, the central bank should target a specific variable, such as inflation, or the money supply, or the exchange rate. I f a sufficiently rich incentive mechanism - a complete contract - can be designed and enforced, the credibility problem can be eliminated completely. If state-contingent payments are not feasible, however, or if narrowly defined tasks are inappropriate, as in fiscal policy, incentive mechanisms are necessarily incomplete. But in order to gain credibility, strategic delegation of the decision-making authority to a policymaker with "distorted" preferences may still be desirable. This insight has been exploited in monetary policy, to advocate the benefit of an independent and "conservative" central bank. It also applies to the election of a conservative policymaker facing the task of selecting a wealth tax, or to the delegation of certain policy choices to a foreign government, as in the case of multilateral exchange rate arrangements, or currency boards 2. 2 International competition is another institutional device %r coping with credibility which is emphasized in the literature but not in this survey. Tax competition, or exchange rate competition, conhibute to overcoming a domestic credibility problem because they can reduce the ex-post incentives to unilaterally increase tax rates or inflation.

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A second incentive constraint is political opportunism, by which we mean that the incumbent government is prepared to introduce distorted policies to increase its chances of re-election. This incentive constraint typically applies when politicians value holding office p e r se and voters, although rational, are uninformed. We study the consequences of political opportunism in monetary policy only, but the empirical implications for fiscal policy have been spelled out in the literature. The main prediction is an electoral cycle in aggregate demand policies: the incumbent government has an incentive to stimulate the economy just before elections to appear more competent in the eyes of uninformed voters, thus boosting of the probability of re-election. This always leads to an electoral cycle in inflation which, depending on the information advantage of the government, could also increase output volatility at the time of elections. The normative implications tend to reinforce those of the credibility literature: central bank independence and monetary or inflation targets reduce the scope for electoral cycles in monetary policy. Other, deeper reforms, such as who should have the right to call the elections and at what time, remain to be investigated. Political ideology may shape policy formation if different parties pursue different "partisan" (i.e. ideological) platforms once in oNce, and if the election outcome is uncertain. Political polarization and political instability thus induce another incentive constraint, which also gives rise to an electoral cycle in aggregate demand, output or public spending. But here the cycle takes place after, rather than before, elections and reflects the winning party's desire to influence economic outcomes. In a dynamic context, this incentive constraint may generate "strategic myopia". The government in office realizes that it may be replaced by a policymaker with different ideological preferences. This gives an incentive to accumulate public debt or postpone investment, so as to influence the future behavior of the opponent. Political ideology also implies strategic manipulation of state variables to influence the voters; for instance, an extremist incumbent may restrain his own future behavior by appropriate institutional reforms to increase his own electability. The strategic manipulation of future opponents and voters are both stronger, the more unstable and polarized the political system. From a normative point of view, the benefits of delegation and targeting in monetary policy are further reinforced. More generally, there may be advantages of institutional checks and balances and institutions that moderate political conflict and policy extremism. The discussion, so far, applies to a single decision-maker facing static or dynamic incentive constraints. Often, however, decision-making power is dispersed among several political actors. This creates another incentive constraint, which we may call divided government. Examples include coalition governments, soft budget constraints on public enterprises or local governments, veto rights held by key individuals in government or by organized groups in society, or the lobbying activities of special interests. Divided government arises almost exclusively in fiscal policy. In a static context its central implication is over-spending, as every decision-maker fully internalizes the benefits of public spending but only a fraction of the cost: this is the so called "common pool" problem. In a dynamic context, myopic behavior emerges: each decision-maker has an incentive not only to over-spend, but also to spend

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sooner rather than later. Leaving tax revenues for tomorrow can be counter-productive, because they are partly appropriated by other decision-makers. Hence, models of divided government also predict debt accumulation and/or under-investment. In some circumstances, the dispersion of veto rights delays stabilization in an unsustainable fiscal situation. The most straightforward institutional remedy is to centralize power in the hands of a single decision-maker (a prime minister, or a president, or the Secretary of the Treasury). Alternatively, one might rely on two-stage budgeting, with a decision on aggregate items (total spending, or total borrowing) preceding the decision on how spending is allocated. Such budgetary solutions entail a trade-offbetween an allocative distortion (a lopsided spending result from centralized decision-making power) and an aggregate distortion (over-spending resulting from inadequate centralization). At a deeper political level, the incentive constraints induced by divided government and political ideology can be traded off. Political reforms that centralize power in the hands of single parties or individuals also exacerbate polarization between the majority and the opposition, and may thus imply that political instability becomes a more binding incentive constraint. The last incentive constraint considered in this chapter arises when there is income heterogeneity, so that tax policies are motivated by pressure .for redistribution. The positive implication is that the overall size of government is determined by the extent of inequality in pre-tax income or, in the case of social insurance policies, by inequality in risk. This, in turn, has implications for the link between inequality and measures of economic performance. But the redistributive motive is also an important force shaping the composition of spending or the structure of taxation. Public financial policies that redistribute along different dimensions become non-equivalent, because they are supported by different coalitions of voters. For instance, public debt and social security redistribute across generations in the same way; nevertheless in a political equilibrium they give rise to different allocations, because they redistribute between rich and poor in different ways. A similar non-equivalence result holds with regard to alternative instruments of geographic redistribution. As in the case of lacking credibility, an incentive constraint on policy formation breaks the Modigliani-Miller theorem of government finance. Some of the topics covered in this survey partly overlap with a companion survey, Persson and Tabellini (1999). There we cover the literature on public economics and public choice, dealing with static allocation issues in fiscal policy, rather than the intertemporal policy issues emphasized here. Neither do we cover the literature on monetary and fiscal policy in an international context, which is surveyed in Persson and Tabellini (1995). Each part starts with a separate introduction, in which we highlight a number of empirical regularities, motivating the sections to follow, and provide a more detailed road map. We comment on the original literature both as we go along and in separate "Notes on the Literature" at the end of each section.

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Part A. Monetary Policy The empirical evidence for the (democratic) OECD countries in the post-war period suggests the following stylized facts: (i) Inflation rates vary greatly across countries and time. But there is a common time pattern: in most countries inflation was low in the 1960s, but very high in the 1970s; it came down in the 1980s and 1990s in all countries, though at different speeds and to different extents 3. (ii) Inflation rates are correlated with real variables, such as growth or unemployment, in the short run. But there is little evidence o f a systematic correlation over longer periods. Across countries, average inflation and average growth tend to be negatively correlated or not correlated at all 4. (iii) There is little evidence o f systematic spillover effects between monetary and fiscal policy. Specifically, higher budget deficits are not systematically associated with higher inflation rates 5. (iv) Inflation increases shortly after elections; budget deficits tend to be larger during election years; there is also some (not very strong) evidence that monetary policy is more expansionary before elections. On the other hand, real variables such as growth or unemployment are not systematically correlated with election dates. (v) Output displays a temporary partisan cycle just after elections: newly appointed left-wing governments are associated with expansions, right-wing governments with recessions. This cycle tends to occur in the first half o f the inter-election period and is more pronounced in countries with two-party systems. Inflation displays a permanent partisan cycle: higher inflation is associated with left-wing governments 6 (vi) Average inflation rates and measures of central bank independence are negatively correlated; this holds up when controlling for other economic and institutional variables (even though the correlation is less robust). There is also some evidence that fixed exchange rates are associated with lower inflation. Real variables, on the other hand, have no systematic correlation with the monetary regime (although the variance o f the real exchange rate is lower under fixed than floating exchange rates) 7 These stylized facts will be taken as the starting point for Part I. Fact (i) clearly calls tbr a positive model of inflation. Fact (ii) is not well understood and the profession See, for instance, Bordo and Schwartz (1999). 4 Time-series evidence (for the USA) can be found in Stock and Watson (1999), whereas (broad) cross-country evidence can be found in Barro (1997) and in Fischer (1991). s See for instance Grilli et al. (1991). This fact no longer applies if one considers the interwar period or developing countries. In particular hyperinflations are typically associated with fiscal problems. 6 Statements (iv) and (v) are suggested by the comprehensive study by Alesina and Roubini (t997). 7 See Grilli et al. (1991), Cukierman (1992), Jonsson (1995), Eijffinger and de Haan (1996), Mussa ~1986), Baxter and Stockman (1989). The robusmess of these findings has been questioned by Posen (1993, 1995), however.

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is still searching for a satisfactory model of the joint determination of nominal and real variables. But it suggests that a plausible model would encompass the natural rate hypothesis that the Phillips curve is vertical and monetary policy is neutral in the long run, while preserving some scope for aggregate demand policies to affect output in the short run. Fact (iii) suggests that abstracting from fiscal policy may not be a bad first approximation. Facts (iv) and (v) indicate that political variables might be important ingredients in successful positive models of inflation and macroeconomic policy. Fact (vi) finally suggests that the institutional features of the monetary regime particularly the statutes regulating the central bank - should also play a role in a successful model. In Section 2 we formulate and discuss a model of macroeconomic policy and inflation which has been the workhorse in much of the recent literature. We illustrate how credibility problems in monetary policy may arise and how these may be fully or partly resolved by reputation. Section 3 extends the simple model with political institutions and incentives. We illustrate how political business cycles and partisan cycles, consistent with the stylized facts above, may come about. Designing nqonetary institutions to tackle the distortions created by credibility problems and political cycles is the topic of Section 4.

2. Credibility of monetary policy In this section, we first formulate and discuss a model of macroeconomic policy and inflation, in the spirit of Kydland and Prescott (1977), Fischer (1977) and Barro and Gordon (1983a), which has been the starting point for much of the recent literature. In subsection 2.1 we set up the model and make general comments. Subsection 2.2 derives a normative benchmark. In subsection 2.3 we emphasize how the credibility problems tied to the central banks' ability to temporarily boost the economy result in excessively high equilibrium inflation - the celebrated "inflation bias". Subsection 2.4 briefly illustrates how reputation may provide full or partial solutions to such credibility problems, drawing on the work by Barro and Gordon (1983b), Backus and Driffill (1985), Canzoneri (1985) and others that - in turn - borrow heavily from the literature on repeated games. 2.1. A simple positive model o f monetary policy

The demand side of our model economy is represented by :~: = m + v + # ,

(2.1)

where o~ is inflation, m is the money growth rate, v is a demand (or velocity) shock, and ?2 is a "control error" in monetary policy. Letting output enter the implicit money demand function underlying Equation (2.1) complicates the algebra, but does not yield

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important additional insights. The supply side of the model assumes that nominal wage setting (unilaterally by firms, unilaterally by labor unions, or bilaterally by bargaining between these actors) aims at implementing an exogenous, but stochastic, real wage growth target ~o 8. Letting er° denote rationally expected inflation, nominal wage growth w then becomes w = (o + :r e.

(2.2)

Employment (or output growth), x, satisfies x= y-(w-er)-e,

where 7 is a (potentially stochastic) parameter, and e is a supply shock. Combining this relation with Equation (2.2), we obtain an expectations-augmented short-run Phillips curve

x = 0 + (er

ere)_ e,

(2.3)

where 0 - 7 - ~o can be interpreted as the stochastic natural rate of employment (output growth). We assume that all shocks are i.i.d., orthogonal to each other, have (unconditionally) expected values of zero, well-defined variances ~7~,~ { , and so on. The timing of events is as follows: (0) rules of the monetary regime may be laid down at an institution design stage; (1) the value of 0 is observed both by the private sector and the policymaker; (2) er~ is formed, given the information about 0; (3) the values of v and e are observed; (4) the policymaker determines m; (5) /~ is realized together with er and x. The assumed timing captures the following concerns: Some shocks, related to the labor market, are commonly observable and can therefore be embodied in privatesector wage-setting decisions, here captured by expectations formation. Other shocks can only be embodied in policy. This distinction is best interpreted as reflecting the ease with which monetary policy decisions are made, relative to the laborious wage-setting process, but could also reflect a genuine information advantage of the policymaker (which is perhaps only plausible for financial sector shocks). O f course, it is this advantage that allows monetary policy to stabilize the economy. Finally, there is some unavoidable noise in the relation between policy and macroeconomic outcomes.

As is well-!~lown, the "surprise supply" formulation wc end up with below could also be derived from a model of price-setting finns, or from a Lucas-style "island model".

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Clearly, Equation (2.1) and the assumed information implies that rationally expected inflation is Jr° --E(ar ] 0 ) = E(m I 0),

(2.4)

where E is the expectations operator. Substituting Equations (2.1) and (2.4) into (2.3), we have x=O+m-E(m[

O)+v~-~

&

(2.5)

The model thus entails the usual neutrality result: only unanticipated aggregate demand policy affects real variables. But if policy responds to shocks, it can still stabilize employment. 2.2. Ex ante optimal monetary policy

We follow the rational expectations literature in thinking about policy as a rule. Suppose society has the quadratic loss function E[L(0r, x)] : ½E[(ar - yg*)2+ ~(X --

X*)2],

(2.6)

where a~* and x* are society's most preferred values for inflation and employment, and ,~ is the relative weight on fluctuations in these two variables. As the objective is quadratic in macroeconomic outcomes, which in turn are linear in the shocks, the optimal policy rule is of the form m - k + k ° O + k V v ~k%';

(2.7)

that is, policy potentially responds to all shocks observable to the policymaker. Suppose furthermore that the policymaker can make a binding commitment to the rule (2.7) at the institution design stage (0), i.e. before the observation of 0. Clearly, since E(v) = E(E) = 0, this implies private sector expectations: E(m [ O) = k + k°O.

(2.8)

By Equations (2.1), (2.5), (2.7) and (2.8), macroeconomic equilibrium under the rule is

Jc - k +k°O+ (k ~ + 1) v + U E + t~, x - O+(k~+ 1) v + g + ( k e - 1)e.

(2.9) (2.10)

What is the optimal rule? Substitute Equations (2.9) and (2.10) into (2.6), take expectations over all shocks, and set the derivatives of the resulting expression with regard to the intercept and the slope coefficients in Equation (2.7) equal to zero. The following results emerge:

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(i)

k - :~* and k ° = 0. The optimal rule provides an "anchor for inflationary expectations". Expectations are right where society wants them to be, namely at the preferred rate o f inflation: E(Jv [ 0) - zc*. The optimal rule is thus neither conditional on the observable shock to the natural rate, 0, nor on society' s output target, x*. Such conditionality would be embodied in expectations; it would therefore do nothing to stabilize employment, only add costly noise to inflation. (ii) k ~ = - 1 . Demand (velocity) shocks are fully stabilized. As policy also operates via aggregate demand, a complete stabilization o f demand shocks nullifies their effects on inflation as well as on employment. (iii) k e = ~ / ( i + 30. Supply shocks are stabilized according to the policymaker's tradeoff between inflation and employment fluctuations. The higher the weight on employment, the more these shocks are stabilized. The optimal state-contingent policy rule can thus be written as /l m = Yg* - v + ( 1 ~ 6 . Macroeconomic omcomes -- indexed by R - when the rule is ~bllowed are Jr j~ = ~* + ~ - ~ e q 1 xa = 0- ~e+/~.

/~,

(2.11) (2.12)

Results such as these have been - and continue to be - very influential for academic economists' thinking about policy. They suggest that delivering low inflation and stable employment is essentially a technical (not a strategic) problem: inflation can be kept low by clearly announcing a rule aiming at low average inflation. Demand shocks should be completely stabilized. The inflation and employment consequences o f supply shocks should be traded off according to society's preferences. Control errors are unavoidable, but can perhaps be reduced by better forecasting or operating procedures in monetary policy. Even though this picture is too rosy for a realistic positive model o f macroeconomic policy, it still provides a useful normative benchmark that we can use to evaluate the outcome in the positive models below. In the remainder o f the chapter, we simplify the stochastic structure by setting v = /~ = 0. Demand shocks, as we saw, present no problem for the policymaker in this class o f models, provided that they can be identified in time and that there are no other policy goals such as interest-rate smoothing. Control errors do present problems, but are unavoidable 9. With these simplifications, there is no meaningful

9 Abstracting from conUol errors is irmocuous as long as the public can monitor monetary policy perfectly and as long as policymaker competency and efforts are exogenous. Below, we comment on where control errors would matter. Moreover, in a richer (dynamic) setting with expectations entering the aggregate demand function, demand shocks and control errors may give rise to incentive problems similar to those discussed below.

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distinction in the model between m and st. For simplicity, we therefore assume that the policymaker sets .re directly. Why don't we eliminate the shocks to the natural rate 0, with a similar motivation? The answer is that such shocks do not affect the solution under commitment, whereas they do affect policy in an interesting way under alternative assumptions about the policymaking process. 2.3. Discretion and credibility

In reality, decisions on monetary policy are taken sequentially over time, rather than once and for all. Assuming ex ante commitment to a state-contingent policy rule rhymes badly with this practice. In our static model, reality is better captured by an alternative timing: policy is chosen under "discretion" when the policy instruments are set at stage (4) above, after wages have been set (37e formed) and shocks have been realized. This adds an ex post incentive compatibility condition to our positive model: policy has to be optimal ex post - when it is actually enacted. This additional credibility constraint makes the solution less advantageous for the policymaker (and society). The policymaker still sets sr (that is, m), seeking to minimize the loss in Equation (2.6). But all uncertainty has been resolved at the new decision stage, so the expectations operator is redundant. Consider how the loss is affected by a marginal expansion, for given :U and e. Using Equations (2.3) and (2.6), we have dL(yG x)

d~

-Ljr(zc, x)+L~(Jv, x)-~2 - ( z r - ~ * ) + ) ~ ( O + ( z C (lJ~

~)-~'-x*),

(2.13)

where a subscript denotes a partial derivative. By Equation (2.13), the benchmark policy rule is not incentive compatible under discretion. Suppose that wage setters believed in an announcement of that rule, implying that :ve - sT*. Using the optimal-rules outcome in Equations (2.1 1)-(2.12), and evaluating the derivative in Equation (2.13) at the point prescribed by the ex ante optimal policy rule, we get dL(~R'Xa)dz z~::z* = X(O x*). If preferred employment (output) exceeds tile natural rate (if x* > 0), ar~ expansioii reduces the loss, rendering the ex ante sub-optimal policy rule ex post inoptimal. Once wages have been set, the marginal inflation cost - the first term on the RHS of Equation (2.13) - is always smaller than the marginal employment benefit - the second term on the RHS 10. Thus, the ex post incentive-compatibility constraint is binding and the low-inflation rule is not credible.

l0 To make this more clear, consider the case when c - 0, such that tile optima| rule prescribes the policy sTR = ~*, implying xR = 0. Then, by Equation (2.13) the marginal inflation cost is acmalty zero (to first order), whereas the marginal employment benefit is positive (if x* > 0).

1410

17 Persson and G. Tabellini

A credible policy must simultaneously fulfill two conditions: (i) the policy is e x optimal, ~y dL = 0, given :re and e; (ii) expectations are rational, i.e. ~e = E(s~ I 0). In game-theoretic terms, those are the conditions for a Nash Equilibrium in a game with many atomistic private wage setters (desiring to minimize the deviation of the realized real wage w - ~e, from the targeted real wage co) moving before the policymaker 11. Condition (i) requires that the expression in Equation (2.13) equals zero. Taking expectations of that expression, condition (ii) can be expressed as E(zc ] 0) = ~* + 3,(x* - 0). Combining the two conditions, we get

post

a -D = st* + ,~(x* - 0) + ~ e , +A,

(2.14)

where the D superscript stands for discretion. The employment outcome remains as in Equation (2.12) except that /~ = 0 by assumption, if we assume x* - 0 > 0, the discretionary policy outcome in Equation (2.14) and the commitment outcome in Equations (2.11)-(2.12) illustrate the celebrated "inflation bias" result: equilibrium inflation is higher under discretion than under commitment to a rule, whereas employment is the same, independently of the policy regime. The bias is more pronounced the higher is ;, (the more valuable is employment on the margin) and the higher is x* relative to 0 (the higher is preferred employment relative to the natural rate); both factors contribute to a greater "temptation" for the policymaker to exploit his short-run ability to boost employment by expansionary policy once wages are fixed. Since the natural rate 0 is random, whereas the employment target x* presumably is constant (or at least more stable than 0), inflation is also more variable under discretion than under the rule. The inflation bias is due to two key assumptions. The first is the sequential timing of monetary policy decisions. The second is the assumption that the employment target is higher than the natural rate, that is: x* - 0 > 0. This assumption must reflect a lack of policy instruments: some distortion in the labor or product market keeps employment too low. The government does not remove this distortion; either because it does not have enough policy instruments or because the distortion is kept in place by some other incentive problem in the policy-making process. These assumptions capture important features of monetary policymaking in the real world. In this static model, the policy response to the supply shock e is not distorted: shocks are stabilized in the same way under discretion and commitment. This equivalence does not, however, carry over to a dynamic model where employment (but not the employment target) is serially correlated. In such a dynamic model, the future inflation bias depends on current employment (since the future equilibrium employmem depends on current employment). To reduce the future inflation bias, the

1 The equilibrium would also apply identically to a simultaneous game between the government and a single trade union. If the union moved before the government, the equilibrium might differ slightly, but the fundamental incentive problem would not be affected.

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policymaker thus responds more aggressively to supply shocks under discretion than under commitment. Moreover, the systematic inflation bias increases, as an ex post expansion today expands both current and future employment 12 The "distortion" in the policymaking process can be described as follows: under discretion, the policymaker (correctly) fails to internalize the mapping from actual policy to expected policy. He is not being foolish: he really cannot influence private sector expectations. This is what we mean when saying that a (low inflation) policy "lacks credibility". Yet, actual policy maps into expected policy in equilibrium when private agents have rational expectations. Under commitment, on the contrary, the policymaker internalizes this equilibrium mapping; indeed announcing the optimal policy rule brings rationally expected inflation down precisely to the preferred rate of inflation. The conclusions are pretty stark. First, a desirable policy rule does not become credible just by announcing it; is thus pointless to recommend a noncredible policy rule. Second, the inability to commit to a policy rule has obvious costs. Institutional reforms that give policymakers greater commitment ability can thus be desirable. This simple model of monetary policy credibility is often criticized with reference to the plausible objection that "real world policymakers are not trying to surprise the private sector with unexpected inflation". But this criticism misses the point of the analysis. The model does not predict that the policymaker tries to generate policy surprises in equilibrium. On the contrary, in equilibrium the policymaker would like to bring inflation down but refrains from doing so as his lack of credibility would turn any anti-inflationary policy into a recession, in other words, the model predicts an inertia of expectations to a suboptimally high inflation rate, and a difficulty in curbing these expectations down to the socially efficient rate. What the model does rely on, however, is an assumption that the policymaker would want to generate policy surprises outside o f equilibrium to a more favorable outcome. Is this a plausible positive model of inflation? Some observers, like McCallum (1996), apparently do not think so. A convincing rebuttal should address the question already posed by Taylor (1983), who - in his discussion of Barro and Gordon (1983b) - asked why society has not found ways around the credibility problem in monetary policy, when it has found ways around the credibility problem of granting property rights to patent holders. This question is best addressed in connection with a closer discussion of the institutions of monetary policymaking, so we come back to it in Section 4. What are the observable implications of the analysis so far? One implication is that a binding credibility problem would show up by the central bank reacting to variables that entered the private sector's information set (before policy is set), whereas the

12 Svensson (1997a) proves this result formally, drawing on earlier work by Lockwood et al. (1998) and Jonsson (1997). See also Obstfeld (1997b) for a related result in a dynamic model of seignorage. Beetsma and Bovenberg (1998) show that stabilizationbias mises also when monetary and fiscal policy are pursued by different authorities with diverging objectives.

14t2

T. Persson and G. Tabellini

reaction function would not include such variables under commitment. Hence, the unconditional variance of inflation is higher under discretion. If the credibility problem is caused by a high )~, the model indeed predicts a positive correlation between average inflation and the variance of inflation, in conformity with international evidence. The discretionary model also suggests a plausible explanation of the secular trend in inflation experienced by the industrialized countries and mentioned in the introduction. The 1950s and 1960s were a period without serious supply shocks and with a low natural rate of unemployment (low variance of e, high realizations of 0), which made it easy to keep inflation low. Enter the 1970s with severe supply shocks (high realizations of E) pushing up the natural rate (to capture this in the model would require serial correlation in employment) and inflation; we may then interpret the rise in inflation as the result of policymakers maintaining their earlier high employment objectives (x* staying constant or falling by less than 0). The gradual decline in inflation from the mid-1980s and onward, despite continued high natural rates (in Europe), can be understood to derive from policymakers gradually adapting their employment ambitions to the structural problems in the labor market (x* drifting downwards over time) and from the institutional reforms in central banking arrangements in a number of countries in the recent decade. Naturally, learning from past policy mistakes is also likely to have played an important role. To date, time-series implications of this type have received too little attention in the credibility literature 13. Instead, the literature has focused on normative issues of institutional reform, and to some extent on explaining cross-sectional differences in macroeconomic outcomes by different institutions. 2.4. Reputation

One can criticize the simple model discussed so far for being static and failing to capture the repeated nature of policymaking. Specifically, the model rejects repeated interaction with the public and hence ignores reputational forces. A branch of the literature has studied reputational forces in detail. The main result is that a link from current observed policy to future expected policy can indeed discipline the policymaker and restore credibility. With repeated interaction, a policymaker operating under discretion faces an intertemporal trade-off: the future costs of higher expected inflation, caused by expansion today, may more than outweigh the current benefits of higher employment. To illustrate the idea, consider the model of subsection 2.3, repeated over an infinite horizon. The policymaker's intertemporal loss function, from the viewpoint of some arbitrary period s, can be written as E~.

[±

6' "L(JG xt)

,

(2.15)

[=S

1.~ See,however,the recentpapers by Parkin(1993), Barro and Broadbent(1997) and Broadhent(1996).

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where 6 is a discount factor. To simplify the algebra, we assume the static loss function to be linear, not quadratic, in employment: (2.16)

L(Tg, x) = ~2rl 2 _ /~.,x.

With the simpler loss function, the ex ante optimal policy rule is simply to have zero inflation all the time and to accept employment x = 0 - e (since ~* = 0 and employment volatility is not costly), while the static equilibrium under discretion has inflation equal to )~ and employment still at x = 0 - e. We now show that, even under discretion, reputation can indeed create strong enough incentives to enforce zero inflation. As an example, assume that wage setters set wages on the basis o f the following expectations: ~[=

0 iff ~ = ~ [ , 3, otherwise.

u= t-1 ..... t-T,

(2.17)

Equation (2.17) says that wage setters trust a policymaker who sticks to zero inflation in period t to continue with this same policy in the next period. But if they observe any other policy in period t, they lose this trust and instead expect the discretionary policy to be pursued for the next T periods. A policymaker confronted with such expectation formation, in effect, faces a non-linear incentive scheme: he is "rewarded" for sticking to the rule, but he is "punished" if deviating from it. Consider a policymaker that enjoys the trust of the public (i.e. :Vs~ = 0). When is the punishment strong enough to outweigh the immediate benefit of cheating on the rule? To answer formally, note that the optimal deviation (found by minimizing the static loss function, given e and COs ~ = 0) is simply ~. = 3,, thus implying employment x~. = )~ + Os - es. After some algebra, the current benefit from cheating can then be expressed as B = L(0, 0s -- e,) - L(,~, ,~ + 0~ - e,) = ~,~.~ 2

(2.18)

Due to the simpler loss function, the benefit is independent o f the realizations of 0 and e. The punishment comes from having to live with higher expected and actual inflation in the next T periods. Why higher actual inflation? As the expectations in Equation (2.17) are consistent with the static Nash Equilibrium outcome in subsection 2.3, it is indeed optimal for the policymaker to bear the punishment if it is ever imposed. In other words, the private sector's expectations will be fulfilled, both in and out o f equilibrium 14. Thus, the cost of a deviation is C=Es

6 t "(L(.,t, 0,-et)--L(O, Ot-e,))

~ Lt=s+

.... 6

)-Z2,

(2.19)

1

14 By this argument the analysis identifies a sequentially rational (subgame perfect) equilibrium. For other expectation formation schemes, in which expectations changed more drastically after a deviation, we would have to impose a separate incentive-compatibility constraint, namely that it is indeed optimal to carry out and bear the ptmishment after a deviation [see Persson and Tabellini (1990, ch. 3) on this point].

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T. Persson and G. Tabellini

which is clearly stationary if we assume that 0 is i.i.d, over time. Obviously, the policymaker finds it optimal to stick to the zero-inflation rule as long as B ~< C. Inspection of Equations (2.19) and (2.18) reveals that this is more likely the higher the discount factor c5 and the longer the horizon T for which inflationary expectations go up after a deviation. Many extensions of this basic framework are feasible; and some have been pursued in the literature. For instance, if we retained the quadratic loss function of the previous subsection, the benefit of cheating would be an increasing function of the actual realization of 0, while the cost would depend on the variance and the expected value of 0. As a result, even with reputation, equilibrium inflation would continue to depend on the actual realization of 0: a high value of 0 makes the incentivecompatibility condition more binding, as it increases the benefit B but not the cost C. The lowest sustainable inflation rate (defined by the condition that B = C) would be an increasing function of 0. Thus, reputation would reduce average inflation but would not change the main positive implications of the model of the previous section. Canzoneri (1985) studied a framework with shocks to inflation that are unobservable to private agents both ex ante and ex p o s t ; an example could be the /~ shocks in Equation (2.1) above. If observed inflation exceeds some threshold, such monitoring problems give rise to temporary outbreaks of actual and expected inflation, because the public cannot clearly infer whether high inflation is due to large shocks or to deliberate cheating. Backus and Driffill (1985), Barro (1986), Tabellini (1985, 1987) and Vickers (1986) studied reputational models where the private agents are uncertain about the policymakers "type" (as his )~ in the model above). They use the information embodied in current observations of policy to learn about this type, and the policymaker sets policy optimally with a view to this private learning process. Such models illustrate how a "dovish" policymaker (someone with a high )~ or without access to a commitment technology) can temporarily borrow the reputation of a "hawkish" policymaker (someone with a low )~ or with access to a commitment technology). They also illustrate how a hawkish policymaker may have to impose severe output costs on the economy to credibly establish a reputation. This differs from the equilibrium considered above, where the policymaker merely maintains a reputation he is lucky enough to have. Cukierman and Meltzer (1986) also studied credibility and private learning but in a richer dynamic setting, where parameters in the central bank's objective function vary stochastically over time. The central insight of the reputation literature is that ongoing interaction between a policymaker and private agents can mitigate the inflation bias and restores some credibility to monetary policy. Whether the problem is entirely removed is more controversial, however, and depends on details of the model and the expectations formation mechanism. Even though the insight is important, the reputation literature suffers from three weaknesses. As in the theory of repeated games, there is a multipleequilibrium problem, which strikes with particular force against a p o s i t i v e model of monetary policy. Moreover, the problem of how the players somehow magically

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Political Economics and Macroeconomic Policy

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coordinate on one of the many possible equilibria is worse when the ganle involves a large number of private agents rather than a few oligopolists. Finally, the normative implications are unclear. The existence of reputational equilibria with good outcomes is not helpful to a country where inflation is particularly high at a given moment in time. The lack of suggestions for policy improvements is another reason why researchers largely turned away from reputational models, towards an analysis of the policy incentives entailed in different monetary policy institutions Js 2.5. N o t e s on the literature

Textbook treatments of the general material in this section can be found in Persson and Tabellini (1990, Chs. 1-4), and in Cukierman (1992, Chs. 9-11, 16), both covering the literature up to around 1990. The literature on credibility in monetary policy starts with Kydland and Prescott (1977), who included a brief section with the basic insight of the static model in subsection 2.3. Barro and Gordon (1983a) formulated a linearquadratic version and pushed its use as a positive model of monetary policy. Calvo (1978) studied the credibility problem of monetary policy in a dynamic model, where the short-run temptation to inflate arises for public-finance reasons. Obstfeld (1997b) provides an insightful analysis of the credible policies in a dynamic seignorage model. Dynamic models of the employment motive to inflate were developed by Lockwood and Philippopoulus (1994), Lockwood et al. (1998), and Jonsson (1997). Parkin (1993) argues that the great inflation of the 1970s can be explained by an increase in the natural rate in the kind of model dealt with here. Ball (1996) points to indirect evidence that many disinflationary episodes in the 1980s lacked credibility. Barro and Gordon (1983b) started the theoretical literature on reputation in monetary policy, drawing on the work on trigger strategies in repeated games with complete information. Backus and Driffill (1985), Tabellini (1985, 1987) and Barro (1986) developed incomplete information models of reputation, emphasizing how a dovish policymaker can borrow a reputation from a super-hawkish policymaker who only cares about inflation and not at all about employment. Vickers (1986) instead emphasized how a policymaker who seriously wants to fight inflation may have to engage in costly recessionary policies in order to signal his true identity to an incompletely informed public. Reputation with imperfect monitoring of monetary policy was first studied by Canzoneri (1985). Grossman and Van Huyck (1986) and Horn and Persson (1988) studied reputational models dealing with the inflation tax and exchange rate policy, respectively. Rogoff (1987) includes an insightful discussion about the pros and cons of the reputational models of monetary policy.

15 Some interesting recent work, however, suggests an institutional interpretation of some of these reputational equilibria arguing that some institutional arguments are more conducive to reputation building than others; see Jensen (1997), al Nowaihi and Levine (1996) and Herrendorf(1996). The ideas are related to Schotter (1981) and to the view that international institutions may facilitate cooperation in hade policy [see Staiger (1995) tbr a survey].

1416 3o Political

T Persson and G. Tabellini

cycles

The empirical evidence for the democratic OECD countries during the post-war period suggests systematic pre-electoral expansionary policies - fact (iv) in the introduction as well a post-election partisan cycle in real variables and inflation - fact (v). These "facts" vary somewhat depending on the country and the time period considered, and their robustness has not been checked with the same standards as, say, in the modern macroeconometric literature attempting to identify innovations in monetary policy 16 But they are interesting enough to motivate this line of research. The empirical evidence also indicates that there is so-called "retrospective voting": the likelihood of election victory for the incumbent government or legislature depends largely on the state of the economy; as expected, a higher growth rate boosts the reelection probability of the incumbent iv. It is then tempting to "explain" fact (iv) the political business cycle - by opportunistic governments seeking re-election by taking advantage of the voters' irrationality. But how can we claim that the same individuals act in a rational and forward-looking way as economic agents, but become fools when casting their vote? One of the puzzles any rational theory o f political business cycles must address is thus how to reconcile retrospective voting with the evidence of systematic policy expansions before elections. This puzzle is addressed in subsection 3.1, under the assumption that voters are rational but imperfectly informed, and that 'the government is opportunistic and mainly motivated by seeking re-election. This section builds on work by Lohman (1996), Rogoff and Sibert (1988) and Persson and Tabellini (1990). The correlations between macroeconomic outcomes and the party in office are easier to explain, provided that we are willing to assume policymakers to be motivated by ideology (have preferences over outcomes) and, once in office, prepared to carry out their own agenda. These assumptions lead to a theory of "partisan" political business cycles, which is summarized in subsection 3.2, following the pioneering work by Alesina (1987). 3.1. Opportunistic gooernments

Throughout this section~ we discuss political business cycles in the simple monetary policy model of Section 2, as does most of the literature. But the ideas generally apply to aggregate demand management, including fiscal policy. We deal in turn with "moral

~ Faust and Irons (1999) criticize the literature on partisan cycles in the USA tot failing to control for simultaneity- and omitted-variable bias and argue that the support for a partisan cycle in output is much weaker than what a cursory inspection of the data would suggest. Mishra (1997) uses modern panel data estimation techniques trying to control for similar biases in a panel of 10 OECD countries. He finds strong support for a post-electoral partisan cycle and weaker support for a pre-electoral cycle. J; See, for instance, Fair (1978).

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hazard" and "adverse selection", where the labels refer to the informational asymmetry between voters and the elected policymaker. 3.1.1. Moral hazard in monetary policy

The model in this first subsection is adapted from Lohman (1996), whose work builds on that by Persson and Tabellini (1990) and Holmstrom (1982). Its main insight is that elections aggravate the credibility problem of monetary policy, because they raise the benefit of surprise inflation for the incumbent. Consider a version of the model in subsection 2.4. Voters are rational, have an infinite horizon and are all identical. Their preferences are summarized by a loss function defined over inflation and employment, identical to Equations (2.15) and (2.16) above - and are thus linear in employment. Political candidates have the same objectives, defined over output and inflation, as the voters. In addition, they enjoy being in office: their loss is reduced by K units each period they hold office. Candidates differ in their ability to solve policy problems. One candidate may be particularly able to deal with trade unions, another to deal with an oil-price shock, a third is better able to organize his administration. This competence is reflected in output growth (employment): a more competent candidate brings about higher growth, ceteris paribus. To capture this, we write the Phillips curve exactly as in Equation (2.3), except that we set 0 to zero; we thus consider only e shocks, but change their interpretation. Throughout this section, e captures the competence of the incumbent policymaker, not exogenous supply shocks. We assume that the competence of a specific policymaker follows a simple MA-process: e, = -~h - /~t-1, where ~/ is a mean zero, i.i.d, random variable, with distribution F(.) and density f ( . ) (in this formulation a positive realization of ~/ leads to high output). Competence is assumed to be random, as it depends on the salient policy problems, but partially lasting, as the salient policy problems change slowly and as competence may also depend on talent. Serially correlated competence is the basis of retrospective voting: as competence lasts over time, rational voters are more likely to re-elect an incumbent who brought about a high growth rate. In the very first period of this repeated game, we assume r/0 = 0. The timing in a given period t is as follows. The previous period's policy instrument and inflation & 1 are observed. Wages (and expected inflation) are determined. The policymaker sets the policy instrument for t. Competence is realized and output growtb xt is observed by everybody. Finally, if t is an election year - which happens every other year -~ elections are heldo Two remarks should be made about these assumptions. First, unlike in Section 2, the policymaker does not have any information advantage over private agents: when policy is set, the current competence shock ~/i is unknown to everyone, including the incumbent. The voters do not face an adverse selection problem in that the policymaker cannot deliberately "signal" his competence. This assumption distinguishes the model in Lohman (1996) from the earlier work by Rogoff and

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71 Persson and G. Tabellini

Sibert (1988), Rogoff (1990) and Persson and Tabellini (1990). The voters still face a moral hazard problem: through his monetary policy action, the incumbent can appear better than he really is. The voters understand these incentives, but can do nothing about them, as policy is unobservable. A model o f this kind was first studied by Holmstrom (1982) in a standard principal-agent set-up, where the agent has career concerns, subsection 3.1.3 discusses the alternative, and more complicated, setting when the policymaker is better informed about his own competence than the voters. Second, at the time o f the elections, voters only observe output growth and wages (expected inflation), but not inflation or policy. This assumption is not as bad as it may first appear. Inflation typically lags economic activity. A n d even though monetary policy instruments are immediately and costlessly observed, this information is meaningless unless the voters also observe other relevant information that the policymaker has about the state o f the economy. To properly understand an expansion o f the money supply six months before the elections, voters would have to know the policymaker's forecasts o f money demand and other relevant macroeconomic variables. Assuming that policy itself is unobservable is just a convenient shortcut to keep the voters signal-extraction problem as simple as possible is Finally, we make two other simplifying assumptions. Once voted out o f office, an incumbent can never be reappointed. The opponent in any election is drawn at random from the population and his pre-election competence is not known. Thus the expected competence o f any opponent is zero. 3.1.2.

The equilibrium

First, consider wage-setters. They have the same information as the policymaker and Call thus compute equilibrium policy and perfectly predict inflation. Hence, in equilibrium sr - Jv~ in every period. Next, consider voters. By observing output and knowing the previous period shock to competence, tk 1, they can correctly infer the current competence o f the incumbent by using Equation (2.3): tlt = xt - rlt i 19. The equilibrium voting rule is then immediate. Voters always prefer the policymaker with the highest expected competence. As the opponent has zero expected competence, the voters re-elect the incumbent with probability one i f and only i f xt > r/t--l, as in this c a s e t h > 0 (if xf --= rk 1, we can assume that the voters randomize, as they are indifferent). To an outside econometrician, who observes x~ but not t/l-l,

18 As Lohman (1996) observes, however, this assumption is not easily made consistent with a surprise supply formulation (like in Section 2) where employment (output growth) is determined by realized real wages in a one-sector setting. Lohman instead formulates her model as a Lucas island model where firms observe tile local inflation but not economy-wide inflation (the policy instrument). i9 Voters know that Jr = JU. Also, recall that in period 0 we have, by assumption, tl0 0. Hence in period 1: x I = t/l, and output fully reveals the policymaker's competence. Knowing r/l , in period 2, voters can intbr r/2 from x2 = t12+ th, and so on.

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Political Economics and Macroeconomic Policy

this voting rule appears consistent with retrospective voting: the probability of reelection, Pr(~h i ~< x t ) - F ( x ~ ) , increases with output growth in the election period. Next, consider the policymaker's optimization problem. In @ e l e c t i o n years, he can do nothing to enhance future re-election probability, as competence shocks last only one period and are observed with the same lag. Hence, the equilibrium inflation rate minimizes the static loss in Equation (2.1 6) with respect to ~, subject to Equation (2.3) and taking yL"e as given. As in subsection 2.4, this yields 76 = X. O n - e l e c t i o n years entail different incentives: by raising output growth through unexpected inflation, the incumbent policymaker would increase his election probability. In equilibrium, wagesetters correctly anticipate these incentives, and raise expected inflation accordingly, so that output continues to grow at its natural rate. To formally derive these results, we first compute the equilibrium probability of re-election from the point of view of the incumbent. Recall that he is re-elected iff [xt > t/t_,], or - by Equation (2.3) and our definition of E - iff [tit > gete - Jrt I • When setting policy, the incumbent has not yet observed t/t. His perceived probability of reelection is 1 - Prob(r/t ~< xe _ ~ ) ~ 1 -- F(aVre - a~t), where F(.) is the cumulative distribution of t/. This probability is clearly an increasing function of unexpected inflation. Next, we need some additional notation. Let V R and V N be the expected equilibrium continuation values of reappointment and no reappointment, at the point when policy in an on-election year is chosen. Furthermore, let ~ be equilibrium inflation during on-election years, to be derived below. Simple algebra establishes that: VN _

~2 q_ 6~-g2

2(1 - 62) ,

K(1 + 6)

vR _ VN _

1

~2(1

(3.1)

F(0))'

where 1 F(O) is the equilibrium probability of re-election perceived by the incumbent in all . f u t u r e elections (he recognizes that future inflation surprises are not possible in equilibrium). Intuitively, the expected value of winning the elections - the difference V R - V N - depends on K, the benefits from holding office, but not on the equilibrium policies, ,~ and Yv, since those are the same irrespective of who wins. Note also that these continuation values do not depend on the policymaker's competence, as competence is not known when policy is set. We are now ready to formulate the problem of an incumbent during an on-election year. The incumbent takes expected inflation as given and chooses current inflation to minimize E[L t ]

[½yc 2 - )~(Jv - off) - K + 6(1 - - F ( s r ? - Jvt)) V ~ + 6F(¢c~ - Jrt) V N I .

(3.2) The first two terms in Equation (3.2) capture the expected loss in the current period. The last two terms capture the expected value of future losses, as determined by reappointment or not in the upcoming elections. Taking the first-order condition for a

Persson and G. Tabellini

1420

given ~e and then imposing the equilibrium condition Jr - :re yields the equilibrium inflation rate during on-election years: 6(1 + 6)f(O) = ~q-(~f(O)(VN - v R ) = "~ q - K 1 - 6 2 ( 1 - F(0))'

(3.3)

where the last equality follows from Equation (3.1). The LHS of Equation (3.3) is the marginal cost of inflation. The RHS is the marginal benefit: 3. is the usual benefit of higher output growth~ present at all times; the second term is tile additional on-election-year benefit; higher output growth increases the chance of re-election. This additional benefit of surprise inflation undermines credibility and makes policy more expansionary during on-election years. Thus, equilibrium inflation right after the election is higher, the more the policymaker benefits from holding office, as measured by K, and the more surprise inflation raises the probability of reappoinmlent, as measured by the density f(0). Finally, as the incentives to inflate before elections are perfectly understood by private agents, expected inflation is also higher, and equilibrium output growth is not affected. Thus, the equilibrium is consistent with stylized fact (iv) in the introduction. Elections aggravate the credibility problem, as the incumbent cares even more than usual about output growth. 3.1.3. A d v e r s e s e l e c t i o n

What happens when policy is instead chosen after the incumbent has observed the realization of current competence th, but the sequence of events is otherwise exactly as before? In this setting, studied by Rogoff and Sibert (1988), Rogoff (1990) and Persson and Tabellini (1990), the policymaker enjoys an information advantage over wage-setters, who do not know the realization of t/t when forming expectations. Output fluctuations can still reveal the policymaker's type, but in a less straightforward fashion: voters have to deal with an adverse selection problem, where output can be used as a deliberate signal of the incumbent's competence. To cope with this more intricate problem, we postulate that in each period tl can only take one of two values: ~ > 0 and tl < 0 with probabilities P and (1 - P ) , respectively. As before, ;'/is i.i.d, and has an expected value E(t/) = P ~ + (1 - P)~ = 0. We refer to an incumbent with a high (low) realization of t/as competent (incompetent). The opponent's competence is still unknown to everyone. In the moral hazard model, all incumbent types choose the same action, because e x a n t e they were all identical. Here, a more competent incumbent has stronger incentives to surprise with higher inflation. There are two reasons for this. First, a more competent incumbent cares more about winning the elections, since he knows that he can do a better job than his opponem. Second, a more competent incumbent also has a lower cost of signalling his competence through high output growth. Here, we only sketch the arguments needed to characterize the equilibrium A full derivation is provided by

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Persson and Tabellini (1990, Ch. 5). As a first step, compute the expected net value o f winning the elections:

(1 + 6 ) K V R - V N = A,r/+ 1 - 62(1 - P )

(3.4)

Comparing Equations (3. l) and (3.4), the net value of winning now depends on the competence o f the incumbent: a competent incumbent knows he is more likely to bring about higher future output growth than his opponent, and hence values office more. A incompetent incumbent realizes the converse - and is less eager to be re-elected 2°. The equilibrium inflation rate trades off this net value of winning against the short-run cost o f signalling. Both types want to appear competent and are prepared to artificially boost the economy through unexpected inflation to increase the chances of winning. But the competent type can signal at a lower cost: he needs to inflate less to produce any level o f output growth. As the value o f winning is also higher for the competent type, a "separating equilibrium" generally emerges: rational voters re-elect the incumbent only if output growth exceeds a minimum threshold. The threshold is so high that only a competent incumbent finds it optimal to reach it through unexpected inflation. The incompetent type instead prefers to keep inflation low, knowing he will not be re-elected. Recall that wage-setters have to form inflation expectations without knowing which incumbent type they face. expost, they will always be wrong, even though their ex ante inflation forecast is rational. If the incutnbent is incompetent, he chooses the short-run optimal inflation rate Uv = X in the model), which is lower than expected; hence, the economy goes through a recession. If the incumbent is competent, inflation is higher than expected and the economy booms. How do the conclusions o f this model compare with the stylized facts? Clearly, retrospective voting applies: voters reward pre-electoral booms with reappointment and punish pre-electoral recessions. Output is not systematically higher before elections; on average, inflation is higher just after the elections, but this cycle is weaker than in the moral hazard model, as only the competent type now raises equilibrium inflation. Overall, the predictions of this model are not inconsistent with the stylized facts. Which model is more satisfactory? The moral hazard model has more clear-cut predictions and makes less demanding assumptions about the rationality of the voters. Moreover, multiplicity of equilibria is an additional problem in the adverse selection model. With enough data, one could discriminate between the two models: output

2o We assume that K is sufficiently high that even an incompetent incmnbent values being re-elected. Note also that here the equilibrium probability of winning future elections coincides with P, the probability of a high realization of~t. That is, in equilibrium a competent incumbent is alwaysreappointed and an incompetent one is not. This is a feature of all separating equilibria, that will be discussed below; some equilibria may exist that are not separating, but we neglect them here. Persson m~d Tabellini (1990) contains a more general discussion of this issue.

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volatility before the elections and inflation volatility after the elections are higher only in the adverse selection model. Note that these two models also have different normative implications. With moral hazard, the political cycle is entirely wasteful, whereas it conveys valuable information to voters in the adverse selection model 21 . 3.2. Partisan gooernments

The prior section relied on two crucial assumptions. All voters are alike and policymakers are opportunistic: their main purpose is re-election to enjoy the rents from office. Elections serve only one purpose: to select the most competent policymaker. But voters are not alike, and policymakers are also motivated by their own "ideological" view of what ought to be done and which group o f voters to represent. Therefore, elections serve another goal: they resolve conflicts and aggregate preferences. The policy outcome then hinges on the partisan interests o f the elected government. In monetary policy, and more generally aggregate demand policies, one crucial concern is the relative weight assigned to stabilizing output. For left-wing governments output and employment may weigh more heavily than prices; if so, they will also pursue more expansionary aggregate demand policies than right-wing governments. Elections thus create uncertainty about economic policy. This uncertainty is greater in a two-party system with very polarized parties. It may create a post-electoral cycle in the policy instruments, and a resulting macroeconomic cycle. We now extend our simple monetary policy model to illustrate these ideas, showing how one can account for stylized fact (v) in the introduction. The ideas originate with the work o f Alesina (1987, 1988). 3.2.1. The model

Consider the same model as in the previous section, but suppose that individual voters differ in their relative evaluation o f output and inflation. The preferences o f voter i are still described by an intertemporal loss function like (2.15), but the static loss o f individual i has an idiosyncratic relative weight on output: Li(zc, x) = ~:vl 2

)~ix.

(3.5)

Two political candidates or parties, called D and R, have the same general loss function as the voters, with relative weights )LD > )~R. The D candidate thus cares more

21 Rogoff (1990) shows in a closely related adverse selection model of fiscal policy that society may actually be worse off if one tries to curtail pre-election signalling through, say, a balanced budget amendment (the loss of losing the information may more than outweigh the gain of eliminating the distortions associated with signalling). In a recent paper, however, al Nowaihi and Levine (1998) demonstrate that political cycles can be avoided and social welfare increased by delegating monetary policy to an independent central bmlk faced with an inflation contract of the type discussed in subsection 4.3 below.

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about output growth and less about inflation than the R candidate. The candidates' preferences are known by everybody, but the outcome of the election is uncertain. For simplicity, there are no competence or supply shocks: output growth is described by Equation (2.3), without any e so that x = 0 + ¢c - ¢ce. The timing of events is as follows: Wages are set at the beginning of each period. Elections are held every other period, just after wages are set for that period. Thus, wage contracts last through half the legislature and cmmot be conditioned on the election outcome. Finally, to capture the electoral uncertainty about policy, we assume that candidates can only set policy once in office. In other words, electoral promises are not binding and the policy must be ex post optimal, given the policymaker's pret~rences. 3.2.2. Economic equilibrium

Under these assumptions, voters are perfectly informed and the state of the economy does not reveM anything to them. Hence, policymaker I chooses the same inflation rate in office whether it is an on- or off-election period. Given the assumed timing, it is easy to verify that ¢d = )~I, I = D, R. In off-election periods, this inflation rate is perfectly anticipated by wage-setters, and output grows at the natural rate: x = 0. But just before the elections, wage-setters do not know which policymaker type will win. Suppose they assign probabilities P and (1 - P ) to the events that D and R win. During on-election periods, expected inflation is thus :ve = )~R + p()~o _ )~R). If party R wins, it sets 7c = XR < ¢ce and causes a recession in the first period of office: output is x = -P(3. D -tlR). If D wins, the opposite happens: actual inflation is higher than expected and a boom occurs: x = (1 - P ) ( ) ~ - 3.R). Thus, uncertain election outcomes may cause economic fluctuations. But this political output cycle occurs after the election and is due to different governments having different ideologies, in contrast to the previous model where the political output cycle is due to signalling and occurs beJore elections. interpreting these ideological differences along a left-right political dimension, we get a possible explanation for stylized fact (v). The model predicts that left-wing governments stimulate aggregate demand and cause higher inflation throughout their tenure, while the opposite happens under right-wing governnaents. An election victory of the left brings about a temporary boom just after the elections; victory of the right is instead tbllowed by a recession. These partisan effects are more pronounced under a more polarized political system (i.e. with large differences between tlD and )~R in the model), or more generally if the elections identify a clear winner, like in two-party systems. Alesina and Roubini (1997) argue that these predictions are consistent with the evidence for industrial countries. 3.2.3. Political equilibrium

The partisan model tbcuses on the role of party preterences in elections. Voters anticipate what each party would do if elected, and choose the party closest to their

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17. Pe~5'son and G. Tabellini

ideal point. Thus, the probability that one party or the other wins is entirely determined by fluctuations in the distribution of voters' preferences for the two parties. Moreover, as electoral promises are not binding and voters are rational and forward-looking, the policy platforms of the two candidates do not converge towards the median voter. In the model, voters face a trade-off. If R wins, inflation is lower but output is temporarily lower, while the opposite happens if D wins. How voters evaluate this trade-off depends on their relative weight parameter )~i. Computing the losses to a generic voter after an R and a D victory, respectively, and taking differences, it is easy to verify that voter i strictly pret~rs R to win if

,V < ½(1 + 6)(,~ R + X~)).

(3.6)

The probability (1 ~-P) that R wins is the probability that the relative weight of the median voter ~" satisfies inequality (3.6). Electoral uncertainty thus ultimately relies on the identity of the median voter being unknown, because of random shocks to the voters' preferences or to the participation rate. Ceteris paribus, right-wing governments enjoy an electoral advantage: because all policymakers suffer from an inflation bias, a high value of )~ is a political handicap 22. Inequality (3.6) implies that a voter whose ideological view is right in between R and D [that is, such that ,~i _ ½(3j~+ )j))] votes for the right-wing candidate. This suggests that an incumbent can act strategically to increase its chances of re-election. Specifically, a right-wing government can make its left-wing opponent less appealing to the voters by increasing the equilibrium inflation bias. This could be done by reducing wage indexation, by issuing nominal debt (to raise the benefits of surprise inflation), or by creating more monetary policy discretion, via a less disciplining exchange rate regime or weaker legislation regarding central bank independence, or even by current monetary policy if unemployment is serially correlated. These ideas have their roots in the literature on strategic public debt policy, further discussed in Section 6 below. On the normative side, electoral uncertainty and policy volatility are inefficient, and voters would be better off ex-ante by electing a middle-of-the-road government that enacted an intermediate policy. But in the assumed two-party system, there is no way of eliminating this unnecessary volatility. The stark result that there is no convergence to the median position, is weakened under two circumstances. One, studied by Alesina and Cukierwian (1988), is uncertainty about the policymaker type. Then each candidate has an incentive to appear more moderate, so as to raise the probability of winning the next election. The second, studied by Alesina (1987), is repeated interactions. Then the two candidates can sustain self-enforcing cooperative agreements: a deviation from a moderate policy would be punished by the opponent who also reverts to more extreme behavior once in office. Alternatively, cooperation could be enforced by the v o t e r s

22 This observation is related to the argument about the benefits of appointing a conservative central banker discussed in subsection 4.3 below.

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punishing a government that enacted extreme policies. Naturally, there is the same problem of multiple equilibria as in the reputational equilibria of subsection 2.4. Institutional checks and balances can also moderate policy extremism. In a presidential system, for instance, actual policies often result from a compromise between the legislature and the executive. The model of partisan policymakers suggests that the voters would take advantage of these institutional checks and balances to moderate the behavior of the majorities. Alesina and Rosenthal (1995) argue that the voters' attempt to moderate policy extremism can explain split ticket voting in Presidential systems (i.e., the same individuals voting for different parties in Presidential and Congressional elections) and the mid-term election cycle (the party who won the last general elections loses the interim election). 3.3. N o t e s on the litetz~ture

Alesina and Roubini (1997) present existing and new evidence on electoral cycles in OECD countries. They also survey the theoretical work on political cycles in aggregate demand policy. Alesina and Rosenthal (1995) focus on the United States in particular. The evidence for a partisan cycle is scrutinized by Faust and Irons (1999) (for the USA) and by Mishra (1997) (for a panel of OECD countries). Fair (1978), Fiorina (1981) and Lewis-Beck (1988) discuss the evidence on retrospective voting in the USA and elsewhere. The first models of political business cycles with opportunistic government are due to Nordhaus (1975) and Lindbeck (1976). The first theory of a partisan political cycle is due to Hibbs (1977). All these papers relied on the assumption that private agents are backward-looking, both in their economic and voting decisions. The model of an opportunistic govermnent and adverse selection with rational voters, summarized in subsection 3.1.3, was developed by Rogoff and Sibert (1988) in the case of fiscal policy, and adapted to monetary policy by Persson and Tabellini (1990). Rogoff (1990) generalized the fiscal policy results to two-dimensional signalling by the incumbent. Ito (1990) and Terrones (1989) considered political systems in which the election date is endogenous and chosen by the incumbent himself, after having observed his own competence. The moral hazard model studied in subsection 3.1.1 is very similar to a principalagent problem with career concerns developed by Holmstrom (1982). It was studied in the context of monetary policy by Lohman (1996) and, in a somewhat different set-up, by Milesi-Ferretti (1995b). Ferejohn (1986) and Barro (1973) study a more abstract moral hazard problem where an incumbent is disciplined by the voters through the implicit reward of reappointment. The model of partisan politics with rational voters is due to Alesina (1987, 1988). This model is extended by Alesina et al. (1993) and by Alesina and Rosenthal (1995) to allow for ideological parties who also differ in their competence. Milesi-Ferretti (1994) discusses how a right-wing incumbent might increase his popularity by reducing the extent of wage indexation; similar points with regard to nominal debt and the choice of

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T. Persson and G. Tabellini

an exchange rate regime were investigated by Milesi-Ferretti (1995a,b). Jonsson (1995) discusses strategic manipulation of monetary policy for political purposes when there is autoregression in employment. Uncertainty about the policymaker's ideological type is considered in Alesina and Cukierman (1988). The role of moderating elections, in theory and in the US data, is studied by Alesina and Rosenthal (1995).

4. Institutions and incentives

Theoretical work on institutions and incentives in monetary policy has developed over the last ten years. Below, we give a selective account of key ideas in that development. We do not follow the actual course of the literature over time, but we exploit what, in retrospect, appear to be the logical links between different ideas. The main issue is how the design of monetary institutions can remedy the incentive problems discussed in Sections 2 and 3. Even though we focus on lack of credibility, some results extend to the political distortions of Section 3. The ideas in this section rely on a common premise: institutions "matter". A constitutional or institution-design stage lays down some fundamental aspects of the rules of the game, which cannot be easily changed. Once an independent central bank has been set up, an international agreement over the exchange rate has been signed, or an inflation target has been explicitly assigned to the central bank, it has some such staying power, in the sense that changing the institution e x p o s t is costly or takes time. This premise is questioned by some critics [in particular by McCallum (t996) and Posen (1993)], who argue that some of the proposed institutional remedies discussed in this section "do not fix the dynamic inconsistency" that is at the core of this literature, they "merely relocate it". The criticism is correct, in that the institutions are assumed to enforce a policy which is e x p o s t suboptimal from society's (or the incumbent government) point of view. Hence, there is always a temptation to renege on the institution. But the staying power of institutions need not be very long to be effective. In the model that dominates the literature, what is needed is a high cost for changing the institution within the time horizon of existing nominal contracts. Beyond the contracting horizon, expectations would reflect any constitutional change, which removes the distinction between e x p o s t and e x a n t e optimality. As already remarked in subsection 2.4, the cost of suddenly changing the institution could also be a loss of reputation. By focusing political attention on specific issues and commitments, institutions alert private individuals if govermnents explicitly renege on their promises. To pick up the thread from Section 2, one purpose of successful monetary institutions is to make monetary policy a bit more like patent legislation. In our view, real-world monetary institutions do have such staying power. They can be changed, but the procedure for changing them often entails delays and negotiations between different parties or groups that were purposefully created when the institution was designed. We thus think that the premise of the literature is generally appropriate. But it would be more convincing to derive

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the institutional inertia as the result o f a well-specified non-cooperative strategic interaction between different actors, something the literature - so far - has failed to do 23. 4.1. Fixed exchange rates." simple rules and escape clauses

Pegging the value o f the exchange rate to gold or to some reserve currency has been a common device, particularly in smaller countries, to anchor inflationary expectations, discipline domestic price and wage setting, or prevent political interference in monetary policy. Such attempts have met with mixed success. A m o n g the industrialized countries during the post-war period, the Bretton Woods system and (part of) the European Exchange Rate Mechanism (ERM) were reasonably successful. But unilateral attempts o f some European countries to peg their exchange rates in the 1970s and 1980s often ended up in failure: with lack o f credibility generating a spiral of repeated devaluations, domestic wages and prices running ahead of foreign inflation. What can explain such differences? To shed light on this question, let us study a slight modification of the static model in Section 2. A small open economy is specialized in the production o f a single good which is also produced by the rest o f the world. The central bank controls 37 through the exchange rate, given a foreign inflation rate denoted 37*. The rest of the model, including the expectations-augmented Phillips curve (2.3), the rational-expectations assumption, the objective function o f the policy maker (2.6), and the timing o f events are as in subsection 2.2 or 2.3; except that we assume not only 0, but also 37* to be known when wages are set (7c° are formed). Note that 37* denotes both foreign and target inflation, as pegging the exchange rate to a low-inflation currency can be seen as an explicit or implicit attempt to target a low inflation rate. Under discretion, the model is formally identical to that in subsection 2.3 and thus generates the inflation and employment outcomes in Equations (2.12) and (2.14). As E(37) > 37*, the model is consistent with the idea o f a devaluation spiral, fuelled by low credibility among wage-setters and a devaluing exchange rate. Consider now the following institution. At stage (0), society commits to a simple rule o f holding the exchange rate fixed, or of letting it depreciate at a fixed rate k. There is commitment, in the sense that the rate o f depreciation k is chosen at the start of each period, and cannot be abandoned until one period later. The rule is simple, because it cannot incorporate any contingencies. In practice, simple commitments of this kind can be enforced by multilateral agreements such as the Bretton Woods system or the ERM, where the short-rnn interests of other countries are hurt if one country devalues. Policy commitments to complex contingent rules would require implausible assumptions on verifiability and foresight.

23 Jensen (1997) in tact studies a simple model related to the contracting solution to be studied in subsection 4.3 - where the government can renege on the initial institution at a continuous (nonlump sum) cost. In this setting institution design generally improves credibility, but cannot remove the credibility problem cmnpletely.

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What is the optimal rule? As the depreciation rate is known in advance of wage setting and expectation formation and is not contingent on the e shocks, it is neutral with respect to real variables. Hence, the optimal rule has k = 0. Under this simplicity constraint, a fixed exchange rate is thus the optimal commitment. This results in the following equilibrium outcome: ~s = jr., x s _ 0 - e, where the S superscript stands for simple rule. Is the simple rule better than discretion? It depends. The rule brings about lower average inflation, but employment is more variable. A formal comparison of the two regimes can be made by substituting Equations (2.12)-(2.14), and the previous expression for ~s and x s, into Equation (2.6) and taking expectations o f the difference in their payoffs. Recalling that E(O) = 0, this gives

E[L(~t)'xD)]-E[L(~S'xS)] = 2)'2- {E(x*)2 + o~ - -(1- ~ 2 ; ).

J

The first two "terms on the RHS capture the benefit of credibility under the simple rule the sum of the squared average inflation bias and its variance. The last term is the loss from not being able to stabilize employment. A simple rule is better than discretion if the gain o f credibility is larger than the loss o f stabilization policies. This trade-off between credibility and flexibility is a recurrent theme in the literature on institution design. The benefit o f the simple rule is further enhanced if, under discretion, monetary policy is also distorted by the electoral incentives discussed in Section 3. Another monetary regime, often advocated though harder to enforce, is a commitmerit to a k% money growth rule. Suppose we add a simple quantity-theory equation to our model, where money demand depends on output growth (or employment), so that + x = m + v. The policy instrument is m, like in Section 2. Under a simple money growth rule, velocity shocks v destabilize employment and prices. A simple exchange rate peg, on the other hand, automatically offsets velocity shocks. But a money supply rule might better stabilize supply shocks; as these destabilize both output and prices, the price response acts as an automatic output stabilizer. In the limit, if ~, = 1, a k% money rule mimics the optimal policy response to a supply shock 24. The assumption that an exchange rate peg, once announced, cannot be abandoned until next period, may be too stark. Multilateral exchange rate agreements often have escape ,clauses: European countries have temporarily left the ERM or realigned their central parities when exceptional circumstances made it difficult to keep the exchange rate within the band. An escape clause can be thought o f as follows. Define normal times as a range of possible realizations o f the unobservable supply shock: e C [eL(o), EU(o)]. Inside this interval, the central bank remains committed to the simple rule. During exceptional times, defined by the complementary event, an 24 A literature dating back to the 1970s has studied the choice between alternative rules in richer models - for surveys, see Genberg (t989) and Flood and Mussa (1994). Recent contributions to the comparison of exchange rate versus money based stabilizations of inflation are surveyed by Calvo and V6gh (1999).

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escape clause is invoked. The central bank abandons the simple rule and pursues a discretionary (ex p o s t optimal) policy, given inflationary expectations. At normal times, the exchange rate is fixed and output is destabilized by (small) supply shocks. There is also a p e s o problem: as the escape clause will be invoked with positive probability, expected inflation is always positive. Normal times with actual inflation at zero, thus has some unexpected deflation and employment below the natural rate. At exceptional times, on the other hand, the central bank abandons the rule and sets an ex p o s t optimal policy to stabilize (unusually large) supply shocks. But less inflation is now needed compared to the regime with pure discretion, because expected inflation is lower. Hence, a simple rule with an escape clause strikes a better balance between credibility and flexibility, by allowing for flexibility when it is most needed. Indeed, Flood and Isard (1989) have shown that a rule with an escape clause always dominates pure discretion and, if supply shocks are sufficiently volatile, it also dominates a simple rule. As Obstfeld (1997a) has stressed, however, escape-clause regimes can give rise to multiple equilibria. Intuitively, expected inflation depends on how often the escape clause is invoked. At the same time, the e x p o s t decision whether or not to invoke the escape clause depends on expected inflation. As higher inflationary expectations make it more tempting to abandon the rule, high inflationary expectations may become self-fulfilling. How can a regime with an escape clause be implemented? In a multilateral exchange rate regime where realignments have to be approved by an international body, the bounds would depend on the bargaining power of the devaluing (revaluing) country, which, in turn, would depend on the details of the institution (the prospective sanctions, the procedure for making the decisions, etc.). In a domestic context, we could suppose that at the institution design stage (before 0 is realized) society sets a pair of fixed costs [ct'(0), cU(0)] incurred whenever the escape clause is invoked. These costs would capture the public image loss for the central banker from not fulfilling his mandate, or the costs for the government of overriding a central bank committed to the simple rule. They would implicitly define bounds eL(0) and eu(0), that leave the central bank indifferent between sticking to the simple rule and bearing the cost of no stabilizing policies, or paying tile cost and invoking the escape clause, in neither of these interpretations it is reasonable to assume that the costs could be calibrated very carefully ex ante. For instance, costs may have to be state-dependent or symmetric; cL(O) = c j~, cU(O) = c ~j or c u = c1" = c. Such plausible constraints would prevent society from reaping the full value of the escape-clause regime, but still generally improve on the discretionary outcome. Flood and Marion (1997) point out that an important consideration behind the ex ante choice of c might be to prevent multiple equilibria. 4.2. Central b a n k independence

The first example of strategic delegation in monetary policy is the independent and conservative central banker, suggested by Rogoff (1985). To illustrate the idea in our simple model, we continue to make a formal distinction between society and the central bank. Society's true preferences take the form (2.6). At the institution design stage (0)

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o f the model, society appoints a central banker. The central banker is independent: once appointed, society can no longer interfere with his decisions. (Towards the end o f this subsection, we ask how reasonable this assumption really is.) Prospective central bankers have loss functions o f the form (2.6), but differ in their personal values of)L 25. The appointment thus boils down to the choice o f a parameter, say )~. The private sector observes )~B and forms its inflationary expectations accordingly. The appointed central banker sets monetary policy freely at stage (4), according to his own private preferences. As already discussed in subsection 2.3, this choice gives the equilibrium outcomes

XB ~(2, B, 0, e) - :v* + ,~B(x* -- 0) + 1 ~ - - ~ E, 1

x(,!, B, O, e) -- 0 - 1 + ~,R e. Note that the outcomes do not only depend on the realized shocks, but also on the bankers' preferences. These expressions illustrate a basic trade-off in the strategic delegation: a central banker more hawkish on inflation, i.e. someone with a lower 2,B, has more credibility in keeping inflation low, but is less willing to stabilize supply shocks. To formally study delegation, consider society's expected loss function, as a function of the central banker type: E[L(~B)] = 1E[(x()~ B, O, e ) - go*) 2 + ~ ( x ( ) f , O, e) -x*)21,

(4.1)

where the expectation is tal{en over 0 and E, for any 3~~. Next, insert the expressions for equilibrium inflation and employment into Equation (4.1) and take expectations. The derivative of the resulting expression with regard to At is dE[L(Jf)] d)~~

)~(x .2 + a0) + ( ) f - "~)(1 +a~)~B)3 '

(4.2)

The first term is the expected credibility loss of choosing a central banker with a higher ,~B. The second term measures the expected stabilization gain. The optimal appointment involves setting this expression equal to zero. Evaluating the derivative (4:2) at the extreme points implies that ~, > 3,~ > 0 26 Thus, by optimally choosing an independent central banker, society strikes a different compromise between credibility and flexibility than in the fixed exchange rate regime. 25 This suggests a heterogeneity in the population with regard to the relative weight placed on inflation versus employment, which ore formal model abstracts from. As discussed in Section 3, however, such heterogeneity can be formally introduced in the model without any difficulties. Alesina and Grilli (1992) indeed show that strategic delegation of the type to be discussed below would take place endogenously in a model where heterogeneous voters elect the central banker directly. 26 Equation (4.7) is a ~burth-order equation in ,~B, which is difficult to solve. But as the derivative is negative at )f = 0, positive for all 2~ > 2~, and the second-order condition is fulfilled for any ,~e in the interval (0, ,~), we kaaowthat the solution must be inside the interval (0,)~).

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But it is still a compromise: it is optimal to appoint a central banker who is more conservative on inflation than society itself (to address the inflation bias), but still not ultraconservative (to preserve some of the benefits of stabilization). Note also that fluctuations in the inflation bias arising from observable 0 shocks remain. If 3~8 could be chosen after the realization of 0, society would want to meet a more serious incentive problem - a smaller 0 - with a more hawkish central banker - a smaller XB. In practice, the extent of the incentive problem is serially correlated over time, so that making appointments at discrete points is probably a good way of dealing with this problem. Like in the escape-clause model, we could give society or government the option of overriding the central bank decision in exceptional circumstances. The override option could involve firing the central banker, introducing ad-hoc legislation or an explicit override clause under a prespecified procedure (the latter arrangement is indeed observed in the central bank legislation of many countries). An implicit escape clause mitigates the ex p o s t suboptimality of central bank behavior, inducing even a conservative central banker to stabilize extreme supply shocks to the same extent as society would do 27. This option should not be overemphasized, however; escape clauses can hardly be optimally designed ex ante. Moreover, as already noted in the introduction, if the government has an override option, why does it not use it all the time to get the policy it wants ex p o s t ? We may also note that having an independent central bank also protects society from the distortions introduced by the electoral business cycles discussed in Section 3. In this case, however, only independence is required, and no special emphasis on inflation relative to other macroeconomic goals. Waller (1989) was probably first in formulating a model of central bank independence under partisan politics 2s. Waller and Walsh (1996) study the optimal term length of central bankers in the context of partisan cycles, where society's objectives may change over time. The literal interpretation that society picks a central banker type is not very satisfactory: individual priorities or attitudes towards inflation and employment are often unknown and vaguely defined. Moreover, individual attitudes are probably less important than the general character and tradition of the institution itself. A better interpretation is that, at the constitutional stage, society drafts a central bank statute spelling out the "mission" of the institution. Thus, the parameter ,~ reflects the priority assigned to price stability relative to other macroeconomic goals. As instrument independence is a necessary condition for delegation to work, we should expect such a strategic setting of goals to work better if combined with institutional and legislative features, lending independence to the central bank and shielding it from short-run political pressures. In this interpretation, the model yields observable implications: countries or time periods in which the central bank statute gives priority to price stability and protects central bank independence should have lower average inflation and higher employmem 27 This is indeed proved by Lohman (1992). 28 Fratianni et al. (1997) formally analyze the role of central bank independence in the absence of a traditional credibility problem, but in the presence of explicit electoral incentives.

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(or output) volatility - since if )~B < )~, stabilization policies are pursued less vigorously. Moreover, electoral business cycles in inflation or output should be less pronounced with greater central bank independence. By now, a number o f studies have constructed measures o f central bank independence based on central bank statutes, also taking the priority given to the goal o f price stability into account 29. Crosscountry data for industrial countries show a strong negative correlation between those measures of central bank independence and inflation, but no correlation between output or employment volatility and central bank independence. Thus, central bank independence seems to be a free lunch: it reduces average inflation, at no real cost. Different interpretations o f this result have been suggested. Alesina and Gatti (1996) note that an independent central bank could reduce electorally induced output volatility, as would be predicted by the models of Section 3, and Lippi (1998) provides evidence that could support this proposition. Posen (1993, 1995) argues that the cross-country correlation between central bank independence and lower inflation is not causal, and suggests that both may be induced by society's underlying preferences for low and stable inflation. Finally, Rogoff (1985) also suggests another interpretation o f the model: the conservative central banker might be interpreted as a targeting scheme supported by a set of punishments and rewards. Having a conservative central banker is formally equivalent to having an additional term in inflation in his loss function, 0 ( B -- X)(J'g -- 3"g*) 2, where Z ~ > Z. The central banker thus has the same objective function as everybody else, but faces additional sanctions if actual inflation exceeds the target. In this simple model, a conservative central banker is thus equivalent to an inflation target 3o. This alternative interpretation has been picked up by a more recent literature, asking which targets are more efficient, and more generally how a targeting scheme should be designed to optimally shape the central bank ex-post incentives. 4.3. Inflation targei~ and inflation contracts'

Central banks have traditionally operated with intermediate targets, like money or the exchange rate. in the 1990s, several central banks started to target inflation: whereas some central banks imposed the procedure on themselves, the transition has been mandated by some governments 31. Such targeting schemes have recently been studied 29 See in particular Bade and Parkin (1988), Grilli et al. (1991), Alesina and Summers (1993), Cukierman (1992) and Eijffmger and Schaling (1993). 30 Rogoff (1985) compares an inflation target to other nominal targets, such as money and nominal income. He shows that strategic concerns of the type considercd here, can indeed overturn the ranldng of intermediate targets, based on parameter values and relative variance of shocks, in the traditional non-strategic literature on monetary targeting. 31 A substantial literature discusses real-world inflation targeting. See in particular Leiderman and Svensson (t995), Haldane (1995), McCallum (I996), Mishkin and Posen (1997) and Ahneida and Goodhart (1996). In practice, an inflation target means that the central bank is using its own inflation Jorecast as ml intermediate target; see Svensson (1997b) for instance

Ch. 22." Political Economics and Macroeconomic Policy

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from the point of view of the theory of optimal contracts. Society, or whoever is the principal of the central bank, presents its agent - the central b a n k with punisbments or rewards conditional on its performance. The question is what constitutes an optimal contract, and what kind of behavior it induces on the agent. We illustrate the basic ideas of this recent literature in our simple model of credibility. The optimal contract can easily be modified so as to implement the optimal monetary policy even in the presence of political distortions, but we do not pursue this extension. Much of the discussion in this subsection is based on results in Persson and Tabellini (1993) and Walsh (1995a). The central bank holds the same quadratic preferences as everybody in society. It operates under discretion, setting policy at stage (4). At the constitutional stage (0), the government formulates a publicly observable complete contract for the central bank which formulates state-contingent punishments (or rewards) conditional on realized inflation: P(2C; O, e) -po(O, e) +Pl (0, e) ~ + ½P2(O, e) at;2.

(4.3)

Our goal is to optimally set the terms pi(O, 0, i = 0, l, 2, that define the contract. We only include up to second-order terms in the contract, since that is sufficient for our purposes. Units are normalized so that, at stage (4), the central bank minimizes the sum of the loss function and its punishment with respect to inflation: L(zc, x)+ P(jr; 0, e). Going through the same steps as in subsection 2.3 (deriving the central bank optimum condition for inflation, given the contract and expected inflation, solving for rationally expected inflation, and combining the resulting expressions), we get the equilibrium condition ( l + p 2 ( 0 , e))jr

,~(1 + p2(0, e)) Jr* pj(O,e)+X(x*--O)+ l + • + p 2 ( O , e ) e .

(4.4)

The benchmark optimum in Equation (2.11) can be implemented by settingp2(0, e) = 0 and pl(O, e) = pl(O) = X(x* - 0). Since the constant po(O, e) does not afl?ct any of the central bank marginal incentives, it can be set freely - for instance, it can be set negative enough that the participation constraint is satisfied: the central bank leadership finds it attractive enough in expected terms to take on the job. Thus a remarkably simple linear performance contract - imposing a linear penalty on inflation - removes the inflation bias completely. The credibility-flexibility trade-off has disappeared: average inflation is brought down to the target, at no cost of output volatility. Once the simple contract has been formulated, the central bank has the right incentives to implement ex ante optimal policy. Note that the optimal contract is not conditional on e; this is because the marginal incentives to stabilize the economy are correct under discretion (in the terminology of Section 2, there is an inflation bias but no stabilization bias). But the slope of the penalty for inflation is conditional on 0; as the incentive to inflate the economy also varies linearly with 0. To see the intuition for this result, think about the punishment for inflation as a Pigovian corrective tax. As

T. Persson and Ca. Tabellini

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discussed in subsection 2.3, the distortion we want to address is that the central bank does not internalize the effect o f its policy on inflationary expectations, when acting expost. Since expected inflation E ( ~ I 0) is a linear projection o f Jr, a linear penalty for inflation makes the central bank correctly internalize the marginal cost o f its policy 32. To see this formally, substitute Equation (2.3) into the objective function (2.6) and calculate the equilibrium marginal cost o f expected inflation in state 0 as:

dE[L(~,x) l O] d~ e

= ,Vx* - O) =p~(O, e).

That there is no credibility-flexibility trade-off with an optimal contract contrasts with the previous subsection, where - under a quadratic inflation target - lower expected inflation was associated with distorted stabilization policy. A quadratic inflation target is thus not an optimal contract. The Rogoff (1985) targeting solution, discussed at the end o f the last section, is equivalent to an inflation contract with 1 B P2 = (X ~ - 2'), Pl = (2"B _ 2")st*, and P0 = ~(X - 2")(zc*)2. This clearly gives the central banker incorrect marginal incentives. Nevertheless, the optimal linear inflation contract can be reinterpreted as similar to an inflation target. As the intercept can be set freely, we can write the optimal contract as

P ( x ; O)

=~o + pL ( O)(x - zc*);

(4.5)

the central banker is punished linearly, but only for upward deviations from society's preferred inflation rate. Walsh (1995b) shows that the marginal penalty on inflation can be interpreted as resulting from an arrangement where the governor o f the central bank faces a probability o f being fired which increases linearly in inflation. Such an arrangement resembles the Price Targeting Agreement in force in New Zealand since 1990. Other looser interpretations would be to associate the penalty with altered central-bank legislation, a lower central-bank budget, or a loss o f prestige of the institution and the individuals heading it, for failing to deliver on a publicly assigned or self-imposed "mission". Naturally, it may be impossible to specify the penalty exactly as a linear function o f inflation. But to approximate an optimal incentive scheme, the punishment for upward deviations from an inflation target should not increase too rapidly with the size of the deviation. In fact, if the central bank is risk averse, the optimal contract entails a diminishing marginal penalty on inflation (to reintroduce linearity in the incentive scheme). Svensson (1997a) has proposed an alternative interpretation o f inflation targets, related to - but somewhat different from - the optimal performance contract interpretation. In his formulation the central bank is not assumed to have any generic

32 Indeed, tinearity of the optimal contract is preserved for any general loss ~unctions~ and not just for the quadratic one.

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preferences over macroeconomic outcomes; instead society can impose a specific quadratic objective function on the central bank o f the form in Equation (2.6). Suppose that society manages to assign a loss function with a lower goal for inflation, say avB(0) rather than ~*, to the central bank. Then the optimal central bank goal for inflation is ~ ( 0 ) = 0c* - ,a.(x* - 0). Pursuing this goal would eliminate the inflation bias, without giving up on stabilization policies. That is, the lower inflation goal is equivalent to our previous setting with a central bank minimizing L + P, where L is society's loss function and P is an inflation contract o f the form in Equation (4.3), with parameters p2 = 0, p~ = )~(x* - 0) and P0 = ½[)~(x* - 0) 2 - 2~*)~(x* - 0)]. This representation of an inflation target suggests an alternative explanation for the empirical observation discussed in the previous subsection. A lower zce is associated with lower inflation but not with higher output variability, as in the data. It is not without problems to associate this scheme with real-world institutions, however. Suppose that the optimal inflation rate for society, sT*, is about 2%, and that the average inflation bias, )~(x* - 0), is about 5% (not an outrageous number, given the recent monetary history of many European countries). The central bank should then be given an inflation goal, S~(0), o f - 3 % . But in equilibrium, tile central bank would not take any action to bring inflation below 2%, which may present it with some problems when explaining its policy to the public. A second, more important, problem relates to enforcement. How can we ensure that the central bank accepts to evaluate the costs and benefits o f the policy according to the imposed objective function, rather than according to society's preferences? A plausible answer is that the central bank is held accountable for its actions and that there is a performance based scheme o f rewards or punishments that makes the central bank behave in the desired fashion. But then we are back to the performance contract interpretation o f inflation targets explicitly suggested by Equation (4.5) 33 A natural question is whether to base the contract on inflation or on other measures of performance, such as money, the exchange rate, or nominal income. Persson and Tabellini (1993) show that if the central bank is risk neutral, if the constraints faced by the central bank (i.e. the behavioral equations o f the economy) are linear, as assumed so far, and if the marginal penalties under the contract can be contingent on 0, there is an equivalence result: alternative targets yield the same equilibrium. With relevant non-linearities, however, an inflation-based contract is simpler; to replicate the ex ante optimal policy with other measures o f performance, the contract must be contingent on a larger set of variables, such as shocks to money demand, or to the money multiplier. In this sense, an inflation target dominates targeting schemes based on other nominal variables: simplicity implies enhanced accountability and thus easier enforcement. Intuitively, the whole purpose of optimal contracts is to remove an inflation bias. This is most easily done by means o f a direct penalty on inflation, rather than in a

3~ The best assignment if society could really freely impose an objective f~nction on CB, would be to set x*(O) = 0, thereby eliminating the inflation bias completely.

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more rotmd about way, by targeting other variables that are only loosely related to inflation. What happens if the contract cannot be made state-contingent, so that P0, pl and p2 in Equation (4.3) each have to be constant across 0? This question and its answer are related to the problem in Herrendorf and Lockwood (1997), who study delegation in a model with observable shocks, and to the problem in Beetsma and Jensen (1998), who study delegation via an optimal contract when the central banker's preferences are tmcertain e x ante. To find the optimal incomplete contract in this case, we first plug the solution for Jr in Equation (4.4) with the slope coefficients constant, as well as the associated solution for x, namely x= 0-

1 +P2

1 +~+P2

E,

into the quadratic objective function. We then take expectations o f the resulting expression over 0 and e and maximize with regard to Pl and P2. After tedious but straightforward algebra, we can write the optimality conditions as ~. /!)1 -- ~x* --P2

,

(l +/92) 3 -- a2 P2 (1 + ~t,+p2) 3 02.

(4.6)

These conditions are both intuitive. It is easy to show that the first condition says E(3r) = 3:*: unconditionally expected inflation should coincide with society's preferred rate o f inflation. The second condition says that the coefficient on the quadratic term in the contract should be a positive hacreasing function o f the relative importance o f observable to unobservable shocks (the left-hand side is increasing in p2). Thus, when fluctuations in the observable incentives to inflate cannot be handled by a statecontingent linear punishment, the constrained optimum gives up a little bit on (firstbest) stabilization in order to diminish the costly fluctuations in Jr. Asp~ contains a term in Jr*, we can rewrite the optimal non-state contingent contract as

P(~c) - p o + P l ~ +p2(a: - ~.)2, with P2 given by Equation (4.6) and Pl - ( ~,x* +P2g~) • According to this expression, the central bank should be targeting society's preferred rate of inflation and face an extra reward for low inflation. It is perhaps not too far-fetched to interpret the inflation targeting schemes enacted in the 1990s in many countries as an instance o f this arrangement 34. The simple contracting model discussed here has been extended in several directions. I f some shocks are observable, but not verifiable and hence not contractible, the central :~ In the model of Beetsma and Jenscn (1998) with uncertain CB pre~brences, the optimal inflation target may instead be above society's target.

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bank can be required to report the value of these shocks. Persson and Tabellini (1993) show that the optimal contract is related both to the inflation outcome and to the central bank announcement; it is structured in such a way as to induce optimal behavior as well as truth telling. Policy announcements matter not because they convey information to the private sector (that already observes everything), but because they change central bank incentives, by providing a benchmark against which performance can be assessed e x p o s t 35. Walsh (1995a) shows that the optimal contract can also handle costly effort by the central bank. Dolado et al. (1994) as well as Persson and Tabellini (1996) extend the contract approach to the international policy coordination problems that arise when central banks fail to internalize the international externalities of their monetary policies, al Nowaihi and Levine (1998) show how delegation via inflation contracts may eliminate political monetary cycles. McCallum (1996) and others have argued that the contracting solution makes little sense, because it just replaces one commitment problem with another: who enforces the optimal contract? This question reintroduces the general question about institutional reforms raised at the beginning of this section, although it might apply more forcefully to a more ambitious incentive scheme such as the optimal contract. As in the case of the fixed-exchange rate regimes of subsection 4.1, enforcement is more likely if agents have heterogenous ex p o s t benefits of inflation and agents hurt by inflation are given a prominent role in the enforcement. Interestingly, Faust (1996) argues that a desire to balance redistributive interests for and against surprise inflation was a clear objective in the mind of the framers of the Federal Reserve. As stated before, we also do believe that changing institutions takes time. The public image of a policymaker who emphatically announces an inflation target, would be severely tarnished, if he explicitly abandoned it shortly afterwards. This is one of the main reasons why in the real world inflation targets can alter the ex p o s t incentives of policymakers. The emphasis of the contracting solution on accountability and transparency is helpful for thinking more clearly about these issues, and about the trade-offs that emerge if the reward scheme cannot be perfectly tailored to mimic the optimal contract. We cannot demand much more than that from simple theoretical models. But where the literature should go next is probably not to other variations of the objective function in the simple linear-quadratic problem. Instead it would be desirable to model the different steps and the incentives in the enforcement procedure as a well-defined extensive-form, non-cooperative game. 4.4. Notes on the literatuFe

The literature on institutions in monetary policy has been surveyed in textbook fbrm by Persson and Tabeltini (1990), Cukierman (1992) and Schaling (1995).

3s In the reputationat model of Cukierman and Liviatan (1991), by contrast, atmouncements matter because they convey information about the policymaker'stype.

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Z Pelwson and (7. Tabellini

The formal theoretical literature on central bank independence starts with Rogoff (1985), whose analysis of the conservative central banker is the basis of the model in subsection 4.3, although the treatment of society's problem as a principal agent problem is suggested by Barro and Gordon (1983b) in an anticipatory footnote. Giavazzi and Pagano (1988) discuss the commitment ability in multilateral fixed exchange rate regimes, although their analysis is carried out in a richer dynamic framework than the simple model of subsection 4.1. Flood and Isard (1989) introduce the formal analysis of the rules with escape clauses. Lohman (1992) discusses the implementation of an escape clause, by costly government override, in a monetary policy model that also includes delegation to a Rogoff-type central banker. Obstfeld (1997a) applies an escape-clause model in his analysis of realignments within the ERM, emphasizing the possibility of multiple equilibria. Bordo and Kydland (1995) argue that the classical gold standard worked like a rule with escape clauses. Flood and Marion (1997) include an insightful discussion of escape-clause models and speculative attacks. The optimal contracting solution to the credibility problem, in subsection 4.3, was developed by Walsh (1995a) and by Persson and Tabellini (1993), and was further extended by Beetsma and Jensen (1998) and by Herrendorf and Lockwood (1997). Insightful recent general discussions about the appropriate institutional framework for monetary policy can be found in Fischer (1995), McCallum (1996) and Goodhart and Vinals (1994). Cukierman and Lippi (1998) study theoretically and empirically how the optimal central banking arrangement varies with the structure of labor markets. The early real-world experience with inflation targeting is surveyed in Leiderman and Svensson (1995). More recent surveys include Haldane (1995) and Mishkin and Posen (1996). A number of studies - including Bade and Parkin (1988), Alesina (1988), Grilli et al. (199 l), Cukierman (1992) and Eijffinger and Schaling (1993) - have developed empirical measures of central bank independence and studied their relation to inflation and other macroeconomic outcomes in a cross-section of countries during the last few decades. Capie et al. (1994) study historical evidence on inflation before and after major central bank reforms in twelve countries since the end of the 19th century. Jonsson (1997) uses pooled time-series and cross-section data from the OECD countries since the early 1960s and finds that the negative relation between central bank independence and inflation is robust to the control of a number of other institutional and economic variables. Posen (1993) criticizes this kind of finding and argues that it is caused by an omitted variable problem, the causal variable for both independence and inflation being the resistance against inflation in the financial community. A survey of empirical studies is found in Eijffinger and de ttaan (1996). Each subsection above refers to additional relevant studies on specific topics.

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Part B. Fiscal Policy This part o f the chapter focuses mainly on intertemporal aspects of fiscal policy, such as government debt issue and taxation o f wealth. A companion piece [Persson and Tabellini (1999)] surveys the research on static "public finance" problems. The main stylized facts regarding the intertemporal aspects o f post-war fiscal policy in the industrialized countries include: (i) Tax rates on capital vary considerably across countries and fluctuate over time, with an upward trend. In many countries, estimates of effective tax rates on capital are quite high and often higher than tax rates on consumption or labor 36. (ii) Many countries have accumulated large debts, even in peace time. For most countries, debt accumulation in the post-war period started in the early 1970s. The cross-sectional pattern o f deficits is far from homogeneous; some countries have been endemically in deficit and built up massive debts, whereas others have not 37 (iii) Large deficits and debts have been more common in countries with proportional rather than majoritarian and presidential electoral systems, in countries with coalition governments and frequent government turnovers, and in countries with lenient rather than stringent government budget processes 3s. It is difficult to account for these regularities by the theory of optimal taxation or, more generally, any theory that assumes policy to be set by a benevolent social planner. According to Chamley (1986), the optimal capital tax should decline over time, asymptotically approaching zero, as the long-run elasticity o f investment is very high compared to that of other tax bases. Similarly, Barro's (1979) tax-smoothing model o f deficits can successfully explain war-time deficits, but not the persistent accumulation o f debt that has occurred in many industrial countries since the 1970s. Moreover, the correlations between policies and political institutions suggest that political and institutional factors play an important role in shaping fiscal policy. In this second part o f the chapter, we survey some recent literature that speaks to these stylized facts on the basis o f positive models o f fiscal policy. As in monetary policy, these recent contributions try to explain departures from socially optimal outcomes by various incentive constraints in the policy formation process. In Section 5 we discuss credibility again, abstracting from politics and individual heterogeneity. In Section 6 we add politics to our basic model o f fiscal policy and discuss alternative explanations for large government borrowing. 3~ Mendoza et al. (1996), building on earlier work by Mendoza et al. (1994), compute effective tax rates for a sample of 14 industrial countries, during the period 1965-1991. For the most recent six-year period, the average capital tax rate for these countries was close to 40%, higher than both the average labor tax rate and the average consumption tax rate. Furthemmre, the average tax rate on capital was higher than that on labor and consumption during every five-year period since 1965, and kept rising over time. 37 See ibr instance Elmendorf and Mankiw (1999) and Alesina and Perotti (1995b). 3s See von Hagen and Harden (1995), Alesina and Perotti (1995b), Grilli et al. (1991), Roubffli and Sachs (1989).

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17 Persson and G. Tabellini

5. Credibility of fiscal policy We first discuss the ex p o s t incentive compatibility constraints that imply a lack of credibility for desirable tax policies. Many insights parallel those in monetary policy. But by adding microeconomic foundations, we can now make more meaningful welfare statements. And by adding an explicitly dynamic setting, we can investigate how state variables link policy decisions over time. As in monetary policy, sequential (or discretionary) decision-making and a lack of policy instruments may imply that the government lacks credibility and loses control of private sector expectations. The economy gets trapped in a third-best equilibrium, where the government relies excessively on a highly distorting policy instrument. The most obvious example is the "capital levy problem". But credibility problems are not confined to capital taxation: they are the norm rather than the exception in a dynamic economy. These issue are discussed in subsection 5.1. Subsection 5.2 treats another consequence of lack of credibility: the possibility of multiple equilibria and confidence crises, features often observed in countries with high punic debts. In a dynamic economy current policy credibility depends on previous policy decisions; for instance, it depends on the size and denomination of the outstanding public debt; this new dimension is discussed in subsection 5.3. Finally, as in monetary policy, reputation can mitigate the adverse effects of the ex p o s t incentive constraint and institutions can be designed to relax it. These remedies are briefly discussed in subsection 5.4. 5.1. The capital l e w problem

According to the standard theory of optimal taxation, capital should be taxed at a much lower rate than labor or consumption. Moreover, the tax rate on capital income should generally decrease over time and approach zero asymptotically. The reason is that the elasticity of investment tends to be higher than those of labor supply and consumption, and it is even higher over longer horizons, as there are more opportunities for intertemporal substitution. This prescription sharply contrasts with stylized fact (i) above. Lack of credibility offers a reason why even a benevolent government can end up with such a suboptimal tax structure 39. 5.1.1. The m o d e l

Consider a two-period closed economy, t -- 1,2, with one storable commodity. A representative consumer has preferences defined over consumption in both periods, ca, and leisure in the second period, x, represented by u - U ( c l ) + c 2 + V(x).

(5.1)

In the first period, the consumer either consumes his exogenous and untaxed endowment, e, or invests a non-negative amount in a linear storage technology with 39 The next two subsections draw oil Persson and Tabellini (1990, ch. 6).

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unitary gross returns. In the second period, he devotes his unitary time endowment to labor l, or leisure time x, and consumes all his income and wealth after having paid taxes. His budget constraints are cl + k = e,

(5.2)

c2 = (1 - 0) k + (1 - r) l,

(5.3)

where k is the investment in the storage technology, 0 and r are the capital and labor income tax rates, and the real wage is unity. Finally, the government must finance a given amount o f second-period per-capita public consumption, g. Thus, the government budget constraint is (5.4)

g = rl + Ok.

Taxes are only paid in the second period, and lump-sum (i.e. non-distorting) taxes are not available. We follow the public-finance tradition o f treating the set o f available Ramsey taxes as exogenous; but ultimately, the non-availability of (personalized) lump-sum taxes must be due to some heterogeneity that can only be imperfectly observed by the government. What is the optimal tax structure in this economy? And what is the equilibrium tax structure if the government lacks credibility? We address both questions in turn. 5.1.2. The ex ante optimal policy

To derive a normative benchmark, we assume that at the start of period 1 - before any private decision is made - the government commits to a tax structure (0, r) for period 2. The decision is observed by the private sector, and cannot be changed. There is no uncertainty, and period-2 public consumption, g, is known already in period 1. We first describe how the private sector responds to the tax rates. The private sector first-order conditions are: U c ( e - k ) >~ 1 - 0 ;

Vx(l-l) = l-r,

(5.5)

where the equality in the first condition applies at an interior optimum with positive investment. Each tax rate thus drives a wedge between the relevant marginal rates of transformation and substitution. Optimal policy seeks to minimize the resulting distortions. Inverting these two expressions, we obtain the private sector savings function k = Max[O,K(1 - 0)], where K(1 - O) ~- e - Ucl(1 - 0), and labor supply function l = L(1 - r) _--_ 1 - vxl(1 - r). The partial derivatives Ko and Lr are both negative. By the separability and quasi-linearity o f the utility function, each tax base depends on its own tax rate only. For future reference, it is useful to define the

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elasticities of these two tax bases with respect to their own net of tax returns, as ek(0) and el(O, respectively 4°. The optimal tax structure maximizes consumer welfare, subject to the private sector and government budget constraint (5.2)-(5.4), and the private sector first-order conditions (5.5). Solving this optimization problem yields the following version of the Ramsey Rule41: 0

r

(5.6)

1 - 0 ek(O) = ~ e l ( r ) .

Equation (5.6) implicitly defines the ex a n t e optimal tax structure. What are its general properties? First, optimal tax rates are higher on the more inelastic tax base. Second, it is always optimal to tax both bases, as long as both elasticities are finite and strictly positive. Finally, both tax rates move in the same direction if the revenue requirements change; higher public consumption drives up both tax rates, in proportion to their elasticities. If, as empirically plausible, labor supply is much more inelastic than investment, the optimal tax rate on labor is much higher than that on capital. As taxes are distorting, the economy reaches a second best - not a first best. 5.1.3. E q u i l i b r i u m u n d e r d i s c r e t i o n

Suppose instead that the policy decision is taken at the start of period 2, after period-1 investment decisions have been made. This timing is much more plausible, as a sovereign country can change its tax structure at any time, under a normal legislative procedure. Under this timing, however, every tax structure promised in period 1 is not credible. A credible tax structure must be optimal e x p o s t ; from the vantage point of period 2. More precisely, a credible equilibrimn tax structure satisfies three requirements. (i) Individual economic decisions are optimal, given the expected policies and the decisions of all other individuals in the economy. (ii) The tax structure is e x p o s t optimal, given outstanding aggregate capital and individual equilibrium responses to the tax structure. (iii) Individual expectations are fulfilled and markets clear in every period. Let us consider each of these requirements. (i) Optimal individual behavior is still summarized by the functions K and L and by the corresponding elasticities. But the investment function and the corresponding elasticity are now defined over the expected, not the actual, capital tax rate, as the tax structure is decided in period 2, after the investment decision. Thus, k = K(1 0 e) and ei~(0e). We call this elasticity the ex a n t e elasticity of investment, since it is defined over 0 e rather than 0. 4o These elasticities are, respectively: (1 0) ek(O) -

K

dK d(1 - 0)

U,~ KUcc > 0,

el(r) ~

(1 r) dL L d(1 v)

41 See Persson and Tabellini (1990, ch. 6), for a derivation.

V~

LV~ >0.

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(ii) The ex p o s t optimal tax structure also continues to be described by the Ramsey Rule (5.6), but with one important proviso. The investment elasticity that enters Equation (5.6) is the ex p o s t elasticity, that is the elasticity with respect to the actual tax rate 0, since that is what the government is choosing. By the argument at point (i), this e x p o s t elasticity is zero: k depends on 0 e, not on 0. Equation (5.6) then implies that for any given capital stock k the ex p o s t optimal capital tax rate, 0", must satisfy 0* - Min[1, g / k l .

(5.7)

The optimal labor tax rate r follows from the govenmaent budget constraint. In particular, r - 0 if 0* = g / k < 1. This result is very intuitive. When tax policy is chosen, the supply of capital is completely inelastic at k, whereas the supply of labor continues to have a positive elasticity, as it is chosen by the private sector after observing tax policy. Hence, the government finds it ex p o s t optimal to set either a fully expropriating capital tax rate of 1, or a tax rate sufficiently high to finance all of public consumption with capital taxes, driving labor taxes to 0. (iii) Rational individuals correctly anticipate government policy. Hence, 0 e = 0* and k = K(1 - 0"). Combining this last result with Equation (5.7), the equilibrium tax rate is defined by 0* = M i n [ 1 , g / K ( 1 - 0")]. We illustrate the possible equilibria in Figure 1. The solid curve is the ex a n t e revenue function for different values of 0. Tax revenues first grow with the tax rate, but at a decreasing rate, since the tax base shrinks as 0 rises. Once we reach the "top of the Laffer Curve", tax revenue begins to shrink, as the reduction in the tax base more than offsets the higher tax rate. l f g is sufficiently high (higher than point G) only one equilibrium exists, in which 0* = 1 and k = 0 (point C in the diagram). Irrespective of private expectations, the government fully expropriates any outstanding capital stock. Anticipating this, nobody invests. It is easy to verify that all three requirements for an equilibrium are fulfilled. Private individuals optimize and have correct expectations about policy. And the government also optimizes, for even with no capital outstanding, 0 = 1 is (weakly) optimal, as confirmed by Equation (5.7). This equilibrium is disastrous: there is a prohibitive tax on capital, but still a large tax on labor which is the only available tax base. Yet, the government can do nothing to change the outcome. No promise to tax capital at a rate lower than 1 would be believed, because it would not be ex p o s t optimal for the government to fulfill it. If g is below point G in Figure 1, this disastrous outcome continues to exist together with two other equilibria. Suppose that government spending corresponds to the horizontal line in Figure 1. Then points A and B are also equilibrium outcomes. At point A, every consumer expects 0 e = 0 a and invests K(1 - 0a). Hence, the government can just finance g by setting 0 exactly at 0 A, while keeping the labor tax equal to 0. Thus, the government is at an ex p o s t optimum. The same argument establishes that point B is also an equilibrium.

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oK(1 -o) G

C 0

0A

0B

l

0

Fig. 1.

These equilibria are clearly Pareto ranked: A is better than B which is better than C. They are all worse than the e x a n t e optimal tax structure, since they tax capital too heavily and labor too lightly (except at point C where both bases are taxed too heavily). If the government is unable to commit, the economy is trapped in a third-best, or worse, allocation. 5.1.4. E x t e n s i o n s

Results similar to those above, apply to the taxation o f other forms o f wealth, in particular to public debt and real money balances; in the case of money, naturally, the tax takes the form of inflation. The logic is always the same. Once an investment decision has been made, the tax base is fixed and it becomes ex p o s t optimal to tax it as much as needed, or as much as possible. Moreover, credibility problems are not confined to wealth taxes, but are generic in a dynamic economy with sequential policy decisions. The reason is that the e x p o s t and e x a n t e elasticity o f tax bases generally differ from each other. In general this difference is not as stark as with wealth taxes, where the ex p o s t elasticity is zero. In the case o f other tax bases than wealth, we can no longer conclude that the optimal tax rate is always higher e x p o s t than e x ante. To gain some intuition for why, consider an increase in a labor tax rate in a given period t. If the tax increase is u n a n t i c i p a t e d , the household substitutes from labor into leisure in the current period. But if the tax increase was a n t i c i p a t e d in period t - 1, some intertemporal substitution has already taken place: the household works less in period t, but has already worked more in period t - 1. We cannot generally tell whether an anticipated or an unanticipated tax hike is more distorting, however. Intertemporal substitution increases the distortion at time t, the period of higher taxes, as the tax base is more elastic. But this greater distortion is offset by a larger tax base in period t 1, when the household is working more in

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anticipation of higher future taxes. In general, therefore, we can say that optimal tax rates are different, but not whether they are higher ex ante or e x post 42. We close this discussion with two remarks. First, characterizing the equilibrium with sequential government decisions is relatively easy in a two-period economy, and doable in a finite-horizon economy. But it becomes very difficult in an infinite-horizon economy 43. Second, so far we have considered a representative consumer economy in which the government lacks a non-distorting tax and has incentives to raise revenues in less distorting ways. Lump-sum taxation may, however, not be enough to avoid lack of credibility. If the goverlmaent also has distributive goals, but not enough lump-sum taxes and transfers to reach its desired income distribution, the optimal tax policy may still lack credibility despite the availability of (non-personalized) lump-sum taxation. What matters ultimately is thus a scarcity of policy instruments relative to objectives. 5.2. Multiple equilibria and confidence crises'

When discussing reputational equilibria in monetary policy, we argued that multiple equilibria indicated an incomplete theory. Here, multiplicity of equilibria instead reflects an indeterminacy in the economy, and helps explain the occurrence of sudden speculative attacks or capital flights that have plagued many economies. Absent a commitment technology, policy is driven by private expectations rather than the other way around. Equilibria under discretion thus become intrinsically fragile, as investors face a difficult coordination problem. The ex post optimal policy depends on aggregate investment. But aggregate investment depends on the simultaneous decisions of many atomistic individuals, which in turn depend on expectations about policy. Thus, there is a strategic complementarity. A single investor expecting nobody else to invest also finds it optimal not to invest: he realizes that aggregate capital will be small, and hence full expropriation is inevitable. Thus, individual expectations are self-fulfilling and, as they are not nailed down by any economic fundamentals, can fluctuate widely. The resulting policy uncertainty is yet another drawback of a discretionary policy environment. These problems arise in many policy decisions. Consider public-debt repayment in a two-period economy, and suppose that in the second period debt can be partially defaulted or taxed away, at a cost proportional to the size of the default. Calvo (1988) shows that we then get multiple equilibria, in a good equilibrium, every investor expects the debt to be fully repaid and demands a low interest rate. To avoid the cost of default, the government indeed services the outstanding debt. In a bad equilibrium, every investor expects partial default and demands a higher interest rate. The cost of servicing this debt is now higher, and with distorting taxes the government prefers a partial default; hence, default expectations are self-fulfilling. The equilibrium with default is Pareto inferior, as the net amount serviced is the same, but default costs are borne. 42 For a further &scussion, see Persson and Tabellini (1990, ch. 8). 43 See also the survey by Krusell et al. (1997).

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Another example, studied by Velasco (1994) and Giavazzi and Pagano (1990), concerns exchange-rate crises in a high public debt economy. By assumption, the cost o f outright default is prohibitive, but the outstanding debt could be monetized away. In a good equilibrium, investors expect the exchange rate peg to be viable and the domestic interest rate equals the foreign interest rate; at this low interest rate, it is optimal to service the outstanding public debt by tax revenue alone. In a bad equilibrium, investors expect the peg to collapse. They demand a higher interest rate, which raises the cost o f servicing the debt through tax revenue; at the higher interest rate, it becomes optimal to fulfill the expectations, the peg is abandoned and the debt is partially monetized through higher inflation 44. Related coordination problems arise in s e q u e n t i a l (as opposed to simultaneous) investment decisions. Alesina et al. (1990) and Cole and Kehoe (1996a,b) study an infinite-horizon economy with a large public debt. Like in Calvo (1988), default is costly, but the cost is assumed to be a lump sum cost. In the good equilibrium, the debt is rolled over forever at low interest rates, and distorting taxes are raised to pay interest on the debt. In the bad equilibrium, there is a debt run, as nobody wants to buy the outstanding debt for fear that - next period - investors will refuse to roll it over. Faced with such a situation, it is indeed e x p o s t optimal for the government to default on the debt, rather than repaying it all at once. Thus the investors' fears are indeed rational and self-fulfilling. Here, the coordination problem thus concerns investment decisions at different points in time. 5.3. P u b l i c d e b t m a n a g e m e n t

The papers discussed in the previous subsection have implications for debt management policies, as the occurrence of a confidence crisis depends on the maturity structure or currency denomination o f outstanding debt. For instance, tile debt-run equilibrium discussed by Alesina et al. (1990) disappears if the outstanding debt has a long enough maturity, whereas it is more likely with a short-maturity debt that must be rolled over every period. Similarly, the results in Giavazzi and Pagano (1990) suggest that issuing foreign currency debt can reduce the risk o f capital flight, as investors are already protected against depreciation. More generally, public debt management policies alter the future incentives of the monetary and fiscal authorities in many subtle ways, even if the ex a n t e and ex p o s t elasticities o f all tax bases are the same. This point was first noted in the seminal paper by Lucas and Stokey (1983) with regard to the maturity structure o f public debt. They start from the observation that fiscal policy typically alters real interest rates. The resulting wealth effect can benefit or harm the government, depending on the composition o f its balance sheet. With a lot of long-term debt, a higher long-term 44 A high cost of servicing the debt is not the only reason why an exchange rate peg may not be credible~ in a related argument, Bensaid and Jeanne (1997) show that multiple equilibria can arise if raising the interest rate to det?nd an exchange-rate peg is too costly lbr the government.

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real interest rate depreciates the outstanding debt and acts like a non-distorting capital levy. Alternatively, if it has long-term assets and short-term liabilities, the government benefits from a policy that reduces the short-term real interest rate. Under sequential decision making, the government's ex a n t e optimal policy may not be credible: the government may have an incentive to deviate from it e x p o s t , in order to change the value o f its outstanding assets and liabilities. Conversely, these incentives give an additional role for public debt management policies: if the maturity and contingency structure o f the debt is rich enough, it can be revised over time so as to maintain credibility o f the e x a n t e optimal tax policy under sequential decision making, even if ex a n t e and e x p o s t elasticities of relevant tax bases differ from each other 45. Naturally, these results only hold if the economy is closed or large enough to affect intertemporal world prices. Not only the maturity structure o f the public debt shapes policy incentives. Its composition into nominal and indexed debt plays a similar role, as the real value of the former, but not the latter, depends on the price level 46. Based on this observation, Persson et al. (1987) show that the capital-levy incentive for the government to dilute the real value o f its outstanding nominal liabilities - such as the money stock - can be relaxed if the govermnent holds claims on the private sector, denominated in nominal terms, if the nominal claims and liabilities are balanced, the e x a n t e Ramsey solution may be sequentially sustained. But nominally denominated liabilities can also offer valuable insurance against unanticipated fluctuations in government spending, if the government does not have access to contingent debt. Calvo and Guidotti (1990) study the choice between nominal and indexed debt as a trade-off between credibility and flexibility. The upshot is thus that the structure of the public debt becomes a strategic variable that can be manipulated by a government to relax incentive constraints which it will meet in the future. As a result, the "government capital structure" again becomes nonneutral, even if a Modigliani-Miller theorem about the irrelevance of the govenmaent financial structure would apply in the absence o f these incentive constraints. In this section, we have only considered governments that continue to make decisions in the future with full certainty. But the idea of using public financial policies strategically to influence future fiscal policy decisions, obviously extends to the case which is more relevant for real-world democracies (dictatorships), where elections (coups and revolutions) shift the identity and policy preferences o f governments over time. Strategic public financial policies have indeed received attention in the literature on the politics of public debt that we survey in Section 6.

45 "Rich enough" generally means that there are as many goverrmlent debt instruments as there are policy instruments. ,16 Public debt denominated in foreign currency is similar to indexed debt in this regard, but will not be considered here.

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5.4. R e p u t a t i o n a n d e n J b r c e m e n t

As in monetary policy, repeated interaction creates incentives to maintain a reputation, which may mitigate the capital-levy problem. Suppose that future expected capital tax rates depend on the current tax structure. Even though existing capital is taken as given by the government, it still perceives future investment to respond to current tax rates, through expected future tax rates, and this discourages overtaxation. Chari and Kehoe (1990) have studied this reputation mechanism in an infinitely repeated version of the simple two-period model of subsection 5.1. The equilibrium with reputation comes arbitrarily close to the ex a n t e optimal Ramsey rule, under appropriate assumptions about the government discount factor and the length of the punishment period. Kotlikoff et al. (1988) show that a related enforcement mechanism may be available in an overlapping-generations economy. A misbehaving government is not deterred by investors' expectations, but by the threat that future generations of tax payers will withdraw their intergenerational transfers to a generation that breaks "the social contract" by overtaxing capital. Naturally, multiplicity of equilibria remains in both models. When we consider default on public debt, however, reputational equilibria encounter additional difficulties. Suppose that a defaulting government is "punished" by savers, who refuse to buy public debt in the future. The punishment thus consists of not being able to smooth tax distortions overtime, in the face of fluctuating public spending or tax bases. Is this sufficiently strong to deter default? Bulow and Rogoff (1989) argue that it is not. Suppose that a defaulting government can never borrow again, but can nevertheless still invest budget surpluses in assets earning the market rate of return (for instance, by accumulating reserves of a foreign asset). Then, a simple arbitrage argument implies that the government is always better off defaulting rather than repaying its debt 47. Thus, simple reputation models cannot explain public debt repayment. There must be other reasons why governments honor their debts: either reputational spillovers across policy instruments, or other costs in a default, such as distress in the banking system, arbitrary redistributions, or sanctions credibly enforced by the international community. In Part I, we discussed various institutional reforms that might raise the credibility of desirable policies. In the case of fiscal policy, such reforms are less effective, however, as the tasks of a sovereign legislature cannot be narrowly defined. Nevertheless, some institutional devices could mitigate the capitaMevy problem. Political delegation to a conservative policymaker is one way. International tax competition is another. As discussed in a companion survey [Persson and Tabellini (1995)], capital controls or international tax agreements that limit tax competition exacerbate the domestic credibility problems, and could thus be counterproductive. 47 Bulow and Rogoff (1989) develop their argument in the case of sovereign loans that finance consumption or investment, with no tax distortions, for arbitrary concave utility and production function. But their result generalizes to a model with tax distortions.

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5.5. Notes' on the literature

Much of this section is based on Persson and Tabellini (1990, chs. 6-8). There is a large game-theoretic literature on dynamic games with sequential decision-making. What started this line of research are again the papers by Kydland and Prescott (1977) and Calvo (1978). The book by Basar and Olsder (1982) provides a game-theoretic analysis of these problems in an abstract setting. The "capital levy problem" has a long history in economics. Eichengreen (1990) provides a historical account. It has been formally analyzed (although with numerical solutions) in a two-period economy by Fischer (1980). An early treatment of surprise inflation to tax real money balances is Auernheimer (1974), but Calvo (1978) is the classic here. A large literature deals with speculative attacks and multiple equilibria. In this section we have only focused on multiple equilibria that arise when policy is endogenous and there is a credibility problem. Confidence crises on public debt have been studied by many authors; in particular by Calvo (1988), Alesina et al. (1990), Cole and Kehoe (1996a,b) and Giavazzi and Pagano (1990). Multiple equilibria with discretionary monetary policy have also been extensively treated in the literature, in particular by Obstfeld (1997a), Bensaid and Jeanne (1997), Chari et al. (1996) and Velasco (1994). Reputation and capital taxation is discussed by Kotlikoff et al. (1988), Chari and Kehoe (1990) and, more recently, by Benhabib and Rustichini (1996), while Grossman and Van Huyck (1988) and Chari and Kehoe (1993) applied reputation to a model of public debt repayment. The idea that reputation can fail in the case of sovereign debt repayment is due to Bulow and Rogoff (1989), whereas Chari and Kehoe (1993) show that enforcement problems on both sides of the market can restore a role for reputation. Reputational spillovers across contracts are discussed by Cole and Kehoe (1994). Political delegation and capital levies are modeled in Persson and Tabellini (1994c) and discussed by North and Weingast (1989) in a fascinating historical context. The literature on international tax competition and credibility is surveyed by Persson and Tabellini (1995). The credibility of optimal tax structures in a general intertemporal context and without capital has been studied by Lucas and Stokey (1983). Their seminal paper discusses both debt management and the credibility of tax policy. Subsequently, Persson and Svensson (1984) and Rogers (1987) reinterpret and clarify some of the general issues concerning the credibility of optimal intertemporal taxation. The debt management implications of the Lucas and Stokey paper are also generalized and interpreted, by Chari et al. (1992) and by Persson and Svensson (1986). Persson et al. (1987) extend the Lucas and Stokey result to a monetary economy, whereas M. Persson et al. (1997) show that the temptation to generate surprise inflation may be much stronger than the theoretical literature suggests, once the full set of nominal rigidities in public expenditure and tax programs are taken into account. Rogers (1987) discusses strategic debt management and credible tax policy in an economy with endogenous

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government consumption, while Rogers (1986) considers distributive goals. Missale and Blanchard (1994) study how the maturity structure required to make a low-inflation policy incentive compatible varies with the level of debt. Calvo and Guidotti (1990) study the credibility-flexibility trade-off in the optimal decomposition of public debt into indexed and non-indexed securities. Finally, Missale et al. (1997) as well as Drudi and Prati (1997) have studied public debt management as a signal of the government resolution to enact stabilization policies.

6. Politics of public debt As noted in the introduction to Part II, many industrial countries have accumulated large debts in peace time. Moreover, debt and deficits appear to be correlated with specific political and institutional features. The goal of this section is to survey the literature that addresses these issues. We begin with the idea that deficits may be a by-product of political instability. Section 5 emphasized that governments can manipulate their debt structure to resolve their own future credibility problems. Subsection 6.1 takes up this thread, showing how the debt level itself can be used strategically to bind the hands of succeeding governments with different political preferences, in a way first suggested by Alesina and Tabellini (1990) and Persson and Svensson (1989). This idea typically applies to political systems with two parties and a government that clearly represents the view of a cohesive political majority. The debt level can also be used to enhance the incumbent government's re-election probability, in a way first suggested by Aghion and Bolton (1990) and also discussed in Section 3. We construct a simple two-period example that incorporates both of these mechanisms. The remainder of the section then looks at political systems with more dispersed political powers, as in the case of coalition govermnents or powerful political interest groups. In subsection 6.2, we discuss why such a situation may be particularly prone to generate deficits. The argument is a dynamic version of the common-pool problem formulated by Levhari and Mirman (1980) - in the context of natural resources and applied to government debt by Velasco (1999). In subsection 6.3 we follow the approach of Alesina and Drazen (1991), showing how the struggle between powerful groups, about who will bear the cost of necessary cuts in spending, may lead to a war of attrition delaying the elimination of existing deficits. In both these subsections, we reduce the full-blown dynamic models found in the literature to simple two-period examples. In subsection 6.4, finally, we discuss briefly how the politics of intergenerational redistribution may trigger government deficits, as suggested by Cukierman and Meltzer (1989), Tabellini (1991) and others.

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6.1. Political instability in a two-party system 6.1.1. Economic equilibrium

Consider a two-period economy without capital, but otherwise similar to that of subsection 5.1. A continuum of individuals have identical preferences over consumption and leisure. First we describe their preferences over private economic outcomes and their private economic behavior, for a given economic policy. Individual preferences over public policy and different parties are described later. Preferences over private economic outcome are given by the utility function: (6.1)

U = C 1 + C 2 + V ( X l ) + V(x2).

Every consumer faces the same constraints. Leisure and labor in period t, xt and lt, must sum to unity. Budget constraints are c2=(1

cl+b=(1-rl)ll,

rz)12+Rb,

where Tt is a labor tax rate, R is the gross interest rate, and b is the holding of public debt - the only available form of saving. By the absence of discounting and the linearities in the utility function, an interior equilibrium f o r b requires R = 1. Recognizing this, we can write the equilibrium consolidated budget constraint as Cl +C2 = (1 - ' g l ) l l

+ ( 1 - T 2 ) I 2.

Solving the consumer problem, leads to labor supply functions L(1 - rt) identical to those of subsection 5.1. Public spending only takes place in period 2. Let g denote total per capita public consumption. Using R = 1, the government budget constraints are - b = rill,

b+g-

T212.

It is useful to re-express private utility as an indirect utility function defined over the policy variables b and g. Private equilibrium utility is only a function of the two tax rates T~ and r2. From the govermment budget constraints, these tax rates can be expressed as functions of b and g. Thus we can rewrite Equation (6.1) as J ( b , g ) - Max[c1 + c2 + V(xl) + V(x2)]. This indirect utility function has intuitive properties. First, Jg < 0, is the private marginal cost of government spending which is increasing in g: Jgg < 0. Second, Jb is the private marginal cost of government debt. The symmetry of labor supply implies > O as Jt, ~

1 b ~< -~g.

(6.2)

That is, when tax rates are equal over time, tax distortions are optimally smoothed out (orb = 0). But if more (less) than half the revenue necessary to finance g is raised in

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period 1, so that b < - ½ g (> -½g), private utility could be enhanced by higher (lower) debt issue. Finally, as taxes are distortionary and as higher b adds to the government's tax bill in period 2, the cross-derivative Jbg is negative 48.

6.1.2. The political system Individuals belong to two different groups, which we label d and r, o f given sizes s and (1 - s ) . The two groups are identified with the supporters of two political parties: D and R. Individuals and parties differ in their preferred allocation of public spending over two types o f public consumption: gd and gr. The two types of public consumption each require one unit o f output, but they provide different utilities to the two parties and their individual supporters. For simplicity we assume that individuals belonging to group d (r) only care about gd (g,.) and that each party only cares about the utility o f its own supporters. If elected, party I thus maximizes the utility function

u1 = J(b, g) + H(gi).

(6.3)

Thus, party I correctly internalizes the welfare effects of economic policy on private economic outcomes, according to the indirect utility function J defined over debt and total spending, and evaluates the benefits o f public consumption for its constituency according to the (concave) H function, defined over gi. Political parties are "outcome motivated" rather than "office motivated". It is easy, however, to amend the model with a separate benefit o f holding office, as in Section 3. Finally, we assume that relative group size s is a random variable, the realization o f which determines the election outcome. We define P = Pr(s ~< 0.5) as the probability, from the viewpoint of period 1, that party R wins. This electoral uncertainty can be due to a random participation rate, or to uncertainty about the relative popularity of parties on other policy dimensions. Below we suggest an explicit model for P, but for now we take it as exogenous.

6.1.3. Equilibrium policy Events in the model unfold as follows: (1) One o f the parties holds office in period 1; this party sets debt (tax) policy b. (2) Economic decisions in period 1 are made. (3) The elected party takes office and sets public spending. (4) Economic decisions in period 2 are made. As before, we consider a sequentially rational equilibrium, and we characterize it by backward induction.

48 Note that our formulation of the model rules out credibility problems of the type discussed in Section 5. The asstuned preferences imply that labor supply fimctions depend on the current after-tax wage only, so that there is no difference between ex ante and ex post elasticities. Also, incentives for debt repudiation do not arise, because the government is a creditor and has no opportunity to manipulate the equilibrium interest rate.

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Optimal private decisions at stages (2) and (4) are already subsumed in the indirect utility function. Suppose party I holds office in period 2. It chooses g so as to maximize its objective in Equation (6.3), given the outstanding debt level b. The first-order condition for good i is Jg(b, g) + Hg(g i) = O.

(6.4)

Thus party I spends on good i only (good j # i has only costs and no benefits) and equates the marginal cost of supplying good i to its marginal benefit (to group i). Clearly, this condition defines a reaction function gi = G(b) which is the same for both parties. Since higher debt implies higher period-2 tax distortions, any government type is less willing to spend on public goods if it inherits a higher public debt; hence: Gb < 0. We can look at the period-1 incentives to issue debt at stage (1). The identity of that government does not matter for the results, but to fix ideas we suppose that party D is the incumbent. Its expected payoff, given the expected election outcome, depends on debt policy according to the incentive constraint imposed by equilibrium policy choices in period 2: E(uD (b)) - J (b, G( b)) + (1 - P ) H ( G ( b ) ] . Optimal debt policy thus has to satisfy & + [Jg + (1 - P ) Hg]@, : & - P H g G b : O,

(6.5)

where the second equality follows once we impose condition (6.4). Condition (6.5) has an intuitive interpretation. To strengthen the intuition, first consider the special case in which party R stands no chance at winning - that is, P - 0 for any b. Then Equation (6.5) reduces to Jh = 0. In words, a government that is certain of re-election chooses the efficient debt policy, smoothing completely over time the tax distortions from the financing of its preferred public good. When re-election is not certain, however, other incentives come into play. The larger is the probability that the opponent will win, the more party D deviates from the efficient debt policy, as is evident from the second term. As this term is positive, party D sets Jt~ < 0 whenever P > 0. A positive probability of losing the election leads to excessive debt issue - or more precisely to an insufficient surplus today [recall Equation (6.2)]. Whereas the incumbent government fully internalizes the benefits of borrowing associated with tax smoothing, it does not fully internalize the cost of lower public spending in the future, because these costs are borne only if the government is re-elected. Thus, the over-issue of debt is larger the slimmer is the re-election probability. To express the intuition in an alternative way: it is optimal for the party-D government to tie the hands of a prospective party-R government, as that party will spend on a good not valued by the natural constituency. This strategic motive, creating

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facts for a successor with different preferences, was first stressed by Persson and Svensson (1989) and Alesina and Tabellini (1990). 6.1.4. Endogenous election outcomes As mentioned already in Section 3, governments also manipulate state variables to increase their chances of re-election. We now modify our model to show how this incentive applies to public debt, illustrating an idea first stressed by Aghion and Bolton (1990). Consider the same model, but suppose that parties and individuals also differ along a second - not explicitly modeled - dimension capturing aspects of public policy that do not directly affect the economy. Specifically, we assume that individual utility depends on the identity of the party holding office, in addition to the public good it provides. But we allow individuals belonging to the same group to have different preferences over policymakers in this second dimension. Thus, we postulate the following overall preferences for individual j in group i, for i = D, R: u ij = J ( b , g ) + H ( g i) + ( U +/3)K o,

(6.6)

where H(.) is the same concave function as in Equation (6.3), and the dummy variable K z) equals 1 if party D holds office in period 2, and 0 if party R holds office. The parameter aJ is distributed around a mean value of 0 in the population of each group, according to the symmetric and unimodal distribution function F(-). In period 1 the precise value of/3 is not known, but only its expected value E(/3). The aJ parameter thus measures an idiosyncratic "ideological" (and exogenous) bias for party D, and to the extent that/3 is positive, party D enjoys a popularity advantage. That is, individuals evaluate public consumption according to their group affiliation, and each party cares about its natural constituency. But voters also trade off the economic benefits obtained from their party against other (exogenous or noneconomic) aspects of public policy, according to the parameters a and [3. These "non~ economic" determinants of political preferences are not related to group affiliations in any precise way. This specification of political preferences implies that group affiliation does not completely determine how individuals vote, so that the vote share of each party is endogenous. Finally, we assume that the relative size of the two groups, given by s, is now a fixed parameter, not a random variable. The timing of events is as before, except that just before the date of elections the realization of aggregate popularity,/3, becomes known. What determines the election outcome? At the time of elections, debt policy b is given by previous decisions. Consider voter j in group d. She votes for party R if and only if J ( b , g ) + H(G(b)) + a j +/3 > J(b,g), or if aJ > - ( H ( G ( b ) ) + [3). Thus, unless party D is generically unpopular ~3 < 0), only group-d individuals with a strong idiosyncratic ideological bias against party D vote for party R. Next, consider voter j in group r. She votes for party R if and only i f J ( b , g ) + aJ +/3 > J ( b , g ) + H(G(b)),

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or if aJ > H ( G ( b ) ) - / 3 . Not surprisingly, a group-r voter is more likely to support party R, since she draws economic benefits from its election. Combining these conditions and using the law of large numbers, we get the total vote share for party R: SR(b,/3) = s F ( - H ( G(b)) - [3) + (1 - s) F ( H ( G(b)) - [3),

where fi is a random variable; everything else is known or chosen by the incumbent government. Thus, before knowing the realization of/3, the probability that R wins is P(b)

-

p[[se(b,/3) >~ 0.51.

We want to know how this probability depends on public debt. As a preliminary step, note that dSR db - HgGh[(1 - s))C(H(G(b)) - [3) - s f l ( - H ( G ( b ) ) -/3)], where f is the derivative (density) of F. As HgG~ is negative, the sign hinges on the expression in square brackets. Consider first the case/3 = 0. By symmetry of F, we see that the vote share of party R goes up for any/3 if s > (1 - s ) . Intuitively, higher b leads to lower furore spending, which increases party R's advantage among voters in group d, but it reduces it among voters in group r. if group d is larger, the 1 Then, by former effect prevails. Consider next the case in which s = (1 - s) = g. symmetry and unimodality of F, the vote share for R goes up as b increases if and only if/3 < 0. Again the voters in group d are more important, not because the whole group is larger, but because at the margin the voters in group d are more mobile when party D is generally unpopular. It follows from this discussion that Pb > 0 is more likely the larger is s and the smaller is E(/3). That is, from the point of view of a party-D incumbent, issuing more debt reduces the probability of re-election (Pb > 0) if its economic policies benefit a large group of voters (s is large) or if it is unpopular among all the voters (/3 < 0). It is now easy to characterize the equilibrium debt issued by a party-D government Going through the same steps as in the previous subsection, the optimality condition for public debt - the analog of (6.5) is & - P ( b ) Hg Gb - P b H ( G ( b ) ) - O.

(6.7)

The first two terms on the left-hand side of Equation (6.7) are identical to those in Equation (6.5) and have the same meaning. The government trades off the efficiency considerations of public debt (captured by Jb) and the strategic effects on the future spending decisions of its opponent (captured by P H x G v ). The last term captures the effect of debt on the re-election probability. If issuing debt enhances the re-election

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chances for party D, so that Pb < 0, this effect adds to the incentives to issue debt, but when Pb > 0 it pulls in the opposite direction. From the previous discussion we know that Pb < 0 is more likely when s is small and when E([3) > 0. Intuitively, a party-D government whose spending policies benefit only a small "minority" - one for which s is small - enhances it re-election chances by constraining its own future spending, that is by issuing more debt, since this makes him more attractive to swing voters in the larger group r. Similarly, a party-D government whose non-economic policies are generically popular finds it more beneficial to go after swing voters in the opposition party's natural constituency, group r. 6.1.5. Discussion

What happens if the disagreement between the two parties is not as extreme as we assumed, so that both parties always spend on both goods, g~ and gr, although the preferred composition of public spending differs across parties? The answer depends on the shape of the utility function: more debt forces future spending cuts, but which public good is cut the most depends on preferences. If lower total spending is associated with a more similar mix of the public goods by the two parties, Tabellini and Alesina (1990) show that more instability (a lower probability of re-election) still leads to larger equilibrium debt 49. The model thus yields the empirical prediction that political polarization (i.e. sharp disagreement between the majority and the opposition) and political instability (i.e., frequent government turnovers) lead to larger debt accumulation. The simple idea that political instability causes government to behave myopically can be applied in more general models. Adding government spending in period 1 does not change the argument in any respect. Similarly, the results go through if policies are chosen directly by the voters, rather than by the government, as long as there is a probability that the current majority will be replaced by a future majority with different preferences. In fact, the prediction is more general and really applies to any intertemporal aspect of public policy, such as the choice of public investment [Glazer (1989) and Part Ill below], or the implementation of tax reforms [Cukierman et al. (1992)]. If" political disagreement concerns the overall size of public spending, rather than its composition, the result that public debt policy is economically inefficient continues to apply. But-now the direction of the inefficiency depends on which government is in office. Persson and Svensson (1989) show that a conservative government facing a more liberal opposition has an incentive to borrow, to force future spending cuts if the liberal is elected; but a liberal government has the opposite incentives and underissues debt (runs an excessively large surplus). Hence the empirical prediction that on average left-wing governments are more disciplined than their opponents, because they are more willing to raise tax revenue. ~t9 Tabellini and Alesina (1990) tbrmulate this condition in a precise way, referring to thc concavity index of the function H.

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As we saw in the introduction to this part, the general idea that govenmlent turnover is positively associated with debt issue is consistent with the stylized facts. Some of the models' specific predictions regarding public debt issue have been taken to the data by Ozler and Tabellini (1991) for developing countries and by Lambertini (1996) for industrial countries, with supportive results in the first paper but not in the second one

50 ,

Stretching the model somewhat, it also predicts that minority governments would be more prone to issue debt, as the two strategic effects pull in this direction for a government with a small natural constituency (a small s tends to raise P and to make Pb negative) 51. For a government with popular candidates, the two effects pull in opposite directions, though. The specific positive implications concerning the effect o f debt on re-election probabilities are not necessarily robust, but depend on the assumptions about voters' preferences in Equation (6.6). But the general idea, that public financial policies can also be used to manipulate the relative popularity of the two parties, is sound and has many other applications besides public debt. Clearly, these determinants of economic policy would be even more important if parties were also opportunistic, i.e., also cared about staying in office p e r se. Finally, note that all of these predictions are confined to a two-party system, and in particular to a political system in which a government, once elected, behaves as a single decision-maker. We now turn to coalition governments.

6.2. Coalition governments

To see why coalition governments may issue debt, consider a two-period, two-group, two-party model, silnilar to that in the previous section. As tax distortions are not central to the argument here, we assunae taxes to be exogenous and lump-sum. Furthermore, we abstract from elections and popularity and instead assume that the two parties share office, both in period 1 and period 2. Public spending occurs in each period. As before, the two groups have sharply different preferences over the composition o f public consumption. We can write the utility of a typical group-i individual as u i = cl ~ c2 + H ( g { ) + H(g~) = 2 ( y -- r) + H(g{) + H ( g '2),

where y and r are exogenous per capita incomes and per capita taxes assumed to be equal over time.

50 Petterson (1997) test the Persson-Svensson and Aleshla-Tabellini models of strategic debt issue on panel data from Swedish municipalities. He finds support for the former model but not for the latter. 51 Questioning the stylized fact cited in the Introduction to Part II, Edin and Ohlsson (1991) argue that minority governments, rather than coalition govermnents, are associated with larger debt issue.

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To simplify further, let us assume that s = ½, so groups (or parties) d and r are of equal size. The government budget constraints are g,--(g~+g~):r+b,

g2

(g~+g~):r-b.

It is easy to see that in this setting the optimal cooperative policy (giving equal weight to the two groups) would set b = 0, and g~ = gI T f o r i = d, r a n d t = 1,2, sincethat would smooth the benefits of government spending optimally across groups and time. This is not the equilibrium outcome, though, if groups do not cooperate. In each period, the coalition partners simultaneously and non-cooperatively propose a spending level for their constituency. Period-2 debt is always honored. I f jointly feasible, these proposals are implemented; if infeasible, each group gets a share of the feasible spending level in proportion to its proposal. More precisely, using p(g~) to denote the proposal of group i in period t we assume that 52

gl

f p(g~)

if

] @

~2r

f p(gi2)

if

(p(gl)+p(gi/)) <~2r, otherwise,

~, p(gl)+p(gi )

g~ = /

(p(g~) +p(gJ)) <~ r - b,

P(g£) n ( r - b )

k P(g'2)+P(g~)

(6.8)

otherwise

Clearly, this model implicitly assumes a weak budget process, where each of the coalition partners is given responsibility for one separate part of the government budget, and none of them has responsibility for the overall budget constraint. We can also interpret the model as referring to a very weak government where spending ministers are in the hands of powerful interest groups. Given the relation between proposals and outcomes in Equation (6.8), there is a unique Nash equilibrium in period 2: each party proposes that the whole remaining pool of government resources, r - b, be allocated to its own group. Bidding for the whole pie in period 2, by setting p(g~) = (r - b), is costless. Such a proposal is a dominant strategy, as any lower proposal reduces the share of group i. Equilibrium spending thus satisfies g~ = g~/= ½(T - b).

(6.9)

6.2.1. Equilibrium debt issue In period 1 the situation is diffbrent, because insisting on high spending eats up future resources. This cost is not high enough, though, to prevent equilibrium over-issue of ~ We also asstune that no group can bid for m o r e than the total available resources. Thus, P(gl) <~ 2"r and p(g~) <~ r - b for i - r, d.

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debt. To see this, consider how debt links spending in periods 1 and 2. Given future equilibrium spending in Equation (6.9) and the budget constraints (6.7), we can write the objective of party I in period 1 as u1 = 2(y - T) + H ( g l ) + H [ z " - (g{ + g J)/2]. When contemplating its spending proposal and taking party Y's proposal as given, party I thus does not internalize more than half the cost of current spending. The optimal proposal satisfies

As the proposals of both parties are identical, they are clearly feasible: the second expression in parentheses is positive, satisfying the feasibility constraint in Equation (6.9). They are thus implemented and the equilibrium spending profile for group i satisfies

H ~ ( g l ) - ' g H g ( g 2 ')

- 0.

AS e~l °-i > g£ for i = d, r, it follows from Equation (6.8) that b > 0. This result is an instance of the familiar common pool argument: as the property rights to future income are not well defined, each of the parties only internalizes a fraction of the cost of current spending and debt issue. The result is a collective irrationality, which departs radically from the cooperative solution. Naturally, with N > 2 groups the problem becomes even worse, because now each party only internalizes I / N of the future costs of debt issue. This model can be generalized in several directions. Velasco (1999) studies a genuine multi-period model. This gives richer debt dynamics, including the possibility of delayed endogenous stabilizations. Chari and Cole (1993) study a two-period model which combines ideas from this and the previous subsection. Legislators facing a free-rider problem that drives spending too high try to constrain future spending and avoid collective irrationality by issuing more debt. Lizzeri (1996) applies a related idea to a very different model of redistribution, originally formulated by Myerson (1993). He considers a two-period economy where elections are held every period. Candidates can make binding promises before elections, over how to redistribute the available resources across voters and over time. Rational voters reward myopic behavior, however, favoring a candidate who promises to distribute all resources today. The reason is that resources left for the future can be taken away by the opponent if the first-period incumbent is not re-elected 53.

53 Tile commonpool problem has also been extensivelystudied in a static context. Persson and 'Ihbellini (1999) smvey that literature.

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6.2.2. A stronger budget process

The over-issue o f debt is obviously caused by a flawed government budget process, where each party o f the coalition (each group) is given decision-making authority over part of the budget, but nobody is given decision-making authority over the aggregate outcome. Which institutional reforms could address this problem? A natural idea is to centralize decision-making authority completely to one of the parties (or perhaps to reform the electoral system, to make majority governments, rather than coalition governments, more likely). I f the same party fully controlled all spending decisions, it would indeed appropriately internalize the cost o f overspending and o f debt issue. Such centralization o f decision-making power could be abused, however. In the model o f subsection 6.1, party I would spend all the revenue evenly over time on its own group, if it had the power to do so. The allocation o f spending across time would thus be fine, but the allocation across groups would be terrible. Moreover, in such a world, electoral uncertainty would re-introduce the incentives for debt issue considered in that section. This problem could be mitigated by institutional "checks and balances", for instance by splitting agenda-setting power between the two groups, giving, say, party D agenda-setting power over the budget size and party R agenda-setting power over its allocation 54. It turns out that a simple institution can implement the socially optimal allocation in the model. The solution is to split the decision in stages. First public debt is chosen. Then the allocation o f g t across different types o f public goods is sequentially determined, first in period 1 and then in period 2, with a separate budget constraint for each period. Suppose that the allocation o f spending is made according to Equation (6.8), except that (r + b) replaces 2 r in the expression for first-period spending on the RHS of Equation (6.8). It is easy to see that both groups now agree to a balanced budget (b = 0), as any other choice would be inefficient for both of them. Since there is unanimity, any mechanism for choosing b would give the same result. Interestingly, the empirical evidence in yon Hagen (1992), von Hagen and Harden (1995) and Alesina et al. (1996) suggests that certain features of the budget process makes it less likely that countries run into public debt problems. One o f the indicators that make up the index of budget stringency in their work is precisely whether the budget process entails a decision on the overall budget, before the decision on its allocation 5s.

54 Fhe effects of some of these checks and balances are investigated in a difterent set up by T. Persson et al. (1997). s5 Hallerberg and yon Hagen (1997) argue that countries with majoritarian electoral systems (and which thus are more likely to have one-party governments) have chosen to centralize power to the finance minister in the budget process, whereas coantries with proportional electoral systems (more likely to have coalitions and minority governments) instead have tried to limit their deficits by adopting formal budget targets.

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Ch. 22." Political Economics and Macroeconomic Policy 6. 3. D e l a y e d stabilizations

In this section we do not focus on why budget deficits arise, but on why it may take time to get rid of them once they have arisen. Following Alesina and Drazen (1991), we illustrate the possibility o f delayed stabilizations when two parties in a coalition government, or two powerful interest groups, both have an incentive to let the other party bear the brunt o f the necessary adjustment. Alesina and Drazen's continuoustime model built on the biological war-of-attrition model o f Riley (1980) and on the public-goods model o f Bliss and Nalebuff (1984). We adapt their analysis to our simple two-period setting. In the model of the previous section, assume that aggregate government spending has got stuck at a level higher than aggregate tax revenue. In particular, assume that gd + gr = g = r +/3, with/3 > 0. As before, tax revenue is exogenously fixed at the same level in each period. We study two possible outcomes: (i) Stabilization is delayed, in which c a s e g ~ + g ~ " = gl = r + / 3 , b = /3, a n d g ~ + g ~ = g2 = r - j 3 . (ii) Stabilization occurs in period 1, in which case aggregate overspending is cut by [3 so that gl = r = g2 and hence b = 0. The allocation o f spending cuts across the two groups in case (ii) depends on how stabilization came about. We return to this question below. We are interested in the probability that stabilization is delayed, and what factors make delay more likely. To simplify the algebra, we assume that the utility o f group i is linear in gi. We assume that the costs o f debt policy enter additively in the utility function. They can be thought o f as either a suboptimal spending allocation over time, or other costs associated with debt issue - perhaps part of the deficit is financed by a distortionary inflation tax. We thus write utility o f group i as u i = 2 ( y - z') + g{ + g i9 - lcib.

(6.10)

The parameter t¢i measures the cost to group i of postponing the stabilization. A crucial assumption is that this cost is private information to group i. G r o u p j only knows that K"i is distributed on the interval [0, ?(] according to the distribution function F(lfi). The corresponding parameter tcJ has the same distribution, but the realizations o f ~ci and tcJ are independent. All political action takes place at the beginning o f period 1, when each party, simul. taneously and non-cooperatively, makes a proposal p/ of whether to stabilize (pl = s) or not (pI = n). If both parties propose n, the stabilization is delayed. But i f at least one party proposes s, stabilization takes place. If only one party "gives in" and proposes s, that party bears the main burden of the necessary cutbacks. Specifically, we assume: gi(n,n)=½(r+/3),

g ~ ( n , n ) = ½(r -/3),

g~(s, n) = g[(n, s) = ~i r - a , g~(n,s)=g~(s,n)=½"r+a, g~(s, s) = gr, '

i=d,r,

t = 1,2, t=l,2~ t=1,2,

i=d,r,

(6.11)

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where gi(pt),pD) denotes how spending on group i depends on the two proposals, and where a > 0 measures the advantage of not giving in. Implicit in Equation (6.11) is the idea that the political process gives veto rights to some party or interest group. Thus, this model applies to countries ruled by coalition governments, or more generally to a situation where the executive is weak and faces effective opposition by organized interests in the legislature or outside of Parliament. Consider one of the parties, say party D. It compares expected utility when proposing n, denoted by E[u d I pd = n], and when proposing s, denoted by E[u d ] pd _ s]. Let q = Pr[p" = s] be the probability that party R proposes s (q is determined in equilibrium). Then, Equations (6.10)-(6.11) and some algebra imply E[ ud I S = n ] - E [ ud [ S = s] = a - ( l

q)tedb.

(6.12)

Thus, it is more advantageous to propose n if the gains from not giving in are large (a is large), if the costs of deficit finance for group d is low (k d is low), and if the probability that party R proposes s is high (q is high). Clearly, party D says no whenever ted is below some critical number K. But, since party R faces an identical decision problem, it also proposes n whenever te" < K. Thus it must be the case that (1 - q ) = F ( K ) . Using that and setting the expression in (6.12) equal to zero, we can implicitly define the equilibrium value of K by: X F ( K ) = all3.

The LHS of this expression is increasing in K. Therefore, K = K ( a , fi), with Ka > 0 and Kf~ < 0. We can now answer the main questions, namely how often we would observe a delayed stabilization and what factors make equilibrium delay more likely. Delayed stabilization requires that both groups propose n. As teJ and te" are independently distributed, the unconditional probability o f observing delay is (1 - q)(1 - q) -- F ( K ( a , f i ) ) F ( K ( a , fi)). The likelihood of delay is thus increasing in a, the gain from winning the war of attrition when the other party gives in first. If we interpret a as a measure of cohesion in the political system, this result thus says that delayed stabilizations and prolonged deficits are more likely in polarized political systems. Note that if a = 0, there is never any delay; postponing adjustment only implies losses for each party. The likelihood of delay is also decreasing in fi, the initial fiscal problem. The model is consistent with the general idea that a worse fiscal crisis makes adjustment more likely; here we get that result because the expected cost of waiting becomes individually larger with a higher ft. Thus, the model supports the general idea that financial crises and times of economic distress resulting from budgetary instability are catalysts of reform, and

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should not be feared too much [Drazen and Grilli (1993)]. The mechanism causing delay in the model, namely a conflict over how to distribute the losses from cutbacks in government programs, also rhymes well with casual observation. Finally, the model can be used to study the consequences of financial aid to developing countries and conditionality [Casella and Eichengreen (1995)]. To be effective, external financial aid should not ease the pain of an unsustainable situation (in terms of our model, it should not reduce fi), for this would simply delay the stabilization. Effective financial aid should instead be conditional on a stabilization taking place and shrink over time if the stabilization is postponed, to increase the incentives to give in early for the rivaling parties. 6.4. Debt and intergenerational politics

The models in this section all focus on how debt redistributes tax distortions, or benefits of government spending, over time. But they ignore another role of debt: redistribution across generations. They also all assume any outstanding debt to be honored by the government that inherits it. But as we have seen in Section 5, this requires a strong form of commitment. Reputational or institutional forces facilitate commitments, but then they should really be part of the argument; such forces may also not go all the way. In conventional representative-agent macroeconomics, debt issue and pay-as-yougo social security are identical policies. Several authors have addressed the political determinants of such policies in a median-voter setting without altruism - see Browning (1975) for an early contribution, Boadway and Wildasin (1989), and Cooley and Soares (1999). In these papers, future social-security policies are honored by assumption (at least in the next period); i.e. commitment is assumed. Working agents not too far from retirement favor introducing pay-as-you-go social security, as this allows them to free ride on younger agents. Old-age agents are, of course, also in favor. Therefore a majority of voters typically favors social security and equilibrium policy depends, in a predictable way, on age-earning profiles and the population growth rate. Cukierman and Meltzer (1989) analyze budget deficits in a similar way, but introduce inter-generational altruism. The degree of altruism varies across households: some households leave positive bequests, but others are bequest-constrained. Nonconstrained voters, who can undo any intergenerational redistribution, are only concerned with the general equilibrium effects of the policy, and not on how it redistributes across generations. But a budget deficit is favored by the bequestconstrained voters, because it allows them something they cannot do privately redistribute resources towards themselves. In a median voter equilibrium, the size of the budget deficit depends of the efficiency effects and the number of bequest-constrained voters. Even though these contributions introduce important aspects of politics, they still hinge on the commitment assumption. At any moment social security strictly benefits

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only a minority (the retired) but imposes a cost on a majority (the workers). A similar problem exists for debt. Why then does the majority not repeal the policy? Reputational concerns may help, if honoring the current program enhances the probability that it will be honored in the future. But as we have already discussed in Section 5, this argument is not without problems. Tabellini (1990, 1991) suggests one should allow intra-generational heterogeneity in income, when thinking about these questions. Pure intergenerational policies rarely exist, at least when generations are altruistically linked. Social security programs thus redistribute not only from kids to parents, but also from rich to poor. Similarly, public debt default would have both intergenerational and intragenerational effects (as the rich are likely to hold more debt). A policy redistributing across generations may therefore be upheld in equilibrium, without ex ante commitments, by a coalition of voters that contains members of different generations who belong to similar income groups. But the coalitions that form ex p o s t to support existing social security and outstanding debt are different. Social security is supported by the old and the kids of poor parents, whereas debt is supported by the old and the kids of rich parents. These two intergenerational policies are thus not equal under heterogeneity and lack of commitment. As in Section 5, incentive constraints in policymaking violate the Modigliani-Miller theorem of government finance. Majority voting is not the only way of thinking about how the policy preferences of different generations get aggregated in the political process. In many societies, different age-groups - the old, in particular - have well-organized interest groups that lobby and take other political action to support policies benefitting their members. Rotemberg (1990) discusses the repayment of government debt as the outcome of bargaining between living generations. Grossman and Helpman (1996) formulate a dynamic model of intergenerational redistribution where policy commitments are again not feasible. In the model, pressure groups of living generations make contributions to the government conditional on the support given to their members. The model has multiple expectational equilibria, which remind of the equilibria in capital taxation studied in Section 5. But it is the expectations of the current goverm'nent - rather than the expectations of private agents - about the policy of the next government that introduce the self-fulfilling property. One can easily end up in a very bad equilibrium, where the pressure groups get engaged in a very stiff and costly competition for policy favors and Where capital formation suffers.

6.5. N o t e s on the literature

A huge literature deals with the politics on government deficits. Here we only refer to the more recent contributions, that typically study general equilibrium models with rational voters and politicians. A broader survey of the public choice literature is Mueller (1989). Much of the modern macroeconomic literature on public debt is surveyed in Alesina and Perotti (1995a).

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The idea that political instability induces a govermnent to use public debt strategically, to influence the future policies of its opponent, was first independently studied by Alesina and Tabellini (1990) and Persson and Svensson (1989). The model of subsection 6.1 is related to Alesina and Tabellini (1990), while Persson and Svensson (1989) studied a model where parties disagree on the overall size (as opposed to the composition) of public spending. Since then, many other papers have applied this idea to intertemporal fiscal policy. In particular, Tabellini and Alesina (1990) provide a generalization of these results, Alesina and Tabellini (1989) study capital flight and external borrowing, Tabellini (1990) looks at these models in the context of international policy coordination, Glazer (1989) applies the same idea to the choice of duration in public investment, Cukierman et al. (1992) analyze tax reforms from this point of view and provide empirical evidence that political instability is associated with more inefficient tax systems, and Roubini and Sachs (1989), Grilli et al. (1991), Ozler and Tabellini (1991) and Lambertini (1996) analyze the empirical evidence. Finally, the result that public debt policies also affect the re-election probability was first studied in this context by Aghion and Bolton (1990). Modeling the voters' preferences as entailing a trade-off between economic and non-economic dimensions, as we do in subsection 6.1, is a common strategy in some of this literature - see in particular Lindbeck and Weibull (1987). The dynamic "common pool" problem has a long history. It has been studied in industrial organization, where it refers to dynamic games among oligopolists facing an exhaustible resource, such as an oil field or a fishery [Levhari and Mirman (1980), Benhabib and Radner (1992)]. In fiscal policy, it was studied by Tabellini (1987) in a dynamic game of monetary and fiscal policy coordination, and by Velasco (1999) in a setting more similar to that of this model. This idea is also at the core of the more empirically oriented literature on budgetary procedures, such as Alesina and Perotti (1995a), von Hagen and Harden (1995), and Hallerberg and yon Hagen (1997). There is also an interesting (mainly empirical) line of research, that has investigated the effects of various restrictions on government borrowing. Most of this literature has studied the variety of institutional arrangements in US states. See for instance Bohn and Inman (1996), Poterba (1994), and Eichengreen and yon Hagen (1996). The model of delayed stabilizations is due to Alesina and Drazen (1991), who in turn have elaborated on earlier ideas by Riley (1980) and Bliss and Nalebuff (1984). Since then, the model has been extended in several directions, among others, by Drazen and Grilli (1993), Casella and Eichengreen (1995) and Alesina and Perotti (1995b). Finally, a large literature deals with intergenerational redistribution. Besides the papers quoted in the previous subsection, a separate line of research has investigated the sustainability of social-security systems in reputational models [Kotlikoff eta!. (1988), Boldrin and Rustichini (1996)].

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Part C. Politics and Growth Distorted fiscal policies, such as those emerging from the political equilibria in Part II, are likely to affect economic performance. It is therefore natural to ask whether political factors and political institutions are correlated with long-run economic growth. Here, too, there are some stylized facts. Most notably, after controlling for the conventional determinants o f growth: (i) Inequality in the distribution o f income or wealth is significantly and negatively correlated with subsequent growth in cross-country data. On the other hand, the evidence on the effect o f growth on the distribution o f income (the Kuznets curve) is quite mixed, both in cross section and time series data 56. (ii) Political instability, as measured by more frequent regime changes, or political unrest and violence, is significantly and negatively correlated with growth in cross-country data 57. (iii) Better protection of property rights is positively and significantly correlated with the growth. Whereas political rights and the incidence o f democracy are strongly correlated with the level o f income, there are no robust findings regarding the effect o f democracy on economic growth. 58 A recent literature has tried to explain these regularities in a setting where both economic growth and fiscal policies are endogenous. Section 7 surveys this literature.

7. Fiscal policy and growth Subsection 7.1 illustrates how income inequality can produce a negative effect on investment and growth, because it provides stronger incentives for redistributive policies that hurt growth-promoting investment. This idea was suggested by Alesina and Rodrik (1994) and Persson and Tabellini (1994b). As in these papers - and a great deal of subsequent work - we rely on a simple median-voter model inspired by Roberts (1977) and Meltzer and Richards (1981). Subsection 7.2 then illustrates how political instability can hurt growth, by inducing the incumbent government to follow more myopic policies, as in the work by Svensson (1996) and Devereux and Wen (1996). The argument here is closely related to that on strategic debt policy in subsection 6.1. Finally, subsection 7.3 briefly discusses how poor protection o f property rights may hurt investment and growth, as in Tornell and Velasco (1992)

56 This finding was first obtained by Atesina and Rodrik (1994) and Persson and Tabellmi (1994b). For a recent and comprehensive survey of the empirical evidence on inequality and growth, see Perotti (1996). 57 On this point see Alesina et al. (t996) and Barro (1991). 58 On the relation be~ieen property rights and growth see Knack and Keefer (1995). A survey of the voluminous literature on the links fi-om democracy to growth can be found in Przeworski and Limongi (1993).

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and Benhabib and Rustichini (1996). The underlying ideas are closely related to the dynamic common-pool problem discussed in subsection 6.2. 7.1. I n e q u a l i t y

and growth

Consider again a two-period economy inhabited by a continuum of heterogenous agents. Everyone has the same quasi-linear preferences over private consumption in periods 1 and 2 and over government (per capita) consumption in period 2. The utility of consumer i is:

u' = u(c~)+ c~ +H(g)

(7.1)

The budget constraints are C i1

e i - r - k i,

(7.2)

C2i = (1 - O) A ( 1 ) k i,

where k i is private investment, r and 0 lump-sum and capital taxes, and A ( I ) the gross return to private capital, which is increasing in public investment 1. We abstract from credibility problems; the government can commit to these policy instruments before private capital accumulation. Finally, e i is the endowment of agent i. These endowments are distributed in the population with mean e and a distribution function for the idiosyncratic part F ( e i - e). To proxy empirical income distributions, we assume that F is skewed to the right: the median value o f e i - e, labeled e" - e and defined by F ( e " - e) ½, is negative. Assuming a balanced budget in every period, the government budget constraint in per capita terms is: I = "r,

(7.3)

g = OA(l)k,

(7.4)

where k denotes per capita (average) capital. Following the approach of subsection 5.1, we can derive equilibrium private investment from Equations (7.1)-(7.3) as k i = e - I - UcI(A(I)(1

- 0)) + ( e i - e) =~ K ( O , I )

+ ( e i - e),

where the common investment function satisfies K0 < 0 and K1 > 0. It is again convenient to express the utility from private consumption as an indirect utility function defined over the policy variables: ji(o,[,

e i) --~

Max[U(ci0 + c~]

=U(e-I-K(O,I))+(I = J(O,I)

O)A(I)K(O,I)+A(I)(t-O)(e

i

e)

~ A ( I ) (1 - O)(e i - e).

(7.5) By the envelope theorem, the direct welIhre cost of the capital tax Jo = - A ( I ) K is negative. Moreover, the welfare effect of public investment, .11 = -U~ + (1 - O ) A t K , is

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Z Persson and (5. Tabellini

monotonically decreasing in I (by Ucc < 0 and AH < 0). Substituting Equation (7.5) into (7.1) and using (7.3), we obtain individual-/policy preferences over the two policy instruments 0 and I: u i = j i ( o , I, e i) + H ( O A ( I ) K ( O , I)).

These policy preferences are linear in the idiosyncratic variable e i. They therefore fulfill a monotonicity (single-crossing) condition, such that the preferred policy of the agent with endowment e m will be a Condorcet winner, even though the policy space is two-dimensional. If we imagine that policy decisions are taken at the begilming of period 1 by direct democracy, the winning proposal is thus the policy preferred by this decisive voter. I f the second-order conditions are fulfilled 59, the equilibrium values for I and 0 thus satisfy dl + It~,O(KAI + A K D + (em -- e)(1 - O)AI = O, Jo + H g A ( K + OKo) - (e" - e ) A = O.

(7.6)

To understand these conditions, first assume that the distribution is symmetric, so that e m = e. Then the third terms in both conditions are zero, and Equation (7.6) characterizes the optimal policy for the average agent, which by quasi-linear preferences - would be chosen by a utilitarian planner. The first condition says that it is optimal to provide more public investment than would maximize private indirect utility (i.e. Jr < 0) due to the beneficial effects on the future tax base and hence on public spending (if public debt were allowed this result would be different). The second condition equates the average private marginal cost of raising revenue (Jo < 0) with the marginal benefit it generates via public consumption. But if e m < e, redistributive effects come into play. The decisive voter's capital falls short of average capital by exactly (e m - e). This implies that I is smaller and 0 is higher than in the hypothetical planning solution. The reason is that the decisive w,ter does not benefit from public investment as much as the average capital holder, and he also does not suffer as much from capital taxes. To see this formally, notice that the third term in the first equation of (7.6) is negative and the third term in the second equation is positive. By the second-order conditions, ! has to be lower and 0 has to be higher than in the social planner's solution. We thus see that inequality hampers growth via two different channels. The growth rate from period 1 to period 2, given by [ A ( 1 ) K ( O , I ) / e ] - l, is increasing in I (both directly and indirectly) and decreasing in 0. Furthermore, the higher is inequality, as measured by the distance between median and average income, the lower is growth as equilibrium public investment is smaller and capital taxation - as well as government consumption - is higher. ~') As hi all optimal taxation problems, this assumption is not necessarily innocuous, but can involve restrictive assumptions on underlying fimctional forms.

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Alesina and Rodrik (1994) and Persson and Tabellini (1994b) developed this kind of reduced-form prediction in related but explicitly dynamic models. Whereas Persson and Tabellini (as we have done) focused on the size distribution of income, Alesina and Rodrik focused on the functional distribution of income between labor and capital. Both papers also took the reduced-form prediction to the data - here Alesina and Rodrik too look at the size distribution of income. And they indeed found a strong negative effect of inequality on growth in a cross section of post-war data from a broad sample of countries 60. These papers stimulated a body of subsequent work scrutinizing both the empirical and the theoretical argument. Whereas the reduced-form relation from inequality to growth indeed seems empirically robust, the structural links implied by the theory have not generally found support in later empirical work 61. Thus, it has been hard to identify both the implied link from inequality to redistribution and the link from redistribution to growth, as emphasized in the recent surveys by Perotti (1996) and Benabou (1996). The model in this section suggests that these links could be pretty subtle, however (with opposite effects of inequality on government consumption and investment, for example, and ambiguous effects on total government spending). Moreover, the failure to find a robust link from tax rates and redistribution to economic growth is a problem for conventional growth theory, not just for political theories of growth. The literature has also searched for other reasons why inequality and growth may be inversely related. Perotti (1996) stresses that one link may run via political instability or via other, non-political, channels such as education. Benabou covers a whole range of recent theoretical work showing that the links between income distribution, policy and growth may run in different directions. For instance, redistribution may promote growth when agents are credit constrained, or when it promotes education.

7.2. Political instability and growth We now modify the previous model as follows. First, every private agent has the same first-period endowment: that is, e i = e and the average investment function K(O,I) applies for everyone. Instead, as in subsection 6.1, agents belong to two different groups, d and r, and public spending is of either of two types: gJ (benefitting only group d) or g" (benefitting only group r). Second, and again following subsection 6.1, policy is not set by majority rule but by an incumbent government D that acts so as to maximize the utility of group-d agents. The incumbent may be replaced by an alternative government R in the future.

r,0 Perssonand Tabellini (1994b) also round a similar relation in a small historical panel of industrialized countries with data going back to the late 19th century. ~l Later empirical work based on better data has also questioned an empirical finding by Persson and Tabellini (1994b) that was interpreted as giving indirect support for the theory-,namely that the relation between inequality and growth was only present in democracies and not in dictatorships.

Z Persson and G. Tabellini

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For simplicity, we take the re-election probability (1 - P ) as exogenous. It is natural to interpret P as a measure o f political instability. Third, to introduce a meaningful policy choice in period 2, policies are chosen sequentially. Thus, public investment I is chosen in period 1, before private capital, and the capital tax rate 0 is chosen in period 2. To avoid the capital-levy problem discussed in Section 5, we assume that in period 2 the private sector can still avoid some of the tax, though at a cost, by reallocating some o f its accumulated capital to a non-taxed asset with a lower return. We could think o f this as tax avoidance, or capital flight. A convenient formulation, following Persson and Tabellini (1992), is to rewrite the period-2 budget constraint as c2 = (1 - O)A(I)(k - f ) + f - M ( f ) , where M ( f ) is a concave and increasing function o f the amount f shielded from taxation and where we have recognized that everybody makes the same savings decision. It is easy to show that average savings are still given by the function K(O, I) and that tax avoidance is given by the function F ( O , I ) with Fo > 0 and FI < 0 62. The government's tax base can thus be written as a function K ( O , I ) = A ( I ) K ( O , I ) - F(O,I). The ex ante properties o f this function (that is from the viewpoint of period 1) are the same as before: decreasing in 0 and increasing in I. in period 2, when K and I are given from previous decisions, the ex post tax base K 2 ( 0 , I ) is still decreasing in 0 but with a smaller slope (intertemporal substitution possibilities are eliminated). The bottom line after these modifications is similar to the previous section: we can write the ex ante indirect utility of an agent in group i as u i = J(O, I) + H ( g i) - J (0, I) + H(OK(O, I)).

(7.7)

We can also define ex post indirect utility (for given K and I) as j2(O, I) + H ( O K --2 (O,D). Both J(O,I) and j2(0, I) have the same qualitative properties as the corresponding function in subsection 7.1. Any government holding power in period 2 spends all revenue on the public good favored by its own constituency. The expost optimal tax rate is given by the condition: +H

(K 2 +

= 0,

(7.8)

which has the same interpretation as the second condition in Equation (7.6). Thus, both prospective governments will set the same tax rate. Condition (7.8) implicitly defines the optimal tax rate as a function o f past public investment O(I), with slope o, =

4 + --2 ° Jgo + HggKo0

(i? The first--order condition for optimal tax avoidance is for the consumer to set A(I)(1 Mr(f) = 0. When this condition is inverted, we get the desired tax avoidance function.

O)

1 -I

Ch. 22.. PoliticalEconomics and MacroeconomicPolicy

1471

Unless H is very concave, Ol > O, as the numerator is positive and the denominator is negative (by the second-order condition). Public investment enlarges the tax base and this drives up the optimal tax rate. The incumbent party-D government in period 1 chooses I so as to maximize

E ( S ) : PJ(O(1),I) + (1

P)[J(O(I),I) + H(O(1)K(O(1),I))]

= J(O(I), I) + (1 - P)[H(O(I)K(O(1), 1-))]. We can rewrite the first-order condition to this problem with Equation (7.8), recognizing that J~ = Jo and g2 = ~ at the equilibrium tax rate. Some additional algebra gives

Jl +Hg[OKI + O(Ko --K2o)Ol] PHg[OKI + 0I(K + OKo)] = O.

(7.9)

Suppose first that D is certain to be re-elected: P = 0. Then the optimal choice o f / b o i l s down to the familiar weighting of private welfare (the first term) against government revenue (the second term), where the latter are fully internalized as the government is certain to remain in office. The resulting condition is the same as the second condition in Equation (7.6) of the previous subsection, adjusted for the different timing of tax policy and for the lack of heterogeneity. But when re-election is uncertain, P > 0, future government revenue is less valuable and policy myopia sets in. As the third term in Equation (7.9) is negative, a higher probability P of losing office makes public investment less attractive and reduces it in equilibrium. Higher instability not only draws down public investment, but reduces growth in this model. Second-period income, c2 + g = A(I)K(O, I ) - M(F(O, I)), unambiguously goes down as I falls. The direct negative effects of lower public investment and the indirect negative effects of higher waste due to more tax avoidance always outweigh the positive effects of the smaller equilibrium capital tax. Much of the informal discussion of why political instability is harmful for growth seems to suggest a direct effect of uncertainty or unpredictability on private investment. We know, however, that uncertainty in returns has ambiguous effects on private investment. Here a different mechanism is at work: political instability induces more myopic fiscal policies, which in turn cause lower public investment and growth. This is related to Svensson (1998), who shows that political instability may make a forwar& looking government abstain fi'om improvements in the legal system that enforce private property rights. He also finds empirical support for this idea. Political instability [as measured by Alesina et al. (1996)] indeed reduces the protection of private property rights [as measured by the same index as in Knack and Keefer (1995)] in a wide crosscountry sample. And controlling for property-rights protection, political instability drops out of a cross-country investment regression. The theoretical paper by Devereux and Wen (1996) emphasizes a somewhat different mechanism: political instability induces incumbent governments to leave smaller assets to their successors, thereby forcing theln to tax capital at a higher rate; the expectation of higher taxes drives down private investment, which leaves a smaller tax base for the successor government.

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7. 3. Property rights and growth

As mentioned in the introduction, the data support the idea that poor enforcement of property rights is harmful for investment and growth. This idea is also derived from some recent theoretical work. Benhabib and Rustichini (1996) study a growth model where two groups try to redistribute consumption towards themselves at the expense of the economy's capital stock. They show how such incentives may arise both at low and high levels of income, and how they may be exacerbated by greater inequality in the two groups' incomes. Their model abstracts from the political mechanism and the channels of redistribution, however. Tornell and Velasco (1992) focus on redistribution through the fiscal policy process in a linear (Ak) growth model. Their argument, as Benhabib and Rustichini's, is another instance of the common pool problem discussed in subsection 6.3. The common pool is now a part of the economy capital stock rather than the government tax base, but the incentive to over-exploit this common pool is the same. Because the redistribution is supposed to take place via the governlnent policy process, the poorly enforced property rights are closely related to weak government. Tornell (1995) studies a related model, but allows for endogenous property rights. in particular, property rights can be created and destroyed at a cost. He shows that the economy can go through a cycle with low property-rights protection at low and high levels of income. I f so, this pattern is perfectly foreseen and leads to gradually falling growth rates at intermediate levels of income. Lane and Tornell (1996) show that an exogenous positive shock due to productivity or the terms of trade may actually reduce the growth rate in an economy with powerful interest groups and poorly defined property rights. The mechanism is again a coordination failure between the interest groups, whereby the initial increase in the incentives to invest is more than outweighed by an increase in redistributive transfers. Svensson (1996) produces a related result, where the incentives of the interest groups to hold back on their demand for transfers vary negatively with government income. 7.4, Notes" on the literature

Beyond the papers cited in the text, early contributions to the theory of income distribution," investment and growth were made by Perotti (1993), who studied human capital accumulation, and tax-financed subsidies in the presence of borrowing constraints, by Bertola (1993) who studied tax policy and the functional distribution of income, by Glomm and Ravikumar (1992) who studied private versus public provision of education, and by Saint-Paul and Verdier (1993) who also studied redistributive policies that finance public education in a setting with wealth-constrained individuals. Perotti (1996) and Benabou (1996) provide additional references to recent empirical work. Finally, Caballero and Hammoar (1996) focus on the rents created by factor specificity and how the distribution of those rents affects the incentives to invest. As stated in the text, few theoretical models spell out the mechanisms whereby political

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instability is harmful for growth. As emphasized by Benabou (1996), there is thus scope for new work to provide better theoretical underpinnings for the empirical findings. Sharper theory is also needed to sort out the empirical channels whereby politics interacts with growth. This is not going to be easy, however, given the strong empirical correlations between inequality, instability and lacking enforcement of property rights. We want to end with a methodological note. In this section, as in the previous one, we have relied exclusively on simple two-period examples. This avoids a major difficulty: a full-fledged treatment o f the dynamic interactions between collectively chosen policy decisions and income distribution rapidly becomes analytically complex. As a result, the dynamic models studied in the literature have often relied on simplifying assumptions: dynamic links are assumed away in the model's economic structure, voting only takes place at an initial point in time rather than sequentially over time, or agents are assumed to be myopic and ignore some o f the dynamic implications of their actions. The clearest formulation of a general solution concept for dynamic political models with heterogenous agents is made in Krusell and Rios-Rull (1996). This paper also makes a contribution by showing how the endogenous build-up of vested interests, as agents acquire monopoly skills in operating new technologies, can lead to a growth cycle: the political majority at different points in time will shift between less and more growth-promoting policies. Krusell et al. (1997) survey parts of the literature on politics and growth from a methodological angle. They also show how to go from their proposed solution concept to quantitative (numerical) applications.

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Herrendorf, B., and B. Lockwood (1997), "Rogoff's 'conservative' central breaker restored", Journal of Money, Credit and Banking 29:476-495. Hibbs, D. (1977), "Political parties and macroeconomic policy", American Political Science Review 71:1467-1478. Holmstrom, B. (1982), "Managerial incentive problems a dynamic perspective", in: Essays in Economics and Management in Honor of Lars Wahlbeck (Swedish School of Economics, Helsinki). Horn, H., and T. Persson (1988), "Exchange rate policy, wage formation and credibility", European Economic Review 32:1621-1636. Ito, T. (1990), "The timing of elections and political business cycles in Japan", Journal of Asian Economics 1:135 146. Jensen, H. (t997), "Credibility of optimal monetary delegation", American Economic Review 87: 911-920. Jonsson, G. (1995), "Institutions and macroeconomic outcomes - The empirical evidence", Swedish Economic Policy Review 2:181-212. Jonsson, G. (1997), "Monetary politics and unemployment persistence", Journal of Monetary Economics 39:303 325. Knack, S., and R Keefer (t995), "Institutions and economic peribrmance: cross-country tests using alternative institutional measures", Economics and Politics 7:207 227. Kotlikoff, L., T. Persson and L.E.O. Svensson (1988), "Social contracts as assets: a possible solution to the time-consistency problem", American Economic Review 78:662-677. Krusell, E, and V, Rios-Rull (1996), "Vested interests in a positive theory of stagnation and growth", Review of Economic Studies 63:601-631. Krusell, E, V. Quadrini and V Rios-Rull (1997), "Politico-economic equilibrium and economic growth", Journal of Economic Dynamics and Control 2t :243~72. Kydland, EE., and E.C. Prescott (1977), "Rules rather than discretion: the inconsistency of optimal plans", Journal of Political Economy 85:473M90. Lambertini, L. (1996), "Are budget deficits used strategically'?", mimeograph (UCLA). Lane, E, and A. Tornell (1996), Power, growth and the voracity effbct, Journal of Economic Growth 1:213-241. Leiderman, L., and L.E.O. Svensson, eds (1995), inflation Targets (CEPR, London). Levhari, D., and L. Mirman (1980), "The great fish war: an example using the Cournot-Nash solution", Bell Journal of Economics 11:322-334. Lewis-Beck, M. (1988), Economics and Elections: The Major Western Democracies (University of Michigan Press, Ann Arbor, MI). Lindbeck, A. (1976), "Stabilization policies in open economies with endogenous politicians", American Economic Review Papers and Proceedings 66:1-19. Lindbeck, A., and J. Weibull (1987), "Balanced budget redistribution as the outcome of political competition", Public Choice 52:272-297. Lippi, E (1998), "On central bank independence and the stability of policy targets", Scandinavian Journal of Economics 100:495-512. Lizzeri, A. (1996), "Budget deficits and redistributive politics", mimeograph (Princeton University). Lockwood, B., and A. Philippopoulus (1994), "Insider power unemployment and multiple inflation equilibria", Economica 61:59 -77. Lockwood, B., M. Miller and L. Zhang (1998), "Designing monetary policy when unemployment persists", Economica 65:327-345. Lohman, S. (1992), "The optimal degree of conmritment: credibility and flexibility", American Economic Review 82:273-286. Lohman, S. (1996), °'Democracy and inflation", mimeograph (UCLA). Lucas, R.E., and N.L. Stokey (1983), "Optimal fiscal and monetary policy in an economy without capital", Journal of Monetary Economics 12:55-94.

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von Hagen, J., and I. Harden (1995), "National budget processes and fiscal performance", European Economy, Reports and Studies 3. Waller, C. (1989), "Monetary policy games and central bank politics", Journal of Money, Credit and Banking 21:422-431. Waller, C., and C.E. Walsh (1996), "Central bank independence, economic behavior, and optimal term limits", American Economic Review 96:1139-1 t 53. Walsh, C.E. (1995a), "Optimal contracts for central bankers", American Economic Review 85:150-167. Walsh, C.E. (t995b), "Is New Zealand's Reserve bank act of 1989 an optimal central bank contract?", Journal of Money Credit and Banking 27:1179-1191.

Chapter 23

ISSUES

IN THE

DESIGN

OF MONETARY

POLICY

RULES *

BENNETT T. McCALLUM Carnegie Mellon University and National Bureau of Economic Research

Contents Abstract Keywords 1. Introduction 2. Concepts and distinctions 3. Special difficulties 4. Choice o f target variable 5. Choice o f instrument variable 6. Issues concerning research procedures 7. Interactions with fiscal policy 8. Concluding remarks References

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The author is indebted to Peter B. Clark, 'lodd Clark, Charles Evans, Robert Flood, Marvin Goodfriend, Charles Goodhart, An(hew Haldane, Robert Hetzel, Lars Joining, Allan Meltzer, Edward Nelson, Christopher Sims, Lars Svensson, John Taylor, John Whittaker, and especially Michael Woodford for helpful suggestions and criticisms. Handbook qf Macroeconomics, Volume 1, Edited by AB. laylor and M. WoodJbrd © 1999 Elsevier Science B.V. All rights reserved

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Abstract

This chapter begins with a number of important preliminary issues including the distinction between rules and discretion in monetary policy; the feasibility of committed rule-like behavior by an independent central bank; and optimal control vs. robusmess strategies for conducting research. It then takes up the choice among alternative target variables - with the most prominent contenders including price level, nominal income, and hybrid (inflation plus output gap) variables - together with the issue of growth-rate vs. growing-level target path specifications. One conclusion is that im'tation and nominal income growth targets, but not the hybrid target, would have induced fairly similar policy responses in the US economy over 1960-1995. With regard to instrument choice, the chapter argues that both nominal interest rate and monetary base measures are feasible; this discussion emphasizes the basic conceptual distinction between nominal indeterminacy and solution multiplicity. Accordingly, root-mean-square-error performance measures are estimated for interest rate and base instruments (with nominal income target) in the context of a VAR model. Other topics emphasized in the chapter include the operationality of policy-rule specifications; stochastic vs. historical simulation procedures; interactions between monetary and fiscal policies; and the recently-developed fiscal theory of the price level.

Keywords JEL classification: E52, E58

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1. Introduction The topic o f rules for the conduct o f monetary policy has a long and distinguished history in macroeconomic analysis, with notable contributions having been made by Thornton (1802), Bagehot (1873), Wicksell (1907), Fisher (1920, 1926), Simons (1936), M. Friedman (1948, 1960), and others 1. A major reorientation in the focus of the discussion was provided as recently as 1983, however. In particular, Barro and Gordon (1983a) built upon the insights of Kydland and Prescott (1977) in a manner that put an end to the previously widespread notion that policy rules necessarily involve fixed settings for the monetary authority's instrument variable. This step served to separate the "rules vs. discretion" dichotomy from the issue o f "activist vs. nonactivist" policy behavior and thus opened the door to possible interest in policy rules on the part o f actual monetary policymakers - i.e., central bankers. In fact there has been a great increase in apparent interest in rules by policymakers during recent years - say, 1990-1996. Evidence in support o f that claim is provided by several studies conducted at the Federal Reserve's Board o f Governors of the rule introduced by John Taylor (1993b), such as Brayton et al. (1997) and Orphanides et al. (1998), as well as by discussions of this rule in speeches by members o f the Board [e.g., Blinder (1996)]. In the United Kingdom, interest by the Bank o f England in Taylor's rule as well as an alternative due to McCallum (1988, 1993a) is clearly indicated in an article by Stuart (1996) that attracted considerable attention in the British press. Numerous analytical studies of these rules 2 have been conducted by central bank economists from a number of countries 3. To some extent this upsurge in interest is related to the arrival o f inflation targeting as a leading candidate for the provision o f a practical guideline for monetary policy, significant applications having been introduced during 1990-1993 in Canada, New Zealand, Finland, Sweden, and the United Kingdom 4. There are, to put it mildly, numerous issues concerning monetary policy rules on which professional agreement is far from complete, even among academics that is, even neglecting the split between academic and central-bank views, which itself has probably diminished in recent years. The main purpose o f this chapter is to survey the most critical of these issues. The first to be discussed, which concerns the fundamental nature of policy rules and an independent central bank's capacity to

1 For other early rule proposals, see Laidler (1996) and Humphrey (1992). Also see Jonung (1979) for an interesting discussion of the Swedish experience of the 1930s. 2 Including proposals of Meltzer (1984, 1987), Hall (1984), Hall and Mankiw (1994), Feldstein and Stock (1994), and Gavin and Stockman (1990). 3 An incomplete list of notable studies would include those mentioned above plus Hess, Small and Brayton (1993), Clark (1994), Croushore and Stark (1995), Dueker (1993), Dueker and Fischer (1995), Estrella and Mishkha (1997), Judd and Motley (1991, 1992), Haldane and Salmon (1995), King (1996), and Jefferson (1997). Many more have been added since this chapter was written, most featuring Taylor's rule. 4 There is a sizable and growing litcrature on inflation targeting that will be mentioned below.

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behave in accordance with a rule - i.e., the commitment problem - is reviewed in Section 2. Next, Section 3 takes up some special difficulties that bedevil all attempts to design good policy rules and also to study ones previously proposed, namely, the lack of agreement (especially among academics) concerning models of monetary policy effects - and the associated social costs of inflation and unemployment - plus the existence of ongoing changes in economic structure relevant to monetary policymaking (e.g., improvements in payments technology). Two major substantive areas of rule design, the specification of target and instrument variables, are then taken up in Sections 4 and 5. In the first of these, the choice among basic target variables - such as exchange rate, price level, or nominal income measures - is considered along with the desirability of specifying target paths in trendstationary or difference-stationary form (i.e., levels vs. growth rates). In the second, the classic dispute between advocates of interest-rate and monetary-base (or bank reserve) instruments is reviewed, brief discussions being given of the rather extreme views that one or the other is actually infeasible as an instrument. The following pair of sections, 6 and 7, take up a number of analytical issues involving the study of candidate rule specifications. Among these are the design of simulation exercises; issues involving operationality (i.e., feasibility of specified instruments and information sets); and the interaction of monetary and fiscal policy rules. Finally, a brief conclusion is included as Section 8. Since the author has been writing on the subject of monetary rules for well over a decade, it would be futile to pretend that the chapter's discussion will be entirely "balanced" or "unbiased". What is intended, rather, is that important alternative points of view are mentioned and presented with reasonable accuracy even where agreement is lacking. Another recent overview is provided by Clarida, Gali and Gertler (1999).

2. Concepts and distinctions The crucial point that a policy rule can be activist has already been mentioned. Of course this is a matter of definition; thus the use of a terminological system that does not permit rules to be activist i.e., to involve policy instrument settings that are conditional on the state of the economy - cannot be ruled out on strictly logical grounds. But since the publication of Barro and Gordon (1983a), standard usage in the profession has been virtually unanimous in permitting activist rules and in basing the "rules vs. discretion" distinction on the manner in which (typically activist) instrument settings are determined. Roughly speaking, discretion implies period-byperiod reoptimization on the part of the monetary authority whereas a rule calls for period-by-period implementation of a contingency formula that has been selected to be generally applicable for an indefinitely large number of decision periods. The foregoing distinction is satisfying and straightforward to apply in the context of the simple "workhorse" model that features a surprise Phillips curve as utilized by Kydland and Prescott (1977), Barro and Gordon (1983a,b), and a host of subsequent

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writers. When it comes to practical application to the behavior o f actual central banks, however, the distinction is not so easily drawn. Suppose that a particular central bank, which presumably cares about both inflation and unemployment outcomes, is observed regularly to be more stimulative when recent unemployment is high and/or current macroeconomic shocks threaten to increase unemployment. How does one decide whether this central bank's behavior should be classified as discretionary or rule-based but activist? Within a simple model one can calculate the settings implied by each type of behavior, or simply observe whether inflation exceeds its target value on average (i.e., whether the discretionary inflation bias is present). But such steps are not possible for an actual central bank, because there will typically not be any clear-cut agreement concerning the nature and magnitude o f shocks that have occurred in specific historical periods or even (in many cases) agreement as to the prevailing target inflation rate expressed in precise quantitative terms - even for analysis within the central bank itself. Taylor (1993b) explicitly addressed the problem of distinguishing "rule-like" from discretionary behavior in practice, recognizing that no actual central bank would be likely to follow literally a simple formula for its instrument settings but contending that the distinction could be of importance nevertheless 5. The key, Taylor suggested, is that rule-like behavior is systematic in the sense of"methodical, according to a plan, and not casual or at random". Clearly, being systematic is a necessary condition for rule-like behavior, but even those central bankers who defend discretionary behavior do not think of it as unsystematic. Accordingly, McCallum (1993b) argues that being systematic is not sufficient and points out that discretionary behavior in the workhorse model can, even with the inclusion o f random shock terms, be accurately represented by systematic application o f a simple formula. The needed additional criterion, McCallum suggests, is that the monetary authority "must also design the systematic response pattern [so as] to take account o f the private sector's expectational behavior" (p. 217), i.e., to optimize once, not each period. Taking such account is basically what Barro and Gordon (1983a) specified in their characterization, within the workhorse model with rational expectations, o f policy according to a rule. There is then no attempt to exploit temporarily given inflationary expectations for brief output gains 6. Qualitative knowledge of the policymaking process o f an actual central bank may then be sufficient in some cases to determine whether or not policy responses are designed to try to exploit temporarily given expectations.

5 Taylor, like Judd and Motley (1992), envisions the genuine possibility that central bard~ policy committees would enrich their considerations by referring to the instrument settings suggested by a numerical rule, e.g., taking them as a starting point for their policy deliberations. 6 It may be asked why a one-time optimization will not involve the exploitation of expectations that happen to exist at the time. But my meaning of systematic implies that the same actions are specified each time the same conditions are faced, so the response pattern cannot be different for the "first" or "first few" periods. Basically, the optimization calculation must be made fi:om the perspective of a dynamic stochastic steady state.

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It is interesting to note, parenthetically, that although Milton Friedman has never embraced the concept o f activist rules, in one o f his most carefully considered arguments on b e h a l f o f nondiscretionary monetary policy the crucial advantage o f a rule is said to be that decisions are made in the form o f a policy applicable to many distinct cases, not on a case-by-case basis, with such a form o f policymaking having favorable effects on expectations. In particular, Friedman (1962) suggests that monetary policymaking is in important ways analogous to freedom-of-speech issues, in the sense that adopting a rule that applies in general will on average lead to different and preferable - outcomes than those generated by decision making on a case-by-case basis. After presenting the analogy and remarldng on "our good fortune o f having lived in a society that did adopt the self-denying ordinance o f not considering each case o f [contested] speech separately" (1962, p. 241), Friedman contends that: Exactly the same considerations apply in tile monetary area. if each case is considered on its [individual] merits, the wrong decision is likely to be made in a large fi'action of cases because the decision-makers are ... not taking into account the cumulative consequences of the policy as a whole. On the other hand, if a general rule is adopted for a group of cases as a bundle, the existence of that rule has favorable effects on people's attitudes ... and expectations that would not follow even from the discretionary adoption of precisely the same [actions] on a series of separate occasions. ]~ Friedman (1962, p. 241) Thus we see that the logic o f Friedman's argument is basically the same as that identified by Barro and Gordon (1983a) and is entirely compatible with "activism," i.e., conditioning clauses in the rule 7. A controversial issue is whether it is feasible for an independent central bank to behave in a rule-like fashion. The most straightforward point o f view- is that expressed b y Taylor (1983, 1993b), McCallum (1995b, 1997b), Kydland and Prescott (1977), and Prescott (1977), namely, that an independent central bank is perfectly free to choose its instrument settings as it sees fit. Since it will generate superior outcomes on average i f it does so in a rule-like manner, and is presumably capable o f understanding that, the well-managed central bank will in fact behave in such a maimer. This requires it to adopt instrument settings that are different, however, from those that would appear optimal i f it were making a fresh optimization calculation each period (i.e., not considering the cases as a group). Thus many authors have suggested that, since there is no tangible "commitment technology" to guarantee that future choices will be made similarly, independent central banks are inevitably destined to behave in a discretionary fashion, making a fresh optimization calculation each period. One o f the strongest explicit statements o f this position has been made by Chari, Kehoe and Prescott (1989, p. 303), as follows: "We should emphasize that in no sense can societies choose between commitment [and] time-consistent [i.e., discretionary] equilibria. Commitment technologies are like teclmologies for making shoes in an A r r o w - D e b r e u

"1 An example of a conditioning clause in the fieedom-of-speech example would be one pertaining to cases of false alarms shouted in "crowded theaters".

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model - they are either available or not". But while this form o f language is rather extreme, the position taken is probably more representative o f academic thought over (say) 1984-1994 than is the pragmatic Taylor-McCallum position. That is, most analyses o f the consequences o f various issues simply presume, often without explicit justification, that central bank behavior will be o f the uncommitted discretionary type ~. In many cases it is contended that there is a necessary tradeoff between commitment and flexibility, which the Taylor-McCallum position denies. The justification typically given, explicitly or implicitly, for tile assumption o f (suboptimal) discretionary behavior is that although rule-like behavior is superior on average, it remains true that within each period prevailing expectations are "given" so each extra bit o f inflation or monetary ease will add output or reduce unemployment, implying that the discretionary choice would typically be superior from the perspective of that single period. Furthermore, the public understands this feature o f policy choice, according to the usual position, so individuals will expect the central bank to behave discretionarily, thereby making the discretionary action preferable (from the singleperiod perspective). But to conclude that the central bank will therefore consistently choose the discretionary outcome is analytically to adopt a particular equilibrium concept - see Chart, Kehoe and Prescott (1989). The solution concept preferred by Taylor, McCallum, Lucas (1976, 1980), and Prescott (1977) is simply rational expectations in a competitive model with a monetary authority that behaves as a Stackelberg leader vis-a-vis the private sector 9. To the present writer the latter concept seems more plausible 10, but the key point here is that neither o f the two modes of central bank behavior - rule-like or discretionary - has as yet been firmly established as empirically relevant or theoretically appropriate. Also, it would seem to be indisputable that there is nothing tangible to prevent a central bank from behaving in a rule-like

A particularly strildng example of tile importance of this assumption is provided by Svensson (1996), who argues that in the workhorse model, extended to inchide persistence of output or unemployment in the surprise Phillips relationship, price-level targeting will lead to less inflation variability (as well as less price-level variability) than will inflation targeting. This dramatic result depends, however, upon the presence of discretionary behavior on the part of the monetary authority. It does not obtain if the central bank is behaving in a rule-like fashion. Svensson (1996) recognizes this point but his discussion emphasizes the discretionary case. This exposition does not explicitly refer to thc reputational models pioneered by Barro and Gordon (1983b), the reason being that the author finds these models implausible. Of course the argunlent here advanced relies upon reputational effects, but does not utilize the type of equilibria featured in the reputation literature. i0 Empirically it is unlike the usual position consistent with tile "free lunch" finding that increased CB independence provides improved inflation performance without increased output employment variability. On this finding, see Fischer (1995) or Debelle and Fischer (1995, p. 201). It should be noted, incidentally, that my hypothesis is quite different from that of Mervyn King (1996), who suggests that CBs do not aim for output in excess of the natural rate value (as they do in the worldlorse model). The latter implies, since inflation and output desires are reflected in separate terms in King's loss function, that actual CBs would not want to keep output above the natural rate value even if they could do so without generating any inflationary tendency.

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fashion 11 so that there is no necessary (i.e., inescapable) tradeoff between "flexibility and commitment", as has often been suggested ~2. This position does not deny that central banks are constantly faced with the temptation to adopt the discretionary policy action for the current period; it just denies that succumbing to this temptation is inevitable. In practice, adoption o f rule-like decision making procedures is one mechanism for combating these temptations.

3. Special difficulties To economists who do not specialize in monetary or macroeconomic issues, it may seem surprising or perhaps a matter for professional embarrassment that a large volume o f debate can be sustained on the subject o f monetary policy rules. Surely, the argument would go, it should not be terribly difficult to conduct an optimal control exercise using some reasonably good macroeconometric model and thereby discover what an o p t i m a l monetary policy rule would be. This would have to be done for a number o f different economies, o f course, but the problems involved are in principle almost negligible and in practice are easily surmountable. Admittedly, the model would have to be one that is structural - policy invariant - so as not to be subject to the Lucas critique (1976), but that necessity has been well understood for many years by now 13 In fact, however, such an argument fails entirely to recognize one basic and fundamental difficulty that underlies a large fraction o f the issues concerning monetary policy rules. This difficulty stems from the lack o f professional agreement concerning the appropriate specification o f a model suitable for the analysis o f monetary policy issues. There are various aspects o f such a model that different researchers would emphasize. Many would suggest that money demand theory is quite undeveloped and inadequate for policy analysis. The viewpoint taken in McCallum (1997a), by contrast, contends that it is the dynamic connection between monetary policy actions and real aggregative responses that is the main source o f difficulty 14. Others, including

1t In the workhorse model, policy settings of both the committed and discretionary type may be expressed as resulting from policy feedback equation of the form or, = a o + a l E ~ 1 ~ +a2u~, with different coefficient values. Here E t l¢gt represents prevailing expectations and u~ is a current macroeconomic shock. There is nothing tangible to prevent a~ choices that represent conmaitment. t2 The absence of any inescapable tradeoffis implicit in the central bank contracting approach pioneered by Walsh (1995) and Persson and Tabellini (1993). 13 Taylor (1979) conducted an optimal policy exercise in the context of a dynamic macro model with rational expectations almost 20 years ago. 14 In this reference, the argument is stated as follows. It is not just that the economics profession does not have a well-tested quantitative model of the quarter-to-quarter dynamics, the situation is much worse than that: we do not even have any basic agreement about the qualitative nature of the mechanism. This point can be made by mentioning some of the leading theoretical categories, which include: rcal business cycle models; monetary misperception models; semi-classical price adjustment models; models with overlapping nominal contracts of the Taylor variety or the Fischer variety or the Calvo Rotemberg

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King (1993) and Fuhrer (1997) would point to weaknesses in modeling investment or consumption behavior, and o f course empirical understanding o f exchange rates and other open-economy influences is widely regarded as highly unsatisfactory. But whatever the particular model component that is singled out for special criticism, it seems extremely hard to avoid the conclusion that agreement upon macroeconomic model specification is predominantly absent - and that different models carry highly different alleged implications for monetary policy. The upshot, clearly, is that in practice one cannot simply conduct an optimal control exercise with an "appropriate" model. That approach simply collapses in response to the question "What is the appropriate model?" In light of this mundane but fundamental difficulty, the research strategy recommended by several writers including Blanchard and Fischer (1989, p. 582), McCallum (1988, 1997a), and to some extent Brunner (1980) - is to search for a policy rule that possesses "robustness" in the sense o f yielding reasonably desirable outcomes in policy simulation experiments in a wide variety o f models. In effect, the same type o f approach is collectively utilized by the various teams o f researchers participating in the Brookings projects directed by Ralph Bryant [Bryant et al. 1988, 1993)] ts. It is worth mentioning briefly that the research strategy based on robustness may serve to some extent as a protection against failures o f the Lucas-critique type. That critique is best thought o f not as a methodological imperative regarding model building strategies, but as a reminder o f the need to use policy-invariant relations in sinmlation studies and especially as a source o f striking examples in which policy invariance is implausible. The construction o f a policy-invariant model faces a major difficulty, however, in the above-mentioned absence o f professional agreement about model specification. Thus it would seem sensible to consider a variety o f models in the hope that one will be reasonably well specified - and therefore immune to the critique - and search for a rule that will perform satisfactorily in all o f them 16. O f course, there is no need for such a project to be carried out by a single researcher; furthermore, attempts to make each contending model policy invariant would enhance the effectiveness

type; models with nominal contracts set as in the recent work of Fuhrer and Moore; NAIRU models; Lucas supply function models; MPS-style markup pricing models; and so on. Not only do we have all of these basic modeling approaches, but to be made operational each of them has to be combined with some measure of capacity output - a step that itself involves competing approaches - and with several critical assumptions regarding the nature of different types of unobservable shocks and the timeseries processes generating them. Thus there are dozens or perhaps hundreds of competing specifications regarding the precise nature of the connection between monetary policy actions and their real short-term consequences. And there is little empirical basis for much narrowing of the range of contenders. 15 For the optimal-design point of view, see Fair and Howrey (1996). 16 From the perspective of the robustness approach, there is something to be said in favor of expressing "satisfactorily" in terms of nominal variables - even though individuals are concerned ultimately with real magnitudes because the relationship between monetary policy instruments and nominal variables may be less subject to Lucas-critique difficulties than is the case with real variables. An argument to this effect is attempted in McCallum (1990b, pp. 21-22).

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o f the overall project. Thus there is no necessary conflict between a robustnessoriented strategy and studies by individual researchers that involve construction o f single models [e.g., Ireland (1997), Rotemberg and Woodford (1997)]. The lack of professional agreement over model specification also makes it difficult to reach any firm conclusions about the proper goals o f monetary policy, as is discussed at the end o f this section, before the related but more pragmatic issue o f target variables is taken up. Other issues that are of greater technical interest but less fundamental importance - for example, issues concerning operationality and the simulation techniques appropriate for investigating a rule's properties - will be considered below, in Section 6. In any discussion of monetary policy, but especially in ones involving the design o f rules, it is useful to adopt a terminology regarding goals, objectives, targets, instruments, etc., that clearly reflects basic conceptual distinctions and at the same time is reasonably orthodox (or at least non-idiosyncratic). With those criteria in mind, we shall below use the word goals" to refer to the ultimate but typically nonoperational objectives of the monetary authority, and the term target to refer to an operational variable that takes precedence in the actual conduct of policy. The leading contenders for a central bank's target variable would be some comprehensive price index, nominal GDP or some other measure of nominal spending, a monetary aggregate, or a foreign exchange rate - with growth rates rather than (growing) levels perhaps pertaining in the case o f the first three. The choice among target variables will be considered in some detail in Section 4. At the opposite end o f the scale from goals are instrument variables, i.e., the variables that central banks actually manipulate more or less directly on a daily or weekly basis in their attempts to achieve specified targets. For most central banks, some short-term interest rate would be regarded as the instrument variable, but some analysts continue to promote the monetary base (or some other controllable narrow aggregate) in that capacity. It must be said that a term such as "operating target" would probably be nearer to standard for central bank economists or even policy-oriented academics, and there is a sense - to be described momentarily - in which it is more accurate than "instrument variable". But in an article such as the present one it would seem desirable to employ a terminology that promotes a clear distinction between target and instrument variables. Thus we seek to avoid ambiguous usage such as "interest rate targeting" to refer to a central bank's weekly instrument (or operating target) settings, rather than its policy-governing target variable. The sense in which "operating target" would be preferable to "instrument" is as follows. Many actual central banks choose not to manipulate their interest rate instruments in a literally direct fashion but rather to conduct open-market operations only once a day with quantities chosen so as to be expected to yield a market-influenced interest rate that lies within (or close to) some rather narrow band. The USA's Federal Reserve, for example, typically enters the Federal Funds market only once a day (normally around 10:30-10:45 a.m.) so the end-of-day or daily average value of the Federal Funds rate (FF rate) can depart from the open-market desk's "target value" by

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20-30 basis points on any given day. Thus writers such as Cook and Hahn (1989) or Rudebusch (1995) will distinguish between "actual" and "target" values at the daily level. But the Fed keeps the FF rate within a few basis points o f its operating target on average over periods as short as a week. Thus there is little harm, in a study such as the present one, in using the term instrument variable and pretending that the Fed controls its interest instrument directly. There is, it should be said, a significant amount of debate over the feasibility of a central bank's using one variable or another as its instrument (even in our sense). Those issues will be taken up in Section 5. In our terminology, then, a policy rule might be thought o f as a formula that specifies instrument settings that are designed to keep a target variable close to its specified target path. If rt and xt were the instrument and target variables, then, the simplest prototype rule might be o f the form r, = rt-i +)~(x~ 1 xi-l),

X < 0,

(3.1)

which specifies that the instrument setting should be decreased if xt fell short o f its target value x T in the previous period. Somewhat more realistic examples involving more variables and other timing patterns will be considered below. Some writers have taken the position that the specification o f a policy rule is complete when a target variable has been selected and a target path (or perhaps a tolerance range) has been designated. Hall and Mankiw (1994, p. 79), for example, recommend that the central bank behave so as to keep each period's externallygenerated forecast o f future nominal income equal to a value given by a selected target path, but beyond that "we see no need to tel! it how to go about achieving the peg." Also, Svensson (1997a) distinguishes between "instrument rules" and "target rules" and expresses a preference for the latter, which specify target values but not instrument settings 17. The position taken in the present chapter, however, is that a monetary policy rule is by definition a formula that specifies instrument settings, with the choice of a target variable and path constituting only one ingredient. For some particular target choices it might be the case that the problem o f designing instrument settings would be extremely simple or uninteresting, but in general such will not be the case. McCallum's series o f rule studies (1988, 1993a, 1995a), for example, was undertaken partly in response to a claim by Axilrod (1985) - who was at the time a principal monetary policy advisor at the Fed's Board of Governors - that the achievement of nominal GNP targets was technically infeasible. From this practical perspective, the investigation o f a rule expressed in terms of a feasible instrmnent variable becomes

J7 As a related matter, Svensson has suggested that behavior conforming to a rule of the form (3.1) should not be referred to as involving a x t target; that terminology should be reserved (he suggests) to cases in which the central bank's instrument is set so as to make Etxt~/= xt*+j. But a rule such as (3.1) with 3.(x~i - E~xt~:i) on the right-hand side leads to equivalent behavior in the limit as )~---,oo,and so is a compatible but more general formulation.

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an essential portion of the selection of a desirable target. For there is little point in designating a particular target if in fact it is not achievable. Svensson's (1997a) preference for what he terms target rules is not based on any lack of interest in the instrument-target relationship, but stems (apparently) from a point of view that does not recognize the difficulty emphasized above, namely, the absence of a satisfactory model of the economy. Thus Svensson presumes that any change in knowledge about the economy's workings will typically require some change in an instrument rule, whereas "with new information about structural relationships ... a target rule implies automatic revisions of the reaction function" [Svensson (1997a), pp. 1136-1137]. Indeed, if the central bank were conducting policy by conducting optimal control exercises each period with a single model, it would be true that changes in the latter would typically entail changes in the implied instrument rule. But under the presumption presented above, that it would be unwise to design a rule optimally on the basis of any single model, Svensson's conclusion does not follow. Instead, if an instrument rule has been designed so as to work reasonably well in a wide variety of models, then new information about the economy's structure is unlikely to entail any change in rule specification even when the rule designates instrument settings. Terminologically, moreover, it seems best to distinguish between the choice of policy rules and policy targets. The selection of a target variable is an extremely important aspect of systematic policy-making and may involve sophisticated analysis, as in the work of Svensson. But nevertheless a target is just that, a target. A rule, by contrast, is a formula that can be handed to a central banker for implementation without any particular knowledge of the analysts' views about model specification or objectives, in any event, in what follows it will typically be presumed that the term monetary policy rule refers to a formula or guide such as Equation (3.1) for period-by-period setting of instrument values in response to specified conditions. In evaluating candidate formulas such as Equation (3. l), it would clearly be desirable to have at hand an established specification of the appropriate ultimate goals of monetary policy. In that regard there exist important issues, such as whether a CB should keep actual or expected inflation close to some normative value, what that normative value is, and precisely how variability of output - or is it output relative to capacity (measured how?) or consumption? - should be weighed in relation to the inflation criterion. Now, in optimizing models that are specified at the level of individuais' tastes and technology, such as Ireland (1997) and Rotemberg and Woodford (1997), the answers to such questions are unambiguous and implicit in the solution to the optimal control problem. But again the fundamental difficulty mentioned above intrudes in a crucial manner, for these answers will depend nonnegligibly upon the specification of the model at hand 18. Consequently, the marked

is One rather prominent issue is whether there exists some externality that makcsthe appropriateoutput reference value greater than the natural-rate value that is relevant for price and wage behavior. Another crucial issue concerns the validity or invMidityof strict natural-rate hypothesis, i.e., the proposition that

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absence o f professional agreement regarding model specification implies that there can be (at least at present) no consensus as to the CB goals that are appropriate from the perspective o f an economy's individuals. In practice, nevertheless, there seems to be a substantial anaount o f agreement about actual (not ideal) CB objectives; namely, that many CBs strive to keep expected inflation close to zero (allowing for measurement error) and to keep output close to a capacity or natural-rate value that is itself a variable that grows with the capital stock, the labor force, and technical progress 19. Although it cannot be established that these objectives are optimal, it would seem to this writer that they probably provide a fairly good specification o f appropriate CB macroeconomic goals.

4. Choice of target variable After a long dose o f preliminaries, let us now finally turn to substantive issues in the design o f a monetary rule. In this section we shall be concerned with the choice o f a target variable - both its idemity and the question o f whether its path should be specified in growth-rate or level form. For the reasons just outlined, our discussion will be pragmatic rather than theoretical in nature. In recent years, the most fashionable target variable for the monetary authority has been a nation's inflation rate - in other words, a comprehensive price-level variable with its target path set in growth-rate terms. A great deal has been written about inflation targeting in policy-oriented publications, and substantial scholarly efforts have been contributed by A l m e i d a and Goodhart (1996), Bernanke and Mishkin (1997), Goodhart and Vinals (1994), McCallum (1997a), and others, as well as the individual authors represented in books edited by Leiderman and Svensson (1995) and Haldane (1995). Other leading target-variable choices are aggregate spending magnitudes such as nominal GNP or G D P - often in growth rate form - and a "hybrid" variable that sums inflation and real output measured relative to some sort o f trend or reference value 2°. A l l o f these choices presume, however, that the economy in question does not have its monetary policy dedicated to an exchange rate target, so a brief prior discussion o f exchange rate policy should be appropriate.

output cammt be kept above its natural-rate value permanently by any monetary policy strategy, even one that features a permanently increasing (or decreasing) rate of inflation [Lucas (i972)]. J9 This variable capacity value may, however, exceed the natural-rate value, as mentioned in footnotes 10 and 18, and as is typically assumed in the CB credibility literature. 2o The magnitude of inflation rates depends upon the length of a single time period whereas the percentage (or fractional) deviation of output from its reference path does not. The usual convention with this hybrid variable is to add percentage inflation rates measured lbr annual periods to percentage output deviations. It would be equivalent to use inflation over a quarter plus one-fom'th of the relative output deviation. Use of fractional units for both variables would also be equivalent, with appropriate adjustments in the response coefficient. This last convention will be utilized below.

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Perhaps the most basic of all monetary policy choices is whether or not to adopt a fixed exchange rate. The principal considerations involved in this choice are those recognized in the optimal currency area literature began by Mundell (1961) and extended by M c K i n n o n (1963) and Kenen (1969). Basically, these all boil down to the question of whether the lnicroeconomic (i.e., resource allocation) advantages of an extended area with a single medium of exchange outweigh the macroeconomic (i.e., stabilization policy) disadvantages of being unable to tailor monetary policy to local conditions 2j. Some analysts [e.g., Bruno (1993), Fischer (1986)] have contended that there are some macroeconomic advantages of a fixed exchange rate22 but the arguments seem actually to be based on political or public-relations considerations, not economic costs and benefits 23. Thus in the case o f small economies for which large fractions of their market exchanges are international in character, and which tend frequently to experience the same macroeconomic shocks as their neighbors and trading partners, it is clearly advantageous to forgo the flexibility of an independent monetary policy by keeping a fixed exchange rate (and common currency) with a specified currency or basket of currencies 24. And at the other extreme, the macroeconomic advantages o f a floating exchange rate would seem to be clearly dominant for pairs of nations such as the USA, Japan, and the prospective European monetary union. The main point of the previous paragraph is that the advantages that might lead a nation to choose to have a fixed exchange rate, and thus to dedicate its monetary policy actions to that criterion, are basically either microeconomic or political in nature. Thus the type of considerations involved are quite different than those that are involved in the selection among macroeconomic target variables such as inflation, nominal spending growth, or the above-mentioned hybrid variable. Because of the scope of the present chapter, we shall henceforth focus our attention on the latter type of choice 25.

21 If a set of countries is to have permanently fixed exchange rates, it would seem that from a purely economic perspective there are extra benefits (reduced transaction costs) with no extra costs of having a common currency. (No ongoing costs, that is; there may obviouslybe significantchangeover costs, as in the EMU example.) As for rates that are fixed, but not permanently,the European experiences of 1992 and 1993 support Friedman's (1953) classic argmnent that such an arrangement is undesirable because of the self;destructive speculativeimpulses that are encomaged. 22 From the monetary-policyperspective, a moving peg or narrow bm~dfalls into the same category as a fixed exchmlge rate, since it entails the dedication of monetary policy to its maintenance. 23 This statement is applicable to much of the literature relating to the planned European monetary union, of course. 24 A relatively clear-cut example is provided by Luxembourg, which has had a monetary union with Belgium since 1921 (except for an intenuption during World War II), Belgian francs serving as a legal tender in both nations, Luxembourgalso issues franc notes and coins, but has kept these interchangeable -with their Belgian counterparts. 25 It should be recognized, however, that it would be possible to consider a target that consists of a weighted average of (say) exchange rate changes and inflation. This example couid alternatively be thought of as an inflation target with an unusual specificationof the price index to be utilized.

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In the literature on this subject, which is large, the most popular approach is to determine how well the various targets would perform in terms of yielding desirable values of postulated social and/or policy-maker objective fimctions, with these pertaining primarily to root-mean-square (RMS) deviations from desired values of variables such as inflation or real GDP relative to capacity 26. Such studies may be conducted with theoretical or estimated models, but in either case need to take account of the various types of macroeconomic shocks that may be relevant - need to take account, that is, of the variance, covariance, and autocovariance magnitudes of the shock processes. Some of the leading examples of theoretical studies are those of Bean (1983), West (1986), Aizenman and Frenkel (1986), Henderson and McKibbin (1993), Frankel and Chinn (1995), Ratti (1997), and Ireland (1998), while welllcnown simulation studies with estimated models have been conducted by Taylor (1979, 1993a), Feldstein and Stock (1994), Haldane and Salmon (1995), and the individual authors in Bryant et al. (1988, 1993). In some of these studies it is pretended, for the sake of the issue at hand, that the selected target variables are kept precisely on their target path; the Bean, West, Aizemnan-Frenkel, Frankel-Chinn, Ratti, and (in part) Henderson-McKibbin studies are of that type. Others, however, focus on RMS deviations in simulations with policy rules expressed in terms of instrument variables. Proponents of the first approach would argue, presumably, that they prefer to keep the issue of whether a variable can be controlled separate from the evaluation of its effects if well-controlled. Those who disagree would point out that there is little need to know such properties tbr variables that in fact can be controlled only very poorly. Indeed, they might argue that unless controllability is taken into account, the issue is simply that of specifying an appropriate social objective function; i.e., that "targeting" is not the matter under investigation. In this regard it is worth keeping in mind the point emphasized above, namely, that there is in fact no professional agreement on the appropriate specification of a dynamic macroeconomic model. This implies not only an absence of agreelnent on the "true" social objective function, but also the absence of agreement on a matter as basic as the listing of relevant macroeconomic shocks. Keynesians and real-businesscycle analysts, for example, would disagree sharply as to the very nature of the relevant shock processes. For the candidate target variables mentioned above, other than the hybrid variable, an important question is whether it is preferable to specify a growth-rate target or one of the growing-levels type, i.e., whetber the target should be specified in a differencestationary or trend-stationary manner. This issue is often discussed under the heading of "inflation vs. price-level targeting," but similar considerations would apply if the target variable were nominal GDP, some other measure of nominal spending, or even

~' These are the two valiables that are most closely related to the utility t~mctions of individuals m explicit optimizing models such as those of Ireland (1997) or Rotemberg and Woodtbrd (1997).

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a money-stock variable 27. Specifically, the weakness o f the growth-rate choice is that it will - by treating past target misses as bygones - introduce a random walk (or more general unit root) component into the time-series processes for all nominal variables, including the price level. Thus there will exist a possibility that the price level would drift arbitrarily far away from any given value (or predetermined path) as time passes, implying considerable uncertainty as to values that will obtain in the distant future. By contrast, the main disadvantage with a levels-type target path is that the target variable will be forced back toward the preset path after any disturbance that has driven it away, even if the effect o f the disturbance is itself o f a permanent nature. Since any such action entails general macroeconomic stimulus or restraint, this type o f targeting procedure would tend to induce extra cyclical variability in demand conditions, which may imply extra variability in real output i f price-level stickiness prevails. Furthermore, variability in output and other real aggregative variables is probably more costly in terms o f human welfare than is an equal amount o f variability in the price level about a constant or slowly-growing path. Also, although it is not entirely clear that fully permanent shocks are predominant, most time-series analysis seems to suggest that the effects o f shocks are typically quite long lasting - indeed, are virtually indistinguishable from permanent. Consequently, it would seem desirable not to drive nominal variables back to preset paths - or at least not to do so quickly and frequently. Thus, it seems preferable to adopt a nominal target o f the growth-rate type, rather than the growing-levels type 28. One reason for the foregoing conclusion is that very few transactions are based on planning horizons as distant as 50 years. A more representative long-lasting arrangement might be more like 20 years in duration. But price-level uncertainty 20 years into the future might not be very large even i f the (log o f the) price level included a unit root component. Suppose that the log price level were to behave as a pure random walk relative to a preset target path (say, a zero-inflation path). Then i f it is assumed that the random, unpredictable component at the quarterly frequency has a standard deviation o f 0.0045 (which is approximately the standard deviation o f one-step ahead forecast errors for the U S A over 1954-1991) 29, it follows that a 95% confidence interval for the (log) price level 20 years ahead would be only about 8% (plus or minus) 3°. This, it seems to the writer, represents a rather small amount o f price level

27 Here and below the language will often be stated in terms of nominal variables such as nominal GDP or a price index when it is the natural logarithm of that variable that is actually meant. 28 For alternative argmnents that reach this conclusion, which is taken for granted by Feldstein and Stock (1994), see Fischer (1995) and Fillion and Tetlow (1994). The opposing position is taken by Hall and Mankiw (1994) and Svensson (1996) [but see footnote 8 above]. 29 Thus it is being tentatively assumed that the control error, if inflation targeting were adopted, would have a mean of zero and a variance equal to that of the currently-prevailing one-step-ahead forecast error, which might be taken as an approximation of the minimum feasible control error variance. 3o I am taking the control error to be serially lmcorrelated. Then the 80-period ahead error would have variance (80) (0.00452) -0.00162 whose square root is 0.040. Thus two standard deviations equals 0.08

Ch. 23." Issues in the Design of Monetary Policy Rules

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uncertainty - at least in comparison with the magnitudes that prevailed over the 1960s, 1970s, and 1980s, because of non-zero and uncertain trend rates. The foregoing argument seems moderately persuasive to the present writer, but it is clearly not compelling and the conclusion is certainly not accepted by all analysts. Furthermore, even if it were accepted, it might be possible to obtain the benefits of trend stationarity by adopting a target that is a weighted average of ones o f the growth-rate and growing-level types 31. Accordingly, in the simulations reported below, consideration will be given to growth-rate, growing level, and weighted average types. Now let us consider some points regarding the comparative merits of three leading target-variable possibilities. Because they seem at present to command the most support, we will discuss (i) the inflation rate, (ii) the growth rate o f nominal GDP, and (iii) the above-mentioned hybrid variable. As some notation will be useful, henceforth let xt, Yt, and Pt denote logs of nominal GDP, real GDP, and the price level (as represented by the deflator so that xt = Yt +Pt), with time periods referring to quarteryears. Then the three contending target variables in their simplest form are Apt, Act, and ht - A p t + 0.253~t, where yt - y t -j~t with )Tt denoting the reference value of real GDR In choosing among these three contenders, a straightforward approach would be to select the target variable that corresponds most closely to the central bank's views about social objectives that are influenced by monetary policy. From that perspective, it would appear that the hybrid variable ht might be the most appropriate of the three, a point o f view taken implicitly by Blinder (1996), with Axt arguably ranking second 32 But among actual central banks that have adopted formal numerical targets, virtually all have (as o f early 1997) opted for inflation targets. So apparently the straightforward approach is not the only one that needs to be considered. There are undoubtedly several reasons for this tendency for actual central banks to choose Apt over the others as their formal target, but three o f these seem justifiable and in any event deserve to be mentioned. First, it is believed by a large number of policymakers and a large number o f scholars that monetary policy has, from a

so a 95% confidence interval will have width roughly ±0.08 or ±8 percent. If the control error is serially correlated, then the relative effect of the unit root term will depend on the autocorrelation pattern but is likely to be more serious. 31 If used in a rule of form (3.1), this sort of weighted-average target would be equivalent to a pure growing-levels target with both "proportional" and "derivative" feedback. 32 The case for nominal income targeting is that it should, from a long-term perspective, provide almost as good inflation control as direct inflation targeting, since average real outpnt growth will be virtually independent of monetary policy and reasonably ~brecastable, while probably providing somewhat better automatic stabilization of real variables. About the latter advantage one cannot be certain, because of the absence of professional understanding mentioned in footnote 14. The basic logic of nominal income targeting applies, moreover, to other aggregative measures of nominal spending, not just to nominal GDP or GNP per se. The sharp criticism of nominal income targeting recently expressed by Ball (1997) is, it is argued below, fundamentally misguided.

1500

B.T. McCallum

long-rml perspective, no substantial effect on fit = Y t - ) S t 33. In other words, while monetary policy may have significant effects on output relative to capacity, these are only temporary. Therefore, so the argument goes, central banks should concentrate their attention on the Apt variable that their policy actions affect strongly on a longrun basis 34. Second, measurement of)Tt and therefore )~t is difficult and controversial, even in comparison to measurement o f Aps. We have described Yt as a capacity, trend, or reference value, but that does not define the appropriate variable even in conceptual terms, much less in operationally measurable terms 35. in particular, errors in measuring )Tt are likely to be much larger than errors in measuring the long-term average value o f Ayt, which is all that is necessary for correct design o f a Axt target. Thus the ht target is more demanding o f knowledge concerning the economy than is either o f the other contenders under discussion. The third reason is related to the other two, especially the first. It is that communication with the public is thought by practitioners to be much easier when only the inflation variable is involved. Typical citizens have an understanding o f the concept o f inflation, so the argument goes, but not o f the national income accounting concepts xt andyt, much less the reference value)Tt. In addition, it must be mentioned that in practice actual inflation targets are typically based on yearly average inflation rates, and with those values forecasted to prevail 1-2 years into the future 36. Since inflation forecasts are in practice based in part on recent levels or growth o f real output, the three target variables under consideration may be fairly closely related to each other. Furthermore, inflation targets are usually accompanied by provisions stating that the occurrence o f "supply shocks" - such as crop failures, terms-of-trade changes, or indirect tax-rate changes - will entail temporary modification o f the current inflation target measures. Thus, for example, the New Zealand legislation includes several such escape clauses - termed "caveats" that are built into the Reserve Bank's targeting procedures 37. Because o f considerations such as these, it would probably be unrealistic (and unreasonable) to expect that a truly compelling argument could be made for any one 33 This proposition, often termed the "natural rate hypotlaesis", is subscribed to by a large fraction of macroeconomic researchers. 34 This position is explicitly expressed by McCallum (1997a) and by Reserve Bank of New Zealand (1993). 35 In recent years there has been a tendency, most marked in media discussions but also present in professional literature, to speak as if "natural rate" and "NAIRU" conccpts and theories were equivalent. To the present writer that is far from being the case. The strict version of the natural rate hypothesis, due to Lucas (1972), is the proposition that there is no monetary policy that will keep output permanently high in relation to its natural rate (i.e., market clearing) value. By contrast, the NAIRU (non-acceleratinginflation rate of unemployment) approach posits a stable relationship between tmemployment (or output relative to its reference value) and the "acceleration" magnitude, i.e., the change in the inflation rate. But the latter implies that permanent acceptance of a positive acceleration magnitude (i.e., increasing inflation) will result in a permanent increase in output relative to its reference value, in stark contradiction to the natural rate hypothesis. 36 Of course the same sort of averaging could be applied to the Axt and h~ variables. 37 On this subject, see Reserve Bank of New Zealand (1993).

Ch. 23: Issues in the Design of Monetary Policy Rules'

1501

0.06 l

o.o4.1

t

0.02 -

0.00 -0.02.

-004

~ 60

_ 65

[--

~ 70

_ 75

80

~ 85

DLXGAP ....... DLPGAP . . . . .

90

95

ZERO I

Fig. 1. Gap measures for inflation and nominal GDP targets, 196~1995. of the candidate target measures. Consequently, it should be of interest to compare actual past values of the three leading measures with those values that would have been called for if corresponding targets had been in place. For the purpose of this exercise, it will be assumed that the desired value of Apt is 0.005, which amounts to approximately two percent inflation on an annual basis. Also, for simplicity it will be assumed that 37t values are given by deterministic trends obtained by regression ofyt on time for the sample period under consideration. This last assumption is unsatisfactory, of course - as will be discussed again - but should suffice for the limited purpose at hand of making comparisons. Let us first consider the time period 1960.1-1995.4, with United States GDP data used for xt and with Yt based on GDP in 1992 fixed-weight prices (i.e., using the fixedweight rather than the chain-weight deflator). Over this period, the 37t trend variable is given by the expression fit = 7.520749 + 0.006881t (with t = 1 in 1947.1). Therefore, Aft = 0.006881 is assumed and the target value for Axt is 0.011881, with 0.005 being the target value for both Apt and h , For each of the three variables we calculate the gap between actually observed values and these retrospective, hypothetical target values. These gaps are denoted Ap(gap)t - Apt - 0.005, Ax(gap)t = A& - 0.011881, and h(gap)t = Apt + 0.25yt- 0.005. Their values for the first two variables (over 1960.1-1995.4) are plotted in Figure 1 and those for the second and third are plotted in Figure 2. In Figure 1 we see that the Ap~ and Axt targets both suggest that monetary policy was excessively expansive most of the time between 1965 and 1989. The Ax(gap) measure is considerably more variable from quarter to quarter than the Ap(gap) measure, basically because Ayt is more variable than Apt. Averaging over the whole period, the two measures give the same signals simply because the A& target value was calculated

1502

B.T. McCallum 0.06

0.04

0.02

0,00

-0.02.

-0.0460

65 [

70

75

80

85

DLXGAP ....... HGAP . . . . .

90

95

ZERO]

Fig. 2. Gap measures for hybrid and nominal GDP targets, 1960-1995.

so as to yield the desired inflation rate given the realized average growth rate of output over the sample period, Of course, actual policymakers could not know this rate in advance, when choosing their target value for Axt. Thus desired inflation would tend to differ from the average realized value to the extent that average output growth is forecast incorrectly. The magnitude of this error would not be large, however, when averaged over long spans of time. By and large, a striking feature of Figure 1 is that the two target variables do not give greatly different signals when averaged over periods as short as 2-3 years. Nevertheless, there are a few quarters when the Axt variable suggests that policy should be loosened whereas the Apt variable suggests the opposite, and this situation prevails for over a year during 1990-1991. Those analysts who favor Axt targeting believe, of course, that keeping Axt values steady would result in smaller fluctuations in Yt than would a policy of keeping Ap~ values steady. Whether such is the case in fact will depend upon the precise nature of the economy's short-term, dynamic Phillips relation, a point emphasized in McCallum (1988, 1997a) 3s. Figure 2 compares gap values for ht and Axt targets. In this case there is much more divergence in signals, with the hybrid measure calling for more monetary expansion over lengthy periods during the early 1960s and 1990s, and tighter monetary policy during much of the 1970s, in. comparison with the zk~ct measure. (Of course both measures signal that policy was too inflationary from 1965-1989, as before.) These features of the plots in Figure 2 are basically a consequence of the fact that a linear trend line for yt implies negative residuals in the early 1960s and 1990s and many

3~ See fbotnote 14 above.

Ch. 23:

1503

Issues in the Design of Monetaly Policy Rules

0.06. 0.04. 0.02-

-0.02-

8'5' '86 '87 '88 I

DLXGAP85

89

90

91

92

93

..... HGAP85 . . . . .

94

95

ZERO]

Fig. 3. Gap measures for hybrid and nominal GDP targets, 1985 1995. positive residuals during the 1970s, which it does because o f the sustained period o f rapid growth in real G D P from 1960 to 1973. To emphasize this last point, Figure 3 gives results for the same type o f exercise but with the sample period limited to 1985.1-1995.4. Here it will be noted that the h(gap)t values are quite different from those for 1985-1995 in Figure 2, solely because the y~ trend line is estimated differently and yields a significantly different residual pattern 39. Now there are no major discrepancies that persist as long as in Figure 2, although the two measures give quite different policy signals over most o f 1990 and 1992, the Axt target calling for a relatively more expansionary monetary stance in the former year and a more restrictive stance in the latter year. The sizable difference between the h(gap)t figures shown in Figures 2 and 3 illustrates the main weakness o f the hybrid target variable, namely, its sensitivity to alternative calculations o f y t reference values. Proponents o f the hybrid variable might argue that more sophisticated measures o f f t should be used, and it is certainly true that our linear trends are not conceptually attractive. But neither are, say, HodrickPrescott (HP) filtered series, for reasons emphasized by Cogley and Nason (1995) plus a recognition o f what the HP filter would imply about US GNP for the period 1929-1939 4°. Other measures exist, but have attracted little professional support. In

39 It also has a reduced slope, which changes the definition of Ax(gap) to Axt 0.010336. 40 If the HP filter were applied to US real GNP over a period including 1929-1939, the HP "trend" series would turn down fairly sharply during the early 1930s. If this series were used as one's measme of trend or capacity output, it would then be concluded that the Great Depression was not very serious i.e., that output was low over 1932 1938 largely because capacity was low. But measured unemployment figures suggest strongly that this conclusion would be misleading.

B.T. McCallum

1504

0.06 . 0'04 t 0.024 0.00-

--7~, ~

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-0,02-

'6's ....

7'0 ....

7'6 ....

6'0 ....

6'2 ....

9'0 ....

9's

DLXFGAP ....... DLPFGAP ..... ZERO] Fig. 4. Gap measures for inflation and nominal GDP values forecast 4 quarters ahead, 1960-1995. sum, there is no widely accepted and conceptually sound measure for f~, but use o f the hybrid target variable requires such a measure and its value is rather sensitive to the particular measure adopted. One weakness o f the indicators presented in Figures 1-3 is that they pertain to currently-measured values of the target gaps whereas in practice actual central banks focus upon gaps expected to prevail several months in the future. Also, Svensson (1997a) has argued rather convincingly that "inflation forecast targeting" has several attractive features. Consequently, indicators o f expected future gaps were obtained by regressing gap values on information variables observed 4 to 7 quarters in the past. The variables used in these regressions are Axt, Apt, Ab, and Rt (four lagged values o f each), where bt is the log of the monetary base and Rt is the 3-month Treasury bill interest rate. Also one lagged value o f fit was included; a second lagged value would create perfect collinearity among the regressors. Values o f these forecasted future gaps are presented in Figures 4 and 5, where the measures should be interpreted as giving policy signals one quarter in advance of the dates shown. Clearly, the values are smoothed greatly for zXxt and Apt, relative to the previous graphs, but the overall messages remain the same: that there is apparently little basis for choice between Axt and Apt while the ha indicator appears to give signals that are quite different. Recently, Ball (1997) has put forth, in rather strong language, some striking propositions regarding target variables 41. Among these are claims to the effect that efficient monetary policy 42 consists o f a special case o f a Taylor rule that is equivalent

41 Some of these have been noted favorably by Svensson (1997a,b). 42 The paper's concept of"efficient monetary policy" is one that focuses on the variances of inllation and output (relative to capacity) while assmning tmrealistically that the central bank has full contemporaneous

Ch. 23:

1505

Issues in the Design of Monetary Policy Rules

0.06 . 0.04 t 002

,,,

',

,:

",

" ~ , ' "~" i

0.00-"

;';

", , ,"~' ',', "\l L';, -^""

b'

,J -'V

-0.02

i , ,615 ....

7~0 ....

I --DLXFGAP

7~5 ....

810 ....

8~5 ~

90

95

....... HFGAP ..... ZERO]

Fig. 5. Gap measures for hybrid and nominal GDP values forecast 4 quarters ahead, 1961~1995. to a partial-adjustment variant of inflation targeting (even when output variance is important); that efficient monetary policy requires much stronger responses to output fluctuations than is implied by historical practice or Taylor's (1993b) suggested weights; and that nominal income targeting would be "disastrous" as it would give rise to non-trend-stationary behavior o f output and inflation processes. These results are shown to hold, however, only in a single theoretical model, with no attempt being made to determine their robustness. In fact, the last one depends sensitively upon details of the utilized model that are not justified either theoretically or empirically. The model's Phillips curve, in particular, has a superficial similarity in appearance to the Calvo Rotemberg specification as exposited by Roberts (1995), but differs by being backward rather than forward-looking. If a forward-looking version were utilized, the implied coefficient relating inflation to current output would have the opposite sign and Ball's instability result would be overturned, as it would be with several other prominent Phillips curve specifications,

5. Choice of i n s t r u m e n t variable In this section we consider the choice o f a variable to serve as the instrument through which a central bank's policy rule will be implemented. It is well known that, although a substantial number o f academic economists have favored use o f a monetary base or

knowledge of all variables (oil this, see Section 6 below)• Thus it simply assumes away thc first-order problem of designing an operational rule that will generate the desired mean value tbr :r~ while avoiding explosions.

1506

B. Z McCaHum

reserve aggregate instrument, almost all actual central banks utilize some short-term interest rate in that capacity. Before turning to a review o f their relative desirability, however, it will be appropriate to consider the sheer feasibility o f interest rate and monetary base instruments, since there are a few scholars who have contended that one or the other would be infeasible in some sense. In this category the most well-known argument is that of Sargent and Wallace (1975). That paper put forth the claim that, in a model in which all private agents are free of money illusion and form their expectations rationally, the economy's price level would be indeterminate if the central bank were to use an interest rate as its instrument. Specifically, the Sargent-Wallace (1975) paper included a result suggesting that if the interest rate Rt were set each period by means of a policy feedback rule that specifies Rt as a linear function o f data from previous periods, then all nominal variables would be formally indeterminate. Sargent (1979, p. 362) summarized this conclusion as follows: "There is no interest rate rule that is associated with a determinate price level. ''43 Subsequently, however, McCallum (1981, 1986, p. 148) showed that the SargentWallace claim was actually incorrect in such a model; instead, all nominal variables are fully determinate provided that the policy rule utilized for the interest rate instrument involves some nominal variable, as suggested previously by Parkin (1978) and in the classic static discussion of Patinkin (1961). The problem with the alleged proof o f Sargent and Wallace is that it showed that the model at hand imposed no terminal condition on the price level, but did not consider the possibility of an initial condition. In the present context it is important to distinguish between two quite different types of price-level behavior that have been referred to in the literature as involving "indeterminacy". Both involve aberrational price level behavior, but they are nevertheless very different both analytically and economically. Consequently, McCallum (1986, p. 137) proposed that they be referred to by terms that would recognize the distinction and thereby add precision to the discussion. The proposed terms are "nominal indeterminacy" and "solution multiplicity (or nonuniqueness)" 44, The former refers to a situation in which the model at hand fails for all nominal variables (i.e., variables measured in monetary units) to pin down their values. Thus money stock values and values o f (say) nominal income, as well as the price level, would not be defined by the model's conditions. Paths o f all real variables are nevertheless typically well defined. In terms of real-world behavior, such a situation could conceivably obtain

43 Sargent and Wallace (1982) advanced arguments quite different from those of their 1975 paper, and attributed this difference to their use in (1982) of a model with agents who solve explicit dynamic optimization problems, in contrast to the linear IS-LM model with a Lucas supply function in (1975). in fact, however, the main relevant difference is that the 1982 analysis is based on a model in which monetary and nonmonetary assets cannot be distinguished and hldeterminacy does not actually prevail in any case. On this, see McCallum (1986, pp. 144-154). An important recent contribution is Benassy (1999). 44 Actually,McCallam (1986) proposed "indeterminacy~ for the tormer, but the addition of the adjective is clearly desirable.

Ch. 23:

Issues in the Design of Monetary Policy Rules

1507

if the monetary authority failed entirely to provide a nominal anchor 45. This type of phenomenon has been discussed by Gurley and Shaw (1960), Patinkin (1949, 1961), Sargent (1979, pp. 360-363), Sargent and Wallace (1975), McCallum (1981, 1986), and Canzoneri, Henderson and Rogoff (1983), among others. Solution multiplicity, by contrast, refers to aberrational behavior usually described as involving "bubbles" or "sunspots" that affect the price level. In these situations it is typically the case that the path of the money stock - or some other nominal instrument controlled by the monetary authority - is perfectly well specified. Nevertheless, more than one path for the price level - often an infinity of such paths - will satisfy all the conditions of the model. In terms of real world behavior, arbitrary yet selfjustifying expectations is the source of this type of aberration. It has been discussed by a vast number of writers including Taylor (1977), Sargent and Wallace (1973), McCallum (1983), Brock (1975), Black (1974), Obstfcld and Rogoff (1983), and Flood and Hodrick (1990). Nominal indeterminacy is a static concept that concerns the distinction between real and nominal variables whereas solution multiplicity is an inherently dynamic concept involving expectations. An important application of this distinction is to the "indeterminacy" results of Brock (1975, pp. 144-147) and Woodford (1990, pp. 1119-1122). These results pertain to cases in which (base) money is manipulated by the central bank and involve non-uniqueness of rational expectations equilibria when the imposed money growth rates are low, close to the Chicago Rule rate that satiates agents with the transaction-facilitating services of money. But since these equilibria involve wellspecified paths of nominal money holdings, the non-uniqueness is clearly not of the nominal indeterminacy type. Instead, it is of the solution multiplicity type, involving price level bubbles or sunspots. Such theoretical multiplicities may or may not be of practical significance 46, but in any event are not examples of "price level indeterminacy" in the sense of Gurley and Shaw (1960), Patinkin (1949, 1961), S argent (1979, pp. 360-363), or Sargent and Wallace (1975). To some readers, this fact may diminish the force o f Woodford's (1990, 1994) argument in favor of an interest rate instrument. Let us now return to the issue of instrument feasibility, switching to the extreme opposite side of the debate. In a recent article, Goodhart (1994) has argued not just that monetary base control by a modern central bank is undesirable, but that it is essentially infeasible. In particular, Goodhart states that "virtually every [academic?] monetary economist believes that the CB can control the monetary base . . . " so that if the CB does not do so, then "it must be because it has chosen some alternative

45 And the system lacked sufficient inertia or money illusion to make the nominal paths determinate requirements that are actually almost inconceivable. 46 It is unclear whether there is any compelling evidence in support of tile notion that macroeconomic bubbles or stalspots are empirically relevant [Flood and Hochick (1990)]. In any event, it is a plausible hypothesis that, in cases with an infinity of solutions, there is a single bubble-free or fundamentals solution that obtains in practice.

1508

B.T. McCallum

operational guide for its open market operations" (p. 1424). But, he asserts, "almost all those who have worked in a CB believe that this view is totally mistaken; in particular it ignores the implications o f several o f the crucial institutional features o f a m o d e r n commercial b a n k i n g system, notably the n e e d for unchallengeable convertibility, at par, b e t w e e n currency and deposits, and secondly that commercial b a n k reserves at the CB receive a zero, or below-market, rate o f interest" [Goodhart (1994), p. 1424]. T h e n as the discussion proceeds it b e c o m e s clear that Goodhart is h i m s e l f taking a position that is predominantly, if n o t entirely, supportive o f the opinions o f those who have worked in a CB. Thus he asserts, o n his own account, that "if the CB tried to r u n a system o f m o n e t a r y base control, it would fail" (p. 1425). A n d he goes on to outline the putative flaws in logic or factual knowledge that invalidate the cited views o f academic economists (pp. 1424-1426). In fact, however, although Goodhart's discussion is apparently i n t e n d e d to be c o n c e r n e d with feasibility, the actual a r g u m e n t a t i o n presented pertains to desirability. Specifically, the m a i n analytical points are those made in the first three complete paragraphs o f p. 1425, which argue that tight base control would lead in practice to overnight interest rates that at the end o f most days would equal either the CB's penal rate or a value "near zero ''47. H a v i n g developed that point, Goodhart concludes as follows: "Some economists might prefer such a staccato pattern o f interest rates, b u t it would not seem sensible to practitioners" (p. 1425). But clearly this is an a r g u m e n t that pertains to the desirability, not the feasibility, o f tight base control 48 H a v i n g concluded, then, that neither interest rate nor m o n e t a r y base i n s t r u m e n t s are infeasible 49, we turn to the task o f considering their relative desirability 5°. In that

47 If required-reserve averaging is practiced, then the statements referred to pertain only to days near the end of reserve maintenance periods. 48 More extensive but still inconclusive arguments are presented by Whittaker and Theunissen (1987) and Okina (1993). The latter presumes lagged reserve requirements, an arrangement that is inappropriate with a base instrument [McCallum (1985)]. 49 A different objection to use of a base instrument is that central batiks do not literally control the stun of currency and reserves, since currency is demand determined and only the non-borrowed component of total reserves is directly controlled, since banks can use the discount window to add to or subtaact from reserve holdings. But there are three flaws with this position. First, since the base can be read from the CB's own balance sheet, it can observe it frequently and make whatever adjustments are needed to keep the magnitude closer to its target. Second, the CB could, if it chose, close the discount window. Third, it would be possible to consider the non-borrowed base as the instrument under discussion. s0 Brief mention should be made of a study by Howitt (1992), who finds that an interest rate peg would lead to dynamic instability in a model that includes a sticky-price Phillips curve and a generalized adaptive form of dynamic "learning behavior" rather than rational expectations. Whether or not one finds the latter feature appealing, Howitt's results do not pertain to the issue at hand since the type of "pegging" that he is concerned with involves keeping Rt at some preset value indefinitely, not varying Rt period by period in an instrument capacity. Several writers have shown that, under rational expectations, nominal indeterminacy does not prevail with an interest rate peg. Canzoneri, Henderson and Rogoff (1983) and McCallum (1986) have established this in models of the IS-LM-AS type under the assumption that the peg is a limiting version of a money supply rule designed to reduce interest rate fluctuations.

Ch. 23." Issues in the Design of Monetary Policy Rules

1509

regard, m o s t proponents o f a base instrument do not deny that such a r e g i m e w o u l d involve substantially m o r e variability o f short-term interest rates than is e x p e r i e n c e d under today's typical procedures, w h i c h involve interest-rate instruments and shortterm interest rate smoothing 51. B a s e proponents w o u l d contend, however, that with a base instrument it m a y be possible to design simple p o l i c y rules that are m o r e effective f r o m a m a c r o e c o n o m i c perspective than are c o m p a r a b l e rules with interestrate instruments 52, 53. In order to illustrate the plausibility o f that contention, let us consider s o m e counterfactual historical simulations o f the general type u s e d by M c C a l l u m (1988, 1993a, 1995a) with quarterly U S data. In order to keep the m o d e l specification from biasing the results, the m a c r o e c o n o m e t r i c m o d e l in these simulations will be an unconstrained V A R w i t h four lags included for each o f the four variables Ayt, Apt, Abt, and Rt 54 H e r e Rt is the t h r e e - m o n t h treasury bill rate, bt is the log o f the St. Louis Fed adjusted m o n e t a r y base, and G N P data is utilized for Yt and Pt. The estimation and s i m u l a t i o n p e r i o d is 1954.1-1991.4. We have seen above that there has not b e e n a large discrepancy, historically, between signals p r o v i d e d by Ax~ and Apt targets, when the target values are gauged so as to imply the s a m e average inflation rate. Accordingly, let us concentrate our attention on rules for Abt and Rt designed to keep xt close to three target paths, all o f w h i c h provide e x p e c t e d Axe, values o f 0.01125 ( i . e , approximately 4.5 n o m i n a l G N P growth per year,

Woodford (1990, 1994) and Sims (1994) extend tlfis type of result to a "pure peg" and conduct their analysis in general equilibrium models with explicit optimization on the part of individual agents. 51 The concept of interest rate smoothing that I have in mind is keeping R~ close to Rt 1, but there is no major conflict here with concepts such as a tendency to minimize E(Rt-Et iRt)2 [Goodfriend (1987)]. 52 The reason why design of a simple interest rate rule may be more difficult stems fxom the ambiguity of nominal interest rates as indicators of monetary tightness or ease. High interest rates, that is, are associated with tight monetary policy from a short-run or point-in-time perspective, but with loose monetary policy from a long-ran (i.e., maintained) perspective. This means that the interest rate effects of an open market action are in opposite directions ~?omshort-term and long-term perspectives. Accordingly, the design of a policy rule for the control of target variables would seem to be more complex and dynamically delicate if an interest rate is the instrument variable than if a nominal quantity variable serves in that capacity. 53 One objection to use of a base instrument lbr the USA is that much of the currency component of the base - which is by far the larger component - is believed to be held outside the comatry. Recently, Jefferson (1997) has indicated that use of only that portion held in the country [as estimated by Porter and Judson (1996)] alters the estimated relationship between the base and nominal GDR and yields improved base-rule simulation results for the period 1984-1995. 54 The use of an unconstrained VAR is undesirable because such a model is almost certainly not policy invariant. However, the small "structural models" used in McCallum (1988) are biased in favor of the base instrument because the real monetary base (and no interest rate) appears as an explanatory variable in these models' common aggregate demand relation. In Hess, Small and Brayton (1993), by contrasi, the small macro model discussed on pp. 1 4 ~ t might be considered to be biased in favor of an interest rate instrument. The author hopes to conduct simulations with a more appropriate model in the near future.

1510

B. Z M c C a l l u m

designed to yield 2.0 percent inflation). These three paths will be of the growth-rate, growing level, and weighted average types. For the monetary base instrument, the rule to be considered is

Abt = 0 . 0 1 1 2 5 - ~ ( x t

1 - b t 1 - x t 17+bt 17)-t-/~(x] 1 - x t 1),

(5.1)

where ,~ > 0 is a policy adjustment parameter and the target variable x; can be defined in various ways 55. To yield a growing-levels target, we would have x 21 = xt11 + 0.01125 whereas a growth-rate version would use instead x23 = xt 1 + 0.01125. Besides these, we will consider x[ 2 = 0.2x] l + 0.8x)"3, where the weights are chosen semi-arbitrarily but so as to give more importance to the growth-rate target. According to the policy rule (5.1), monetary base growth is set in each quarter so as to equal the target value for nominal GNP growth minus average base velocity growth over the past four years 56, plus a cyclical correction term that reacts to past target misses. Note that x~31-&l =(xt2+0.01125)-x*l

.... 0.01125

A&.I

and that x;21 x,-1 = 0.2(x~ll

x , q ) + 0.8(0.01125-zZv, 1)

= 0.2(Xtll-Xt 1)+ 0"8(z~Xt 1 --/~Ct 1) so that use of x22 is equivalent to having a growing-levels target but using derivative as well as proportional feedback, in the terminology o f Phillips (1954). So as to obtain some indication of robustness to rule specification, a range of ;. values from 0 to 1 will be examined. For the interest instrument rule, no velocity growth term is needed so the comparable rule can be expressed as Rt = Rt-I -

100~.(x2

1 - xt-I).

(5.2)

Thus, the value of the interest rate instrument is lowered relative to the previous quarter when target spending x; exceeds the actual level in the previous quarter. The - 1 0 0 factor is inserted so as to make the same range o f )~ values as in Equation (5.1)

55 This is the type of rule studied in McCallmn (1988, 1993a, 1995a). 56 The velocity connection term serves implicitly as a forecast of the average growth rate of base velocity over the indefinite future, i.e., the long-lasting component of velocity growth that is due to institutional change (not growth due to cyclical effects, which are accounted for in the third telan). More sophisticated methods of forecasting the permanent component of both velocity growth and real output growth would be used in practice by actual central banks.

Ch. 23." Issues in the Design of Monetary Policy Rules

1511

Table 1 RMS errors with base/interest instruments, rules (5.1) and (5.2), VAR Model, US Data 1954.1-1991.4 ~ = 0.00

3.=0.25

Ni 1

0.0503 1.153

0.0235 expl a

0.0376 expl

expl expl

x~2

0.0133 0.2415

0.0ll3 expl

0.0184 expl

expl expl

x~3

0.0097 0.0184

0.0112 expl

0.0188 expl

expl expl

x~ I

0.0503 1.153

0.0284 0.0619

0.0232 0.0381

0.0201 0.0254

x~2

0.0133 0.2415

0.0109 0.0155

0.0106 0.0123

0.0114 0.0147

x~3

0.0097 0.0184

0.0100 0.0105

0.0105 0.0107

0.0118 0.0142

RMS error relative to:

~ = 0.50

,~= 1.00

Panel A: x~ 1 target

Panel B: x2 2 target

Panel C: x~ 3 target

x~J

0.0503 1.153

0.0418 0.3321

0.0361 0.t825

0.0292 0.0959

x~'2

0.0133 0.2415

0.0123 0.0680

0.0117 0.0378

0.0116 0.0217

x~3

0.0097 0.0184

0.0099 0.0104

0.0102 0.0100

0.0111 0.0123

a expl, explosive oscillations.

a p p r o p r i a t e a g a i n 57. T h e s a m e trio o f x~ definitions is e m p l o y e d as with the b a s e instrument. Table 1 r e p o r t s results o f c o u n t e r f a c t u a l h i s t o r i c a l s i m u l a t i o n s e a c h u s i n g rule (5.1) or (5.2) w i t h V A R e q u a t i o n s for Ayt, Apt, a n d e i t h e r Rt or A b , In these, e s t i m a t e d r e s i d u a l s for Aye, Ap~, a n d e i t h e r Rt or Abt are f e d into the s y s t e m as e s t i m a t e s o f s h o c k s that o c c u r r e d historically, w i t h the s i m u l a t i o n s b e g i n n i n g w i t h initial c o n d i t i o n s

57 The factor 100 is needed because R/ is expressed in tern~ls of percentage points whereas Ab~ is in logarithmic (i.e., fractional) units. Comparability is not complete, however, because R t is measured as percentage points on a per annum basis. Use of -400 as the scale factor would, however~ result m dynamically unstable behavior for most 3~values over 0.25.

B.T. McCallum

1512

as o f 1954.1 and running for 152 periods 5s. The table's entries are RMS errors, i.e., deviations o f xt from target values x~, with the top figure in each pair pertaining to the Abt instrument and the bottom figure to the Rt instrument. The three panels A, B, and C refer to simulations with the three target values (x2 l, x~ 2, x~3), and for each simulation the RMS error performance is reported relative to each o f the three target paths. Thus, we are able to see if performance relative to alternative criteria is sensitive to the target utilized, for each o f the targets. Comparing the three panels we see that when tile levels target is used (with only proportional feedback) performance is very bad with the Rt instrument, explosive fluctuations in xt resulting with ,~ = 0.25, 0.5, and 1.0. Even with the base instrument, the levels target does not perform too well and leads to instability when ;~ = 1.0. With = 0.25, somewhat better performance relative to the xj'1 target path obtains than when x~ 2 or x~3 is the target, but the difference is not large. Panel C, by contrast, shows that when the pure growth rate target xt 3 is adopted, successful stabilization o f x~ is achieved for all )~ values with both instruments. Performance relative to the growing levels path x; 1 is much better in Panel B with the x; 2 target, however, and brings about very little deterioration in performance relative to the pure growth rate criterion (i.e., the x; 3 path). Accordingly, the weighted average criterion xt 2 seems quite attractive, as was noted for Japan in McCallum (1993a). Equivalently, application o f a limited amount o f proportional as well as derivative feedback is evidently desirable 59 As for the comparison between monetary base and interest rate instruments, the results in Table 1 are distinctly more favorable to the former. In only one o f 30 separate comparisons 6° is the R M S error value smaller with the Rt instrument 61. And, more significantly, the number o f cases in which explosive oscillations result is larger with the interest instrument. These cases, should be noted, all involve the growing-levels target, xt ~. Some proponents o f an interest instrument might argue that it is important that Rt be adjusted relative to a reference level, rather than to the previous quarter's value. Following the practice o f Taylor (1993b), therefore, let us also consider performance o f a rule o f the following type:

R t = 10010.029 + (Pt 1 --Pt 5)] - 100~(xt-1 -xt-1).

(5.3)

s8 Stochastic simulations, with shocks generated randomly, have been conducted by Judd and Motley (t992) in a related study mentioned below in Section 6. 59 Judd and Morley's (1992) findings with regard to the use of some proportional control are less encouraging, evidently because their mixture is more heavily weighted toward proportional control. Also, they do not consider performance relative to the x*lt path when x*2~ is the target utilized. 60 Note that the first-colurrm cases are the same with the three different targets, since with ~ - 0 there is no feedback from target misses. (,I Michael Wood~brd has emphasized to me that there is no inherent interest in comparing base and interest instruments with equal values of k; that we want to compare entire families. These comments are correct. But Table 1 attempts to do that by scaling the 3, values - recall that the factor -100 has been inserted in Equation (5.2) - so that instrument instability occurs for about the same value of (scaled))~.

1513

Ch. 23: Issues' in the Design o f Monetary Policy Rules

Table 2 RMS errors with level-style interest instruments, rule (5.3), VAR Model, US Data 1954.1-1991.4 = 0.00

3,= 0.25

x~ x~,2 x~3

0.3825 0.0809 0.0118

0.1541 0.0326 0.0104

x~l x~2 x~3

0.3825 0.0809 0.01 t 8

0.2996 0.0630 0.0111

RMS error relative to:

2~- 0.50

2 - 1.00

Panel A: x~ 1 target

0.0915 0.0208 0.0108

0.0551 0.0169 0.0143

0.24l 6 0.0507 0.0110

0,1702 0.0366 0.0129

Panel B: x; z target

Panel C: x~ 3 target

x~t x~2 x~3

0.3825 0.0809 0.0118

0.3687 0.0780 0.0118

0.3559 0.0754 0.0120

0.3328 0.0711 0.0153

Here the (p~_j pt 5) term uses the past year's inflation rate as a forecast o f the next quarter's so as to make the rule one that sets a real interest rate in relation to the (annualized) target value o f 0.029, which is designed to be consistent with a long-run real interest rate o f 2.9 percent. The latter follows Taylor's (1993b, p. 202) suggestion of using the sample average rate o f growth o f real output. The feedback term is as before. Results are presented in Table 2 for cases using rule (5.3) that are exactly analogous to those in Table 1. |t will be seen that the performance is better than with interest instrument rule (5.2) for all 12 comparisons when x~ 1 is the target, i.e., when a levels target is utilized. A m o n g the 18 remaining comparisons, however, rule (5.3) outperforms (5.2) in only a single case. So, it is unclear whether the levels form o f interest instrument rule is superior to the form that calls for adjustment of R~ relative to the previous quarter's value. In comparison to the base instrument, rule (5.3) avoids the explosive outcome in the case in which 3, = 1 and the levels target x~ 1 is used, and also does better relative to the x23 path in two more cases (with the levels target). But for all cases in which the growth rate target x~ 3 or the weighted average target x/" is used, the R M S error is larger with rule (5.3) than with (5.1) - and is substantially larger when the criterion path is either x~ 1 or x~2. It must be emphasized that the foregoing is just a single illustration, not a study purporting to be conclusive - especially since the model used is o f the VAR t y p e

1514

B.T.. M c C a l l u m

Nevertheless, the apparent superiority o f the base instrument gives rise to the question o f why it is that, in actual practice, almost all central banks utilize operating procedures that are akin to use o f an interest rate instrument. It is almost certainly the case that use o f a base instrument would entail more short-term interest rate variability, but it is unclear that this would have any substantial social costs 62. One hypothesis is that interest rate instruments and interest rate smoothing are practiced because financial communities dislike interest variability and many central banks cater to the wishes o f financial institutions with which they have to work in the course o f their central-banking duties. The extent o f interest-instrument preference by CBs suggests, however, that there are additional reasons. Accordingly, Goodfriend (1991) and Poole (199l) have made interesting efforts to understand the Fed's attachment to an interest rate instrument. Despite their contribution o f various insights, however, the question remains unanswered 63. M y own thoughts on the subject suggest two intelligible reasons for a CB to prefer a R~ instrument, one having to do with beliefs concerning possible instrument instability and the other involving the CB's role as a lender o f last resort. Regarding the former, consider a grossly simplified base money demand function that includes lagged as well as current interest rates: bz = ao + a l R t + (x2Rt ] + th,

6It < O.

(5.4)

Here the absence o f price level and income/transaction variables reflects the presumption that their movements are slow in comparison to those of bt and Rt 64. N o w suppose that the CB were to manage bf exogenously 65. Then Rt will behave as R~ -- [30 + [3 t Rt 1 + [32 rh + [~3

(bt determinants),

(5.5)

where/31 = - a 2 / a l . Thus, if a2 < 0, there will be oscillations in Rt. More importantly, if la2t > lal I, then the system will be explosive. B e l i e f that market demand for the monetary base is such that la21 > la~ I represents the actual state of affairs would then lead one to believe that use o f a base instrument would be disastrous, as suggested by Goodhart. And, in fact, there is some reason to

(,2 Between 19'75 and 1987 the Swiss National Bank used procedures that were akin to use of a base instrument. [See Rich (1987, pp. 11-13).] Short-term interest rate variability in Switzerland was much greater than in other economies, but macroeconomic performance was excellent. (In 1987 there were two major institutional changes, involving new required-reserve structures and a new clearing system, that seriously disrupted monetary control and resulted in altered operating procedures.) 63 It is possible that Goodhart's (t 994) belief, that a base instrument would be infeasible, is shared by many central bankers. But why? One possible reason is developed in the next two paragraphs. 64 This simplification should not be misleading for the purposes at hand, although it would be ~5tal for many other issues. In Equation (5.4), th is a stochastic disturbance term. 65 Here l do not literally mean exogenous, but rather that bt is varied for macroeconomic reasons, not so as to s m o o t h R t values.

Ch. 23: Issues in the Design of Monetary Policy Rules

1515

think that such beliefs might be held by central bankers. In particular, econometric estimates o f base money demand functions (direct or indirect) sometimes indicate that la2l > la~l in fact. Central bank analysts would be aware o f these estimates. My own belief is that it is not true that fa2 ] > ]ctl [ holds in reality, for time periods of one month or longer, so that the posited CB attitude is unjustified. 66 But it could be prevalent, nevertheless, even if my belief is correct. A second intelligible reason for CB interest instrument preference concerns the lender-of-last-resort (LLR) role. That role is to prevent financial crises that involve sharply increased demands for base money [Schwartz (1986), Goodfriend and King (1988)]. To prevent such crises, the CB needs to supply base money abundantly in times o f stress [Bagehot (1873)]. This is usually conceived o f as occurring by the route o f discount-window lending. But Goodfriend and King pointed out that a policy involving interest rate smoothing i.e., not allowing R: to change much relative to Rt t - would amomatically provide base money in times o f high demand 67. Then if a CB is going to practice R~ smoothing it is quite natural for it to use a R~ instrument 6s. This last discussion leads one to consider the possibility o f using an interest rate instrument - and smoothing its movements at a high frequency (e.g., weekly) so as to keep monetary base values close to target levels implied by a policy rule such as (5.1). The motivation, of course, is the notion that quarterly base rules seem to function better macroeconomically than interest rules. The preliminary investigation in McCallum (1995a) attempts to study this question while accounting realistically and in quantitative terms for shock variances and market responses in the US economy. The results suggest that the federal funds rate could be manipulated weekly to approximate monetary base values that are designed to hit desired quarterly-average nominal GNP targets, with considerable smoothing o f the funds rate on a weekly basis (only about twice as much weekly variability as now obtains).

6. Issues concerning research procedures In this section consideration will be given to a number o f issues concerning procedures used in investigations of the properties o f monetary policy rules. One set of issues has to do with the operationality of various rule specifications while another set focuses

G6 In part my belief stems from the fact that for base demand in period t the value ofR t 1 is an irrelevant bygone, so Rt 1 does not belong in a properly specified demand function. There are reasons, involving omission of expectational variables, why econometric studies would nevertheless tend to find strong R~ ~ effects. On this, see McCallum (1985, pp. 583 585). 67 As would a practice of keeping R~ from rising above some preset penal rate. 68 Goodfriend (1991, p. 15) and Poole (1991, pp. 37-39) observe, however, that this is not a stricl logical necessity. Also, many actual CBs apparently do not accept the Goodfriend-King argument that the LLR role can be fulfilled by Rt smoothing without discount-window lending.

1516

B. Z McCallum

on the types of simulations used to generate model outcomes. Regarding the latter, a weakness of the simulation results reported above in Section 5, and also those in McCallum (1988, 1993a, 1995a), is that they are based on simulation exercises with a single set of shock values, i.e., shocks estimated to have occurred historically. As explained by Taylor (1988) and Bryant et al. (1993), there are several advantages to be obtained by using true stochastic simulations with a large number of shock realizations generated by random selection from (multivariate) distributions that have covariance properties like those of the historical shock estimates. The studies of Judd and Motley (1991, 1992) for example, improve upon those of McCallum (1988) by conducting "experiments" each of which consists of 500 stochastic simulations with a given model, policy rule, and policy parameter values, rather than a single simulation with the historical residuals used as shocks. One obvious advantage of stochastic simulations over historical counterfactuals is that they avoid the possibility that the historical residuals happen to possess some particular quirk that makes performance unrepresentative for the shock moments being utilized. Another advantage is that sample-mean values of shocks may not equal zero, as they must by construction in the case of historical residuals. This feature is especially important in considering the consequences of rules that feature difference stationarity (rather than trend-stationarity) of nominal variables. The residual values used as shocks in the simulations in Tables 1 and 2, for example, sum to zero for each equation's shock tenn. Thus the extent of a tendency for xt (say) to drift away from a levels target path such as xt 1 is understated by the results in those tables 69. Bryant et al. (1993, pp. 373-375) suggest that, in addition, stochastic simulations are helpful from a robustness perspective. Perhaps the most ambitious project undertaken to date on the characteristics of alternative monetary policy rules is the Brookings-sponsored study reported in Bryant et al. (1993). In this study, which is a follow-up to Bryant et al. (1988), eight prominent modeling groups (or individuals) reported on policy rule simulation exercises conducted with the following multicountry models: GEM, INTERMOD, MSG, MX3, MULTIMOD, MPS, LIVERPOOL, and TAYLOR. These studies were designed to explore the macroeconomic consequences of adopting different target variables for monetary policy, with contenders including nominal GDP (in levels form) and the hybrid variable discussed above in Section 4, as well as monetary aggregates and the exchange 'rate. Most impressively, the conference organizers took pains to arrange for the various modeling groups all to consider the same range of policy alternatives, thereby creating the possibility of obtaining results that would gain m credibility as a consequence of being relatively robust to model specification. At the strategic level of research design, therefore, this Brookings project possessed the potential for contributing greatly to knowledge concerning the design of monetary

69 Understated, but not entirely absent; thne plots of xt hldicate the absence of any path-restoring behavior except toward the end of the 152-quartersimulation (and sample) period.

Ch. 23: lssues in the Design of Monetary Policy Rules

1517

and fiscal policy rules (even in the face of potential weaknesses of the models' specifications). It is argued in McCallum (1993b, 1994), however, that this potential was significantly undermined by the particular generic form of policy rule specified for use by all the modeling groups. The alleged problem is that the rule form permits rule specifications that are not operational and, in addition, suggests performance measures that can be seriously misleading. The rule form in question, which has also been used in several other studies, may be written as Rt - Rbt

=/l(zt

- z~),

(6.1)

where Rt is an interest rate instrument and zt is a target variable such as nominal GDP. Here the "b" superscripts designate baseline reference paths for the variables, baseline paths that may be defined differently by different investigators. Also, the performance of various targets is evaluated by measures such as E[(zt - - Z bt ~~2 l J, which pertain to target variable(s) for the rule and perhaps also other criterion variables. In terms of operationality there are two problems with this rule form (6.1)7o. The more obvious is that it is unrealistic to pretend that monetary policymakers can respond to the true value of current-period realizations of zt for several leading specifications of the latter. It is reasonable to assume that contemporaneous observations are available for interest rates, exchange rates, or other asset-market prices. It would be unreasonable, however, to make such an assumption for nominal or real GDP (or GNP) or the price level. One could make arguments pro and con in the case of monetary aggregates such as M1 or M2, but in the case of national-income values, data are not produced promptly enough for actual central bankers to respond to movements without an appreciable lag. Ignoring that lag, as is done throughout the Bryant et al. (1993) studies, clearly makes it possible for the simulated performance to be significantly better than could be obtained in reality. Furthermore, simulations that ignore this lag also intend to understate the danger of instrument-induced instability, a bias that is quite important because instrument instability is one of the most serious dangers to be avoided in the design of a policy rule. The second and less obvious way in which rules like (6.1) are not operational involves the baseline values R ) and z ). ttere the problem is that an actual policymaker could not implement any rule of form (6.1) without knowledge of these reference paths. But by definition these paths may be related to each other by the model being investigated, so the policy rule is model-specific and therefore of reduced interest to a practical policymaker. In terms of misleading performance measures, the problem is that the instrumem variable under consideration may be one that can be used to smooth out fluctua~ tions in zt but not to control the long-term growth o f z , Then by using fluctuations in z,

70 It should be noted favorablythat the instrument variable is operational and realistic.

1518

B. 717.McCallurn

relative to the baseline path z b in a performance measure like E [ ( z t - - z b ) 2 ] , the investigator may conclude that Rt is a desirable instrument when in fact it is highly unsuitable 71. Another type of nonoperationality involves the specification of instrument variables that would, in actual practice, be infeasible in this capacity. Broad monetary aggregates such as M2 or M3 would seem clearly to fall into this category and, under typical current institutional arrangements, probably the same applies to variants of M1. Studies that pretend that such variables are feasible instrument have declined in frequency in recent years, as the practice of specifying an interest instrument has gained in popularity [e.g., Taylor (1993a), Bryant et al. (1993), Fuhrer and Moore (1995)]. Objections based on the operationality criterion have been directed at rules that use nominal GDP or GNP targets, even when these rules refer only to values lagged by at least one quarter. The point is that national income statistics are not produced often enough or quickly enough, and are significantly revised after their first release. But this criticism seems misguided since the essence of nominal income targeting is to utilize some rather comprehensive measure of aggregate (nominal) spending; the variable does not need to be GDP or GNP p e r se. Other measures could readily be developed on the basis of price and quantity indices that are reported more often and more promptly -in the USA, for example, one could in principle use the product of the CPI and the Fed's industrial production index (both of which are published monthly). It might even be possible to develop a monthly measure that is more attractive conceptually than GDP, by making the price index more closely tailored to public perceptions of inflation and/or by using a quantity measure that treats government activity more appropriately.

7. Interactions with fiscal policy The relationship between monetary and fiscal policy has been quite an active topic recently, possibly in part as a response to the magnitude and duration of fiscal deficits experienced in many developed countries and/or to controversies concerning proposed fiscal rules for the planned European monetary union. It is obviously impossible to discuss in this chapter all of the many ramifications of monetary/fiscal policy interactions, but it seems important to recognize some recent arguments which suggest that it is necessary, or at least desirable, for the monetary authority to take account of fiscal policy behavior when designing its monetary policy rule 72. Such a recommendation is implicitly critical of the policy rules discussed in previous sections and runs counter to the spirit of much current central-bank thinking, as expressed for example in the practice of inflation targeting. Consequently, three strands of literature will be considered. :1 Some examples are described in McCallum (1994). 72 Among these contributions are papers by Alesina and Tabellini (1987), Debelle and Fischer (1995), Leeper (1991), Sims (1994, 1995), and Woodford (1994, 1995).

Ch. 23: Issues in the Design of Monetary Policy Rules

1519

An early paper on the subject that has received a great deal of attention is the Sargent and Wallace (1981) piece entitled "Some Unpleasant Monetarist Arithmetic". As many readers will be aware, that paper's principal contention was that an economy's monetary authority cannot prevent inflation by its own control of base money creation if an uncooperative or irresponsible fiscal authority behaves so as to generate a continuing stream of primary fiscal deficits 73. Whether the central bank has control over inflation is viewed as depending upon, in the words of Sargent and Wallace (1981, p. 7), "which authority moves first, the monetary authority or the fiscal authority. In other words, who imposes discipline on whom?" Having posed the problem in that way, the Sargent-Wallace paper then goes on to suggest that it might well be the fiscal authority that dominates the outcome. In fact, however, the paper's analysis proceeds by simply assuming that the fiscal authority dominates, an assumption that is implicit in the procedure of conducting analysis with an exogenously given path of primary deficits. Proceeding in that fashion, the Sargent-Wallace paper seems to show that even a determined central bank could be forced by a fiscal authority to create base money along a path that is inflationary when a non-inflationary path is intended. It is argued by McCallum (1990a, pp. 984-985), however, that this suggestion is unwarranted. It is of course true that fiscal authorities may be able to bring political pressure to bear on central banks in ways that are difficult to resist. But the SargentWallace analysis is not developed along political lines; instead it seems to invite the reader to conclude that a politically independent central bank could be dominated in some technical sense by a stubborn fiscal authority. My basis for disputing this is that an independent central bank is technically able to control its own path of base money creation, but fiscal authorities cannot directly control their own primary deficit magnitudes. The reason is that deficits are measures of spending in excess of tax collections, so if a fiscal authority embarks on a tax and spending plan that is inconsistent with the central bank's (perhaps non-inflationary) creation of base money, it is the fiscal authority that will have to yield. Why? Simply because in this circumstance, it will not have the purchasing power to carry out its planned actions 74. In other words, the fiscal authority does not actually have control over the instrument variable - the deficit - that it is presumed to control in the Sargent-Wallace experiment. Thus a truly determined and independent monetary authority can always have its way, technically speaking, in monetary versus fiscal conflicts. This simple point is one tha~ seems to the author to be of great importance in the design of central bank institutions. The point is also intimately related to a quite recently developed body of theorizing that takes a strongly "fiscalist" stance, leading examples of-which include Woodford

73 The result pertains to primary deficits, i.e., deficits exclusive of interest payments, but not to deficits measured in the conventional interest-inclusive way. 74 This is directly implied by the government's budget constraint which limits purchases to revenue raised by taxes, net bond sales, and base money creation. In this regard it should be recognized that the government cannot compel pfivatc agents to buy its bonds (i.e., lend to it), since such would represent taxation.

1520

B.77 McCallum

(1994, 1995), Sims (1994, 1995), and Leeper (1991). Perhaps the most dramatic theme in this literature is the presentation o f a "fiscal theory o f the price level" [Woodford (1995, pp. 5-13), Sims (1994)]. For an introductory exposition and analysis, let us consider the simplest case, which involves a Sidrauski-BrockT5 model with constant output y and utility function u(ct, mr)+ [3u(ct+l, m r + t ) + . . , with u ( c , m ) = (1 - a ) - I A l c 1-~ + (1 - rl) IA2ml-rl, where a, , / > 0 and fi = 1/(1 + p ) with p > 0. Also we assume t / < 1, in order to facilitate presentation o f the fiscalist theory, not the counter-argument outlined subsequently. In this setup, the households' firstorder conditions include mt+l _ A R 1/8 Pt+l t , 1 P, 1

l + R, - / 3 P, '

A =

R, > 0

(7.1)

(7.2)

for all t = l, 2 . . . . . Here Pt is the money price o f output, Mt is nominal money at the start o f period t, mt = M t / P , ca is consumption during t, and R¢ is the rate o f interest on government bonds, the household's budget constraint being Pt(Y

vt) - Ptct + Mt+l - M t + (1 + Rt)-I Bt+l _ Bt '

(7.3)

where vt is lump-sum taxes and Bt is the nominal stock o f bonds at the end o f t. In per-household terms, the government budget constraint with zero purchases is - P t v t = Mt+j - M r + (1 + Rt) 1Bt+l - B~,

(7.4)

so vt is the per-household value o f the fiscal surplus. If the government chooses time paths for M t and vt (or Bt), then Equations (7.1)-(7.4) give equilibrium values for ct, Pt, Rt, and Bt (or vt) provided that two transversality conditions are satisfied, these requiring that [3tMt/Pt and [3tB/pt approach zero as t---+ oo. Note that Equations (7.3) and (7.4) imply ct = y , the constancy o f which is utilized in formulations (7.1) and (7.2). Following the fiscalist argument v6, now suppose that the value o f Mr is kept constant at M and that vt = v > 0 for all t = 1, 2 . . . . . Then the price level is determined as follows. The GBR can be written as

b._, = (1 +RO

[b,-v~] = B1 b , - l

(7.5)

implying that bt = B,/P~ will explode as t ~ o c , since 1/fi > l, unless it is the case that B1/P1 = o/(1 -/~), which would induce bt to remain constant at the level bt = v / ( l [3) 75 That is, a model in which infinite-lived households with time-separablc preferences makc their decisions in a optimizing fashion and interact with each other and the government (monetary authority and fiscal authority) on competitive markets. Woodford's (1995) version of the model, and ours, does not include capital goods but that feature of the setup is not relevant to the issues at hand. 76 I am indebted to Michael Woodford for special efforts to explain the argumcnt to me, bm lie is certainly not responsible for the point of view expressed here.

Ck. 23: Issues in the Design of MonetalT Policy Rules

1521

thereafter. Therefore, so the theory says, PI = B1 (l -/3)/v is determined by the fiscal surplus magnitude v and the initial stock of nominal debt B1. At the same time, Equations (7.1) and (7.2) imply a difference equation relating Pt+~ to Pt in an unambiguously explosive fashion, starting from P1, provided that PI exceeds a critical value Pc. That explosion in Pt makes M / P t approach zero and so, with bt constant, both transversality conditions are satisfied although Bt is exploding. Thus the fiscal theory of the price level asserts that with a constant money stock and constant fiscal surplus, the price level explodes as time passes, starting from a level that is directly related to the size of the pre-existing nominal bond stock and to the magnitude of the maintained surplus. No other path could be an equilibrium because it would imply an exploding bt, which would violate a transversality condition. The foregoing is an ingenious argument but, in the opinion of the writer, is open to a crucial objection. It is that there is another equilibrium - typically ignored by fiscalist writers that does not rely upon explosive-bubble behavior of the price level. This more fundamental "monetarist" equilibrium features Pt+l = P t - MPl/'t/A, i.e., a constant price level, together with values Bt+l = 0 for all t = 1, 2 , . . . . With these paths for Pt and Bt it is clear that Equations (7.1)-(7.3) and both transversality conditions are satisfied. It might be objected that this solution does not satisfy the budget constraint (7.4) for the values of vt = v specified by the fiscalist writers, but it has been argued above that the fiscal surplus is actually not a variable that can legitimately be specified as exogenous 77. What the monetarist solution says is that if the fiscal authority tried to keep vt = v as in the fiscalist solution, then households would refuse to purchase the bonds that are required to be sold by the fiscal authority. It would be necessary to distinguish between bonds supplied in (7.4) and bonds demanded in (7.3), with Bt = 0 in the latter. If there were an initial stock of bonds outstanding, B I ~ 0, then they would be retired in period 1 with a resulting real primary surplus of B1/P1. In sum, a formally correct and arguably more plausible solution than the fiscalist candidate is one in which the price level remains constant, with a magnitude that is proportional to the money stock. At the same time, the stock of bonds offered for sale by the fiscal authority may be explosive bm if so these bonds will not be purchased by optimizing households. The fiscal authority's realized surplus will then be zero after the initial period leaving us with a traditional non-fiscalist result 78. There are, of course, several other cases and more complex models featured in the recent fiscalist literature~ indeed, a rather bewildering variety. But it would appear to the present writer that the sta'iking fiscalist outcomes typically result from emphasizing the possibility of bubble

77 This is also the basis for the argument hi a recem paper by Buiter (1998), which reaches conclusion,s predominantly compatible with those presented here. 78 Note that it is not being claimed that this is the only solution, but merely that it is a solution (and one that might be thought likely to prevail by analysts who are skeptical of the empirical importance of macroeconomic bubbles).

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solutions while ignoring the existence of a non-bubble or fundamentals solution that would deliver an entirely traditional policy message. 79, 8o The third strand of the monetary-fiscal interaction literature to be discussed is represented by papers by Alesina and Tabellini (19 87) and Debelle and Fischer (1995). In the former, the workhorse Barro-Gordon model is extended by assuming that real government purchases are controlled by a fiscal authority (FA) that may have different objectives - concerning the level of these purchases as well as inflation and output than those of the central bank (CB). The FA's revenues come from non-lump-sum (distorting) taxes and money growth, government debt being excluded from the m o d e l In this setting, Alesina and Tabellini derive outcomes pertaining to both discretionary and rule-like behavior by the CB 81. Their most striking result is that when preferences of the CB and the FA are sufficiently different 82, equilibrium outcomes with monetary policy commitment can be inferior 83 to those obtained under discretion. This result is with independent behavior by the CB and FA, so the message is that monetary-fiscal policy cooperation is needed. In a more recent paper, Debelle and Fischer (1995) have modified the AlesinaTabellini framework by also including a social objective function, one that can be different from those of the CB and FA. Only the latter cares, in their setup, about the level of government purchases. In this model, Debelle and Fischer conduct analysis always assuming discretionary behavior by the CB but under different assumptions regarding the Stackelberg leadership positions of the CB and FA. A major aim of the analysis is to determine the optimal value, in terms of society's preferences, of the "conservativeness" of the CB, i.e., the relative importance that it assigns to ilfftation. It is not optimal, they find, for the CB's preferences to match those of society - i.e.,

79 Dotscy (1996) shows that a reahstic specificationof parameter values gives rise to a more traditional policy message than one promoted in the fiscalist literature, for an issue concerning the responsiveness of the CB to fiscal variables under the assumption that the fiscal anthority's policy rule tends to prevent debt explosions. 8o One other feature of the recent fiscalist literature is its contention that pegging the nominal interest rate at a low value will result in a correspondinglylow inflation rate and in no indeterminacyproblem, implying that such a policy would be preferable to the maintenance of a low growth rate of the (base) money supply. The analyticalkey to this argument is that explosive price level (bubble) solutions, which are possible with a low money stock growth rate, would be precluded by a constant interest rate in models with a well-behaved (possibly constmat) real rate of interest - see, e.g., Equation (7.2) above. It has been established above, however, that when money growth is exogenous, the possible aberration reflects multiple (bubble) solutions, not nominal indeterminacy.But the empirical relevance of bubble solutions for macroeconomicvariables is dubious, this writer would contend, and if such solutions are not relevant then the theoretical disadvantage for the low money growth policy is itself irrelevant. 81 In the absence of debt, the FA has no incentive for dynamic inconsistency, i.e., no commitment problem. 82 The CB is assumed to assign at least as much weight to the inflation rate (relative to each of the other goal variables) as does the FA. 83 Inferior in terms of both authorities' prelbrences; the private sector is assumed to care only about real wages.

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the private sector. And they find that it is undesirable socially for the FA to dominate (in a Stackelberg sense) the CB, requiring the CB bank to finance FA deficits 84 An objection to this last strand of analysis stems from its reliance on the presumption that an economy's CB and FA will have preferences that differ from each other's and from social (i.e., household) preferences. While such might be the case in some nations, one would expect that in democratic societies, CBs and FAs will be aware of and tend to reflect the basic preferences of the population. That tendency might be combatted by various devices, but it seems likely that (e.g.) attempts to appoint CB governors with tastes more anti-inflationary than society's would often result in ex-post surprises regarding these tastes. Also, one might expect that fiscal or monetary legislation would be overturned fairly promptly if it were to yield results that are truly inconsistent with the preferences of the society's voters. In any event, it would seem that designing institutions nnder the presumption that CB and/or FA preferences differ from those of the society at large is unlikely to be fruitful.

8. Concluding remarks This final section will consist of a brief and perhaps opinionated recapitulation of conclusions obtained for the main topics of discussion. First, in actual practice the defining characteristics of rule-like behavior are that the central bank conducts policy in a systematic fashion, and while doing so systematically abstains from attempts to exploit existing expectations for temporary gains in output. Central banks can behave in this committed manner if they choose; there are dynamic-inconsistency pressures on them to act in a more discretionary fashion, but there is nothing tangible to prevent committed behavior. Indeed, the adoption o f a monetary policy rule is one technique for overcoming discretionary pressures. In terms of research strategy, the chapter's discussion has promoted the robustness approach - i.e., searching for a rule that works reasonably well in a variety of models rather than the more straightforward approach of deriving an optimal rule relative to a particular model, No strong claims are made in this regard, however, and the value of the optimal design approach is recognized. The importance of operationality of any proposed rule is also emphasized, as well as the merits of stochastic simulations as opposed to simpler historical counterfactual simulations. Regarding the choice of a target variable, the chapter suggests that in practice the difference between an inflation target and one that aims for nominal spending growth, at a rate designed to yield the same target inflation rate on average, is unlikely to be large. More dissimilar is the hybrid target variable that adds together inflation and output relative to capacity. This hybrid variable is probably more closely related to

~4 Of course, it is argued above that tile FA will not be able to dominate if the CB has independence (i.e., can choose its own base money creation rates),

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actual central bank objectives, but the absence o f any reliable and agreed-upon method o f measuring capacity or trend output creates a major drawback for this variable. Also, it is argued that the magnitude o f future price-level uncertainty, introduced by the unit root component that results from a growth-rate type of target, is probably rather small. Thus growth-rate targets appear somewhat more desirable than growing-level targets as the latter requires stringent actions to drive any nominal target variable back toward its predetermined path after shocks have led to target misses. Turning to the choice o f an instrument variable, the chapter presents a small bit o f evidence designed to illustrate why it is that a number o f academic economists are inclined to prefer quantity instruments, such as the monetary base, rather than short-term interest rates. The exposition includes arguments against some literature claims that either short-term nominal interest rates or the monetary base are infeasible as instruments. In this discussion, particular emphasis is given to the distinction between two quite different types o f abberational price level behavior, namely, nominal indeterminacy and multiple solutions. The former has to do with the distinction between real and nominal variables while the latter concerns self-fulfilling dynamic expectational phenomena - i.e., bubbles. Also, the former pertains to all nominal variables whereas the latter involves real variables. Finally, with regard to prominent fiscalist positions two points are made. First, the recently developed fiscal theory o f price-level determination typically leads to a solution that is not unique; there also exists a less exotic bubble-free solution that has a much more traditional (indeed, monetarist) flavor. This conclusion stems from recognition that central banks can dominate in any conflicts with fiscal authorities. Also, there are some results in the literature that suggest that monetary/fiscal cooperation is important, but these depend upon the assumption that central banks and fiscal authorities have fundamentally different objective fimctions. It is doubtful whether such an assumption can play a fruitful role in the design o f desirable central bank institutions and behavior patterns.

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Whittaker, J., and A.J. Theunissen (1987), "Why does the reserve bank set the interest rate?", South Al?ican Journal of Economics 55:16-33. Wicksell, K. (1907), "The influence of the rate of interest on prices", Economic Journal 17:213-220. Woodford, M. (1990), "The optimum quantity of money", in: B.M. Friedman and F.H. Hahn, eds., Handbook of Monetary Economics, vol. 2 (North-Hollazld, Amsterdam) 1065-1152. Woodford, M. (1994), "Monetary policy and price level determinacy in a cash-in-advance economy", Economic Theory 4:345-380. Woodford, M. (1995), "Price-level determinacy without control of a monetary aggregate", CarnegieRochester Conference Series on Public Policy 43:1-46.

Chapter 24

I N F L A T I O N STABILIZATION A N D B O P C R I S E S IN DEVELOPING

COUNTRIES

*

GUILLERMO A. CALVO

University of Maryland CARLOS A. VEGH**

UCLA

Contents Abstract Keywords 1. Introduction 2. Understanding chronic inflation 2.1. 2.2. 2.3. 2.4. 2.5. 2.6.

Inflation as an optimal tax Shocks and accommodation Multiple equilibria The "provinces" efl~ct Delayed stabilization In conclusion

3. Evidence on the real effects of stabilization in chronic-inflation countries

1533 1533 1534 1536 1537 1538 1539 1540 1540

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1541 1543 1547

3.1. Exchange-rate-based stabilization: empirical regularities 3.1.1. Stabilization time profiles 3.1.2. Panel regressions 3.1.3. Do exchange-rate-based stabilizations sow the seeds of their own destruction? 3.2. Money-based stabilization: empirical regularities 3.3. Recession now versus recession later 3.4. A word of caution

1550 1553 1554 1557 1559

4. Exchange-rate-based stabilization I: inflation inertia and lack of credibility

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4.1. Inflation inertia

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" We are grateful to Francesco Daveri, David Gould, Amartya Lahiri, Carmen Reinhart, Sergio Rodriguez, Jorge Roldos, Julio Santaella, John Taylor, Aaron Tornell, Martin Uribe, Sara Wong, Mike Woodford, Carlos Zarazaga, participants at the conference on "Recent Developments i~ Macroecononomics", organized by the Federal Reserve Bank of New York (February 1997), and, especially, Ratna Sahay and Miguel Savastano for insightful comments and discussions. ** Corresponding author. Department of Economics, UCLA, 405 Hilgard Avenue, Los Angeles~ CA 90095-1477. E-lnaih [email protected]. Website: http://vegh.sscnet.ucla.edu.

Handbook of Macroeconomics, Volume 1, Edited by ~B. Taylor and M, Wood~fbrd © 1999 Elseuier Science B.V. All rights reserved 1531

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4,2. Lack of credibility 1569 5. Exchange-rate-based stabilization ll: durable goods, credit, and wealth effects 1573 5.1. Durable goods 1573 5,2. Credit market segmentation 1575 5,3. Supply-sideeffects 1577 5,4. Fiscalpolicy 1580 5,5. And the winner is ... 1581 6. Money-based stabilization 1582 6,1. A simple model 1582 6,2. Extensions to other money-basedregimes 1587 6,3. Money anchor versus exchange-rate anchor 1588 7. Balance-of-payments crises 1590 7,1. Liquidity 1591 7~2. The Krugman model 1592 7,3. Krugman model: critique and extensions 1595 7.3.1. Bonds 1595 7.3.2. Sterilization 1595 7.3.3. lnterest rate policy 1596 7,4. The current account approach 1597 7.5. Financial considerations 1599 7.5.1. Volatilityof monetary aggregates 1599 7.5.2. Short-matmity debt 1601 7.5.3. Domestic debt and credibility 1603 7.5.4. Credibility,the demand for money and fiscal deficits 1603 8. Concluding remarks 1604 References 1607

Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries

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Abstract High and persistent inflation has been one of the distinguishing macroeconomic characteristics of many developing countries since the end of World War II. Countries afflicted by chronic inflation, however, have not taken their fate lightly and have engaged in repeated stabilization attempts. More often than not, stabilization plans have failed. The end of stabilizations - particularly those which rely on a pegged exchange rate - has often involved dramatic balance-of-payments crises. As stabilization plans come and go, a large literature has developed trying to document the main empirical regularities and to understand the key issues involved. This chapter undertakes a critical review and evaluation of the literature related to inflation stabilization policies and balance-of-payments crises in developing countries. The chapter begins by trying to rationalize the existence of chronic inflation in a world of rational agents. It then offers an empirical analysis of the main stylized facts associated with stopping chronic inflation. It is shown that the real effects of disinflation depend on the nominal anchor which is used. Exchange-rate-based stabilizations lead to an initial output and consumption boom - which is particularly evident in the behavior of durable goods - real exchange rate appreciation, and current account deficits. The contractionary costs typically associated with disinflation emerge only later in the program. In contrast, in money-based stabilizations, the contraction occurs in the beginning of the program. The chapter then proceeds to review several explanations for these puzzling phenomena, emphasizing the real effects of lack of credibility, inflation inertia, and consumption cycles generated by durable goods purchases. The chapter also documents the fact that most exchange-rate-based stabilizations end up in balance-of-payments crises. The Mexican crisis of December 1994 brought back to life some of the key questions: Do exchange-rate-based stabilizations sow the seeds of their own destruction by unleashing "unsustainable" real exchange rate appreciations and current account deficits? Or are credibility problems and self-fulfilling prophecies at the root of these crises? The remainder of the chapter is devoted to analyzing the main ideas behind this unfolding literature.

Keywords JEL classification: E52, E63, F41

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G.A. Caluo and C.A. V~gh

1. Introduction

High and persistent inflation has been one of the distinguishing macroeconomic characteristics of many developing countries - particularly in Latin America - since the end of World War II. Pazos (1972) coined the term "chronic inflation" to refer to this phenomenon. In his view, chronic inflation is quite a different creature from the much more spectacular hyperinftations studied by Cagan (1956). First, unlike hyperinflations whose duration is measured in terms of months, chronic inflation may last for decades. Second, countries learn how to live with high and persistent inflation by creating various indexation mechanisms which, in turn, tend to perpetuate the inflationary process. As a result, inflation does not have an inherent propensity to accelerate and, if it does, soon reaches a new plateau. Countries afflicted by chronic inflation, however, do not take their fate lightly. Quite to the contrary, in the last four decades they have engaged in repeated stabilization attempts which, more often than not, have failed. The end of stabilizations - in particular those which rely on a pegged exchange rate - has often involved dramatic balance-of-payments crises with costly devaluations and losses of international reserves. With increasingly open capital markets, some of these crises now send shock waves throughout the world, as vividly illustrated by the Mexican crisis of December 1994. In the last ten years, however, countries such as Chile, Israel, and Argentina have succeeded in reducing inflation close to international levels. Still, most developing countries continue to struggle through stabilization attempts, and some former socialist economies have also begun to face similar cycles of inflation and stabilization. The currency crises that hit South East Asia during the second half of 1997 were also a startling reminder that no region is immune to boom-bust cycles which were once thought as being mainly a Latin American disease. Over the course of the last four decades, a myriad of major stabilization plans went by, leaving behind a rich legacy of issues and puzzles. In retrospect, the stabilization plans implemented in the late 1970s in the Southern Cone countries - Argentina, Chile, and Uruguay - proved to be a turning point. Designed by US-trained technocrats, these plans were in some sense the first ones to openly recognize the constraints imposed on monetary policy by open financial markets. Trying to make the most of such constraints, policymakers decided to abandon the "closed-economy" monetary policies of the past - aimed primarily at controlling the money supply - and switch to "open-economy" policies based on setting a declining rate of devaluation which would quickly bring domestic inflation in line with tradable-goods inflation (given by world inflation plus the rate of devaluation). To the consternation of policymakers, however, the inflation rate failed to converge to tradable-goods inflation, which resulted in a large real appreciation of the domestic currency. More puzzling still, in spite of the real appreciation, real economic activity - particularly private consumption -- expanded in the early years of the programs. Later in the programs, a recession set in, eve1~before the programs collapsed. In the mid-1980s, major programs in Argentina, Brazil, and Israel brought back to

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life some o f the same, and still mostly unresolved, issues. In spite o f the use o f wage and price controls to supplement an exchange rate peg, real appreciation remained an integral part o f the picture. More puzzling, however, was the reemergence o f the pattern of an initial b o o m and a later recession. The Israeli recession was viewed as particularly hard to rationalize because o f its occurrence in a fiscally sound and largely successful stabilization program. Based on these new programs - and a reexamination of older programs going back to the 1960s - Kiguel and Liviatan (1992) and V6gh (1992) argued that the outcome observed in the Southern-Cone stabilizations is a pattern common to most stabilization plans which have relied on the exchange rate as opposed to a monetary aggregate - as the main nominal anchor. Specifically, the beginning o f an exchange-rate-based stabilization is characterized by an economic boom and sustained real appreciation. Later in the programs - and often aggravated by the collapse o f the program - a contraction takes hold. In contrast, the scanty evidence on money-based stabilization in chronic-inflation countries lends support to the notion that, as in low-inflation countries, the recession takes place at the beginning o f the program [Calvo and V6gh (1994b)]. Hence, it would appear that under money-based stabilization, the costs (in terms o f output losses) would be paid up-front, whereas, under exchange-rate-based stabilization, these costs would be postponed until a later date. The intriguing idea that choosing between the two nominal anchors may imply choosing not t f b u t w h e n to bear the costs o f disinflation has been dubbed the "recession-now-versus-recession-later" hypothesis. The twin puzzles o f the b o o m - r e c e s s i o n cycle in exchange-rate-based stabilizations and the recession-now-versus-recession-later hypothesis have been the driving force behind recent developments in the area o f inflation stabilization in developing countries. An emerging empirical literature has attempted to document these phenomena in a systematic way, while an extensive theoretical literature has advanced various hypotheses - such as inflation inertia and lack o f credibility - to explain the real effects of disinflation. A critical review and evaluation o f this literature constitutes the core of this chapter i. A third puzzle is the fact that most exchange-rate-based stabilizations end up in balance-of-payments (BOP) crises. The literature, however, has had precious little to say so far about the possible links between the dynamics o f exchange-rate-based stabilizations and BOP crises. The Mexican crisis o f December 1994 which put an end to an exchange-rate-based stabilization plan initiated seven years earlier - brought back to life some o f the key questions: Do exchange-rate-based stabilizations sow the Not suprisingly, most of the literature has been respired by the experiences of chronic inflation countries, which constitute a rich laboratory for the discussion of inflation and stabilization in developing countries. To focus the discussion, we follow this tradition and confine our discussion on inflation and stabilization mostly to chronic inflation countries. We will thus ignore some rare episodes of fullblown hyperinfations (like Bolivia in the mid-1980s) - which have more in common with Cagan's classic hyperinflations [see V6gh (1992)]. We will also mostly ignore the inflationary experience of the transition economies, as the dramatic transformation from plan to market raises some special issues [see, for example, De Melo, Denizer and Gelb (1995), and Sahay and V6gh (1996)].

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seeds of their own destruction by unleashing "unsustainable" real appreciations and current account deficits? Or are credibility problems and self-fulfilling prophecies at the root of these crises? The remainder of the chapter is devoted to analyzing the main ideas behind this unfolding literature. O f course, the potential for BOP crises is a more general issue, which goes back to Krugman's (1979) seminal contribution, and applies to any pegged exchange rate system. Hence, while many of the issues to be discussed have broader relevance, we focus on factors which may be of particular importance for developing countries. The chapter proceeds as follows. Section 2 focuses on how to explain the existence of chronic inflation in a world of rational economic agents. Section 3 examines the main empirical regularities of inflation stabilization in chronic-inflation countries. Section 4 begins the theoretical discussion on exchange-rate-based stabilization by focusing on two key thctors: inflation inertia and lack of credibility. Section 5 continues the analysis of exchange-rate-based stabilization by highlighting the role of consumer durables, credit market segmentation, supply-side effects, and fiscal policy. Section 6 examines money-based stabilization. Section 7 discusses the causes and mechanics of balance-of-payments crises. Section 8 concludes.

2. Understanding chronic inflation For the purposes of this chapter, the rate of inflation in period t is defined as the proportional rate of growth of the price level (usually the consumer price index) from period t - l to period t. An essential ingredient in the definition of inflation is the "price level", that is to say, the relative price of goods in terms of money. Therefore, one cannot have inflation without money, and one cannot have inflation without goods. During high inflation - unless something very unusual is happening to the demand tot money or to the demand t0r or supply of goods - the supply of money also grows at a high rate. Hence, although inflation is a phenomenon that results from the interaction of monetary and real phenomena, monetary factors are likely to dominate. The situation, however, is not symmetric: it does not follow from the above observations that real phenomena, like output or domestic absorption, are largely independent of money. This would be true only under very special circumstances~ including (i) no nominal rigidities, and (ii) no effects of changes in nominal interest rates on consumption (see below). As the ensuing analysis will reveal, the channel from money to output is particularly relevant during stabilization programs. The empirical evidence is quite clear about the following two points: inflation is closely tracked by money supply, and inflation - particularly, changes in the rate of inflation - affects real variables. The latter represents a formidable challenge faced by stabilization programs. As will be argued below, however, the real effects of either inflation or stopping inflation are not necessarily rooted in fundamentals but may, to a large extent, be due to factors - like policy credibility - which suitable institutional/political arrangements may help to modify.

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Under ideal circumstances, stopping inflation may be a socially painless process. Those circumstances, however, require appropriate fiscal adjustment. One serious difficulty in that respect is that there is more than one way to effect a fiscal adjustment, and each o f these ways has different implications for various groups in society. Consequently, it is not easy to reach wide consensus on any particular policy. This has two important consequences: (i) delayed stabilization, and (ii) adoption o f incomplete stabilization programs. Point (i) rationalizes inflation persistence, while point (ii) explains the prevalence of short-lived stabilization programs. But what sets inflation in motion in the first place? And, in particular, how can the phenomenon of high and persistent inflation be explained in a world of rational economic agents? 2 Although it would seem fair to say that the profession is still struggling to provide an answer to these questions and is far from reaching a consensus, the existing literature provides several useful insights. 2.1. Inflation as an optimal tax

One explanation, due to Phelps (1973), is that in a world o f distorting taxes, governments may find it optimal to depart from Friedman's (1969) celebrated optimum quantity of money rule, which calls for setting the nominal interest rate to zero. Phelps's (1973) result is quite intuitive. It follows from the observation that at Friedman's optimum quantity o f money rule, the marginal cost of the inflation tax (i.e., the nominal interest rate) is, by definition, nil. Thus, at the margin, increasing fiscal revenue thi'ough money creation has no cost. In contrast, the marginal benefit o f lowering any distorting tax is unambiguously positive. Therefore, starting from a zero nominal interest rate, it is welfare-improving to increase the inflation tax and lower any other distorting tax used to collect revenue. Thus, Phelps's result calls for a positive inflation tax 3. A key assumption in Phelps (1973) and the ensuing literature is that there is no fundamental difference between the inflation tax and other "conventional" taxes. It has long been recognized, however, that the costs of collection, enforcement, and evasion associated with the inflation tax are negligible compared to those o f other taxes. As Keynes (1924, p. 46) put it, inflationary finance "is the form o f taxation which the public finds hardest to evade and even the weakest Government can enforce, when it can enforce nothing else". An inefficient tax system may make it optimal to resort to 2 An alternative explanation tbr the existence of chronic inflation is simply that policymakers in these countries are systematically ignorant or incompetent. We find this explanation both implausible as a description of the real world and maintercsting from a theoretical point of view (given that we do not have good theories of "ignorance" or "incompetence"). Hence, the basic premise of this section is that chronic inflation is a phenomenon in search of a "rational" explanation. 3 A large literature has developed which analyzes the robustness of Phelps' (1973) findings [see the critical survey by Woodford (1990)]. Modeling money as an intermediate input, Kimbrough (1986) shows an interesting case in which Friedman's rule holds even though all available taxes arc distorting. Kimbrough's result, however, holds only under rather restrictive assumptions [see Woodford (1990), Guidotti and V6gh (1993), and Correia and Teles (t996)].

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the inflation tax even in cases in which Friedman's optimum quantity of money rule would otherwise be optimal [see Aizenman (1987) and V6gh (1989)]. The above arguments - valid as they may be as normative propositions - appear rather insufficient to rationalize chronic high inflation in developing countries. First, high inflation is a phenomenon that the society is typically trying to get rid of and, thus, could hardly be expected to be optimal in accord with Phelps's (1973) prescriptions. Second, while the evidence does show a long-run relationship between fiscal deficits and inflation [see, for example, Fischer, Sahay and V6gh (1997)], crosscountry econometric studies for developing countries have not found support for the main empirical implication of Phelps's (1973) hypothesis that there should be a positive correlation between the inflation tax and other conventional taxes [see Edwards and Tabellini (1991)]. In fact, the inflation tax appears to act more as a residual source of government revenue. Third, empirical estimates show that inflation is often larger than the level that maximizes revenue from inflation [see, for example, Easterly and Schmidt-Hebbel (1994)] 4. This implies that lower inflation and higher revenues from inflation could be simultaneously achieved - a glaring contradiction of Phelps's (1973) prescription. In sum, although the optimal taxation approach could explain perhaps the persistence of low levels of inflation, it would seem that other factors are needed to explain the actual pattern of inflation observed in chronic inflation countries. 2.2. Shocks and accommodation

While fiscal deficits may constitute the original sin that gives rise to inflation, the persistence of inflation may involve policy accommodation which transforms temporary domestic or external shocks into permanent increases in the inflation rate [see, in particular, Bruno and Fischer (1986) and Bruno (1993, Chapter 3)]. For example, consider a shock which calls for a real appreciation of the domestic currency. Authorities may dislike real appreciation because, say, it might be detrimental to exports. Therefore, incipient real appreciation would lead authorities to devalue. Since conditions after the shock require a more appreciated equilibrium real exchange rate, such a policy reaction cannot provide a definitive solution to the authorities' problem. After the first devaluation, domestic prices will rise to regain lost ground and attempt, once again, to climb a little higher (in order to generate the equilibrium real appreciation). Thus, another devaluation will eventually follow - and, of course~ prices will continue rising, setting in motion an inflationary process quite unrelated to fiscal revenue considerations/t la Phelps 5. 4 Although measuring the seigniorage-maximizinginflation rate is not without problems [see Easterty~ Mauro and Schmidt-Hebbel(1995)]. 5 Empirical evidence on the inflationary consequences of real exchange rate targeting in Brazil, Chile, and Colombiamay be found in Calvo, Reinhart and V6gh (1995). At a theoretical level,the inflationary conseqnences of real exchange rate targeting have been analyzed by Adams and Gros (1986), Lizondo

Ch. 24: Inflation Stabilization and BOP Crises in Deoeloping Countries

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More generally, monetary accommodation is typically reflected in the fact that key nominal variables - the rate of devaluation, the rate of monetary growth, and nominal wage growth - are linked to past inflation through accommodative policy rules and institutional arrangements such as backward-looking wage indexation. A greater degree of accommodation will be reflected in more inflation inertia. Bruno (1993) shows how nominal variables linked to past inflation may generate an autoregressive process for the inflation rate. Under these circumstances, temporary shocks to the inflation rate lead to permanent increases in the inflation rate. Bruno and Melnick (1994) further show that the higher is the degree of monetary accommodation, the higher is the new inflation plateau. While the process of shocks and accommodation captures some important elements of chronic inflation processes, it is less clear whether it can be argued that inflation is unduly high, in the sense of not being socially optimal. Presumably, policymakers accommodate shocks because not doing so would bring about undesirable consequences. In fact, one can show simple examples in which, in response to temporary shocks, it may be optimal to keep constant the real exchange rate by generating higher inflation [see Calvo, Reinhart and V6gh (1995)]. In the same vein, it is often argued that not accommodating expected inflation by printing money could bring about a severe liquidity crunch and thus lower output. Hence, this view leaves unresolved the issue of why society would periodically wish to get rid of inflation. 2.3.

Multiple equilibria

A more clear-cut case of socially suboptimal inflation is multiple equilibria. An example that we find particularly relevant [Calvo (1992)] is one in which there is a stock of public debt denominated in domestic currency, D. Let the one-period nominal interest rate be denoted by i. Then, next period's full service of the debt (i.e., principal plus interest) will be (1 + i)D. Let us choose units of measurement so that the present price level equals 1, and indicate the one-period expected inflation rate by ~e. Thus, if, say, the equilibrium real interest rate is zero, we have that i = sr e. Therefore, if actual inflation is zero, the real burden of servicing domestic debt would be (1 + ~°)D. This could very well be a large number. On the other hand, if the government fulfills the private sector's expectations and sets actual inflation equal to expected inflation, the real burden of the debt is just D. Thus, the temptation not to stop inflation in its tracks may be irresistible. A numerical example may help bringing the above point home. Suppose that the stock of debt is just 20 percent of GDP, and consider the case of Brazil (in the late 1980s) where the monthly rate of inflation was about 30 percent. If inflation is stopped but the private sector expected it to continue at previous levels, the nominal interest rate will remain at 30 percent per month. Therefore, just interest on the debt will (1991), Montiel and Ostry (1991), Calvo, Reinhart and V6gh (1995), Uribe (1995), and Lahiri (1997) See also Heymaimand Leijonhufvud (1995) for a more general analysis of these issues.

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amount to 6 percent of GDP per month. This sizable cost of stopping inflation may, quite plausibly, lead authorities to relent by either keeping inflation at the original high levels, or adopting a very gradual stabilization program. 2.4. The "provinces" eJfect

Another explanation is what one might call the "provinces effect." Provinces, municipalities, state enterprises, etc., are entities that, at best, attempt to maximize social welfare by controlling a small set of levers. In particular, for these institutions, inflation is a p u n i c good, generated by total government expenditure, to which their individual expenditure adds an insignificant amount. Therefore, in choosing "provincial" expenditure, each entity will overlook the adverse welfare consequences of inflation on all other entities. Consequently, like with any other public good, too much inflation (i.e., too little price stability) will be generated 6. While this approach provides an attractive rationale for the existence of inflation, it still needs to explain cross-sectional variation in inflation outcomes. In other words, why should this effect be more relevant in, say, Argentina than in the USA? 2.5. Delayed stabilization

We now come to a more recent explanation for the persistence of high inflation; namely, the "war of attrition". This is an extremely useful idea formally developed by Alesina and Drazen (1991) 7. Suppose that inflation is unduly high for any of the reasons discussed above. Thus, policymakers would know that inflation could be brought under control if institutions were changed, or some appropriate transfers were put in place. So, why do they not act upon this knowledge and stop inflation in its tracks? Alesina and Drazen's (1991) explanation is that, since there is more than one way to get out of the inflation quagmire, and each way has different welfare implications across groups, it may be optimal for each group to wait for another group to give in. Eventually, the most "anxious" group will give in, adjustment will take place, and inflation will stop. In the meantime, inflation will remain high. Note, however, that Alesina and Drazen's (1991) model per se does not rationalize the advent of high inflation. Thus, Alesina and Drazen's model would need to be appended with some inflation-causing factor, or factors, in order to be able to track empirical evidence. An interestingapplication of the Alesina-Drazen tramework is the fbrmalizatlon of the idea that, in practice, things must get worse before they get better, in other words, oftentimes societies need to go through a truly devastating hyperinflationary ¢~ See Aizemnan (1992), Velasco (1993), Sanguinetti (1994), Mondino, Sturzenegger and Tommasi (1996), Zarazaga (1996), and Jones, Sanguinetti and Tomrnasi (1997). 7 Of course, the perception of inflation as the outcome of an unresolved distributive struggle is not new, and goes back to Hirsclmaan (1963) [see tteymann and Leijonhufvud (1995) fbr a detailed discussion]. It should also be noted that these last two factors - the "provinces" effect and delayed stabilization are part of a large, and growing, literature on the polical economy of reform [see Tommasi and Velasco (t996) for a survey].

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outburst before a political consensus for a stabilization emerges. In the war-of-attrition framework just described, Drazen and Grilli (1993) show how a higher rate of inflation may be welfare-improving by bringing forward the expected time of resolution. The earlier resolution of the war of attrition may thus more than offset the short-term costs of higher inflation. 2.6. In conclusion

Based on the analysis thus far, we believe there is no single explanation for the phenomenon of chronic inflation. In fact, we would argue that, when taken together and in the proper dynamic sequence, the five factors discussed above probably explain the key features of processes of chronic inflation. At a fundamental level, governmems with inefficient tax-systems will always find it optimal to resort to some inflation (inflation as an optimal tax). The "provinces effect" is likely to add another - socially suboptimal - layer to the optimal public finance level of inflation. Once inflation has emerged, the economy as a whole naturally develops various indexation mechanisms (including accommodative policy rules) aimed at minimizing, for a given inflation rate, the real effects of inflation. Heavy indexation of the economy makes relative prices less responsive to various shocks, which sets the stage for temporary shocks to have permanent effects on the rate of inflation (the "shocks and accommodation" view). At this stage, the inflationary process will probably bear little relation to its original cause (the fiscal deficit), fueling the perception that putting the fiscal house in order may, after all, not help in dealing with the inflation problem. By now, the government's incentives to tackle the problem seriously are greatly diminished. After inflation has become entrenched in the public's mind, it may be too costly for the government not to validate the public's expectations (multiplicity of equilibria). In addition, and even if the government finally managed to credibly commit to a low level of inflation, political battles over the distribution of the fiscal adjustment needed to implement a stabilization may prolong chronic inflation (delayed stabilization). In the end, things may indeed need to get worse - by, say, having a hyperinflationary outburst - before they get better.

3o Evidence on the real effects of stabilization in chronic-inflation countries It is perhaps fair to say that until recently the dominant opinion in the professioit was that stopping inflation would bring about a sharp fall in output and domestic absorption. In fact, the notion that disinflation is contractionary is so entrenched m the literature that the question asked has typically been n o t / f b u t by how much outpul would fall in response to an anti-inflationary program. The best-known manifestation of this approach is the so-called "sacrifice ratio," or cumulative percent output loss per percentage point reduction in inflation. Okun (1978, p. 348), summarizing the findings of several papers on the USA, awaes that "the cost of a 1 point reductio~ in the basic inflation rate is 10 percem of a year's GNP, with a range of 6 percent

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to 18 percent." Fischer (1986b) estimates a sacrifice ratio of 5 to 6 - at the lower end of the Okun range - for the USA for the period 1979-1986. Based on a review of fourteen episodes in eight countries, Gordon (1982) concludes that, by and large, contractionary policies - especially "cold turkey" policies - aimed at bringing down inflation have entailed large output costs. More recently, Ball (1994) examined 28 disinflation episodes in nine OECD countries using quarterly data and found that, with one exception, disinflation is always costly, with the sacrifice ratio ranging from 2.9 for Germany to 0.8 for France and the United Kingdom. The conventional view about the output costs of disinflation has also been taken to apply to open economies, indeed, in traditional open-economy models, disinflation is expected to cause an initial recession regardless of the nominal anchor which is used (the exchange rate or the money supply), as argued by Fischer (1986a). Therefore, the choice of the nominal anchor is based on a comparison of the sacrifice ratio involved in the two alternative strategies. By examining the sacrifice ratio under different parameter configurations, Fischer (1986a) concludes that the exchange rate should be the preferred nominal anchor. A similar conclusion is reached by Chadha, Masson and Meredith (1992). Based on simulations using MULTIMOD (a large-scale, multi-region macroeconometric model), they conclude that, for the United Kingdom, the sacrifice ratio is cut almost in half under an exchange-rate anchor compared to a money anchor. The intuition behind the view that "disinflation is always and everywhere contractionary" owes much to the unemployment-inflation trade-off, Phillips-curve literature. Particularly influential has been the staggered-contracting approach pioneered by Fischer (1977) and Taylor (1979, 1980). In these models, wage contracts are preset for a number of periods. Hence, credibility of the policy is not enough to generate a costless disinflation. Only a fully-credible gradual disinflation, which would take into account the structure of labor contracts, could reduce inflation with no output cost. For the case of the USA, Taylor (1983) concludes that it would take tbur years to disinflate from a rate of wage increase of 10 percent per year to 3 percent without creating unemployment. The conventional view has not gone unchallenged. In an influential paper, Sargent (1982) has argued that inflation was stopped virtually overnight with little or no output costs in the hyperinflations which developed in Austria, Germany, Poland, and Hungary in the aftermath of World War I. Based on this evidence, he argues that disinflation need not be contractionary if it is accompanied by a credible change in regime, which drastically alters the public's perceptions about future government policies. However, even if Sargent's (1982) conclusions regarding the output costs of stopping hyperinflation were accepted, such hyperinflations are seen as extreme episodes whose lessons are not necessarily applicable to much more mundane, garden~ variety inflations 8.

8 Notice that tile averagemonthly rate of inflation in these tbur episodes in the twelvemonths preceding stabilization ranged fiom a low of 33.3% in Hungary to a high of 455.1% in Gemaany[see V6gh (1992),

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1543

Perhaps a more fundamental challenge to the conventional view began to emerge in the late 1970s when major stabilization plans were implemented in the SouthernCone countries of Latin America (Argentina, Chile, and Uruguay). The cornerstone of these programs was the announcement of a predetermined path for the exchange rate, which involved setting a declining rate of devaluation 9. Contrary to Phillips-curve based predictions, the resulting decline in inflation was accompanied by a boom in consumption and no signs of higher unemployment. Moreover, the expansion took place in spite of a sharp appreciation of the real exchange rate. The contractionary costs associated with disinflation appeared only later in the programs, often before the programs finally collapsed. As it turned out, the puzzling phenomenon of an initial expansion followed by a later recession observed during the Southern-Cone "tablitas" appears to be a common pattern of exchange-rate-based stabilizations [see Kiguel and Liviatan (1992) and V6gh (1992)]. In sharp contrast, money-based stabilizations - which are much less common in chronic-inflation countries - have typically led to an initial recession, as the conventional view would have it. The remainder of this section takes a detailed look at some of the empirical evidence on these issues.

3.1. Exchange-rate-based stabilization." empirical regularities Table 1 lists twelve major exchange-rate-based stabilizations in chronic inflation countries in the last 35 years. These programs - which took place in Argentina, Brazil, Chile, Israel, Mexico, and Uruguay - have been studied in great detail and constitute the main motivation behind much of the literature in the area 10, 11. Based Table 2]. Garber (1982) and Wicker (1986) have both taken issue wit1 Sargent's (1982) conclusions. See also V~gh (1992) and Bruno (1993, Chapter 1). 9 In popular parlance, the announced schedule would be referred to as the "tablita" (Spanish for "little table"). In Chile, the exchange rate was eventually fixed. 10 Case studies include but are certainly not limited to the following. On the Argentine plans, see De Pablo (1974), Fernandez (1985), Canavese and Di Tdla (t988), Heymann (199l), and Dornbusch (1995). On the Brazilian plans, see Kafka (1967), Modiano (1988), and Cardoso (1991). On Chile, sec Corbo (1985) and Edwards and Cox Edwards (1991). On the Israeli plan, see Bruno (1993) and Bufman and Leiderman (1995). On Mexico, see Dornbuschand Werner(1994) and Santaella and Vela (1996). On the Uruguayan plans, see Finch (1979), Hanson and de Melo (1985), Viana (1990), and Talvi (1995). See also Foxlcy (1980), Diaz-Alejandro (1981), Ramos (1986), Corbo, De Melo and Tybout (1986), Kiguel and Liviatan (1989), Edwards (1991), and Ag6nor and Montiel (1996, Chapter 8). 11 The literature has often distinguished between "orthodox" programs (which do not rely on prices and/or wages controls) and "heterodox" programs (which do, and thus have "multiple nominal anchors") Of the programs listed in Table l, five were "orthodox" plans (the three "tablitas", the Argentine 1991 Convertibility plan, and the Uruguayan 1990 plan); the rest were "heterodox" plans. Except tbr tile behavior of inflation and domestic real interest rates (see below), the response of key macroeconomics variables to major stabilizationplans has been very similar, regardless of whether the plans were orthodox or heterodox. Hence, for the purposes of our analysis,not much will be made of this distinction.It should be noted, however, that the policy debate over the desirabilityof price and wage controls has been intensc: see, for instance, Dornbusch and Simonsen (1987), Dornbusch, Sturzenegger and Wolf (1990), Bruno (1993), Leidernlan (1993), and Meltzer (1994).

1544

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Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries

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1546

G.A. Calvo and C.A. V&gh

on these episodes, the literature has identified the following main empirical regularities associated with exchange-rate-based stabilization 12: (i) Slow convergence of the inflation rate (measured by the CPI) to the rate of devaluation. In heterodox programs, inflation has typically fallen faster due to temporary price controls 13 (ii) Initial increase in real activity -particularly, real GDP and private consumption followed by a later contraction. It is less clear whether the same pattern applies to investment 14 (iii) Real appreciation of the domestic currency. (iv) Deterioration of the trade balance and current account balance. (v) Ambiguous' impact response o f domestic real interest rates. Ex-post domestic real interest rates have generally decreased in the initial stages of orthodox plans. However, they appear to have increased substantially in the early stages of the heterodox programs of the mid- 1980s. To take a closer look at the main stylized facts, we constructed a panel of annual observations for four countries (Argentina, Chile, Israel, and Uruguay), which covers 16 years (1978-1993), for a total of 64 observations 15. The panel includes seven of the twelve exchange-rate-based stabilizations listed in Table 1 (the "tablitas" implemented in 1978 in Argentina, Chile, and Uruguay, the Israeli 1985 plan, the Argentine 1985 Austral plan, the Uruguayan 1990 plan, and the Argentine 1991 Convertibility plan) and ten macroeconomic variables (devaluation rate, inflation rate, rates of growth of GDP, private consumption, durable goods consumption, fixed investment, and public consumption, all expressed in per capita terms, real exchange rate, current account deficit as a proportion of GDP, and real lending rate) 16.

~2 See Kiguel and Liviatan (1992), Vdgh (1992), Calvo and V6gh (1994b), Reinhart and V6gh (1994, 1995b), and De Gregorio, Guidotti and V6gh (1998). 13 Although less well-documented,casual empiricism suggests that wholesale price inflation (which captures the behavior of tradable goods inflation) converges quite rapidly. t4 Both Kiguel and Liviatan (1992) and Reinhart and V6gh (1995b) report mixed results ~br investment. Real estate boom-bust cycles also appear to be a hallmark of many of these programs; see Rebelo and V6gh (1995) and Guerra (1997b). Some spotty data also suggest that output in the non-tradable sector typically expands more rapidly than in the tradable sector [Rebelo and V~gh (1995)]. ~5 The numerous caveats that apply to the empirical exercises which follow are discussed at the end of the section. I(~ The sample chosen was dictated by data availability. The sources of data are as tbllows. Data oll GDP, private consumption, and durable goods consumption were provided by the Central Banks of Argentina, Israel, Uruguay, and the Chilean Ministry of Finance. For Argentina and Uruguay, durable goods consumptionis proxied by cat sales. Real exchange rate data for Israel were providedby the Bank of Israel. All other data are from International Finance Statistics (IMF). Fixed investment corresponds to gross fixed capital formation adjusted by the GDP deflator. (Ideally, we would have liked to have private fixed investment, but data are hard to come by.) The real exchange rate is a real effective exchange rate, as computed by the IMF, defined as a nominal effective exchange rate index adjusted for relative movements in national price or cost indicators of the home country and its main trading partners. Following common practice, the index is presented in such a way that an increase rcflects

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries,

1547

3.1. l. Stabilization time profiles As a first pass at the data and to illustrate the dynamic response of the different variables to the implementation of an exchange-rate-based stabilization program, we constructed profiles in "stabilization" time (as opposed to "calendar" time)17 Stabilization time is denoted by T + j , where T is the year in which the stabilization program was implemented and j is the number of years preceding or following the year of stabilization ( j = - 2 , . . . , 4) 18. We then computed the average value of each variable in stabilization time. The resulting stabilization time profiles, presented in Figures 1 and 2, thus portray the dynamic behavior of key macroeconomic variables for a "representative" exchange-rate-based stabilization plan. Vertical bars indicate the year before stabilization (time T - 1) and, where applicable, dashed lines denote the mean of the corresponding variable for the entire sample (i.e., for all 64 observations) Panel A in Figure 1 illustrates the behavior of the rates of devaluation and inflation 19 The U-shaped profile for the rate of devaluation (the nominal anchor) reflects the fact that, more often than not, policymakers either switch to a more flexible exchange-rate arrangement (often after a brief period with a fixed exchange rate) or abandon the program altogether. While inflation is highly responsive to the reduction in the rate of devaluation, it remains above the rate of devaluation and then lags it as the rate of devaluation increases. Panel B shows that the real exchange rate (set to 100 in the year before the stabilization) appreciates for three consecutive years (falling below 80 in year T + 2) before beginning to depreciate, following the higher rate of devaluation. The current account deteriorates up to year T + 3 reaching a deficit of 4.8 percent of GDP - and then reverses course (Panel C). While the rate of growth of public consumption falls in the year of stabilization presumably reflecting an initial fiscal adjustment it shows no systematic behavior

a real depreciation. Real interest rates were computed by deflating nominal rates by the same year's inflation rate. Population series from International Finance Statistics (IMF) were used to compute per capita figttres. 17 Fischer, Sahay and V6gh (1996) have used this approach to analyzing stabilization policies m transition economies. See also Easterly (1996). ~a If the program began in the last quarter of a given year, the following year is taken as 7'. Thus, T is 1978 for the Chilean tablita, 1979 for the Argentine and the Uruguayan tablitas, 1985 for the Austral and Israeli plans, and 1991 for the Convertibilityand the Uruguayan 1990 plans. We should also note that we did not allow for any overlapping(i.e., any given year in calendar time correspondsto at most one point in stabilization time). Hence, in the case of Argentina,the fust observation in stabilizationtime for the Austral plan is 1984 (which corresponds to T 1) and the last one is 1988 (7' + 3). Finally,note that the nmnber of observations for each year in stabilizationtime may differ, since some stabilizations episodes do not have observations for all years in stabilizationtime (i.e,, from T - 2 through T + 4). For instance, there are 7 observations for T - 1, T, and T + 1, but only 4 for T + 4 and 3 for T - 2. 19 Sincethe mean is essentially the same (179.3 percent for the devaluation rate and 177.9 percent fo~ the inflation rate), the panel contains only one horizontal line.

1548

G.A. Caluo and C.A. Vdgh

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Ch. 24:

Inflation Stabilization and BOP Crises in Deoeloping Countries A. Real GDP growth (percent per year)

6

1549

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for two consecutive years) and increase sharply afterwards. As indicated earlier, tile accepted wisdom is that real interest rates have increased on impact in heterodox plans. This does not show up in annual data, suggesting that the initial rise in real interest

1550

G.A. Calvo and C.A. Vdgh

rates in heterodox plans has manifested itself basically as "spikes" immediately after the implementation of the plans 21. Figure 2 presents the evidence related to the boom-recession cycle in the growth of per capita GDP, consumption, and fixed investment. Panel A shows that real GDP growth increases above the sample mean in the year of stabilization and peaks in T + l. In T + 2, growth is back to its mean and decreases sharply thereafter. The same pattern is observed for private consumption (Panel B) and durables consumption (Panel C). In orders of magnitude, however, the cycle in durables goods is much more pronounced than the one in private consumption, which is in turn more pronounced than the one in real GDR At the peak, durable goods consumption is rising at 47.7 percent per year, private consumption at 8.9 percent, and real GDP at 4.7 percent. Fixed investment growth follows a similar pattern (Panel D). Finally, Panels E and F show the behavior of private consumption and fixed investment as a proportion of GDR It can be seen that the boom in private consumption is also quantitatively important even relative to GDP. At its peak (in T + 1), the ratio of private consumption to GDP reaches 74.3 percent (compared to a mean of 68.8 percent). In contrast, Panel F shows that the ratio of fixed investment to GDP falls in T and surpasses its mean level only in T + 3 before falling precipitously. The stabilization time profiles thus point to the presence of a boom-recession cycle associated with exchange-rate-based stabilization. Although it is empirically difficult to distinguish a late recession in both successful and unsuccessful programs from the output collapse that typically accompanies the end of failed programs, Figures 1 and 2 are consistent with the idea that the late recession may take hold before the programs collapse. Notice that real activity (i.e., GDP and consumption in Figure 2, Panels A and B) slows down already at T + 2 and falls below the sample mean at T + 3, which could reflect the effects of rising real interest rates (Figure 1, panels E and F) and cumulative real exchange appreciation (Figure 1, Panel B). The fact that this contraction is taking place while the current account deficit continues to grow (Figure 1, Panel C) suggests that the contraction is not related to the real effects of an eventual collapse. 3.1.2. Panel regressions

By and large, the profiles in stabilization time presented in Figures 1 and 2 are consistent with the stylized facts that have been emphasized in the recent literature. However, while the raw data presented in this manner is clearly suggestive, these plots cannot answer the key questions of whether the boom-recession cycle in GDR consumption, and investment has been significant in a statistical sense or whether it may have been caused by factors other than the exchange-rate-based stabilization 21 This idea is supported by tile quarterly data presented in V6gh (1992) and the evidencem Km,linslg¢ and Leiderman (1998). These "spikes" are partly related to the sudden drop in inflation when wages and price controls axe part of the stabilization package.

Ch. 24." Inflation Stabilization and BOP Crises' in Developing Countries

1551

programs themselves. While a definite answer to these questions is far from trivial and remains a challenge for future research - some simple e c o n o m e t r i c exercises m a y shed light o n these important issues. Specifically - and following R e i n h a r t and V r g h (1994, 1995b) - we ran p a n e l regressions o n d u m m y variables i n t e n d e d to capture the early a n d late stages o f a program, a n d test whether growth in per capita GDP, consumption, and fixed investment during those periods was significantly different from trend growth 22. We also test for the significance o f the time pattern o f public consumption 23. The regressions control for c o m m o n external shocks, as suggested by Echenique and Forteza (1997) 24. The sample for the panel regressions remains the same as that used for the stabilization time profiles: four countries (Argentina, Chile, Israel, and U r u g u a y ) with 16 observations each ( 1 9 7 8 - 1 9 9 3 ) for a total o f 64 observations. We define the "early" d u m m y as taking a value o f one in the first three years o f the programs 25. I f the p r o g r a m lasted less than three years (as was the case for the Argentine "tablita" and the Austral plan), then the "early" d u m m y takes a value o f one in the first two years o f the program. I n all cases, the "late" d u m m y takes a value of one in the two years immediately following the "early" stage 26. Notice that the "late" d u m m y has b e e n defined for all programs, regardless o f whether they actually failed or not. W h i l e this makes the criterion more stringent (compared to defining the "late" d u m m y only for those programs that fail), it is m o r e in accordance with the idea that the late recession takes place in both successful and u n s u c c e s s f u l programs. As control variables, we chose the Libor rate (adjusted by US inflation), average growth in OECD countries - both o f which are i n t e n d e d to capture the world business cycle and terms o f trade 27.

22 See also De Gregorio, Guidotti and Vrgh (1998), Gould (1996), and Echenique and Forteza (1997). 23 As will become clear in Section 5, this evidence is relevant for some theories that have emphasized the effects of fiscal policy in explaining the real effects of exchange rate-based stabilization. 24 Of course, one would like to control also for the effects of domestic reforms, which have accompanied several (although certainly not all) of these programs. To that effect, one could construct a "liberalization index" - which would take into account trade, financial, and structural reforms - along the lines of work by De Melo, Denizer and Gelb (1995) for transition economies. This remains an issue for future research. 25 The year in which the program was implemented is included as part of the "early" dmnmy if the program started in the first three quarters. Otherwise, the following year is taken as the first year of the "early" dummy. 26 Specifically, the years in which the "early" and "late" dunmaies take a value of one are the following: Argentine tablita, early = 1 for 1979 and 1980, late = 1 for 1981 and 1982; Austral plan, early- 1 for 1985 and 1986, late-1 for 1987 and 1988; Convertibility plan, early = 1 for 1991, 1992, and 1993; Chilean tablita, early 1 for 1978, 1979, and 1980, late= 1 for 1981 and 1982; Israel 1985, early= 1 tbr 1985, 1986, and 1987, late = 1 for 1988 and 1989; Uruguayan tablita, early = 1 for 1979, 1980 and 1981, late= 1 for 1982 and 1983; Uruguay t990, early=l for 1991, 1992, and 1993. 27 All data were obtained from the International Monetary Fund. Both Libor and OECD growth are expressed in percentage terms. The terms of trade index measttres the relative price of exports in terms of imports. TM

1552

G.A. Calvo and C.A. V~gh

Table 2 Exchange-rate-based stabilization: Panel regressionsa Dependent variables Growth in real GDP (1) Early dummy Late dummy Libor (real) OECD growth Terms of trade No. of obs.

1.84"* (0.73) 3.49*** (0.82) -0.31 ** (0,14) 0.71"** (0.20) -0.03 (0.02) 64

Growth in Growthin real private real durables consumption consumption (2) (3) 3.33** (1.57) -4.60** ( 1.93) -0.68"* (0.31) 0.21 (0.47) 0.02 (0.03) 64

14.74" (7.89) -29.61 .... (l 0.01) --3.3 l** (1.59) 1.97 (2.44) -0. l 8 (0.20) 64

Growthin real fixed investment (4)

Growth in real public consumption (5)

0.80 (3.76) 4.46 (4.62) -2.81"** (0.77) 0.78 (1.15) -0.10 (0.10) 64

-3.78 (2.58) -5.42* (3.19) -1.18*" (0.52) 0.76 (0.78) 0.04 (0.06) 64

a All dependent variables are expressed in per capita terms. The sample includes Argentina, Chile, Israel, and Mexico for the period 1978-1993. Standard errors are given in parentheses. The method of estimation was a 2-step GLS procedure which allows for groupwise and cross-group heteroscedasticity and groupwise autocorrelation. The regressions include fixed effects (not reported). Significance at the 10, 5, and 1 percent level is indicated by one, two, and three asterisks, respectively.

The summary results of the panel regressions are reported in "Iable 2. Let us first focus on the first three columns (GDP, private consumption, and durables consumption). The "early" and "late" dummies have the expected signs (positive for "early" and negative for "late") and are significant (at least at the 10 percent level) in all three cases. For example, column (2) indicates that growth in private consumption per capita is 3.33 percent higher (relative to trend growth) during the early stages of the program and 4.60 lower in the late stages. The size of the coefficients also tends to support the idea ± suggested by Figure 2 - that the boom-recession cycle is the most pronounced for durable goods and the least pronounced for GDP, with consumption falling somewhere in between. The initial rise in durable goods consumption is more than four times larger than the rise in private consumption, which is in turn almost twice as high as the rise in GDP per capita. Increases in Libor (in real terms) negatively affects all three variables (and are always significant). This result is consistent with the notion that fluctuations in international interest rates also play a key role in generating boom-bust cycles in developing countries [see, for example, Calvo, Leiderman and Reinhart (1993)]. OECD growth matters only for GDP growth, while the effects o f terms o f trade are never significant.

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

1553

In sharp contrast, the cycle in fixed investment is not statistically sigqlificam [Table 2, column (4)]. Changes in real world interest rates (i.e., real Libor) fully explain the cycles in fixed investment. In any event, this should perhaps not come as a big surprise since casual evidence for a majority of programs suggests that the main force behind the expansionary phase is the sharp increase in private consumption. It is also consistent with evidence from Bruno and Easterly (1998) and Easterly (1996), who find that growth following inflation crises is not driven by investment. Finally, column (5) in Table 2 indicates that the initial fall in public consumption is not statistically significant. We may thus conclude that the econometric evidence is consistent with the notion that exchange-rate-based stabilization leads to boom-recession cycles in real GDP, private consumption, and consumption of durable goods, even when account is taken of external factors. The evidence is inconclusive with regard to investment. 3.1.3. Do exchange-rate-based stabilizations sow the seeds' o f their own destruction?

A notable aspect of exchange-rate-based stabilization programs is that, as noted iu Table 1, a vast majority have ended in balance-of-payments crises. In fact, of all the major programs listed in Table 1, the Argemine 1991 Convertibility plan is so far the only successful plan which has maintained the exchange rate at the level chosen at the inception of the program 28. Eight of the twelve plans ended in full-blown crises with large losses of international reserves. Naturally, the stabilization time profiles in Figures 1 and 2 appear to capture this pattern. In T + 4, the current account sharply reverses course (Figure 1, Panel C), suggesting that a "crisis" has occurred 2,7 This "crisis" time coincides with a resumption of high inflation, a real exchange rate depreciation, and a collapse in GDP, consumption, and investment. As argued by Reinhart and V6gh (1995b), the dynamics unleashed by exchange-rate. based stabilization plans are likely to be partly responsible for the demise of several programs. Prolonged periods of real exchange-rate appreciation and growing current account deficits are seldom sustainable, especially when domestic and external shocks compound the problems. Corrective devaluations do not always work, particularly in a world of increasing financial globalization, as the example of Mexico in December 1994 dramatically showed. These regimes are also prone to financial and speculative attacks which may be unrelated to problems of current account sustainability. The evidence thus suggests that understanding the links between the dynamics of exchange° rate-based stabilizations and the eventual collapse of most of these programs should

2a The lsraeli 1995 plan was also a successfulplan in terms of obtaining a lasting reduction in inflation. tlowever, there were severaldevaluations along the way and finally an exchange rate band was adopted. 2,7 Kaminsky and Reinhart (t995) show that BOP crises are associated with a sharp rise in exports. which shotdd lead to a dramatic improvementin both the trade and current account balances.

1554

G.A. Calvo and C.A. Vdgh

be an integral part o f the research agenda (an analysis of these issues is carried out in Section 7).

3.2. Money-based stabilization: empirical regularities Money-based programs in chronic inflation countries have been much less common than programs based on the exchange rate 3o. Table 3 presents the main features o f five major money-based programs undertaken in the last 25 years 3l . As the table makes clear, monetary regimes vary across episodes and pure money-based programs (i.e., a clean floating regime) are rare 32 Hence, for the purposes of this chapter, the term "money-based" stabilization should be broadly understood as including assorted dirty floating regimes and dual exchange rate systems with a fixed commercial rate (or equivalent systems). The rationale for lumping these regimes together is that in all cases the monetary authority has, to a lesser or greater extent, control over the money supply. This is, o f course, in contrast to an exchange-rate-based regime (under perfect capital mobility) in which the money supply is fully endogenous. As will be discussed in detail in Section 5, one should expect regimes in which the monetary authority has control over the money supply to deliver similar outcomes to those that would obtain under a pure money-based regime. Hence, to contrast stylized facts with theory, it makes sense to adopt such a classification. The following empirical regularities have been identified in money-based programs [see Calvo and V6gh (1994b)]: (i) Slow convergence of inflation to the rate of growth of the money supply. (ii) Real appreciation of the domestic currency. (iii) No clear-cut response of the trade balance and the current account. I f anything~ there seems to be a short-run improvement in the external accounts. (iv) Initial contraction in economic activity. A sharp, though short-lived, contraction in real GDP, consumption, and investment seems to follow the implementation of money-based programs. (v) Initial increase in domestic real interest rates. These empirical regularities are less surprising in that they seem to broadly conform with available evidence for industrial countries. To illustrate some of these empirica! regularities, we constructed a panel with five countries (Argentina, Brazil, Chile~

30 As discussed below, there are good reasons to expect the exchange rate to be the preferred anchor in chronic inflation countries. 31 For case studies, see Harberger (1982), Corbo (1985), Edwards and Cox Edwards (1991), Mcdeiros (1994), Kiguel and Liviatan (1996), and Favaro (1996). 32 Note that, by definition, a pure money-based program implies a clean floating. The reverse, however, is not necessarily true: a clean floating might be adopted in conjunction with, say, interest rate or inflatiol~ targeting [see, for instance, Masson, Savastano and Sharma (1997) and V6gh (1997)]. These monetary regimes, however, have not been observed in any major stabilization effort in high inflation countries.

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T'+3

T+4

Fig. 3. Money-based stabilization. D o m i n i c a n Republic, and Peru) with 25 years o f annual data (19'71-1995), for a total o f 125 observations 33, 34 The stabilization time profiles are illustrated in Figure 3. Panel A shows that the inflation rate falls dramatically in the first year after stabilization but begins to rise again s o o n afterwards 3s. A l t h o u g h the inflation rate does r e m a i n above the rate of m o n e y growth, inflation persistence appears to be m u c h less p r o n o u n c e d that in exchange-rate-based p r o g r a m s (recall Figure 1, Panel A). R e a l G D P growth falls in the year o f stabilization f r o m -3.8 to - 7 . 3 percent, but recovers soon after and is 33 Again, data availability dictated the sample size. Since we now focus on a smaller member of variables, the time series available are longer than before. However, the small nunther of programs and the rather short duration of some of them calls for c:~ution in the interpretation of the evidence. 34 For these programs, T is 1975 for the Chilean plan and 1990 for the Collor, Bonex, Dominican Republic, and Peruvian plans. To avoid overlapping with other, exchange-rate-based plans and giving priority to the actual plan which was in effect the Bonex plan is associated with two dtupanies (1989 and 1990), the Collor plan goes back only until T - 1, and the Chilean 1975 plan goes forward only until T + 1. 35 The fact that inflation actually rises in the year of stabilization (T) is heavily influenced by the Peruvian program.

Ch. 24:

lnflation Stabilization and BOP Crises in Deueloping Countries"

155'7

above the sample mean in T + 3 (Panel B). The evidence is thus consistent with a short-lived but sharp contraction in economic activity. It should be noted, however, that real GDP growth is already below its mean in the year before the program. The real exchange rate appreciates throughout the program (Panel C), while the current account shows no clear pattern (Panel D). Lack of data prevented us from looking at real interest rates. Quarterly data presented in Calvo and V6gh (1994b), however, are consistent with the notion of an initial rise in real interest rates. 3.3. R e c e s s i o n n o w v e r s u s r e c e s s i o n later

A comparison of the real activity in money-based and exchange-rate-based stabilizations raises an important issue. The timing of the recessionary effects of disinflation programs appears to differ across nominal anchors: in money-based plans the contraction occurs early in the program, while in exchange-rate-based programs it seems to occur late in the program (compare Figure 2, Panel A with Figure 3, Panel B). This phenomenon has been dubbed the "recession-now-versus-recessionlater" hypothesis. To test this hypothesis, we carried out two econometric exercises for the rate of growth of real per capita GDP for as large a sample as possible. The sample includes the period 1971-1995 for eight countries (Argentina, Brazil, Chile, Dominican Republic, Israel, Mexico, Peru, and Uruguay) for a total of 200 observations. The sample comprises 14 stabilization plans: 9 exchange-rate-based stabilizations (all of those described in Table 1 except for the first three) and the five money-based stabilizations listed in Table 3. Table 4 shows the results of fixed effects regressions on stabilization dummies, controlling for external factors 36. Three regressions are shown: the first two ("individual regressions") attempt to identify the effects of exchange-rate-based stabilization time dummies and money-based stabilization time dummies separately (i.e., each regression includes only the time dummies corresponding to a particular anchor). The third ("joint regression") includes all stabilization time dummies simultaneously. Let us first focus on exchange-rate-based stabilization. First, regressions (I) and (3) indicate that growth in the two years before exchange-rate-based stabilization is not statistically different from trend growth 37. Hence, exchange-rate-based stabilizations appear to have been implemented in "normal" times 3s. Growth in the first two years of stabilization (T and T + 1) is significantly above trend growth in the individual regression. In the joint regression, growth is significantly above trend in T + 1. In both cases, growth is significantly below trend four years after stabilization (i.e., in T + 4)~ External factors have the expected signs and are always significant. 36 For the 12 plans analyzedbefore, T remains the same. For the two new plans in the sample (Cruzado and Mexican plan), T is 1986 for the Cruzado plan and 1988 for the Mexican plan. We do not allow for overlapping. 37 Of course, since all regressions include fixed effects, trend growth varies across cotmtries. 38 This casts doubts on the idea that the booms associatedwith exchange-rate-basedstabilizations began prior to the implememationof the programs, as has been argued by Kydland and Zarazaga (1997).

1558

G.A. Calvo and C.A. Vdgh

Table 4 Real GDP per capita growth before and after stabilization a individual regresssions Exchange-ratebased (1) T- 2 T- 1

-0.46 (1.09) 0.94

(l.08) 7" T+ 1

2.00* (1.03) 2.91"**

Moneybased (2)

Joint regression Exchange-ratebased

Money -based (3)

-6.86*** (1.56) -4.18 ....

-0.71 (1.18) 0.47

(1.59)

(1.13)

-10.83"** (1.60) -3.84**

1.42 (1.11) 2.34**

-6.96*** (1.66) -4.45 ....... (1.59) -10.98 ...... (1.59) -3.87 (1.58) -2.84 (1.76) -1.12 (1.77) 0.49 (1.71)

(i .03)

(1.55)

(l. 11)

-0.21 (1.04) 0.49 (1.10) 1.99" (1.11) -0.62*** (0.13)

-3.20" (l.71) -0.83 (1.71) 0.39 (1.64) -0.58*** (0.13)

-0.61 (1.11) -0.26 (1.20) -2.33** (1,17)

OECD growth

0.55*** (0.16)

0.57*** (0.17)

0.55*** (0.17)

Terms of trade

0.012" (0,0069) 200

0.013' (0.0067) 200

0.013" (0.0067)

T+2 T+3 T+4 Libor (real)

No. of observations

-0.60 .... (o.13)

200

Dependent variable is real ¢SDP per capita growth. The sample comprises Argentina, Brazil, Chile, Dominican Republic, Israel, Mexico, Peru, and Uruguay ~br the period 1971-1995. Standard errors are given in parentheses. The method of estimation was a 2-step GLS procedm'e, which allows for groupwise and cross-group heteroscedasticity and groupwise antocorrelation. All regressions include fixed country effects (not reported). Significance at the 10, 5, and 1 percent level is indicated by one, two, and three asterisks, respectively. a

In m o n e y - b a s e d stabilizations, growth in the two years before stabilization is significantly below trend growth [regressions (2) and (3)]. M o n e y - b a s e d stabilizations thus appear to have b e e n i m p l e m e n t e d in "bad" times. Growth is sharply below trend in the year o f stabilization and continues to be significantly below trend in the tirst year (in both the individual and j o i n t regressions) and second year after stabilization (in the individual regression). External factors have the expected signs and are always significant. These results are thus consistent with the idea o f an early recession in m o n e y - b a s e d stabilization, and an early b o o m followed by a contraction in exchange-rate-based

Ch. 24: lnflation Stabilization and BOP Crises in Deueloping Countries,

1559

stabilization. A caveat to be noticed is the fact that growth was significantly below trend before the stabilization in money-based programs. This raises the possibility that the initial recession might simply be the continuation o f that trend 39. While the regressions reported in Table 4 are certainly revealing, they may be asking too much o f the data. The reason is that we are really interested in the behavior of growth in the "early" and "late" stages o f stabilization programs, rather than in specific years (i.e., we are interested in "joint significance"). Hence, as before, we ran panel regressions with early and late dummies, and control variables 4°. Table 5 shows the same regression estimated by three different methods: OLS, fixed effects, and a 2-step GLS with fixed effects. The results do not vary much across different method of estimations. In all cases, the early and late dummies for exchange-rate-based stabilization are significant and so is the early dummy for m o n e y - b a s e d stabilization. In other words, growth in the early stages o f an exchange-rate-based stabilization is significantly higher than trend growth and significantly below trend growth in the late stages. In money-based stabilizations, growth is significantly below trend growth in the early stages and not significantly different from trend growth in the late stages. Of the control variables, real Libor and OECD growth are always significant. These results are thus consistent with the recession-now-versus-recession-later hypothesis. 3.4. A word o f caution A final word o f caution is in order. Research on the empirical regularities o f stabilization in chronic inflation countries is still very much work in progress. In fact, we would argue that too little empirical work - relative to theoretical work - has been done in the area. Needless to say, this type o f analysis faces formidable obstacles, including small samples (in particular o f money-based programs), the definition o f inflation stabilization episodes, the classification o f episodes by type o f nominal anchor, the quality o f the data, and the need to control for other shocks (both domestic and external). Much work remains to be done and the results presented here should be taken as suggestive and pointing out directions to follow, rather than as conclusive evidence. At a methodological level, we think it is important to distinguish between two alternative approaches. One approach - the one adopted in this section might be t9 In addition, Gould (1996) has argued that the state of the economy be%re stabilization influences the choice of the nominal anchor, with "bad" times inducing policymakers to choose money as the main anchor. 40 For tile seven plans which were already part of the previous sample, the danmaies are the same but, since the sample is now longer, the late dummy takes a value of 1 during 1994 and 1995 for both the Convertibility plan and the Uruguayan 1990 plan. For the seven new plans, the years in which "early" and "late" take a value of I are the following: Bonex plan: early = 1 for 1990 (no late dummy); Cruzado plan: early= 1 for 1986, late= 1 for 1987 and 1988; Chile 1975, early= 1 for 1975 and 1976, late= 1 for 1977; Dominican Republic, early = 1 for 1990, 1991 and 1992, late = 1 for 1993 and 1994; Mexico, early= 1 for 1988, 1989, and 1990, late 1 for 1991 and 1992; Peru, early 1 for 1990, 199I, and 1992~ late= l for 1993 and 1994. TM

TM

1560

G.A. Catuo and C.A. V~gh

Table 5 Real GDP per capita growth: Panel estunates a OLS (l) Exchange-rate-based stabilization: Early dummy Exchange-rate-based stabilization: Late dummy Money-based: Early dummy Money-based: Late dmnmy Libor (real) OECD growth Terms of trade Adjusted R 2 No. of observations

2.31"* (0.96) -2.33** (1.10) 4.90 *0* (1.40) 1.59 (1.66) -0.50 (0.13) 0.55*** (0.19) 0.01" (0.006) 0.18 200

Fixed effects (2) 2.40** (1.03) -2.18* (1.16) -5.46*** (1.44) 0.72 (1.69) -0.61 . . . . (0.14) 0.45** (0.19) -0.005 (0.015) 0.25 200

2-step GLS (3) 1.73"* (0.75) - 1.64"* (0.80) -6.29 .... (1.30) -1.89 (1.22) 0.62 (0.13) 0.62 .... (0.16) 0.01 (0.007) 200

a Dependent variable is expressed in per capita terms. The sample includes Argentina, Brazil, Chile, Dominican Republic, Israel, Mexico, Peru, and Uruguay for the period 1971-1995. Standard errors are given in parentheses. The 2-step GLS procedure allows for groupwise and cross-group heteroscedasticity and groupwise autocorrelation. The regressions include fixed effects (not reported). Significance at the 10, 5, and 1 percent level is indicated by one, two, and three asterisks, respectively.

d u b b e d the "episodic" approach. This approach involves selecting the best-kdlown stabilization episodes, which have received a great deal o f attention. A t the other extreme, we have a " m e c h a n i c a l " approach, where stabilization episodes are defined based on the behavior o f inflation. For example, Easterly (1996) defines a stabilization as an episode characterized by a switch from a period o f two years or more with an a n n u a l rate o f inflation above 40 percent to a period o f two years or more with an a n n u a l rate o f inflation below 40 percent. Both approaches have problems. The "episodic" approach is subjective and will tend to omit lesser-known episodes 41. The " m e c h a n i c a l " approach defines a stabilization b y its outcome, which is clearly problematic. Conceptually, an inflation stabilization p r o g r a m involves a drastic reduction in the rate o f growth o f a policy i n s t r u m e n t (the exchange rate or the m o n e y supply) and n o t necessarily the attainment o f a 41 It should be noted, though, that omitting smaller programs is not necessarily a bad thing. To isolate better the effects of a given phenomenon, it makes sense to select episodes in which the phenomenon in question relative to many other factors which are difficult to control for - was of overriding importance.

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

t561

policy objective (a fall in the inflation rate). In fact, both theory and evidence provide numerous examples of stabilizations which involve a rather slow reduction (or even an initial increase) in inflation. Whatever the merits of both approaches, in the second~ best world of empirical analyses, there is surely something to be learned from both of them. Within the episodic approach, Echenique and Forteza (1997) argue that the results reported in Reinhart and V6gh (1994, 1995b) - in particular, the initial boom under exchange-rate-based stabilization - are not robust to the inclusion of external factors (they do not look at either private consumption or durable goods consumption). The revised estimates reported above do not support such a claim, except for investment. In any event, controlling for other factors - both domestic and external - is clearly an important endeavor as it would imply that, quantitatively speaking, models of exchange-rate-based stabilization should be able to account only for a fraction of the actual booms observed. Gould (1996) argues that, after adjusting for initial conditions which make the choice of the nominal anchor endogenous, growth actually improves in either case. Using the "mechanical approach" described above, Easterly (1996) argues that stabilization from high inflation has been expansionary (in terms of GDP and consumption) regardless of the nominal anchor. In other words, he does not find evidence of money-based stabilization being contractionary. The difference may reflect the very different sample - out of 28 episodes, Easterly (1996) classifies all but 9 as money-based stabilization - and the fact that he considers only successful programs. In accordance with our findings, however, Easterly (1996) also argues that higher investment is absent in the early stages of stabilization. The notion that inflation stabilization may be associated with higher growth also receives support from the transition economies. Using a 25-country sample, Fischer, Sahay and V6gh (1996) conclude that inflation stabilization has been expansionary for the transition economies - regardless of the nominal anchor - but that resorting to a fixed exchange rate has had an additional positive effect on growth. A more general critique is that of Kydland and Zarazaga (1997) who argue based on a review of the literature on disinflation in chronic-inflation countries anO an analysis of business cycles in Argentina - that nominal exchange rate shocks do not seem to have had any noticeable real effects, even during exchange-rate-based stabilizations. More specifically, they argue that business cycles in Argentina could be explained by real shocks. It is worth stressing, however, that the stabilization literature has certainly not claimed that stabilizations are the main source of business fluctuations in high-inflation countries; it has only claimed that stabilization programs have reai effects. The latter is, of course, perfectly consistent with the idea that real shocks may be the main source of business cycle fluctuations over long periods of time42~ 4~ A case in point is Uruguay. Hoflknaisterand Vdgh (t996) find that over tile period 1975--1990nominal shocks explain only a small fraction of output movements.For the tablita period (1979-1983), however~ a historical decomposition suggests that nominal shocks played a central role.

1562

G.A. Calvo and CA. V~gh

Furthermore, for any given country, major stabilizations are relatively rare events. This small-sample problem has led researchers in this area to work with panels (i.e., crosscountry analysis). It is thus doubtful whether time-series, business-cycle analysis for a particular country might be able to pick up the real effects of stabilization. Even if such effects were there, the "recurrent" sources of business cycle fluctuations - whatever they may be, and this literature certainly takes no position on this - would probably dominate.

4. Exchange-rate-based stabilization I: inflation inertia and lack of credibility Given the main characteristics of chronic inflation processes - decades of high inflation and a rich history of failed stabilization attempts - it is perhaps not surprising that the two main explanations advanced for the stylized facts discussed in Section 3 rely on inflation inertia and lack of credibility. 4. l. Inflation inertia

Rodriguez (1982) was the first to point out that, under conditions of high capital mobility, a credible decline in the rate o f devaluation may provoke an initial expansion. The main motivation behind his model was the fall in real interest rates observed in the initial stages of the Argentine tablita [see also Fernandez (1985)]. In the model, a reduction in the devaluation rate leads, through the interest parity condition, to lower domestic nominal interest rates. If inflationary expectations are sticky (i.e., adaptive expectations ?t la Cagan), then the real interest rate will fall, stimulating aggregate demand in the short run. The initial expansion, however, will eventually be followed by a contraction, as inflation inertia leads to a sustained real exchange rate appreciation. Rodriguez's (1982) major contribution was thus to show that, even though Phillips-curve type implications will eventually hold, short-run dynamics may push the economy in the opposite direction. Notice, incidentally, that the argument relies on some form of expectational inertia 43. The above explanation has prima facie high predictive power, as it reproduces quite well the stylized facts documented in the previous section, including the boom-recession cycle and the U-shaped path of the real exchange rate. It also provides us with a simple model suggesting the possible traps that one might encounter in a stabilization effort. For example, if the process is not well understood, policymakers may reach the conclusion that stabilization has generated a higher sustainable level of output and economic activity. Since expansion is normally accompanied by higher 4:3 Dornbusch (1982), in contrast, assumes that agents display rational expectations (i.e, are forwardlooking), but that the inflation rate is predetermined and thus exhibits a large degree of inertia. While Dotvabusch (1982) does not focus on the initial output effects of disinflation, he emphasizes the eventual recession brought about by the c:maulativereal appreciation of the domestic currency.

1563

Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries

fiscal revenue, policymakers may be induced to slacken their control on government expenditure, enhancing the economy's overheating and further widening the fiscal deficit when recession sets in. Further, as emphasized at the time by Dornbusch (1982) - and more recently by Dornbusch and Werner (1994) - sticky-inflation-based models call attention to the problem of "overvaluation" and the public's expectations that a corrective devaluation would have to take place at some point to restore "equilibrium" relative prices. Rodriguez's (1982) model postulates reduced-form aggregate demand functions which depend on the real interest rate and the real exchange rate. In particular, the model assumes that a higher real interest rate unambiguously lowers aggregate demand. These appear to be highly plausible assumptions. However, Calvo and V6gh (1994a) show that such assumptions are rather strong and are not necessarily supported by models consistent with optimizing behavior. This can be illustrated by a simple example. Consider a small open economy perfectly integrated with the rest of the world in goods and capital markets. The representative household's instantaneous utility depends (separably) on consumption of tradables, c T, non-tradables (or home goods), c y, and real monetary balances in terms of tradables, m 44. Thus, lifetime utility as of time 0 can be written as: .fo °~ [o(c/) + u(c~) + z(mt)] exp(-/3t) dt,

(4.1)

where/3(> 0) is the rate of time preference, and 0(% u(.) and z(.) are strictly increasing and strictly concave functions. The individual has a constant endowment flow of tradable goods, yV, while output of nontradables, yN, is demand-determined (i.e., in equilibrium, yN = c N for all t). Tile law of one price holds for the tradable good. The (constant) world real imerest rate is denoted by r. (It will be assumed that there is no foreign inflation, so that r is also the world nominal interest rate.) Therefore, the individual's lifetime constraint is given by: b0 -I m0 +

T + y_N + rt Ct

)

exp(--rt) dt =

c T ~ cN I itmt ,

Ct

)

e x p ( r t ) dL

(4.2)

where b0 denotes tile individual's initial stock of net foreign assets, et denotes the real exchange rate (i.e., the relative price of tradable goods in terms of non-tradable goods), it is the nominal interest rate, and Tt are government lump-sum transfers. Given perfect capital mobility, the interest parity condition it = r + Et holds, where e~ is the rate of devaluation. 44 As will become clear below, the other assumptions in the present example make our key ~esuits invariant with respect to the price deflator in the definition of real money balances.

G.A. Calvo and C.A. V@h

1564

To abstract from fiscal issues, we assume that the government returns back to the consumer all of its revenues. Hence, the government's lifetime budget constraint indicates that the present value of transfers must equal the initial stock of governmentheld foreign assets (i.e., international reserves), denoted by Ro, and revenues from money creation:

/0

rt exp(-rt) dt = Ro +

/0

(tht + etmt) e x p ( r t ) dr.

(4.3)

Combining (4.2) and (4.3), taking into account non-tradable goods market equilibrium, the interest parity condition, and the transversality condition limt _, 0 mt exp(-rt) -- 0, yields the economy's resource constraint ko + yT L = ~0occ] exp(-rt) dr, F

(4.4)

where k ( - b + R) is the economy's net stock of foreign assets. Equation (4.4) thus constrains this small economy's lifetime consumption of tradable goods to be equal to tradable goods wealth. Maximization of lifetime utility (4.1) with respect to the budget constraint (4.2) yields the following first-order conditions 45: v'(c~) = A,

(4.5)

X ,

(4.6)

z'(mt) = 26,

(4.7)

u'(c~) et

where X is the time-invariant Lagrange multiplier. Equations (4.5) and (4.6) are the familiar conditions whereby, at an optimum, the household equates the marginal utility of consumption to the shadow value of wealth, Z, times the relative price of the good (uaity in the case of tradables and 1/e in the case of non-tradables). Similarly, at an optimum, the marginal utility of real money balances is set equal to the shadow value of wealth times the opportunity cost of holding real money balances, i [Equation (4.7)]. Equation (4.5) indicates that optimal consumption of tradable goods is constant along a perfect fo~resight path. From Equation (4.4), it then follows that cf = rko + y T a constant, for all t ~> 0. Further, notice that unanticipated changes in the devaluation rate will not affect consumption of tradable goods. Consequently, from Equation (4.5), the Lagrange multiplier, ~, is invariant with respect to (unanticipated) changes in the rate o f devaluation 46. This feature will greatly simplify the ensuing analysis.

Backward-looking indexation is introduced along the lines of Calvo and V6gh (1994a). The home goods sector operates under sticky prices (i.e., the nominal price 45 As usual, we assume that [3 - r to eliminate inessential dynamics. 46 Of course, the multiplieris always invariantto anticipated changes.

Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries'

1565

of home goods, pN, is a predetermined variable). Let the rate of inflation (of nontradables) be indicated by Jr. We assume that srt = co, + O(c N _yN),

0 > 0,

(4.8)

where iPN stands for full-employment output ofnon-tradables, and co is a predetermined variable which satisfies cbt - X(3rt --cot),

y > 0.

(4.9)

The variable co can be interpreted as the rate o f growth of nominal wages. Hence, Equation (4.8) says that inflation of home goods is equal to the rate of growth of nominal wages plus excess aggregate demand 47. In turn, equation (4.9) indicates that wage inflation increases (decreases) as price inflation (in terms of nontradables) exceeds (falls short of) wage inflation. This assumption is meant to capture backwardlooking wage indexation mechanisms, whereby the rate o f growth o f nominal wages is adjusted whenever the inflation rate exceeds the current level of wage growth. To illustrate the implications of this set-up, integrate backwards Equation (4.9) and substitute the resulting expression for ~ into Equation (4.8) to obtain l

Jet

Yq,e x p [ - x ( t - s)] ds + O(cNt --ipN).

(4.10)

0(3

Equation (4.10) shows that current inflation depends on a weighted average of past inflation rates - with inflation rates in the recent past receiving the greatest weight and current excess aggregate demand, which is what the notion of "inflation inertia" is usually taken to mean [see, for instance, Dornbusch and Simonsen (1987)]. We will now study the implications of a once-and-for-all reduction in the rate of devaluation, which is the central exercise in Rodriguez (1982). Given the invariance of the Lagrange multiplier with respect to changes in el, it follows from first-order condition (4.6) that we can safely write c y as an increasing function of the real exchange rate, et; that is, c N = q)(et), with O~(et) > 0. HencG by Equations (4.8) and (4.9), we have &t-~ g0[0(et) - 2N ].

(4.1 1)

Furthermore, by definition, et ~ EtPF*/PtN, where G is the nominal exchange rate (m units of domestic currency per unit of foreign currency, p T . is the (constant) f o r e i g n

47 Note that, in this specification, )~ is not a predetermined variable (i.e., it could jump on impact if consumption of home goods does so).

1566

G.A. Calvo and C.A. V~gh

03' £H

~=0

\

"

I

!I

...................................\ .....................~ i A

..........................

6-=0

ess

e >

Fig. 4. Inflation inertia: dynamic system. currency price o f the tradable good and pN is the price o f home goods48. Using this definition and Equation (4.8), it follows that - et - cot - 0[~b(e~)_~N].

(4.12)

et

Equations (4.11) and (4.12) constitute a system o f differential equations in cot and et, which can be shown to be locally stable 49. Since both cot and et are predetermined variables, this ensures that under perfect foresight - and for a given set o f p a r a m e t e r s all equilibrium paths converge to the steady-state. Suppose that initially (i.e., for t < 0), the devaluation rate is expected to remain constant at the value e H. Hence, in the initial steady state (point A in Figure 4), ;r~ = e u and O(e~) = ~N. At time 0, policymakers announce an unanticipated and permanent reduction in the devaluation rate from e H to e L. The new steady state is denoted by point B, where inflation o f home goods is e L, while the real exchange rate remains unchanged. The dynamics o f the adjustment to the new steady state are illustrated by the arrowed path in Figure 4. The time path o f the main variables is illustrated in Figure 5. Nominal wage growth falls monotonically over time (Panel B). The real exchange rate declines (appreciates) 48 Note that the real exchange rate is a predetermined variable because E is a policy variable and pN is a predetermined variable. 49 The trace of the matrix associated with the linear approximation around the steady state is -es~00~(ess) < 0 (where a subscript "ss" denotes steady-state values) and the determinam is 7ess0~b~(ess) > 0, which implies that both roots have negative real parts. For expositional simplicity, roots will be assumed to be real.

1567

Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries

A. Rate of devaluation

B. Nominal wage growth

t

co1' H

gL I i

time

e'

0

C. Real exchange rate

time

D. Consumption of home goods 0N

ess /- s/"

0

/I:'

E,

time

t~ Inflation rate

t~

time

F. Domestic real interest rate

at r

gH i

/--'---

\\~ ,,

~L ,

"

//

0

tl

time

0

t1

time

Fig. 5. Disinflationunder inflation inertia. in the early stages of the program, and then returns to its initial steady-state value (Panel C). Given that consumption of tradables remains constant, consumption of nontradables (Panel D) falls in the early stages (as its relative price, l/e, increases) and increases later on. Hence, during the initial stages of the stabilization program, consumption of home goods (and thus output of home goods) falls - i.e., it does not rise in line with the stylized facts. At some point in time (denoted by fl in Figure 5)~ inflation of home goods must fall below its long-run equilibrium value (Panel E) in order for the real exchange rate to return to its unchanged steady-state value. It is this protracted period of deflation needed to restore equilibrium relative prices which underlies the call for a step devaluation at some point during the adjustment

t568

G.A. Calvo and C.A. V~gh

program [see, for instance, Dornbusch and Werner (1994)]. Indeed, in this model, a devaluation at time tl in Figure 5 (which corresponds to point C in Figure 4) would immediately take the economy to its new steady state, provided that workers also agreed to reduce the rate of nominal wage growth, w, to e L. It should be noticed that consumption of non-tradables falls in the early stages of the program in spite of the fact that the domestic real interest rate, rd(~- i--2g), decreases on impact (Figure 5, Panel F). The reason is that, in utility-maximization models, the real interest rate determines the slope of the consumption path but not the level of consumption. Hence, the initial fall in r d implies that, as long as r d < r, consumption of non-tradable goods will follow a declining path. Calvo and V6gh (1994a) extend this analysis to the case in which instantaneous utility is represented by a constant-elasticity-of-substitution utility function. They show that the results obtained in the context of Dornbusch-Rodriguez models hold true only if the intertemporal elasticity of substitution exceeds the elasticity of substitution between tradables and nontradables. In that case, consumption of both tradable and non-tradables goods increases on impact, which implies that the current account goes into deficit. The relative magnitude of these parameters is, of course, an empirical issue. Estimates provided by Ostry and Reinhart (1992), however, cast some doubts on the relevance of backward-looking models since they show that, for a number of developing countries, the intertemporal elasticity of substitution is typically smaller than that between tradables and nontradables 50. An important feature of Calvo and V6gh's (1994a) formulation is that the stabilization does not bring about a wealth effect, in the sense that wealth in terms of tradable goods remains unchanged. This appears as the natural assumption to make when the purpose of the exercise is to isolate the effects of inflation inertia on the outcome of an exchange-rate-based stabilization. However, in a more general model with capital accumulation and endogenous labor supply, the wealth effect associated with a permanent reduction in the rate of devaluation will cause an increase in consumption of tradable goods and, given that the real exchange rate cannot change on impact, a corresponding increase in consumption of non-tradable goods [see Rebelo and V6gh (1995), Figure 11]. Hence, wealth effects associated with supply-side effects (analyzed in more detail below) could help explain the initial boom under backwardlooking indexation even under the more plausible parameter configuration in which the intertemporal ~elasticity of substitution is smaller than the elasticity of substitution between tradables and non-tradables goods.

5o The more common criticism of Rodriguez (1982) is the assumption of adaptive expectations an assumption that has fallen out of favor among the profession. This criticism is, however,misplaced since Rodriguez's (1982) results still hold under rational expectations, as shown in Calvo and V6gh (1994a). In other words, the key assumption in Rodriguez (t982) is not adaptive expectations but rather that aggregate demand depends negatively on the real interest rate (provided, of course, that there is some other source of inflation inertia).

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

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4.2. Lack o f credibility A common characteristic o f stabilization plans is imperfect credibility. As pointed out in Section 2, there are fundamental reasons for stabilization programs to be less than fully credible. Since stabilization is costly from a political point o f view, why would anybody expect that, as a general rule, stabilization programs have no chance to fail? Implementing a program that succeeds in all states of nature is unlikely to be optimal from the policymaker's point o f view. Suppose, for the sake o f concreteness, that authorities announce a stabilization plan in which the exchange rate is set at a lower and constant level forever, but the private sector believes that the program may eventually be abandoned. To keep matters simple, let us further assume that everybody believes that the program will be abandoned at time T > 0 (where time 0 represents "today"), and the rate of devaluation will, once again, become high after time T (see Figure 6, Panel A). Assuming perfect capital mobility, the latter implies that the nominal interest rate will be low from time 0 to time T, and expected to be high afterwards 51. Will this have real effects? The answer is negative in the money-in-the-utility-function framework used in subsection 4.1 to illustrate the effects o f backward-looking indexation. In that model, the nominal interest rate does not affect any goods-markets equilibrium condition. Thus, the real economy (under flexible prices) would be undisturbed by the monetary experiment. However, separability between money and goods in the utility function is a very special, and probably unrealistic, assumption. It implies that the marginal utility of money is independent o f expenditure, a condition that is likely not to hold if money is used for transactions 52. Following Calvo (1986), let us assume that transactions require holding cash in advance 53. Thus, using the same notation as before, we postulate 54 m, = a(cJ' + CN),

a > 0.

(4.1 3)

et

The consumer's preferences are now given by: .f~/0 [v(cT) + u(c~)] exp(-fit)dt.

(4.14)

51 Note that, formally, lack of credibility is modeled as a temporary stabilization~ which explains the label "temporariness hypothesis", often used in the literature. 52 It should be noted, however, that the basic results of Section 4.1 hold true even under non-separability of real money balances (say, under the cash-in-advance specification explored below). Since we studied a permanent reduction in the devaluation rate, it would still be the case that consumption of traded goods remains unchanged under a cash-in-advance specification. s3 We adopt a cash-in-advance, flexible-prices specification to illustrate the essential mechanisms behind lack-of-credibility in the simplest possible model. The same results would obtain under a money-in-theo utility-function specification provided that the cross-derivative between consumption and real money balances is positive [see Calvo (1986)]. s4 For the derivation of the cash-in-advance constraint in continuous time, see Feenstra (1985)

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G.A. Catvo and C.A. V&gh

After substituting Equation (4.13) into (4.2), we obtain a lifetime constraint that involves only c~ and c~ as choice variables (and whose corresponding Lagrange multiplier will be denoted by ~). Maximization of Equation (4.14) subject to this lifetime budget constraint yields

v'(clF) = ~(1 + air),

(4.15)

u'(c~) = ~(1 + air).

(4.16)

el

The term involving the nominal interest rate i, 1 + ai, has a straightforward interpretation. Under the present assumptions, individuals must hold a stock of cash before making purchases. This means that, in addition to the market price of the good (unity for the tradable good and 1/e for the non-tradable good), the cost of the good is augmented by the opportunity cost of holding the needed real money balances. The eIfective price of consumption is thus 1 + ai for tradable goods and (1 + ai)/e for non-tradables. For the present discussion, we can simplify the supply side even further and assume that the domestic supplies of tradables and nontradables are fixed at y:r and yN, respectively. Then, by Equations (4.15) and (4.16), and home goods-market equilibrium (i.e., c~ = yN), it follows that

et

.'(cy)

u,(yN).

(4.17)

Hence, in equilibrium, the real exchange rate and consumption of tradable goods move in opposite direction, in other words, any shock that causes consumption of tradable goods to increase will also entail a real exchange rate appreciation (i.e., a fall in et). Consider now the effects of a non-credible stabilization program as described above (Figure 6). Since the representative individual expects a policy reversal at time T, it implies that he/she will expect the nominal interest rate i to be low from 0 to T, and high afterwards. Thus, by Equation (4.15), consumption of tradables will be high between 0 and T and low afterwards. Given that the present discounted value of c'r must satisfy the resource constraint (4.4), the path of consumption of tradable goods must look like that in Panel B of Figure 6. Intuitively, since the consumer expects the good to be cheaper between 0 and T than after T, he/she substitutes consumption away from the future (when consumption is expected to be relatively expensive) and towards the present (when consumption is cheaper). The current account deteriorates on impact and worsens throughout the stabilization as debt service increases (or net interest income falls), as illustrated in Panel C of Figure 6. Unlike tradable goods whose supply is rendered perfectly elastic by the rest of the world - non-tradable goods are in fixed supply. Hence, the excess demand for non-tradable goods between 0 and T will have to be met by a rise in their relative price (i.e., a fall in et), as follows ti-om Equation (4.17) (Panel D of Figure 6).

1571

Ch. 24." Inflation Stabilization and BOP Crises in Deueloping Countries B. Consumption of traded goods

A. Rate of devaluation

A

CT '~

H~ r

Li ~i

¸

rko+y T

i

L

0

T

time

time

D. Real exchange rate

C. Current account e

0

T

time

0

T

time

Fig. 6. Temporary stabilization. At the beginning of the program there is thus a boom in the consumption of tradables and a real appreciation, which is eventually followed by a contraction in the consumption of tradables and a real depreciation 55. Thus, this model displays two basic stylized facts that have accompanied exchange-rate-based stabilization programs, as argued in Section 3. It is also noteworthy that, unlike the previous explanation based on inflation inertia, this model does not rely on an initial fall in real interest rates. Hence, it could also explain the stylized facts even in programs in which only nominal, but not necessarily real, interest rates fall in the early stages 56. By introducing price stickiness into this model, Calvo and V~gh (1993) have shown that a temporary stabilization may account for other key stylized facts discussed in Section 3: (i) the joint occurrence of an output boom and a real exchange rate ss The real effects at time T will occur regardless of whether the program is actually abandonedor not, provided that if it is not abandoned, the program becomes fully credible at T. Formally,it can be shown that permanentchanges in the rate of devaluationare everywhere superneuh-al. 56 An interesting extension of the basic model is to assume that T is a stochastic variable, as in Calvo and Drazen (1998), which leads to richer dynamicpatterns for consumption.In particular, they show thal in the absence of state-contingentassets, consumptionrises on impact and continues to increase as long as the policy is in effect. See also Lahiri (1996a,b), Mendoza and Uribe (1996), and Venegas-Martinez (1997). Fm-thervariations of the basic model include Obstfeld (1985), who studies a gradual, tablita-type stabilization, and Talvi (1997), who analyzes tile endogenous impact of higher consumption on fiscal revenues.

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G.A. Calvo and C.A. VSgk

appreciation in the early stages of the program; (ii) a recession in the non-tradable goods sector (i.e., a fall in output below its full-employment level) which may take place before the program is discontinued; and (iii) inflation remaining above the rate o f devaluation until the time at which the program is expected to be discontinued 57. Hence, in this case, inflation persistence is not due to some ad-hoc backward-looking mechanism but rather to lack of policy credibility. The model thus suggests that the fact that inflation remains high is not prima-facie evidence o f stickiness in the rate of inflation 58. It should be noted that in the exercise illustrated in Figure 6, lack of credibility is socially costly, because a central planner would set consumption o f tradables constant and equal to rko + y rr, instead o f setting a path displaying the boom-bust pattern shown in Panel B of Figure 6. Hence, even though consumption rises as a noncredible exchange-rate-based stabilization program is put into effect, the stabilization still proves to be a socially costly process. This conclusion, though, depends critically on the fact that, in cash-in-advance models (with no labor-leisure choice), there are no benefits associated with a reduction in inflation (i.e., the real equilibriurn is independent of permanent changes in the inflation rate). In contrast, in transactioncosts models, lower inflation is beneficial because it frees time for productive activities. In such a set-up, a temporary stabilization may be welfare-improving if the benefits (in terms of freed resources) o f temporarily lower inflation more than offset the intertemporal distortion caused by a non-constant path o f the nominal interest rate [see Reinhart and V6gh (1995a)]. Hence, policymakers may still find it optimal to implement stabilizations plans that may not be fully credible, provided they command a "reasonable" level of credibility. Lack o f credibility thus provides a rich framework to explain the main stylized facts observed in exchange-rate-based disinflations. The most common criticism o f this type o f model is that it relies critically on intertemporal consumption substitution, which is believed to be small or not significantly different from zero. Reinhart and V6gh (1995a) have examined the empirical relevance o f the "temporariness" hypothesis, by estimating the intertemporal elasticity o f substitution for five chronic-inflation countries (Argentina, Brazil, Israel, Mexico, and Uruguay). Using these estimates, they compute the predicted increases in consumption for seven major stabilization plans

5'7 In this model, the domestic real interest rate falls on impact. As discussed in Section 3, howeve,, real interest rates have typically increased on impact in heterodox programs. This often reflects tight credit policy in the early stages of the programs. For instance, the Israeli 1985 plan had an explicit target tbr bank credit, which was to be achieved by a combination of higher reserves requirements and a higher discount rate [Barkai (1990)]. The idea is for money to act as an additional nominal anchor in the early stages of the plan. This could be modeled by assuming that the stock of money is predetermined at each point in time due to the presence of capital controls [Calvo and V~gh (1993)]. Ag6nor (1994) incorporates fiscal considerations into a model with imperfect capital mobility to address this issue, 58 Within this fiamework, Ghezzi (1996) has analyzed the important but still little understood question of when to abandon an initial peg and switch to a more flexible exchange rate regime (a common occurrence in practice, as argued in Section 3).

Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries

1573

(the three Southern Cone tablitas, the Argentine 1985 Austral plan, the Brazilian 1986 Cruzado plan, the Israeli 1985 plan, and the Mexican 1987 plan) and compare them to the actual increases. They conclude that, in spite of low (but statistically significant) elasticities of substitution - ranging from 0.19 to 0.53 - this mechanism has a good explanatory power in four out of the seven episodes. It is the case, however, that nominal interest rates must fall substantially for this mechanism to be quantitatively important, which explains why the model appears to perform poorly for the SouthernCone tablitas 59. If anything, however, the estimates provided by Reinhart and V6gh (1995a) should probably be viewed as a lower bound for the importance of the "temporariness" hypothesis. The reason is that the model does not incorporate durable goods which, as argued in Section 3, appear to play a central role in the initial consumption boom. The presence of durable goods is likely to increase the quantitative importance of intertemporal substitution for two reasons. First, the introduction of durable goods might yield higher intertemporal elasticities of substitution, as found by Fauvel and Sampson (1991) for Canada. Second, in addition to intertemporal consumption substitution, durable goods introduce the possibility of intertemporal p r i c e substitution because goods can be stored [Calvo (1988)].

5. Exchange-rate-based stabilization lI: durable goods, credit, and wealth effects The explanations discussed in the previous section rely on what we view as two key characteristics of chronic inflation processes: inflation persistence and lack of credibility. There are other elements, however, which may have played an important role in stabilization plans in chronic inflation countries. We first discuss the role of durable goods consumption and credit market segmentation. We then turn to a discussion of wealth effects, which may result from either supply-side responses or fiscal policy. 5.1. Durable goods

As shown in Section 3, the consumption boom that characterizes exchange-rate-based stabilization programs has been particularly evident in the behavior of durable goods. This pattern of durable goods consumption has inspired an alternative explanation for the boom-bust cycle put forward by De Gregorio, Guidotti and V6gh (1998) (henceforth DGV). This hypothesis, which is unrelated to inflation inertia or lack 59 It is worth pointing out that trying to explain all of the observed consumption booms may bc misleading, as other factors such as lower international interest rates - may account for part of the boom.

1574

G.A. Calvo and C.A. V~gh

ci BI

IA!B ]

-4

-3

I

0,

DAD

-2

-1

0

1

time

Fig. 7. Consumption of durable goods.

of credibility, is capable of generating a boom-bust cycle even in a fully credible program. Suppose that there are transactions costs associated with the purchase of durable goods. This implies that individuals buy durable goods only at discrete intervals of time. in the aggregate, however, sales of durable goods are smooth over time since different individuals purchase durable goods at different points in time 6°. This is illustrated in Figure 7. There are four consumers (whose purchases of durable goods are represented by the squares labeled A, B, C, and D) who buy durable goods at different points in time (i.e., every four periods). Hence, before time 0, aggregate sales o f durables goods are constant. Consider now a stabilization plan implemented at time 0. Furthermore, suppose that there is a wealth effect associated with the stabilization (more on this below). Then, some consumers will be inclined to anticipate their purchase o f durable goods and perhaps buy a more expensive durable good. In other words, next year's new Honda becomes today's new Mercedes. In terms o f Figure 7, consumers B and C (who, in the absence of the stabilization plan, would have replaced the durable good at time t = 1 and t = 2, respectively) decide to buy the durable good at t = 0 (the picture abstracts from "size" effects). Consumer D, who just replaced his/her durable good at t = -1, also anticipates his/her purchase but to t = 1. In this simple example, there are no purchases of durables at t = 3 and t = 4, due to the initial bunching o f purchases at t = 0 and t = 1. The initial boom (in period 0) is thus followed by a bust in periods 2 and 3. Hence, this model is capable of accounting for the boom-bust cycle without resorting to inflation inertia or lack o f credibility 61. A key difference between this story and the previous two (inflation inertia and lack of credibility) lies in the policy implications. Under the temporariness (i.e., lack of credibility) hypothesis, the boom-bust cycle is a clear indication that policymakers have not done enough at the outset to convince the public that the program is 6o In the absence of transaction costs and given fliat durable goods depreciate over time consumers would find it optimal to buy in each period the amount of durable goods that they are planning to consume during that period. Buying a greater amount would imply a loss for next period. Technically, it is assumed that consumers follow (S,s) rules and choose optimally the trigger points. 61 Furthemore, if idiosyncratic shocks were introduced into the pictm'e, aggregate purchases of durable goods would eventually return to the pattern prevailing before the plan was implemelated.

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

1575

sustainable over time. Hence, one would expect policymakers to worry when the initial boom emerges, and perhaps consider measures aimed at enhancing the program's credibility. In the same vein, inflation inertia (due to backward-looking indexation) also reflects some unresolved institutional problems which clearly endanger the whole stabilization strategy [as in the Chilean tablita; see Edwards and Cox Edwards (1991)]. In such a case, policymakers should try to cut the link between current and past inflation. In sharp contrast, the boom-bust cycle emphasized by DGV (1998) is a direct consequence of the policymakers' ability to implement a fully credible stabilization plan. The eventual consumption bust is the natural counterpart of the initial "bunching" in consumption, and any policy measures aimed at counteracting it are likely to be suboptimal. In DGV (1998), the wealth effect formally comes about because the fall in inflation leads to an increase in real money balances which, in turn, frees time spent in transacting to be used in productive activities. This channel is consistent with models (to be examined below) that emphasize supply-side effects of disinflation. The durablegoods consumption cycle described above, however, is independent of how this wealth effect comes about, and would also hold under alternative scenarios which may not involve, strictly speaking, a wealth effect. One such scenario, which we find particularly attractive and examine next, relies on the existence of credit market constraints. 5.2. Credit market segmentation

A boom in domestic absorption, which lies at the heart of the initial expansion and real exchange rate appreciation, can only happen if domestic residents are able to borrow from the rest of the world, or lower their holdings of foreign assets (i.e., capital repatriation). The examples examined so far rely on the fiction of a representative individual. There is thus no room for some individuals to borrow abroad and lend at home, while the rest engage in higher domestic borrowing and spending. Developing countries, however, are typically characterized by large segments of the population which do not have direct access to international borrowing and lending 62 A relevant scenario with two types of borrowers is one in which type l, say, has perfect access to international capital markets (like in the above examples), and type lI can only borrow at home. In addition, type-II individuals borrow in terms of domestic currency and are constrained to loan contracts displaying a constant nominal interest rate or a constant string of nominal installments. These are, admittedly, very special loans but their simplicity may make them cost-effective for medium-ticket durable consumption loans (i.e., television sets). In this setup, lower inflation/devaluation may induce a consumption boom, even though the program is fully credible. To see this, consider the realistic case in which borrowers pay back their debts in the form of a constant stream of nominal installments. ('~ See, lbr instance, Rojas-Suarez and Weisbrod (1995) who show that domestic bank lending is mote prevalent ha developingthan in developedcountries.

1576

G.A. Calvo and C.A. VOgh

6050if)

Ill

40-

/

E

~ i = 0.50 \ \

C

30-

\ \ \ \

I1)

\ \

20-

\\

10

\ --.

i = 0.20

"x l'l-I~ IiTH]

Y~ il i i i ii1~

0

..........

i illtlt

ii H i H lii

5

i = 0.03 ii H ii i I i iii

H i j ii i i i i i i i i i i H i i i i H i H i~ i i i i i ii i i Iii

10

i i1'1'1 i"i i

15

20 time

Fig. 8. Real instaUments for various nominal interest rates (percent per year, r = 0.03).

Thus, abstracting from credibility and country-risk problems, and asstmaing that the real (and nominal) international interest rate is r, the domestic nominal interest rate, i, will be equal to r + e. We now assume, for simplicity, that loans are given in perpetuity and that the rate of devaluation is expected to be constant. Hence, an individual who borrows a sum S will have to pay an installment equal to iS in perpetuity. Furthermore, normalizing the present price level, P0, to unity, and assuming a constant real exchange rate, we get that domestic inflation will also be equal to e. The real value of the installments is then given by (r-~e) S P~

(r+e) S exp(et) '

t~>0,

where t = 0 is the time at which the loan is granted. Consequently, the higher is the rate of devaluation, the higher will be the nominal interest rate, i, and thus the higher will be the real value of the first few installments. When inflation is high, the real value of the first few installments could be exorbitantly large, deterring credit. Figure 8 illustrates the effects of a lower inflation rate on the time path of real payments. In the three cases depicted, r = 0.03. The rate of devaluation takes three different values: 0, 0.17, and 0.47, so that i = 0.03, 0.20, and 0.50, respectively. The figure shows how the rate of inflation/devaluation can dramatically affect the time path of real payments. When i - 0.03, the path of real installments is flat. When i = 0.50, real installments in the early periods are the highest. Naturally, changes in the inflation

Ch. 24: Inflation Stabilization and BOP Crises in Deoeloping Countries

1577

(devaluation) rate do not affect the present discounted value of real installments as o f time 0, which equals S. Formally, note that

,f0 ~

i S exp(-rt) dt = S, exp(et)

so that changes in e affect real payments, but not the value o f the integral. Therefore, a substantially lower rate o f devaluation may make credit affordable to type-II individuals. The ensuing consumption boom puts upward pressure on retailing a highly labor-intensive activity - contributing to further real appreciation of the currency. Notice that the boom so generated may be socially desirable because it signifies an improvement in the credit market. Furthermore, if the newly available credit is directed towards durable goods consumption - as is likely to be the case purchases will fall later on during the program along the lines o f DGV (1998), contributing to an eventual downturn in economic activity. Hence, this type of scenario should be quite successful in explaining several stylized facts. Existence o f credit segmentation may also help to rationalize these phenomena even in the case in which there are no loan-contract constraints on type-II individuals. This would be so, for example, if type-I individuals take the implementation of the stabilization plan as a signal that the government is starting to "get its house in order". High inflation reflects the existence of tensions among policy objectives. Hence, until a stabilization program is implemented, foreign investors and type-! individuals may feel that placing their funds in the country in question exposes them to some kind of surprise taxation (particularly, if the funds are placed in highly visible domestic banks) 63. Thus, by assuaging the investors' fears, a stabilization program - which enjoys some but not necessarily complete credibility - may bring about a lowering of interest rates for type-II individuals, stimulating expenditure 64. 5.3. Supply-side effects'

All the explanations examined so far are based on demand-side considerations. This is perhaps only natural considering that much of the literature was inspired by the Southern-Cone tablitas of the late 1970s where, to most casual observers, the most striking fact was the increase in consumers' demand for goods (particularly durable goods). In more recent programs - such as Mexico 1987 and Argentina's 1991 Convertibility plan - it has been argued that monetary stabilization may have played an important role in unleashing supply-side responses in labor and investment [see 63 Domestic banks play a key role in making funds available to type-iI individuals, because their comparative advantage stems f?om their better knowledge of the local mmket. 64 Again, if some of the higher consumption falls on durable goods, a boom-bust pattern may emerge along the lines of DGV (1998). Moreover, there is, in principle, no reason in this example for social welfare to be negatively affected by the rise in consumption.

1578

G.A. Caluo and C.A. F~gh

Rebelo (1993), Roldos (1995, 1997), Uribe (1997a), and Lahiri (1996a, 1996b)] 6s. While the evidence presented in Section 3 casts some doubts on the general empirical relevance o f the investment channel, supply-side effects may well have contributed to the initial boom in some instances and thus deserve attention 66. The role o f capital accumulation in generating a steady rise in the relative price of non-tradables (i.e., a real exchange rate appreciation) is emphasized by Rebelo (1993) in the Portuguese context. I f reforms increase the economy's steady-state capital stock, then as the capital-labor ratio rises, the price o f the capital-intensive good (the tradable good) falls. Roldos (1995) and Uribe (1997a) present models in which domestic money is needed to buy (or install) capital goods, in the spirit o f Stockman (1981). As a result, inflation drives a wedge between the real return o f foreign assets and that o f domestic assets, which implies that the domestic capital stock is a decreasing function of the inflation rate. A reduction in the inflation rate thus leads to a higher desired capital stock, and hence to an expansion in aggregate demand and investment. Since the supply o f non-traded goods is assumed to be relatively inelastic in the short-run, the expansion in aggregate demand leads to an increase in the relative price o f non-traded goods (i.e., a real appreciation) and a trade account deficit. A somewhat unsatisfactory aspect o f some o f these models is that they rely on some features - gestation lags, adjustment costs, and particularly the assumption that the investment good be a "cash good" - which do not have a clear economic interpretation. In particular, there is no evidence that would seem to tie investment to the level o f cash transactions. From a qualitative point o f view, however, this assumption is not necessary for this type o f model to generate the effects just described, as made clear by Lahiri (1996a). In his model, the nominal interest rate introduces a distortion between consumption and leisure [as in Roldos (1997)]. When inflation falls, labor supply increases. This, in turn, leads to a rise in the desired capital stock and, hence, in investment. Rebelo and V6gh (1995), however, argue that the assumption that investment be in some way related to cash transactions is critical for the q u a n t i t a t i o e performance o f a broad class o f models 67. A more fundamental problem o f supply-side based models is that, given that the driving force behind such models are wealth effects, they cannot explain the late

o5 It should be noted that these programs were also accompanied by important structural reforms. As stressed in Section 3, it would be important - though far from trivial - to disentangle the effects of these reforms from those of the exchange rate-based stabilization per se. Clearly, we would not want to ascribe to monetary stabilization supply-side effects which may be due to real reforms. 66 There is little systematic evidence on labor supply responses in exchange rate-based stabilization. For some evidence on Mexico and Argentina, see Roldos (1995). 67 Similar results would obtain if money were used as a factor of production [see Uribe (i 997b)]. This channel could be rationalized by assuming - following the credit channel literature - that firms do not have access to capital markets and must resort to bank credit to finance the need for short-term working capital [see Bernanke and Gertler (1995) and, in the context of stabilization policies, the discussion below on Edwards and V6gh (1997)]. Bank-intermediated capital has been used to improve the quantitative predictions of some monetary models; see, for instance, Chaff, Jones and Manuelli (1995).

Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries

1579

contraction observed in many programs. To this end, supply-side considerations must be supplemented by either lack of credibility or some nominal rigidity 68. To illustrate how supply-side effects may be combined with temporary stabilization to replicate some of the stylized facts of exchange-rate-based stabilizations, we proceed to analyze a simple model which incorporates a consumption-leisure choice in the same cash-inadvance specification presented in Section 4. Consider a one-good economy in which the representative household maximizes

f

(5.1)

o~ , ( c~ , gt ) exp(-fit) dt,

where g~ denotes leisure, subject to the lifetime constraint (which already incorporates the cash-in-advance constraint mt a C Tt ) 69.. ( 1 - g t + vt) e x p ( - r t ) d t =

bo+mo+

f0

cT(l +ai~) e x p ( - r t ) d t .

(5.2)

First-order conditions imply that (assuming fi = r): Ucv(cT, gt) = ~(1 + air),

(5.3)

uc~(cT,g,) (5.4)

ue(ctr,gt) - 1 + air,

where ~ is the Lagrange multiplier associated with constraint (5.2). Note how the nominal interest rate introduces a wedge between consumption and leisure, as Equation (5.4) makes clear. Taking into account the government's intertemporal budget constraint, it is easy to show that /co +

(1 - gt) exp(-rt) dt -

f0

cll exp(-rt) dr.

(5.5)

Two important observations, which illustrate some of the points noted above, follow easily from Equations (5.3), (5.4) and (5.5). First, a permanent reduction in the rate of devaluation, and thus in i, would cause a once-and-for all increase in consumption and output. Hence, this would explain the initial expansionary effects, but not the eventual contraction, observed in exchange-rate-based stabilizations. Second, if the utility function were separable (i.e., Ucle(') = 0), then a temporary (i.e., non-credible) stabilization of the type studied in Section 4.2 would lead to a consumption cycle similar to that illustrated in Panel B of Figure 6, but to a p e r m a n e n t increase in output 6s Sec Rcbeto and V6gh (1995), Lahiri (1996a,b), Mendoza and Uribc (1996), and Edwards and Vdgh (1997). (,9 The function u(.) is assumed to be sta-ictlyincreasing and strictly concave, and goods are assumed to be normal. The household's time endowment is taken to be one. Production is given by 1 - g.

1580

G.A. Calvo and C.A. V~gh

(i.e., a permanent fall in leisure). Hence, the output cycle cannot be rationalized with a separable utility function. Suppose now that the cross-derivative is negative; that is, UcTe(.) < 0. Then it follows from Equations (5.3) and (5.4) that at time T, consumption falls and leisure increases (i.e., work effort decreases). This piece of information, together with Equation (5.5), implies that at time 0 both consumption and labor effort rise. Hence, such a specification of preferences would lead to a boom-bust cycle in both consumption and output. An extension of this simple model - which would generate the boom-recession cycle in output even with separable preferences - is to introduce a costly banking system and assume that firms need bank credit to pay the wage bill [Edwards and V6gh (1997)]. In such a framework, a fall in consumption at time T leads to a fall in demand deposits and, hence, to a reduction in the supply of bank credit. The resulting "credit crunch" leads to higher lending rates, a lower level of bank credit, and a recession. More generally, the idea that the banking system may amplify both booms and busts through changes in bank credit appears quite attractive to explain the issues at hand, from both a theoretical and a quantitative point of view. 5.4~ Fiscal policy

The elimination of large public sector deficits is clearly a necessary condition for a lasting reduction in inflation. It is thus not surprising that programs in which the fiscal adjustment was either absent or short-lived got quickly off track, the best° known examples being the Argentine 1978 tablita and 1985 Austral plan, and the Brazilian 1986 Cruzado plano In successful plans (like the Israeli 1985 plan and the Argentine 1991 Convertibility plan), however, the fiscal adjustment has often been quite important. Such adjustment typically involves some combination of tax increases and cuts in government spending. While this is consistent with the initial fall in public consumption shown in the stabilization time profile (Figure 1, Panel D), the panel regressions reported in column (5) of Table 2 indicate that the coefficient on the "early" dummy is not significant. Still, there is an important branch of the literature which has focused on the expansionary effects of the fiscal policies that often accompany major exchange-ratebased stabilizations. In Helpman and Razin (1987), the reduction in the inflation tax generates a wealth effect due to the lack of Ricardian equivalence. In Drazen and Helpman (1988), the wealth effect comes through the expectation of a future reduction in government spending. Rebelo (1997) considers a scenario in which, in the absence of reforms, government expenditure increases, thus raising the present value of the resources needed to finance that spending. By bringing the fiscal situation in order, a stabilization leads to a wealth effect that may produce a boom even though taxes increase in the short run 7°. 70 See also Giavazzi aald Pagano (1990) and Bertola and Drazen (1993), who analyze the possibly expansionary role of fiscal policy in the stabilizations of Denmark in 1982 and Ireland in 1987.

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

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Rebelo and V6gh (1995) examine the effects of reductions in public consumption and increases in taxes in a two-sector, general equilibrium model. A fall in government consumption of tradable goods leads to a consumption boom and a real appreciation, but investment falls and the current account improves. A reduction in public consumption of non-tradables leads to a counterthctual real depreciation. Hence, cuts in fiscal expenditures seem to have limited power in explaining the stylized facts of exchange-rate-based stabilization. On the other hand, tax increases are recessionary. Finally, as with supply-side effects, fiscal-based explanations would not be able to generate an eventual recession, unless of course the policy is reversed.

5.5. A n d the w i n n e r is . . .

In the end, we would want to have a sense of whether a "winner" emerges among all the competing theories aimed at explaining the empirical regularities associated with exchange-rate-based stabilization which have been examined in the last two sections. To focus on essentials, the above models have abstracted from features which, while "realistic", would have diverted attention away from the key channels. While this is the logical route to follow, it makes a comparison across models difficult since not all channels are operating simultaneously. To remedy this, Rebelo and V6gh (1995) have evaluated, both qualitatively and quantitatively, all the hypotheses examined in the last two sections (except for the one related to durable goods) in a single, two-sector model with a labor-leisure choice and capital accumulation. They conclude that, qualitatively, the only two hypotheses that may explain a boom-recession cycle are lack of credibility and price or wage stickiness (inflation inertia). (In their model, an initial wealth effect stemming from supply-side etfects helps the inflation-inertia hypothesis in generating an initial consumption boom.) This is, of course, consistent with the evaluation that follows from the simpler models analyzed above. Quantitatively, however, Rebelo and V6gh (1995) find that supply-side effects seem critical to account for any sizeable fraction of the observed outcomes. Still, baseline parametrizations fall short of explaining the observed consumption booms and real appreciations. While there are configurations of the technology that are consistent with the data, there is still little information to assess whether these configurations are empirically plausible. Hence, further work on the structure of the supply-side and on the differential response of the tradable and non-tradable goods sector - which would allow us to build more refined quantitative models - would be particularly usefuk Finally, it is worth stressing the importance of disentangling the effects of stabilization from other reforms. The reason is that we may be asking models to explain "too much" in quantitative terms. In other words, the poor quantitative performance of a broad class of models found by Rebelo and V6gh (1995) may be due not to a lack of "good" models but rather to the fact that we may be trying to explain all of the observed consumption booms and real appreciation as a result of exchange-rate-based stabilizations.

G.A. Calvo and C.A. Vdgh

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6. Money-based stabilization The use of a money anchor to bring down chronic inflation has been much less common than the use of an exchange-rate anchor. Available evidence, however, suggests that these stabilizations have led to an initial recession, higher real interest rates, and real exchange rate appreciation (Section 3). As discussed earlier, the monetary regimes prevailing in these plans have borne little resemblance to the textbook case of a "pure" money anchor (i.e., a clean floating exchange rate), and have ranged from dirty floating to dual exchange rate systems (with a pegged commercial rate). Nonetheless, a common feature of such regimes is that money has been, albeit to varying degrees, the predominant nominal anchor. Therefore, to fix ideas, we will focus on the textbook case of a pure money anchor. We will then argue that, qualitatively, deviations from this benchmark would not alter the basic results.

6.1. A simple model From an analytical point of view, the two key elements needed to reproduce the stylized facts illustrated in Section 3 are (i) an interest-rate elastic money demand and (ii) sticky prices. We will introduce these two critical elements in the simplest possible way 71. We generate an interest-rate elastic money demand by introducing money in the utility function. We will therefore keep the utility function postulated in Equation (4.1), but assume that it takes a log-specification72: /o ~ [log(etT) + log(c~) + log(mt)] exp(-/3t) dt.

(6.1)

The household maximizes Equation (6. l) subject to (4.2). The first-order conditions imply that (again, assuming that fi = r)

c~ = etc~, 1

-

~.i,,

(6.2)

(6.3)

mt

where 2~ is the Lagrangean multiplier associated with lifetime constraint (4.2). On the supply side, we follow Calvo's (1983) staggered-prices formulation a continuous-time version of the overlapping-contracts models A la Fischer (1977) and Taylor (1979, 1980) - whereby the price level is sticky (i.e., it is a predetermined 71 In the absence of sticky prices, there would be no difference between money-based and exchange rate-based stabilization. The reason is that, under money-based stabilization, the real money supply could change at any point in time fllrough changes in the price level. 72 This model is a simplified version of Calvo and V6gh (1994c). See also Dornbusch (t980) and Fischer (1986a, 1988).

Ch. 24: Inflation Stabilization and BOP Crises"in Developing Countries

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variable at each instant in time), output o f home goods is demand-determined, and the rate of change in inflation is a negative function of excess aggregate demand: _

2c, - - i f (

CN

t -Y

-N

),

~ > 0.

(6.4)

Equation (6.4) can be derived by assuming that finns set prices in a non-synchronous manner taking into account the future path o f aggregate demand and the average price level prevailing in the economy [see Calvo (1983)]. At any point in time, only a small subset of firms can change their price. The price level is therefore a predetermined variable. If excess demand develops at some point in time, a small subset of firms will change their price and inflation rises. The subset o f firms that will change their price diminishes over time, which implies that inflation o f home goods falls over time. Hence, the change in the rate of inflation is negatively related to excess demand in the non-traded goods sector 73. As in the previous section, the interest parity condition implies that it = r + ft. Output of non-tradable goods is demand determined so that c N = yN for all t. The resource constraint continues to be given by Equation (4.4). To solve the model, we proceed in two stages, in the first stage, we show that the path of real money balances, mt (= Mt/EtPT*), is governed by an unstable differential equation. Note that - # , - et,

(6.5)

mt

where/~t(--- ~lJMt) denotes the rate of growth of the money supply, which is the policy instrument in a money-based stabilization. Substituting into Equation (6.5) the interest parity condition and first-order condition (6.3), we have that rht

1 - ~t + r - =--.

mt

(6.6)

,~,mt

Around the steady state, Equation (6.6) is an unstable differential equation 74. Hence, following an unanticipated and permanent reduction in/~t, mt adjusts instantaneously to its higher steady-state value. Hence, from Equation (6.3), it and thus ~t also adjust instantaneously to their lower steady-state values. 73 Note that in this formulation, the price level of home goods (,oN) is sticky (i.e., it is a predermined variable) but the inflation rate of non-tradable goods (~) is fully flexible (i.e., it is a forward-looking variable). It is also worth stressing that the formulation embedded in Equation (6.4) is not inconsistent with the one postulated in (4.8), where the level of the inflation rate of home goods depends positively on excess aggregate demand. The reason is that, in equilibrium, the staggered-prices formulation given by Equation (6.4) may still generate a Phillips-curve relation in which inflation is above its steady-state value when excess aggregate demand develops. 74 Notice that, as before, ~ is invariant to changes in ~t~.

t584

G.A. Cairo and C.A. V~gh

fi:=O !I

I

I ii

~H,I

A /

B/

gL

/

//

/

./ fi=O

/C

L

V

nss

n

Fig. 9. Money-based stabilization: dynamic system. Intuitively, if et fell on impact below ~t~, then mt would be increasing over time, which necessitates of a lower i (and lower e) to equilibrate the money market, which further increases mr, and so on. Thus, for mf not to diverge, the rate of depreciation, and thus the nominal interest rate, must adjust instantaneously. In the second stage, we form a dynamic system in real money balances in terms of home goods and the rate of inflation. To that effect, let us define real money balances in terms o f home goods; that is, nt = M / P N. Then, ht

- ~t, - st,.

(6.7)

/'/t

The second dynamic equation follows fiom Equation (6.4), taking into account Equation (6.2) and the fact that, from the definition o f mr and nz, et = nt/mt: ~, = ~@N _ n , c ] ) . mt

(6.8)

Equations (6.7) and (6.8) constitute a system o f differential equations in n and Jc, for given c T, m¢, and the policy variable gt. Around the steady state, the system is saddlepath stable, as it should be since n is the only predetermined variable (Figure 9 depicts the corresponding phase diagram)75. J5 Thc deteirninant associated with the linear approximation aroand the steady state is -~nssC~s/mss < O, which indicates that there is one positive and one negative root.

Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries

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Suppose that initially (i.e., for t < 0), the public expects the rate of money growth to remain constant forever at #H. This initial steady state is characterized by C~lss = rko +yT, cN = •N, ess

-

fiN rko + yT '

(6.9) (6.10) (6.11)

&~ = /~n,

(6.12)

iss = r + #n, ~N nss r + #H'

(6.13)

d = F~ rss

(6.15)

(6.14)

where, as before, the domestic real interest rate, r °, is defined as i - ar. In terms of Figure 9, the initial steady state is at point A. Suppose now that, at time 0, policymakers announce a permanent and unanticipated reduction in the money growth rate from b~u to #L. The new steady state becomes point B where real money balances in terms of home goods are higher and inflation is lower. On impact, the system jumps from point A to point C and then travels along the saddle path towards its new steady state, point B. The path of the main variables is illustrated in Figure 10. Real money balances (in terms of home goods) increase gradually over time (Panel B). On impact, inflation falls below its new steady-state value and then increases over time (Panel C). The path of the real exchange rate (Panel E) follows from the fact that ~t/e~ = et - &. The real exchange rate must fall (i.e., appreciate) on impact to allow for a subsequent real exchange rate depreciation. The initial fall in the real exchange rate is effected through a fall in the nominal exchange rate, given that the price level of home goods is a predetermined variable. The path of consumption of home goods (Panel D) can be derived from Equation (6.2) and the path of the real exchange rate. Since consumption of traded goods does not change - and continues to be equal to permanent income of traded goods - consumption of home goods falls on impact as the relative price of home goods (i.e., the inverse of the real exchange rate) increases. It then increases as home goods become cheaper over time. The path of the domestic real interest rate (Panel F) follows from the definition r d = it - art. The domestic real interest rate increases on impact - as the inflation rate of home goods falls below the nominal interest rate - and then falls towards its unchanged steady state. What is the driving force behind these results? It is best to think about the equilibrium condition in the money market, which is given by: nl -

(6.16) it We think of the left-hand side of Equation (6.16) as the real money supply in terms of non-tradable goods and of the right-hand side as real money demand. Upon the

1586

G.A. Caluo and C.A. V@h B. Real money balances

A. Rate of monetary growth n

! /

/-

/

rlss

O

/~!

time

0

time

D. Consumption of home goods

C. Inflation rate cN~ ~N

g H

j_-

//

//

/

[ 0

time

0

E. Real exchange rate

time

F. Domestic real interest rate

e

ess' ,

f--

j_--

_-- . . . . . r

O

time

- - 4

--

O

7:~:

=

time

Fig. 10. Money-basedstabilization: time paths.

announcement of a lower rate of money growth, expected inflation and thus the nominat interest rate fall. For a given c N this increases real money demand in terms of home goods. Real money supply, n( = M/PN), however, cannot change on impact because neither Mt (a policy variable) nor pN (a predetermined variable) change. Hence, the fall in the nominal interest rate generates an incipient excess demand for real money balances. To equilibrate the money market, consumption of home goods (and thus output) needs to fall. For consumption of home goods to fall, home goods must become more expensive (i.e., the real exchange rate must fall). Since consumption of home goods must return to its initial steady-state, the domestic real interest rate must increase to induce a rising path of consumption of home goods.

Ch. 24.. Inflation Stabilization and BOP Crises in Developing Countries'

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This simple model thus reproduces the main stylized facts associated with moneybased stabilization illustrated in Section 3: an initial recession, a real exchange rate appreciation, and higher domestic real interest rates. The model does not exhibit, however, inflation persistence. To generate that result, we would need to introduce either inflation inertia or lack of credibility, along the lines of Section 4 [see Calvo and V6gh (1994c)]. The model also predicts no change in the trade and current account balances. As a first approximation, unchanged external accounts are not really at odds with the facts, as argued in Section 3. To generate an alternative prediction, we would need to get rid of the separability between c N and c T, which would considerably complicate the solution method because the system would cease to be block-recursive. 6.2. Extensions to other money-based regimes

Would the basic results change if we deviated from the extreme case of a pure money anchor (i.e., a clean floating)? The answer is no. Consider first a dirty floating, whereby the monetary authorities intervene in foreign exchange markets to influence the nominal exchange rate. In the example just analyzed, policymakers might want, on impact, to buy foreign exchange (i.e., accumulate international reserves) in exchange for domestic money to prevent the nominal exchange rate from appreciating too much. In terms of the model, the effects of intervention could be captured in a very simple way by assuming that, on impact, policymakers increase the nominal money supply so as to prevent the nominal exchange rate - and thus the real exchange rate - from appreciating (while still reducing the rate of growth to /~L)76. Since m(= M / E P r*) jumps immediately to its higher steady-state value, it follows that a higher M0 implies a higher E0 (relative to the case in which the nominal money supply is not changed on impact). In other words, the larger the initial increase in the level of the money supply, the smaller the initial nominal and real appreciation. In terms of Figure 9, this implies that, depending on how much the money supply increases, the system would jump on impact to a point along the saddle path between points C and B and then proceed towards point B. Qualitatively speaking, then, the impact efI~cts would be the same. Quantitatively, the initial real appreciation and thus the initial recession would be lessened. An extreme case of the "intervention" policy just described is a situation in which the initial level of the money supply is increased as much as needed for tile nominal exchange rate not to change on impact. In this case, the system would jump immediately to its new steady state (Point B in Figure 9). Neither the nominal nor the real exchange rate would change and the initial recession would be avoided altogether. This case is typically ruled out as implausible on the basis that, in practice, a large initial increase in the stock of money would likely be interpreted as an increase in the rate of growth of money, which would severely affect the credibility of the whole '16 Of course, this is not, strictly speaking, intervention since there is no accmnulation of reserves (I.e.. money is introduced through a "helicopter" drop).

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G.A. Caloo and C.A. FOgh

program. Still, it helps rationalizing the monetary authorities' incentives to intervene in foreign exchange markets. From a theoretical point of view, if policymakers can manipulate at will the initial money stock, then to generate a recession it would be necessary to introduce inflation inertia, along the lines analyzed in Section 3. Consider now the case in which there are capital controls. From a monetary point o f view, capital controls give policymakers the ability to have further control over the money supply (if they did not have it to begin with). In the case of a floating rate (or dirty floating), then it should make little difference. In fact, adding capital controls to the model above - by, say, assuming that the private sector's stock of net foreign assets is given and cannot change - would not change anything since the restriction would not be binding (recall that the current account is zero throughout the adjustment). Mixed regimes - such as dual exchange rates with a predetermined commercial rate - should also lead to an initial recession 77. The key is that the initial nominal money supply will still be a policy instrument (unlike a predetermined exchange rate regime in which the initial nominal money supply adjusts endogenously to satisfy real money demand). Hence, any disinflationary policy which leads to a reduction in expected inflation and thus to an increase in real money demand - will lead to a "liquidity crunch" and an initial recession. In sum, the effects o f disinflation in any monetary regime which involves significant capital controls should be qualitatively similar to those of a textbook money-based stabilization 78. 6.3. Money anchor versus exchange-rate anchor

As noted earlier, a money anchor is much less common than an exchange-rate anchor in stabilization programs in chronic-inflation countries. Although far from being a panacea for stopping inflation, policymakers' revealed preference for an exchange-rate anchor may be rationalized on a number of grounds. First, the behavior o f money velocity may be quite difficult to predict in the transition from high to low inflation, especially in chronic-inflation countries where the distinction between monies and quasi-monies is particularly blurred. Therefore, as a practical matter, it may be quite difficult to gauge how "tight" a given monetary rule is likely to be, and whether a "stable" relationship will hold in the aftermath o f disinflation. In contrast, using the exchange rate has the intrinsic advantage tha~, given the endogeneity o f the money supply, there is no need in principle to have any infolmation about money demand and velocity. 77 Models of dual exchange rates using tile samc type of framework emphasized thIoughout this chapter may be found in Obstfeld (1986a), Guidotti and V6gh (1992), and Calvo, Reinhart and V6gh (1995). 78 As noted in Section 3, there may be regimes with a clean floating which do not necessarily have a monetary aggregate as the main nominal mlchor [see Masson, Savastano and Sharma (1997) for a taxonomy of monetary regimes]. These regimes, however, have been rare in major stabilization programs. Still, V~gh (1997) shows an example in which nominal and real interest rate rules are equivalent to a money-based reghne.

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A second, and related, issue is that prolonged periods of high inflation lead to a high degree of dollarization of the economy 79. In such a situation, the "relevant" money supply (i.e., the one which affects inflation and real activity) is likely to include (the domestic-currency value of) foreign currency holdings and deposits. Since this component cannot be controlled by policymakers, a reduction in the domestic component of the money supply may have little effect on total liquidity, and, hence, on inflation. In effect, policy simulations of money-based disinflation for the case of Uruguay [Hoffmaister and V6gh (1996)] suggest that reducing the rate of growth of either M1 or M2 (which do not include foreign currency deposits) results in an extremely slow disinflation compared to using the exchange rate. In sharp contrast, if policymakers c o u l d (which, of course, they cannot) control M3 (M2 plus foreign currency deposits), then the speed of disinflation would be roughly the same as that achieved with an exchange-rate anchor. A third issue is that, by the simple virtue of being a price rather than a quantity, the exchange rate provides a much clearer signal to the public of the govermnent's intentions and actual actions than a money supply target. Thus, if the public's inflationary expectations are influenced to a large extent by the ability to easily track and continuously monitor the nominal anchor, the exchange rate has a natural advantage. Based on the considerations just discussed, it should not come as a surprise that, by and far, disinflation programs in chronic-inflation countries have relied on the exchange rate as the main nominal anchor (with the August 1990 Peruvian program being the most notable exception). Revealed preferences, therefore, would seem to support the view - with which we would certainly agree - that the exchange rate should be viewed as the more suitable nominal anchor in chronic-inflation countries. This is also consistent with Uribe's (1994) findings on the welfare costs of money-based versus exchange-rate-based stabilization. By performing different simulations of Calvo and V6gh's (1994c) model, he argues that exchange-rate-based stabilization is generally less costly, in terms of welfare, than money-based stabilization. An important caveat against the use of an exchange-rate anchor is in situations of very little credibility. For instance, in a countW in which a series of failed exchangerate-based stabilizations has led the public to identify the initial boom and current account deficit as a signal of an unsustainable stabilization effort, it would probably be wise to try to switch strategies and opt for a money anchor. The main reason is that theory suggests [see Calvo and V~gh (1994c)] that the effects of imperfect credibility differ drastically under each regime: lack of credibility is more disruptive under an exchange-rate anchor because it reduces the benefits (inflation falls by less) at the same time that it increases the size of the real dislocations (the boom-bust cycle becomes more pronounced). In contrast, in money-based stabilization, lack of credibility reduces

"19 See Calvo and V6gh (1992) and Savastano(1996).

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G.A. Calvo and C.A. V~gh

both the benefits (in terms of lower inflation) but also the initial recession. Hence, if the public is perceived as being highly skeptical, a money anchor may be less risky 8°.

7. Balance-of-payments crises As argued in Section 3, most exchange-rate-based stabilization programs end in balance-of-payments (BOP) crises (recall Table 1). These programs typically unleash dynamics - consumption booms, sustained real appreciation, current account deficits which call into question their sustainability 81. This, in turn, fuels speculation o f a possible abandonment o f the exchange-rate anchor. Once the survival of the program has been called into question, financial factors - such as a large stock o f shortterm debt - often aggravate the situation and may induce self-fulfilling crises. Whether balance-of-payment crises are ultimately caused by worsening fundamentals or self-fulfilling elements is a matter o f ongoing debate 82. But even if the ultimate demise o f the peg responds to some self-fulfilling event, it is still the case that fundamentals go a long way in determining the potential vulnerability of the system [Obstfeld and Rogoff (1995)]. Naturally, the potential for balance-of-payments crises is a more general issue and applies to any pegged exchange rate system, whether the peg is part of an explicit fifflation stabilization program or not (as most recently exemplified by the South East Asian crises of the second half o f 1997). However, even when the peg was not instituted as part o f a program, crises tend to occur as the economy enters a recession, following a prolonged boom in economic activity, credit expansions, real exchange rate appreciation, and current account deficits [Kaminsky and Reinhart (1995)] ~3. These are, of course, essentially the same dynamics as those generated by exchange-rate-based stabilizations (recall Figures 1 and 2). We suspect this is no coincidence, since it may be argued that pegged exchange rates keep inflation down (mainly by linking inflation of tradable goods to world inflation) at the expense o f an appreciating currency. We would thus suspect that some of the mechanisms discussed in Sections 4 and 5 may help in explaining the dynamics leading to balance-of-payment crises in general. This area has enjoyed a renaissance o f sorts in the aftermath o f the Mexican crisis. Researchers have gone back to gh'ugman's (1979) seminal paper on the mechanics of balance-of-payments crises and refined it in several important ways. Hence, after a brief discussion o f liquidity considerations, we take Krugwnan's (1979) model as the starting 80 Another argLmlent for a money anchor is given in Tornell and Velasco (1995), who ague thai a money anchor might provide more fiscal discipline. 81 Naturally, a fiscal disequilibrium will only reinforce the sense of tmsustainability. 82 See Krugman (1996) and the comments therein by Kehoe and Obstfeld 83 See also Bordo and Schwartz (1996), Dornbusch, Goldfajn and Valdes (1995), Eichengreen, Rose and Wyplosz (1995, 1996), Frankel and Rose (1996), Obstfeld (1995), and Sachs, Tornell and Velasco (1996). For an early analysis of devaluation crises, see Harberger (1981).

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries'

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point o f this section. We then discuss the notion of current account sustainability. Finally, we examine the role o f financial factors and lack o f credibility in precipitating balance-of-payment crises.

7.1. Liquidity Balance-of-payments crises take different forms. A common characteristic is that the government finds itself unable to comply with financial obligations. A n example is when the government is committed to keeping a fixed exchange rate (against, say, the US dollar), and the public wishes to exchange domestic money for dollars in an amount that exceeds the international reserves available for this operation. As a result, the government has to abandon its exchange-rate policy. However, the loss of reserves may occur for other reasons. For instance, reserves may be lost if the country has shortterm liabilities, bonds, that cannot be rolled over in the capital market, and exceed the level o f available international reserves 84. A BOP crisis does not necessarily involve insolvency, i.e., the country's inability to pay. As a general rule, countries undergoing BOP crises have ample resources to meet their financial obligations. In practice, the problem is that the country does not have enough financial assets that can be swiftly activated to meet its financial obligations. Thus, at the core o f a BOP crisis, there is typically a mismatch between the "liquidity" o f financial obligations and that of government financial assets. This mismatch is associated with another dominant characteristic of BOP crises, namely, they take place within a relatively short period of time (normally within a month), a fact that contributes to dramatize the event 85. The word "liquidity" in the above paragraph is just a signpost, not a definition. A good definition o f liquidity is highly elusive. We will discuss the concept in the context of a special environment. Let p(t, v) be the output price o f a given asset at time t, if the asset was placed on the market at time v ~< t. We say that the asset is perfectly liquid ifp(t, t) = p(t, v) for all t and v (and all states o f nature). In other words, an asset is perfectly liquid if there is no advantage to the seller in announcing his/her intention to sell in advance o f the actual transaction. Otherwise, ifp(t, t) < p(t, v), we say that the asset displays some illiquidity. The asset's degree of liquidity could be measured by

~(t, v)

p(t, t) p(t, v)"

Some simple models assume only two types o f assets, namely (i) perfectly liquid assets, and (ii) assets for which g(t, v) = 0 for all v < t; that is, assets that would have no 84 This was a key ingredient in the December 1994 balance of payments crisis in Mexico. See, for instance, Sachs, Tornell and Vetasco (1995) and Calvo and Mendoza (1996). ~5 This should not be interpreted to mean thai the ftmdamental reasons behind a balance of payments crisis are so short-lived - just the symptoms are.

G.A. Calvo and C.A. V~gh

1592

market value if they had to be liquidated in no time's notice 86. In this case, a BOP crisis would take place if the liabilities that the government is called upon to service at time t exceed the stock of liquid assets. In the models to be discussed here the liquidity properties of an asset are postulated, not explained.

7.2. The Krugman model This is an elegant model that captures the essential features mentioned above. We will present a version along the lines of the utility-based models used in previous sections of this chapter [see, for example, Calvo (1987) and Obstfeld (1986b)]. For present purposes, it is enough to assume that all goods are fully tradable, and that the representative individual is endowed with a constant flow of tradable goods per unit of time. Hence, using the same notation, lifetime utility is given by j0 °~ Iv(c/) + z(mt)] exp(-[Jt) dt.

(7.1)

As in Section 4, let the country be fully integrated in goods and capital markets and thus face a constant international price of the tradable good and a constant world real interest rate, r, which equals the subjective discount rate. The consumer's intertemporal budget constraint is thus given by Equation (4.2) (abstracting from the terms that relate to non-traded goods). The first-order conditions are therefore (4.5) and (4.7). Therefore, as before, Equation (4.5) implies that, along a perfect foresight equilibrium path, consumption is constant. The exchange rate is assumed to be fixed if there are enough reserves to sustain the value of the domestic currency (i.e., if reserves are above or at their "critical" level, which we assume to be zero). The exchange rate is sustained by intervening in the foreign exchange market. Thus, the fixed rate is abandoned once the public wants to turn domestic into foreign currency in an amount that exceeds the stock of liquid assets set aside for this operation. In Krugman (1979), these assets are identified with (international) reserves, R. While the fixed exchange rate regime lasts, perfect capital mobility implies that the domestic nominal interest rate equals the international one; that is, it = r. After the fixed rate is abandoned, the exchange rate is allowed to float, and exchange rate intervention is stopped. Hence, again denoting by et the rate of devaluation/inflation, perfect capital mobility implies that it = r + et. We assume that the central bank transfers net profits to the fiscal budget, which implies that the central bank's capital is constant. Hence, from the central bank's balance sheet, it follows that

X/It - E t k t + NbA~, 86 Lucas's (1990) cash-in-advancemodel has this characteristic.

(7.2)

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

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where M is high-powered money, E is the nominal exchange rate (i.e., the price o f foreign exchange in terms o f domestic currency), R denotes reserves denominated in foreign exchange, and NDA stands for net domestic assets (i.e., domestic credit)87. The government's only source of expenditures are lump-sump transfers to households. It finances an exogenously given level of transfers, r, with central bank credit and proceeds from international reserves (which we assume earn the international interest rate, r). Thus, (7.3)

E t T = N b A I + rE~Rt.

Since during the fixed-rate period, it = r and hence, by Equation (4.7), the demand for money is constant (implying 3)/t = 0), we have: Rt = - ( r - rRt).

(7.4)

In other words, under fixed exchange rates the loss of international reserves equals the budget deficit (given by government transfers minus interest revenues from international reserves) 8s After fixed rates are abandoned, Rt = Rt - 0, and hence, by Equations (7.2) and (7.3), hh + elmt = T.

(7.5)

Assuming, for simplicity, that the individual initially holds no foreign assets or liabilities, it follows from first-order condition (4.5) and the lifetime constraint that crt = f r o + yT for all t. Hence, combining first-order conditions (4.5) and (4.7) and solving for mr, we get the familiar demand-for-money expression: mi - L(i, rRo +yT),

Li < 0,

Lrt~0+yv> 0.

For simplicity, we will tbcus on steady states (i.e., rh~ (7.5) and (7.6), we have that eL(r ~ e, f r o + S )

= r.

(7.6) 0). Thus, by Equations

(7,7)

The left-hand side of Equation (7.7) corresponds to revenue from the creation of money at steady state, while the right-hand side is the amount to be financed by these means. Clearly, Equation (7.7) will in general display multiple equilibria because the demand for money is negatively sloped with respect to e. However, since equilibrium 87 Equation (7.2) implicitly assLmaes with no loss of generality that the central bank does not monetize nominal capital gains on international reserves. Typically the central bank creates a fictitious non-monetary liability instead. ~8 It is assumed that the initial fiscal deficit is positive; i.e., r -- rRo > O.

G.A. Caluo and C.A. Vdgh

1594 IR R

AIR

i

0

\

T T* time

Fig. 11. Krugmat~ crisis.

multiplicity is not a key theme in Krugman (1979), we will assume that the economy settles down on the lowest rate o f devaluation consistent with Equation (7.7), which will be indicated by e*. Clearly, if r > 0, then after the currency peg is abandoned, the economy jumps to a higher inflation plateau, and stays there forever. It follows from expression (7.6) that at "switch point," i.e., the point in time T at which the currency peg is abandoned, the demandJbr money" collapses. This is a key feature of the model. Figure 11 depicts the central characteristics o f an equilibrium path for international reserves assuming that the government runs a fiscal deficit (i.e., ~ - r R o > 0) and that the nominal exchange rate is a continuous function o f time (this assumption will be rationalized later). From 0 to T reserves are driven by Equation (7.4). The system is abandoned at time T - and not when reserves reach zero because, as pointed out above, at switch time the demand for money takes a sudden dip equal to L(r, rRo + S ) - L ( r + e, fro + S ) = AR. Since the exchange rate is assumed not to jump at time T, it follows that the government suffers a loss of reserves equal to AR at time T. Clearly, switch point T is uniquely determined. Thus, the model is able to capture some of the main characteristics of a BOP crises outlined above. To close we will now briefly discuss the continuity of the exchange rate path E. In the first place, we will constrain E to be piece-wise continuous and everywhere righthand differentiable. These are technical assumptions which help to make sure that the problem is well-defined in a mathematical sense, and that irrelevant nonuniqueness situations are ruled out. Notice that jumps in E are not ruled out. Suppose that, contrary to our assumption above, E jumps at t ~> T, and let M[ be the left liminf of M at t. I f M t > 0, then the representative individual suffers a capital loss on account of his/her money holdings at time t. Thus, assuming that the demand for money goes to zero as the nominal interest rate diverges to plus infinity, a plausible regularity condition, it follows that it will never be optimal to undergo that kind of capital loss, which implies that M S = 0. Thus, if t > T, there will be an excess supply o f money at t, which is inconsistent with equilibrium. Suppose now that t = T, and,

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1595

hence, the jump takes place exactly at switch point. Since M t- = 0, then the BOP crisis would have occurred before time T, which is a contradiction. This proves that E is continuous everywhere as assumed above. Finally, it is worth stressing that, since the interest rate on international reserves is equal to the international interest rate, the current account will be zero at all times. Notice, however, that external balance equilibrium does not prevent the occurrence of a BOP crisis. This is worth keeping in mind when we discuss the current account approach below. 7.3.

Krugman model: critique and extensions

We now extend the above model in several useful directions. 7.3.1. Bonds

Domestic debt (outside the central bank) may be introduced and thus account for an element that has played a prominent role recently. Thus, Equation (7.3) would become: E~r - N b A t + rEiRt - itD~ + L)t,

(7.8)

where D stands for instant-maturity government debt outside the central bank (in nominal terms). Actually, bond issuance could completely finance the deficit and, thus, NDAt = 0. Under those circumstances, no reserves would be lost during the fixed rates period. However, domestic debt D would increase without bound and, at some point, no more debt could be placed in the market becanse, otherwise, the government would not satisfy its intertemporal budget constraint. This is an interesting example because it is not unusual for governments to try to mask the fiscal disequilibrium in this manner. International reserves, which are closely watched by the private sector, would in this fashion be insulated from fiscal disequilibrium (prior to the BOP crisis). 7.3.2. Sterilization

The Krugman model assumes that the mo~etary authority makes no attempt at sterilizing the effects of reserve accumulation. Money supply is not a target. Thus, the model assumes that at switch time the monetary authority will not interfere with the run against domestic money and allow money supply to fall. In practice, money is not simply cash but includes bank deposits. Therefore, a fall in the money stock is normally associated with a cut in bank credit. This is a cause of trouble especially if the event is not fully anticipated 89. Of course, if bank credit is easily substitutable ~9 Under perfect foresight, everybody knows the exact timing of the BOP crisis. However, the model is easily and realistically extended to the case in which, say, the demand for money has a stochastic component and hence, there is always an element of surprise in the timing of the crisis [see Flood and Garber (1984)].

1596

G.A. Caluo and C.A. VOgh

for other type of credit, the bank credit crunch would cause no major disruption. But in LDCs this is not the case. Consequently, the central bank is induced to intervene through open market operations to provide the bank credit that would disappear as a result of the collapse in money demand at switch time. Flood, Garber and Kramer (1996) argue that there are several important instances in which central banks have attempted to fully sterilize the collapse in money demand. Interestingly, they show that this policy, if anticipated, would lead to a BOP crisis happening immediately, i.e., at time 0. There would be no fixed exchange rate period like the interval [0, T) in the Krugman model. The proof is straightforward. For money to remain constant (i.e., full sterilization) at time T, after-crisis inflation should equal inflation before crisis (which is zero). But this would imply that there is no crisis mid the exchange rate is constant forever. However, Equation (7.4) implies that sooner or later international reserves will be driven down to zero, and a crisis will take place, a contradiction. Thus, the only possibility left is for the crisis to take place at t - 0. In other words, the fixed-exchange-rate regime collapses upon the announcement. To have a more vivid picture of this instantaneous crisis, let us assume that at the time of the announcement real monetary balances fall short of total reserves (implying that an attack against domestic currency cannot be successful unless it triggers an expansion of domestic credit). The government's announcement is followed by an immediate attack on the domestic currency. Since authorities try to stabilize the stock of money, they intervene increasing domestic credit. Given that the demand for money has collapsed, the additional liquidity infusion only results in a loss of international reserves. This will continue until reserves are depleted. At that point authorities lose control of the exchange rate. Since there are no reserves, the exchange rate is the adjustment variable. Hence, the currency will devalue (the price level will rise) until real monetary balances are consistent with the equilibrium expected rate of devaluation/inflation. Anticipated sterilization although inconsistent with fixed rates under the above assumptions could, however, be sustained under other set of plausible assumptions. F'ood, Garber and Kramer (1996) and Kumhof (1997) show that fixed-rates-cumsterilization is consistent with a situation in which government bonds are imperfect substitute with international bonds. Calvo (1996b) shows that the same holds if it is costly to move in and out of money. 7.3.3. Interest rate policy

Another important aspect of reality which is not captured in Krugman's (1979) model is the possibility of the central bank actively defending the currency by raising shortterm interest rates. Sweden, for instance, raised short-term interest rates to around 500 percent per year in September 1992 to stave off a speculative attack [see, for instance, l~ugman (1996)]. More recently, both Hong Kong and Brazil sharply raised interest rates to defend their currencies in the aftermath of the South East Asian currency crisis. While not always successful, higher interest rates often buy time for

Ch. 24: inflation Stabilization and BOP Crises in Deoeloping Countries

1597

the government to try to uphold the system's credibility by adopting more fundamental measures. Lahiri and V6gh (1997) model interest rate policy by assuming that the government controls the interest rate on highly liquid government debt - along the lines of Calvo and V6gh (1995) - and show that by announcing a policy of higher interest rates in the event o f a crisis, the crisis may be postponed until international reserves actually reach zero (i.e., at a point like T* in Figure 11). At that point, the central bank is forced to float but there is no run (i.e., the money supply remains constant). This result of "crisis with no run" might also explain situations in which centTal banks abandon a peg with no dramatic loss of international reserves. 7.4. The current account approach

This approach has become popular after Mexico's 1994 BOP crisis since some observers have claimed that the crisis originated in the fact that Mexico was spending "beyond its means". In other words, Mexico's current account deficit was "too large." (It is worth recalling that in Krugman's model a BOP crisis could take place even though the current account deficit is nil to the extent that a payments crisis involves a liquidity shortage, irrespective of the country's overall solvency.) More generally and as shown in Section 3 - exchange-rate-based stabilizations typically lead to large current account deficits. Whether or not such imbalances are sustainable is thus a critical question when it comes to evaluate the reasons behind these programs' collapse. The sustainability literature is based on the budget-constraint equation for the conntry as a whole 9o. To illustrate, let us denote b y f and CAD net international debt and current account deficit (both as a share o f GDP), respectively. Then, ]; : CAm,

- 72;,

(7.9)

where t/is the rate o f growth o f output. Sustainability analysis focuses on steady states. Thus, settingj; = 0, the steady-state - sustainable - current account deficit satisfies CADss = r/fs~,

(7.10)

where, as in earlier sections, the subscript "ss" denotes "steady state". This equation establishes a relationship between steady-state debt and current account deficit. In the absence of growth (i.e., r/ = 0), then the sustainable current account deficit is necessarily equal to zero. In contrast, with positive growth a sustainable current accoum deficit is possible. This analysis is unable to give us a definite answer on C~4Dss until we pin down J;s. Recent experience shows that the capital market is reluctant to keep lending to LDCs exhibiting levels o f indebtedness that exceed 80 percent o f GDP [Williamson 90 For an elaboration, see Milesi-Ferretti and Razin (1996)~

G.A. Calvo and C.A. Vdgh

1598

(1993)]. Hence, this additional piece of information allows us to write the sustainability condition (7.10) as follows: CADss <~ 0.8tl.

(7.11)

Thus, a country that can be expected to grow at 4 percent per year cannot sustainably run a current account deficit exceeding 3.2 percent. Since 4 percent growth was, if anything, an upper bound for Mexico, this analysis would conclude that its 8 to 9 percent current account deficits were grossly unsustainable. Notice that CADt = ~ - TSt, where TS denotes the trade surplus (including nonfinancial transfers) as a share of GDR and r f denotes debt service (r is the international rate of interest). Therefore, by Equation (7.10),

Thus, if we again set the growth rate to 4 percent (i.e., rl = 0.04) and, in addition, we assume the international interest rate to be 10 percent per annum (i.e., r = 0.10), then, by Equation (7.12), at the steady state the economy must run a trade balance surplus of 0.06£s as a share of GDR The trade balance surplus increases with the steady-state debt/GDP ratio, fss. In particular, at the upper bound forJ;s (80 percent of GDP) the trade balance surplus would be 4.8 percent of GDP. Presumably, the reason for capital markets to be unwilling to extend credit to LDCs beyond 80 percent of GDP is that it may become tempting for those countries to renege on their debt obligations. Temptation, in turn, is likely to be related to the sacrifice associated with servicing the debt. Gross sacrifice of servicing the debt can be measured by the associated trade balance surplus. The previous computation suggests that the capital market becomes nervous about a cotmtry's willingness to repay when debt service represents only about 5 percent of GDE Notice that the net sacrifice from servicing the debt could be much less once one takes into account international penalties from debt delinquency. Thus, one criticism of current account sustainability computations is that they are highly sensitive to the definition of sustainable debt/GDP ratios. Besides, the above example shows that the implied critical sacrifice levels are low when compared to other capital market transactions. For example, mortgages in the USA are easy for a household to get if total mortgage payments are less than 25 percent of the household's income. Thus, if this ratio were also relevant for countries' debt then, using the above parameters, the critical steady-state debt/GDP ratio would be 4.16 ( = 0 . 2 5 / ( r - r/), where r - ~/ - 0.06). Therefore, recalling Equation (7.10), a country growing at 4 percent per year could run a sustainable current account deficit of more than 16 percent of GDP! Of course, countries are not mere households because they are protected by sovereignty clauses. However, prior to the crisis Mexico had given very clear signals that it wanted to belong to the First World and signed treaties that would have made it very costly to engage in strategic repudiation of international debt (or any debt, for that matter).

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries"

1599

A more fundamental criticism is that steady-state computations could be very misleading for countries that are undergoing deep economic reforms. The current account deficit could in those instances be a temporary phenomenon associated with reform. Once we move away from the steady-state straightjacket, this approach has precious little to say. Finally, the current account approach does not address the BOP-crises issue as such. If the utility function is separable in money and consumption as in expression (7.1), the demand for money would be impervious to solvency issues. Thus, if we further assume that the government runs no fiscal deficit and there is no expansion in domestic credit, then the currency will never be under attack and a BOP crisis will never take place. 7.5. Financial considerations

Financial factors are likely to play a key role in precipitating balance-of-payment crises. We now review several such factors, which we deem particularly relevant. 7.5.1. Volatility o f monetary aggregates"

The Krugman model focuses on fiscal deficits as the key determinant o f reserves losses. However, even in the absence of domestic credit expansion, international reserves in a fixed-exchange-rate regime may rise or fall as a consequence o f fluctuations in the demand for money. This is not a minor consideration for LDCs since some of them exhibit substantially higher fluctuations in their demand for money than advanced industrial countries. To illustrate the significance of these considerations, let us examine the case in which the (log) demand for money follows a random walk and, to abstract from the effects highlighted in Krugman's model, let us assume that the demand for money is totally inelastic with respect to the nominal interest rate, and that there is fiscal balance. To simplify the exposition, we will continue making the assumption that domestic prices equal the nominal exchange rate, which is kept constant unless there is a BOP crisis. Letting m denote the demand for real monetary balances, then we postulate (in discrete time) that log mt~l = logm~ + Lt,

(7.13)

where m stands for real monetary balances and Lt is an i.i.d, random variable. Under these circumstances, the demand for money can fall and create a BOP crisis even though there is no fiscal deficit. If ~t exhibits a mean-zero normal distribution, then the larger its variance, the larger will be the probability of a BOP crisis given an initial level of international reserves. Estimates of Equation (7.13) show Mexico, for instance, with a relatively high standard deviation (about 4 percent per month), while a country like Austria that has successfully pegged to the Deutsche Mark for about 15 years shows a standard deviation which is only about 1 percent per month [see Calvo (1996a)].

1600

G.A. Caluo and C.A. Vdgh

In addition, balance-of-payments problems could be exacerbated by external factors. For example, Calvo and Mendoza (1996) show that there is a significant effect from US short-term interest rates on Mexico's demand for money (specifically, M2). This was reflected in a sizable fall in the demand for money during 1994 and, we suspect, lay at the heart of the Mexican difficulties at the end of the year. Mexico and other Latin American countries experienced sizable capital inflows in the first half of the 1990s. As argued by Calvo, Leiderman and Reinhart (1993), about 50 percent of these flows stem from external factors, among which US interest rates hold a prominent role. Capital inflows gave rise to an expansion in consumption and investment which, in turn, increased monetary aggregates. Thus, the above-mentioned link between domestic monetary aggregates and external rates of interest may stem from direct opportunity-cost or indirect absorption-type considerations. Experience in several countries, and most notably in Mexico, suggests that the fluctuations in monetary aggregates provoked by external factors - and more specifically, by capital flows - could be substantial [see Calvo, Leiderman and Reinhart (1996) and Calvo and Mendoza (1996)]. An equation like (7.13), enhanced by taking explicit account of external factors, would be needed to assess the implication of different reserve levels. To illustrate, consider the simple case in which external factors are fully captured by the random term in Equation (7.13). We proceed as follows. Let u~ = m S R , where R stands for international reserves, and m is interpreted as the monetary base. Hence, a BOP crisis in period t + 1 will take place if ms - mt+l > Rt. Or, equivalently, if log mt+l = ~t~l < log u/ - _1 mr

ut

(7.14)

Clearly, the probability of a BOP crisis is an increasing function of v. Notice that this "vulnerability" index is totally independent of the popular index given by the ratio of reserves to one-month worth of imports. The latter hails back to periods in which reserves were held to ensure smooth trade, while the index developed here is associated with the probability of a BOP crisis as a result of financial fluctuations. In the above example there exists a direct connection between m and R because we assume m stands for base money (i.e., monetary liabilities of the central bank). I f instead m stood for M2, the connection is more indirect and depends on how the central bank reacts to shocks in the larger monetary aggregates. If the central bank is not responsible for banking problems but defends the exchange rate parity by intervening and swapping base money for international reserves, then the same analysis developed above is applicable, except that one would need to derive the demand tbr base money from Equation (7.13) - which would now apply to M2 - minimum reserve requirements, and an equation describing the demand for banks' excess liquidity. In turn, if the central bank is responsible for ensuring adequate banks' liquidity, then the central bank may be led to expand domestic credit whenever M2 falls, h~ the extreme case in which banks are fully insulated from any liquidity loss as a

Ch. 24: Inflation Stabilization and BOP Crises in Deueloping Countries

1601

consequence of a fall in M2, then M2 is equivalent to base money and the above example is fully applicable. It is worth noting, however, that in practice M2 is much larger than money base and, hence, the probability of a BOP crisis, given international reserves, is likely to be even higher (unless the volatility of M2 is substantially lower than that of base money). However, by providing liquidity to offset the fall in M2 the central bank does not prevent M2 from falling. Thus, if a central bank is keen on not letting monetary aggregates fall, then it will increase domestic credit even more and provoke a large loss of reserves after just a small contraction in monetary aggregates. This seems to have been the case in Mexico during 1994. As noted above, Calvo and Mendoza (1996) show that the demand for M2 fell in 1994. Since banks held sizable domestic public debt in their portfolios, rolling back private debt could have been prevented simply by an open market operation that lowered domestic public debt in banks' portfolios by an amount equal to the fall in M2. However, the central bank went beyond that and prior to the crisis succeeded in stabilizing the level of M2. This meant a sizable expansion of banks' credit to the private sector (more than 40 percent from January to December 1994). This is quite remarkable given that these measures were undertaken concurrently with a sizable loss of international reserves. This illustrates how much a central bank may be willing to risk in order to safeguard the financial system. Similar behavior was observed in Thailand and Malaysia during the more recent currency crises in South East Asia. 7.5.2. Short-maturity debt

As pointed om above, the BOP crisis literature has on the whole ignored the role of domestic debt, and followed Krugman (1979) in assuming that fiscal deficits are fully monetized. However, the assumption that fiscal deficits are fully monetized is becoming increasingly unrealistic as governments have started to have access to international capital markets. It has thus become increasingly possible to finance fiscal deficits by floating domestic or international public debt. The maturity structure of this debt varies across countries but it is perhaps fair to say that emerging-markets' governments are likely to exhibit a debt maturity structure slanted towards the short end of the spectrum. Mexico again shows an extreme case in this respect: in December 1994 about US$10 billion of domestic debt was due to mature in January, and about US$30 billion during 1995 (these are large numbers compared to the US$6 billion stock of international reserves held by Mexico prior to the crisis). As argued in Calvo (1998) the demand for emerging markets' assets (including public debt) could be highly volatile for two basic reasons. In the first place, the effective rate of return on these assets depends on policy - like everywhere else but with the added complication that policy in emerging markets is itself highly volatile, reflecting imperfect knowledge of structural parameters and, most importantly~ relatively unstable political equilibria. The instability of the latter has likely increased after the breakdown of communism. Therefore, assessing the "state of nature" in an

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G.A. Cairo and C.A. VOgh

emerging market could be quite costly. It is not enough to know the particulars of the investment project since, in general, its profitability will depend on govertmaent regulations. Thus, a project could be very lucrative and yet be unattractive to foreign investors if, for instance, profits are expected to be subject to high taxes (either directly or through the imposition of, for example, foreign exchange controls). Consequently, assessing the state of nature in a given emerging market is likely to entail large "fixed" costs. The second basic ingredient for high volatility of demand for emerging markets' assets is the so-called "globalization" phenomenon, which is characterized by the fact that investors diversify their portfolios across a large number of emerging markets. Portfolio diversification, in the absence of Tequila or contagion effects, helps to lower portfolio risk. Interestingly, however, the benefit from portfolio diversification does not depend on specific knowledge about the actual state of nature in these economies. For risk hedging, it is enough that the return on the different assets across countries not be perfectly correlated. Thus, for instance, by the law of large numbers, risk could become very low if the different investment projects were stochastically mutually independent. It is intuitive, and can be rigorously shown in a canonical example [Calvo (1998)], that under the above circumstances (i.e., high information costs and globalization), (i) investors will be very sensitive to "news" about expected returns, and (ii) their incentives to learn about the state of nature in each emerging market will eventually decrease as the number of emerging markets rises. Consequently, in a globalized capital market, investment in emerging markets' assets is likely to be highly sensitive to rumors and relatively unresponsive to "fundamentals." The above-mentioned phenomenon poses no direct threat of a BOP crisis to the extent that it only involves fluctuations in stock market prices. However, if a large share of domestic debt is coming due in the short run, adverse changes in investors' sentiments about a given emerging market may cause a BOP crisis, particularly if the exchange rate is held fixed. The only available policy under those circumstances (short of devaluing) is to raise interest rates on newly-issued domestic debt. Unfortunately, since investors are ill-infurmed about fundamentals, the interest-rate hike could possibly be taken as a sign of weakness and not of strength, since they may feel that higher interest rates are due to the "market" being aware of serious difficulties. Furthermore, even if investors were better informed, the bonds-attack could lead to socially costly cr{ses. As an illustration, consider a simple two-period example in which all public debt has one-period maturity and the international riskless interest rate is zero. We assume that debt can be repaid in full, independently of the repayment schedule. However, output is a function of the debt-repayment schedule. Suppose that the economy is controlled by a social planner and is subject to the standard intertemporal budget constraint. Under these circumstances, a social planner will choose the optimal debt-repayment schedule by maximizing the social utility function subject to the budget constraint~ A social optimum is attained if the country can freely choose the share of total debt that will be repaid each period. However, if bond-holders insist on getting fully repaid

Ch. 24." Irtflation Stabilization and BOP Crises in Deoeloping Countries'

1603

in the first period, we assume that the effort to comply with the financial obligation is so counterproductive that output next period would fall to zero. Thus, even though the country is able to fully repay its outstanding debt in period 1, no rescheduling would now be possible because potential investors (rationally) expect output to be zero in period 2. Thus, the existence of large short-term maturity debt may give rise to multiple equilibria, and make the country vulnerable to socially costly bond-attacks [see Calvo (1998) and Cole and Kehoe (1996)]. 7.5.3. D o m e s t i c debt and credibility

In addition, the existence of domestic-currency denominated public debt can generate BOP difficulties if the exchange rate policy is not fully credible. Suppose the government announces a fixed exchange rate but the public believes that the currency will be devalued next period by e times 100 with probability p. Then, if investors are risk neutral (in terms of foreign currency) the nominal interest rate satisfies 1÷

itp + (1 + i,)(1 - p ) = 1 + r,

l+e

(7.15)

where i and r and are the domestic and international one-period interest rates, respectively. Clearly, if e and p are positive numbers, then the domestic interest rate will exceed the international one. This phenomenon is called the "peso problem" and is a common feature of exchange-rate-based stabilization programs. Suppose the government has a fixed debt level d and that, under full credibility (i.e., e = 0), the fiscal deficit is zero (i.e., r - rRt + rd = 0). Assuming, for simplicity, that fiscal deficits are fully monetized, it follows that, if there is an expectation of a devaluation (but the currency is not devalued), the discrete version of Equation (7.4) would be given by Rt+l - Rt = -(72 - rRt + itd),

with the fiscal deficit now being positive since it > r due to the peso problem. Hence, the peso problem may put into motion Krugman's BOP-crisis machinery 91. Thus, lack of credibility may result in an unsustainable balance of payments even though "fundamentals" could be fully in line with a sustainable situation. 7.5.4. Credibility, the d e m a n d f o r money and fiscal deficits

Credibility problems may be reflected through other more subtle, but equally important, phenomena. As argued in Section 3, there is typically a consumption boom in the early stages of an exchange-rate-based stabilization. Therefore, the demand for money ~)l A related scenario is discussed by Guidottl and V6gh (1999). In their model, the Krugman machinery is put into motion by the probability of a devaluation associated with a fiscal consolidation.

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G.A. Calvo and C.A. V~gh

will contain a cyclical component associated with tile stabilization program. Higher monetization at the start of the program may give the impression to policymakers that the program enjoys a high degree of credibility. An argument one commonly hears from policymakers is that higher monetization reflects the return of flight capital due to the higher confidence inspired by the stabilization plan. While this is partially true, policymakers may wrongly conclude that the higher stock of real monetary balances is a permanent positive shock. However, if monetization is provoked by the expectation that the program will be abandoned in the non-too-distant future, then the real stock of money will eventually collapse, possibly generating a BOP crisis. In a recent study, Talvi (1997) shows that if tax revenue is an increasing function of consumption, then prior to crisis the fiscal deficit could shrink, giving the false impression that the fiscal house is in order. In an example, Talvi (1997) shows that the fiscal deficit is nil before tile crisis, only to explode afterwards. This pattern of the fiscal deficit is understandably quite confusing to the average policymaker. It is not unusual for the initial slackening of the fiscal constraint to be read as an indication that tax evasion has fallen and, hence, that the higher fiscal revenue has a significant permanent component. As a result, considerable political pressure is built up for more government spending. Unfortunately, if imperfect credibility is the key reason for the initial consumption boom and policymakers give in to pressures to increase government expenditure, then after-crisis fiscal deficits could reach dangerously high levels - which will become apparent only after a crisis erupts and policymakers have little room to manoeuver.

8o Concluding remarks We have concluded our long journey through the fascinating world of inflation stabilization and balance-of-payment crises in developing countries. After examining the possible rationale behind the existence of chronic inflation in many developing countries, we carried out some simple econometric exercises which support tile existence of two main puzzles in the area of inflation stabilization. First, exchangerate-based stabilization leads to an initial boom in real GDP, private consumption, and durable goods consumption. The recession typically associated with disinflation programs appears only later in the programs. Second, money-based stabilization leads to an early recession, suggesting that the timing of the contraction depends on the nominal anchor which is used (the "recession-now-versus-recession-later" hypothesis). We did not, however, find support for the existence of an investment cycle in exchange-rate-based stabilizations. Nor did we find evidence of a significant fall in public consumption around the time of stabilization. We then reviewed the main theories aimed at explaining these puzzles. We first focused on theories that emphasize expansions in demand: inflation inertia, lack of credibility (temporary policy), and durable goods. The first, inflation inertia, relies oil a fall in real interest rates to generate the initial boom. However, within an optimizing

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framework and in the absence of any wealth effect, this theory would require some implausible parameter configurations to rationalize the initial boom. Also, it would have a hard time explaining the boom in programs in which real interest rates rise on impact. The second, lack of credibility, conforms quite well with the stylized facts. Quantitatively, however, it faces the problems of low intertemporal elasticities of substitution. The third, which relies on the timing of purchases of durable goods, may also reproduce the consumption cycle, lts quantitative relevance has not been evaluated yet. We then turned to explanations that rely on wealth effects. The first emphasizes supply-side responses - both in labor supply and investment - to the removal of the inflation distortion. While these theories can explain the boom, they cannot explain the late recession. In addition, the fact that the investment cycle was not found significant casts some doubts on the relevance of this mechanism. A second source of wealth effects - cuts in government spending - faces a similar problem Quantitatively, however, supply-side effects appear to be a critical component of any story aimed at explaining the empirical regularities associated with exchange-rateo based stabilization. To explain the stylized facts of money-based stabilization, we resorted to an optimizing version of traditional sticky-prices model '~ la Taylor-Fischer. A reduction in the rate of money growth decreases expected inflation and thus the nominal interest rate. This induces an incipient excess demand for real money balances. To restore money-market equilibrium, consumption (and thus output) of home goods needs to fall. This is effected through a real appreciation of the domestic currency. It is worth stressing that sticky prices are essential to this type of model. Without this feature, money-based stabilization would yield the same results as exchange-rate-based stabilization. Hence, a model designed to explain both the stylized facts of exchangerate-based and money-based stabilization - and, in particular, the recession-nowversus-recession-later hypothesis - requires sticky prices and an interest-rate elastic money demand [see Calvo and V6gh (1994c)]. Since most exchange-rate-based stabilizations end in thll-blown balance-of-payment crises - typically accompanied by banking crises - we took a detailed look at both the mechanics and causes of balance-of-payments crises in the final leg of our journey (Section 7). While the starting point of this section was Krugman's (1979) seminal paper on balance-of-payments crises, most of the issues touched upon have come to light after the December 1994 Mexican crisis, and represent very much research in progress. It was argued that simple extensions of Krugman's (1979) model may account for some missing links in the original story: (i) bond-financing may mask the fiscal problems by preventing reserve losses; (ii) imperfect substitutability between domestic and foreign assets opens the door for the central bank to sterilize the effects of reserve losses on money supply; and (iii) an active interest rate policy allows the central bank to postpone the abandonment of the peg and avoid a run in the final stages. We then analyzed the current account approach; that is, the view that large currem account deficits may be unsustainable and lead to balance-of-payments crises. While

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this channel could provide a concrete link between the dynamics of exchange-ratebased stabilizations and their demise, it still has precious little to say outside the steady state. In addition, the mechanics through which a BOP crisis would occur are unclear. Finally, we highlighted the role of financial considerations and credibility as contributing factors in unleashing balance-of-payments crises. Under high information costs and globalization, demand for emerging markets' assets is likely to be highly sensitive to rumors and relatively unresponsive to fundamentals. Changes in investors' sentiments could make it difficult for the government to roll-over a large stock of shortterm debt, leading to a bond-led attack. A large stock of short-term debt may also result in self-fulfilling crises. Lack of credibility in the peg - and thus high nominal interest rates - may also put into motion the Krugman-type machinery in the face of a large stock of domestic debt. Where do we go from here'? In the area of inflation stabilization, much work remains to be done on the empirical regularities of disinflation in chronic inflation countries. Numerous problems need to be addressed, including sample selection and small samples for money-based programs. Small samples for successful exchangerate-based programs also pose a problem since the econometric finding of a late recession is clearly influenced by events in failed programs. A critical aspect in econometric work is to control for other domestic factors, such as trade and structural reforms. Disentangling the effects of stabilization from other reforms is important not only to make sure that the empirical regularities remain such, but also because we may be asking theoretical models to explain "too much", quantitatively speaking. It would also be important to document in a systematic way the behavior of the homegoods sector relative to the traded-goods sector. Some available evidence suggests that the initial boom is much more evident in the home-goods sector. The behavior of investment should also be looked at in more detail. The goal of this research agenda would be to establish how much needs to be explained and then build more refined quantitative models to evaluate the alternative hypotheses, along the lines of Rebelo and V6gh (1995). It is clear that we are still far away from a good understanding of the links between the dynamics of exchange-rate-based stabilizations and their ultimate demise. While Krugman's (1979) model and variations thereof provide a good description of the mechanics of BOP crises, they offer in general little insight into the more fundamental causes of such crises - over and above the obvious implication that a deterioration in the fiscal balance during a program will put into motion Krugman-type dynamics. We feet that the notion of current account sustainability needs substantial refinement before it can offer a consistent and complete account of the facts, but is an area definitely worth pursuing. In this respect, a productive area of research would be to focus on the role of the financial and banking sectors in amplifying the expansionary cycle and possibly contributing to the downturn and eventual crisis. A particularly relevant channel has to do with the real estate market. A sizeable fraction of the lending boom goes to finance real-estate operations [see, for instance, Guerra (1997a)]. These loans are usually made

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using as collateral temporarily high asset prices. In the context o f the temporariness hypothesis, G u e r r a (1997b) shows an example in which the fall in asset prices (i.e., land prices) before the a b a n d o n m e n t o f the p r o g r a m m a y trigger a b a n k i n g crisis. While this does not explain the end o f the program, it does provide a link b e t w e e n the d y n a m i c s o f these p r o g r a m s and b a n k i n g crises.

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Lahiri, A., and C.A. V6gh (1997), "Krugman balance of payments crises: are they for real?", mimeograph (UCLA). Leiderman, L. (1993), Inflation and Disinflation: The Israeli Experiment (University of Chicago Press, Chicago, IL). Lizondo, J.S. (t991), "Real exchange rate targets, nominal exchange rate policies, and inflation", Revista de An~ilisis Econ6mico 6:5-22. Lucas Jr, R.E. (1990), "Liquidity and interest rates", Journal of Economic Theory 50:237-264. Masson, RR., M.A. Savastano and S. Sharma (1997), "The scope for inflation targeting in developing countries" Working Paper 97/130 (International Monetary Fund). Medeiros, C. (1994), "A case of a monetary stabilization program: the Dominican Republic's economic program, 1990-1993", mimeograph (International Monetary Fund). Meltzel, A.H. (1994), "Book review: Heterodox policy and economic stabilization", Journal of Monetary Economics 34:581-600. Mendoza, E., and M. Uribe (1996), "The syndrome of exchange rate-based stabilizations and the uncertain duration of currency pegs", International Finance Discussion Papers No. 548 (Board of Governors of the Federal Reserve System). Milesi-Ferretti, G.-M., and A. Razin (1996), Current-Account Sustainability, Princeton Studies in International Finance No. 81. Modiano, E.M. (1988), "The Cruzado first attempt: the Brazilian stabilization program of February 1986", in: M. Bruno, G. Di Tella, R. Dorubusch and S. Fischer, eds., Inflation Stabilization: The Experience of Israel, Argentina, Brazil, Bolivia, and Mexico (MIT Press, Cambridge, MA) 215~58. Mondino, G., E Sturzenegger and M. Tormnasi (1996), "Recurrent high inflation and stabilization: a dynamic game", International Economic Review 37:981496. Montiel, E, and .l. Ostry (1991), "Macroeconomic implications of real exchange rate targeting in developing countries", IMF Staff Papers 38:872 900. Obstfeld, M. (1985), "The capital inflows problem revisited: a stylized model of Southern-Cone disinflation", Review of Economic Studies 52:605 625. Obstfeld, M. (1986a), "Capital controls, the dual exchange rate and devaluation", Journal of International Economics 20:1-20. Obstfeld, M. (1986b), "Speculative attack and the external constraint in a maximizing model of the balance of payments", Canadian Journal of Economies 19:1-22. Obstfeld, M. (1995), "International currency experience: new lessons and lessons relearned", Brooking Papers on Economic Activity 1:t 19 220. Obstfeld, M., and K. Rogoff (1995), "The mirage of fixed exchange rates", Journal of Economic Perspectives 9:73-96. Okun, A.M. (1978), "Efficient disinflationary policies", American Economic Review, Papers and Proceedings 68:348-352. Ostry, J., and C.M. Reinhart (1992), "Private saving and terms of trade shocks", IMF Staff Papers 39:495-517. Pazos, E (1972), Chronic Inflation in Latin America (Prager Publishers, New York). Phelps, E.S. (1973), "Inflation in the theory of public finance", Swedish Journal of Economics 75:6'7 82. Ramos, J. (1986), Neoconservative Economics in the Southern Cone of Latin America, 1973 1983 (Johns Hopkins University Press, Baltimore, MD). Rebelo, S.T. (1993), "Inflation in fixed exchange rate regimes: the recent Portuguese experience", in: E Tortes and E Giavazzi, eds., Adjustment and Growth in the European Monetary Union (Cambridge University Press, Cambridge) 128 149. Rebelo, S.T. (1997), "What happens when countries peg their exchange rates? (The real side of monetary reforms)", Working Paper No. 6168 (NBER). Rebelo, S.T., and C.A. V6gh (1995), "Real effects of exchange rate-based stabilization: an analysis of competing theories", in: B.S. Bernanke and J.J. Rotemberg, eds., NBER Macroeconomics Annual (MIT Press, Cambridge, MA) 125-174.

Ch. 24:

Inflation Stabilization and BOP Crises" in Deueloping Countries

1613

Reinhart, C.M., and C.A. V6gh (1994), "Inflation stabilization in chronic inflation countries", mimeograph (International Monetary Fund). Reinhart, C.M., and C.A. V6gh (1995a), "Nominal interest rates, consumption booms, and tack of credibility: a quantitative examination", Journal of Development Economics 46:357-378. Reinhart, C.M., and C.A. V~gh (1995b), "Do exchange rate-based stabilizations carry the seeds of their own destruction?", mimeograph (International Monetary Fund). Rodriguez, C.A. (1982), "The Argentine stabilization plan of December 20th", World Development 10:801 811. Rojas-Suarez, L., and S.R. Weisbrod (1995), "Financial fragilities in Latin America: the 1980s and 1990s', Occasional Paper No. 132 (International Monetary Fund). Roldos, J. (1995), "Supply-side effects of disinflation programs", IMF Staff Papers 42:158-183. Roldos, J. (1997), "On gradual disinflation, the real exchange rate, and the current account", Journal of International Money and Finance 16:37 54. Sachs, J., A. Tornell and A. Velasco (1995), "The collapse of the Mexican peso: what have we learned?", Working Paper No. 5142 (NBER). Sachs, J., A. Tornell and A. Velasco (1996), "Financial crises in emerging markets: tile lessons fiom 1995", Working Paper No. 5576 (NI3ER). Sahay, R., and C.A. V~gh (1996), "Inflation and stabilization in transition economies: an analytical interpretation of the evidence", Journal of Policy Reform 1:75-108. Sanguinetti, E (1994), "Intergover~maental transfers and public sector expenditure: a game theoreticapproach", Estudios de Economia (Universidad de Chile) 21:181~ 12. Santaella, J., and A. Vela (1996), "The 1987 Mexican disinflation program: an exchange rate-based stabilization?", Working Paper 96/24 (International Monetary Fund). Sargent, T.J. (1982), "The ends of four big inflations", in: R.E. Hall, ed., Inflation: Causes and Effects (University of Chicago Press, Chicago, IL) 41-97. Savastano, M.A. (1996), "Dollarization in Latin America: recent evidence and policy issues", in: E Mizen and E.J. Pentecost, eds., The Macroeconomics of International Currencies: Theory, Policy and Evidence (Edward Elgar, London) 225 255. Stockman, A. (1981), "Anticipated inflation and the capital stock in a cash-in-advance economy", Journal of Monetary Economics 8:387 393. Talvi, E. (1995), "Fiscal policy and the business cycle associated with exchange rate-based stabilizations: evidence from Uruguay's 1978 and 1991 programs", Working Paper Series 313 (Inter-Americau Development Bank). Talvi, E. (t997), "Exchange rate-based stabilization with endogenous fiscal response", Journal of Development Economics 54:59-75. Taylor, J.B. (1979), "Staggered wage setting in a macro model", American Economic Review, Papers and Proceedings 69:108-113. Taylor, J.B. (1980), "Aggregate dynamics and staggered contracts", Journal of Political Economy 88: 1--23. Taylor, J.B. (1983), "Union wage settlements during a disinflation", American Economic Review '13: 981-993. Tommasi, M., and A. Velasco (1996), "Where are we in the political economy of reform?", Journal of Policy Reform h 187~38. Tornell, A., and A. Velasco (1995), "Fixed versus flexible exchange rates: which provides mo~c fiscai discipline?", Working Paper No. 5108 (NBER). Uribe, M. (1994), "Comparing the welfare costs and the initial dynamics of alternative temporaiy stabilization policies", mimeograph (Board of Governors of the Federal Reserve System). Uribe, M. (1995), "Real exchange rate targeting and macroeconomic instability", International Finance Discussion Papers No. 505 (Board of Governors of the Federal Reserve System). Uribe, M. (1997a), "Exchange-rate-based inflation stabilization: the initial real effects of credible plans", Journal of Monetary Economics 39:197--221.

1614

G.A. Calvo and C.A. VSgk

Uribe, M. (1997b), "A note on the analytics of credible exchange rate-based disinflation when money facilitates firms' transactions", mimeograph (Board of Governors of the Federal Reserve System). V6gh, C.A. (1989), "Government spending and inflationary finance: a public finance approach", IMF Staff Papers 36:657-677. V6gh, C.A. (1992), "Stopping high inflation: an analytical overview", IMF Staff Papers 39:626-695. V6gh, C.A. (1997), "Monetary policy, interest rate rules, and inflation targets", mimeograph (UCLA). Velasco, A. (1993), "A model of endogenous fiscal deficits and delayed fiscal reforms", C.V. Start Center Report 93-4 (New York University). Venegas-Martinez, E (1997), "Temporary stabilization: a stochastic analysis", mimeograph (CIDE, Mexico). Viana, L. (1990), "Uruguay's stabilization plan of 1968", mimeograph (CERES, Uruguay). Wicker, E. (1986), "Terminating hyperinflation in the dismembered Hapsburg monarchy", American Economic Review 76:350 364. Williamson, J. (1993), "Issues posed by porttblio investment in developing countries", in: S. Claessens and S. Gooptu, eds., Portfolio Investment in Developing Countries, Discussion paper No. 228 (World Bamk). Woodford, M. (1990), "The optimum quantity of money", in: B.E Frie&nan and EH. Hahn, eds., Handbook of Monetary Economics (North-Holland, Amsterdam) 1067-1152. Zarazaga, C.E. (1996), "Recurrent hyperinflations in a dynamic game with imperfect monitoring in the appropriation of seignorage", mimeograph (Federal Reserve Bank of Dallas).

Chapter 25

GOVERNMENT DEBT DOUGLAS W. ELMENDORF Federal Reserve Board N. GREGORY MANKIW Harvard University and NBER

Contents Abstract Keywords 1. I n t r o d u c t i o n 2. T h e data 2.1. Debt and dcficits in the USA and other countries 2.2. Measurement issues 2.2.1. Adjusting for economic conditions 2.2.2. Assets and liabilities beyond the official debt 2.2.3. Capital budgeting 2.2.4. Generational accounting 2.3. Future fiscal policy 3. T h e c o n v e n t i o n a l v i e w o f debt 3.1. How does debt affect the economy? 3.1.1. The short run: increased demand for output 3.1.2. The long run." reduced national saving and its consequences 3.1.3. Other effects 3.2. How large is the long-run effect of debt on the economy? 3.2.1. The parable of the debt fairy 3.2.2. A closer look at the effect of debt on private savings 3.2.3. A closer look at international capital flows 3.2.4. A closer look at the marginal product of capital 3.2.5. The deadweight loss of servicing the debt 3.2.6. Summary 4. R i c a r d i a n e q u i v a l e n c e 4.1. The idea and its history 4.1.1. The essence of the Ricardian argument 4. 1.2. A brief history of the Ricardian idea 4.1.3. Why Ricardian equivalence is so important Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor and M. Woodfbrd © 1999 Elsevier Science B. K All rights reserved 1615

1616 1616 1617 161'7 1618 1620 1620 1621 1623 1624 1625 1627 1628 1628 1628 1630 1632 1632 1634 1636 1638 1639 1639 1640 1640 1640 1642 1644

1616 4.2. The debate over Ricardian equivalence: theoretical issues 4.2.1. Intergenerational redistribution 4.2.2. Capital market imperfections 4.2.3. Permanent postponement of the tax burden 4.2.4. Distortionary taxes 4.2.5. Income uncertainty 4.2.6. Myopia 4.3. The debate over Ricardian equivalence: empirical issues 4.3.1. Testing assumptions about household behavior 4.3.2. Testing the implications for consumption 4.3.3. Testing the implications for interest rates 4.3.4. Testing the implications for international variables 5. Optimal debt policy 5.1. Fiscal policy over the business cycle 5.2. Fiscal policy and national saving 5.2. i. Lifb-cycle saving 5.2.2. lntergenerational saving 5.3. Tax smoothing 6. Conclusion References

D. W. Elmendorf and N.G. Mankiw

1645 1645 1648 1649 1651 1652 1653 1654 1654 1655 1657 1658 1659 1659 1660 1660 1661 1662 1663 1663

Abstract

This chapter surveys the literature on the macroeconomic effects of government debt. It begins by discussing the data on debt aud deficits, including the historical time series, measurement issues, and projections o f future fiscal policy. The chapter then presents the conventional theory o f government debt, which emphasizes aggregate demand in the short run and crowding out in the long run. It next examines the theoretical and empirical debate over the theory o f debt neutrality called Ricardian equivalence. Finall); the chapter considers various normative perspectives about how the government should use its ability to borrow.

Keywords J E L classification: E6, H6

Ch. 25:

Government Debt

1617

1. Introduction

An important economic issue facing policymakers during the last two decades of the twentieth century has been the effects of government debt. The reason is a simple one: the debt of the US federal government rose from 26% of GDP in 1980 to 50% of GDP in 1997. Many European countries exhibited a similar pattern during this period. In the past, such large increases in government debt occurred only during wars or depressions. Recently, however, policymakers have had no ready excuse. This episode raises a classic question: how does government debt affect the economy? That is the question that we take up in this paper. It will not surprise the reader to learn that macroeconomists are divided on the answer. Nonetheless, the debates over government debt are fascinating and useful to study. They are fascinating because they raise many fundamental questions about economic behavior. They are useful to study because learning the sources of disagreement can help an impartial observer reach a judgment of his own. Our survey of the effects of government debt is organized as follows. Section 1 considers some of the data on government debt. These data give some sense of the history of government debt in the USA and elsewhere. This section also discusses some recent projections for the beginning of the twenty-first century. Section 2 then examines the conventional view of the effects of government debt. We call this view "conventional" because it is held by most economists and ahnost all policymakers. According to this view, the issuance of government debt stimulates aggregate demand and economic growth in the short run but crowds out capital and reduces national income in the long run. Section 3 turns to an alternative view of government debt, called Ricardian equivalence. According to this view, the choice between debt and tax finance of government expenditure is irrelevant. This section discusses the basis of this idea, its history and importance, and the debate over its validity. Section 4 moves from positive to normative analysis. It considers various perspectives on the question of how the government should use its ability to borrow. The discussion highlights the potential significance of colmtercyclical fiscal policy, optimal national saving, and intertemporal tax smoothing.

2. The data In this section we present some basic facts about government debt and deficits in the USA and other countries. We give the official data, and then examine a number of issues regarding the appropriate measurement of fiscal policy. We conclude the section by considering projections of future fiscal policy in a number of countries.

D. W. Elmendorf and N.G. Mankiw

1618 Panel A Debt as e Percentage

Percent 120 - -

of GNP

1791 - 1996

100

88

60

40

20

o

r 1790

~ 1810

I, 1830

J

I 1850

i

~ 1870

~ 1890

I 1910

i

I 1930

i

i 1950

p 1970

1990

Panel B

Deficit as a P e r c e n t a g e o f G N P 1791 - 1996

Percent 30 - -

I 1790

I 1810

~

I 1890

J

I 1858

i

I 1879

~

I

i

1890

I 1910

i

I 1930

I

i 1950

I 1970

,

I 1980

Fig. I.

2.1. Debt and deficits' in the USA and other countries We begin with data f r o m the U S A . Panel A o f Figure 1 shows U S federal debt as a p e r c e n t a g e o f gross national product over the past 200 years 1. It is c o m m o n to exclude the debt o f state and local governments, as we do, although for many p u r p o s e s it is m o r e appropriate to consider the consolidated debt o f all levels o f government. M o s t

We take GNP data from Berry (1978, Table IB) tor 1791 to 1868, tiom Romer (1989) for 1869 to 1928, and from the National Income and Product Accotmts since 1929. The end-of-year debt comes from Bureau of the Census (1975, series Y493) for 1791 to 1939, from Congressional Budget Office (CBO) (1993, Table A-2) for 1940 to 1961, and from CBO (1997a, Table F-4) since 1962. We splice the series multiplicatively at the break points and convert dcbt from fiscal-year to calendar-year form.

Ch. 25:

Goeernment Debt

1619

state governments hold positive net assets, because they are prohibited from running deficits in their operating budgets, and because the assets they accumulate to fund employee pensions exceed the debt they issue to finance capital projects. The figure shows federal debt "held by the public", which includes debt held by the Federal Reserve System but excludes debt held by other parts of the federal government, such as the Social Security trust fund. The primary cause of increases in the US debt-output ratio has been wars: the War of 1812, the Civil War, World War I, and World War II all produced noticeable upswings in federal indebtedness. The Great Depression and the 1980s are the only two peacetime intervals when this ratio increased significantly. Between these sharp increases, the debt-output ratio has generally declined fairly steadily. An important factor behind the dramatic drop between 1945 and 1975 is that the growth rate of GNP exceeded the interest rate on government debt for most of that period. Under such circumstances, the government can collect taxes equal to only its non-interest spending, finance the interest payments on the outstanding debt by issuing more debt, and still watch its debt grow more slowly than the economy. This situation has potentially important implications for the effect of government debt, as we discuss later. Panel B of Figure 1 shows the US federal budget deficit as a share of GNP over the past 200 years 2. These deficit numbers are for the so-called "unified budget", which includes both "on-budget" items like national defense and "off-budget" items like Social Security, thus capturing essentially all of the fiscal activities of the federal government. Once again, the effect of wars is quite apparent. The small deficits between 1955 and 1975 were consistent with a declining debt-output ratio for the reason just mentioned: although the debt was growing, output was growing faster. After 1975, larger deficits and a less favorable relationship between the interest rate and the growth rate caused the debt-output ratio to rise. Government debt and deficits in other industrialized countries span a wide range, as shown in Table 1. The first column presents general government net financial liabilities as a percentage of GDR This measure differs in several respects from that shown in panel A of Figure 1: it includes all levels of government, nets out financial assets where the data are available, and normalizes by GDP rather than GNP. Nevertheless, the US value for 1996 matches the last point shown in the figure. The second and third columns show the budget surplus and primary budget surplus as percentages of GDP. The primary surplus equals taxes less all non-interest spending. The highest reported debt-income ratios are in Italy and Belgium; their high debt service payments induce substantial budget deficits despite primary budget surpluses.

2 The budget sm~pluscomes from Bureau of the Census (1975, series Y337) for 1791 to 1928, fi~om Bureau of the Census (1975, series Y341) for 1929 to 1961, and from Congressional Budget Office (1997a, Table F-4) since 1962. We convert these numbers from a fiscal-year basis to a calendar-year basis. Note that the deficit does not equal the annum change in federal debt. Roughly speaking, the change in debt reflects the government'scash outlays and receipts, while the unified deficit involves a limited amount of capital budgeting. We return to this issue below.

1620

D. Pg Elmendolf and N.G. Mankiw Table 1 Debt and deficits in industrialized countries in 1996, in percent of GDP a

Country

Net debt

Budget surplus

USA

49

-2

1

Japan

14

4

-4

Germany

48

-4

-1

France

39

-4

-l

112

-7

3

44

-4

-1 4

Italy United Kingdom

Primary budget surplus

Canada

70

2

Australia

29

-1

0

Austria

51

-4

0

Belgium

127

-3

5

Denmark

46

-2

Finland

-8

3

-1 4

1

Greece

n.a.

-7

Iceland

37

-2

1

Ireland

n.a.

-1

3

Korea

4

-22

4

Netherlands

48

2

2

New Zealand

n.a.

3

4

Norway

-28

6

7

Portugal

n.a.

4

1

53

-5

1

Spain Sweden

26

4

-1

TOTAL of these cotmtries

45

-3

0

Data are from OECD (1997, pages A33, A35, and A38) and include all levels of government. "n.a." denotes not available. a

2.2. Measurement issues' T h e official US data o n federal g o v e r m n e n t d e b t and deficits o b s c u r e a nu-mbe~ o f i n t e r e s t i n g and i m p o r t a n t issues ip a s s e s s i n g fiscal policy. We n o w d i s c u s s s o m e o f t h e s e m e a s u r e m e n t issues.

2.2.1, Adjusting f o r economic conditions Official data on d e b t and deficits are o f t e n a d j u s t e d to reflect t h r e e e c o n o m i c variables: the p r i c e level, interest rates, a n d the b u s i n e s s cycle. T h e a d j u s t m e n t for the p r i c e level

1621

Ch. 25." Government Debt

occurs because the real value of the debt is, for many purposes, more important than the nominal value. For the level of the debt, the price-level adjustment is obvious: if D is the debt and P is the price level, then the real debt is D/P. For the deficit, however, the price-level adjustment is somewhat more subtle. It is natural to define the real deficit to be the change in the real value of the debt. In this case, the real deficit equals the nominal deficit (deflated by the price level) minus the inflation rate times the existing debt. That is, d(D/P) _ d D / d t dt

P

dP/dt D P

P"

The inflation correction, which is represented by the second term on the right-hand side of this equation, can be large when inflation is high or the outstanding debt is large. Indeed, it can turn a nominal budget deficit into a real budget surplus. The second adjustment is for the level of interest rates. The adjustment arises because the market value of the debt may be more important than the par value. When interest rates rise, outstanding debt falls in value, and when interest rates fall, the opposite occurs; of course, a given rate change will cause debt with a longer maturity to be revalued more than shorter-term debt. The market value of US debt over time can be calculated using the data and procedures outlined in Seater (1981), Butkiewicz (1983), and Cox and Hirschhorn (1983). The annual change in the market value can differ noticeably from the annual change in the par value, but the series follow the same broad trends. The third common adjustment to the budget deficit is for business cycle conditions. Because the deficit rises automatically when economic activity slows, and vice versa, the budget deficit in a given year may offer a misleading impression of underlying fiscal policy. The "standardized employment deficit" [Congressional Budget Office (1997a)] eliminates the effects of the business cycle on the budget. This deficit is based on estimates of what spending and revenue would be if the economy were operating at normal levels of unemployment and capacity utilization. 2.2.2. Assets' and liabilities beyond the official debt

Debt held by the public is the largest explicit liability of the federal government, but i~ is not the only liability. Moreover, the federal government also holds significant assets. As emphasized by Eisner and Pieper (1984) and Eisner (1986), all of these assets and liabilities should be considered in any overall accounting of the government's financial situation. Unfortunately, it is quite difficult to assess the value of many government assets and liabilities. Some valuation problems are primarily technical. For example, a large share of the government's physical capital is defense-related, and many of these goods are not sold in (legal) markets. As another example, federal insurance of bank deposits may prove to be either very costly to the government or very inexpensive, and it is difficult to assess the probabilities of the alternative outcomes.

1622

D. ~ Ehnendolf and ~ G. Mankiw

Tabie 2 US federal governmentexplicit assets and liabilitiesa Category

Estimated value in 1995 ($ billions)

Liabilities

Debt held by the public (excluding the Federal Reserve) Federal pension liabilities Insurance liabilities Other

3219 1513 66 498

Assets

Financial assets Physical assets Net liabilities

576 1737 2983

a Data are from Office of Management and Budget (1996).

Other valuation problems are more conceptual. Do the furore Social Security benefits specified by current law constitute a government liability in the same sense as explicit debt? The answer to this question depends at least partly on how the liability is perceived by households. If households believe that these benefits will be paid with the same probability that the explicit debt will be honored, then it may be sensible to count the present value of the benefits as government debt. In this specific case, the additional debt could be roughly three times the explicit debt, as Feldstein (1996a) estimates the present value of Social Security benefits less taxes for current adults at roughly $11 trillion in 1995. Similar questions arise for civil service and military retirement benefits, Medicare, and other entitlement programs. The important general point is that the appropriate measure of government indebtedness largely depends on people's behavior. As a result, deciding what measure of fiscal policy is best requires taking a stand on the correct model of economic behavior. Attempts to measure a range of explicit government assets and liabilities include the presentations of historical federal balance sheets by Eisner (1986), Bohn (1992), and Office of Management and Budget (1996). OMB's estimates for 1995 are summarized in Table 2. The largest liabilities are debt held by the public (excluding the Federal Reserve) and expected pension liabilities for federal military and civilian employees. OMB also includes the expected cost of contingent liabilities that arise from loan guarantees and insurance programs. The federal government's financial assets include gold and loans owed to the government; its physical assets include both reproducible plant and equipment (about three-quarters of which relates to national defense) and non-reproducible capital such as land and mineral deposits. OMB does not include in these estimates the cost of future Social Security payments and other "continuing commitments", arguing that the appropriate way "to examine the balance between

Ch. 25: Government Debt

1623

future Government obligations and resources is by projecting ... total receipts and outlays" (p. 20). As it turns out, OMB estimates the government's assets to be worth roughly as much as its non-debt liabilities in 1995, so net explicit liabilities are close to the value o f debt. Indeed, net liabilities appear to have followed debt fairly closely in recent decades, despite sometimes significant differences in their annual changes. Debt increased by about $2.4 trillion between 1975 and 1995, while OMB estimates that liabilities rose about $2.6 trillion. Yet, these measures diverged sharply before 1975. Bohn estimates that the net worth o f the federal government was roughly the same share o f GNP in 1975 as in 1947, as a dramatic decline in the debt share was offset by a drop in military assets and a rise in government employee pension obligations. 2.2.3. Capital budgeting

One way to incorporate some government assets into the regular budget process is to create separate capital and operating budgets. In this way, current outlays would include not the acquisition o f capital goods, but the depreciation o f previously purchased capital. One effect o f capital budgeting is that it would allow the government to spend money on capital assets without running an explicit deficit. Some observers view this situation as an inducement to profligate spending, particularly because it is difficult to decide exactly what constitutes capital, and many types o f spending could acquire that label. For whatever reason, the US federal government (unlike many state governments) does not rely on a capital budget as a central element o f its budget process. Nevertheless, the principle o f capital budgeting does affect budget numbers in two ways. First, the unified budget includes some specific kinds o f capital budgeting. Since 1992, for example, government credit programs have been counted not in terms o f their current outlays, but in terms o f the present value o f their expected future outlays. Thus, the deficit cost o f a direct student loan is not the loan amount itself, but the net cost o f providing the loan, taking into account the probability o f default. Because the government's cash outlays reflect the total amount o f the loan, the increase in the debt exceeds the deficit. A similar pattern is repeated for some other fiscal activities where the budget amounts differ from the contemporaneous cash outlays or receipts 3. Second, the federal budget as recorded in the National Income and Product Accounts does treat government consumption and investment in physical capital differently 4.

3 Formally, the change in debt equals the deficit less so-called "other means of financing". Much of this category consists of short-term differences between the deficit and borrowing needs, but some other means of financing (such as direct student loans) involve quite long-term divergences. 4 This treatment in the National Income and Product Accounts was introduced in 1996. There are a number of other discrepancies between unified budget principles and NIPA budget principles. These include geographic differences, timing conventions, and some shifting of items between the revenue and expenditure sides of the budget.

1624

D. W. Elmendorf and N.G. Mankiw

Government consumption includes an estimate of the depreciation of government capital, and government purchases of new capital are tallied separately. The federal government's investment in physical capital is fairly modest, with gross investment less than 15% of consumption expenditures in 1994.

2.2.4. Generational accounting

One prominent alternative to standard debt and deficit accounting is "generational accounting", proposed by Auerbach et al. (1991) and Kotlikoff (1992). These authors argue that the conventional deficit and explicit debt "simply reflect economically arbitrary labeling of government receipts and payments", so that the measured deficit "need bear no relationship to the underlying intergenerational stance of fiscal policy" (p. 56). Generational accounts measure fiscal policy by its impact on different generations, not by the annual flows of spending and taxes. Generational accounts are constructed by extrapolating current policies through the lifetimes of all people currently alive, and calculating the net taxes they would pay under those policies. The net taxes of future generations are then set at a level which satisfies the government's intertemporal budget constraint. These calculations provide important information about how fiscal policy redistributes resources across generations. For example, most of the transfer from young to old during the postwar period occurred not in the 1980s when measured deficits were high, but between the 1950s and 1970s when deficits were low but Social Security benefits were being enhanced. Nevertheless, generational accounts do suffer from some problems, as explored by Cutler (1993) and Congressional Budget Office (1995). One set of problems involves technical issues in constructing the accounts. For example, it is unclear what is the appropriate discount rate for future taxes, and different discount rates produce very different quantitative results. A second issue is whether the labelling of government receipts and payments truly is arbitrary. For instance, the methodology of generational accounting treats Social Security payments and interest payments on govermnent debt as essentially equivalent. Yet it is surely easier for the government to reduce future Social Security benefits than to reduce future coupon payments on existing debt securities. The label "govenmlent debt" appears to have some true meaning. A final important problem springs from the fact that generational accounting is inextricably tied to a specific model of individual behavior. In particular, the methodology assumes that people are life-cycle consumers without a bequest motive, so that their behavior and well-being depend on their assessment of government policies over their entire lifetimes and only over their lifetimes. If individuals are liquidity-constrained or myopic, however, then their behavior and well-being may be more sensitive to current taxes than to the present value of the future taxes they expect to pay. Conversely, if individuals have altruistic bequest motives (a possibility we discuss extensively later), then their behavior and well-being will be sensitive to future

Ch. 25: Government Debt

1625

taxes that will be paid by their descendants. In either case, generational accounts fail to provide a good gauge of fiscal policy for either positive or normative purposes. 2.3. Future fiscal policy Current patterns of taxes and spending are unsustainable in most industrialized countries over the next twenty-five years. The primary causes of this situation are the aging of their populations and the rising relative cost of medical care. Table 3 presents the elderly dependency ratio - defined as the population age 65 and over as a percentage of the population ages 20-64 - for a number of countries. Between 1990 and 2030, longer lifespans and continued low birthrates will sharply increase the ratio of retirees to working adults. The US population is projected to age less dramatically than the population of many other industrialized countries, but the increase in retirees per worker in the USA is still expected to exceed 50%. In most countries, health care has absorbed an increasing share of national income over the past several decades. The cost of producing most specific medical services may not have increased, but the cost of providing medical care that meets the socia! standard clearly has risen. Predicting future developments in this area is difficult, but most analysts expect the relative cost of medical care to continue to increase for some time. A large share of government outlays involves transfers from working adults to retirees or the financing of health care. (Of course, these categories overlap heavily.) Thus, the aging of the population and the increasing cost of health care will put a significant strain on government finances over the coming decades. Table 4 shows projections tbr the effect of population aging on various countries' budget surpluses and debts under the assumption that current tax and spending rules remain unchanged. The numbers show only the direct effect of aging, and ignore the problem of paying interest on the accumulating debt. The projections are highly uncertain as well. Table 3 Elderly dependencyratiosa Country Japan Germany France Italy United Kingdom Canada USA

1990

2030

19 24 23 24 27 19 2i

49 54 43 52 43 44 36

a Data are from CongressionalBudget Office (1997b).

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D. Pg ElmendoJjand N.G. Mankt'w

Table 4 Projected effect of population aging on fiscal conditions in industrializedcountries, in percent of GDP ~ Country

Primary budget surplus

Change in debt from 2000 to 2030

1995

2030

USA

0.4

-3.8

44

Japan

-3.4

-8.7

190

Germany

-0.6

-6.6

45

1.6

-4.5

62

3.4 -2.8

5.9 1.4

109 27

Canada

1.5

-1.0

39

Australia

0.0

-1.4

37

Austria

2.7

-7.7

171

Belgium

4.3

-0.5

42

Denmark

2.0

2.3

124

Finland

4.3

-8.8

213

Iceland

- I. 1

-3.3

41

France Italy United Kingdom

Ireland

1.8

0.0

2

Netherlands

1.4

-6.0

142

Norway

3.2

4.7

135 110

Portugal Spain Sweden

0.6

-5.6

- 1.1

4.4

66

5. l

-2.7

117

a Data are from Roseveare et al. (1996) and refer only to the direct effect of population aging without incorporating the effect of higher interest payments on the larger outstanding debt. The primary budget surplus equals taxes less non-interest spending.

Nevertheless, they show a marked deterioration in the fiscal situation of almost every country. For the USA, Congressional Budget Office (1997b) (CBO) has performed a careful analysis of the fiscal outlook. The analysis incorporates the need to pay interest on the accumulating debt, as well as the feedback between debt and the economy. Table 5 summarizes CBO's results. Without economic feedbacks, government debt more than doubles as a share of output by 2030; including feedbacks, this share rises three-fold. A large part of this looming fiscal problem is the expected rise in future payments for Social Security and Medicare. Dealing with this long-term fiscal imbalance will likely be one of the most significant challenges facing policymakers during the next century.

Ch. 25.

1627

Government Debt

Table 5 CBO baseline projections for the US budget, in percent of GDP a Variable

1995

2030

2050

-1

5

6

3 2

6 11

12 18

50

125

267

Primary deficit Interest payments Total deficit

-1 3 2

5 12 17

n.a. n.a. n.a.

Debt

50

159

n.a.

Without economic feedbacks

Primary deficit Interest payments Total deficit Debt With economic feedbacks

a Data are from Congressional Budget Office (1997b) and assume that discretionary spending grows with the economy after 2007. "n.a." signifies that the values were too extreme to be reported by CBO. 3. T h e c o n v e n t i o n a l v i e w o f d e b t

In this section we present what we believe to be the conventional view o f the effects o f government debt on the economy. We begin with a qualitative description o f those effects, focusing on the impact o f debt on saving and capital formation, and thereby on output and income, on factor prices and the distribution o f income, and on the exchange rate and foreign transactions. We also review some other economic and non-economic consequences o f government borrowing. Following our qualitative analysis, we try to quantify some o f the long-run effects o f debt in a very rough way. Although quantifying these effects precisely is an arduous task, we think it important to have some quantitative sense o f what is at stake. Therefore, we present a ballpark estimate o f the impact o f debt, which is interesting in itself and also illuminates some o f the critical assumptions underlying all quantitative analyses o f government debt. Our analysis assumes that government spending on goods and services is not affected by debt policy. That is, we examine the effects o f issuing a given amount o f debt and reducing taxes temporarily by an equal amount. Because the government must satisfy an intertemporal budget constraint, and because debt cannot grow forever as a share o f income, this temporary tax reduction will generally be accompanied by a future tax increase. For most o f this section, we simply assume that the present value o f that tax increase equals the current increase in debt. We defer more careful consideration o f the budget constraint to the last part o f the section, where we re-examine the effects o f debt in a world with uncertainty. The analysis also assumes, except where stated otherwise, that monetary policy is unaffected by debt policy. By

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D. W.Elmendorfand N.G. Mankiw

excluding possible monetization of the debt, we can couch our discussion in real, rather than nominal, terms. 3.1. How does debt affect the economy?

The government's debt policy has important influence over the economy both in the short run and in the long run. We begin by discussing the short-run effects of budget deficits. We then turn to the long-run effects, of which the most important is a reduction in national wealth. In particular, we explain both how deficits affect national saving and how the change in saving affects many aspects of the economy. We also consider several other long-run effects of government debt. 3.1.1. The short run: increased demand Jbr output

Suppose that the government creates a budget deficit by holding spending constant and reducing tax revenue. This policy raises households' current disposable income and, perhaps, their lifetime wealth as well. Conventional analysis presumes that the increases in income and wealth boost household spending on consumption goods and, thus, the aggregate demand for goods and services. How does this shift in aggregate demand affect the economy? According to conventional analysis, the economy is Keynesian in the short rim, so the increase in aggregate demand raises national income. That is, because of sticky wages, sticky prices, or temporary misperceptions, shifts in aggregate demand affect the utilization of the economy's factors of production. This Keynesian analysis provides a common justification for the policy of cutting taxes or increasing government spending (and thereby running budget deficits) when the economy is faced with a possible recession. Conventional analysis also posits, however, that the economy is classical in the long run. The sticky wages, sticky prices, or temporary misperceptions that make aggregate demand matter in the short run are less important in the long run. As a result, fiscal policy affects national income only by changing the supply of the factors of production. Ttm mechanism through which this occurs is our next topic. 3.1.2. The long run." reduced national saving and its consequences

"lb understand the effect of government debt and deficits, it is crucial to keep in mind several national accounting identities. Let Y denote national income, C private consumption, S private saving, and T taxes less government transfer payments. The private sector's budget constraint implies that: Y-C4S+T.

National income also equals national output, which can be divided imo four types of spending: Y=C+I.~G+NX,

Ch. 25." Government Debt

1629

where I is domestic investment, G is government purchases of goods and services, and N X is net exports of goods and services. Combining these identities yields: S + ( T - G) = I + N X .

This identity states that the sum of private and public saving must equal the sum of investment and net exports. The next important identity is that a nation's current account balance must equal the negative of its capital account balance. The current account balance is defined as net exports N X plus net investment income by domestic residents and net transfers; for the most part, we ignore these last two, smaller pieces. The negative of the capital account balance is called net foreign investment, or N F I , which is investment by domestic residents in other countries less domestic investment undertaken by foreign residents. Thus, the third identity is simply: NX = NFI,

so that international flows of goods and services must be matched by international flows of funds. Substituting this identity into the other two identities yields: S + ( T - G) = I ~ N F I .

The left side of this equation shows national saving as the sum of private and public saving, and the right side shows the uses of these saved funds for investment at home and abroad. This identity can be viewed as describing the two sides in the market for loanable funds. Now suppose that the govermnent holds spending constant and reduces tax revenue, thereby creating a budget deficit and decreasing public saving. This identity may continue to be satisfied in several complementary ways: private saving may rise, domestic investment may decline, and net foreign investment may decline. We consider each of these possibilities in turn. To start, an increase in private saving may ensue for a number of reasons that we discuss below. In fact, some economists have argued that private saving will rise exactly as much as public saving falls, and the next section of the paper examines this case at length. For now, we adopt the conventional view that private saving rises by less than public saving falls, so that national saving declines. In this case, total investment - at home and abroad - must decline as well. Reduced domestic investment over a period of time will result in a smaller domestic capital stock, which in turn implies lower output and income. With less capital available, the marginal product of capital will be higher, raising the interest rate and the return earned by each unit of capital. At the same time, labor productivity would be lower, thereby reducing the average real wage and total labor income. Reduced net foreign investment over a period of time means that domestic residents will own less capital abroad (or that foreign residents will own more domestic capital).

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D. W. Elmendorf and N.G. Mankiw

In either case, the capital income o f domestic residents will fall. Moreover, the decline in net foreign investment must be matched by a decline in net exports, which constitutes an increase in the trade deficit o f goods and services. As this connection between the budget deficit and the trade deficit became better known in the U S A during the 1980s, it led to the popular term "twin deficits". Pushing the trade balance into deficit generally requires an appreciation o f the currency, which makes domesticallyproduced goods relatively more expensive than foreign-produced goods 5. 3.1.3. Other eJJects

Although increasing aggregate demand in the short run and reducing the capital stock in the long run are probably the most important effects of government budget deficits, debt policy also affects the economy in various other ways. We describe several o f these effects here. First, government debt can affect monetary policy. A country with a large debt is likely to face high interest rates, and the monetary authority may be pressured to try to reduce those rates through expansionary policy. This strategy may reduce interest rates in the short run, but in the long run will leave real interest rates roughly unchanged and inflation and nominal interest rates higher. In the USA, at least in recent years, monetary policy has apparently not responded to fiscal policy in this way. For example, the US debt-income ratio rose sharply during the 1980s, and the US inflation rate declined sharply. Nevertheless, successive Chairmen o f the Federal Reserve Board have warned o f the possible link between the budget deficit and inflation 6. In extreme cases, a country with a large debt may have difficulty financing an ongoing deficit through additional borrowing and, as a result, will be tempted to raise revenue through seigniorage. I f the fiscal authority can force the monetary authority to finance ongoing deficits with seigniorage, then, as Sargent and Wallace (1981) argue, inflation is ultimately a fiscal phenomenon rather than a monetary one'7. This

5 For more complete analyses of tile imernational effects of debt, see Frenkel and Razin (1992, chs. 7, 8, 10 and 11) and Obstfeld and Rogoff (1996, ch. 3). 6 Paul Volcker told~Congress in 1985 that "the actual and prospective size of the budget deficit ... heightens skepticism about our ability to control the money supply and contain inflation" (p. 10). Alan Greenspan said in 1995 that he expected that "a substantial reduction in the long-term prospective deficit of the United States will significantly lower very long-term il~lation expectations vis-a-vis other countries" (p. 141). 7 Woodford (1995) proposes an alternative "fiscal theory of the price level", based on the effect of prices on the real value of government debt and thus on aggregate demand. Wood~brdconsiders an economy of infinitely-lived households, and hypothesizes an increase in govermnent debt with no offsetting change in future taxes or spending. This policy makes households wealthier and increases aggregate demand. If aggregate supply is unchanged, both goods market equilibrium and the government's budget constraint require that the price level increases enough to reduce real debt to its initial value. The mechanism is quite similar to the Pigou Patin!dn (1965) real-balance effect, except that it allows for households thai appear to be Ricardian, and it involves total government liabilities rather than just outside money. In

Ch. 25:

Government Debt

1631

monetization of the debt is the classic explanation for hyperinflation. For example, staggering budget deficits as a share of national income were the root cause of hyperinflations in 1920s Germany and 1980s Bolivia. As Sargent (1983) explains, inflation can fall sharply in such a country when government borrowing is reduced and the central bank commits not to finance future deficits. Yet, this line of reasoning is not very important for most developed countries today, as seigniorage represents a very small share of total government revenue 8. A second effect of government debt is the deadweight loss of the taxes needed to service that debt. The debt-service payments themselves are not a cost to a society as a whole, but, leaving aside any payments to foreigners, merely a transfer among members of the society. Yet effecting that transfer in a world without lump-sum taxes will create some distortion of individual behavior that generates a deadweight loss. Thus, a policy of reducing taxes and running a budget deficit means smaller deadweight losses as the debt is being accumulated but larger deadweight losses when the debt is being serviced with higher taxes. A third effect of government debt is to alter the political process that determines fiscal policy. Some economists have argued that the possibility of government borrowing reduces the discipline of the budget process. When additional government spending does not need to be matched by additional tax revenue, policymakers and the public will generally worry less about whether the additional spending is appropriate. This argument dates back at least to Wicksell (1896), and has been echoed over the years by Musgrave (1959), Buchanan and Wagner (1977), and Feldstein (1995) among others. Wicksell claimed that if the benefit of some type of government spending exceeded its cost, it should be possible to finance that spending in a way that would receive unanimous support from the voters; he concluded that the government should only undertake a course of spending and taxes that did receive nearly unanimous approval. In the case of deficit finance, Wicksell was concerned that "the interests [of future taxpayers] are not represented at all or are represented inadequately in the tax-approving assembly" (p. 106). Musgrave noted that when budget balance is altered for stabilization purposes, "the function of taxes as an index of opportunity cost [of government spending] is impaired" (p. 522). Buchanan and Wagner asserted that a balanced-budget rule "will have the effect of bringing the real costs of public outlays to the awareness of decision makers; it will tend to dispel the illusory 'something for nothing' aspects of fiscal choice" (p. 178). And Feldstein wrote that "only the 'hard budget constraint' of having to balance the budget" can force politicians to judge whether spending's "benefits really justify its costs" (p. 405). It is also possible that the existence of government debt reduces the fiscal flexibility of the government. If moderate levels of debt have only small negative effects, but contrast to the Sargent-Wallace analysis, Woodlbrd's point does not depend on any particular response by the monetary anthority to changes in fiscal policy. 8 For further analysis of the connections between fiscal policy and monetary policy, see Aiyagari and Gertler (1985), Leeper (1991), McCallum (1984), and Sims (t994).

1632

D. W. Elmendorf and N.G. Mankiw

larger debts are perceived to be quite costly, then a country with a moderate debt will be constrained from responding to calls for greater spending or lower taxes. This constraint on future policymakers is, in fact, one of the explanations sometimes given for why goverlmaents choose to accumulate large debts. A fourth way in which government debt could affect the economy is by making it more vulnerable to a crisis of international confidence. The Economist (4/1/95) noted that international investors have worried about high debt levels "since King Edward III of England defaulted on his debt to Italian bankers in 1335" (p. 59). During the early 1980s, the large US budget deficit induced a significant inflow of foreign capital and greatly increased the value of the dollar. Marris (1985) argued that foreign investors would soon lose confidence in dollar-denominated assets, and the ensuing capital flight would sharply depreciate the dollar and produce severe macroeconomic problems in the USA. As Krugman (1991) described, the dollar did indeed fall sharply in value in the late 1980s, but the predicted "hard landing" for the US economy did not result. Krugman emphasized, however, that currency crises of this sort have occurred in countries with higher debt-output ratios, particularly when much of that debt is held by foreigners, as in many Latin American countries in the 1980s. A fifth effect of government debt is the danger of diminished political independence or international leadership. As with the danger of a hard landing, this problem is more likely to arise when government borrowing is large relative to private saving and when the country experiences a large capital inflow from abroad. Friedman (1988) asserted: "World power and influence have historically accrued to creditor countries. It is not coincidental that America emerged as a world power simultaneously with our transition from a debtor nation ... to a creditor supplying investment capital to the rest of the world" (p. 13). 3.2. How large is the long-run eJJect of debt on the economy? So far we have described the effects of government debt in qualitative terms. We now present rough quantitative estimates of some of these effects. We begin with an extremely simple calculation of the effect on national income of a reduced capital stock, and we then explore the sensitivity of our results to three key assumptions. Our ballpark estimate is, in fact, broadly consistent with the few other quantitative analyses in the literature. We also note the magnitude of the deadweight loss caused by the taxes needed to finance the debt service. We calibrate our calculations for the US economy, but the approach is applicable to other countries as well. 3.2.1. The parable o f the debt Jhiry As we have discussed, a primary effect of govermnent debt is the crowding out of capital and the consequences that result from this crowding out. How large are these effects? To answer this question, consider the parable offered by Ball and Mankiw (1995). hnagine that one night a debt fairy (a cousin of the celebrated tooth fairy)

Ch. 25: GooernmentDebt

1633

were to travel around the economy and replace every government bond with a piece o f capital o f equivalent value. How different would the economy be the next morning when everyone woke up? It is straightforward to calculate the effect o f this addition to the capital stock. I f factors o f production earn their marginal product, then the marginal product o f capital equals the capital share o f income ( M P K x K / Y ) divided by the capital-output ratio (K/Y). In the U S A between 1960 and 1994, the gross return to capital was roughly onethird o f income, and the capital-output ratio averaged a little over three 9. The implied marginal product o f capital is about 9.5%. More precisely, this figure represents the gross marginal product; it shows how much an extra dollar o f capital adds to gross output and income. If the country wants to maintain that dollar o f capital, however, then it needs to do replacement investment to offset depreciation. Depreciation amounts to roughly 3.5% o f capital, so the net marginal product o f capital is about 6%. In other words, each dollar o f capital raises gross national product by 9.5 cents and net national product by 6 cents. When the debt fairy magically reverses the effects o f crowding out, the amount o f capital increases by the amount o f federal government debt, which in the U S A is about one-half o f gross output. Our estimates o f the marginal product o f capital imply that gross output would be increased by about 4.75%, and net output by about 3% 10. In 1997, these increases amount to about $400 billion and $250 billion, respectively. The story o f the debt fairy is appealing because it offers a simple way to calculate the effects o f government debt on national income. But is this calculation realistic? The debt-fairy calculation implicitly makes three assumptions: (1) Deficits do not affect private saving, so debt crowds out other forms of private wealth one for one. (2) The economy is closed, so crowding out takes the form o f a reduced capital stock. (3) The profit rate measures the marginal product o f capital, so it can be used to gauge the effects o f a change in the capital stock.

9 These data are drawn fiom the National Income and Product Accotmts of the Colmnerce Department's Bureau of Economic Analysis (BEA). Net capital income is the sum of corporate profits, rental income, net interest, and a share of proprietors' income (all with appropriate adjustments for inventory valuation and capital consumption). Gross capital income equals net income plus depreciation. We use national income plus depreciation as the measure of total output and income. The capital stock is BEA's net stock of fixed reproducible tangible wealth excluding consumer durables. Including the value of inventories and land in the measure of capital would depress the estimated return on capital. On the other hand, Feldstein et al. (1983) note that "pre-tax" corporate profits in the national income accounts actually represent profits qfier the payment of state and local property taxes; adding these taxes back into profits would raise the estimated rates of return. Finally, some authors measure the benefit of additional saving by the return to nonfinancial corporate capital. Because corporate capital is more heavily taxed than other capital, it earns a higher pre-tax return. Yet, there is no reason to assume that any addition to the capital stock would flow disproportionately to corporations. 10 The actual effect of adding tbis much capital would be somewhat smaller, because the marginal product would decline as the capital stock increased.

1634

D. Igz?Etmendorf and N.G. Mankiw

Let us consider how relaxing each of these assumptions might alter the conclusion that current US government debt reduces US national income by about 3%. 3.2.2. A closer look at the effect o f debt on private savings'

The debt fairy replaces each dollar of government debt with one dollar of capital. Is this dollar-for-dollar substitution appropriate? More concretely, if the US government had run sufficient surpluses during the past twenty years to reduce its debt to zero, would national wealth now be larger by the amount of the actual current debt? In actuality, an increased flow of government borrowing will affect the flow of private saving through several channels. First, private saving will rise because some households will save part of the tax reduction to consume later in life. Second, forwardlooking consumers will realize that the increasing debt will force higher future interest payments by the government and, thus, higher future taxes. Third, greater government borrowing will affect interest rates and wages, and these general-equilibrium effects in turn will affect private saving. Fourth, the government's debt policy may affect distortionary capital taxes, which in turn affect private saving. For all of these reasons, the size of the budget deficit affects tile amount of private saving. Understanding the long-run effect of debt on capital therefore requires a formal, general equilibrium model, with particular attention paid to household saving behavior. Conventional analysis focuses on models with overlapping generations of life-cycle consumers introduced by Samuelson (1958) and Diamond (1965). Because this model incorporates people at different stages of their life-cycle who differ in both their level of wealth and marginal propensity to consume out of wealth, aggregation is often difficult in realistic models with more than two generations. Blanchard (1985) resolves this problem by making assumptions about the aging process that simplify aggregation analytically. Auerbach and Kotlikoff (1987) and other researchers resolve this problem by simulating a more complicated model numerically. Before turning to the results from these well-known analyses, however, it is instructive to examine a simple, stylized example. Consider an economy in which every person lives for a fixed number of periods. Assume that the interest rate is given (either because this is a small open economy or because the technology is linear in capital and labor). Also assume that the consumers choose the same level of consumption in each period of life (either because their rate of time preference happens to equal the interest rate or because they have Leontief preferences). Now consider how an increase in government debt affects the steady state. Higher debt means higher interest payments and higher taxes. If those taxes are distributed equally across people of different ages, then each person's after-tax income is reduced by the amount of those interest payments (per capita) in each period. Because consumers still want to smooth consumption, they respond to this higher tax burden by reducing consumption in each period by the same amount. As a result, after-tax income and consumption fall equally, private saving is unchanged, and private wealth is unchanged. Each dollar of debt crowds out exactly one dollar of capital, as assumed by the debt fairy parable.

Ch. 25.. Government Debt

1635

To see what happens when various assumptions are relaxed, we turn to the Blanchard and Auerbach-Kotlikoff analyses. Blanchard develops a continuous-time overlappinggenerations model in which people have log utility and face a fixed probability of dying in each period. He examines the effect of accumulating additional government debt and then holding debt at its new level forever. To establish notation, let D denote debt and W denote national wealth (domestic capital plus net foreign assets), so private wealth equals D + W. For a small open economy, Blanchard confirms the result from our simple example: steady-state d W / d D equals -1 if the rate o f time preference equals the world interest rate. I f the world interest rate and the rate o f time preference differ, crowding out may be larger or smaller than one for one 11 Matters become more complicated in a closed economy. In this case, as capital is crowded out, the interest rate rises, and households are encouraged to save. As a result, the absolute value of d W / d D is smaller in a closed economy than in an open economy 12. Calculations using the Blanchard model indicate that the difference between open and closed economies is substantial, but this result appears highly sensitive to the assumption of log utility, according to which households are very willing to substitute consumption between periods in response to a higher interest rate. Most research in the consumption literature suggests a much smaller intertemporal elasticity o f substitution than unity 13. Auerbach and Kotlikoff (1987) construct a large-scale general equilibrium model, and simulate the model to examine the effects o f alternative debt, tax, and Social Security policies. The numerical simulations reveal not only the steady-state changes in capital and other variables, but also the transition path to the new steady state. The model assumes that people have an economic lifetime o f 55 years, have perfect foresight about future economic conditions, and make rational choices regarding their consumption and labor supply. The government raises funds through distortionary taxes and satisfies an intertemporal budget constraint. A production function for net output

11 Let p bc the probability of dying in each period or, as suggested by Blanchard and Summers (1984), a "myopia coefficient" that reflects mortality or myopia. Let r equal the world interest rate and 0 the rate of time preference. Then Blanchard reports that dW dD

p p~ 0 p+rp+O r"

12 Blanchard and Fischer (1989, p. 131) report that, in the steady state, dK dD

p(p + O) (p + r)(p + O - r ) - F H C '

where K is the capital stock, C is consumption, and F is thc aggregate net production fimction. 13 For attempts to use variants of the Blanchard model to estimate the cost of various debt policies, see Romer (t988) and Evans (1991).

1636

D. 14(Elmendolf and N.G. Mankiw

completes the model, which describes a closed economy. Auerbach and Kotlikoff choose values for the key parameters based on the empirical literature. Note, in particular, that they assume that the intertemporal elasticity of substitution is 0.25. Auerbach and Kotlikoff examine the effect of reducing taxes and accumulating debt over a certain number of years, and then boosting taxes to hold the debt at its new per capita level forever. This debt policy reduces saving and capital by transferring resources from younger and future generations, who have a low or zero marginal propensity to consume, to older generations, who have a high marginal propensity to consume. Capital is also diminished by the higher rate of distortionary income taxes in the long run, although the initial reduction in the tax rate can actually crowd-in capital in the short run. Auerbach and Kotlikoff analyze deficits equal to 5% of output that last for one year, 5 years, and 20 years; they do not report the resulting levels of debt, but these can be calculated approximately based on the size of the deficits and the interest rate. For all three experiments, the decline in capital appears to be extremely close to the increase in debt 14. We conclude this discussion by emphasizing that the short-rml effect of a budget deficit on consumption and saving is a poor gmide to the long-run effect of debt on national wealth. In a model with life-cycle consumers, government debt may have only a small short-run effect, as confirmed by Blanchard (who finds that initial saving adjusts by only several percent of a change in debt) and Auerbach and Kotlikoff (who find that at the end of a 20-year tax cut, the capital stock is reduced by only onefifth of its eventual decline). Nonetheless, debt has a much larger effect on life-cycle consumers in the long run. Auerbach and Kotlikoff's closed-economy model shows approximately one-for-one crowding out; Blanchard's formulas suggest smaller effects in a closed economy but roughly one-for-one crowding out in an open economy. On balance, the debt fairy's one-for-one substitution of capital for debt may be on the high side of the truth, but it seems a reasonable approximation. 3.2.3. A closer look at international capital flows

When the debt fairy changes government debt into national wealth, the increment to national wealth is assumed to take the form of domestic capital, witb no change in net ownership o£ foreign assets. This is clearly not a realistic description of an opet~ economy. Yet, alternative assumptions about international capital flows would have little effect on the estimated impact of government debt. In actuality, net international capital flows are fairly small. Feldstem and Horioka (1980) examined five-year averages of domestic investment and saving across countries and found these two variables moved almost exactly one for one with each other. More recent estimates suggest that the strength of this relationship declined somewhat in

14 'rile increases in debt fiom the tlucc alternative policies are roughly 5, 30 mid 200% of output. The corresponding declines in the capital stock are 5, 29 and 182% of output.

Ch. 25." Government Debt

1637

the 1980s. Nonetheless, these estimates indicate about 75% of a long-term change in national saving adds to domestic investment and only 25% goes to investment abroad 15. Because many countries allow capital to move freely across their borders, it is surprising that net international capital flows are not larger in the long run. The literature has considered many possible explanations 16. For our purposes, though, the key point is that the existence of international capital flows - or the lack of such flows has little impact on the ultimate cost o f government debt. Suppose that the debt fairy transformed each dollar o f reduced debt into an extra dollar o f net foreign assets, rather than an extra dollar of domestic capital. In this case, which is the extreme opposite o f our original assumption, the debt reduction would not raise domestic output at all Instead, it would raise foreign output, and some of that output would flow back to this country as the return on our additional overseas assets. As long as the return to wealth is the same at home and abroad, the location of the extra wealth does not affect our income. Another way to understand this point is to note the distinction between domestic income and national income. Domestic income is the value o f production occurring within a nation's borders; this is identically equal to domestic output or GDP. Tomorrow's domestic output and income depend on today's domestic investment. But the consumption o f domestic residents depends on t h e i r income, which is the value o f production accruing to a nation's residents. This is called national income, and it is identically equal to national output or GNR Tomorrow's national output and income depend on today's national saving, wherever this saving is ultimately invested. Naturally, this strong statement requires several caveats. First, the statement ignores the tax implications of the location of capital. Governments receive a higher effective tax rate on capital located in their countries than on capital owned by their residents but located abroad. Thus, the social return to domestic investment is higher than the social return to foreign investment, even if the private (after-tax) returns are the same. Second, additional capital accunmlation does not reduce the marginal product of capital as quickly if the capital can flow abroad. As we saw in our earlier discussion of the Blanchard model, the effect of debt on the capital stock is reduced if changes in the capital stock affect the interest rate and thereby private saving. Third, the location of nationally-owned capital does affect the distribution of income. If the domestic capital stock increases, so does the wage, while the return to capital and the interest rate fall; domestic workers benefit and owners o f domestic capital are

15 See Feldstein and Bacchetta (1991) and Dornbusch (1991). ~0 Frankel (1991), Mussa and Goldstein (1993), and Gordon and Bovenberg (1996) review the evidence regarding international capital mobility and discuss a number of explanations for the observed immobility. For a recent attempt to explain the Feldstein-Horioka puzzle within the context of neoclassical growth theory, see Barro et al. (1995).

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hurt 17. An increase in the ownership of capital located abroad does not have these effects. Fourth, international capital flows change the composition of domestic production. If a smaller deficit raises net foreign investment, then net exports will rise, while if it increases only domestic investment, then of course investment spending will rise. Moreover, the budget deficit affects the exchange rate if there are significant international capital flows, but not otherwise. On balance, it seems that the issuance of government debt has only a small effect on international capital flows in the long run and that those flows have only a small effect on the return to extra saving. Acknowledging the openness of the economy, therefore, does not substantially alter the estimated impact of government debt. 3.2.4. A closer look at the marginal product oJcapital

In describing the impact of the debt fairy, we calculated the marginal product of capital using the capital share of national income and the capital-output ratio. This calculation was based on the standard premise that the factors of production, including capital, are paid their marginal product. Now we reconsider whether that calculation was appropriate. In recent years, there has been a wave of research that proposes a new view of capital. As Mankiw (1995) discusses, a variety of empirical problems with the basic neoclassical growth model would be resolved if the true capital share in the production function is much larger than the one-third measured from the national income accounts. One reason that the true capital share might be larger than the raw data suggest is that capital may have significant externalities, as argued by Romer (1986, 1987). If the social marginal product of capital is well above the private marginal product that we observe, then reducing government debt and raising the capital stock would have much larger effects than the debt fairy parable suggests. Another possible reason for a large capital share is that the correct measure of capital includes human capital, such as education and training, as well as tangible physical capital, like plant and equipment. Mankiw et al. (1992) propose an extension of the basic Solow (1956) model in which there are fixed saving rates for both physical capital and human capital. They show that cross-country data are consistent with this model and an aggregate production function of the tbrm Y=K1/3HI/3L 1/3. If the share of income devoted to human-capital accumulation is unchanged by debt policy, then the reduction in income caused by the crowding out of physical capital will also reduce the stock of human capital; in this case, government debt reduces income substantially more than our earlier calculation indicated. By contrast, if the stock of human capital remained fixed, then our earlier calculation would be correct.

17 Bccausc some owners of domestic capital are foreigners, this shill actually raises national income slightly.

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3.2.5. The deadweight loss of servicing the debt When discussing the qualitative effects of debt, we reviewed a number of issues beyond the impact of debt on the capital stock. The only one of those effects that is readily quantifiable is the deadweight loss of the additional taxes needed to meet the debt service burden 18. Of course, the deadweight loss of taxation was reduced during the period when taxes were lower and the debt was accumulated, and optimal debt policy requires balancing these effects. Our concern here, however, is just with the cost of an ongoing debt. If the government builds up a certain debt, and then decides to hold that debt constant in real terms, the additional debt service per dollar of accumulated debt is r, the real interest rate on debt. If 3. is the deadweight loss per dollar of tax revenue, then the loss per dollar of debt is ~r. The total real return on intermediate-maturity government debt averaged about 2% between 1926 and 1994 (Stocks, Bonds', Bills' and Inflation, 1995). A standard choice for ;. is Ballard, Shoven and Whalley's (1985) estimate of one-third, although Feldstein (1996b) argues that incorporating distortions to the form of compensation and the demand for deductions - in addition to the usual distortions to labor and capital supply - makes the true 3, much larger. If )~ equals onehalf, then 2r=0.01, and with the US debt-income ratio at one-half, the deadweight loss from servicing the debt is about half a percent of output.

3.2.6. Summary As concern about current and prospective US budget deficits has grown, quantitative estimates of the effect of debt have begun to appear in official US government documents. For example, in the 1994 Economic Report of the President (pp. 85 87), tile Council of Economic Advisers assumed that the President's deficit-reduction plan would boost national saving by 1% of output each year for 50 years. Then the Report used a simple Solow growth model to show the effect of that extra saving on the economy. It concluded that the additional saving would eventually raise output by 3.75%. More recently, the Congressional Budget Office (1997b) constructed a complex model of the economy and the federal budget and simulated the model through the year 2050. Because current law would produce an explosive rise in the national debt over that period, CBO's results do not reflect steady-state effects. In the simulation that includes the economic effects of increasing debt, debt rises by 30% of output by 2020, resulting in output that is 2% smaller than it otherwise would be. Over the following decade, debt increases by another 80% of output, and output is diminished by more than 8% relative to the same baseline. Thus, these calculations are similar in spirit to those found in the academic literature.

is Auerbaeh and Kotlikoff's (1987) estimates of the weffare effects of debt policy include this cost, but isolating its significance from their published results is not possible.

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We have now quantified, in a very rough way, some long-run effects of government debt on the economy. The debt fairy parable implied that each dollar of debt reduces net output by about 6 cents each year. More careful consideration of the strong assmnptions embodied in that parable suggested that this estimated cost is at least in the right ballpark. The deadweight loss from the taxes needed to service the debt adds about another one cent per dollar of debt. Thus, the US debt of the late 1990s, which equals about half of annual output, is reducing net output by about 3.5%. In 1997, this amounts to around $300 billion per year. Is this cost large? Labor productivity has increased by about one percent per year in the USA since 1975, so reducing output by three to four percent is like giving up three to four years of productivity growth. That is a significant loss, but it does not qualify as a disaster. One final comparison of the cost of the current debt is with the effect of the upcoming demographic transition in the USA. Congressional Budget Office (1997b) projects that, under current law, population aging and rising health care costs will boost non-interest spending of the federal government by five percent of output between 1996 and 2025. if tile current debt were maintained in real terms, it would represent about one-third of real output in 2025 (because of economic growth). Thus, eliminating that debt would add about two percent to national income, or almost half of the extra income needed to cover the additional government spending.

4. Ricardian equivalence So far our discussion has focused on the conventional analysis of government debt. By "conventional", we mean that this analysis describes the views held by most economists and almost all policymakers. There is, however, another view of government debt that has been influential in the academic debate, even if endorsed by only a minority of economists. That view is called Ricardian equivalence after the great 19th century economist David Ricardo, who first noted the theoretical argument. In recent years, the Ricardian view has been closely associated with Robert Barro, whose work has given the view renewed vigor and prominence. 4.1. The idea and its' history

Ricardian equivalence is a type of neutrality proposition: it states that a certain type of government policy does not have any important effects. In this section we discuss the general idea, its history, and its importance as a theoretical benchmark. In the following sections we examine the various dimensions of the debate over the validity of Ricardian equivalence as a description of the real world. 4.1.1. The essence o f the Ricardian argument

Suppose that the government cuts taxes today without any plans to reduce gover~ur~ent purchases today or in the future. As we have seen, conventional analysis concludes

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that this policy will stimulate consumption, reduce national saving and capital accumulation, and thereby depress long-term economic growth. By contrast, the theory of Ricardian equivalence asserts that this policy will not alter consumption, capital accumulation, or growth. The situation with the tax cut and budget deficit is e q u i v a l e n t to the situation without it. The Ricardian argument is based on the insight that lower taxes and a budget deficit today require (in the absence of any change in government purchases) higher taxes in the future. Thus, the issuing of government debt to finance a tax cut represents not a reduction in the tax burden but merely a postponement of it. If consumers are sufficiently forward looking, they will look ahead to the future taxes implied by government debt. Understanding that their total tax burden is unchanged, they will not respond to the tax cut by increasing consumption. Instead, they will save the entire tax cut to meet the upcoming tax liability; as a result, the decrease in public saving (the budget deficit) will coincide with an increase in private saving of precisely the same size. National saving will stay the same, as will all other macroeconomic variables. In essence, the Ricardian argument combines two fundamental ideas: the government budget constraint and the permanent income hypothesis. The government budget constraint says that lower taxes today imply higher taxes in the future if government purchases are unchanged; the present value of the tax burden is invariant to the path of the tax burden. The permanent income hypothesis says that households base their consumption decisions on permanent income, which depends on the present value of after-tax earnings. Because a debt-financed tax cut alters the path of the tax burden but not its present value, it does not alter permanent income or consumption. Thus, all of the predictions of the conventional analysis of government debt no longer hold. Another way to view the Ricardian argument is suggested by the title of Robert Barro's classic 1974 paper "Are Government Bonds Net Wealth?" To the owners of government bonds, the bond represents an asset. But to taxpayers, government bonds represents a liability. A debt-financed tax cut is like a gift of government bonds to those getting the tax cut. This gift makes the holder of the bond wealthier, but it makes taxpayers poorer. On net, no wealth has been created. Because households in total are no richer than they were, they should not alter their consumption in response to the tax cut. It is important to emphasize that the Ricardian argument does not render all fiscal policy irrelevant. If the government cuts taxes today and households expect this tax cut to be met with future cuts in government purchases, then households' permanent income does rise, which stimulates consumption and reduces national saving. But note that it is the expected cut in government purchases, rather than the tax cut, that stimulates consumption. The reduction in expected future government purchases would alter permanent income and consumption because they imply lower taxes at some time, even if current taxes are unchanged. Because the Ricardian view renders some fiscal policies irrelevant but allows other fiscal policies to matter, providing a convincing test of this view has proven difficult. For example, in the early 1980s, a debt-financed tax cut advocated by President Reagan

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in his first administration was followed by a substantial rise in government debt and a fall in national saving. Some observers, such as Benjamin Friedman (1992), see this episode as a natural experiment that decisively rejects Ricardian equivalence. Yet it is possible that consumers expected this tax cut to mean smaller government in the future; smaller government was, in fact, President Reagan's intention, and to some extent it has been the result. Moreover, other developments, such as a booming stock market, occurred at the same time and surely had some effect on household decisions. In this case, higher consumption and lower national saving could coincide with a tax cut without contradicting Ricardian equivalence. Because neither interpretation of history can be ruled out, both the conventional and Ricardian views of government debt continue to have adherents within the economics profession.

4.1.2. A brief history o f the Ricardian idea The modern literature on Ricardian equivalence began with Robert Barro's 1974 paper. Not only did this paper clearly set out the Ricardian argument but it also anticipated much of the subsequent literature by discussing many of the reasons why Ricardian equivalence might not hold. What the paper did not do, however, was credit Ricardo with the idea. It was not until James Buchanan's 1976 comment on Barro's paper that the term Ricardian equiualence was coined. Ricardo was interested in the question of how a war might be funded. In an 1820 article, he considered an example of a war that cost 20 million pounds. He noted that if the interest rate were 5%, this expense could be financed with a one-time tax of 20 million pounds, a perpetual tax of 1 million pounds, or a tax of 1.2 million pounds for 45 years. He wrote, in point of economy, there is no real difference in either of the modes; for twenty millions in one payment, one million per annum for ever, or 1,200,0000 pounds for 45 years, are precisely of the same value ... Ricardo also was aware that the question raises the issue of intergenerational linkages (which we discuss more fully in a later section): It would be difficult to convince a man possessed of 20,000 pounds, or any other sum, thai a perpetual payment of 50 pounds per annum was equally burdensome with a single tax of 1000 pounds. He would have some vague notion that the 50 pounds per annum would be paid by posterity, and would not be paid by him; but if he leaves his fortune to his son, and leaves it charged with this perpetual tax, where is the difference whether he leaves him 20,000 pounds with the tax, or 19,000 pounds without it? Although Ricardo viewed these different methods of government finance as equivalent, he doubted whether other people in fact had the foresight to act in so rational a manner: The people who pay taxes ... do not manage their private affairs accordingly.We are apt to think that the war is burdensome only in proportion to what we are at the moment called to pay for il in taxes, without reflecting on the probable duration of such taxes.

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And, indeed, Ricardo did not dismiss g o v e r n m e n t debt as an insignificant p o l i c y concern. B e f o r e the British parliament, he once declared, This would be the happiest country in the world, and its progress in prosperity would go beyond the powers of imagination to conceive, if we got rid of two great evils - the national debt and the corn laws 19. B e c a u s e R i c a r d o doubted the practical validity o f R i c a r d i a n equivalence, O ' D r i s c o l l (1977) suggested the t e r m Ricardian non-equiualence, although this phrase has never caught on. W h e t h e r or not Ricardo was a Ricardian, he n o w gets credit for first noting the possible irrelevance o f g o v e r n m e n t debt. M o r e recently, several sources have suggested the possibility o f debt neutrality, as Barro in fact noted in his 1974 paper. In 1952, Tobin p o s e d the Ricardian question: How is it possible that society merely by the device of incurring a debt to itself can deceive itself into believing that it is wealthier? Do not the additional taxes which are necessary to carry the interest charges reduce the value of other components of private wealth? Tobin v i e w e d this R i c a r d i a n logic as raising an intriguing theoretical question, but he never suggested that it m i g h t actually h o l d in practice. The R i c a r d i a n a r g u m e n t also appears in Patinkin's (1965, p. 289) classic treatise, Money, Interest, and Prices, which was based on a 1947 dissertation at the U n i v e r s i t y o f Chicago. In c o n s i d e r i n g whether g o v e r n m e n t b o n d s should be treated as part o f h o u s e h o l d wealth, Patinkin wrote, The difficulty with this approach is that tile interest burden on these bonds must presumably be financed by future taxes. Hence if the private sector discounts its future tax liabilities in the same way that it discounts future interest receipts, the existence of government bonds will not generate any net wealth effect. Patinkin does not c l a i m originality for this idea. In a footnote, he says, "This p o i n t is due to Carl Christ, w h o cites in turn discussions w i t h M i l t o n Friedman". In 1962, M a r t i n Bailey's textbook explained clearly (p. 75) the possibility "that households regard deficit financing as equivalent to taxes". B a i l e y explains: [Govermnent debt] implies future taxes that would not be necessary if the expenditures were financed with current taxation. If a typical household were to save the entire amount that was made available to it by a switch from current taxation to deficit financing, the interest on the saving would meet the future tax charges to pay interest on the government bonds, while the principal saved would be available to meet possible future taxes imposed to repay the principal on the govermnent bonds. If the household has a definite idea of how it wants to allocate its total present and future resources among consumption at different points of time, and if it recognizes that the shift from current taxation to deficit financing does not change its total resources at all l~om a long-run point of view, then it will indeed put entirely into saving any 'income' made available to it by a government decision to finance by bond issue rather than current taxation.

19 Quoted m Buchholz (1989, p. 73). Ricardo's opposition to the corn laws (which restricted the imporl of grain from abroad) suggests that he took his theory of comparative advantage more seriously than he did his theory of debt neutrality.

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That is, the household will consume exactly the same amount, whichever form of financing is used. Bailey even points out in a footnote that "the same argument applies if no repayment [of the debt's principal] is expected, if the typical household plans to leave an estate". Bailey does not cite Ricardo, but in the text's preface he refers to this section and notes, "a claim to original authorship must be shared with at least two other persons, Gary Becker and Reuben Kessel, who independently developed the same material for their respective courses". The idea of Ricardian equivalence, therefore, has had a long and distinguished history. Yet there is no doubt that Robert Barro's 1974 paper was a turning point in the literature on government debt. Barro stated the conditions for Ricardian equivalence more clearly than the previous literature had, and he laid out explicitly the intergenerational model needed to establish the result. (We discuss this model below.) Perhaps the greater thoroughness in Barro's treatment of the issue is founded in his apparent belief in debt neutrality. Previous authors, including Ricardo, raised the theoretical possibility of neutrality but often doubted its practical applicability. In a way, Barro can be viewed as the Christopher Columbus of Ricardian equivalence. Columbus was not the first European to discover America, for Leif Ericsson and others had come before. Instead, Columbus' great confidence in the importance of his mission ensured that he was the last European to discover America: after Columbus, America stayed discovered. Similarly, Robert Barro was not the first economist to discover Ricardian eqnivalence, but he was surely the last. Since Barro's work, Ricardian equivalence has maintained its place at the center of the debate over government debt, and no one will be able to discover it again. 4.1.3. Why Ricardian equioalence is so important

Although most economists today agree with David Ricardo and doubt that Ricardian equivalence describes actual consumer behavior, the idea of Ricardian equivalence has been extraordinarily important within the academic debate over government debt. There are two reasons for this. The first reason is that a small but prominent minority of economists, including Robert Barro, have argued that Ricardian equivalence does in fact describe the world, at least as a first approximation. This small group has provided a usefut reminder to the rest of the profession that the conventional view of government debt is far from a scientific certitude. The inability of macroeconomists to perform true experiments makes macroeconomic knowledge open to debate. Although we believe that policymakers are best advised to rely on the conventional view of government debt, we admit that there is room for reasonable disagreement. The second and more significant reason that Ricardian equivalence is important is that it offers a theoretical benchmark for much further analysis. There are many parallels both inside and outside of economics. Mathematicians study Euclidean geometry (even though we now kalow that we live in a non-Euclidean world);

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physicists study frictionless planes (even though all real planes exhibit some friction); and economists study Arrow-Debreu general-equilibrium models with complete and perfectly competitive markets (even though markets in actual economies are neither complete nor perfectly competitive). The theoretical benchmark in economics that is most similar to Ricardian equivalence is the Modigliani-Miller theorem. Modigliani and Miller established conditions under which a firm's choice between debt and equity finance is irrelevant. Similarly, Ricardian equivalence is the claim that the govermnent's choice between debt and tax finance is irrelevant. Few finance economists believe that the Modigliani-Miller theorem describes actual fix'ms' financing decisions. Nonetheless, the theorem provides a starting point for many discussions in corporate finance. Similarly, even if Ricardian equivalence does not describe the world, it can be viewed as one natural starting point in the theoretical analysis of government debt. As the next section should make clear, trying to explain why Ricardian equivalence is not true can yield a deeper understanding about the effects of government debt on the economy. 4.2. The debate ouer Ricardian equivalence: theoretical issues

Although most economists today are skeptical of the Ricardian proposition that government debt is irrelevant, there is less consensus about why government debt matters. The conventional view (which we discussed earlier) begins with the premise that a debt-financed tax cut stimulates consumption. There are various reasons why this might be the case. 4.2.1. Intergenerational redistribution

One reason governrnent debt might matter is that it represents a redistribution of resources across different generations of taxpayers. When the government cuts taxes and issues government debt today, the government budget constraint requires a tax increase in the future, but that tax increase might fall on taxpayers who are not yet living. This redistribution of resources from future to current taxpayers enriches those who are now living; current taxpayers respond to the increase in their resources by consuming more. This intergenerational redistribution is tbe mechanism that makes government debt matter in basic overlapping-generations models, such as those of Diamond (1965) and Blanchard (1985). Barro's 1974 paper built on Becker's (1974) theory of the family to provide a clever rejoinder to this argument. Barro argued that because future generations are the children and grandchildren of the current generation, it is a mistake to view them as independent economic actors. Instead, Barro suggested that current generations might behave altruistically toward future generations. In the presence of this intergenerational altruism, it is no longer natural to presume that current generations will take advantage of the opportunity to consume at the expense of future generations.

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Barro proposed the following model of the family. Suppose that the total utility of generation t, denoted Vt, depends on consumption during its lifetime Ct and on the utility of its children Vt+l, discounted by some factor/3: vt = u ( G ) +/3vt+L. Recursive substitution establishes that

Vt = U(Ct) -}-/3U(CI+I) +/32U(Ct+2 ) q_/33U(Ct+3 ) + . . . That is, the utility of generation t depends on its own consumption and the consumption of all future generations. In essence, the relevant decisionmaldng unit is not the individual, who lives only a finite number of years, but the family, which continues forever. As a result, the family member alive today decides how much to consume based not only on his own income but also on the income of future members of his family. Ricardian equivalence is, therefore, preserved: a debt-financed tax cut may raise the income an individual receives in his lifetime, but it does not raise his family's permanent income. Instead of consuming the extra income from the tax cut, the individual saves it and leaves it as a bequest to his descendants, who will bear the future tax liability. The debate over Ricardian equivalence is, therefore, in part a debate over how different generations are linked to one another. This issue has broad significance for macroeconomics. As Kotlikoff and Summers (1981) established, a large fraction of wealth in the US economy is eventually bequeathed rather than consumed by its current owner 2°. It is possible that many bequests are accidental rather than intentional; that is, people might leave bequests because they die unexpectedly before consuming their entire wealth. Yet the fact that annuity markets (even if imperfect) are used so rarely suggests that consumers must have some desire to leave bequests. The altruism model proposed by Barro is one possible model of the bequest motive, but there are others. Another popular model is the "joy of giving" or "warm glow" model, according to which a person's utility depends on the size of his bequest rather than on the utility of his children. That is,

V, = U(Ct) + G(B~), where G(Bt) represents the utility from giving a bequest of size B , Closely related to this model is the "strategic bequest motive" proposed by Bernheim et al. (1985); according to this model, parents use bequests to induce certain types of behavior from their children, such as visiting home more frequently. These alternative models of the bequest motive do not give individuals any reason to look ahead to their children's

20 For oilier discussions of the role of intergenerational transt~rs in wealth accumulation, see Gate and Scholz (1994), Kesslerand Masson (1989), Kotlikoff (1988), and Modigliani (1988).

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tax liabilities and, therefore, do not yield Ricardian equivalence in the presence of policy-induced intergenerational redistributions. It is sometimes mistakenly claimed that the effects of government debt depend on whether people have finite lives (as is the case in the Diamond overlapping-generations model) or infinite lives (as is effectively the case in the Barro intergenerational-altruism model). The key issue, however, is not the finiteness of life but the introduction over time of new taxpayers without links to the past. [This point was established by Philippe Weil (1989).] To see this, imagine an economy in which consumers die (according to some Poisson process) but no new consumers are ever born. In this economy, all future tax liabilities must fall on people who are currently living, so Ricardian equivalence would hold, despite the finiteness of life. By contrast, consider an economy in which new consumers are born over time but, once born, live forever. In this economy, some of the future tax liabilities implied by government debt would fall on future arrivals, and Ricardian equivalence would fail to hold. The Barro model of intergenerational altruism, which links all future arrivals to those currently living, has attracted a variety of theoretical criticisms. One of the more entertaining is that offered by Bernheim and Bagwell (1988), who build on the well established tenet that human reproduction is sexual and that, as a result, people share common descendants. Indeed, if one looks back and forth among everyone's future family trees, one quickly concludes that the entire world population is connected through a web of familial relationships. This observation, together with intergenerational altruism, yields profound predictions. According to the Barro model, a transfer of a dollar (in present value) between Doug Elmendorf and one of his descendants does not affect anyone's consumption. Similarly, a transfer between Greg Mankiw and one of his descendants does not affect anyone's consumption. But if Elmendorf and Mankiw have common descendants, as surely they must, then a transfer between Elmendorf and Mankiw does not affect anyone's consumption. Indeed, because everyone is connected through common descendants, the entire distribution of income is irrelevant - a prediction that is surely false. Bernheim and Bagwell use this argument as a reductio ad absurdum to conclude that the Barro model cannot describe the relationships among generations. A less intriguing, but ultimately more persuasive, critique of the Barro model of intergenerational altruism arises from the work of Evans (1991), Daniel (1993), and Smetters (1996). Suppose that we consider a standard model of intergenerational altruism but add the seemingly innocuous wrinkle that the degree of altruism (as measured above by the parameter fi) differs across families. Even if all consumers have some degree of altruism, it is likely in the presence of heterogeneity that many consumers will not have operative bequest motives. In the steady state of such a model, the interest rate is determined by the time preference of the most patient family (that is, the family with the highest fi). At this interest rate, other families will choose to hit the corner solution of zero bequests and, therefore, will act like a series of overlapping generations: they will save for life-cycle reasons but will leave no bequests. For these zero-bequest families, transfers of resources across generations will have real effects.

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Despite the failure o f Ricardian equivalence in this model, the level o f government debt does not matter for aggregate variables in the economy's steady state. Because the time preference of the most patient family pins down the steady-state interest rate, it also pins down the capital stock and the level o f output. A debt-financed tax cut, for instance, will stimulate consumption, crowd out capital, and raise the real interest rate for a period o f time, but the most patient family will respond by increasing saving until, eventually, the capital stock and real interest rate return to their former levels. This result suggests that Ricardian equivalence may work better as a long-run theory than as a short-run theory. Finally, it is worth noting that, for some purposes, the importance o f these intergenerational issues may be overstated. Poterba and Summers (1987) claim that, even without intergenerational altruism, people may have long enough time horizons to make Ricardian equivalence approximately true in the short run for some policy interventions. For example, imagine that the government cuts taxes today, issues government debt with an interest rate of 5%, and then services the interest payments with higher taxes over the infinite futm'e. In this case, about 77% of the future taxes occur within 30 years, indicating that the redistribution o f the tax burden toward future generations, though not zero, is relatively small. Moreover, because the marginal propensity to consume out of wealth for life-cycle consumers is relatively small, the redistribution that does occur has only a small effect on consumption. Thus, the immediate result may be an increase in private saving approximately equal to the budget deficit. Poterba and Smnmers argue that if Ricardian eqnivalence fails in a substantial way in the short run, the explanation must lie not in the intergenerational redistribution caused by government debt but in some other mechanism 21. 4.2.2. Capital market imperfections

The simplest, and perhaps most compelling, explanation for the failure o f Ricardian equivalence is the existence of capital market imperfections. For households thal discount future utility highly or that expect rapidly rising income, the optimal consumption path may require consuming more than their income when young (and less when old) by borrowing in financial markets. The possibility of default and bankruptcy, however, may prevent these households from borrowing for the purposes o f current consumption. In this case, the optimal strategy is to consume all o f current income and hold exactly zero assets.

2I Even if private saving does rise approximately one-tbl~one with the budget deficit in thc short run, there could be substantial crowding out of capital in the long run. The Auerbac~Kotlikoff simulations discussed earlier suggest that the full effects of government debt take a long time to appeal in life-cycle models. Thus, the Poterba-Summers argument raises the possibility -- in contrast to the model with heterogeneous altruism just discussed - that Ricardian equivalence may work well as a short-run theory but not as a long-run theory.

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In the presence of such a binding borrowing constraint, Ricardian equivalence will no longer hold. A debt-financed tax cut effectively gives the constrained household the loan that it wanted but could not obtain from private lenders. The household will respond by increasing consumption, even with the knowledge that the result is higher taxes and lower consumption in the future. The potential importance of capital market imperfections is highlighted by the small amount of wealth that many people hold compared to the level of government debt in our economy. In recent years, the federal government debt has been about half of national income. If Ricardian equivalence held, the typical household should be holding additional wealth equal to half of annual income. Yet many households have wealth far below that level. To reconcile Ricardian equivalence with these facts, one would need to believe that in the absence of government debt, most households in the economy would have substantially negative net wealth. This seems implausible: few consumers are able to obtain substantial loans without tangible collateral. Thus, it seems that government debt has allowed many households to consume more than they otherwise would. The literature contains some debate over whether capital market imperfections should cause a failure of Ricardian equivalence. Hayashi (1987) and Yotsuzuka (1987) present examples of endogenous capital market imperfections based on asymmetric information that preserve Ricardian equivalence. In these models, asymmetric information about future income, together with the possibility of default, prevents households from borrowing against future income. Yet because taxes are assumed to be lump sum, there is no information problem about the stream of tax payments; as a result, the borrowing constraint does not affect the ability of households to trade off taxes today and taxes in the future. In this case, a debt-financed tax cut causes the borrowing constraint to adjust in such a way as to leave consumption opportunities unchanged. As Bernheim (1987) points out, however, this result is crucially dependent on the assumption that taxes are lump sum. I f taxes rise with income, then the asymmetry in information about future income causes a similar asymmetry in information about future tax liabilities, in this more realistic case, these models yield the more conventional result that a debt-financed tax cut relaxes the borrowing constraint, allowing households to consume more. 4.2.3. Permanent postponement o f the tax burden

When a person first hears the case tbr Ricardian equivalence, a natural response is, "Yes, that theory might apply if a budget deficit today required higher taxation in the future. But, in fact, the government never has to pay offits debts. When the government cuts taxes and runs a budget deficit, it can postpone the tax burden indefinitely". This simple argument, it turns out, raises a number of complex questions for economic theory. The first point to make is that Ricardian equivalence does not require that the government ever pay off its debts in the sense of reaching zero indebtedness. Imagine

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that the government cuts taxes for one year by dD, increases the government debt by that amount, and then leaves government debt at the new higher level forever. To service this additional government debt would require additional taxes of r × d D every year, where r is the interest rate on the debt. The present discounted value of these higher taxes is dD, which exactly offsets the value of the tax cut. Hence, if consumers look ahead to all future taxes, Ricardian equivalence holds, even though the government never retires the additional debt it has issued. Matters become more complicated if the government does not raise taxes to finance the interest on this additional debt but, instead, finances these interest payments by issuing even more debt. This policy is sometimes called a "Ponzi scheme" because it resembles investment scams in which old investors are paid off with money from new investors. If the government pursues such a Ponzi scheme, the government debt will grow at rate r, and the initial tax cut and budget deficit do not imply higher taxes in the future. But can the government actually get away with this Ponzi scheme? The literature has explored this question extensively 22. An important issue is the comparison between the interest rate on government debt r and the growth rate of the economy g. If r is greater than g, then government debt will increase faster than the economy, and the Ponzi scheme will eventually be rendered infeasible: the debt will grow so large that the government will be unable to find buyers for all of it, forcing either default or a tax increase. By contrast, if r is less than g, then government debt will increase more slowly than the economy, and there is nothing to prevent the government from rolling over the debt forever. The comparison between r and g has broader generaPequilibrium implications, however, and these implications help explain the effects of government debt. In standard neoclassical growth theory, r reflects the marginal product of capital, and g reflects population growth and technological change. These two variables can be used to gauge whether the economy has reached a dynamically efficient equilibrium. If r is greater than g, then the economy is efficient in the sense of having less capital than at the "Golden Rule" steady state. By contrast, if r is less than g, then the economy is inefficient in the sense of having accumulated too much capital. In this case, a reduction in capital accumulation can potentially increase consumption in all periods of time. A govermnent Ponzi scheme, like the "asset bubbles" studied by Tirole (1985), is both feasible and desirable in such an economy because it helps ameliorate the problem of oversaving. Dynamic inefficiency and successful, Pareto-improving Ponzi schemes offer an intriguing theoretical possibility, but they are not of great practical relevance for the US economy or other economies around the world. Economists today do not believe that households are saving too much, driving the return to capital below the economy's

22 See, for instance, Ball et al. (1998), Blanchard and Weil (t992), Bohn (1993), and O'Connell and Zeldes (1988).

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growth rate. And, indeed, Abel et al. (1989) present evidence for dynamic efficiency. Hence, Ricardian equivalence cannot be refuted by asserting that the government can roll over the debt forever. Yet one nagging fact remains: in the US economy, the interest rate on government debt has on average been less than the growth rate of the economy. Abel et al. reconcile this fact with their finding of dynamic efficiency by noting that government debt and economic growth have different risk characteristics. They present an example o f a dynamically efficient economy in which uncertainty about economic growth drives down the return on risk-free assets, such as government debt, below the average growth rate. Thus, one cannot judge dynamic efficiency (and the feasibility of government Ponzi schemes) simply by comparing the average return on risk-free assets with the average growth rate 23.

4.2.4. Distortionary taxes The Ricardian equivalence proposition is based on the assumption that taxes are lump sum. If instead taxes are distortionary, then a postponement o f the tax burden affects incentives and thereby behavior. These microeconomic distortions could have a large macroeconomic impact, making Ricardian equivalence a poor approximation to reality. To see the potential importance o f distortionary taxation, imagine an economy described by the standard Ramsey growth model except that taxes, rather than being lump-sum, are raised with a proportional income tax with rate r. The following equations describe the steady state:

y=f(k),

Ty-rD+g,

r-if(k),

(1

r)r =p.

The first equation is the production function. The second equation states that tax revenue ry equals the interest on the debt rD plus government spending g. The third equation states that the interest rate r equals the marginal product of capital. (Both interest income and capital income are assumed to be taxed at the same rate, so the tax does not affect this equation.) The fourth equation states that the after-tax interest rate equals the rate of subjective time preference p; this is the steady-state condition for the Ramsey model. Given these equations, it is straightforward to see how an increase in government debt affects the economy. Higher debt leads to higher debt service; a

23 Ball et al. (1998) build on these ideas and consider policies in dynamically efficient economies called "Ponzi gambles" in which the government cuts taxes and rolls over the resulting debt for as long as is possible. In their model, debt can raise the welfare of all generations in those realizations of history in which taxes do not need to be increased. Yet the policy is a gamble because the government is sometimes forced to raise taxes. Moreover, those tax increases are especially undesirable because they occur in realizations of history in which future generations are already burdened by low economic growth.

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higher debt service requires a higher tax rate; a higher tax rate implies a higher beforetax interest rate; and a higher interest rate requires a smaller steady-state capital stock. As in the traditional analysis, government debt crowds out capital, even though the mechanism here is quite different. We can easily calibrate the magnitude of this effect for this model. By fully differentiating this system we obtain an expression to show how much debt crowds out capital:

dDdk - { r -~D Jf "l + -l - r ' )~/ f "~}

'

If we specialize the production function to Cobb-Douglas y - U ~, then this expression becomes: dk { D r+(1 -(1dD - a) ~

r ) l - ce~-I ~}

For the US economy, taxes take about one-third of income ( T - 1/3), capital earns about one third of income (a = 1/3), and the debt equals about one-seventh of the capital stock (D/k = 1/7). For these paranaeter values, dk/dD =-1.11. That is, an extra dollar of government debt reduces the steady-state capital stock by slightly over one dollar. This example shows that substantial crowding out can occur simply because of distortionary taxation 24. Although this example is sufficient to show the potential importance of distortionary taxation, more realistic analyses of debt policy go beyond this special case. In the steady state of the Ramsey model, national saving is infinitely elastic at the rate of time preference. Other models, such as the life-cycle model of Auerbach and Kotlikoff (1987), would predict a more limited saving response to a change in the after-tax rate of return. In addition, it is important to consider the dynamic effects of tax changes, as in Judd (1987) and Dotsey (1994), and the effects of taxes on labor supply, as in Trostel (1993) and Ludvigson (1996). Perhaps the only certain conclusion is that in a world with distortionary taxation, Ricardian equivalence is unlikely to provide a good first approximation to the true effects of debt policy.

4.2.5. Income uncertainty Another possible reason tbr the failure of Ricardian equivalence is that government debt may alter consumers' perception of the risks they face. This possibility was

24 The numerical results presented here are, of course, sensitive to a variety of detailed asstm~ptions. If we introduce depreciation, so that the production function is.f (k) - k c*- 6k, then the degree of crowding as measured by dk/dD falls. If we take a broad view of capital, so that a is larger than t/3, then the degree of crowding rises.

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explored by Chan (1983), Barsky et al. (1986), Kimball and Mankiw (1989) and Croushore (1996). These authors begin with the axioms that taxes are levied as a function of income and that furore income is uncertain. Therefore, when the government cuts taxes today, issues government debt, and raises income taxes in the future to pay off the debt, consumers' expected lifetime income is unchanged, but the uncertainty they face is reduced. If consumers have a precautionary saving motive, this reduction in uncertainty stimulates current consumption. Put differently, consumers discount risky uncertain income and uncertain future taxes at a higher rate than the interest rate on government bonds; a postponement of the tax burden, therefore, encourages current spending. The potential importance of this mechanism is highlighted by the recent interest in buffer-stock theories of saving. [See, for instance, Carroll (1997).] In these models, consumers are impatient (in the sense of having a high subjective discount rate) but are nonetheless prudent (in the sense of having a precautionary saving motive). As a result, consumers maintain a small amount of saving in order to protect themselves against unlikely but very adverse shocks to their income. If consumers do not pay significant taxes when these unlikely, adverse outcomes are realized, then a postponement of the tax burden will stimulate current consumption. 4.2.6. Myopia

When non-economists are explained the idea of Ricardian equivalence, they often have trouble taking the idea seriously. The reason for this response goes to the heart of how economists view human behavior. Rational, optimizing, forward-looking homo economicus is a creature of the economist's imagination. Economists are trained in the power of this model, but non-economists are often more skeptical. In particulai, non-economists are doubtful about whether people have the foresight to look ahead to the future taxes implied by government debt, as is required for Ricardian equivalence to hold. It is hard to incorporate this sort of myopia into economic theory. Yet there have been some attempts to model short-sightedness. Strotz (1956) and Laibson (1997), for instance, consider preferences according to which consumers give excessive weight to current utility (compared to the benchmark case of exponential discounting). As a result, consumers exhibit time-inconsistent behavior and can be made better off through a binding commitment to increased saving. This model can explain the popular notion that people save too little, but it cannot by itself explain a failure of Ricardian equivalence. In this model, the time-inconsistent consumer faces a standard intertemporal budget constraint, so a postponement of the tax burden does not alter the consumer's opportunities. This consumer saves too little but, without a binding borrowing constraint or other imperfection, is fully Ricardian in response to fiscal policy. Although the ILicardian behavior of Strotz-Laibson consumers shows that myopia by itself need not undermine Ricardian equivalence, this result does not necessarily

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render myopia irrelevant in this debate. The impatience implicit in the Strotz-Laibson preferences can explain the prevalence of liquidity constraints and buffer-stock saving, which in turn highlights the deviations from Ricardian equivalence emphasized earlier. In addition, it is possible that the Strotz-Laibson approach to modelling myopia is not the best one. Developing better models of myopic behavior remains a challenge for future research. 4.3. The debate over Ricardian equivalence. empirical issues'

The theoretical literature just discussed offers various reasons why government debt may affect consumption and capital accumulation. Yet these deviations from Ricardian equivalence do not prove that the proposition is a bad first approximation of the actual economy. To reach such a judgment, one must assess the quantitative importance of these theoretical deviations from the Ricardian benchmark. Some of the research discussed earlier bears on this issue. As noted above, calculations using the Blanchard model of finite lifetimes imply that debt can crowd out a significant amount of capital, and Auerbach and Kotlikoff's simulations show that the combination of finite lifetimes and distortionary taxes can generate roughly one-for-one crowding out. Moreover, many of the theoretical analyses cited in the previous section include calibrations that illustrate the potential importance of the channels through which debt may affect the economy. Simulations, however, are no substitute for evidence. In this section we review the empirical evidence on the validity of Ricardian equivalence. We begin with tests of the assumptions underlying the proposition and conclude that a substantial fraction of households probably do not behave as the proposition assumes. We next turn to tests of the proposition's implications for various macroeconomic variables. Despite substantial research in this area, we believe that the results are ultimately inconclusive 25. 4.3.1. Testing assumptions about household behaoior

When testing theories, economists typically focus on the theories' implications rather than their assumptions. Yet, because testing the implications of Ricardian equivalence raises substantialdifficulties, examining the underlying assumptions is also worthwhile. The key assumption is consumption smoothing both within lifetimes and across generations. That is, households are assumed to choose consumption and saving based on a rational evaluation of an intertemporal budget constraint that includes both current: and future generations. One piece of evidence that many households do not behave in this way is the small amount of wealth that they hold. This situation may arise from a combination of

25 Our review of this litcrattue is necessarily brieE For more thorough discussions with additional citations, see Bernheim (1987) and Seater (1993).

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impatience and borrowing constraints, as described earlier, or because some people are not very forward-looking. In either case, a deficit-financed tax cut would spur consumption. Numerous papers also present evidence that people do not smooth consumption fully over time. Campbell and Mankiw (1989) use aggregate data to show that consumption is more sensitive to current income than the basic consumptionsmoothing model predicts. Hall and Mishkin (1982), Zeldes (1989), and Carroll and Summers (1991) make the same point using household data. Further confirmation comes from households' responses to changes in taxes and government benefits; for example, see Poterba (1988), Wilcox (1989), and Shapiro and Slemrod (1995). In these studies, deviations from the life-cycle model are economically as well as statistically significant. Some studies, such as Runkle (1991), Attanasio and Browning (1995), and Attanasio and Weber (1995), have argued that income and consumption data are in fact consistent with the consumption-smoothing model. But the weight of the evidence from the consumption literature is that consumption smoothing is far from complete. In our view, this conclusion casts serious doubt on the empirical plausibility of Ricardian equivalence. 4.3.2. Testing the implications Jbr consumption A large and contentious literature has focused on the implication of Ricardian equivalence that a reduction in current taxes with no change in current or future government spending should not affect household consumption. The standard approach is to estimate a traditional aggregate consumption function, with consumer spending as the dependent variable and income, wealth, fiscal policy, and various other controls as independent variables. Ricardian equivalence is rejected if the coefficients on taxes and debt are significantly different from zero. Although this approach seems to offer a direct test of the Ricardian view, there are a number of problems with its implementation. The fit'st problem is the treatment of expectations. The behavior of forward-looking households depends on expectations of fiscal policy, not just the measures of current fiscal policy that are included in these regressions. Suppose that the current level of taxation reflects expectations of fitture government spending. (This is in fact implied by the theory of tax smoothing, which we discuss later.) In this case, a significant negative coefficient on current taxes in the consumption function does not necessarily violate Ricardian equivalence. A second problem is simultaneity. Some of this literature estimates the consumption function with ordinary least squares. This approach is valid only if the shocks to the consumption function do not affect fiscal policy or other right-hand side variables. Other papers attempt to address this problem using instrumental variables, but finding persuasive instruments is close to impossible 26. ~' For a discussion of tile identification problem in the context of tests of Ricardian equivaJcncc, see Cardia (1997).

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D. lie Elmendorf and N.G. Mankiw

A third problem in this literature is that the number of observations is small compared with the number of highly correlated explanatory variables, h~ addition to the basic fiscal variables, some authors include measures of the marginal tax rate, while others separate taxes and spending by the level of government. Still others decompose the income and fiscal variables into permanent and transitory components as a way of capturing expectations. Although there may be good reasons to include these variables as a matter of theory, their addition compounds the problem of multicollinearity. One way to increase the independent variation in the explanatory variables is to use a longer estimation period, but this procedure can introduce spans in which consumption is clearly distorted, such as during wars. A final problem is that these specifications may have little power to distinguish between the Ricardian and conventional views of fiscal policy. As discussed earlier, life-cycle consumers' marginal propensity to consume out of a temporary tax cut may be only a few cents on the dollar. This value may be statistically indistinguishable from the Ricardian benchmark of zero effect. Nonetheless, the difference between a small and a zero marginal propensity to consume is economically important, for a small short-run drop in saving can cumulate to a large long-run decline in the capital stock. Various recent papers have tried to avoid some of these problems by building on the Euler equation approach pioneered by Hall (1978). By looking at the firstorder condition for a representative consumer, rather than an aggregate consumption function, some of the problems in measuring expectations are avoided. Yet the problem of power remains. The first-order condition for a finite-horizon consumer in the Blanchard model is not very different from the first-order condition for an infinitehorizon consumer. Nonetheless, policy can have substantially different effects in the two cases, especially in the long run. With these problems in mind, it is perhaps not surprising that this literature has failed to reach a consensus on the validity of Ricardian equivalence. Some researchers have concluded that equivalence is a reasonable description of the world; for example, see Kormendi (1983), Aschauer (1985), Seater and Mariano (1985), Evans (1988) and Kormendi and Meguire (1986, 1990, 1995). Other researchers have reached the opposite conclusion; for example, see Feldstein (1982), Modigliani and Sterling (1986, 1990), Feldstein and Elmendorf (1990), Evans (1993), and Graham and Himarios (1991, 1996). Our view is that this literature considered as a whole is simply inconclusive. Many studies that fail to reject Ricardian equivalence are also unable to reject the life-cycle model, as their standard errors are large relative to the difference in coefficient values implied by the alternative hypotheses 27. Further, some studies that find insignificant

2"1 For example, see Evans (1988), Kormendi and Meguire (1990), and Seater and Mariano (1985). The latter paper presents an extreme example of lack of power: the authors cannot reject the hypothesis that the coefficienton taxes equals zero, but neither can they reject that it equals minus one.

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effects o f taxes on consumption also find insignificant effects o f government spending, which is inconsistent with both Ricardian and life-cycle models and suggests that this framework does not reflect the true effects o f fiscal policy %. More generally, most results in this literature appear very sensitive to small differences in specification 29. 4.3.3. Testing the implications f o r interest rates

Ricardian equivalence implies that a debt-financed reduction in government revenue should not affect interest rates. The conventional view o f debt generally implies the opposite. A n important set o f papers tests this implication by examining the effect o f the budget deficit on interest rates after controlling for government spending and other influences. As with the literature concerning the consumption effects of fiscal policy, research into interest-rate effects appears straightforward, but numerous problems quickly arise. Indeed, some o f the problems in the two literatures are quite similar. One problem is that interest rates depend on expectations o f fiscal policy and other variables and those expectations are hard to measure. A number of studies use forecasts from vector autoregressions as a proxy for expectations, but the quality of those proxies is unclear. Vector autoregressions assume that variables follow a stable time-series process, and they do not incorporate non-quantitative information. Both of these points are likely to be important, especially for fiscal policy variables, which are the outcome o f a political process. Measurement error in the proxies for expectations biases the estimated coefficients toward zero and, thus, toward the null hypothesis of Ricardian equivalence. A second problem with this approach as a test o f Ricardian equivalence is thai there is no natural metric for gauging the size of interest-rate effects. For the effect o f taxes on consumption, there are natural Keynesian and life-cycle benchmarks as well as the Ricardian benchmark. Indeed, this feature was critical in assessing whether tests of Ricardian equivalence had any power against alternative descriptions o f the world. But no such alternative benchmarks exist for interest rates, because the size of the movements expected under non-Ricardian views depends on a host of elasticities. In particular, if international capital flows have an important effect on the domestic

28 For example, see Seater and Mariano (1985). 29 For example, some of the strongest evidence in favor of Ricardian equivalence comes from the especially thorough investigation conducted by Kormendi (1983) and Kormendi and Meguire (1986, 1990, 1995). Yet, Kormendi and Meguire (1990) show that although theh results are robust to a variety of changes in specification (Table 1), they are not robust to the seemingly innocuous choice of deflator (Table 2). For further discussion of Kormendi and Meguire's specification, see the exchanges between them and Barth et al. (1986), Modigliani and Sterling (1986, 1990), and Graham (1995). As another example of the sensitivity of results, Graham and Himarios (1991, 1996) show that the estimates of Aschauer (1985) and Evans (1988) are not robust to alternative formulations of the Euler equation or measures of consumption.

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financial market, interest rates may not respond much to fiscal policy even if Ricardian equivalence is invalid. With these caveats in mind, it is worth noting that this literature has typically supported the Ricardian view that budget deficits have no effect on interest rates. Plosser (1982) pioneered the approach of measuring expected policy using vector autoregressions. Further work in this vein by Plosser (1987), Evans (1987a, 1987b) and Boothe and Reid (1989) has confirmed Plosser's original conclusion that a zero effect o f deficits cannot be rejected 3°. Our view is that this literature, like tile literature regarding the effect o f fiscal policy on consumption, is ultimately not very informative. Examined carefully, the results are simply too hard to swallow, for three reasons. First, the estimated effects o f policy variables are often not robust to changes in sample period or specification 31. Second, the measures of expectations included in the regressions generally explain only a small part of the total variation in interest rates. For example, the average R-squared of Plosser's basic monthly regressions [Plosser (1987), Tables 6 and 7] is 0.06, and the corresponding value of Evans' basic quarterly regressions [Evans (1987b), Table 1] is 0.09. This poor fit suggests some combination of measurement error in expectations and the omission o f other relevant (and possibly correlated) variables. Under either explanation, the estimated coefficients on the policy variables must be viewed with skepticism. Third, Plosser (1987) and Evans (1987b) generally cannot reject the hypothesis that government spending, budget deficits, and monetary policy each have no effect on interest rates. Plosser (1987) also reports that expected inflation has no significant effect on nominal interest rates. These findings suggest that this framework has little power to measure the true effects o f policy. 4.3.4. Testing the implications Jor international variables

Ricardian equivalence implies that a debt-financed reduction in government revenue should not affect the exchange rate or the current account. In contrast, the conventional view o f debt implies that the exchange rate should appreciate in these circumstances and the trade deficit should increase. Several researchers have tested these implications and reached conflicting conclusions. Evans (1986) applies to exchange rates the methodology used by Plosser and Evans to study the effect of budget deficits on interest rates. He concludes that US budget

30 Dii-Ierentsorts of analyses by Evans (1985), Hoelscher (1986), and Wachtel and Yomlg (1987) have reached mixed conclusions. 31 For example, Plosser (1987, Table 10) reports sharply different coefficient estimates during the 1968 1976 and 1977-1985 sample periods and using monthly data as opposed to quarterly data. As another example, Evans (1987a, Tables 1 and 2) estimates that budget deficits had a small and statistically insignificant effect on nominal interest rates during the 1950s, 1960s and 1970s, but an effect that was large, statistically significant, and surprisingly negative between 1979 and 1984. Of course, the effect of budget deficits may well have changed over time, but an estimated shift of this magnitude signals some problem with specification.

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deficits tend to cause a depreciation o f the dollar, in contrast to both the Ricardian and conventional views. Evans' analysis is subject to the same problems that plague the interest-rate literature discussed above 32. Moreover, a decline in the dollar should cause a strengthening o f tbe trade balance. Yet Bernheim (1988) and Rosensweig and Tallman (1993) conclude that US trade deficits worsen when the US budget deficit increases. In the end, the empirical literature examining the effects o f fiscal policy on consumption, interest rates, and international variables fails to offer clear evidence either for or against the Ricardian hypothesis. If the evidence is so weak, why then do most economists feel confident in rejecting Ricardian equivalence as a description o f the world? The answer, we believe, is that most economists are incredulous about the assumptions that are needed to support the Ricardian view o f government debt. In this case, the debate over theory is more persuasive than the debate over evidence.

5. Optimal debt

policy

Disagreement about the appropriate amount o f government debt in the USA is as old as the country itself. Alexander Hamilton (1781) believed that "a national debt, if it is not excessive, will be to us a national blessing", while James Madison (1790) argued that "a public debt is a public curse". Indeed, the location o f the nation's capital was chosen as part o f a deal in which the federal government assumed the Revolutionary War debts o f the states: because the Northern states had larger outstanding debts, the capital was located in the South. Attention to the national debt has waxed and waned over the years, but has been intense during the past two decades. Similarly, government debt and deficits have been a focus of recent public debate in many European countries. The appropriate use o f government debt depends on how debt affects the economy. As we have seen in the theoretical debate over Ricardian equivalence, debt could potentially have many different effects. As a result, the literature on optimal debt policy is broad in scope, ttere we focus on the three effects that are most often viewed as important: the use of debt policy to reduce the magnitude o f economic fluctuations, the use o f debt policy to increase national saving, and the use o f debt policy to reduce tax distortions by smoothing taxes over time. 5.1. Fiscal polioT over the business cycle

Although some economists argue that fluctuations in aggregate output represent an optimal response to shifts in preferences or technology, most economists believe that some output variability arises from rigidities or coordination failures. These changes

32 For example, fewer than half of the estimated coefficientsreported by Evans (1986, Tables 1 and 7) are statistically distinguishable fi'om zero.

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in output, and especially shortfalls of output relative to the potential determined by the available factors of production, are socially costly. In this case, timely adjustments to the government deficit and debt may raise social welfare. This notion of "countercyclical fiscal policy" dates at least to Keynes, and Blinder and Solow (1973) present one of the classic analyses. Countercyclical fiscal policy arises automatically from the design of tax and transfer programs. When output and income are high, tax liabilities rise and eligibility for government benefits falls, reducing the budget deficit; when output and income are low, these effects reverse and the deficit widens. These "automatic stabilizers" are important quantitatively. The Congressional Budget Office (1997a) estimates that when real output falls by 1%, tax revenue declines by about 1%. Countercyclical fiscal policy may also be implemented on a discretionary basis. For example, during the 1975 recession, Gerald Ford and Congress agreed to a small cut in personal income taxes. Over time, however, this sort of policy has fallen into disfavor. During the 1990 recession, for instance, taxpayers received a reduction in tax withholding but not tax liability. Part of this shift in views comes from a realization that an explicitly temporary change in taxes has only a small effect on the consumption of even moderately forward-looking consumers. Moreover, there are generally long lags in enacting discretionary changes in fiscal policy, so any effect on aggregate demand may be poorly timed. Finally, and perhaps most important, there is an increased appreciation for the ability of the Federal Reserve to conduct effective countercyclical monetary policy. 5.2. Fiscal policy and national saving

The most important long-run effect of government debt under tile conventional viewis to reduce national wealth. Thus, optimal debt policy in the long run depends primarily on optimal national saving. Current public debate often takes as given the netion that saving should be increased. Proving this point, however, is by no means straightforward. Bernheim (1994), Lazear (1994) and Hubbard and Skinner (1996) provide recent discussions of why more saving might be desirable. Examining this topic in detail is beyond the scope of this paper, but we consider briefly the issues that relate to government debt. We consider first whether debt policy should be used to make people save more for their own retirement, and then whether debt policy should be used to make current generations leave more wealth to future ones. 5.2.1. LiJe-cycle saving

Feldstein (1985) argues that people should do more saving within their lifetimes because the marginal product of capital exceeds their marginal rate of substitution between present and furore consumption. This wedge arises, he argues, because of the taxation of capital income. He is surely right that capital taxation distorts households'

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consumption decisions. But does this imply that debt policy should be used to increase national saving? The answer is not obvious. Suppose that people are life-cycle consumers whose consumption is distorted by capital taxation. Eliminating the distortion would be desirable, but this goal cannot be achieved simply through debt policy. For instance, if the govertmaent raises lumpsum taxation today, reduces government debt, and thereby reduces lump-sum taxation later within these consumers' lifetimes, Ricardian equivalence obtains, and national saving does not change. By contrast, Ricardian equivalence fails to hold if the future tax reductions benefit future generations. In this case, national saving rises because the income effect of current taxation reduces current generations' consumption. Nonetheless, the distortion between current and future consumption of any given generation is unchanged. That is, the increase in national saving induced by debt policy does not mitigate the distortionary effects of capital taxation. When considering how policy affects national saving, it is important to distinguish between the allocation of constmaption across a person's lifetime and the allocation of consumption across generations. Capital taxation inefficiently encourages consumption when a person is young compared to consumption when the same person is old. In a life-cycle model, however, debt policy does not affect this comparison. Instead, debt policy affects the consumption of current generations compared to the consumption of future generations. Thus, in a life-cycle model with rational consumers and distortionary capital taxes, life-cycle saving is inefficiently low, but debt policy cannot remedy the problem. 5.2.2. Intergenerational saoing

Debt policy can affect national saving by transferring resources among generations of life-cycle consumers. One approach to intergenerational equity in the context of debt policy is to focus on the appropriate distribution of paying for government services. The "benefit principle" implies that current spending should be financed out of current taxes, but capital spending should be financed over the life of the capital. Musgrave (1959) advocated this approach, terming it "pay-as-you-use finance" (p. 558)33. This principle provides one justification for the practice of financing wars which are expected to benefit future as well as current generations - largely through debt issuance. Another approach to intergenerational concerns about government debt is to consider the overall welfare of different generations using an explicit social welfare function. As Romer (1988) notes, a utilitarian social planner discounts income at the rate 6 = O + g / o , where 0 is the intergenerational discount rate for utility, g is the growth rate of income, and a is the intertemporal elasticity of substitution (which equals

33 Musgrave also argued that the budget deficit should vary over the business cycle for stabilization purposes.

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the inverse of the elasticity of marginal utility with respect to consumption), income growth matters here because it reduces the utility gained from an extra dollar of income. If the net marginal product of capital r exceeds 6, then deferring consumption to future generations is socially optimal. Applying this criterion is by no means straightforward. Obviously, one must determine how much to discount the utility of future generations. One might argue that zero is the most consistent with people choosing a social welfare function "behind a veil of ignorance" [Rawls (1971)] about the generation to which they belong. If 0 = 0 , g=0.01, and 0=0.33, the social discount rate 6 is 0.03. If r=0.06, which is the value we used earlier, the net gain from deferring consumption ( r - 6 ) is 0.03. One is thus led to conclude that increased national saving would be desirable. Yet the opposite conclusion arises if o--0.1, so that 6 is 0.1. In this case, economic growth together with sharply diminishing marginal utility ensures that the marginal utility of future generations is low, so there is little benefit to saving on their behalf. In the end, therefore, the utilitarian approach to intergenerational saving illuminates the key parameters that determine optimal national saving, but it does not allow us to reach an easy conclusion on whether national saving is in fact too low or too high.

5.3. Tax smoothing

Another approach to analyzing optimal debt policy, advocated by Barro (1979), emphasizes the distortionary nature of taxation. The deadweight loss from a tax depends roughly on the square of the tax rate. Thus, the distortion-minimizing way to finance a given stream of government spending is to maintain a smooth tax rate over time. If future government spending were known with certainty, the optimal tax rate would be constant. Because future government spending is uncertain, the optimal tax rate sets the present value of revenue equal to the present value of expected spending. As information about spending becomes available, the optimal tax rate changes. Under this view, the budget deficit is simply the difference between government spending and the amount of revenue generated by this tax rate, and the debt will rise and fall accordingly over time. Barro's tax-smoothing model is follnally parallel to Friedman's permanent-income hypothesis. According to the permanent-income hypothesis, households smooth consumption by basing it on their expected permanent income; they save and borrow in response to transitory changes in income. According to the tax-smoothing model, governments smooth tax rates by basing tax rates on expected permanent government spending; they increase or decrease government debt in response to transitory changes in spending or revenue. Barro (1979) finds that the tax-smoothing theory of debt explains fairly well the behavior of US debt since 1920, and Barro (1987) reaches a similar conclusion for British debt from 1700 through World War I. Much of the variation in spending that Barro studies is related to wars. Thus, the tax-smoothing logic provides another

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Government Debt

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justification (in addition to intergenerational equity) for a c c u m u l a t i n g government debt during wars and paying off the debt during peacetime.

6. Conclusion This essay has touched o n some o f the major issues in the debates over the effects o f g o v e r n m e n t debt. Because o f the broad scope o f this topic, we have had to be selective. We have i g n o r e d m a n y important related subjects, such as the m a n a g e m e n t o f g o v e r n m e n t debt with instruments o f varying maturities, the debate over inflationindexed debt, the pros a n d cons o f alternative rules for setting fiscal policy, and the theories o f political e c o n o m y that attempt to explain w h y and w h e n governments issue debt. We trust that readers who have m a d e it to this c o n c l u s i o n will understand why we avoided these additional fascinating but extensive topics.

References Abel, A.B., N.G. Mankiw, L.H. Summers and R.J. Zeckhauser (1989), "Assessing dynamic efficiency: theory and evidence", Review of Economic Studies 56:1--20. Aiyagari, S.R., and M. Gertler (1985), "The backing of government bonds and monetarism", Journal of Monetary Economics 16:19-44. Aschauer, D.A. (1985), "Fiscal policy and aggregate demand", American Economic Review 75: t 17 127. Attanasio, O.R, and M. Browning (1995), "Consumption over the life cycle and over the business cycle", American Economic Review 85:1118-1137. Attanasio, O.E, and G. Weber (1995), "Is consumption growth consistent with intertemporal optimization? Evidence from the consumer expenditure survey", Journal of Political Economy 103:1121-1157. Auerbach, A.J., and L.J~ Kotlikoff (1987), Dynamic Fiscal Policy (Cambridge University Press, Cambridge). Auerbach, A.J., J. Gokhale and L.J. Kotlikoff (1991), "Generational accounts: a meaningful alternative to deficit accounting", Tax Policy and the Economy 5:55-110. Bailey, M.J. (1962), National Income and the Price Level (McGraw-Hill, New York). Ball, L., and N.G. Mankiw (1995), "What do budget deficits do?", in: Budget Deficits and Debt: Issues and Options (Federal Reserve Bank of Kansas City) 95 119. Ball, L., D.W. Elmendorf and N.G. Manldw (1998), "The deficit gamble", Journal of Money, Credit and Banking 30(4):699-720. Ballard, C., J.B. Shoven and J. Whalley (1985), "General equilibrium computations of the marginal welfare cost of taxes in the United States", American Economic Review 75:128-138. Barro, R.J. (1974), "Are government bonds net wealth?", Journal of Political Economy 82:1095-1117. Barro, R.J. (1979), "On the deternlinationof the public debt", Journal of Political Economy 87:940-971. Barro, R.J, (1987), "Government spending, interest rates, prices, and budget deficits in the United Kingdom, 1701-1918", Journal of Monetary Economics 20:221-247. Barro, R.J., N.G. Mankiw and X. Sala-i-Martin (1995), "Capital mobility in neoclassical models of growth", American Economic Review 85:103-115~ Barsky, R.B., N.G. Mankiw and S.R Zeldes (1986), "Ricardian consumers with Keynesian propensities", American Economic Review 76:676-691. Barth, J.R., G. Iden and ES~ Russek (1986), "Govermnent debt, government spending, and private sector behavior: comment", American Economic Review 76:1158-1167.

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Becket, G.S. (1974), "A theory of social interactions", Journal of Political Economy 82:1063-1093. Bernheim, B.D. (1987), "Ricardian equivalence: an evaluation of theory and evidence", in: S. Fischer, ed., NBER Macroeconomies Annual (MIT Press, Cambridge, MA) 263-303. Bernheim, B.D. (1988), "Budget deficits and the balance of trade", Tax Policy and the Economy, 1-31. Bernheim, B.D. (1994), "Comment", in: D.A. Wise, ed., Studies in the Economics of Aging (University of Chicago Press, Chicago, IL) 171-179. Bernheim, B.D., and K. Bagwell (1988), "Is everything neutral?", Journal of Political Economy 96: 308-338. Bernheim, B.D., A. Shleifer and L.H. Strummers (1985), "The strategic bequest motive", Journal of Political Economy 93:1045-1076. Berry, T.S. (1978), Revised Annual Estimates of American Gross National Product, Bostwick Paper No. 3 (The Bostwick Press). Blanchard, O.J. (1985), "Debt, deficits, and finite horizons", Journal of Political Economy 93:223 247. Blanchard, O.J., and S. Fischer (1989), Lectures on Macroeconomics (MIT Press, Cambridge, MA). Blanchard, O.J., and L.H. Summers (1984), "Perspectives on high world real interest rates", Brookings Papers on Economic Activity 1984(2):273-334. Blanchard, O.J., and R Weil (t992), "Dynamic efficiency, the riskless rate, and debt Ponzi games under uncertainty", Working Paper No. 3992 (NBER). Blinder, A.S., and R.M. Solow (1973), "Does fiscal policy matter?", Journal of Public Economics 2:319-337. Bobal, H. (1992), "Budget deficits and government accounting", Carnegie-Rochester Conference Series on Public Policy 37:1-84. Bohn, H. (1993), "Fiscal policy and the Mchra Prescott puzzle: on the welfare implications of budget deficits when real interest rates are low", Working Paper No. 8-93 (Department of Economics, University of California at Santa Barbara). Boothe, P.M., and B.G. Reid (1989), "Asset returns and government budgets in a small open economy", Journal of Monetary Economics 23:65-77. Buchanan, J.M. (1976), "Barro on the Ricardian equivalence theorem", Journal of Political Economy 84:337 342. Buchanan, J.M., and R.E. Wagner (1977), Democracy in Deficit: The Political Economy of Lord Kcynes (Academic Press, New York). Buchholz, T.G. (1989), New Ideas from Dead Economists: An Introduction to Modem Economic Thought (Penguin, New York). Bureau of the Census (t975), Historical Statistics of the United States, Colonial Times to 1970, Part 2 (Washington, DC). Butkiewicz, J.L. (1983), "The market value of outstanding govermnent debt: comment", Journal of Monetary Economics 11:373-379. Campbell, J.Y., and N.G. Mankiw (1989), "Consumption, income and interest rates: reinterpreting the time series evidence", in: S. Fischer and O.J. Blanchard, eds., NBER Macroeconomics Annual (MII Press, Cambridge, MA) 185-216. Cardia, E. (1997), "Replicating Ricardian equivalence tests with simulated series", American Economic Review 87:65-79. Carroll, C.D. (1997), "Buffer-stock saving and the life cycle/permanent income hypothesis", Quarterly Journal of Economics 112:1-55. Carroll, C.D., and L.H. Smmners (1991), "Consumption growth parallels income growth: some new evidence", in: B.D. Bernheim and J.B. Shoven, eds., National Saving and Economic Performance (University of Chicago Press, Chicago, IL) 305-343. Chan, L.K.C. (1983), "Uncertainty and the neutrality of government financing policy", Journal of Monetary Economics 11:351 372. Congressional Budget Office (1993), Federal Debt and Interest Costs (Washington, DC, May).

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Congressional Budget Office (1995), Who Pays and When? An Assessment of Generational Accounting (Washington, DC, November). Congressional Budget Office (1997a), The Economic and Budget Outlook: Fiscal Years 1998 2007 (Washington, DC, January). Congressional Budget Office (1997b), Long-term Budgetary Pressures and Policy Options (Washington, DC, March). Council of Economic Advisers (1994), Economic Report of the President (Washington, DC, February). Cox, W.M., and E. Hirschhorn (1983), "The market value of outstanding government debt: monthly, t 942 1980", Journal of Monetary Economics 11:261-272. Croushore, D. (1996), "Ricardian equivalence with wage-rate uncertainty", Journal of Money, Credit and Banking 28:279-293. Cutler, D.M. (1993), "Book review of Laurence Kotlikoff's generational accounting", National Tax Journal 56:61-67. Daniel, B.C. (1993), "Tax timing and liquidity constraints: a heterogeneous-agent model", Journal of Money, Credit and Banking 25:176-196. Diamond, RA. (1965), "National debt in a neoclassical growth model", American Economic Review 55:1126-1150. Dornbusch, R. (1991), "Comment on Feldstein and Bacchetta", in: B.D. Bernheim and J.B. Shoven, eds., National Saving and Econmnic Performance (University of Chicago Press, Chicago, IL) 220-226. Dotsey, M. (1994), "Some unpleasant supply side arithmetic", Journal of Monetary Economics 33: 507 524. Eisner, R. (1986), How Real is the Federal Deficit? (Free Press, New York). Eisner, R., and EJ. Pieper (1984), "A new view of the federal debt and budget deficits", American Economic Review 74:11-29. Evans, E (1985), "Do large deficits produce high interest rates?", American Economic Review 75:68-87. Evans, E (1986), "Is the dollar high because of large budget deficits?", Journal of Monetary Economics 18:227-249. Evans, R (1987a), "Interest rates and expected future budget deficits in the United States", Journal of Political Economy 95:34-58. Evans, E (1987b), "Do budget deficits raise nominal interest rates? Evidence from six countries", Journal of Monetary Economics 20:281-300. Evans, R (1988), "Are consumers Ricardian? Evidence for the United States", Journal of Political Economy 96:983-1004. Evans, R (1991), "Is Ricardian equivalence a good approximation?", Economic Inquiry 29:626-644. Evans, R (1993), "Consumers are not Ricardian: evidence from nineteen countries", Economic Inquiry 31:534-548. Feldstein, M. (1982), "Government deficits and aggregate demand", Journal of Monetary Economics 9:1-20. Feldstein, M. (1985), "Debt and taxes in the theory of public finance", Journal of Public Economics 28:233-245. Feldstein, M. (1995), Overview panelist, in: Budget Deficits and Debt: Issues and Options (Federal Reserve Bank of Kansas City) 403~412. Feldstein, M. (1996a), "The missing piece in policy analysis: social security retbrm', American Economic Review 86:1-14. Feldstein, M. (1996b), "How big should govermnent be?", National Tax Association Proceedings, 314-326. Feldstein, M., and E Bacchetta (1991), National saving and international investment, in: B.D. Bernt~eim and J.B. Shoven, eds., National Saving and Economic Performance (University of Chicago Press, Chicago, IL) 201 220. Feldstein, M., and D.W. Elmendorf (1990), "Government debl, government spending, and private sector behavior revisited: comment", American Economic Review 80:589-599.

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Feldstein, M., and C. Horioka (1980), "Domestic saving and international capital flows", Economic Journal 90:314 329. Feldstein, M., L. Dicks-Mireaux and J.M. Poterba (1983), "The effective tax rate and the pretax rate of return", Journal of Public Economics 21:129-158. Frankel, J.A. (1991), Quantifying international capital mobility in the 1980s, in: B.D. Bernheim and J.B. Shoven, eds., National Saving and Economic Performance (University of Chicago Press, Chicago, IL) 227 260. Frenkel, J.A., and A. Razin (1992), Fiscal Policies and the World Economy (MIT Press, Cambridge, MA). Friedman, B.M. (1988), Day of Reckoning (Random House, New York). Friedman, B.M. (1992), "Learning from the Reagan deficits", American Economic Review 82:299 304. Gale, W.G., and J.K. Scholz (1994), "Intergenerational transfers and the accumulation of wealth", Journal of Economic Perspectives 8:145 160. Gordon, R.H., and A.L. Bovenberg (1996), "Why is capital so immobile internationally? Possible explanations and implications for capital income taxation", American Economic Review 86:1057-1075. Graham, EC. (1995), "Government debt, government spending, and private-sector behavior: comment", American Economic Review 85:1348-1356. Graham, EC., and D. Himarios (1991), "Fiscal policy and private consumption: instrumental variables tests of the 'consolidated approach'", Journal of Money, Credit and Banking 23:53-67. Graham, EC,, and D. Himarios (1996), "Consumption, wealth, and finite horizons: tests of Ricardian equivalence", Economic Inquiry 34:527-544. Greenspan, A. (1995), General discussion, in: Budget Deficits and Debt: lssucs and Options (Federal Reserve Baak of Kansas City) 139-149. Hall, R.E. (1978), "Stochastic implications of the life cycle-permanent income hypothesis: theory and evidence", Journal of Political Economy 86:971-987. Hall, R.E., and ES. Mishkin (1982), "The sensitivity of consumption to transitory income: estimates from panel data on households", Econometrica 50:461481. Hamilton, A. (1781), Letter to Robert Morris (April 30). Hayashi, E (1987), "Tests for liquidity constraints: a critical smvey", in: T. Bewley, ed., Advances in Econometrics: Fifth World Congress (Cambridge University Press, New York). Hoelscher, G. (1986), "New evidence on deficits and interest rates", Journal of Money, Credit and Banking 18:1-17. Hubbard, R.G., and J.S. Skinner (1996), "Assessing the effectiveness of saving incentives", Journal of Economic Perspectives 10:73-O0. Judd, K. (1987), "Debt and distortionary taxation in a simple perfect foresight model", Journal of Monetary Economics 20:51-72. Kessler, D., and A. Masson (1989), "Bequest and wealth accumulation: are some pieces of the puzzle missing?", Journal of Economic Perspectives 3:141-152. Kimball, M.S., and' N.G. Mankiw (1989), "Precautionary saving and the timing of taxes", Journal of Political Economy 97:863-879. Kormendi, R.C. (1983), "Government debt, government spending, and private sector behavior", American Economic Review 73:994--1010. Kormendi, R.C., and R Meguire (1986), "Government debt, government spending, and private sector behavior: reply", American Economic Review 76:1 180-1187. Kormendi, R.C., and R Meguire (1990), "Government debt, government spending, and private sector behavior: reply and update", American Economic Review 80:604-617. Kormendi, R.C., and P Meguire (1995), "Government debt, govenunent spending, and private sector behavior: reply", American Economic Review 85:t 357-1361. Kotlikoff, L.J. (1988), "Intergenerational transfers and savings", Journal of Economic Perspectives 2:41-58.

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Ricardo, D. (1820), "Funding system", reprinted in: E Sraffa, ed., The Works and Correspondence of David Ricardo (Cambridge University Press, Cambridge). Romer, C.D. (1989), "The prewar business cycle reconsidered: new estimates of gross national product, t869-1928", Journal of Political Economy 97:107. Romer, D. (1988), "What are the costs of excessive deficits?", in: S. Fischer, ed., NBER Macroeconomics Annual (MIT Press, Cambridge, MA) 63-98. Romer, EM. (I986), "Increasing returns and long-run growth", Journal of Political Economy 94:1002-1037. Romer, PM. (1987), "Crazy explanations for the productivity slowdown", in: S. Fischer, ed., NBER Macroeconomics Annual (MIT Press, Cambridge, MA) t 63-202. Rosensweig, J.A., and E.W Talhnan (1993), "Fiscal policy and trade adjustment: are the deficits really twins?", Economic Inquiry 31:580594. Roseveare, D., W. Leibfritz, D. Fore and E. Wurzel (t996), "Ageing populations, pension systems and government budgets: simulations for 20 OECD countries", Working Paper No. 168 (OECD Economics Department). Runkle, D.E. (1991), "Liquktity constraints and the permanent-income hypothesis: evidence from panel data", Journal of Monetary Economics 27:73 98. Samuelson, PA. (1958), "An exact consumptionqoan model of interest, with or without the social contrivance of money", Journal of Political Economy 66:467~482. Sargent, T.J. (1983), "The ends of four big inflations", in: R.E. Hall, ed., Inflation: Causes and Effects (University of Chicago Press, Chicago, IL) 41-93. Sargent, T.J., and N. Wallace (1981), "Some unpleasant monetarist arithmetic", in: Quarterly Review, Federal Reserve Bank of Minneapolis (Fall). Seater, J.J. (1981), "The market value of outstanding government debt, 1919-1975", Journal of Monetary Economics 8:85-101. Seater, J.J. (1993), "Ricardian equivalence", Journal of Economic Literature 31:142-190. Seater, J.J., and R.S. Mariano (1985), "New tests of the life cycle and tax discounting hypotheses", Journal of Monetary Economies 15:195-215. Shapiro, M.D., and J. Slemrod (1995), "Consumer response to the timing of income: evidence from a change in tax withholding", American Economic Review 85:274-283. Sims, C.A. (1994), "A simple model for the determination of the price level and the interaction of monetary and fiscal policy", Economic Theory 4, 3:381 399. Smetters, K.A. (1996), "Ricardian equivalence: long-run leviathan", mimeograph (Congressional Budget Office). Solow, R.M. (1956), "A contribution to the theory of economic growth", Quarterly Journal of Economics 70:65-94. Stocks, Bonds, Bills and Inflation (1995), Yearbook (Ibbotson Associates, Chicago, IL). Strotz, R.H. (1956), "Myopia and inconsistency in dynmnic utility maximization", Review of Economic Studies 23:165-180. The Economist (1995), "Caught in the debt trap", April 1. Tirole, J. (t985), "Asset bubbles and overlapping generations", Econometrica 53:1499-1528. Tobin, J. (1952), "Asset holdings and spending decisions", reprinted: 1971, in: Essays in Econonfics, vol. 1 (North-Holland, Amsterdam). Trostel, EA. (1993), "The nonequivalence between deficits and distortionary taxation", Journal of Monetary Economics 31:207~27. Volcker, EA. (1985), Statement to the committee on banking, finance and urban affairs, U.S. House of Representatives (Washington D.C.) February 7. Wachtel, E, and J. Young (1987), "Deficit announcements and interest rates", American Economic Review 77:1007-1012. Well, E (1989), "Overlapping families of infinitely-lived agents", Journal of Public Economics 38: 183 198.

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Wicksell, K. (1896), "A new principle of just taxation", reprinted: 1958, in: R.A. Musgrave and A.T. Peacock, eds., Classics in the Theory of Public Finance (MacMillan Press, London). Wilcox, D.W. (1989), "Social security benefits, consumption expenditure, and the life cycle hypothesis", Journal of Political Economy 97:288-304. Woodford, M. (1995), "Price-level determinacy without control of a monetary aggregate", Carnegie~ Rochester Conference Series on Public Policy 43:1-46. Yotsuzuka, T. (1987), "Ricardian equivalence in the presence of capital market imperfections", Journal of Monetary Economics 20:411-436. Zeldes, S.E (1989), "Consumption and liquidity constraints: an empirical investigation", Journal of Political Economy 97:305-346.

Chapter 26

OPTIMAL FISCAL AND MONETARY POLICY* V.V. CHARI

University o f Minnesota and Federal Reserve Bank of Minneapolis PATRICK J. KEHOE

University o f Pennsylvania, Federal Reserve Bank of Minneapolis, and National Bureau of Economic Research

Contents

Abstract Keywords Introduction 1. The primal approach to optimal taxation 1.1. The Ramsey allocation problem 1.2. Elasticities and commodity taxation

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1.3. Uniform commodity taxation

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1.4. Intermediate goods

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2. Fiscal policy 2.1. General framework

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2.2. Capital income taxation

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2.2.1. In a steady state 2.2.2. In a non-steady state 2.3. Cyclical properties 2.3.1. Debt taxation as a shock absorber 2.3.2. Tax-smoothing and incomplete markets 2.3.3. A quantitative illustration 2.4. Other environments

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2.4.2. Open economy models 2.4.3. Overlapping generations models

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3. Monetary policy 3.1. Three standard monetaty models 3.1.1. Cash~redit

* The views expressed herein are those of the authors and not necessarily those of the Federal Rescrvc Bank of Minneapolis or the Federal Reserve System.

Handbook o f Macroeconomics, Volume I, Edited by .lB. 'laylor and M~ WbodJord © 1999 Elsevier Science B.V. All rights reserved 1671

1672 3.1.2. Money-in-the-utility-function 3.1.3. Shopping-time 3.2. From monetary to real 3.3. Cyclicalproperties 4. Conclusion References

v..v.Chari and P.J. Kehoe 1728 1732 1733 1736 1742 1743

Abstract We provide an introduction to optimal fiscal and monetary policy using the primal approach to optimal taxation. We use this approach to address how fiscal and monetary policy should be set over the long run and over the business cycle. We find four substantive lessons for policymaking: Capital income taxes should be high initially and then roughly zero; tax rates on labor and consumption should be roughly constant; state-contingent taxes on assets should be used to provide insurance against adverse shocks; and monetary policy should be conducted so as to keep nominal interest rates close to zero. We begin by studying optimal taxation in a static context. We then develop a general framework to analyze optimal fiscal policy. Finally, we analyze optimal monetary policy in three commonly used models of money: a cash--credit economy, a moneyin-the-utility-function economy, and a shopping-time economy.

Keywords primal approach, Ramsey problems, capital income taxation, Friedman rule, tax smoothing J E L classification: E5, E6, E52, E62, H3, H21

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Introduction

A fundamental question in macroeconomics is, How should fiscal and monetary policy be set over the long run and over the business cycle? Answering this question requires integrating tools from public finance into macroeconomics. The purpose of this chapter is to lay out and extend recent developments in the attempts to do that within a framework which combines two distinguished traditions in economics: the public finance tradition and the general equilibrium tradition in macroeconomics. The public finance tradition we follow in this chapter stems from the work of Ramsey (1927), who considers the problem of choosing an optimal tax structure in an economy with a representative agent when only distorting taxes are available. The general equilibrium tradition stems from the work of Cass (1965), Koopmans (1965), Kydland and Prescott (1982), and Lucas and Stokey (1983). Within the public finance tradition, our framework builds on the primal approach to optimal taxation. [See, for example, Atkinson and Stiglitz (1980), Lucas and Stokey (1983), and Chari et al. (1991).] This approach characterizes the set of allocations that can be implemented as a competitive equilibrium with distorting taxes by two simple conditions: a resource constraint and an implementability constraint. The implementability constraint is the consumer budget constraint in which the consumer and the firm first-order conditions are used to substitute out for prices and policies. Thus both constraints depend only on allocations. This characterization implies that optimal allocations are solutions to a simple programming problem. We refer to this optimal tax problem as the Ramsey problem and to the solutions and the associated policies as the Ramsey allocations and the Ramsey plan. We study optimal fiscal and monetary policy in variants of neoclassical growth models. This analysis leads to four substantive lessons for policymaking: • Capital income taxes should be high initially and then roughly zero. • Tax rates on labor and consumption should be roughly constant. • State-contingent taxes on assets should be used to provide insurance against adverse shocks. • Monetary policy should be conducted so as to keep nominal interest rates close to zero. The basic logic behind these policymaking lessons is that Ramsey policies smooth distortions over time and states of nature. Smoothing tax distortions over time implies that capital tax rates should be roughly zero and labor and consumption taxes should be roughly constant [Lucas and Stokey (1983) and Chari et al. (1994)]. Ramsey policies also imply that heavily taxing inelastically supplied inputs is optimal. Thus Ramsey policies involve taxing capital income at initially high rates, but then dropping these rates, to zero in the long run. [See Judd (1985) and Chamley (1986).] Since keeping capital, labor, and consumption taxes roughly constant is optimal, the government needs some source of revenue to ensure that taxes need not be sharply changed when the economy is hit by shocks. One way to provide such revenue insurance is to have explicitly state-contingent debt, in the sense that the rate of return

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on the debt varies with the shocks. Another way is to have non-state-contingent debt with taxes on interest income which vary with the shocks. Revenue insurance can also be provided by having taxes on capital income that vary with the shocks while still being roughly zero on average. In terms of monetary policy, Friedman (1969) advocates a simple rule: set nominal interest rates to zero. In the models we consider, the Friedman rule is optimal if the consumption elasticity of money demand is one. We think that this rule deserves attention because the weight of the empirical evidence is that the consumption elasticity of money demand is indeed one. [See Stock and Watson (1993).] Throughout the chaptm, we emphasize that the primal approach, in essence, involves finding optimal wedges between marginal rates of substitution and marginal rates of transformation. Typically, many tax systems can decentralize the Ramsey allocations. Thus optimal tax theory yields results on optimal wedges, and thus the prescriptions for optimal taxes depend on the details of the particular tax system. For example, in the one-sector growth model, a tax system which includes any two of consumption, labor, and capital income taxes can decentralize the Ramsey allocations, in such a model, it is optimal to set intertemporal marginal rates of substitution equal to intertemporal marginal rates of transformation in the long run. With a tax system that consists of capital and labor taxes, this is accomplished by setting capital income taxes equal to zero. With a tax system that consists of consumption and labor taxes, this is accomplished by making consumption taxes constant. Thus the Ramsey allocations can be implemented either with zero capital income taxes or with constant consumption taxes. Throughout this chapter, we focus on economies in which the government effectively has access to a commitment technology. As is well known, without such a technology, there are time inconsistency problems, so the equilibrium outcomes with commitment are not necessarily sustainable without commitment. Economies with commitment technologies can be interpreted in two ways. One is that the government can simply commit to its future actions by, say, restrictions in its constitution. The other, and the way we prefer, is that the government has no access to a commitment technology, but the commitment outcomes are sustained by reputational mechanisms. [See, for example, Chari et al. (1989), Chari and Kehoe (1990, 1993), and Stokey (199l) for analyses of optimal policy in environments without commitment.] Throughout this chapter we also restrict attention to proportional tax systems. The results we develop all come from environments with an infinite number of periods and include some combination of uncertainty, capital, debt, and money. Many of the basic principles, however, can be developed in a simple static context in which the ideas are easiest to digest. In Section l, in a static context, we develop two of the three main results in public finance which show up repeatedly in macroeconomic models. First, under appropriate separability and homotheticity conditions on preferences, it is optimal to tax goods at a uniform_ rate. Second, if all consumption goods, types of labor income, and pure profits can be taxed, then it is optimal not to tax intermediate goods. The uniform commodity tax result shows up

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repeatedly in analyses of fiscal policy, and this result and the intermediate-goods result show up repeatedly in analyses of monetary policy. We defer to the next section the development of the third main result, that it is optimal to set taxes on capital income equal to zero in the long run. In Section 2, we lay out a stochastic neoclassical growth model to analyze fiscal policy. We begin with a deterministic version of this model to highlight the long-run properties of optimal fiscal policy. In this version, we develop the results of Chamley (1980, 1986) on the optimality of zero capital-income taxation in a steady state, the generalizations by Judd (1985) to environments with heterogeneous agents, and some qualifications by Stiglitz (1987) when there are restrictions on the tax system. Next, we show that for a commonly used class of utility functions, optimal capital taxes are zero not only in a steady state, but also after the first period. Next, we consider a stochastic model without capital to highlight how optimal fiscal policy should respond to shocks. We illustrate how, by using debt as a shock absorber, taxes on labor income are optimally smoothed in response to shocks to government consumption and technology [as in Lucas and Stokey (1983) and Chari et al. (1991)]. We then contrast these results with the assertions in Barro (1979) about tax-smoothing in a reduced-form model. We argue that the work of Marcet et al. (1996) on taxation with incomplete markets partially affimas Barro's assertions. We also consider the quantitative features of optimal fiscal policy in a standard real business cycle model [as in Chari et al. (1994)]. We go on to discuss how the results developed in a closed economy with infinitely lived agents and only exogenous growth extend to other environments. We first show that in an endogenous growth framework along a balanced growth path, all taxes are zero. [See Bull (1992) and Jones et al. (1997).] Essentially, in this framework, capital income taxes distort physical capital accumulation, and labor income taxes distort human capital accumulation. Hence it is optimal to front-load both taxes. We then consider an open economy and show that under both source-based and residencebased taxation, optimal capital income taxation is identically zero. The intuition for these results is that with capital mobility, each country faces a perfectly elastic supply of capital and therefore optimally chooses to set capital income tax rates to zero. [See Atkeson et al. (1999) and Garriga (1999).] Finally, we consider an overlapping generations model and show that only under special conditions is the tax rate on capital income zero in a steady state. The conditions are that certain homotheticity and separability conditions hold. [See Atkeson et al. (1999) and Garriga (1999).] In Section 3, we lay out a general framework for the analysis of monetary policy. We consider three commonly used models of money: a cash-credit monetary economy, a money-in-the-utility-function monetary economy, and a shopping-time monetary economy. For each model, we provide sufficient conditions for the optimality of the Friedman rule. These conditions for the cash-credit economy and the money-in-theutility-function economy are analyzed by Chari et al. (1996), while conditions for the shopping-time economy are analyzed by Kimbrough (1986), Faig (1988), Woodford (1990), Guidotti and V6gh (1993), and Correia and Teles (1996), as well as by

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Chaff et al. (1996). The common features of the requirements for optimality are simple homotheticity and separability conditions similar to those in the public finance literature on optimal uniform commodity taxation. There have been conjectures in the literature - by Kimbrough (1986) and Woodford (1990), among others - about the connection between the optimality of the Friedman rule and the intermediate-goods results. For all three monetary economies, we show that when the homotheticity and separability conditions hold, the optimality of the Friedman rule follows from the intermediate-goods result. Finally, we report results for a quantitative monetary business cycle model. We find that if debt has nominal non-state-contingent returns, so that asset markets are incomplete, inflation can be used to make real returns contingent, so that debt can serve as a shock absorber.

1. The primal approach to optimal taxation The general approach to characterizing competitive equilibria with distorting taxes described in this section is known in the public finance literature as the primal approach to taxation. [See Atkinson and Stiglitz (1980).] The basic idea is to recast the problem of choosing optimal taxes as a problem of choosing allocations subject to constraints which capture the restrictions on the type of allocations that can be supported as a competitive equilibrium for some choice of taxes. In this section, we lay out the primal approach and use it to establish some basic principles of optimal taxation, together with the results on uniform commodity taxation and intermediategoods taxation. The rest of this chapter applies these basic principles of optimal taxation to a variety of environments of interest to macroeconomists. These environments all have an infinite number of periods and include some combination of uncertainty, capital, debt, and money. As such, the derivations of the results look more complicated than the derivations here, but the basic ideas are quite similar. 1.1. The Ramsey allocation problem

Consider a model economy in which n types of consumption goods are produced with labor. The resource constraint is given by F ( c l + gl . . . . , c,, + g~, l) = 0,

(1.1)

where ci and gi denote private and government consumption of good i, I denotes labor, and F denotes a production process that satisfies constant returns to scale. The consumer's problem is to maximize utility: max U(cl . . . . , c,,, l) subject to Z p i ( l i

(1.2) + r,.)ci = 1,

(1.3)

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where p~ is the price of good i and vi is the ad valorem tax rate on good i. Thus there are n linear commodity taxes. We normalize the wage to 1. A representative firm operates the constant returns technology F and solves

l

(1.4)

subject to F(xl .... ,x,, l) = 0,

(1.5)

Zpixi

max

(x,/)

-

i

where xi denotes output of good i. The government budget constraint is

fff2pigi

=

i

(1.6)

Z p i ~ . C i. i

Market clearing requires that ci+gi

=Xi

for

i =

1,... ,n.

(1.7)

Throughout this chapter, we take government expenditures as given. A competitive equilibrium is a policy Jr = (r/)7=l; allocations c, l, and x; and a price system p that satisfy the following: (i) tile allocations c and l maximize Equation (1.2) subject to (1.3), (ii) the allocations x and l solve Equation (1.4), (iii) the government budget constraint (1.6) holds, and (iv) the allocations c and x satisfy condition (1.7). Throughout this chapter, we assume that first-order conditions are necessary and sufficient and that all allocations are interior. The sufficiency of the first-order conditions for firms and consumers holds under appropriate concavity assumptions, and interiority can be assured with appropriate monotonicity and Inada conditions. Proposition 1. The allocations in a competitive equilibrium satisfy

F(cl + gt . . . . . cn + g~,, l) -- 0

(1.s)

and the implementability constraint Z

Uici + U/1 = O.

(1.9)

i

Furthermore, given allocations which satisfy Equations (1.8) and (1.9), we can construct policies and prices which, together with the given allocations, constitute a competitive equilibrium. R e m a r k : The literature usually refers to Equation (1.9) as the implemenlability constraint because it is a constraint on the set of allocations that can be implemented as a competitive equilibrium with distorting taxes. This constraint can be thought of as the consumer budget constraint with both the taxes and the prices substituted out by using first-order conditions.

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Proof: We first prove that the allocations in a competitive equilibrium must satisfy Equations (1.8) and (1.9). Condition (1.8) follows from substituting the market-clearing condition (1.7) into (1.5). To derive Equation (1.9), notice that the consumer's firstorder conditions are

Ui = api(1 + zi) -gl

for

i= 1,...,n,

= 0~

Zpi(1 + Ti)ci -- [,

(1.10) (1.11) (1.12)

i

where a is the Lagrange nmltiplier on the budget constraint. Substituting Equations (1.10) and (1.11) into (1.12) gives (1.9). Next, we prove that i f c and l satisfy (1.8) and (1.9), then a price systemp, a policy Jr, and an allocation x, together with the given allocations, constitute a competitive equilibrium. We use the first-order conditions for the firm, which are

Pi =--Fi/Ft

for

i = 1,...,n.

(1.13)

We construct x, p, and zc as follows: xi - ci + gi, Pi is from (1.13), and s~- is from l+ri-

UiFI UIFi"

Given our assumptions on the utility function, the first-order conditions are necessary and sufficient for consumer and firm maximization. With x, p, and ¢c so defined, (c, l,x,p, zc) clearly satisfies firm maximization. When a = -Ul, conditions (1.10) and (1.11) clearly are also satisfied. Substituting for Ui and Ul in Equation (1.9), we have Z

ciaPi(1 + ri)

al

O.

i

Dividing by a and rearranging gives Equation (1.12). The government budget constraint is satisfied by Walras' law. D We can now define a type of optimal tax equilibrium in which the government objective is to maximize the utility of consumers. We think of the government as first choosing policies and of private agents as then choosing their actions. Let H denote the set of policies for which a competitive equilibrium exists. A Ramsey equilibrium is a policy Jr = (ri)i~_l i n / / ; allocation rules c(.), l(.), and x(.); and a price function p(.) that satisfy the following: (i) the policy Jr solves max g(c(sr'), l(jr')) subject to Z p i ( j r ' ) g i i

Zpi(~') r~ci(jr')

(1.14)

i

and (ii) for every Jr', the allocations c(jr'), l ( S ) , x(jr'), the price system p ( S ) , and the policy Jr' constitute a competitive equilibrium.

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Notice that we require optimality by consumers and firms for all policies that the government might choose. This requirement is analogous to the requirement of subgame perfection in a game. To see why this requirement is important, suppose we had not imposed it. That is, suppose we required optimality by consumers and firms only at the equilibrium policies, but allowed allocation and price rules to be arbitrary elsewhere. Then the set of equilibria is much larger. For example, allocation rules that prescribe zero labor supply for all policies other than some particular policy would satisfy all the equilibrium conditions. Since the government's budget constraint is then satisfied only at the particular policy, the government optimally chooses that policy. We think that such equilibria do not make sense. That is, we think the requirement that consumers and firms behave optimally for all policies is the sensible way to solve the government's problem of forecasting private behavior. If the competitive equilibrium associated with each policy is unique, clearly the Ramsey equilibrium is also unique. If there are multiple competitive equilibria associated with some policies, our definition of a Ramsey equilibrium requires that a selection be made from the set of competitive equilibria. In this case, there may be many Ramsey equilibria, depending on the particular selection made. In this chapter, we focus on the Ramsey equilibrium that yields the highest utility for the government. In such a Ramsey equilibrium, a particular allocation and price system are realized, namely, c, l, and p. We call these the Ramsey allocations and prices'. We then have the following proposition as an immediate corollary of Proposition 1. Proposition 2. The Ramsey allocations solve the Ramsey problem, which is to choose c and 1 to maximize U(c,l) subject to conditions (1.8) and (1.9). We have studied an economy in which the government uses consumption-goods taxes to raise revenues and have shown how the problem of solving for the Ramsey equilibrium reduces to the simpler problem of solving for the Ramsey allocations. Other tax systems lead to the same Ramsey problem. For example, consider a tax system that includes taxes on the n consumption goods as well as taxes on labor income. It can be shown that the Ramsey allocations can be supported by a tax system that uses any n of the n + 1 instruments. For example, the Ramsey allocations can be supported by taxes on consumption goods 2 through n and labor income or by taxes on consumption goods alone. The fact that the Ramsey allocations can be decentralized in many ways implies that it is more useful to think about optimal taxation in terms of the implied wedges between marginal rates of substitution and marginal rates of transformation rather than in terms of the particular tax system used to decentralize the Ramsey allocations. The form of the Ramsey allocation problem depends on the assumption that the tax system contains at least n independent instruments. We call such a tax system complete. An example of an incomplete tax system is one in which taxes on the first consumption good and labor are constrained to be zero. For such an incomplete tax

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V..I(Chari and P.J. Kehoe

system, the analog of Proposition 1 is that a set of allocations is part of a competitive equilibrium if and only if the set satisfies conditions (1.8) and (1.9), together with

U~ U/

F1 Ft

Intuitively, this constraint captures the fact that the government has no tax instruments that drive a wedge between the marginal rate of substitution of the first consumption good and labor and the marginal rate of transformation of the same commodities. The reader will find proving this analog useful in part, because the proof illustrates that condition (1.9) must hold regardless of the nature of the tax system. That is, when the tax system is incomplete, the implementability constraint is unchanged, and the new constraints that reflect this incompleteness must be added to the Ramsey problem. 1.2. Elasticities and commodity taxation We can use the Ramsey allocation problem to derive some simple results on optimal commodity taxes. We show that with additively separable preferences, tax rates depend on income elasticities, with necessities being taxed more than luxuries. The discussion here closely follows Atkinson and Stiglitz (1980, chap. 12). Consider the first-order conditions for the Ramsey problem: (1 + ~) Ui - 3.UiHi = y~.,

(1.15)

(1 + 3.) U~ - ~UzHt = -yFz,

(1.16)

where ~ and 7 are the Lagrange multipliers on the implementability constraint and the resource constraint, respectively; Hi =-- - ( ~ i Uj.icj + UiiI)/Ui; and Hi - ( ~ j Uiicj + Uid)/Uz. Using Equations (1.10), (1.ll), and (1.13) in (1.15) and (1.16) and simplifying gives T,1+~

,~(~. - H I ) 1 +)L-,~H~'

Rearranging shows that the relative tax rates for two goods i andj are determined by

r#(1 + Ti) ~/(1 + Tj)

Hi - H t ~ - Hi

(1.17)

Now, Equation (1.17) is not an explicit formula for optimal tax rates, since tile //i, Hi, and Hr terms depend on endogenous variables. Nevertheless, (1.17) shows that if Hi > Hi, then vi > rj. Suppose next that the utility function is additively separable. Then

-

Uii ci

ui

(1.18)

Let c(p, m), l(p, m) denote the solution to the problem of rnaximizing utility subject to ~ p i c i = l + m, where m is nonlabor income, so that ci(p, m) is the demand function

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for good i. Letting a denote the Lagrange multiplier on the budget constraint, we can differentiate the first-order condition Ui(c(p, m)) = a ( p , m ) p i with respect to nonlabor income m to obtain Oc~

Oa

Ui Oa

U"om = P * ~ -

a Om

or

H,

10ci Ci 017/1

10a

-

17 (31"tl

(1.19)

so that Hi _ t b

/qj

(1.20)

t/i'

where t/i is the income elasticity of demand for good i. Thus necessities should be taxed more than luxuries. The standard partial equilibrium result is that goods with low price elasticities of demand should be taxed more heavily than goods with high price elasticities. In general equilibrium, this result does not necessarily hold. It does hold if preferences are additively separable and there are no income effects. That is, utility is quasi-linear and is given by Vi(ci)

- 1.

(1.21)

i

For such a utility function, Equation (1.20) is not helpful because the income elasticities for all the consumption goods are zero. It is easy to show that for a utility function of the form (1.21), Hi = 1/ei, where e/= -(Oci/Opi)Pi/C i is the price elasticity of demand. To see this, differentiate the first-order condition with respect to Pi,

U,.(c(p, m), lq_,, m)) = api,

(1.22)

to obtain OCi Uii ,~-- = a, opi

(1.23)

where a is constant because of quasi-linearity. Substituting Equations (1.22) and (1.23) into (1.18) gives Hi - 1/ei. Since ri > r/ when Hi >/-/.1, consumption goods which are relatively more price inelastic (have low e,.) should be taxed relatively heavily. To summarize, with additive separability, the general result is that tax rates depend on income elasticities, with necessities taxed more than luxuries. Moreover, the familiar

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intuition from partial equilibrium that goods with low price elasticities should be taxed heavily does not necessarily apply in a general equilibrium setting.

1.3. Uniform commodity taxation Here we set up and prove the classic result on uniform commodity taxation. This result specifies a set of conditions under which taxing all goods at the same rate is optimal. [See Atkinson and Stiglitz (1972).] Consider a utility function of the form

U(c, l) - W(G(c), l)

(1.24)

where c = ( c i , . . . , cn) and G is homothetic. Proposition 3. I f utility satisfies' condition (1.24) that is', utility is weakly separable across consumption goods and is homothetic in consumption then Ui/Uj = Fi/Fj for i = 1.... , n. That is, optimal commodity taxation is uniform in the sense that the Ramsey taxes satisfy "ci = ~- for i = 1 , . . . , n. Proof: Substituting the firm's first-order conditions (1.13) into the consumer's first-

order condition, we have that

u~ l+ri-

U1Fi

Thus ~ - rj if and only if ~ / F / - Uj/~. Note that a utility function which satisfies condition (1.24) satisfies

cj

cj

'~

J

-'~

for all

i, k.

(1.25)

J

To see this, notice that from homotheticity, it follows that

Ui(ac, l) Uk(ac, l)

Ui(c, l) gk(c, l)

or

[ Ui(c, 1) ] Ui(ac, l) = [ Uk(c,l)J Ul,(ac, l). Differentiating Equation (1.26) with respect to c~ and evaluating it at a gives (1.25).

(1.26) =

1

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Consider next the first-order condition for ci from the Ramsey problem, namely,

where, again, ~ is the multiplier on the implementability constraint and 7 is the multiplier on the resource constraint. From Equation (1.25), we have that there is some constant A such that ~ / c / U / j = A ~ for all i. Using this fact and the form of utility function, we can rewrite Equation (1.27) as (1 + 3") WLGi + ,~ [AWl Gi + lW12Gi] ~ ~Fi.

(1.28)

Since Equation (1.28) holds for all i and j, Gi/Fi ~ Gj/Fj for all i a n d j and Ui _ WLG i _ W1Gi _ Uj

[] Note that the Ramsey allocations can be decentralized in many ways. For example, taxes on goods can all be set to an arbitrary constant, including zero, and remaining revenues raised by taxing labor income. Consider some generalizations of this proposition. Suppose that the utility function is homothetic and separable over a subgroup of goods, in the sense that the utility function can be written as

U ( c l , . . . , c¢,,~(ck+l . . . . . c,),l) with ~b homothetic. Then it is easy to show that the Ramsey taxes Tk+L = ... - r~. Next, if there is some untaxed income, then we need to modify Proposition 3. Suppose that we add to the model an endowment of good 1, Yl, which is not taxed. Then the implementability constraint becomes

Uici + U1l = Ulyl.

Z i

Then even if U satisfies U(0(Cl .... , c,0, l) with 0 homothetic, it is not true that optimal taxes are uniform (because of the extra terms Uljyl from the derivatives of Utyl). If we add the assumption that U is additively separable across c l , . . . , co, then the Ramsey taxes for goods 2 through n will be uniform, but not equal to the tax on good 1. Next, suppose that the tax system is incomplete in the sense that the government is restricted to setting the tax on good 1 to some fixed number, say, TI = 0. Then the Ramsey problem now must include the constraint U~ _ F1 in addition to the resource constraint and the implementability constraint. Then even if U satisfies condition (1.24), optimal commodity taxes on goods 2 through n are not

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necessarily uniform. Finally, in order to connect this result on uniform commodity taxation to some of the later results, suppose that the utility function is defined over an infinite sequence of consumption and labor goods as U(cl, c2 . . . . ,11,12,...). The assumption that the utility is of the form V(q~(Cl. . . . . ct .... ),11,12,...) with homothetic and separable between consumption and all labor goods 11,/2.... , together with the assumption that the utility function is additively separable across time with constant discount factor/3, restricts the utility function to the form ~ C 1 c7

]

I

1.4. Intermediate goods' Here we establish the classic intermediate-goods result for a simple example. (This example turns out to be useful when we study monetary economies.) Recall the standard result in public finance that under a wide variety of circumstances, an optimal tax system maintains aggregate production efficiency. [See Diamond and Mirrlees (1971).] In the context of an economy with multiple production sectors, transactions between firms can be taxed. Taxing such transactions distorts the relations between the marginal rate of transformation in one sector and the marginal rate of transformation in another sector and yields aggregate production inefficiency. In such a setup, the standard result on aggregate production efficiency immediately implies that taxing intermediate goods is not optimal. Consider an economy with three final goods .... private consumption x, government consumption g, and labor l - and an intermediate good z. The utility function is U(x, l)~ The technology set for producing the final consumption good using labor ll and the intermediate good is described by

f ( x , z , ll) <~ O,

(1.29)

w h e r e f is a constant returns to scale production function. There is a technology set for producing the intermediate good and government consumption using labor/2 described by

h(z,g, 12) <~ O,

(1.30)

where h also is a constant returns to scale production function. The consumer's problem is to maximize

U(x, l~ + 12) subject to p(1 4 r ) x ~. w(l~ + h)~

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where p and w are the prices of the consumption good and labor and T is the tax on the consumption good. The firm that produces private consumption goods maximizes profits px - wll - q(1 + t})z

subject to condition (1.29); q is the price of intermediate goods, and ~7 is the tax on intermediate goods. The firm that produces intermediate goods and government consumption goods maximizes profits qz + rg - wI2,

where r is the price of government consumption, subject to condition (1.30). We can easily show that the Ramsey allocation problem is given by max U(x, Ii + 12) subject to conditions (1.29), (1.30), and xUx + (ll +/2) Ut = 0.

(1.3l)

We then have Proposition 4. The solution to the Ramsey allocation problem satisfies production efficiency; namely, the marginal rates o f transformation are equated across technologies. Equioalently, setting the tax on intermediate goods tl = 0 is optimal. Proof: For this economy, production efficiency is equivalent to

f~

-

h~

(1.32)

Solving the Ramsey allocation problem, we obtain the following first-order conditions for z, ll, and 12, respectively: vf~ = -#hz,

(1.33)

Ut + 3,(xUix + UI + lUa) + of - O,

(1.34)

UI + 2(xUtx + Uz + 1UH) +/zh/= O,

(1.35)

where v, /~, and )L are the multipliers on (1.29), (l.30), and (1.31). Combining Equations (1.34) and (1.35) gives of =/~hl, which, combined with (1.33), establishes Equation (1.32). The first-order conditions for profit maximization for the firms imply that ,fi_ q(l+t])_ f w

hz( l

h,

+

~/).

Thus, if condition (l.32) holds, Equation (1.36) implies that r/-- 0. [2

(1 .36)

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V.V.Chari and PJ. Kehoe

The intermediate-goods result holds in general settings in which there are (possibly infinitely) many goods and many production technologies. We have assumed that the production technologies satisfy constant returns to scale. If there are increasing returns to scale, then there are standard problems with the existence of a competitive equilibrium. If there are decreasing returns to scale, then the intermediate-goods result continues to hold, provided that pure profits can be fully taxed away. It turns out that the result for uniform commodity taxation follows from the intermediate-goods result. To see this, consider a utility function o f the form U ( c , l) - W ( G ( c ) , l),

(1.37)

where c = ( c l , . . . , c n ) and G is homogeneous o f degree 1. We can reinterpret this economy as an economy with a single consumption good x, which is produced using n intermediate-goods inputs ( c l , . . . ,c,~) with the constant returns to scale technology x = G(c). The intermediate-goods result requires that in an optimal tax system, the taxes on the intermediate-goods inputs be zero, so that there are taxes only on final goods x and 1. This is clearly equivalent to a uniform tax on (cl . . . . , cn).

2. Fiscal policy In this section, we begin by setting out a general framework for analyzing optimal fiscal policy in a stochastic one-sector growth model. We use a deterministic version o f this model to develop results on the taxation of capital income, in both the short and long run. We first show that the optimal capital income taxes are zero in a steady state, even if there are heterogeneous consumers. We then show that for a class of utility functions, there is only one period with nonzero capital income taxes, following which capital income taxes are zero along a transition to the steady state. We then turn to the cyclical properties of optimal fiscal policy. In a stochastic model without capital, we illustrate how debt can act as a shock absorber. We briefly discuss how incomplete markets can alter these results. We then illustrate the main features o f optimal fiscal policy over a business cycle using a calibrated version of the model with capital. Finally, we discuss how these results are altered in three other environments: an endogenous growth model, an open economy model, and an overlapping generations model. 2.1. G e n e r a l f r a m e w o r k

Consider a production economy populated by a large number of identical, infinitely lived consumers. In each period t = 0, 1.... , the economy experiences one o f finitely many events st. We denote by s t = ( s o , . . . , st) the history o f events up to and including period t. The probability, as of period 0, o f any particular history s t is t~t(st). The initial realization so is given. This suggests a natural commodity space in which goods are differentiated by histories.

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In each period t, the economy has two goods: a consumption-capital good and labor. A constant returns to scale technology which satisfies the standard Inada conditions is available to transform capital k(s t-l) and labor l(s t) into output via F(k(st-X), l(st), st). Notice that the production function incorporates a stochastic shock st. The output can be used for private consumption c(st), government consumption g(sX), and new capital k(st). Throughout, we will take government consumption to be exogenously specified. Feasibility requires that

c(s ~) + g(s t) + k(s ~) = F(k(s ~-1), l(sl), st) + (1 - 6) k(s I-I ),

(2.1)

where 6 is the depreciation rate on capital. The preferences of each consumer are given by

Z

[3~lz(s ~) U(c(s~), l(s~)),

(2.2)

t,S t

where 0 < [2 < 1 and U is strictly increasing in consumption, is strictly decreasing in labor, is strictly concave, and satisfies the Inada conditions. Government consumption is financed by proportional taxes on the income from labor and capital and by debt. Let T(s t) and O(s t) denote the tax rates on the income from labor and capital. Government debt has a one-period maturity and a state-contingent return. Let b(s ~) denote the number o f units of debt issued at state s t and Rb(S t+l) denote the return at any state s L+I = (s ~, st+l). The consumer's budget constraint is

c(st)+k(st)+b(s t) <~ [1

T(st)] w(st) l(st)+Rk(st)k(st-l)+Rb(sl)b(sl-1),

(2.3) where Rk(s t) = 1 + [1 - O(st)][r(s ~) - 6] is the gross return on capital after taxes and depreciation and r(s t) and w(s t) are the before-tax returns on capital and labor. Consumers' debt holdings are bounded by b(s ~) >~ - M for some large constant M. Competitive pricing ensures that these returns equal their marginal products, namely, that

r(s t) = Fk(k(s t l), l(st), st), w(s') = Fl(k(s t 1), l(st), s,).

(2.4) (2.5)

Consumers' purchases o f capital are constrained to be nonnegative, and the purchases of government debt are bounded above and below by some arbitrarily large constants. We let x(s t) = (c(sl), l(st),k(st), b(st)) denote an allocation for consumers at s t and let x = (x(st)) denote an allocation for all s t. We let (w, r,R~,) = (w(st), r(st),Rh(s~)) denote a price system. The government sets tax rates on labor and capital income and returns tbr government debt to finance the exogenous sequence o f government consumption. The government's budget constraint is

b ( s t ) _ Rb(st)b(st-I)+g(s t)

r(st)w(s,)l(s,)__O(s,j[r(st)_6]k(s

l 1).

(2.6)

We let 3"c(st) = (T(st), O(st)) denote the government policy at s t and let zc - (~(st)) denote the infinite sequence of policies. The initial stock of debt, b 1, and the initial stock o f capital, k-l, are given.

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Notice that for notational simplicity, we have not explicitly included markets in private claims, so all borrowing and lending is between consumers and the government. Since all consumers are identical, such claims will not be traded in equilibrium; hence their absence will not affect the equilibrium. Thus we can always interpret the current model as having complete contingent private claims markets. A competitive equilibrium for this economy is a policy a~, an allocation x, and a price system (w,r, Rb) such that given the policy and the price system, the resulting allocation maximizes the representative consumer's utility (2.2) subject to the sequence of budget constraints (2.3), the price system satisfies (2.4) and (2.5), and the government's budget constraint (2.6) is satisfied. Notice that we do not need to impose the feasibility condition (2.1) in our definition of equilibrium. Given our assumptions on the utility function, constraint (2.3) is satisfied with equality in an equilibrium, and this feature, together with (2.6), implies (2.1). Consider now the policy problem faced by the govenunent. We suppose that there is an institution or a commitment technology through which the government, in period 0, can bind itself to a particular sequence of policies once and for all. We model this by having the government choose a policy g at the beginning of time and then having consumers choose their allocations. Formally, allocation rules are sequences of functions x(gc) = (x(s t [ at)) that map policies ~ into allocations x(ar). Price rules are sequences of functions w(a~) ~- (w(s t [ a~)) and r(av) = (r(s t I a~)) that map policies av into price systems. Since the government needs to predict how consumer allocations and prices will respond to its policies, consumer allocations and prices must be described by rules that associate government policies with allocations. We will impose a restriction on the set of policies that the government can choose. Since the capital stock in period 0 is inelastically supplied, the government has an incentive to set the initial capital tax rate as high as possible. To make the problem interesting, we will require that the initial capital tax rate, O(so), be fixed at some rate. A Ramsey equilibrium is a policy av, an allocation rule x(.), and price rules w(.) and r(.) that satisfy the following: (i) the policy zc maximizes

~13t~(s ') U(c(s' I aO, l(s' l =)) I~S t

subject to constraint (2.6), with allocations and prices given by x(ag), w(g), and r(gr); and (ii) for every gl, the allocation x(~1), the price system w(avl), r(ar'), and Rb(~'), and the policy ~' constitute a competitive equilibrium. We now turn to characterizing the equilibrium policies and allocations. In terms of notation, it will be convenient here and throughout the chapter to let Uc(s t) and U1(s ~) denote the marginal utilities of consumption and leisure at state s t and let Fk(s t) and Fl(s t) denote the marginal products of capital and labor at state s t. We will show that a competitive equilibrium is characterized by two fairly simple conditions: the resource constraint

c(s') -~ g(s*) + k(s ~) = f'(k(s'-t), l(st), s,) + (1 - 6) k(s t q)

(2.7)

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and the implementability constraint ~y~(s

t) [Uc(s')c(s~) + U~(st) l(st)] = Uc(so)[R~(so)k-~ +Rb(so)b-1],

(2.8)

l,s t

where Rk(so) = I + [1 - O(so)][Fk(so) - b]. The implementability constraint should be thought of as an infinite-horizon version of the budget constraint of either the consumer or the government, where the consumer and firm first-order conditions have been used to substitute out the prices and policies. We have

Proposition 5, The consumption, labor, and capital allocations and the capital tax rate and return on debt in period 0 in a competitive equilibrium satisfi2 conditions (2.7) and (2.8). Furthermore, given allocations and period Opolicies that satisfy (2. 7) and (2.8), we can construct policies, prices, and debt holdings that, together with the given allocations and period-O policies, constitute a competitive equilibrium. Proof: We first show that a competitive equilibrium must satisfy (2.7) and (2.8). ] b see this, note that we can add (2.3) and (2.6) to get (2.7), and thus feasibility is satisfied in equilibrium. Next, consider the allocation rule x(¢c). The necessary and sufficient conditions for c, 1, b, and k to solve the consumer's problem are given as follows. Let p(s ~) denote the Lagrange multiplier on constraint (2.3). Then by Weitzman's (1973) and Ekeland and Scheinkman's (1986) theorems, these conditions are constraint (2.3), together with first-order conditions for consumption and labor:

[3tg(s t) Ue(s t) < 0, [3tl~(st) Ul(s t) <~-p(st)(1 - r(st))w(st), with equality if l(s t) > 0;

(2.9) (2.10)

first-order conditions for capital and government debt:

[p(st)--~+p(st+l)Rb(st+l)l b(st)=O~

(2.11)

[p(st)--~-~p(st~')Rk(s"') ] ~+1 s

(2.12)

k(st) = O;

and the two transversality conditions

~ p ( s ~ ) b(s~) .... o,

(2.13~

t

s t

t lim ~-2p(s ~) k(s ~) - O.

(2.14)

S /

We claim that any allocation which satisfies (2.3) and (2.9)-(2.14) must also satisfy (2.8). To see this, multiply (2.3) byp(st), sum over t and s t, and use (2.11)-(2.14) to obtain

}~p(s~)~c(s')-[1 t,s t

~(sl)] w(s~)l(s')} =p(so)[Rk(so)k ~+Rb(so)b

~].

(2.15)

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Using (2.9) and (2.10) and noting that interiority follows from the Inada conditions, we can rewrite Equation (2.15) as

V~(s') [G.(s') c(s ~) + Ut(s') l(s')] = G ( s 0 ) [R~(s0) k ~ + Rb(s0) b l]. t,s t (2.16) Thus (2.7) and (2.8) are necessary conditions that any competitive equilibrium must satisfy. Next, suppose that we are given allocations and period-0 policies that satisfy (2.7) and (2.8). We construct the competitive equilibrium as follows. First, note that for an allocation to be part of a competitive equilibrium, it must satisfy conditions (2.3) and (2.9)-(2.14). Multiplying (2.3) by p(s t) and summing over all periods and states following s" and using (2.9)-(2.14), we get

V~(s~)

t=~+l s,

(2.17)

Thus any competitive equilibrium debt allocation must satisfy (2.17), and hence (2.17) defines the unique debt allocations given consumption, labor, and capital allocations. The wage rate and the rental rate on capital are determined by (2.4) and (2.5) from the capital and labor allocations. The labor tax rate is determined from (2.5), (2.9), and (2.10) and is given by

V~(s9

[1 - "v(s~)]/~)(s~).

(2.18)

We can use Equations (2.3), (2.9), (2.11), and (2.12) to construct the capital tax rate and the return on debt. From these conditions, it is clear that given the allocations, the tax rate on capital and the return on debt satisfy

~(st) Uc(s t) = ~ [3~(st÷l) Uc(st÷l) Rk(gtl sttllst

#(s t) U~(s t) .... ~

fitt(s t F1 ) U~.(s t+l )Rb(S

1),

t+l

),

(2.19)

(2.20)

s/+1 ]st

c(s '+~) + k(s "~1) + b(s '~1) = [1 - r(s'+l)] w(s '+1) l(s ~+~)+/~(s ~+j)/c(s') + gb(s '+1) O(s'),

(2.21)

where Rl,(s ~+~) - 1 + [1 - O(st~l)][r(s t+l) - 6]. It turns out that these conditions do not uniquely determine the tax rate on capital and the return on debt. To see this, suppose that st+l can take on one of N values. Then counting equations and unknowns in Equations (2.19)-(2.21) gives N + 2 equations and 2N unknowns in each period and state. Actually, however, there is one linear dependency across these equations. To see

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this, multiply (2.21) by [3#(s t*l) Uc(s ~+1) and sum across states in period t + 1. Use (2.17), (2.19), and (2.20) to obtain an equation that does not depend on Rb and 0. Since we can replace any of the N equations from (2.21) with this equation, there are only N + 1 equations left to determine Rb and 0. Thus there are N - 1 degrees of indeterminacy in setting the tax rate on capital and determining the return on debt. One particular set of policies supporting a competitive equilibrium has the capital tax rate not contingent on the current state. That is, suppose for each s ~, 0(st,&+l) = 0(s l)

for all

st+~.

(2.22)

We can then use (2.19) to define O(s t) and use the period-t + 1 version of (2.21) to define Rb(st+l), It is straightforward to check that the constructed return on debt satisfies (2.20). Another set of policies supporting the same competitive equilibrium has the return on debt not contingent on the current state. [For details, see Chari et al. (1994), and for a more general discussion of this kind of indeterminacy, see Bohn (1994).] [] If the competitive equilibrium associated with each policy is unique, clearly the Ramsey equilibrium is also unique. If there are multiple competitive equilibria associated with some policies, our definition of a Ramsey equilibrium requires that a selection be made from the set of competitive equilibria. We focus on the Ramsey equilibrium that yields the highest utility for the government. Given our characterization of a competitive equilibrium, the characterization of this Ramsey equilibrium is immediate. We have

Proposition 6. The allocations in a Ramsey equilibrium solve the Jbllowing programming problem." f3' #(s t) U(c(s t), l(sr ))

max ~_~ Z S t

(2.23)

t

subject to (2.7) and (2.8). For convenience, write the Ramsey allocation problem in Lagrangian form:

max ~_~[3tl~(st) { W(c(s'),l(s'),)~)- XU~.(so)[Rk(so)k_~ + Rb(so)b-~]}

(2.24)

t~S t

subject to (2.7). The function W simply incorporates the implementability constraint into the maximand and is given by

W(c(s'), l(st), J.) - U(c(s'), l(s')) + • [U~(s t) c(s') + Ul(s') l(s')],

(2.25)

where 3. is the Lagrange multiplier on the implementability constraint, (2.8). ]'he firstorder conditions for this problem imply that, for t ) 1, Wz(s')

We(s9

Fl(st)

(2.26)

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1692 and

Wc(st)=Zfilz(s~+l Is*)W~(s t+l) [ 1 - 6 + F k ( s t + l ) ]

for

t=0,1,2 .....

S t+l

(2.27) A property of the Ramsey allocations which is useful in our analysis of the cyclical properties of optimal fiscal policy is the following. If the stochastic process on s follows a Markov process, then from Equations (2.26) and (2.27) it is clear that the allocations from period 1 onward can be described by time-invariant allocation rules c(k, s; ~), l(k,s; )0, k'(k,s; )0, and b(k, s; 3.). The period-0 first-order conditions include terms related to the initial stocks of capital and debt and are therefore different from the other first-order conditions. The period-0 allocation rules are thus different from the stationary allocation rules, which govern behavior from period 1 onward. Thus far, we have considered a tax system with capital income taxes and labor income taxes. A wide variety of other tax systems lead to the same Ramsey allocation problem. For example, consider a tax system that includes consumption taxes, denoted r~(st), as well as labor and capital income taxes. For such a system, the implementability constraint is given by

~ [ 3 ~ ( s t) [Uc(s ~) c(s t) + Ul(s')/(st)] -- (1go(s°) + v~0) [Rk(So)k-i +Rb(S0) b-l] [,S t

(2.28) where Re(so) = 1 + [1 - O(so)][Fk(so) - 6] and r~0 is the tax rate on consumption in period 0. The first-order conditions of the competitive equilibrium with such a tax system are given by c/~(s')

Uc(st)

_

I

T(s')

~ + ~rlts

,~

,.

)

(2.29)

and

Uc(sf) -Uc(st+l) Rk(sZ+l), l+r,:(s t) ~-~ /3/~(s" l I St)l + ~(st+,)

(2.30)

S I+l ]S t

where Rg(s t+l) - 1 + [1 - O(st+l)][Fk(s t'l) - 6]. Inspection of these first-order conditions shows that if an allocation satisfies the implementability constraint (2.28) and the resource constraint (2.1), it can be decentralized as a competitive equilibrium under a variety of tax systems. Examples of such tax systems include those with only consumption taxes and labor income taxes and those with only consumption taxes and capital income taxes. More complicated examples include those in which tax rates on capital and labor income are required to be the same, but are allowed to be different from tax rates on consumption. The message of this analysis is that optimal tax theory implies optimal wedges between marginal rates of substitution and marginal rates of

Ch. 26." Optimal Fiscal and Monetary Policy

1693

transformation and is typically silent on the detailed taxes used to implement these wedges. Recall that with a capital and labor income tax system, we ruled out lump-sum taxes by imposing a constraint on period-0 capital income taxes. In a consumption and labor tax system, an analogous constraint is necessary. Notice that if consumption taxes are constant so that Tc(s t) = re0 for all s t and that if labor is subsidized appropriately so that r(s t) = -re0, then (2.29) and (2.30) become the undistorted first-order conditions. By setting r~0 arbitrarily high, it is possible to satisfy (2.28) at the lump-sum tax allocations and thus to achieve the undistorted optimum. One way to rule this out is to impose an upper bound on T~.0. (There seems to be some confusion about this point in the literature.) 2.2. C a p i t a l i n c o m e taxation 2.2.1. In a steady state

Here we develop the results on the optimality of zero capital income taxes in a steady state, and we consider various generalizations and qualifications for that result. For simplicity, we consider a nonstochastic version o f the model in which the stochastic shock in the production function is constant and government consumption is also constant, so g ( s t) = g. Suppose that under the Ramsey plan, the allocations converge to a steady state. In such a steady state, We. is constant. Thus, from Equation (2.27), 1 =/3(1 - 6 + Fk).

(2.31)

The consumer's intertemporal first-order condition (2.19) in a steady state reduces to 1 =/311 + (1 - O)(Fk - 6)].

(2.32)

Comparing (2.31) and (2.32), we can see that in a steady state, the optimal tax rate on capital income, 0, is zero. This result is due to Chamley (1980, 1986). A natural conjecture is that with heterogeneous consumers, a nonzero tax on capital income is optimal to redistribute income from one type of consumer to another. We examine this conjecture in an economy with two types o f consumers, indexed i = 1,2, whose preferences are given by OG

V " [jtUi( c. lit),

(2.33)

t-O

where cit and [it denote the consumption and labor supply o f a consumer o f type i. Notice that the discount factors are assumed to be the same for both types of consumers. The resource constraint for this economy is given by c~t + c2t + g + kt~ l = F ( k t , 11~, lzt) + (1 - 6) kt,

(2.34)

where the production function F has constant returns to scale. Notice that the production function allows for imperfect substitutability between the two types o f labor

V.V. Chari and P.J. Kehoe

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and capital. For this economy, the implementability constraints for the two types of consumers i = 1,2 are given by

Z

fit (V~tci t + U/,lit) = Uico(Rkok'o + Rbobio),

(2.35)

t where k~ and bi~ denote the initial ownership o f capital and debt by consumers o f type i 1. If the tax system allows tax rates on capital income and labor income to differ across consumer types, then it is straightforward to establish that the resource constraint and the two implementability constraints completely characterize a competitive equilibrium. For the Ramsey equilibrium, we suppose that the government maximizes a weighted sum of consumers' utilities of the form oo

o(3

601 ~-~fi t U 1(Clt, llt)+co2 Z / 3 t U 2 (cat, 12t), t 0 tO

(2.36)

where the welfare weights coi C [0, 1] satisfy cot + (92 = 1. The Ramsey problem is to maximize Equation (2.36) subject to the resource constraint (2.34) and the implementability constraints (2.35). Let us define

W(c,t, c2f, ILt, 12t, )~1, ;-2) = ~

[coiUi(ci,, li,) + ,~i(U{,cit + U];l,,) 1

(2.37)

i-1,2

for t ~> 1; and for t = 0, W equals the right-hand side o f Equation (2.37) evaluated at t = 0 minus ~ ~ U~o(Rkok i i Here 3,i is the Lagrange multiplier on the ~i + Rbobo). implementability constraint for the consumer o f type i. The Ramsey problem is, then, to maximize O(3

~_~ fit W(CII, CZt, 11;, lat, "~'1,/~2) t-O subject to the resource constraint (2.34). The first-order conditions for this problem imply that

W~f--fiW~.~+l(1-6+Fkt~l)

for

i=1,2

and

t=0,1,2 .....

(2.38)

In a steady state, W , is a constant, and thus 1 = [3(1 - 6 + F~),

(2.39)

which as before implies that the steady-state tax on capital income is zero. This resait is due to Judd (1985). I Notice in (2.35) tile initial assets arc denoted k~ and b~, while in (2.8) they are denoted k I and b i. Throughout the chapter hi deterministic environments initial assets have a subscript 0, while in stochastic environments initial assets have a subscript -1. This unfortunate inconsistency stems from the traditiov, of using kt ~t to denote the capital choise in period t.

1695

Ch. 26." Optimal Fiscal and Monetary Policy

This result also holds when type-1 consumers are workers who supply labor, cannot save or borrow, and hold no initial capital, while type-2 consumers are capitalists who own all the capital but supply no labor. Then we replace Equation (2.35) for type-1 consumers with

U~tclt + Ul~llt = 0

for all t.

(2.40)

Notice that in the solution to the Ramsey problem, Equation (2.38) continues to hold for the capitalists, and thus the steady-state tax on capital income is zero. Notice also that this result shows that even if the Ramsey planner puts zero weight on the capitalists, taxing capital in the long run is still not optimal. The reason is that the cumulative distortion o f the capital taxes on intertemporal margins makes even the workers prefer the static distortion o f marginal rates that comes from labor income taxes. Now suppose that the tax system does not allow tax rates on either capital income or labor income to differ across consumer types. These restrictions on the tax system imply extra constraints on the allocations that can be achieved in a competitive equilibrium. Consider first the restriction that tax rates on capital income do not differ across consumers. To derive the restrictions that this adds to the Ramsey problem, consider the consumers' intertemporal first-order conditions, which can be written as U~t - fi [1 + (1 Uc(t+ 1

Ot+l)(Fktq

1 -

6)].

(2.41)

Since the right-hand side of Equation (2.41) does not vary with i, the restriction U]t =-U2'2t Uct+l

(2.42)

holds in any competitive equilibrium. Thus Equation (2.42) is an extra restriction that must be added to the Ramsey problem. Let/~ denote the Lagrange multiplier on (2.42). Defining

ui + J' where xt - (cmczt,ll~,12t,Zi,Z2), we can use the same argument as before, with V replacing W, to conclude that the steady-state tax on capital income is zero. Consider next the restriction that tax rates on labor income do not vary across consumers. Consider the consumers' first-order conditions for labor supply, which can be written as -

Uict Flit

1 -

Tt.

(2.43)

V.V. Chari and P..J Kehoe

L696

Since the right-hand side of Equation (2.43) does not vary with i, the restriction v,',

_ e,,,

Uclt U~t

(2.44)

F/2I

holds in any competitive equilibrium and thus must be added to the Ramsey problem. We proceed as before and, with no confusion, define

{ U/~U;2

Fm ~

(2.45)

where vt is the Lagrange multiplier on (2.44). A first-order condition lbr the Ramsey problem is

-~V/,+t + V+t, - / 3 G t , + l

[Fk,+~ + (l

-

O)].

In a steady state, this reduces to

vc! Clearly, unless Vk - 0, the steady-state tax on capital income is not zero. Inspection of Equation (2.45) shows that Vk = 0 if and only if Filt/F12t does not depend on k. Recall that the production function is separable between k and (11,I2) if Fm/F12t does not depend on k. Such separable production functions can be written in the form F(k, ll,/2) = F(k, H(ll,/2)) for some function H. [For some related discussion, see Stiglitz (1987).] This analysis of fiscal policy with restrictions suggests that other restrictions on tax rates may lead to nonzero taxation of capital income in a steady state even in a representative agent model. Consider an economy with identical consumers, and consider another restriction on the tax system, namely, that tax rates are equal for all periods. Suppose, for example, that taxes on capital income are restricted to being equal for all periods l?om period 1 onward, while labor tax rates are unrestricted. Using the consumer's first-order conditions, we see that G/

G,+I

-- /3 [1 q- (1 -- 0t+l)(~'kt+l

(2.46)

- ~)]

together with the restriction that 0t~ 1 = 01 for all t > 1, implies the following restriction across allocations: fiU~.f+~

1 F~-1,t+i~L-~5- L~-~c i - 1 F~,j--~

for all

t > 1.

(2.47)

The appropriate Ramsey problem, then, has constraints of the torm (2.47), as well as the imptementability constraint and the resource constraint. We leave it to the reader

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Optimal Fiscal and Monetary Policy

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(as a difficult exercise) to show that, under suitable conditions, the optimal tax on capital income is positive, even in the steady state. The intuition is that with no such restrictions, it is optimal to front-load the capital income taxes by initially making them large and positive and eventually setting them to zero. When taxes are constant, it is optimal to try to balance these two opposing forces and make them somewhat positive tiu'oughout. The discussion of the extra constraints on the Ramsey problem implied by restrictions on the tax system suggests the following observation. Zero capital income taxation in the steady state is optimal if the extra constraints do not depend on the capital stock and is not optimal if these constraints depend on the capital stock (and, of course, are binding). Another possible restriction is that there is some upper bound on tax rates. Suppose, for example, that capital tax rates are at most 100 percent. Then in addition to satisfying the analogs of conditions (2.7) and (2.8), an allocation must satisl}¢ an extra condition to be part of a competitive equilibrium. Rewrite the analog of Equation (2.19) as Ucz - - ~ U c t ~ l ( ] .@ ( l - Ot.l l )(Fkl+l - c~)).

(2.48)

Then if an allocation satisfies Fk~+~ >~ 6 and

0t+ 1

(2.49)

~ 1, Equation (2.48) implies that

U~ >~ fiU~t+L.

(2.50)

Thus we can simply impose (2.50) as an extra constraint. With this constraint, for suitable restrictions on the utility function, the optimal policy is to set the tax rate to its upper bound for a finite number of periods. After that, the tax takes on an intermediate value for one period and is zero thereafter. 2.2.2. In a non-steady state

in the preceding subsection, we showed that in a variety of circumstances, in a steady state, the optimal tax on capital income is zero. Sometimes one can establish a much stronger result, namely, that optimal capital income taxes are close to zero after only a few periods. [See Chamley (1986), for example.] In this subsection, we show that for a commonly used class of utility functions, it is not optimal to distort the capital accumulation decision in period 1 or thereafter. The class of utility functions we consider are of ~/he fbrm cl-O U(c, l) = l-.S a + V(l).

(2.5l)

One might conjecture that if utility functions of this fbrm have the property that optimal capital income taxes are exactly zero after period 1, then for utility functions that are in

1698

V..g Chari a n d P..£ K e h o e

some sense close to these, keeping capital income tax rates close to zero after period 1 is also optimal. To motivate our result, we write the consumer's first-order condition for capital as qt+ 1 ( 1 -- 6 + F k t + 1 ) -- 1 = qt+ 10t v 1 ( F k t + 1 -- (~),

(2.52)

where qz+l - flUct+/Uc: is the Arrow-Debreu price of a unit of consumption in period t + 1 in units of consumption in period t. Now, in an undistorted equilibrium, the consumer's first-order condition has the same left-hand side as (2.52), but the righthand side equals zero. Thus the right-hand side of (2.52) measures the size of the wedge between the distorted and undistorted first-order conditions for capital accumulation in period t. We then have Proposition 7. For utility functions o f the form (2.51), it is not optimal to distort the capital accumulation decision at period 1 or thereafter. Namely, the optimal tax rate on capital income received in period t is zero f o r t ~ 2. Equivalently, qt+lOt+l(F~t+l-6) = 0 Jbr all

t ~> 1.

(2.53)

Proof: For t >~ 1, the first-order conditions for the Ramsey problem imply that Wct+ l . .

1 =/3~O

- 6 + Fk~+i),

(2.54)

where W is given in Equation (2.25). For t ~> 1, the consumer's first-order conditions for capital imply that Uct+l

1 =/3~

[1 + (1 - O,-,q)(Fk~+l - 6)1.

(2.55)

Now, for any utility function of the tbrm (2.51), we can easily show that

W.+l Uct+l We, U.

(2.56)

Substituting Equation (2.56) into (2.54) and subtracting the resulting equation from (2.55) gives the result. E] Proposition 7 implies that the tax rate on capital income received in period t is zero for t ~> 2 and is typically different from zero in period 1. In period 0, of course, the tax rate is fixed by assumption. This result is much stronger than the standard Chamley result, which refers to steady states, and the logic behind this result is actually more connected to the uniform tax results than to the rest of the Chamley-type results. To see this, suppose that the tax

Ch. 26." Optimal Fiscal and Monetary Policy

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system allows the government to levy only proportional taxes on consumption and labor income. For this tax system, the analog of the restriction o f the initial tax on capital income is that the initial consumption tax is given. Then with a utility function of the form (2.51), consumption taxes are constant in all periods except period 0. In a continuous-time version o f the deterministic model with instantaneous preferences given by Equation (2.51), Chamley (1986) shows that the tax rate on capital income is constant for a finite length o f time and is zero thereafter. The reason for Chamley's different result is that he imposes an exogenous upper bound on the tax rate on capital income. If we impose such an upper bound, the Ramsey problem must be amended to include an extra constraint to capture the restrictions imposed by this upper bound. (See the example in Subsection 2.2.1.) In the deterministic version of the model, with preferences given by Equation (2.51), the tax rate is constant at this upper bound for a finite number of periods, there is one period o f transition, and the tax rate is zero thereafter. In the stochastic version of the model, constraints o f this kind can also be imposed. One can derive an upper bound endogenously. Consider the following scenario. At the end of each period t, consumers can rent capital to firms for use in period t + 1 and pay taxes on the rental income from capital in period t + 1. Or consumers can choose to hide the capital, say, in their basements. If they hide it, the capital depreciates and is not available for use in t + 1. Thus, if they hide it, there is no capital income, and consumers pay zero capital taxes. 2.3. Cyclical properties 2.3.1. D e b t taxation as a shock absorber

In this subsection, we illustrate how state-contingent returns on debt can be used as a shock absorber in implementing optimal fiscal policy. One interpretation of state-contingent returns on debt is that the government issues debt with a non-statecontingent return and uses taxes or partial defaults to make the return state-contingent. We show that under reasonable assumptions, during periods o f high government expenditures such as wartime, the government partially defaults on debt, and during periods o f low government expenditures such as peacetime, it does not. Many o f the insights here are developed in Lucas and Stokey (1983) and Chaff et al. (1991). We illustrate this shock-absorber role in a version o f our model o f fiscal policy with no capital. Specifically, we assume that F ( k , 1,z) = zl, where z is a technology shock. The resource constraint is c(s t) + g ( s t ) ~" z ( s ' ) l(s')

and the consumer's first-order condition for labor supply is

ul(st) - I1 r(s')] z(~) gc(s t)

(2.57)

V.E Chari and P.J Kehoe

1700

The first-order condition tbr debt is

(2.58)

Uc(s t) = ~ [3~(St+l) Vc(st+l)Rb(xt+l)/[A(st). st+~

For convenience, let H(s t) - Uc(s t) c(s ~) + Ul(s t) l(st). Notice that the resource constraint and the consumer's first-order condition imply H(s t) = Uc(st)[v(st)z(s t) l(s t) g(st)]. Thus H(s t) is the value of the (primary) government surplus at s t in units of current marginal utility. The implementability constraint reduces to

~_~ fig(st) H(st) = U~(so) R0 b t.

(2.59)

t,S t

Expression (2.17) reduces to

(2.60) t=r+l

s t

Now imagine that the government promises a non-state-contingent (gross) rate of return on government debt R(s t 1) and then levies a state-contingent tax v(s t) on the gross return on government debt. That is, R and v satisfy

Rh(s ~) = [1 - V(s~)]/~(s~<). Consider next determining the tax rate and the return on debt. The after-tax return on debt [1 - v(sr)] R(s r-l) in some period r and state s" is obtained as follows. Multiplying the consumer budget constraint by fit p(s ~) U~:(st) and summing from period r and over all periods and states from period r + 1 onward, we obtain the familiar requirement that the value of the government's after-tax debt obligation must equal the expecteC present value of government surpluses:

t=r+l

,v t

(2.61) While the after-tax returns are determined by Equation (2.61), the gross returns and file tax rates on debt are not separately determined. The reason is that both consumers and the govermnent care only about the after-tax return on debt. Obviously, there are many ways of combining (before-tax) gross returns and tax rates to give the same after-tax

Ch. 26:

Optimal Fiscal and Monetary Policy

1701

returns. More formally, if v and R support a particular set o f Ramsey allocations, so do any v and R' that satisfy [1 - v(s~)]R'(s ~ 1) : [1 - v(s")]R(s r 1)

for all

r and s '~.

(2.62)

We resolve this indeterminacy by normalizing gross returns R to satisfy

k(s' 1)= ~(st+L)U~(s'-l)

(2.63)

where s t - (s t-l, st). Notice that the normalization in Equation (2.63), together with (2.62), implies that tax rates on debt satisfy

#(s t [ s I L) U,.(Sl)V(S t)

0

for all

tands t 1

(2.64)

S t

where/~(s t [ s t 1) = l~(st+l)/t~(st). Next, we derive the first-order conditions fbr the Ramsey problem. Let 3. denote the Lagrange multiplier on the implementability constraint. The first-order conditions for t ~> 1 imply that

z(s t) u,.(s') + U;(s') + Z [z(s')H~(s') + H;(s')] = 0,

(2.65)

where H,.(s t) and Hl(s t) denote the derivatives o f H ( s t ) . For t - 0, the first-order condition is the same as (2.65), except that the right-hand side is replaced by

,~ [z(so) G c ( s o ) + Gl(so)] [1 - V(So)] R_lb_l. These first-order conditions can be used to prove the following proposition: Proposition 8. For t >~ 1, there exist .functions ~, 7, and ~ such that the Ramsey consumption allocations, labor allocations, and labor tax rates can be written as

c(s') ' C'(gt,zD,

l(s') = 7(g,z,),

c(s') = ~(gt,z,).

Moreover, if b ~ = O, then c(so), l(so), and ~C(so) are given by these same functions. Proof: For t /> 1, substituting from the resource constraint for l(s t) into (2.65) gives one equation o f the form F ( c , g , z ; ) O = 0. Solving this gives the Ramsey consumption allocation as a function o f the current levels o f government consumption, the technology shock, and the multiplier. From the resource constraint and from Equation (2.57), we know that the labor allocation and the labor tax rate are a function of these same variables. For t = 0, the same procedure gives allocations and the labor tax rate in period 0 as a function of go, z0, and 5~. We can solve for )~ by substituting

V.V Chari and P.J. Kehoe

1702

the allocations into the implementability constraint (2.59). Clearly, for b-1 = 0, the first-order conditions for t = 0 are the same as the first-order conditions for t ~> 1. [] Proposition 8 says that the allocations and the labor tax rate depend only on the current realizations of the shocks and not separately on the entire history o f realizations. This proposition implies that labor tax rates inherit the stochastic properties of the underlying shocks. For example, if government consumption is i.i.d. and the technology shock is constant, then tax rates are i.i.d. (This result does not hold in general with capital.) If government consumption is persistent, then so are the tax rates. This result of standard neoclassical theory sharply contrasts with claims in the literature that optimal taxation requires labor tax rates to follow a random walk. [See Barro (1979), Mankiw (1987), and our discussion in the following subsection, 2.3.2.] To understand the nature of the Ramsey outcomes, we consider several examples. In all o f them, we let technology shocks be constant, so z(st) = 1 for all s t. We begin with a deterministic example that illustrates how Ramsey policies smooth distortions over time. E x a m p l e 1. Consider an economy that alternates between wartime and peacetime. Specifically, let gt = G for t even and gt = 0 for t odd. Let the initial indebtedness R l b 1 = 0. We will show that the government runs a deficit in wartime and then pays off the debt in the ensuing peacetime. Consider the first-order condition for the Ramsey problem in peacetime. Using the resource constraint, we have that (1 + )L)[U,.(O) + Ul(O)] + ,~c[U~.,..(O) + 2 U~.I(O)+ Ua(O)] - 0, where the partial derivatives are evaluated at gr = 0. By strict concavity, the second bracketed term is negative. Since the multiplier ~ is positive, the first term is positive. From Equation (2.57), we have that U~. + Uz -- rUc. Thus r(0) > 0. When we use Proposition 8, Equation (2.59) implies that H ( G ) +/3H(0) = 0, which can be rewrittetJ as

Uc( G)[ T( G) l(g ) - G] + [3U,,( O)['~( O) l(O)] - O. That is, the discoumed value of the government surplus is zero over the two-period cycle o f government consumption. Since the government runs a surplus in peacetime, it must run a deficit in wartime. Here the government sells debt b(G) - G -- r(G) l(G) in wartime and retires debt in the next peacetime. The gross return on the debt from wartime to peacetime is R ( G ) = Uc(G)/[3U~(O), and with our normalization, the tax rate on debt is always zero. E x a m p l e 2. Consider an economy that has recurrent wars with long periods of peace in between. Specifically let gt = G for t = 0, T, 2T, ..., and let gt - 0 otherwise. Let

1703

Ch. 26." Optimal Fiscal and Monetary Policy

the initial indebtedness R-lb-x = over each T-period cycle, that is,

0.

Again, by Proposition 8, the budget is balanced

G ( G ) [ T ( G ) l(G) - G] + fiU~(O)[v(O) l(O)] + . . . +/3 ~ 1U~(O)[r(O) l(O)] = O. Here, as in Example 1, the government runs a deficit in wartime and a constant surplus in peacetime. The war debt is slowly retired during the following T - 1 periods of peace. The government enters the next wartime with zero debt and restarts the cycle. Specifically, the government issues debt of level G - v(G) l(G) in wartime. In the first period of peacetime, the government sells

G(G) fiu.(o) ---

[G

r(G) I(G)].- r(0) l(0)

units of debt. In the second period, it sells

G(G)_ [G - ¢(G) I(G)]- -rS-°~l--(-°) r(0), l(0),

fi2 Uc(O)

and so on. Clearly, the debt is decreasing during peacetime. E x a m p l e 3. Here we will illustrate the shock-absorbing nature of optimal debt taxes. Let government spending follow a two-state Markov process with a symmetric transition matrix with positive persistence. The two states are g: = G and gt = 0. Let Jr=Prob{gt~l=GIg,-G}=Prob{g,+l=01g:

0} > 31

Therefbre, the probability of staying at the same state is greater than the probability of switching states. Let go =- G, and let the initial indebtedness R 1b 1 be positive. The government's period t budget constraint is

b(s t) = [1 - v(st)] R(s t-l) b(s: 1) + g ( s ' ) - T(s') l(s').

(2.66)

From Proposition 8, the allocations and the labor tax rates depend only on the current realization gt for t ~> 1. Under the Markov assumption, Equations (2.60) and (2.63) imply that the end-of-period debt b(s t) and the interest rate R(s t) depend only on the current realization gt. From Equation (2.66), we know that the tax rate on debt depends on the current and the previous realizations. Let b(g:), R(g:), and v(g~-i ,g~) denote the end-of-period debt, the gross interest rate, and the tax rate on debt, For a large class of economies, we can prove the following proposition: Proposition 9. Suppose that in the solution to the Ramsey problem, tt(0) > H(G) > O; that is, the value of government surpluses is larger in peacetime than in wartime, the

1704

V.Y Chari and P..Z Kehoe

government's debt is always positive, the marginal utility of consumption is greater in wartime U~(G) than in peacetime Uc(O), and both b(G) and b(O) are positive. Then v(0, G) > v(G, G) > 0 > v(O, 0) > v(G, 0).

(2.67)

That is, the debt tax rates' are most extreme in periods of' transition: they are highest in transitions from peacetime to wartime and lowest in transitions from wartime to peacetime. Furthermore, debt is taxed in wartime and subsidized in peacetime. R e m a r k : It is possible to show that the assumptions in this proposition are satisfied for a large class of economies if the initial debt is sufficiently large. Proof: Let V(G) and V(0) denote the expected present value of govermnent surpluses

when the economy is in state G and state 0, respectively. These surpluses are given by the left-hand side of Equation (2.61) multiplied by the marginal utility of consumption in that state, which can be written recursively as V(G) = H(G) + fi[jr V(G) + (1 - Jr) V(0)],

(2.68)

V(0) = H(0) +/3[¢cV(0) + (1 - Jr) V(G)].

(2.69)

Solving these, we obtain Jr)H(O)+(I-/3Jr)H(G) ~ D /3(1 - ¢v)H(G) + (1 -/3jr)H(O) V(0) = , D V(G) -

fi(1

(2.70) (2.71)

where D = (1 -/3go) 2 -/32(1 -Jr)2 > 0. From Equation (2.60), we obtain

/3[:rV(G) + (1 - Jr) V(0)] , U~.(G) /3[jrV(O) + (1 sD V(G)] b(0) = , uc(0) b(G) =

(2.72) (2.73)

and from Equation (2.63), we obtain gc(c) R(G) . . . . . . . . . . . . . . . . . . . , /3[~Uc(G) + (1 - :r) Uc(O)] ~

uc(o) R(0) =/3[jrUe(0) + (1 --Jr) U~.(G)]"

(2.74) (2.75)

Combining these, we obtain expressions for the befbre-tax obligations of the government: JrV(G) + (1 - aT) V(0) R(G) b(G) = JrUc(G) + (1 - :v) Uc(O)' R(O) b(O) --

Jr V(0) + (1 - Jr) V(G) Jr U~:(0) + (1 -- Jr) Uc(G)

(2.*76) (2./7)

Ch. 26.. OptimalFiscal and Monetary Policy

1705

Since H(G) < H(0), Equations (2.70) and (2.71) imply that V(G) < V(0). Using this result, :w > ½, and U~(0) < U~(G), we can see that Equations (2.76) and (2.77) imply that

R(G) b(G) < R(O) b(O).

(2.78)

We can rewrite Equation (2.61) as

V(&)

[1 - v(gt-a,gt)] R(&-I) b(&-l) - Uc(gt)"

(2.79)

The right-hand side of Equation (2.79) depends only on the cm'rent state; thus (2.78) implies that v(0, G) > v(G, G) and v(0, 0) > v(G, 0). To establish Equation (2.67), we need only show that v(G, G) > 0 > v(0, 0). But this follows from (2.64) and (2.'79), using V(G) < V(0) and Uc(0) < Uc(G). [] The intuition for these results is as follows. The Ramsey policy smooths labor tax rates across states. This smoothing implies that the government runs a smaller surplus in wartime than in peacetime. With persistence in the shocks, the expected present value of surpluses starting from tile next period is smaller if the economy is currently in wartime than if it is in peacetime. The end-of-period debt is, of course, just the expected present value of these surpluses. [See Equation (2.60).] Thus the end-of'period debt is smaller if tile economy is in wartime than if it is in peacetime, so

D(G) < b(O). As was shown in (2.78), R(G)b(G) < R(O)b(O). Thai is, the obligations of the government if there was war in the preceding period are smaller than if there was peace. Suppose the economy is currently in wartime, so gt = G. The current deficit and end-of-period debt are the same regardless of the history. Thus, if the inherited debt obligations are larger, the only way to meet the government budget constraint is to tax debt at a higher rate. So a transition from peacetime to wartime results in higher debt taxes than does a continuation of wartime. Similar intuition applies for the comparisons of transitions from wartime to peacetime with continuations of peacetime. 2.3.2. Tax-smoothing and incomplete markets Here we develop Barro's (1979) result on tax-smoothing and compare it to the work of Marcet et al. (1996) on optimal taxation with incomplete markets. In a wellknown paper, Barro (1979) analyzes a reduced-form model of optimal taxation. Ithis theoretical development, there is no uncertainty and the government chooses a sequence of tax rates ~t on income to maximize

t=Z-~o(1 + r ) "

1706

EV. Chari and P.J. Kehoe

where Yt is income in period t and r is an exogenously given interest rate, subject to budget constraints of the form bt = (1 + r ) b t

I + g t - "6Yt,

where g~ is government spending, b-t is given, and an appropriate boundedness condition on debt is imposed. These constraints are equivalent to the present value budget constraint Z "rty: _ gt t=0 (1 +r)t l=0 ( l + r ) t + b °

(2.80)

Barro shows that in this deterministic setup, optimal tax rates are constant. Barro goes on to assert that the analog of this result with uncertainty is that optimal taxes are a random walk. In an environment with uncertainty, the properties of optimal policy depend on the structure of asset markets. If asset markets are complete, the analogous present value budget constraint is

r(sgy(s') t~S t

1 +.(s,)

g(s') -

l,s t

i-+r( -Z +b°

With this asset structure, optimal tax rates are clearly constant across both time and states of nature. If asset markets are incomplete, then the analysis is much more complicated and depends on precise details of the incompleteness. Suppose, for example, that the only asset available to the government is non-state-contingent debt. The sequence of budget constraints for the government can be written as

b(s') = (l + ,) b(s' t) + g(s ~) _ r(~)y(s,) together with appropriate boundedness conditions on debt. Substituting the first-order conditions to the government's problem into the budget constraints and doing some manipulations yields

~ [ 3 ' '~(~' t s ) f--F

S t

U r ( s I ) y ( s t)

T(St)y(st)]

.... (1 +~)b(: ~).

U~(s")y(s9

(2.82)

The restriction that debt is not state-contingent is equivalent to the requirement that the left-hand side of Equation (2.82) is the same for any two states in period r in the sense that for all s r l,

t--r

u~(s~)y(s') [g(s~) - ~(s')y(~')l U~(s")y(s")

St

U~(s')y(s') I = r

s'

(2.83)

[g(,,)

Ur(s ~'/ ) y ( s

r(st)y(st)j F/

)

>

where s ~ = (s: ~,s.) and s"' - (s" 1,s~,) tbr all s,.,s.,. Analyzing an economy with incomplete markets requires imposing, in addition to (2.81), an infinite number of

Ch. 26:

Optimal Fiscal and Monetary Policy

1707

constraints of the form (2.83). This problem has not yet been solved. An open question is whether optimal tax rates in such an environment follow a random walk. In our general equilibrium setup, restrictions on government policy also impose extra constraints. Suppose that neither capital tax rates nor the return on debt can be made state-contingent. Then the additional restrictions that the allocation must satisfy so that we can construct a competitive equilibrium are given as follows. Substituting Equations (2.17) and (2.18) into the consumer's budget constraint yields, after some simplification,

t=v

(2.84)

xr

- {1 + [1 - O(s ~ l)][Fl~(s")- c5]} k(s '-1)

:Ro(s r l)b(s'

1),

where 0(s r 1) satisfies (2.85) Sr

The requirement that the debt be non-state-contingent is, then, simply the requirement that the left-hand side of Equation (2.84) with O(s ~ -l) substituted from (2.85) be the same for all st. Furthermore, we need to impose bounds on the absolute value of the debt to ensure that the problem is well posed. We then have that if an allocation satisfies these requirements, together with the resource constraint (2.7) and the implementability constraint (2.8), a competitive equilibrium can be constructed which satisfies the restriction that neither the capital tax rate nor the return on debt be state-contingent. Clearly, computing equilibria with non-state-contingent capital taxes and return on debt is a difficult exercise. Marcet et al. (1996) analyze an economy with incomplete markets but without capital. When government consumption is serially uncorrelated,, they find that the persistence properties of tax rates are a weighted average of a random walk and a serially uncorrelated process. They also find that the allocations are close to the complete markets allocations. They argue that their results partially affirm Barro's (1979) assertion. In Section 3, we consider a model in which debt is nominal and non-state-contingent. There we show that inflation can be used to make the real returns state.-contingent and that the Ramsey allocations are identical to those in an economy with real statecontingent debt. This result is reminiscent of our result that even if debt returns are not state-contingent, as long as capital tax rates are state-contingent, the Ramsey allocations are identical to those in an economy in which all instruments are statecontingent. This feature suggests that for actual economies, judging the extent of market incompleteness can be tricky.

1708

EV. Chari and P.J. Kehoe

2.3.3. A quantitative illustration

Here we consider a standard real business cycle model and use it to develop the quantitative features of optimal fiscal policy. We follow the development in Chari et al. (1994). In quantitative stochastic growth models, preferences are usually specified to be of the form el(c, l) -

[c 1 ~(L - l)y]v' ~p

where L is the endowment of labor. This class of preferences has been widely used in the literature [Kydland and Prescott (1982), Christiano and Eichenbaum (1992), Backus et al. (1992)]. The production technology is usually given by F ( k , l,z, t) = UZ(ePt+~l) 1 a.

Notice that the production technology has two kinds of labor-augmenting technological change. The variable p captures deterministic growth in this change. The variable z is a technology shock that follows a symmetric two-state Markov chain with states zt and zh and transition probabilities Prob(zt~l = zi I zt = zi) = ~ for i = l, h. Government consumption is given by gt = ge pt, where again p is the deterministic growth rate and g follows a symmetric two-state Markov chain with states gf and gh and transition probabilities Prob(gt+t = gi i gt = gi) = ~ for i = l,h. Notice that without shocks to technology or government consumption, the economy has a balanced growth path along which private consumption, capital, and government consumption grow at rate p and labor is constant. Zhu (1992) shows that in economies of this form, setting capital income tax rates to be identically zero is not optimal. We ask whether capital tax rates are quantitatively quite different from zero. Recall from the proof of Proposition 5 that certain policies are uniquely determined by the theory, while others are not. Specifically, the labor tax rate is determined, while the state-by-state capital tax rate and return on debt are not. From Equation (2.19), however, we know that the value of revenues fi'om capital income taxation in period t + 1 in terms of the period-t good is uniquely determined. To turn this variabie into a tax rate, consider the ratio of the value of these revenues to the value of capital income, namely;

O~(s ,) = )2 q(s~'t) O(s~l)[F/,(s~) 6] q(s'+l)[Fk(s t+l) - 6] ~

(2.86)

where q(s t*l ) = [3[.1(stt i ] s t) U~.(st~l)/Uc(s i) is the price of a unit of consumption at state s t+l in units of consumption at s t. We refer to Oe(s ~) as the ex ante tax rate on capital income.

Ch. 26:

Optimal Fiscal and Monetary Policy

1709

Table 1 Parameter values for two models" Model

Parameters and values

Baseline model

Preferences

y - 0.80

Technology

a = 0.34

~p- 0 6 = 0.08

fi - 0.97 p = 0.016

Gover,tment consumption

g/= 350

g h - 402

¢ = 0.95

Technology shock

z l - 0.04

z h = 0.04

~ = 0.91

L = 5475

Markov chains for

High risk aversion model

Preferences

q~= -8

a Source: Chari et al. (1994). Next, in defining the last variable that is uniquely determined by the theory, it is useful to proceed as follows. Imagine that the government promises a non-statecontingent rate of return on government debt ?(s t ~) and levies a state-contingent tax v(s ~) on interest payments from government debt. That is, ? and v satisfy

Rh(s t) = 1 + ?(s ~ L)[1 - v(st)],

(2.87)

and ~ q ( s t ) v ( s t) = 0, where q(s t) is the price of a unit of consumption at state s ¢ in units of consumption at state s t-l. Thus ?(s t 1 ) is the equilibrium rate of return on a unit purchased in period t - 1 at s t 1, which yields a non-state-contingentreturn ?(s t` l) at all states s t. It is clear from (2.21) that the theory pins down Rl,(s t) k(s f 1) ~ Rb(S t) b(s t 1). Given our definition of v, it is also clear that the theory pins down the sum of the tax revenues from capital income and the interest on debt, which is given by

O(s t) [Ft(s t) - 6]/~(s ~ 1)+ v(s')~(s' ')b(s'-l).

(2.88)

We transform these revenues into a rate by dividing by the income from capital and debt to obtain the tax rate on private assets, given by

rl(st)= O(s')[l~'k(st)

6]k(st ~)+ v(st)~(s t L)b(s' ~) [Fk(s t) - 6] k(s t 1) + ?(s t l)b(s, 1)

(2.89)

We consider two parametrizations of this model. (See Table 1.) Our baseline model has ~p = 0 and thus has logarithmic preferences. Our high risk aversion model has ~p = - 8 . The remaining parameters of preferences and the parameters tbr technology are those used by Chari et al. (1994). We choose the three parameters of the Markov chain for government consumption to match three statistics of the postwar US data:

ggChari and R J K e h o e

1710 Table 2 Properties of the fiscal policy modelsa

Percentage in models

Income tax rates

Labor Mean

Baseline

High risk aversion

23.87

20.69

Standard deviation

0.10

0.04

Autocorrelation

0.80

0.85

Capital

Mean

0.00

0.06

Standard deviation

0.00

4.06

Autocorrelation

0.83

Private assets

Mean

1.10

0.88

Standard deviation

53.86

78.56

Autocorrelation

-0.01

0.02

a All statistics are based on 400 simulated observations. The means and standard deviations are in percentage terms. For the US economy,the tax rates are constructed as described by Chari et al. (1994). For the baseline model, the capital tax rate is zero; thus, its autocorrelationis not defined. the average value of the ratio of government consumption to output, the variance of the detrended log of government consumption, and the serial autocorrelation of the detrended log of government consumption. We construct the Markov chain tbr the technology parameters by setting the mean of the technology shock equal to zero, and we use Prescott's (1986) statistics on the variance and serial correlation of the technology shock to determine the other two parameters. For each setting of the parameter values, we simulate the Ramsey equilibrium for our economy, starting from the steady state of the deterministic versions of our models. In Table 2, we report some of the resulting properties of the fiscal variables in our models. In the baseline model, the tax rate on labor income fluctuates very little. For example, i f the labor tax rate were approximately normally distributed, then 95 percent of the time, the tax rate would fluctuate between 23.67 percent and 24.07 percent. The tax on capital income is zero. This is to be expected because with ~p = 0, the utility function is separable between consumption and leisure and is homothetic in consumption, and the utility function thus satisfies the conditions discussed in Subsection 2.2.2. In the baseline model, the tax on private assets has a large standard deviation. Intuitively, we know that the tax on private asset income acts as a shock absorber. The optimal tax rate on labor does not respond much to shocks to the economy. The government smooths

Ch. 26:

Optimal Fiscal and Monetary Policy

1711

labor tax rates by appropriately adjusting the tax on private assets in response to shocks. This variability of the tax on private assets does not distort capital accumulation, since what matters for the capital accumulation decision is the ex ante tax rate on capital income. This can be seen by manipulating the first-order condition for capital accumulation. In Table 2, we also report some properties of the fiscal policy variables for the high risk aversion model. Here, too, the tax rate on labor income fluctuates very little. The tax rate on capital income has a mean o f - 0 . 0 6 percent and a standard deviation of 4.06 percent so that the tax rate is close to zero. We find this feature interesting because it suggests that, for the class of utility functions commonly used in the literature, not taxing capital income is optimal. Here, as in the baseline model, we find that the standard deviation of the tax rate on the income from private assets is large. 2.4. Other environments' 2.4.1. Endogenous growth models' Thus far, we have considered fiscal policy in models in which the growth rate of the economy is exogenously given. We turn now to models in which this growth rate is determined by the decisions of agents. Our discussion is restricted to a version of the model described in Lucas (1990). Analysis of optimal policy in this model leads to a remarkable result: Along a balanced growth path, all taxes are zero. Bull (1992) and Jones et al. (1997) discuss extensions to a larger class of models. Consider a deterministic, infinite-horizon model in which the technology for producing goods is given by a constant returns to scale production function F(kl, h~lj~), where kt denotes the physical capital stock in period t, ht denotes the human capital stock in period t, and lli denotes labor input to goods production in period t. Human capital investment in period t is given by htG(12t), where 12t denotes labor input into human capital accumulation and G is an increasing concave function. The resource constraints for this economy are ct + g + kt+l = F(kl, htllt) + (1 - Ok) kt

(2.90)

hx+L = htG(lzt) + (1 - 6h) h,~

(2.91)

and

where et is private consumption, g is exogenously given government consumption, and 6/, and Oh are depreciation rates on physical and human capital, respectively. The consumer's preferences are given by oo

~

[3' c'] ° v(lt, + let)~(1 - a),

t-O

where v is a decreasing convex function. Government consumption is financed by proportional taxes on the income from labor and capital in the goods production sector

1712

EV. Chari and RJ Kehoe

and by debt. Let rt and 0t denote the tax rates on the income from labor and capital. Government debt has a one-period maturity. Let bt+l denote the number of units of debt issued in period t and Rbtbt denote the payoff in period t. The consumer's budget constraint is ct + k~+j + bt+l ~< (1 - rt) wthtllt + Rekt + Rbtbt,

(2.92)

Rkt - 1 + ( 1 - Ot)(rt - c5) is the gross return on capital after taxes and depreciation and 1"1 and wt are the before-tax returns on capital and labor. Note that human capital accumulation is a nonmarket activity. The consumer's problem is to choose sequences of consumption, labor, physical and human capital, and debt holdings to maximize utility subject to (2.91) and (2.92). We assume that consumer debt holdings are bounded above and below by some arbitrarily large constants. Competitive pricir~ ensures that the returns to factor inputs equal thei,~ marginal pre~ducts, nameIy, tha~ where

rl = f k ( k . h~l~),

(2.93)

wt = Ft(kt, hfllt).

(2,94)

We let xt = (ct, lit, 12t, kt, kt, bt) denote an allocation for consumers in period t and let x = (st) denote an allocation for all t. The government's budget constraint is b,+ l = Rbtb~ + g - rtwthtll~ - Ot(r~ - (3)k,

(2.95)

We let zct = (rt, 0t) denote the goverrmaent policy at period t and let s~ ~- (zc~) denote the infinite sequence of policies. '1"he initial stock of debt, b 1, and the initial stock of capital, k-l, are given. A competitive equilibrimn is defined in the usual way. We have the following proposition. Proposition lO. The consumption allocation, the labor allocation, the physical and human capital allocations, the capital tax rate, and the return on debt in period 0 in a competitive equilibrium satisfy (2.90), (2.91), and O(3 "~ [3 [ ct

Uct = Ao,

(2.96)

t-0

where

A0 -- C:~.0{[I + (1 -00)(~0 - 6)1 l,o +R~0b0}

U~o [l~0 + 1 - 6h + (~(l~0)] G'(12o)

j

Furthermore, given any allocations and period-O policies' that satisfy (2.90), (2.91Z (2.96), and

Ul,

[3U/~.!

hLG'(12~) - ht+l G'(lzt+l) [ 1 -

C~h -I-

G(12, l )] +

[3U~z+l ll~+l ht+~ '

(2.97)

we can construct policies, prices, and debt holdings whick, together wztk the given allocations and period-O policies, constitute a competitive equilibrium.

Ch. 26:

Optimal tqscal and Monetary Policy

1713

Proof: The procedure we use to derive the implementability constraint is to express the consumer budget constraint in period-0 form with the prices substituted out. Recall that in the model with exogenous growth, this procedul"e implied that the capital stock from period 1 onward did not appear in the implementability constraint. It turns out that when human capital is accumulable, human capital does not appear in the implementability constraint from period 1 onward either. The consumer's first-order conditions imply that (2.98) (2.99)

-[YU1, = )~t(1 - rt)wtht, -ill U# -= ~tthtG' (12,),

(2.100)

-ktt + ktt ~1 [1 - Oh + G(121+l)] + )~t+l (1

(2./01)

t)+O wt+lllt+l - O.

Multiplying Equation (2.101) by ht~l, substituting for /tt~ and gt+~ from (2.99) and (2.100), and using Equation (2.91), we obtain --

2t(1 ---Tt)wlhl+L '~t+l(1-- Tt+l)w~+lht+2 + G'(lzt) G'(12,+1)

+ "~t+l (1 -- Z)+I ) W t + 1 l t t . l l h t t

1 - O.

(2.102) From Equation (2.102) and a standard transversality condition, we know that ~,o )to(1 - Z'O)Wohl Z )~t+l(l - "gt~i) wt+tllt+lht, 1 = t =o G'(12o)

(2.103)

Similarly, we can show that ~l+lRk,.+lk~+l = 2okt + Z t-o

,~tkt.

(2.104)

t=l

Next, we multiply the consumer budget constraint (2.92) by ~.t and sum from period 0 onward. When we use (2.103) and (2.104), (2.96) follows. To derive (2.97), we substitute (2.99) into (2.102). We leave it to the reader to prove the converse. [] The Ramsey problem is to maximize consumer utility subject to conditions (2.90), (2.91), (2.96), and (2.97). Recall that human capital accumulation occurs outside the market and cannot be taxed. In any competitive equilibrium, the Euler equation for human capital accumulation is undistorted. Therefore, there is no tax instrument that can be used to make the Euler equation for human capital accumulation hold for arbitrary allocations. In contrast, for arbitrary allocations, the Euler equation for physical capital can be made to hold by choosing the tax on capital income appropriately. This incompleteness of the tax system implies that the undistorted Euler equation for human capital accumulation is a constraint on the set of competitive allocations. We have the following proposition.

1714

V.V. Chari and P..J Kekoe

Proposition 11. Suppose that the Ramsey allocations converge to a balanced growth path. In such a balanced growth path, all taxes are zero. Proof." We prove that along a balanced growth path, the first-order conditions for the Ramsey problem are the same as those for a planner who has access to lump-sum taxes. (This, of course, does not mean that the government can achieve the lump-sum tax allocations, because there are distortions along the transition path.) Let W(ct, lit + 12t; )0 = U ( c , lit + 12t) + ~ctUct, where ~ is the Lagrange multiplier on (2.96). For our specified utility function, W(ct, lit + 12t; ~) = [1 + ~(1 - o')] U(ct, lit + [2t). The Ramsey problem is to maximize t

[3 W(cf, lit + [2t; ~.) - )~Ao subject to (2.90), (2.91), and (2.97). Consider a relaxed problem in which we drop condition (2.97). Since the objective function in this rewritten problem from period 1 onward is proportional to that of a social planner who has access to lump-sum taxes, the solutions to the two problems are the same along a balanced growth path. This solution also satisfies condition (2.97). Thus, along a balanced growth path, the Ramsey problem has the same solution as the lump-sum tax problem. The solutions to these last two problems differ along the transition paths only because the two problems imply different allocations for period 0 and therefore for the capital stocks for the beginning of period 1. [] The reader may be concerned that this result depends on the ratio of government consumption to output going to zero. To see that this concern is not warranted, consider an extension of the model described above. Consider an environment in which the government chooses the path of government consumption optimally. To see this, suppose that the period utility function is given by U(cl, li + 12) + V(g), where V is some increasing function of government consumption. The government problem in this setup is to choose both tax rates and government consumption to maximize the consumer utility. We can solve this problem in two parts. In the first part, government consumption is taken as exogenous and tax rates are chosen optimally. In the second part, government consumption is chosen optimally. The proof described above obviously goes through for extensions of this kind. For V(g) - a g I °/(1 -(f)~ it is easy to show that along a balanced growth path, govermnent consumption is a constant fraction of output. 2.4.2. Open economy models' So far, we have considered models of a closed economy. We turn now to considering issues that arise in an open economy. The elasticity of capital supply is likely to be

Ch. 26." Optimal Fiscal and Monetary Policy

1715

much greater in an open economy than in a closed economy because in the open economy capital is mobile and can flow to the country with the highest rate o f return. We consider a small open economy that takes the rates o f return on saving in the rest o f the world as given. In so doing, we abstract from the interesting strategic issues that arise when more than one authority sets taxes, and we abstract from general equilibrium linkages between an economy's fiscal policy and world prices. In an open economy, in addition to the standard taxes a government can levy on its citizens, a government can tax foreign owners o f factors that are located in its country. To allow this possibility, we allow there to be source-based taxes as well as residence-based taxes. Source-based taxes are taxes that governments levy on income generated in their country at the income's source, regardless o f ownership. Residencebased taxes are taxes that governments levy on the income o f their residents regardless o f the income's source. We show that source-based taxes on capital income are zero in all periods and that, with a restriction that ensures that the economy has a steady state, residence-based taxes on capital income are zero in all periods as well. This result is much stronger than the corresponding result for closed economies. [See Razin and Sadka (1995) for some closely related work.] Consider a model with both source-based and residence-based taxation. We model source-based taxes as those levied on a firm and residence-based taxes as those levied on consumers. Let r[ denote the world rental rate on capital absent any domestically levied taxes. The firm's problem is to solve

m a x f ( k t , l t ) - (1 + 02~)r[lq- (1 + rj~)writ, where 0fi and Tji are the source-based tax rates on capital and labor. The first-order conditions are Ot~r,*

Fk, - r ,*,

(2.105)

"Cj~wt = Fit - wt.

(2.106)

Consumers solve O<3

max ~

[3' U(ct, lt)

(2.107)

t-0

subject to o~

oG

p,c, = t~O

--

(2.

o8)

t-O

where pt = 1T~= i(1/&), R~.- 1 v ( l -O~.~,)(r~--6), P0 = 1, 0~. and ~2 are the residence° based tax rates on capital and labor, and initial assets are set to zero for convenience. The consumer first-order conditions are summarized by U#

- w t ( 1 - ~>t),

fiU~. 1 1 U~., Rt+~"

(2.109) (2.110)

V.g Chari and P.J Kehoe

1716

The economy-wide budget constraint (which is simply the sum of the consumer and government budget constraints) is given by oo

oQ

Zqt[ct+g+kt+l--(1 t=0

6)kt] = ~-~qtF(kt,

lt),

(2.111)

t=0

where qt = l T s = 1(1/R2) and R2 = r* + 1 - 6 . Notice that the economy as a whole borrows and lends at the before-tax rate R2, while consumers borrow and lend at the after-tax rate R~.. Intuitively, we know that any taxes on borrowing or lending levied on consumers are receipts of the government and cancel out in their combined budget constraint. Notice also that in the closed economy models studied in earlier sections, the competitive equilibrium has consumer budget constraints, a government budget constraint, and a resource constraint. In this small open economy, there is no resource constraint, and it is convenient to replace the govermnent budget constraint by the economy-wide budget constraint. To derive the constraints for the Ramsey problem, substitute the consumer first-order conditions into Equation (2.108) to get the implementability constraint c'/d

~l~'[Gtc,

+ U~,l,] = o,

(2.112)

t=0

where we have used the fact that Equation (2.110) implies that pt = fit U~./Uco. Next, notice that the first-order conditions of the firm and the consumer can be summarized by Equations (2.105), (2.110), and UI, _ F)a ( 1 - Tj_).

U,

(2.113)

(1 + rj~)

Thus, tbr each marginal condition, there is at least one tax rate so that the tax system is complete and there are no additional constraints on the Ramsey problem. Thus, with both source- and residence-based taxes available, the Ramsey problem is to maximize Equation (2.107) subject to (2.111) and (2.112). With purely source-based taxation, rct= Oct --- O, so from Equation (2.110) it is clea~ that for such a tax system, the Ramsey problem has the additional constraint fiUcg+l

Ucl

1

R/+1"

With purely residence-based taxation, r# = 0/* = 0, so from Equation (2.105) it is clear that the Ramsey problem has the additional constraint

Yt,, = r;.

Ch. 26:

1717

Optimal Fiscal and Monetary Policy

Consider the Ramsey problem when both source- and residence-based taxes are available. For convenience, write the problem as oo

max Z

[3' W(ct, lt, 3.)

l-O

subject to (2.111), where W(c,, It, 3,) condition for capital implies that

U(ct, lt) + )~ [Uact + U#lt]. The first-order

F~t = rt*,

(2.114)

while the first-order condition for consumption implies that fiWd+l

1

We,

Rt+ I

(2.115)

From Equation (2.114) it is clear that setting @ = 0 for all t is optimal. Next, note that this small economy will have a steady state only if flR[ - 1

(2.116)

for all t. Under this parameter restriction, Equation (2.115) implies that Wet = Wc, l, and thus the Ramsey allocations are constant, so in particular, Uct = Uct)l. Equations (2.110) and (2.116) imply that Oct = 0 for all t. Under a system with only source-based taxes, the Ramsey problem is to maximize ~--,t = o [3 W ( c , It, )~) subject to conditions (2.111) and (2.115). If we consider a relaxed version of this problem with the constraint (2.115) dropped, the above analysis makes clear that the solution to this relaxed problem satisfies this dropped constraint and hence solves the original problem. The first-order condition for capital then implies (2.114); hence, 0j~ = 0 tbr all t. Similarly, under a system with only residence-based taxes, the Ramsey problem is to maximize ~ - o fit W ( c , lt, )0 subject to conditions (2.111) and (2. 114). If we consider a relaxed version of this problem with the constraint (2.114) dropped, the above analysis makes clear that the solution to this relaxed problem satisfies this dropped constraint and hence solves the original problem• The first-order condition for consumption in the relaxed problem is (2.115). Under the parameter restriction (2.116), Wct = We, l, so Uc, = Ua+l. Hence, equations (2.110) and (2.116) imply that Oct = 0 for all t. In sum: Proposition 12. Under a system with both source- and residence-based taxes, 0/~ = O~.t = O.for all t. Under a system with only source-based taxes, O/t = O.fi~r all t. Under a system with only residence-based taxes, with the additional restriction (2.116), Oct = 0 f o r all t.

1'718

V.E Chari and t~J Kehoe

Notice that the Ramsey allocations from the problem with both source- and residence-based taxes can be achieved with residence-based taxes alone. With the additional restriction (2.116), the allocations from the problem with both types of taxes can be achieved with source-based taxes alone. The intuition for why sourcebased taxes are zero is that with capital mobility, each country faces a perfectly elastic supply of capital as a factor input and therefore optimally chooses to set capital income taxes on firms to zero. The intuition for why residence-based taxes are zero is that under (2.116) the small economy instantly jumps to a steady state, and so the Chamleytype logic applies for all t. 2.4.3. Ot;erlapping generations models' The discussion thus far has focused on models with infinitely lived agents. There is also an extensive literature on optimal policy in overlapping generations models. [See, for example, Atkinson (197l), Diamond (1973), Pestieau (1974), and Atkinson and Sandmo (1980); the surveys by Auerbach (1985) and Stiglitz (1987); and the applied work of Auerbach and Kotlikoff (1987) and Escolano (1992).] The results in this literature are much weaker than those in standard models with infinitely lived agents. One reason is that in a life cycle model, agents have very heterogeneous preferences over the infinite stream of consumption goods. For example, in a twoperiod overlapping generations model, an agent of generation t values consumption goods only in periods t and t + 1. In this subsection, we show that tax rates on capital income in a steady state are zero if certain homotheticity and separability conditions are satisfied. This result is well known. For an exposition using the dual approach, see, for example, Atkinson and Stiglitz (1980). Here we follow the primal approach used by Atkeson et al. (1999) and Garriga (1999). In this sense, the proposition we prove is more closely connected to the results on uniform commodity taxation than to the results on zero capital taxation in infinitely lived agent economies. We briefly develop a formulation of optimal fiscal policy in an overlapping generations model. Consider a two-period overlapping generations model with a constant population normalized to 1. The resource constraint is clt + c2t + kt+l + g = F(kt, lit, 12t) + (1 - (3) I¢/~

(2.117)

where clt and c2L denote the consumption of a representative young agent mad a representative old agent in period t, IjL and 12t denote the corresponding labor inputs, k1 denotes the capital stock in t, and g denotes government consumption. Each young agent in t solves the problem max U (cm lit) + fiU (c2t L~I,12i+t) subject to Clt + kt+| + bt+t - (1 --- Tit) W l t l l t

and c2,+j - (1

~:2t~l) Wzt+ll2t+l "4:-[1 + (1 - Ot+l)(rt+ 1 -- 6)] kt+l + e t + l b t + l ,

Ch. 26:

Optimal Fiscal and Monetary Policy

t719

where rl: and T2/ are the tax rates on the two types o f labor inputs and O: is the tax rate on capital income. The government budget constraint is TltWltllt + T2tw2tl2t + Otrtk/ + bt+l = g + R t b .

To define an optimal policy, we need to assign weights to the utility of agents in each generation. We assume that the government assigns weight )~t to generation t with )~ < 1. Then the Ramsey problem can be written as O(3

max U(c2o,/20)/X + ~

Xt [U(cl:, ll/)+

[~U(c2t+l, 12/+1)]

t-0

subject to the resource constraint for each t and

R(Clf,llt)+[3R(c21~-l,12,~-l) = 0

for each t,

(2.118)

where R(c, l) =-- cU:(c, l) + 1U:(c, l) and U(C20,/20) is the utility of the initial old. There is also an implementability constraint for the initial old, which plays no role in our steady-state analysis. Constraints (2.118) are the implementability constraints associated with each generation. It is straightforward to show that if the solution to the Ramsey problem converges to a steady state with constant allocations (cl,, lit, C2t+l, 12t+l, kt~ 1) = (Cl, 11, c 2 , / 2 , k), then the Ramsey allocations satisfy

1 2

F/, + 1 - 6.

(2.119)

In a steady state, the first-order condition for capital accumulation is

Uc(cl,ll) ~g~.(c2,~)

1 +(1 - O ) ( F x - 6 ) .

(2.120)

Inspecting these equations, we see that unless

1

U~(c~, ll)

,~

[~Uc(c2,/2)

(2.121)

the tax rate on capital income is not zero. In general, we would not expect this condition to hold. Notice the contrast with infinitely lived representative consumer models in which, in a steady state, the marginal utility of the representative consumer U,(c, l:) is constant. In an overlapping generations model, we would not expect the marginal utility o f a consumer to be constant over the consumer's lifetime. If the utility function is of the form C1 o

U(c, l) = - 1 - ~ + V(1) then we can show the following:

(2.122)

1720

EV.. Chari and P.J. Kehoe

Proposition 13. I f the utility Jimction is o f the Jbrm (2.122), then in a steady state, the optimal tax on capital income is zero.

Proof: To prove this, consider the first-order conditions for the Ramsey problem for consumption evaluated at a steady state: U~.l + atR~.l - ~tt,

(2.123)

/3[Ue2 + atRc2] = ;t,~,,

(2.124)

where )~t~tt and )~tat are the multipliers on (2.117) and (2.118), respectively. We can easily see that at and b~t are constant in a steady state. With a utility function of the form (2.122), &. is proportional to Uc so that (2.123) and (2.124) imply (2.121). [] The key properties used in proving this result are homotheticity of the utility function over consumption and the separability of consumption and leisure. In this sense, this proposition is more closely connected to the results on unitbrm commodity taxation than to the results on zero capital taxation in infinitely lived agent economies. When )~ = fl and F ( k , 11,12) = F ( k , 11 + 12) then one can show that for all strictly concave utility functions the optimal tax on capital income is zero in a steady state. [See Atkeson et al. (1999).]

3. Monetary policy In this section, we study the properties of monetary policy in three monetary economies. Friedman (1969) argues that to be optimal, monetary policy should follow a rule: set nominal interest rates to zero. For a deterministic version of our economy, this would imply deflating at the rate of time preference. Phelps (1973) argues that Friedman's rule is unlikely to be optimal in an economy with no lump-sum taxes. Phelps' argument is that optimal taxation generally requires using all available taxes, including the inflation tax. Thus Phelps argues that the optimal inflation rate is higher than the Friedman rule implies. In this section, we set up a general framework that allows us to analyze Phelps' arguments. We analyze them in three standard monetary economies with distorting taxes: a cash--credit model, a money-in-the-utility-function model, and a shopping-time model. The conditions for the optimality of the Friedman rule in the first two economies are analyzed by Chari et al. (1996), while those for the shopping-time model are extensively analyzed in the literature. [See Kimbrough (1986), Faig (1988), Woodford (1990), Guidotti and V6gh (1993), and Correia and Teles (1996), as well as Chariet al. (t996).] In this section, we show that the Friedman rule is optimal when simple homotheticity and separability conditions are satisfied. These conditions are similar to the ones developed in the uniform taxation results in Section 1. We explore the cmmection between tile optimality of the Friedman rule and the intermediate-goods result. For all three monetary economies, when the homotheticity

Ch. 26." Optimal Fiscal and Monetary Policy

1721

and separability conditions hold, the optimality of the Friedman role follows from the intermediate-goods result. To prove this, we show that under such conditions, all three monetary economies can be reinterpreted as real intermediate-goods economies, and the optimality o f the Friedman rule in the monetary economies follows directly from the intermediate-goods result in the reinterpreted real economies. In contrast, when these conditions do not hold, there is no such connection. To prove this, we show that when these conditions do not hold, there are two possibilities. First, there are monetary economies in which the Friedman rule holds which cannot be reinterpreted as real intermediate-goods economies. Second, there are monetary economies which can be reinterpreted as real intermediate-goods economies but in which the Friedman result does not hold. Finally, we conduct some numerical exercises designed to develop quantitative features o f optimal monetary policy. We find that if debt has nominal non-statecontingent returns, inflation can be used to make real returns state-contingent so that debt can serve as a shock absorber.

3.1. Three standard monetary models 3.1.1. Cash-credit Consider a simple production economy populated by a large number of identical, infinitely lived consumers. In each period t = 0, 1. . . . , the economy experiences one o f finitely many events st. We denote by s t = (so . . . . . st) the history of events up to and including period t. The probability, as o f period 0, of any particular history s t is #(st). The initial realization so is given. In each period t, the economy has three goods: labor and two consumption goods, a cash good and a credit good. A constant returns to scale technology is available to transform labor l(s t) imo output. The out-put can be used for private consumption o f either the cash good c l(s t) or the credit good c2(s t) or for government consumption g(s t). The resource constraint in this economy is thus

c~ (s') + c2(s t) + g(st) = l(st).

(3.~)

The preferences of each consumer are given by

t

Z [~t[~(st) U(CI(St)' C2(SI)' [(SI))' st

(3.2)

where the utility function U is strictly concave and satisfies the Inada conditions. In period t, consumers trade money, assets, and goods in particular ways. At the start of period t, after observing the current state st, consumers trade money and assets in a centralized securities market. The assets are one-period, non-state-contingent nominal

v.v. Chari and RJ Kehoe

1722

claims. Let M(s t) and B(s t) denote the money and the nominal bonds held at the end o f the securities market trading. Let R(s t) denote the gross nominal return on these bonds payable in period t + 1 in all states S t+x = ( s t , s t l 1). Notice that the nominal return on debt is not state-contingent. After this trading, each consumer splits into a shopper and a worker. The shopper must use the money to purchase cash goods. To purchase credit goods, the shopper issues nominal claims, which are settled in the securities market in the next period. The worker is paid in cash at the end o f each period. This environment leads to the following constraint for the securities market:

M(s,)+ B(st)= R(s t 1)B(s,-l)+ M(s,-l) p(s t 1)cl(st 1) _p(s t 1)c2(s,-1 ) + p ( s t u)[1 __ r(s t l)] l(s,-I),

(3.3)

where p is the price o f the consumption goods and T is the tax rate on labor income. The real wage rate is 1 in this economy given our specification of technology. The lefthand side of Equation (3.3) is the nominal value o f assets held at the end of securities market trading. The first term on the right-hand side is the value of nominal debt bought in the preceding period. The next two terms are the shopper's unspent cash. The fourth term is the payments for credit goods, and the last term is the after-tax receipts from labor services. We will assume that the holdings of real debt B(st)/p(s t) are bounded above and below by some arbitrarily large constants. Purchases o f cash goods must satisfy the following cash-in-advance constraint:

p(s t) cl (s t) <~M(st).

(3.4)

We assume throughout that the cash-in-advance constraint holds with equality. We let

x(s t) = (cl(st), c2(st), l(st),M(st),B(sl)) denote an allocation for consumers at s t, and we let x = (x(st)) denote an allocation for all s ~. We let q = (p(st),R(st)) denote a price system for this economy. The initial stock o f money M 1 and the initial stock o f nominal debt B-I are given. Money is introduced into and withdrawn from the economy through open market operations in the securities market. The constraint facing the government in this market is

M ( s ' ) - M ( s l - I ) + B(s t) = R(s I 1)B(st-l)~ p(st-l)g(s t 1)-p(st-I) r(SL-l) l(st-1).

(3.5) The terms on the left-hand side o f this equation are the assets sold by the government. The first term on the right is the payments on debt incurred in the preceding period, the second term is the payment for government consumption, and the third term is tax receipts from labor income. Notice that government consumption is bought on credit. We let Jr = (r(st)) denote a policy for all s t. Given this description of an economy, we now define a competitive equilibrium. A competitive equilibrium is a policy ~, an allocation x, and a price system q such

Ch. 26: OptimalFiscal and Monetary Policy

1723

that given the policy and the price system, the resulting allocation maximizes the representative consumer's utility and satisfies the government's budget constraint. In this equilibrium, the consumer maximizes Equation (3.2) subject to (3.3), (3.4), and the bounds on debt. Money earns a gross nominal return of 1. I f bonds earn a gross nominal return of less than 1, then the consumer can make profits by buying money and selling bonds. Thus, in any equilibrium, R(s 0 ~> 1. The consumer's first-order conditions imply that U~(st)/U2(s t) = R(st); thus in any equilibrium, the following constraint must hold:

gl(s t) >~ g2(st).

(3.6)

This feature of the competitive equilibrium constrains the set of Ramsey allocations. Consider now the policy problem faced by the government. As before, we assume that there is an institution or a commitment technology through which the government can bind itself to a particular sequence of policies once and for all in period 0, and we model this technology by having the government choose a policy ~ = (r(s0) at the beginning of time and then having consumers choose their allocations. Since the government needs to predict how consumer allocations and prices will respond to its policies, consumer allocations and prices are described by rules that associate allocations with government policies. Formally, allocation rules and price functions are sequences of functions x(jr) = (x(s t t :r)) and q(jr) = (/)(s t ] ~ ) , R ( s t [ ~)) that map policies Jr into allocations and prices. A Ramsey equilibrium is a policy Jr, an allocation rule x(.), and a price system q(.) that satisfy the following: (i) the policy Jr maximizes

}-~'[Y~(s9 g(cx(st l m, c2(s' l m, l(st l jr)) I~S r

subject to (3.5), with allocations given by x(jr), and (ii) ~br every Jr', the allocation x ( ~ ' ) and the price system q(~t), together with the policy Jr', constitute a competitive equilibrium. As is well known, if the initial stock of nominal assets held by consumers is positive, then welfare is maximized in the Ramsey problem by increasing the initial price level to infinity. If the initial stock is negative, then welfare is maximized by setting the initial price level so low that the government raises all the revenue it needs without levying any distorting taxes. To make the problem interesting, we set the initial sum of nominal assets of consumers M 1 + R I B 1 to zero. For convenience, let Ui(sO for i = 1,2, 3 denote the marginal utilities at state s t. Using standard techniques [for example, from Lucas and Stokey (1983), Chari et al. (1991), and Section 1], we can establish the implementability constraint: Proposition 14. The consumption and labor allocations in a competitive equilibrium satisfy conditions (3.1), (3.6), and the implementability constraint

Z/{tg(st) [c,(s~) U~ (s~)+ c2(s~)U~(st)+/(s t)U3(st)] = O, l

S t

(3.7)

1724

V.V. Chari and P.J. Kehoe

Furthermore, allocations that satisfy (3.1), (3, 6), and (3.7) can be decentralized as a competitive equilibrium. The Ramsey problem is to maximize consumer utility subject to conditions (3.1), (3.6), and (3.7). Consider utility functions of the form (3.8)

U(cI, c2, l) ~- V(w(c1, c2), [),

where w is homothetic. We then have Proposition 15. For utility functions of the .]'brm (3.8), the Ramsey equilibrium has R(s t) = 1 .for all st. Proof: Consider for a moment the Ramsey allocation problem with constraint (3.6) dropped. We will show that under (3.8), constraint (3.6) is satisfied. Let Z denote the Lagrange multiplier on (3.7) and fitkt(s t) y(s t) denote the Lagrange multiplier on (3.1). The first-order conditions for ci(s t) :for i - 1,2 in this problem are (l +Z) Ui(s ~) +Z

cj(s t) Uji(s t) + l(s t) U3i(s t) = y(st).

(3.9)

U =

Recall from Section ] that a utility function which satisfies (3.8) also satisfies

v'2 c:(s') ~l(s') @, C:(s9 ~2(s t) Z_., j=l

V 1(S t)

Z_,

j=l

(3.10)

U2(s t)

Next, dividing Equation (3.9) by Ui and noting that U3i/Ui have that

+ ,ts r v-7~f ~

= VI2/VI

for i

=- 1 , 2 ,

we

(3.1 l)

Using Equation (3.10), we have that the left-hand side of (3.11) has the same value for i - 1 and for i = 2. Therefore, Ul(st)/U2(s t) = 1. Since the solution to the less-constrained problem satisfies (3.6), it is also a solution to the Ramsey allocation problem. From the consumer's first-order condition, we have that UI (st)/U2 (s t) = R(st) and thus that R(s t) = 1. [] Now let us relate our results to Phelps' (1973) arguments for taxing liquidity services. Phelps (1973, p. 82) argues that "if, as is often maintained, the demand for money is highly interest-inelastic, then liquidity is an attractive candidate for heavy taxation at least from the standpoint of monetary and fiscal efficiency". Our results suggest that the commction between the interest elasticity of money demand and the desirability of taxing liquidity services is, at best, tenuous.

Ch. 26: Optimal Fiscal and Monetary Policy

1725

To see this, suppose that the utility function is of the form clj ~

U ( c l , c2, l)

~

c~ ~

+~

+ V(1).

(3.12)

Then the consumer's first-order condition UE/U2 = R becomes m o -

-

(c - m) a

- R,

(3.13)

where m is real money balances and c - cl + c2. The implied interest elasticity of money demand r/is given by 1

R 1/°

r/= ~ - R ~ / - r

1"

(3.14)

Evaluating this elasticity at R = 1 gives r/ = 1/2a, and thus the elasticity of money demand can range from zero to infinity. Nevertheless, all preferences in this class satisfy our homotheticity and separability conditions; hence the Friedman rule is optimal. Phelps' partial equilibrium intuition does not hold up for reasons we saw in Section 1. As we noted there, in general equilibrium, it is not necessarily true that inelastically demanded commodities should be taxed heavily. The homotheticity and separability conditions are equivalent to the requirement that the consumption elasticity of money demand is unity. To see this, consider a standard money demand specification: log m = a0 + ai log c + f ( R ) , w h e r e f ( R ) is some invertible function of the interest rate. If al - 1, so the consumption elasticity of money demand is unity, this formulation implies that m/c = e a°+jO~), or that there is some function h such that h(m/c) = R. The consumer's first-order condition is U1/U2 = R. Thus UI/U2 must be homogeneous of degree 0 in m and c if the consumption elasticity of money demand is unity. This formulation immediately implies the homotheticity and separability conditions. Note two points about the generality of the result. First, restricting w to be homogeneous of degree 1 does not reduce the generality of the result, since we can write w(.) = g ( f ( . ) ) , where g is monotone and f is homogeneous of degree 1, and simply reinterpret V accordingly. Second, the proof can be easily extended to economies with more general prodnction technologies, including those with capital accumulation. To see how, consider modifying the resource constraint (3.1) to f (Cl(Sl), C2(St),g(xt), l(st), k(s'), k(sl-l)) = O,

(3.15)

where k is the capital stock a n d f is a constant returns to scale function, and modifying the consumer's and the government's budget constraints appropriately. Let capital

1726

Vii

Chari and PJ. Kehoe

income net of depreciation be taxed at rate O(s~), and let capital be a credit good, although the result holds if capital is a cash good. For this economy, combining the consumer's and the firm's first-order conditions gives

U1 (s ~) _ R(s,fl(s'). Thus the optimality of the Friedman rule requires that Ul(st)/U2(s The constraint requiring that R(s t)/> 1 now implies that

~) = ft(st)/J2(st).

g~(s') ./i(s') u2(s,--5 >~ A(s'~'

(3.16)

and the implementability constraint (3.7) now reads t

s,

(3.17)

= vc(s0) {[l - 0(s0)] [./i(s0) - 6)]} k

~,

where k_ 1 is the initial capital stock. Since the tax on initial capital O(so) acts like a lump-sum tax, setting it as high as possible is optimal. To make the problem interesting, we follow the standard procedure of fixing it exogenously. The Ramsey allocation problem is to choose allocations to maximize utility subject to conditions (3.15), (3.16), and (3.17). For preferences of the form (3.8), the analog of Equation (3.11) has the right-hand side multiplied by f(s') for i = 1,2. This analog implies that U1(st)/U2 (s t) = fl (st)/f2 (st), and thus the Friedman rule holds. We now develop the connection between the optimality of the Friedman rule and the uniform taxation result, in this economy, the tax on labor income implicitly taxes consumption of the cash good and the credit good at the same rate. In Section l, we showed that if the utility function is separable in leisure and the subutility function over consumption goods is homothetic, then the optimal policy is to tax all consumption goods at the same rate. If R(s t) > 1, the cash good is effectively taxed at a higher rate than the credit good, since cash goods must be paid for immediately, but credit goods are paid for with a one-period lag. Thus, with such preferences, efficiency requires that R(s t) = 1 and therefore that monetary policy follow the Friedman rule. To make this intuition precise, consider a real barter economy with the same preferences (3.2) and resource constraint (3.1) as the monetary economy and with commodity taxes on the two consumption goods. Consider a period-0 representation of the budget constraints. The consumer's budget constraint is

~ q(s t) {[1 + rl(s~)] ci (s t) + [1 + T2(st)] C2(st)} ~ ~ q(s ~) l(st), t

(3.18)

St

and the government's budget constraint is

~ q(st)g(st)= ~ Z q(s~)[ T'(st)c''(s~) + T2(st)c2(s~)] ' t

St

•

(3.19)

St

where q(s t) is the price of goods in period t and at state sq A Ramsey equilibrium for this economy is defined in the obvious fashion. The Ramsey allocation problem for

Ch. 26." Optimal Fiscal and Monetary Policy

1727

this barter economy is similar to that in the monetary economy, except that the barter economy has no constraint (3.6). The consumer's first-order conditions imply that Ul(s t)

1 -b Tl(S t)

U2(s9

1 + r2(sg

Thus Ramsey taxes satisfy Tt(s t) = r2(s ~) if and only if in the Ramsey allocation problem of maximizing Equation (3.2) subject to (3.1) and (3.7), the solution has Ui(sZ)/Uz(s t) = 1. Recall from Proposition 3 in Section 1 that for utility functions of the form (3.8), the Ramsey equilibrium has ~q(s t) = r2(s t) for all s t. Thus, with homotheticity and separability in the period utility function, the optimal taxes on the two consumption goods are equal at each state. Notice that this proposition does not imply that commodity taxes are equal across states. [That is, Ti(s t) may not equal Tj(sr) for t ~ r and for i,j = 1,2.] We have shown that if the conditions for uniform commodity taxation are satisfied in the barter economy, then in the associated monetary economy, the Friedman rule is optimal. Of course, since the allocations in the monetary economy must satisfy condition (3.6) while those in the barter economy need not, there are situations in which uniform commodity taxation is not optimal in the barter economy but in which the Friedman rule is optimal in the monetary economy. To see this, consider the following. Example. Let preferences have the form 1 oi

1 o2

U(Cl, c2, l) - icl~ al + ~_-U~ c2 + V(l).

(3.20)

The first-order conditions for the Ramsey problem in the barter economy imply that

Ul(s t) U2(s t)

cl(s t) a~ -

c2(st)-~

1 +).(1 -

a2)

1 + )~(1 - 01)"

(3.21)

Clearly, Ul(s t) >~ U2(s ~) if and only if CVl ~ o 2. For cases in which al = 02, these preferences satisfy condition (3.6), and both uniform commodity taxation and the Friedman rule are optimal. If as > a2, then neither uniform commodity taxation nor the Friedman rule is optimal. What is optimal is to tax good 1 at a higher rate than good 2. In the barter economy, this higher taxation is accomplished by setting rl (s t) > r2 (s t), while in the monetary economy, it is accomplished by setting R(st) > 1. More interestingly, when a~ < a2, uniform commodity taxation is not optimal, but the Friedman rule is. To see this, note that when a~ < {72, the solution in the monetary economy that ignores the constraint Ul(s t) >~ U2(s t) violates this constraint. Thus this constraint must bind at the optimum, and in the monetary economy, U1 (s t) = Ue(st). Thus, in the barter economy, taxing good 1 at a lower rate than good 2 is optimal, and this is accomplished by setting rl (st) < r2(s~). In the monetary economy, taxing

v.v. Chari and P..L Kehoe

1728

good 1 at a lower rate than good 2 is not feasible, since R(s t) ~> 1, and the best feasible solution is to set R(s t) = 1. in this subsection, we have focused on the Lucas and Stokey (1983) cash-credit version of the cash-in-advance model. It turns out that in the simpler cash-in-advance model without credit goods, the inflation rate and the labor tax rate are indeterminate. The first-order conditions for a deterministic version of that model are the cash-in= advance constraint, the budget constraint, and

Ult _ Rt U2i 1 - Tt'

1 Ult _ R~p: [3 U2t Pt+l

where the period utility function is U(ct, lt) and Rt is the nominal interest rate from period t to period t + 1. Here, only the products R / ( 1 - vt) and Rtp/pt+~ are pinned down by the allocations. Thus the nominal interest rate, the tax rate, and the inflation rate are not separately determined. The Ramsey allocation can be decentralized in a variety of ways. In particular, trivially, both the Friedman rule and arbitrarily high rates of inflation are optimal.

3.1.2. Money-in-the-utility-fimction In this section, we prove that the Friedman rule is optimal for a money-in-the-ntilityfunction economy under homotheticity and separability conditions similar to those above. Consider the tbllowing monetary economy. In this economy, labor is transformed into consumption goods according to c(s ¢) + g(s t) = l(st).

(3.22)

(We use the same notation here as in the last subsection.) The pretbrences of the representative consumer are given by

Z ~_~ffl~(st) U(M(st)/P(St)' c(st)' l(st))' t

(3.23)

S t

where the utility function has the usual monotonicity and concavity properties and satisfies the Inada conditions. In period t, the consumer's budget constraint is

p(s t) c(s,)+ M ( s t ) + B(s ~) = M(st-l) + R(s t a) B(s ~ 1) +p(s~)[ 1 _ T(st)] l(st). (3.24) The holdings of real debt B(s~)/p(s ~) are bounded below by some arbitrarily large constant, and the holdings of money are bounded below by zero. Let M l and

Ch. 26: OptimalFiscal and Monetary Policy

1729

R_IB 1 denote the initial asset holdings of the consumer. The budget constraint of the government is given by B(s t) = R(s t 1)B(st 1)+p(st)g(st ) _ [M(s t) _ M ( s t

1)] _p(st)[1

_ r(st)ll(sZ). (3.25) A Ramsey equilibrium for this economy is defined in the obvious fashion. We set the initial stock of assets to zero for reasons similar to those given in the preceding section. Let m(s t) = M(st)/p(s t) denote the real balances in the Ramsey equilibrium. Using logic similar to that in Proposition 14, we can show that the consumption and labor allocations and the real money balances in the Ramsey equilibrium solve the Ramsey allocation problem max

Z Z f

(3.26)

ff t~(s~) U (m(s~)' c(st)' l(s~) )

S t

subject to the resource constraint (3.22) and the implementability constraint

~ [Y [m(s~) U~(s') + c(s') U2(s~)+ l(s ~) U3(s ~)]

- o.

(3.27)

These two constraints, (3.22) and (3.27), completely characterize the set of competitive equilibrium allocations. We are interested in finding conditions under which the Friedman rule is optimal. Now the consumer's first-order conditions imply that Ut(s')

U2(s9

_ 1

1

R(st)

(3.28)

Thus, for the Friedman rule to hold, namely, for R(s f) = 1, it must be true that Ui (s t) _ O.

U2(s t)

(3.29)

Since the marginal utility of consumption goods is finite, condition (3.29) will hold only if Ul(s t) = 0, that is, if the marginal utility of real money balances is zero. Intuitively, we can say that under the Friedman rule, satiating the economy with real money balances is optimal. We are interested in economies for which preferences are not satiated with any finite level of money balances and for which the marginal utility of real money balances converges to zero as the level of real money balances converges to infinity. That is, for each c and l, l i m m ~ Ul(m,c,l) = 0 and l i m m ~ U2(m,c,l) > 0. Intuitively, in such economies, the Friedman rule holds exactly only if the value of real money balances is infinite, and for such economies, the Ramsey allocation problem has no solution. To get around this technicality, we consider an economy in which the level of real money balances is exogenously bounded by a constant. We will say that the

V.V.Chari and P..J Kehoe

1730

Friedman rule is optimal if, as this bound on real money balances increases, the associated nominal interest rates in the Ramsey equilibrium converge to one. With this in mind, we modify the Ramsey allocation problem to include the constraint

m(s t) <~ Fn,

(3.30)

where ffz is a finite bound. Consider preferences of the form

U(m, c, l) = V(w(m, c), l),

(3.31)

where w is homothetic. We then have Proposition 16. l f the utility Jimction is' of the form (3.31), then the Friedman rule is"

optimal. Proof: The Ramsey allocation problem is to maximize Equation (3.23) subject to (3.22), (3.27), and (3.30). Consider a less-constrained version of this problem in which constraint (3.30) is dropped. Let/3t/~(st)y(s t) and 3, denote the Lagrange multipliers on constraints (3.22) and (3.27). The first-order conditions for real money balances and consumption are

(l+Z) Ul(St)+~[m(st)Ull(St)+c(st)U21(st)+l(st)U31(xt)]

=0

(3.32)

and (1 + )~) U2(s l) +,I, [m(s ~) U12(s t ) + c(s t) U22(s t) + l(s t) U32(st)] = ]/(st).

(3.33)

Since the utility function satisfies condition (3.31), it follows (as in Section 1) that

m(s~) gll(s~) + c(s~) g21(s ~) m(s~) Ui2 + c(s~) U22(s ') = gl (s ~) g2(s ~)

(3.34)

Using the form of Equation (3.31), we can rewrite conditions (3.32) and (3.33) as

(1 + ~) +.,~

[m(s t) Ull(S l) + c(s') U21(st)

[

Ul (s')

+ l(~t) V21(st) ] = 0

(3.35)

"~ " Vl(s') I

and (1 -I- ~) -l-,~ [ re(St) Ul2(St)u2(st) + C(St) U22(st)

. ~. v:l(s')] _ y(s ~)

+ ,ts ~

l

cl2(s~)

(3.36)

From Equation (3.34), we know that ]/(s~) g2(sO

0

(3.37)

m the less-constrained problem. Hence the associated m(s t) is arbitrarily large, and thus for any finite bound N, the constraint (3.30) binds in the original problem. The result then follows from (3.28). []

Ch. 26." Optimal Fiscal and Monetary Policy

1731

Again, restricting w to be homogeneous does not reduce the generality of the result. Clearly, the Friedman rule is optimal for some preferences which do not satisfy condition (3.31). Consider m [ ~l

U(m,c,l)- 1-al

c I o~ +

+ V(I).

(3.38)

Note that for cases in which (Yl ~ 02, Equation (3.38) does not satisfy condition (3.31). The first-order condition for the Ramsey problem for money balances m ( s t ) , when the upper bound on money balances is ignored, is [1 +)~(1

O~)]m ( s l ) -°~ - O.

(3.39)

Unless the endogenous Lagrange multiplier ,~ just happens to equal (oi - 1) 1, Equation (3.38) implies that the Friedman rule is optimal. In related work, Woodford (1990) considers the optimality of the Friedman rule within the restricted class of competitive equilibria with constant allocations and policies. Woodford shows that if consumption and real balances are gross substitutes, then the Friedman rule is not optimal. Of course, there are functions that satisfy our homotheticity and separability assumptions which are gross substitutes, for example, m I (y

g ( m , c, l) = ~

c 1 (r

+~

+ v(1).

The reason for the difference in the results arises from the difference in the implementability constraints. Woodford's problem is max U ( m , c, l)

(3.40)

subject to c+g

<~ l,

U t m + U2c + U3l - (1 - [ 3 ) U l ,

(3.41) (3.42)

where (3.42) is the implementability constraint associated with a competitive equilibrium with constant allocations. The first-order conditions for our problem are similar to those fbr Woodford's problem, except that his include derivatives of the right-hand side of condition (3.42). Notice that in Woodford's problem, iffi = 1 and preferences satisfy our homotheticity and separability conditions, then the Friedman rule is optimal. Notice, too, that if the model had state variables, such as capital, then constant policies would not typically imply constant allocations. To analyze the optimal constant monetary policy for such an economy, we would analyze a problem similar to that in Equation (3.26) with extra constraints on allocations that capture these restrictions. [These restrictions would be similar in spirit to those in (2.47).]

v.v Chari and P..J.Kehoe

1732

3.1.3. Shopping-time In this subsection, we prove the optimality o f the Friedman rule in a shopping-time monetary economy under appropriate homotheticity and separability conditions. Consider a monetary economy along the lines of Kimbrough (1986). Labor is transformed into consumption goods according to

c(st)+ g(s t) <~l(st).

(3.43)

The preferences of the representative consumer are given by

~ [3~l~(s~) U (c(s~), l(s t) + O(c(st), M(st)/p(st))), t

(3.44)

St

where U is concave, U1 > 0, U2 < 0, 01 > 0, and q~2 < 0. The function ~(Cl, M/p) describes the amount o f time needed to obtain c units of the consumption good when the consumer has M/p units of real money balances. We assume that q~l > 0 so that with the same amount of money, more time is needed to obtain more consumption goods. We also assume that q~2 < 0 so that with more money, less time is needed to obtain the same amount of consumption goods. The budget constraints of the consumer and the government are the same as (3.24) and (3.25). The Ramsey equilibrium is defined in the obvious fashion. Let m(s t) -M(st)/p(s t) and set the initial nominal assets to zero; we can then show that the consumption and labor allocations and the real money balances in the Ramsey equilibrium solve the problem max Z

[

Z / 3 ~ #(s~) St

U( c(st)' l(st) + O(c(s~)' m(st) ))

subject to condition (3.43) and

Z t

~ [~t~(St) {c(st) st

I ~71(st) + 01(st)

g2(st)]

-t-

[(S t) g2(s t)

-~

m(st)O2(s t) U2(s')} - 0. (3.45)

From the consumer's first-order conditions, we know that 02 = 0. We then have Proposition 17.

R(s s) - 1 if and only if

[[ ~ is homogeneous of degree k and k >~ 1, then the Friedman rule

is optimal. Proof: The first-order conditions for the Ramsey problem with respect to l(s ~) are given by

m(s t) and

U202+,~[cU1202+U2202(Olc+~2m+l)+U202+u2(O12c+O22m)]=O

(3.46)

U2 +• [cUI2

(3.47)

and +

U22(~1C -I- ~2m + I) + U2] + 7 - 0,

where 7 is the multiplier on the resource constraint and we have dropped reference to s t

Ch. 26." Optimal Fiscal and Monetary Policy

1733

Suppose first that 02 ;e 0 SO that the optimal policy does not follow the Friedman rule. Then, from Equations (3.46) and (3.47), we have that ~U2(012c Jr 022 m)

02

+ y = O.

(3.48)

Now, under the condition that 0(c, m) is homogeneous of degree k and k >~ 1, we have that 02(ac, ]tm) = ak-102(C , m). Differentiating with respect to a and evaluating at a = 1, we have that c012 + m022 = (k - 1)02, and thus CO12 q- toO22

02

~> 0.

(3.49)

Since 3. ~> 0, U2 < 0, and y > 0, conditions (3.48) and (3.49) contradict each other. [] Note that this proof does not go through if q~(c, m) is homogeneous of degree less than 1. Using the dual approach, however, Correia and Teles (1996) prove that the Friedman rule is optimal for this shopping-time economy when 0(c, m) is homogeneous of any degree. 3.2. From monetary to real

In this subsection, we examine the relationship between the optimality of the Friedman rule and the intermediate-goods result developed in Section 1. The relationship is the following. First, if the homotheticity and separability conditions hold, then in the three monetary models we have studied, the optimality of the Friedman rule follows from the intermediate-goods result. Second, if these conditions do not hold, then in all three economies, the optimality of the Friedman rule and the intermediate-goods result are not connected. To establish these results, we proceed as follows. We begin by setting up the notation for a simple real intermediate-goods economy and review the intermediategoods result for that economy. We then show that when our homotheticity and separability conditions hold, the cash-credit goods and the money-in-the-utilityfunction economies can be reinterpreted as real economies with intermediate goods. For these two monetary economies, we establish that the optimality of the Friedman rule in the monetary economy follows from the intermediate-goods result in the reinterpreted real economy. It is easy to establish a similar result for the shoppingtime economy. This proves the first result. Next, we consider monetary economies which do not satisfy our conditions. We establish our second result with a couple of examples. We start with an example in which the monetary economy can be reinterpreted as a real intermediate-goods economy but in which the Friedman rule does not hold in the monetary economy. We then give an example of a monetary economy in which the Friedman rule does hold, but this economy cannot be reinterpreted as a real intermediate-goods economy.

t734

EV. Chari and P.J. Kehoe

The cash-credit economy can be reinterpreted as a real production economy with intermediate goods. Under our homotheticity and separability assumptions, the period utility is U(w(cl~, c2t), 4) and the resource constraint is cll + c2l +gt = 4.

(3.50)

Since the gross nominal interest rate cannot be less than unity, the allocations in the monetary economy must satisfy

wl(cl,, c2~) >>.w2(c1~, c2~).

(3.51)

The reinterpreted economy is an infinite sequence of real static economies. In each period, the economy has two intermediate goods zlt and z2t, a final private consumption good xt, labor 4, and government consumption gt. The intermediate goods zlt and z2t in the real economy correspond to the final consumption goods c~t and c2t in the monetary economy. The period utility function is U(xt, 4). The technology set for producing the final good xt is given by f l ( x , , z l , , z z t , 4) = x , - - w ( z l , , z 2 , ) <<.O, f2(xt,zlt,Z2t,4)

= w2(zlt,Z2t)-Wl(Zlt,z2t)

~ O,

(3.52) (3.53)

while the technology for producing the intermediate goods and government consumption is given by h(zlt, z2t, gt, 4) = zl~ + z2t + gt - It <<.O.

(3.54)

The real econon'ly and the monetary economy are obviously equivalent. The intermediate-goods result for the real economy is that the Ramsey allocations satisfy production efficiency. For this economy, because the marginal rate of transformation between zl and z2 is 1 in the intermediate-goods technology, production efficiency requires that WI W2

1.

(3.55)

Recall that in the monetary economy, the Friedman rule is optimal when Equation (3.55) holds. Thus the intermediate-goods result in the real economy implies the optimality of the Friedman rule in the monetary economy. Does this implication hold more generally? Whenever the monetary economy can be reinterpreted as an intermediate-goods economy, is the Friedman rule optimal in the monetary economy? No. Suppose that the utility function U(cl, c2, l) is of the separable form V(w(cl, c2), 1), but that it does not have a representation in which w exhibits constant returns to scale. Suppose that w instead exhibits decreasing returns. For example, suppose that w(cl, c2) = (Cl + k)~c 21-~, where k is a constant. In the

Ch. 26:

Optimal Fiscal and Monetary Policy

1735

intermediate-goods reinterpretation, the constant k can be thought of as a scarce factor inelastically supplied by the consumer. The intermediate-goods result holds, provided that the returns to the scarce factor are fully taxed away. I f the returns to the scarce factor cannot be taxed, then the intermediate-goods result does not hold. It is easy to show that the Friedman rule is not optimal in the monetary economy. In a sense, the Friedman rule is not optimal because in the monetary economy, there is no sensible interpretation under which the parameter k can be taxed. Next, one might ask, Is it true that whenever the Friedman rule is optimal in the monetary economy, there exists an analogous intermediate-goods economy? Again, no. Consider, for example, Ramsey allocation problems in which the constraint U1 >~ U2 binds, but in which the utility function is not separable in consumption and leisure. The Friedman rule is optimal, but the monetary economy cannot be reinterpreted as an intermediate-goods economy. In this subsection, we have shown that under our homotheticity and separability assumptions, the optimality of the Friedman rule follows from the optimality of uniform commodity taxation. We have also shown that the optimality of the Friedman rule follows from the intermediate-goods result. These findings are not inconsistent because the uniform taxation result actually follows from the intermediate-goods result. (See Section 1.) The construction of the intermediate-goods economy for the money-in-the-utilityfunction economy is straightforward. Recall that in the monetary economy, under our homotheticity and separability conditions, the period utility function is U ( w ( m t , ct), lt) and the resource constraint is ct + gt = l~. The reinterpreted economy is again an infinite sequence of real static economies. In each period, the economy has two intermediate goods zl~ and z2t, a final private consumption good xt, labor lt, and government consumption gt. The intermediate goods zit and z2t correspond to money mt and the consumption good ct in the monetary economy, respectively. The technology set for producing the final good xt is given by f ( x t , Z l t , Z 2 t , lt) = Xt - W(Zlt,Z2t) <~ O.

The technology set for producing intermediate goods and consumption is given by k ( x t , z l t , z 2 t , lt) - z2t + g t -It <~ O.

The real and monetary economies are obviously equivalem. Production efficiency in the intermediate-goods economy requires that the marginal rates of transformation between zl and z2 in the two technologies be equated. Since the marginal rate of transformation between zl and z2 in the intermediate-goods technology is z e r o (h2/h3 = 0), we have wl/w2 = 0. Thus production efficiency in the intermediate-goods economy implies optimality of the Friedman rule in the monetary economy.

1736

EV. Chari and P..~ Kehoe

3.3. Cyclical properties We turn now to some quantitative exercises which examine the cyclical properties of optimal monetary policy in our cash-credit goods model. For some related work, see Cooley and Hansen (1989, 1992). In these exercises, we consider preferences of the form U(c,

l)

= {[C 1 Y ( L - l)Y] qJ -

1}/%

where L is the endowment of labor and

c = [(1 - or) c'[ + ac#] i/v. The technology shock z and government consumption both follow the same symmetric two-state Markov chains as in the model in Section 2. In the baseline model, for preferences, we set the discount factor/3 = 0.97; we set ~p = 0, which implies logarithmic preferences between the composite consumption good and leisure; and we set 7 = 0.80. These values are the same as those in Christiano and Eichenbaum (1992). The parameters cr and v are not available in the literature, so we estimate them using the consumer's first-order conditions. These conditions imply that Ult/U2t = Rt. For our specification of preferences, this condition can be manipulated to be

( (7 ]u(E-V)RI/O k T2~ ) '

C2t

cl,

v)

(3.56)

With a binding cash-in-advance constraint, ci is real money balances and c2 is aggregate consumption less real money balances. We measure all the variables with US data: real money balances by the monetary base, Rt by the return on threemonth Treasury bills, and consumption by consumption expenditures. Taking logs in Equation (3.56) and running a regression using quarterly data for the period 1959-1989 gives a = 0.57 and v = 0.83. Our regression turns out to be similar to those used in the money demand literature. To see this, note that Equation (3.56) implies that Clt Clt + C2t

- [1 + (

L

kT-

a

,~1/(1 V)R,/(1_v) ] 1

/

'

J

(3.57)

Taking logs in Equation (3.57) and then taking a Taylor's expansion yields a money demand equation with consumption in the place of output and with the restriction that the coefficient on consumption is 1. Our estimates imply that the interest elasticity of money demand is 4.94. This estimate is somewhat smaller than estimates obtained when money balances are measured by MI instead of the base.

Ch. 26.

Optimal Fiscal and Monetary Policy

1737

Table 3 Properties of the cash-credit goods monetary models Rates

Percentage in models Baseline

High risk aversion

I.I.D.

Labor income tax

Mean

20.05

20.18

20.05

Standard deviation

0.11

0.06

0.11

Autocorrelation

0.89

0.89

0.00

Correlation with shocks Government consumption Technology Output

0.93

-0.93

0.93

-0.36

0.35

-0.36

0.03

-0.06

0.02

Inflation

Mean

-0.44

4.78

-2.39

Standard deviation

19.93

60.37

9.83

0.02

0.06

-0.41

0.37

0.26

0.43

Technology

-0.21

-0.21

-0.70

Output

-0.05

-0.08

-0.48

-2.78

Autocorrelation Correlation with shocks Government consumption

Money growth

Mean

-0.70

4.03

Standard deviation

18.00

54.43

3.74

0.04

0.07

0.00

Autocorrelation Correlation with shocks Government consumption Technology Output

0.40

0.28

0.92

-0.17

-0.20

0.36

0.00

-0.07

0.02

We set the initial real claims on the government so that, in the resulting stationary equilibrium, the ratio of debt to output is 44 percent. This is approximately the ratio of US federal government debt to GNP in 1989. For the second parametrization, we set ~[~ = - 8 , which implies a relatively high degree o f risk aversion. For the third, we set ~p = 0 and make both technology shocks and government consumption i.i.d. In Table 3, we report the properties of the labor tax rate, the inflation rate, and the money growth rate for these three parametrizations of our cash-credit goods model. In

v.g Chari and l~J Kehoe

1738

all three, the labor tax rate inherits the persistence properties of the underlying shocks (as it did in Subsection 2.3.1). Consider the inflation rate and the money growth rate. Recall that for these cashcredit goods monetary models, the nominal interest rate is identically zero. Table 3 shows that the average inflation rate and the money growth rate are roughly zero. This result may, at first glance, be puzzling to readers familiar with the implications of the Friedman rule in deterministic economies. If government consumption and the technology shock were constant, then the price level and the money stock would fall at the rate of time preference, which is 3 percent per year. In a stochastic economy, the inflation rate and the money growth rate vary with consumption. Therefore, the mean inflation rate depends not only on the rate of time preference, but also on the covariance of the inflation rate and the intertemporal marginal rate of substitution. Specifically, the consumer's first-order conditions imply that

] =/3Et[UI(StM)/U 1(st)] R(sg)p(St)/p(sl+l),

(3.58)

where Et is the expectation conditional on s t. Under the Friedman rule, R(s t) = 1. Using the familiar relationship that the expectation of a product of two random variables is the sum of the product of the expectations of these variables and their covariance in Equation (3.58) and rearranging, we obtain

Et [p(sf)/p(st~l)] = 1//3

covt(p(st)/p(s t*l), Ui (st+l)/Uj (st)) Et [ U1 (s t+~)/U~ (s 9]

(3.59)

In a stationary deterministic economy, Equation (3.59) reduces to Pt/Pt+l = 1//3 so that following the Friedman rule is equivalent to deflating at the rate of time preference. In our stochastic economy, periods of higher-than-average consumption (and hence lowerthan-average marginal utility) are also periods of lower-than-average inflation (and hence higher-than-average p(s t)/p(st+l)). Thus the covariance term in Equation (3.59) is negative. Taking unconditional expectations on both sides of Equation (3.59), we have that following the Friedman rule implies that E[p(st)/p(s t+l)] > 1//3. For all three parametrizations, the autocorrelation of the inflation rate is small or negative. Thus, in each, the inflation rate is far from a random walk. The correlations of inflation with government consumption and with the technology shock have the expected signs. Notice that these correlations have opposite signs, and in the baseline and high risk aversion models, this leads to inflation having essentially no correlation with output. The most striking feature of the inflation rates is their volatility. In the baseline model, for example, if the inflation rate were normally distributed, it would be higher than 20 percent or lower than - 2 0 percent approximately a third of the time. The inflation rates for the high risk aversion model are even more volatile. The money growth rate has essentially the same properties as the inflation rate. The inflation rates in these economies serve to make the real return on debt state-contingent. In this sense,

Ch. 26:

1739

Optimal Fiscal and Monetary Policy A: Government Consumption Shock

0,75.

B: Technology Shock

Labortax rate

0.75

0.5.

0,5

o o 0.

0.25

0 Inflation rate

-025 .

-0.25

-0.5 0

0.2

0.4

0.5

0.8

Autocorrelation of government consumption shock

0.2

0,4

0.6

08

Autocorrelation of technology shock

Fig. I. Persistence plots of inflation rates and labor tax rates versus shocks to government consumption and technology: (a) govermnent consumption shock; (b) technology shock.

debt, together with appropriately chosen monetary policy, acts as a shock absorber. The inflation rates are volatile in these economies because we have not allowed for any other shock absorbers. The results for the high risk aversion model are basically similar to those for the baseline model, with two exceptions. First, the correlation o f the labor tax rate with the shocks has opposite signs from the baseline model. Changing the risk aversion changes the response o f the marginal rate of substitution o f consumption and leisure to the shocks. This change in the response alters the sign o f the correlation. Second, and more significantly, the inflation rate in the high risk aversion model is substantially more variable and has a higher mean than the inflation rate in the baseline model. The reason for the difference is that the higher variability in the inflation rate increases the covariance term in Equation (3.59) and thus increases the average inflation rate. The results for the i.i.d, model are similar to those for the baseline model, with two exceptions. In the i.i.d, model, the autocorrelation o f the labor tax rate and the autocorrelation o f the inflation rate are quite different from their values in the baseline model. The labor tax rate has basically the same persistence properties as the underlying shocks - and so does the price level. A standard result is that if a random variable is i.i.d., its first difference has an autocorrelation o f - 0 . 5 . The inflation rate is approximately the first difference o f the log o f the price level. Thus, in our i.i.d. model, the autocorrelation of the inflation rate is close to -0.5. We investigated the autocorrelation properties o f the labor tax rate and the inflation rate as we varied the autocorrelation (or persistence) o f the underlying shocks. We found that the autocorrelation of both the labor tax rate and the inflation rate increased as we increased the persistence of the underlying shocks. Specifically, we set one shock at its mean value and varied the persistence of the other shock. In Figure 1A, we plot the autocorrelations o f the labor tax rate and the inflation rate as functions of the autocorrelation of government consumption. In Figure 1B, we plot the autocorrelations

V.V. Chari and P.J. Kehoe

1740 A: S h o c k to G o v e r n m e n t C o n s u m p t i o n 12

E~

oco o ~ 7>-

/ 0

5

1

15

1'0

20

period

B: Labor Tax Rate

8 20

19. 5

10

15

period

C: inflation Rate 60--40o~ 200-20 ~rO 10

period

V

15

F~ig. 2. Responses to government consumption shock: (a) the shock to governmentconsumption; (b) labor tax rate; (c) inflation rate.

o f these rates as functions of the autocorrelation o f the technology shock. In both o f these figures, the autocorrelations o f the rates increase as the autocorrelations o f the shocks increase. The inflation rate and money growth rate are close to i.i.d. These rates are positively correlated with government consumption and negatively correlated with the technology shock. As with the labor tax rate, these shocks have opposing effects on inflation and similar effects on output, implying that the correlation of inflation and money growth with output is roughly zero. To gain some intuition for the labor tax rates and the inflation rates, we simulated a version o f the baseline model in which technology shocks were set equal to their mean levels so that the only source of uncertainty is government consumption. In Figure 2, we report a 20-period segment o f our realizations. In Figure 2A, we see the shock to government consumption: this variable is constant at a low level from

Ch. 26." Optimal Fiscal and Monetary Policy

1741

period 0 to period 5, is then high from period 6 to period 12, and returns to its low level from period 13 to period 20. In Figure 2B, we plot the optimal labor tax rates. These tax rates follow the same pattern: they are constant between periods 0 and 5, when government consumption is low; are slightly higher between periods 6 and 12, when government consumption is higher; and return to their low level between periods 13 and 20, when government consumption returns to its low level. The striking feature is that labor tax rates hardly fluctuate in response to the shocks. In Figure 2C, we plot the optimal inflation rate. There is a large inflation rate from period 5 to period 6, when government consumption rises to its higher level, and a large deflation rate from period 12 to period 13, when government consumption falls. In periods without a change in government consumption, the inflation rate is roughly zero. To gain an appreciation of the magnitude of the shock absorber role of inflation, it is useful to trace through the effects of shocks on govenmlent debt, revenues, and expenditures. Using the analog of Proposition 7 for this economy, we can show that the allocations c(st), l(st), real money balances re(st), and real debt B(st)/p(s t) depend only on the current state st, while the change in the price level p(s~)/p(s ~ 1) depends on st 1 and st. We write these functions as c(st), l(st), m(st), b(st), and ~(st-1, st). Consider now the government's budget constraint under the assumption that the economy in period t - 1 is at the mean level of government consumption and the mean level of the technology shock. Denote this state by ~. Consider two scenarios. Suppose first that the economy in period t stays at ~. We can rearrange the government's budget constraint to obtain

b(S)-

, ~,~

[g(~)- r(~)z(S)l(~)]-

m(S)

(3.60)

Suppose next that the economy in period t switches to state s', where g is higher and the technology shock is at its average level. The government budget constraint can then be written as

b(s') -

R(s) b ~(~,s')

+~

1

[

[ g ( s ) - T(~)z(~)/(~)]- m(s')

1

0r(S,s')J '

(3.61)

In both (3.60) and (3.61), the term on the left is the new debt. The first term on the right is the inberited debt obligations net of the inflation tax. The second term on the right is the inflation-adjusted government deficit from period t 1. The inflation adjustment reflects that both government consumption and tax revenues are credit goods that are paid for with a one-period lag. The last term on the right is the seigniorage. Subtracting Equation (3.60) from (3.61) gives the accounting identity A New debt -= A Value of old debt + A Tanzi effect- A Seigniorage, (-23)

(19)

(+1)

(3.62)

(+5)

where the Tanzi effect is the difference in the inflation-adjusted deficit. [See Tanzi (1977).] (The numbers in parentheses are discussed below.)

1742

v.v Chari and t~J Kehoe

We can use our simulation to calculate the terms in Equation (3.62). We normalize the economy so that mean output is 100 units of the consumption good. We consider an innovation in government consumption of 1 unit of this consumption good. This innovation leads to an increase in the present value of government consumption of 28 units of the consumption good. The numbers in parentheses below the terms in Equation (3.62) are the changes in the relevant terms in units of the consumption good. The value of the old debt falls by 19 units because the sharp rise in inflation acts as a tax on inherited nominal debt. In our economy, the government debt is positive when the shocks are at their mean values. The government runs a surplus to pay the interest on the debt. A rise in the inflation rate erodes the value of the nominal surplus, leading to a Tanzi effect of 1 unit. The large inflation rate is, of course, due to a sharp rise in the money growth rate. The government collects 5 units of additional seigniorage by printing this money. Thus the new debt falls by 23 units. Since the present value of govenmaent consumption rises by 28 units, the present value of labor tax revenues needs to rise by only 5 units. This result implies that labor tax rates need to change by only a small amount. In this economy, the volatile inflation rate acts as a shock absorber, allowing the labor tax rate to be smooth. In essence, the government pays for 82 percent (23/28) of the increase in the present value of government spending by increasing the price level sharply, which taxes inherited nominal claims, and for only 18 percent (5/28) by increasing the present value of labor taxes. Note that our autocorrelation results are quite different from those of Mankiw (1987). Using a partial equilibrium model, he argues that optimal policy implies that both labor taxes and inflation should follow a random walk. It might be worth investigating whether there are any general equilibrium settings that rationalize Manldw's argument. In the models considered in this subsection, nominal asset markets are incomplete because returns on nominal debt are not state-contingent. The government, however, can insure itself against adverse shocks by varying the ex post inflation rate appropriately. These variations impose no welfare costs because private agents care only about the expected inflation rate and not about the ex post inflation rate. A useful extension might be to consider models in which ex post inflation imposes welfare costs. An open question is whether optimal inflation rates will be roughly a random walk if the welfare costs are high enough.

4. Conclusion

In this chapter we have analyzed how the primal approach can be used to answer a fundamental question in macroeconomics: How should fiscal and monetary policy be set over the long run and over the business cycle? We use this approach to draw a number of substantive lessons for policymaking. Obviously, these lessons depend on the details of the specific models considered. By and large we have considered

Ch. 26:

OptimalFiscal and Monetary Policy

1743

environments without imperfections in private markets, such as externalities and missing markets. In m o d e l s with such imperfections, optimal p o l i c y not only m u s t be responsive to the efficiency considerations we have emphasized, but also must attempt to cure the private m a r k e t imperfections.

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Cooley, T.E, and G.D. Hansen (1992), "Tax distortions in a neoclassical monetary economy", Journal of Economic Theory 58:290-316. Correia, I., and E Teles (1996), "Is the Friedman rule optimal when money is an inte~xnediate good?", Jomnal of Monetary Economics 38:223-244. Diamond, EA. (1973), "Taxation and public production in a growth setting", in: J.A. Mirrlees and N.H. Stern, eds., Models of Economic Growth (Wiley, New York) 215-235. Diamond, EA., and J.A. Mirrlees (1971), "Optimal taxation and public production I: Production efficiency", American Economic Review 61:8-27. Ekeland, I., and J. Scheinkman (1986), "Transversality conditions for some infinite horizon discrete time optimization problems", Mathematics of Operations Research 11:216-229. Escolano, J. (1992), "Optimal taxation in overlapping generations models", manuscript (University of Minnesota). Faig, M. (1988), "Characterization of the optimal tax on money when it functions as a medium of exchange", Journal of Monetary Economics 22:137-148. Friedman, M. (1969), "The optimum quantity of money", in: The Optimum Quantity of Money and other Essays (Aldine Publishing Company, Chicago, 1L) 1-50. Garriga, C. (1999), "Optimal fiscal policy in overlapping generations models", manuscript (University of Barcelona). Guidotti, EE., and C. V6gh (1993), "The optimal inflation tax when money reduces transactions costs: a reconsideration", Journal of Monetary Economics 31:189-205. Jones, L.E., R.E. Manuelli and EE. Rossi (1997), "On the optimal taxation of capital income", Journal of Economic Theory 73:93-117. Judd, K.L. (1985), "Redistributivc taxation in a simple perfect foresight model", Journal of Public Economics 28:59-83. Kimbrough, K.R (1986), "The optimum quantity of money rule in the theory of public finance", Journal of Monetary Economics 18:277-284. Koopmans, T.C. (t965), "On the concept of optimal growth", in: The Econometric Approach to Development Planning (Rand McNally, Chicago, IL). Kydland, EE., and E.C. Prescott (1982), "Time to build and aggregate fluctuations", Econometrica 50:1345-1370. Lucas Jr, R.E. (1990), "Supply-side economics: an analytical review", Oxford Economic Papers 42: 293 -316. Lucas Jr, R.E., and N.L. Stok~,y (1983), "Optimal fiscal and monetary policy in an economy without capital", Journal of Monetary Economics 12:55 93. Mankiw, N.G. (1987), "The optimal collection of seigniorage: theory and evidence", Journal of Monetary Economics 20:327-341. Marcet, A., TJ. Sargent and J. Seppala (1996), "Optimal taxation without state-contingent debt", manuscript (Stanford University). Pestieau, EM. (1974), "Optimal taxation and discoLmt rate for public investment in a growth setting", Journal of Public Economics 3:217 235. Phelps, E.S. (1973), "Inflation in the theory of public finance", Swedish Journal of Economics 75:67-82. Prescott, E.C. (1986), "Theory ahead of business cycle measurement", Federal Reserve Bank of Minneapolis Quarterly Review 10(Fa11):9-22. Ramsey, EE (1927), "A contribution to the theory of taxation", Economic Journal 37:47-61. Razin, A., and E. Sadka (1995), "The status of capital income taxation in the open economy", FinanzArchiv 52:21-32. Stiglitz, J.E. (1987), "Pareto efficient and optimal taxation and the new new welfare economics", in: AJ. Auerbach and M. Feldstein, eds, Handbook of Public Economics, vol. 2 (North-Holland, Amsterdam) 991-1042. Stock, J.H., and M.W. Watson (1993), "A simple estimator of cnintegrating vectors in higher order integrated systems", Econometrica 61:783 820.

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Stokey, N.L. (1991), "Credible public policy", Journal of Economic Dynamics and Control 15:627-656. Tanzi, V (1977), "Inflation, lags in collection, and the real value of tax revenue", International Monetal3r Fund Staff Papers 24:154~167. Weitzmun, M.L. (1973), "Duality theory for infinite horizon convex models", Management Science 19:783-789. Woodford, M. (1990), "The optimum quantity of money", in: B.M. Friedman and EH. Hahn, eds., Handbook of Monetary Economics, vol. 2 (North-Holland, Amsterdam) 1067 1152. Zhu, X. (1992), "Optimal fiscal policy in a stochastic growth model", Journal of Economic Theory 58:250-289.

AUTHOR INDEX

Alrmlan, H.M. 368, 535 Anderson, E. 564 Anderson, E.W. 368, 369 Ando, A., s e e Modigliani, F 762 Andolfatto, D. 994, 1158, 1173, 1203, 1207, 1221 Andres, J., s e e Blanchard, O.,I. 1214 Araujo, A. 323 Arellano, M. 787 Arifovic, J. 455,465, 472, 521-523, 525-52'7, 531 An'ow, K. 664, 1033, 1042 Arrow, K.J. 1218 Arthur, W.B. 454, 476, 534 Ascari, G. 1041 Aschauer, D.A. I656, I657 Asea, R, s e e Mendoza, E. 1439 Ashenfelter, O. 618, 11038, 1039 Askildsen, J.E. 1074 Atkeson, A. 575, 610, 786, 847, 1298, 1675, 1718, 1720 Atkinson, A.B. 1673, 1676, 1680, 1682, 1718 Attanasio, O.P 564, 607, 608, 610-613, 752, 753, 756, 759, 769, 777, 779, 781,783, 784, 787, 789 794, 796, 797, 802, t264, 1655 Auerbach, A.J. 380, 549, 576, 588, 590, 591, 593, 616, 82I, I624, 1634, t635, 1639, 1652, 1718 Auerbach, A.J., s e e Feldstein, M.S. 904, 906 Auernheimer, L. 1449 Auster, R. 474 Autor, D. 57'7 Axilrod, S.H. t493 Azariadis, C. 262, 264, 271, 289, 389, 395, 516, 527, 658, 660, 661, 1035

Abel, A.B. 818, 831, 834, 835, 994, 1069, 1237, t251, 1253, 1265, t266, 1268, 127I, 1272, 1284, 1285, 1651 Abowd, J. 567, 568, 570, 571,616, 759 Abraham, J. 1039 Abraham, K.G. 1058 Abraham, KJ. 1183, 1221 Abramovitz, M. 208 Abramowitz, M. 865, 887 Acemoglu, D. 852, 1215 Adam, M. 500 Adams, C. 1538 Adelman, EL., s e e Adehnan, 1. 9 Adelman, I. 9 Ag&nor, RR. 1543, 1572 Aghion, P. 264, 665, 672, 715, 719, t 157, 1208, 1210, 1213, 1377, 1450, 1454, 1465 Aiyagari, S.R. 442, 547, 552, 566, 567, 983, 1140, 1293, 1631 Aizenman, J. 1497, 1538, 1540 Akaike, H. 217 Akerlot, G. 1344 Akerlof, G.A. 198, 397, 1034, 1035, 1039, 1157, 1200 al Nowaihi, A. 1415, 1422, 1437 Alesina, A. 162, 277-279, 692, 1404, 1416, 1422-1426, 1430, I432, 1438, 1439, 1446, 1449, 1450, 1454, 1460, 1461, 1464--1466, 1469, t471, 1518, 1522, 1540 Alesina, A., s e e Tabellini, G. 1456, 1465 Alessie, R. 774, 775 Allais, M. 661, 1309 Allen, D.S. 871 Allen, E 576 Ahneida, A. 1432, 1495 Alegoskoufis, G.S. 166, 214, 215 Altonji, J. 615 Alto@, J., s e e Hayashi, E 796 Alto@, J.G. 789 Altug, S. 584, 595,611,612, 785, 786, 792 Alvarez, E 575,996 Ambler, S. 944, t062, 1067 Americml Psychiatric Association t325

Bacchetta, E 1344 Bacchetta, E, s e e Feldstein, M 1637 Bachelier, L. 1316 Backus, C.K. 549 Backus, D. 1017, 1031, 1270, 1405, 1414, 1415 Backus, D.K. 9, 42, 45, 938, 1316, 1708 i-1

I-2 Bade, R. 1432, 1438 Bagehot, W. 155, 1485, 1515 Bagwell, K. 1125 Bagwell, K., s e e Bemheim, B.D. 1647 Bailey, M.J. 1643 Bairoch, P 719, 724 Baker, J.B. 1125 Balasko, Y. 427, 506 Balassa, B.A. 705 Balke, N.S. 6, 61, 114, 204, 205, 221 Ball, L. 42, 72, 199, 1023, t037, 1039, 1041, 1127, 1415, 1499, 1504, 1542, 1632, 1650, 1651 Ball, R. 1321 Ballard, C. 1639 Banerjee, A., s e e Aghion, P 1377 Bange, M.M., s e e De Bondt, W.E 1321 Banks, J. 751, 758, 759, 770, 783, 788, 790--792 Banks, J., s e e Attanasio, O.R 756, 759, 793, 794 Bannerjee, A.'~ 1332 Bansal, R. 1255 Barberis, N. 1294, 1322 Barclays de Zoete Wedd Securities 1238 Barkai, H. 1572 Barnett, S. 831 Barnett, W. 538, 540 Barone, E. 702 Barro, R.L 101, 157, t58, 173, 237, 245, 246, 252, 269, 271,272, 277-281,284, 643,651, 657, 659, 671, 675, 681, 683-685, 688, 689, 6 9 1 - 6 9 4 , 696, 943, 974, 1023, 1055, 1155, 1404, 1405, 1411, 1412, 1414, 1415, 1425, 1438, 1439, 1466, 1485-1489, 1637, 1641, 1642, 1645, 1662, 1675, 1702, 1705, 1707 Barsky, R. 43,558, 564, 565 Barsky, R., s e e Solon, G. 579, 1058, 1102, 1106 Barsky, R., s e e Warnel, E.J. 1019 Barsky, R.B. 182, 215, 216, 1149, 1237, t277, 1294-1296, 1653 Barth, J.R. 1657 Bartle, R.G. 76 Barucci, E. 525 Basar, T. 1449 Basu, S. 399, 402, 433, 983, 992, 994, 1069, 1080-1082, 1096, 1097, t117, 1142 Bates, D.S. 1310, 1324 Batmaol, W.J. 252, 269

Author

Index

Baxter, M. 9, 11, 12, 45, 203, 380, 430, 934, 938, 974, 980, 992, 1296, 1404 Bayoumi, T. 161,211,216, 217, 219 Bayoumi, T., s e e Mussa, M. 208 Bazaraa, M.S. 331 Bean, C., s e e Blanchard, O.J. 1214 Bean, C.R. 785, 1497 Beaudry, R 99, 395, 413, 592, 1264 Beaulieu, J.J. 801,802, 876 Becker, G. 592, 653 Becker, G.S. 317, 1645 Becker, G.S., s e e Ghez, G 615, 752, 759 Becker, R. 369 Beetsma, R. 1411, 1436, 1438 Bekaert, G. 1281 Bell, D.E. 1313 Bellman, R. 336, 340 Belsley, D. 882, 887, 888, 892 Beltratti, A. 524, 525 Ben-David, D. 265, 278 Ben Porath, Y. 577, 582 Benabou, R. 1017, 1018, t031, 1128, 1129, 1469, 1472, 1473 B~nabou, R. 268 Benartzi, S. 1290, 1312, 1313 B6nassy, J. 507 Benassy, J.-R 1506 Benhabib, J. 283, 395, 399-405, 408, 412-414, 417, 419, 421,423-427, 431,433-435,437, 442, 505, 550, 847, 1145, 1449, 1465, 1467, 1472 Benigno, R, s e e Missale, A. 1450 Benjamin, D. 161 Bennett, R. 395 Bensaid, B. 1446, 1449 Benveniste, A. 476, 531 Benveniste, L.M. 321 Bergen, M., s e e Dutta, S. 1019, 1020 Bergen, M., s e e Levy, D. 1014, 1015, 1019 Bergen, RR. 1041 Berger, L.A. 1330 Bergstr6m, V. 538 Bernanke, B.S. 68, 72, 76, 83, 89, 91-93, 114, 144, 178, 182-184, 800, 856, 857, 1036, 1343, 1345, 1346, 1352, 1357, 1361, 1363, 1365, 1369, 1371, 1373, 1376 1378, 1495, 1578 Bernard, A.B. 254, 271,287, 288 Bernard, V.L. 1321 Bernheim, B.D. 1646, 1647, 1649, 1654, 1659, 1660

Author

Index

Berry, M., s e e Dreman, D. 1320 Berry, T.S. 1618 Bertocchi, G. 474 Bertola, G. 643, 708, 801,821, 834, 835, 840, 843, 1187, 1222, 1472, 1580 Bertsekas, D.E 326 Besley, T. 856 Betts, C.M. 217 Beveridge, S. 1062, 1143 Bewley, T. 566, 1155 Bhaskar, V. 1037 Bianchi, M. 290, 292 Bikhchandani, S. 1332 Bils, M. 694, 910, 912, 983, 1053, 1059, 1069, 1070, 1072, 1075, 1076, 1078 1081, 1085, 1087, 1102, t104, 1119, 1120, 1130 Bils, M.J. 579 Binder, M. 271, 1092 Binmore, K. 462 Binmore, K.G. 1188 Bisin, A. 427 Bismut, C., s e e Benaboa, R. 1017, 1018, 1031 Bizer, D. 380 Bjorck, A., s e e Dahlquist, G. 337 Black, E 417, 1280, 1310, 1331, 1507 Blackwell, D. 320 Blad, M., s e e BSnassy, J. 507 Blanchard, O.J. 40-42, 211, 216, 21'7, 391, 416, 471,504, 643, 660, 818, 852, 877, 887, 888, 890, 892, 906, 912, 1013, 1030, 1033, 1034, 1036, 1041, 1112, 1130, 1162, 1173, 1176, 1183, 1184, 1194, 1202, 1214, 1221, 1266, 1491, 1634, 1635, 1645, 1650 Blanchard, O.J., s e e Missale, A. 1450 Blank, R. 579 Blinder, A. 587, 750, 1018-1020, 1038 Blinder, A.S. 41,876, 881,887, 893, 903, 904, 907, 908, 910, 1018, 1085, 1118, 1344, 1485, 1499, 1660 Blinde~, A.S., s e e Bernanke, B.S. 83, 91, 93 Bliss, C. 1461, 1465 Bliss, R., s e e Fama, E.E 1280 Blomstrom, M. 277, 279, 280 Bloomfield, A. 156 Blume, L.E. 321,322, 4 7 4 Blume, L.E., s e e Bray, M. 474 Blundell, R. 572, 602, 611,612, 620, 764, 770, 779, 781,783,788, 790-792, 797 Blundell, R., s e e Banks, J. 758, 759, 770, 783, 788, 79~792

I-3 Boadway, R. t463 Bodnar, G. 1318 B6hm, V. 475, 646 Bohn, H. 1465, 1622, 1650, 1691 Boldrin, M. 362, 399, 400, 506, 962, 1062, 1284, 1297, 1465 Bolen, D.W. 1325 Bollerslev, T. 1236, 1280 BoRon, R, s e e Aghion, R 1377, 1450, 1454, 1465 Bona, J.L. 313 Boothe, EM. 1658 Bordo, M.D. 152, 155-160, 162, 164-167, 182, 184, 185, 194, 202-204, 207-209, 211,215, 217-221, 1404, 1438, 1590 Bordo, M.D., s e e Bayoumi, T. 161 Bordo, M.D., s e e Betts, C.M. 217 Borenstein, S. 1124 Boschan, C., s e e Bry, G. 8 Boschen, J.E 139 Boskin, M.J. 618 Bossaerts, P. 454 Bosworth, B., s e e Collins, S. 653 Bourguignon, E, s e e Levy-Leboyer, M. 222 Bovenberg, A i . , s e e Gordon, R.H. 1637 Bovenberg, L . , s e e Beetsma, R. 1411 Bowen, W. 619 Bowman, D. 1313 Boyd, W.H., s e e Bolen, D.W. 1325 Boyle, M., s e e Paulin, G. 751 Boyle, R 380 Boyle, RR, s e e Tan, K.S. 334 Brainard, WC. 817 Brauch, R., s e e Paulin, G. 751 Braun, R.A. 974 Bratm, S.N., s e e gxane, S.D. 876, 877 Bray, A. 1290 Bray, M. 454, 463,465, 466, 473-475, 527 Brayton, F. 1043, 1344, 1485 Brayton, E, s e e Itess, G.D. 1485, 1509 Breeden, D. 1246 Breiman, L. 289 Bresnahan, T.F. 911,912 Bretton Woods Commission 208 Broadbent, B. 1412 Broadbent, B., s e e Barro, R.J. 1412 Broadie, M., s e e Boyle, R 380 Brock, W.A. 319, 407, 455, 528, 532, 547, 552, 556, 942, 951, 1507 Brown, C. 585 Brown, R, s e e Ball, R. 1321

I-4 Brown, S. 1242 Browning, E. 1463 Browning, M. 598, 606, 607, 610 612, 750, 752, 771,778, 787, 792, 798, 803 Browning, M., s e e Attanasio, O.R 607, 608, 610, 611,613, 779, 789, 791, 1655 Browning, M., s e e Blundell, R. 611,612, 779, 781,783, 790, 791 Broze, L. 487, 488 Brugiavini, A. 775 Brugiavini, A., s e e Banks, J. 770, 788 Brmnberg, R., s e e Modigliani, E 761 Brumelle, S.L., s e e Puterman, M.L. 336, 338 Brunner, A.D. 104 Brmmer, K. 1"79, 183, 191, 1025, 14911 Bruno, M. 471, 1090, 1496, 1538, 1539, 1543, 1553 Bry, G. 8 Bryant, R.C. 1043, 1491, 1497, 1516-15t8 Bryant, R.R. 1313 Buchanan, J.M. 1631, 1642 Buchholz, T.G. 1643 Buckle, R.A. 1019 Bufman, G. 1543 Buiter, W. 1030, 1521 Bulirsch, R., s e e Stoer, J. 334 Bull, N. 1675, 1711 Bullard, J. 466, 507, 509, 515, 526 Bullard, J., s e e Arifovic, J. 527 Bulow, J. 1448, I449 Burdett, K. 1173, 1196 Bureau of the Census 1618, 1619 Burns, A.E 5, 8, 931,934 Burns, A.E, s e e Mitchell, W.C. 8, 44 Burnside, C. 399, 930, 980-985, 994, 1078, 1142, 1162 Burtless, G. 618, 620 Butkiewicz, J.L. 1621

Caballe, J. 578 Caballero, R.J. 399, 749, 771,794, 801, 802, 821-823, 828, 830, 832, 834-838, 840-842, 844, 846, 847, 852, 855, 856, 994, 1032, 1157, 1158, 1160, 1187, 1210, 1211, 1213, 1472 Caballero, R.J., s e e Bertola, G. 801, 821, 834, 840, 843, 1187 Cagan, R 157, 161,203, 1534 Cage, R., s e e Paulin, G. 751 Calmfors, L. 1214

Author

Index

Calomiris, C.W. 169, 181, 183, 187, 191, 1376 Calvo, G.A. 389, 397, 408, 419, 422, 1030, I032, 1034, 1114, t346, 1360, 1363, 1389, 1400, 1415, 1428, 1445 1447, 1449, 1450, 1535, 1538, 1539, 1546, 1552, 1554, 1557, 1563, 1564, 1568, 1569, 1571-1573, 1582, 1583, 1587-t589, 1591, 1592, 1596, 1597, 1599-1603, 1605 Cameron, S. 589 Campbell, J. 92 Campbell, JR. 846, 847, 994 Campbell, J.Y. 763, 764, 769, 784, 930, 961, 1120, 1140, 1141, 1145, 1150, 1235-1238, 1251, 1255, 1257, 1258, i26t, 1264-1266, 1268, 1270, 1272, 1274, 1275, 1280, 1284, 1286, 1290, 1320, 1655 Canavese, A.J. 1543 Canetti, E.D., s e e Blinder, A.S. 1018, 1118 Canjels, E. 55 Canova, E 283,376, 377, 379 Cantor, R. 1344 Canzoneri, M.B. 159, 160, 1405, t414, 1415, 1507, 1508 Capie, E 154, 163,222, 1438 Caplin, A. 849, 850 Caplin, A.S. 801,910, 1031, 1032 Card, D. 580, 1016, 1148 Card, D., s e e Abowd, J. 567, 568, 570, 571, 616, 759 Card, D., s e e Ashenfelter, O. 1038, 1039 Cardia, E. 1655 Cardia, E., s e e Ambler, S. 1062, 1067 Cardoso, E. 1543 Carey, K., s e e Bernanke, B.S. 178, 182 Carlson, J. 473 Carlson, J.A. 904 Carlson, J.A., s e e BucMe, R.A. 1019 Carlson, J.B. 104 Carlstrom, C. 1348, 1357, 1368, 1378, 1379 Carlton, D. 1129 Carlton, D.W. 1018 1020 Carmichael, H.L. 1155 Carpenter, R.E. 876, 881,912, 1344 Carroll, CD. 567, 572, 573, 593, 759, 762, 769, 771,785, 788, 793, 1264, 1344, 1653, 1655 Case, K.E. 1323 Casella, A. 1463, 1465 Caselli, E 277-279, 283, 284, 286

Author Index

Cass, D. 244, 246, 247, 295, 389, 516, 643, 649, 662, 942, 948, 1673 Cass, D., s e e Balasko, Y. 427 Castafieda, A. 380 Cazzavilan, G. 426 Cecchetti, S.G. 182, 217, 876, 1015, 1016, 1018, 1019, 1251, 1265, 1270, 1272, 1294, 1296 Cecchetti, S.G., s e e Ball, L. 1037 Chadha, B. 1031, 1542 Chah, E.Y. 775 Chamberlain, G. 283, 286, 785 Chamberlain, T.W. 1334 Chamley, C. 400, 851, 1439, 1673, 1675, t693, t 697, 1699 Champsaur,, R 538, 463 Chan, L. 1321 Chan, L.K.C. 1653 Chandler, L.V 176 Chang, C . C , Y . , s e e Chamberlain, T.W. 1334 Chari, V.V. 72, 124, 397, 422, 672, 697, 698, 700, 701, 709, 715, 720, 722, 723, 974, 1036, 1037, 1040-1042, 1371, 1448, 1449, 1459, 1488, 1489, 1578, 1673--1676, 1691, 1699, 1708-1710, 1720, 1723 Chari, V . V . , s e e A t k e s o n , A . 1675, 1718, 1720 Chattetjee, S. 996, 1126 Chatterji, S. 475, 507 Chattopadhyay, S.K., s e e Chatte~ji, S. 475, 507 Chen, N. 1281 Chen, X. 476, 532 Cheung, C.S., s e e Chamberlain, q~W. 1334 Chevalier, J.A. 1122, 1123 Chiappori, RA. 391,395, 516 Childs, G.D. 882 Chinn, M., s e e Frankel, J. 1497 Chirinko, R.S. 815, 817, 1058, t066, 1086, t344, 1367 Chiswick, B., s e e Beckcr, G. 592 Cho, D. 278 Cho, I.-K. 455, 465, 524, 525 Cho, J.O. 974, 976, 1025, 1036 Cho, J.O., s e e Bils, M. 983, 1075, 1079, 1104 Chou, R.Y. 1236, 1280 Chou, R,Y., s e e Bollerslev, T 1236, 1280 Choudhri, E.U., s e e Bordo, M.D. 184, 194 Chow, C.-S. 326, 334 Chow, G.C. 1294 Christensen, L.R. 673, 688

I-5 Christiano, LJ. 43, 67 70, 83, 84, 89, 91-94, 99, 108, 109, 114, 115, 124, 137, 143, 144, 314, 329, 330, 339, 347, 349, 350, 355, 362, 364, 367, 369, 370, 376, 377, 379, 426, 504, 547, 764, 881, 888, 909, 952, 962, 974, 1011, 1017, 1018, 1021, 1030, 1038, 1089, 1100, 1296, 1365, 1369, 1708, 1736 Christiano, L.J., s e e Aiyagari, S.R. 1140 Christiano, L.J., s e e Boldrin, M. 962, 1284, 1297 Christiano, L.J., s e e Chari, V.M 72, 1449, 1673, 1675, 1676, 169I, 1699, 1708 1710, 1720, 1723 Chtmg, K.L. 299 Clarida, R. 95, 96, 136, 422, 1364, 1368, 1486 Clark, D., s e e Kushner, H. 476 Clark, J.M. 816 Clark, K.B. 602, i173 Clark, EB., s e e Mussa, M. 208 Clark, T.A. 173 Clark, T.E. 1091, 1485 Cochrane, J. 1120 Cochrane, J.tt. 101, 211, 796, 1234, 1246, 1249, 1296 Cochrane, J.H., s e e Campbell, J.Y. 1237, t251, 1284, 1286 Coe, D.T. 265 Cogley, T. 211,395, 547, 967, 1142, 1503 Cohen, D. 271 Cohen, D., s e e Greenspan, A. 798, 844, 847 Cohn, R., s e e Modigliani, E i321 Cole, H.L. 576, 1163, 1194, 1201-1203, 1207, 1446, 1449, 1603 Cole, H.L., s e e Chari, V.V. 1459 Coleman, T. 601 Coleman, W.J. 367, 380 Coleman II, W.J. 114 Coleman II, WJ., s e e Bansal, R. 1255 Collins, S. 653 Conference Board 43 Congressional Budget Office 1618, 1619, 1621, 1624-1627, 1639, 1640, 1660 Conley, J.M., s e e O'Ban; W.M. 1332 Conlon, J.R. 1032 Constantinides, G.M. 559, 567, 781,803, 1237, 1284, 1291, 1293 Constantinides, G.M., s e e Ferson, W.E. 1284 Contini, B. 1177, 1178, i180, 1200, 1222 Cook, T. 194, 195, 1493

I-6 Cooley, T.E 42, 69, 97, 101, 115, 124, 137, 376, 380, 408, 411, 549, 847, 954, 962, 974, 1376, 1463, 1736 Cooley, T.E, s e e Cho, J.O. 974, 976, 1025, 1036 Cooper, R. 204, 398, 824 Cooper, R., s e e Azariadis, C. 395 Cooper, R., s e e Chatterjee, S. 996, 1126 Cootncr, EH. 1316 Corbo, V 1543, 1554 Correia, I. 974, 1537, 1675, 1720, 1733 Cossa, R. 584 Council of Economic Advisers 1639 Cox, D. 705 Cox, W.M. 1621 Cox Edwards, A., s e e Edwards, S. I543, 1554, 1555, 1575 Crawford, V.P. 475 Crossley, 32, s e e Browning, M. 610, 798 Croushore, D. 1485, 1653 Crucini, M.J. 178, 705 Crucini, M.J., s e e Baxter, M. 1296 Cukiennan, A. 1404, 1414, 1415, 1432, 1437, 1438, 1450, 1456, 1463, 1465 Cukierman, A., s e e Alesina, A. 1424, 1426 Cukierman, A., s e e Brunner, K. 1025 Cummings, D., s e e Christensen, L.R. 673, 688 Cmmnins, J.G. 822, 856, 1344 Cunliffe Report 161 Currie, D. 454, 504 Cushman, D.O. 95, 96 Cutler, D.M. 797, 1290, 1320, 1321, 1624 Cyrus, T., s e e Frankel, J.A. 280 Dahlquist, G. 337 Daniel, B.C. 1647 Daniel, K. 1322 Dantbine, J.-R 329, 370, 952, 962, 1002, 1157 Darby, M.R. 166 Dasgupta, R 655,656 d'Autume, A. 487 DaVanzo, J. 618 Daveri, E 1220 Davidson, J. 750 Davies, J.B. 766 Davis, D. 1033 Davis, RJ. 333 Davis, S,J. 1151, 1152, 1160, 1161, 1176, 1178, 1180, 1194, 1199

Author

Index

Davis, S.J., s e e Attanasio, O.P. 796, 797 Davutyan, N. 156 Dawid, H. 523, 527 De Bondt, W.E 1307, 1320, 1321, 1323 de Fontnouvelle, R, s e e Brock, W.A. 528 De Fraja, G. 1037 De Gregorio, J. 1546, 1551, 1573, 1575, 1577 de Itaan, J., s e e Eijffmger, S. 1404, 1438 de la Torre, M. 41 De Melo, J., s e e Corbo, V 1543 de Melo, J., s e e Hanson, J. 1543 De Melo, M. 1535, 1551 De Pablo, J.C. 1543 de Soto, H. 695 Deaton, A. 752, 756, 764, 771,775, 776, 783, 785, 787, 794, 798, 1344 Deaton, A., s e e Blinder, A. 750 Deaton, A., s e e Browning, M. 611, 612, 752, 787, 792 Deaton, A.S. 1264 Deaton, A.S., s e e Campbell, J.Y. 764 Debelle, G. 1489, 1518, 1522 DeCanio, S. 454, 463 DeCecco, M. 155 Degeorge, E 1321 DeKock, G. 158 DeLong, J.B. 252, 279, 695, 1042, 1290, 1324

DeLong, J.B., s e e Barsky, R.B. 1237, 1277, 1294-1296 den Haan, W.J. 271,347, 354, 369, 994, 1166, 1194, 1203, 1204, 1206, 1207 Denardo, E.V 320 Denison, E.E 237, 653 Denizer, C., s e e De Melo, M. 1535, 1551 Denson, EM. 40 Desdoigts, A. 290 DeTray, D.N., s e e DaVanzo, J. 618 Devereux, M. 952, 1466, 1471 Devereux, M., s e e Alcssie, R. 775 Deverettx, M., s e e Beaudry, P. 395, 413 Devereux, M.B. 1126 Devereux, M.B., s e e Beaudry, P. 99 Devine, T.J. 1166 Dewatripont, M., s e e Aghion, E 1157 Dezhbakhsh, H. 1039 Di Tella, G., s e e Canavesc, A.J. 1543 Diamond, E 796 Diamond, P., s e e Shafir, E. 1316 Diamond, P.A. 661, 1157, 1161, 1162, 1t73, 1188, 1634, 1645, 1684, 1718

Author

Index

Diamond, RA., s e e Blanchard, O.J. 41, 42, 1162, 1173, 1183, 1184, 1194, 1202, 1221 Diaz-Alejandro, C.E 1543 Diaz-Gimenez, J., s e e Castafieda, A. 380 Dickens, WT., s e e Akerlof, G.A. 198 Dickey, D.A. 53, 54, 212 Dickinson, J. 618 Dicks-Mireaux, L., s e e Feldstein, M. 1633 Diebold, EX. 6, 11 Dielman, T., s e e Kallick, M. 1325 Dixit, A. 824, 829, 844, 1115, 1121, 1126 Dixit, A.K., s e e Abel, A.B. 835 Dixon, H. 537 Dodd, D.L., s e e Graham, B. 1323 Dolado, J. 1437 Dolado, J.J. 1214 Dolde, W. 1318 Dolde, W.C., s e e Tobin, J. 773 Domar, E. 640 Dombergel, S. 1019 Dominguez, K. 164, 182 Domowitz, I. 1020, 1083, 1093 Doms, M. 823, 838 Donaldson, J.B., s e e Constantinides, G.M. 1293 Donaldson, J.B., s e e Danthine, J.-R 329, 370, 952, 962, 1002, 1157 Doob, J.L. 299 Dornbusch, R. 198, 1043, 1543, 1562, 1563, 1565, 1568, 1582, 1590, 1637 Dotsey, M. 370, 952, 974, 1032, 1043, 1 5 2 2 , 1652 Drazen, A. 1463, 1465, 1541, 1580 Drazen, A., s e e Alesina, A. 162, 1450, 1 4 6 1 , 1465, 1540 Drazen, A., s e e Azariadis, C. 262, 264, 2 ' 7 1 , 289, 527, 658, 660 Drazen, A., s e e Bertola, G. 1580 Drazen, A., s e e Calvo, G.A. 1571 Drcman, D. 1320, 1323 Dreze, J. 770 Drifflll, J., s e e Backus, D. 1405, 1414, 1 4 1 5 Driskill, R.A. 1042 Drudi, E 1450 Drugeon, J.R 426 Dueker, M.J. 1485 Duffle, D. 380 Duffle, D., s e e Constantinides, G.M. 567, 781, 1237, 1291 Duffy, J. 257, 439, 473, 500 Duffy, J., s e e Arifovic, J. 527

I-7 Duffy, J., s e e Bullard, J. 526 Duguay, R 215 Dumas, B. 561,564 Dunlop, J.T. 939, 1059 Dunn, K.B. 800, 1284 Dunne, T., s e e Donas, M. 823, 838 Dupor, B. 994 Durkheim, 1~. 1331 Durlauf, S.N. 254, 262 264, 268, 270, 271, 287, 289, 303,550, 905407 Dtalauf, S.N., s e e Bernard, A.B. 254, 271,287, 288 Dutta, RK 380 Dutta, S. 1019, 1020 Dutta, S., s e e Levy, D. 1014, 1015, 1019 Dutton, J. 156 Dyl, E.A. 1334 Dynan, K.E. 770

Easley, D., s e e Blume, L.E. 321,322, 474 Easley, D., s e e Bray, M. 474 Easterly, W. 277~79, 281, 675, 703, 1538, 1547, 1553, 1560, 1561 Easterly, W., s e e Bruno, M. 1553 Eaton, J. 719 Eberly, J.C. 801,802, 1344 Eberly, J.C., s e e Abel, A.B. 831, 834, 835, 994 Echenique, E 1551, 1561 Eckstein, O. 1344 Eden, B. 1019, 1023 Edin, D.A. 1457 Edwards, S. 1538, 1543, 1554, 1555, 1575, 1578-1580 Edwards, S., s e e Cukierman, A. 1456, 1465 Edwards, W. 1322 Eichenbaum, M. 83, 94, 96, 99, 100, 137, 184, 549, 550, 785, 799, 800, 803, 885, 888, 905407, 912, 957, 1084 Eichenbatun, M., s e e Aiyagafi, S.R. 1t40 Eichenbaum, M., s e e Burnside, C. 399, 930, 980-985, 994, 1078, 1142, 1162 Eichenbaum, M., s e e Chari, VV 72, 1449 Eichenbaum, M., s e e Christiano, L.J. 43, 6?70, 83, 84, 89, 91 94, 99, 108, 115, 124, 137, 143, 144, 376, 377, 379, 764, 974, 1011, 1021, 1038, 1089, 1100, 1365, 1369, 1708, 1736 Eichenbamn, M.S., s e e Christiano, L.J~ 881, 888

I-8 Eichengreen, B. 152, 154-157, 160, 162-164, 168, 178, 185, 187, 189, 204, 208, 209, 211,219, 1449, 1465, 1590 Eichengreen, B., s e e Bayomni, T. 211, 216, 217, 219 Eichengreen, B., s e e Bordo, M.D. 162 Eichengreen, B., s e e Casella, A. 1463, 1465 Eijffinger, S. 1404, 1432, 1438 Eisner, R. 817, 1310, 1621, 1622 Ekeland, I. 1689 E1 Karoui, N. 835 Elias, VJ. 673 Ellison, G. 475, 1124 Ellson, R.E., s e e Bordo, M.D. 157 Elmendorf, D.W. 1439 Elmendorf, D.W., s e e Ball, L. 1650, 1651 Elmendorf, D.W., s e e Feldstein, M. I656 Emery, K.M. 215 Emery, K.M., s e e Balke, N.S. 114 Engel, E., s e e Caballero, R.J. 801, 802, 821, 835-838, 840-842, 994, 1032, 1158 Engelhardt, G. 1344 Engle, R., s e e Bollerslev; T. 1280 Engle, R.E 50 Engle, R.E, s e e Chou, R.Y. 1236, 1280 Engkmd, R 9 Epstein, L.G. 556, 558, 564, 565, 744, 769, 1250, 1256 Erceg, C. 1041 Erceg, C.J., s e e Bordo, M.D. ]82 Eriksson, C. 1208 Erlich, D. t314 Ermoliev, Y.M., s e e Arthur, W.B. 476 Escolano, J. 1718 Esquivel, G., s e e Caselli, E 277-279, 283,284, 286 Esteban, J.-M. 264 Estrella, A. 43, 1281, 1485 Evans, C. 982 Evans, C.L. 105 Evans, C.L., s e e Bordo, M.D. 182 Evans, C . L . , s e e Christiano, L.J. 67, 68, 70, 83, 84, 89, 91-94, 99, 108, 137, 143, 144, 1011, 1021, 1038, 1089, 1100, 1365, 1369 Evans, C.L., s e e Eichenbaum, M. 83, 9 4 , 96, 137 Evans, G.W. 425, 426, 453-455, 461-465,468, 470, 472.478, 480, 481, 483, 484, 487, 489-492, 495-497, 500, 502, 504-507, 509-513,516, 518-521,526-528, 530 532, 1025, 1125

Author

Index

Evans, M. 182 Evans, E 283, 1635, 1647, 1656 1659 Faig, M. 1675, 1720 Fair, R. 1416, 1425 Fair, R.C. 876, 1077, 1491 Fair, R.C., s e e Dominguez, K. 182 Falcone, M. 326 Fallick, B.C. 855 Fama, E.E 1235, 1280, 1281, 1307, 13t6, 1320-1323 Farber, H. 1200 Farmer, R. 662, 1002 Farmer, R.E. 391,395, 396, 411-414, 427-430, 434, 437, 500, 505 Farmer, R.E., s e e Benhabib, J. 395, 399-402, 408, 412-414, 417, 425,427,431,433-435, 442, 505 Farrell, J. 1121 Faust, J. 69, 217, 1416, 1425, 1437 Fauvel, Y. 1573 Favaro, E. 1554, 1555 Fay, J.A. 1077, 1103 Fazzari, S.M. 818, 1344 Fazzari, S.M., s e e Carpenter, R.E. 881, 912, 1344 Fazzari, S.M., s e e Chifinko, R.S. 1066, 1086 Featherstone, M. 1332 Federal Reserve Board 176 Feenberg, D. 60 Feenstra, R. 1569 Feenstra, R.C., s e e Bergen, ER. 1041 Feiwel, G.R. 535 Feldman, M. 474 Feldstein, M. 44, 197, 1485, 1497, 1498, 1622, 1631, 1633, 1636, 1637, 1639, 1656, 1660 Feldsteh~, M.S. 904, 906 Felli, E. 1083, 1122 Fellner, W. 641,657 Ferejohn, J. 1425 Fernald, J.G., s e e Basu, S. 399, 402, 433, 994, 1117, 1142 Fernandez, R. 1543, 1562 Ferris, S.E 1314 Ferson, W.E. 1284 Festinger, L. 1314 Fethke, G. 1037 Fiebig, D.G., s e e Domberger, S. 1019 Filippi, M., s e e Contini, B. 1177, 1178, 1180, 1222 Fillion, J.E 1498

Author

Index

Finch, M.H.J. 1543 Finegan, T.A., s e e Bowen, W. 619 Finn, M. 981, 1091 Fiorina, M. 1425 Fischer, A.M., s e e Dueker, M.J. 1485 Fischer, S. 182, 197, 202, 215, 216, 1025, 1026, 1155, 1404, 1405, 1438, t449, 1489, 1496, 1498, 1538, 1542, 1547, 1561, 1582 Fischer, S., s e e Blanchard, O.J. 471,643, 660, 1013, 1033, 1034, 1036, 1491, 1635 Fischer, S., s e e Bruno, M. 1538 Fischer, S., s e e Debelle, G. 1489, 1518, 1522 Fischhoff, B. 1319, 1326 Fischhoff, B., s e e Lichtenstein, S. 1318 Fishe, R.RH. 173 Fisher, I. 154, 157, 203, 1316, 1321, 1343, 1372, 1377, 1485 Fisher, J. 92 Fishel, J., s e e Boldrin, M. 962, 1284, 1297 Fisher, J., s e e Christiano, L.J. 314, 347, 349, 350, 355, 362, 364, 962, 1296 Fishe~; J.D.M. 910, 1368, 1375, 1376, 1378 Fisher, /.D.M., s e e Campbell, J.R. 846 Fishlow, A. 155 Flandreau, M. 154 Flannery, B . E , s e e Press, W.H. 329-334, 343, 348, 356, 365 Flavin, M. 572, 749, 763, 784 Flenmfing, J.S. 773 Flood, R.P 152, 158, 202, 408, 1428, 1429, 1438, 1507, 1595, 1596 Flood, R.R, s e e Garber, EM. 165 Florovsky, G. 1326 Forbes, K. 277, 278 Ford, A.G. 155 Fore, D., s e e Roseveare, D. 1626 Foresi, S., s e e Backus, D.K. 1316 Forteza, A., s e e Echenique, E 1551, 1561 Fortune, R 1310 Foufoula-Georgiou, E., s e e Kitanidis, EK. 326 Fourgeaud, C. 454, 465, 473, 475 Fox, B.L. 326 Foxley, A. t543 Fral~kel, J. 1497 Frankel, J.A. 280, 281, 1590, 1637 Franses, RH. 289 Fratianni, M. 143t Freeman, R. 577 Fregert, K. 1016 French, K. 1280

I-9 French, K.R., s e e Fama, E.E 1235, 1281, 1320, 1323 Frenkel, J.A. 203, 1630 Frenkel, J.A., s e e Aizenman, J. 1497 frennberg, R 1238 Friedman, B.M. 43, 44, 1632, 1642 Friedman, D. 475 Friedman, J.H., s e e Breiman, L. 289 Friedman, M. 46, 48, 61, 137, 154, 160, 162, 168, 172, 176, 179, 180, 185, 189, 195, 203, 222, 275, 376, 572, 761, 762, 943, 1011, 1173, 1325, 1485, 1488, 1496, 1537, 1674, 1720 Froot, K. 1266, t316 Frydman, R. 453, 454, 474, 528, 536, 539 Fuchs, G. 464, 474 Fudenberg, D. 455,475, 1155 Fudenberg, D., s e e Ellison, G. 475 Fuerst, T. 99, 974, 1378 Fuerst, T., s e e Carlstrom, C. 1348, 1357, 1368, 1378, 1379 Fuhrer, J.C. 454, 905, 908, 1039, 1040, 1491, 1518 Fuhrer, J.C., s e e Carroll, C.D. 769, 785 Fuk~da, S.-i. 875 Fuller, W.A., s e e Dickey, D.A. 53, 54, 212 Fullerton, D. 576, 588, 616 Funkhouser, R. 699 Futia, C. 299 Galbraith, J.K. 1182 Gale, D. 389, 475, 849, 851, 1376 Gale, D., s e e Chamley, C. 851 Gale, W.G. 1646 Galeotti, M. 909, 1086, 1124 Gali, J. 395,405-407, 426, 429, 434, 993, 994, 1117, 1119, 1120, 1129 Gall, J. 67, 69, 217 Gall, J., s e e Benhabib, J. 424 Gall, J., s e e Clarida, R. 96, 136, 422, 1364, 1368, 1486 Gallarotfi, G.M. 154 Gallego, A.M. 321,322 Galor, O. 262, 263, 272, 660 Gandolfi, A.E., s e e Darby, M.R. 166 Garber, RM. 165, 1323, 1543 Garber, RM., s e e Eichengreen, B. 187, 189 Garber, EM., s e e Flood, R.E 408, 1595, 1596 Garcia, R. 790 Garibaldi, E 1180, 1222 Garratt, A. 504

1-10 Garratt, A., s e e Currie, D. 454, 504 Garriga, C. 1675, 1718 Gaspar, J. 324, 369 Gastil, R.D. 689 Gatti, R., s e e Alesina, A. 1432 Gavin, W. 1485 Geanakoplos, J.D. 395, 458, 1322 Gear, C.W. 346 Geczy, C.C., s e e Brav, A. t290 Gelb, A., s e e De Melo, M. 1535, 1551 Genberg, H. 165, t428 Geoffard, EY., s e e Chiappori, EA. 391 Gerlach, S., s e e Bacchetta, R 1344 Gersbach, H. 1376 Gertler, M. 83, 92 94, 1040, 1343, 1348, 1366, 1373, 1374, 1376-1378 Gertler, M., s e e Aiyagari, S.R. 1293, 1631 Gertler, M., s e e Bernanke, B.S. 92, 144, 183, 856, 857, 1036, 1345, 1346, 1352, 1357, 1365, 1369, 1371, 1373, 1376 1378, 1578 Gertler, M., s e e Clarida, R. 95, 96, 136, 422, 1364, 1368, 1486 Geweke, J. 34, 334 Geweke, J., s e e Barnett, W. 540 Geweke, J.E 89 Ghali, M., s e e Surekha, K. 908 Ghez, G. 615, 752, 759 Ghezzi, R 1572 Ghosh, A.R. 202, 207, 208 Giavazzi, E 167, 203, 1438, 1446, 1449, 1580 Giavazzi, E, s e e Missale, A. 1450 Gibson, G.R. 1307 Gigerenzer, G. 1308, 1318 Gilbert, R.A. 195 Gilchrist, S. 847, 1344 Gilchrist, S., s e e Bernanke, B.S. 856, 1036, 1345, 1373, 1376 Gilchrist, S., s e e Gertler, M. 83, 92 94, 1366, t373, 1374, 1376 Gill, RE. 329 Gilles, C., s e e Coleman II, W.J. 114 Gilson, R.J. 1154 Giovannini, A. 156, 158, 160, 166, t69, 380 Giovannini, A., s e e Giavazzi, E 167 Gizycki, M.C., s e e Gruen, D.K. 1316 Glasserman, R, s e e Boyle, R 380 Glazer, A. 1456, 1465 Glomm, G. 712, 1472 Glosten, L. 1280 Goetzmann, W., s e e Brown, S. 1242

Author

Index

Goetzmaml, W.N. 1242, 1252, 1314, 1320, 1333 Goff, B.L. 159 Gokhale, J. 750 Gokhale, J., s e e Auerbach, A.J. 1624 Goldberg, EK., s e e Attanasio, O.R 777 Goldfajn, I., s e e Dornbusch, R. 1590 Goldstein, M., s e e Mussa, M. 208, 1637 Gomes, J. 994, 1159 Gomme, R 962, 1062 Gomme, R, s e e Andolfatto, D. 1173 Gomme, R, s e e MacLeod, W.B. 1157 Goodfriend, M. 88, 120, 121, 156, 173, 191, 194~196, 764, 1013, 1117, 1346, 1509, 1514, 1515 Goodhart, C . , s e e Capie, E 154 Goodhart, C.A.E. 193 Goodhart, C.A.E., s e e Almeida, A. 1432, 1495 Goodharl, C.E.A. 1438, 1495, 1507, 1508, 1514 Goodman, A. 797 Goolsbee, A. 839, 843, 848 Gordon, D.B. 128, 134 Gordon, D.B., s e e Barro, R.J. 158, 1155, 1405, 1411, 1415, 1438, 1485-1489 Gordon, D.B., s e e Leeper, E.M. 69 Gordon, R. 1030 Gordon, R.H. 1637 Gordon, R.J. 40, 46, 48, 49, 181, 1542 Gordon, R.J., s e e Balke, N.S. 6, 61,204, 205, 221 Gorman, W.M. 553, 556, 782, 803 Gorton, G., s e e Calomiris, C.W. 181 Gottfries, N. 463, 1121, I122 Gould, D.M. 1551, 1559, 1561 Gourieroux, C. 487 Gourieroux, C., s e e Broze, L. 487, 488 Gourieromx, C., s e e Fourgeaud, C. 454, 465, 473, 475 Gourinchas, E-O. 609, 1344 Graham, B. 1323 Graham, F.C. 1656, 1657 Grandmont, J.-M. 439, 454, 460, 464, 474., 475, 48t, 507, 514, 526, 661 Granger, C. 34 Granger, C.W.J. 88l, 903 Granger, C.WJ., s e e Engle, R.E 50 Gray, J.A. 1025, 1026, 1038 Green, D., s e e MaCurdy, T.E. 619, 620 Green, E. 575

Author

Index

Green, H., s e e Beaudry, R 592 Greenberg, D., s e e Burtless, G. 618 Greenberg, D.H., s e e DaVanzo, J. 618 Greenspan, A. 199, 798, 844, 847, 1630 Greenwald, B. 857, 1122, 1377 Greenwood, J. 380, 550, 576, 664, 692, 962, 980, 995 Greenwood, J., s e e Cooley, T.E 847 Greenwood, J., s e e Gomes, J. 994, 1159 Greenwood, J., s e e Gomme, E 962, 1062 Gregory, A.W. 376, 377 Gregory, A.W., s e e Devereux, M. 952 Grier, K.B. 253 Griffiths, M., s e e Dolado, J. 1437 Griliches, Z. 54l Grilli, V. 95, 1404, 1432, 1438, 1439, 1465 Grilli, V, s e e Alesina, A. 1430 Grilli, V, s e e DeKock, G. 158 Grilli, V., s e e Drazen, A. 1463, 1465, 1541 Grilli, V.U. 169 Gros, D., s e e Adams, C. 1538 Gross, D. 857, 1344 Gross, D.B., s e e Goolsbee, A. 839 Grossman, G.M. 264, 639, 672, 715, 1210, 1464 Grossman, H.J. 158, 1415, 1449 Grossman, S.J. 801, 1237, 1242, 1246, 1268, 1291, 1293 Grout, P.A. 852 Gruen, D.K. 1316 Guerra, A. 1546, 1606, 1607 Guesnerie, R. 439, 454, 460, 464, 465, 474, 475, 506, 511,516, 526 Guesnerie, R., s e e Chiappori, RA. 391, 395, 516 Guesnerie, R., s e e Evans, G.W. 464 Guidotti, RE. 1537, 1588, 1603, 1675, 1720 Guidotti, RE., s e e Cairo, G.A. 1447, 1450 Guidotti, RE., s e e De Gregorio, J. 1546, 1551, 1573, 1575, 1577 Guiso, L. 772 Guiso, L., s e e Galeotti, M. 909 Guide, A.M., s e e Ghosh, A.R. 202, 207, 208 Gultekin, M. 1317 Gultekin, N.B., s e e Gultekin, M. 1317 Guo, J.-T., s e e Farmer, R.E. 395,427-430, 434, 505 Guo, J.-12 416, 427 Gurley, J.G. I507 Gust, C. 1041 Guttman, E, s e e Erlich, D. t314

1-11 Haberler, G. 185 Hahn, E 661 H a h n , T . , s e e Cook, T. 194, 1493 Hahn, W. 479 Hairault, J.-O. 1036 Haldane, A.G. 1432, 1438, 1485, 1495, 1497 Haley, W.J. 585 Hall, G. 911 Hall, R.E. 399, 556, 573, 595, 607, 608, 673, 679, 680, 683 686, 702, 765, 767-769, 784, 789, 791, 794, 817, 856, 930, 982, 1068, 1070, 1079, 1089, 1092, 1095, 1096, 1141-1143, 1145, 1151-1153, 1157, 116~ 1164, t200, 1261, 1485, 1493, 1498, 1655, 1656 Hall, S., s e e Currie, D. 454, 504 Hall, S., s e e Garratt, A. 504 Hallerberg, M. 1460, 1465 Haltiwanger, J., s e e Caballero, R.J. 821, 837, 838, 840-842, 1158 Haltiwanger, J., s e e Cooper, R. 824 Haltiwanger, J.C. 881 Haltiwanger, J.C., s e e Abraham, K.G. 1058 Haltiwanger, J.C., s e e Davis, S.J. 1151, 1152, 1160, 1161, 1176, 1178, 1180, 1194, 1199 Hamermesh, D. 577 Hamilton, A. 1659 Hamilton, J. 963 Hamilton, J.D. 12, 72, 80, 182, 1118, 1265 Hammerlin, G. 344 Hammour, M.L., s e e Caballero, R.J. 846, 847, 852, 855, 856, 1157, 1158, 1160, 1187, 1210, 1211, 1213, 1472 Hannerz, U. 1332 Hansen, B. 1194 Hansen, B.E. 38, 39 Hansen, G.D. 547, 551,602, 976, 977, 1200 Hansen, G.D., s e e Cooley, T.E 69, 97, 101, 115, 124, t37, 380, 408, 411,974, 1736 Hansen, L.E 547, 555, 556, 558, 57~574, 768~ 769, 784, 882, 915, 1234, 1246, 1249, 1250, 1261, 1294, 1295 Hansen, L.R, s e e Anderson, E.W. 368, 369 tlansen, L.R, s e e Cochrane, J.H. 1234, 1246, 1249 Hansen, L.E, s e e Eichenbaum, M. 549, 550, 785, 799, 800, 803 Hanson, J. 1543 Hansson, B., s e e Frennberg, R 1238 Harberger, A.C. 1554, 1590

1-12 Harden, 1., s e e yon Hagen, J. 1439, 1460, 1465 Hardouvelis, G.A. 1281 Hardouvelis, G.A., s e e Estrella, A. 43, 1281 Harris, R., s e e Cox, D. 705 Harrison, A. 277, 279, 280 Harrison, S.G., s e e Christiano, L.J. 426 Harrison, S.H. 402 Harrod, R. 640 Hart, O. 852,1154 Hartwick, J. 656 Harvey, A.C. 9 Harvey, C.R. 1236, 1280 Hashimoto, M. 1152 Hassett, K.A. 815, 818, 843, 1344 Hassett, K.A., s e e Auerbach, A.J. 821 Hassett, K.A., s e e Cummins, J.G. 822, 856, 1344 Hassett, K.A., s e e Fallick, B.C. 855 Hassler, J. 9, 1238 Haug, A.A., s e e Dezhbakhsh, I-I. 1039 Haugen, R.A., s e e Ferris, S.R 1314 Hause, J.C. 569 Hausman, J. 620 Hausman, J., s e e Burtless, G. 620 Hawley, C.B., s e e O'Brien, A.M. 776 Hayashi, E 773,775, 776, 785, 788, 790, 796, 800, 818, 1649 Head, A., s e e Devereux, M.B. 1126 Heal, G., s e e Dasgupta, E 655, 656 Heal, G.M., s e e Ryder Jr, H.E. 1284 Heaton, J. 380, 547, 569, 803, 1242, 1255, 1284, 1293 Heckman, J.J. 576, 578, 579, 582, 584-587, 590, 592, 593, 595, 601-603,605, 615 617, 620-624, 752, 759, 1166 Heckman, J.J., s e e Ashenfelter, O. 618 Heckman, J.J., s e e Cameron, S. 589 Heckman, J.J., s e e Cossa, R. 584 tteckman, J.J., s e e Killingsworth, M.R. 550, 601, 1148 Heijdra, B.J. 1119, 1120, 1126 Heinemann, M. 495, 525 Hellwig, M., s e e Gale, D. 13']6 Helpman, E. 203, 1580 Helpman, E., s e e Coe, D.T. 265 Helpman, E., s e e Drazen, A. 1580 Helpman, E., s e e Grossman, G.M. 264, 639, 672, 715, 1210, 1464 Hendershott, RH. 1333 Henderson, D.W. 1497

Author

Index

Henderson, D.\¥, s e e Bryant, R.C. 1491, 1497, 1516 Henderson, D.W., s e e Canzoneri, M.B. 160, 1507, 1508 Hendry, D., s e e Davidson, J. 750 Hercowitz, Z. 664 Hercowitz, Z., s e e Barro, R.J. 1023 Hercowitz, Z., s e e Greenwood, J. 550, 664, 962, 980 Herrendorf, B. 1415, 1436, 1438 Hess, G.D. 9, 1485, 1509 Hester, D.A. 871 Heston, A., s e e Summers, R. 238, 301, 640, 673-675, 677, 680, 681,689, 720 Hetzel, R.L. 180 Heymann, D. 506, 1539, 1540, 1543 Hibbs, D. 1400, 1425 Hildenbrand, W. 535, 537 Himarios, D., s e e Graham, EC. 1656, 1657 Himmelberg, C.R, s e e Gilchrist, S. 1344 Hiriart-Urruti, LB. 331 Hh'schhorn, E., s e e Cox, W.M. 1621 Hirschman, A. 1540 Hirshleifet, D., s e e Bikhchandani, S. 1332 Hirshleifer, D., s e e Daniel, K. 1322 Hobijn, B., s e e Franses, RH. 289 Hodrick, R. 9, 12, 34, 428, 931,932 Ho&'ick, R.J., s e e Bekaert, G. 1281 Hodrick, R.J., s e e Flood, R.R 1507 Hoelscher, G. 1658 Hoffmaister, A. 1561, 1589 Hoffman, D.L. 51,412 Hoffmann, K.-H., s e e Hanmaerlin, G. 344 Holbrook, R. 569 Holmstrom, B. 1376, 1417, 1418, 1425 Holt, C.A., s e e Davis, D. 1033 Holt, C.C. 882, 885, 888, 909, 910, 912 Holtham, G., s e e Bryant, R.C. 1491, 1497, 1516 Holtz-Eakin, D., s e e Blinder, A.S. 41 Hommes, C.H. 529, 532 Hommes, C.H., s e e Brock, W.A. 455, 528, 532 Honkapohja, S. 464, 481,507, 535 Honkapohja, S., s e e Evans, G.W 425, 426, 454, 455, 461,464, 465,468, 470, 472-478, 480, 481,483,484, 487, 489492, 495~497, 502, 504-507, 509--513, 516, 518-521, 526 528, 530-532, 1025 Hooker, M.A., s e e Fuhrer, J.C. 454

Author

Index

[-looper, E, s e e Bryant, R.C. 1043, 1491, 1497, 1516-1518 Hopenhayn, H. 672, 708, 994 Hopenhayn, H.A. 844 Horioka, C., s e e Feldstein, M. 1636 Horn, H. 1415 Hornstein, A. 549, 996 Hornstein, A., s e e Fisher, J.D.M. 910 Horvath, M. 994 Horvath, M., s e e Boldrin, M. 962, 1062 Hoshi, T. 1344 Hosios, A.J. 1193, 1224 Hotz, VJ. 792, 803 Houthakker, H.S. 803 Howard, R. 336 Howitt, R 389, 399, 455, 506, 507, 514, 515, 517, 521,527, 1174, 1508 Howitt, R, s e e Agbion, R 264, 665, 672, 715, 719, 1208, 1210, 1213 Howrey, E.R, s e e Fair, R.C. 1491 Hoynes, H.W., s e e Attanasio, O.P. 753 Hsieh, C.-T. 673, 687 Hubbard, R.G. 567, 569, 572, 573, 593, 771, 776, 794, 797, 856, 1344, 1376, 1660 Hubbard, R.G., s e e Cummins, J.G. 822, 1344 Hubbard, R.G., s e e Domowitz, I. 1020, 1083, 1093 Hubbard, R.G, s e e Fazzari, S.M. 818, 1344 Hubbard, R.G., s e e Gertler, M. 1376 Hubbard, R.G., s e e Hassett, K.A. 815, 818, 843, 1344 Huberman, G., s e e Kahn, C. 1154 Huffman, G.W. 437 Huffman, G.W., s e e Greenwood, J. 380, 962, 980 HuggeR, M. 380, 576, 593 Halten, C. 664 Flultgren, "12 1100 Humphrey, T.M. 1485 tttmlphreys, B.R. 909 Hurd, M.D. 780 Hybels, J., s e e Kallick, M. 1325 Hyslop, D., s e e Card, D. 1016 Ibbotson, R. 1321 lden, G., s e e Barth, J.R. 1657 Ikenberry, G.J. 163 Im, K. 283 lmrohoroglu, A. 797 Ingberg, M., s e e Honkapohja, S. 535 lngram, B. 984

1-13 Inman, R., s e e Bohn, H. 1465 Intriligator, M., s e e Griliches, Z. 541 Ireland, RN. 129, 194, 1036, 1492, 1494, 1497 Irish, M., s e e Browning, M. 611, 612, 752, 787, 792 Irons, J.,see Faust, J. 1416, 1425 Irwin, D.A. 178 lsard, E, s e e Flood, R.E 158, 1429, 1438 Islam, N. 283-285, 287, 653 Ito, T. 1425 Iwata, S., s e e Hess, G.D. 9 Jackman, R. 1221 Jackman, R . , s e e L a y a r d , R. 1098, lt76, 1177, 1221 Jackwerth, J.C. 1310 Jaeger, A., s e e Harvey, A.C. 9 Jaffee, D.M. 1376 Jagannathan, R., s e e Glosten, L. 1280 Jagannathan, R., s e e Hansen, L.E 547, 1234, 1246, 1249 James, H., s e e Bernanke, B . S . 183, 184 James, W. 1330 Janis, I. 1332 Jappelli, 32 776, 780, 790, 1344 Jappelli, T., s e e Guiso, L. 772 Jeanne, O. 156, 1041 Jeanne, O., s e e Bensaid, B. 1446, 1449 Jefferson, P.N. 1485, 1509 Jegadeesh, N. 1321 Jegadeesh, N., s e e Chan, L. 1321 Jensen, H. 1415, 1427 Jensen, H., s e e Beetsma, R. 1436, 1438 Jensen, M. 1344 Jeon, B.N., s e e yon Furstenberg, G.M. 1333 Jermann, U.J. 1296 Jennann, U.J., s e e Alvarez, E 575 Jermann, U.J., s e e Baxter, M. 980, 992 Jewitt, I., s e e Buiter, W. 1030 Jimeno, J.E, s e e Blanchard, O.J. 1214 Jimeno, J.E, s e e Dolado, J.J. 1214 John, A., s e e Cooper, R. 398 Johnson, H.G. 702, 704, 705 Johnson, P, s e e Goodman, A. 797 Johnson, RA., s e e Durlauf, S.N. 254, 263,264, 270, 271,289, 303 Johnson, RG., s e e Banks, J. 751 Johnson, S.A. 345, 381 Jones, C.I. 237, 264, 290, 292, 672, 696, 714-716, 718, 719

1-14 Jones, C.I., s e e Hall, R.E. 673, 679, 680, 683-686, 702, 856 Jones, L.E. 245, 257, 261, 380, 672, 709, 711-713, 720, 1675, 1711 Jones, L.E., s e e Chaff, V.V. 715, 1578 Jones, M. 1540 Jonsson, G. 1404, 1411, 1415, 1426, 1438 Jonung, L. 159, 1485 Jonung, L., s e e Bordo, M.D. 152, 215, 217, 220, 221 Jonung, L., s e e Fregert, K. 1016 Jorda, O. 881 Jorgenson, D. 664 Jorgenson, D.W. 817 Jorgenson, D.W., s e e Christensen, L.R. 673, 688 Jorgenson, D.•, s e e Hall, R.E. 817 Jorion, E, s e e Goetzmann, W.N. 1242, 1252, 1320 Jovanovic, B. 702, 848, 1200 Jovanovic, B., s e e Greenwood, J. 664, 692 Judd, J.R 1485, 1487, 1512, 1516 Judd, K. 590, 1652 Judd, K., s e e Bizer, D. 380 Judd, KJ., s e e Gaspar, .I. 324, 369 Judd, K.L. 314, 324, 340, 343, 347, 348, 350, 354, 1673, 1675, 1694 Judson, R. 663 Judson, R., s e e Porter, R. 1509 Juhn, C. 569, 619 Jun, B. 474 Juster, E32 777 Juster, 32, s e e Barsky, R. 558, 564, 565 Kaas, L . , s e e B6hm, V. 646 Kafka, A. 1543 Kahaner, D. 329, 333 Kahn, C. 1154 Kahn, C.M., s e e Blanchard, O.J. 391,504 Kahn, J., s e e Crucini,,M.J. 178, 705 Kahn, J.A. 897, 910 Kalm, J.A., s e e Bils, M. 910, 912, 1053, 1078, 1079, 1085 Kahneman, D. 1308, 1309, 1311 Kahneman, D., s e e Thaler, R.H. 1313 Kahneman, D., s e e Tversky, A. 1308, 1315, 1319, 1330 Kalaba, R., s e e Belhnan, R. 340 Kaldol; N. 237, 238, 240, 640, 941 Kalecki, M. 1054 Kallick, M. 1325

Author

Index

Kamihigashi, 32 428 Kaminsky, G.L. 1550, 1553, 1590 Kandel, S. 1235, 1252, 1253, 1265, 1270, 1272 Kandori, M. 475 Kane, A., s e e Chou, R.Y. 1236, 1280 Kaniovski, Y.M., s e e Arthur, W.B. 476 Kaplan, S.N. 856, 1344 Karatzas, L, s e e El Karoui, N. 835 Karras, G., s e e Cecchetti, S.G. 217 Kashyap, A.K. 137, 877, 881,886, 903,906, 912, 1018, 1344, 1374, 1376 Kashyap, A.K., s e e Cecchetti, S.G. 876 Kashyap, A.K., s e e Hoshi, 32 1344 Kashyap, A.K., s e e Hubbard, R.G. 1344 Katz, L. 577, 578 Katz, L., s e e Autor, D. 577 Katz, L.E, s e e Abraham, K.J. 1183, 1221 Katz, L.E, s e e Cutler, D.M. 797 Katz, L.W., s e e Blanchard, O.J. 1176 Kaufman, H. 1344 Keane, M.P. 608, 609, 786, 790 Keefer, E, s e e Knack, S. t466, 1471 Kehoe, RJ., s e e Atkeson, A. 847, 1675, 17t8, 1720 Kehoe, PJ., s e e Backus, C.K 549 Kehoe, RJ., s e e Backus, D.K. 9, 42, 45, 938, 1708 Kehoe, EJi, s e e Chari, V.V. 124, 397, 422, 672, 697, 698, 700, 701, 709, 720, 722, 723, 974, 1036, 1037, t040-1042, 1371, 1448, 1449, 1488, 1489, 1673-1676, 1691, 1699, 1708 1710, 1720, 1723 Kehoe, RJ., s e e Cole, H.L. 1449 Kehoe, T.J. 314, 380, 389, 391,574, 575 Kehoe, T.J., s e e Cole, H.L. 1446, 1449, 1603 Kehrei, K.C., s e e Moffitt, R.A. 618 Kelly, M. 271 Kemmerer, E.W. 173 Kendlick, D.A., s e e Armnan, H.M. 535 Kenen, RB. 165, 1496 Kennan, J. 803 Kessler, D. 1646 Keynes, J.M. 158, 161, 1055, 1059, 1537 Kiefer, J. 476 Kiefcr, N.M., s e e Burdett, K. l t 73 Kiefer, N.M., s e e Devine, T.J. 1166 Kiguel, M. 1535, 1543, 1546, 1554, 1555 Kihlstrom, R.E. 563 Kiley, M.T. 422, 423, 1041, 1117, 1129 Killian, L. 87

Author

Index

Killingsworth, M.R. 550, 601, 1148 Kim, J. 129, 1036 Kim, K. 377, 379 Kim, M., s e e Nelson, C.R. 1320 Kim, S. 95 Kim, S.-J. 672, 711-714 Kimball, M., s e e Barsky, R. 558, 564, 565 Kimball, M., s e e Carroll, C.D. 762, 771 Kimball, M.S. 556, 770, 1036, 1041, 1056, 1114, 1117, 1127, 1653 Kimball, M.S., s e e Basu, S. 983, 992, 994, 1069, 1080, 1081, 1117 Kimbrough, K.R 1537, I675, 1676, 1720, 1732 Kindahl, J., s e e Stigler, G. t018 Kindleberger, C.R 162 King, M. 199, 1333, 1485, 1489 King, R.G. 9, 46, 54, 69, 101,278, 369, 391, 429, 435, 545, 549, 649, 672, 689, 692, 7ll-713,929, 931,932, 939, 941,945,953, 954, 971, 995, 1036, 1041, 1043, 1062, 1140, 1364, 1367, 1491 King, R.G., s e e Barro, R.J. 974 King, R.G., s e e Baxtel, M. 9, 11, 12, 430, 934, 974 King, R.G., s e e Dotsey, M. 974, 1032, 1043 King, R.G., s e e Goodfriend, M. 1013, 1117, 1346, 1515 King, S. 101 Kirby, C. 1320 Kirman, A.R 475, 528, 536, 539-541 Kitanidis, RK. 326 Kiyotaki, N. 524, 852, 857, 1353, 1356, 1376, 1378, t379 Kiyotald, N., s e e Blanchard, 03. 1033, 1034 Kiyotaki, N., s e e Boldrin, M. 399 Kleidon, A.W. 1320 Klein, B. 202, 215, 216 Klein, L. 94t Klemperer, RD. / 121 Klenow, PJ. 663,673, 679, 680, 683 686, 694, 702, 705,707 Klenow, RJ., s e e Bils, M. 694 Klenow, EJ., s e e Heckman, J.J. 578 Klock, M., s e e Silbennan, J. 1316 Knack, S. 1466, 1471 Kneese, A. 656 Knowles, S. 277, 278 Kocherlakota, N. 574, 954, 985, 1234, 1251, 1253 Kocherlakota, N., s e e Cole, H.L. 576

1-15 Kocherlakota, N., s e e Ingram, B. 984 Kocberlakota, N.R. 271,673,694 Kochin, L., s e e Benjamin, D. 161 Kollintzas, T. 904-907 Kollman, R. 1085 Kon-Ya, E, s e e Shiller, R.J. 1316 Konings, J., s e e Garibaldi, P 1180, 1222 Koopmans, T. 931,942, 948 Koopmans, T.C. 244, 246, 247, 295, 643, 649, 1673 Koopmans, TJ. 9 Kormendi, R.C. 278-281,671, 1656, 1657 Kornai, J. 703 Kortum, S., s e e Eaton, J. 719 Kosobud, R., s e e Klein, L. 941 Kosters, M.H. 618 Kotkin, B., s e e Bellman, R. 340 Kotlikoff, L. 1448, 1449, 1465 Kotlikoff, L., s e e Hayashi, E 796 Kotlikoff, L.J. 780, 1624, 1646 Kotlikoff, L.J., s e e Auerbach, A.J. 380, 549, 576, 588, 590, 591, 593, 616, 1624, 1634, 1635, 1639, 1652, 1718 Kotlikoff, L.J., s e e Gokhale, J. 750 Koyck, L.M. 816 Kramer, C., s e e Flood, R.R 1596 Krane, S.D. 876, 877 Kremer, M., s e e Blanchard, O.J. 852 Kremer, M., s e e Easterly, W. 277, 278, 281, 675 Kreps, D.M. 540, 557, 1256 Kreps, D.M., s e e Bray, M. 474 Kreps, D.M., s e e Fudenberg, D. 475 K~%ger, S. 380, 843, 847 Krishnamurthy, A. 1376, 1378 Kroner, K.E, s e e Bollerslev, T. 1236, 1280 Krueger, A., s e e Autor, D. 577 Kateger, A.O. 673, 679, 699 Krueger, J.T. 104, 105 Krugman, R 1215, 1536, 1590, 1592, 1594, 1596, 1601, 1605, 1606, 1632 Krusell, R 380, 547, 566, 567, 994, 1293, 1445, 1473 Krusell, P, s e e Greenwood, J. 664 Kuan, C.-M. 476 Kugler, P. 1281 Kuh, E., s e e Meyel, J.R. 8t7 Kumhof, M. 1596 Kurz, M. 474 Kushner, H. 476 Kushner, H.J. 476

1-16 Kusko, A.L. 1327 Kuttner, K., s e e Evans, C.L. 105 Kutmer, K.N., s e e Friedman, B.M. 43, 44 Kuttner, K.N., s e e Kruegm; J.T. 104, 105 Kuznets, S. 941 Kuznets, S., s e e Friedman, M. 572 Kwiatkowski, D. 2t2 Kydland, EE. 9, 42, 158, 428, 547, 549, 578, 929, 953, 956, 957, 962, 980, 98t, 1058, 1059, 1140, 1141, 1145, t167, 1195, 1400, 1405, 1415, 1449, 1485, 1486, 1488, 1557, 1561, 1673, 1708 Kydland, EE., s e e Backus, C.K. 549 Kydland, EE., s e e Backus, D.K. 1708 Kydtand, EE., s e e Bordo, M.D. 158, t60, 185, 215, 1438 Kydland, EE., s e e Hotz, V.J. 792, 803 Kyle, A.S,, s e e Campbcll, J.Y. 1290 La Porta, R. 1240, 1320 Labadie, R, s e e Giovamaini, A. 380 Labadie, RA., s e e Coleman II, W.J. 114 Lach, S. 1019 Ladron de Guevara, A. 317 Laffont, J., s e e Gourieroux, C. 487 Laffont, JJ., s e e Kihlstrom, R.E. 563 Laffont, J.-J. 538 Lahiri, A. 1539, 1571, 1578, 1579, 1597 Lai, K.S. 876 Laibson, D. 1653 Laidler, D. 1485 Lakonishok, J. 1323 Lakonishok, J., s e e Chan, L. 1321 Lain, R-S., s e e Cecchetti, S.G. 1251, 1265, 1270, 1272, 1294, 1296 Lam, ES. 802 Lambert, J.D. 346 Lambertini, L. 1457, 1465 Lamo, A.R. 290 Lamont, O.A., s e e Kashyap, A.K. 881, 912, 1344, 1374 Landi, L., s e e Barucci, E. 525 Lane, R 1472 Langer, E.J. 1329 Lansing, K., s e e Guo, J.-T. 416 Lapham, B.J., s e e Devereux, M.B. 1126 Laroque, G., s e e Fuchs, G. 464, 474 Laroque, G., s e e Grandmont, J.-M. 464, 474, 475, 481,507 Laroque, G., s e e Grossman, S.J. 801 Lau, L. 664

Author

Index

Lau, S.H.E 1037 Lawrance, E. 607 609 Layard, R. 1098, t176, 1177, 1221 Layard, R., s e e Jackman, R. 1221 Layne-Farrar, A., s e e Heckman, J.J. 578 Lazaretou, S. 159 Lazear, E.R 1660 Lazear, E.R, s e e Hall, R.E. 1152 LeaNte of Nations 162 Leahy, J. 844, 1332 Leahy, J., s e e Caballero, R.J. 823, 828, 830 Leahy, J., s e e Caplin, A. 849, 850 Learner, E.E. 282 Lebow, D.E. 215, 1016 Lebow, D.E., s e e Blinder, A.S. 1018, 1t18 Lee, C. 1324 Lee, J.-W., s e e Barro, R.J. 277-281,671, 68I, 683-685, 688, 689, 691-694 Lee, J.-W. 703 Lee, J.Y. 395 Lee, K. 284 Lee, T.H., s e e Granger, C.W.J. 881,903 Leeper, E.M. 69, 74, 83, 93, 101, 128, 132, 134, 137, 418, 420, 1036, 1089, 1369, 1518, 1520, 1631 Leeper, E.M., s e e Faust, J. 69, 217 Leeper, E.M., s e e Gordon, D.B. 128, 134 Lefort, E, s e e Caselli, E 277-279, 283, 284, 286 Lehmann, B.N. 1321 Leibfritz, W., s e e Roseveare, D. 1626 Leiderman, L. 1432, 1438, 1495, 1543 Leiderman, L., s e e Bufman, G. 1543 Leiderman, L., s e e Calvo, G.A. 1552, 1600 Leiderman, L., s e e Kamhlsky, G.L. 1550 Leijonhufvud, A. 152, 202, 215 Leijonhufvud, A., s e e Heymann, D. 1539, 1540 Lemarechal, C . , s e e Hiriart-Urruti, LB. 331 LeRoy, S.F. 1235, 1319 Lettau, M. 470, 472, 524, 527, 1293, 1297 Leung, C. 271 Levhari, D. 1450, 1465 Levin, A. 283, 1017, 1031, 1035, 1036, 1038 Levin, A., s e e Brayton, E 1043, 1344, 1485 Levine, D.K., s e e Fudenberg, D. 455, 475 Levine, D.K., s e e Kehoe, T.J. 380, 389, 391, 574, 575 Levine, J. 1332 Levine, P., s e e al Nowaihi, A. 1415, 1422, 1437

Author

Index

Levine, R. 269, 277-282, 390, 423, 671, 694, 1376 Levine, R., s e e King, R.G. 278, 689, 692 Levy, D. 1014, 1015, 1019 Levy, D., s e e Carpenter, R.E. 876 Levy, D., s e e Dutta, S. 1019, 1020 Levy-Leboyer, M. 222 L~vy-Strauss, C. 1331 Lewis-Beck, M. 1425 Li, J.X. 326 Li, Y., s e e Jolmson, S.A. 345, 381 Lichtenstein, S. 13 l 8 Lichtenstein, S., s e e Fischhoff, B. 1319 Lilien, D.M. 1160, 1183, 1221 Lilien, D.M., s e e Hall, R.E 1153 Lillard, L. 569, 572 Limongi, E, s e e Przeworski, A. 1466 Lin, C., s e e Levin, A. 283 Lindbeck, A. 1098, 1425, 1465 Lindert, R 156 Lioni, G., s e e Contini, B. 1177, 1178, 1180, 1222 Lippi, F. 1432 Lippi, E, s e e Cukierman, A. 1438 Lippi, M. 217 Lipsey, R.E., s e e Blomstrom, M. 277, 279, 280 Lia, C.Y., s e e CoLflon, J.R. 1032 Liviatan, N., s e e Cukierman, A. 1437 Liviatan, N., s e e Kiguel, M. 1535, 1543, 1546, 1554, 1555 Lizondo, J.S. 1538 Lizzeri, A. 1459 Ljung, L. 474, 476, 481,482 Ljungqvist, L. 1214 Lo, A.W. 132i Lo, A.W., s e e Campbell, J.Y. 1255, 1257, 1258, 1261, 1266, 1270, 1320 Loayza, N.V. 708 Lochner, L., s e e Cossa, R. 584 Lochner, L., s e e Heckman, J.J. 576, 578, 582, 584, 586, 587, 590, 592, 593 Lockwood, B. 1411, 1415 Lockwood, B., s e e Herrendorf, B. 1436, 1438 Lohman, S. 1416-1418, 1425, 1431, I438 Londregan, J., s e e Alesina, A. 1425 Long, J. 929, 952, 953, 994 Loomes, G. 1313 Lopez-de-Silanes, E, s e e La Porta, R. 1240 Lorentz, A.L. 344 Lothian, J.R., s e e Darby, M.R. 166

1-17 Loury, G.C. 299 Lovell, M.C. 881, 893, 908, 910 Lown, C., s e e Bernanke, B.S. 1343 Lucas, D.J. 1035, 1036, 1042 Lucas, D.J., s e e Heaton, J. 380, 547, 569, 1255, 1293 Lucas, R. 398, 424, 425, 641, 651, 929, 932, 953 Lucas, R.E. 46, 50, 380, 1158, 1446, 1449 Lucas, R.E., s e e Stokey, N.L. 314, 318021, 346, 951,998, 999 Lucas Jr, R.E. 67, 88, 158, 238, 245, 264, 265, 293, 454, 457, 463, 474, 545, 547, 554, 559, 561, 575, 578, 582, 583, 615, 616, 672, 710-715, 720, 797, 1022 1024, 1043, 1195, 1268, 1489, 1490, 1495, 1500, 1592, 1673, 1675, 1699, 1711, 1723, 1728 Lucas Jr, R.E., s e e Atkeson, A. 575 Lucas Jr, R.E., s e e Stokey, N.L. 271,299 Ludvigson, S. 785, 788, 1344, 1652 Lundvik, E, s e e Hassler, J. 9, 1238 Lusardi, A. 608, 790, 791 Lusardi, A., s e e Browning, M. 606, 771 Lusardi, A., s e e Garcia, R. 790 Lutmaer, E.G.J. 575 Lyons, R.K., s e e Caballero, R.J. 399

Maberly, E.D., s e e Dyl, E.A. 1334 Macaulay, ER. 173 MacAvoy, RW., s e e Funkhouser, R. 699 Maccini, L.J. 881,893, 894, 903, 907 Maccini, L.J., s e e Blinder, A.S. 887, 904, 910, 1344 Maccini, L.J., s e e Durlauf, S.N. 905 907 Maccini, L.J., s e e Haltiwanger, J.C. 881 Maccini, L.J., s e e Humphreys, B.R. 909 MacDonald, R., s e e Bordo, M.D. 156 Mace, B.J. 796 Mackay, D. 1307 MacKinlay, A.C., s e e Campbell, J.Y. 1255, 1257, 1258, 1261, 1266, 1270, 1320 MacKinlay, A.C., s e e Lo, A.W. 1321 MacLeod, W.B. 1157, 1186 MaCurdy, T.E. 551, 567-569, 5'72, 592, 595, 615, 616, 619-62t, 752, 759, 767, 792, 975, 1148, 1149 MaCurdy, T.E., s e e Attanasio, O.R 792 MaCurdy, T.E., s e e Blundell, R. 602, 620 MaCurdy, T.E., s e e Heckman, J.J. 615 Maddala, G.S. 275

1-18 Maddison, A. 288, 673~i75, 677, 678, 720, 721 Madison, J. 1659 Mailath, G.J., s e e Kandori, M. 475 Makhija, A.K., s e e Ferris, S.R t314 Malcomson, J.M., s e e MacLeod, W.B. 1157, 1186 Malinvaud, E., s e e Blanchard, O.J. 1214 Malkiel, B. t316 Mankiw, N.G. 135, 158, 159, 173, 216, 244246, 252-255, 269-271,277~79, 289, 397, 567, 653, 655, 660, 673, 679--686, 694, 749, 785, 790, 800, 961, 1281, 1290, 1292, 1638, 1702, 1742 Mankiw, N.G., s e e Abel, A.B. 1266, 1651 Mankiw, N.G., s e e Ball, L. 42, 1023, 1632, 1650, 1651 Mankiw, N.G., s e e Barro, R.J. /637 Mankiw, N.G., s e e Barsky, R.B. 1653 Mankiw, N.G., s e e Campbell, J.Y. 769, 784, 1261, 1264, 1290, 1655 Mankiw, N.G., s e e Elmendorf, D.W. 1439 Mankiw, N.G., s e e Hall, R.E. 1485, 1493, 1498 Mankiw, N.G., s e e Kimball, M.S. 1653 Mann, C.L., s e e Bryant, R.C. 1043, 1491, 1497, 1516-1518 ManueUi, R.E, s e e Chaff, VV 715, 1578 Manuelli, R.E., s e e Jones, L.E. 245, 257, 261, 380, 672, 709, 711 713,720, i675, 1711 Mao, C.S., s e e Dotsey, M. 370, 952 Marcet, A. 314, 326, 348, 351,454, 455, 464, 465, 468, 473476, 480, 494, 499, 525, 528-530, 532, 1675, 1705, 1707 Marcet, A., s e e Canova, E 283 Marcet, A . , s e e den Haan, W.J. 347, 354, 369 Margarita, S., s e e Beltratti, A. 524, 525 Margaritis, D. 474 Mariano, R.S., s e e Seatel; J.J. 1656, 1657 Maffger, R.R 1344 " Marimon, R. 455, 464, 472, 475, 523, 53l, 1214 Marmlon, R., s e e Evans, G.W. 483, 509, 527, 528, 531 Marion, N., s e e Flood, R.R 1429, 1438 Mark, N.C., s e e Cecchetti, S.G. 1251, 1265, 1270, 1272, 1294, 1296 Marris, S. 1632 Marschak, J. 582, 1043 Marshall, A. 203 Marshall, D.A., s e e Bekaert, G. 1281

Author

Index

Marshall, D.A., s e e Marcet, A. 326, 348, 351, 455 Marston, R., s e e Bodnar, G. 1318 Marston, R.C. 164 Martin, J.R 1181 Mas-Colell, A., s e e Kehoe, T.J. 380 Masciandaro, D., s e e Grilli, V 1404, 1432, 1438, 1439, 1465 Masson, A., s e e Kessler; D. 1646 Masson, E, s e e Chadha, B. 1542 Masson, ER. 1554, 1588 Matheny, K.J. 395, 441 Matsukawa, S. 1037 Matsuyama, K. 395, 399 Matthieson, D., see Mussa, M. 208 Mauro, R 277 Mauro, E, s e e Easterly, W. 1538 Maussner, A. 528 Mayhew, S. 1310 McAfee, R.R, s e e Howitt, R 389, 399, 506, 517, 521 McCallum, B.T. 83, 173, 184, 198, 203, 408, 487, 488, 496, 503, 1022, 1026, 1043, 1411, 1426, 1432, 1437, 1438, 1485, 1487, 1488, 1490, 1491, 1493, 1495, 1500, 1502, 1506-1510, 1512, 1515-1519, 1631 McCulloch, J.H., s e e Dezhbakhsh, H. /039 McElroy, M. 619 McFadden, D. 1314, 1316, 1328 McGrattan, E.R. 348, 974 McGrattan, E.R., s e e Anderson, E.W. 368, 369 McGrattan, E.R., s e e Chari, V.V. 124, 397, 422, 672, 697, 698, 700, 701, 709, 720, 722, 723, 974, 1036, 1037, 1040-1042, 1371 McGrattan, E.R., s e e Marimon, R. 455, 475, 523 McGuire, W.J. 1332 Mclntire, J.M., s e e Carlson, J.B. 104 McKelvey, R.D. 380 McKibbin, WJ., s e e Henderson, D.W. 1497 McKinnon, R. 1496 McKinnon, R.I. 166, 207 McLaughlin, K.J. 1016, 1152 McLean, I., s e e Eichengreen, B. t57 McLennan, A. 474 McLennan, A., s e e McKelvey, R.D. 380 McManus, D.A. 908 Means, G.C. 1082 Meckling, W., s e e Jcnsen, M. 1344 Medeiros, C. 1554, 1555

Author

Index

Medoff, J.L., s e e Fay, J.A. 1077, 1103 Meehl, P. 1319 Meghir, C. 611, 613, 775, 804 Meghir, C., s e e Arellano, M. 787 Meghir, C., s e e Attanasio, O.R 793,794 Meghir, C., s e e Blundell, R. 611, 612, 779, 781,783,790-792 Meghir, C., s e e Browning, M. 607, 611,778 Meguire, R, s e e Konnendi, R.C. 278-281,671, 1656, 1657 Mehra, R. 547, 961, 1234, 1236, 1249, 1251, 1264, 1268, 1270, 1272, 1289, 1312 Mehra, R., s e e Constantinides, G.M. 1293 Mehra, R., s e e Danthine, J.-R 329, 370, 952 Meigs, A.J. 191 Melenberg, B., see Alessie, R. 774 Melino, A., s e e Blanchard, O.J. 912 Melino, A., s e e Epstein, L.G. 558, 565 Melino, A., s e e Grossman, S.J. 1242 Melnick, R., s e e Bruno, M. 1539 Meltzer, A.H. 162, 169, 174-176, 178, 179, 185, 204, 215-217, 222, 1466, 1485, 1543 Meltzer, A.H., s e e Brunner, K. 179, 183, 191, 1025 Meltzer, A.H., s e e Cukierman, A. 1414, 1450, 1463 Mendoza, E. 1439, 1571, 1579 Mendoza, E., s e e Calvo, G.A. 1591, 1600, 1601 Meredith, G., s e e Chadha, B. 1542 Melton, R. 1275 Merton, R.K. 389, 1333 Merz, M. 994, 1158, 1173, 1203, 1207 Metivier, M., s e e Benveniste, A. 476, 531 Metzler, L.A. 867 Meyer, J.R. 817 Mihov, I., s e e Bernanke, B.S. 72, 76, 83, 89, 114, 1365, 1369 Milesi-Ferretti, G.-M., s e e Mendoza, E. 1439 Milesi-Ferretti, G.-M. 1425, 1 4 2 6 , 1597 Milgrom, R 475, 1322 Millard, S.R 1217, 1220 Miller, B.L. 566 Miller, M., s e e Lockwood, B. 1411, 1415 Miller, M., s e e Modigliani, E 1343 Miller, R.A., s e e Altug, S. 584, 595, 611, 612, 785, 786, 792 Mills, E 1082 Mills, J., s e e Erlich, D. 13t4 Mills, L.O., s e e Boschcn, J.E 139 Mills, T.C. 204

1-19 Mills, T.C., s e e Capie, E 163, 1438 Mincer, J. 581,592, 684 Minehart, D., s e e Bowman, D. 1313 Mirman, L., s e e Levhari, D. 1450, 1465 Mirman, L.J., s e e Brock, W.A. 319, 547, 552, 556, 942, 951 Miron, J.A. 173, 216, 876, 907, 1242 Miron, J.A., s e e Barsky, R.B. 1149 Miron, J.A., s e e Beaulieu, J.J. 876 Miron, J.A., see Feenberg, D. 60 Miron, J.A., s e e Mankiw, N.G. 173, 216, 1281 Mirrlees, J.A. 1154 Mirrlees, J.A., s e e Diamond, RA. 1684 Mishkin, ES. 101, 183, 216, 1023, 1380, 1432, 1438 Mishkin, ES., s e e Bernanke, B.S. 1495 Misl~dn, ES., s e e Estrella, A. 1485 Mishkin, ES., s e e Hall, R.E. 607, 608, 789, 1655 Mishra, D. 1416, 1425 Missale, A. 1450 Mitchell, B.R. 222 Mitchell, W.C. 8, 44, 1053 Mitchell, W.C., s e e Burns, A.E 5, 8, 931,934 Mitra, K. 530, 532 Mnookin, R.H., s e e Gilson, R.J. 1154 Modiano, E.M. 1543 Modigliani, E 761,762, 780, 1321, 1343, 1646, 1656, 1657 Modigliani, E, s e e Dreze, J. 770 Modigliani, E, s e e Holt, C.C. 882, 885, 888, 909, 910, 912 Modigliani, E, s e e Jappelli, T. 780 Modigliani, E, s e e Samuelson, P.A. 643 Moffitt, R. 752, 787 Moffitt, R.A. 618 Moler, C., s e e Kahaner, D. 329, 333 Mondino, G. 1540 Monfort, A., s e e Gourieroux, C. 48"] Monfo, S., s e e Robbins, H. 4'76,478 Montgomery, E. 1017, 1018 Montiel, E 1539 Montiel, E, s e e Agdnor, RR. 1543 Monta'ucchio, L. 330 Montrucchio, L., s e e Boldfin, M. 362 Moore, B.J. 455, 475, 496 Moore, G.H. 1059 Moore, G.H., s e e Zarnowitz, V. 40 Moore, G.R., s e e Fuhrer, J.C. 905, 908, 1039, 1040, 1518

1-20

Author

Moore, J., s e e Kiyotaki, N. 852, 857, 1353, 1356, 1376, 1378, 1379 Moreno, D. 481 Morgan, D. 1374 Morrison, C,J. 1086 Mortensen, D.T. 1157, 1158, 1162, 1163, 1173, 1182, 1183, 1187, 1188, 1194, 1198, 1203, 1208, 1217, 1220, 1222 Mortensen, D.T., s e e Burdett, K. 1173, 1196 Mortensen, D.T., s e e Millard, S.R 1217, 1220 Morton, T.E, 338 Mosser, EC. 910 Motley, B., s e e Judd, J.E 1485, 1487, 1512, 1516 Mroz, T.A. 618 Maoz, T.A., s e e MaCurdy, T.E. 592, 752 Muellbauer, J., s e e Deaton, A. 783 Mueller, D. 1464 Mulligan, C.B. 346, 1150 Mundell, R.A. 1496 Murphy, K. 581 Murphy, K., s e e Juhn, C. 569, 619 Murphy, K., s e e Katz, L. 577, 578 Murphy, K.M. 262, 278, 1082 Mmxay, C.J., s e e Nelson, C.R. 11 Murray, W., s e e Gill, RE. 329 Musgrave, R.A. 1631, 1661 Mussa, M. 208, 1404, 1637 Mussa, M., s e e Flood, R.P. 152, 202, 1428 Mussa, M.L., s e e Frenkel, J.A. 203 Muth, J.E 457, 473,484 Muth, J.E, s e e Holt, C.C. 882, 885, 888, 909, 910, 912 Myerson, R. 1459 Nakanmra, A. 618 Nakamura, M., s e e Nakamura, A. 618 Nalebuff, B., s e e Bliss, C. 1461, 1465 Nance, D.R. 1318 NaI~kervis, J.C., s e e McManus, D.A. 908 Nash, S., s e e Kahaner, D. 329, 333 Nason, J.M., s e e Cogley, T. 395, 547, 967, 1142, 1503 Natanson, I.R 342 NBER

8

Neale, M.A., s e e Northcrafl, G.B. 1315 Negishi, T. 559 Nelson, C.R. 11, 211, 213, 264, 969, 1264, 1320 Nelson, C.R., s e e Beveridge, S. 1062, 1143 Nelson, D.B. 182

Index

Nelson, E, 1035 Nerlove, M. 283,284 Neumann, G.R., s e e Burdett, K. 1173 Neusser, K. 941 Neves, J., s e e Correia, I. 974 Neves, R, s e e Blundell, R. 792 Ng, S., s e e Garcia, R. 790 Nickell, S., s e e Layard, R. 1098, 1176, 1177, 1221 Nickell, S.J. 823 Nicolini, J.E, s e e Marcet, A. 455,530, 532 Niederreiter, H. 334 Nilsen, O.A., s e e Askildsen, J.E. 1074 Nishimura, K., s e e Benhabib, J. 403~405, 425, 435 Nordhaus, W. 1400, 1425 North, D. 1449 Northcrafl, G.B. 1315 Novales, A. 803 Nurkse, R. 163,203 Nyarko, Y. 465, 474 O'Barr, W.M. t332 O'Brien, A.M. 776 O'Brien, A.P. 181 Obstfeld, M. 159, 164, 165, 407, 1411, 1415, 1429, 1438, 1449, 1507, 1571, 1588, 1590, 1592, 1630 Obstfeld, M., s e e Froot, K. 1266 O'Connell, S.A. 1650 Odean, T. 1314, 1323 O'Driscoll, G.P. t643 OECD 1181, 1182, 1215, 1620 Office of Management and Budget 1622 Officer, L. 155 Ogaki, M., s e e Atkeson, A. 610, 786 Ohanian, L.E. 1036 Ohanian, L.E., s e e Cooley, T.E 42, 962, 974 O'Hara, M., s e e Blume, L.E. 321,322 Ohlsson, H., s e e Edin, D.A. 1457 Okina, K. 1508 Okun, A.M. 1014, 1541 Oliner, S . D . 137, 820, 1374, 1376 Oliner, S.D., s e e Cummins, J.G. 856 Olsder, G., s e e Basar, T. 1449 Olshen, R.A., s e e Breiman, L. 289 Oppers, S. 154 Orphanides, A. 198, 1485 Ortega, E., s e e Canova, E 376, 377, 379 Ortigueira, S., s e e Lads'on de Guevara, A. 3 t 7 Ostry, J. 1568

Author

Index

Ostry, J., s e e Montiel, P 1539 Ostry, J.D., s e e Ghosh, A.R. 202, 207, 208 Owen, ED., s e e Knowles, S. 277, 278 Ozlel; S. 1457, 1465 Ozler, S., s e e Alesina, A. 277 279, 1460, 1466, 1471 Paarsch, H., s e e MaCurdy, T.E. 619, 620 Pacelli, L., s e e Contini, B. 1177, 1178, 1180, 1222 Packal6n, M. 525 Padilla, J., s e e Dolado, J. 1437 Pagan, A., s e e Kim, K. 377, 379 Pagan, A.R. 9, 69, 108 Pagano, M., s e e Giavazzi, E 203, 1438, 1446, 1449, 1580 Pagano, M., s e e Jappelli, T. 776 Papageorgiou, A. 334 Papageorgiou, C., s e e Duffy, J. 257 Paquet, A., s e e Ambler, S. 944 Parekh, G. 87, 109 Parente, S.L. 672, 674, 702, 708 Parke, W.R., s e e Davutyan, N. 156 Parker, J., s e e Barsky, R. 43 Parker, J., s e e Gourinchas, P-O. 609, 1344 Parker, J.A. 1120 Parker, J.A., s e e Solon, G. 579, 1058, 1102, 1106 Parkin, M. 1037, 1412, 1415, 1506 Parkin, M., s e e Bade, R. 1432, 1438 Pashardes, R, s e e Blundell, R. 781 Paskov, S.H. 334 Patel, J., s e e Degeorge, E 1321 Patinkin, D. 407, 1506, t507, 1630, 1643 Paulin, G. 751 Paxson, C., s e e Deaton, A. 798 Paxson, C., s e e Ludvigson, S. 788 Pazos, E 1534 Peles, N., s e e Goetzmann, W.N. 1314 Pencavel, J. 550, 601,605, 975, 1148 Peralta-Alva, A. 374 Perli, R. 402, 431,435 Perli, R., s e e Benhabib, J. 425, 426, 437 Perotti, R. 1466, 1469, 1472 Perotti, R., s e e Alesina, A. 1439, 1464, 1465 Perron, R 264 Perry, G.L., s e e Akerlof, G.A. 198 Persson, M. 1447, 1449 Persson, T. 278, 692, 1400, 1403, 1413, 1415-1418, 1420, 1421, 1425, 1433, 1435, 1437 1440, 1442, 1445, 1448-1450, 1454,

1-21 1456, 1459, 1460, 1465, 1466, 1469, 1470, 1490 Persson, T., s e e Engkmd, R 9 Persson, T., s e e Hassler, J. 9, 1238 Persson, T., s e e Horn, H. 1415 Persson, T., s e e Kotlikoff, L. 1448, 1449, 1465 Persson, T., s e e Persson, M. 1447, 1449 Pesaran, H. 487 Pesaran, M.H., s e e Binder, M. 271 Pesaran, M.H., s e e lm, K. 283 Pesaran, M.H., s e e Lee, K. 284 Pestieau, RM. 1718 Petersen, B.C., s e e Carpenter, R.E. 881, 912, 1344 Petersen, B.C., s e e Domowitz, I. 1020, 1083, 1093 Petersen, B.C., s e e Fazzari, S.M. 818, 1344 Petterson, R 1457 Pflug, G., s e e Ljung, L. 476 Phaneuf, L. 1028, 1039, 1041 Phelan, C. 380, 575, 796 Phelan, C., s e e Atkeson, A. 1298 Phelps, E. 944, 1025, 1026, 1039 Phelps, E.E., s e e Frydman, R. 453, 454, 474, 528, 536, 539 Phelps, E.S. 46, 168, 1059, 1098, 1121, 1122, 1157, 1173, 1176, 1192, 1220, 1537, 1538, 1720, 1724 Philippopoulus, A., s e e Lockwood, B. 1415 Phillips, A.W. 1510 Phillips, A.W.H. 46 Phillips, L.D., s e e Lichtenstein, S. 1318 Phillips, PC.B., s e e Kwialkowski, D. 212 Picard, P 1157 Pieper, RJ., s e e Eisner, R. 1621 Pierce, J.L. 195 Piketty, T., s e e Aghion, P. 1377 Pindyck, R. 1072 Pindyck, R.S. 835, 910, 912 Pindyck, R.S., s e e Abel, A.B. 835 Pindyck, R.S., s e e Caballero, R.J. 844 Pippenger, J. 156 Pischke, J.-S., s e e Jappelli, T. 790 Pischke, J.-S. 764 Pissarides, C.A. 774, 1163, 1173, 1183, 1184, 1188, 1193, 1194, 1200, 1203, 1207, 1209, 1220 Pissarides, C.A., s e e Garibaldi, E 1180, 1222 Pissarides, C.A., s e e Jackman, R. 1221

1-22 Pissarides, C.A., s e e Mortensen, D.T. t158, 1182, 1183, 1194, 1198, 1203, 1208 Plosser, C.I. 952, 954, 958, 961, 963, 1094, 1658 Plosser, C.I., s e e King, R.G. 9, 54, 369, 391, 429, 435, 549, 929, 931, 941, 945, 954, 995 Plosser, C.I., s e e Long, J. 929, 952, 953, 994 Plossel, C.I., s e e Nelson, C.R. 11,211, 213, 264, 969 Plutarchos, S., s e e Benhabib, J. 437 Polemarchakis, H.M., s e e Geanakoplos, J.D 395, 458 Policano, A., s e e Fethke, G. 1037 Pollak, R.A. 803 Pollard, S. 161 Poole, W. 192, 1514, 1515 Poonia, G.S., s e e Dezhbakhsh, H. 1039 Popper, K. 376 Porter, R. 1509 Porter, R.D., s e e LeRoy, S.F. 1235, 1319 Porteus, E.L., s e e Kreps, D.M. 557, 1256 Porfier, E 1068, 1126 Portier, E, s e e Hairault, J.-O. 1036 Posen, A. 1404, 1426, 1432, 1438 Posen, A., s e e Mishkin, ES. 1432, 1438 Poterba, J.M. 159, 1235, 1320, 1465, 1648, 1655 Poterba, J.M., s e e Cutler, D.M. 1290, 1320, 1321 Poterba, J.M., s e e Feldstein, M. 1633 Poterba, J.M., s e e Kusko, A.L. 1327 Power, L., s e e Cooper, R. 824 Pradel, J., s e e Fourgeaud, C. 454, 465, 4'73, 475 Praschnik, J., s e e Hornstein, A. 549 Prati, A. 162 Prati, A., s e e Alesina, A. 1446, 1449 Prati, A., s e e Drudi, E 1450 Prescott, E.C. 178, 365, 545, 675, 700, 702, 930, 934, 952, 954, 956, 957, 961, 963, 982, 1033, 1296, 1488, 1489, 1710 Prescott, E.C., s e e Chaxi, V.V. 1488, 1489, 1674 Prescott, E.C., s e e Cooley, T.E 376, 549, 954 Prescott, E.C., s e e Hansen, G.D. 602 Prescott, E.C., s e e Hodrick, R. 9, 12, 34, 428, 931,932 Prescott, E.C., s e e Kydland, EE. 9, 42, 158, 428, 547, 549, 929, 953, 956, 957, 962, 980, 981, 1058, 1059, 1140, 114t, 1145,

Author

Index

1167, 1195, 1400, 1405, 1415, 1449, 1485, 1486, 1488, 1673, 1708 Prescott, E.C., s e e Lucas Jr, R.E. 547, 554 Prescott, E.C., s e e Mehra, R. 547, 961, 1234, 1236, 1249, 1251, 1264, 1268, 1270, 1272, 1289, 1312 Prescott, E.C., s e e Parente, S.L. 672, 674, 708 Prescott, E.C., s e e Stokey, N.L. 951,998, 999 Prescott, E.S. 380 Press, W.H. 329-334, 343, 348, 356, 365 Preston, I., s e e Banks, J. 759, 783, 790, 791 Preston, 1., s e e Blundell, R. 572, 764, 797 Priouret, R, s e e Benveniste, A. 476, 531 Pritchett, L. 237 Pritchett, L., s e e Easterly, W 277, 278, 281, 675 Przeworski, A. 1466 Psacharopoulos, G. 685 Puterman, M.L. 336, 338, 339 Quadrini, V., s e e Cooley, T.E 1376 Quadrini, V, s e e Krusell, E 1445, 1473 Quah, D. 254, 263, 268, 272, 275, 283, 287, 288, 290-292, 294, 299 Quah, D., s e e Leung, C. 271 Quah, D.T., s e e Blanchard, O.J. 211, 216, 217 Quah, D.T., s e e Durlauf, S.N. 550 Quandt, R.E. 34 Quattrone, G.A. 1329 Rabin, M. 1319 Rabin, M., s e e Bowman, D. 1313 Rabinowitz, P., s e e Davis, EJ. 333 Radner, R. 952 Radner, R., s e e Benhabib, J. 1465 Ramey, G. 281,852, 1157, 1159 Ramey, G., s e e den Haan, W.J. 994, 1166, 1194, 1203, 1204, 1206, t207 Ramey, G., s e e Evans, G.W. 455, 461,462 Ramey, V.A. 67, 876, 885, 897, 902, 905-907, 909, 911,914, 1084, 1089 Ramey, V.A., s e e Bresnahan, T.E 911,912 Ramey, VA., s e e Chah, E.Y. 775 Ramey, V.A., s e e Ramey, G. 281 Ramos, J. 1543 Ramsey, E 643, 649 Ramsey, ER 1673 Rankin, N. 1025 Rankin, N., s e e Dixon, H. 537 Rapping, L., s e e Lucas Jr, R.E. 615, 616

Author

Index

Rasche, R.H., s e e Hoffman, D.L. 51,412 Ratti, R.A. 1497 Ravikttmar, B., s e e Chatterjee, S. 1126 Ravikumar, B., s e e Glomm, G. 712, 1472 RaMs, J. 1662 Ray, D., s e e Esteban, J.-M. 264 Rayack, V~ 579 Razin, A. 1715 Razin, A., s e e Frenkel, J.A. 1630 Razin, A., s e e Helpman, E. 203, 1580 Razin, A., s e e Mendoza, E. 1439 Razin, A., s e e Milesi-Ferretti, G.-M. 1597 Rebelo, S.T. 245, 260, 261, 709, 952, 1546, 1568, 1578-1581, 1606 Rebelo, S.T., s e e Burnside, C. 399, 930, 980, 982 985, 994, 1078, 1142 Rebelo, S.T., s e e Correia, I. 974 Rebelo, S.T., s e e Easterly, W. 703 Rebelo, S.T., s e e Gomes, J. 994, 1159 Rebelo, S.T., s e e King, R.G. 9, 54, 369, 391, 429, 435, 545, 549, 649, 672, 711-713, 929, 932, 945,954, 995, 1062, 1140 Rebelo, S.T., s e e Stokey, N.L. 578, 583, 672, 709, 711,714, 954 Redish, A. 154, 155, 166 Redish, A., s e e Betts, C.M. 217 Redmond, J. 161 Reichenstein, W. 101 Reichlin, L., s e e Evans, G.W. 1125 Reichlin, L., s e e Lippi, M. 217 Reid, B.G., s e e Boothe, PM. 1658 Reinbart, C.M. 1545, 1546, 1551, 1553, 1561, 1572, 1573 Reinhart, C.M., s e e Calvo, G.A. 1538, 1539, 1552, 1588, 1600 Reinhart, C.M., s e e Kaminsky, G.L. 1553, 1590 Reinhart, C.M., s e e Ostry, J. 1568 Renelt, D., s e e Levine, R. 269, 277-282, 390, 423, 671,694 Reserve Bank of New Zealand 1500 Resnick, L.B., s e e Levine, J. 1332 Restoy, F. 1272 Revelli, R., s e e Contini, B. 1177, 1178, 1180, 1200, 1222 Revenga, A., s e e Blanchard, O.J. 1214 Rey, R, s e e Aghion, R 1157 Ricardo, D. 1642 Rich, G. 1514 Richard, S.E, s e e ttansen, L.P 556 Richards, S., s e e Meltzer, A.H. 1466

1-23 Rietz, T. 1252, 1272, 1296 Riley, J. 1461, 1465 Rios-Rull, J. 943 Rios-Rull, J.-V., s e e Castafieda, A. 380 Rios-Rull, J.-V. 380 Rios-Rull, V., s e e Krusell, P. 1445, 1473 Ritter, J.R. 1321 Ritter, J.R., s e e Ibbotson, R. 1321 Rivers, D. 840 Rivlin, T.J. 343 Rob, R., s e e Jovanovic, B. 702 Rob, R., s e e Kandori, M. 475 Robb, R., s e e Heckman, J.J. 752 Robbins, H. 476, 478 Roberds, V~, s e e Hansen, L.E 573,574 Roberts, H.V. 1307 Roberts, J., s e e Milgrom, P 475 Roberts, J.M. 1013, 1033, 1040, 1116, 1118, 1505 Roberts, J.O., s e e Lebow, D.E. 215 Roberts, K. 1466 Robertson, J.C., s e e Pagan, A.R. 69, 108 Robinson, D. 217 Robinson, J. 1054, 1120 Robinson, S., s e e Meltzer, A.H. 204, 216, 217, 222 Rockafellar, R.T. 325 Rockoft, H. 155, 157 Rockoff, H., s e e Bordo, M.D. 160 Rodriguez, C.A. 1562, 1563, 1565, 1568 Rodr~guez-Clare, A., s e e Klenow, RJ. 663,673, 679, 680, 683-686, 694, 702, 705, 707 Rodrik, D., s e e Alesina, A. 278, 692, 1466, i469 Rogers, C. 1449, 1450 Rogers, D., s e e Fullerton, D. 576, 588, 616 Rogerson, R. 551,602, 97~978, 1145 Rogerson, R., s e e Benhabib, J. 402, 550, 1145 Rogerson, R., s e e Bertola, G. 1222 Rogerson, R., s e e Cho, J.O. 976 Rogerson, R., s e e Cole, H.L. 1163, 1194, 1201 1203, 1207 Rogerson, R., s e e Greenwood, J. 550, 995 Rogerson, R., s e e Hopenhayn~ H. 672, 708, 994 Rogerson, R., s e e Parente, S.L. 702 Rogoff, K. 961, 1415- 1418, 1420, 1422, 1425, 1429, 1432, 1434, 1438 Rogoff, K., s e e Bulow, J. 1448, 1449 Rogoff, K., s e e Canzoneri, M.B. 1507, 1508

1-24 Rogoff, K., s e e Obstfeld, M. 407, 1507, 1590, 1630 Rojas-Snarez, L. 1575 Roland, G., s e e Persson, T. I460 Roldos, J. 1578 Roll, R. 1328 Romer, C.D. 6, 69, 92, 137, 183, 187, 204, 205, 1618 Romer, D. 237, 643, 649, 651, 661,930, 1013, I034, 1140, 1157, 1163, 1635, i661 Romer, D., s e e Ball, L. 1023, 1037, 1041, 1127 Romcr, D., s e e Franket, J.A. 280, 281 Romer, D., s e e Mankiw, N.G. 244-246, 252255, 269-271,277--279, 289, 653, 655, 660, 673,679-683, 685, 686, 1638 Romer, D.H., s e e Romer, C.D. 69, 92, 137 Romer, RM. 238, 245, 260, 261,264, 265, 271, 278, 280, 398, 424, 425, 641, 651, 665, 672, 705-707, 715-717, 719, 1638 Romer, P.M., s e e Evans, G.W. 425, 426, 506, 521 Rose, A., s e e Akerlol, G.A. 1200 Rose, A.K, s e e Eichengreen, B. 1590 Rose, A.K., s e e Frankel, J.A. 1590 Rosen, A., s e e Meehl, R 1319 Rosen, S. 584, 585, 976 Rosensweig, J.A. 1659 Rosenthal, H., s e e Alesina, A. 1425, 1426 Roseveare, D. 1626 Ross, L. 1319 Ross, S., s e e Brown, S. 1242 Ross, S.A. 1331 Rossana, R.J. 879, 881, 886, 907 Rossana, R.J., s e e Maccini, L.J. 881, 893, 894, 903, 907 Rossi, RE., s e e Jones, L.E. 380, 672, 711--713, 1675, 1711 Rotemberg, J.J. 67, 68, 395, 397, 406, 407, 423, 429, 434, 838, 910, 974, 996, 1020, 1033, 1034, I036, 1040, 1041, 1043, 1044, 1055, 1056, 1058, 1062, 1063, 1067-1069, 1074, 1081, 1082, 1088--1090, 1092, 1093, 1106, 1107, 1114, 1116, 1118, 1123q125, 1129, 1143, 1144, 1365, 1464, 1492, 1494, 1497 Rotemberg, J.J., s e e Mankiw, N.G. 785 Rotemberg, J.J., s e e Pindyck, R. 1072 Rotemberg, J.J., s e e Poterba, J.M. 159 Rothschild, M. 823 Rotwein, E. t011

Author

index

Roubini, N. 1439, 1465 Roubini, N., s e e Alesina, A. 277~79, 1404, 1423, 1425, 1460, 1466, 1471 Roubini, N., s e e Grilli, V 95 Roubini, N., s e e Kim, S. 95 Rouwenhorst, K.G. 1296 Royer, D., s e e Balasko, Y 506 Rubinstein, A. 1188 Rubinstein, A., s e e Bilmlore, K.G. 1188 Rubinstein, M. 554-556 Rubinstein, M., see Jackwerth, J.C. 1310 Rudd, J.B., s e e Blinder, A,S. 1018, 1 t 18 Rudebusch, G.D. 69, t04, 196, 1493 Rudebusch, G.D., s e e Diebold, EX. 6 Rudebusch, G.D., s e e Oliner, S.D. 137, 820, 1374, 1376 Rudebusch, R.G. 11 Rudin, J. 1040 Ruhm, C. 1152 Runlde, D., s e e Glosten, L. 1280 Run!de, D., s e e Keane, M.R 608, 609, 786, 790 Runkle, D.E. 789, 790, 1 6 5 5 Rtmkle, D.E., s e e Geweke, J.E 89 Runkle, D.E., s e e Mankiw, N.G. 135 Russek, ES., s e e Barth, J.R. 1657 Rust, J. 314, 317, 336 Rust, J., see Amman, H.M. 535 Rustichini, A., s e e Benhabib, J. 400, 847, 1449, 1467, 1472 Rustichini, A., s e e Boldrin, M. 400, 1465 Ryder, H. 587 Ryder k; H.E. 1284

Sabelhaus, J., s e e Gokhale, J. 750 Sachs, J. 1590, 1591 Sachs, J., s e e Bruno, M. 1090 Sachs, J., s e e Roubini, N. 1439, 1465 Sachs, J.D. 252, 703 Sack, B., s e e Galeotti, M. 909 Sadka, E., s e e Razin, A. 1715 Sahay, R. 1535 Sahay, R., s e e Fischer, S. 1538, 1547, 1561 Saint Marc, M. 222, 223 Saint-Paul, G. 1162, 1472 Saint-Paul, G., s e e Blanchard, O.J. 1214 Sakellaris, R, s e e Barnett, S. 831 Salad-Martin, X. 269, 277, 279--282, 659, 694

Author

1-25

Index

Salad-Martin, X., s e e Barro, R.J. 237, 245, 246, 252, 269, 271, 272, 278, 284, 643, 651,657, 659, 671,675, 1637 Salge, M. 499 Sahnon, C.K., s e e Haldane, A.G. 1485, 1497 Salmon, M. 525 Salmon, R, s e e Kirman, A.R 536, 539-541 Saloner, G., s e e Rotemberg, J.J. 910, 1058, 1093 Salter, W.E.G. 848 Sampson, L., s e e Fauvel, Y. 1573 Samuelson, RA. 46, 643, 661, 1311, 1634 Samwick, A. 609 Samwick, A.A., s e e Carroll, C.D. 567 Sandmo, A., s e e Atkinson, A.B. 1718 Sandroni, A. t293 Sanguinetti, E 1540 Sanguinetti, R, s e e Heymann, D. 506 Sanguinetti, R, s e e Jones, M. 1540 Santaella, J. 1543 Santos, M., s e e Caballe, J. 578 Santos, M.S. 321-323, 326, 327, 335, 353, 354, 382, 590, 1266 Santos, M.S., s e e Bona, J.L. 313 Santos, M.S., s e e Ladron de Guevara, A. 317 Santos, M.S., s e e Peralta-Alva, A. 374 Sargent, T. 162, 198, 929 Sargent, T., s e e Ljungqvist, L. 1214 Sargent, T., s e e Lucas Jr, R.E. 582 Sargent, T., s e e Marimon, R. 455, 523 Sargent, T.J. 73, 121, 135, 417, 418, 453, 455, 457, 458, 464, 465, 489, 504, 523, 524, 529-531,763,888, 1023, 1024, 1145, 1506, 1507, 1519, 1542, 1543, 1630, 1631 Sargent, T.J., s e e Anderson, E.V¢~ 368, 369 Sargent, T.J., s e e Cho, I.-K. 455, 465, 524, 525 Sargent, T.J., s e e Evans, G.W. 530 Sargent, T.J., s e e Hansen, E.P 558, 573, 574, 882, 915, 1294, 1295 Sargent, rl:J., s e e Marcet, A. 454, 464, 465, 468, 473-476, 480, 494, 499, 525, 528, 529, 532, 1675, 1705, 1707 Sattinger, M. 577, 578 Saunders, A. 181 Sauvy, A. 222 Savage, L.J. 1308, 1324 Savage, L.J., s e e Friedman, M. 1325 Savastano, M.A. 1589 Savastano, M.A., s e e Masson, RR. 1554, 1588

Savin, N., s e e Bray, M. 454, 465, 466, 473, 475, 527 Savin, N., s e e Ingrain, B. 984 Savin, N.E., s e e McManus, D.A. 908 Savouri, S., s e e Jackman, R. 1221 Sayers, R.S. 156 Sbordone, A. 983 Sbordone, A., s e e Cochrane, J. 1120 Sbordone, A.M. 1078, 1099, 1108, 1118, 1128 Scammell, W.M. 156 Scarpetta, S. 1214 Schaling, E. 1437 Schaling, E., s e e Eijffinger, S. 1432, 1438 Schaller, H., s e e Moore, B.J. 455 Scharfstein, D., s e e Chevalier, J.A. 1122, 1123 Scharfstein, D., s e e Hoshi, T. 1344 Scheinkman, J., s e e Ekeland, L 1689 Scheinkman, J., s e e He&man, J.J. 579 Scheinkman, J.A. 566 Scheinkman, J.A., s e e Benveniste, L.M. 321 Schiantarelli, E, s e e Galeotti, M. 909, 1086, 1124

Schmidt, R, s e e Kwiatkowski, D. 212 Schmidt-Hebbel, K., s e e Easterly, W. 1538 Schmitt-Groh6, S. 406, 407, 416, 418, 429, 431,435 Schmitt-Groh6, S., s e e Benhabib, J. 419, 421, 423 Schmitz Jr, J.A. 672, 695 697, 699 Schnadt, N., s e e Capie, E 154 Scholes, M., s e e Black, E 1310, 1331 Scholz, J.K., s e e Gale, W.G. 1646 SchSnhofer, M. 515 Schopenback, R, s e e Erlich, D. 1314 Schotter, A. 1415 Schuh, S. 877, 881,912 Schuh, S., s e e Davis, S.J. 1151, 1152, 1160, 1161, 1178, 1194, 1199 Schuh, S., s e e Fuhrer, J.C. 905, 908 Schuh, S., s e e Humphreys, B.R. 909 Schultz, T.V~ 653 Schmnaker, L.L. 344, 345 Schwartz, A., s e e Thaler, R.H. 1313 Schwartz, A.J. 156, 161, 173, 180, 204, 1515 Schwartz, A.J., s e e Bordo, M.D. 159, 165, 184, 194, 203,204, 208, 217, 1404, 1590 Schwartz, A.J., s e e Darby, M.R. 166 Schwartz, A . . I . , s e e Friedman, M. 6l, 137, 154, 162, 172, 176, 179, 180, 185, 189, 222

1-26 Schwert, G.W. 1236, 1280 Schwert, G.W., s e e French, K. 1280 Seater, J.J. 162!, 1654, 1656, 1657 Sedlacek, G., s e e Heckman, J.J. 578, 579 Sedlacek, G.J., s e e Hotz, V.J. 792, 803 Segal, I.B. 1157 Senhadji, A.S., s e e Diebold, EX. 11 Sentana, E., s e e King, M. 1333 Seppala, J., s e e Marcet, A. 1675, 1705, 1707 Seslnick, D. 746, 751 Shafir, E. 1316, 1324, 1329 Shafir, E., s e e Tversky, A. 1324 Shapiro, C. 1157 Shapiro, C., s e e Farrell, J. 1121 Shapiro, M. 938, 980 Shapiro, M., s e e Barsky, R. 558, 564, 565 Shapiro, M.D. 138, 818, 1069, 1075, 1655 Shapiro, M.D., s e e Dominguez, K. 182 Shapiro, M.D., s e e Mankiw, N.G. 135 Shapiro, M.D., s e e Ramey, V.A. 67, 1089 Sharma, S., s e e Masson, RR. 1554, 1588 Sharpe, S. 1344 Shaw, E.S., s e e Gurley, J.G. 1507 Shaw, K. 584 Shay, R.R, s e e Juster, ET. 777 Shea, J. 402, 608, 790, 983, 1117 Sheffrin, S.M., s e e Driskill, R.A. 1042 Shefrin, H. 1313, 1317, 1321, 1330 Shell, K. 389, 391,516 Shell, K., s e e Balasko, Y. 427 Shell, K., s e e Barnett, W. 540 Shell, K., s e e Cass, D. 389, 516, 662 Shepard, A., s e e Borenstein, S. 1124 Sherali, D.H., s e e Bazaraa, M.S. 331 Sheshinski, E. 1031, 1037 Sherry, C.M., s e e Bazaraa, M.S. 331 Shiller, R.J. 173, 1234, 1235, 1238, 1249, 1290, 1316, 1317, 13t9, /320, 1323, 1324, 1327, 133~1332 Shiller, R.J., s e e Campbell, J.¥. t235, 1265, 1280, 1320 Shiller, R.J., s e e Case, K.E. 1323 Shiller, R.J., s e e Grossman, S.J. 1242, 1246, 1268, 1291 Shin, M.C., s e e Puterman, M.L. 339 Shin, Y., s e e Im, K. 283 Shin, Y., s e e Kwiatkowski, D. 212 Shleifer, A. 1317, 1324 Shleifer, A., s e e Barberis, N. 1294, 1322 Sh!eifer, A., s e e Bei~nheim,B.D. 1646 Shleifer, A., s e e DeLong, J.B. 1290, 1324

Author

Index

Shleifer, A., s e e La Porta, R. 1240 Shleifer, A., s e e Lakonishok, J. 1323 Shleifer, A., s e e Lee, C. 1324 Shleifer, A., s e e Murphy, K.M. 262, 278, 1082 Shoemaker, C.A., s e e Johnson, S.A. 345, 381 Shor, N.Z. 331 Shoven, J.B. 705, 708 Shoven, J.B., s e e Ballard, C. 1639 Sibert, A., s e e Rogoff, K. 1416, 1417, 1420, 1425 Sichel, D., see 0liner, S.D. 820 Siegel, J.J. 1312, 1313 Silberman, J. 1316 Simkins, S. 931 Simmons, B. 163 Simon, H.A., s e e Holt, C.C. 882, 885, 888, 909, 910, 912 Simons, H.C. 852, 1485 Simonsen, M.H., s e e Dornbusch, R. 1543, 1565 Sims, C.A. 34, 44, 69, 83, 93, 95, 99, I05, 121, 128, 129, 131, 132, 134, 144, 397, 418, 539, 673, 694, 1509, 1518, 1520, 1631 Sims, C.A., s e e Hayashi, E 788 Sims, C.A., s e e Leeper, E.M. 69, 74, 83, 93, 101, 128, 132, 134, 1036, 1089, 1369 Sinai, A., s e e Eckstein, O. 1344 Singer, B. 292 Singer, B., s e e Heckman, J.J. 1166 Singleton, K. 1270 Singleton, K.J., s e e Dural, K.B. 800, 1284 Singleton, K.J., s e e Hansen, L.E 547, 555, 556, 768, 769, 784, 882, 1234, 1246, 1250, 1261 Siow, A., s e e Altonji, J.G. 789 Skinner, B.E 1328 Skinner, J.S. 771,772 Skinner, J.S., s e e Hubbard, R.G. 567, 569, 572, 573, 593, 771,776, 794, 797, 1660 Slade, M.E. 1015 Slemrod, J,, s e e Shapiro, M.D. 1655 Slovic, P., s e e Fischhoff, B. 1319 Small, D.H., s e e Hess, G.D. 1485, 1509 Small, D.H., s e e Orphanides, A. 1485 Smetters, K.A. 1647 Smith, A.A., s e e Krusell, E 380, 547, 566, 567~ 994 Smith Jr, A.A., s e e Krusell, E 1293 Smith, C.W., s e e Nance, D.R. 1318 Smith, E.L. 1312

Author

1-27

Index

Smith, G.W., s e e Devereux, M. 952 Smith, G.W., s e e Gregory, A.W. 376, 377 Smith, R., s e e Alogoskoufis, G.S. 166, 214 Smith, R.R, s e e Lee, K. 284 Smithson, C.W., s e e Nance, D.R. 1318 Shower, D., s e e Blanchard, O.J. 1214 Soares, J., s e e Cooley, T.E 1463 S6derlind, R, s e e Hassle1; J. 9, 1238 S6derstr6m, T., s e e Ljung, L. 476 Soerensen, J.R 528 Solnick, A., s e e Judd, K.L. 340 Solon, G. 579, 1058, 1102, 1106 Solon, G., s e e Barsky, R. 43 Solow, R.M. 237, 244, 246, 257, 643, 656, 664, 681,929, 930, 942, 950-952, 1140, 1207, 1638 Solow, R.M., s e e Blanchard, O.J. 1214 Solow, R.M., s e e Blinder, A.S. 1660 Solow, R.M., s e e Hahn, F. 661 Solow, R.M., s e e Samuelson, RA. 46 Sommariva, A. 222 Sonnenschcin, H., s e e Hildenbrand, W. 535, 537 Sorger, G., s e e Honmles, C.H. 529, 532 Souleles, N., s e e Jappelli, T. 790 Spear, S.E. 465 Spear, S.E., s e e Marimon, R. 455, 531 Spiegel, M.M., s e e Benhabib, J. 283 Spilerman, S., s e e Singer, B. 292 Spulber, D., s e e Caplin, A.S. 801, 1031, 1032 Spynnewin, E 803 Srba, E, s e e Davidson, J. 750 Srinivasan, T.N. 705 Stacchetti, E., s e e Jones, L.E. 720 Stafford, E, s e e Holbrook, R. 569 Stafford, E, s e e Ryder, H. 587 Staiger, D. 49, 50 Staiger, R. i415 Staiger, R.W., s e e Bagwell, K 1125 Stambaugh, R.F., s e e French, K. 1280 Stambaugh, R.E, s e e Kandel, S. 1235, 1252, 1253, 1265, 1270, 1272 Stark, T., s e e Croushore, D. 1485 Starr, R.M., s e e Chah, E.Sq 775 Startz, R., s e e Nelson, C.R, 1264 Statman, M., s e e Shefrin, H. 1313, t317, 1330 Stedinger, J.R, s e e Johnson, S.A. 345, 38I Stein, J.C., s e e Kashyap, A.K. 137, 881,912~ 1344, 1374, 1376 Stengel, R.E 904

Stephen, E, s e e Ryder, H. 587 Sterling, A., s e e Modigliani, E 1656, 1657 Stigler, G. 1018 Stigler, G.J. 1173 Sfigler, S.M. 275 Stiglitz, J., s e e Dixit, A. 1115, 1121, 1126 Sfiglitz, J., see Greenwald, B. 857, 1122, 1377

Stiglitz, J., s e e Jaffee, D.M. 1376 Stiglitz, J.E. 1675, 1696, 1718 Stiglitz, J.E., s e e Atkinson, A.B. 1673, 1676, 1680, 1682, 1718 Stiglitz, J.E., s e e Shapiro, C. 1157 Stock, J.H. 9, 11, 39, 43, 45, 50-54, 821, 878, 919, 934, 938, 939, 1011, 1021, 1404, 1674 Stock, J.H., s e e Feldstein, M. 44, 1485, 1497, 1498 Stock, J.H., s e e King, R.G. 54, 941 Stock, J.H., s e e Staiger, D. 49, 50 Stockman, A. 1578 Stockman, A.C. 549 Stoclcman, A.C., s e e Baxter, M. 203, 938, 1404 Stockman, A.C., s e e Darby, M.R. 166 Stockman, A.C., s e e Gavin, V~ 1485 Stockman, A.C., s e e Ohanian, L.E. 1036 Stocks, Bonds, Bills arid Inflation 1639 Stockton, D.J., s e e Lebow, D.E. 215, 1016 Stoer, J. 334 Stoker, Z, s e e Blundell, R. 770, 788 Stokey, N., s e e Alvarez, E 996 Stokey, N., s e e Lucas Jr, R.E. 559, 561 Stokey, N., s e e Milgrom, R 1322 Stokey, N.L. 271,299, 314, 318-321,346, 578, 583, 672, 705, 709, 711, 714, 951, 954, 998, 999, 1674 Stokey, N.L., s e e Lucas, R.E. 380, 1446, 1449 Stokey, N.L., s e e Lucas Jr, R.E. 158, 1673, 1675, 1699, 1723, 1728 Stone, C.J., s e e Breiman, L. 289 Sh'ang, G. 82 Strongin, S. 83.-85, 87, 114 Strotz, R.H. 1653 Strotz, R.H., s e e Eisner, R. 1310 Stroud, A.H. 334 Stuart, A. 1485 Stulz, R.M. 1317 Sturzeneggcr, E, s e e Dornbusch, R. t543 Sturzenegge~; F., s e e Guo, J.-T. 427 Sturzenegger, E, s e e Mondino, G. 1540

1-28

Author

Suarez, J. 1378 Subrahmanyam, A., s e e Daniel, K. 1322 Sugden, R., s e e Loomes, G. 1313 Suits, D., s e e Kallick, M. 1325 Stmmlers, L.H. 961 Summers, L.H., s e e Abel, A.B. 1266, 1651 Summers, L.H., s e e Alesina, A. 1432 Surmaaers, L.H., s e e Bemheim, B.D. 1646 Summers, L.H., s e e Blanchard, O.J. 416, 1635 Summers, L.H., s e e Carroll, C.D. 759, 793, 1655 Summers, L.H, s e e Clark, K.B. 602, 1173 Summers, L.H., s e e Cutler, D.M. 1290, 1320, 1321 Summers, L.H., s e e DeLong, J.B. 279, 695, 1042, 1290, 1324 Summers, L.H., s e e Easterly, W. 277, 278, 281, 675 Summers, L.H., s e e Kotlikoff, L.J. 780, 1646 Summers, L.H., s e e Mankiw, N.G. 785 Summers, L.H., s e e Poterba, J.M. 1235, 1320, 1648

Summers, R. 238, 301, 640, 673 675, 677, 680, 681,689, 720 Sun, T. 1270 Sundaram, R.K., s e e Dutta, RK. 380 Sundaresan, S.M. 1284 Sundel, S., s e e Marimon, R. 455, 472, 531 Surekha, K. 908 Sussman, O., s e e Suarez, J. 1378 Svensson, J. 1466, 1471, 1472 Svensson, L.E.O. 156, 197, 417, 1033, 1034, 1273, 1411, 1432, 1434, 1489, 1493, 1494, 1498, 1504 Svensson, L.E.O., s e e Englund, R 9 Svensson, L.E.O., s e e Kotlikoff, L. 1448, 1449, 1465 Svensson, L.E.O., s e e Leiderman, L. 1432, 1438, 1495 Svensson, L.E.O., s e e Persson, M. 1447, 1449 Svensson, L.E.O., s e e Persson, T. 1449, 1450, 1454, 1456, 1465 Swagel, R, s e e Alesina, A. 277~79, 1460, 1466, 1471 Swan, T.W 244, 246, 247, 643 Sweeney, J., s e e Kneese, A. 656 Swoboda, A., s e e Genberg, H. 165 Symansky, S.A., s e e Bryant, R.C. 1491, t497, 1516 Szafarz, A., s e e Adam, M. 500

Szafarz, A.,

see

Index

Broze, L. 487, 488

Tabellini, G. 1414, 1415, 1450, 1456, 1464, 1465 Tabellini, G., s e e Alesina, A. 1446, 1449, 1450, 1454, 1465, 1518, 1522 Tabellini, G., s e e Cu!derman, A. 1456, 1465 Tabetlini, G., s e e Daveri, E 1220 Tabellini, G., s e e Edwards, S. 1538 Tabellini, G., s e e Grilli, V. 1404, 1432, 1438, 1439, 1465 Tabeltini, G., s e e Ozler, S. 1457, 1465 Tabellini, G., s e e Persson, T. 278, 692, 1400, 1403, 1413, 1415 1418, 1420, 1421, 1425, 1433, 1435, 1437-1440, 1442, 1445, i448, 1449, 1459, 1460, 1466, 1469, 1470, 1490 Taber, C., s e e Heckman, J.J. 576, 578, 582, 584, 586, 587, 590, 592, 593 Taguas, D., s e e Blanchard, 03. 1214 Tallarini Jr, T.D., s e e Hansen, L.E 558, 1294, 1295 Tallman, E.W, s e e Rosensweig, J.A. 1659 Talvi, E. 1543, 1571, 1604 Tan, K.S. 334 Tanner, S., s e e Banks, J. 758, 792 Tanzi, V. 1741 Tarshis, L. 939, 1059 Tauchen, G. 367 Taylol, A., s e e Obstfeld, M. 164, 165 Taylor, C. 1330 Taylor, J.B. 46, 182, 314, 397, 408, 417, 422, 454, 474, 487, 489, 495, 545, 1011, 1013, 1015, 1017, 1025, 1027 1031, 1037 1039, 1042, 1043, 1113, 1364, 1411, I485, 1487, 1488, 1490, 1497, 1505, 1507, t512, 1513, 1516, t518, 1542, 1582 Taylor, J.B., s e e Phelps, E. 1025, 1026 Taylor, L.D, s e e Houthakker, H.S. 803 Taylor, S.E. 1330 Tejada-Guibert, J.A., s e e Johnson, S.A. 345, 381 Teles, R, s e e Correia, I. 1537, 1675, 1720, 1733 l'elmer, C.I., s e e Backus, D.K. 1316 Temin, R 162, 179, 180, 183, 184 Temple, J. 276 Terlizzese, D., s e e Guiso, L. 772 Terna, R, s e e Beltratti, A. 524, 525 Terrones, M. 1425 Teruyama, H., s e e Fukuda, S.-i. 875 Tesar, L., s e e Mendoza, E. 1439

Author

Index

Tesar, L., s e e Stockanan, A.C. 549 Tetlow, R., s e e Fillion, J.E 1498 Teukolsky, S.A., s e e Press, W.H. 329-334, 343, 348, 356, 365 Thaler, R., s e e Froot, K. 1316 Thaler, R., s e e Lee, C. 1324 Thaler, R.It. 1313, 1317 Thaler, R.H., s e e Benartzi, S. 1290, 1312, 1313 Thaler, R.H., s e e De Bondt, W.E 1307, 1320, 1323 Thaler, R.H., s e e Shefrin, H. 1317 Thaler, R.H., s e e Siegel, J.J. 1312 The Economist 1238, 1632 Theunissen, A.J., s e e Whittaker, J. 1508 Thomas, J. 994 Thomas, J.K., s e e Bernard, V.L. 1321 Thomas, T.J. 161 Thompson, S.C., s e e Taylor, S.E. 1330 Thomson, J.B., s e e Carlson, J.B. 104 Thornton, H. 1485 Thurow, L. 759 Tieslau, M.A., s e e Hoftinan, D.L. 412 Tillmann, G. 474 Timberlake, R.H. 169, 174 Timmermann, A.G. 454, 455, 500, 530 Tinbergen, J. 817 Tirole, J. 1266, 1650 Tirole, J., s e e Fudenbelg, D. 1155 Tirole, J., s e e Holmstrom, B. 1376 Titman, S., s e e Jegadeesh, N. 1321 Tobin, J. 773, 817, 818, 1643 Tobin, J., s e e Brainard, W.C. 817 Tobin, J., s e e Eichengreen, B. 168 Todd, R, s e e Heckman, J.J. 578, 582 Todd, R., s e e CNistiano, L.J. 1365 Toharia, D., s e e Blanchard, O.J. 1214 Toma, M. 174, 177, 187, 190 Toma, M., s e e Goff, B.L. 159 Tommasi, M. 1540 Torrmlasi, M., s e e Jones, M. 1540 Tommasi, M., see Mondino, G. 1540 Topel, R. 578 Topel, R., s e e Juhn, C. 619 Topel, R., s e e Murphy, K. 581 Tornell, A. 1466, 1472, 1590 Tornell, A., s e e Lanc, R 1472 Tornell, A., s e e Sachs, J. 1590, 1591 Townsend, R.M. 453,461,474, 529, 795, 796, 1350, 1376

1-29 Townsend, R.M., s e e Phelan, C. 380, 575, 796 Traub, J.E 338 Traub, J.E, s e e Papageorgiou, A. 334 Trehan, B. 159 Tria, G., s e e Felli, E. 1083, 1122 Triffin, R. 157, 165 Trostel, PA. 1652 Tryon, R., s e e Brayton, E 1043, 1344, 1485 Tsiddon, D. 1031 Tsiddon, D., s e e Lach, S. 1019 Ysitsiklis, J.N., s e e Chow, C.-S. 326, 334 Tsutsui, Y., s e e Shiller, R.J. 1316 Tullio, G. 156 Tullio, G., s e e Sommariva, A. 222 Tullock, G., s e e Grief, K.B. 253 Tuncer, B., s e e Krueger, A.O. 699 Turnovsky, S. 474 Tversky, A. 1308, 1315, 1319, 1324, 1330 Tversky, A., s e e Kahnelnan, D. 1308, 1309, 1311 Tversky, A., s e e Quattrone, G.A. 1329 Yversky, A., s e e Shafir, E. 1316, 1324, t329 Tversky, A., s e e Thaler, R.H. 1313 Tybout, J., s e e Corbo, V. 1543 Tylor, E.B. 1331 Uldig, H. 70 Uhlig, It., s e e Lettau, M. 524, 1297 Uhlig, H., s e e Taylor, J.B. 314 United Nations 681 Uppal, R., s e e Dumas, B. 564 Uribe, M. 1539, 1578, 1589 Uribe, M., s e e Benhabib, J. 419, 421,423 Uribe, M., s e e Mendoza, E. 1571, 1579 Uribe, M., s e e Schmitt-Groh~, S. 416, 418, 431 US Bureau of the Census 585 Uzawa, H. 578, 651,710 Valdes, R., s e e Dornbusch, R. 1590 Valdivia, V, s e e Cln'istiano, I,.J. 504 Van Huyck, J.B., s e e Orossman, H.J. 158, 1415, 1449 van Wincoop, E., s e e Beau&y, P 1264 Van Zandt, T., s e e Lettau, M. 470, 472 Vasicek, O. 1270 V6gh, C . , s e e Guidotti, RE. 1675, 1720 V6gh, C.A. 1535, 1538, 1542, 1543, 1546, 1550, 1554, t588 V6gh, C.A., s e e Bordo, M.D. 158

1-30 V6gh, C.A, s e e Calvo, G.A~ 1428, 1535, 1538, 1539, 1546, 1554, 1557, 1563, 1564, 1568, 1571, 1572, 1582, 1587-1589, 1597, 1605 V+gh, C.A., s e e De Gregorio, J. 1546, 1551, 1573, 1575, I577 V~gh, C.A., s e e Edwards, S. 1578-1580 V~gh, C.A., s e e Fischer, S. 1538, 1547, 1561 V~gh, C.A., s e e Guidotti, RE. 1537, I588, 1603 V6gh, C.A., s e e Hoffmaister, A. 1561, 1589 V~gb, C.A., s e e Lahiri, A. 1597 V~gh, C.A., s e e Rebelo, S.T. 1546, 1568, 1578, 1579, 1581, 1606 V+gh, C.A., s e e Reinhart, C.M. 1545, 1546, 1551, 1553, 1561, 1572, 1573 V~gh, C.A., s e e Sahay, R. 1535 Vela, A., s e e Santaella, J. 1543 Velasco, A. 416, 1446, 1449, 1450, 1459, 1465, 1540 Velasco, A, s e e Sachs, J. 1590, 1591 Velasco, A., s e e Tommasi, M, 1540 Velasco, A., s e e Tornell, A. 1466, 1472, 1590 Venable, R., s e e Levy, D. 1014, 1015, 1019 Venegas-Martinez, E 1571 Ventura, G., s e e Huggett, M. 380 Veracierto, M. 994 Verdict, 3,., s e e Saint-Paul, G. 1472 Vetterling, WT., see Press, W.H. 329 334, 343, 348, 356, 365 Viana, L. 1543 Vickers, J. 1414, 1415 Vigo, J,, s e e Santos, M.S. 321,322, 326, 327, 335 Vinals, J., s e e Goodhart, C.E.A. 1438, 1495 Vishny, R.W, s e e Barberis, N. 1294, 1322 Vishny, R.W, s e e La Porta, R. 1240 Vishny, R.W., s e e Lakonishok, J. 1323 Vishny, R.W., s e e Murphy, K.M. 262, 278, 1082 Vishny, R.W., s e e Shleifer, A. 1324 Visscher, M., s e e Prescott, E.C. 700 Vires, X. 474, 532 Vires, X., s e e Jun, B. 474 Volcker, P.A. 1630 yon Furstenberg, G.M. 1333 yon Hagen, J. 1439, 1460, 1465 yon Hagen, J., s e e Eichengreen, B. 1465 yon Hagen, J., s e e FratiaImi, M. 1431 yon Hagen, J., s e e Hallerberg, M. 1460, 1465 yon Weizs~icker,C. 641,650, 657 Vredin, A.E., s e e Bergstr6m, V. 538

Author

Index

Vuong, Q.H., s e e Rivers, D. 840 Wacbtel, R 1658 Wachtel, P., s e e Evans, M. 182 Wachter, S.M., s e e Goetzmann, WN. 1333 Wadhwani, S., s e e King, M. 1333 Wagner, R.E., s e e Buchanan, J.M. 1631 Waldmann, R.J., s e e DeLong, J.B. 1290, i324 Walk, H., s e e Ljtmg, L. 476 Walker, M., s e e Moreno, D. 481 Wallace, N., s e e Sargent, ZJ. 417, 418, 489, 1024, 1506, 1507, 1519, 1630 Waller, C. 1431 Walle~, C., s e e Fratianni, M. 1431 Wallis, K., s e e Kreps, D.M. 540 Walsh, C.E. 1433, 1434, I437, 1438, 1490 Walsh, C.E., s e e Trehan, B. 159 Walsh, C.E., s e e Waller, C. 1431 Wang, EA. 1322 Wang, J. 1237, 1293 Wm~g, L.-T., s e e Dezhbakhsh, H. I039 Wang, T., s e e Dumas, B. 564 Warner, A.M., s e e Sachs, J.D. 252, 703 Warner, E.J. 1019 Wascher, W., s e e Lebow, D.E. 1016 Watson, J., s e e den Haan, W.J. 994, 1166, 1194, 1203, 1204, 1206, 1207 Watson, J., s e e Ramey, G. 852, 1157, 1159 Watson, M,W. 6, 50, 547, 931 Watson, M.W, s e e Bernanke, B.S. 144 Watson, M,W, s e e Blanchard, O.J. 1266 Watson, M.W., s e e Canjels, E. 55 Watson, M.W., s e e King, R.G. 46, 54, 939, 941 Watson, M.W., s e e Staiger, D. 49, 50 Watson, M.W, s e e Stock, J.H. 9, 43, 45, 50--52, 821, 878, 919, 934, 938, 939, 1011, 1021, 1404, 1674 Webb, S., s e e Goo&nan, A. 797 Webber, A., s e e Capie, E 222 Weber, G. 774 Weber, G., s e e Alessie, R. 774, 775 Weber, G., s e e Attanasio, O.E 611-613, 756, 769, 781, 783, 784, 787, 790, 791, 793, 794, 1264, 1655 Weber, G., s e e Bhmdell, R. 781 Weber, G., s e e Brugiavini, A. 775 Weber, G., s e e Meghir, C. 61t, 613, 775, 804 Weber, M. 133t Weder, M. 403,437 Wehrs, W., s e e Carlson, J.A. 904

Author

Index

Weibull, J., s e e Lindbeck, A. 1465 Weil, D.N., s e e Mankiw, N.G. 173, 216, 244246, 252-255, 269-271,277-279, 289, 653, 655, 660, 673,679q583, 685, 686, 1638 Weil, P. 547, 1235, 1250, 1253, 1256, 1647 Weil, R, s e e Blanchard, O.J. 1650 Weil, R, s e e Restoy, E 1272 Weingast, B., s e e North, D. 1449 Weinstein, M.M. 182 Weisbrod, S.R., s e e Rojas-Suarez, L. 1575 Weiss, A., s e e Greenwald, B. 1122 Weiss, L., s e e Scheinkman, J.A. 566 Weiss, Y. 583 Weiss, Y., s e e Blinder, A. 587 Weiss, Y., s e e Lillard, L. 569, 572 Weiss, Y., s e e Sheshinski, E. 1031, 1037 Weitzman, M.L. 1689 Welch, E 579 Welch, I., s e e Bikhchandani, S. 1332 Wen, LE, s e e Devereux, M. 1466, 1471 Wen, L. 427, 431 Wenzelburgm, J., s e e B6hm, V. 475 Werner, A., s e e Dornbusch, R. 1543, 1563, 1568 West, K.D. 871,876, 880, 882, 885, 887, 888, 894, 896, 897, 900, 902, 905 908, 913, 919, 1028, 1041, 1320, 1497 Whalley, J. 705 Whalley, J., s e e Ballard, C. 1639 Whalley, J., s e e Shoven, J.B. 705, 708 Whalley, J., s e e Srittivasan, T.N. 705 Wheatley, S. 1242, 1261 Wheelock, D.C. 177, 179 Wheelock, D.C., s e e Calomiris, C.W 187, 191 Whinston, M.D., s e e Segal, I.B. 1157 White, E., s e e Bordo, M.D. 159 White, E.N. 180 White, H. 524 White, H., s e e Chen, X. 476, 532 White, H., s e e Kuan, C.-M. 476 Whited, T. 1344 Whited, T., s e e Hubbard, R.G. 1344 Whiteman, C. 487 Whitt, W. 326 Whittaker, J. 1508 Wickens, M.R., s e e Robinson, D. 217 Wicker, E. 162, 176, 177, 179 181, 1543 Wicksell, K. 203, 1485, 1631 Wieland, V, s e e Orphanides, A. 1485 Wigmore, B.A. 163, 183

1-31 Wilcox, D. 1242 Wilcox, D., s e e Kusko, A.L. 1327 Wilcox, D.W. 1655 Wilcox, D.W, s e e Carroll, C.D. 769, 785 Wilcox, D.W, s e e Cecchetti, S.G. 876 Wilcox, D.W., s e e Kashyap, A.K. 137, 877, 886, 903, 906, 912 Wilcox, D.W., s e e Orphanides, A. 198, 1485 Wilcox, D.W., s e e West, K.D. 908 Wildasin, D., s e e Boadway, R. 1463 Wilkinson, M. 881 Williams, J.C., s e e Brayton, E 1043, 1344, 1485 Williams, J.C., s e e Gilchrist, S. 847 Williams, J.C., s e e Wright, B.D. 347, 348 Williamson, J. 1597 Williamson, O.E. 852 Williamson, S. 1376 Willis, R., s e e Heckman, J.J. 602, 623 Wilson, B., s e e Saunders, A. 181 Wilson, C.A. 408 Wilson, R. 5 5 4 , 796 Winter, S.G., s e e Phelps, E.S. 1121 Woglom, G. 1127 Wohar, M.E., s e e Fishe, R.P.H. 173 Wojnilower, A. 1344 Wolf, H., see Dornbusch, R. 1543 Wolf, H., s e e Ghosh, A.R. 202, 207, 208 Wolff, E. 664 Wolfowitz, J., s e e Kiefer, J. 476 Wolinsky, A. 1188 Wolinsky, A., s e e Binmore, K.G. 1188 Wolinsky, A., s e e Rubinstein, A. 1188 Wolman, A.L., s e e Dotsey, M. 974, 1032, 1043 Wohnan, A.L., s e e King, R.G. 1036, 1041, 1043, 1364, 1367 Wolters, J., s e e Tullio, G. 156 Wong, K.-E 108 Wood, G.E., s e e Capie, E 163, 1438 Wood, G.E., s e e Mills, T.C. 204 Woodford, M. 389, 395, 406, 407, 409, 418, 421-423, 439, 454, 473~476, 481,483, 507, 516, 518, 521,662, 1036, 1157, 1507, 1509, 1518-1520, 1537, 1630, 1675, 1676, 1720, 1731 Woodford, M., s e e Bernanke, B.S. t361, 1363 Woodford, M., s e e Boldrin, M. 506 Woodford, M., s e e Farmer, R.E. 395, 396 Woodford, M., s e e Guesnerie, R. 439, 454, 460, 465, 474, 475, 506, 511,516, 526

1-32 Woodford, M., s e e Kehoe, T.J. 380 Woodford, M., s e e Lucas Jr, R.E. 1023 Woodford, M., s e e Rotemberg, J.J. 67, 68, 395, 406, 407, 429, 434, 974, 996, 1020, 1041, 1043, 1044, 1055, 1056, 1062, 1063, 1067 1069, 1074, 1081, 1082, 1088 1090, 1092, 1093, 1106, 1107, 1118, 1123-1125, 1129, 1143, 1144, i365, 1492, 1494, 1497 Woodford, M., s e e Santos, M.S. 1266 Woodward, EA., s e e Baker, J.B. 1125 Wooldridge, J., s e e Bollerslev, Z 1280 Wozniakowski, H., s e e Traub, J.E 338 Wright, B.D. 347, 348 Wright, M.H., s e e Gill, RE. 329 Wright, R. 1158 Wright, R., s e e Benhabib, J. 402, 550, 1145 Wright, R., s e e Boldrin, M. 399 Wright, R., s e e Burdett, K. 1196 Wright, R., s e e Greenwood, J. 550, 995 Wright, R., s e e Hansen, G.D. 976 Wright, R., s e e Kiyotaki, N. 524 Wright, R., s e e Parente, S.L. 702 Wright, R., s e e Rogerson, R. 978 Wurzel, E., s e e Roseveare, D. 1626 Wynne, M. 974 Wynne, M.A., s e e Huffman, G.W 437 Wyplosz, C . , s e e Eichengreen, B. 168, 1590 Xie, D. 425 Xie, D., s e e Benhabib, J. 425 Xie, D., s e e Rebelo, S.T. 952 Xu, "L 344 Pashiv, E. 1200 Yellen, J.L., s e e Akerlof, G.A. 397, 1034, 1035, 1039, 1157, 1200 Yeo, S., s e e Davidson, J. 750 Yi, K.-M., s e e Kocherlakota, N.R. 271 Yin, G.G., s e e Kushner, H.J. 476 Yong, W., s e e Bertocchi, G. 474 Yorukoglu, M., s e e Cooley, T.F. 847

Author

Index

Yorukoglu, M., s e e Greenwood, J. 576 Yotsuzuka, T. 1649 Young, A. 664, 672, 673,687, 716 Young, J., s e e Wachtel, E 1658 Yu, B., s e e Hashimoto, M. 1152 Yun, T. 1026, 1036

Zarazaga, C.E. 1540 Zarazaga, C.E., s e e Kydland, EE. 1557, 1561 Zarnowitz, V 9, 40 Zeckhauser, R., s e e Degeorge, E 1321 Zeckhauser, R.J., s e e Abel, A.B. 1266, 1651 Zeira, J., s e e Galor, O. 262, 263 Zejan, M., s e e Blomstrom, M. 277, 279, 280 Zeldes, S.R 566, 607-609, 771,789, 790, 802, 1344, 1655 Zeldes, S.E, s e e Barsky, R.B. 1653 Zeldes, S.R, s e e Hubbard, R.G. 567, 569, 572, 573, 593, 771,776, 794, 797 Zeldes, S.E, s e e Mankiw, N.G. 790, 1290 Zeldes, S.R, s e e Miron, J.A. 876, 907 Zeldes, S.R, s e e O'Connell, S.A. 1650 Zellner, A. 34 Zenner, M. 497 Zha, T., s e e Cushman, D.O. 95, 96 Zha, T., s e e Leeper, E.M. 69, 74, 83, 93, 101, 128, 132, 134, 1089, 1369 Zha, T., s e e Sims, C.A. 69, 83, 93, 99, 128, 129, 131, 132, 134, 144 Zhang, L., s e e Lockwood, B. 1411, 1415 Zhou, Z., s e e Grossman, S.J. 1237, 1293 Zhu, X. 1708 Zilcha, I., s e e Becker, R. 369 Zilibotti, E, s e e Gali, J. 405, 426 Zilibotti, F., s e e Marimon, R. 1214 Zin, S.E., s e e Epstein, L.G. 556, 558, 564, 744, 769, 1250, 1256 Zingales, L., s e e Kaplan, S.N. 856, 1344

SUBJECT INDEX

accelerator 884, 890, 896, 909 accelerator model 816, 817 accelerator motive 867, 902 activist vs. non-activist policies 1485 actual Jaw of motion (ALM) 466, 472, 490, 511 adaptive expectations 453,465 adaptive learning 464, 472, 493, 510 stability under 471 adaptively rational expectations equilibrium 532 adjustment costs 800, 1072 employment 1075 hours 1075 in investment 1296 non-convex 821, 839 production 867, 892, 893,900 hazard 835, 836, 840 speed of 881,889, 908 age distribution 753, 848 aggregate convexity 843 aggregate demand 1617, 1628, 1630 aggregate httman capital 583, 590 593 aggregate productivity 1195 aggregate productivity shock 1204 heterogeneous 1214 aggregate shocks 578, 582, 865 aggregation 548-594, 604, 605, 614, 615, 745, 781,804, 836, 849, 910 across commodities 782 AK model 672, 673, 709-715, 720, 733 allocation rules 1688, 1723 alternative dating 499 amplification 841, 1145, 1158, 1159, 1161 anchoring 1314-1317, 1322 animal spirits 395, 5t7, 521,941 anomalies 1307, t308, 1316, 1317, 1321, 1322, 1333, 1334 approximation error 326 345, 351-382 arbitrage 1246 ARMA models 489, 496, 501 Arrow-Debrcu equilibrium 795

asset-price chaunel 1378 asset prices, variable 1356 asset pricing models with t~edback 500 asset pricing with risk neutrality 498 associated differential equation 519 asymmetric fixed costs 825 asymmetry in adjustmen! of employment 1158 asymptotic stability 479, 639 autarky 853 automatic stabilizers 1660 average cohort techniques 787

backlog costs 884 backstop technology 656 balance-of-payments (BOP) crises 1534, 1535, 1553 balanced-budget rule 1631 balanced growth path 50, 392, 393, 424, 425, 427 band-pass filter, s e e BP filter bank lending channel 1376 Barro, R. 1640, 1642 1646 Bayesian learning 474 Bayesian updating 461,465 Belgium 1619 Bellman's Principle of Optimality 9 9 8 bequest motive 745, 780, 1624, 1646, 1647 strategic 1646 best practice 848 /3-convergence 659 Beveridge curve 1194, 1196, 1221, 1222 bilateral bargaining problem 1157 black market premium 671,688, 689, 691 694, 703 Blanchard Kahn technique 505 Bolivia 1631 boom recession cycle 1550, 1552, 1581 bootstrap methodology 79 BOP crises, s e e balance-of-payments crises borrowers' net worth 1345 1-33

1-34 borrowing constraint 566, 575, 593, 595, 597, 598, 772, 775, 1293 s e e also capital market inaperfections; credit market imperfections; liquidity constraints Boschen-Mills index 139 142 bottlenecks 842, 843 bounded rationality 454, 464 BP (band-pass) filter 12, 933, 934 Bretton Woods 152, 153, 163-168, 188, 190, 192, 199, 202-204, 206-209, 211,213, 215, 218-220 Brownian motion 825, 845 regulated 845 bubble-free solution 1524 bubble solutions 1522 bubbles 499 explosive 499 budget deficit 1619 budget surplus 16t9 buffer-stock saving 771, 1653, 1654 building permits 45 Burns Mitchell business cycle measurement 932 business cycles 865, 927 1002, 1620, 1621, 1659 s e e also cycles; fluctuations in aggregate activity facts about 934, 938, 939, 956 general equilibrium models 67 in RBC model 968 measuring 932 persistence of 939 table of stumnary statistics 956, 957 US facts 934 USA 935--938, 956 Cagan model of inflation 497 calculation equilibrium 462 calibration 545, 550, 567, 601,614, 6t6 Canada 45 capacity utilization 41,427, 431,930 modeling of 980 rate of 981 steady-state rate of 984 capital 1617, 1687 broad measure 701 desired 816, 842 frictionless 832, 838 human 673, 678, 679, 681--687, 701, 7t0, 713, 714, 716--718, 720, 732, 734

Subject lndex s e e also human capital organizational 700, 701 physical 678-683, 701, 710, 713, 714, 721, 732 specific 1154 stockof 1629, 1630, 1632, 1633, 1636-1638, 1648, 1652, 1656 target 820 unmeasured 701,702 vintage 702 capital accumulation 942, 1203 general equilibrium nature of 946 optimal 946 perpetual inventory method 944 capital budgeting 1623 capital controls 1588 capital imbalances, establishments' 837 capital hltensities 641,644, 679, 680, 682, 685, 686 capital investment decision 1349 capital/labor substitution 856 capital market imperfections 1648, 1649 see also borrowing constraint; credit market imperfections capital taxation 166i, 1708 optimality of zero 1693 capital utilization 848 CARA utility 794 cash-in-advance constraint 397, 1722 cash-credit model 1720, 1721 "catching up with the Joneses" 1284 certainty equivalence 762 Chamley result 1698 characteristics model 578, 579, 582, 602 characterization of equilibria 487, 489 Chotesky factor 80 classification 262, 289, 303 classifier systems 465, 523 closed economy 1714 closed-form solution 769 club-convergence 660 Cobb-Douglas production function in RBC model 944, 950 "cobweb" model 456 coefficient of relative risk aversion 1249 cohort data 781 cohort effects 576, 577, 590-592, 617, 753, 754 cointegration 50, 750, 820, 838, 877-881, 885 887, 903, 1266 collateral 857

Subject Index

commitment 574, 575, 1488, 1523 technology 1688, 1723 vs. flexibility 1489 commodity space 1686 comparative advantage 547, 548, 577-579, 584, 587 comparative dynamics measured by impulse response 967, 968, 970 competitive equilibrium 844, 845, 1677, 1688, 1722 competitive trajectory 650 complementarity 1161 complements 599, 601,611-613, 855 complete markets 553, 558, 563, 595, 602, 786, 1688 computation of (approximate) solutions 525 computational general equilibrium (CGE) 705, 708 computational intelligence 465 computational tool 455 conditionally linear dynamics 475,481 conditioning 556, 594, 597-599, 601,605, 612, 613 consistent expectations equilibria 529 constant returns to scale 639, 83l, 1687 in RBC model production function 995 consmner expectations 45 consumer theory 603 consumer's budget constraint 1264, 1712, 1728 consumption 40, 545, 546, 548-558, 560-564, 566, 567, 572-576, 587, 590, 594-603, 605 614, 616, 621, 1276 behavior in US business cycles 938 empirical 1344 estimates 605-6t4 'excess' sensitivity 524 growth 1233, 1242, 1276 inequality in 797 pemlanent-income hypothesis 943 private 1687 procyclical 433 M35 smoothing 805 in RBC model 967 fime-averaged data 1242 consumption-based asset pricing 1249 consumption expenditare 745 Consumption Expenditure Survey (CEX) 750 consumption per capita 643 consumption taxes 1692 contract multiplier 1028

1-35 contractual problems 849 control rights 852 control variables 688, 689 convergence 240, 245-2'76, 284-288, 290, 295, 296, 659 global 486 local 519 probability of 480 speed of 531,659 convergence analysis 454, 477M79 convertibility 153, 160 convertibility rules 209, 213 convex adjustment costs 818, 823 coordination failures 461 coordination of beliefs 391 corner solutions 804 cost of capital 817, 1344 cost shifters 906, 912 cost shock 867, 884, 899, 907, 908, 912 Costa Rican tariff reform 707 costly state verification 1349 creative destruction 848, 1210, 1213 credibility 1536, 1603 credit chains 1378 credit constraints 856 credit market 847 imperfections 1343 see also borrowing constraint; capital market imperfections segmentation 1575, 1577 cross-country regression 276, 281 cross-section least-squares regression 269 cross-sectional density 840 of establishments' capital imbalances 837 cross-sectional growth regression 252, 269 273, 275, 276, 284~289, 671,675, 694 literature 688 crossover 522 crowding out 1632, 1633, 1636, 1638, 1648, 1652, 1654 currency crises 1534 current account deficit 1598 Cmxent Population Survey 796 curse of dimensionality 843, 847 customer markets 1120 cycles 460, 507, 509, 526, 865 deadweight loss 1631, 1632, 1639, 1640, 1662 debt contract 1350 debt-deflation 1372

1-36 debt neutrality 1644 deb~income ratio 1630 debt-output ratio 1619 decentralized economy 547, 575, 576, 602 decision rule 888-890 deficits 1617 nominal 1621 real 1621 demand shocks 865, 884, 889-892, 895, 898, 1055 demographic transition 658 demographic variables 793 demographics 547, 551 615, 744 and retirement behavior 758 depreciation 642, 1633 detrending and business cycle measurement 932 difference models of habit 1284 difference-stationary models 764 difference-stationary process 211,215, 1497 differential equation 472 diminishing returns 639 separately to capital and augmented labor 653 dirty floating 1587 discount factor 548, 555-557, 561, 567, 588, 595, 606, 607, 609, 610, 616 disinflation, output costs of 1542 disiunction effect 1324 disparity in GDP 675 disparity in incomes 674 distribution dynamics 263,290-295, 299 distribution of country incomes 674 distribution of relative GDP 674 dividend growth 1233, 1242, 1276 dollarization t589 domestic debt 1595, 1601 domestic policy regime 153, 202 Dornbusch-type model 502 DSGE, see dynamic stochastic general equilibrium models durability 798, 1242 durable goods 549, 746, 799, 1550, 1552, 1573, 1575 dynamic economic models 312, 313 Dynamic New Keynesian (DNK) framework 1346 dynamic programming 834 dynamic stochastic general equilibrium (DSGE) models 930, 1139, 1145, 1150, 1157, 1166

S u b j e c t Index

models with job search

1158

earnings 546, 567-573, 577-588, 592, 593, 598, 605, 615, 623 s e e also wages structural equation 582 variance 569-572, 578, 586 econometric approaches 237 economic growth 1617, 1641, 1651 economic relationship 852 education 577, 578, 580, 584, 602, 607, 609, 613,615, 622, 623,653 eductive approaches 462, 464 effective labor 650 efficiency of termh~ations 1152 efficiency units 566, 658 s e e also labor in efficiency units efficiency wages 577, 578, 1098, 1157, 1159, t 160 efficient equilibrium 854 efficient markets 1307, 1308, 1316, 1319 1322, 1333 elastic labor supply 1145 elasticity 545, 546, 550-552, 563, 579, 580, 592-594, 596-601,605, 607, 610, 614-617, 620 of capital supply 1714 long run 838 of demand, varying 1119 of intertemporal substitution 552, 557, 561, 564, 597, 600, 601,614, 615, 769, 791, 1148, 1250 of investment 857 of labor supply schedule 1147 of substitution 645 election 522 embodied technology 1207 embodiment-effect 664 employment 39 employment contract 1153 employment fluctuations 1173, 1194 enaployment protection t215, t217 employment relationship 1157 endogenous fluctuations 506, 531 endogenous growth models 238, 241,243,245, 257, 259, 261, 264, 265, 269, 271, 297, 506, 651,653, 1711 entry 1067 variable 1125 entry and exit 551,602, 615,616, 824, 844 envelope theorem in RBC model 998

1-37

Subject Index

"episodic" approach 1560 e-SSE 520 Epstein-Zin-Weil model 1259 equipment 840 equity premium puzzle 1234, 1245, 1249, 1250 error correction model 750 E-stability 463, 466, 468, 471~473,488, 490, 491,504, 511 iterative 463 strong 473, 483, 491,512 weak 473,483, 512 Euler equation 314, 345~47, 349-352, 354, 355, 364, 368, 371, 373, 374, 381, 382, 555-558, 566, 567, 575, 597, 598, 606, 607, 609, 611,621,650, 765, 767, 794, 805 undistorted 1713 Euler equations 745, 791 excess bond returns 1276, 1277, 1280 excess sensitivity 772, 784, 785, 790 excess smoothness puzzle 747 excess stock returns 1249, 1276, 1277 excess volatility 1319, 1320 excessive destruction 856 exchange rate 527, 531, 1658 anchor 1588 and markups 1122 arrangements 167, 203 exchange-rate-based stabilization 1535, 1543, 1553, 1559 empirical regularities 1546 existence of competitive equilibrium in RBC model 1002 exit, delayed 850 see also entry and exit exogenous growth models 261 exogenous technological progress 650 expectation functions 453, 461,464 expectational stability, s e e E-stability expectations, average 528 expectations hypothesis of term structure 1281 experience 582, 584, 590, 602 experimental evidence 530 exports 41 extensive margins 843 external effects 390, 399M01, 403--405, 424-427, 43l, 433435, 437 external finance premimn 1345 external habit models 1284 externalities in RBC model 1002

factor-saving bias 641 factors of production 909 Family Expenditure Survey (FES) 746, 750 family income 564, 569, 589 Federal Reserve I53, 168, 169, 172-182, 184-202, 219 feedback derivative 1510 proportional 1510 feedback rule 68, 71 feedforward networks 524 financial accelerator t 345 financial development 671,688, 692 financial markets, role in economic growth 1376 firing cost 1186, t214, 1222 fiscal authorities 1524 fiscal deficits 1538, 1594, 1604 fiscal increasing returns 416 fiscal policy 672, 692, 694, 712, 715, 1580, 1617, 1624 countercyclical 1617, 1660 fiscal theory of price-level determination 1520, 1524 fixed costs 390, 426, 435, 828, 848, 911 flow-fixed costs 831 fixed effect 787 flexible accelerator 816, 865, 893, 903 flexible cyclical elasticity 842 flexible neoclassical model 817 floating exchange rate 1582 fluctuations in aggregate activity 547, 549, 552, 556, 569, 1053 see also business cycles induced by markup variation 1055, 1104 France 45 free entry condition 844, 845 fYictionless neoclassical model 817 Friedman rule 1720 Frisch demands 595 597, 603 Frisch labor supply 1146 full-order equilibrium 530 functional forms 550, 583,584, 588, 598, 601, 607, 611,623 fundamental solution 498 fundamental transformation 852 gain sequence 469, 475 decreasing 469 fixed 469 small 470

1-38 general equilibrium 543-625, 888 generational accounting 1624 genetic algorithms 465, 521,525 Germany 45, 1631 global culture 1332, 1333 GLS 788 gold standard 153-190, 199-220 Golden Rule 1650 Gorman-Laneaster technology 800 government budget constraint 1687, 1719 consumption 671, 69l, 694, 1687, 1736 rate to GDP 688, 689 debt 16t7, 1687 production 672, 695, 701 production of investment 699 purchases 41 purchases and markups 1120 share 692 in GDP 671,689 in investment 695, 696 in manufacturing output 696 in output 693 gradual adjustments 823 gradualism 849 Granger causality 34 Great Depression 153, 163, 175, 178, 180-184, 199, 200, 213, 1343 Great Inflation of the 1970s 153 great ratios of macroeconomics 939, 940 gross domestic product (GDP) per capita 674 per worker 671 gross substitutes 1731 growth cycles 9 growth accounting 678, 687, 688 growth miracles in East Asia 709 growth-rate targets 1524 maximum growth rate 677, 726, 728, 732 habit formation 798, 802, 1237, 1284 habits 564, 802 Harro4-Domar models 640 hazard rate constant 839 effective 836 increasing 840 hedging demand 1275 Iterfindaht index 824 heterogeneity 546, 547, 552, 553

Subject Index

in firms 1366 in learning 527 in values of job matches 1152 of preferences 545, 558, 563 unobserved 779, 831 heterogeneous agents 843, 1237, 1290 heterogeneous consumers 1686 Hicks composite commodity 766 Hicksian demand decomposition in RBC model 971 hiring rate 1161 histogram 840 historical counterfactual simulations 1523 history-dependent aggregate elasticity 841 Hodrick-Prescott filter, see HP filter hold-up problems 852 home production 402, 417, 431,702 home sector 435 homotheticity 1725, 1728, 1733 Hotelling's rule 657 HP (Hodrick-Prescott) filter 12, 932, 933 human capital 527, 546, 547, 576, 577, 583-592, 594, 639, 653, I638, 1712 hump-shaped impulse responses 405, 436, 1374 hump-shaped profiles 755 hyperinflation (seignorage) 509, 520, 531, 1631 hysteresis and threshold effects 455, 530 i.i.d, model 1739 identification problem 75-78 global identification 76, 77 local identification 76 undefidentification 76, 77 idiosyncratic risk 795, 1290 idiosyncratic shocks 840 in productivity 1183 imbalances 826 imperfect competition 665 implementability constraint 1677, 1689, 1719, 1729 implicit collusion 1123 imports 41 impulse 1140 impulse response measure of comparative dynamics 967 to productivity in RBC model 967 impulse response functions 74, 81, 85, 86, 90, 98, 100, 102, 107, 110, 112, 133, 140, 397, 41t, 430, 431,880, 894

Subject Index inaction range 832 Inada conditions 645 income distribution, cross-country 671 income elasticity 1681 income inequality 797 income processes 569, 574, 610 income tax 672 income uncertainty 1652 incomplete contracts 853, 854, 856 incomplete markets 566-576, 1742 indeterminacy 491, 494, 506, 1161, 1506, 1691 nominal 418, 1506, 1524 of price level 215, 216, 415, 4t7, 419, 423 real 413, 415, 416, 418, 419, 423 indicator, cyclical 1062 indivisible labor model, role in RBC model 977 industry equilibrium 888,889 inequality 745, 795 infinite-horizon consumption program 647 inflation 42, 1534, 1536, 1630 and business cycles 939 and markups 1128 inertia 1562 level 198 persistence 166, 211,213-215 rate 1738 autocorrelation 1738, 1739 variability 207 inflation correction 1621 inflation forecast targeting 1504 inflation-indexed bonds 127t inflation-indexed consol 1269 inflation targeting 1499, 1505 vs. price-level targeting 1497 inflation tax 1538, 1720 inflationary expectations 1281 intbrmation externality 849 information pooling 849 information set 455 informational problems 849-85 i, 858 infrequent actions 825 instability 481,519 of interest rate pegging 514 of REE 507 institutional faetors 852 instrument feasibility 1507 instrument instability 1517 instrument variable 1492, 1524 instrm~ental variables (IV) estin~ator 787

1-39 instrumental variables (IV) regression 1261 insurance 745, 795 integrated world capital market 1297 interest rate 43, 1620, 1621, 1629, 1630, 1634, 1635, 1637, 1639, 1648, 1652, 1653, 1657 1659 nominal 1524 interest rate instrument t514 interest rate policy 1596 interest rate smoothing 1509 intermediate-goods result 1684, 1720, 1733 intermediate-goods taxation 1676 intermediate input use 1081 internal habit models 1284 international capital flows 1636 1638 International Financial Statistics (IFS) 1238 international reserves 1594 intertemporal allocation 761 intertemporal budget 555, 561,647, 661 intertemporal budget constraint 1259, 1268 intertemporal CAPM 1275 intertemporal channel 1142 intertemporal elasticity of labor supply 1149 of substitution in leisme 1147 intertemporal marginal rate of substitution 1245 intertemporal non-separabilities 775 intertemporal optimization 745 intcrtemporal substitution 1055, 1150 "intervention" policy 1587 intradistribution dynamics 274, 292 intratemporal first-order conditions 775 inventories, target 894 inventodcs of finished goods 887 inventory fluctuations 1084 procyclical 872-882, 898, 900, 909 inventory investment 865 inventory-sales ratio 871 inventory-sales relationship 867 investment 40, 641 collapse 851 competitive equilibrium 844 delays 1365 distortions 672, 695-698 empirical 1344 expected 839 frictionless 832 lumpy 822, 823 share in output 693,699 spike 823, 824, 857

1-40 investment (eont'd) tax incentives 843 US manufacturing 840 investment episode 823 investment output ratio 714 irrational expectations 1237, 1293 irregular models 490, 493, 505 irreversibility constraint 832 irreversible investment 822, 828, 832 iso-elastic utility function 606, 607, 610 Italy 1619 Ito's lenmla 825 Japan 45 Jensen's inequality 1247 job-finding rate, cyclical behavior of 1162 job loss 1151 job search t143, 1150, 1158, 1162 job-specific capital I152 job to job flows 1198, 1200 job-worker separations 1184 jobs creation 846, 1150, 1158, 1161, 1173, 1176, 1178, 1185, 1201, 1219 cost 1187, 1193, 1215, 1222 creation and destruction, international comparison 1178 destruction 846, 1150, t 158, 1160, 1166, 1173, 1176, 1178, 1185, 1197, 1201, 12t9 rate 1151, 1152 flow 1197 international comparison 1180 reallocation 1222 termination 1152 cost 1193 joint production 853 joint surplus 1157 just-in-time 871 Kaldor facts about economic growth 941 Keynes, J.M. 1660 Keynesian analysis [ 628 Keynesian consumption function 761 Kreps-Porteus axiomatization 744 Krugman model 1592 Kuhn Tucker multiplier 774 labor 1687 bargaining strength 1219 labor-augmentation 651

Subject Index

labor contract 1154 labor force 1174 labor force status 602, 603, 607, 611, 614, 623 labor hoarding 1076, 1078, 1097 labor in efficiency units 650 see also efficiency units labor income 1237, 1275, 1290 labor market 855 policy 1214 restrictions 672, 695 labor power 1220 labor productivity 42 labor regulations 852 labor share 1059 labor supply 546-553, 562, 577, 585, 587, 592, 594, 596, 598, 599, 601,602, 605, 606, 608, 610 62l, 623, 744, 777, 792, 1150, 1296 elasticity 975, t371 in RBC model 975 empirical 1148 endogenous in RBC model 945 extensive margin 976 female 6 t 1 fixed costs of working 976 indivisible labor model 976 male 611 substitution effect 975 unobserved effort of 930 labor tax rate, autocorrelation 1739 lack of credibility 1569, 1572, 1581 Latin America 1543 laws of large numbers 837 leading example 488, 493 learning 453,488 by doing 664 in games 475 in misspecified models 528 least squares learning 465,467, 526 social 849 stability under 496 statistical 493 lean~ing dynamics, persistent 455 learning equilibria 515 learning rules 439, 454 econometric 472 finite-memory 474 fixed-gain 51 I statistical 465 learning sunspot solutions 494 learning transition 531

Subject Index

Legendre--Clebsch condition 904 levels accounting 678-687 leverage 1280 life cycle 583, 586-588, 593, 595, 601, 603, 604, 609, 615, 620, 621, 744, 749, 752, 754, 760, 792, 793 life cycle-permanent income model 760 life expectancy 691-693 lifetime budget constraint 647 see also intertemporal budget likelihood function 840 linear allocation rules 554, 563, 564 linear commodity taxes 1677 linear filter l 1 linear model 467, 487, 842 with two forward leads 501 linear-quadratic model 457, 865, 876, 882, 903, 904 liquidity 1255, 1591 liquidity constraints 745,772, 773, 789, 1654 see also borrowing constraint liquidity variables 817 log-linearization 788 long-term bonds 1255, 1280 low-equilibrium trap 646 Lucas aggregate supply model 457 Lucas critique 1491 Lucas program 67 lumpy project 823 Lyapunov theorems 479 M2 44 M1 velocity 50 machinery, price of 696 macroeconomics 639 magical thinking 1328, 1329 maintenance 823 maintenance investment 839 major and infrequent adjustments 823 managed float 152, 153, 167, 202, 204, 207 manufacturers 870 marginal cost schedule 1054 declining 1066 marginal production costs 867, 890, 892, 896, 899, 902, 905, 907 marginal profitability of capital 830 marginal rate of substitution 549, 551,554-557, 559, 560, 598, 622, 765 heterogeneity 620-623 marginal utility 767 market capitalization 1239

1-41 market clearing 1021 I024, 1026, 1035 expected 1021, 1024-1027 market imperfection 390, 405, 424, 426, 433 market structure 546, 553, 558, 575, 598 market tightness i 185 market work 550, 594, 601 Markov chain 1708, 1736 Markov process 1264 markup 399, 400, 406, 407, 426, 429, 431, 1053 average 1068 countercyclical 406, 1113 for France 1068 cyclical 1092 desired 1056 measurement 1058 models of variation 1055, 1112 procyclical 1113, 1128 variable 406, 407 variation in desired 1129 Marshallian demands 597 martingale 767 martingale difference sequence 487 match capital 1152 matching function 1183 matching model 1163 Maximum Principle 650 measure of financial development 691 measurement error 518, 546, 56I, 572 574, 609, 616, 1242 "mechanical" approach 1560 mechanism design 1154 Medicare 1622, 1626 men 550, 552, 607, 615, 620 mental compartments 1317 menu costs 397 microeconomic data 543 625, 745 microeconomic lumpiness 824 microfoundations 761 military purchases 1088 Mincer model 568, 569, 581,582, 584, 592 minimal state variable solutions, see MSV solutions mismatch 1221 mismeasarement of average inflation 1254 Modigliani-Miller theorem t343 monetary accormnodation 1539 monetary base 44, 1507, 1524 monetary economies 1720 monetary model with mixed datings 500

1-42

Subject & d e x

monetary policy 692, 695, 715, 1012, 102~ 1037, 1281, 1630, 1660, 1720 optimal, cyclical properties of t736 monetary policy rule 1364 monetary policy shocks 65-145 effect 69 on exchange rates 94-96 on US domestic aggregates 91-94 on volatility 123-127 identification schemes 68 70, 1369 Bernanke-Mihov critique 115-123 Bernanke Mihov test 11%121 empirical results 121 123 Coleman, Gilles and Labadie 114, 115 narrative approach 13(>141 see also Romer and Romer shock pitfalls 134 136 plausibility 100-104 assessment strategies 114-123 problems t43-145 interpretations 71-73 non-recursive approaches 127-134 output effects 1129 recm'siveness assumption 78-127 see also recursiveness assumption responses to 1368 monetary regimes 153, 168, 178, 202, 204, 211,216, 220 nmney 44, 1011 1013, 1020-1029, 1031-1033, 1035, 1036, 1040, 1041 money anchor 1588 money-based stabilization 1535, 1543, 1554, 1558, 1582 money demand 50, 598, 1603, 1736 consumption elasticity of 1725 interest elasticity of 1736 money growth rate 1738 money-in-the-utility-function model 1720, 1728

money supply 1536 money velocity 1588 see also M1 velocity monopolies 695 monopolistic competition 1033-1036, 1041, 1042 monotonicity 830 Morgan Stanley Capital International (MSCI) 1238 MSV (minimal state variable) solutions 488, 493, 502 and learning 503

locally (in)deternfinate 490 non-MSV solutions 493 multiple competitive equilibria 1679 multiple equilibria 1539, 1603 multiple REE, see under R E E multiple solutions 487, 1506, 1524 multiple steady states 460 multiple strongly E-stable solutions 501 multiplicity of steady states 658, 662 multivariate models 502 with time t dating 505 mutation 522 Muth model 465, 484, 525 myopia 1653, 1654 Nash bargain, generalized 1189 National Account 751,752 national accounting identities 1628 National Bureau of Economic Research (NBER) 6,8 national income 1617 national saving 1628, 1629, 1637, 1639, 1641, I652, 1659-1662 natural experiments 822 natural rate 1176 nalnral resources 639 negative income tax experiments 1148 neoclassical exogenous growth model 243,261, 673 neoclassical growth model 245, 246, 252, 259, 269, 272, 276, 639, 695, 697, 701, 1140 basis for RBC model 942 neoclassical theory of investment 817 net convergence effect 692, 693 net present value rule 835 net worth and the demand for capital 1352 neural networks 465, 524 neurons 524 noise case of small 513 intrinsic 507 noise traders 1290 noisy k-cycle 5/3 noisy steady states 483, 509 nominal anchor 207, 211, 215, 216, 1535, 1542, 1557 nominal income targeting 1505 non-durables 746 non-nested models 840 non-random attrition 787 non-Ricardian policy 418

1-43

Subject Index

non-Ricardian regime 418 non-separability of consumption and leisure 759 non-state-contingent nominal claims 1722 Non-Accelerating Inflation Rate of Unemployment (NAIRU) 46 nonlinear models 468 nonlinearity 828, 839 nonparametric techniques 532 numerical algorithms 320, 324, 326, 328, 348, 358, 378 numerical solutions 318, 326, 352, 805 obsolescence 848 OECD 685, 718, 719, 1174 OECD adult equivalence scale 757 oil prices, effects of 1089 one-sector model 639 one-step-ahead forward-looking reduced form 506 open economy 1714 open market operations 1722 openness 703 operationality 1486, 1523 opportunism 851,858 opportunity costs 854 optimal control 1490 optimal debt policy 1639, 1659, 1660, 1662 optimal fiscal policy 1686 optimal investment path 834 optimal national saving 1617 optimal tax theory 1692 optimal trajectory 650 optimal wedges 1692 optimum quantity of money rule 1537 option to wait 832, 834 ordinary differential equation (ODE) approximation 468, 478 orthogonality conditions 785 out-of-sanrple forecasting 840 out-of-steady-state behavior 649 output 1687 output levels 206 output variability 208, 211 overconfidence 1319-1323, 1325, 1326, 1328 overhead labor 1065 overidenfifying restrictions 768 overlapping contracts models 495, 1582 overlapping generations model 390, 395, 397, 398, 427, 458, 546, 549, 576-594, 660, 1634, 1635, 1645 1647

overparanletrization 473 overreaction 1319 1322 overtaking 650 overvaluation 1563

panel data 275, 283-287, 295, 781 Pareto weights 55%564, 796 partial adjustment model 821,838 participation 574, 601, 1218 path dependence of adaptive learning dynamics 455 peacetime 1699 Penn World Table 674, 680 pent-up demand 841 perceived law of motion (PLM) 466, 472, 490, 511 perceptron 524 perfect competition 831 perfect foresight 650 perfect insulation 846 perfect-insurance hypothesis 796 periodic or chaotic dynamics 646 see also cycles permanent-income hypothesis 749, 1641, 1662 permanent shocks 216-219 perpetual inventory method 680 persistence 870 882, 891, 893, 900, 902, 904, 1142, 1162, I166, 1739 of business cycles, see persistence under business cycles of fluctuations 527 of inflation 1537 peso problem 1252 pessimism 1295 Phillips cm've 46, 1056, 1363, 1542 planner's problem in RBC model 997, 1002 policy 455 affecting labor markets 672 distorting investment 695 impeding efficient production 672 policy accommodation 1538 policy ftmction 320-381 political rights 671,689 political stability 671,688, 692 Ponzi scheme 1650 population aging 1625, 1640 population growth 941 endogenous 639 power utility 1249

1-44 precautionary saving 744, 770, 1253, 1288, 1653 preference parameters 550, 555, 556, 558, 567, 601, 605 preferences 546-550, 552, 553, 556-558, 564, 565, 567, 572, 582, 593, 601, 604, 605, 607, 608, 610, 614, 616, 617, 623 additive 594 conditional 778 fimctional forms 550 Gorman polar 766, 783 heterogeneity 545, 552, 558-565, 567, 593, 594, 609, 621,623 homogeneity 553 556, 577 of representative agent in RBC model 942 quadratic 762, 770 present-value model of stock prices 1264 log-linear approximation 1265 present-value neutrality 573 price elasticity 1681 price functions 1723 price puzzle 97-100 price rules 1688 price-cost margin 1053 s e e also markup price-dividend ratio 1265, 1266, 1276 prices 42 of maclfinery 696 of raw materials 1082 pricing, equilibrium 555, 602, 845 primal approach 1676 primary budget 1619 principal-agent problems 1345 principles of optimal taxation 1676 private and public saving 1629 private information 574-576, 849 production costs, non-convex 897, 911 production economy 1686 production efficiency 1684, 1735 production function 548-550, 578, 579, 581, 583-586, 588, 590, 591,594 non-Cobb-Douglas 1064 production possibilities surface 401 production smoothing 876, 877, 884, 895, 1085 production to order 887 production to stock 887 productivity 552, 553, 566, 583, 602, 1057 cyclical 938, 1094 deterministic growth of 943 general 1192, 1193

Subject I n d e x

growth of 942 shocks 930, 943, 965, 972 amplification of 963 modeled as first-order autoregressive process 963 persistence of (serial correlation) 952, 963 RBC model's response to 964 remeasurement of 982 slowdown 664 profit function 830 profits 1057 cyclical 1100 projection facility (PF) 480 propagation of business cycles 865 propensity to constune 762 property rights 852, 856 proportional costs 825 proportional taxes 1687 prospect theol2¢ 1308 1313 protection of specific investments 1154 "provinces" effect 1540 proxies for capital utilization 1080 prudence 771 PSID 783 public consumption 1581 public debt 1601, 1603 public finance 1676 public saving 1629, 1641 putty-clay models 847, 848 q-theory

817 Tobin's q averageq 817,818 "flexible q" 818 marginal q 818 fragility of 828 quadratic adjustment cost model 823, 838 Quandt Likelihood Ratio (QLR) 34 quantitative perfunnance 1578, 1581 quantitative theory 671-673, 695-719 see also dynamic stochastic general equilibrinm models quasi-magical thinking 1329, 1330 see also

Ramsey allocation problem 649, 1679, 1691, 1692, 1713, 1719, 1723, 1729 Ramsey equilibrium 1678, 1688, 1723, 1'729, 1732 Ramsey growth model 1651, 1652 Ramsey prices 1679

1-45

Subject Index

random walk 767, 1316, 1319, 1702, 1706, 1738, 1742 geometric 825 range of inaction 826 rate of arrival of shocks 1193 rate of discount 1193 rate of return 566, 577, 582, 595, 606, 610 ratio models of habit 1284 rational bubbles 499, 1266 rational expectations 453 transition to 454 rational learning 461 rationalizability 464 rationing 857 RBC models, see real business cycle Reagan, R, 1641 rea~ balance model 489, 496 real business cycle (RBC) 394, 402, 413,427, 428, 437, 442, 505, 843, 928, 1296 amplification of productivity shocks in 958, 967 as basic neoclassical model 942 baseline model 1143, 1709, 1736 failures 1144 calibration 953-955,959 competitive equilibrium 999 concave planning problem 1002 contingent rules 1000 criticisms 961 depreciation rate of capital 944 discount factor 942 modified 945 endowments in 943 cxtensions 994 firm's problem 1001 government spending and taxes in 974 high risk aversion model 1709 high-substitution version calibration 985, 987 decision rules for 985 ingredients of 984 probability of technical regress 989, 990 role of capacity utilization in 985 role of indivisible labor in 985 sensitivity to measurement of output 992 sensitivity to parameters 990, 991 simulation of 986 household's problem 1000 importance of consumption smoothing in 967

Inada conditions on production function 996 interest rate effects 973 internal propagation in 967 labor demand for 956 supply of 956 Lagrangian for 946 lifetime utility 996 market clearing 1001 production function in 943 RBC model as basic neoclassical model 942 simulations of 957 solution certainty equivalence 952 dynamic programming 951 linear approximations 949 loglinear approximations 952 rational expectations 951 steady state of 947 transtbrmation to eliminate growth 944 transitional dynamics of 948 transversality condition for 946 wage effect in 973 wealth effects in 971 with nominal rigidities 974 real exchange rate 1547 real interest rate 1220, 1233, 1276, 1286 measurement of 939 real marginal cost 1053 real shocks 1174 real wage 1296 reallocation of workers 1160, 1183, 1199 recession now versus recession later 1535, 1557 recursive algorithm 468, 475, 479, 486 recursive least squares 467 recursive least squares learning 494 recursive utility 557 recursiveness assumption 68, 73, 78 127 benchmark identification schemes 83 -85 F F policy shock 87, 88 influence of federal funds futmes data 104--108 NBR policy shock 88 NBR/TR policy shock 89 problems 97 results 85 robustness 96, 97 sample period sensitivity 108 1i4

1-46 recursiveness assumption (cont'd) relation with VARs 78-83 REE (rational expectations equilibria) 452 cycles 458 multiple 454, 467 reduced order lhnited information 529 unique 484 reflecting barriers 828 regime switching 426 regression tree 289 regular models 490 regulation barrier 832 relative price of inves~lent to consumption 696 698, 700, 701 reluctance to invest 828, 832 renegotiation 1153, 1t55 renewable/nonrenewable resources 655,656 rental prices 588, 590, 592 of capital 1000 reorganization 1160, 1161 representative agent 556, 557, 560, 561, 563, 587, 601, 838, 1249, 1259, 1268 in RBC model altered preferences in indivisivle labor 977 altruistic links 943 preferences of 942 representative household 643 representativeness heuristic 1319, 1322, 1327 reproduction 522 research and development (R&D) 664, 672, 692, 695, 708, 709, 715-7!9 residence-based taxation 1715 restricted perceptions equilibrium 529 restrictions in job separation 1222 restrictions on government policy t707 retailers 869 retirements 839 returns to scale 639 decreasing 656 increasing 652, 653,664, 828, 830, 1066 social 460, 509, 521 Ricardian equivalence 418, 1617, 1640 1659, 1661 Ricardian regime 418 Ricardo, D. 1640 risk 546, 547, 552, 554-558, 563 567, 569, 572, 575,593,606 risk adjustment 555, 557, 558 risk aversion 547, 552, 556 -558, 564-566, 606, 771

Subject Ndex risk premium 1246, 1247, 1250 risk price 1236, 1280 risk-sharing in indivisible labor version of RBC model 977 riskfree rate puzzle 1235, 1252 robustness approach 1491, 1523 Romer and Romer shock 137-142 rnte-like behavior i487, 1522 rule-of-thumb decision procedure 524 rules I52-154, 156, 158, 160, 166, 168, 184, 200, 208, 219, 220 rules vs. discretion 1485 Rybczinski theorem 404 (S, s) model 801,802, 831,910, 911 sacrifice ratio 1541 saddle point 405, 649 saddle point stability 490 Sargent and Wallace model 489 saving 641 private 1628, 1629, 1632--1634, 1637, 1641, 1648 'saving lot a rainy day' equation 764 scale effects 672, 715, 716, 718, 719 school attainment 691 school enrolhnent 681,684 post-secondary 683 primary 683 secondary 68l.-683 schooling 576 578, 581 592 sclerosis 856 scrapping 844, 847, 855, 856 endogenous 844 search and matching approach 1173, 1183 search efficiency 1162 search equilibrium 1186 search externalities 506 seasonal adjustment 1242 seasonal variations in work volulne 1149 second-best solutions 849 secondary job loss 1163 sector-specific external effects 402 sectoral shifts hypothesis 1221 securities market 1722 seignorage model 460, 471, 509, 525, 530, 1741 selection criterion 468 selection device 454 self-fulfilling fluctuations 506 separability 556, 602, 603, 607, 608, 612, 613, 617, 1725, 1728, 1733

Subject lndex

tests 611 separation rate 1151 Sharpe ratio 1249 shock absorber 1699, 1710, 1739 shock propagation 1203 shocks and accommodation 1539 shopping-time model 1720, 1732 shopping-time monetary economy 1732 short-term bonds 1280 shurt-tenn maturity debt 1603 o-convergence 659 Sims Zba model 128-134 empirical results 131-134 skill-biased technology shock 1215, 1216, 1218 skills 546, 547, 569, 576-579, 581,582, 584, 586-588, 590-594, 623 slow adaption 480 slow speed of adjustment 8"77,894 small durables 798 small open economy 1715 small sample 820 small versus large finns t373 smooth pasting conditions 827 Social Security 1619, 1622, 1624, 1626, 1635 Solow residual 930, 1140, 1141 as productivity measure 962 in growth accounting 962 mismeasurement 962 solvency conditions 575 specificity 851,852, 856 spectral analysis 11 SSE, see stationary sunspot equilibria stability conditions 454 stabilization 1534, 1562 stabilization goals 153 stabilization time profiles 1547 stable equilibrium point 481 stable roots 393 staggered contracts model 1012, 1013, 1024, 1027, 1030, 1032, 1039 staggered price and wage setting 1012, 1013, 1027, 1030, 103t, 1033, 1035-1037, 1040 staggered price setting 397, 422, 423, 1129, t363 staggered-prices formulation t582 standardized employment deficit 1621 state-contingent claims 555, 602 state-contingent returns on debt 1687, 1699 state-dependent pricing 1031, 1032 state dynamics 477

1-47 state prices 1294 stationary distribution of RBC model 999 stationary sunspot equilibria (SSE) 408, 517 e-SSE 517 near deterministic solutions 520 steady states 468, 507, 525, 549-551,576, 592, 598, 639 of RBC model 944 sterilization 1595 sticky price models 503, 1113 stochastic approximation 468, 475, 476 stochastic discount factor 1234, 1245 log-normal 1246 stochastic growth model 546 577, 592 stochastic simulations 1516, 1523 stock market 1310, 1312, 1313, 1315, 1316, 1320-1328, 1331, 1333 stock market volatility puzzle 1235, 1236, 1268, 1276, 1280 stock prices 43 stock return 1233, 1240 stockout costs 884, 885 Stolper-Samuelson theorem 404 Stone price index 783 storage technologies 574, 575 strategic complementarity 1129 strategic delays 858 strong rationality 464 structural model 462 structural shifts 530 structalres 840 subgame perfection 1679 subjective discount factor 548, 552, 561, 593, 595, 609, 616 subsistence wage 657 substitutes 577, 590, 591,613,616 sm~ costs 858 sunspot equilibria 454, 515 sunspot paths 662 sunspot solutions 495 see also learning sunspot solutions sunspots 489, 515 supply of capital 846 supply price of labor 1192, 1193 supply shocks 1129 supply-side responses 1577 surplus 853 surplus consumption ratio 1286 survivorship bias 1242 sustainability 1597

1-48 T-mapping 467, 471,512 Tanzi effect 1741 target points 826 target variables 1492, 1523 tariff 672, 695, 703-707 taste shift 778 tax see also labor tax rate; capital taxation distortionary 165l, 1652, 1654 on capital income 1686 on employment 1220 on international trade 703 policy 672, 708 rate 1441 on private assets 1709 reforms 822 smoothing 1655, 1659, 1662, 1705 intertelnporal 1617 source-based 1715 system 1679 Taylor expansion 1265 Taylor rule 1364 technological change 1708 technological embodiment 848 technological progress 641, 1207, 1213 disembodied 1207, 1208 endogenous 639 Harrod-neutral, Hicks-neutral 944 labor-augmenting 944 purely labor-augmenting 650 techimlogical regress, probability of in RBC models 930 technology adoption 672, 708 technology shocks 1141, 1142, 1736 temporariness hypothesis 1569, 1572 temporary shocks 216 temporary work 1165 term premimn 1255 term structure of interest rates 1270 termination costs 708 thick-market externality 1161 threshold externalities 527 thresholds 258-262, 276, 289 time-additive utility function 661 time aggregation 881 time-consistent behavior 1488 time dependency 799 time-dependent pricing 1031, 1032 time-inconsistent behavior 1653 time preference 547, 588 time preference rate 1253

Subject Index

time series 264, 272, 287, 288 time series volatility 756 time to build 832, 850 time-vary/ng aggregate elasticity 841 timing assumption 469 Tobin's q 817, 1296 see also q-theory total factor productivity (TFP) 42, 673, 678, 687, 688, 702 trade deficit 1630, 1658, 1659 trade policy 672, 692, 694, 702 training 577, 582-584, 586-592, 653 transition rates 1166 transversality conditions 392, 393,400, 650 Treasury bills 1233 trend-stationary models 764 trend-stationary process 10, 211, 1497 trigger points 830 tuition costs 583, 588, 590 twin deficits 1630 two-stage least squares estimation 1261 tmcertainty 545-547, 556, 558, 564, 566, 567, 569, 572, 574, 575, 593, 605, 606, 620, 621,623,744, 1627, 1653 underinvestment 852, 854 underreaction 1319-1322 unemployment 546, 569-571, 578, 579, 1143, 1150, 1158, 1161, I162, 1173, 1174, 1194, 1214 experiences of OECD countries 1213 natural level 1157 rise in 1182 serial correlation 1163 unemployment compensation 1217 unemployment income 1214 unemployment inflow and outflow rates 1181 unemployment rates 1176 unemployment spell duration hazard 1184 tmemployment-skill profile 1216 unified budget 1619 uniform commodity taxation 1676, 1726 union bargaining 1098 uniqueness of equilibrium in RBC model 1002 unit root 11 United Kingdom 45 tmivariate models 488, 497 unstable equilibrium point 481 utility function 548-550, 556-558, 560, 594, 596, 597, 599-601,606, 607, 610

1-49

Subject Index

momentary in RBC model 944 offsetting income and substitution effects 944 utility recursion 557 utilization of capital 1079 vacancies 41, 1194 vacancy chain 1200 vacancy dmation hazard 1184 value function 319-327, 329, 335, 336, 340, 345, 351-355, 357-359, 365,368, 378 value matching 827 variable costs 828 variety, taste for 705 vector autorcgression (VAR) 73,438 definition 73 vintage capital models 847, 848 volatility employment 1157 inventories 869, 870 monetary aggregates 1599 vote share 1455 wage bargaining 1130 wage contract 1173, 1186 wage inequality 1182, 1214, 1218, 1219

wages 42, 547, 550-553, 556, 566-569, 572, 577-579, 581,587, 593, 595-601,603-607, 611, 612, 616, 617, 619, 621, 623, 1181, 1629, 1637 see also earnings cyclical 939 equilibrium 556 fixed 1157 marginal 1069 rigidity 1055 war of attrition 1540 wars 1619, 1642, 1656, 1661-1663, 1699 wealth distribution 556, 561,567, 572, 593 wealth-output ratios 1240 wealth shock 1372 welfare costs of macroeconomic fluctuations 1297 welfare theorems, role in RBC analysis 1001 wholesalers 869 within-period responscs 599 women 550, 552, 607, 615, 620, 623 worker flows 1180 into unemployment 1164 worker turnover 1176 works in progress inventories 887 yield spread

1256, 1280