Exchange Rate Volatility, Trade, and Capital Flows under Alternative Exchange Rate Regimes (Japan-US Center UFJ Bank Monographs on International Financial Markets)

Exchange Rate Volatility, Trade, and Capital Flows under Alternative Exchange Rate Regimes Recent years have seen a substantial increase in the volatility of exchange rates. This trend has prompted economists and financial analysts to question if the observed behavior of exchange rates is consistent with a rational model. Does that volatility, further, hinder trade? What are financial markets' effects on countries' investment decisions, and how would changes in fixed exchange rates affect growth and welfare? What are the requirements to make such changes feasible? Professors Sercu and Uppal examine these issues in the context of dynamic generalequilibrium models, explicitly considering the role of financial markets while allowing for commodity markets to be segmented across countries. They show that the theoretical models for exchange rates in this context are quite different from those put forth by monetary theorists and proponents of purchasing power parity arguments. The authors also find that an increase in exchange rate volatility may be associated with either an increase or decrease in trade, and they conclude by identifying the particular conditions under which a regime of fixed exchange rates maximizes welfare. Piet Sercu is Professor of International Finance at the Catholic University of Leuven. He has also taught at the Flemish Business School in Brussels and held visiting professorships at Cornell and New York Universities, the University of British Columbia, and the London Business School. Professor Sercu served in 1995 as President of the European Finance Association and was awarded the 1996 Francqui Chair of Economics at FUNDP, Namur, Belgium. He has published in journals such as the Journal of Finance, Journal of Banking and Finance, and Journal of International Money and Finance and is the coauthor with Raman Uppal of International Financial Markets and the Firm (1995). His current research focuses on general equilibrium models of exchange rate pricing, international trade and consumption, and forward and future markets. Raman Uppal is Associate Professor in the Faculty of Commerce and Business Administration, University of British Columbia, and has served as Visiting Professor of Finance at the Catholic University of Leuven and at the Sloan School of Management, Massachusetts Institute of Technology. His recent research focuses on understanding how market imperfections affect the welfare of investors, their optimal portfolios and hedging strategies, aggregate trade and capital flows, and exchange rate and other asset prices. He is coauthor with Piet Sercu of the above-named text, and Professor Uppal's articles have appeared in journals such as the Journal of Finance, Journal of Financial and Quantitative Analysis, Journal of International Money and Finance, and Review of Financial Studies.

Japan-U.S. Center Sanwa Monographs on International Financial Markets Selection Committee Ryzuo Sato, New York University (Ex Officio Chairman and Editor) Akiyoshi Horiuchi, University of Tokyo Paul Krugman, Massachusetts Institute of Technology Marti Subrahmanyam, New York University James Tobin, Yale University Richard Zeckhauser, Harvard University The Sanwa Bank has established "The Sanwa Bank Research Endowment Fund on International Financial Markets" at The Center for Japan-U.S. Business and Economic Studies of The Stern School of Business, New York University, to support research on international financial markets. One part of this endowment is used to offer an award for writing a monograph in this field. The Sanwa award is made annually on a competitive basis by the Selection Committee, and the winning published titles and proposals are listed below. 1992, Richard C. Marston, University of Pennsylvania: International Financial Integration: A Study of Interest Differentials between the Major Industrial Countries (published 1995; paperback ISBN 0 521 59937 7) 1993, Willem H. Buiter, University of Cambridge, Giancarlo Corsetti, Yale University, and Paolo A. Pesenti, Federal Reserve Bank of New York: Financial Markets and European Monetary Cooperation: The Lessons of the 1992-1993 Exchange Rate Mechanism Crisis (published 1998; ISBN 0 521 49547 4, paperback ISBN 0 521 79440 4) 1994, Lance E. Davis, California Institute of Technology, and the late Robert E. Gallman, University of North Carolina, Chapel Hill: Evolving Financial Markets and International Capital Flows: Britain, the Americas, and Australia, 1865-1914 (ISBN 0 521 55352 0) 1995, Piet Sercu, Catholic University ofLeuven, and Raman Uppal, University of British Columbia: Exchange Rate Volatility, Trade, and Capital Flows under Alternative Exchange Rate Regimes (published 2000; ISBN 0 521 56294 5) 1996, Robert P. Flood, International Monetary Fund, and Peter M. Garber, Brown University: Speculative Attacks on Fixed Exchange Rates 1997, Maurice Obstfeld, University of California, Berkeley, and Alan M. Taylor, University of California, Davis: Global Capital Markets: Growth and Integration 1998, Pravin Krishna, Brown University: Regional Trading Blocs and Preferential Trading Systems 1999, Kose John, New York University: Corporate Governance and Agency Problems: Theory and Empirical Evidence

Exchange Rate Volatility, Trade, and Capital Flows under Alternative Exchange Rate Regimes Piet Sercu Catholic University ofLeuven

Raman Uppal University of British Columbia

CAMBRIDGE UNIVERSITY PRESS

CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521562942 © Piet Sercu and Raman Uppal 2000 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2000 This digitally printed first paperback version 2006 A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Sercu, Piet. Exchange rate volatility, trade, and capital flows under alternative exchange rate regimes / Piet Sercu, Raman Uppal. p. cm. — (Japan-U.S. Center Sanwa monographs on international finance markets) Includes bibliographical references. ISBN 0-521-56294-5 (hb) 1. Foreign exchange rates — Mathematical models. I. Title. II. Series. III. Uppal, Raman. HG3823 .S465 2000 332.4'5 21 - dc21 ISBN-13 978-0-521-56294-2 hardback ISBN-10 0-521-56294-5 hardback ISBN-13 978-0-521-03423-4 paperback ISBN-10 0-521-03423-X paperback

99-040246

To my parents, Jan Sercu and Therese Reynaert, and to my wife, Rita Mosselmans Piet Sercu

To my grandparents, Jaswant Singh and Gobind Kaur Raman Uppal

Contents

Acknowledgments Guide to Notation 1

2

3

page xiii xv

Introduction and Overview 1.1 Our Objective and the Contribution of Our Work 1.2 Outline of the Monograph and Summary of Major Results

1 1

Modeling Exchange Rates: A Survey of the Literature 2.1 Exchange Rates and National Price Levels 2.2 Spot Exchange Rates, Forward Exchange Rates, and Interest Rates 2.3 Exchange Rates and the Balance of Payments 2.4 Asset Models of the Exchange Rate 2.5 Exchange Rate Models with Microeconomic Foundations

5 6

A Simple General-Equilibrium Model of an International Economy 3.1 Motivation for the Modeling Assumptions 3.1.1 Advantages of the General-Equilibrium Modeling Approach 3.1.2 Modeling the Distinction between Nations 3.1.3 Monetary Policy and Exchange Rate Regimes 3.1.4 Advantages of the General-Equilibrium Approach for Empirical Tests 3.2 Details of the Basic Model of an Endowment Economy 3.3 Extension of the Basic Model to a Production Economy 3.3.1 The Dynamics of the Spot Exchange Rate 3.3.2 The Nominal Exchange Rate in the Production Economy 3.4 Other Extensions

2

9 11 12 15 17 17 17 18 22 22 23 29 32 33 34 ix

Contents

4

5

6

7

The Spot Exchange Rate in a Large Class of General-Equilibrium Models 4.1 The Economy and the Equilibrium Exchange Rate 4.2 Characterizing the Level of the Exchange Rate 4.2.1 The Exchange Rate under Homothetic, CRRA Utility 4.2.2 Purchasing Power Parity 4.2.3 Implications of the General Model for PPP Tests on First-Differenced Data 4.3 Empirical Tests of PPP 4.3.1 Review of the Empirical Methodology Used to Test PPP 4.3.2 Data 4.3.3 ADF and Cointegration Tests of PPP 4.4 Empirical Tests of the Model with Homothetic CRRA Utility 4.5 Conclusion Forward Exchange Rates in a Model with Segmented Goods Markets 5.1 Related Literature 5.2 Implications of General-Equilibrium Model for UIP in Real Terms 5.3 The UIP Relation in Nominal Terms 5.4 Conclusion International Trade Flows, Exchange Rate Volatility, and Welfare 6.1 Background and Related Literature 6.2 The Economy 6.3 The Relation between Trade and Exchange Rate Risk 6.3.1 The Effect of Output Volatility on Exchange Risk and Expected Trade 6.3.2 The Effect of Segmentation on Exchange Rate Volatility and Trade 6.4 Discussion of the Model and Its Implications for Empirical Work 6.5 Conclusion International Capital Flows and Welfare 7.1 The Risk-Sharing Gains from Financial-Market Integration 7.2 Other Sources of Gains from Financial-Market Integration

35 36 39 39 42 43 45 45 48 48 52 54 57 58 60 63 64 66 67 70 73 73 75 76 78 82 83 85

Contents

7.3 7.4

The Welfare Costs of Segmented Commodity Markets International Financial Flows 7.4.1 Determining the International Financial Flows 7.4.2 Analysis of International Financial Flows Conclusion

87 90 91 94 97

Tariff Policy with International Financial Markets 8.1 Optimal Tariff Rates and Financial-Market Integration 8.1.1 The Model with Endogenous Tariff Policy 8.1.2 Results on Optimal Tariffs 8.2 Tariff Policy, Financial Markets, and Welfare 8.3 Implications of Financial Markets for Policy Coordination 8.4 Conclusion

99 100 100 101 102

7.5 8

9

10

Endogenous Monetary Policy and the Choice of Exchange Rate Regime 9.1 Money and Exchange Rate Regimes: A Review 9.1.1 Money Demand 9.1.2 Money Supply and the Government's Economic Role 9.1.3 The Exchange Rate Regime 9.2 The Model 9.3 The Derived Utility of Absorption and Effects of Monetary Policy 9.3.1 The Derived Utility of Absorption 9.3.2 The Effect of Monetary Policy on Hiring and Production Decisions 9.3.3 The International Sharing Rule 9.3.4 The Nominal Exchange Rate 9.4 The Exchange Rate under Alternative Monetary Rules 9.4.1 An Idealized EMS: Fully Coordinated Monetary Policy 9.4.2 The Nash Game 9.4.3 Monetary Union 9.5 Conclusion

103 103 104 104 105 107 108 110 113 113 115 116 117 118 119 121 122 123

Concluding Thoughts

125

References Author Index Subject Index

129 147 151

Acknowledgments

Over the past ten years, our research effort has been devoted to understanding the behavior of exchange rates, the relation of exchange rates to interest rates, international trade and cross-country capital flows, and the effect on these variables of tariff and monetary policy. Given our focus on large developed economies, such as Japan, the United States, and countries in Western Europe, our view has been that the economic models used to analyze the relation between exchange rates and trade in goods and financial capital should be general equilibrium in nature rather than those of small open economies. In 1995, our proposal was chosen for the fourth Sanwa Monograph Award. In this monograph we present the results of our research based on general-equilibrium models, along with a description of related work on the analyses of exchange rates, trade flows, financial flows, and monetary policy in international economies. We gratefully acknowledge the support of the Sanwa Bank through its promotion of the Sanwa Monograph Program. We are particularly indebted to Professor Ryuzo Sato and Professor Rama Ramachandran of the Center for Japan-U.S. Business and Economic Studies at New York University for their encouragement. We would also like to acknowledge the help of two anonymous referees who made several suggestions for improving the substance and exposition of this monograph. While working on this research we received helpful comments from several individuals, whom we would like to thank: David Backus, Richard Baillie, Anton Barten, Suleyman Basak, Geert Bekaert, Martin Boileau, Jim Brander, Menzie Chinn, Marnik Dekimpe, Harris Delias, Mick Devereux, Glen Donaldson, Silverio Foresi, Ken Froot, Mike Gallmeyer, Geert Gielen, Robert Hodrick, Michelle Lee, Kai Li, Ronald MacDonald, Geert Rouwenhorst, Gonzalo Rubio, Gregor Smith, Frans Spinnewyn, Jim Storey, Rene Stulz, Linda Van de Gucht, Simon van Norden, Tom Vinaimont, Simon Wheatley, and seminar participants at Boston University, Carnegie Mellon University, Erasmus University, HEC School of Management, Catholic University of Leuven, Massachusetts Institute of Technology, Northwestern University, Universidad del Pais Vasco, University of Alberta, University of British Columbia,

Acknowledgments

University of Vienna, the 1995 meetings of the Center for European Policy Research, the 1995 and 1997 meetings of the European Finance Association and the European Financial Management Association, the 1996 conference on Exchange Rates at the National Bureau for Economic Research (NBER), and the 1995, 1996, 1997, and 1998 meetings of the Western Finance Association. We are especially beholden to Prakash Apte, Paul De Grauwe, Bernard Dumas, Burton Hollifield, Khang Min Lee, Maurice Levi, Vasant Naik, Cynthia Van Hulle, and Tan Wang with whom we have worked on issues related to those discussed in this monograph and from whom, in the course of this research, we have learned much. Raman Uppal was visiting Catholic University of Leuven and MIT during the course of this project and would like to thank these institutions for the hospitality extended to him. Finally, we would like to thank our home institutions, Catholic University of Leuven and the University of British Columbia, for providing us with a rich intellectual environment over the past ten years.

Guide to Notation

English Alphabet ck(t) ck](t) dki(t) F(t) F(t, t + 1) FP(t, t + 1) gk i j k K(t) Lk mk Mk nB(t) n Pk (t) Pk Pki(t) pkj{t) rk qk(t) RP(t, t + 1) S{t)

vector of consumption quantities ckj(t) of good j (=1, . . . , N) in country k consumption of good j in country k at time t the dividend paid by security /, in units of currency k net foreign investment account forward exchange rate at time t for a transaction at F{tJ

V(t)~S{t)'the f ° r w a r d exchange rate premium consumption of the government (public) good in country k subscript used to refer to a particular security subscript used to refer to a particular good subscript used to refer to a particular country (k = 1 is home country) stock of physical goods located in the home country at time t supply of labor (time spent working) in country k money supply in country k YlNj=\ ckj(t)Pkj(O, nominal spending in country k number of bonds owned by the domestic resident number of shares of the firm k owned by the domestic resident log Uk(t) the price of security / in units of currency k the local currency price of good j in country k the interest rate in country k the endowment in country k at time t E,[S{t+\)\-F{tj+\)^ t h e foreign-exchange risk premium nominal exchange rate (value of one unit of foreign currency)

Guide to Notation

Tk

uk V(Mkit), pk(t)) viMkit), pkit)) , Kiit)] wk Wit)

Z(t) Zkit) V[Ktit),

,t]

log of the nominal exchange rate for country k tax in country k time-additive utility function (with a constant discount rate) utility function of the representative investor in country k indirect utility of nominal spending in country k indirect utility of nominal spending in the linear homogenous case maximum undiscounted value of central planner's objective function wage rate in country k wealth of the home investor at time t amount of goods exported from country k cumulative amount of goods exported from country k quantity of private good that is used by government to produce gk the real exchange rate random white noise affecting the production process in country k maximum value of central planner's objective function

Greek Alphabet impatience parameter for country fc's future consumption function indicating a positive monotone transformation, reflects risk aversion relative risk aversion r](t)

fl

n*

~ dv./dc. k' d e £ r e e of relative risk aversion (in real terms) slope of the upper ray of the region of no trade aV( ?Q(0 A ' (0) ' m a r g i n a l indirect utility of nominal spending in country k instantaneous mean return of the home production process price level, computed on the basis of marginal consumption price level, computed on the basis of average consumption

Guide to Notation Ok a r Vk(ck(t)) co(t)

xvii

a constant reflecting the relative wealth of two countries instantaneous volatility of the aggregate production process proportional cost for transferring goods from one country to another function that is linear homogenous in consumption quantities ln[ATi (t)/K2(t)], log of the ratio of physical capital at home and abroad

1

Introduction and Overview

1.1

Our Objective and the Contribution of Our Work

As summarized by Krugman (1989), there are two prominent puzzling facts since the collapse of the Bretton Woods system. First, why has the floating-rate regime led to an increase in the volatility of real exchange rates? The consensus expectation in the late 1960s and the early 1970s was that real rates would be more stable, but the experience has been quite to the contrary (see Frankel, 1993, chap. 10). Second, why has the impact of these enormous swings in the real exchange rate on national outputs and inflation rates been so limited? Baxter and Stockman (1989) and also Frankel and Rose (1995) provide empirical evidence that, except for an increase in real exchange rate volatility, other macroeconomic aggregates have not been affected by the change in the exchange rate system in the 1970s. Perhaps more controversially, Krugman also holds that the large fluctuations in the value of, in particular, the U.S. dollar relative to the deutsche mark and the Japanese yen, are irrational bubbles. Furthermore, international capital flows have not smoothed out fluctuations in outputs and investments as expected. Many academics and politicians also think that the volatility of the exchange rate hinders international trade and international investments and conclude that a return to a system of fixed exchange rates, if feasible, would be desirable. One illustration of such a system is the European Union's singlecurrency plan. In light of these considerations, and given the widespread perception that an increase in exchange rate volatility leads to a reduction in the level of international trade, various questions arise. Is the observed behavior of the exchange rate consistent with a rational model? Does exchange rate volatility hinder trade? What type of capital flows are consistent with a rational model? What are the channels and dynamics of the international transmission of shocks and what is the role of financial markets in dealing with these shocks? What is the effect of financial markets on a country's investment decisions and, through such decisions, on its growth and welfare? What is the effect of capital markets on a nation's optimal tariff policy? How would a return to fixed foreign-exchange rates affect macroeconomic aggregates and welfare, and 1

2

Exchange Rate Volatility

what are the requirements to make this feasible? Finally, how are the answers to these questions affected by the segmentation of the real sectors of international economies? While addressing these issues, our focus is on a world consisting of large developed economies. Thus, the model that we consider is a general-equilibrium one, rather than that of a small open economy. Moreover, consistent with the current state of the financial system, our analysis considers explicitly the role of financial markets in the determination of spot and forward exchange rates, trade flows, capital flows, and the setting of tariff and monetary policy.1 At the same time, our model allows for commodity markets to be segmented across countries so that nations are distinct.

1.2

Outline of the Monograph and Summary of Major Results

The remaining chapters in this monograph can be divided into three parts. The first part, consisting of Chapters 2 and 3, provides background information. In Chapter 2, we survey existing models of international economies, and in Chapter 3 we describe a simplified version our general model - one that is limited to a single consumption good and only two countries that are symmetric in their initial endowments and preferences - and also elucidate on the motivation for the assumptions that we make. The model is described in two versions: in the first, output is given exogenously and in the second the production decision is modeled explicitly. Our main objective in Chapter 3 is to contrast the general-equilibrium modeling approach with previous models of international economies, and to build some intuition in the context of these simple models that will be useful when analyzing variants of these models in later chapters. The principal contribution of this chapter is to show how one can develop a fairly simple framework to analyze macroeconomic quantities and policies. In the second part of the monograph, comprising Chapters 4, 5, and 6, our focus is on macroeconomic variables. The variables that we study are the spot exchange rate, the forward exchange rate, short-term interest rates, and trade flows. In Chapter 4 we extend our basic model to a multicountry, multigood setting that allows for international differences in preferences and endowments. We then derive the exchange rate in this setting. The contribution of this chapter is both on the modeling front, and in the empirical testing of the model. On the theoretical side, we show that the implications of the general-equilibrium model 1

Andersen and Moene (1995) present work on the effect of the opening of financial markets on macroeconomic variables.

Introduction and Overview of the exchange rate are quite different than those implied by the monetary theory of exchange rates and purchasing-power parity (PPP). On the empirical front, we show that our model nests several specifications tested in the literature and that the general model provides a better explanation of exchange rate behavior than the standard models. In Chapter 5 our attention shifts from the spot exchange rate to the forward exchange rate and interest rates. Using a model with endogenous production, we study the implications of segmented commodity markets for the behavior of the forward exchange risk premium. We describe how a model with proportional shipping costs, and therefore deviations from PPP, can generate exchange rate behavior that is closer to the data than predicted by earlier models. In Chapter 6 we examine trade flows and the relation between exchange rate volatility, trade, and welfare. Existing models analyze exchange rate volatility in a partial-equilibrium setting (see, e.g., De Grauwe, 1988; Franke, 1991; and Viaene and de Vries, 1992), whereas the model that we construct is a general-equilibrium one, which implies that it is internally consistent and permits welfare analysis. We find that while an increase in exchange rate volatility always lowers welfare, the increase in exchange rate volatility could be associated with either an increase or a decrease in trade. That is, the model offers one explanation for the empirical observation that there is little evidence of a negative relation between exchange rate volatility and the volume of international trade. Finally, in the third part of the monograph, we look at policy issues. In Chapter 7 we investigate the policy of opening financial markets. We start by discussing the effect of opening financial markets on welfare. One implication of our model is that integration of financial markets can have a substantial effect on welfare. The welfare gains can be direct ones, arising from improved risk sharing, or indirect ones, arising from the ability to invest in high-return, high-risk production technologies because of the improved opportunities to share risk across countries. A second finding is that the gains from opening financial markets are significant even when commodity markets are not perfectly integrated. The policy implication is that it is important to encourage theflowof financial capital even in the absence of perfect commodity market integration. In the models that we develop, we also find that the volume of capital flows exceeds the volume of trade flows; this is consistent with the data, which show that less than 20% of transactions in capital markets are related to trade flows. In Chapter 8 we examine the interaction between financial markets and the choice of tariff rates. We describe how the structure of financial markets influences directly the choice of optimal tariff rates: whereas in the absence of capital markets the optimal tariff is strictly positive, with perfectly integrated

4

Exchange Rate Volatility

financial markets the welfare-maximizing tariff rate is zero. Thus, there is an additional source of welfare gains from the integration of financial markets: besides the gains from risk sharing and improved production decisions, welfare improves also because the optimal tariff rate is driven down to zero. It turns out that the welfare gain from the reduction in tariffs is substantially larger than the gain from risk sharing. The analysis described in this chapter also suggests that financial markets can play an important role in coordinating international trade policy. Although money has been introduced in the basic models described in Chapter 3, and the models with money have been used in our analysis of spot and forward exchange rates in Chapters 4 and 5, the process driving money supply has been taken to be exogenous in these chapters. In Chapter 9 we examine monetary policies and the choice of an exchange rate regime in an economy where money supply is determined endogenously. In the context of a specific model, we identify the particular conditions under which a regime of fixed exchange rates is welfare maximizing. Chapter 10 contains our conclusions and some thoughts for future research. In this chapter, we also discuss the issues that we have not touched upon in our analysis.

Modeling Exchange Rates: A Survey of the Literature

With the collapse of the fixed exchange rate system established at Bretton Woods, the behavior of exchange rates changed dramatically. The demise of the fixed exchange rate system came at about the same time as the oil crisis, which meant that the substantial increase in exchange rate volatility was accompanied by high inflation. These changes in the economic environment led to a renewed interest in understanding movements in exchange rates and their effects on prices, wages, and employment. In this chapter, we survey different approaches to modeling exchange rates. In this survey, we limit our attention to the literature on exchange rate determination; the literature related to the other issues addressed in later chapters of the monograph is discussed in those chapters. Our discussion starts with the early models of exchange rates, lists the weaknesses of each model from both a theoretical and an empirical perspective, and then progresses to the next, more sophisticated, model.1 In this presentation, rather than attempting to provide the minute details of each model in the literature,2 we focus on highlighting the essential features of each modeling approach and relating it to our work in the chapters to follow. In the next chapter, we describe the features of the model that we use for the analysis in this book and contrast this model with other models described in this chapter. Limitations of our model, and the extensions to it that might lead to interesting insights, are listed in Chapter 10. Traditionally, economists have tried to explain the behavior of exchange rates based on three variables: price levels, interest rates, and the balance of payments. Hence, in Section 2.1 we consider models that relate the exchange rate to national price levels; in Section 2.2 we discuss the relation between spot 1

2

For a general overview of exchange rate models, see Isard (1995). De Grauwe (1990) presents a historical account of the development of exchange rate theories placed in the context of macroeconomic events. For the interested reader we provide references to articles where the details of each model are available.

6

Exchange Rate Volatility

exchange rates, forward rates, and interest rates in money markets. We examine exchange rate models based on the balance of payments in Section 2.3. In Section 2.4 we evaluate monetary models with and without flexible prices and also models based on the portfolio balance approach. Finally, in Section 2.5 we discuss general-equilibrium models of exchange rates.

2.1

Exchange Rates and National Price Levels

Although Cassel (1918) was the first to use the phrase "purchasing-power parity" (PPP), the idea that exchange rates should be related to the national price levels can be traced back to the School of Salamanca in Spain in the sixteenth century.3 In a single-good setting, the quantity of goods one can buy with one unit of currency defines the purchasing power of the currency. In an economy with many goods, purchasing power is defined in terms of a representative bundle of goods. One PPP condition, called absolute PPP, relates the absolute price levels in two countries to the level of the exchange rate between them. If, at a particular time t, the cost of the representative consumption bundle translated into domestic terms equals the cost of the representative bundle at home, we say that absolute PPP holds.4 If we denote the prices of the representative bundles at home and abroad by P\(t) and /M0> respectively, then absolute PPP holds when:

where S(t) is the number of units of the currency of country 1 required to buy one unit of the currency of country 2. As a theory of exchange rate determination, absolute PPP states that the exchange rate must adjust so that the foreign price level translated at the spot rate is the same as the domestic price level. Relative PPP, on the other hand, states that the percentage change in the exchange rate must equal the difference between the inflation at home and abroad. Although PPP is an intuitively appealing concept, there is little theoretical justification for it. In Chapter 4 we show that in a general-equilibrium model with optimizing agents, PPP holds only under very restrictive conditions. Most economists would also agree that empirically PPP is not a very good model for describing exchange rates in the short run. Thus, most of the recent debate 3 4

See Grice-Hutchinson (1952). In testing the PPP relation, one should compare the cost of the same consumption bundle across the two countries. In practice, the representative consumption bundles are different across countries, and so in testing for PPP one may need to construct a basket of goods that is identical across countries; see Kravis et al. (1975).

Modeling Exchange Rates: A Survey of the Literature

7

has centered around whether PPP is a good description of exchange rates in the long run.5 Balassa (1964) and Samuelson (1964) developed exchange rate models that link deviations from PPP to differences in productivity in an attempt to explain the empirical regularity that currencies of more developed economies tend to be overvalued by PPP standards. These models assume that there is a nontradable good in each country, and one perfectly tradable good. Balassa and Samuelson argue that the relative prices are determined by relative production costs and, hence, by relative productivities in the sectors producing traded and nontraded goods. Nontradables are associated with services and tradables with industrial goods; and in a more developed economy the weight for services in the consumption bundle, and therefore also in the price index, is larger than it is in a less developed economy. Deviations from absolute PPP are then explained as follows. The productivity of labor in the industrial sector relative to that in the service sector is higher the more developed the economy. Thus, if country 2 is the more developed country, then the relative price of nontradables versus tradables is higher in country 2 than in country 1. If equal weights are assigned across countries, this produces a real exchange rate in excess of unity; and this conclusion holds a fortiori if the weight for services is higher in the richer country. Similarly, it is argued that, over time, relative prices of services tend to rise everywhere; however, as the weight for services is higher in the richer country, this effect leads to an appreciation of the real value of the currency of the more developed country, country 2. The equilibrium model that we develop in Chapter 4 is consistent with this argument. Empirical evidence for PPP in the short run is weak; long and persistent deviations from PPP have been documented extensively in the empirical literature. To test the relative PPP hypothesis, one common regression equation that is used in the literature is:

where the left-hand-side variable is the percentage change in the exchange rate between times t and t + 1, and the term within the square brackets on the righthand side is the difference between the domestic and foreign inflation rates over this period. The null hypothesis that relative PPP holds implies that the slope coefficient, b, should be equal to unity and the intercept, a, should equal zero. A frequently cited study of relative PPP is the one by Cumby and Obstfeld (1984) where they test an equation that is similar to the one given here. They reject the relative PPP hypothesis for all five countries (against the United 5

Froot, Kim, and Rogoff (1995) use 700 years of data to evaluate the relation between exchange rates and commodity prices.

8

Exchange Rate Volatility

States) in their sample. This test was extended to the case of eleven countries by Roger Huang (1987), and PPP was rejected for most of these countries as well. Other empirical tests of PPP, which focus on the time series properties of the real exchange rate, have also found that the PPP relation is quite weak. Some authors tested (and often could not reject) the hypothesis that deviations from relative PPP accumulated randomly over time (Roll, 1979; Adler and Lehman, 1983). That is, it seemed that even in the long run relative PPP would fail. But these discouraging results appear partly due to the fact that the tests being conducted by these authors are not very powerful. Abuaf and Jorion (1990), using a different methodology, show that cumulative deviations from relative PPP tend to halve after three years - that is, cumulative deviations from relative PPP have some tendency to correct themselves in the long run. In other words, the variance of PPP deviations does not increase proportionately with time. These results are consistent with those of other tests: for example, Huizinga (1987) and Huang (1990), using a wide range of techniques, have found some support for the hypothesis that exchange rates have a tendency to revert back to their PPP values over the long run. Chapter 4 describes in greater detail these and other tests that are based on cointegration analysis.6 We conclude that the relative PPP relation may have some power in the medium to long run (several years rather than several months). Relative PPP may also hold rather well in the short run if the source of shocks is nominal.7 It may also do well when inflation is high, as was the case in Germany around 1930 and after the Second World War, and in Brazil in the 1970s. McNown and Wallace (1989) conduct an empirical study of relative PPP in high-inflation countries such as Argentina (where prices increased by a factor of 250,000 between 1976 and 1986), Brazil, Chile, and Israel and find support for PPP. But even in these cases there are substantial period-by-period deviations from relative PPP - deviations as large as 800% per month. Thus, the exchange rate and the difference in inflation levels across countries usually do not fully and perfectly offset each other, consistent with the Keynesian view of the world. The sluggish response of prices to changes in the nominal exchange rate also implies that movements in the real and nominal exchange rates are closely related. As pointed out by Krugman (1990, 1993), the close relation between real and nominal exchange rates suggests that nominal shocks do have real effects. Bayoumi and Eichengreen (1994) and Eichenbaum and Evans (1992) find that 6 7

Froot and Rogoff (1995) provide an extensive survey of this literature. This was already recognized by Cassell (1922).

Modeling Exchange Rates: A Survey of the Literature

nominal shocks can explain a large proportion of the variance of the exchange rate since the end of the Bretton Woods agreement. Clarida and Gali (1994) obtain similar results using a very different identification scheme. These results indicate that a country can use monetary policy to affect the real exchange rate.8 However, given the large variation in the nominal spot rate relative to that in inflation rates, it is unlikely that exchange rates can be explained by international inflation differentials in the short run. More likely the short-term variation in exchange rates is caused by interest rate changes, or news about the relative state of the domestic and foreign economies, or even changes in the prices of other assets.

2.2

Spot Exchange Rates, Forward Exchange Rates, and Interest Rates

The PPP approach to determining the exchange rate is based on the view that the demand for currencies is derived from the demand for goods. But, as early as the nineteenth century, policy makers knew that they could influence the demand for money, and hence the exchange rate, by changing interest rates. There are, in fact, two relations between interest rates and exchange rates. The first one, covered interest rate parity, is an arbitrage-based relation. It states that, in the absence of impediments to international capital flows, the return from investing in a domestic riskless asset should be the same as that from investing in a foreign riskless asset and covering the exchange risk with a forward contract: [1 + r,(f, t + 1)] = [1 + r2(f, t + 1)] x

F

where r^t, t + 1) is the riskless rate between t and t + 1 in country k and F(t, t + 1) is the forward exchange rate between time t and t + 1. This relation between spot exchange rates, forward rates, and interest rates was known to Italian bankers as far back as the Renaissance. As far as we know, the first published version of this relation is in Cournot's Recherches sur les principes mathematiques de la theorie des richesses (1838). This relation was later rediscovered by Paul Einzig (1937), a reporter for the Financial Times, who picked it up from London bankers. Marston (1995) examines this relation for the G-5 countries and finds that the returns from investing in any of these currencies is the same in both national and Eurocurrency markets. 8

We will analyze such a setting in Chapter 9.

10

Exchange Rate Volatility

The second relation, uncovered interest rate parity (UIP), relates the current forward rate to the future spot rate. This relation hypothesizes that the return from investing in a riskless domestic asset should be the same as the expected return from investing in a riskless asset denominated in terms of the foreign currency - even when the foreign investment is not hedged with a forward contract: [ l + r , ( M + l)] = [ l + r 2 ( M + l ) ] x

S(t)

where Et is the expectation conditional on all information available at time t. To obtain an equation for the determination of the current spot rate, the UIP equation is rewritten with the current exchange rate as the dependent variable:

The problem in using regression analysis to test the UIP relation as it is expressed here is that the right-hand side is in terms of expectations, which are unobservable; all one can observe is the realized value of the spot rate at time t + 1, S(t + 1). This problem is solved by noting that in an informationally efficient market, the deviation between the market's forecast and the actual outcome must be totally unpredictable. Thus, tests of UIP are joint tests of the relation and of market efficiency. With the assumption of efficient markets, one can rewrite the preceding equation in terms of the observed spot rate, S(t + 1), and its forecast error, e(t, t + 1). In terms of percentage changes, this gives us:

[

L

S(t)

J

[\+r2(t,t+\)]

which, using the covered interest parity relation, can be expressed as

For notational ease, one can define the percentage change in the spot rate as s(t, t + 1), and the percentage difference between the forward and spot rates as the forward premium FP(t, t + 1): »

and

This allows us to rewrite equation (2.1) as: (2.2)

s(t, t + 1) = a + 0 FP(t, t + 1) + e(t, t + 1).

Under UIP, s(t, t + 1) = FP(t, t + 1) + e(t, t + 1) so the null hypothesis is that a = 0andj8 = 1.

Modeling Exchange Rates: A Survey of the Literature

11

Although UIP would lead us to expect a value of /3 that is statistically close to 1, Froot and Thaler (1990) report that the average slope coefficient obtained from seventy-five empirical studies is, in fact, —0.88. While some studies find a slope coefficient that is positive, not a single study finds a slope that is equal to or greater than unity; details of this literature are provided in Baillie and McMahon (1989b), Engel (1994), Hodrick (1987), Lewis (1995), and Marston (1995). Note that since )3 is typically not equal to zero in the regression tests of UIP, the forward premium does have some power to predict the future spot rate although the sign of the relation is often opposite to what we would expect under UIP. In practice, however, the unpredictable component e(t, t + 1) is very large in comparison with the predictable component, FP(t, t +1), and thus the exchange rate remains difficult to forecast. Because of the overwhelming evidence from many regression tests, we can safely conclude that /3 is significantly below unity. That is, the forward rate is a biased predictor of the future spot rate. One interpretation is that investors are not risk-neutral and that the bias in the forward rate's prediction of the spot rate reflects a risk premium.9 Fama (1984) provides a nice characterization of the risk premium: his analysis shows that to explain the bias in the forward rate, the risk premium needs to be large in magnitude and strongly negatively correlated with the forward premium. In Chapter 5, we provide the details of Fama's analysis and then evaluate this risk premium in a general-equilibrium model where commodity markets are segmented, giving rise to deviations from PPP.

2.3

Exchange Rates and the Balance of Payments

The balance-of-payments (BOP) theory is a Keynesian flow approach to the determination of the exchange rate. According to the BOP theory of exchange rates, the supply and demand for a currency arise from the items of the current and capital accounts of the BOP. The objective of the BOP theory of exchange rates is to explain (a) why exchange rates and prices are not as predicted by PPP and (b) why we see continuous capital flows between countries. The explanation offered for these two observations is based on a Keynesian view of the world that prices of goods are sticky in the short run. Moreover, given that prices adjust slowly to a change in economic conditions, economies are in a state of persistent disequilibrium leading to the flow of capital between countries. According to the early proponents of the BOP approach to exchange rates,10 the current account is determined by prices of goods at home (P\) and prices 9 10

Other explanations for a slope coefficient of less than unity are discussed in Chapter 5. See, for example, Marshall (1923), Lerner (1944), Robinson (1947), and Metzler (1949).

12

Exchange Rate Volatility

of goods abroad, translated into domestic terms using the spot rate (SP2), with the added assumption that the functional relation between the current-account balance and the relative prices abroad and at home, SP2/ P\, is greater than unity. The main point made by these models is that the exchange rate can affect the current account only if it changes domestic absorption relative to domestic production. The limitations of this early elasticities approach are that it assumes the demand for exports and imports depends only on prices and ignores the role of other variables (such as income), and it also ignores items of the capital accounts. Moreover, this analysis is static rather than intertemporal and is not based on microeconomic principles. The Mundell (1960, 1961, 1963) and Fleming (1962) approach added to the goods and money markets a consideration of the international flow of capital. The transactions in the capital account are assumed to depend on the relative interest rates at home and abroad. The functional relation between the domestic interest rate and foreign investment is assumed to be positive; that is, an increase in the interest rate at home attracts foreign investment and leads to an inflow of international funds. Analogously, the relation between the capital-account balance and the foreign interest rate is negative. Finally, the capital account depends also on the exchange rate S, because the value of S will determine the value of the foreign return in terms of domestic units. Thus, in contrast to the PPP theory of exchange rates, the BOP theory acknowledges that the demand for a currency may arise also from investors' direct and portfolio investment decisions. Within this framework, the foreign interest rate and price level are assumed to be constant, and then one can analyze the effects of domestic monetary and fiscal policies. One of the major results of the Mundell-Fleming framework is that the relative effectiveness of monetary and fiscal policies depends on the exchange rate regime and the mobility of financial flows. A major weakness of this approach, however, is that it ignores the fact that investors can hold assets with different risk-return trade-offs, and that agents would make this choice in an optimal fashion.1' In contrast, when we evaluate tariff policy in Chapter 8 and monetary policy in Chapter 9, we consider an intertemporal framework, where investors choose portfolios of financial assets in an optimal fashion.

2.4

Asset Models of the Exchange Rate

The asset approach to exchange rate determination shifted attention from the trade balance to capital flows as a determinant of exchange rates. We can divide 1

' See Frenkel and Razin (1987) and Krugman and Obstfeld (1991) for extensions of the MundellFleming model.

Modeling Exchange Rates: A Survey of the Literature

13

the asset models of the exchange rate into two groups: those that consider only moneys (Johnson, 1972), and those that consider portfolios of risky assets (Branson, 1968; Girton and Henderson, 1973).12 The monetary approach was developed by Mussa (1976), Frenkel (1976), and Bilson (1978, 1979). Its building blocks are the quantity theory of money, UIP, and PPP. It shows that the exchange rate today is the discounted value of future expected money stocks and output levels at home and abroad. Thus, the monetary approach views the exchange rate like any other asset price and, hence, the value of the spot rate changes whenever relevant information is released. In that respect, the asset approach overcomes a major limitation of the PPP approach: because the arrival of new information is much more frequent than changes in relative commodity prices, the asset approach can potentially explain the frequent changes observed in the exchange rate. The monetary approach is also different from the BOP (Keynesian) approach because it does not assume that prices are sticky or that the economy is in a state of constant disequilibrium. The monetary model relies on the assumption that PPP holds. Given the poor performance of PPP in the data, Dornbusch (1976) developed a rationalexpectations model in which prices are sticky in the short run, but the exchange rate, treated as an asset price, can respond to new information instantly.13 He then shows that in such a model, the exchange rate could overshoot: for example, in response to an unanticipated monetary shock, the exchange rate responds more than proportionately to the shock in order to compensate for the stickiness in prices of goods. In the long run, as prices adjust, the exchange rate then returns to its equilibrium value. In contrast to the monetary approach, the portfolio-balance approach does not assume that investors ignore risk and, therefore, regard domestic and foreign bonds as perfect substitutes. In this model, risk-averse investors choose how to allocate their wealth across different risky assets. The demand for these assets depends on expectations of changes in the exchange rate. Meese and Rogoff (1983) find that the empirical performance of the flexibleprice model, the model with sticky prices, and the portfolio-balance approach to be very poor; these structural models typically fail to outperform a randomwalk model in predicting exchange rates out of sample, even when one assumes that the driving variables could be forecasted perfectly. Various extensions of these structural models, such as a model with time-varying parameters 12 13

See Branson and Henderson (1985) for a survey of these models. A review of this paper, and related models, can be found in Obstfeld and Stockman (1985) and also in Obstfeld and Rogoff (1996).

14

Exchange Rate Volatility

(Wolff, 1987; Schinasi and Swamy, 1989)14 and models with nonlinearities (Diebold and Nason, 1990; Meese and Rose, 1991) outperform the randomwalk model, but not by much.15 The poor performance of models based on fundamentals, especially at short horizons, suggests that changes in nominal exchange rates must either be due to unobservable fundamentals or to nonfundamental factors such as speculative bubbles. However, the observed difference in exchange rate volatility under different exchange rate regimes suggests that the first explanation is unlikely, and Frankel and Rose (1995) show that the evidence in favor of speculative bubbles is also not strong. From a theoretical viewpoint, a shortcoming of these models is that they are static and partial-equilibrium models in that they take the return process on risky assets to be exogenous. In the general model that we describe in Chapter 4, returns on risky assets are determined by market-clearing conditions, and the demand for these assets is the outcome of an intertemporal optimization exercise. Moreover, the exchange rate in our model is nonlinear and characterized by changing coefficients. The models described here were developed to understand the behavior of a freely floating exchange rate. However, as attention of policy makers shifted toward a regime where there were limits on the flexibility of exchange rates, models were developed to analyze the dynamics of the exchange rate within a target zone.16 Krugman (1991), assuming that the target zone was perfectly credible, showed that the distribution of the exchange rate would be U-shaped, implying that the exchange rate would spend most of its time near the edges of the zone.17 Dumas (1992) showed that one could obtain a similar result in a general-equilibrium model where the commodity markets of the two countries were segmented by shipping costs. The details of the model by Dumas are given in Chapter 3, and the implications of this model for UIP and capital flows are explored in Chapters 5 and 7, respectively. 14

15

16 17

Another approach, especially for characterizing the behavior of exchange rates at high frequencies, is to use time-series models. For a description of the high-frequency properties of nominal exchange rates, see de Vries (1994). For time-series models of the exchange rate, see Baillie and McMahon (1989a, 1989b) and Baillie and Bollerslev (1989, 1990). See Dornbusch (1988), Meese (1990), and Frankel and Rose (1995) for a review of such models and tests of their empirical performance; Baillie and McMahon (1989b) also provide extensive details on the econometric evidence. See also De Grauwe (1994), Evans and Lothian (1993), and Mark (1995). Engel and Hakkio (1993) conclude that a target zone system for the U.S. dollar, yen, and mark is unlikely to lead to a decline in exchange rate volatility. Other models in the target zone literature allow for the possibility of a change in the zone itself (through a shift in the central parity). This literature is surveyed in Svensson (1992) and Bertola(1994).

Modeling Exchange Rates: A Survey of the Literature

2.5

15

Exchange Rate Models with Microeconomic Foundations

To address the shortcomings of the static models described here, intertemporal models of the real exchange rate with strong microeconomic foundations have emerged. The early contributors to this approach were Lucas (1982), based on the work in Lucas (1978), Helpman and Razin (1979, 1982), and Stockman (1980, 1983, 1987). Under this approach, the equilibrium exchange rate is a consequence of the optimizing behavior of individuals who can invest in financial claims and face an intertemporal budget constraint.18 Some of these models are partial-equilibrium models because they assume that one country is small and, therefore, takes world prices as given; other models are general equilibrium in nature and allow each country's decisions to affect world prices. The early models assumed that all goods were perfectly tradable (Stockman, 1980; Lucas, 1982; Hodrick, 1987). This, however, implied that the real exchange rate was always equal to unity. Later models assumed that in each country at least one good was nontradable: see, for instance, Stulz (1987), Devereux (1989), Stockman and Delias (1989), and Stockman and Tesar (1995). Based on this work, Backus, Kehoe, and Kydland (1992) developed international real business-cycle models to evaluate the ability of dynamic generalequilibrium models to match features of the international business cycle data. Dumas (1992), instead of assuming that some goods are nontraded, introduces a cost for transferring goods from one country to another; thus, in this setting whether a particular good is traded or nontraded on a given date is determined endogenously. To extend the models of real exchange rates to include a role for money, several approaches have been adopted. In the first, money is introduced via a cash-in-advance constraint (Lucas, 1982, 1990; Svensson, 1985a, 1985b; Fuerst, 1992; Bekaert, 1994). Grillio and Roubini (1992) extend the Lucas (1990) modeling device of a participation constraint to a two-country setting; they use this model to show that the exchange rate can exhibit excess volatility.19 Alternatively, money is introduced through the utility function: see Sidrauski (1967) and Brock (1974) for early contributions (in the context of a closed economy) followed by Karekan and Wallace (1980), McCallum (1983), LeRoy (1984), Feenstra (1986), Danthine and Donaldson (1986), Stulz (1986a, 1986b), Bakshi and Chen (1996), and Basak and Gallmeyer (1998). Finally, one can introduce a stochastic demand for money via a transaction-cost technology, as in Bansal et al. (1993), Bekaert (1996), and Bekaert, Hodrick, and Marshall (1996). 18 19

See Dumas and Solnik (1995) for empirical tests of a particular equilibrium model of exchange rates. For a discussion of these models, and an extension to a continuous-time setting, see Wang (1998).

16

Exchange Rate Volatility

Another stream of the literature developed models of price stickiness: Svensson and van Wijnbergen (1989) extended the Lucas (1982) model to require that prices must be set one period in advance (by monopolistically competitive firms). More recently, Obstfeld and Rogoff (1995a) have modeled imperfections in the commodity market via the assumption of monopolistic competition and nominal price rigidity (and the results are quite different from those in the Mundell-Fleming model). Because all goods are freely traded in these models, however, there are no deviations from PPP. These models were followed by the model of Chari, McGratten, and Kehoe (1996), which employs staggered price setting, and that of Kollmann (1997, 1998), where prices have to be set two to four periods in advance.20 Devereux (1997b) provides a survey of recent models of the real exchange rate. He divides the class of models with money nonneutralities into two sets: first, the "liquidity approach," where the focus is on the effect of monetary policy via the financial markets; and second, the "sticky-price" approach, where money has an effect because prices are sticky in the short run. Devereux argues that the empirical evidence supports many aspects of the general-equilibrium approach to exchange rates based on sticky prices. Allen and Stein (1995) also provide strong empirical evidence in support of equilibrium models of the exchange rate in the medium and long term. The framework that we use in this monograph belongs to this class of intertemporal, general-equilibrium models. Our model can be considered an extension of the Lucas (1982) model, and in its most general version (see Chapter 4) allows for multiple goods, some tradable, others nontradable, and still others that are tradable at a cost. We allow for international differences in commodity prices by introducing a cost for shipping goods across countries. We introduce money using the cash-in-advance constraint, where it will have an effect on real variables because of the assumption that prices (wages) may be sticky in the short run (see Chapter 9). The next chapter provides the details of a simple version of this model. 20

Extensions of Obstfeld and Rogoff's (1995a) model are also in Hau (1997a, 1997b). See also Atkeson and Kehoe (1997).

3

A Simple General-Equilibrium Model of an International Economy

In this chapter, we describe the basic framework that we use to undertake most of our analysis. In Section 3.1 we motivate our modeling assumptions and provide empirical support for these assumptions. In Section 3.2 we provide the details of the analytical model of a two-country endowment economy that we use throughout our analysis. In Section 3.3 we extend this model to allow for endogenous production decisions. Other extensions to the simple model that will be undertaken in the chapters to follow are described in Section 3.4.

3.1

Motivation for the Modeling Assumptions

Our objective is to understand the exchange rates between developed economies. We also wish to analyze the influence of financial markets on the flow of goods and financial capital between such economies, and through these flows, the effect on welfare and growth. Given these objectives, the framework we consider has the following characteristics: 1. The model is of a dynamic, stochastic, general-equilibrium world economy in which decision rules for individual agents are derived from optimizing behavior. 2. The model is one in which the economies of individual countries are distinct in that their commodity and financial markets need not be perfectly integrated. 3. Monetary policy and the exchange regime matters, in the sense that they affect the allocation of real resources. We indicate below why these three features are important for a model used to address the issues considered in this monograph. 3.1.1

Advantages of the General-Equilibrium Modeling Approach

Given that the focus of our analysis is on large developed economies such as the countries of Western Europe, Japan, and the United States, it is important that we consider a general-equilibrium model where prices are determined 17

18

Exchange Rate Volatility

endogenously rather than one where the country of interest is assumed to be "small" so that its actions have no impact on prices. Moreover, because the real and financial decisions of investors are interlinked, a general-equilibrium approach is needed to analyze simultaneously the effect of these decisions on prices in commodity and capital markets. Our general-equilibrium model is also firmly based on dynamic optimization rather than on ad hoc linear behavioral rules.1 As Stockman (1988a, p. 534) states, "Dynamic stochastic general equilibrium models based on individual optimization generally give different results from the kind of models that were previously in general use. The results obtained in the older models often failed to be robust to these ad hoc assumptions about portfolio allocations." Helpman and Razin (1979a) likewise list a dynamic optimization-based, general-equilibrium approach as one of the requirements for a framework used to compare alternative exchange rate regimes. Their other requirements, all of which are satisfied by the model that we consider, are that: the economy's real resource constraint should be independent of the exchange rate regime; all demand functions should be derived from intertemporal utility-maximizing behavior, and these utility functions should also be used for making welfare comparisons; exchange rates should be determined endogenously; and the financial transactions that agents can engage in should not depend on the exchange rate regime. The general-equilibrium analysis also enables us to make welfare comparisons, and, thus, we can study issues related to changes in policies. In contrast, older models studying policy changes are subject to the Lucas critique because they postulated the decision rules of individual agents rather than deriving them from optimizing behavior.2 Finally, our model provides stronger testable restrictions for empirical work, as will be described in greater detail.

3.1.2

Modeling the Distinction between Nations

In the model we develop, countries are distinct from one another in an economically material way, which is necessary if one is to explain the stylized facts of international data. Dumas (1994) lists four stylized facts about international data that cannot be explained in perfectly integrated markets: deviations from purchasing-power parity tend to persist for long periods of time; investors' portfolios are biased toward domestic assets; cross-country consumption correlations are low; and there are violations of uncovered interest rate parity. Our model is consistent with all four facts. 1 2

See also the model in Gavin (1989). A survey of such models is provided in the previous chapter.

A Simple General-Equilibrium Model of an International Economy

19

Factors that could make "countries" distinct include: segmentation of commodity (and labor) markets, segmentation of capital markets, differences in output functions (supply factors), and differences in commodity preferences or attitudes toward risk (demand factors). The effects of different output and commodity-preference functions have been extensively studied in the (neo)classical theory of trade and are therefore well understood. Moreover, these differences are much less important for the issues that we wish to study. Thus, in our analysis, we typically assume that preferences and output processes are the same across countries and our focus is on the segmentation of commodity and capital markets. We explain how we model the segmentation of commodity and capital markets, why it is important to model this segmentation, and what it implies for our results. 3.1.2.1 Segmentation of Commodity Markets. In the literature on international macroeconomics, segmentation of commodity markets has typically been modeled either by introducing nontraded goods (e.g., Stulz, 1987, and Stockman and Delias, 1989) or costs for transferring goods across countries (e.g., Black, 1973, and Dumas, 1992).3 Ideally, one should allow for both types of commodity market segmentation. This is because nontraded goods constitute a large proportion of total expenditure; for example, OECD countries spend 60% to 80% of their incomes on services, which are essentially nontradable. Moreover, as noted in Stockman and Tesar (1995), it is important that a model include nontraded and partially tradable goods because a model with just one (tradable) good is likely to overstate the linkages between economies. Stockman (1990, p. 136) likewise states that, "Both theory and evidence on open economies suggest the inclusion of nontraded goods and multiple traded goods. Nontraded goods are quantitatively important and can play a role in breaking the link between foreign and domestic consumption."4 Krugman (1989) also stresses the importance of "home bias in consumption" for the analysis of the trade balance. Along with nontraded goods, tariffs and especially nontariff barriers5 are also a significant source of segmentation. Deardorff and Stern (1990) report that the average tariff in industrialized countries is about 6.6% (their table A7). Deardorff (1989) reports, on the basis of several studies, the low (high) estimates of ad valorem equivalents of nontariff barriers for the various traded goods in the major industrialized countries (in his tables 4 and B5). For example, in the United States the low (high) estimates range from 0% (0%) for machinery to 14.5% (20.5%) for food products. For Japan, the low (high) estimates are 3 4 5

Chapter 2 contains additional references to articles using these modeling approaches. See Devereux, Gregory, and Smith (1992) and Kollmann (1995, 1996) for evidence on low consumption correlations across countries. The nature of these barriers is described in van Nunen (1990).

20

Exchange Rate Volatility

0% (0%) for machinery and 27.1% (58.1%) for food. Melo and Tarr (1992, p. 200), based on their study of the textile, automobile, and steel industries in the United States, estimate that the average tariff that would generate the same welfare costs as those resulting from quotas in the three sectors is 49%. Cooper (1986) also provides empirical evidence on the openness of the U.S. economy. Finally, besides tariffs and nontariff barriers, factors such as pricingto-market (Marston, 1990) and transportation costs play a role in segmenting international commodity markets. Given the importance of nontraded goods and of tariffs and other trading costs, in its most general version our model (presented in Chapter 4) allows for three classes of goods: nontraded goods, traded goods (in the strict sense - that is, goods that are traded all the time), and tradable goods that are traded only if the cost of trading is smaller than the benefit. The three classes of goods, as well as the proportional costs we introduce for shipping goods internationally, are important to obtain a reasonable model for the real exchange rate and for the pattern of trade. A model in which all goods can be traded without friction is unrealistic; in such a model commodity prices would be equated across countries, thus flatly denying the possibility of a major phenomenon that we study: widely fluctuating real exchange rates. The introduction of shipping costs in a one-good setting is obviously a step in the right direction. This modeling choice is supported by the recent work of Engel and Rogers (1995), who study price differences for the same good across the United States and Canada. They find that distance matters: price differences increase with distance, even within a country. Second, national borders are important: price differences across U.S. and Canadian cities that are just across the border from each other are of the same magnitude as the price differences across two U.S. cities that are 2,500 miles away from each other. Wei and Parsley (1995) study the variability of commodity prices in OECD countries. They also find that distance is a significant determinant of price variability. The shipping cost specification is also supported by the recent tests by Obstfeld and Taylor (1997) and O'Connell and Wei (1997) that use Threshold AutoRegressive statistical models (TAR) and the Smooth Transition AutoRegressive models (STAR) in Michael, Nobay, and Peel (1997).6 3.1.2.2 Segmentation of Capital Markets. Highlighting the importance of financial markets, Keynes stated that, "The exchange rate is determined in the stock market." Along the same lines, according to Stockman (1988a, p. 546), "a serious model of exchange rates must be based on a general equilibrium model of financial markets." In our view, it is important that a model of developed 6

See also O'Connell (1996, 1998).

A Simple General-Equilibrium Model of an International Economy

21

economies include an explicit analysis of capital markets and capital flows for three reasons. First, from an empirical point of view, the volume of international financial transactions is very large (at least U.S. $1.5 billion daily in just the exchange markets), of which only a small proportion is estimated to be related to trade in goods and services. Second, results from general-equilibrium models in the presence of financial markets are very different from those obtained under incomplete markets. Likewise, as Stockman (1988a) remarks, the development of the financial sector influences the equilibrium in the real sector in significant ways, and government restrictions on capital flows (quantitative or tax-based) alter the real equilibrium in a way that is not a priori obvious.7 Thus, it is important to specify the structure of asset markets and the role of international financial flows. Third, there is some controversy as to whether the capital flows, enormous as they are, actually play the role that economists expect them to play.8 If true, this may have policy implications. Segmentation of capital markets can be modeled in at least three ways. One way is to introduce a tax on capital transactions, as in Black (1974) and Stulz (1981a). Alternatively, one could impose capital controls so that trade is possible in only a limited number (or quantity) of financial claims, usually implying that financial markets are incomplete. This approach is adopted in Subrahmanyam (1975), Errunza and Losq (1985), Sellin and Werner (1993), Basak (1995), and Lee (1998). Finally, one could explicitly model informational asymmetries as a source of home bias (as in Brennan and Cao, 1996). Although the third approach is beyond the scope of our current research agenda, our model can incorporate the first two types of capital market segmentation. Thus, our analysis extends the work of Cole and Obstfeld (1991), Sellin and Werner (1993), and Basak (1995), by allowing us to consider the effect on welfare of the interaction between imperfectly integrated commodity markets and capital markets (see Chapter 7).9

See Bayoumi (1997) for empirical evidence on the effect of capital flows on real activity. The absence of formal capital controls is not a sufficient condition for perfect integration. On the individual level, although theory predicts a high degree of international diversification (Solnik, 1974; Sercu, 1980; Adler and Dumas, 1983), in practice portfolios are characterized by substantial home bias (French and Porterba, 1991; Uppal, 1993; Cooper and Kaplanis, 1994). On the macroeconomic level, it is a puzzle why fluctuations in investment are mostly financed by fluctuations in savings rather than by international capital flows (Feldstein and Horioka, 1980; Krugman, 1989). However, Obstfeld (1986) shows that even in a model with high capital mobility, it is possible to generate the correlations between saving and investment observed in the data. A review of this literature can be found in Tesar (1991); Baxter and Crucini (1993) show that productivity shocks in a real business cycle model can also generate high correlations between national savings and investments. Our work also extends the analysis in Feeney (1994), where she evaluates whether trade in goods and financial securities are complements or substitutes; her analysis is in a setting where the country of interest is assumed to be small.

22

Exchange Rate Volatility

3.1.3

Monetary Policy and Exchange Rate Regimes

Having described segmentation of commodity and capital markets as the crucial factors that distinguish countries in our model, we now turn to the monetary sector and the choice of monetary policy and the exchange rate regime. Stockman (1983) lists the conditions under which a model of an international economy may be neutral to the exchange rate regime: Ricardian equivalence holds; there are no informational asymmetries about the policy maker; the exchange rate peg should not be maintained through assets that are not included in the efficient portfolios of households; unanticipated changes in future nominal prices should not affect the wealth of individuals; and, finally, money should not play any real role. The remarkable break in the volatility of the real exchange rate around 1973 strongly suggests that monetary arrangements can have significant effects. To obtain a model that does not preclude the possibility of any such effect, we permit monetary policy to influence real wages and, through that, the allocation of real resources. Thus, depending on the focus of our analysis, we consider both models where the monetary rule is given exogenously (Chapters 4 and 5) and where the choices of exchange rate regime and of monetary policy are endogenous (Chapter 9). 3.1.4

Advantages of the General-Equilibrium Approach for Empirical Tests

We now describe the advantages of the general-equilibrium modeling approach for understanding the data. In the empirical literature on exchange rates, researchers have typically tested reduced forms of theoretical models.10 In this case, although it is possible to determine whether a reduced-form model is rejected or not, one cannot identify the reason for the rejection. The main strength of our work is that the tests we consider are of a structural, general-equilibrium model. Because we are testing a particular structural model, it is possible to identify the source of any model rejection. That is, the empirical tests of the theoretical model (and those based on calibrations) indicate which features of a model must change if one wishes to explain the date. Moreover, as shown in Chapter 4, tests for several competing models can be implemented in nested form. Another potential advantage of testing a well-specified model is that the model yields the precise nonlinear relations between the relevant variables or parameters and imposes restrictions not only on expected values but also on higher moments. For instance, in the model described in Section 3.3, the 10

See Chapter 2 for references to the body of work testing structural models in reduced form. Edison and Melvin (1989) provide a survey of empirical work on the determinants of exchange rate regimes.

A Simple General-Equilibrium Model of an International Economy

23

exchange rate is nonlinear; and in Chapter 6 our model predicts a particular nonlinear functional form for the relation between exchange rate volatility and the volume of trade. Thus, tests can be formulated to take advantage of the knowledge of higher moments and of the particular functional form and thus will have much more power to reject a particular null hypothesis. Working with a general-equilibrium model is useful also because empirical tests that are in terms of consumption variables can often be restated in terms of financial variables (such as interest rates) by using the first-order conditions implied by the theoretical economy. Thus, this can eliminate the need for consumption data that are difficult to collect and are generally not of as good quality as financial data. This will prove to be useful when we evaluate the model using numerical calibration techniques, as in Chapters 5 and 7. A related advantage of the general-equilibrium approach is that it has immediately testable implications in terms of the aggregate data that are available. In contrast, partial-equilibrium models based on the behavior of a single firm, such as the ones used to analyze the relation between exchange rate volatility and trade, are inconsistent with the aggregate data that are used for empirical tests of this relation.

3.2

Details of the Basic Model of an Endowment Economy

In this section we present a general-equilibrium model of an international endowment economy and describe how to solve for the exchange rate, consumption policies, and trade volume. To simplify the exposition, we will start with the most basic version of our model. In the next section we extend the model to allow for endogenous production. Finally, in Section 3.4 we describe the various extensions to this model that we consider in later chapters.1' In the basic model, we assume that there are only two countries. The home and foreign country (k = 1 and 2, respectively) are similar in three respects. First, they are assumed to be populated by a large and equal number of infinitely lived consumers. Second, their financial markets are perfectly integrated, complete, and frictionless. Third, the countries are assumed to have started out with identical endowments, the firms generating the endowments are assumed to be perfectly competitive, and the parameters of the stochastic processes that determine future endowments are identical.12 The factors that distinguish one economy from another are the following. First, after the initial date the outputs of the good generally differ across countries, and costs for shipping goods across countries make 11 12

A glossary containing a guide to the notation used in this monograph is included in the frontmatter. These assumptions about symmetry across countries are relaxed in Chapter 4.

24

Exchange Rate Volatility

the commodity markets less than perfectly integrated. Second, each country has its own money, and the nominal stocks of money may differ across countries. In every period, each country is endowed with a quantity of a single good that is homogenous across countries, imperfectly tradable, and nonstorable. In each country, the available quantity of the good, qk(t), is assumed to be characterized by discrete-time, exogenous stochastic processes, as in Lucas (1982). There is a proportional cost,r, for shipping the good internationally. This cost is modeled as a waste of resources: if one unit is shipped, only 1/(1 H-r) units actually arrive. The simplest way to introduce money in the model is by using the cash-inadvance constraint and the timing convention used in Lucas (1982).13 Denote the money supply in country k by m/dt) and let the evolution of m^t) be given by a deterministic or stochastic process. We assume that domestic money is used to purchase goods consumed in the home country and foreign money for goods consumed abroad. The domestic and foreign goods prices referred to in this book are expressed in units of the corresponding country's currency. These prices may change over time because the local money supply changes, or because quantities available for consumption change. Let Ck(t) be the consumption quantity of the good in country k, and Xk(t) the exports from country k (before transactions costs). Given our assumption of complete and frictionless financial markets and perfectly competitive commodity markets, the decentralized solution is identical to that of the central planner because individuals can implement the optimal solution of the central planner through trading in financial claims. If we assume that the utility function in each country, u^, is time-additive with constant relative risk aversion (CRRA), (3.1)

VS

the central planner's objective is to choose the amounts of trade so as to maximize the aggregate utility: 14 (3.2a)

13

14

Max Et

That is, we assume that investors can purchase goods only with currency. The timing convention is such that investors learn about the current state of the world, including monetary shocks, before trading in the markets for securities and consumption goods. Given that investors can hold riskless securities with a positive nominal return, money will be held only within a period (to buy the known amount of current period consumption), and not across periods. The absence of weights preceding the utilities reflects the assumption that the two countries have started out with identical amounts of the good and that the endowment processes have identical parameters across countries. In the decentralized solution, the initial endowments determine the initial relative wealth of the two countries; and this, in complete markets, then determines how the claims on future consumption are distributed among the countries.

A Simple General-Equilibrium Model of an International Economy

25

subject to: (3.2b)

ci(r) =

(3.2c)

c2(t) = q2(t) - x2(t) •

1+T JC|(O 1+T

(3.2d) where 5 is the impatience parameter and r\ > 0 is the degree of relative risk aversion (RRA). To solve the problem in (3.2a), note that the utility function in (3.1) is time-separable, trade affects consumption only within the same period, and the constraints apply period by period. It follows that we can rewrite the intertemporal problem in (3.2a) as a static problem, Max C l ( r ) I -r]

+

C2(r)

1 -r]

subject to (3.2b, c, d).

We now explain the implications of the shipping cost. Given that it is costly to transfer the good from one country to another, it will be optimal to trade only when the price of the tradable good at home is sufficiently different from the price abroad. Note that in constraints (3.2b) and (3.2c), a shipment of x\(t) from the home country leads to an increase in foreign consumption of only xi (0/(1 + r), and likewise for shipments in the other direction. In the absence of shipping costs, it would be optimal to set the relative amount of consumption in the two countries equal to unity and correct any deviation of q2(t)/q\ (0 from unity by shipping goods. But in the presence of shipping costs, there will be a no-trade zone within which deviations of c2{t)/c\{t) from unity will be left uncorrected (see Figure 3.1). Only if q2(t)/q\(t) is outside the no-trade region will goods be exported from one country to another, and the shipped amounts will be such that C2(0/^i(0 remains on the nearest boundary of the no-trade region. We identify this region later. From the first-order conditions of this static problem, we immediately obtain the condition that indicates when to ship goods across countries. This condition implies that the ratio of the marginal utilities of the home and foreign investor are bounded above and below by the transactions cost:

0.3)

J_<^iyBc2 l+r

-

8KI[.]/3CI

=

c^r:< (t)~i

~

Equivalently, relative consumption is bounded by:

m

1

" ^ <[. + „•/.-..

26

Exchange Rate Volatility

45-degree line

1+T

Region of Domestic Exports

Figure 3.1. The region of no trade in an endowment economy. When the weights assigned by the central planner to the two countries are the same, then the critical loci that separate the no-trade domain from the region with trade are symmetric around the 45-degree line and are as follows: domestic exports if qi(t)/q\(t) < K\ foreign exports \f qi{t)/q\(t) > K; no trade otherwise. The figure also shows the amounts of exports from country 1, x\, and (net) imports into country 2, x\/(\ -f r), that arise if the output point is given by (q\, qi) m the zone of domestic exports. For any given output vector (q\,q2) outside the no-trade zone, a smaller r (i.e., a narrower no-trade zone) requires a larger amount of trade to bring consumption to the nearest bound. Thus, when initial endowments of the two countries are equal, we obtain a no-trade region that is symmetric around the 45-degree line.15 Figure 3.1 illustrates this: for qi(t)/q\(t) > K there will be exports from the foreign country; for q2(t)/q\(t) < \/K there will be exports from the home country; and there 15

With unequal weights in the objective function (3.2a), the region of no shipping would not be symmetric around the 45-degree line. This, however, would not affect the conclusion that the ratio of marginal utilities can deviate from unity, nor would it affect the inferences made.

A Simple General-Equilibrium Model of an International Economy

27

is no trade when \/K < qi(t)/q\(t) < K. Having identified the region of no shipping and the sharing rule for consumption, we now determine the real and nominal exchange rates. In an economy with only a single tradable good the real exchange rate, Z(t), is given by the ratio of the marginal utility of consumption of the tradable good abroad to that at home:16 _ du2[c2(t)]/dc2

rc2(Q-p

In an economy with one good and no transactions costs (r = 0), such as in Lucas (1982), the real exchange rate is always equal to unity. That is, the central planner's trade decision would always equalize marginal utilities of consumption across countries. In the presence of transactions costs, however, it is no longer optimal to correct every imbalance in the marginal utility of consumption at home and abroad at each date; the tradable good will be transferred across countries only when the imbalance in the marginal utilities of consumption is large enough to compensate for the cost of shipping goods. Thus, from equation (3.3), the real exchange rate, Z(t), is bounded by the transactions costs: (3.4)

— — < Z(t) < 1 + r. 1 +r

Let S(t) = Z(t)[p\(t)/p2(t)] denote the nominal spot exchange rate, in terms of domestic currency per unit of foreign currency. The cash-in-advance constraint is, (3.5)

mk(t) > ck(t)

pk(t),

where pk(t) is the price level in country k, and mk(t) is the money holdings. If one assumes that the nominal interest rates at home and abroad are positive, then equation (3.5) holds with equality. Using this assumption and equation (3.4), the nominal exchange rate is, (3.6a)

S{f) = Z{t)ris"

i • - * " " - " - ' 1 " Pi(')

m2(t)/p2(t)]

p2(t)

[m2(t)\

[P2(t)\

The inequalities in (3.6b) can be interpreted as bounds that the nominal exchange rate must satisfy to preclude arbitrage opportunities in the goods 16

This property is discussed in greater detail in Chapter 4.

28

Exchange Rate Volatility

market.17 To see this, note that in order to import one (net) unit of the tradable good from abroad into the home country, the importer has to buy (1 + r) units of this good at the foreign price p2(t) per unit. In the absence of arbitrage opportunities, the all-in cost of the foreign good must be no lower than the domestic price p\(t): S(t) p2(t) (1 + r) > p\(t). A symmetric relation for exports gives us the other bound in (3.6b). To obtain some insight about the model described here, we can compare its implications for the exchange rate to the exchange rate obtained from the monetary model, which is based on a money-demand equation for each country and the assumption of PPP. The money-demand equations implied by the cashin-advance constraint are a special case of the money-demand equations of the monetary approach to the exchange rate, in the sense that we restrict the demand elasticities and the velocities of money to be equal to unity in each country. But the main reason why our model differs from the monetary model is that we allow for the possibility of no trade and for deviations from PPP. To see the similarities and the differences between these models, note that in a one-good economy c^it) corresponds to real transactions volume in the standard monetary model. With unit elasticities and velocities, the monetary model then simplifies to

(3.7)

S(t) =

m\(t)c2(t) m2(t)c\(t)'

One can then show that, for periods when there is trade, the predictions of models (3.6) and (3.7) are similar. The first relation in (3.6b) holds as an equality if there are imports, whereas the second relation holds as an equality if there are exports. After substituting the cash-in-advance constraint, c*(f) Pk(t) = k = {1,2}, into these equalities and into (3.6a), our model simplifies to (1 + r)

when there are exports,

1 u

u

when there are imports. Thus, when trade is in the same direction for two or more consecutive periods, models (3.6) and (3.7) have identical implications for changes in the exchange rate - the reason being that, under those circumstances, relative PPP holds. But in the no-trade region, the exchange rate in our model behaves very differently 17

Benninga and Protopapadakis (1988) derive one-sided "forward" bounds when trading takes time. They also express the exchange rate in terms of general state prices, but do not have a closed-form solution. Dumas (1988, appendix I) shows how the shipping cost in our model can be reinterpreted as one that arises because shipping takes time. For a model with fixed rather than proportional shipping costs, see Shrikhande (1992).

A Simple General-Equilibrium Model of an International Economy

29

from that in the monetary model. Given that most estimates of r\ exceed unity, the

exchange rate in our model, S(t) = [c2(t)/c\ (t)] x~r* x [m\ (t)/m2(t)], is decreasing in relative consumption rather than being proportional to it. This difference arises because in the monetary approach the real exchange rate is fixed at unity, whereas in our model the real exchange rate equals [c2(t)/c\(t)~\~r]. In Chapter 4 we use an extended version of this model to characterize exchange rates in terms of observable variables. In Chapter 6 we use this model to examine the relation between exchange rate volatility and trade. In Chapter 8 we endogenize the tariff cost of shipping goods internationally, and then in Chapter 9 we introduce sticky wages so that money is no longer neutral.

3.3

Extension of the Basic Model to a Production Economy

In the previous section we have presented a bare-bones model of an international endowment economy with distinct nations. In this section, we describe an extended version of the two-country model developed there that explicitly accounts for the production decision. This model is similar to the one in Dumas (1992) and Hollifield and Uppal (1997).18 The advantage of analyzing a production economy is that it allows us to study intertemporal decisions such as savings and investment. The only other difference compared with the model of an endowment economy is that the model with endogenous production is set in continuous time. The reason for this is that in many cases it will not be possible to solve this model analytically, and one will have to resort to numerical methods; in such situations, it will be easier to solve the differential equations that characterize the solution to the continuous-time model rather than the corresponding difference equations for a model set in discrete time. We now assume that there is one production technology in each country and that the goods produced in the two countries are perfect substitutes in consumption and production. We assume that the production technologies have the same expected return and volatility in the two countries and, as before, the domestic and foreign representative consumers have identical preferences given by constant relative risk aversion (CRRA) utility functions. We also assume that the representative consumers in the two countries start out with equal wealth. Thus, the only factors that distinguish one country from another are, as before, (a) production in each country is subject to a country-specific shock, and (b) it is costly to export the physical good from one country to another. That is, each country is characterized by a unique innovation in its production process and these shocks are not perfectly shared.19 18 19

See also the certainty model in Black (1973). Stockman (1988b), in a study of seven European countries, finds that country-specific shocks have had a substantial influence on output growth since the mid-1960s.

30

Exchange Rate Volatility

It is assumed that the goods are produced using a stochastic constant-returnsto-scale technology, which is characterized by its instantaneous expected rate of return, /z, and instantaneous standard deviation, a. We also assume that there are no barriers to entry in an industry. With these assumptions, perfect competition obtains and the value of the domestic [foreign] industry is equal to the value of the existing stock of the domestic [foreign] good, K\{t) [K2(t)]. The physical good that is produced in each country can be consumed, exported to the other country, or reinvested in the production process. To account for the export of the good from one country to another, we introduce two processes, X\(f) and X2(t), with Xi(0) = X2(0) = 0. These processes regulate the joint process for the stock of the domestic and foreign goods, K\(t) and K2(t).20 The processes, X\(t) and X2(t), represent the cumulative amounts of the goods exported, since time 0, from the home to the foreign location, and from the foreign to the home location, respectively. The regulated processes for K\(t) and K2(t), adjusted for consumption and either exports or imports between the two countries, are described as follows:

(3.8a)

dK\{t) = \jiK{(t)dt + aKi(t)dz\(t)] - cx(t)dt - dXx(f) + (1

-r)dX2(t),

(3.8b) dK2(t) = [fiK2(t)dt + aK2(t)dz2(t)] - c2(t)dt - dX2{t) where K\(0) = K2(0) = A'o, and the output shocks at home and abroad, dz\{t) and dz2(t), may be correlated. Given that the home and foreign investor are identical and that the production shocks have the same variance, in an economy with perfectly integrated commodity markets it would be optimal to diversify production risk by always maintaining equal stocks of the good at home and abroad. That is, it would be optimal to regulate the processes for K\(t) and K2{t) continuously so that K\(t) = K2(t). However, as explained earlier in the context of the endowment model, in the presence of the trading cost it is not optimal to correct an imbalance in the relative quantity of the good at home and abroad at each instant because the benefits obtained by exporting or importing the good may be less than the cost incurred in doing so. Dumas (1992) and Davis and Norman (1990) have shown that, as in the endowment model, in the presence of transfer costs 20

The theory of instantaneous control of Brownian motion, first examined in Benes, Shepp, and Witsenhausen (1980), is developed in Harrison and Taksar (1983) and Harrison (1985). For a rigorous treatment, see Davis and Norman (1990). For a simple exposition of the mathematical theory, see Dixit (1991) and Dumas (1991). Dixit (1992) and Pindyck (1991) provide a review of the applications of this theory to various economic problems.

A Simple General-Equilibrium Model of an International Economy

31

there will exist a region of the state space within which it is optimal not to export or import the good. With proportional transfer costs and isoelastic utility functions, this no-trade region is a cone, delineated by two rays with slope X and I/A originating from the origin (as in Figure 3.1). Given that the transfer costs are proportional, the optimal shipping policy is to trade the minimal amount of physical goods necessary to stay within the no-trade region. The objective of each representative agent is to maximize expected lifetime utility, Max E /

Jo

Qxp(-8t)-^-—

1 -*/

dt,

rj>0,8>

0,

which is the continuous-time analog of equation (3.1). Given our assumption of complete and frictionless financial markets, the objective function of the central planner is to maximize equation (3.9),21 the equally weighted sum of the domestic and foreign expected lifetime utility, subject to equation (3.8): (3.9)

V[K{(t),K2(t\t]=

Max dtu( We further note that the problem in equation (3.9) is an infinite-horizon one, and that the processes in equation (3.8) are Markovian and time-homogeneous. Thus, the solution to equation (3.9) is stationary Markov. We will therefore work with the undiscounted value function, V[K\(t), K2(t)], where V[K\(t), K2{t), t] = exp(-St)V[KX (0, K2(t)].22 Also, the value function is homogenous of degree 1 — r] in K\ and K2\ this allows us to reduce the state space from two variables to only one, co(t) = \n[K\(t)/K2(t)].23 The first-order conditions for domestic and foreign consumption are: c{[K\(t), K2(t)] = V\[Ki(t),

K2(t)YXh\

c2[Kx(t), K2(t)] = V2[Kx(t)9

K2{t)YX/\

where subscripts on V denote partial derivatives. The real exchange rate, as in equation (3.4), is: (3.10) 21 22

23

This is the analog of equation (3.2a). That this transformation is appropriate can be seen by direct substitution of e~8t V[K\ (t), ^CO] into the Bellman-Jacobi equation for V[K\(t), / ^ ( O , t]. A similar transformation is made in

Ingersoll(1987,p.74).

The advantage of using this particular definition of the imbalance is that it makes it easier to interpret the results. This is because the conditional variance of the process for co{t) is constant, and, therefore, the drift of this process is sufficient to characterize the process.

32

Exchange Rate Volatility

After substituting in the optimal consumption policies, the Hamilton-JacobiBellman equation that characterizes the solution to the problem in equation (3.9) is:

(3.H) o = (-±-\vl«-l)/" \\ -t]J

+ (^L-]v^-zl)/11 -8V \\-T]J

+ Vl2cf2KlK2[dzi(t)x

dz2(t)l

Also, V[K\(t), K2(t)] must satisfy the value-matching and smooth-pasting boundary conditions.24 The solution25 to the central planner's problem in (3.9) can be obtained by solving the differential equation in (3.11), subject to the boundary conditions. This solution allows us to determine optimal consumption, the optimal export-import policies, and also the process for the log of the imbalance in the accumulation of capital in the two countries, a>(t) = \n[K\(t)/K2(t)]:

where dz = (dz\ — dz2)/V2 is a standardized Brownian motion. 3.3.1

The Dynamics of the Spot Exchange Rate

Dumas (1992) finds that in the preceding model, the real exchange rate given in equation (3.10) has several properties that are consistent with the data: the exchange rate is heteroskedastic, with a tendency to revert back to PPP. Moreover, the deviations from PPP generated by the proportional shipping cost are persistent. This implies that even though there is some mean-reversion tendency, these deviations can last a very long time.26 The stationary (unconditional) probability distribution is U-shaped, indicating that the probability mass of the exchange rate is concentrated in the area close to the edges of the no-trade region. To see the intuition underlying the last result, note that the drift of the process for co(t) is positive. That is, imbalances in K\/K2 tend to increase 24

25 26

The value-matching boundary conditions state that one exports or imports goods only when the change in lifetime expected utility is exactly offset by the cost incurred by trading the good; these conditions are: when K\/K2 = I/A. then (1 — x)V\ = V2, and when K\/K2 = A. then Vi = (1 — T ) V2. The smooth pasting conditions ensure that the decision to ship is made optimally: when K\/K2 = I/A. : (1 — T)V\\ = V\2 and (1 — r)V2i = Vn\ and analogously for the case when K\/K2 = A.. It can be shown that if 8 > (1 — r])[/jL — 0.5 r\ a2], then a solution to this problem exists and is unique. Abuaf and Jorion (1990) find the half-life of exchange rate deviations from PPP is about three years.

A Simple General-Equilibrium Model of an International Economy

33

rather than decrease, implying that the deviations from the law of one price are persistent. To understand the reason for this, consider the situation where the home capital stock increases relative to that abroad. In the decentralized setting, the foreign investor owns a fraction of the domestic capital stock in order to diversify output risk; thus, the increase in the domestic capital stock should lead to a higher dividend being paid out to the foreign investor. Because of the shipping cost, however, it is not optimal to ship the foreign investor's share of the dividend. Instead, the foreign investor invests this dividend in the domestic production process, leading to an increase in the already larger domestic capital stock. This additional investment has the effect of increasing the foreign investor's wealth; consequently, in order to consume more (because of the wealth effect), she decreases investment locally, thereby decreasing the already smaller foreign capital stock. Consequently, the capital stock in the home country, relative to that in the foreign country, tends to increase rather than decrease. A major implication of the results in Dumas is that the linear mean equations typically used in empirical characterizations of the exchange rate are unlikely to identify a process that, as this model shows, is nonlinear with heteroskedasticity. Moreover, the long-run behavior of the derived exchange rate is very different from its behavior in the short run, implying that an appropriate empirical model must distinguish between these two. 3.3.2

The Nominal Exchange Rate in the Production Economy

The model just described is of a real economy. As in the model of the endowment economy described in Section 3.2, we introduce money via the cash-in-advance constraint in equation (3.5). In this simple setup, we assume that the exogenously given process for money in the domestic economy is,

dm\(t) = iim]m\(t)dt + crmim\(t)dzmi(t), where /xm, is the drift of the money supply process, ani] is its volatility, and dzm] is the Wiener shock. We denote the covariances between the shock to money supply and the shocks to domestic and foreign output as crK]in] and oKimx. The conditional covariance of domestic money and the capital imbalance is denoted by awm,; the covariance of foreign money and the capital balance from the foreign perspective is cr_wm,. The process for the foreign-money supply is given analogously. Again, if we assume that the nominal interest rates at home and abroad are positive, the cash-in-advance constraints bind in equilibrium, implying that the process for domestic prices is: dIn p\(t) = dInm\(t) -

dInc{(t).

34

Exchange Rate Volatility

Denote the nominal spot exchange rate by S(t), and define s(t) = In S(t) = e(t) + Inp(t) — In/?. Then, the stochastic process for the log of the nominal exchange rate is as follows: ds(t) = ([/Zm, - fJLnt2] - 0.5[a^ - O^J) dt + CTmidzmi(t) - om2dzm2{t)

dZ(t),

where we remind the reader that Z(t) denotes the real exchange rate while Zkif) is the Wiener shock. In Chapter 5 we use this model to study the relation between forward and spot exchange rates; and in Chapter 7 we use it to examine how the presence of financial markets influences social welfare.

3.4

Other Extensions

We now list other extensions to the model described here that we consider in later chapters. In Chapter 4, on exchange rates, we extend the model to multiple countries that can differ in terms of their preferences and endowments. Also, we allow for multiple goods with different degrees of tradability: these goods can be tradable without cost, tradable at a cost (fixed or proportional), or nontradable. We will also see that one does not need to assume explicitly the cash-in-advance constraint; money can enter as an argument of the utility function. In fact, for the task of exchange rate determination, it turns out that it is not necessary to specify the exact role that money plays in the economy. Also, one can relax the assumption on preferences: while the utility function still needs to be time-additive, it is not restricted to be homothetic, nor of the hyperbolic absolute risk aversion (HARA) class. In Chapter 7, on capital flows, we consider explicitly the role of financial markets by computing the equilibria for both the case of integrated financial markets and also when they are segmented. In this chapter, we also see that one is not limited to CRRA time-additive utility: one can extend the analysis to recursive utility functions, proposed by Kreps and Porteus (1978), Epstein and Zin (1989), and Duffie and Epstein (1992), that allow one to distinguish between risk aversion and the elasticity of intertemporal substitution. In Chapter 8, on tariffs, we no longer assume that the shipping cost is exogenous; instead, we will interpret the shipping cost as an endogenously determined tariff that the government chooses to realize its objectives. Then, in Chapter 9, we endogenize monetary policy and also the choice of the exchange rate regime.

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

In this chapter we characterize the exchange rate in a general-equilibrium setting using an extended version of the model described in Chapter 3. Relative to the monetary models of the exchange rate, equilibrium models offer the advantage of being based on strong microeconomic foundations. However, existing equilibrium models of the exchange rate, like the basic model described in the previous chapter, often depend on very specific assumptions about the number of goods and countries, the utility functions and production processes, and the type of frictions in the international-goods markets. See, for example, Stockman (1980), Lucas (1982), Domowitz and Hakkio (1985), S vensson (1985a, 1985b), Hodrick and Srivastava (1986), Stulz (1987), Stockman and Delias (1989), Dumas (1992), Engel (1992a, 1992b), Backus and Smith (1993), Bekaert (1994), and Sercu, Uppal, and Van Hulle (1995). In contrast, the framework we develop in this chapter is one where utility functions are quite general and can differ across countries, and where commodity markets may be imperfect. We find that with financial markets that are complete and integrated, the nominal exchange rate mirrors differences in initial wealths and marginal indirect utilities of nominal spending. Differences in marginal indirect utilities may arise from commodity market imperfections and/or differences in consumption preferences, time preferences, or risk aversions. To relate these marginal indirect utilities to observable variables so that one can evaluate the model empirically, we then restrict utility functions to be homothetic with constant relative risk aversion (CRRA). In this CRRA model, we show that the nominal exchange rate is loglinear in time and in the nominal spendings and price levels of the two countries. Thus, according to the CRRA model there are, generally, three missing variables in the standard purchasingpower parity (PPP) equation: time, and the nominal spendings in the two countries. Moreover, the elasticities of the exchange rate with respect to the price indices need not be identical across countries, and their signs are likely to differ from what PPP predicts. We find that PPP holds only under very restrictive assumptions: if either relative risk aversion (RRA) equals zero and time 35

36

Exchange Rate Volatility

preferences are identical across countries, or if there is a fully pooled equilibrium with one (composite) good that can be traded costlessly. On the empirical front, the questions we ask are, first, whether we can reject PPP and, second, whether the addition of the variables implied by the CRRA model improves our ability to explain the behavior of exchange rates. By nesting PPP as a special case of the CRRA equilibrium model of exchange rates, we can test a much richer set of hypotheses than the ones addressed in the standard cointegration analysis of PPP. Analyzing exchange rates, prices, and differentialtrend-corrected aggregate consumption data in a Johansen and Juselius (1992) cointegration framework and in error-correction regressions, we reject the standard PPP hypothesis and find evidence in support of the CRRA model. In Section 4.1 we present an equilibrium model of exchange rates that is a generalized version of the model described in Chapter 3. In Section 4.2 we derive the level of exchange rate for the case where preferences are homothetic and exhibit constant relative risk aversion; we also determine the conditions that yield PPP. Then we examine empirical tests of PPP in Section 4.3 and compare the results to those from tests of the CRRA model of exchange rates in Section 4.4.

4.1

The Economy and the Equilibrium Exchange Rate

In this section we first describe a model of a multicountry, multigood economy with imperfect commodity markets. We impose only a few (very standard) restrictions on preferences, and none on the endowment processes. In the second part of this section, we characterize the exchange rate in this general setting. The economy that we consider consists of M > 2 countries. We focus on two arbitrarily selected countries that are referred to as the home country (subscript k = 1) and the foreign country (k = 2). Each country has a representative consumer with a standard, strictly quasi-concave utility function defined over N > 1 goods. Across countries these representative individuals may differ in terms of risk aversion, consumption preferences, and initial wealths. The outputs of each of the TV goods can be stochastic over time. The economies could be exchange economies where output is given by exogenous endowment processes (as in Stockman, 1980, and Lucas, 1982) or production economies with endogenous investment decisions (as in Dumas, 1992, and Stulz, 1987). The specification of the production or endowment processes is quite general: some goods may be produced everywhere, while other goods may be produced only in some countries. International shipment of these goods may be costly for some or even all of these goods; these shipping costs are assumed to be purely variable costs (as in the models described in Chapter 3). Given these costs for transferring goods across countries, some goods may be traded all

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

37

the time, some may be ixdidable in the strict sense (i.e., traded only if the price difference is sufficiently large to justify incurring the shipment costs), and some goods may be de facto nontradable.1 For simplicity, money is introduced into the model via the Lucas (1982) cash-in-advance constraint.2 We assume that financial markets are complete and perfect. Thus, the outcome of decentralized consumption and investment decisions is identical to the solution of a central planner's problem of the form M

(4.1)

9kEt\ J^ Uk(ck(t))\

Max£ r k=2

which is the multicountry analog to equation (3.2a) in the case of the basic twocountry model described in Chapter 3. This optimization is constrained by an opportunity set that depends on the currently available outputs, the production functions, and the technology for transferring goods across countries.3 We do not need to specify the opportunity set explicitly. In (4.1), ck(t) is the vector of consumption quantities ckj(t) of good j ( = 1 , . . . , N) consumed by the representative individual in country k ( = 1 , . . . , M) and Uk is the utility function of the representative investor in country k. The relative weight assigned by the central planner to each of the other countries, 0k, generally is a function of the initial distribution of wealth in the equivalent decentralized problem.4 In turn, these initial wealths depend on the initial endowments, the characteristics of the (stochastic) investment functions or endowment processes, the frictions in the international markets for consumption and capital goods, and the utility functions. For example, one sufficient (but not necessary) set of assumptions to obtain 0k — 1 is when the utility functions, the initial endowments, and the parameters of the output processes of all countries are identical. Given these assumptions, we now derive the exchange rate. Define the net endowment of each good in each country as the amount available for consumption. In an exchange economy the net endowments are, of course, identical to the 1

2

3 4

Other frictions could be introduced, like shipment lags (goods sent from one country at time t arrive only at time t + 1) and transaction lags (a trade arranged at time t is implemented at time t + 1 only). It can be shown that neither transaction lags nor shipment lags affect any of our conclusions. Essentially the same results would be obtained if real money balances were introduced as an argument in the utility function, except that the price index will contain the interest cost of money balances - see, for instance, Stulz (1987). See equations (3.2b, c, d) for a particular example of these constraints. In a decentralized economy with a complete capital market, there exists a portfolio strategy that allows investors to implement the central planner's solution. For example, consider the case where 6k = 1, utility functions are equal, and shipment costs are zero. The central planner's solution then is to give each of the M countries an equal amount of consumption. The portfolio strategy that implements this plan is that each country holds 1/M-th of the shares of each productive asset, so that each country can obtain 1/M-th of world output.

38

Exchange Rate Volatility

gross endowments, whereas in a production economy we need to set aside the resources needed for the optimal investments identified from the solution of the problem defined in equation (4.1). If the objective function in (4.1) is maximized, it must be impossible to further increase the utility from current consumption in one country without reducing either consumption in another country or investments. Denote the aggregate utility of the central planner from immediate consumption by (boldface) U(.): M

(4.2)

U(c(O) = tfi(c,(O) + ][>t/*(c*(O). k=2

Thus, in the optimum identified from (4.1), U(c(f)) must be at its maximum subject to the feasibility conditions. From this Pareto optimality of consumption, it follows that the relative price for any pair of goods can be read off as the marginal rate of substitution (MRS), along U(c(t)), in the optimum. Let us choose, as the pair of goods, one unit of good j located in country 1 and one unit of the same good j located in country 2. The local-currency prices of these goods are denoted by p\j(t) and P2j(t). Because the relative price has to be computed from nominal prices expressed in a common numeraire, we need a reference currency and an exchange rate. Without loss of generality, we select currency 1 as the numeraire, and use S(t) to denote the nominal exchange rate (units of country 1 currency per unit of currency 2). Here, we write the condition that equates the relative price to the MRS:5

S(t)p2j(t)

=

dV(t)/dc2j(t)

We can now link the nominal exchange rate to the marginal indirect utility function. The indirect utility function, V(Mk(t), pAt)), is defined as (4.4)

V(Mk(t), pk(t)) = Max |t/*(c*(f)) - A*(f) (t)

ckj(t)pkj(t)-Mk(t) where Mk (t) is the amount of nominal spending, expressed in units of currency k. The marginal indirect utility of nominal spending in country k is the multiplier, A(0, in the preceding optimization problem:

dV(Mk(t\pk(t)) This corresponds to equation (3.6a) in the basic model.

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

39

Then, we have our first result: the nominal exchange rate, S(t), is proportional to the ratio of the marginal indirect utility of total nominal spending in the two countries:6 (4.5, We wish to study the implications of this result for the real exchange rate and deviations from PPP. The focus is on the level of the exchange rate and most of this discussion is confined to the special case of time-additive homothetic utility functions.

4.2

Characterizing the Level of the Exchange Rate

In this section we first discuss the general implications for the exchange rate equation (4.5) when preferences are restricted to be homothetic and the discount factors for the utility of future consumption are constant over time. This assumption of constant time preference is abbreviated as CTP. Following this, we derive the exchange rate under the additional assumption of constant relative risk averse (CRRA) utility functions, and show that PPP holds only as a very special case. The motivation for restricting the analysis to homothetic utility functions is that these induce a price index, without which popular concepts like the real exchange rate or PPP deviations are not well defined. The assumption of constant relative risk aversion is motivated by the desire to express the level of the exchange rate in terms of observable variables. 4.2.1

The Exchange Rate under Homothetic, CRRA Utility

With time-additive utility functions and a constant discount rate, lifetime utility Yju(ck(O, t) is of the form ^JSjwfotW). When, in addition, utility is homothetic, the period-by-period utility function uk(ck(t)) can be written as O[u^(cjt(0)], where vk(ck(t)) is linear homogenous in the consumption quantities and <&k is a positive, monotone (and, usually, concave) transformation. The function vk(ck(t)) c a n be thought of as summarizing the consumption preferences (which, for homothetic functions, are independent of wealth or total 6

To see this, substitute (4.2) into (4.3) to relate the central planner's MRS to the marginal utilities of the two countries: S(t)p2j{t)/p\j(0

= 029U 2 (t)/dc 2 j (t)/dU\(t)/dc\j(t).

Then solve for the

exchange rate: (c2(t))/i)c2j(t) PI jit) = 02 3U\ (c\(t))/'dc\jU) P\i(t) HU2

5(0-

To obtain (4.5), we substitute dUk(t)/dckj(t) = Ak(t) pkj(t), obtained from the optimization problem defined in (4.4).

which is the first-order condition

40

Exchange Rate Volatility

spending), while the curvature of the transformation, O(.), reflects the degree of risk aversion. This separation of consumption preferences from risk aversion makes it possible to characterize the level of the exchange rate in terms of the level of nominal spending, the price level, and relative risk aversion. If the function $>[vk(ck(t))] is at its maximum value given a consumption budget constraint, then vk(ck(t)) must also be at its maximum value subject to the same constraint. It is well known (see, e.g., Samuelson and Swamy, 1974) that the solution of the linear-homogenous problem,

vk(Mk(t), pk{t)) = Max \vk(ck(t)) - Xk{t)\Yckj(t)

pkj{t) - Mk(t)]\,

is of the form vk(t) = Mk(t)/Ylk(pk(t)). The function Uk(pk(t)) is independent of nominal spending, Mk(t), and is linear homogenous in the prices. Accordingly, Uk(pk(t)) is interpreted as the price level in country k, and vk(t) = Mk(t)/Uk(pk(t)) the total real spending. These properties of homothetic functions allow us to specialize the result in equation (4.5): with homothetic utility functions, the nominal exchange rate, S(t), and the real exchange rate, Z(t) 9 are given by:7

and ,4.7, Given that the marginal utilities of aggregate real spending are not observable, equations (4.6) and (4.7) cannot be used to study the empirical behavior of the level of the nominal and real exchange rates; we will make the additional assumptions that investors have CRRA utility functions, with risk aversion Equations (4.6) and (4.7) follow upon using the relations 8rk Vk[Mk(t), Pk(t)] = vk(t) = Mk(t)/Ylk(t), which means that we can specify the marginal indirect utility of nominal spending as: dVk(Mk(t),

Pk{t))

8Mk(t)

d<$>k{vk{t)) dvk(t)

dvk{t)

8Mk(t)

dvk(t)

Uk(pk(t))

To understand the role of (82/81Y, note that different impatience factors mean that the two countries are depleting their wealths at different rates. Thus, (82/81Y continuously updates the initial 62 so as to capture this divergence of the two countries' wealths. Stated differently, (<$2/<5i)' reflects one of the causes (besides frictions in the goods markets) of divergence between undiscounted marginal utilities, d$>k/dvk; in that sense it eliminates the effect of the trendwise divergence of these marginal utilities on the exchange rate rather than predicting that there should be a time trend in the exchange rate.

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

41

given by r]k. This allows us to link, in a tractable way, the marginal utilities of real consumption to real consumption quantities for which data are available. Specifically, with CRRA the exchange rate becomes a loglinear function of both the price level and the level of nominal spending in the two countries, with the constraint that the elasticities of each country's price level and nominal spending sum to unity. Thus, with homothetic preferences and constant relative risk aversion, the nominal exchange rate is:8

S'2 I - r ~

2

s\ i

-r

when JJ ^ 1. In the log-utility case (tj = 1),

Equations (4.8) and (4.9) encompass many existing models of the exchange rate, which have typically been derived in settings with one or two goods (whereof at least one good is tradable only at a cost) and constant relative risk aversion. For example, assuming two countries with identical relative risk aversions and discount factors, Sercu et al. (1995) derive (4.8) and (4.9) for the special case of a single (imperfectly tradable) good, while Backus and Smith (1993) derive (4.8) for the case of constant elasticity of substitution (CES) consumption preferences defined over one perfectly tradable good and one nontradable good. Stulz (1987) derives equation (4.9) from a two-country production economy with log investors that have equal discount factors and identical Cobb-Douglas preferences defined over a perfectly tradable good and a nontraded good.9 Thus, we see that all these special versions generalize to cases where there are N goods (regardless of their degree of tradability) and K countries, and where the degrees of relative risk aversion and time preference, as well as the commodity preferences, can differ across countries. Equations (4.8) and (4.9) can be derived by recalling that constant relative risk aversion utility functions have the form

9

The equations then follow upon substituting Vk(t) = Mk(t)/T\k(t) into these functions and deriving the marginal utilities as in (4.6). The exchange rate equation in Stulz (1987) also contains interest rate terms. This is because he introduces money via the utility function; as a result, the interest cost of holding money balances becomes one of the prices in Tlk(t).

42

Exchange Rate Volatility

Our model also nests the monetary economies considered in Bakshi and Chen (1997) and Basak and Gallmeyer (1998), where the focus is on determining the prices of financial securities rather than expressing the exchange rate in terms of observable variables and relating it to PPR Bakshi and Chen characterize the exchange rate and prices of financial assets in terms of exogenous variables in an exchange economy where money is neutral. However, they restrict utility to log functions and the endowment processes to lognormal distributions; also, they consider only an equilibrium with perfect pooling, that is, without deviations from PPP. Basak and Gallmeyer characterize the exchange rate in an exchange economy with money in the utility function. In contrast to these models, we can characterize the exchange rate in terms of observable variables without having to specify exactly what role money plays in our economy. 4.2.2

Purchasing Power Parity

Relative PPP holds when

S(t) whereas absolute PPP holds when, in addition, 02 = 1.10 Two alternative sufficient sets of conditions for PPP are: 1. Commodity markets are frictionless and agents have identical, homothetic utility functions - irrespective of their time and risk preferences. Then also 02 = 1 (absolute PPP holds). 2. Agents have linear homogenous utility functions (% = 0) and equal impatience across countries (8\ =82) - irrespective of market imperfections and international differences in consumption preferences.1' 10

Note that absolute PPP is a useful concept only if we have absolute measures of the price level, that is, the cost in units of local currency of a basket that corresponds to some (arbitrarily scaled but internationally common) reference consumption bundle. The CPI data that are available are not absolute measures of the cost of a basket in the sense just defined; rather, CPIs are indices of costs relative to the cost of a basket that differs across countries and was measured in some reference period that might also differ across countries. Given that we have only relative price data, and that consumption bundles that differ across countries, we have to rely on relative PPP. 1 ' Case (1) follows from the fact that under the assumptions of frictionless markets, relative prices are equal all over the world. Given identical and homothetic utility functions, it follows that the consumption bundles have the same (relative) composition across countries: at any time t there is but one composite good in the world, with time-varying composition proportional to the aggregate consumption amounts of the individual goods. The quantities of this aggregate good consumed per country are just the Vjt(O's. Equation (4.7) implies that the real exchange rate is the marginal rate of substitution along an indifference curve 4>i(ui(0) + ^2^2(^2(0)- As the composite good can be transferred internationally costlessly, this marginal rate of substitution of v\(t) for V2(t) always equals unity. Case (2) follows immediately from setting <J>(I>A(O) = and 82 =S\ in (4.6).

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

43

From the foregoing result we see that it is possible to obtain PPP as a special case of the CRRA model: equation (4.10) can be obtained by setting the RRA coefficients, rjk, in (4.8) equal to zero and eliminating the time trend on the righthand side. In case (1) this is valid by direct assumption. In case (2) the terms in r] and 8 cancel out because under the assumptions of perfect markets and identical homothetic consumption preferences - that is, one common composite good - the marginal utilities of real spending are equalized; specifically, if, in (4.6), 8t2d®2(t)/dv2(t) equals 8\d<$>\{t)/dvx{t), then PPP obtains. 4.2.3

Implications of the General Model for PPP Tests on First-Differenced Data

In the traditional test of relative PPP, one regresses changes in the log exchange rate on inflation differentials across countries: (4.11)

A l n S = a + £ [ A l n n i - A l n n 2 ] + e,

with the null hypothesis that /3 = 1.12 Our theoretical analysis has the following implications for these tests. First, consider the special case of our model where consumption preferences are homothetic, time preference is constant, and relative risk aversion is equal across countries and constant over time. In this case, equation (4.8) simplifies to: (4.12)

AlnS = <$! -82 + rj[A\nMl - AlnM 2 ]

-rj)[AlnUi

- Alnn 2 ].

Given that rj is commonly accepted to be larger than unity, as long as we control for nominal spending, equation (4.12) suggests that an increase in domestic inflation should lead to an appreciation of the home currency (a decrease in S) not to a depreciation, as PPP predicts. In light of this, the puzzle in standard regression tests of relative PPP is not why we do not observe exchange rates that are equal, on average, to inflation differences. Rather, the puzzle is why we often observe a positive association between exchange rate changes and inflation differentials at all. To understand this, note that in the standard regression tests of relative PPP given in (4.11), the nominal spending variables are omitted. Given that growth rates of nominal spending are positively correlated with inflation rates, the true (negative) effect, 1 — r], of inflation is to some extent confounded with the 12

For a review of estimations that take into account errors in variables, see, for instance, Apte, Kane, and Sercu (1994) or Betton, Levi, and Uppal (1995). Stulz (1987) provides a theoretical analysis of the effect of nontraded goods on the real exchange rate, and Kravis et al. (1975) offer empirical evidence.

44

Exchange Rate Volatility

positive effect, ij, of the omitted spending variable. As a result, the empirical coefficients of the regression slope of A In .Son A ln(I~Ii/n2) no longer estimate r\ but are biased toward unity.13 As Sercu, Uppal, and Van Hulle (1995) note, this is especially true in low-frequency data and in samples drawn from periods of hyperinflation where the correlation between growth in nominal spending and inflation is likely to be high. In addition to these observations, we also note the following. First, in the case where preferences are nonhomothetic, there is an additional omitted variable, marginal inflation, denoted by A In Uk(t), which is imperfectly proxied for by the consumer price index (CPI) measure of inflation, A In Tlk(t). Thus, the coefficient for CPI inflation in a regression of A In S on A l n n i / n 2 is expected to be closer to zero than in the case of homothetic preferences. Second, even in the homothetic-utility version of the model, a second omitted variable shows up, namely the time preferences. The implied correlation between the prices and the (omitted) time-preference variables then introduces further biases in the regression estimates. Third, in the more general equations (4.8) and (4.9), the coefficients for the true inflation rates and the growths in nominal spending need not be identical across countries because the degree of risk aversion need not be equal across countries.14 Imposing a single coefficient for AlnMj and — AlnM 2 will produce estimates whose expected values are equal to neither rj\ nor 772 (and likewise for the coefficients of the inflation terms). Fourth, the risk aversion coefficients need not be constant over time. Thus, the standard constant-coefficient linear regression test for PPP may be inappropriate. In view of all this, the poor results that are commonly obtained in regression tests of relative PPP may simply be the result of misspecification of the test equation rather than some kind of excess volatility or irrationality.15 Our general model also has implications for empirical work on other exchange rate models. For example, a test of the CTP/CRRA model is provided by Backus and Smith (1993). They assume equal relative risk aversions, r\, and 13

Alternatively, one could rearrange (4.12) as - Aln(M 2 /n 2 )] + [A In 111 - A l n n 2 ] , and argue that the difference of the two real consumption-growth rates has a low variability, so that the omitted-variable bias is small and the coefficient of the inflation differential comes out positive. In their regression tests of relative PPP, Apte et al. (1994) allow for different coefficients across countries, and they test for equality. The only instances where the equality hypothesis is not rejected is when the power of the test is low. See the survey article by Frankel and Rose (1995) for a discussion of the presence of bubbles in exchange rates.

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

45

discount rates, S. The resulting model, A l n S ( r ) ^ = »/Aln has two implications. The coefficients of determination of the changes in the log exchange rate and in the log real-consumption ratio should be equal, and the autocorrelation of the log of the real exchange rate changes should have the same sign as the autocorrelation of changes in the log real-consumption ratio. Backus and Smith reject the equilibrium model based on the foregoing. However, given that these tests assume homothetic preferences, as well as equal risk aversions and discount rates across countries, what they reject is only a special case of the equilibrium model.16

4.3

Empirical Tests of PPP

In this section, we provide a brief overview of the existing methodology used in testing PPP, describe our data set, and then undertake these tests for our data set. Our objective in testing the standard PPP hypothesis is to establish a base case for comparison with tests of the CRRA model that are reported in Section 4.4. 4.3.1

Review of the Empirical Methodology Used to Test PPP

Rather than requiring PPP to hold exactly, most of the empirical literature adopts the weaker hypothesis that PPP holds as a long-run relation. Specifically, the hypothesis is that real exchange rates have no unit roots; or, alternatively, one determinant of the (time-varying) drift in the spot rate is assumed to be partial correction of the beginning-of-period deviation from PPP. A first type of test of long-run PPP can be found in Abuaf and Jorion (1990), who apply AugmentedDickey-Fuller (ADF) tests to real exchange rate data. The test equation is: nus(r-i) where AZ^ y* represents lagged changes in the left-hand-side variable and & is the adjustment speed. Abuaf and Jorion reject a unit root - the estimate of & is significant. This is consistent with long-run PPP as defined previously, but may also be consistent with the CRRA model.17 16

17

Kollmann (1995, n. 9) examines the predictions of the Backus and Smith (1993) model and finds that the data reject the restriction that the risk aversion coefficients are identical across countries. Even when these coefficients are allowed to differ across countries, he finds little support for the model with homothetic preferences and complete financial markets. The reason is that, even when there are shipment costs, trade is still likely to bound the divergence between the marginal utilities whether or not risk aversion is positive. Thus, in itself the evidence of stationary real exchange does not say anything about the CRRA model.

46

Exchange Rate Volatility

Another strand of the empirical PPP literature employs cointegration analysis. Cointegration analysis was pioneered by Granger (1981) and developed by, among others, Engle and Granger (1987), Phillips (1990), and Stock and Watson (1988) and more recently by Johansen (1988, 1991) and Johansen and Juselius (1990, 1992). The original Engle and Granger (1987) cointegration approach adopts a bivariate framework, whereas the more recent and more powerful approach developed in Johansen (1991) uses a multivariate framework that allows for the existence of multiple cointegrating vectors and a richer specification of short-run dynamics. Nessen (1994), Froot and Rogoff (1995), and Edison, Gagnon, and Melick (1997) provide reviews of the use of cointegration analysis to test PPP. A lucid and relatively nontechnical exposition of cointegration analysis can be found in Dickey and Rossana (1994). Cointegration analysis differs from ADF tests on real exchange rates in at least three ways. First, rather than fixing, a priori, the coefficients of the log CPIs at unity, the coefficients are unrestricted. That is, in its simplest form the equation that underlies a bilateral test is A In 5(0 = ak + AZ* yk - ft [£0 In S(t - 1) - £ u s In n u s (f - 1) + pklnnk(t-l)] + ek(t). In tests of this equation, Azk contains the lagged inflation rates and exchange rate changes for the two countries being considered. The hypotheses is that ft should be positive, and that the PPP predictions, pus/Po = 1 = Pk/Po, should be consistent with the data.18 A second difference relative to ADF tests is that cointegration analysis can be extended to allow for a second long-run relation among the three variables. In a bilateral test between the United States and country k, the generalized model is: (4.13)

A In Sk(t) = ak- fti [fti In Sk(t - 1) - AJSI In n u s ( r - 1)

+ pki In n*(f - 1)] - ft2[£o2 In Sk(t - 2) - £ US2 In n u s ( r - 2) + pk2 In Uk(t - 2)] + Az* yk + s(t). Each long-term relation in (4.13) now has its own cointegration vector p and its speed-of-adjustment parameter f. According to the PPP hypothesis, one of the cointegration vectors should be p = (1, 1, I). 19 Note that Flores et al. (1996) test the PPP hypothesis using a multivariate framework. In their tests, they allow for the speed of mean reversion to differ across countries. Thus, our model provides theoretical support for this specification. 18 19

Note that, here, the null is PPP (i.e., there is a stationary real rate) while in the ADF test the null is the presence of a unit root; in this sense, the two tests are complementary. The possible presence of a second vector could reflect policy coordination; for example, a successful fixed-rate policy may require a long-term relation between the two price levels. A third cointegration relation would not be consistent with the unit-root properties in the series.

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

47

Lastly, cointegration can be extended to multilateral data. In the multicountry version of (4.13), Az* yk is expanded to allow for short-term dynamic impacts from lagged inflation rates for all five countries and lagged exchange rate changes for all four pairs; and the error-correction term is likewise expanded to allow for up to eight long-term relations between the nine variables (four exchange rates and five CPIs). Thus, the multicountry version of the model is (4.14)

A lnS(r) = ak + ? [Y(t - 1) 0] + Az y + e(t)

where: A In S(0 is the vector of all five exchange rate changes between dates t — 1 and t. Y = [In S\, In S2, In S3, In S4, In n u s , In n , , In n 2 , In n 3 , In n 4 ] . P is a 9 x r matrix containing nine coefficients for each of the r cointegration relations, where r < 8. £ is a matrix of adjustment speeds for each of the four exchange rates to each of the r long-term relations. Az contains lagged changes in the variables in Y. y contains the coefficients of Az. PPP posits that ft should contain at least the following cointegration vectors: country country country country

1 versus U.S. 2 versus U.S. 3 versus U.S. 4 versus U.S.

px ppp = [1,0, 0,0, 1, 1,0,0,0]' # u w = [0, 1,0,0, 1,0, 1,0,0]' &!PPP = [0, 0, 1,0, 1,0,0, 1,0]'

J&U>PP = [0,0,0, 1, 1,0,0,0, 1]'

Thus, in a multilateral analysis, a PPP test should find at least four cointegration vectors, but again there could be more than just these four. The PPP prediction for P is verified with the Johansen-Juselius likelihood ratio (LR) test (or, more recently, the more powerful test of Horvath and Watson, 1995).20 Nessen (1994) does reject the PPP hypothesis. Combined with the Abuaf and Jorion (1990) evidence of stationarity in the real exchange rate, such a rejection of the PPP hypothesis would suggest that there are missing variables in the model - for example, spending data and a time trend - that are correlated with the price variables. A third, and closely related, testing methodology is to employ panel analysis of the bilateral model (4.14).21 Examples are Nissen (1997) and Koedijk et al. (1996), with the proviso that they a priori restrict /3us and pk to be equal and specify Az to contain the contemporaneous inflation difference (rather than 20

21

Edison et al. (1997) show how the power of these cointegration tests can be improved using the Horvath and Watson (1995) procedure. See also MacDonald and March (1994). Expanded data sets have been considered also by Frankel and Rose (1996), Froot et al. (1995), Lothian (1997), Lothian and Taylor (1996), Wei and Parsley (1995), and Taylor (1995). Related work includes Engel, Hendrickson, and Rogers (1996) and O'Connell (1996).

48

Exchange Rate Volatility

lagged inflation rates and exchange rate changes). Nissen and Koedijk et al. find significant values for the adjustment speed, and obtain f3 estimates that are close to unity, as predicted by PPP. This in itself does not reject the CRRA model, because the missing variable, the real spendings, may be uncorrelated with the price data. In a next step, Nissen and Koedijk et al. also include the ratio of the two countries' real spending as an additional regressor and find no evidence of any effect on the real exchange rate - a result that differs markedly from ours as explained below. 4.3.2

Data

The data we use are quarterly consumption spending series, CPI data in the last month of the quarter, and end-of-quarter exchange rate data from International Finance Statistics (IFS) for the United States (US), Japan (JP), Germany (DE), the United Kingdom (UK), and Switzerland (CH), over the period ranging from the first quarter of 1974 to the last quarter of 1994.22 We take the U.S. dollar as the reference currency (currency " 1 " in the theoretical part) and convert all exchange rates into U.S. dollars per unit of foreign currency. In what follows, the other country is referred to as country k = {DE, JP, UK, CH}. 4.3.3

ADF and Cointegration Tests of PPP

The first step of the empirical analysis is to test whether the series all have unit roots. This is done using the ADF statistic, and Table 4.1 contains the results. Not surprisingly, the null hypothesis that the nominal data have unit roots cannot be rejected for any of the series. Note, however, that, unlike in Abuaf and Jorion (1990), in Table 4.1 the hypothesis of a unit root cannot be rejected even for the real exchange rates. The likely cause is the loss of power from our use of a relatively short sample of quarterly data, rather than the long series of annual data used by Abuaf and Jorion. We now proceed with the cointegration tests. These are complementary to the ADF tests on real exchange rates in the sense that PPP is the null in the JohansenJuselius test, whereas in the ADF tests the null is the unit-root hypothesis for 22

Other economies had severe exchange controls for a substantial part of the sample period (France, Italy, Spain, Scandinavia, all newly industrialized countries [NICs] and less developed countries [LDCs]), or suffered from missing data (Belgium). It is true that the United Kingdom, and especially also Japan, had exchange controls until the early 1980s, but it was felt that these two major exchange rates could not be excluded from the tests. Dropping Japan from the tests does not affect the conclusions. We also used money supplies to proxy for aggregate consumption, which allows us to use monthly rather than quarterly observations. The drawbacks are that one then is assuming a cointegration relation between a country's spending and its money supply, which weakens the power of the test. The results with money were not clearer, to say the least, than the ones reported here.

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

49

Table 4.1. Augmented Dickey-Fuller tests, quarterly data 1974-1994 Country

\nSk

\nUk

\nMk

Germany (DE) United Kingdom (UK) Japan (JP) Switzerland (CH) United States (US)

-2.13 -1.62 -2.29 -3.00 -2.36 -0.71 -2.68 -2.43 -1.33 -2.29 -2.22 -2.54 — -1.00 -0.16

lnS*^ -2.11 -2.32 -2.72 -2.41 —

ln^ -2.23 -3.07 -1.86 -1.69 -2.37

Notes: There are 84 degrees of freedom (87 observations, adjusted for two lags and one ADF slope coefficient), and the critical value for 50 df (100 df) is -3.50 (-3.45). The unit root null hypothesis cannot be rejected for any of the variables. ADF tests onfirstdifferences (not shown) reject the hypothesis of a second unit root. real exchange rates - that is, PPP does not hold. The new tests require several preliminary steps. Given that the nominal variables satisfy the 1(1) assumption, the first stage in the analysis is to establish the correct lag length in Az* yk. We do this by running the standard vector autoregressions (of exchange rate changes on lagged changes in all variables) and increasing the lag length until the BoxLjung statistic for serial correlation among residuals becomes insignificant at the 5% level for all the equations. We find that, with quarterly data, two lags always suffice, and for consistency we include two lags throughout the analysis. The next step is to estimate the number of cointegration relations in the data, using the Johansen-Juselius maximum-eigenvalue (Amax) and Trace statistics.23 The tests are done on each of the four bilateral data sets for country k relative to the United States and also on the combined data set. Cheung and Lai (1993) and Richards (1995) provide small-sample properties of the likelihood ratio tests, and Godbout and van Norden (1995) discuss the implications of these results for cointegration tests of PPP. We adopt the Cheung and Lai (1993) correction for the small-sample bias. The A.max tests for the entire data set, shown in the lower part of Table 4.2, indicate the presence of at least two vectors across the five countries. The tests in the bilateral data sets, on the other ^max = —T log(l — L r +i) and TR = —T Xl/Lr+i 1°SO ~" ^/)» where T is the sample size, p the number of variables, and L, is the z'-th ordered eigenvalue. The kmax statistic tests the hypothesis that there are r (< p — 1) cointegration relations against the alternative that there are r + 1 such relations. The trace statistic tests the hypothesis that there are r (< p — 1) cointegration relations against the alternative that there are p — 1 such relations. The tests often yield different conclusions. MacKinnon, Haug, and Michelis (1996) provide critical values. Because these tests are known to have low power, Johansen and Juselius (1992) recommend using 90% critical values rather than the usual 95%. The software used is that in Hansen and Juselius (1995).

50

Exchange Rate Volatility

Table 4.2. Tests for number ofcointegration relationships in {In Sk, Inn*, l n n u s } data ^-max

Trace (r)

r

Eigenvalue

Germany-United States (p = 3) 0 1 2

0.2572 0.0494 0.0031

24.38 4.16 0.25

28.79 4.41 0.25

Japan-United States (p = 3) 0 1 2

0.5075 0.2059 0.0257

58.08* 18.91* 2.14

79.13* 21.05 2.14

Switzerland-United States (p = 3) 0 1 2

0.3518 0.0578 0.0087

35.55* 4.88 0.72

41.15 5.60 0.72

United Kingdom-United States (p = 3) 0 1 2

0.3191 0.1805 0.0646

31.51* 16.32 5.47

53.31* 21.80 5.47

A// countries (p = 9) 0 1 2 3 4 5 6 7 8

0.7918 0.5500 0.4244 0.3771 0.2895 0.2349 0.1982 0.0346 0.0274

128.67* 65.47 45.29 38.81 28.03 21.95 18.11 2.88 2.28

351.50* 222.83* 157.36 112.07 73.46 45.23 23.47 5.16 2.28

(r vs. r + 1)

Notes: The table shows Eigenvalues, Amax, and Trace statistics for various hypothesized values of the number of cointegration relations, r. The table reports results for four bilateral data sets and the five-country multilateral data set. The data set includes exchange rates and CPIs but not spending data. An asterisk indicates rejection at the 10% level. Nonrejected values of r by both criteria are printed in boldface.

hand, show that, for Switzerland and the United Kingdom, there is at least one relation and probably even two for Japan. For Germany, there is no compelling evidence of a long-run vector, but on the other hand the test has low power and

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

51

Table 4.3. Johansen-Juselius likelihood tests of PPP on {In Sk, lnl"!*, lnn u s } data Country

X2-test

p-value

Tests in bilateral data sets Germany Japan Switzerland United Kingdom

13.95 16.58 28.51 3.92

0.00 0.00 0.00 0.05

Tests in full data set Germany United Kingdom Switzerland Japan All countries

24.25 20.89 24.71 24.17 66.90

0.00 0.00 0.00 0.00 0.00

Notes: The table shows the y}-statistics and probability values for the PPP hypothesis, in the data set

without spending data. In the bilateral data set, and in the country-by-country tests on the entire data set, the PPP-vector is imposed one country at a time; that is, in each such test the other cointegration vectors are left unrestricted. In the test labeled "all countries," the four PPP-vectors are imposed simultaneously, and the test assumes there are, in all, six cointegrating vectors, the lowest number that cannot be rejected from the bilateral tests in Table 4.2. there is no reason why DEM would behave differently from the other currencies. Thus, we cannot reject the hypothesis that there is at least one cointegrating vector per bilateral data set and four in the entire data set. Given that there are at least four long-run relations present in the data set under consideration, we next test whether one can reject that these relations are the ones suggested by PPP. In a bilateral data set, we hypothesize that fi0] = /3US1 = fikl = 1, and we perform a Johansen-Juselius x 2 likelihood ratio test, again corrected for small-sample effects following Richards (1995). In each of the bilateral tests shown in Table 4.3, the PPP-specification of the ft vector is rejected.24 We also test the PPP prediction about the /?s in the multicountry data set. In the lower part of Table 4.3, we first impose the constraints listed in (4.13) 24

Because the alternative tests derived in Horvath and Watson (1993) are more powerful than the Johansen-Juselius tests employed here, our rejection of PPP is conservative.

52

Exchange Rate Volatility

one at a time (i.e., leaving the other r — 1 long-run relations unconstrained; we assume there are, all together, r = 5 cointegration vectors in the combined data set). In all cases, the proposed restriction is rejected. Lastly, we impose all four PPP constraints simultaneously. In light of the country-by-country test results, it is not surprising that this joint test of PPP is also rejected. This failure of PPP confirms the findings of others (see, e.g., Nessen, 1994;25 Froot and Rogoff, 1995).

4.4

Empirical Tests of the Model with Homothetic CRRA Utility

In this section, our objective is to compare the performance of the CRRA model in equation (4.8) to the PPP equation in (4.10) using the Johansen and Juselius (1992) cointegration tests. In these tests, we extend the PPP test equation by introducing the variables suggested by the CRRA model - real spendings and possibly also a time trend to allow for divergences between the real consumptions caused by different time preferences. To verify whether spending does play a role in the long-run equilibrium value of the exchange rate, we introduce consumption data and a time trend into the models discussed in Section 4.3.1. The Johansen and Juselius (1992) and Horvath and Watson (1995) tests now are no longer applicable because, unlike PPP, the CRRA model does not provide a specific hypothesis about the long-run cointegration vector. That is, whereas PPP implies that all fls should equal unity, the CRRA model says that, in the error-correction version of the CRRA model in equation (4.8),26 (4.15)

A In S(t) = cik + Kkt + AZusttJS.* + AZ* yk + ek(t) - ft [In S(t - 1) - £ u s In Tlm(t - 1) + h In Uk(t - 1) - £* s In MVs(t - 1) + fl;s In A#us(f - 1)],

the P coefficients should equal r]us, *7*> 0 — ^?us), and (1 — rjus), respectively; and the problem obviously is that our knowledge about these parameters is, at best, sketchy. However, we can still use the cointegration analysis to verify the presence of cointegration among the five nominal variables in equation (4.15). As an alternative to the nominal formulation in (4.15), we can also write the 25

26

Relative to Nessen (1994), our cointegration analysis uses more recent results on critical values when testing for the number of cointegration relations, and includes a correction for small samples. In this equation, ak = In[6^(1 - T?US)/O - Ik)] and Kk =

Table 4.4. Xmax and Trace tests on the number of cointegration relations for nominal data consisting of{\nSk, A-max

Trace (r)

r

Eigenvalue

Germany-United States (p = 5) 0 1 2 3 4

0.3425 0.3290 0.2852 0.2386 0.0087

34.38 32.72 27.53 22.35 0.72

117.69* 83.31* 50.59 23.07 0.72

Japan-United States (p = 5) 0 1 2 3 4

0.5347 0.2994 0.1932 0.1384 0.0815

62.74* 29.17 17.60 12.22 6.97

128.70* 65.97 36.79 19.19 6.97

Switzerland-United States (p = 5) 0 1 2 3 4

0.4278 0.3435 0.2793 0.1855 0.1373

45.78 34.50 26.86 16.83 12.11

136.09* 90.30* 55.80* 28.94 12.11

United Kingdom-United States (p = 5) 0 1 2 3 4

0.4327 0.3732 0.2596 0.1749 0.0869

46.48* 38.30 24.64 15.76 7.46

132.64* 86.16* 47.86 23.42 7.46

0.8540 0.7481 0.7066 0.6614 0.5862 0.4974 0.4753 0.3942 0.3455 0.2984 0.2339 0.2061 0.1630 0.1113

157.80na 113.07na 100.55 88.79 72.35 56.41 52.88 41.10 34.76 29.05 21.85 18.92 14.59 9.68

811.81na 654.0 lna 540.94 440.39 351.60 279.25 222.84 169.96 128.86 94.10 65.05 43.20 24.27 9.68

/4// countries (p = 14) Ona jna

2 3 4 5 6 7 8 9 10 11 12 13

(r vs. r + 1)

Notes: The table shows Eigenvalues, A.max, and Trace statistics for various hypothesized values of cointegration relations r, where p is the number of variables. The table reports results for four bilateral data sets and the five-country multilateral data set. The data include exchange rates, CPIs and nominal spendings. An asterisk indicates rejection at the 10% level. Nonrejected values of r by both criteria are printed in boldface. As critical values are available for only up to 12 variables, no critical values are reported (na) for the hypotheses of 0 or 1 cointegration relation for the multilateral nominal data set, "all countries (p = 14)."

54

Exchange Rate Volatility

model in real terms,

(4.16)

A In Sk(t) = ak + AZmym,k + AZ*n + e(t) f Sk(t - \)TLk(t-\) + tk\ In U

L

«-—

ln

Mm(t-\)

n us (r-i)

and verify the presence of at least one cointegration relation among the three real variables. We analyze the variables both in nominal and real terms, starting with the results for the nominal data. The empirical results, summarized in Table 4.4, from tests within the fivevariable bilateral data sets with nominal variables always reject the hypothesis of zero cointegration relations. As we have already rejected the hypothesis that one of these relations is PPP, this evidence is encouraging. As found previously in Table 4.2, also here the multilateral tests on nominal data seem to have less power to detect long-term relations. Table 4.5 summarizes the results based on real data. The bilateral tests provide little evidence of a long-run relation for Japan. For Germany, the Trace and A.max statistics for the hypothesis of no long-run relations fall short of the 10% critical values by one or two decimals. Lastly, the tests cannot reject that there is at least one cointegration vector in the data for Switzerland and the United Kingdom. This evidence from the real data set suggests that the cointegration relations picked up among the nominal variables go beyond the relations between nominal exchange rates and prices found in Table 4.2.

4.5

Conclusion

Much of the literature on exchange rate determination is based on PPP, with PPP being justified on the basis of the consumption opportunity set (frictionless commodity arbitrage). In contrast, the standard microeconomics-based equilibrium paradigm views relative prices - and, hence, also exchange rates - as determined not just by consumption opportunity sets but also by marginal utilities. We accordingly characterize the exchange rate in a general-equilibrium economy with imperfect commodity markets but complete and frictionless capital markets. Wefindthat, in general, the real exchange rate is related to differences in initial wealth and time preferences, and also to differences in marginal utilities of total nominal spending. In the special case of homothetic-utility functions with constant relative risk aversion, the model implies that there are missing variables in the PPP equation, the nominal spendings in the two countries and possibly also time, and that the ceteris paribus effect of higher domestic prices

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

55

Table 4.5. Xmax and Trace tests on number of cointegration relations between real exchange rates and real spending data ^-max

Trace (r)

r

Eigenvalue

(r vs. r + 1)

Germany-United States (p = 3) 0 1 2

0.2553 0.1870 0.0190

24.17 16.97 1.57

42.71 18.55 1.57

Japan-United States (p = 3) 0 1 2

0.1611 0.1507 0.0261

14.40 13.39 2.17

29.96 15.56 2.17

Switzerland-United States (p = 3) 0 1 2

0.3272 0.1076 0.0009

32.50* 9.34 0.07

41.91 9.41 0.07

United Kingdom-United States (p = 3) 0 1 2

0.2932 0.1324 0.0006

28.45* 11.65 0.05

40.15 11.70 0.05

All countries (p = 9) 0 1 2 3 4 5 6 7 8

0.6330 0.5187 0.4137 0.3267 0.2894 0.1817 0.1103 0.0514 0.0306

82.19* 59.97 43.79 32.44 28.01 16.44 9.58 4.33 2.55

279.30 197.11 137.14 93.35 60.91 32.90 16.46 6.88 2.55

Notes: The table shows Eigenvalues, Amax, and Trace statistics for various hypothesized values of cointegration relations r, where p is the number of variables. The table reports results for four bilateral data sets and the five-country multilateral data set. An asterisk indicates rejection at the 10% level. Nonrejected values of r by both criteria are printed in boldface. is a drop in the value of foreign currencies rather than a rise (as predicted by PPP). Unlike related models in the equilibrium model, these conclusions do not need any assumption of equal risk aversions, time preferences, or consumption preferences.

56

Exchange Rate Volatility

We use both cointegration and regression analysis to test the equilibrium exchange rate model with homothetic utility as well as constant relative risk aversion and time preference. When spending data are excluded from the model, as in standard cointegration tests of PPP, we reject PPP; this confirms that similar results obtained by others are robust to the Cheung and Lai (1993) and Richards (1995) correction for small samples. When we consider a data set consisting of real exchange rates and real consumption data, we establish the existence of at least three bilateral relations among the real data. This empirical support encourages us to explore, in the chapters that follow, some of the model's theoretical implications. Thus, Chapter 5 considers the relation between spot rate changes and forward premia; Chapter 6 examines the link between exchange rate volatility and the expected volume of trade; and Chapter 7 explores the role of capital flows in this model.

5

Forward Exchange Rates in a Model with Segmented Goods Markets

In the previous chapter our focus was the spot exchange rate. In this chapter we study the relation between forward exchange rates, spot exchange rates, and interest rates. In particular, we examine the effect of segmented commodity markets on the relation between the forward exchange rate premium and the change in the future spot rate. The relation between forward exchange rates and future spot rates has been the subject of numerous studies. Empirical tests typically find that when one regresses changes in spot rates on forward premia, the slope coefficient is less than one and often negative. This result is called the forward bias puzzle. For example, Froot and Thaler (1990) report in their survey that the average coefficient on the forward premium, across seventy-five studies, is —0.88. Other surveys of this literature can be found in Baillie and McMahon (1989b), Engel (1994), Hodrick (1987), Lewis (1995), and Marston (1995). In this chapter our objective is to examine the effect of segmentation of international commodity markets on the relation between the forward premium and the change in the spot rate. Segmentation of commodity markets gives rise to PPP deviations, which are an important feature of exchange rate data. Typically, the theoretical models that have been used to analyze predictable deviations from uncovered interest parity (UIP) have assumed that PPP holds. However, empirical studies such as Bekaert (1994), Canova (1991), Gokey (1994), Levine (1989,1991), and Mishkin (1984) find that predictable deviations from PPP are highly correlated with predictable violations of UIP; Engel (1994) provides a discussion of these tests. Drawing on the work in Hollifield and Uppal (1997), we first present the theoretical implications of the effect of segmentation on the forward bias in a dynamic general-equilibrium model. We then describe a numerical analysis of a calibrated version of the model. In Section 5.2 we show the theoretical implications of the real model for spot and forward exchange rates and report the population moments of the real economy based on a numerical analysis of

57

58

Exchange Rate Volatility

the economy calibrated to U.S. data. In Section 5.3 we describe implications for the nominal economy, based on the findings for the real economy.

5.1

Related Literature

The relation between spot and forward exchange rates is the focus of numerous studies. Under the assumption of rational expectations, various authors have tested the UIP relation by regressing changes in the log of the exchange rate on the forward premium and various predetermined variables. The UIP hypothesis implies that the coefficient on the forward premium should be unity, the intercept should be zero, and any predetermined variables used to predict the change in the spot rate should have a coefficient of zero.1 However, studies typically find that the coefficient on the forward premium is smaller than one and often negative. Two major hypotheses have been advanced to explain these results: either market participants make systematic expectation errors (Lewis, 1989; Alapat, 1994) or there are time-varying risk premia in the forward exchange market. The articles studying time-varying risk premia include Backus, Gregory, and Telmer (1993), Baillie and Bollerslev (1989), Bansal et al. (1993), Bekaert et al. (1996), Bekaert (1994), Canova and Marrinan (1993), Cumby (1988), Domowitz and Hakkio (1985), Engel (1992a), Fama (1984), Hansen and Hodrick (1983), Hodrick (1987), Hodrick and Srivastava (1984), Korajczyk and Viallet (1992), Macklem (1991), Mark (1985), and McCurdy and Morgan (1991), among others. Fama (1984) makes the important empirical observation that the risk premium for holding forward contracts is more variable than the expected change in the spot rate, and the correlation between the two is negative. One can obtain this characterization as follows. Recall from Chapter 2 that with the assumption of efficient markets, one can rewrite the UIP relation in terms of observed spot rate, S(t + 1), and its forecast error, e(t, t + 1). In terms of percentage changes, this gives us:

(5.1)

| - •^

— l = «+ l|

v

'

m

- \ + e ( t , t + l).

Defining the percentage change in the spot rate as s(t, t + 1) and the percentage difference between the forward and spot rates as the forward premium

and

See also the discussion in Chapter 2.

Forward Exchange Rates in a Model with Segmented Goods Markets

59

we can rewrite (5.1) as: (5.2)

s(t, t 4 1) = a 4 P FP(t, t 4 1) 4 e(t, t 4 1).

Now, define the risk premium at time t, RP(t, t + l), as:

S(t)

=RP(t,t + 1).

Adding and subtracting S(t) in the numerator on the left-hand side of the preceding expression yields: /g,[S(r

V

+

l)]-S(»\ _ /F(,,,

s(o

) V

= RP(t,t + \),

which, in terms of s(t, t 4 1) and FP(t, t 4 1), is: Ets(t, t 4 1) - FP(f, t + 1) = /?P(r, r + 1). Writing the preceding equation in terms of observable variables leads to the following test equation: (5.3)

s(t, t + 1) - FP(t, t + 1) = RP(t, r + 1)4- ^(r, r 4 1),

where e(t,t + \), the forecast error, should be unpredictable given the available information. In the time-series regression test of the equation given in equation (5.2), the slope coefficient is:

However, from equation (5.3) we know that: (5.5)

s(t, t 4 1) = FP(t, t 4 1) 4 RP{t, f + l ) + e(t, t 4 1).

Fama (1984) combines equations (5.3) and (5.4) to characterize the risk premium. Substituting the expression in (5.5) for s(t, 14 1) into (5.4), we can rewrite P as: (5 6)

-

p

~

cov(FP, FP) 4 cov(/?P, FP) 4 cov(e, FP) var(FP)

The term cov(e, RP) is zero since in an efficient market the risk premium contains no information about e(t, 14 1). So equation (5.6) reduces to:

var(^)

60

Exchange Rate Volatility

From (5.7) we see that the deviation of the slope coefficient, /3, from 1 gives us information about variation in the risk premia. The regression coefficient can still equal unity as long as RP(t, t + 1) is uncorrelated with FP(t, t + 1). Conversely, an estimate for f5 that is different from unity suggests either inefficiency or the existence of a risk premium that is correlated with FP(t, t + 1). If /3 < 1, as is empirically the case, the implication is that cov(RP, FP) < 0. Assuming efficiency, Fama finds that variation of the risk premium over time is greater than the variation of the expected change in the spot rate and the variation of the forward premium. These results imply that, if markets are efficient, a change in the forward premium is typically associated with an even larger change in the risk premium, and the change in the risk premium is opposite in direction to the change in the forward premium. These results suggest that to explain why the forward rate is a biased predictor of the future spot rate, the risk premium needs to be large in magnitude and strongly negatively correlated with the forward premium. Models used to study the risk premium are typically based either on international versions of the capital asset pricing model (CAPM) with time-varying conditional moments, or on versions of the consumption-based asset-pricing models of Lucas (1982) and Svensson (1985b). Generally, these studies find it difficult to explain all major features of the data. In contrast to earlier work already described, in this chapter we examine UIP in a general-equilibrium economy with optimizing agents but where the optimization is subject to the segmentation of the commodity markets. This focus on the imperfection of the real sectors is in contrast to the work of Bekaert (1994) and Bansal et al. (1993), where their focus is on monetary disturbances but PPP is assumed to hold.2 Stulz (1981b, 1987) also theoretically studies the effect of deviations from PPP on UIP. In his models, deviations from PPP arise as a consequence of nontraded goods rather than a proportional shipping cost.

5.2

Implications of General-Equilibrium Model for UIP in Real Terms

The real exchange rate is the shadow price of goods abroad relative to the price of domestic goods. In the two-country, single-consumption-good model of a production economy described in Chapter 3, the real exchange rate given in equation (3.10) is:

Vt[Ki (t),K2(t)Y 2

For a review of the empirical evidence on deviations from PPP, see Chapter 2. For specific tests of PPP, see Chapter 4.

Forward Exchange Rates in a Model with Segmented Goods Markets

61

where subscripts on V denote partial derivatives, and V is the central planner's (undiscounted) value function defined in equation (3.9). In the absence of a cost for transporting goods from one country to another, the marginal valuation of output would be equated across countries at all points in time; that is, V\[K\(t), K2(t)] =V2[K\(t), K2(t)], implying that the real exchange rate is constant at one. However, in the presence of the proportional shipping cost, the real exchange rate will vary stochastically between 1 — r and 1/(1 - r). To derive the relation between the real exchange rate and the home and foreign interest rates, we first need to derive the interest rates in terms of the value function. The results in Cox, Ingersoll, and Ross (1985) allow us to state that the domestic real interest rate, r\(t), is: r\(t) = 8

T/,

. ,

V\(t)dt

= M + -TTTT^W*7 '

V\(t)

and the foreign interest rate is given similarly. We can then show that the relation between the expected change in the log of the real exchange rate, denoted e{t) = In Z(0, and the domestic and foreign interest rates is:3 Et[de(t)] = [r,(f)-r 2 (O] * [ 1 + 0 ( 0 ] ^

= [n(t)-r2(t)]dt-RP™\t)dt, where

and the risk premium in the real economy is:

RP™\t)dt = - 0 ( 0 x [r,(0 - r2{t)l Examining the equation for the expected change in the exchange rate, we see that the effect of segmentation of commodity markets on the real exchange rate is captured by the variable 0(0- The variable 0(0 can be interpreted in the following way. The term r\ is the relative risk aversion (RRA) parameter of the consumers in the economy, while the term [/x — r(t)]/a2 gives the production risk premium in the home economy. If one interprets K\(t) and K2(t) as the value of the portfolio of stocks for all the firms located in each country (the local market portfolio), then the term [/x — r\ ( 0 1 / ^ 2 is the market risk premium. Thus, 0 ( 0 is the difference between the RRA of the representative agent and the sum of the market risk premia in the two economies. We now explain how 0 ( 0 is affected by the degree of segmentation of commodity markets. 3

The empirical relation between real interest rates and real exchange rates has been studied by Baxter (1994), Campbell and Clarida (1897), Edison and Pauls (1993), and Meese and Rogoff (1988).

62

Exchange Rate Volatility

In a perfectly pooled economy, the production risk premium in each of the countries would be equal to rj/2 and thus the term 0(0 is equal to zero. On the other hand, with 100% shipping costs, the production risk premium in each country is constant and equal to r\. Thus, in this case, 0(0 = — T) < 0; but now the interest rates in the two countries are constant and equal to one another, implying that the premium for real exchange rate risk is zero.4 For levels of shipping costs between 0 and 100%, however, 0(0 is negative and stochastically varying over time. The intuition for 0(0 being negative is that, in an economy with segmented markets, the sum of the production risk premia at home and abroad is greater than it would be in a perfectly pooling equilibrium. Given that the term 0 ( 0 is negative in the presence of shipping costs, UIP (in terms of real variables) will not hold in this model. The fact that 0 ( 0 < 0 implies that the ftPreal(0 is always of the opposite sign as the (real) forward premium, [r\(t) — r 2 (0L thus satisfying one of the Fama conditions necessary to get a UIP slope coefficient that is less than unity. To evaluate the magnitude of this effect, Hollifield and Uppal undertook a calibration exercise. The parameter values chosen for the calibration exercise correspond to data from Summers and Heston (1991) and are similar to the parameter values used in Obstfeld (1994). RRA is allowed to range from 2 to 30. Based on the estimates in Deardorff and Stern (1990) and Deardorff (1989) that are reported in Chapter 3, the shipping cost is allowed to range from a low of 5% to as high as 70%. The results of the calibration exercise indicate that, consistent with the findings of empirical studies, the model always generates a slope coefficient that is less than unity. For the set of parameter values examined, however, the slope coefficient is never negative - not even for extreme levels of risk aversion or transactions costs. For example, even when the shipping cost is 70% and RRA is 15, the slope coefficient is 0.48. The reason for this is that 0 is zero at the boundaries of the cone and takes its lowest value at the middle of the cone. But, as we have already discussed in Chapter 3, the probability mass of the stationary distribution has much more mass close to the boundaries of the cone - that is, in the regions where the two economies are more likely to trade with each other and, therefore, are least segmented. While higher shipping costs decrease the minimum value that 0 takes, it also increases the size of the cone and reduces the mass assigned to the middle region of the cone. Given that these two effects are in opposite directions, even with high shipping costs the model of the real economy cannot reduce the UIP slope coefficient to below zero. 4

The real interest rates are equal in this case because in both countries the production technologies and preferences are identical and the output shocks are independently and identically distributed.

Forward Exchange Rates in a Model with Segmented Goods Markets

63

To summarize, the analysis of the UIP regression in the real economy shows that the model generates a slope coefficient that is less than unity but not negative. The intuition underlying this result is the following. The segmentation of commodity markets leads to large imbalances in the stock of goods at home and abroad, implying that there are deviations from absolute PPP. However, the imbalance in the stock of goods at home and abroad is persistent, and therefore the deviations from relative PPP are not substantial. There are two reasons for the persistence in the imbalance in the stock of goods at home and abroad; the first one explains why the imbalance tends to increase rather than decrease, and the second one explains why the imbalance does not get corrected. Imbalances in capital tend to increase rather than decrease because the drift of co(t) is positive - as explained in Chapter 3. The correction to imbalances associated with large deviations from absolute PPP is small because, with proportional costs, it is optimal to ship only infinitesimal amounts. Given that there are only small deviations from relative PPP, the premium for real exchange rate risk that the real model generates is such that the slope coefficient drops to below one but not below zero.

5.3

The UIP Relation in Nominal Terms

The model we have analyzed is of a real economy. Typically, empirical tests of UIP are based on nominal data. Hence, in this section we report the relation between the exchange rate and interest rates when all variables are expressed in nominal terms. Hollifield and Uppal first derived the nominal UIP slope coefficient in terms of the moments from the real economy and a term that captures the interaction between the monetary and real sectors. Then, they used the estimates of the moments from the numerical analysis of the real model to determine the magnitude of this interaction term for the model to match the UIP regression in the data. Given that the focus here is on the effect of imperfections in the real sector, rather than that of the monetary sector, money is introduced using the cash-inadvance constraint - as described in Chapter 3 - so that it has no effect on the real allocations but it still can generate inflation risk premia in nominal interest rates. Hollifield and Uppal show that for the special case in which risk aversion is large, the nominal risk premium can be written as: t ) ( a

0 -n)(
m i

-

64

Exchange Rate Volatility

Now, the risk premium for nominal exchange rate risk consists of three parts: the first term captures the effect of real factors; the second term is the conditional volatility of money supplies, and the third term measures the interaction between the real and monetary sectors. If real interest rates were constant (which would be the case if there was no shipping cost), then any predictable deviations from UIP would arise from predictability in the conditional variances and covariances involving money supplies. To see the role of the shipping costs, observe that in the two polar cases, where either there are no shipping costs or there is a 100% shipping cost, the real interest rates in the two countries would be constant and equal to each other, and the predictable deviations from UIP would be driven solely by the volatility of monetary shocks and the conditional covariances between money and output shocks. Thus, it is only when 0 < r < 1 that the real exchange rate has an impact on the nominal risk premium. In this case, the UIP slope coefficient in the nominal model depends on only two sets of quantities: the first set comprises the moments of the real model, and the second set consists of the covariance between the imbalances in K\ relative to K2 and money supplies. The calibration exercise in the previous section provides us the first set of terms, which are used to infer the value of acoM required to obtain a UIP regression coefficient that is negative, as is found in the data. The value for a(onu required to get a negative UIP regression coefficient is approximately zero. This value is not very sensitive to either the level of shipping costs or RRA that one assumes in the model, and it is quite low compared with what is found in the data.

5.4

Conclusion

We have described how one can derive the relation between exchange rate changes and interest rates in a general-equilibrium model where deviations from PPP arise endogenously from the segmentation of commodity markets. The model can generate predictable deviations from UIP, and these can be expressed in terms of domestic and foreign interest rates. The results of calibrations to calculate the UIP regression coefficient in the theoretical model, both in terms of real interest rates and exchange rates and in terms of nominal variables, indicate that the real model can successfully generate a regression coefficient that is less than unity. However, the real model cannot generate a negative regression coefficient as found in the data; the nominal model can generate a negative regression coefficient only if money supply shocks and relative returns on capital in the two countries are negatively correlated. The work in this chapter indicates that the ability of equilibrium models to replicate stylized features of the data can improve as one generalizes the

Forward Exchange Rates in a Model with Segmented Goods Markets

65

model. In this chapter, allowing for deviations in PPP by introducing a cost for transferring goods across countries results in a model that can generate a UIP regression slope coefficient that is less than unity. In related work, Backus et al. (1993) find that allowing for more general preferences - such as habit persistence - can also improve the performance of the model along certain dimensions. These results imply that it might be worthwhile to extend the model described here in other directions.

6

International Trade Flows, Exchange Rate Volatility, and Welfare

Our objective in this chapter is to evaluate the conjecture that an increase in exchange rate volatility leads to a decrease in the volume of international trade. Most empirical tests do not find a strong negative relation between exchange rate volatility and the volume of international trade. Our theoretical analysis provides a potential explanation for these results. We also address two weaknesses in the existing literature on exchange rate volatility and international trade, as pointed out by Peree and Steinherr (1989): the existing theoretical models are partial equilibrium in nature, and in the empirical work a linear relation between trade and exchange rate risk is postulated while the true relation might be nonlinear.1 Specifically, our work determines a nonlinear relation between exchange rate volatility and the volume of international trade and does this in the context of a general-equilibrium model. The model that we use to illustrate our arguments is similar to that described in Chapter 3. In contrast to existing partial-equilibrium work studying the relation between international trade and exchange rate volatility, in our model the exchange rate and the prices of financial securities are determined endogenously. Our major result is that in this general-equilibrium setting an increase in exchange rate volatility may be associated with either an increase or a decrease in the volume of international trade, depending on the source of the change in volatility. Because even in our simple model there exists no unambiguous relation between exchange rate volatility and trade, it is clear that, in more complicated models (and in the real world), there need not be a clear relation either. After providing some background for our discussion, we describe in Section 6.2 the economy that we use in our analysis and determine the optimal quantities of exports and imports. In Section 6.3 we show that in this setting the relation between exchange rate volatility and the volume of international trade 1

Peree and Steinherr (1989) also mention that it is not clear how one should measure exchange rate risk and that the aggregate trade equations ignore the competitive structure of product markets. While the exchange rate volatility in our theoretical model is well defined, we do not address the issue of industrial structure.

66

International Trade Flows, Exchange Rate Volatility, and Welfare

67

is positive when output risk increases, and negative when the shipping cost increases. In Section 6.4 we discuss the implications of our modeling assumptions, and relate the results of our theoretical model to the empirical evidence on the relation between exchange rate volatility and trade.

6.1

Background and Related Literature

In the academic literature, both theoretical and empirical, there is no consensus about the relation between exchange rate risk and the volume of trade. After discussing the theoretical models and then the empirical work, we describe how our analysis extends the existing literature. A more detailed review of this literature can be found in the International Monetary Fund (1984), Peree and Steinherr (1989), Edison and Melvin (1990), and Cote (1994). In the early theoretical literature, a number of models were constructed to support the view that an increase in exchange rate volatility leads to a reduction in the level of international trade. These models (e.g., Clark, 1973; Baron, 1976a; Hooper and Kohlhagen, 1978; Broil, 1994) consider firms exposed to exchange risk.2 A typical argument in this literature is that higher exchange risk lowers the risk-adjusted expected revenue from exports and therefore reduces the incentives to trade. These results, however, are derived from partial-equilibrium models. For example, most of this literature assumes that exchange rate uncertainty is the sole source of risk in the decision maker's portfolio and either ignores the availability of hedges (forward contracts, or nonlinear hedges like options and portfolios of options) or takes the prices of the hedge instruments (or at least some of the determinants of these prices) as given. Taking into account the firm's option to hedge (linearly) its contractual exposure, some other partial-equilibrium models question whether risk-averse entrepreneurs would always view a higher exchange risk as a deterrent to trade. For example, Ethier (1973) and Baron (1976b) show that exchange rate volatility may not have any impact on trade volume if firms can hedge using forward contracts. Viaene and de Vries (1992) extend this analysis to allow for the endogenous determination of the forward rate; then, exchange rate volatility has opposing effects on importers and exporters (who are on opposite sides of the forward contract). In this case, Viaene and de Vries find that the net effect of exchange rate volatility on trade is ambiguous. Also De Grauwe (1988) shows that aversion to risk is not sufficient to obtain a negative link between exchange risk and expected trade; the direction of the association depends critically on the 2

Cushman (1983) argues that the relevant source of uncertainty for the firm is about the real rather than the nominal exchange rate; he finds similar results for the case where profits depend on the real exchange rate.

68

Exchange Rate Volatility

degree of risk aversion. This is because, in general, an increase in risk has both an income effect and a substitution effect that work in opposite directions (Goldstein and Kahn, 1985). Thus, even though firms are worse off with an increase in exchange rate risk, their response may be to export more rather than less. Delias and Zilberfarb (1993) make a similar point using a portfolio-choice model.3 While these models allow the firm to hedge or at least diversify its exchange risk, they often still ignore the firm's option to adjust its production in response to the exchange rate. Models that focus on the firm's flexibility tend to conclude that a higher exchange risk actually stimulates trade. When firms are allowed to respond optimally to exchange rate changes, the revenue per unit of an exportable good (De Grauwe, 1992; Sercu, 1992) or the entire cash flow from exporting (Franke, 1991; Sercu and Van Hulle, 1992) becomes a convex function of the exchange rate. From this it follows that expected unit revenue or the expected cash flow increases when the volatility of the exchange rate increases, which then acts as a stimulant to trade rather than as a deterrent.4 These models, however, still take the demand functions or the cash flow function as given, and therefore ignore the issue of how the changes in the economy that cause an increase in exchange risk affect the demand or cash flow function. Moreover, all these models assume that the exchange rate is exogenous and is therefore not affected by the actions of the firms; and these existing models typically analyze a single firm, whereas the data that are used in the empirical tests described later are of the aggregate economy (Bini-Smaghi, 1991; Goldstein and Khan, 1985). Results from the empirical analysis of the relation between trade volume and exchange rate volatility are similarly mixed, matching the lack of consensus on the theoretical side. In empirical tests, typically, it is the real rather than the nominal exchange rate that is studied (see, e.g., Asseery and Peel, 1991; De Grauwe, 1988; Gagnon, 1993; Gotur, 1985; Koray and Lastrapes, 1989; Kroner and Lastrapes, 1993; Peree and Steinherr, 1989). Exchange rate risk is measured using one of the following: the standard deviation of the level of the exchange rate or the standard deviation of the percentage change in the exchange rate, the difference between the actual spot rate and that predicted by the forward rate (so as to measure the unanticipated change), or a time-series model such as generalized autoregressive conditional heteroskedasticity (GARCH) for exchange risk (Asseery and Peel, 1991; Pozo, 1992; McKenzie and Brooks, 1997). Most empirical work fails to find a strong negative relation between exchange rate volatility and the volume of international trade. For example, Koray and 3 4

See also Cole (1988). This literature is similar to the trade literature on hysteresis; see, for example, Baldwin (1988), Baldwin and Krugman (1989), and Dixit (1989a, 1989b). For a comprehensive review of this modeling approach, see Dixit and Pindyck (1994).

International Trade Flows, Exchange Rate Volatility, and Welfare

69

Lastrapes (1989) and Lastrapes and Koray (1990) use vector autoregressive (VAR) models to examine if exchange rate volatility affects the volume of trade.5 They find that exchange rate volatility explains only a small part of imports and exports. Gotur (1985) also finds that there is little support for a relation between exchange rate volatility and trade. Gagnon (1989) finds similar results based on simulations of a dynamic optimizing model with adjustment costs. In cross-section work, Brada and Mendez (1988), using a gravity model of bilateral trade, find that even though exchange rate volatility reduces trade, its effect is smaller than that of restrictive commercial policies. Frankel and Wei (1993), using an instrumental variables approach, also conclude that the effect of exchange rate volatility on trade is small. On the other hand, Asseery and Peel (1991), using an error-correction framework, and Kroner and Lastrapes (1993), using a multivariate GARCH-in-mean model, find that an increase in volatility may be associated with an increase in international trade. McKenzie and Brooks (1997) even find that U.S.-German imports and exports are positively and significantly associated with exchange rate volatility modeled as an autoregressive conditional heteroskedasticity (ARCH) process. Thus, the overall conclusion is that the negative effects of exchange rate volatility, if present, are small.6 To explain these findings of the empirical studies in a framework that does not have the limitations of the theoretical models just discussed, we again need a general-equilibrium model of the aggregate economy as in, for instance, the (neo)classical trade literature. However, the standard free-trade models assume that all commodity markets are perfect; that is, the drawback of the neoclassical approach is that commodity price parity is postulated to hold at all times and for all goods, implying that there is no real exchange rate risk.7 Another drawback of the standard free-trade models is that, by requiring period-by-period equilibrium on the trade balance, they ignore the existence of capital markets. Accordingly, our objective is to consider a model of the macroeconomy that has the internal consistency of the general-equilibrium models of international trade, but where capital markets are allowed to play their normal economic roles, and where commodity markets are sufficiently segmented to allow for deviations from commodity price parity and changes in the real exchange 5 6 7

The advantage of the vector autoregressive (VAR) approach is that it does not impose exogeneity on the variables in the system (consistent with our general-equilibrium approach). See, also, Caballero and Vittorio (1989). In a perfect-markets setting, PPP deviations can still arise because of international differences in commodity preferences. However, Engel (1993) and Rogers and Jenkins (1995) find that, as a source of PPP deviations, violations of commodity price parity are far more important than differences in commodity preferences. Engel and Rogers (1995) also show that within-country deviations from the law of one price are much smaller than cross-country deviations, which is consistent with the friction in our model for trading goods across countries.

70

Exchange Rate Volatility

rate.8 In our model, the financial markets are assumed to be complete and perfectly integrated, reflecting the fact that, at least for developed economies, international capital markets are far less subject to restrictions than commodity markets. Thus, in our model consumers can make cross-border financial investments to finance or hedge future imports; likewise, firms can make optimal hedging decisions; and the prices of all contracts are determined in a generalequilibrium framework. Commodity markets, on the other hand, are assumed to be segmented internationally - there is a proportional cost for transferring goods across countries.

6.2

The Economy

In this section, we start with the endowment economy described in Chapter 3, and state only the additional assumptions required for our analysis of trade and exchange rate volatility. Recall that the model in Section 3.2 is of a world economy with two countries (k = 1,2) that have perfectly integrated financial markets but segmented commodity markets. In every period, each country has a stochastic endowment of a single nonstorable good that is homogenous across countries and can be traded internationally only at a cost. The endowment in country k at time t of this good is denoted by qk(t). These stochastic endowments are given exogenously, as in the exchange economy of Lucas (1982). Although the results in this section on the equilibrium levels of trade and the real exchange rate are distribution-free, in the next section we do specify a distribution for the endowment processes to identify the implications of various shocks for both expected trade and the variance of the real exchange rate; specifically, we shall let the endowment processes for the goods be given by log random walks, with constant mean, fik — 0.5crA2, and variance, o^, k = {1,2}:

j \ / = i \

k = {1,2}.

The correlation between the outputs of the good at home and abroad, p, is assumed to be less than unity. As in Chapter 3, the home and foreign country (k = 1 and 2, respectively) are assumed to be populated by a large and equal number of infinitely lived 8

Sutherland (1996) builds on the model of Obstfeld and Rogoff (1995a) to evaluate the effect of financial-market integration on volatility of macroeconomic variables. He finds that with increased integration, volatility typically declines; the only exception is when the source of the shocks is monetary.

International Trade Flows, Exchange Rate Volatility, and Welfare

71

consumers with identical preferences over the single good: (6.1)

Uk[ck(t)] = j^—[ck(t)]l-\

0 < 17 < oo,

n # I, 9

where ck(t) denotes the consumption of the good in country k. The central planner's objective is to choose the decision rule for exports so as to maximize the equally weighted aggregate lifetime utility of the two countries given in equation (3.2a). The central planner's decision rules for consumption and trade are summarized later. The intuition underlying the optimal consumption and trade policies is given in Chapter 3. With a strictly positive shipping cost, the first-order conditions imply that there will be a no-trade zone within which international imbalances in the weighted marginal utility of consuming the good will be left uncorrected notably when the cost of shipping outweighs the utility gained by reducing the international imbalance in the consumption of this good. That is, trade occurs only when the ratio of the two outputs falls outside a particular region. Thus, it is possible to divide the state space into three critical regions or metastates, indexed by /, where / = {0, 1,2}: in region 0 of the state space, there is no trade; in region 1, country 1 exports the good; and in region 2, country 2 exports the good. These three regions are shown in Figure 3.1. It will be convenient to express our results in terms of these three regions. Many of our results also depend on the ratio of optimal consumption rather than levels; we will use /c,(r) = [c2(t)/c\(t)] to denote this ratio at time t and in region i. In each of the states / = {1, 2, 3}, the optimal consumption ratio across countries for the good is: (6.2)

1+r/

9

qi(t)

\\+TJ

[/ = 1 : country 1 is exporting]

(l+r)l/1?

it" 1 ^" 7 > (1 + T ) ' / I '

[ / = 2 : country 2 is exporting]

qiit) q\U)

otherwise

[i — 0 : no trade].

q\{t)

The special case where r\ = 1 is represented by the log utility function. This utility specification yields the samefirst-orderconditions as the ones obtained by setting r\ equal to unity in the case tor the utility function in (6.1), and the same expressions for trade and the real exchange rate. Thus, the implications for the log utility function are similar to the ones we derive for the case i) jt 1.

72

Exchange Rate Volatility

The optimal export policies follow from the consumption behavior just described. Equation (6.3) gives the optimal amount of the good that should be exported from country 1, and (6.4) gives the optimal exports of the good from country 2: <">

(6.4)

x2(t) =

, ( 1 + T ) + 1 M a x ( g 2 ( O - K2qi (0, 0).

To obtain equations (6.3) and (6.4), note that in the absence of trade, we have c2(t)/c\(t) = q2(t)/q\(t), implying that x\(t) = x2(t) = 0. In the region / = 1, with exports from country 1, (6.2) implies that country 1 must be exporting an amount xi (0 such that c2(t)/c\ (f)) = (1 + r)~ 1/?? . The amount of good being exported from country 1 can then be identified from the sharing rule c2(t) = K\C\(t) (with K\ defined in (6.2)) and the market-clearing condition c\(t) = q\(t) — x\(t) and c2(t) = q2(t) + x\{t)/{\ + r). The solution is

„.

X\{t)

=

q\(f)-qi{f)/KX

which is positive because we are considering states where q\(t)K\ > q2(t). This condition also implies that, in these states, x2(t) = 0. We can obtain x2(t) in similar fashion. Lastly we derive the real exchange rate, which in a one-good economy is given by the ratio of the marginal utility of consumption abroad to that at home, Z(t) = [c2(t)/c\(t)]~ri.l0 Substituting into this expression the consumption ratios derived in (6.2) gives: -« = 1 + r (6.5)

Z(t) =

\qw)/

1

if i = 1

if / = 2.

From equations (6.2) to (6.5), we see that it is possible to express explicitly the real exchange rate and the volume of international trade as functions of r, rj, and the state variables (the outputs of the two goods). Now, we can examine how a change in either r or the volatility of the relative endowment process affects the expected volume of trade and the volatility of the exchange rate. 10

This is the same as the expression in equation (3.4).

International Trade Flows, Exchange Rate Volatility, and Welfare

6.3

73

The Relation between Trade and Exchange Rate Risk

In this section, we examine the change in exchange rate volatility and expected trade for two experiments: first, where there is a change in the volatility of the relative endowment processes; second, where there is a change in the degree of commodity market segmentation, measured by r. 6.3.1

The Effect of Output Volatility on Exchange Risk and Expected Trade

To consider the effect of an increase in volatility in the endowment processes on the expected level of trade, we obtain analytical expressions for the expected volume of domestic and foreign exports by noting that the expression for the realized volume of domestic [foreign] exports in (6.3) [(6.4)] is similar to the payoff of an option to exchange two risky assets at the rate K2 [1/K\]. The properties of such options have been studied in the finance literature by Margrabe (1978). Thus, we can use the insights from the theory of option pricing to determine the expected volume of trade. Given the assumption that the distribution of the two endowment processes is jointly lognormal, we obtain an expression for the expected foreign exports that is similar to the value of an option to exchange two risky assets whose prices are lognormally distributed. From option-pricing theory, we also know that the value of an option is increasing in the volatility of the underlying stochastic process. In our context, the expected volume of foreign exports is a positive function of the volatility of the relative output process, q2(T)/q\(T). This follows from the result that the conditional expectation at time t, of foreign exports at a later date 7\ is given by the expression in (6.6), which is a nonlinear positive function of the variance of q2(T)/q\(T): ,,,, (6.6)

,™ Et[qi(T)-\N{d\) - K2Et[qx(T)}N{d2) vf Et(x2(T)) = , K2/(\ + T)+ 1

where Et(qk{T)) = qk(t)exp{/jk(T

- t)},

k = {1, 2}

0 2 = o\ — 2po\o2 +
q\T)

a\ =

N(d) = the probability thatz < d, where z is a unit-normal random variable.

74

Exchange Rate Volatility

Equation (6.6) shows that the expected volume of foreign exports is increasing in the volatility of the relative endowment process. Similarly, we can show the same is true for domestic exports. Given that total trade is the sum of domestic and foreign exports, based on the results in Black and Scholes (1973) and Merton (1973), we conclude that the expected volume of trade increases with an increase in the volatility of the relative endowment process. We now evaluate the effect of an increase in output risk on the variance of the real exchange rate. Like others before us, we choose to study the log of the exchange rate because of its symmetry. From (6.5): —r]\r\K\ = ln(l + r )

(6.7)

lnZ(O =

if

, qi(t) -rj\n-

"" if K\ <

q\(0

~

q2(t)

< K2\

^x "

if ^ - >K2. q\(t)

Thus, the log real exchange rate is proportional to a truncated variate, ln[^2(O/<7i(OL where the values of the log output ratio that fall outside the no-trade region [ln/cj, \r\K2] are replaced by the (constant) bounds In K\ and In K2- Given the expression for the exchange rate in (6.7) and the assumption that \n[qi(T)lq\(T)\ is normally distributed, var,(lnZ(7)) is a positive function of the volatility of relative output. That is, an increase in the volatility of the relative output leads to an increase in the volatility of the exchange rate. To see the intuition underlying this result,11 consider, for simplicity, a situation where the bounds on the log exchange rate, ±ln(l + r), are symmetric around the expected log exchange rate. An increase in the variance of the relative output does not affect these bounds. Given the symmetry of the bounds around the mean, the effect of an increase in volatility of q2(J)/q\(T) is to increase the probability that Z(T) is at one of its bounds. That is, when the volatility of either q\(T) or q2{T) increases, more and more of the probability mass of In Z(T) is shifted away from the middle of the distribution toward the bounds. This leads to an increase in the variance of the log exchange rate. One can show formally that for the case of a lognormal distribution this conclusion holds also in situations where the bounds on the log exchange rate are not symmetric around its expected value. Thus, from the first experiment on the relation between trade and exchange rate volatility, we conclude the following: when there is an increase in the 1

' A formal proof can be found in Sercu (1997).

International Trade Flows, Exchange Rate Volatility, and Welfare

75

volatility of the relative endowment process, there is an increase in both exchange rate volatility and the expected volume of trade. Thus, when the source of the shock in the exchange risk is a change in the risk of the outputs, there is a positive association between expected trade and exchange rate volatility. 6.3.2

The Effect of Segmentation on Exchange Rate Volatility and Trade

In this section we analyze how exchange rate volatility and the expected volume of trade change as we vary r, the parameter that determines the degree of segmentation between international commodity markets. Let us consider the effects of a drop in the shipment cost. Figure 3.1 implies that a decrease of r boosts expected trade, for two (related) reasons. First, the zone of no trade shrinks; that is, the probability of trade becomes larger. Second, for any given output point outside the no-trade zone, a narrower no-trade zone also means that a larger amount of trade is needed to reduce the difference in the international consumption levels to the level justifiable by transaction costs. The shrinking no-trade zone also means that the bounds on the exchange rate become tighter; therefore, the variance of the exchange rate decreases. Thus, with a lognormal output ratio, a drop in the shipment cost implies (1) a decrease in exchange rate volatility and (2) an increase in the expected volume of trade. Hence, when there is a change in the shipment cost, there is a negative association between expected trade and exchange rate volatility. We can illustrate this result by comparing an economy with international commodity markets that are partially segmented (0 < r < oo) to one where they are perfectly integrated (r = 0). Let us first examine how expected trade volumes would react to a complete elimination of the shipment cost. Recall that there is no trade in the region where

With zero shipping costs, this region of no trade shrinks to a single line - the 45-degree line - because K\ and K2 collapse to unity. Thus, the probability of trade increases; in addition, for a given output combination for which trade is nonzero, the amount of exports is higher than it would have been under a positive r. Thus, compared to an economy with segmented commodity markets (r > 0), the expected volume of trade will be larger in an economy where r equals zero.12 12

In terms of options, when one shrinks T to zero, the trade function becomes like the payoff from a straddle rather than that from a strangle; and the former is more sensitive to changes in volatility than the latter.

76

Exchange Rate Volatility

We next compare the volatility of the exchange rate in an economy with partially segmented markets to one where r equals zero. When r = 0, the real exchange rate always equals a constant (unity), implying that the variance of the exchange rate vanishes entirely regardless of the riskiness of relative output. To sum up the example, when r is reduced to zero, expected trade rises and exchange rate volatility drops to zero. Compared with the result in the previous experiment, where trade and exchange rate volatility were positively related, the predictions about the relation between the expected volume of trade and exchange rate volatility are now reversed: here, with increased segmentation of the commodity markets, the expected volume of trade decreases while exchange rate volatility increases. Thus, from these two experiments we conclude that an increase in exchange rate volatility may be associated with either an increase or a decrease in the volume of trade.

6.4

Discussion of the Model and Its Implications for Empirical Work

In the previous section, we showed that an increase in exchange rate volatility need not always be associated with a decline in trade. This is because, in a general-equilibrium setting, both the volume of trade and the volatility of exchange rates are endogenous quantities; thus, the relation between the volume of trade and the volatility of exchange rates can be either positive or negative depending on the underlying source for the change in exchange rate volatility. In this section, we discuss the sensitivity of these results to our modeling assumptions and the implications of the results of our theoretical model for empirical work. We start by noting that if in a stylized and simple model like ours there is no unique relation between the volume of trade and exchange rate volatility, then a unique relation is unlikely in a more general model. That is, the relation between exchange rate volatility and the volume of trade will be ambiguous even in models that are more general. Our modeling choices have been motivated by the desire to obtain all results analytically, without having to resort to numerical methods. However, it is possible to extend the model in several directions and still show that the relation between exchange rate volatility and international trade is ambiguous. We will describe some possible extensions here. We first consider the sensitivity of our results to our assumption of lognormal distributions for the output shocks. From equations (6.3) and (6.4), we see that the expressions for trade are convex in q\(t) and ^ ( 0 - Thus, the result in Section 6.3.1, that an increase in the riskiness of q\(t) and ^ ( 0 leads to an

International Trade Flows, Exchange Rate Volatility, and Welfare

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increase in the expected volume of trade, does not depend on a particular distribution for the endowment process. Similarly, our conclusion that a drop in the shipment cost stimulates expected trade is distribution-free. Sercu (1997) shows that the positive link between increased output risk and exchange rate volatility holds for distributions other than the lognormal. Thus, the conclusions from Section 6.3.1 are robust to assumptions about distributions. However, other assumptions, such as a constant shipping cost and only a single tradable good, are more difficult to relax. The approach we adopted to make the existence of two countries economically meaningful was to consider a one-good international market with a cost for shipping goods internationally. A second common way to make the two countries distinct is to assume that, besides a perfectly tradable good, there is a second, fully nontradable good. Examples of this approach include Backus and Smith (1993), Stockman and Delias (1989), Stulz (1987), and Tesar (1993). With a nontraded good added to the model, our conclusions would remain unchanged as long as the output process for this good is nonstochastic or the two goods are separable in utility. Indeed, under either of these assumptions K\ and K2 would still be nonstochastic and all our earlier inferences would, therefore, continue to hold. However, in a more general model with nontraded goods, the KS would become functions of a second stochastic variable, relative output of the nontradable good. In the "option" interpretation of the trade functions, these KS determine both the strike price and the size of the option contract (as can be seen from equations (6.3) and (6.4)), and the variability of the KS is directly proportional to the variability of the relative output of the nontradable good. Not surprisingly, then, a higher output risk in the nontradable goods sector has an ambiguous effect on trade. The same holds if there are multiple, imperfectly tradable goods: the K for each good then depends on the outputs of other goods, making it difficult to draw general inferences about the effect that increased output risk in one sector has on trade in another good. Similar conclusions hold with respect to exchange rate volatility. We now make some observations about the implications of our theoretical results for empirical tests of the relation between the volume of international trade and the volatility of exchange rates. As noted in the Introduction, existing empirical evidence on this relation is mixed: evidence of a negative relation between trade and exchange rate is weak, at best. In light of our analysis, these ambiguous results could mean that the two forces discussed in the model were both active, and counteracted each other with different relative intensities across countries, sectors, and periods. For instance, after 1972 there was a rise in both exchange rate volatility and uncertainty about economic activity. Thus, our model suggests that this increase in uncertainty should have contributed to an increase in trade. However, to make this inference, one needs to control

78

Exchange Rate Volatility

for the simultaneous change in the barriers to trade. While it is true that in the post-1972 period there were efforts to liberalize world trade further, this period was also characterized by an increase in nontariff barriers. Of course, one needs to be careful in distinguishing between tariffs (that raise revenue to finance the production of public goods) and the dissipative shipment cost representing trade frictions in our model. Still, one would expect that, like pure shipment costs, tariffs and nontariff barriers inhibit trade, thus counteracting the predicted effect of increased uncertainty in endowments. A second comment is that, even if the effect of changing liberalization of trade is somehow controlled for, the predicted positive association between exchange rate volatility and trade due to variations in output risk need not be obvious in small-sample data. First, sample parameters (such as average trade and ex post exchange rate volatility) are noisy estimates of the population parameters used in our analysis. Second, if trade is already intense and can be expected to remain so in the future, the effect of increased output risk on both the variance of the real exchange rate and on the expected volume of trade is small.13 A third potential reason why empirical studies may have failed to detect a strong relation between trade and exchange rate volatility is that the relation implied by our general-equilibrium model is nonlinear. Thus, the linear regression model frequently used by empirical studies to estimate the relation between trade and exchange rate volatility is misspecified.

6.5

Conclusion

In this chapter we examine the conjecture that exchange rate volatility leads to a decline in trade. We argue that both trade and exchange rate volatility are endogenous quantities, and thus, it is misleading to relate one to the other as if one of them were exogenous. We endogenize both variables by considering a model of a stochastic general-equilibrium economy with international commodity markets that are partially segmented. In contrast to existing work on the effects of exchange rate volatility on trade, in our model the exchange rate is determined endogenously. We find that it is possible to have either a negative or a positive relation between trade and exchange rate volatility, depending on the source of the increase in exchange rate volatility. In particular, in this chapter we report two experiments. In the first experiment, the source of increased volatility 13

With respect to expected trade, this is because strict convexities occur only at the points K\ or /Q. Thus, if it is unlikely that these critical values will be reached, the effect of the convexity on the expected level of trade is small. With respect to the real exchange rate, when the probability of trade is very high, the effect of riskiness of the endowments on the variance of the real exchange rate is small because the exchange rate then is highly likely to be at one of its bounds. Thus, under these circumstances exchange rate variability is already small and is hardly affected by variations in output risk.

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in the exchange rate is an increase in the volatility of the endowment processes; in this case, trade increases along with exchange rate volatility. In the second experiment, the degree of segmentation of commodity markets increases. In this case, too, exchange rate volatility increases, but it is now associated with a decrease in trade. Because both kinds of change can occur in the real world, our model provides a potential explanation for the results of empirical studies that typically fail to find a strong negative relation between exchange rate volatility and the volume of international trade. Several other scenarios not detailed in this chapter, such as the existence of other goods (either perfectly tradable or nontradable), lead to similar results about the ambiguous relation between trade and exchange rate volatility. The model also has welfare implications. Our model implies that the volatility of the real exchange rate may be associated with (1) a drop in the volatility of fundamentals and (2) a reduction in the physical impediments to trade. In both cases, the decrease in real exchange risk is beneficial in terms of welfare: to risk-averse agents, a lower consumption risk increases expected utility regardless of whether consumption risk is reduced by lower costs in international trade or by lower output risk. Whereas a reduction in trade barriers is associated with an increase in the volume of trade, a drop in the volatility of fundamentals may be associated with a fall in trade. That is, even though welfare increases in both cases, the effect on the endogenous variable, trade, may differ.14 Thus, in pursuing a policy of reducing exchange rate variability, policy makers should not consider, as a separate factor, the effect that their policy has on trade. Understanding the relation between exchange rate volatility and commodity trade is fundamental for choosing between different exchange rate regimes and for setting policies for trade in commodity markets and capital markets.15 The findings reported in Allen and Stein (1995) suggest that fundamentals can explain a major proportion of the trends in real exchange rates over the medium and long run. The empirical results indicate that changes in savings and productivity, and for small countries changes in the terms of trade and 14

15

Manuelli and Peck (1990) show, in the context of an overlapping-generations model, that the volatility of the nominal exchange rate may not necessarily have negative implications for welfare. This is because different nominal exchange rates may be associated with the same real allocation. The fact that the nominal exchange rate may be indeterminate in such models was first discussed in Kareken and Wallace (1981). King, Wallace, and Weber (1992) also illustrate that the nominal exchange rate may not be related to fundamentals, though the real allocations differ across equilibria only if financial markets are incomplete. In contrast to these models, our focus is on the volatility of the real exchange rate, and in our model financial markets are complete. Dominguez (1997) studies empirically the effect on exchange rate volatility of central bank intervention in currency markets.

80

Exchange Rate Volatility

the world interest rate, account for a large proportion of the movements in the real exchange rates. This evidence suggests, consistent with our model, that to reduce the volatility of real exchange rates one needs to reduce the volatility of fundamentals: monetary policies are unlikely to have long-term effects on the real exchange rate, and fixed exchange rates serve only to slow down the speed of adjustment. As explained in De Grauwe (1990), on the basis of the work in Poole (1970), attempts to stabilize the exchange rate without trying to reduce the variability of the fundamentals will generally not lead to an improvement in welfare. Although much attention has been paid to the "excess" volatility of nominal exchange rates - Isard (1995, p. 3) points out that, "exchange rates varied month-to-month roughly five times as much during 1974-1994 as the prices of consumer goods and the services in the United States and Japan, and eight times as much as the consumer prices in Germany" - it is important to recognize that, over the same period the currency exchange rates have exhibited somewhat less month-to-month variability than major stock market price indices and comparable or lower variability than the prices of many primary commodities. Also, Eichengreen (1994) finds that the volatility of output was lower under floating exchange rates than it was during the period of the Bretton Woods agreement. That is, there seems to be no simple association between the exchange rate regime and the volatility of GDP.16 Similar evidence is reported also in De Grauwe (1990, pp. 171-172). Given that our model of the exchange rates is based on fundamentals, it does not allow for the possibility of excess volatility: in our framework, all movements in exchange rates are linked to changes in the underlying fundamentals. Consequently, all financial transactions (short- and long-term) are related to fundamentals,17 and thus in such a setting proposals to reduce exchange rate volatility by limiting capital flows, via policies such as target zones or the taxes proposed in Tobin (1978), Summers and Summers (1989), and Eichengreen, Tobin, and Wyplosz (1995), can lead only to a reduction in welfare.18 The welfare loss from limiting access to capital markets is considered in Chapter 7. The analysis in this chapter is only a first step in analyzing the relation between exchange rate volatility and international trade. However, to make 16 17

18

A discussion of exchange rate regimes is given in Chapter 9. Claessens, Dooley, and Warner (1995) study the volatility of different types of capital flows and find that direct investment is no more persistent over time than short-term investment; that is, there may not be a clear relation between the holding period and the desirability of the investment. For an extensive discussion of the issues related to the implementation, feasibility, and desirability of the Tobin tax, see Reinhart (1991), Frankel (1996), and the articles in Haq, Kaul, and Grunberg(1996).

International Trade Flows, Exchange Rate Volatility, and Welfare

81

inferences about tariff and monetary policy in the context of exchange rate volatility, our model would have to be extended. To study tariff policy, one needs to interpret the shipping cost in our model as a nondissipative tariff that is determined endogenously. One would also have to model how the proceeds of the tariff are to be used in the economy. Similarly, to study the role of monetary policy, one needs to introduce money in the model in a way that it affects real allocations and also specify how the government's seigniorage income is used in the economy. These extensions are discussed in Chapters 8 and 9.

7

International Capital Flows and Welfare

In contrast to the preceding chapter where our focus was on trade flows, in this chapter we examine financial flows. This gives us an opportunity to evaluate the role of financial markets, which until now we had assumed were perfectly integrated across countries. In this analysis, we continue to consider commodity markets that are not fully integrated but compare scenarios where financial markets are perfectly segmented and where they are perfectly integrated. This exercise, therefore, allows us to analyze the linkages between the real and financial sectors of an open economy. Helpman and Razin (1978a), in early work, examine the relation between thefinancialand real sectors of international economies; Arndt and Richardson (1987) and Allen and Stein (1990) discuss why it is important to study the issues that arise in this context. Financial flows between nations arise from saving and investment decisions, decisions that are made on the basis of intertemporal considerations. In order to account for the intertemporal nature of these decisions, we work with the model of a production economy described in Chapter 3. Obstfeld (1982) and Cole and Obstfeld (1991) explain why it is necessary to account for the intertemporal considerations that arise only in the context of a production economy. Our main results are the following. First, we show that the welfare gains from the integration of financial markets can be substantial when financial markets are the only vehicle for risk sharing. We also explain that financial-market integration may have benefits over and above those arising from improved risk sharing. For example, Obstfeld (1994) shows that the availability of foreign financial claims for risk sharing may have an effect also on production decisions: nations with integrated financial markets will be willing to invest more in high-risk, high-return production technologies. Feeney (1994) makes a similar point; that is, trade in securities and commodities are complements rather than substitutes. Having investigated the importance of financial integration while assuming that commodity markets are integrated, we then reverse the experiment: taking as given that financial markets are integrated in the developed economies of 82

International Capital Flows and Welfare

83

today, we then evaluate the effect of commodity market segmentation.1 We find that the welfare loss from the segmentation of goods markets can be substantial. This welfare loss can be partly alleviated by the ability of investors to trade in foreign financial claims. However, trade in financial securities is only an imperfect substitute for trade in commodities: even with perfectly integrated, frictionless, and complete financial markets, the loss arising from the barriers to trade in goods can be significant. A policy implication of these results is that while it is optimal to facilitate international financial transactions until barriers to trade are fully dismantled, it is also important to pursue agreements that permit the free flow of goods across countries. Finally, we also analyze the volume of financial flows that arise as a consequence of the imperfect integration of commodity markets. We show that the volume is directly related to the degree of segmentation of the international commodity markets. We begin in Section 7.1 by evaluating the gains that arise from the opening of financial markets - that is, the gains from risk sharing, as opposed to the gains from trade in goods. In Section 7.2 we examine the results from Obstfeld (1994), where it is shown that the welfare gains from integrating financial markets may arise from not just risk sharing but also from the possibility that firms can change their investment strategies when it is possible to share risk internationally. In Section 7.3 we gauge how the welfare gains identified in the first section and also those measured by Obstfeld are affected by the segmentation of commodity markets: based on the analysis in Dumas and Uppal (1998), we report that even when commodity markets are not perfectly integrated, the gains from financial capital flows can be substantial. In Section 7.4 we analyze capital flows and relate them to volatility in the economy and the degree of commodity market segmentation.

7.1

The Risk-Sharing Gains from Financial-Market Integration

In this section we consider a special case of production economy described in Chapter 3, one where goods markets are perfectly integrated (where the shipping cost is zero). This assumption will be relaxed in later sections. With this assumption, the processes for K\(t) and K2O), adjusted for consumption 1

Cho, Eun, and Senbet (1986), Gultekin, Gultekin, and Penati (1989), Hietala (1989), and Wheatley (1988) provide evidence in support of integrated financial markets. Direct evidence on the absence of capital controls in developed economies is given in Halliday (1989). See Errunza (1989) and Errunza and Padmanabhan (1992) for related work.

84

Exchange Rate Volatility

and exports/imports between the two countries, are: (7.1a) (7.1b) where K\(0) = K2(0) = Ko. These equations are the same as the ones in (3.7a) and (3.7b), but with r = 0. The objective of the central planner is given in equation (3.9), and the Hamilton-Jacobi-Bellman equation that characterizes the solution is given in equation (3.11). Given that in the single-consumption-good model under consideration the production processes of the two countries have identical risk and return, and that preferences are identical across nations, trade between the countries occurs only for the purpose of risk sharing and not for the traditional reason comparative advantage. Thus, we can analyze the welfare gain of integrating financial markets by examining the role that financial securities play in enabling countries to share risk. In the absence of financial markets, the capital account will be zero implying that the current account is also zero - that is, there is no trade between the two countries. In this case, the optimization problem of the central planner can be solved by considering each country individually. According to the approach in Merton (1971), the aggregate lifetime expected utility of the central planner, defined in equation (3.9), is given by: (7.2)

V a u t [K,(0, K2(t)] =

1 -T)

where r)

On the other hand, when financial markets are perfectly integrated, the aggregate lifetime expected utility of the central planner is given by: (7.3)

Vopt[K{(t), K2(t)] = — 1

K2(t)]l~\

[K{(t) +

-t]

where — O.25?7 a2

J

That is, in a world with integrated capital markets (and zero shipping costs), one unit of capital at home is identical to one unit of foreign capital stock. Thus, one can solve the problem considering only the aggregate capital stock,

International Capital Flows and Welfare

85

We can now evaluate the effect of financial markets on welfare. Our measure of the welfare cost, compensating variation in initial endowments, is the same as that used in Cole and Obstfeld (1991) and Obstfeld (1994). The compensating variation is the reduction, a, in initial endowments [ATi(O) and £2(0)] that is required in the economy with perfectly integrated financial sectors so that the lifetime expected utility in this economy is reduced to the same level as that in the economy with segmented financial markets. That is, a is the quantity that makes V ^ R l - a)ff,(f), (1 - a)K2(t)] = V aut [^i(O, K2(t)]. In our numerical calibration, we choose parameters that are similar to those used by Cole and Obstfeld (1991). We set the subjective discount rate, <5, to 0.02 per annum, and the mean rate of growth in output, /x, to 0.02 per year. We consider three levels of relative risk aversion (RRA = 1.5, 2, and 4) and three levels of volatility (a = 0.025, 0.050, 0.075).2 The welfare cost of segmented capital markets is reported in Table 7.1. As one would expect, the welfare cost of segmented financial markets increases with volatility and with the degree of risk aversion. The welfare cost ranges from a low of 1.17% (for low volatility of 2.5% and a low risk aversion of 1.5) to a high of 33.95% (for a volatility of 7.5% and risk aversion of 4). Thus, we see that financial markets can have a substantial influence on welfare by allowing investors to share risk across countries. Although the gains from risk sharing reported here are large, it is important to caution the reader that financial markets are not the only way to share risk. For instance, Cole and Obstfeld (1991) show in a two-good model that endogenous changes in the relative prices of the home and foreign good allow investors to share most of the risk even in the absence of financial markets. Tesar (1995) and Mendoza (1991) also report that the gains from risk sharing could be quite small. In contrast to these papers, Obstfeld (1994), Lewis (1995), and Van Wincoop (1996) report much larger gains from risk sharing. In the next section (and also in the next chapter), we see that the welfare effect from opening financial markets may exceed the gains from direct risk sharing.

7.2

Other Sources of Gains from Financial-Market Integration

In the preceding section, we have evaluated the impact of opening financial markets on welfare via the direct channel of risk sharing. Obstfeld (1994), however, makes the important point that the ability to share risk may affect 2

Costello (1993, table 3) estimates the per-annum volatility of output growth to be the following: 0.0521 for Italy, 0.0466 for Canada, 0.0435 for Germany, 0.0354 for the United Kingdom, 0.0535 for the United States, and 0.0789 for Japan.

86

Exchange Rate Volatility

Table 7.1. Welfare cost of segmented financial markets (a)

Panel A: a =0.025 RRA=1.5 RRA = 2.0 RRA = 4.0

0.011719 0.015686 0.031871

Panel B: a = 0.050 RRA = 1 . 5 RRA = 2.0 RRA = 4.0

0.046867 0.063476 0.135496

Panel C: a = 0.075 RRA = 1 . 5 RRA = 2.0 RRA = 4.0

0.105377 0.145541 0.339488

Notes: We report the welfare cost, a, of segmented commodity markets for different levels of segmentation of commodity markets, parameterized by the effective tariff rate, r. The welfare cost is computed as the permanent reduction, a, in initial endowments that is required in the economy with perfectly integrated financial (and real) sectors so that lifetime expected utility in this economy is reduced to the same level as that in the economy with segmented markets. That is, a is defined as the quantity that makes V ^ K l - a)K\(t), (1 - a)K2(t)] = V[K\(t), ^2(01- All values reported are for the case where K{(0) = K2(0), /x = 0.02, and 8 = 0.02. welfare through other channels as well. To illustrate this, he develops a model where the source of these indirect gains is a shift in investment strategies. 3 In Obstfeld's model, there are two production technologies in each country: one, a low-risk technology with relatively low return, and the other with a high return but also higher risk. In the absence of international financial markets, investors allocate a certain proportion of total resources to the high-return technology and the rest to the low-return technology. Integrated financial markets, however, increase the opportunities to share risk; thus, investors are willing to 3

In the next chapter we describe another potential source of indirect gains - a change in tariff policy.

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87

invest a greater share of wealth in the high-risk, high-return production technology. Hence, financial integration leads to an improvement in welfare not only through risk sharing but also because integration of financial markets allows countries to choose technologies with higher returns.4

7.3

The Welfare Costs of Segmented Commodity Markets

In the welfare gains reported in the previous two sections, it was assumed that commodity markets are perfectly integrated. This implies that the gains from risk sharing, both direct and indirect, can be fully realized. However, the presence of costs for transferring resources across countries will constrain the amount of welfare gains that can be realized from financial-market integration. In this section, we take as given that financial markets are fully integrated and evaluate the effect of commodity market segmentation on aggregate welfare. As in our basic model (see Chapter 3), we model the segmentation of commodity markets by introducing a proportional shipping cost, r, so that it is costly to export the physical good from one country to another. Thus, for every unit of good that is exported from one country, only (1 — r) arrives in the other country. Thus, the regulated processes for K\(t) and K2(t), adjusted for consumption and exports or imports between the two countries, are the ones given by equations (3.8a) and (3.8b). We now need to solve the differential equation in (3.11) subject to the law of motion for the production processes in (3.8) and the appropriate boundary conditions.5 Although the aggregate utility level in this case, V[K\(t), K2(t)', T > 0], cannot be obtained in closed form, it can be computed by solving numerically the differential equation in (3.11). In Figure 7.1 we present the lifetime expected utility of the central planner for different degrees of segmentation of the commodity markets, plotted against the log of the ratio of the capital stock at home to that abroad, co{t) = \n[K\(t)/K2(t)\. From this figure we make two observations. First, as one would expect, the aggregate level of welfare increases with an increase in the degree of integration between the home and foreign commodity markets (decrease in r). Second, for a given r, the level of welfare declines as the imbalance in the quantity of goods at home and abroad increases. This is a consequence of the fact that the (unconstrained) optimal policy for diversifying the risk from the two production processes, given that the two production processes are uncorrelated, is to have the quantity of goods at home equal that abroad. In 4 5

See Feeney (1994) for a similar analysis in a small-country model. The boundary conditions are given in Chapter 3.

-160

T

- 1 6 5 -•

- 1 7 0 •-

ig-175

+

s

1 -180 +

-185 -•

- 1 9 0 -•

-195 •

-1.5

-1 -0.5 0 0.5 Imbalance in quantity of goods at home and abroad: Log(Kl/K2)

1

1.5

Figure 7.1. Lifetime expected utility. This figure shows the lifetime expected utility of the central planner for different levels of integration (r) of the international commodity markets. The utility is plotted as a function of the imbalance in the quantity of goods located at home and abroad. Note that the tolerated imbalance in the stock of goods located at home and abroad (region of no shipping) increases with an increase in r. From the figure, we see that as the level of integration increases (r decreases), the utility level increases. Also, for a given level of r, the utility level increases as the imbalance in the goods at home and abroad decreases (max at K\ = K2). In this figure, /z = 0.11, p = 0.10, a = 0.50, and RRA is 1.5. The symbols indicate the proportional tariff levels considered: triangle = 0, diamond = 0.10, letter x = 0.20, square = 0.30.

International Capital Flows and Welfare

89

Table 7.2. Welfare cost of segmented financial markets (a) Magnitude of the effective tariff (T) 0.05

0.10

0.20

0.50

Panel A: a =0.025 R R A = 1.5 RRA = 2.0 RRA = 4.0

0.001849 0.001917 0.002101

0.003392 0.003544 0.003866

0.006027 0.006496 0.007338

0.010616 0.012896 0.017817

Panel B: o = 0.050 R R A = 1.5 RRA = 2.0 RRA = 4.0

0.004938 0.005304 0.006525

0.008552 0.009102 0.010843

0.015133 0.016114 0.018720

0.032103 0.036109 0.044174

Panel C: a = 0.075 R R A = 1.5 RRA = 2.0 RRA = 4.0

0.009888 0.011009 0.015416

0.016290 0.017945 0.024388

0.027482 0.029983 0.039164

0.058141 0.064434 0.081266

Notes: We report the welfare cost, a, of segmented financial markets for different levels of volatility and RRA. The welfare cost is computed as the permanent reduction, a, in initial endowments that is required in the economy with perfectly integrated financial sectors so that the lifetime expected utility in this economy is reduced to the same level as that in the economy with segmented financial markets: a is the fraction that makes

V°&[(\ - a)K\(t), (1 - a)K2(t)] = V[K{(t), K2(t); 1 > r > 0]. All values reported are for the case where K\ (0) = K2(0), fi = 0.02, and 8 = 0.02.

the presence of the transfer cost, however, this imbalance is not corrected every instant; thus, as the imbalance in the quantity of goods at home and abroad increases, the welfare level falls. Note that for the cases where r > 0, even when the quantity of goods at home is initially equal to that abroad, the aggregate level of welfare is not the same as in the case where the goods markets are perfectly integrated (r = 0). This is because of the rational anticipation that, when an imbalance in the stock of goods at home and abroad occurs, it will not be optimal to correct this instantaneously because r > 0. To estimate the magnitude of the welfare loss from the segmentation of the international commodity markets, we report a set of simulation results in Table 7.2. As before, our measure of the welfare cost is the reduction, a, in initial endowments [ K\ (0), ^ ( 0 ) ] that is required in the economy with perfectly integrated real (and financial) sectors so that the lifetime expected utility in this economy is reduced to the same level as that in the economy with segmented

90

Exchange Rate Volatility

commodity markets:

Vopt[(l - a)Kx(t), (1 - a)K2(t)] = V[Kx(t), K2(f)\ 1 > r > 0]. We use the same parameters as before; the only additional parameter that we need to specify is the effective tariff rate (r). Based on the evidence in Deardorff and Stern (1990) and Melo and Tarr (1992) reported in Chapter 3, we consider the following values for r: 0.05, 0.10, 0.20, and 0.50. From Table 7.2 we see that for a = 0.025 and r = 0.05 the welfare cost of the segmentation of commodity markets is of the order of 0.2%. This cost increases as the volatility levels increase. For example, when a = 0.075 and RRA = 4, then the welfare loss for the case where r = 0.05 is 1.5%. The welfare loss from the segmentation of the commodity markets is even greater when the degree of segmentation of the real sector is more severe. In the extreme case where r = 0.50, a = 0.025, and RRA = 4, the welfare loss is as large as 1.7% and this increases to 8.1% as a increases to 0.075. Thus, we observe that the deadweight loss from the imperfection of the real markets cannot be completely offset by trading in financial markets. That is, financial securities provide only an imperfect hedge against the additional output risk that arises when a friction prevents optimal diversification of production across the two countries. Even though these simulations suggest that the welfare cost of effective tariffs can be quite large, the important point is that these costs are much smaller than those from segmented financial markets. The same point is made also in Dumas and Uppal (1998), in the context of the two-good model considered in Obstfeld (1994).6

7.4

International Financial Flows

Having analyzed the effect of financial markets on welfare, in this section we analyze the volume of financial flows between the home and foreign country when financial markets are perfectly integrated but there is a cost for transferring goods across countries. To do this, we need to extend the solution of the central planner to the disaggregate level of the home and foreign representative investors. We undertake the analysis of capital flows in two parts: in the first part, we start by defining financial capital flows and then show how they can be determined; then, in the next subsection, we analyze these flows and relate them to exchange rate volatility and the parameters of the model. 6

In their analysis, Obstfeld (1994) and Dumas and Uppal (1998) use a recursive utility function instead of the standard time-additive expected utility function. Dumas, Uppal, and Wang (1998) explain how for a multiagent economy one can extend the standard stochastic dynamic programming formulation for expected utility to the case of recursive utility.

International Capital Flows and Welfare

7.4.1

91

Determining the International Financial Flows

Given that the commodity markets are segmented, the home and foreign investors do not hold identical portfolios. Therefore, the equilibrium, in contrast to Lucas (1982), is a not a perfectly pooled one. Thus, in response to output shocks, investors across countries consume and save different quantities, and this produces a nonzero current-account balance between the two countries. Trade in financial assets between investors is the complement of the currentaccount balance. We use the Cox and Huang (1989) martingale pricing approach to determine the financial flows that arise between nations in equilibrium.7 The trade in financial assets between countries depends on the menu of securities that investors can hold. We assume that investors can own equity in the domestic and foreign risky technologies. In addition to the investment in the risky production technologies, each investor may also invest in an instant maturity, zero-net-supply bond that is riskless in terms of the domestic good. These securities are sufficient to complete the market.8 We choose the domestic good, K\(t), to be the numeraire, and the real exchange rate, Z(t), the relative price of the foreign good in terms of the domestic good, is given in equation (3.10). Note that in the presence of costs for exporting goods from one country to another, the marginal rates of consumption in the home and foreign country need not be equal. That is, the real exchange rate will typically not be equal to unity. For example, when the foreign good is scarce relative to the domestic one, the exchange rate will be greater than unity. Denote the value of domestic and foreign equity by P\(t) and P2(t), respectively. Given our assumption that the home good is the numeraire, it follows that Pi (0 = A^ (r), and P2(t) = Z(t)K2(t), where Z(t) is the real exchange rate (the price in domestic units of the foreign good). Let B(t) denote the price of the bond that is riskless in terms of the domestic good. The stochastic processes for P\{t) and P2(t), can be derived using Ito's lemma: (7.4)

dPx{t) = [Atp,(0Pi(0 - ci(0]dt +
(7.5)

dP2(t) = [nPl(t)P2(t) - Z{t)c2{t)]dt + ox{t)Px(t)dzx(t) + O2(t)P2(t)dz2(t),

7

8

The Cox and Huang (1989) approach requires that one first identify the optimal consumption policy for an investor and then find a self-financing portfolio strategy that generates this flow of consumption. In the economy being considered in this article, the information structure is generated by N (=2) Brownian motions. Duffle and Huang (1985) show that for markets to be dynamically complete in the presence of N sources of uncertainty, one requires the existence of at least N risky assets and one risk-free asset. Uppal (1993, lemma 2) shows that, in the model being considered, the riskless asset is never held in equilibrium.

92

Exchange Rate Volatility

where

+ 0.5 and

Let n = {rcPl (0, nPl(t), nB(t)} denote the portfolio of the home investor and m = {mP] (r), m P2 (0, mB(t)} the portfolio of the foreign investor. Here, nP] (t) is the number of shares of the domestic firm held by the home investor, nPl(t) is the number of shares of the foreign firm held by the domestic investor, and nB(t) is the investment in the domestic bond, which has an instantaneous interest rate, in terms of the home good, of r(t). The elements of m are defined similarly. We normalize the total number of shares outstanding in the domestic and foreign firm to one. Given this normalization, and the fact that bonds are in zero net supply, implies that n + m = {1, 1,0}. We denote the wealth of the domestic investor by W(t), which is given by the value of her portfolio at time t:

(7.6)

W(t) = np> (f)Pi(f) + nP2(t)P2(t) + nB(t)B(t).

Given the Markovian nature of the model, and the infinite horizon assumption, the wealth of the home investor depends only on the current value of the stock price at home and abroad; that is, W(t) = W[P\(t), /MOlWe are now ready to define the capital flows between the two countries. We start by defining the net foreign investment account at time t, F(t), which gives the home ownership of foreign assets, net of domestic assets owned by foreigners.

F{t) = nPl(t)P2(t) - [mp\t)Px{t) + mB(t)B(t)] = np>(t)P2(t) - {[1 - nPi(t)]P(t) - nB(t)B(t)} nPi(t)P2(t) + nB(t)B(t) =

W(t)-Pl(t\

where the second line is derived using the fact that n P| and m P], the total number of shares outstanding in the domestic firm, are equal to one and that the bonds are in zero net supply. The last line follows from the definition of wealth in (7.6).

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Changes in the net foreign investment account arise from two sources: (1) from the net acquisition of foreign assets and (2) from changes in the (local) market values of assets and changes in exchange rates. However, the capital flows recorded in the balance-of-payments account do not include capital gains. Thus, to obtain the financial capital flows we exclude the capital gains component from the change in the net foreign investment account. The change in net foreign investment account is given by dF(t) = d W(t) — dP\(t). Using Ito's lemma, this is:

(7.7)

WP]dPl(t)+Wp2dP2(t)-dPl(t)+l-WP]P][dP](t)]2

dF(t) =

+ WP]P2[dP](t)dP2(t)]+l-Wp2p2[dP2(t)]2 = [WP] +

-\]dP](t)+WP2dP2(t)

WP]

+ -Wp2 where (7.7) is obtained by using the results in (7.4) and (7.5). Note that the change in the market value of the domestic firm is given by dP\(t), and that the (translated) value of the foreign firm, by dP2(t). Thus, the first two terms in equation (7.7) give the capital gains on the shares held by the domestic investor (typically excluded in the balance-of-payments accounts), and the terms on the last line are the capital flows - that is, the change in the net asset position.9 We can therefore define the volume of capital flows by setting the dP\(t) and dP2(t) terms equal to zero. We now define the value of a country's capital flows as the net purchase of assets, per unit of time. This flow, which can be determined by the change in the wealth of the home country that occurs as a result of the accumulation of assets rather than from capital gains, is given by: (7.8)

X

-WPlPl[dP\{t)}2

+ WPlP2[dPldP2(t)]

+

l

-WP2P2[dP2(t)]2.

We can also define the current-account balance of a country. The currentaccount balance is the difference between a country's income and its absorption. The country has two sources of income: first, dividend and capital gains from 9

It can be shown that the number of shares of the domestic firm that the home investor holds, nPx (t), is given by Wp] [P\(t), /^COl and the number of shares of the foreign firm, nP2(t), is ), Piit)]. Therefore, the change in these positions is given by the second derivatives

\ P2{t)l

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Exchange Rate Volatility

the shares that it holds and, second, interest on any loans that it has made. The total dividend paid out by the domestic firm is given by c\ (t), and the dividend of the foreign firm, in domestic terms, is Z(t)c2(t). The home country's share of the dividend from the domestic firm is determined by the proportion of total shares that the investor owns and is given by nPl(t)c\(t). The home country's share of foreign dividends is nPl(t)Z(t)c2(t). Thus, the current-account balance, excluding capital gains, can be defined as theflow,per unit of time, of payments received as interest and dividends, less its absorption:10 (7.9)

[/iPl(Oc,(O + np\t)Z{t)c2{t) + nB(t)r(t)] - cx(t).

As is clear from (7.8), to determine the capital flows one only needs to obtain the process for W[P\(t), P2(t)]. The differential equation describing W[P{(t), P2(t)] in the region 1/[A(1 - r)] < Px/P2 < X(l - r) can be derived using Ito's lemma and the individual investor's budget constraint: (7.10)

0=-rlW

+ ci + Wpl(rlPi-cl)+Wp2(rlP2-Zc2)+^WplplP?
+ 2 ^ f t ^ 2 2 h 2 ( 0 + ^1(0] + WPiP2Pl P2[oax{t)} with the associated boundary condition, WP][ P\ (f), /MO] = Wp2[P\(t), P2(t)], which is the (value-matching) boundary condition requiring that goods be exported from one country to another only when the return from exporting fully offsets the cost - that is, when the effect on wealth, of exporting (or importing) goods, is zero. 7.4.2

Analysis of International Financial Flows

In this section, we present results on the direction and the volume of capital flows, based on the numerical solution of the differential equation for wealth, which is derived in the previous section. We first analyze how an increase in the integration of international commodity markets affects the volume of capital flows. We show that with increasing integration, the (conditional) volume of capital flows declines. We then analyze how the risk aversion parameter affects the volume of capital flows andfindthat the volume offinancialflowsis directly related to the difference between the degree of risk aversion and unity.11 10

1]

Absorption consists of just c{t), because dP\(t) is interpreted as capital gains rather than a change in portfolio investment. As one would expect, the current-account balance is equal to the capital flows, and the global (domestic and foreign) capital flows add up to zero. Recall that the relative risk aversion of the log investor is unity. As is well known, for an investor with log utility the wealth effect and the substitution effect exactly offset each other; hence, a change in the investment opportunity set leads has no effect on the savings (and capital flows) of this investor.

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95

Observe that financial flows serve as a substitute for trade in goods and foreign direct investment:12 when trade in goods is not optimal at a particular instant, then agents trade securities instead, in anticipation of exports or imports in the future. That is, there are capital flows even in the absence of trade in goods. This is consistent with the empirical observation that only a small proportion of the total trade in international financial securities is related to the flow of goods and services. In the two extreme cases, where the shipping cost is zero and where there is a 100% shipping cost, the volume of international capital flows is zero. This is because in the first case there is no impediment to trade in goods, and thus one does not need the compensating trade in financial securities. In the second case, when goods markets are perfectly segmented, the likelihood of commodity trade in the future is zero. Because there is no future trade in goods that needs to be financed, the volume of capital flows is zero again. To further analyze financial capital flows, we need to solve the differential equation in (7.10). Substituting this solution into (7.8) or (7.9) allows us to obtain the international capital flows. Given that the interest rates, the exchange rate, and the optimal consumption and export policies are determined endogenously, it is not possible to solve this differential equation in closed form. Therefore, we analyze the capital flows using numerical methods. Confirming our intuitive argument, we find that the volume of capital flows, for the general case where 0 < r < 1, is directly related to the degree of segmentation of the goods markets. That is, the volume of financial flows increases with an increase in r. We show the volume of financial flows, for different levels of segmentation (T), in Figure 7.2. From the figure, we see that as the trading cost, r, increases, the volume of financial flows increases.13 This result is a consequence of the fact that the flow of financial capital is a substitute for trade in goods, albeit an imperfect one. Thus, as r increases and investors are constrained from transferring the physical commodity, trade in financial claims increases to offset this constraint to some extent. This substitutability between trade in financial securities and real goods is analogous to the insight in Mundell (1957) that trade in goods may make trade in factors of production redundant. Cole and Obstfeld (1991) examine the reverse issue: if no asset trade is possible, then how good a substitute is trade in 12

13

Feeney (1994) also analyzes the relation between trade in commodities and trade in financial securities to see if they are substitutes or complements; she makes the assumption that the country being analyzed is small and, hence, does not affect world prices. Note also, that as the transfer cost increases, the no-trade region is wider. That is, in the presence of a larger trading cost, it is optimal to tolerate a larger imbalance in the stock of goods at home and abroad before deciding to transfer goods.

0.003 T

1.50

-0.003

±

Imbalance in quantity of goods at home and abroad: Log(Ki/K2)

Figure 7.2. Volume of capital flows. This figure shows that the volume of capital flows increases as the degree of segmentation of the commodity markets increases. That is, the capital flows increase as r increases, implying that financial flows are a substitute for trade in real goods. In this figure, fi = 0.11, p = 0.10, a = 0.50, and the degree of (RRA) 1 — y = 1.50. The symbols indicate the proportional tariff levels considered: square = 0.10, letter x = 0.20, diamond = 0.30.

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97

commodities. They find, in the context of their model, that trade in goods is a fairly good substitute for trade in financial assets and can substantially reduce the welfare loss from the inability to trade in financial markets. Atkeson and Bayoumi (1993) also discuss the role of financial capital flows as a substitute for physical capital mobility. The analysis of financial flows in this section also extends the work of Stockman and Svensson (1987). Their model accounts for financial flows arising from a change in the location of wealth but does not consider the effects of a change in the ownership of wealth. The model constructed here explicitly accounts for the effect of both: a change in the distribution of physical goods across countries and a change in the allocation of wealth across countries.14

7.5

Conclusion

In this chapter we study the impact of imperfections in the physical goods market on international financial flows in a general-equilibrium setting. We model a two-country, two-good economy in which financial markets are complete and frictionless but the markets for real goods are segmented by a proportional cost for exporting goods from one country to another. Investors compensate for this constraint on their ability to allocate physical resources optimally (between the home and foreign country) by trading in financial claims. The ability to trade in financial assets reduces the welfare loss from the segmentation of commodity markets. Thus, financial capital flows are a substitute for the flow of real goods. With complete, frictionless, and perfectly integrated commodity markets, the welfare loss from the segmentation of commodity markets is not substantial. This loss increases with the risk aversion of investor and with the aggregate volatility of output growth in the world economy. A policy implication of this result is that it is important to remove barriers to trade, and until organizations such as the International Trade Organization (ITO) and the North American Free Trade Association (NAFTA) can remove all barriers to trade in goods, policy makers should facilitate the flow of financial capital. 14

Our work also extends the literature studying the relation between international capital flows and the terms of trade. In contrast to the existing models studying the Harberger-Laursen-Metzler effect - Harberger (1950) and Laursen and Metzler (1950) argue, based on a static theory of savings, that a temporary deterioration in the terms of trade leads to a current-account deficit because real income falls as the terms of trade worsen, and thus households run a currentaccount deficit to maintain consumption levels - such as Obstfeld (1982), Persson and Svensson (1985), Sachs (1981), Stulz (1988), and Svensson and Razin (1983), the model in this article is a general-equilibrium one in which domestic and foreign interest rates are determined endogenously and production is modeled explicitly. See, also, Dooley, Frankel, and Mathieson (1987), Obstfeld (1986), and Tesar (1991).

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Exchange Rate Volatility

The equilibrium in this model is not a pooling one. That is, given the segmentation of the commodity markets, investors at home do not hold the same portfolio as investors abroad. Thus, in response to output shocks, they trade financial assets. We analyze the financial flows that arise as the two countries trade in financial markets to hedge themselves against production shocks. Given that financial flows are a substitute for trade in commodities, we find that the volume of capital flows increases with the degree of segmentation of the commodity markets and with investors' risk aversion. In contrast to the existing literature on international capital flows, our results are obtained in a generalequilibrium model in which the interest rate and the real exchange rate are determined endogenously. Some of the issues not considered here are the effectiveness of monetary policy and the choice of the exchange rate regime in the presence of financial markets. We examine these issues in Chapter 9.

8

Tariff Policy with International Financial Markets

In this chapter our objective is to examine tariff policy in the presence of capital markets. In particular, we address the following issues: (1) how does the degree of integration of financial markets affect the optimal tariff rate; (2) what is the magnitude of the welfare gains arising from the change in tariff rates on the opening of financial markets, and how do these gains compare with the direct gains from risk sharing; and (3) can financial markets play a role in coordinating international policy. The model that is used to analyze these issues is an extended version of the basic framework described in Chapter 3. The major difference is that now commodity markets are segmented because of an explicit tariff instead of a shipping cost - that is, one needs to interpret the exogenous shipping cost as an endogenously determined tariff rate, as done in Lee (1998) and Devereux and Lee (1998). The choice of optimal tariff policy has been studied at length.l Johnson (1954) framed the choice of optimal tariff in terms of the terms-of-trade argument. Kennan and Riezman (1988) extended the results in Johnson by relaxing the assumption of constant-elasticity offer curves. Other models of strategic tariff interactions between governments include McMillan (1986) and Dixit (1987). These models, however, do not consider stochastic endowments or the role of financial markets. Helpman and Razin (1978b) are among the first to study the effect of financial markets on tariffs. They find that a tariff does not protect the import-competing industry in a small open economy when consumers can trade in securities and the tariff proceeds are not redistributed to the consumers as lump-sum transfers. Stockman and Delias (1986) find that domestic welfare drops with higher domestic tariffs (or higher foreign tariffs). This relation is obtained despite the improvement in the terms of trade with domestic import tariffs, and their finding is opposite to that derived in a static model without asset markets. Although 1

For the definitive guide, see Frenkel and Razin (1994).

99

100

Exchange Rate Volatility

Helpman and Razin (1978b) and Stockman and Delias (1986) show the importance of considering financial markets in evaluating tariff policy, the tariff policy in question is not endogenously determined in these models. Barari and Lapan (1993) generalize Stockman and Dellas's work by allowing the government to choose an optimal tariff. They assume the foreign government to be passive in their analysis and examine the home government's tariff choice in two extreme economies, namely financial autarky and complete financial markets. The work described in this chapter differs from the preceding models in two ways. First, the choice of the domestic and international tariff rates is endogenous - determined by the two governments behaving strategically in a Nash game. Second, the Nash equilibrium tariff is determined also for the intermediate case of an economy with incomplete financial markets, whereas previous analyses are based on a study of the two extreme cases, that of financial autarky and complete financial markets. In Section 8.1 we describe the modeling choices in Lee (1998) and the implications of this model for optimal tariff rates in the presence of international capital markets. In Section 8.2, using the analysis in Devereux and Lee (1998), we describe the welfare implications of capital market integration. Then, in Section 8.3, we discuss the implications of these results for international policy coordination.

8.1

Optimal Tariff Rates and Financial-Market Integration

8.1.1

The Model with Endogenous Tariff Policy

Lee (1998) extends the basic model of Chapter 3 by modeling the segmentation of commodity markets by a proportional tariff rate rather than a shipping cost. The tariff is chosen optimally by the government, and the tariff proceeds are redistributed to investors in the form of a lump-sum transfer. She considers a two-date, two-country economy, where the representative investor in each economy has a stochastic endowment of two nonstorable goods. Each of these two goods is homogeneous across the two countries. It is assumed that each country "specializes" in one good, that is, has a larger endowment of this good; thus, good 1 is typically exported by country 1, while good 2 is typically exported by country 2. In this economy, each investor chooses the quantity to consume and the quantity of each good to trade. In addition, investors also choose how to allocate their wealth across the available financial securities. The main difference in the individual's problem, compared with that in Chapter 3, is that now an investor's wealth includes also the lump-sum transfer of the tariff collected by the government.

Tariff Policy with International Financial Markets

101

The problem that the government (policy maker) faces is to choose the optimal tariff for the next period in order to maximize the utility of its citizens (here the representative investor). Each government assumes that the other one will choose its own tariff level optimally. The equilibrium tariff is determined by solving simultaneously the problem of the individual investors, who take the tariff rate as given, and the Nash tariff game between the two governments. 8.1.2

Results on Optimal Tariffs

We now describe the outcome of the foregoing optimization problem for different financial market structures. Three financial market structures are considered: financial autarky, where investors cannot trade any financial claims; complete financial markets, where investors can hedge the endowment risks in every state; and incomplete financial markets, where only some financial claims are available so that the hedging is not perfect in all states. A tariff has two effects: a wealth effect via an improvement in the terms of trade; and a price effect that distorts the price of the good at home relative to that abroad. Under complete segmentation of financial markets, the wealth effect dominates, and thus the optimal tariff is always strictly positive. A positive tariff reduces the demand for the import good in the home country by driving down the world price of the import good relative to the world price of the export good in the economy. Therefore, a positive tariff improves the world terms of trade for the home country. Because the home country is endowed with a larger quantity of its export good relative to its import good, the improvement in its terms of trade increases the value of its endowment and creates a positive wealth effect, while having the opposite effect on the foreign country. Consequently, in a Nash tariff game, each government has the incentive to choose a positive tariff. On the other hand, with complete and perfectly integrated financial markets, the optimal tariff is zero. The reason for this is that in the presence of financial markets investors can hedge against changes in the terms of trade. That is, with complete financial markets, investors can hedge perfectly against the wealth effects arising from a change in the terms of trade. Thus, the only consequence of the tariff is the price distortion that it creates between the domestic price and the foreign price for the good. Given that now the tariff has only a negative effect, the optimal tariff is zero. In the intermediate case, where some financial claims are available but the financial market is not complete, the government can influence the terms of trade partially. Thus, the optimal tariff turns out to be positive, although it is smaller than that under complete segmentation of the capital markets. To conclude, we see that there are important interactions between decisions made in commodity markets and financial markets. Given that financial markets

102

Exchange Rate Volatility

are fairly well developed and closely integrated across the large economies that are the focus of our study, this analysis implies that a policy maker must pay close attention to financial markets when setting trade policy. In the next two sections, we see that financial markets can play a significantly positive role on welfare and policy.

8.2

Tariff Policy, Financial Markets, and Welfare

In the preceding section we have seen that the structure of financial markets influences the choice of tariff. We now examine the magnitude of this effect on welfare. In Chapter 7 we compared welfare under integrated financial markets to that under segmented markets. We saw that substantial risk-sharing gains could be realized by permitting investors to diversify risk by trading in financial claims. We also described how the opening of financial markets could induce a change in production choices, thus generating further welfare gains. In this section, we will see a second such source of indirect welfare gains arising from the effect financial markets have on tariff policy. That is, the overall gains from trade in financial markets are higher than those estimated in models where trade policy is held constant. Devereux and Lee (1998) estimate the magnitude of these indirect gains arising from financial market integration. The model used by Devereux and Lee (1998) is similar to that described in the previous section. The only difference is that the tariff is allowed to be contingent on the state of nature rather than being predetermined. This is motivated by the assumption that governments may not be able to precommit to a tariff policy and may wish to adjust this policy after observing the realization of the endowment shocks. Thus, the timing of events is as follows: (1) financial markets open and trade in securities occurs; (2) the endowment shocks are realized; (3) governments choose tariffs optimally in a Nash game; and (4) there is trade in goods. Even with these changes to the model, the basic result is the same as in the previous section: while the optimal tariff in the absence of financial markets is positive, the tariff in the presence of perfectly integrated and complete financial markets is zero. That is, financial markets not only allow for optimal risk sharing but also eliminate the gains from tariffs so that governments endogenously decide on a free-trade policy. Devereux and Lee call this the "trade dividend" of financial markets. They also provide empirical evidence to support this result: they find that countries with financial markets that are open are also the ones with low tariff rates. To estimate the magnitude of the welfare gains from the opening of financial markets, Devereux and Lee extend their model to an infinite-horizon setting and

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103

calibrate it to data for the United States and Japan. They find that the welfare gains arising from the fact that the optimal tariff in the presence of financial markets is zero are about sixteen times as large as the direct gains from the risk sharing facilitated by financial markets. They also report that compared with the gains from integrating financial markets while taking trade policy to be exogenous, the gains with endogenous trade policy are between six times to fifty times as large, depending on the particular choice of parameter values. 8.3

Implications of Financial Markets for Policy Coordination

In this and the previous chapters we have seen that the opening of financial markets can have a significant impact on welfare, over and above what pure risk sharing would suggest. However, the opening of financial markets has another important consequence: financial markets may reduce the need for international coordination of policy. In the model just described, in the absence of financial markets government would ideally like to precommit to a zero tariff. But when governments cannot coordinate their tariff policies, the outcome of the Nash game is one where tariffs are positive. On the other hand, withfinancialmarkets, even in the absence of any other coordinating mechanism, the equilibrium tariff is zero.2 That is, financial markets effectively play the role of a coordinating mechanism. 8.4

Conclusion

In response to the three questions raised at the start of this chapter, we find that the opening of financial markets can have a significant effect on the choice of tariff policies, that financial markets can provide an endogenous mechanism for coordinating international trade policy, and that the welfare effect of opening financial markets now includes the direct gains from risk sharing and the indirect effects from the lower tariff (for reasonable parameter values, the indirect effects are about sixteen times as large as the indirect effects). This is the second indirect source of welfare gains from the opening of financial markets that we have highlighted and complements our description, in the previous chapter, of how the opening of financial markets could encourage countries to shift investments towards high-risk, high-return technologies. 2

This result is in contrast to the finding of Chang (1997), who finds that the opening of financial markets makes policy coordination more desirable. In this model, however, the policy game is about the choice of debt levels, which are directly related to the interest rates rather than the relative price of goods.

9

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

Money has not played a great role in any of the chapters thus far. In Chapters 4 and 5 we linked nominal spending to the money supply via a cash-in-advance constraint, but the supply of money was given exogenously. In this chapter, at last, we give money an important role as a control variable that influences economic activity. We then use the model to address the issue of whether fixed exchange rates are desirable. For a survey of the literature on macroeconomic performance under alternative exchange rate regimes, see Alogoskoufis (1994). Canzoneri and Rogers (1990) discuss the costs and benefits of the European Union (EU) in particular.1 We briefly review the different ways of modeling supply and demand for money2 and the issues associated with exchange rate regimes in Section 9.1. In the remainder of the chapter, we formally analyze the issue of the desirability of fixed exchange rates in a model that contains money as well as a government and still has maximal resemblance to the models discussed in the preceding chapters. Section 9.2 describes the assumptions of this model, and the basic implications of the model are derived in Section 9.3. Section 9.4 examines the conditions under which the exchange rate will be constant over time, given optimal monetary policies.

9.1

Money and Exchange Rate Regimes: A Review

In this introductory section we first discuss alternative ways of modeling money demand. We then turn to the issue of money supply, and especially the government's use of the seigniorage income. Lastly, we bring up the issue of (nominal) exchange rate regimes. 1

2

There is a large literature comparing alternative exchange rate systems; for some of the early work in this area, see, for instance, Helpman and Razin (1979a), Greenwood and Williamson (1987), Helpman and Razin (1987), Persson and Svensson (1989), and Stockman (1988c). Eichengreen (1994) provides an empirical analysis of the relation between a country's choice of exchange rate regime and business cycle effects. See also the discussion on models of nominal exchange rates in Chapter 2.

104

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

9.1.1

105

Money Demand

Money is said to be useful as a numeraire, a store of value, and as a way to avoid the inconvenience of pure barter trade (hence the transaction demand and precautionary demand for money, possibly reinforced by money's status as sole legal tender). In formal economic models, the role of numeraire can, of course, be assigned to any good, so money is modeled either as a store of value or as the least-cost medium of exchange. The store-of-value aspect is emphasized in the overlapping-generations approach.3 In such a model, active young agents coexist with retired, older agents, and the former save money to provide for consumption in the retirement stage of their life. This approach has some drawbacks. In reality, money provides "convenience" services rather than interest or cash dividends. In its role as a store of value, it is therefore dominated by bonds and other financial assets that provide purely financial returns. In short, in a model of this class one has to ignore the existence of purely financial assets; otherwise money will not be held at all. Stated differently, one cannot ignore money's chief raison d'etre of being the least-cost medium of exchange. However, it is not easy to formally model the least-cost-medium-of-exchange aspect of money. The standard ways of introducing money are via the cash-in-advance constraint and via moneyin-the-utility-function; and neither approach formally models the search costs that would have incurred in the absence of money.4 We briefly describe both approaches. One can invoke (and somewhat stretch) the legal-tender characteristic of money and postulate that producers-vendors will simply not accept any other form of payment. This view leads to the cash-in-advance approach, pioneered by Clower (1967): at the beginning of the period consumers have to hold ready the cash they want to spend during that period. In some versions of this approach, the cash needs to be picked up at the end of the preceding period, while in other variants people acquire money at the beginning of the period itself. The distinction between the two may matter for at least two reasons. First, if consumers hold the money "overnight," they bear the interest cost.5 In contrast, if consumers acquire money just before shopping starts, money is held overnight by the firms (who distribute it, at the beginning of 3 4 5

See Karekan and Wallace (1980). The first article in which search costs are explicitly accounted for in developing a theory of money demand is Kiyotaki and Wright (1989). Denoting the nominal risk-free rate by R, one can decompose money balances as M = M/(l + R) + M • R/( 1 + R), where the component M/( 1 + R) is the bond equivalent of money balances (i.e., part of the investment decision) while M • R/( 1 + R) is the consumption part - the cost of interest foregone.

106

Exchange Rate Volatility

the next period, as dividends and wages). In a rational and complete market, however, this distinction should not be important: if corporations hold the money overnight, then their money balances (and the cost of interest foregone) still show up in the stock prices and, hence, in the consumers' intertemporal budget constraints.6 A more important distinction, therefore, is whether cash is acquired before the relevant information about the consumption period is known. If consumers can pick up the cash after all news has been made public and after asset markets have traded, the consumers know perfectly what their planned expenditures for the period will be; and in view of the cost of foregone interest on the idle money balances, they will not carry any cash overnight. Thus, in such a model, money balances exactly equal nominal expenditures in the period, as in a quantity theory with a velocity of unity.7 The cash-in-advance approach gets more complicated if the decision about cash balances has to be made before all relevant news is divulged and asset prices have been determined: then optimal expenditures are still uncertain at the time cash balances are acquired, and the precautionary motive for money also plays a role.8 The standard alternative to imposing a cash-in-advance constraint is to model real money balances as providing direct utility. This money-in-the-utility assumption is derived from the observation that people value leisure and can reduce searching time if they hold money. With money in the utility function, (real) money balances become akin to other goods, and the nominal price of holding money is the present value of the nominal interest forgone. Compared with the cash-in-advance approach, one difference is that in a moneyin-the-utility-function model, consumers do not actually spend their balances. Despite the differences between the two ways of modeling the demand for money, their implications are often similar: see Feenstra (1986), and especially Guidotti (1989), who shows the equivalence between the cash-in-advance and the money-in-the-utility approaches in the context of a two-country world. Perhaps more important, therefore, is the way that money is supplied, or, more precisely, what the government does with its seigniorage income.

6

7

8

In much of the literature, investors just hold (nominal or real) bonds, no stocks. Thus, in an incomplete market, the equivalence between corporate and individual-consumer balances does not hold. Note that the velocity, as defined here, is identified relative to consumption expenditures over one (undefined) period, rather than total added value over one year, as common estimates of velocity are. Thus, the unit level of the velocity is not necessarily a problem. Its assumed constant nature is more problematic, though. See Svensson (1985a, 1989); Obstfeld and Rogoff (1996) discuss other variants of the basic cash-in-advance scenario.

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

9.1.2

107

Money Supply and the Government's Economic Role

Probably the simplest approach to account for seigniorage in a microeconomics-based model is to assume that the government transfers back its seigniorage income to the residents, by way of a lump-sum transfer (see, e.g., Obstfeld and Rogoff, 1996, for many applications of this approach). Alternatively, the government can be viewed as an income-maximizing entity (Cagan, 1956), an approach that raises interesting questions related to the rationality of expectations. One could also adopt the stance taken by Fama and Farber (1979), or in Chapter 8 of this book, where the government uses its seigniorage income, possibly along with tax revenues, to produce a public good. In the Keynesian tradition, the government spends cash not just to sustain or improve the economic infrastructure but also to influence economic activity. The standard assumption is that prices and wages are sticky, so that additional demand leads to increased output rather than to pure inflation (as monetarist orthodoxy would have predicted). The early Keynesian approach, being built on behavioral equations rather than microeconomic optimization subject to budget constraints, sidestepped the issue of how the government is financing its outlays. However, it is probably clear that the main source of its purchasing power must be seigniorage. Taxation would just shift demand from the private sector to the public sector rather than increasing total expenditures.9 Likewise, public borrowing just means that taxation or monetization is postponed, and in the stylized framework adopted in much of the literature (and in this book) the effects of postponing taxation or monetization are similar to immediate taxes or seignorage because rational agents anticipate the future cost of taxes or inflation ("Ricardian equivalence"). In the more recent, microeconomics-based literature, monetary policy can still have an important impact on economic activity if, as in the Keynesian literature, prices or wages are assumed to be sticky.10 Svensson and van Wijnbergen (1989) develop a model where monopolistically competitive firms are assumed to set prices one period in advance. Obstfeld and Rogoff (1995a), Chari et al. (1996), Kollmann (1997, 1998), and Hau (1997a, 1997b) also consider models where prices are rigid in the short run. Atkeson and Kehoe (1997) consider the effect of monetary shocks in a model where both asset markets and commodity markets are segmented. 9

10

Unless taxation succeeds in mobilizing money balances that, for unstated reasons, are kept idle. This is again similar to money creation in the sense that idle money hoards are not part of the effective money supply. See, also, the articles by Kimrough (1993) and Martin (1994) and the review paper by Devereux (1997b).

108

Exchange Rate Volatility

An assumption of sticky prices or wages is easily justified on empirical grounds. In many European countries, for instance, wages are set in periodic (say, two-yearly) bargaining rounds, possibly influenced and/or canonized by the government. Occasionally, European governments have imposed price and wage freezes, not only after devaluations but also during the high-inflation period of the 1970s and early 1980s or as a way of restoring the competitiveness of their economies. If, in a cash-in-advance model, wages are sticky while prices are not (or less so), an increased money supply boosts economic activity by reducing the real cost of labor. If prices are sticky, an increased money supply boosts demand and hence output. Thus, monetary policy does influence economic activity.

9.1.3

The Exchange Rate Regime

Once both money supply and demand have been included in the model, the nominal exchange rate enters into the picture, and the issue of an optimal exchange rate regime arises. Ever since the value of money became based on faith rather than on its gold or silver content, many governments have sought to stabilize the relative values of different moneys. This has notably been the case in the Bretton Woods system and, after its gradual collapse in 1972-1973, especially in the "Snake" and European Monetary System's (EMS) "Exchange Rate Mechanism" among countries of the European Economic Community (EEC, now EU). The constraints imposed upon monetary policy by a fixed nominal exchange rate depend, among other things, on whether PPP holds or not. In a model with PPP, the question of sustainability of a fixed exchange regime boils down to the issue of whether inflation rates can be kept aligned at a reasonable cost to the partners in the system. In contrast, in a setting as adopted in the preceding chapters, where the real rate can move within a band defined by the cost of shipping and is determined by national outputs (see Chapter 3), a fixed exchange rate regime has to take into account not just the inflationary impact of monetary policy but also its effect on the real exchange rate (via money's effect on real outputs). The leeway for real-exchange-rate movements also increases the government's room for independent monetary policies. Much of the literature has focused on whether an independent monetary policy is compatible with fixed exchange rates, and under what circumstances an independent monetary policy is desirable. This literature consists of many variants - partial-equilibrium models, Keynesian-type behavioral models, or microeconomics-based generalequilibrium models - many of which are reviewed in Isard (1995), Obstfeld and Rogoff (1996), and De Grauwe (1997).

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

109

The formal economic issue regarding the economic cost of fixed exchange rates11 has been complemented by arguments that are much more difficult to model in a general-equilibrium setting. Adopting a familiar argument from the (stock market) microstructure literature, one can first argue that, if uncertainty about future exchange rates is small or nil, competitive market makers in currency markets will quote narrower bid-ask spreads, thus reducing transaction costs for the world economy.12 While this advantage may seem small, the elimination of exchange risk can also have indirect effects similar to reduced transaction costs. As discussed in Chapter 5, it is often argued that exchange rate risk lowers the risk-adjusted value of future export revenue, so that volatility may hinder international trade. In addition, low or zero exchange rate uncertainty will make the (perishable) investment required in setting up international-trade relations or distribution networks less risky; thus, in a lowrisk regime there will be more arbitrage activity between goods markets and less room for price discrimination. A similar argument can be made with respect to domestic and foreign direct investments (which, like entry costs in export markets, often have an important irreversible component): with fixed exchange rates, new ventures, whether abroad or at home, are less likely to be suddenly rendered uncompetitive. Also, the advantages of fixed rates are not confined to more investment and higher employment: in addition, more competitive pressure from foreign competitors, whether producing at home or abroad, may shake up traditional producers that behave like monopolists sheltered by exchange risk walls. Lastly, for currencies with a reputation of inflation and depreciation, adopting a fixed exchange rate is likely to lower the real interest rates and, thus, further boost investment and lower the cost of government debt. These arguments all assume full credibility of the fixed rate. However, one might invoke the September 1992 EMS crisis and argue that fixed-rate systems that stop short of monetary unions can never be fully credible.13 The logical issue then is whether a system with small chances of a very large change in exchange rates is actually much better than a system with frequent but small changes. Or, if monetary union is seen as the only viable alternative, the issue 11 12 13

See Mundell (1961) and McKinnon (1963) for early arguments, and Bayoumi (1997) and De Grauwe (1997) for more recent discussions of these issues. See Haq et al. (1996) for a discussion of the proposal by Tobin (1978) to reduce exchange rate volatility via a tax on short-term transactions in capital markets. Buiter, Corsetti, and Pesenti, (1997) present a detailed discussion of this crisis; S vensson (1994), based on evidence from the same crisis, concludes that fixed exchange rates are more fragile and difficult to maintain than previously thought, and may also conflict with price stability. Obstfeld and Rogoff (1995b) discuss the difficulties of maintaining fixed exchange rates in the presence of integrated capital markets.

110

Exchange Rate Volatility

then becomes whether it is not overly costly to give up not only the exchange rate but also a country-specific monetary policy as a tool for steering the economy.14 It is a difficult task to introduce all of these features into one single model. Thus, in this chapter we limit ourselves to considering the extent to which the traditional arguments against fixed rates apply in a general-equilibrium model with complete financial markets but imperfectly integrated goods markets. Specifically, in an economy where financial markets allow agents to hedge against all relevant risks and where real exchange rates are allowed to move (albeit within a band), is monetary policy effective and are optimal policies compatible with a fixed-rate regime?

9.2

The Model

In many ways, the framework we use is similar to the earlier setting described in Chapter 3. The economy consists of two countries, indicated by subscripts k = {1, 2}, each populated by alarge and equal number of identical, price-taking individuals and firms. Thus, each country can again be thought of as having one representative consumer and a representative firm. As in earlier chapters, financial markets are frictionless and complete, and countries are assumed to start out with equal endowments.15 The completeness of the financial market and the competitive nature of the real markets again imply that, in the absence of market failures, the outcome of decentralized decisions corresponds to the optimal production and consumption plan that would have been chosen by a central planner. Thus, unlike in an incomplete-markets model there is no need to spell out the budget and portfolio constraints and identify the optimal investment choice. As before, international trade in the goods markets is possible only at a cost: when country k exports one unit, only 1/(1 + r) units arrive in the other country. A last similarity with earlier chapters is that agents have utility functions that are isoelastic. The present model, however, differs from earlier chapters in many important respects. One prominent innovation relative to earlier chapters is that the present model is not one of an endowment economy. That is, firms are no longer passively receiving an output whose size is beyond their control, but are now actively producing their output good, using (internationally immobile) labor as their inputs and making their hiring and firing decisions optimally in response to output prices and wages. Because labor plays a role 14

15

The usual attitude is that, with a fixed exchange rate, a country cannot have its own monetary policy anyway; however, we show later that this is not necessarily true if commodity markets are less than perfectly integrated. See also De Grauwe (1997). See Martin (1994) for an analysis of the impact of country size on a country's optimal monetary policy in the context of a two-country Lucas endowment model.

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

111

in this model, the cash income of an individual agent consists not only of dividends paid out (in cash) by an internationally diversified portfolio and the net disinvestments (if desired), but also of wage income. The unit wage is fixed exogenously, reflecting either a sticky-wages situation (the price of labor is set one period in advance) or an income policy on behalf of the government.16 As an example of the latter situation, we can mention Belgium, where the government has the legal right to intervene in central wage bargaining between unions and employers if the emerging wage growth rate deviates from the average of the main trading partners. This assumption of fixed wages in the short run provides a way to make monetary policy relevant: unexpected inflation lowers real wages and, therefore, boosts output in the economy. A major difference relative to earlier chapters, already touched in the introduction, is that money and the government now play a prominent role. On the demand side, we have chosen to maintain the cash-in-advance assumption introduced in Chapter 3. In modeling the supply side, we let the government affect the real economy in two ways. First, the government can choose its level of spending on the production of the public good, which directly affects the utility of private consumption. The government finances its purchases using income from seigniorage and taxation.17 This brings us to the second way the government affects economic life: wages being sticky, the monetization component of government spending leads to inflation, lower real wages, and, therefore, increased production. We now describe the model in more mathematical detail. The utility function of a resident of country k is isoelastic (i.e., exhibits constant relative risk aversion) relative to a composite consumption indicator defined over a public good (gk) and a private good (ck). In addition, the objective function depends on the amount of time spent working (Lk):

(9.i)

uk(t) =

L '[ '

^

1 -r\' with y / > 0 , £ > 0 , £ < l .

Notice that the utility from consumption is assumed to be separable from that from leisure, a standard assumption in this literature and in related business cycle models. A special case allowed in equation (9.1) is fi = l - that is, the marginal utility of leisure equals B, a constant. This special case will 16 17

See Kollmann (1998) for a similar model where prices have to be set two to four periods in advance. We could, of course, have allowed the government to borrow too, but because of Ricardian equivalence, this additional feature would not have affected the results.

112

Exchange Rate Volatility

be crucial when we consider the compatibility of optimal monetary policy with a fixed exchange rate regime. It may, therefore, be useful to note that there is some evidence from the business cycle literature that this linear specification fits observed data rather well (see, e.g., Hansen, 1985; Kollmann, 1998). The private good is produced in both countries. The production function relies on (local) labor, Lk(t), as its sole input and is subject to country-specific productivity shocks that are modeled as changes in the scale factor Ak(t): (9.2)

Qk(t) = ^±Lk{tf, a

1 > a > 0.

Although Ak(t) may change unexpectedly from period to period, it is assumed to be known with certainty within each production period. As in earlier chapters, international trade in the private good is possible if the autarky solution would imply inadmissibly large deviations between the marginal utilities (as specified in Section 9.3.3). Thus, if there is trade, total output Qk(t) is supplemented (or reduced) by the amount of net imports (or exports). Let lower-case qk(t) denote the quantity available for local spending after taking into account net trade. Of this quantity ("absorption"), a benevolent government appropriates a fraction yk(t), leaving the remainder for private consumption: (9.3)

ck(t) = [\

-yk(t)]qk(t).

The public good is then produced from the government's purchases of the private good using a technology similar to equation (9.2):18 (9.4)

gk(t) = YJ^l[yk(t)qk(t)Y,

0 < y < 1.

Y

The government's spending is financed through money creation (AM*) and taxes (Tk). Thus, in nominal terms its budget equation is given by (9.5)

pk(t) yk(t) qk(t) = AMk(t) + Tk(t),

where pk(t) is the nominal price of the private good, expressed in local-currency units. All money that has been issued by the government is held by the private 18

The formulation (9.4) could have been replaced by one in which the government uses labor as its input, but this hardly affects the results. If gk(t) had been modeled as a result of the government's use of labor, we could still have computed "absorption" of the private good, qk{t), as the sum of (a) actual private consumption of that private good and (b) production foregone because of the government's use of labor. Thus, in the current framework the notion of "absorption" just becomes somewhat less abstract than it would have been had we chosen to model a government that buys labor instead of the fruits of labor.

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

113

sector because of a cash-in-advance constraint. Firms announce their outputs, and capital markets are open for transactions, before the government and the private consumers spend their income.19 To buy goods, the government or the consumers are constrained to use the currency of the producer's country. Thus, the cash-in-advance constraint - Mk(t) = pk{t)Qk{t) - allows us to determine the nominal price of the private good as follows:

The implications of this model are explained in two steps. In Section 9.3 we derive some features that hold irrespective of the exchange rate regime. Section 9.4 then looks at optimal monetary policies and their implications for the exchange rate.

9.3

The Derived Utility of Absorption and Effects of Monetary Policy

Before proceeding with the formal derivation and discussion of the model's implications for the choice of the exchange rate regime, we want to spell out some features that are relevant regardless of the exchange rate regime: the derived utility function defined over absorption - that is, the amount of the private good corrected for net exports, qk(t) - if we assume that the government maximizes welfare (Section 9.3.1); the effects of monetary policy on the labor and goods markets (Section 9.3.2); the sharing rules in an open economy (Section 9.3.3); and the exchange rate (Section 9.3.4). 93.1

The Derived Utility of Absorption

As we shall show, the function that identifies the maximum utility achievable out of a locally available quantity qk(t) ("absorption") is quite similar to the one adopted in previous chapters - except, of course, the time-varying state variable that reflects the time-varying productivity in the public sector, Yk(t). Specifically, the derived utility of consumption is (9.7) 19

1 - rj

In the beginning of the period, all cash is with the firms. These firms hire labor, produce, and announce their output. The government announces its purchase plan and pays. Firms distribute all their cash, A/*(/) = Mk(t — 1) + AMk(t) + Tk(t) to their workers and shareholders, who use it to pay taxes and for consumption. Thus, after trading is over all cash is back with the firms. Note that individuals that want to spend more (or less) than their cash-dividend and wage income can trade securities among each other, but in the aggregate these trades cancel out. Thus, total private - domestic and foreign - and government spending adds up to Mk(t).

114

Exchange Rate Volatility

where (9.8a) (9.8b) (9.8c)

s= \-r]

^ — {\-r1')[(\-ef)

=

-V'l

y J

This result can be derived as follows. First substitute (9.2)-(9.4) into (9.1); the utility-of-consumption function can then be rewritten as

(9.9)

v(q(t), r(0) = r^—l ( — [y*(0**(0" i-nf

\(\-e')(\-ri')

y J

1 -

where the last line follows from (9.8a)-(9.8b). In (9.9), [yk(t)l'e[ 1 - yk(t)]e]]"" is maximized with respect to yk(t)ifyk(t) = s. Substituting this into (9.9) and using (9.8c) then leads to (9.7). A few comments on our modeling choices are in order. First, the technological uncertainty factor in (9.7), Tk(t), has a role that is mathematically very close to what is achieved by adding into the Cobb-Douglas preference function a nontraded good with its own specific input.20 Thus, little additional mileage can be achieved, in this model, by adding a purely nontraded good. Second, the optimal level of government spending given total available output, qk(t)9 does not yet commit the country to a specific monetary policy, because any desired level of yk(t) can be obtained using an infinitely large number of combinations of AMk(t) and Tk(t) (see equation (9.5)). The difference between the two policy 20

A nontraded good that shares its sole production factor with the traded good will behave very much like the latter good, so a truly nontraded good should not use the same input.

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

115

tools is, of course, that monetization affects inflation - and thus, in a stickywages model, the real wage - whereas taxation does not. Therefore, once yk(t) is set, monetary policy can still be used to set the real wages at any desired level, and fiscal policy can then be adjusted to obtain the optimal mix of consumption of private and public goods. Also note that, once the absorption quantity qk(t) has been determined (by a combination of productivity levels and monetary policies, as explained below), it is always optimal to use fiscal policy Tk{t) to set yk(t) equal to e\ because in our sticky-wages model taxes do not affect outputs, fiscal policy cannot be used to achieve any other objective. 9.3.2

The Effect of Monetary Policy on Hiring and Production Decisions

Individual firms act as price takers in the factor and goods markets and hire labor so as to maximize profits. The supply of labor is fully elastic at the (within the period, exogenous) nominal wage level fixed in the last period but, from (9.6), the price of the output good is endogenously affected by aggregate output (and, of course, monetary policy). We now derive the following relations: (9.10) and (9.11)

Lk(t)=cc^\.

Equation (9.11) is the cornerstone of monetary policy in this model: it shows how an increase in money supply increases demand for labor (whose real cost has fallen, as nominal wages are fixed in the short run). The ultimate effect, as (9.10) shows, is that output increases. These results can be established as follows. The objective function of the representative firm is to maximize its profits: (9.12)

Max -^-Lk{tf Mk(t) |_ a

\pk(t) - Lk(t) wk(t), J

where the price of the good, pk(t), and the wage rate, wk(t), are taken as given at the individual producer's level. The first-order condition of (9.12), Ak(t)La~x pk(t) = wk(t), is readily solved for Lk(t): (9.13)

"

r

~""' "

[Mk(t)Ak(t)\

1 \-a

116

Exchange Rate Volatility

where the last line follows from the quantity theory equation, (9.6). Substituting (9.13) into the production function (9.2), we obtain »,«,

a

lMk(t)Ak(t)\

Solving (9.14) for Qk(t) leads to (9.10). The latter equation can then be substituted into (9.13); upon simplification, (9.11) obtains. 9.3.3

The International Sharing Rule

Once the two national outputs, Quit), have been determined (as the result of the monetary decisions and the levels of productivity, Ak(t)), we can identify the national absorptions qk(t).2{ We show that the national sharing rules are very similar to those in Chapter 5. Setting ®k(t) = rk(t)(l~e')il~n'\ the rules (and their derivation) are similar to the counterparts from Chapters 3 and 5:22

then country 1 is exporting and

then country 2 is exporting and ,oi*™ ,^ ' ^l(

(9 16b)

6l(0+62(0/0

0 =

then there is no international trade; that is, (9.17)

$i(0=8i(0,

$2(0=62(0.

Although formally similar to the sharing rules obtained in Chapter 3, there is one important difference. Specifically, the expressions in (9.15) and (9.16) 21

22

Note that, here, we take Qk(t) as given, and we just study how a decentralized economy with competitive goods markets and a complete financial market will distribute these outputs internationally. The question of how the gross outputs Qkit) themselves have been set does not arise yet. The conditions on output are easily translated into conditions on relative money supply using equations (9.10) and (9.11).

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

117

now depend also on the time-varying factors 0*(O> which are proportional to the productivities in the government sector, Vk(t). The sign of (1—77) is determined by the sign of (1— rf), as can be seen from (9.8b). When rj' = 1 - the log-utility case - the investor ignores this productivity factor. In the log case, the marginal utility of consuming the private good is independent of how much of the public good is available;23 thus, the marginal utility of private consumption is not affected by shocks in the government's production technology. In general, however, a shock to Tk{t) has both wealth and income effects. If rjf > 1, a rise in r*(f) means that there is more of the public good; simultaneously, the higher value of F*(f) also lowers 0^(0 and, therefore, lowers consumption of the private good. That is, when v[ > 1, the two goods act as substitutes: with a more productive government and a better infrastructure, consumers are happy with a lower share in world output. The opposite holds when rj' < 1. 9.3.4

The Nominal Exchange Rate

To discuss the welfare and policy implications of exchange rate regimes, we also need to see how monetary policy affects the nominal exchange rate or, conversely, how a constraint on the nominal exchange rate determines monetary policy. In the seminal models in this field, shipment costs are absent, and therefore PPP holds. A common approach then is to assume an asymmetric structure, where the dominant country (say, country 2) sets its monetary policy in its own interest, and the satellite country (country 1) has to accommodate. In these models, a fixed-rate regime then requires the satellite country to match the dominant partner's preferred inflation rate. In our setting, however, PPP holds at best in a relative sense, namely when there is trade (i.e., when p\ (t) = piit) S(t) (1 + T ) ± ! , depending on the direction of trade); and when there is no trade, the real exchange rate's position within the admissible band, (1 + r)" 1 to (1 + r), is affected by monetary policy. Because the real exchange rate depends on monetary policy, a fixed-rate regime no longer boils down to just an inflation target. At this point, it suffices to indicate how the equilibrium nominal rate would be set in the absence of a specific regime. From Chapter 4, in a complete financial market as the one considered here, the nominal exchange rate equals the ratio of the marginal utilities of nominal spending. Here, nominal spending is not equal to the money supply, Mk(t) = pk(t) Qk(t), since Qk{t) includes government spending and net exports. Denote private spending as Mk{t) = pk{t)eqk(t). Because prices are kept constant in the computation of the marginal utility of 23

Just note that ln((g*(t)£Ck(t)]~e)) = s\ngk{t) + {\ - e) In ck{t); thus, the derivative with respect to, say gk(t), does not depend on the level of Ck(t) and vice versa.

118

Exchange Rate Volatility

nominal spending, we then have

(9.18)

SM-*™'9*** dVx{t)/dMx{t) = dV2(t)ldq2{t) P2(t) =

~

dV2(t)/dq2(t)M](t)/Ql(t) dV](t)/dq](t)M2(t)/Q2(ty

where the first fraction on the left-hand side is just the real exchange rate, and the last fraction uses the quantity-theory equation.

9.4

The Exchange Rate under Alternative Monetary Rules

In this section we first consider two policies - the cooperative solution and the noncooperative Nash one - and ask the question to what extent these policies are compatible with a fixed exchange rate regime. We find, as one might expect, that cooperative monetary policies combined with sticky wages lead to fixed exchange rates if relative nominal wages are constant over time (i.e., not just within the period), and shocks are symmetric.24 The symmetric-shock condition is familiar in the related literature (see, e.g., Obstfeld and Rogoff, 1996). However, the model produces one exception to the familiar rule: when P = 1 - that is, workers have very flexible working habits and show no increasing reluctance to give up more and more leisure - then the symmetric-shock condition disappears and the constant-relative-wages rule suffices. Recall, from Section 9.2.1, that there actually is some empirical support for the conjecture that ft = 1. In that light, a fixed-rate regime may very well be more feasible, or less costly, than is commonly thought. However, in general, with sticky wages the cooperative solution may not be sustainable and, as in the prisoners' dilemma, may drive shortsighted authorities toward a noncooperative Nash game. In this Nash game, the conclusions from the preceding paragraph remain true only if there is no trade. That is, as soon as there are exports or imports, a fixed-rate regime conflicts with myopically optimal monetary policies even when f$ equals unity. We now discuss both claims. We close this section with a brief digression on a third policy regime, the monetary union. 24

We define a situation with symmetric shocks as one where relative productivity in the private sector, A \ (t)/A2(t), remains constant, and similarly for relative productivity in the public sector, Fi(f)/ F2(t) - even though the absolute productivities themselves may change.

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

9.4.1

119

An Idealized EMS: Fully Coordinated Monetary Policy

In setting up the EMS after the demise of the asymmetric Bretton Woods system, the European Community greatly stressed the need for policy coordination as a sine qua non for stable exchange rates and also allowed for frequent realignments. In this section, we verify under what circumstances an unconstrained cooperative monetary game leads to a constant exchange rate. In the coordinated game, each country chooses its own monetary policy so as to maximize aggregate utility. Thus, the problem facing country k is to

(9.19) MaxV,(f) + V2(t)

a

a

J

In (9.19), V\(t) and V^(0 depend on the absorptions q\(t) and q2{t), respectively; as specified in (9.15b) and (9.16b), the latter depend on one or both gross outputs Qk{t), which, finally, are determined by the respective country's monetary policy and productivity. The central result regarding the exchange rate can be summarized as follows: if we assume optimal monetary policies, the nominal exchange rate is given by:25

(9.20)

i

S(t) =

where (9.21)

M2(t)/w2(t) I-i?

l-e'

, if there is no trade

r,(o/

, if country 1 is exporting

A{(t) .l+rA2(0J

/ifi a)

'

, if country 2 is exporting.

Note that, in the equation that describes relative monetary policy when there is no trade, the outer exponent is positive if, as commonly accepted, rj exceeds unity. Thus, in the absence of trade, when country 2 is ahead of country 1 in terms of tht productivities, the latter country should choose a more expansive The proofs are available on request.

120

Exchange Rate Volatility

monetary policy (i.e., opt for lower real wages and more effort) to mitigate the poor productivity. In contrast, when there is trade, the relative productivity of the government sector, T2{t)/ Fi (£), no longer appears explicitly in the relative monetary policy. One should not conclude from this that optimal monetary policy ignores the government's effectiveness.26 Rather, the effects of relative government efficiency are now shared internationally, through commodity trade - see equations (9.15a) and (19.16a); therefore, the optimal monetary response to differences in government productivity becomes identical across countries and cancels out when one considers relative optimal monetary policy. Note also that, with the sharing of productivity effects through trade, the optimal response through monetary policies reverses: as ft > 1 > a (i.e., the utility cost of foregone leisure exceeds the productivity of labor), the country that is getting ahead in terms of private productivity reacts by having a more expansive monetary policy (i.e., going for a lower real wage) and more effort. The microeconomic intuition behind the reversal of the link between effort and productivity, relative to the no-trade case, is that in the presence of trade the price-wage ratio is less responsive to local output changes; thus, firms have more incentives to hire and produce. On the social welfare level, the logic is one of comparative advantage: it pays to have the more productive labor force work more. Returning to the exchange rate under optimal monetary policies, (9.20) says that the exchange rate is not proportional to the relative money supply, as would have been the case if the quantity theory had also applied to wages (or if effort had not entered into the utility function - i.e., if fi had been equal to zero). With respect to the desirability of a fixed-rate regime, the exchange rate equation tells us that a country does not have to give up its welfare-optimizing monetary policy if the following two conditions hold: (1) a constant-relativewages rule applies; and (2) either the shocks are symmetric - that is, the optimal relative money-to-wages ratio is a constant across countries - or /3 equals unity. Under either of the conditions in (2), the exchange rate equates the nominal wages, so that a constant-relative-wage rule implies a fixed exchange rate:

(9.22)

^np=lormt)/m(t)=k, P M2{t)/w2(t)

then S(t) oc

. w2(t)

The analysis for the symmetric-shock case is familiar: in general, if shocks to the Fs and As are not symmetric, then the optimal policy is to let exchange 26

There is no closed-form solution for monetary policy of a single country when there is trade, but it is easily verified that the optimal response depends on both productivities.

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

121

rates vary in response to these productivity shocks. However, in a sense equation (9.20) also weakens the asymmetric-shock argument against fixed rates, because the conditions under which the optimal exchange rate turns out to be constant become substantially less severe when p approaches 1, that is, when the marginal welfare cost of more effort is a constant rather than increasing in Lk(t). Intuitively, if there is no increasing reluctance to work harder, then monetary policy can fully focus on the output effect by offsetting the shocks to productivity. Of course, the cooperative monetary strategy may fall apart if countries prefer short-term gains and feel that such a decision has no impact on the partner's monetary policy (the noncooperative Nash game). 9.4.2

The Nash Game

In the preceding strategy, the monetary authorities cooperate fully and take into account the effects their actions have on the partner economy. If countries have P = 1 and accept an equal-wage-inflation rule, then they can sustain a constant exchange rate. Not surprisingly, this result no longer obtains under a noncooperative game as soon as there is trade. If the authorities play a Nash game, each chooses its monetary policy so as to maximize its individual utility, ignoring the effect on the other's utility and assuming that the other country will stick to its policy. Thus, country k has as its policy objective: (9.23)

Mk{t)

P L

w

k(t)

A comparison with the cooperative objective function, (9.19), immediately implies that whenever it is optimal to trade, a noncooperating country works less hard than in the cooperative game, because it now ignores the beneficial effects that its own extra labor has on the other country and because its own decision is perceived not to have any effect on the partner's choice of strategy.27 Thus, because of the prisoners' dilemma the cooperative solution cannot be sustained, as every country has an incentive to work less and let the other country bear much of the cost of the lost output. The resulting exchange rate equations are the following: in the absence of trade, (9.24) 27

S(t) =

See Rogoff (1985) for an example of a model where international monetary cooperation is actually counterproductive.

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Exchange Rate Volatility

when country 1 is exporting, ( 9.25)

5(0 _

when country 2 is exporting, (9.26)

S(0="2(r)

+T

The conclusions of the cooperative solution still hold as long as there is no trade, for the simple reason that, if there is no interdependency, then coordination does not matter. Thus, as before, when p = 1, a combination of optimal monetary policies and constant relative wages results in a constant exchange rate; and when p < 1, a fixed exchange rate is optimal only if, in addition, shocks are symmetric. But as soon as we consider the solutions with positive trade, we see that even when p equals unity the exchange rate fluctuates in response to asymmetric productivity shocks 1^(0/ Fi(0> through Kk(t) as defined in (9.15a) and (9.16a). Thus, a fixed-rate regime is incompatible with optimal (noncooperative) monetary policies. 9.4.3

Monetary Union

In both cases discussed thus far, each of the countries had its own monetary policy. A monetary union differs from a fixed-rate system not only in the sense that its fixed-rate commitment is much more final but also in the sense that there is just one monetary policy.28 The mathematics of a monetary union is considerably more complicated than the model developed thus far. For this reason, we just describe the main differences in the setup and verbally describe the conclusions. In a monetary union, seigniorage is split among the participating countries. Thus, in a model where the member states are initially equal, the obvious rule regarding seigniorage would be a 50-50 split. The government's budget equation then is

(9.27) 28

pk(t)qk(t)yk(t) = Tk(t) + ^AAf(f),

See Bayoumi (1997) for a review of the literature on optimum currency areas. Miller and Williamson (1988) and De Grauwe (1997) contain an extensive discussion of the costs and benefits of monetary integration; Dominguez (1996) and Eichengreen (1997) provide empirical evidence on the success of central bank intervention in foreign exchange markets.

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

123

where the total money supply is denoted by (unsubscripted) M(t). An immediate implication of (9.27) is that, as each government no longer has two countryspecific policy tools, one can no longer separate the issue of the government's share in total absorption from the issue of optimal inflation. The second major change in the setup is the cash-in-advance constraint. As money freely circulates across countries, the constraint now is 29

(9.28)

M(t) = px(t)Qx{t) + S(t)P2(t)Q2(t).

Because real market imperfections are not affected by monetary union, the real exchange rate can still fluctuate between 1/(1 + r) and (1 + r). The cooperative formulation of the problem is then to (9.29)

Max

V,(r) + V2(t)

\LpAt) + L?(f) .

Already from the modified setup it is clear that the outcome cannot be as good as the one from a cooperative game with independent monetary policies. Not surprisingly, then, even when f$ equals unity, the exchange rate that results from (9.29) no longer simplifies to (9.22), implying that in the presence of a fixed-rate regime and asymmetric shocks the monetary policies are always suboptimal.

9.5

Conclusion

The formal analysis in the preceding section has examined the proposition that, in the presence of asymmetric shocks, afixedexchange rate regime is incompatible with welfare maximization. We confirmed this proposition provided that f$ < 1; however, when the welfare cost of reduced leisure is invariant to the amount of time spent at work, a fixed-relative wage policy combined with a fixed exchange rate has no welfare costs. A monetary union, in contrast, always implies some welfare cost. Some of the benefits of monetary union are clear: there will be a decrease in transactions costs. A second benefit is that a monetary union will remove one source of uncertainty about relative prices; however, the effects of this on welfare and growth seem to be small (see, e.g., De Grauwe, 1997, table 3.2). There exist large differences across the real sectors of countries. These differences can be accommodated via changes in the exchange rate, monetary 29

Of course, in a true monetary union, S(t) equal unity; however, as in the previous section our approach is to let S(t) be free and to see under what circumstances the resulting exchange rate is constant.

124

Exchange Rate Volatility

policy, and fiscal policy; typically, the easiest way is to allow the exchange rate to change (compared with, say, contractionary fiscal policy). The cost of monetary union is that a country gives up the exchange rate as a policy instrument. In view of the analysis presented in this chapter, one could question the EMS and especially the European Monetary Union (EMU) plans. What, then, might explain the (admittedly, often lukewarm) preference for fixed rates? One could, first, question whether asymmetric shocks can be all that important in economies that are becoming more and more alike and where technological improvements spread quickly. One view is that integration of trade will make the effect of demand shocks more symmetric across regions. On the other hand, Krugman (1991) argues that trade integration may lead to regional concentration - for the automobile industry in the United States, a highly integrated economic area, is highly concentrated - and therefore the effects of shocks might be asymmetric. Recent empirical work by Fatas (1997) and Frankel and Rose (1997) seems to indicate that, with the integration of trade in Europe, the correlations of real activity have increased, making currency union more attractive. However, institutional differences across countries (such as the power of trade unions in the economy) are unlikely to disappear in the near future.30 Another legitimate concern with the asymmetric-shock argument is whether the authorities are as efficient, benevolent, and surgically precise as they are assumed to be in this literature. If monetary policy is blunt and sluggish in its effects, or based on outdated and partial information, or used for political purposes, the arguments for monetary independence lose much of their appeal. For instance, one often cannot help noticing that many European politicians, especially those from fiscally profligate countries, were not overly unhappy to abdicate their role as economic policy makers. 30

See Atkeson and Bayoumi (1993) for a discussion of how financial capital can substitute for physical capital mobility; that is, how agents can diversify against region-specific shocks by holding financial assets whose returns are not correlated with these shocks.

10 Concluding Thoughts

We have developed a general-equilibrium, intertemporal framework of a stochastic world economy. In this framework, decision rules of individual agents with rational expectations are derived based on optimizing behavior, and the prices of goods and financial securities, the interest rate, and the exchange rate are determined endogenously. We have explicitly modeled the segmentation of commodity markets by introducing a cost for shipping goods across countries; thus, our model allows for deviations from the law of one price. We have also considered the effect of the opening international financial markets on welfare. We have used this framework to understand the behavior of the spot and forward exchange rates and international trade in goods and financial claims. We have also evaluated tariff policy, monetary policy, and the choice of the exchange rate regime in this setting. We characterize the spot exchange rate in a fairly general setting: without restricting the number of goods and countries, the utility functions, production processes, or the nature of frictions in international goods markets, but assuming that financial markets are complete and integrated, we show that the nominal exchange rate reflects cross-country differences in initial wealths, and marginal indirect utilities of nominal spending.1 More important, the expression that we get for the exchange rate is a nonlinear one, with changing coefficients. De Grauwe, Dewachter, and Embrechts (1993) report that the behavior of exchange rate returns is complex and nonlinear. To explain this, instead of using a model with fully rational agents,2 they assume that the interaction between traders using fundamentals and those using technical rules (chartists) generates chaotic motion in exchange markets. Consequently, even very simple versions of their models of the exchange rate can generate very complex behavior with some predictability. However, they find that the evidence in favor of 1 2

Differences in marginal indirect utilities may arise from commodity market imperfections and/or differences in consumption preferences, time preference, and risk aversion. In their model, one type of agent does not take into account that there is another type of agent in the economy. 125

126

Exchange Rate Volatility

nonlinearities in exchange rates is stronger than that for chaos. In contrast to this work, our model shows that one can get nonlinear exchange rate returns even in a model where agents are fully rational. For the version of our model with production, we describe the exact nature of this nonlinearity, and the persistence that it generates in exchange rates. In trying to understand forward currency rates, and their relation to spot exchange rates, two main hypotheses that have been advanced are (1) market participants make systematic expectational errors (Lewis, 1989; Alapat, 1994), and (2) there are time-varying risk premia in the forward exchange market. In spite of the large number of articles trying to generate the observed risk premia, this line of research has met with limited success. Rather than abandon the rational expectations view, we examine forward rates in a model where agents behave rationally but where, in contrast to the existing literature, commodity markets are segmented. By allowing for deviations in the law of one price in commodity markets, the ability of the model to generate observed risk premia improves. Similarly, Backus et al. (1993) find that the performance of the general-equilibrium model improves when preferences are generalized to allow for habit persistence. In our analysis of trade flows, we examine the relation between the volatility of real exchange rates and the volume of international trade. The consensus view is that, if there is one change in going from fixed exchange rates under the Bretton Woods system to a regime of floating exchange rates, it is an increase in exchange rate volatility. However, numerous studies examining the effect of this volatility on trade flows find little evidence of a negative impact. We provide a theoretical model consistent with this result. The main point of this analysis is to highlight that both exchange rates and trade flows are endogenous variables. Thus, the association between them depends on the changes in the underlying factors in the economy. Moreover, it is incorrect to identify welfare with the volume of trade; depending on the changes in the underlying factors, it is quite possible that the volume of trade declines but welfare improves. In the last part of the book, we focused our attention on policy regarding the opening of capital markets and also on tariff and monetary policy. In our study of capital flows, calibrations based on data for the United States, Europe, and Japan indicate that the gains from sharing risk in international financial markets can have a significant effect on welfare. Even more important is the insight from Feeney (1994) and Obstfeld (1994) that financial markets can influence welfare also indirectly - for example, by changing the investment decisions of a country. We also measure the gain from the opening of financial markets when commodity markets are not fully integrated: our calibration analysis indicates

Concluding Thoughts

127

that these gains are still large. Thus, the policy implication is that it is worthwhile to pursue the integration of financial markets even if goods (and labor) markets are not yet fully integrated. For the case of tariff policy, we saw that the presence of financial markets could have a strong influence on the optimal tariff. In the models we described, the opening of financial markets serves to reduce the optimal tariff. Moreover, upon integrating financial markets, the welfare gains from tariff reduction are about sixteen times as large as the direct gains from risk sharing. In the chapter on monetary policy, we showed how one could evaluate the choice over fixed and flexible exchange rates in a framework with segmented-goods markets and optimizing agents. Wefindthat in the presence of shocks that are not symmetric across countries, a flexible exchange rate dominates a regime with fixed rates. A fixed exchange rate regime has no welfare costs only when the marginal cost of reducing leisure is constant; a monetary union, on the other hand, always implies some welfare cost in our model. Throughout the work presented in this book, we have adopted the perspective that agents are rational and markets are efficient. While many may consider this view to be an extreme one, we believe that before we abandon the rationalexpectations paradigm, we should explore it fully by allowing for features of the real world that we observe but do not always model: imperfect commodity markets, incomplete financial markets,3 participation constraints and trading costs, more general preference structures that, for example, allow for habit persistence, and separation between risk aversion and the elasticity of intertemporal substitution. In our models, we have assumed that within a country all agents are identical and have homogenous expectations, and that agents are fully informed about the parameters of the economy and that there are no information asymmetries across countries; also, in our analysis of policy issues, we have ignored the issue of credibility. The work described in this book indicates that rational-expectations models that reflect the more realistic features of the economy can have considerably more success in explaining the empirical regularities observed in the data compared with standard models that ignore these factors. The results in Devereux (1997b) and the empirical work in Allen and Stein (1995) suggest that fundamentals can explain a major proportion of the trends in real exchange rates over the medium and long run. We hope that this book, by showing that the ability of rational-expectations models to explain the data improves once we model the real world more accurately, will serve to encourage research in this area. 3

For evidence that international economies are less than perfectly correlated, see Bayoumi (1997), Devereux et al. (1992), Kollmann (1990, 1995, 1996), and Lewis (1996).

References

Abuaf, Niso, and Philippe Jorion. 1990. Purchasing Power Parity in the Long Run, Journal of Finance 45, 157-174. Adler, M., and B. Dumas. 1983. International Portfolio Choice and Corporation Finance: A Synthesis, Journal of Finance 38, 925-984. Adler, M., and B. Lehman. 1983. Deviations from PPP in the Long Run, Journal of Finance 38, 1471-1487. Alapat, P. 1994. An Investigation into the Sources of the Forward Exchange Rate Bias over Time, Working Paper, University of California, Los Angeles. Allen, Polly Reynolds, and Jerome L. Stein. 1990. Capital Market Integration, Journal of Banking and Finance 14, 909-928. Allen, Polly Reynolds, and Jerome L. Stein. 1995. Fundamental Determinants of Exchange Rates, Oxford: Oxford University Press. Alogoskoufis, G. 1994. On Inflation, Unemployment, and the Optimal Exchange Rate Regime, in Handbook of International Macroeconomics, ed. Rick van der Ploeg, Oxford: Basil Blackwell. Andersen, Margot, and David A. Grier. 1992. Robust, Non-Parametric Measures of Exchange Rate Variability, Applied Economics 24, 951-958. Andersen, T., and K. Moene. 1995. Financial Liberalization and Macroeconomic Stability, Oxford: Basil Blackwell. Apte, P., M. Kane, and P. Sercu. 1994. Relative PPP in the Medium Run, Journal of International Money and Finance 13, 602-622. Arndt, S., and J. Richardson. 1987. Real-Financial Linkages among Open Economies: An Overview, in Real-Financial Linkages among Open Economies, ed. S. Arndt and J. Richardson, Cambridge, MA: MIT Press. Asseery, A., and D. A. Peel. 1991. The Effects of Exchange Rate Volatility on Exports Some New Estimates, Economics Letters 37 (October), 173-177. Atkeson, A., and T. Bayoumi. 1993. Do Private Markets Insure against Regional Shocks in a Common Currency Area? Evidence from the US, Open Economies Review 4, 303-324. Atkeson, A., and P. Kehoe. 1997. Revised Exchange Rates in Segmented Commodity Markets, Working Paper, University of Minnesota. Backus, David, Silverio Foresi, and Chris Telmer. 1996. Affine Models of Currency Pricing, Working Paper, New York University. Backus, David, Alan Gregory, and Chris Telmer. 1993. Accounting for Forward Rates in Markets for Foreign Currency, Journal of Finance 48, 1887-1908. Backus, David, Patrick Kehoe, and Finn Kydland. 1992. International Real Business Cycle Models, Journal of Political Economy 100, 745-775. 129

130

References

Backus, David, and Gregor Smith. 1993. Consumption and Real Exchange Rates in Dynamic Economies with Non-Traded Goods, Journal of International Economics 35,297-316. Baillie, R., and T. Bollerslev. 1989. The Message in Daily Exchange Rates: A Conditional Variance Tale, Journal of Business Economics and Statistics 7, 297-305. Baillie, R., and T. Bollerslev. 1990. A Multivariate Generalized ARCH Approach to Modeling Risk Premia in Forward Foreign Exchange Markets, Journal of International Money and Finance 9, 309-324. Baillie, R., and H. McMahon. 1989a. Testing Rational Expectations and Efficiency in the Foreign Exchange Market, Econometrica 51, 553-564. Baillie, R., and H. McMahon. 1989b. The Foreign Exchange Market: Theory and Econometric Evidence, Cambridge: Cambridge University Press. Bakshi, G., and Z. Chen. 1996. Inflation, Asset Prices and the Term Structure of Interest Rates in Monetary Economies, Review of Financial Studies 9, 241-275. Bakshi, G., and Z. Chen. 1997. Equilibrium Valuation of Foreign Exchange Claims, Journal of Finance 52, 799-826. Balassa, B. 1964. The Purchasing Power Parity Doctrine: A Reappraisal, Journal of Political Economy 72, 584-596. Baldwin, R. 1988. Hysteresis in Import Prices: The Beachhead Effect, American Economic Review 78, 773-785. Baldwin, R., and P. Krugman. 1989. Persistent Trade Effects of Large Exchange Rate Shocks, Quarterly Journal of Economics 104, 635-654. Bansal, Ravi, Ron Gallant, Robert Hussey, and George Tauchen. 1993. Nonparametric Estimation of Structural Models for High-Frequency Currency Market Data, Journal of Econometrics 66, 251-287. Barari, M., and H. Lapan. 1993. Stochastic Trade Policy with Asset Markets: The Role of Tariff Structure, Journal of International Economics 35, 317-333. Baron, David P. 1976a. Fluctuating Exchange Rates and the Pricing of Exports, Economic Inquiry 14 (September), 425-438. Baron, David P. 1976b. Flexible Exchange Rates, Forward Markets, and the Level of Trade, American Economic Review 66, 253-266. Barten, A. 1964. Consumer Demand Functions under Conditions of Almost Additive Preferences, Econometrica 32, 1-38. Basak, S. 1995. An Intertemporal Model of International Capital Market Segmentation, Journal of Financial and Quantitative Analysis 31, 161-188. Basak, S., and M. Gallmeyer. 1998. Currency Prices, the Nominal Exchange Rate, and Security Prices in a Two Country Dynamic Monetary Equilibrium, Working Paper, Wharton School, University of Pennsylvania. Baxter, M. 1994. Real Exchange Rates and Real Interest Differentials: Have We Missed the Business-Cycle Relation? Journal of Monetary Economics 33, 5-37. Baxter, M., and M. Crucini. 1993. Explaining Saving-Investment Correlations, American Economic Review 83, 416-436. Baxter, M., and A. Stockman. 1989. Business Cycles and the Exchange Rate Regime: Some International Evidence, Journal of Monetary Economics 23, 377400. Bayoumi, T. 1997. Financial Integration and Real Activity, Manchester: Manchester University Press. Bayoumi, T., and B. Eichengreen. 1994. Macroeconomic Adjustments under BrettonWoods and the Post-Bretton-Woods Float: An Impulse Response Analysis, Economic Journal 104, 813-827.

References

131

Bekaert, G. 1994. Exchange Rate Volatility and Deviations for Unbiasedness in a Cashin-Advance Model, Journal of International Economics 36, 29-52. Bekaert, G. 1996. The Time Variation of Risk and Return in Foreign Exchange Markets: A General Equilibrium Perspective, Review of Financial Studies 9, 427-470. Bekaert, G., and R. Hodrick. 1993. On Biases in the Measurement of Foreign Exchange Risk Premium, Journal of International Money and Finance 12, 115-138. Bekaert, G., R. Hodrick, and D. Marshall. 1996. The Implications of First-Order Risk Aversion for Asset Market Risk Premiums, NBER Working Paper no. 4624. Benes, V, L. Shepp, and H. Witsenhausen. 1980. Some Solvable Stochastic Problems, Stochastics 4, 134-160. Benninga, S., and A. Protopapadakis. 1988. The Equilibrium Pricing of Exchange Rates and Assets When Trade Takes Time, Journal of International Money and Finance 7, 129-149. Bertola, G. 1994. Continuous-Time Models of the Exchange Rates and Intervention, in Handbook of International Macroeconomics, ed. Rick van der Ploeg, Oxford: Basil Blackwell. Betton, S., M. D. Levi, and R. Uppal. 1995. Index-Induced Errors and Purchasing Power Parity: Bounding the Bias, Journal of International Financial Markets, Institutions, and Money 5.2-3, 165-179. Bilson, J. 1978. The Monetary Approach to the Exchange Rates: Some Empirical Evidence, IMF Staff Papers 25, 48-75. Bilson, J. 1979. Recent Developments in the Monetary Models of Exchange Rate Determination, IMF Staff Papers 2, 201-223. Bini-Smaghi, Lorenzo. 1991. Exchange Rate Variability and Trade: Why Is it So Difficult to Find any Empirical Relationship? Applied Economics 23, 927-935. Black, F. 1973. Transportation Costs, Tariffs, and Taxes in a One-Sector Model of Trade, Working Paper, Massachusetts Institute of Technology. Black, F. 1974. International Capital Market Equilibrium with Investment Barriers, Journal of Financial Economics 1, 337-352. Black, F , and M. Scholes. 1973. The Pricing of Options and Corporate Liabilities, Journal of Political Economy 3, 637-654. Bleaney, Michael. 1992. Comparison of Real Exchange Rate Volatility across Exchange Rate Systems, Oxford Bulletin of Economics and Statistics 54, 557-565. Bonser-Neal, C , G. Brauer, R. Neal, and S. Wheatley. 1990. International Investment Restrictions and Closed-End Country Fund Prices, Journal of Finance 45,523-547. Brada, Josef C , and Jose A. Mendez. 1988. Exchange Rate Risk, Exchange Rate Regime and the Volume of International Trade, Kyklos 41, 263-280. Branson, W. 1968. Financial Capital Flows in the U.S. Balance ofPayments, Amsterdam: North Holland. Branson, W., and D. Henderson. 1985. The Specification and Influence of Asset Markets, in Handbook of International Economics, ed. R. Jones and P. Kenen, Amsterdam: North Holland. Breeden, D. 1979. An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities, Journal of Financial Economics 7, 265-296. Brennan, M., and H. Cao. 1996. International Portfolio Investment Flows, Working Paper, University of California at Los Angeles. Brock, W. 1974. Money and Growth: The Case of Long Run Perfect Foresight, International Economic Review 15,150-111. Broil, U. 1994. Foreign Production and Forward Markets, Australian Economic Papers 33, 1-6.

132

References

Buiter, W., G. Corsetti, and P. Pesenti. 1997. Financial Markets and European Monetary Cooperation: The Lessons of the 1992-93 ERM Crisis, Cambridge: Cambridge University Press. Caballero, R. J., and C. Vittorio. 1989. The Effect of Real Exchange Rate Uncertainty on Exports: Empirical Evidence, World Bank Economic Review 3, 263-278. Cagan, Phillip. 1956. The Monetary Dynamics of Hyperinflation, in Studies in the Quantity Theory of Money, ed. Milton Friedman, Chicago: University of Chicago Press. Campbell, J., and R. Clarida. 1987. The Dollar and Real Interest Rates, CarnegieRochester Conference Series on Public Policy 27, 103-140. Canova, F. 1991. An Empirical Analysis of Ex Ante Profits from Forward Speculation in Foreign Exchange Markets, Review of Economics and Statistics 73, 489-496. Canova, F., and J. Marrinan. 1993. Profits, Risk, and Uncertainty in Foreign Exchange Markets, Journal of Monetary Economics 33, 259-286. Canzoneri, M., and C. A. Rogers. 1990. Is the European Community an Optimal Currency Area? Optimal Taxation versus the Cost of Multiple Currencies, American Economic Review 80, 419-433. Cassel, G. 1918. Abnormal Deviations in International Exchanges, Economic Journal 28,413-415. Cassel, G. 1922. Money and Foreign Exchange after 1914, London: Constable. Chang, R. 1997. Financial Integration with and without International Policy Coordination, International Economic Review 38, 547-565. Chari, V., E. McGratten, and P. Kehoe. 1996. Monetary Policy and the Real Exchange Rate in Sticky Price Models of the International Business Cycle, Working Paper, University of Minnesota. Cheung, Yin-Wong, and Kon S. Lai. 1993. Finite-Sample Sizes of Johansen's Likelihood Ratio Tests for Cointegration, Oxford Bulletin of Economics and Statistics 55.3, 313-328. Cho, D., C. Eun, and L. Senbet. 1986. International Arbitrage Pricing Theory: An Empirical Investigation, Journal of Finance 41, 313-329. Claessens, Stijn, Michael Dooley, and Andrew Warner. 1995. Portfolio Capital Flows: Hot or Cool, World Bank Economic Review 9, 153-174. Clarida, R., and J. Gali. 1994. Sources of Real Exchange Rate Fluctuations: How Important Are Nominal Shocks, NBER Working Paper no. 4658. Clark, Peter B. 1973. Uncertainty, Exchange Risk, and the Level of International Trade, Western Economic Journal 11, 302-313. Clower, Robert. 1967. A Reconsideration of the Microfoundations of Monetary Theory, Western Economic Journal 6, 1-8. Cole, H. 1988. Financial Structure and International Trade, International Economic Review 29, 237-259. Cole, H., and M. Obstfeld. 1991. Commodity Trade and International Risk Sharing: How Much Do Financial Markets Matter? Journal of Monetary Economics 28, 3-24. Cooper, I., and E. Kaplanis. 1994. What Explains the Home Bias in Portfolio Investment? Review of Financial Studies 7, 45-60. Cooper, R. 1986. The United States as an Open Economy, in How Open is the U.S. Economy? ed. R. Hafer, Lexington, MA: Lexington Books. Costello, D. 1993. A Cross-Country, Cross-Industry Comparison of Productivity Growth, Journal of Political Economy 101, 207-222. Cote, A. 1994. Exchange Rate Volatility and Trade: A Survey, International Department, Bank of Canada.

References

133

Coval, J. 1996. International Capital Flows When Investors Have Local Information, Working Paper, University of Michigan. Cox, C , and J. Huang. 1989. Optimal Consumption and Portfolio Policies When Asset Prices Follow Diffusion Process, Journal of Economic Theory 49, 33-83. Cox, J., J. Ingersoll, and S. Ross. 1985. An Intertemporal General Equilibrium Model of Asset Prices, Econometrica 53, 385-408. Cumby, R. 1988. Is It Risk? Explaining Deviations from Uncovered Interest Parity, Journal of Monetary Economics 22, 279-299. Cumby, R., and M. Obstfeld. 1984. International Interest Rate and Price Level Linkages under Flexible Exchange Rates: A Review of Recent Evidence, in Exchange Rate Theory and Practice, ed. J. Bilson and R. Marston, Chicago: University of Chicago Press. Cushman, David O. 1983. The Effects of Real Exchange Rate Risk on International Trade, Journal of International Economics 15, 45-63. Daniel, B. 1985. Optimal Foreign Exchange-Rate Policy for a Small Open Economy, Journal of International Money and Finance 4, 523-536. Danthine, J., and J. Donaldson. 1986. Inflation and Asset Prices in an Exchange Economy, Econometrica 54, 585-605. Davis, M., and A. Norman. 1990. Portfolio Selection with Transaction Costs, Mathematics of Operations Research 15, 676-713. Deardorff, A. 1989. A Computational Analysis of Alternative Scenarios for Multilateral Trade Liberalization, Discussion Paper 363, Economic Council of Canada, Ottawa. Deardorff, A., and R. Stern. 1990. Computational Analysis of Global Trading Arrangements, Ann Arbor: University of Michigan Press. De Grauwe, P. 1988. Exchange Rate Variability and the Slowdown in Growth of International Trade, IMF Staff Papers 35, 63-84. De Grauwe, P. 1990. International Money: Post-War Trends and Theories, Oxford: Clarendon Press. De Grauwe, P. 1992. The Benefits of a Common Currency, IMF Staff Papers 35, 63-84. De Grauwe, P. 1994. Exchange Rates in Search of Fundamental Variables, International Economics Research Paper no. 106, Catholic University, Leuven. De Grauwe, P. 1997. The Economics ofMonetary Integration, 3rd ed., New York: Oxford University Press. De Grauwe, P., H. Dewachter, and M. Embrechts. 1993. Exchange Rate Theory: Chaotic Models of Foreign Exchange Markets, Oxford: Basil Blackwell. De Grauwe, P., and Guy Verfaille. 1988. Exchange Rate Variability, Misalignment, and the European Monetary System, in Misalignment of Exchange Rates: Effects on Trade and Industry, ed. Richard C. Marston, Chicago: University of Chicago Press, 77-100. Delias, Harris, and Ben-Zion Zilberfarb. 1993. Real Exchange Rate Volatility and International Trade: A Reexamination of the Theory, Southern Economic Journal 59.4 (April), 641-647. Devereux, M. 1989. Non-Traded Goods and the International Transmission of Fiscal Policy, Canadian Journal of Economics 21, 265-278. Devereux, M. 1997a. Does Monetary Union Require International Fiscal Policy Coordination? Economic and Social Review 23.1, 35-54. Devereux, M. 1997b. Real Exchange Rates and Macroeconomics: Evidence and Theory, Working Paper, University of British Columbia.

134

References

Devereux, M., A. Gregory, and G. Smith. 1992. Realistic Cross-Country Consumption Correlations in a Two-Country, Equilibrium, Business Cycle Model, Journal of International Money and Finance 11,3-16. Devereux, M., and Khang Min Lee. 1999. Endogenous Trade Policy and the Gains from International Financial Markets, Journal of Monetary Economics 43, 35-59. de Vries, C. 1994. Stylized Facts of Nominal Exchange Rate Returns, in Handbook of International Macroeconomics, ed. Rick van der Ploeg, Oxford: Basil Blackwell. Dickey, D. A., and R. J. Rossana. 1994. Cointegrated Time Series: A Guide to Estimation and Hypothesis Testing, Oxford Bulletin of Economics and Statistics 56, 325-353. Diebold, F., and J. Nason. 1990. Nonparametric Exchange Rate Prediction? Journal of International Economics 28, 315-332. Dixit, A. 1987. Strategic Aspects of Trade Policy, in Advances in Economic Theory: Fifth World Congress, ed. Truman F. Bowley, Cambridge: Cambridge University Press, 329-362. Dixit, A. 1989a. Hysteresis, Import Penetration, and Exchange Rate Pass-Through, Quarterly Journal of Economics 104, 205-228. Dixit, A. 1989b. Entry and Exit Decisions under Uncertainty, Journal of Political Economy 97, 620-638. Dixit, A. 1991. A Simplified Treatment of the Theory of Optimal Regulation of Brownian Motion, Journal of Economic Dynamics and Control 15, 657-673. Dixit, A. 1992. Investment and Hysteresis, Journal of Economic Perspectives 6, 107— 132. Dixit, A., and R. Pindyck. 1994. Investment under Uncertainty, Princeton: Princeton University Press. Dominguez, Kathryn. 1996. The International Evidence: An Assessment of Experience with Foreign Exchange Intervention in the G-3, Working Paper, Kennedy School of Government. Dominguez, Kathryn. 1997. Central Bank Intervention and Exchange Rate Volatility, Working Paper, Kennedy School of Government. Domowitz, Ian, and Craig Hakkio. 1985. Conditional Variance and the Risk Premium in the Foreign Exchange Market, Journal of International Economics 19, 47-66. Dooley, M , J. Frankel, and D. Mathieson. 1987. International Capital Mobility: What Do Saving-Investment Correlations Tell Us? IMF Staff Papers 34, 503-529. Dornbusch, R. 1976. Expectations and Exchange Rate Dynamics, Journal of Political Economy 84, 1161-1176. Dornbusch, R. 1988. Real Exchange Rates and Macroeconomics: A Selective Survey, NBER Working Paper no. 2775. Duffle, D., and L. G. Epstein. 1992. Stochastic Differential Utility, Econometrica 60, 353-394. Duffle, D., and C. Huang. 1985. Implementing Arrow-Debreu Equilibria by Continuous Trading of Few Long-Lived Securities, Econometrica 53, 1337-1356. Dumas, B. 1988. Pricing Physical Assets Internationally, Working Paper, University of Pennsylvania. Dumas, B. 1991. Super Contact and Related Optimality Conditions, Journal ofEconomic Dynamics and Control 15, 675-685. Dumas, B. 1992. Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World, Review of Financial Studies 5, 153-180. Dumas, B. 1994. Partial-Equilibrium vs. General-Equilibrium Models of International Capital Market Equilibrium, in Handbook of International Macroeconomics, ed. Rick van der Ploeg, Oxford: Basil Blackwell.

References

135

Dumas, B., and B. Solnik. 1995. The World Price of Foreign Exchange Risk, Journal of Finance 50, 445-479. Dumas, B., and R. Uppal. 1998. Global Diversification, Growth and Welfare with Imperfectly Integrated Markets for Goods, Working Paper, University of British Columbia and HEC. [Forthcoming in Review of Financial Studies.] Dumas, B., R. Uppal, and T. Wang. 1998. Efficient Intertemporal Allocations with Recursive Utilities, Working Paper, University of British Columbia and HEC. Edison, Hali, Joseph Gagnon, and William Melick. 1997. Understanding the Empirical Literature on Purchasing Power Parity: The Post-Bretton Woods Era, Journal of International Money and Finance 16, 1-17. Edison, Hali, and Michael Melvin. 1989. The Determinants and Implications of the Choice of an Exchange Rate System, Working Paper no. 89-1, Arizona State University. Edison, Hali, and Michael Melvin. 1990. The Determinants and Implications of the Choice of an Exchange Rate System, in Monetary Policy for a Volatile Global Economy, ed. William S. Haraf and Thomas D. Willett, Washington, D.C.: AEI Press, 1-44. Edison, Hali, and B. D. Pauls. 1993. A Reassessment of the Relation between Real Exchange Rates and Real Interest Rates: 1974-1990, Journal of Monetary Economics 31, 165-187. Eichenbaum, B., and C. Evans. 1992. Some Empirical Evidence on the Effects of Monetary Policy Shocks on Exchange Rates, Working Paper WP-92-32, Federal Reserve Bank of Chicago. Eichengreen, Barry. 1994. History of the International Monetary System: Implications for Resort in International Macroeconomics and Finance, in Handbook of International Macroeconomics, ed. Rick van der Ploeg, Oxford: Basil Blackwell. Eichengreen, Barry. 1997. European Monetary Unification: Theory, Practice, and Analysis, Cambridge, MA: MIT Press. Eichengreen, Barry, James Tobin, and Charles Wyplosz. 1995. Two Cases for Sand in the Wheels of International Finance, Economic Journal 105, 162-172. Einzig, Paul. 1937. The Theory of Forward Exchange, London: Macmillan. Engel, C. 1992a. On the Foreign Exchange Risk Premium in a General Equilibrium Model, Journal of International Economics 32, 305-319. Engel, C. 1992b. The Risk Premium and the Liquidity Premium in Foreign Exchange Markets, International Economic Review 33, 871-879. Engel, C. 1993. Real Exchange Rates and Relative Prices: An Empirical Investigation, Journal of Monetary Economics 32, 35-50. Engel, C. 1994. The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence, Working Paper, University of Washington. Engel, C , and C. Hakkio. 1993. Exchange Rate Regimes and Volatility, Economic Review 78 (third quarter), 43-58. Engel, C , M. Hendrickson, and J. Rogers. 1996. Intra-National, Intra-Continental, and Intra-Planetary PPP, Working Paper, University of Washington. Engel, C , and J. Rogers. 1995. How Wide Is the Border? American Economic Review 86, 1112-1125. Engle, R. F., and C. W. J. Granger. 1987. Cointegration and Error Correction: Representation, Estimation and Testing, Econometrica 55, 251-276. Epstein, L., and S. Zin. 1989. Substitution, Risk Aversion and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework, Econometrica 57, 937-969.

136

References

Errunza, V. 1989. Capital Flow Controls, International Asset Pricing and Investors' Welfare: A Multi-country Framework, Journal of Finance 44, 1025-1038. Errunza, V., and E. Losq. 1985. International Asset Pricing under Mild Segmentation: Theory and Test, Journal of Finance 40, 105-124. Errunza, V., and P. Padmanabhan. 1992. Tests of Integration, Mild Segmentation and Segmentation Hypotheses, Journal of Banking and Finance 16, 949-972. Ethier, W. 1973. International Trade and the Forward Exchange Market, American Economic Review 63, 494-503. Eun, C , and S. Janakiramanan. 1986. A Model of International Asset Pricing with a Constraint on the Foreign Equity Ownership, Journal of Finance 41, 897-914. Evans, M., and J. Lothian. 1993. The Response of Exchange Rates to Permanent and Transitory Shocks under Floating Exchange Rates, Journal of International Money and Finance 12, 563-586. Fama, Eugene. 1984. Forward and Spot Exchange Rates, Journal of Monetary Economics 14,319-338. Fama, Eugene, and Andre Farber. 1979. Money, Bonds, and Foreign Exchange, American Economic Review 69, 639-649. Fatas, Antonio. 1997. EMU: Countries or Regions? Lessons from the EMS Experience, Working Paper, INSEAD and CEPR Discussion Paper no. 1558. Feeney, J. 1994. Goods and Asset Market Interdependence in a Risky World, International Economic Review 35, 551-563. Feenstra, R. 1986. Functional Equivalence between Liquidity Costs and the Utility of Money, Journal of Monetary Economics 17, 271-292. Feldstein, M., and C. Horioka. 1980. Domestic Saving and International Capital Flows, Economic Journal 90, 314-329. Fleming, J. M. 1962. Domestic Financial Policies under Fixed and under Floating Exchange Rates, IMF Staff Papers 12, 369-380. Flood, R., and A. Rose. 1995. Fixing Exchange Rates: A Virtual Quest for Fundamentals, Journal of Monetary Economics 36, 3-37. Flores, R., P. Jorion, P.-Y. Preumont, and A. Szafarz. 1996. Multivariate Unit Root Tests of the PPP Hypothesis, Working Paper, University of California, Irvine. Franke, G. 1991. Exchange Rate Volatility and International Trading Strategy, Journal of International Money and Finance 10, 292-307. Frankel, Jeffrey. 1986. International Capital Mobility and Crowding-Out in the U.S. Economy: Imperfect Integration of Financial Markets or of Goods Markets, in How Open is the U.S. Economy? ed. R. Hafer, Lexington, MA: Lexington Books. Frankel, Jeffrey. 1993. On Exchange Rates, Cambridge, MA: MIT Press. Frankel, Jeffrey. 1996. How Well Do Foreign Exchange Markets Function: Might a Tobin Tax Help? NBER Working Paper no. 5422. Frankel, Jeffrey, and Andrew Rose. 1995. A Survey of Empirical Research on Nominal Exchange Rates, in Handbook of International Economics, vol. 3, ed. G. Grossman and K. Rogoff, Amsterdam: Elsevier-North Holland. Frankel, Jeffrey, and Andrew Rose. 1996. A Panel Project on Purchasing Power Parity: Mean Reversion within and between Countries, Journal ofInternational Economics 40, 209-224. Frankel, Jeffrey, and Andrew Rose. 1997. Is EMU More Justifiable Ex Post than Ex Ante? European Economic Review 41, 753-760. Frankel, Jeffrey, and Shang-Jin Wei. 1993. Trade Blocs and Currency Blocs, NBER Working Paper no. 3644.

References

137

French, K., and J. Porterba. 1991. Investor Diversification and International Equity Markets, American Economic Review 81, 222-226. Frenkel, Jacob. 1976. A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence, Scandinavian Journal of Economics 78, 200-224. Frenkel, Jacob, and Assaf Razin. 1987. The Mundell-Fleming Model a Quarter Century Later: A Unified Exposition, IMF Staff Papers 34, 567-620. Frenkel, Jacob, and Assaf Razin. 1994. Fiscal Policies and the World Economy, Cambridge, MA: MIT Press. Froot, K. A., M. Kim, and K. Rogoff. 1995. The Law of One Price over 700 Years, NBER Working Paper no. 5132. Froot, K. A., and K. Rogoff. 1995. Perspectives on PPP and Long-Run Real Exchange Rates, in Handbook of International Economics, vol. 3, ed. G. Grossman and K. Rogoff, Amsterdam: Elsevier North-Holland. Froot, K. A., and R. Thaler. 1990. Anomalies: Foreign Exchange, Journal of Economic Perspectives A, 179-192. Fuerst, T. 1992. Liquidity, Loanable Funds and Real Activity, Journal of Monetary Economics 29, 3-24. Gagnon, Joseph E. 1989. Adjustment Costs and International Trade Dynamics, Journal of International Economics 26, 327-344. Gagnon, Joseph E. 1993. Exchange Rate Variability and the Level of International Trade, Journal of International Economics 34, 269-287. Gardener, G. 1983. The Choice of Monetary Policy Instruments in an Open Economy, Journal of International Money and Finance 2, 347-354. Gavin, M. 1989. The Stock Market and Exchange Rate Dynamics, Journal of International Money and Finance 8,181-200. Girton, L., and D. Henderson. 1973. A Two Country Model of Financial Movements as a Stock Adjustment with Emphasis on the Effects of Central Policy, International Finance Discussion Paper 24, Federal Reserve Board. Godbout, Marie-Josee, and Simon van Norden. 1995. Reconsidering Cointegration in Exchange Rates: Case-Studies of Size Distortion in Finite Samples, mimeograph, Bank of Canada. Gokey, T. 1994. What Explains the Risk Premium in Foreign Exchange Returns, Journal of International Money and Finance 13, 729-738. Goldstein, N., and M. Khan. 1985. Income and Price Effects in Foreign Trade, in Handbook of International Economics, ed. R. Jones and P. Kenen, Amsterdam: North Holland. Gotur, Padma. 1985. Effects of Exchange Rate Volatility on Trade: Some Further Evidence, IMF Staff Papers 32, 475-512. Granger, C. W. J. 1981. Some Properties of Time Series Data and Their Use in Econometric Model Specification, Journal of Econometrics 16, 121-130. Greenwood, Jeremy, and Stephen Williamson. 1987. International Financial Intermediation with Aggregate Fluctuations under Alternative Exchange Rate Regimes, Working Paper, University of Western Ontario. Grice-Hutchinson, Marjorie. 1952. The School of Salamanca, Oxford: Clarendon Press. Grillio, Vittorio, and Nouriel Roubini. 1992. Liquidity and Exchange Rates, Journal of International Economics 32, 339-352. Guidotti, P. 1989. Exchange Rate Determination, Interest Rates and an Integrative Approach to the Demand for Money, Journal of International Money and Finance 8,

29-45.

138

References

Gultekin, M., B. Gultekin, and A. Penati. 1989. Capital Controls and International Capital Market Segmentation: The Evidence from the Japanese and American Stock Markets, Journal of Finance 44, 849-869. Halliday, L. 1989. The International Stock Exchange Directory, Institutional Investor (March), 197-204. Hamilton, J. D. 1994. Time Series Analysis, Princeton, NJ: Princeton University Press. Hansen, Gary. 1985. Indivisible Labor and the Business Cycle, Journal of Monetary Economics 16, 309-327. Hansen, H., and K. Juselius. 1995. CATS in RATS Cointegration Analysis of Time Series, Evanston IL: ESTIMA. Hansen, Lars, and Robert Hodrick. 1983. Risk Averse Speculation in the Forward Exchange Market: An Econometric Analysis of Linear Models, in Exchange Rates and International Macroeconomics, ed. J. Frenkel, Chicago: University of Chicago Press. Haq, M , I. Kaul, and I. Grunberg. 1996. The Tobin Tax: Coping with Financial Volatility, New York: Oxford University Press. Harberger, A. 1950. Currency Depreciation, Income, and the Balance of Trade. Journal of Political Economy 58, 47-60. Harrison, J. 1985. Brownian Motion and Stochastic Flow Systems, New York: Wiley. Harrison, J., and M. Taksar. 1983. Instantaneous Control of Brownian Motion, Mathematics of Operations Research 8, 439-453. Hau, Harald. 1997a. Real Exchange Rate Volatility and Economic Openness: Theory and Evidence, Working Paper, ESSEC School of Management. Hau, Harald. 1997b. Exchange Rate Determination: The Role of Factor Price Rigidities and Nontradeables, Working Paper, ESSEC School of Management. Helpman, E., and A. Razin. 1978a. A Theory of International Trade under Uncertainty, New York: Academic Press. Helpman, E., and A. Razin. 1978b. The Protective Effect of a Tariff under Uncertainty, Journal of Political Economy 86, 1131-1141. Helpman, E., and A. Razin. 1979a. Towards a Consistent Comparison of Alternative Exchange Rate Systems, Canadian Journal of Economics 12, 394^-09. Helpman, E., and A. Razin. 1979b. The Role of Savings and Investment in Exchange Rate Determination under Alternative Monetary Mechanisms, Journal of Monetary Economy 13, 307-325. Helpman, E., and A. Razin. 1982. A Comparison of Exchange Rate Regimes in the Presence of Imperfect Capital Markets, International Economic Review 23, 365388. Helpman, E., and A. Razin. 1987. Exchange Rate Management: Intertemporal Tradeoffs, American Economic Review 77, 107-123. Hietala, P. 1989. Asset Pricing in Partially Segmented Markets: Evidence from the Finnish Market, Journal of Finance 44, 697-718. Hodrick, R. J. 1987. The Empirical Evidence on the Efficiency of Forward and Futures Foreign Exchange Markets, Chur, Switzerland: Harwood Academic Publishers. Hodrick, R. J., and S. Srivastava. 1984. The Covariation of Risk Premiums and Expected Future Spot Exchange Rates, Journal of International Money and Finance 5,5-22. Hodrick, R. J., and S. Srivastava. 1986. The Covariation of Risk Premiums and Expected Future Exchange Rates, Journal of International Money and Finance 5 (Supplement), S5-21. Hollifield, B., and R. Uppal. 1997. An Examination of Uncovered Interest Parity in Segmented International Commodity Markets, Journal of Finance 52, 2145-2170.

References

139

Hooper, Peter, and Steven W. Kohlhagen. 1978. The Effect of Exchange Rate Uncertainty on the Prices and Volume of International Trade, Journal of International Economics 8,483-511. Horvath, M., and M. Watson. 1995. Testing for Cointegration When Some of the Cointegrating Vectors Are Known, Econometric Theory 11, 984-1014. Huang, Chi-Fu. 1987. An Intertemporal General Equilibrium Asset Pricing Model: The Case of Diffusion Information, Econometrica 55, 117-142. Huang, Roger. 1987. Expectations of Exchange Rates and Differential Inflation Rates: Further Evidence on PPP in Efficient Markets, Journal of Finance 52, 69-79. Huang, Roger. 1990. Risk and Parity in Purchasing Power, Journal of Money, Credit and Banking 22, 338-356. Huisman, R., K. Koedijk, C. Cool, and F. Nissen. 1997. Extreme Support for the Unbiasedness Hypothesis, Working Paper, Maastricht University. Huizinga, J. 1987. An Empirical Investigation of the Long Run Behavior of Real Exchange Rates, Carnegie-Rochester Conferences Series on Public Policy 27, 149-214. Ingersoll, J. 1987. Theory of Financial Decision Making, Totowa NJ: Rowman and Littlefield. International Monetary Fund. 1984. Exchange Rate Volatility and World Trade, Occasional Paper no. 28. Isard, P. 1995. Exchange Rate Economics, Cambridge: Cambridge University Press. Johansen, S. 1988. Statistical Analysis of Cointegration Vectors, Journal of Economic Dynamics and Control 12, 231-254. Johansen, S. 1991. Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models, Econometrica 59, 1551-1580. Johansen, S., and K. Juselius. 1990. Maximum Likelihood Estimation and Inference on Cointegration-with Applications to the Demand for Money, Oxford Bulletin of Economics and Statistics 52, 169-210. Johansen, S., and K. Juselius. 1992. Testing Structural Hypotheses in a Multivariate Cointegration Analysis of the PPP and the UIP for UK, Journal of Econometrics 53,211-244. Johnson, H. G. 1954. Optimum Tariffs and Retaliation, Review of Economic Studies 21, 142-153. Johnson, H. G. 1972. The Monetary Approach to the Balance-of-Payments Theory, Journal of Financial and Quantitative Analysis 7, 1555-1572. Kareken, John, and Neil Wallace. 1980. Models ofMonetary Economics, Federal Reserve Bank, Minneapolis. Kareken, John, and Neil Wallace. 1981. On the Indeterminacy of Equilibrium Exchange Rates, Quarterly Journal of Economics 96, 207-222. Kennan, J., and R. Riezman. 1988. Do Big Countries Win Tariff Wars? International Economic Review 29, 81-85. Kimbrough, K. 1993. Optimal Monetary Policies and Policy Interdependence in the World Economy, Journal of International Money and Finance 12, 227-248. King, Robert, Neil Wallace, and Warren Weber. 1992. Nonfundamental Uncertainty and Exchange Rates, Journal of International Economics 32, 83-108. Kiyotaki, N., and R. Wright. 1989. On Money as a Medium of Exchange. Journal of Political Economy 97, 927-954. Koedijk, C , F. Nissen, P. Schotman, and C. Wolff. 1996. PPP and Real Expenditure, Working Paper, Maastricht University.

140

References

Koedijk, C , and P. Schotman. 1990. How to Beat the Random Walk, Journal of International Economics 29, 311-332. Kollmann, R. 1990. World Business Cycles and Incomplete International Asset Markets, Working Paper, University of Chicago. Kollmann, R. 1995. Consumption, Real Exchange Rates, and the Structure of International Asset Markets, Journal of International Money and Finance 14, 191-211. Kollmann, R. 1996. Incomplete Asset Markets and the Cross-Country Consumption Correlation Puzzle, Journal of Economic Dynamics and Control 20, 945-961. Kollmann, R. 1997. The Exchange Rate in a Dynamic-Optimizing Current Account Model with nominal Rigidities: A Quantitative Assessment, Working Paper, International Monetary Fund. Kollmann, R. 1998. International Financial Markets and Business Cycles: A General Equilibrium Approach with Money and Nominal Rigidities, Working Paper, University of Paris. Korajczyk, R., and C. Viallet. 1992. Equity Risk Premia and the Pricing of Foreign Exchange Risk, Journal of International Economics 33, 199-219. Koray, Faik, and William D. Lastrapes. 1989. Real Exchange Rate Volatility and U.S. Bilateral Trade: A VAR Approach, Review ofEconomics and Statistics 11,708-712. Kravis, I. B., Z. Kennessey, A. W. Heston, and R. Summers. 1975. A System of International Comparisons of Gross Products and Purchasing Power, Baltimore: Johns Hopkins University Press. Kreps, D., and E. Porteus. 1978. Temporal Resolution of Uncertainty and Dynamic Choice Theory, Econometrica 46, 185-200. Kroner, Kenneth F., and William D. Lastrapes. 1993. The Impact of Exchange Rate Volatility on International Trade: Reduced Form Estimates Using the GARCH-inMean Model, Journal of International Money and Finance 12, 298-318. Krugman, P. 1989. Exchange Rate Inflexibility, Cambridge, MA: MIT Press. Krugman, P. 1990. Equilibrium Exchange Rates, in International Policy Coordination and Exchange Rate Fluctuations, ed. W. Branson, J. Frenkel, and M. Goldstein, 159-187, Chicago: University of Chicago Press. Krugman, P. 1991. Geography and Trade, Cambridge, MA: MIT Press. Krugman, P. 1993. Thinking about Exchange Rate Determination and Policy, in The Exchange Rate, International Trade and the Balance of Payments, ed. A. BlundellWignall, Reserve Bank of Australia, Sydney. Krugman, P., and M. Obstfeld. 1991. International Economics: Theory and Policy, New York: HarperCollins. Lastrapes, William D., and Faik Koray. 1990. Exchange Rate Volatility and U.S. Multilateral Trade Flows, Journal of Macroeconomics 12 (Summer), 341-362. Laursen, S., and L. Metzler. 1950. Flexible Exchange Rates and the Theory of Employment, Review of Economics and Statistics 32, 281-299. Lee, Khang Min. 1998. Tariff Choice under Alternative Financial Market Structures, Working Paper, University of British Columbia and National University of Singapore. Lerner, Abba. 1944. The Economics of Control, New York: Macmillan. LeRoy, S. 1984. Nominal Prices and Interest Rates in General Equilibrium: Money Shocks, Journal of Business 57, 177-195. Levine, R. 1989. The Pricing of Forward Exchange Rates, Journal of International Money and Finance 8, 163-179. Levine, R. 1991. An Empirical Inquiry into the Nature of the Forward Exchange Rate Bias, Journal of International Economics 30, 359-369.

References

141

Lewis, K. 1989. Changing Beliefs and Systematic Rational Forecast Errors with Evidence from Foreign Exchange, American Economic Review 79, 621-636. Lewis, K. 1995. Puzzles in International Financial Markets, in Handbook ofInternational Economics, ed. G. Grossman and K. Rogoff, Amsterdam: North Holland. Lewis, K. 1996. What Can Explain the Apparent Lack of International Consumption Risk Sharing? Journal of Political Economy 104, 267-297. Lewis, K. 1997. Are Countries with Official International Restrictions Liquidity Constrained? European Economic Review 41, 1079-1 111. Lothian, J. 1997. Multi-Country Evidence on the Behavior of Purchasing Power Parity under the Current Float, Journal of International Money and Finance 16, 19-35. Lothian, J., and M. Taylor. 1996. Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries, Journal of Political Economy 104, 488-509. Lucas, R. 1978. Asset Prices in an Exchange Economy, Econometrica 46, 1429-1445. Lucas, R. 1982. Interest Rates and Currency Prices in a Two-Country World, Journal of Monetary Economics 10, 335-359. Lucas, R. 1990. Liquidity and Interest Rates, Journal of Economic Theory 50, 237-264. MacDonald, R., and I. W. Marsh. 1994. On Casselian PPP, Cointegration and Exchange Rate Forecasting, Working Paper, University of Strathclyde. MacKinnon, James, Alfred Haug, and Leo Michelis. 1996. Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration, Department of Economics, Queen's University, Canada. Macklem, R. 1991. Forward Rates and Risk Premiums in Artificial Economies, Journal of International Money and Finance 10, 335-360. Manuelli, Rodolfo, and James Peck. 1990. Exchange Rate Volatility in an Equilibrium Asset Pricing Model, International Economic Review 31, 559-574. Margrabe, W. 1978. The Value of an Option to Exchange One Asset for Another, Journal of Finance 33, 177-186. Mark, Nelson. 1985. On Time Varying Risk Premia in the Foreign Exchange Market: An Econometric Analysis, Journal of Monetary Economics 16, 3-18. Mark, Nelson. 1995. Exchange Rates and Fundamentals: Evidence on Long-Horizon Predictability, American Economic Review 85, 201-218. Marshall, A. 1923. Money, Credit and Commerce, London: Macmillan. Marston, Robert. 1990. Pricing to Market in Japanese Manufacturing, Journal of International Economics 29, 217-236. Marston, Robert. 1995. International Financial Integration: A Study ofInterest Rate Differentials between the Major Industrial Nations, Cambridge: Cambridge University Press. Martin, P. 1994. Monetary Policy and Country Size, Journal of International Money and Finance 13, 573-586. McCallum, B. 1983. The Role of Overlapping Generations Models in Monetary Economics, Carnegie-Rochester Conference Series on Public Policy 18, 9-44. McCurdy, T., and I. Morgan. 1991. Tests for a Systematic Risk Component in Deviations from Uncovered Interest Rate Parity, Review of Economic Studies 58, 587-602. McKenzie, M., and R. Brooks. 1997. The Impact of Exchange Rate Volatility on GermanUS Trade Flows, Journal of International Financial Markets, Institutions, and Money 7, 73-88. McKinnon, R. 1963. Optimum Currency Areas, American Economic Review 53, 717-724.

142

References

McKinnon, R. 1988. Monetary and Exchange Rate Policies for International Financial Stability: A Proposal, Journal of Economic Perspectives 2, 83-103. McMillan, J. 1986. Game Theory in International Economics, London: Harwood. McNown, R., and M. S. Wallace. 1989. National Price Levels, Purchasing Power Parity, and Cointegration: A Test of Four High Inflation Economies, Journal of International Money and Finance 8, 533-546. Meese, R. 1990. Currency Fluctuations in the Post-Bretton Woods Era, Journal of Economic Perspectives 4, 117-134. Meese, R., and K. Rogoff. 1983. Empirical Exchange Rate Models of the Seventies: Do They Fit Out-of-Sample? Journal of International Economics 14, 3-24. Meese, R., and K. Rogoff. 1988. Was It Real? The Exchange Rate-Interest Differential Relation over the Modern Floating Rate Period, Journal of Finance 43, 933-948. Meese, R., and A. Rose. 1991. An Empirical Assessment of Nonlinearities in Models of Exchange Rate Determination, Review of Economic Studies 58, 603-619. Melo, J. de, and D. Tarr. 1992. A General Equilibrium Analysis of US Foreign Trade Policy, Cambridge MA: MIT Press. Mendoza, E. 1991. Capital Controls and the Gains from Trade in Business Cycle Model of a Small Open Economy, IMF Staff Papers 38, 480-505. Merton, Robert. 1971. Optimum Consumption and Portfolio Rules in a Continuous Time Model, Journal of Economic Theory 3, 373-413. Merton, Robert. 1973. Theory of Rational Option Pricing, Bell Journal of Economics and Management Science 4, 141-183. Metzler, Alan. 1949. The Theory of International Trade, in A Survey of Contemporary Economics, ed. H. Ellis, Philadelphia: Blakiston. Michael, P., A. Nobay, and D. Peel. 1994. Purchasing Power Parity Yet Again: Evidence from Spatially Separated Commodity Markets, Journal of International Money and Finance 13,637-657. Michael, P., A. Nobay, and D. Peel. 1997. Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation, Journal of Political Economy 105, 862-879. Miller, M., and J. Williamson. 1988. The International Monetary System: An Analysis of Alternative Regimes, European Economic Review 32, 1031-1054. Mishkin, F. 1984. Are Real Interest Rates Equal Across Countries? An Empirical Investigation of International Parity Conditions, Journal of Finance 39, 1345-1357. Mundell, R. 1957. International Trade and Factor Mobility, American Economic Review 47,321-335. Mundell, R. 1960. The Monetary Dynamics of International Adjustment under Fixed and Flexible Exchange Rates, Quarterly Journal of Economics 74, 227-257. Mundell, R. 1961. A Theory of Optimum Currency Areas, American Economic Review 51,657-665. Mundell, R. 1963. Capital Mobility and the Stabilization Policy under Fixed and Flexible Exchange Rates, Canadian Journal of Economics and Political Science 29, 509517. Mussa, M. 1976. The Exchange Rate, the Balance of Payments and Monetary Union: A Regime of Controlled Float, Scandinavian Journal of Economics 78, 229-248. Nessen, M. 1994. Common Trends in Prices and Exchange Rates-Tests of Long-Run Purchasing Power Parity, Essay I, in Essays on Exchange Rates and International Finance, unpublished doctoral dissertation, Department of Finance, Stockholm School of Economics.

References

143

Nissen, F. 1997. International Financial Markets Dynamics, unpublished doctoral dissertation, Maastricht University. Obstfeld, M. 1982. Aggregate Spending and the Terms of Trade: Is There a HarbergerLaursen-Metzler Effect? Quarterly Journal of Economics 97, 251-270. Obstfeld, M. 1986. Capital Mobility in the World Economy: Theory and Measurement, Carnegie-Rochester Conference Series on Public Policy 24, 251-270. Obstfeld, M. 1994. Risk-Taking, Global Diversification, and Growth, American Economic Review 84, 1310-1329. Obstfeld, M., and K. Rogoff. 1995a. Exchange Rate Dynamics Redux, Journal of Political Economy 103, 624-660. Obstfeld, M , and K. Rogoff. 1995b. The Mirage of Fixed Exchange Rates, NBER Working Paper no. 5191. Obstfeld, M., and K. Rogoff. 1996. Foundations of International Macroeconomics, Cambridge, MA: MIT Press. Obstfeld, M., and A. Stockman. 1985. Exchange Rate Dynamics, in Handbook of International Economics, ed. R. Jones and P. Kenen, Amsterdam: North Holland. Obstfeld, M., and A. Taylor. 1997. Non-linear Aspects of Goods Market Arbitrage and Adjustment: Heckscher's Commodity Points Revisited, CEPR Working Paper no. 1672. O'Connell, P. G. J. 1996. Market Frictions and Relative Traded-Goods Prices, Working Paper, Harvard University. O'Connell, P. G. J. 1998. The Overvaluation of Purchasing Power Parity, Journal of International Economics 44, 1-19. O'Connell, P. G. J., and S. J. Wei. 1997. The Bigger They Are, the Harder They Fall: How Price Differences across U.S. Cities Are Arbitraged, NBER Working Paper no. 6089. Peree, Eric, and Alfred Steinherr. 1989. Exchange Rate Uncertainty and Foreign Trade, European Economic Review 33, 1241-1264. Persson, T., and L. Svensson. 1985. Current Account Dynamics and the Terms of Trade: Harberger-Laursen-Metzler Two Generations Later, Journal of Political Economy 93, 43-65. Persson, T., and L. Svensson. 1989. Exchange Rate Variability and Asset Trade, NBER Working Paper no. 2811. Phillips, P. C. B. 1990. Optimal Inference in Cointegrated Systems, Econometrica 59, 283-306. Pindyck, R. 1991. Irreversibility, Uncertainty and Investment, Journal of Economic Literature 29, 1110-1148. Poole, William. 1970. Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model, Quarterly Journal of Economics 84, 197-216. Pozo, S. 1992. Conditional Exchange Rate Volatility and the Volume of International Trade: Evidence from the Early 1900s, Review of Economics and Statistics 14, 325-329. Rebelo, S., and C. Vegh. 1995. Real Effect of Exchange-Rate Based Stabilization: An Analysis of Competing Theories, NBER Working Paper no. 5197. Reinhart, V. 1991. The 'Tobin Tax,' Asset Accumulation, and the Real Exchange Rate, Journal of International Money and Finance 10,420-431. Richards, A. 1995. Comovements in National Stock Market Returns: Evidence of Predictability, but Not Cointegration, Journal of Monetary Economics 36, 631-654. Robinson, Joan. 1947. The Foreign Exchanges, in Essays in the Theory of Employment, ed. Robinson, Oxford: Basil Blackwell.

144

References

Rogers, John, and Michael Jenkins. 1995. Haircuts or Hysteresis? Sources of Movements in Real Exchange Rates, Journal of International Economics 38, 339-360. Rogoff, Ken. 1985. Can International Monetary Policy Cooperation Be Counterproductive? Journal of International Economics 18, 199-217. Roll, R. 1979. Violations of Purchasing Power Parity and Their Implications for International Commodity Markets, in International Finance and Trade, vol. 1, ed. M. Sarnat and G. P. Szego, Cambridge: Cambridge University Press, 133-179. Rose, Andrew. 1995. After the Deluge: Do Fixed Exchange Rates Allow Intertemporal Volatility Tradeoffs, NBER Working Paper no. 5219. Rose, Andrew. 1996-1997. International Finance and Macroeconomics, NBER Reporter (Winter), 1-7. Roubini, N. 1988. Offset and Sterilization under Fixed Exchange Rates with an Optimizing Central Bank, NBER Working Paper no. 2777. Saa-Requejo, J. 1993. The Dynamics and the Terms Structure of Risk Premia in Foreign Exchange Markets, Working Paper, INSEAD. Sachs, J. 1981. The Current Account and Macroeconomics Adjustment in the 1970s, Brooking Papers on Economic Activity 1, 201-268. Samuelson, P. 1964, Theoretical Notes on Trade Problems, Review of Economics and Statistics 46, 145-154. Samuelson, P., and S. Swamy. 1974. Invariant Index Numbers and Canonical Duality: Survey and Synthesis, American Economic Review 64, 566-593. Schinasi, G., and P. Swamy. 1989. The Out-of-Sample Forecasting Performance of Exchange Rate Models When Coefficients Are Allowed to Change, Journal of International Money and Finance 8, 375-390. Sellin, P., and I. Werner. 1993. International Investment Barriers in General Equilibrium, Journal of International Economics 34, 137-151. Sercu, P. 1980. A Generalization of the International Asset Pricing Model, Revue de I Association Francaise de Finance 1, 91-135. Sercu, P. 1992. Exchange Risk, Exposure, and the Option to Trade, Journal of International Money and Finance 11, 579-593. Sercu, P. 1997. The Variance of Truncated Random Variable and the Riskiness of the Underlying Variables, Insurance: Mathematics and Economics 20, 79-95. Sercu, P., and R. Uppal. 1995. International Financial Markets and the Firm, Cincinnati, OH: South-Western Publishing. Sercu, P., R. Uppal, and C. Van Hulle. 1995. The Exchange Rate in the Presence of Transaction Costs: Implications for Tests of Relative Purchasing Power Parity, Journal of Finance 50, 1309-1319. Sercu, P., and C. Van Hulle. 1992. Exchange Rate Volatility, International Trade, and the Value of Exporting Firms, Journal of Banking and Finance 16, 155-182. Shrikhande, M. 1992. The Cost of Operating Abroad in International Capital Market Equilibrium, Working Paper, Georgia Institute of Technology. Sidrauski, Miguel. 1967. Rational Choice and Patterns of Growth in a Monetary Economy, American Economic Review 57, 534-544. Solnik, B. 1974. An Equilibrium Model of the International Capital Market, Journal of Economic Theory 8, 500-524. Stein, J., and P. Allen. 1995. Fundamental Determinants of Exchange Rates, Oxford: Clarendon Press. Stock, J. H., and M. W. Watson. 1988. Testing for Common Trends, Journal of the American Statistical Association 83, 1097-1107.

References

145

Stockman, A. 1980. A Theory of Exchange Rate Determination, Journal of Political Economy 88, 673-698. Stockman, A. 1983. Real Exchange Rates under Alternative Nominal Exchange-Rate Systems, Journal of International Money and Finance 2, 147-166. Stockman, A. 1987. Exchange Rate Systems and Relative Prices, Journal of Policy Modeling 9.1,245-256. Stockman, A. 1988a. On the Roles of International Financial Markets and Their Relevance for Economic Policy, Journal of Money, Credit, and Banking 20, 531-549. Stockman, A. 1988b. Sectoral and National Aggregate Disturbances to Industrial Output in Seven European Countries, Journal of Monetary Economics 21, 387-409. Stockman, A. 1988c. Real Exchange Rate Variability under Pegged and Floating Nominal Exchange Rate Regimes, Carnegie-Rochester Conference Series on Public Policy 29, 259-294. Stockman, A. 1990. International Transmission and Real Business Cycle Models, American Economic Review, Papers and Proceedings 80, 134-138. Stockman, A., and H. Delias. 1986. Asset Markets, Tariffs, and Political Risk, Journal of International

Economics 2 1 , 1 9 9 - 2 1 3 .

Stockman, A., and H. Delias. 1989. International Portfolio Nondiversification and Exchange Rate Variability, Journal of International Economics 26, 261-290. Stockman, A., and A. D. Hernandez. 1988. Exchange Controls, Capital Controls, and International Financial Markets, American Economic Review 78, 362-373. Stockman, A., and L. Svensson. 1987. Capital Flows, Investment, and Exchange Rates, Journal of Monetary Economics 19, 171 -201. Stockman, A., and L. Tesar. 1995. Tastes and Technology in a Two-Country Model of the Business Cycle: Explaining International Comovements, American Economic Review 85, 168-185. Stulz, R. 1981 a. On the Effects of Barriers to International Investment, Journal ofFinance 36, 923-934. Stulz, R. 198 lb. A Model of International Asset Pricing, Journal of Financial Economics 9.4, 386-404. Stulz, R. 1986a. Asset Pricing and Expected Inflation, Journal of Finance 41, 209-223. Stulz, R. 1986b. Interest Rates and Monetary Policy Uncertainty, Journal of Monetary Economics 17, 331-347. Stulz, R. 1987. An Equilibrium Model of Exchange Rate Determination and Asset Pricing with Nontraded Goods and Imperfect Information, Journal of Political Economy 95, 1024-1040. Stulz, R. 1988. Capital Mobility and the Current Account, Journal of International Money and Finance 7, 167-180. Subrahmanyam, M. 1975. On the Optimality of International Capital Market Integration, Journal of Financial Economics 2, 3-28. Summers, Lawrence, and Victoria Summers. 1989. When Financial Markets Work Too Well: A Cautious Case for a Securities Transactions Tax, Journal of Financial Services Research 3.2-3, 163-188. Summers, R., and A. Heston. 1991. The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950-88, Quarterly Journal of Economics 106, 327-368. Sutherland, Alan. 1996. Financial Market Integration and Macroeconomic Volatility, in Financial Liberalization and Macroeconomic Stability, ed. T. Andersen and K. Moene, Oxford: Basil Blackwell.

146

References

Svensson, L. E. O. 1985a. Money and Asset Prices in a Cash-in-Advance Economy, Journal of Political Economy 93, 919-944. Svensson, L. E. 0.1985b. Currency Prices, Terms of Trade, and Interest Rates: A General Equilibrium Asset Pricing Cash-in-Advance Approach, Journal of International Economics 18, 17-42. Svensson, L. E. O. 1988. Trade in Risky Assets, American Economic Review 78, 375394. Svensson, L. E. O. 1989. Trade in Nominal Assets: Monetary Policy, and Price Level and Exchange Rate Risk, Journal of International Economics 26, 1-28. Svensson, L. E. O. 1992. An Interpretation of Recent Research on Exchange Rate Target Zones, Journal of Economic Perspectives 6.4, 119-144. Svensson, L. E. O. 1994. Fixed Exchange Rates as a Means to Price Stability: What Have We Learned, NBER Working Paper no. 4504. Svensson, L. E. O., and A. Razin. 1983. The Terms of Trade and the Current Account: The Harberger-Laursen-Metzler Effect, Journal of Political Economy 91, 97-125. Svensson, L. E. O., and Sweder van Wijnbergen. 1989. Excess Capacity, Monopolistic Competition, and International Transmission of Monetary Disturbances, Economic Journal 99, 785-805. Taylor, A. 1995. International Capital Mobility in History: Purchasing Power Parity in the Long Run, NBER Working Paper no. 5675. Tesar, L. 1991. Savings, Investment and International Capital Flows, Journal of International Economics 31, 55-78. Tesar, L. 1993. International Risk Sharing and Non-Traded Goods, Journal of International Economics 35, 69-89. Tesar, L. 1995. Evaluating the Gains from International Risk-Sharing, CarnegieRochester Conference Series on Public Policy 42, 95-143. Tobin, James. 1978. A Proposal for International Monetary Reform, Eastern Economic Journal A, 153-159. Uppal, R. 1992. Deviations from Purchasing Power Parity and Capital Flows, Journal of International Money and Finance 11, 126-144. Uppal, R. 1993. A General Equilibrium Model of International Portfolio Choice, Journal of Finance 48, 529-553. van Nunen, A. 1990. Europe 1992: Boundless Optimism Misplaced, in Economic Interdependence and Financial Stability, ed. H. van Gemert, Tilburg, Netherlands: Tilburg University Press. Van Wincoop, E. 1996. How Big Are Potential Welfare Gains from International RiskSharing? Working Paper, Boston University. Viaene, Jean-Marie, and Casper G. de Vries. 1992. International Trade and Exchange Rate Volatility, European Economic Review 36, 1311-1321. Wang, Tan. 1998. Asset Prices in a Continuous-time Liquidity Model of Monetary Economies, Working Paper, University of British Columbia. Wei, S. J. 1996. How Reluctant Are Nations in Global Integration? Working Paper, Harvard University. Wei, S. J., and D. Parsley. 1995. Purchasing Power Disparity during the Floating Rate Period: Exchange Rate Volatility, Trade Barriers and Other Culprits, NBER Working Paper no. 5032. Wheatley, Simon. 1988. Some Tests of International Equity Market Integration, Journal of Financial Economics 21,177-213. Wolff, Christian. 1987. Forward Foreign Exchange Rates, Expected Spot Rates, and Premia: A Signal Extraction Approach, Journal of Finance 42, 395-406.

Author Index

Abuaf, N., 8, 32n26, 45, 47, 48 Adler,M., 8, 21n8 Alapat, P., 58, 126 Allen, P. R., 16,79,82, 127 Alogoskoufis, G., 104 Andersen, T., 2nl Apte,P,43nl2,44nl4 Arndt, S., 82 Asseery, A., 68, 69 Atkeson, A., 16n20,97, 107, 124n30 Backus, D., 15, 35, 41, 44-5, 58, 65, 77, 126 Baillie,R., 11, 14nnl4,15, 57, 58 Bakshi,G., 15,42 Balassa, B., 7 Baldwin, R., 68n4 Bansal,R., 15,58,60 Barari, M., 100 Baron, D. P., 67 Basak,S., 15,21,42 Baxter, M , I,21n8,61n3 Bayoumi, T., 8, 21n7, 97, 109nl 1, 122n28, 124n30, 127n3 Bekaert,G., 15,35,57,58,60 Benes, V., 30n20 Benninga, S., 28nl7 Bertola, G., 14nl7 Betton, S.,43nl2 Bilson, J., 13 Bini-Smaghi, L., 68 Black, E, 19,21,29nl8,74 Bollerslev, T., 14nl4,58 Brada, J. C , 69 Branson, W., 13nl2 Brock, W., 15 Broil, U., 67 Brooks, R., 68, 69 Buiter,W., 109nl3 Caballero, R. J., 69n6 Cagan, P., 107 Campbell, J., 61 n3

Canova, E, 57, 58 Canzoneri, M., 104 Cao,H.,21 Cassel, G., 6, 8n7 Chang, R., 103n2 Chari,V., 16, 107 Chen,Z., 15,42 Cheung, Y. W., 49, 56 Cho,D., 83nl Claessens, S., 80nl7 Clarida, R., 9, 61n3 Clark, P. B., 67 Clower, R., 105 Cole,H.,21,68n3, 82, 85,95 Cooper, L, 21 n8 Cooper, R., 20 Corsetti, G., 109nl3 Costello, D., 85n2 Cote, A., 67 Cournot, A.-A., 9 Cox, J., 61, 91 Crucini, M., 21n8 Cumby, R., 7, 58 Cushman, D. O., 67n2 Dan thine, J., 15 Davis, M., 30 Deardorff, A., 19,62,90 DeGrauwe,P, 3,5nl, 14nl5, 67, 68, 80, 108, 109nll, 110nl4, 122n28, 123, 125 Delias, H., 15, 19, 35, 68, 77, 99, 100 Devereux,M., 15, 16, 19n4,99, 100, 102, 107nl0, 127 de Vries, C , 3, 14nl4,67 Dewachter, H., 125 Dickey, D. A., 46 Diebold, E, 14 Dixit, A., 30n20, 99 Dominguez, K., 79nl5, 122n28 Domowitz, I., 35, 58 Donaldson, J., 15 Dooley,M., 80nl7,97nl4

147

148

Author Index

Dornbusch, R., 13 Duffie,D., 34,91 n8 Dumas, B., 14, 15, 18, 19, 21n8, 28nl7, 29, 30, 32, 33, 35, 36, 83, 90 Edison, H., 22nlO, 46, 47n20, 61n3, 67 Eichenbaum, B., 8 Eichengreen, B., 8, 80, 104nl, 122n28 Einzig, P., 9 Embrechts, M., 125 Engel,C, 11, 14nl6,20, 35,47n21, 57, 58, 69n7 Engle, R. R, 46 Epstein, L., 34 Errunza, V., 21,83nl Ethier, W., 67 Eun,C, 83nl Evans, C , 8 Evans, M., 14nl5 Fama, E., 58, 59-60, 107 Farber, A., 107 Fatas, A., 124 Feeney, J., 21n9, 82, 87n4, 95nl2, 126 Feenstra, R., 15, 106 Feldstein, M , 21n8 Fleming, J. M., 12 Flores, R., 46 Franke, G., 3, 68 Frankel, J., 1,14, 44nl5, 47n21, 69, 80nl8, 97nl4, 124 French, K., 21 n8 Frenkel,J., 12nl 1, 13, 99nl Froot, K., 7n5, 8n6, 11, 46, 47n21, 52,57 Fuerst, T., 15 Gagnon, J., 46, 68, 69 Gali, J., 9 Gallmeyer, M., 15,42 Gavin, M., 18nl Girton, L., 13 Godbout, M.-J., 49 Gokey, T., 57 Goldstein, N., 68 Gotur, P., 68, 69 Granger, C. W. J., 46 Greenwood, J., 104nl Gregory, A., 19n4, 58 Grice-Hutchinson, M., 6n3 Grillio,V., 15 Grunberg, I., 80nl8 Guidotti, P., 106 Gultekin, B., 83nl Gultekin, M., 83nl

Hakkio,C, 14nl6, 35,58 Halliday,L., 83nl Hansen, H., 49n23, 58, 112 Haq,M., 80nl8, 109nl2 Harberger, A. C.,97nl4 Harrison, J., 30n20 Hau,H., 16n20, 107 Haug, A., 49n23 Helpman, E., 15, 18, 82, 99, 100, 104nl Henderson, D., 13 Hendrickson, M., 47n21 Heston, A., 62 Hietala,R, 83nl Hodrick, R. J., 11, 15,35,57,58 Hollifield, B., 29, 57, 63-4 Hooper, P., 67 Horioka, C , 21n8 Horvath,M.,47,51n24,52 Huang, C , 91 n8 Huang, J., 91 Huang, R., 8 Huizinga, J., 8 Ingersoll, J., 31n22, 61 International Monetary Fund (IMF), 67 Isard,P,5nl,80, 108 Jenkins, M., 69n7 Johansen, S., 36, 46, 49n23, 52 Johnson, H. G., 13,99 Jorion, P., 8, 32n26, 45, 47, 48 Juselius, K., 36, 46, 49n23, 52 Kane,M.,43nl2 Kaplanis, E., 21n8 Karekan,J., 15,79nl4, 105n3 Kaul,I.,80nl8 Kehoe,P, 15, 16, 107 Kennan, J., 99 Khan, M., 68 Kim, A., 7n5 Kimbrough, K., 107nl0 King,R.,79nl4 Koedijk, C , 47 Kohlhagen, S. W., 67 Kollmann, R., 16, 19n4,45nl6, 107, Illnl6,112, 127n3 Korajczyk, R., 58 Koray, F, 68-9 Kravis,I.,6n4,43nl2 Kreps, D., 34 Kroner, K. F, 69 Krugman,P, 1,8, 12n 11, 14, 19,21n8, 68n4, 124

Author Index Kydland,R, 15 Kyotaki,N., 105n4

Mundell,R., 12,95, 109nll Mussa, M., 13

Lai, Kon S., 49, 56 Lapan, H., 100 Lastrapes, W. D., 68-9 Laursen, S., 97nl4 Lee, K.M.,21,99, 100, 102 Lehman, B., 8 Lerner, A., llnlO LeRoy, S., 15 Levi,M.,43nl2 Levine, R., 57 Lewis, K., 11,57,58,85, 126, 127n3 Losq,E.,21 Lothian, J., 14nl5,47n21 Lucas, R. E., 15, 16, 24, 27, 35, 36, 37,60,70,91

Nason, J., 14 Nessen, M., 46, 47, 52 Nissen, R, 47 Nobay, A., 20 Norman, A., 30

McCallum,B., 15 McCurdy, T., 58 MacDonald, R., 47n20 McGratten, E., 16 McKenzie, M., 68, 69 MacKinnon, J., 49n23 McKinnon, R., 109n 11 Macklem, R., 58 McMahon, H., 11, 14nnl4,15, 57 McMillan, J., 99 McNown, R., 9 Manuelli,R.,79nl4 March, J. W., 47n20 Margrabe, W., 73 Mark,N., 14nl5,58 Marrinan, J., 58 Marshall, A., llnlO Marshall, D., 15 Marston, R., 9, 11,20,57 Martin, P., 107nl0, 110nl5 Mathieson, D., 97nl4 Meese,R., 13, 14,61 n3 Melick, W., 46 Melo, J. de, 20, 90 Melvin,M.,22nlO,67 Mendez, J., 69 Mendoza, E., 85 Merton, R., 74, 84 Metzler, L., llnlO, 97nl4 Michael, R., 20 Michelis, L., 49n23 Miller, M., 122n28 Mishkin, E, 57 Moen, K.,2nl Morgan, I., 58

149

Obstfeld, M., 7, 12n 11, 13nl3, 16,20,21, 62, 70n8, 82, 83, 85, 90, 95, 97nl4, 107, 108, 109nl3, 118, 126 O'Connell,RG.J.,20,47n21 Padmanabhan, P., 83nl Parsley, D., 20, 47n21 Pauls, B. D., 61 n3 Peck,J., 79nl4 Peel, D., 20, 68, 69 Penati, A., 83nl Peree, E., 66, 67, 68 Persson, T., 97nl4, 104nl Pesenti, P., 109nl3 Phillips, P. C. B., 46 Pindyck, R., 30n20 Poole, W., 80 Porteus, E., 34 Poterba, J., 21n8, 137 Pozo, S., 68 Protopapdakis, A., 28nl7 Razin, A., 12nl 1, 15, 18, 82, 97nl4, 99, 100, 104nl Reinhart, V., 80nl8 Richards, A., 49, 51, 56 Richardson, J., 82 Riezman, R., 99 Robinson, J., llnlO Rogers, C. A., 104 Rogers, J., 20, 47n21,69n7 Rogoff,K.,7n5,8n6,13,16,46,52,61n3,70n8, 106n8, 107, 108, 109nl3, 118, 121n27 Roll, R., 8 Rose, A., 1, 14,44nl5, 47n21, 124 Ross, S., 61 Rossana, R. J., 46 Roubini, N., 15 Sachs, J.,97n 14 Samuelson, P. A., 7, 40 Schinasi, G., 14 Scholes, M., 74 Sellin,P,21 Senbet, L., 83nl Sercu,R,21n8,35,41,43nl2,44,68,74nll,77

150

Author Index

Shepp, L., 3On2O Shrikhande, M., 28n 17 Sidrauski, M , 15 Smith, G., 19n4, 35, 41, 44-5, 77 Solnik, B., 15nl8, 21n8 Srivastava, S., 35, 58 Stein, J. L., 16, 79, 82, 127 Steinherr, A., 66, 67, 68 Stern, R., 19, 62, 90 Stock, J. H., 46 Stockman, A., 1, 13n 13, 15, 18, 19, 20, 21, 22, 29nl9, 35, 36, 77, 97, 99, 100, 104nl Stulz, R., 15, 19, 21, 35, 36, 37n2, 41, 43nl2, 60, 77, 97nl4 Subrahmanyam, M., 21 Summers, L., 80 Summers, R., 62 Summers, V, 80 Sutherland, A., 70n8 Svensson, L. E. O., 14nl7, 15, 16, 35, 60, 97, 97nl4, 104nl, 106n8, 107, 109nl3 Swamy, S., 40 Sway, P., 14 Taksar, M., 30n20 Tarr, D., 20, 90 Taylor, A., 20, 47n21 Telmer, C , 58 Tesar, L., 15, 19, 21n8, 77, 85, 97nl4 Thaler, R., 11,57 Tobin,J., 80, 109nl2

Uppal, R., 21 n8, 29, 35, 43n 12, 44, 57, 63-4, 83, 90, 91 n8 Van Hulle, C , 35, 44, 68 van Norden, S., 49 van Nunen, A., 19n5 van Wijnbergen, S., 16, 107 Van Wincoop, E., 85 Viaene, J.-M., 3, 67 Viallet, C , 58 Vittorio, C , 69n6 Wallace, M. S., 8 Wallace, N., 15, 79nl4, 105n3 Wang, T., 15nl9, 90n6 Warner, A., 80nl7 Watson, M. W., 46, 47, 51 n24, 52 Weber, W., 79n 14 Wei, S.-J., 69 Wei, S. J., 20, 47n21 Werner, I., 21 Wheatley, S., 83nl Williamson, J., 122n28 Williamson,S., 104nl Witsenhausen, H., 30n20 Wolff, C , 13-14 Wright, R., 105n4 Wyplosz, C , 80 Zilberfarb, B.-Z., 68 Zin, S., 34

Subject Index

absorption: derived utility in model of monetary policy effects, 113-15 arbitrage: covered interest rate parity and exchange rates, 9 ARCH (autoregressive conditional heteroskedasticity) process, 69 Augmented-Dickey-Fuller (ADF) tests: differences from cointegration analysis, 46-7; quarterly data, 48-9; of real exchange rate data, 45; unit-root hypothesis for exchange rates, 48-9 balance of payments: approach to exchange rate determination, 11-12; current-account balance, 93—4; relation between current account and relative prices, 11-12 barriers to trade: nontariff barriers as source of segmentation, 19-20; recommended removal, 97 Bretton Woods: exchange rate behavior with collapse of, 5; stabilization of value of moneys, 108 capital flows: analysis in models, 20-21; analysis of international, 94-7; definition of flows between two countries, 9 2 ^ ; determinants of, 90-2; as determinants of exchange rates, 12-14; with integrated financial markets, 90-7; Mundeil-Fleming framework, 12; policy to encourage, 3; relation to trade flows, 3; sharing risk in financial markets, 126 capital markets: analysis in models, 20-1; effect on tariffs in international, 99; risk sharing in integrated, 86-7; segmentation of, 20-1; welfare cost of segmented, 85-6. See also capital flows; financial markets cointegration analysis: applied to multilateral exchange rate data, 47; differences from ADF tests, 46-7; to test PPP empirically, 46; tests for relationships in data, 49-50

commodity markets: in basic model of endowment economy, 23-9; effect of integration or segmentation on capital flows, 94-8; interactions between decisions in financial markets and, 101-2; in model of multicountry, multigood economy, 36-9; segmentation by tariff rate, 100 commodity markets, segmented: effect on trade and exchange rate volatility, 75-6; general-equilibrium model for UIP, 60-3; of international, 19-20, 57; with rational expectations, 126 constant relative risk aversion (CRRA), 35; in basic model of endowment economy, 24-5; in intertemporal production economy, 29 constant time preference (CTP), 39 consumer price index (CPI): relative price data of,42nlO countries: in basic model of endowment economy, 23-9; distinctions among, 18-21; in endowment economy model of trade-exchange rate volatility relation, 70-2; in intertemporal production economy, 29-34; in model of monetary policy effects, 110-18; in model of multicountry, multigood economy, 36-9; with open financial markets, 102; price differences in, 20 covered interest rate parity: relation to exchange rates, 9 CRRA. See constant relative risk aversion (CRRA) CTP. See constant time preference (CTP) data: cointegration and likelihood tests of PPP, 48-52; first-differenced, 43-5; PPP deviations in exchange rate data, 57; stylized facts about international, 18-19 data sources: CPI, 42nlO; in review of empirical testing of PPP, 48

151

152

Subject Index

demand for money: cash-in-advance constraints, 105-6; money-in-the-utility-function, 106 Dickey-Fuller tests, augmented, 48-9 economic shocks, symmetric and asymmetric, 118,124 endogeneity: of exchange rates in general-equilibrium model, 18; of financial markets' mechanism related to trade policy, 103; of production in model of forward exchange risk, 3; in tariff policy model, 100-1; of tariff rates in Nash game, 100, 121-2; of trade and exchange rate volatility, 78; of trade policy, 103; of trade volume and exchange rate volatility in general-equilibrium model, 76-8 endowment economy: in analysis of trade-exchange rate volatility relation, 70-2; basic model of, 23-9; extension of model to production economy, 29-34 endowments: in model of multicountry, multigood economy, 37-9 European Monetary System (EMS): crisis (1992), 109; exchange rate mechanism, 108; idealized, 119-21; need for policy coordination, 119; preference for fixed exchange rates, 124 European Union (EU): single-currency plan, 1 exchange rate models: assets approach, 12-14; balance-of-payments (BOP) approach, 11-12; constant relative risk aversion (CRRA), 35; deviation from PPP of tradable and nontradable goods, 7; general-equilibrium model, 17-18; interest rates in relation spot and forward exchange rates, 9-11; with microeconomic foundations, 15-16; monetary approach, 13; relation of exchange rate to national price levels, 5-6; test of CTP/CRRA model, 44-5 exchange rate regime: effect of changes from fixed to floating, 1,5; monetary policy with fixed rate, 108-9 exchange rate volatility: effects on trade and welfare, 3; effects on trade volume of, 1, 66-9; measurement of risk, 68; nonlinear relation between trade volume and, 66; related to segmented capital markets, 85-6; risk with change in degree of commodity market segmentation, 73, 75-6; risk with change in endowment processes of the economy, 73-5 exchange rates: advantages of generalequilibrium model, 17-18, 22-3; balance-of-payments theory of, 11-13;

capital flows as determinants of, 12-14; conditions for increased volatility, 126; with CRRA, 41; under CRRA utility functions, 39-42; determinants of, 54; nonlinearities in, 126; related to PPP, 6-9; under relative and absolute PPP, 42-3 exchange rates, equilibrium: in model of multicountry, multigood economy, 36-9 exchange rates, fixed: constraints on monetary policy, 108; economic cost of, 109; monetary policies leading to, 118; return to regime of, 1 exchange rates, forward: effect of commodity market segmentation on, 57; as predictor of future spot rate, 10-11; relation to spot exchange rate, 10, 58-60, 126; risk premia, 58; in segmented commodity markets, 126. See also forward bias puzzle; forward premium exchange rates, nominal: in model of monetary policy effects, 117-18; in model of production economy, 33-4 exchange rates, real: effect of commodity market segmentation on, 61; in general-equilibrium model for UIP, 60-3; intertemporal models of, 15; in monetary union, 123—4; relation between trade volume and volatility of, 126; relation to wealth differences and time preferences, 54-6 exchange rates, spot: in model of production economy, 32-3; relation to forward currency rates, 126; relation to forward rate, 10, 58; UIP in determination of current, 10 exogeneity: in model of endowment economy, 24; of trade policy, 103 factors of production: in model of monetary policy effects, 110-18 financial markets: in basic model of endowment economy, 23-9; gains from trade with integrated, 102-3; influence on setting trade policy, 102-3; interactions between decisions in commodity markets and, 101-2; in model of multicountry, multigood economy, 36-9; opening, 102-3, 127; optimal tariff in integrated, 3-4, 101; tariffs in segmented, 101; trade dividend of, 102. See also capital markets forward bias puzzle, 57 forward premium: forward and spot rates in determining, 10-11; UIP hypothesis related to, 58. See also forward bias puzzle free-trade policy: conditions for choice of, 102

Subject Index

GARCH (Generalized Autoregressive Conditional Heteroskedastic) model, 68, 69 government: choice of tariff in Nash game, 102; in model of monetary policy effects, 110-18 hedging: against changes in terms of trade, 101; for exchange rate risk, 67 incentives: in Nash tariff game, 101 interest rates: in basic model of endowment economy, 27; effect of changes on exchange rates, 9; influence on demand for money, 9; relation to exchange rates in nominal terms, 6 3 ^ . See also covered interest rate parity; uncovered interest rate parity (UIP) Johansen-Juselius tests: cointegration, 52-4; likelihood, 51-2; likelihood tests of PPP, 51-2;PPPin,48 Keynesian theory: balance-of-payments approach to exchange rate determination, 11-12; government spending under, 107 law of one price: in model of production economy, 33 monetary policy: choice of exchange rate regime and, 22; constraints of fixed nominal exchange rate, 108; in idealized EMS, 119-21; leading to fixed exchange rates, 118; model of economic effects, 110-18; Nash game, 121-2 monetary union: seigniorage in, 122-3; welfare benefits and costs in, 123-4 money: assumptions of model of supply and demand for, 110-13; cash-in-advance constraints, 105-6, 123; effect of interest rate changes on demand for, 9; implications of model of demand and supply of, 113-18; in models of real exchange rates, 15; money-in-the- utility-function, 106; as store of value in overlapping generations, 105 Nash game: conditions for noncooperative, 118; countries' choice of monetary policy in coordinated, 119; endogenous tariff rates in, 100-1, 121-2; monetary policy choices in, 121-2 prices, relative: determinants of, 54 production economy: additional extensions to model of, 34; extension of endowment

153

economy to, 29-34; gains from financial-market integration, 83-7 purchasing power parity (PPP): absolute and relative, 6-8, 42; ADF and cointegration tests of, 48-52; alternative sufficient sets of conditions for, 42; approach to determining exchange rate, 9; in CRRA exchange rate model, 35-6; deviations in data from, 18, 57; deviations in segmented commodity markets, 57; empirical tests of, 7-8, 43-6; implications for traditional test of relative, 43-4; panel analysis of bilateral, 47-8; relation to exchange rate, 6-9; as special case of CRRA model, 43; test in multilateral analysis, 47 rational expectations, 127 rational-expectations models: explanation of empirical regularities, 127; of monetary policy with PPP holding, 13 relative risk aversion (RRA): in basic model of endowment economy, 25 risk aversion: effect on capital flow volume, 94; related to segmented capital markets, 85-6; relative risk aversion (RRA), 25 risk premia: capital-asset pricing model (CAPM), 60; in forward exchange market, 58-60; forward exchange rates, 58, 126; in general-equilibrium model, 11; for holding forward contracts, 58-60; in prediction of future spot rate, 11; in prediction of spot rate, 11 risk sharing: in financial markets, 85; gains from financial-market integration, 83-5; in integrated financial markets, 86-7 seigniorage: government income from, 106; in monetary union, 122-3 sharing rule: in model of monetary policy effects, 116-17 tariff, optimal, 101-2; in absence of financial markets, 102; choice of optimal policy, 99, 127; in presence of financial markets, 103 tariffs: in complete and integrated financial market, 102; government choice in Nash game, 102; Nash tariff game, 101; segmented commodity markets by rates, 100; as source of segmentation, 19-20; wealth effect and price effect, 101; welfare gain from reduced, 4. See also barriers to trade terms of trade: government influence on, 101; hedging against changes in, 101 Trace test statistic, 49n23

154

Subject Index

trade: effect of exchange rate volatility on, 1, 3, 68-9; in financial securities, 95; integration in Europe, 124; no-trade region in endowment economy, 26-7, 71, 75; regions of trade and no-trade in model of endowment economy, 25-9; relation to exchange rate risk, 73-6; three state space regions, 26-7, 71, 75; trade and no-trade regions in model of production economy, 30-1; trade and no-trade regions in model of trade-exchange rate volatility relation, 70-2 trade flows: relation between exchange rate volatility and trade volume, 126 trade policy: role of financial markets in setting, 102; welfare gains from endogenous, 103 uncovered interest rate parity (UIP): in determination of current spot exchange rate, 10; function of, 10; in general-equilibrium model in real terms, 60-3; in international

data, 18; relation between forward and spot rates under, 58; tests of, 10-11; violations of, 57 VAR (vector autoregressive) models, 69 welfare: comparisons in general-equilibrium model, 18; effect of exchange rate volatility on, 3; effect of financial market integration on, 3; related to exchange rate risk, 79 welfare gains: from financial-market integration, 4, 83-7; from opening of financial markets, 3, 102-3, 127; from segmented capital markets, 85-7; from sharing financial market risk, 126; from trade in financial markets, 102; without fully integrated commodity markets, 126-7 welfare loss: costs of segmented commodity markets, 87-90; from segmented commodity markets, 83, 87-90; from segmented financial markets, 89-90