Kieler Studien • Kiel Studies 334 Dennis Snower (Editor) Kiel Institute for World Economics
Jan Gottschalk
Monetary Policy and the German Unemployment Problem in Macroeconomic Models Theory and Evidence
Springer
Dr. Jan Gottschalk 1217 F Street NE Washington DC 20002
[email protected]
Cataloging-in-Publication Data Library of Congress Control Number: 2005923877 ISSN 0340-6989 ISBN 3-540-25650-4 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Erich Kirchner, Heidelberg Printed on acid-free paper 42/3153 - 5 4 3 2 I 0
Preface
Persistently high unemployment has plagued Germany for the better part of the past 25 years. Whereas most observers would attribute this to supply-side rigidities in the German economy—and a very formidable body of literature has formed over the years to substantiate this view—another camp identifies overly tight demand-side policies, in particular monetary policy, as another cause for high unemployment, advocating a more expansionary monetary and fiscal policy stance as part of the solution. The present study takes a closer look at the latter proposition, with a particular focus on the role of monetary policy for unemployment. Macroeconomic theory has evolved considerably over the past forty years, and views on the long-run effectiveness of monetary policy have changed substantially. These different views provide the background for the policy debate in Germany on the role of demand policies for unemployment, which this study illuminates by providing an in-depth review of the different theoretical strands of macroeconomics and their policy implications. This is complemented by empirical investigations uncovering the implications of different theories for key macroeconomic variables, and testing their consistency with long-run trends in German data. While this study cannot resolve the underlying theoretical differences conclusively, given that macroeconomic theory continues to evolve and that there are inherent limits to econometric testing, it does provide tentative conclusions that point to a role of demand policies for unemployment, but this role is limited in size and in time. This study is the final result of a long process, a process in which I benefited from the help and encouragement of many colleagues and friends without whom the research project on monetary policy and the German unemployment problem could not have been completed. First of all, I would like to thank Professor Gerd Hansen for his support during a critical phase of the project and for his many valuable comments, and Professor Thomas Lux for his support in thefinalphase. In general, the project benefited from many fruitful discussions with my colleagues at the Business Cycle Research Department of the Kiel Institute for World Economics, and I am grateful for the freedom afforded to me by Professor Horst Siebert and Professor Joachim Scheide to pursue the research project. Particularly important for the success of the project was Jorg Dopke, who was my de facto mentor in the Institute and who has been critical for both the theoretical and empirical parts of this book. I am grateful to Christian Schumacher, Ulrich Fritsche and Kai Carstensen for many helpful comments; The theoretical part benefited from suggestions by Christophe Kamps, particularly regarding the programming of the New Keynesian model in Matlab. Of course, all remaining
VI
Preface
errors are mine alone. Moreover, I would like to acknowledge the financial support of the Marga and Kurt Moellgaard Foundation. Finally, I would like to thank Dietmar Gebert and Kerstin Stark for their patience and their valuable contributions to the editing of this study, and its preparation for the print stage.
Washington DC, May 2005
Jan Gottschalk
Contents
1 Introduction 2 Keynesian and Monetarist Views on the German Unemployment Problem 2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation 2.1.1 The Keynesian Perspective 2.1.2 The Monetarist Challenge 2.1.3 The Keynesian Response to the Monetarist Revolution: TheNAIRU 2.2 The Long-Run Phillips Curve and the Source of Business Cycle Fluctuations in Germany 2.2.1 The Unemployment-Inflation Relationship in Germany 2.2.2 Estimating Keynesian and Monetarist Phillips Curves for Germany 2.3 Conclusion
1 5 6 6 12 23 35 35 39 94
3 The Rational Expectations Revolution 3.1 New Classical Economics 3.2 Real Business Cycle Models 3.3 The New Keynesian Research Program 3.3.1 Empirical Evidence on the Effects of Systematic Policy 3.3.2 Revisiting the Policy Ineffectiveness Proposition 3.3.3 The Building Blocks of New Keynesian Economics
96 96 99 102 102 103 106
4 Monetary Policy in the New Keynesian Model 4.1 Deriving the Core Equations of the New Keynesian Model 4.1.1 The New Keynesian Phillips Curve 4.1.2 The New IS Curve 4.1.3 The Interest Rate Rule 4.2 Simulating the New Keynesian Model 4.2.1 The Standard New Keynesian Model
114 115 115 121 128 138 138
VIII
Contents
A.22 The Extended New Keynesian Model 4.2.3 The Sources of Business Cycle Fluctuations in the New Keynesian Model 4.2.4 The Effects of Systematic Policy 4.3 New Keynesian Economics and the Policy Debate in Germany 5
6
Introducing Nonlinearities into the New Keynesian Model 5.1 Nonlinearities in the Aggregate Supply Curve 5.1.1 Nonlinearities in the Supply Curve and Credit Market Imperfections 5.1.2 Nonlinearities in the Supply Curve and Downward Nominal Rigidities 5.1.3 Empirical Evidence on Nonlinearities in the Supply Curve 5.1.4 Policy ImpHcations 5.2 Nonlinearities in the Welfare Function 5.2.1 The Inefficiency Gap and Business Cycle Fluctuations 5.2.2 The Welfare Effects of the Inefficiency Gap Revisiting the Natural Rate Hypothesis 6.1 A Preliminary Look at the Data 6.2 A Framework for Cointegration Analysis 6.2.1 The Aggregate Demand Equation in the VECM 6.2.2 The Aggregate Supply Equation 6.2.3 The Policy Rule 6.3 Results of a Multivariate Cointegration Analysis for Germany 6.3.1 Testing for a Structural Break 6.3.2 Univariate Unit Root Tests 6.3.3 Results of the Multivariate Cointegration Analysis for the Period 1965-1979 6.3.4 Results of the Multivariate Cointegration Analysis for the Period 1979-1998 6.3.5 A Long-Run Phillips Curve 6.4 Explaining the Long-Run Phillips Curve 6.4.1 Asymmetric Information Models 6.4.2 Nonlinearities in the Long-Run Phillips Curve 6.4.3 Disinflation and Hysteresis Effects
144 151 156 163 171 171 173 175 176 178 180 182 197 204 205 205 208 209 211 213 214 216 216 219 222 225 226 227 229
Contents 6.4.4 Using Monetary Policy to Lower the Unemployment Rate Permanently
7
IX
231
6.5 A New Keynesian Model with Hysteresis
232
Concluding Remarks
238
Appendix A. 1 Appendix for Chapter 2 A.2 Appendix for Chapter 6 A.3 An Introduction into the SVAR Methodology A.3.1 Introduction A.3.2 Identification in Macroeconometric Models: A Traditional Perspective A.3.3 The SVAR Methodology A.3.4 Objections to the SVAR Methodology A.3.5 Conclusion References
241 241 243 245 245 246 254 266 274 276
List of Tables
Table 2.1: Sample Correlation of Unemployment and Inflation
38
Table 2.2: Unit Root Tests
40
Table 2.3: Trace Test for the Cointegration Rank
43
Table 2.4: Forecast Error Variance Decomposition in the Keynesian Phillips Curve Model: Contribution of Demand Shocks
61
Table 2.5: Forecast Error Variance Decomposition in the "Natural Rate" Phillips Curve Model: Contribution of Demand Shocks
64
Table 2.6: Forecast Error Variance Decomposition in the "Money as a Monetary Phenomenon" Phillips Curve Model: Contribution of Demand Shocks
70
Table 4.1: Variance Decomposition Using the McCallum Specification of Shock Variances
153
Table 4.2: Variance Decomposition Using the Baseline Specification of Shock Variances
154
Table 4.3: Variance Decomposition for the Baseline Specification with p = 0.6
155
Table 5.1: Cross Correlations between the Inefficiency Gap and Its Components for Various Lags (/)
191
Table 5.2: Welfare Costs (-) and Benefits (+) of Boom/Recession Episodes
203
Table 6.1: VAR Specification Statistics
215
Table 6.2: Results from ADF Tests
217
Table 6.3: Cointegration Statistics for the Period 1965-1979
217
Table 6.4: Cointegration Statistics for the Period 1979-1998
220
Table 6.5: Restrictions on the Cointegration Vectors
220
raZ?/e^7; MisspecificationTests
242
List of Figures
Figure 2.1: The Phillips Curve
8
Figure 2.2: Business Cycle Fluctuations: The Keynesian View
10
Figure 2.3: Business Cycle Fluctuations: The Monetarist View
19
F/gwr^2.^;TheNAIRU
25
Figure 2.5: Indicators of Trend Unemployment in Germany
31
Figure 2.6: Indicators of Trend Unemployment in the USA
32
Figure 2.7: Unemployment and Inflation in Germany, 1951-1998
36
Figure 2.8: Cyclical and Trend Components of Unemployment and Inflation in Germany
38
Figure 2.9: Recursive Estimation of the Trace Test for the Cointegration Rank
45
Figure 2.10a: The Trade-Off between Inflation and Unemployment in the Keynesian Phillips Curve
57
Figure 2.10b: The Effects of Supply Shocks in the Keynesian Phillips Curve Model
58
Figure 2.11a: The Trade-Off between Inflation and Unemployment in the Monetarist Phillips Curve: "Natural Rate" Identification
65
Figure 2.11b: The Effects of Supply Shocks in the Monetarist Phillips Curve Model: "Natural Rate" Identification
66
Figure 2.12a: The Trade-Off between Inflation and Unemployment in the Monetarist Phillips Curve: "Inflation as a Monetary Phenomenon" Identification
68
Figure 2.12b: The Effects of Supply Shocks in the Monetarist Phillips Curve Model: "Inflation as a Monetary Phenomenon" Identification
69
Figure 2.13: Business Cycle Fluctuations in the Unemployment Rate: Keynesian Phillips Curve Model
80
XII
List of Tables
Figure 2.14: Business Cycle Fluctuations in the Inflation Variable: Keynesian Phillips Curve Model
81
Figure 2.15: Historical Decomposition of the Unemployment Rate: Keynesian Phillips Curve Model
82
Figure 2.16: Historical Decomposition of the Inflation Rate: Keynesian Phillips Curve Model
83
Figure 2.17: Business Cycle Fluctuations in the Unemployment Rate: "Natural Rate" Identification
85
Figure 2.18: Business Cycle Fluctuations in the Inflation Rate: "Natural Rate" Identification
86
Figure 2.19: Historical Decomposition of the Unemployment Rate: "Natural Rate" Identification
87
Figure 2.20: Historical Decomposition of the Inflation Rate: "Natural Rate" Identification
88
Figure 2.21: Business Cycle Fluctuations in the Unemployment Rate: "Inflation as a Monetary Phenomenon" Identification
90
Figure 2.22: Business Cycle Fluctuations in the Inflation Rate: "Inflation as a Monetary Phenomenon" Identification
91
Figure 2.23: Historical Decomposition of the Unemployment Rate: "Inflation as a Monetary Phenomenon" Identification
92
Figure 2.24: Historical Decomposition of the Inflation Rate: "Inflation as a Monetary Phenomenon"
93
Figure 4.1: Impulse Response Functions for the Standard New Keynesian Model
140
Figure 4.2: Cross Correlation between Inflation and the Lagged Output Gap in Germany
143
Figure 4.3: Impulse Response Functions for the Extended New Keynesian Model
150
Figure 4.4: Simulating the New Keynesian Model with a Neutral Policy Rule
160
Figure 4.5: The Effects of Systematic Policy
161
List of Tables
XIII
Figure 4.6: The Taylor Rule and the Short-Term Interest Rate for Germany
167
Figure 5.1: A Convex Short-Run Aggregate Supply Curve
172
Figure 5.2: Distribution of the Output Gap Using the Band Pass Filter
177
Figure 5.3: Distribution of the Output Gap Using a Segmented Trend Model Figure 5.4: Disinflation in a Model with a Convex Short-Run Aggregate
177
Supply Curve
179
Figure 5.5: The Business Cycle and Wage and Price Markups
181
Figure 5.6: The Inefficiency Gap
189
Figure 5.7: The Inefficiency Gap and Its Components
190
Figure 5.8a: The Implied Output Gap of the Inefficiency Gap: The Band Pass Filter Estimate Figure 5.8b: The Implied Output Gap of the Inefficiency Gap: The
194
Segmented Trend Model Estimate
195
Figure 5.9: The Price Markup Estimate
196
Figure 5.10: Welfare and the Inefficiency Gap
200
Figure 5.11: Welfare Effects of Business Cycle Fluctuations
201
Figure 6.1: The Relationship between Inflation and Unemployment in Germany, 1965-1999 and 1980-1999 Figure 6.2: The Real Short-Term Interest Rate and Its Mean in Germany Figure 6.3: The Relation between the Vacancy Rate and the Unemployment Rate in Germany Figure 6.4: A Nonlinear Long-Run Phillips Curve Figure 6.5: The Length of Disinflation and Unemployment in Germany and the United States Figure 6.6: Impulse Response Functions for the New Keynesian Model
206 215 225 229 230 236
XIV
List of Tables
Figure Al: Estimating the Phillips Curve: The Time Series
241
Figure A2: Stability of the Reduced-Form Phillips Curve Relationship
242
Figure A3a: Structural Break Test: Full Sample Period
243
Figure A3b: Structural Break Test: 1965-1979
243
Figure A3c: Structural Break Test: 1979-1998
244
Figure A4: The Time Series and Their Trend Components
244
Figure A5: Identifying the Money Supply Schedule
250
Figure A6: The Impulse Response Function of Output in Response to an Impulse in u^
257
List of Symbols
Section 2.1 a(L)
A ^t
m P Ap Ap' u u ^NAIRU W^^
Aw X
y y ^t
^md ^s
A V
0
lag polynomial index of excess demand serially uncorrelated error term money stock price level inflation rate expected inflation rate unemployment rate steady state unemployment rate NAIRU unemployment rate no-shock NAIRU unemployment rate change in nominal wages vector of variables capturing the interest-rate and transactiontechnology influence on money demand (real) level of output natural level of output vector of supply shock variables money demand shock supply side shock productivity component in nominal wage growth velocity sensitivity of unemployment to unexpected inflation
Section 2.2 d^^d
E
demand shocks expectations operator
XVI
List of Symbols
e, F L m s, e^ Xf
vector containing reduced-form shocks forward operator lag operator shock to the inflation process supply shocks vector containing growth in the money stock and in output variables / vector containing endogenous variables
Yxy € e^ £"" £^
long-run effect of variable y on variable x residual in the price or unemployment equations exogenous real shock exogenous monetary policy shock vector containing the real and the monetary policy shock variables
T] A^ p I a (7^
real disturbance contemporaneous effect of variable y on variable x autocorrelation parameter in the inflation process variance-covariance matrix covariance parameter variance parameter
Chapter 4 B cwj G g M MC(i) MC^ (i) N{i) P P{i) P* (i) A/7 R
government bond contract wage negotiated in period / government consumption shock to aggregate demand nominal money stock real marginal costs of firm / nominal marginal costs of firm i labor input into the production of Y{i) aggregate price level price level of the differentiated good i desired price of firm / inflation rate nominal interest rate
List of Symbols J? R* r r U{C, M')
XVII
V W'' w X Y Y(i) y
long-run equilibrium of the nominal short-term interest rate target of the nominal short-term interest rate real rate of interest natural rate of interest time-separable utility function in consumption ( C ) and in the real money stock (M'') lump-sum tax real wage rate nominal wage per unit of labor input output gap aggregate output level output level ofthe differentiated good/ natural level of output
A, a P
technological factor common to all firms in the production of Y(i) discount factor
Y
elasticity of marginal utility of real money balances
e e^ 8^ ^ T] 6 ^^ V 7t ^ ^ 0; ,^2
price elasticity of demand labor supply shock cost-push shock monetary policy shock expectation errors with respect to inflation probability for each firm to keep its price constant price markup preference shock deviation of inflation from the inflation target inflation target elasticity of substitution of consumption central bank reaction function parameters regarding the output gap and deviation of inflation from the inflation target
Chapter 5 A{t) c
trend component in the production function consumption per capita
XVIII List of Symbols c gap gap K,L mc'' mpn fhpn mrs n n n p Uc, Uj^ ulc W{N) w Y y y,c z A
consumption gap inefficiency gap demeaned inefficiency gap capital and labor input, respectively, in the CES production function nominal marginal costs of production marginal productivity of labor estimate of the marginal productivity of labor marginal rate of substitution between labor and consumption labor supply (hours worked per capita) natural rate of employment percent deviation of employment from its natural level aggregate price level marginal utility of consumption and (dis)utility of labor, respectively real unit labor costs net welfare effect of producing one unit of output compensation per unit of labor input output in the CES production function output per capita natural level of output and consumption, respectively variable capturing capital and technological factors in a stylized production function
ju
utility loss or gain from reallocating labor relative to the natural rate of employment marginal disutility of labor variable capturing low frequency shifts in preferences over consumption and leisure elasticity of the natural rate of consumption with respect to the natural rate of output steady state markup
fiP
price markup
p,p
observable component of the price markup
jW"
wage markup
a
relative risk aversion
5 e rf(^Y
List ofSymbols (fi,v,A,d
distribution, homogeneity, efficiency, and substitution parameters in the CES production function, respectively
Chapter 6 F u u X
XIX
z, V, w z, V , w
natural rate of interest unemployment rate natural rate of unemployment vector containing the variables R (nominal interest rate), 4 P (inflation), and u (unemployment) vectors containing stationary disturbances vectors containing constants
a ^ TT 2"
vector containing short-run adjustment parameters vector containing cointegration relationships inflation target variance-covariance matrix
List of Abbreviations
augmented Dickey-Fuller test autoregressive constant elasticity of substitution modified Dickey-Fuller test statistic European Central Bank European Monetary System test statistic for unit root tests proposed by Kwiatkowski et al. (1992) ERAS long-run aggregate supply curve LRN long-run neutrality LRSN long-run supemeutrality LSW proposition Lucas-Sargent-Wallace proposition MA moving average NAIRU non-accelerating inflation rate of unemployment NAWRU non-accelerating wage rate of unemployment NRH-GAP natural rate hypothesis - gradual adjustment of prices OLS ordinary least squares RBC model real business cycle model SRASI linear short-run aggregate supply curve SRASII convex short-run aggregate supply curve SVAR model structural vector autoregression model SVR Sachverstandigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung (Council of Economic Experts) VAR model vector autoregression model VECM vector error correction model ADF test AR CES DFGLS ECB EMS KPSS test
Introduction
Since the early 1980s, the German economy is beset by high unemployment. Moreover, the much more satisfactory labor market performance in other industrialized countries makes the persistently high unemployment rate in Germany even more distressing. A prominent example for the former is the United States, but other examples include also European countries like the Netherlands and the United Kingdom, which managed more recently to reduce their unemployment rates to relatively low levels. The causes of the increase in the unemployment rate from very low levels in the 1960s to almost ten percent since the early 1980s and the appropriate policy responses by the central bank, fiscal policy, and trade unions are the subject of an intense debate in public and in academia. Broadly speaking, the arguments exchanged in this debate can be categorized as belonging to one of two camps. One stresses that the high unemployment rate in Germany reflects rigid labor markets, which prevent real wages from adjusting to clear the labor market. This camp points to the more flexible labor market arrangements in the United States, and argues that this underlies the more successful performance of the United States labor market. The other camp believes that the Bundesbank has maintained overly tight demand conditions over a long period of time in its attempt to disinflate the economy and maintain price level stability, and that this policy has contributed substantially to the persistently high unemployment rate in Germany. According to this line of argument the Federal Reserve Bank of the United States maintained in general more favorable aggregate demand conditions than the Bundesbank did because of the Federal Reserve Bank's obligation to pursue not only a price level stability goal but also to maintain full employment. Hence, critics of the Bundesbank regard the supposedly more successful demand management policies of the Federal Reserve Bank as a key factor for the maintenance of a relatively low unemployment rate in the United States. Since the policy debate in Germany has been going on for almost 30 years, one objective of this study is to take stock of this debate. The second objective is to provide new empirical and theoretical evidence relevant to this debate, thereby hoping to advance the debate. A central element of the policy debate is the role of monetary policy for stabilizing the real economy. Thus, this study is going to focus on the effectiveness of monetary policy regarding real variables in theory and practice. A particularly important question, which will be at the center of this study, is whether monetary policy can have long-run effects on real variables like output and unemployment, since this long-run effectiveness is a central tenet of
2
Chapter 1
Introduction
the position of the second camp. This study reviews this question from different theoretical viewpoints and presents empirical evidence on the basis of several econometric methodologies. To take stock of the policy debate, Chapter 2 begins by outlining the Keynesian and monetarist positions, since the controversy between these two theoretical schools can be considered as the origin of the current debate. In fact, in many instances the public debate continues to be best understood in terms of the Keynesian and monetarist positions. A key difference between the two schools of thought is the long-run effectiveness of monetary policy. Keynesians believe monetary policy has significant long-run effects on real variables, while monetarists are convinced that monetary policy has only long-run effects on prices or other nominal variables. Testing empirically the long-run effects of monetary policy is complicated by the fact that this requires overcoming a difficult identification problem. In this paper, I employ for this purpose a methodology proposed by King and Watson (1994) based on the structural vector autoregression methodology. Since this methodology has not yet been widely used, the methodological appendix provides an introduction. The King and Watson approach addresses the identification problem by imposing either Keynesian or monetarist identifying restrictions on the model, which allow testing the long-run effects of monetary policy both from a Keynesian and monetarist perspective. Moreover, with this approach I can construct time series reflecting the two viewpoints on business cycle fluctuations. This will prove useful when showing that the two camps are not only separated by different theoretical viewpoints, but also by a different interpretation of macroeconomic events in the past thirty years. Beginning in the second half of the 1970s, the introduction of rational expectations began to change macroeconomics fundamentally. In Chapter 3,1 provide an outline of the rational expectations revolution, and discuss several strands of macroeconomic research that emerged from it. The resulting models have potentially far-reaching policy implications; particularly controversial is the role of anticipated monetary policy, since some rational expectations models imply that anticipated policy is ineffective. Since most monetary policy actions represent a systematic response to economic conditions, they are anticipated. If the ineffectiveness proposition were true, monetary policy would have neither short-run nor long-run effects. In this case, stabilization policy would become futile and, moreover, any claim that tight monetary policy could have contributed to Germany's persistent unemployment problem becomes untenable. However, in response to these theoretical developments the so-called New Keynesian research agenda emerged, which aimed to show that anticipated policy can have real effects even in an environment with fully rational agents. I conclude Chapter 3 by presenting an outline of the building blocks of New Keynesian models. By the late 1990s, New Keynesian models have gained widespread acceptance in the academic literature. This reflects mostly the fact that New Keynesian
Chapter 1 Introduction
3
models have come to incorporate many elements of other macroeconomic research strands, and therefore encompass them. In Chapter 4, this study provides a detailed introduction into New Keynesian economics. We first derive the core equations of the New Keynesian model, and discuss optimal monetary policy in this framework. The latter provides us with the New Keynesian view on the objectives of monetary policy, and in particular on the question to what extent monetary policy should aim to stabilize the real economy. Since Chapter 3 has shown that the effectiveness of anticipated monetary policy is a controversial issue, Chapter 4 provides new evidence of the effects of anticipated monetary policy in New Keynesian models. Another subject of controversy is the source of business cycle fluctuations, and, in particular, to what extent these are due to monetary policy disturbances. Since this controversy is relevant to the present study. Chapter 4 provides also new evidence on this issue by computing the variance decomposition for a general version of this model. Chapter 4 discusses also the implications of the New Keynesian model for the policy debate in Germany; it emerges that New Keynesian economics strongly support the monetarist position. In this context, I also discuss the actual conduct of monetary policy by the Bundesbank and compare it to what would constitute optimal policy in a New Keynesian framework. Moreover, I compare the policy of the Bundesbank with that of the Federal Reserve Bank. This proves useful when evaluating the Keynesian claim that there is a significant difference in the way these two central banks set policy, and that the Federal Reserve Bank pursues a policy more concerned with stabilizing output than the Bundesbank does. However, the monetarist policy implications of the New Keynesian model reflect to some extent the fact that this model is inherently linear, while traditional Keynesian models tend to have nonlinear elements. Also, since New Keynesian models are still at a fairly early stage of development, the omission of nonlinear elements does not necessarily mean that these are thought to be unimportant, but that they have not yet been incorporated. To gain a first impression to what extent nonlinearities in the New Keynesian model could change its policy implications, I discuss in Chapter 5 ways to extend this model accordingly. In particular, I consider several approaches to obtain a nonlinear short-run aggregate supply curve, and I discuss a nonlinear welfare function. Based on the welfare function, I construct a new measure for business cycle fluctuations in Germany, and estimate the welfare effects of the latter in Germany. This helps to shed some light on the question whether business cycle fluctuations are important from a welfare perspective and therefore justify a policy intervention to stabilize the economy in the first place. Another reason why the policy implications of New Keynesian models are similar to those of monetarist models is that both type of models rule out any long-run effects of monetary policy. To test this hypothesis within a New Keynesian framework, in Chapter 6 I apply a recently developed approach by
4
Chapter 1 Introduction
Beyer and Farmer (2002) to German data using multivariate cointegration analysis. I find that the data reject this hypothesis, and proceed to discuss several modem macroeconomic approaches which might fit the data better in this regard. To evaluate the implications for monetary policy, I extend the New Keynesian model to incorporate one of those approaches, and present the results of the stochastic simulation. The results indicate that monetary policy may have some potential to lower unemployment permanently, which would lend the New Keynesian model a more Keynesian character in its policy implications. However, this is an issue that needs to be explored further in future work. In Chapter 7,1 present concluding remarks. In sum, this paper cannot resolve the long-standing differences between Keynesians and monetarists, but it does identify the key differences, and by placing this debate in a modem macroeconomic context this paper finally arrives at a research agenda which might eventually help to bridge some of the differences.^
It should be noted from the outset that this study does not aim to provide a comprehensive explanation of the increase in the German unemployment rate over the past thirty years. Rather, this study focuses on the contribution of monetary policy to the unemployment problem. Since the long-run effects of monetary policy on unemployment in many theoretical models are close to zero, nonmonetary factors like structural rigidities in the labor market must in those models be responsible for the bulk of the increase in unemployment. But a comprehensive analysis of the numerous nonmonetary factors that could explain the German unemployment problem is beyond the scope of this study.
Keynesian and Monetarist Views on the German Unemployment Problem
As argued in the introduction, persistently high unemployment rates in Germany have led to a lasting controversy on the causes of unemployment and the appropriate policy response. The opposing viewpoints, and in particular the public exchanges on these issues, have often been based either on Keynesian or on monetarist theories of business cycle fluctuations, leading to very different conclusions regarding the causes and the cure of the unemployment problem. Since this debate is going on since 30 years and is nowhere near a conclusion, this chapter attempts to take stock and offers a review of the arguments exchanged between both sides. A major contribution of this chapter is the new empirical evidence on the Phillips curve relation in Germany. This relation is central to the controversy between the two schools of thought because the slope of the curve is a key parameter determining whether demand policies can have a lasting impact on real variables like the unemployment rate. Since Keynesians and monetarists sharply disagree on this parameter for theoretical grounds, this chapter estimates the Phillips curve using both a Keynesian and a monetarist identification scheme. In addition, the role of demand and supply shocks for fluctuations in unemployment and inflation is investigated using the historical decomposition technique. This serves to explore empirically the explanations offered by the two Phillips curve models regarding the causes of the secular increase in unemployment over the past 30 years. The chapter is organized as follows. Section 2.1 offers a general introduction into the Keynesian and monetarist views on unemployment and inflation. Particular attention is paid to the role of demand management policies in the two paradigms for the stabilization of the real economy, since this is of central importance to the policy debate. This section contains also a discussion of the NAIRU concept, which modifies the traditional Keynesian view in some important aspects. Section 2.2 contains the empirical evidence on the Phillips curve in Germany. Before presenting the estimates of the slope of the Keynesian and monetarist Phillips curves, this section shows that at the business cycle frequency a stable Phillips curve relation is supported by the data. Next, it provides an introduction into the econometric technique used for testing the slope of the Phillips curve and discusses the identification of the Phillips curve models. Having estimated these models, the results for the Keynesian and monetarist Phillips curves
6
Chapter 2 Keynesian and Monetarist Views
are presented, and the results of the historical decomposition are shown. Section 2.3 presents the conclusions of this chapter.
2.1
Keynesian and Monetarist Explanations of Unemployment and Inflation
2.1.1
The Keynesian Perspective
2.1,1.1
The Departure from Classical Economics
The characteristic difference between classical and Keynesian models is that the former assumes that prices (including wages) adjust instantaneously so as to equate supply and demand quantities on all markets, whereas the latter assumes that nominal wages do not adjust within the relevant period (McCallum 1989: 174ff.). The assumption of sticky wages makes it possible in Keynesian models that labor demand does not equal labor supply quantities. In particular, this allows for the existence of involuntary unemployment.^ This departure from classical economics was prompted by the experience of widespread involuntary unemployment in the depression of the 1930s, which classical economics could not account for. Moreover, the observation that changes in aggregate demand, for example due to changes in government demand for goods, are an important source of short-run fluctuations in economic activity was also hard to reconcile with classical economics.-^ In Keynesian models sluggish wage adjustment accounts for both observations. For example, a fall in demand in product markets will reduce labor demand if wages do not fall sufficiently, thereby leading to involuntary unemployment. If prices also adjust sluggishly, the fall in labor demand reduces product demand further. This leads to a situation where recessions are the result of deficient labor and product demand reinforcing each other (Snower 1997: 20). That is, workers are unemployed because firms are not producing enough goods and services, and firms do not increase production because there is not enough demand; and demand is deficient because people are unemployed. Besides accounting for recessions, another implication of sluggish wage adjustment is that the classical dichotomy between real and nominal variables fails, because it is the nominal wage which is slow to adjust (Romer 1993: 5). Hence, movements in nominal variables like the money supply can have large effects on real variables such as output and employment.
^ ^
Other variants of Keynesian models assume instead of sticky wages that prices are sticky. See Romer (1996: 214ff.), for an extensive discussion. See Romer (1993: 5) on these two points.
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation 2.1.1.2
The Phillips Curve
In the early Keynesian models, nominal wages were treated as exogenous, which posed a problem for dynamic analysis and for the formulation of policy advice, because nominal wages are likely to be set conditional on the state of the economy (McCallum 1989: 176ff). Since in Keynesian models economic policy can affect the state of the economy, policy influences the future values of nominal wages even if wages do not respond within the period to the state of the economy. If this effect of policy on future wages is not taken into account, the dynamic analysis misses an important factor and any advice given to policy makers may be flawed. In other words, nominal wages may be treated as predetermined variables, but are unlikely to be exogenous in a complete model of the macroeconomy. Moreover, in Keynesian models, prices are determined as a markup on unit costs at standard rates of output and capacity utilization (Blanchard 1990: 784). Since wage costs are the main determinant of unit costs, treating nominal wages as exogenous precludes analyzing the causes of inflation. To close the model an equation for nominal wages was needed that explains this variable as a function of conditions prevailing in the past. This equation was provided by the seminal paper of Phillips (1958), who suggested that the nominal wage rate could be explained by recent values of the unemployment rate.^ He argued that if the demand for labor was very high relative to the supply of labor, employers would bid up wages very rapidly. As additional workers were hired, the unemployment rate would fall. The larger the discrepancy between labor demand and supply, the larger the upward pressure on nominal wages would become. Excess labor supply would lead, on the other hand, to downward pressure on wages and rising unemployment. Using data from 1861 to 1957 for the United Kingdom he showed empirically that the growth rate of nominal wages was indeed negatively correlated with the rate of unemployment. A hypothetical Phillips curve corresponding to his finding is depicted in Figure 2.1.^ The relationship between the wage growth rate and the unemployment rate is nonlinear, reflecting the finding of Phillips that the strength of the relationship between the two variables depends on the level of the unemployment. In particular, tight labor markets cause the employers to bid wages up rapidly, whereas loose labor markets with high rates of unemployment lead to a slower downward adjustment of wages, because workers resist a reduction in their wages. Phillips' empirical finding appeared to confirm the assumption of sluggish downward adjustment of wages, which is central for the Keynesian view on the causes of recessions and high unemployment.^ This section draws on the discussion of the Phillips curve in Espinosa-Vega and Russell (1997: 6ff.). This figure is reproduced from Espinosa-Vega and Russell (1997: 7). For a more detailed discussion of the Phillips curve, see Espinosa-Vega and Russell (1997: 6ff.).
7
8
Chapter 2 Keynesian and Monetarist Views
Figure 2.1: The Phillips Curve Inflation rate
Unemployment rate The Phillips curve also establishes the link between monetary policy and inflation if one assumes markup pricing. Monetary policy can affect the level of aggregate employment in the economy through its influence on aggregate demand. This implies that monetary policy can exercise control over inflation via the Phillips curve mechanism. Moreover, the Phillips curve suggests that there is a menu of combinations of employment levels and inflation rates the central bank can choose from. In the traditional Keynesian models a demand stimulus through expansionary policy would increase employment without leading to higher inflation because nominal wages and prices were treated as exogenous (see also Espinosa-Vega 1998: 16). With the Phillips curve mechanism providing a link between real and nominal variables, the demand stimulus would still lead to a higher employment level but also to higher inflation. Thus, the Phillips curve suggests that policy makers have to make a trade-off between the unemployment rate and the inflation rate, and macroeconomic policy needs to strike the right balance between sustaining robust economic activity and controlling inflation (Espinosa-Vega 1998: 19; Goodfriend and King 1997: 236). The assumption of a stable Phillips curve, which corresponded well to the experience in the United States in the 1950s and 1960s, implies that fiscal and monetary policy are powerful both in the short run and in the long run.^ In ^
See Goodfriend and King (1997: 236), for a discussion of the empirical evidence on the Phillips curve in the 1950s and 1960s.
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation particular, this implies that money is not supemeutral in the long run:^ If monetary policy increases the rate of growth of the money supply, prices are always one step ahead of nominal wages, because the latter are assumed to adjust only slowly to the rising price level. As a consequence the real wage declines permanently, the employment level increases and unemployment declines.^ Thus, an increase in the rate of growth of money has long-run effects on real variables. ^^ 2.1.1.3
The Case for Aggregate Demand Management Policies
Keynesian economics assign economic policy an important role in sustaining robust economic activity. In contrast to the "natural rate" view, which gained predominance later and which we will discuss below, output was not assumed to fluctuate symmetrically around a "natural" path of output (potential output) but Keynesians thought that in the absence of vigorous demand management policies the average level of output would be below the potential level of output, and therefore it would be inefficiently low.^^ This view implies that the potential level of output is close to the peaks of the business cycles and not somewhere in the mid-range of peaks and troughs (Tobin 1996: 5). Negative demand shocks can push output below its potential level, but positive demand shocks do not push it very much above this level. Tobin (1993: 52) writes: "Excess demand in aggregate is mainly an 'inflationary gap', generating unfilled orders and repressed or open inflation, rather than significant extra output and employment" (Tobin 1993: 52). That is, even though excess demand is an issue in Keynesian models and macroeconomic stabilization therefore requires two-sided counter-cyclical demand management, it is nevertheless maintained that the efficient level of activity is attained only in booms. De Long and Summers note that this positive Fisher and Seater (1993: 402) define long-run neutrality (LRN) and long-run superneutrality (LRSN) of money as follows: "By LRN, we mean the proposition that permanent, exogenous changes to the level of the money supply ultimately leave the level of real variables and the nominal interest rate unchanged but ultimately lead to equiproportionate changes in the level of prices and other nominal variables; by LRSN, we mean the proposition that permanent, exogenous changes to the growth rate of the money supply ultimately lead to equal changes in the nominal interest rate and leave the level of real variables unchanged." For a detailed discussion of the permanent output-inflation trade-off see Romer (1996: 222ff.). 10 But monetary policy is neutral in the long run, if not supemeutral. An increase in the level of the money supply leads to an increase in the price level. Eventually nominal wages adjust to this higher price level, and the real wage, after falling initially, retums to the value it had before the money supply was increased. Consequently this policy impulse has no long-run effects on the level of employment or output. 11 This section draws on De Long and Summers (1988: 437ff). See also Tobin (1996: 4ff).
9
10
Chapter 2 Keynesian and Monetarist Views
view of booms is in line with the public perception which sees them generally as representing the 'good times'. De Long and Summers (1988:439) write: "... booms cause few regrets: there are few complaints after cyclical expansions by people who wish they had not been fooled into working." To illustrate the Keynesian view of business cycles, Figure 2.2 plots for a hypothetical economy the path of potential output as the dotted line and actual output as the solid line.^^ De Long and Summers (1988: 438) summarize the business cycle depicted in Figure 2.2 as follows: "That the business cycle consists of repeated transient and potentially avoidable lapses from sustainable levels of output is a major piece of the Keynesian view: there is often room for improvement, and good policy aims to fill in troughs without shaving off peaks." The proposition that most of the time output is below its sustainable level rests on the presumption that monopoly power is widespread, since monopoly power leads to higher prices than under perfect competition and therefore to inefficient low real activity (De Long and Summers 1988: 437). Moreover, the existence of persistent involuntary unemployment is taken as another indicator that there is slack in the economy. It follows that a demand policy that fills in the troughs without shaving off the peaks would be welfare-enhancing, because this policy would raise the average level of output, which would bring the economy closer to its efficient level of real activity (ibid.). Figure 2.2: Business Cycle Fluctuations: The Keynesian View Output and potential output
Time 12 For a Keynesian approach to measuring the output gap see also the peak-to-peak
method in De Long and Summers (1988: 457ff.).
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation 2.1.1.4
The Keynesian Policy Assignment
According to the Keynesian perspective on business cycle fluctuations, an activist aggregate demand management policy has the potential to be welfareenhancing. With fiscal and monetary policy, economic policy makers have two tools at their disposal to achieve this objective. Even though Keynesian models suggest that monetary policy has powerful effects, in the 1950s and 1960s the role of monetary policy in practice was to support fiscal policy, which had to carry the main burden of stabilization poUcy (Goodfriend and King 1997: 237). It was thought that monetary policy worked primarily by affecting the availability of financial intermediary credit, which is particular important for small businesses and individuals. "Accordingly," Goodfriend and King (ibid.) write, "there was a reluctance to let the burden of stabilization policy fall on monetary policy, since it worked by a distortion of sorts." The task of demand policy to strike the right balance between sustaining a high employment level and keeping inflation under control is complicated by the possibility that wage-price spirals lead to high rates of inflation without stimulating real activity. A wage-price spiral may emerge when trade unions and employers make incompatible claims on national income and each side attempts to increase its income share by increasing wages or prices respectively, which is answered by the other side in kind. In terms of Figure 1 the resulting wage-price spiral leads to an upward shift of the Phillips curve. Economic policy has to respond to this increase in inflation by tightening demand conditions, thereby reducing inflation but incurring higher unemployment. The threat of tight demand conditions represents, of course, a major incentive to the partners in the wagebargaining process to settle their disputes without taking recourse to wage-price spirals. Consequently, trade unions and employers have in the Keynesian policy assignment the task to preserve price level stability, whereas economic policy has to ensure the maintenance of full employment by using its instruments of demand policy to this effect, but only if wages and prices are set in accordance with the price level stability goal. Thus, sustaining full employment and keeping inflation low requires a large degree of coordination between all three parties. The task for economic policy makers in the Keynesian assignment is particularly challenging because they have to make sure that economic activity meets the expectations of trade unions and employers, which requires considerable fine tuning. For instance, an economic boom due to an unexpected surge in foreign demand is likely to favor firms, because these can raise the prices for their products and thereby increase their share in national income, whereas nominal wages have been fixed in advance and cannot respond to booming demand and rising prices. The perceived injustice by trade unions may trigger high wage demands in the next wage round, leading to a wage-price spiral. To prevent this, economic policy has to respond to the surge in foreign demand by tightening domestic demand in order to cool the economy down and to limit the scope for
11
12
Chapter 2 Keynesian and Monetarist Views
price increases of firms. Since economic policy affects the real economy only after lags, this is a highly challenging task.^^
2.1.2
The Monetarist Challenge
2.1.2.1
The Expectations-Augmented Phillips Curve
The monetarist challenge to the Keynesian consensus, which prevailed until the early 1970s, was based both on theoretical and empirical arguments (Blanchard 1990:785ff; Mankiw 1990:5). They showed that on theoretical grounds the traditional Phillips curve is misspecified and proposed instead the expectationsaugmented Phillips curve. Empirically, the monetarist position was substantiated by the experience of stagflation in the 1970s when the expectations-augmented Phillips curve empirically fared much better than its traditional counterpart. Beginning with the theoretical objections to the traditional Phillips curve, Milton Friedman, the "father" of monetarism, pointed out that unemployment is the difference between labor supply and demand. Moreover, according to standard economic theory, households and firms base their decisions on labor supply and demand on real wages and not on nominal wages (Espinosa-Vega and Russell 1997: 8ff; McCallum 1989: 181ff). It follows that instead of the nominal wage it should be the real wage that increases when there is excess demand for labor and falls when there is excess supply (McCallum 1989: 182). That is, the Phillips curve should be formulated in terms of real wages. If instead a relationship between the change in nominal wages and the unemployment rate is postulated, as the traditional Phillips curve does, this implicitly assumes that changes in current nominal wages are equivalent to changes in expected fixture real wages, taking into account the forward-looking nature of wage contracts.^"* Furthermore, Friedman notes that this assumption really encompasses two assumptions: First, price expectations need to be rigid in the sense that people do not expect the price level to change and, hence, a change in nominal wages corresponds to a change in real wages. Second, only if workers do not resist a reduction in their real wages through higher inflation is it possible to obtain a Phillips curve that is stable enough to offer policy makers a usable menu of options. Both assumptions are hard to justify. The first assumption exposes that Keynesian models have not paid very much attention to the process of expectations formation. The second assumption appears odd if one recalls that downward rigidity of nominal wages, which is a central element of Keynesian economics, rests on the assumption that ^^ An interesting discussion of the difficulties of demand management policies in reconciling the expectations of firms and trade unions is found in Sachverstandigenrat(1975:6). ^^ The following line of argument draws on Espinosa-Vega and Russell (1997: 8ff.).
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation workers resist reductions in their real wages. It is not obvious why they would be less opposed to a wage cut if it occurs through an increase in inflation. ^^ Modifying the Keynesian Phillips curve to account for agents forming expectations about future prices changes the short- and the long-run relationship between inflation and unemployment considerably.^^ The expectations-augmented Phillips curve is given by the following equation: (2.1)
Jw, =/(«,_! ) + 4Pf-'^
The change in current nominal wages, Awf, is still a function of recent rates of unemployment, f{uf^i), as postulated in the traditional Phillips curve, but, in addition, the change in nominal wages depends now on expected inflation, ^f. The sign of the short-run relationship between inflation and unemployment is the same as before, but the transmission mechanism differs: An increase in aggregate demand allows firms to increase their prices, which leads to a higher inflation rate. Friedman assumes that expectations are formed adaptively, Apf = 4P/-i» meaning that the increase in current inflation is not expected by workers, since they expect inflation to be equal to the inflation rate in the last period. ^^ The unexpected increase in inflation reduces the real wage received by workers, which increases labor demand by firms, thus employment rises and the unemployment rate falls. Consequently, there is a negative short-run relationship between inflation and unemployment, just as predicted by the traditional Phillips curve. But in the monetarist model the transmission runs from aggregate demand via unexpected inflation to the unemployment rate, while in Keynesian models the transmission runs from aggregate demand via the unemployment rate to nominal wages and inflation. That is, compared to its traditional counterpart, the expectations-augmented Phillips curve postulates exactly the opposite direction of causality. There is also a striking difference in the long-run properties of the traditional and the expectations-augmented Phillips curve: Whereas the former implies that there is a long-run trade-off between the rate of inflation and the unemployment rate, there is no such trade-off in the latter. This follows from the observation that in the long run, when the economy is in steady state, the rate of growth of the nominal wage is equal to Awf = Apf + A, where A depends on productivity ^^ However, Tobin (1993) points out that this behavior would be rational if workers did not care so much about their absolute wage but more about their wage relative to their co-workers. Thus, a worker might be unwilling to accept a nominal wage cut since he does not know for sure if his co-workers will do the same. An increase in inflation, in contrast, ensures that the real wages of all workers are affected in essentially the same way. ^^ The following section draws on McCallum (1989: 181ff.). 17 Small letters denote logarithms throughout the paper. See Taylor (2001: 125) for Friedman's position on expectation formation.
13
14
Chapter 2 Keynesian and Monetarist Views
growth in steady state. ^^ Inserting this condition into (2.1) yields the following steady state relation between inflation and unemployment: (2.2)
47 + /l = /(w) + 4 7 ^
In steady state, expected inflation is equal to actual inflation, /^^ = Ap, and the two terms drop out of (2.2), leaving us with (2.3)
A = /(«).
This expression shows that once the Phillips curve is augmented to account for expectations, the steady state unemployment rate is not related to the steady state inflation rate. Thus, in the long run there is no trade-off between inflation and unemployment anymore. Technically, this means that supemeutrality holds in monetarist models. This has far-reaching policy implications, which we will discuss in more detail below. The disappearance of the long-run trade-off is also called the accelerationist hypothesis (Espinosa-Vega 1998: 18). To illustrate this hypothesis we denote the steady state unemployment rate as u and specify /(w/_i) as w^_i. Moreover, we formulate the expectations-augmented Phillips curve as a relation governing the inflation process and introduce a supply side shock Esj, which proved important for modeling the inflation process in the 1970s when major oil price shocks hit the world economy. This yields (2.4a)
^t=
/^f -a{ut_i-u)^-8s^t^
with
a>0.
Assuming again adaptive expectations we obtain the following version of the expectations-augmented Phillips curve (see also Romer 1996: 412): (2.4b)
Apt = Apt-x - a{ut-x - w) + Ss^t •
With this formulation of the Phillips curve there is a trade-off between the change in inflation and the unemployment rate, but no permanent trade-off between the level of inflation and unemployment (Romer 1996: 229). To hold inflation steady at a given level, unemployment must be at its steady state level. At this level, any rate of inflation is sustainable. But if policy makers try to keep unemployment permanently below its steady state level, this leads to accelerating inflation. The vertical long-run Phillips curve has also implications for the observed relationship between inflation and unemployment. According to the traditional Phillips curve, there is a stable relationship between the two. As noted above, the traditional Phillips curve provides a good description of inflation and unemploy1^ This section draws on McCallum (1989: 182ff).
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation ment in the 1950s and 1960s, which confirms this claim. However, the expectations-augmented Phillips curve suggests that this relationship will break down if economic policy makers attempt to exploit the apparent trade-off between inflation and unemployment. Such an attempt will yield permanently higher inflation rates but will only have a transitory effect on the unemployment rate. The stagflation experience in the 1970s seemed to confirm this prediction (Mankiw 1990: 5). Thus, in contrast to the traditional Phillips curve models, the expectationsaugmented Phillips curve was able to account both for the stable relationship between inflation and the unemployment rate in the 1950s and 1960s, when movements in inflation tended to be short-lived and inflation expectations did not change much, and for the more turbulent 1970s, when this relationship disappeared (Romer 1996: 231). 2.1,2.2
The Natural Rate of Unemployment
The preceding discussion has shown that the expectations-augmented Phillips curve implies that there is a steady state unemployment rate that is independent of the steady state inflation rate. This steady state unemployment rate is also called the "natural rate of unemployment" (Friedman 1968: 8). The defining characteristic of the natural rate is that it is determined by real rather than by nominal forces. Even though it is possible for policy makers to drive the level of actual unemployment below the natural rate by creating a spell of unexpected inflation, they cannot keep unemployment indefinitely below the natural rate, meaning that money is supemeutral.-^^ The unemployment rate is at its natural level when the structure of real wage rates is in equilibrium and the corresponding rate of growth of real wages can be indefinitely maintained as long as capital formation, productivity increases etc. remain on their long-run trends (ibid.). If unemployment is below the natural rate, there is excess demand for labor and real wages tend to rise, whereas an unemployment rate above the natural rate indicates excess labor supply and real wages tend to fall. The similarity to the traditional Phillips curve is not coincidental, as Friedman points out. By reformulating the Phillips curve in terms of real wages he intends to overcome the basic defect of the traditional Phillips curve of not distinguishing between nominal and real wage rates (ibid.). Regarding the determination of the natural rate of unemployment, Friedman writes at the same place: "The 'natural rate of unemployment', in other words, is the level that would be ground out by the Walrasian system of general equilibrium equations, provided there is imbedded in them the actual structural characteristics of the labor and commodity markets, including market imperfections, stochastic vari^^ For a discussion of the natural rate hypothesis see also Romer (1996: 225ff.). Regarding the role of supemeutrality for the monetarist framework, see EspinosaVega(1998: 16).
15
16
Chapter 2 Keynesian and Monetarist Views
ability in demands and supplies, the cost of gathering information about job vacancies and labor availabilities, the costs of mobility, and so on." Friedman emphasizes that the term "natural" does not mean to suggest that the natural rate of unemployment cannot be changed. He points out that many of the market characteristics that determine it are man-made and policy-made. These factors include minimum wages, the strength of trade unions etc. (Friedman 1968: 9). 2,1.2.3
The Monetary Transmission Mechanism
We have noted in the discussion of the expectations-augmented Phillips curve that unexpected inflation has a central role in the transmission mechanism. This raises the question what the link between monetary policy and inflation in a monetarist model is. We have seen that in a Keynesian model this link is fairly indirect and runs from aggregate demand to unemployment and via the traditional Phillips curve to inflation. In the monetarist framework the quantity theory is used to postulate a direct link between money supply and prices, and hence between the rate of growth of the money supply and inflation. According to the quantity theory, the (log of) nominal income, >^/ + /?/, is determined by the (log of) the stock of money, /w^, and velocity, v^ '^^ (2.5)
yt-^Pt=rnt+Vt.
The quantity theory makes assumptions about the determination of money, velocity, and real output. Without these assumptions equation (2.5), which is also called the "quantity equation," is nothing but an accounting identity.^^ Monetarists transform the quantity equation into a theory by assuming that the central bank controls the money supply and, hence, the variable mt in (2.5). Moreover, they assume that there is a stable demand for real money balances, nif- Pf, which are thought to be a function of economic fundamentals such as real income, yf, the interest rate, and the nature of the technology for conducting transactions (Espinosa-Vega 1998: 16). From this follows that there is a stable function describing the path of velocity.^^ The assumption that the demand for real money balances depends on economic fundamentals implies that a change in the money supply engineered by the central bank has no long-run impact on real
21 22 2^
See Goodfriend and King (1997: 238). See also the discussion in Espinosa-Vega (1998: 16). Velocity is defined as Vf = yf - (mf - Pt) - If there is a stable relationship for real money balances of the form rn,- p^= P^y^+ P2^t^^md,t^ where Xf denotes variables capturing the influence of interest rates and transaction technologies on money demand and e^^ ^ denotes a stochastic money demand shock, then there is also a stable relationship for velocity of the form yt-{i^t~Pt) = {^~P\)yt -Pi^t-^md,,'
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation money balances or, more importantly, on velocity.^"^ In other words, the assumptions regarding the determinants of money demand and the stability of this relation have the effect to tie down velocity in (2.5). The quantity equation shows that with these assumptions any change in the money supply leads to an equiproportional change in nominal income. Since monetarists assume that real variables like unemployment or real output cannot be affected in the long run by nominal variables (natural rate hypothesis), this implies that in the long run there is a one-to-one relationship between the money supply and the price level, and between the rate of growth of the money supply and the rate of inflation. Due to the direct link between money and prices, money balances have a much more important role in the monetarist than in the Keynesian transmission mechanism, since the latter emphasize the role of monetary policy for credit availability and for long-term interest rates and deem these variables to be more important than money balances for consumption and investment decisions (Goodfriend and King 1997: 238). Since credit availability is only an issue when financial markets are imperfect and since monetarists in general are skeptical of claims of market failure, they do not assign much importance to this transmission channel. Regarding the role of long-term interest rates, monetarists regard most of the variations in long-term interest rates as reflecting inflation premia and consequently are skeptical of the role of interest rates in the transmission mechanism (Goodfriend and King 1997: 238ff). Moreover, since it was a major part of the monetarist research program to demonstrate the power of monetary policy to influence real activity in the short run, fiscal policy is superseded by monetary policy as the most potent device available to policy makers.^^ Since monetarists argue that inflation is determined by the growth rate of money supply, this suggests that the expectations-augmented Phillips curve given by (2.4a) is somewhat misleading with respect to the monetarist view on the sources of inflation, because it models inflation as a function of labor market conditions. The relation given by (2.4a) is much more compatible with the Keynesian view of the Phillips curve as the link between aggregate demand conditions and inflation than it is with the quantity theory. To account for the fact that in the monetarist framework causality runs from unexpected inflation to the
^^ This does not hold exactly: Monetarists stress that nominal interest rates reflect to a large extent inflation premia. Since nominal interest rates affect money demand, inflation does so too. Noting that inflation is a monetary phenomenon in the monetarist framework, it follows that a change in the rate of growth of money supply has a long-run effect on the demand for real money balances and on velocity. However, monetarists assume that this effect is quantitatively small. 25 The seminal work demonstrating the power of monetary policy is Friedman and Schwartz (1963). Regarding the importance of monetary policy relative to fiscal policy in the monetarist framework see Goodfriend and King (1997: 239; De Long 2000: 91).
17
18
Chapter 2 Keynesian and Monetarist Views
labor market and not into the other direction as in Keynesian models, it is useful to rewrite the expectations-augmented Phillips curve as follows :^^ (2.6)
Ut=u- (fi{Apf - ^f)
+ Es^t, with (Z) > 0,
where the parameter 0 denotes the sensitivity of unemployment to unexpected inflation, 4P/ ~ 4pf • We will see below that the expectations-augmented Phillips curve given by (2.4a) represents a typical modem Keynesian formulation of aggregate supply, while the expectations-augmented Phillips curve given by (2.6) represents the monetarist view on the relationship between inflation and unemployment.^^ 2.1.2.4
The Case Against Aggregate Demand Management Policies
In the monetarist framework there are essentially two objections against an activist policy of aggregate demand management. First, in contrast to the Keynesian framework the gains of such a policy are small, because it is not desirable in the first place to attempt to increase the average level of output, which is the objective of Keynesian demand management. Second, even if this were desirable, monetarists argue that demand policy could not achieve this objective. The first objection follows from the natural rate hypothesis of unemployment, which implies that there is also a natural rate of output. In contrast to the Keynesian view of business cycles, output is assumed to fluctuate in a symmetric fashion around the natural rate of output. This is illustrated in Figure 2.3. A comparison of Figure 2.3 with Figure 2.2 shows that monetarists take a fiindamentally different position on business cycle fluctuations than Keynesian economists. Whereas the latter consider economic booms to be welfare-enhancing, because they help to bring real activity closer to its efficient level, monetarists see booms and recessions as equally welfare-reducing. In other words, the monetarist view implies that the average level of output over a fixU business cycle is also the efficient level of output, while Keynesians believe that without activist demand management policies the average level of output will be inefficiently low. These fiindamental differences regarding the efficiency of the average level of output are a reflection of different assumptions regarding the flexibility of prices, the prevalence of monopoly power, and the causes of involuntary unemployment. Beginning with the controversy about the flexibility of prices, we have noted in Section 2.1.1.1 that Keynesians are distrustful of the ability of wages and prices to adjust sufficiently to clear labor and product markets. Monetarists, in contrast, ^" See also the discussion of the classical and the Keynesian Phillips curve in Sargent and Soderstrom (2000: 41) and the discussion in King and Watson (1994: lOff). ^' For a discussion of the role of the expectations-augmented Phillips curve in New Keynesian models see Roberts (1995).
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation
19
Figure 23: Business Cycle Fluctuations: The Monetarist View Output and potential output
Time
believe that prices are flexible enough to ensure that markets clear rapidly (Burda and Wyplosz 1997: 412). These differences are also apparent in the monetary transmission mechanism, since nominal wage and/or price rigidities play a central role in the Keynesian transmission mechanism of nominal impulses, but not in the monetarist transmission mechanism, where expectation errors are central. The downward rigidity of nominal wages is a particular important assumption in Keynesian models. This assumption is disputed by monetarists. Even though the latter are prepared to concede that institutional aspects like minimum wages may account for some nominal wage rigidity, situations like these are thought to represent the exception rather than the rule (Espinosa-Vega and Russell 1997: 8). Since most workers earn more than the minimum wage, monetarists argue that nothing prevents them from accepting a pay cut to avoid layoffs. And even though unions may be willing to delay a pay cut, because this would benefit unemployed workers at union members' expense, Friedman finds it doubtful whether unions are strong enough or perverse enough to keep wages from adjusting to full employment in the long run (ibid.). In sum, in contrast to Keynesians the monetarists believe that any deficiency of demand can persist only for short periods of time, because in such a situation firms reduce their prices, thereby increasing the real value of money balances and building up demand for their products.^^ 28
For a discussion of the role of the real balance effect in neoclassical theories see Jarchow (1998: 180ff). For a discussion of the Keynesian skepticism of the real
20
Chapter 2 Keynesian and Monetarist Views
Another argument put forward by Keynesians to justify their presumption that the average level of output is inefficiently low is the alleged pervasiveness of monopoly power. Monetarists disagree and prefer the assumption of perfect competition, which was also common in classical economics. As regards the argument that persistent involuntary unemployment indicates that there is slack in the economy, monetarists concede that there is involuntary unemployment, but they argue that this is the result of institutional characteristics of the labor market like minimum wage regulations. In other words, persistent involuntary unemployment is the result of a high natural rate. Since monetary policy cannot reduce unemployment below the natural rate permanently, it is an unsuitable tool to remedy the situation. The limits of demand management policies in monetarist models are vividly illustrated by De Long and Summers (1988). Their starting point is the observation that the essence of the natural rate view is contained in the stylized Phillips curve given by the following equation:^^ (2.7)
Apt = Apf.i - a{yt.i - y).
De Long and Summers proceed by summing the relation (2.7) over time and rearranging, thereby obtaining (De Long and Summers 1988: 439)
(2.8)
T
aT
It is apparent from (2.8) that a macroeconomic policy that does not change the rate of inflation over time, ^j = 4po > cannot affect the average level of output over that period, X ]=\{yt ~y) = ^' This, in turn, shows that the average level of output is pinned down by its natural level, y, if inflation is kept constant over time. In other words, if macroeconomic policy causes a boom in period t it has to cause a recession of similar proportions in the next period to return inflation to its desired level. Otherwise inflation stays indefinitely above this level. De Long and Summers conclude that the natural rate view implies that macroeconomic policies can do no first-order net good or harm on the output side without permanently raising or lowering the inflation rate. De Long and Summers (1988: 440) write: "Why, then, should anyone care about cyclical unemployment? Excess unemployment incurred today because of policy 'mistakes' allows a larger balance effect see Tobin (1993: 59ff.). This issue is also discussed in detail in Chapter 4. ^^ See De Long and Summers (1988: 438). Note that the relation given by (2.7) is closely related to the expectations-augmented Phillips curve given by (2.4b). The only differences are that in (2.7) the supply shock is omitted and the deviation of unemployment from the natural rate is replaced with the deviation of output from its natural level, yt-y -
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation
21
boom tomorrow. The business cycle produces welfare losses only because consumption is not efficiently smoothed across years." This implication of the natural rate view stands in stark contrast to the Keynesian view of business cycle, where demand management policies can have first-order effects on output without permanently affecting the inflation rate, because in Keynesian models inflation is pinned down by labor market conditions. Put another way, in both the monetarist and the Keynesian framework a boom in economic activity goes along with falling unemployment and increasing inflation. In Keynesian models inflation declines again when unemployment rate returns to its equilibrium level after the boom has passed, because the looser labor market conditions exert downward pressure on the inflation rate, while in monetarist models inflation remains high in spite of the increase in unemployment. In the latter type of model it takes a recession which pushes unemployment above its natural level to reduce inflation again. 2.1,2.5
The Monetarist Policy Assignment
In the monetarist framework the best monetary policy can hope to accomplish is to reduce volatility of output fluctuations. But monetarists fear that any attempt at fine-tuning the economy carries also the risk of destabilizing the economy, since the uncertain strength and lags of policy instruments prevent policy makers fl*om knowing exactly what the effects of a given monetary policy action are going to be (De Long 2000: 88). Friedman (1968: 15) writes in this regard: "As a result, we cannot predict at all accurately just what effect a particular monetary action will have on the price level and, equally important, just when it will have this effect." Monetarists attribute the variability in the effects of monetary policy actions to differences in the degree to which policy actions are expected, because expectations determine the degree to which people adjust prices and wages to neutralize the real effects of an injection of money (Goodfriend and King 1997: 239). Since monetarists believe that the risks of an activist monetary policy outweigh the benefits of reducing the volatility of output fluctuations, they recommend that policy should not try to offset minor disturbances to the economy (Friedman 1968: 14). Instead monetary policy should try to prevent monetary policy from becoming itself a source of economic disturbances and aim to provide a stable background for the economy by acting in a predictable way, thereby ensuring that the average level of prices will behave in a known way in the future (Friedman 1968: 13). In other words, monetarists argue that reducing uncertainty regarding the fixture price level should be the overriding objective of the central bank. The best way to achieve this is to avoid discretionary policy and to conduct monetary policy on the basis of fixed policy rules. The most famous rule in this regard is the A:%-rule suggested by Friedman (1968: 16), in which the
22
Chapter 2 Keynesian and Monetarist Views
quantity of money grows at a constant rate sufficient to accommodate trend productivity growth. In contrast to the Keynesian poHcy assignment, where demand management policies have a central role in sustaining full employment, monetary policy has no such task in the monetarist policy assignment. If a persistent increase in the unemployment rate occurs, monetarists attribute this to an increase in the natural rate of unemployment. For a discussion of the monetarist view of the causes of unemployment it is useful to decompose the natural rate of unemployment into two components: The first component consists of the minimum level of frictional and of structural unemployment which cannot be avoided in a dynamic economy. The second component is comprised of the amount of involuntary unemployment, which is attributable to the failure of real wages to clear the labor market. The unavoidable frictional unemployment is related to the process of job creation and destruction, which occurs in any dynamic economy (Burda and Wyplosz 1997: 153ff.). The resulting search process of firms and workers takes some time because of imperfect information on the part of firms seeking workers and of workers who are seeking jobs. The extent of frictional unemployment is closely related to the institutions of the labor market, which determine the efficiency of the matching process and the number of job separations and vacancies. The unavoidable structural unemployment is related to structural change in the economy, which leads to the disappearance of jobs in some sectors and to new jobs in others. Structural unemployment exists because displaced workers often do not have the skills required in the newly available jobs. This means displaced workers will either have to accept a wage cut to maintain their previous job or they will have to invest into new skills. This adjustment process is likely to take some time so that a minimum of structural unemployment cannot be avoided in an economy that is constantly changing. More problematic from the viewpoint of economic policy is the amount of involuntary unemployment, which exists because real wages are too high to equate labor supply and demand. The failure of real wages to adjust sufficiently to clear the labor market may be the result of the monopolistic behavior of trade unions, high minimum wages, generous unemployment benefits or other distortions in the labor market. For the 1970s monetarists often cite excessive wage aspirations of trade unions in the early 1970s, the demand of unions to be compensated for high oil prices following the two oil price shocks, and their failure to adjust to the productivity slowdown that began in the middle of the decade as reasons why real wages became too high and led to an increase in the natural rate of unemployment in Germany in the 1970s and early 1980s.^^ Consequently they ^^ See the discussion of different approaches towards a supply-side explanation of the increase in unemployment in Europe in Bean (1994: 587ff.). A concise theoretical analysis of the role of these supply side factors for high unemployment in Europe is also contained in Sachs (1986). Siebert (1998) discusses supply side factors con-
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation conclude that the obvious remedy to high unemployment is a slowdown in the growth rate of real wages. That is, since monetarists see the German unemployment problem as being foremost a natural rate problem, they argue that a reduction in the natural rate is a task that trade unions have to accomplish and not monetary policy makers.
2.1.3
The Keynesian Response to the Monetarist Revolution: The NAIRU
The stagflation period following the first oil price shock represented a major problem for the traditional Phillips curve. The simultaneous increase in inflation and unemployment during most of the 1970s led to a distinctively positive correlation between inflation and unemployment, which contradicted the prediction of the traditional Phillips curve of a negative long-run correlation between the two variables (Gordon 1997: 13). The experience of the 1970s led Lucas and Sargent (1978) to their famous quip that the traditional Phillips curve was an "econometric failure on a grand scale." One source of the breakdown of the traditional Phillips curve was its failure to account for the effects of aggregate supply shocks on inflation and unemployment.^^ Since an adverse supply shock like an increase in oil prices leads even in Keynesian models to a positive correlation between inflation and unemployment, the oil price shocks in 1973 and 1979 are liable to account for some of the failings of the Phillips curve. But there was also a more fundamental problem: The secular rise in inflation coincided with the attempt of policy makers to stem the increase in unemployment with expansionary demand management policies (see also Espinosa-Vega and Russell 1997: 11). The warnings of monetarists that the Phillips curve will break down when policy makers try to exploit the alleged trade-off between inflation and unemployment were proved correct by the acceleration in inflation occurring during the 1970s. The dismal results of the attempt to "ride the Phillips curve" strengthened the credibility of the monetarist position greatly. In Lucas (1981: 560) words, "We got the high-inflation decade, and with it as clear-cut an experimental discrimination as macroeconomics is ever likely to see, and Friedman and Phelps were right." To rescue the Keynesian position, the traditional Phillips curve had to be adapted. This led to the NAIRU concept, which extended the Keynesian view of the inflation process and equilibrium unemployment in several ways. First, the NAIRU concept recognizes the importance of inflation expectations in the inflation process and augments the traditional downward sloping Phillips curve tributing in Germany to high unemployment. See also Paque (1999) for a discussion of causes of structural unemployment in Germany. ^^ See also the discussion in Romer (1996: 226).
23
24
Chapter 2 Keynesian and Monetarist Views
with a vertical Phillips curve. Second, the NAIRU can be estimated using the socalled triangle model of inflation, where inflation is determined by inertia and demand and supply conditions. Thus, the underlying inflation model is now considerably richer in its specification than was the traditional Phillips curve model of inflation. Third, the NAIRU concept allows for changes over time in the equilibrium rate of unemployment. 2.1,3.1
Augmenting Keynesian Inflation Models with a Vertical Phillips Curve
The NAIRU, standing for A^on-^ccelerating /nflation T^ate of t/nemployment, is defined as the unemployment rate consistent with an unchanging inflation rate. When the unemployment rate is below the NAIRU, there is pressure for the inflation rate to increase; on the other hand, when the unemployment rate is above the NAIRU, there is pressure for the inflation rate to fall (Stiglitz 1997: 3). When the unemployment rate is at the NAIRU, the inflation rate remains constant. Importantly, the NAIRU is consistent with any inflation rate, since it demands only that the inflation rate does not change but does not deflne any specific level for the inflation rate. That is, at the NAIRU the Phillips curve is vertical. From this follows that NAIRU is the unemployment rate at which the Keynesians' downward-sloping Phillips curve intersects the monetarists' vertical Phillips curve. Since the position of the vertical Phillips curve determines in the monetarist framework the natural rate of unemployment, it follows that numerically the NAIRU is identical with the natural rate. This is shown in Figure 2.4.^^ Adding a vertical Phillips curve to the traditional downward-sloping curve meant that Keynesians accepted the monetarist argument that the Phillips curve needs to be augmented to capture the process of expectation formation. Thus, Keynesians adopted the expectations-augmented Phillips curve given by (2.4a) as their inflation model. This implies in particular that Keynesians accepted the monetarist acceleration hypothesis that any attempt to push the unemployment rate below the NAIRU / natural rate will lead to accelerating inflation. It is tempting to use the terms NAIRU and the natural rate interchangeably, because they are numerically identical, but this risks blurring the substantial differences between the two concepts that remain.^^ Both concepts differ in particular with respect to their implications for stabilization policy. Monetarists intended to demonstrate with the expectations-augmented Phillips the ineffectiveness of aggregate demand management policies. However, even though Keynesians integrated the expectations-augmented Phillips curve into their framework, they did not buy this part of the monetarist argument. In fact, the monetarist position regarding the futileness of demand management policies is based on a number of ^^ Figure 2.4 is reproduced from Espinosa-Vega and Russell (1997: 12, Chart 3). •^^ Stiglitz (1997: 3), for example, uses the term natural rate as synonym for NAIRU.
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation
25
Figure 2.4: TheNAIRU Inflation rate
Natural rate
Unemployment rate
assumptions; besides the acceleration hypothesis it is in particular the assumption that prices are flexible enough to clear labor and goods markets which matters in this regard. Keynesians continued to disagree with the latter assumption and maintained their position that nominal rigidities matter and that consequently involuntary unemployment due to lack of demand can persist for a considerable length of time. Thus, acceptance of the expectations-augmented Phillips curve did not invalidate the Keynesian rationale for stabilization policy. Modigliani and Papdemos, who in 1975 originally proposed the NAIRU concept, interpret the NAIRU as a constraint of policy makers to exploit a trade-off that remained both available and helpful in the short run.^"^ In terms of Figure 2.4, this means that Modigliani and Papdemos assert that the economy spends most of the time in a range of unemployment rates well to the right of the NAIRU, implying that on average the economy is at a suboptimal low level of economic activity. Since the Phillips curve is fairly flat in this range, there is a considerable trade-off between inflation and unemployment. Hence, there is scope for monetary policy to raise the average level of economic activity by trying to moving the actual unemployment rate closer to the NAIRU, which can be done without triggering large inflation responses. Only if policy makers try to push the unemployment rate below 34
See the discussion in Espinosa-Vega and Russell (1997: 1 Iff.).
26
Chapter 2 Keynesian and Monetarist Views
the NAIRU, would the problem of accelerating inflation arise, because the shortrun Phillips curve is fairly steep in this range. Thus, seen from this point of view the adoption of the natural rate in form of the NAIRU by Keynesian economists did not represent much of a concession to the monetarist position. However, even though the NAIRU continues to be an important part of New Keynesian models, which summarizes the Keynesian research program of the 1980s and 1990s, it should be noted that the modem brand of Keynesian economics resulting from this research program is considerably more skeptical about the benefits of stabilization policy than Modigliani and Papdemos were when they proposed the NAIRU concept. The traditional Keynesian endorsement of demand management policies is based on the assumptions that the short-run Phillips curve has a convex shape and that nominal rigidities are strong enough to prevent a clearing of goods and labor markets for long periods of time. In New Keynesian models, on the other hand, the Phillips curve is typically assumed to be linear. Hence, the unemployment rate fluctuates in a symmetric fashion around the NAIRU. Since this means that New Keynesian models have adopted a key element of monetarist models, it follows that regarding the benefits of stabilization policy these models are closer to the monetarist position than to the traditional Keynesian position.^^ 2,1.3.2
The Triangle Model of Inflation
The NAIRU model is like its predecessor, the traditional Phillips curve, in the first place an inflation model. Since modeling inflation means modeling the pricesetting behavior of firms, it represents also the Keynesian view on the determination of aggregate supply. The events of the 1970s showed that the traditional Phillips curve was inadequate as an inflation model. It has been replaced in Keynesian economics by the triangle model of inflation, which has been developed by Gordon in the second half of the 1970s and continues up to the present to be widely used for the modeling of inflation and the estimation of the NAIRU.^^ The label "triangle" is meant to summarize the dependence of inflation on three basic determinants: inertia, demand, and supply (Gordon 1997: 14). The most general specification of the triangle model is^^ (2.9)
Apt = a{L)Ap,.^ + Z>(L) A + c{L)z, + e^,
^^ This is why these models could also be called "New monetarist." We return to this issue in Chapter 4. •^" This section draws on Gordon (1997). For a review of the "history" of the triangle model, see Gordon (1997: 18ff.). This model has recently been employed, for example, by the OECD to estimate the NAIRU for several OECD countries. See OECD(2000: 155ff.). ^^ See Gordon (1997: 14). The lag polynomial a{L), for example, denotes a{L) = ao + axL + a2l? +.... + a„L".
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation
27
where the term a{L)Apt-\ models the inertia in inflation, D^ is an index of excess demand (normalized so that A = 0 indicates the absence of excess demand), Zf is a vector of supply shock variables (z^ = 0 indicates the absence of supply shocks), and Ct is a serially uncorrelated error term. The sum of the coefficients in the lag polynomial a{L) is typically constrained to one, because only in this case there is a "natural" rate of the demand variable Df consistent with a constant rate of inflation. The intuition behind this constraint can be clarified by considering the simple case of only one lag of inflation, a^Apt-\, and by modeling Df as the deviation of the actual unemployment rate from its natural rate, Uf-u . Restricting ao to one and omitting the supply shocks yields in this case Ap^ = Apt^x -^bQ{uf - w ) + e^, with Z^o < 0. Thus, this constraint yields the expectations-augmented Phillips curve given by (2.4b). In particular, it ensures that the inflation model conforms to the acceleration hypothesis. Another noteworthy aspect of (2.9) is that it does not include a nominal wage variable.^^ This formulation is not meant to deny that wage costs play an important role in the price-setting decision behavior of firms, but is a reflection of an empirical finding by Gordon. He stated that a specification like the one given in (2.9), which treats wages only implicitly, performs better than models with separate wage growth and price markup equations (Gordon 1997: 17). The role of the lag polynomial a{L) is to model the inertia in inflation. This inertia can be due to nominal rigidity, arising for example through multi-period nominal contracts, or to lags in the expectation formation. The triangle model is compatible with adaptive expectations or with rational expectations, which are often employed in New Keynesian models.^^ Gordon interprets the lag polynomial a{L) as capturing the influences of both the speed of price adjustment and the speed of expectation formation on the dynamics of inflation without separating between the two."^^ The variable D^ in (2.9), which models the inflationary pressures arising from excess demand in the economy, usually includes the output gap, yt-y, the unemployment gap, Uf-u, or the capacity utilization rate. The causation in the triangle model runs from the unemployment gap and the other demand variables to inflation, and not into the other direction as in the monetarist framework. This means that this model is resolutely Keynesian, as Gordon (1997: 18) emphasizes. The ultimate source of excess demand is "excess nominal GDP growth," which Gordon (1997: 15) defines as the extent to which growth of nominal GDP exceeds the growth of potential output. This implies that growth in the money supply is not a unique cause of inflation. Gordon (1997: 18) writes in this 38
For a model with a wage variable as an additional determining variable, see Franz (2000: 3ff.). The New Keynesian model is reviewed in detail below. ^^ See the discussion in Gordon (1997: 16ff).
28
Chapter 2 Keynesian and Monetarist Views
context: "In a literal sense, the triangle model predicts inflation without using information on the money stock. In an economic sense, this implies that any long-term effect of money growth on inflation operates through channels that are captured by the real excess demand variables." Put another way, the quantity equation given by (2.5) of course also holds in the Keynesian framework, because it is an accounting identity. But the quantity theory does not need to hold. In terms of (2.5) this implies that in the Keynesian framework a change in the money stock (or velocity) affects first real output and then prices.^^ The supply shocks in (2.9) are included, because these shocks can cause a positive correlation between inflation and unemployment. Their inclusion ensures that the triangle model is consistent with the positive correlation between the two variables in the 1970s, due to the explicit treatment of supply shocks such as the rise and eventual fall of oil prices (Gordon 1997: 17). 2.1,3.3
Estimating a Time-Varying NAIRUfor Germany and the USA
A model like (2.9) can be used to estimate the NAIRU. To this end we rewrite (2.9) as42 (2.11)
Apt= a{L)Apt.x + b(L){uf -u)-\-c(L)zt
+ e^,
where u represents the natural rate of unemployment. First, we derive from (2.11) the so-called no-shock NAIRU. That is, we are assuming that there are no supply shocks, i.e., Zf = 0 , and no stochastic disturbance, i.e., e^ =0. With this assumption we can rearrange (2.11) to obtain (2.12a)
Apf =a{L)Apf_i -\-b{L)ut -{b^u-\-bxu-\-...-\-bku), or
(2.12b) Apt = a{L)Apt.x + b{L)ut - d, with d = b{\)u .^^ The NAIRU is defined as the unemployment rate consistent with a stable inflation rate, that is, Ap^ - Apf^i =... = Apf.„. Inserting this condition into (2.12b) and solving for the unemployment rate that is consistent with this scenario yields the no-shock NAIRU estimate:^"^ (2.13)
u^^=d/b{l).
^^ In the monetarist framework, in contrast, velocity is assumed to be constant so that changes in the money supply are the only source of changes in the price level. Moreover, a monetary impulse affects directly the price level, and any real effects are the consequence of unexpected changes in the price level. ^^ The following discussion draws on Franz (2000: 5ff). ^^ The term b{l) denotes the sum of the parameters in the lag polynomial b{L). We assume again a{l) = l. 44 Recall that the sum of the lag polynomial a{L) has been constrained to one.
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation Since J = 6(l)w, it follows from (2.13) that the no-shock NAIRU u^^ is identical with the natural rate u . If there are supply shocks, however, the NAIRU and the natural rate do not coincide anymore. With z^ ?t 0, we obtain instead the NAIRU estimate (2.14)
w^^^^^ = ( J + c(L)z,)/6(l).
This shows that if policy makers wish to keep the inflation rate constant when an adverse supply shock like an oil price shock occurs they have to tighten demand conditions in order to increase the unemployment rate, because the NAIRU has increased in this scenario too. That is, the NAIRU estimated in this way is a short-run concept, indicating which unemployment rate in a given year and based on the actual history of unemployment would be associated with a constant rate of inflation (Elmeskov 1998: 31). It follows that in the discussion of the NAIRU it is often usefiil to distinguish between the NAIRU that is obtained after the effects of supply shocks have passed through the economy (the no-shock NAIRU) and the NAIRU that is consistent with stabilizing the inflation rate at its current level in the next period (the short-run NAIRU).^^ Up to now we have assumed that the NAIRU is constant in time. However, the unemployment experience in the past 30 years in Germany suggests that the NAIRU has moved upwards over time. To identify the time-varying NAIRU, we need to specify the stochastic process for this variable."*^ In the following estimation of the NAIRU for Germany and the USA we employ the Elmeskov method which is based on the identifying assumption that the NAIRU is constant between two consecutive periods.^'^ The starting point of the Elmeskov method is a slightly modified version of the expectations-augmented Phillips curve given by (2.4b):
(2.15)
A^pt=-aXut-uf^^^^^).
This model does not control for the effects of supply shocks on inflation and unemployment, which implies that the resulting NAIRU corresponds to the unemployment rate consistent with stabilizing inflation at its current level, regardless of its cause. For example, if inflation is high due to an adverse supply shock hitting the economy, we estimate the unemployment rate that is consistent with stabilizing inflation at this high level. That is, we estimate the short-run NAIRU. ^^ See also the discussion of these NAIRU concepts in the report of the OECD (2000: 157). The OECD calls the no-shock NAIRU the long-term equilibrium unemployment rate and the NAIRU which is consistent with stabilizing inflation at its current level the short-term NAIRU. See Franz (2000: 6ff) for an extensive discussion of this issue. ^'7 See Elmeskov (1993: 94), Elmeskov and MacFarlan (1993: 85), and the discussion of his method in Fabiani and Mestre (2000: 14ff).
29
30
Chapter 2 Keynesian and Monetarist Views
It is noteworthy that the parameter a^ can change in time, which means that the Elmeskov method is not based on the a priori assumption of a stable systematic relationship between inflation and the unemployment gap. If the parameter Uf were known, the NAIRU could be constructed based on observed data for the rate of inflation and the unemployment rate. We can obtain an estimate of a^ by assuming that the NAIRU does not change between two consecutive periods. Differencing (2.15) and using this assumption yields (2.16)
at=-A^PtlAut.
Substituting this resuh into (2.15), an estimate of the NAIRU in any time period can be calculated as (2.17)
w/^^^^^ = w, - {AU I A^pt) A^pt.
Since the parameter a^ is computed as a fraction where the denominator might be close to zero, the resulting estimate can be highly volatile, leading also to a considerable volatility in the NAIRU estimate itself ^^ To overcome this problem, we follow Elmeskov's suggestion and use a Hodrick-Prescott filter with a smoothing factor of 25 to filter the raw data. The Elmeskov method can be applied to a model like (2.15) with consumer prices as the price variable, yielding the NAIRU, or with a nominal wage variable instead of prices, yielding the M)n-y4ccelerating l^age i^ate of L^nemployment (NAWRU) (Elmeskov and MacFarlan 1993: 85). Alternatively the capacity utilization rate can be used instead of price or wage inflation (Elmeskov 1993: 95ff.). Elmeskov denotes the resulting estimate of the unemployment rate consistent with a stable capacity utilization rate as the Okun curve indicator. The resulting estimates for these three measures for West Germany and the USA are displayed in Figures 2.5 and 2.6."*^
^^ See also the discussion in Fabiani and Mestre (2000: 15). ^^ The consumer price series and the unemployment rate for Germany have been obtained from the Bundesbank. The respective Datastream codes are BDUUOIFAA and WGUS0106Q. The wage series has been constructed using data from the Sachverstandigenrat (Council of Economic Experts in Germany) on wage income and the labor force. The time series on capacity utilization is based on the regular ifo Institute survey on capacity utilization in the manufacturing sector (Datastream code: BDIFOCAPE). The U.S. unemployment rate has been obtained from the U.S. Department of Labor (Datastream code: USUNRATEE). The consumer price series (Datastream code: USCP....F) and the wage series (compensation per hour in the business sector; FRED database) have been published by the U.S. Bureau of Labor Statistics. The capacity utilization series is available from the Federal Reserve Bank (Datastream code: USOPERATE).
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation Figure 2.5: Indicators of Trend Unemployment in Germany NAIRU indicator
NAWRU indicator Unemployment rate, percent
Unemployment rate, percent
10-1
u -
3y^
9 ^
•§7^
83 ^ 8 5 8-
^^^^ 6-
Tl"^\
4-
7a
2-
0-
1
-
1
2
-
1
1
0
1
3
1
-
6
-
Change in inflation
Okun curve
\
2
4
NAWRU indicator
8 5 ^>95
^^>v§9
\
\ ,
6-
0
10-
D-
< K\ 93
2
Percent
u -
^V
-
Unemployment and trends
Unemployment rate, percent
8-
4
Year-to-year change in wage inflation
\ 6i 91
4-
^^«S5;^^ 7 7 \
NAIRU Indicator
^79 267^^=v^-^
\ 7 3 65
085
Okun curve
90
95
100
Index of capacity use
105
^69 110
Unemployment rate -i
1
1—
_,
,
,
,
,
p.
65 68 71 74 77 80 83 86 89 92 95 98
31
32
Chapter 2 Keynesian and Monetarist Views
Figure 2.6: Indicators of Trend Unemployment in the USA NAIRU indicator Unemployment rate, percent 10
NAWRU indicator Unemployment rate, percent 10
Iv—^^
1 ^2is ^K 7lX
J
\
^ ? ^
65
98
H
1—
-4
-2 0 2 Change in inflation
1
1—
-
4
-
2
0
2
4
Year-to-year change in wage inflation
Okun curve
Unemployment and trends
Unemployment rate, percent
Percent 10
10-
Unemployment/ rate / " rl \ / V \
lA
/\\A
A .V/ \v1 /1
J
/ !•* ^
NAIRU indicator
\/
\ / \ \ V^^ \ V*.
V \ \
V*'
\ Okun curve
V
IVA
V/NAWRU
indicator •\
90
95 100 105 Index of capacity use
110
1
1
1
1 ——T
1
1
1
1
1
65 68 71 74 77 80 83 86 89 92 95 98
2.1 Keynesian and Monetarist Explanations of Unemployment and Inflation Even though the indicators differ somewhat, they agree in both countries on the respective underlying trends of the NAIRU. The NAIRU increased considerably in both West Germany and the USA throughout the 1970s and reached its peak in the early 1980s. Since the middle of the 1980s the divergence in the labor market performance in the two countries is striking: In West Germany the NAIRU declined in the following fifteen years only marginally from its peak in the early 1980s, whereas in the USA the NAIRU returned in this time period to the low levels it had in the 1960s. The explanation of the superior performance of the American labor market plays an important role for the controversy on the German unemployment problem, since both Keynesians and monetarists cite the USA as an example of what their policies could achieve. The former argue that the reduction in unemployment in the USA is due to a commitment of the Federal Reserve Bank to maintain fiill employment by stimulating demand, while monetarists attribute this success to the flexibility of the American labor market, leading to a low natural rate of unemployment. However, since, as pointed out by Modigliani and Papdemos, the NAIRU represents a constraint on the ability of policy makers to exploit any trade-off between unemployment and inflation, the fact that most of the increase in the German unemployment rate reflects an increase in the NAIRU suggests that more expansionary policies of the Bundesbank would not have led to a markedly lower unemployment rate in the long run. In fact, this finding foreshadows the results from other empirical investigations in this study where we also find that the bulk of the increase in the German unemployment rate is not due to tight demand conditions. Nevertheless, it should be noted that the NAIRU estimates show that demand-induced unemployment has been significant at times. Also, it is possible that part of the estimated increase in the NAIRU is in fact due to demand conditions. The identifying assumption that the NAIRU is constant between two consecutive periods together with the use of the Hodrick-Prescott for smoothing out fluctuations implies that our NAIRU estimators attempt to isolate the trend component of the unemployment rate. If tight demand conditions lead to a permanent increase in the unemployment rate, this would show up in our estimates as an increase in the NAIRU. 2.1.3.4
The NAIRU in Practice
The NAIRU concept is very popular in applied business cycle research. This is borne out by the observation that it pervades current policy discussions, particular so in the USA, and that economists in institutions like the OECD and the ECB regularly concern themselves with the estimation of the NAIRU.^^ A major factor in this regard is the empirical success of NAIRU models to account for in^^ See for example OECD (2000) and Fabiani and Mestre (2000).
33
34
Chapter 2 Keynesian and Monetarist Views
flation dynamics.^ ^ Stock and Watson (1999), for example, investigate the forecasting power of various leading indicators for U.S. inflation and find that excess demand variables perform well in this regard. Stock and Watson (1999: 23) conclude: "The conventionally specified Phillips curve, based on the unemployment rate, was found to perform reasonably well. Its forecasts are better than univariate forecasting models (both autoregressions and random walks), which in many situations have proven to be surprisingly strong benchmarks. Moreover, with few exceptions, incorporating other variables does not significantly improve upon its short-run forecasts. ... The few forecasts that do consistently improve upon unemployment rate Phillips curve forecasts are in fact from alternative Phillips curves, specified using other measures of aggregate activity instead of the unemployment rate." Altimari (2001) investigates leading indicators for inflation in the euro area and finds that money-based indicators usually work best, particularly so for long forecast horizons, but Phillips curve models perform well, too. She writes on page 22: "When evaluated over the 1995-2000 period, the simple Phillips curve's performance is very close to the best money-based models. Over the most recent 1998-2000 period this model produces the smallest forecast errors of all models." However, the finding that excess demand variables like the unemployment gap are reasonable good leading indicators for inflation does not mean that the NAIRU automatically should be assigned an important role in the policy making process. After all, the deviation of unemployment from the NAIRU accounts only for some part of the inflation variability. Stiglitz (1997: 5) writes in this regard: "... our analysis indicates that at least 20 percent of the variation in the inflation rate can be explained by unemployment alone. This figure serves as a reminder that the actual inflation process—and the policy decisions that must be based on it—is much more complicated than the simple link between the NAIRU and inflation." Moreover, NAIRU estimates usually are very imprecise, which limits the usefulness of this variable to guide policy decisions.^^ Nevertheless, the empirical success of the NAIRU concept and the fact that this concept is "resolutely Keynesian" mean that Keynesian economics have made a remarkable comeback from near obliteration.
^ ^ For a recent application of the NAIRU concept to German data see Franz (2000). ^^ The seminal paper in this regard is Staiger et al. (1996).
2.2 The Long-Run Phillips Curve
2.2
35
The Long-Run Phillips Curve and the Source of Business Cycle Fluctuations in Germany
This section uses empirical evidence on the Phillips curve in West Germany to investigate the supemeutrality proposition and to illustrate the differences between the Keynesian and the monetarist positions regarding the source of business cycle fluctuations. To this end we show first that the negative correlation between inflation and unemployment postulated by Keynesian models never disappeared at the business cycle frequency. Thus, despite the criticism of the Phillips curve as an "econometric failure on a grand scale" (Lucas and Sargent 1978) the relation between inflation and unemployment remained even in the 1970s a useful tool to investigate business cycles. Second, to estimate the Phillips curve, this section employs a technique introduced by King and Watson (1994). These authors show that theoretical Keynesian and monetarist macroeconomic models yield identifying restrictions which can be used to estimate empirical models of the Phillips curve reflecting the respective theoretical viewpoints of Keynesian and monetarist models. The empirical analysis proceeds within the framework of structural vector autoregression (SVAR) models.^^ In a first step we identify a demand and a supply shock and trace out the dynamics of the Phillips curve model in response to these shocks. This allows us to quantify the trade-off between inflation and unemployment implied by Keynesian and monetarist Phillips curve models. The supemeutrality proposition, which is central to the controversy between Keynesians and monetarists, is investigated by testing the significance of the long-run trade-off between the two variables. Next, using the historical decomposition technique we attribute the fluctuations in West German unemployment and inflation rates in the past thirty years to demand and supply shocks buffeting the economy. All data refer to West Germany.
2.2.1
The Unemployment-Inflation Relationship in Germany
The evolution of the unemployment rate and the inflation rate in West Germany is shown in Figure 2.1.^^ To help visual inspection the shaded areas mark periods 53 A detailed introduction into the structural vector autoregression methodology is
provided in the methodological appendix. 54 The unemployment rate in Figure 2.7 is the share of unemployed persons relative
to dependent labor. The inflation rate is computed as 100[ln(P^/P^_i2)], where Pt is the consumer price index. The unemployment rate and the consumer price index have been seasonally adjusted using Census XI1 (multiplicative variant). Both time series are available from Datastream (WGTOTUN%F and WGCP....F). Since in 1999:1 the calculation method of the unemployment rate was changed, the sample period ends in the remainder of this paper in 1998:12.
36
Chapter 2 Keynesian and Monetarist Views
Figure 2.7: Unemployment and Inflation in Germany, 1951-1998 Unemployment 12.5
51
55
59
63
67
71
75
79
83
87
91
95
I I I I I I I I I I I I I I I ( I I I I I M M I I M I I M I I III I I il 51 55 59 63 67 71 75 79 83 87 91
rri 95
Inflation 10.0
-2.5
of recessions.^^ For the raw data it is difficult to discern a clear relationship between the two variables. The inflation rate appears to fluctuate around a rate of approximately 2.5 percent, while the unemployment displays in the 1950s a 55 The recession dates are taken from Artis et al. (1997), who developed a procedure to determine peaks and troughs in the business cycle similar to the NBER classification procedure for the United States. They propose classical business cycle turning points for the G7 and a number of European countries based on time series of industrial production for the respective countries. A recession is defined as the time period between a peak and the following trough. For Germany, the authors determine the business cycle turning points for the time period beginning in 1961 and ending in 1993. Dopke (1999) uses their procedure to determine the turning points in Germany for the time period from 1994 until 1999. I am gratefiil to Jorg Dopke for making his results available to me.
2.2 The Long-Run Phillips Curve
31
Strong downward drift and since the early 1980s an upward drift. However, in recessions the unemployment rate rises strongly while the inflation rate falls, so that in these periods the negative correlation between the two variables, which is predicted by the Phillips curve, is visible. In Figure 2.8 we employ the band-pass filter introduced by Baxter and King (1999) to extract the business cycle component fi-om the two time series.^^ To this end, we use the "Bums and Mitchell" band-pass filter, which admits frequency components between 6 and 32 quarters. Baxter and King (1995: 22) recommend this particular filter, because it removes low-frequency trend variation and smoothes high-frequency irregular variation while retaining the major features of business cycles. The cyclical components of the unemployment and the inflation rate are shown in the upper panel of Figure 2.8 while the lower panel shows the trend components. The latter have been estimated using the Hodrick-Prescott filter. ^^ Figure 2.8 shows that the cyclical components of unemployment and inflation are negatively correlated. In particular, it is a salient feature of the German business cycle that inflation almost always reaches its cyclical peak and unemployment its lowest cyclical level just before or shortly after a recession sets in.^^ Once the recession is under way, unemployment increases strongly while inflation falls. To investigate the stability of the relationship of the cyclical components of unemployment and inflation, we divide the sample period into two subperiods, ranging from 1954 until 1979 and from 1980 until 1995. The first sample period covers the Bretton Woods regime of fixed exchange rates and the first years of flexible exchange rates. It also includes the two oil crises in the 1970s. The second period is characterized by the European Monetary System (EMS), establishing fairly stable exchange rates in Europe, and by a firm commitment of the Bundesbank to maintain low inflation rates and its refiisal to continue with activist demand management policies. Table 2.1 shows that the cyclical components are negatively correlated with a remarkable stable correlation coefficient ranging between approximately -0.50 and -0.60 over all sample periods.^^ ^" Here we apply the band-pass filter to the monthly annualized rate of change of the consumer price index defined as Ap^ = 1,200 ln(P^ /^/-i )• For a similar investigation for the USA see King et al. (1995). To account for the start-point and end-point problems of these filter methods, we drop the first three and the three last years of the sample period. See also the discussion in Baxter and King (1995: 9) of this issue. ^' The Hodrick-Prescott filter is the "industry standard" in applied business cycle research for the estimation of trend components of time series. We have set the smoothing parameter lambda to 14,400, which is the suggested value for monthly data. 58 This holds in particular for the large recessions in 1966, 1974, 1980-1982, and 1992-1993. 59 This result is robust with respect to the choice of the sample periods.
38
Chapter 2 Keynesian and Monetarist Views
Figure 2.8: Cyclical and Trend Components of Unemployment and Inflation in Germany Cyclical components
66
70
74
Unemployment
82
86
Inflation
Trend components 10.0
5.0
2.5
0.0
Table 2.1: Sample Correlation of Unemployment and Inflation Sample period 1954-1995 1954-1979 1980-1995
Raw data -0.20 (A: = -10) -0.13 (A: = -10) -0.53 (A: = -10)
Cyclical components -0.57 (A: = -4) -0.62 (A: = -3) -0.51 (A: = -7)
Trend components -0.41 (A: = -12) -0.24 (A: = -12) -0.89 (A: = -3)
Note: The raw data correspond to the unemployment rate and the monthly inflation rate. The cyclical and trend components have been estimated using the band-pass and the Hodrick-Prescott filter, respectively, as discussed above. The cross correlations between unemployment and inflation have been computed for twelve lags and leads. The parameter k in parentheses indicates the lag/lead where the correlation is at its maximum. A value A: < 0 indicates that unemployment leads inflation.
2.2 The Long-Run Phillips Curve
39
The lead of unemployment of three to seven months with respect to inflation is also fairly constant. If one considers the raw data or the trend component, there is no stable relationship between the unemployment rate and the inflation rate, which shows that the Phillips curve is a business cycle phenomenon and not universally valid. In this context it should also be noted that business cycle variations in the unemployment rate account for only a relatively small part of its overall variation, since Figure 2.8 shows that most changes in the German unemployment rate are of a permanent nature.^^
2,2.2
Estimating Keynesian and Monetarist Phillips Curves for Germany
2.2,2.1
Time Series Properties
Before we estimate the Phillips curve models for Germany, we need to determine the stationarity properties of the unemployment rate and the inflation rate. For this purpose we employ a number of unit root tests. The tests proposed by Perron (1997) and Elliott et al. (1996) are variants of the familiar augmented DickeyFuller (ADF) tests with the null hypothesis of nonstationarity. The Perron (1997) test considers as alternative hypothesis stationary fluctuations around a deterministic trend function and makes allowances for possible changes in its intercept or its slope. The modification of the Dickey-Fuller test (DFGLS) statistic suggested by Elliott et al. is intended to improve the power of the conventional ADF test. The third test is a unit root test with the null of stationarity, which has been proposed by Kwiatkowski et al. (1992). The results are reported in Table 2.2. Table 2.2 displays strong evidence that the West German unemployment rate, L'^is a nonstationary variable: All three versions of the ADF test cannot reject the null of nonstationarity at conventional significance levels, while the KPSS test rejects the null of stationarity at the 1% significance level. The tests for the differenced unemployment variable, Au, indicate that this variable is stationary, implying that the unemployment rate is integrated of order one. The consumer price level, P , is found to be a nonstationary variable. The case for the inflation 60
Regarding the second sample period, it is a striking finding that the trend components of the unemployment rate and the inflation rate are extremely highly correlated. Moreover, the negative coefficient is in accordance with the predictions of the traditional Phillips curve. This finding differs markedly from results for the United States. King et al. (1995) have applied the same technique to U.S. data and find no correlation between the trend components in the time period from 1974 until 1992, while the corresponding correlation coefficient for Germany for this time period is -0.83. For the correlation of the cyclical components King et al. report a correlation coefficient of approximately -0.60 over all sample periods, which is very similar to our results for Germany, indicating that Germany and the United States differ mainly in their long-run response to demand shocks.
40
Chapter 2 Keynesian and Monetarist Views
Table 2,2: Unit Root Tests Variable U Au P Ap ^p
Perron (1997) -5.48 -26.68" -3.87 -4.71 -16.16**
DFGLS
ADF
KPSS
Order of integration
-1.17 (c,/) - 8 . 4 6 " (c) -1.42 (c,/) -0.84 (c) -10.43**
-3.40 (c,r) -15.92** (c) -3.55* (c,0 -3.30* (c) -10.43**
0.73** {T) 0.67* (//) 0.92** (r) 0.33 (//) 0.35 (//)
1(1) 1(0) 1(2) 1(1) 1(0)
Note: Asterisks denote: = significant at the 5% level; = significant at the 1% level. A is the difference operator. Perron (1997) denotes the unit root test statistic proposed by Perron (1997) allowing for a shift in the slope of the time trend and a shift of the intercept at an unknown date (in case of the differenced series only the latter is allowed for). The null hypothesis is nonstationarity. The timing of the break is determined by selecting the date which minimizes the /-value of the lagged endogenous variable in the regression. The lag length is chosen on the basis of an LM test for serial correlation. DFGLS denotes the modified DickeyFuller Mest statistic proposed by Elliot et al. (1996). The terms in the parentheses indicate the inclusion of a constant and a trend, respectively. The null is again nonstationarity. The ADF statistic denotes the result of a conventional ADF test. KPSS denotes the test statistic proposed by Kwiatkowski et al. (1992), which tests the null of stationarity around a level (//) or trend stationarity (r). A lag truncation parameter of 12 is used. The sample period for all unit root tests is from 1951:1 until 1998:12. rate, 4P» is less clear-cut. The conventional ADF test rejects the null of nonstationarity at the 5% significance level and the KPSS test does not reject the null of stationarity at conventional significance levels, but both the Perron and the DFGLS test fail to reject the null of nonstationarity. Since the latter two tests are likely to be more powerful than the ADF test, on balance the evidence suggests that the inflation rate is nonstationary. The differenced inflation series, A^p, is stationary, from which follows that the inflation rate is integrated of order one and the price level is integrated of order two. 2.2.2,2
Testing the Superneutrality Proposition
2,2.2,2.1 The Role of Integration and Cointegration for Superneutrality Tests The order of integration of the time series in our Phillips curve models and the possible existence of a cointegration relationship have important implications for testing the significance of the long-run trade-off between inflation and unemployment. We will discuss below that the existence of such a trade-off violates
2.2 The Long-Run Phillips Curve
41
the supemeutrality proposition, and therefore testing the significance of the longrun trade-off is equivalent to a supemeutrality test.^^ Before proceeding, we provide a definition of what is meant by long-run neutrality and supemeutrality. Beginning with the former, long-mn neutrality refers to a one-time, permanent, unexpected change in the level of the money stock. If long-mn neutrality holds, ultimately this change in the money stock leaves the level of real variables unchanged.^^ Regarding the latter, a second hypothetical experiment that more closely resembles actual monetary policy is a situation where the central bank maintains a given growth rate for the money stock for a long period of time and then unexpectedly changes the growth rate to a new level. If this change in the growth rate for the money stock has no long-mn effect on the level of real variables, this is referred to as long-mn supemeutrality. In this hypothetical experiment it is important that the new growth rate for the money stock be maintained for a long period of time, to allow the transition effects to vanish. Theoretically, the change in the growth rate has to be permanent. Also, it is important that the change in policy be unexpected, because an anticipated change in policy in the near future may induce the economy's participants to change their present behavior. For example, they might stockpile on goods before the faster expansion of the money supply begins to push up prices; consequently, inflation might begin to rise in advance of the change in money growth. Since this complicates the story, we will focus below on unexpected permanent shocks to the money supply when investigating the supemeutrality proposition (see also Bullard 1999: 58). Fisher and Seater (1993) have shown that neutrality and supemeutrality tests depend cmcially on the order of integration of the variables involved. For example, considering the money stock as a monetary policy variable and output as the real variable of interest, their results imply that testing the neutrality proposition requires both the money stock and the output variable to be integrated of order one. If the money stock is integrated of order zero, there are no permanent stochastic changes in the money stock, meaning that shocks to the money stock do not change the money stock permanently and so long-mn neutrality is not addressable. If the money stock is integrated of order one and output is integrated of order zero, long-mn neutrality holds by definition and does not need to be tested, because permanent changes in the money stock cannot be associated with permanent changes in output since the latter do not exist. Thus, testing neutrality is possible only when both the money stock and output are integrated of order one, since in this case there are permanent changes in both the level of money stock and output.^^ Testing long-mn supemeutrality requires the monetary policy ^^ See also the discussion in Section 2.1.1.2. and Section 2.1.2.1. 62 The following discussion is based on Bullard (1999: 57ff.) and on Fisher and Seater (1993: 402). 63 For a more detailed discussion see Fisher and Seater (1993: 405ff.).
42
Chapter 2 Keynesian and Monetarist Views
variable to be integrated of order two and the output variable to be integrated of order one. If the money stock is integrated of order one, there are no permanent stochastic changes in the money growth rate and the supemeutrality proposition is not testable. If output is integrated of order zero, it is again evident that permanent changes in the growth rate of money cannot be associated with nonexistent permanent changes in output. When we test supemeutrality within the Phillips curve framework, we treat the price level as the monetary policy variable and unemployment as the real activity variable of interest. Since we find prices to be integrated of order two and unemployment to be integrated of order one, we can test for superneutrality.^"^ It should be noted that treating the consumer price variable as a monetary policy variable does not mean that monetary policy is assumed to have full control over the price level in every period. Rather, we only assume that monetary policy shocks are the source of nonstationarity in prices. Fisher and Seater point out that, in general, cointegration plays no role in testing long-run neutrality and supemeutrality because both concepts are based on how changes in money or its growth rate are ultimately related to changes in other variables (Fisher and Seater 1993: 414). Nevertheless, they also note that cointegration of the money stock and the real activity variable is sufficient to reject long-mn neutrality and, similarly, cointegration of the growth rate of the money stock and the real activity variable is sufficient to reject supemeutrality (ibid.). Thus, if we find a cointegration relationship between the rate of inflation and unemployment, this would constitute strong evidence against the supemeutrality proposition.^^ ^^ Fisher and Seater (1993) show that the relative order of integration in our case implies that long-run neutrality holds by definition. "^ To illustrate the intuition behind this result, we consider following relationship between the output variable y^ and the money variable m^, namely yt = ^y^-i + ^lyt-i -^cio^t +ci\mt-\ -\-a2mf-2 +^rj aiid investigate the implications of a cointegration relationship for the long-run neutrality proposition. We include two lags for each variable to allow for some dynamics. Hansen (1993: 142) shows that in error-correction parameterization this equation becomes Ay^ = a(yt-i - j3mt-\) b2Ayf^i-\-aoAmf-a2Amf_i+ef, "whQTQ a = {b\-\-b2-\) and P = {aQ-¥a\+a2)l (1 -b\-b2). The parameter p gives the long-run response of output to an innovation in the money stock, provided there is a long-run/cointegration relationship between the two variables. The existence of such cointegration relationship depends on the loading parameter a. Kremers, Ericsson and Dolado have shown that one can test for cointegration between yt and m^ by testing the significance of a (see the discussion in Hansen 1993: 148). If a is significantly larger than zero, then output responds to a disequilibrium in the money-output relationship. That is, a permanent change in the money stock would lead in this case to a permanent response of output to restore the long-run money-output relationship. This implies that the long-run neutrality proposition does not hold. Hence, evidence for a cointegration relationship between output and money is sufficient to reject this proposition. Regarding supemeutrality, one could investigate cointegration between unemployment Uf and inflation 4P? by testing the loading parameter a in the
2.2 The Long-Run Phillips Curve
43
To investigate the presence of a cointegration relationship, we test the cointegration rank of a system comprised of inflation and unemployment using the maximum likelihood procedure proposed by Johansen (1988).^^ We begin by setting up a vector autoregressive system comprised of these two variables and use information criteria to determine the appropriate lag length.^^ The Schwarz criterion suggests the inclusion of 2 lags, the Hannan-Quinn criterion suggests 12 lags, and the Akaike criterion 37 lags. However, even with 37 lags severe problems with autocorrelation remain. This indicates that the bivariate system is too small to model all movements in inflation and unemployment in the period from 1951 until 1998 successfully. If we proceed nevertheless with the cointegration rank test, using the bivariate autoregressive system with 37 lags to minimize the autocorrelation problem, the rank test yields evidence in favor of one cointegration vector.^^ The results are shown in Table 2.3, which reports the values of the A -trace statistic testing the null hypothesis of no cointegration relationship ( r = 0) and the null that the rank of the system is at most one ( r = 1). It is apparent from Table 2.3 that the null of no cointegration is rejected at the 5% significance level, whereas the null of at most one cointegration vector is not rejected at conventional significance levels. Imposing a rank of one on the system and normalizing the cointegration vector on the inflation rate yields the following cointegration vector: (2.18)
4 P + 0.11W = 0 .
Table 2.3: Trace Test for the Cointegration Rank Rank r =0 r=\
>^-trace statistic 16.88* 1.01
95% critical values 15.41 3.76
Note: * = = significant at the 5% level. An unrestricted constant but no trend is allowed for in the system.
error-correction model Au^ =a{u^_y -y^4P/-i)~^2^"/-i +^o^^A "^i^^Pt-i "•"^r • ^^ a tums out to be significantly larger than zero, then a permanent change in the inflation rate would lead to a permanent change in the unemployment rate, implying that supemeutrality would not hold. 66 The cointegration analysis has been done using MALCOLM. ^' The data set is the same we have used for the unit root tests. 68 There are also indications of nonnormality in the residuals, but the trace statistic used below to test the cointegration rank is known to be robust to nonnormality so that is less of a problem.
44
Chapter 2 Keynes fan and Monetarist Views
According to this estimate, increasing the inflation rate by one percentage point lowers the unemployment rate in the long-run by 0.11 percentage points. That is, in the long run inflation and unemployment are negatively correlated as predicted by the traditional Phillips curve. And the loading coefficients for both equations turn out to be significant at conventional significance levels, meaning that the unemployment rate responds to disequilibrium in the long-run relationship between the two variables. Put another way, an increase in the inflation rate would lead to disequilibrium and via the loading coefficient to a permanent change in the unemployment rate to restore the long-run equilibrium between the two variables. However, economically the trade-off between inflation and unemployment is negligible. Moreover, testing the stability of the cointegration rank using recursive estimation reveals severe instability (Figure 2.9).^^ This is not surprising since the computation of the correlation coefficients of the trend components of inflation and unemployment over different sample periods already revealed signs of instability. Figure 2.9 shows that the cointegration relationship breaks down in the 1970s when large supply shocks hit the economy.^^ In sum, even though there is evidence for a negative correlation between inflation and unemployment in the long run, the instability of the cointegration vector indicates that this long-run relation does not hold over the entire sample period and, therefore, the significance of the trace statistic in Table 2.3 in itself does not constitute strong evidence against the supemeutrality proposition. 2.2.2.2.2 The Lucas-Sargent
Critique
Testing supemeutrality by estimating the long-run trade-off between inflation and unemployment has been common in the early 1970s but fell in disrepute after fiindamental criticism of this approach by Lucas (1972) and Sargent (1971). However, King and Watson (1994) show that if inflation is integrated of order one, this approach to testing supemeutrality remains feasible.^ ^ Since this issue is of central importance to this chapter, this section provides a short review of the controversy. Early empirical researchers like Gordon (1970) and Solow (1970) investigated long-run supemeutrality by taking the Keynesian version of the expectations-augmented Phillips curves as a starting point, (2.19)
4 P , = aut + b/^f + St,
"^ In the final chapter of this study we extend the variable set to include a short-term interest; this will also prove effective in reducing the instability we observe here. '^ A similar result is obtained when using the Z-model. The difference between the two models is that the R-model controls for changes in the short-run dynamics of the model. Also, when testing the stability of the cointegration space after the rank restriction has been imposed reveals again severe signs of instability. Note that the unit line in Figure 2.9 marks the 95% significance level. ^ 1 See also King and Watson (1992) and King and Watson (1997).
2.2 The Long-Run Phillips Curve
45
Figure 2.9: Recursive Estimation of the Trace Test for the Cointegration Rank Stability of the Cointegration Rank: The R-Model Significance level = 95% 1.6
1.4
H
1.2
1.0
0.8
0.6
0.4
0.2
0.0
T
I I I I I I I I
67
70
73
where e^ denotes the residual in the price equation and all other symbols as before.^^ Equation (2.19) is closely related to the expectations-augmented Phillips curve given by (2.4a), the only difference being that in contrast to (2.4a) the coefficient on expected inflation in (2.19) is not restricted to unity on a priori grounds but is estimated freely. ^^ Expected inflation is modeled as a distributed lag function of actual inflation, (2.20)
Apf = v{L)Ap, = Zv,4^,_i_, /=0
12 73
This section is based on King and Watson (1994: 13ff). The natural rate of unemployment is modeled as a constant in (2.19), which is not explicitly shown to simplify notation. Also, the sign of a in (2.19) is not pinned down on a priori grounds as it is in (2.4a).
46
Chapter 2 Keynesian and Monetarist Views
with the restriction X/lo^/ - ^ ™posed to ensure that if there were a permanent increase in inflation, inflation expectations would ultimately capture it ( 9 4 P ^ / 3 4 P = 1), i.e., permanent inflation expectations errors are ruled out. The short-run slope of the Phillips curve is given by d^t^dut =a. More interestingly, the long-run slope of the Phillips curve is given by dAp/du = a/[l-bv{l)] = a/[l-b]. Thus, if the coefficient b is found to be equal to unity, there is no long-run trade-off between inflation and unemployment since the attempt to lower the unemployment permanently leads to an infinite inflation rate, confirming the monetarist acceleration hypothesis. If, on the other hand, b is found to be smaller than unity, there is a long-run trade-off, confirming the Keynesian standpoint. Solow (1970) finds the long-run Phillips curve slope to be approximately 94p/9w = l , indicating a substantial long-run trade-off between inflation and unemployment.^"* This result was challenged by Sargent (1971) and Lucas (1972). They take the monetarist version of the expectations-augmented Phillips curve as the starting point of their argument, (2.21)
Ut=(fiAp,-rApf-\-€t,
with 0,0^ <0 and where Sf denotes now the residual in the unemployment equation. According to the natural rate hypothesis, the coefficients on actual inflation and expected inflation are identical {0 = 0^)?^ Inflation is assumed to be generated by an autoregressive process, (2.22)
4?^ = pxApt-x + p2^t-2
+ - + Pn^Pt-n + ^/»
where nif is a shock to the inflation process. Moreover, Sargent and Lucas assume that agents have rational expectations, implying that expected inflation is given by
^^ One can also express the argument made by Gordon and Solow in terms of cointegration analysis. Writing (2.19) as an error correction model under the assumption that in (2.20) w = 0 (which simplifies the analysis without affecting the generality of the result) we obtain A^pt = aAUf - (1 - b)[/!^t-\ ~ [^ /(I ~ ^)] ^t-\ ] + ^/ • Hence, if b = l there is no cointegration relationship between inflation and the unemployment rate, since the loading coefficient is zero. However, if b
2.2 The Long-Run Phillips Curve (2.23)
47
4?f = Et-i4)t = P\M-\ + P2M-2 + - + Pn^t-n.
According to this model the reduced-form relationship between unemployment and inflation is given by (2.24)
ut = (pApt - r tpi^t-i
+ ^/.
The reduced form summarizes the information in the data on the relationship between inflation and unemployment. Lucas and Sargent point out that if equations (2.21) to (2.23) represent the true model of the economy, it is possible to observe a statistical relationship between inflation and unemployment in the data in spite of the fact that the Phillips curve is vertical, i.e., the natural rate hypothesis holds. In other words, (24) shows that an empirical researcher investigating the slope of the long-run Phillips curve would find that duldAp = 0 - ^ ^ X l=\Pi' If Z "=i A < 1 the researcher would conclude that there is a long-run trade-off between inflation and unemployment even though none is implied by the structural model (^ = 0^). From this follows that the approach by Gordon and Solow to estimate the long-run trade-off would fail if agents have rational expectations since in this case their estimate of the slope of the long-run Phillips curve really represents a mixture of the slope coefficient and the inflation process. However, King and Watson (1994) argue that if inflation is integrated of order one, the approach by Gordon and Solow yields valid results because a unit root in the inflation process means that X ^^^ Pi = 1 ?^ Put another way, the Lucas-Sargent critique is an early example of the point stressed by Fisher and Seater (1993):^^ If inflation is stationary, S f = i A < l » the relevant superneutrality experiment—^permanent stochastic changes in the inflation rate—are absent from the inflation data, and the slope of the long-run Phillips curve cannot be estimated. But with inflation being integrated of order one (and, hence, prices being integrated of order two), the relevant experiments are present in the data and the long-run slope can be determined. 2.2.2.2.3 The Identification Problem In the preceding discussion we have assumed that the money supply process is exogenous to the model.^^ Since monetary policy is likely to respond endoge^^ King and Watson (1994: 15ff.) show that this result carries over to richer models than the one considered here. ^^ See King and Watson (1994: 15ff) for a detailed discussion. 78 Regarding the Phillips curve, the corresponding assumption is that exogenous monetary policy shocks are responsible for the nonstationary behavior of prices and inflation.
48
Chapter 2 Keynesian and Monetarist Views
nously to developments in the real and nominal spheres, this assumption is very restrictive. Allowing for an endogenous money supply, however, raises the issue of the identification of exogenous monetary policy shocks. This section provides a brief introduction into the identification issue using a simple macroeconomic model with the money stock as the monetary policy instrument and output as the real variable of interest. ^^ In the model presented here, only neutrality can be investigated but the identification principle is the same as in Phillips curve models where supemeutrality is the issue. Having introduced the identification principle in this section, we discuss the identification of exogenous monetary policy shocks in Keynesian and monetarist Phillips curve models in the following two sections. In this section we consider the linear dynamic model given by (King and Watson 1992: 5ff) (2.25)
Yy{L)yt ^Op^^(l>m{F)E,m, -^(^j{F)E,rj,
(2.26)
rp{L)p, = -dy, ^ii/^{F)E,m,
(2.27)
Amt = Amy Ay t + a^y {L)Ayt_x + «mm {L)Amt-x + e^
(2.28)
+y/rj{F)E,r],
Arjt=A{L)e?,
L is the lag operator, Efm is the conditional expectation of m formed at date /, F is the forward operator defined as FJ[Efm^] = Efm^+j, e^ is an exogenous real shock that is meant to capture the stochastic process driving output growth and £•/" is an exogenous monetary policy shock. ^^ Equations (2.25) and (2.26) determine output and prices, respectively. The model allows for gradual output and price adjustment via the lag operator terms Yy{L) and Yp^^) • Moreover, it allows for forward-looking behavior via the forward operator terms. Equation (2.27) gives the reaction function of the central bank. The coefficient X^y shows the contemporaneous effect of output on the money supply. In addition, the central bank is assumed to respond to past output and money growth. Discretionary monetary policy actions are represented by the monetary policy shock term ef. The reaction function is specified in growth rates and omits a possible cointegration relationship between output and money. This is consistent with actual central bank behavior, since central banks like the ECB or the Bundesbank that target money variables or pay otherwise close attention to money stocks typically allow for a base drift in money. That is, if a growth target for money has been missed, most central banks only aim to bring money growth ^^ ^^
This section is based on King and Watson (1992: 7ff.). The lag polynomial a(L) takes the general form a{L) = a„L^.
aQ+ai{L)-^a2L^+...+
2.2 The Long-Run Phillips Curve
49
back on target, but do not try to bring the level of money balances back to its original trajectory. Finally, (2.28) specifies the process of the second stochastic disturbance in the model, the real disturbance r]^. With this model, the final form of the equation for output becomes (King and Watson 1992: 8) P
(2.29)
•
P
•
Ayt = A^ym^rnt + Z«>y4y/-y + IL^im^-j
+ ^t .
where the coefficient Ay^^ gives the contemporaneous response of output to changes in the money supply. Since we are interested in the dynamic relationship between money supply and output, we consider in the remainder of this section the bivariate dynamic simultaneous equations model comprised of the final form output equation and the money supply equation (2.27): p
(2.30a)
.
p
j=\ p
(2.30b)
.
Ayt = Ay^Amt + J^aj^yAyt-j + Y^a-!ym^-j + ^f j=\ .
p
.
Amt = A^yAy^ + Y.^i,yAyt.j + J^^mm^^z-y + ^ r . 7=1
y=i
or, equivalently, these equations can be written as (2.30c)
Oyy {L)Ayt = Uy^ {L)Amt + e^
(2.30d) a^^ {L)Am, = a^y {L)Ay, + e^, p
with
.
p
.
Umm{L) = \- Y.KmLf, amy(L) = X^y + Y^a^yV, 7=1 p a y y { L )
=
1 -
7=1 .
Y . a J , y D
7=1
p ,
O y m i L )
=
Aym
+
.
Z ' ^ J ^ m ^ '
'
7=1
The variance-covariance matrix of the model is given by Z^ = £(6(8/). The stochastic disturbances £ are assumed to be unobserved mean-zero serially independent random variables that are stationary. With this specification of the disturbance terms and together with the typical stability assumptions Zy=i^^ < 1 and Y, %\^iim < 1> the bivariate model given by (2.30) implies that both money and output are integrated of order one and not cointegrated. Thus, this model is suited to investigate the long-run neutrality of money. To simplify notation further, we write the model in stacked form: (2.31)
a{L)Xt=et,
50
Chapter 2 Keynesian and Monetarist Views
a{L)=Y.oifl^'.
and
y=o
x,=
1
Ay; £t =
Anif
cfTl
Pt
ao = J
-A. ym
' ^nny
a^yy
and a J = --
. y=
In the context of structural vector autoregression analysis it is common to consider the moving-average form of a model, expressing all variables as a function of the structural shocks in the model. Introducing this alternative notation will prove useful when we estimate the monetarist Phillips curve model below. The moving-average form of our model is obtained by inverting the AR-form, yielding^ ^ (2.32a) Ay, = eyrf{L)e?^dy^{L)er (2.32b)
Am,=d,„^{L)£?-^d^jL)er,
In stacked form, this model becomes: (2.33) where
Xt=0{L)£t, 6{L) =
Oyrj{L)
dym{L)
1 that is,
00 =
I
, which is related to a{L) by 0{L) - a{L) ^,
^ym
^nny^ym
^
^my^ym
Kiy
1
1 — ^yny^ym
^ ~ A ly^^ym nv^ "^ym
and
0j =
^mm^yy
^my^ym
^mm^yy
^my^ym
-nJ "^iny^ym ^yy
rny ^mm^yy
J
^mm^yy
^my^ym
The long-run multiplier giving the long-run response of output to a one-unit permanent increase in the money stock is yyf„ =ayffj{l)/ayy{l).^'^ The long-run ^^ ^^
See King and Watson (1997: 73). For the conditions which need to hold for the model to be invertible, see King and Watson (1997: 75ff). The term a{\) refers, in general, to the lag polynomial a{L) evaluated at L = 1. That is, a(l) refers to the sum of the coefficients in a{L), i.e. a{l) = aQ +a\-\-a2 +... + a „ . Note that, for example, in Ayt =a{\)Amt the coeffi-
2.2 The Long-Run Phillips Curve
51
neutrality restriction is Yym = ^ P In the moving-average representation the equivalent restriction is Yym -^ym{^)l^mm{^)^ where dym{^) denotes the longrun response of the level of output to a monetary policy shock and drnm{\) denotes the corresponding response of the money stock (King and Watson 1997: 74). Using long-run restrictions like ^^„(1) = 0 in SVAR analysis has been popularized by Blanchard and Quah (1989) and we will use such restrictions below when estimating the monetarist Phillips curve model. Testing long-run neutrality is complicated by the fact that the model given by (2.30) is not identified. That is, without further restrictions imposed on the model its parameters cannot be estimated. To see this, consider the reduced form of model (2.31) (see King and Watson 1992: 9): (2.34)
X, = t
iXt-i+e,,
where ^- = a^^ai and Ct = aQ^Sf. The reduced form summarizes all information in the data on the relationship between the variables in the vector Xf. To obtain estimates of the structural parameters in (2.30), we need first to estimate the reduced-form parameters 0/, with z = l,...,/?, and then we have to retrieve the structural parameters of interest from the reduced-form model, using the following set of equations (ibid.): (2.35)
aQ^ai=-0i, / = l,...,p,
(2.36)
aoi^,V=^„
where 1^ denotes the variance-covariance matrix of the reduced-form model. It is obvious from (2.35) and (2.36) that there are more unknown structural parameters on the left-hand side than there are estimated reduced-form parameters on the right-hand side. Considering (2.36), the reduced-form equation yields three unique parameters in E^, whereas on the left-hand side we have five unknown parameters: /i^^ and X^y in ao, and Gg^j, CTem^ ^^d (Tgrj^s^ in Is, Thus, without fiirther restrictions it is not possible to obtain unique estimates of the structural parameters from the reduced form parameters. In SVAR models it is typically assumed that the structural disturbances e^j and f"^ are uncorrelated, yielding the restriction (yeT],em = ^ • Our bivariate model requires one additional restriction to identify the model. Without this restriction no structural intercient a{}) gives the long-run response of the level of output to a permanent unit change in the money stock. 83 Note that long-run supemeutrality cannot be tested within this model because the money stock is, according to (2.27), integrated of order one and not of order two, as is required for supemeutrality tests. For a modification of this model allowing for supemeutrality tests see King and Watson (1992: 10).
52
Chapter 2 Keynesian and Monetarist Views
pretation of the equations is possible. To this end one could assume, for example, that the model is recursive, so that either A^y = 0 or Xym = 0.^^ With A^y = 0 , equation (2.30b) would become a money supply function where the central bank is assumed not to respond contemporaneously to changes in output growth, i.e., Amt is predetermined.^^ Alternatively, one could identify the output equation by assuming that Ay^ = 0, which would imply that output does not respond to a change in the money supply within the period; this restriction would be justified if there are lags in the monetary transmission mechanism and the measurement period was relatively short (Fisher and Seater 1993: 407). One could also identify the model by imposing the long-run neutrality restriction {Yym-^) on the model; this restriction would identify the money supply function by assuming that monetary policy actions have no long-run effects on output.^^ Another alternative is to assume that the central bank sets the money supply in the long run independently of output, which implies the restriction Ymy = ^ • According to Fisher and Seater (1993), this restriction can be interpreted as asserting the "longrun exogeneity" of the money stock, in the sense that a permanent change in output has no effect on the money stock in the long run.^^ Yet another approach is chosen by King and Watson (1992, 1997) and Weber (1994), with the latter applying the King and Watson approach to data from G7 countries. Instead of reporting results for a single identifying restriction, these authors summarize the results for a wide range of identifying assumptions in graphs, thereby allowing the reader to specify a value for any one of the parameters Ay^, A^y, Yym or Ymy and find the implied estimates for the other three parameters. In this chapter we take another approach and follow King and Watson (1994), Roberts (1993), Bullard and Keating (1995), and Dolado et al. (1997), who derive from Keynesian and monetarist Phillips curve models identifying restrictions for models comprised of unemployment and inflation. It needs to be emphasized that all the resulting models are just-identified, because we are imposing only two just-identifying and no over-identifying restrictions on the models, and, hence, these models are all observationally equivalent, meaning that their reduced forms fit the data equally well.^^ From this follows that we cannot formally test the validity of the individual models. Notwithstanding, these models have ^^ For a survey on identifying restrictions used in the literature, see King and Watson (1997: 76ff.). 85 Since in our model the money stock is the monetary policy instrument, the money supply function is equivalent to a central bank reaction function. 86 The seminal paper in this regard is Blanchard and Quah (1989). For a survey on bivariate SVAR models using long-run neutrality restrictions, see Gottschalk and Van Zandweghe (2001). ^'^ See Fisher and Seater (1993: 408). King and Watson (1997: 77) propose the alternative restriction Yf^y = 1, which would be consistent with a policy aiming at price level stability under the assumption of stable velocity. ^^ See also the discussion in Dolado et al. (1997: 12).
2.2 The Long-Run Phillips Curve
53
different implications regarding the long-run trade-off between inflation and unemployment and regarding the sources of business cycle fluctuations. The latter means that the models yield different interpretations of particular historical episodes. For example, they are likely to disagree on the sources of recessions. This offers an informal way to assess the plausibility of these models, but before doing so, we need to identify the Keynesian and monetarist Phillips curves. 2,2.2.3
The Keynesian Phillips Curve
2.2.2.3.1 Identifying the Keynesian Phillips Curve The essence of traditional Keynesian models is contained in the following two equations, where for expositional convenience we focus on the contemporaneous interaction between inflation and unemployment and leave (for the moment) dynamics aside:^^ (2.37) (2.38)
4P^ ^aut +St Ut=hApt-\-dt.
The first equation is a price equation, representing the wage-price block in Keynesian models. In the spirit of the traditional Phillips curve inflation is assumed here to be a function of the unemployment rate, which is an indicator of aggregate demand conditions. Moreover, inflation is influenced by supply shocks, St. The second equation represents the IS/LM block and determines unemployment as a function of demand shocks, df. In addition, inflation may have an effect on demand. But, as King and Watson (1994: 11) write, "the conventional Keynesian macroeconometric view was that the short-run dependence of real variables on the price level was minor, suggesting small values h in equation (2.38), and that demand variations were dominated by exogenous shocks (<^^)." One may recall that this assumption sets the Keynesian model apart from monetarist models, where (unexpected) inflation plays a major role in determining demand conditions. The following model represents a Phillips curve model with more elaborate dynamics:^^ p
(2.39a)
Aut = ^Ap^Pt
p
+ lL(pu^,i^Pt-i + lLuu^M-i + £s,t i=\
/=1
^^ This section is based on King and Watson (1994: 1 Iff). 90 Dolado et al. (1997: Sff) show that (2.39a), which is interpreted here as represent-
ing the Phillips curve, can be derived from a wage- and price-setting model, assuming imperfect competition and a hysteretic mechanism. Furthermore, they show that (2.39b) can be interpreted as an aggregate demand equation.
54
Chapter 2 Keynesian and Monetarist Views
(2.39b) A^pt = A^uM
+ Z(t>^Ap4^Pt-i + Z04pt/,/^W/-i + ^t/,r,
where Eg^t is a supply and f'j^^ is a demand shock. We will interpret (2.39a) in the remainder of this chapter as representing the Phillips curve. While this equation provides a natural setting for the monetarist version of the Phillips curve, we need to rearrange the Keynesian Phillips curve given by (2.37) so that it determines the unemployment rate. Doing so means that the parameter X^^ in (2.39a) corresponds to \la in (2.37), and Ss^ is proportional to Sf^^ The model is specified in differences to account for our earlier findings that both inflation and unemployment are integrated of order one and that in our bivariate vector error-correction model there is no stable cointegration relationship between the level variables. The objective is to estimate the slope of the long-run Phillips curve. However, rather than computing dApldAu, as Gordon (1970) and Solow(1970) did, we will determine the slope of the Phillips curve as Yu^ = ^irnk^Adut+k /de^M^^t+k /9^J,J}= ^uApW(/>uu{^) -^^ That is, we will be concerned with the relative effects of demand shocks on unemployment and inflation.^^ With the reduced form of model (2.39) given by (2.40a)
Aut = c{L)Aut-x + d{L)A^Pf_i + ^^^^
(2.40b) A^p, = f{L)Au,.,
+ g{L)A^Pt-i +
e^,,
it can be shown
(2.41)
ru4, = [((i-^(iR4, +^(i)M(i-^(i))+'^-^/(i)] >
meaning that the long-run Phillips curve slope is a function of the short-run slope Au^ and the long-run coefficients in the reduced form model (Dolado et al. 1997: 13). Thus, to estimate the long-run slope we need to identify the short-run Phillips curve slope. Identification of the Keynesian Phillips curve model requires two restrictions. The assumption that the demand and supply shocks are mutually uncorrelated ^^ For the interpretation of equation (2.39a) as a monetarist Phillips curve, recall the discussion in Section 2.1.2.3. See in particular (2.6). ^^ The latter coefficients are defined as 0uAp{^)-^/^ ^Y,f=\4>uApj ^^^ ^s ^j,^(l) = ^^ Since in the Keynesian version of the Phillips curve, which was the starting point of the investigation in Gordon (1970) and Solow (1970), unemployment is an indicator of aggregate demand, both approaches to estimating the long-run slope of the Phillips curve are closely related, but in our model we are more explicit about the identification of the demand shock. Furthermore, we consider the reciprocal of the Phillips curve slope coefficient estimated by Solow (1970).
2.2 The Long-Run Phillips Curve
55
provides one of the two identifying restrictions. For the other identifying restriction we follow King and Watson (1994: 17), who argue that the econometric implementations of the traditional Keynesian model (2.37)-(2.38) allowed for little contemporaneous feedback between the wage-price block (summarized by (2.37)) and the IS-LM block (summarized by (2.38)). In particular, they note that early researchers like Gordon (1970) and Solow (1970) used ordinary least square estimators to estimate wage-price equations like (2.37). That is, in early work the unemployment rate was treated as an exogenous variable in the wageprice block (King and Watson 1994: 18). From this follows that they assumed for (2.38) that /z = 0, which yields the other identifying restriction we have been looking for.^^ This restriction implies that u^ and ^^^^ are uncorrelated and, hence, we can estimate the Phillips curve (2.39a) by using the contemporaneous value of Uf as an instrument for the contemporaneous price variable, A^pt .^^ This approach defines a value for A^^ which we will use in the estimation of the long run Keynesian Phillips curve trade-off It should be noted that the restriction we use here to identify the Keynesian Phillips curve does not impose a long-run vertical Phillips curve on the model. Even though NAIRU models are often specified to include a vertical Phillips curve in the long run, we do not impose any long-run restrictions on our Phillips curve model in order to be able to test empirically the slope of the long run Keynesian Phillips curve. 2,2.2,3.2 The Long-Run Trade-Off in the Keynesian Phillips Curve Model In a first step we estimate the reduced form of model (2.39).^^ We determine the appropriate lag length using information criteria. With the effective sample period beginning in 1954:1 and ending in 1998:12 we find, however, that there are severe problems with autocorrelation in the system even if we specify the system on the basis of the Akaike information criterion, which tends to overparameterize the system.^^ Nevertheless, the system does not display any signs of instability when we investigate its stability using recursive Chow breakpoint tests. Thus, as in the cointegration analysis the problem appears to be that the bivariate system is too small to model all movements of our unemployment and inflation variables over the past 50 years. Considering shorter sample periods helps alleviating this problem. With the effective sample period beginning in ^^ See also the discussion in King and Watson (1997: 93). ^^ See King and Watson (1994: 18). These authors also note that, following the "price equation" estimation strategy used by Gordon (1970) and other researchers in the Keynesian tradition, equation (39a) can equivalently be estimated by OLS using the reverse regression of A'^Pt onto AUf and relevant lags. For the unemployment rate and the price level we use the same time series as before. We compute the inflation rate, Apt, as the monthly annualized rate of change of the consumer price index, i.e. Apt = 1,200 ln(F^ //J_i). Recall that we experienced the same problem when testing for cointegration.
56
Chapter 2 Keynesian and Monetarist Views
1970:1, there are no more signs of autocorrelation or heteroscedasticity in the residuals at the system level, but problems with nonnormality remain.^^ Single equation misspecification tests show that the unemployment equation, which represents the Phillips curve in our model, is well specified, but the null hypotheses of no autocorrelation and normally distributed residuals are clearly rejected in the price equation. The time series for A^p is depicted in the lower panel of Figure Al in the Appendix and it is apparent that this series displays a lot of high frequency noise. It is likely that our Phillips curve model does not adequately model this component in the price variable since it is a business cycle model, which would account for the residuals in the price equation not being white noise. Since the high frequency noise in the price variable is not of major interest to us, we will continue using this model in spite of the problems with the normality assumption at the system level. In Figure A2 we show the results for 1-step ahead Chow forecast tests (first row), «-step ahead Chow forecast tests (second row), and Chow breakpoint tests (third row). These tests show no signs of instability in the single equations (first and second column) or in the system (third column).^^ This confirms our earlier finding that the Phillips curve relation is stable at the business cycle frequency. Having specified the reduced-form Phillips curve model, we estimate the parameter A^^ using the approach outlined above. ^^^ This yields a value of 0.6006 for /iw4p- Surprisingly, our estimate of A^^, which is equivalent to \la in (2.37), has a positive sign instead of the negative sign we would expect from the Phillips curve relation. Nevertheless, Figure 2.10a shows the response of unemployment and inflation to a demand shock, also called impulse response fimctions, and it is apparent that our identification strategy yields a plausible estimate of the Keynesian Phillips curve. The demand shock has been scaled so that the inflation rate is eventually reduced by one percentage point. In the long run this leads to an increase in the unemployment rate by 1.61 percentage points. That is, the Keynesian Phillips curve suggests that there is a substantial long-run trade-off between inflation and unemployment. As we argued in Section 2.1.1, this long-run trade-off is an essential part of the traditional Keynesian paradigm, so this finding supports our assertion that our identification strategy yields indeed a Keynesian Phillips curve.
^° Detailed results are shown in Table Al in the Appendix. The previous recursive analysis of the cointegration rank has shown that over this time period no cointegration relationship between unemployment and inflation is present. ^^ We use one quarter of the sample period (seven years of data) to obtain an initial estimate of our Phillips curve system before proceeding with recursive estimation of the system. ^^^ I am grateful to Mark W. Watson for making available his RATS programs used in the King and Watson (1994) paper. These programs are available from his homepage.
2.2 The Long-Run Phillips Curve Figure 2.10a: The Trade-Off between Inflation and Unemployment in the Keynesian Phillips Curve Reaction of unemployment to a demand shock
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Reaction of inflation to a demand shock
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Phillips curve trade-off 30i.'li
' I "
20I
'i
i
100-
-10-20-
^ 1 , 1 , "
-
-30-
5
> '
'"! 'I'V' y^ r ' l ' .'": V ' . V ' '
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
57
58
Chapter 2 Keynesian and Monetarist Views
Figure 2.10b: The Effects of Supply Shocks in the Keynesian Phillips Curve Model Reaction of unemployment to a supply shock
-0.0
-0.8 H
-1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
\
1
1
r
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Reaction of inflation to a supply shock 0.00
-0.25
-0.50
-0.75
-1.00
-1.25
-T
5
1
1
1
1
1
1
1
1
r-^—I 1
1
1
1
1
1
1
r
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
2.2 The Long-Run Phillips Curve
59
To investigate the significance of the long-run response of unemployment and inflation to the demand shock we employ a bootstrapping procedure to generate a two standard error confidence band. This is shown in Figure 2.10a by the dotted lines.^^^ The unemployment response is clearly significant, but the inflation response is very imprecisely estimated and not significantly different from zero. With the inflation response forming the denominator of our estimate of the longrun Phillips curve slope it is no surprise that the Phillips curve trade-off is not significantly different from zero either. In fact, since the Phillips curve trade-off is computed as a fraction where the denominator might be close to zero, it follows that the resulting estimate is bound to be highly volatile. This is shown in the third panel of Figure 2.10a. The insignificance of the long-run trade-off means that, contrary to our expectations, the Keynesian Phillips curve model does not reject the supemeutrality proposition.^^^ However, since this reflects largely the insignificant response of inflation to a demand shock and we have seen above that the reduced form of our price equation is not well specified this should not be seen as constituting strong evidence against the Keynesian position. ^^^ Nevertheless, the imprecise estimate of the inflation response and the resulting large uncertainty about the slope of the long-run Phillips curve implied by the Keynesian model raises some doubts whether this model presents an adequate description of the inflation and unemployment dynamics in Germany. In particular, we will see below that the monetarist Phillips curve model does not suffer to the same extent from these problems. Regarding the short-run responses. Figure 2.10a shows that it takes approximately two years until the unemployment and the inflation rates reach their new steady state values. The unemployment rate increases on impact and continues to increase gradually over the next two years. Since in Keynesian models the unemployment rate is an indicator of aggregate demand conditions, this suggests that, following an adverse demand shock, aggregate demand conditions do not deteriorate immediately but do so gradually. With respect to inflation. Figure 2.10a shows that in the first three months there is a positive response, consistent with our positive estimate of ^ ^ . Since in Keynesian models a negative demand shock might be the result of a tax increase or higher interest rates charged in the financial sector, an initial positive price response is not implausible if firms try to pass higher costs on to customers via higher prices. One year 101 The bootstrapping procedure is based on 1000 draws. 102 See also King and Watson (1997: 90ff) for an application of this methodology as
supemeutrality tests for U.S. data. 103 To obtain a better estimate of the long-run trade-off it would appear promising to
augment the Phillips curve models with other (exogenous) variables to control for shocks to the inflation variable which are not related to the Phillips curve model. For such an extension, see Dolado et al. (1997) or King and Watson (1994: 27ff). Moreover, Weber (1994: 20) finds strong evidence against a vertical Phillips curve in a Keynesian Phillips curve model. His results are discussed in more detail below.
60
Chapter 2 Keynesian and Monetarist Views
after the demand shock has occurred, inflation begins to fall permanently. This delayed inflation response is consistent with the Keynesian view of sticky prices. Given the large increase in unemployment, the inflation response seems to be small. However, such a small response is consistent with the observation by Blanchard (1990: 784) that in the early 1970s there was a wide consensus that prices did not seem to respond much to demand conditions. All in all, our Keynesian Phillips curve model appears to yield a plausible estimate of the shortrun Keynesian Phillips curve. In Figure 2.10b, we consider the response of unemployment and inflation to a supply shock which has been scaled so that it reduces the inflation rate on impact by one percentage point. Such a shock could correspond, for example, to a technological innovation, which increases productivity, or to a reduction in oil prices. In general, we expect a supply shock to push unemployment and inflation into the same direction. In Figure 2.10b, we observe that in the first year following the shock unemployment remains virtually unchanged but then begins to fall slightly. Inflation, on the other hand, responds strongly to the supply shock, falling on impact by one percentage point. This fall in inflation is quickly reversed, but inflation remains permanently below the base line.^^^ This suggests that in response to a supply shock it is the unemployment rate that is sticky while prices are flexible. That is, firms pass lower oil prices, for example, quickly on to customers while keeping employment unchanged. It should be noted that this follows directly from our identifying restriction: By assuming /? = 0 in (2.38) we specify that prices can respond on impact to all shocks while unemployment is restricted to respond instantaneously only to demand shocks. King and Watson (1997: 93) write that "for today's 'new Keynesians' this may appear to be a very unreasonable identifying restriction (and so must any evidence about the Phillips curve that follows from it). However, the identifying restriction is consistent with the traditional Keynesian model of the late 1960s." Another way to summarize the information that is contained in the impulse response functions is to consider the forecast error variance decomposition of our two variables. As the name suggests, this measure decomposes the variance of the forecast error. The intuition of the variance decomposition can be understood by revisiting the impulse response functions for the unemployment variable depicted in the first panels in Figures 2.10a and 2.10b: on the basis of the changes in the unemployment rate induced by the demand and supply shocks, one can compute for a given forecast horizon and a given shock the variance in unemployment due to this specific shock. Once one has computed the total variance of unemployment due to both shocks for a given horizon, the variance decomposition for this horizon is obtained by calculating the contribution of the ^^^ The base line represents the value a variable would have taken in the absence of the disturbance considered in the experiment underlying the impulse response analysis and is given here by the zero line.
2.2
The Long-Run Phillips Curve
61
Table 2.4: Forecast Error Variance Decomposition in the Keynesian Phillips Curve Model: Contribution of Demand Shocks Inflation 0 1 6 12 18 24 36 48 96
100.00 100.00 99.74 99.69 99.58 99.41 99.21 99.11 98.99
0.46 0.81 0.71 0.31 1.78 5.62 13.50 18.66 25.86
individual shocks to the total variance. In Table 2.4 we compute the forecast error variance decomposition of the unemployment rate and the inflation rate for the Keynesian Phillips curve model. In particular, Table 2.4 shows the contribution of demand shocks to the variance in these two variables. The variance decomposition shows that demand shocks are responsible for virtually all fluctuations in the unemployment rate at all horizons. For inflation, demand shocks are unimportant at short horizons. At the business cycle frequency they account for a small amount of the variance in inflation, which increases as the forecast horizon becomes longer. In summary, our empirical Keynesian Phillips curve model shows that demand conditions are a very important determinant of fluctuations in the unemployment rate. However, one cannot conclude from this analysis that all changes in the unemployment rate are due to changes in demand, because the fact that our Phillips curve model is specified in differences implies that we are modeling essentially the cyclical component of unemployment and inflation; the trend component, on the other hand, has been removed by the differencing procedure. Our preliminary data analysis in Section 2.2.1 has already shown that at the cyclical frequency a strong negative, Phillips curve-type relationship is present in the data. This explains why in the Keynesian model we find an important role of demand conditions for unemployment, since shifts in demand conditions lead in the Keynesian interpretation of the Phillips curve to movements in the unemployment rate along the Phillips curve. But our previous analysis has also shown that the cyclical component explains only a small part of the overall increase in unemployment since the early 1970s. Most of the increase in unemployment is due to an increase in the trend rate of unemployment, and our cointegration analysis has shown that at the trend frequency we do not find a stable Phillips curve relationship. Hence, our empirical Phillips curve model shows that demand management policies in a Keynesian framework can be powerfiil by shifting un-
62
Chapter 2 Keynesian and Monetarist Views
employment and inflation along a nonvertical Phillips curve, but in the past thirty years supply shocks have led to unfavorable shifts in the Phillips curve itself. The latter accounts for our finding that in the long run the Phillips curve is not stable. Thus, even though using the Keynesian identification we find a strong Phillips curve relationship that is attributable to the effects of demand shocks on unemployment and inflation, in practice it becomes impossible to use demand management policies to maintain a low unemployment rate because of the effects of supply shocks on the Phillips curve itself. 2.2.2.4
The Monetarist Phillips Curve
Roberts (1993) argues that the monetarist paradigm suggests two long-run restrictions, which can be used to identify our Phillips curve model. From the natural rate hypothesis follows that a demand shock and, in particular, a monetary policy shock cannot have a long-run effect on the level of a real variable like unemployment. That is, we can impose the supemeutrality restriction Yu/ip = 0 to identify the monetarist Phillips curve. Moreover, the monetarist assertion that "inflation is always and everywhere a monetary phenomenon" yields another identifying long-run restriction: Roberts (1993: 923ff) points out that this means that even though nonmonetary shocks like oil price shocks may have a temporary effect on inflation, inflation is ultimately under control of the central bank and, hence, only central bank actions can have a permanent effect on inflation. Roberts (1993: 924) writes: "By this argument, if there is any non-stationary element to inflation, it must be the result of changes in the rate of inflation that the central bank chooses to tolerate. These changes in the target inflation rate can be thought of as shocks to the preferences for inflation, either of society or simply of the central bank. ... The preceding analysis suggests a natural set of restrictions on a vector autoregression, since a central bank need not change its inflation objectives in response to other exogenous shocks, and so these shocks can be constrained to have no effect on inflation in the long run." To see how the Phillips curve model is identified using long-run restrictions we consider the moving-average representation of model (2.39), (2.42a)
Aut = 0us(L)e,^, + 0udiL)sj^t
(2.42b) A^p, = 0Aps{L)e,, +
0^AL)e,,,
The natural rate hypothesis implies that ^^^(1) = 0 and the "inflation is a monetary phenomenon" restriction implies ^475(1) = 0. Together with the assumption that the demand and supply shocks are uncorrelated we have three identifying restrictions, yielding one overidentifying restriction which can be tested. Blanchard and Quah (1989) have shown how to impose these long-run restrictions on vector autoregression models. However, when we impose these
2.2 The Long-Run Phillips Curve
63
restrictions on the reduced form Phillips curve model we used above to estimate the Keynesian Phillips curve, it becomes apparent that even though the resulting impulse response functions appear plausible, the overidentifying restriction is nevertheless clearly rejected by the data.^^^ That is, the monetarist model does not entirely fit the German data. Since we do not know which of the two monetarist identifying restrictions are rejected by the data, we proceed by considering two just-identified monetarist models, one representing the natural rate hypothesis and the other the "inflation as a monetary phenomenon" restriction. In the next section, where we investigate the sources of business cycle fluctuations implied by the two models, we hope to shed some more light on the plausibility of these models. 2.2.2.4.1 The Long-Run Trade-Off in the ''Natural Rate'' Phillips Curve Model The discussion of the monetarist challenge to Keynesian economics has shown that in monetarist models it is assumed that in the Phillips curve equation (2.39a) the direction of causality runs from (unexpected) inflation to the unemployment rate and not into the other direction as in the Keynesian Phillips curve. Also, in monetarist models inflation is the indicator of demand conditions while the unemployment rate indicates the supply response. Since in monetarist models inflation is assumed to be determined largely by monetary policy shocks, the demand shock in the aggregate demand equation (2.39b) is interpreted here as representing for the most part monetary policy shocks. ^^^ Imposing the "natural rate" restriction ^^^(1) = 0 on the Phillips curve model implies a value of-0.0044 for / ^ ^ . This means that in the "natural rate" model there is practically no short-run response of the unemployment rate to a demand shock. Thus, this model has very different unemployment-inflation dynamics than the Keynesian model where we observe a large contemporaneous response of the unemployment rate to a demand shock {X^^ - 0.6006). Moreover, Figure 2.11a shows that in the "natural rate" model the unemployment rate barely changes at any horizon in response to a demand shock. In this context it is interesting to notice that our "natural rate" identification happens to be very close to the y^^ = 0 restriction used by King and Watson (1994) and Dolado et al. (1997) to identify a Real Business Cycle (RBC) model. This type of model postulates that real activity variables like unemployment are determined only by real shocks like technological innovations and not by nominal shocks like monetary policy shocks. Moreover, prices are assumed to be completely flexible. Our "natural rate" model appears to have RBC characteristics, since the demand
^^^ The model has been estimated using MALCOM. The significance level of the test statistic for the overidentifying restriction is 2.04e-21. 106 In Keynesian models, on the other hand, this shock is assumed to represent largely fiscal policy shocks and other real demand shocks.
64
Chapter 2 Keynesian and Monetarist Views
shock leads on impact to a very strong inflation response which practically neutralizes the effect of this shock on the real sphere. ^^^ Given these characteristics, there is, of course, no Phillips curve trade-off neither in the short run nor in the long run. Figure 2.11b shows the response of unemployment and inflation to a supply shock, which again has been scaled so that it reduces inflation on impact by one percentage point. In contrast to the Keynesian identification there is a very strong unemployment response. This is consistent with the RBC view that real shocks are behind most movements in unemployment. Inflation falls initially below the base line, consistent with our requirement that a supply shock pushes inflation and unemployment into the same direction, and then rises slightly above it as the real economy approaches its new steady state level. Regarding the forecast error variance decomposition. Table 2.5 shows that demand shocks do not matter in the "natural rate" model for the unemployment rate at any forecast horizon. But demand shocks account for all fluctuations in inflation at short horizons and at the business cycle frequency. At longer forecast horizons supply shocks gain in importance. This shows that in this model supply shocks can have long-run effects on inflation, contradicting the monetarist proposition that "inflation is always and everywhere a monetary phenomenon." In sum, compared to the Keynesian Phillips curve model, the "natural rate" model takes the opposite view on the role of demand conditions for fluctuations in unemployment and inflation. In this model, there is no trade-off between inflation and unemployment at any frequency, meaning that both the short-run and long-run Phillips curves are practically vertical. Hence, a change in demand conditions leads to an immediate price response and no unemployment response. Table 2.5: Forecast Error Variance Decomposition in the "Natural Rate" Phillips Curve Model: Contribution of Demand Shocks Period 0 1 6 12 18 24 36 48 96
Unemployment
Inflation
1.14 1.08 2.36 1.15 0.63 0.40 0.22 0.16 0.07
96.98 96.20 96.57 97.71 98.08 96.23 90.99 87.24 81.94
^^' Note that the inflation rate in Figure 2.1 la is expressed as an annualized rate.
2.2 The Long-Run Phillips Curve Figure 2.1 la: The Trade-Off between Inflation and Unemployment in the Monetarist Phillips Curve: "Natural Rate" Identification Reaction of unemployment to a demand shock
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Reaction of inflation to a demand shock 1.20.0-1.2-2.4-3.6-4.8-6.0-7.2-
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 Phillips curve trade-off
2.01.51.00.50.0-
-0.5-1.0-1.5-2.0-
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
65
66
Chapter 2
Keynesian and Monetarist Views
Figure 2.1 lb: The Effects of Supply Shocks in the Monetarist Phillips Curve Model: "Natural Rate" Identification Reaction of unemployment to a supply stiock
~i
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
r
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Reaction of inflation to a supply shock 0.75 0.50-] 0.25-1 0.00 -0.25 -I -0.50 -\ -0.75 -] -1.00 -1.25
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
2.2 The Long-Run Phillips Curve
67
Changes in supply conditions, on the other hand, are the driving force behind fluctuations in the unemployment rate. Interestingly, in this model supply shocks play also some role for inflation fluctuations: in the long run, a positive supply shock that lowers unemployment leads to an increase in inflation. Technically speaking, the "natural rate" model has to display this somewhat counterintuitive relation to be able to account for the negative relation between the two variables that is clearly present in the data, as shown by our preliminary analysis in Section 2.2.1: since demand conditions do not have any effect on unemployment, it falls to the supply shocks to reproduce this negative relationship at longer frequencies, even though a positive relationship would be more intuitive. 2.2.2.4.2 The Long-Run Trade-Offin the ^^Inflation as a Monetary Phenomenon'^ Phillips Curve Model In this section we assume that inflation is a monetary phenomenon. According to the quantity theory this means that the permanent component of inflation is determined by permanent changes in the growth rate of money. ^^^ To identify this model, we impose the restriction O^sW = 0 on the Phillips curve model. ^^^ This yields a value of -0.0295 for A^^^. Thus, the short-run response of the unemployment rate to a demand shock is larger (in absolute terms) than under the natural rate restriction but still considerably smaller than under the Keynesian identification. Figure 12a shows the resulting impulse response functions. It appears that this monetarist model is an intermediate case between the Keynesian model and the "natural rate" model. There is a strong contemporaneous response of inflation to the demand shock which helps to insulate the real economy from this disturbance, but in contrast to the natural rate restriction the inflation response is not strong enough to fully neutralize its effect on the unemployment rate. Following the demand shock the unemployment rate gradually increases and reaches its new long-run level after about two years when it has increased by 0.44 percentage points. The unemployment response is significant, so is the slope of the long-run Phillips curve. It is a surprising finding that the monetarist model of the Phillips curve entails a significant long-run trade-off between inflation and unemployment. Formally, this means that the supemeutrality proposition is rejected, contradicting a central tenet of the monetarist view. Nevertheless, the long-run trade-off is fairly small, indicating a very steep long-run Phillips curve. Figure 2.12b shows the response of unemployment and inflation to a supply shock. The inflation response is relatively short-lived and after approximately 18 months inflation is back at its base line. Note that the supply shock has been ^^^ See also the discussion in Bullard and Keating (1995: 478). ^^^ A similar approach to identify the monetarist Phillips curve has been used by Bullard and Keating (1995) and Dolado et al. (1997).
68
Chapter 2 Keynesian and Monetarist Views
Figure 2.12a: The Trade-Off between Inflation and Unemployment in the Monetarist Phillips Curve: "Inflation as a Monetary Phenomenon" Identification Reaction of unemployment to a demand stiock
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 Reaction of inflation to a demand shock
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 Phillips curve trade-off
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
2.2 The Long-Run Phillips Curve
69
Figure 2.12b: The Effects of Supply Shocks in the Monetarist Phillips Curve Model: "Inflation as a Monetary Phenomenon" Identification Reaction of unemployment to a supply shock
-|
5
1
\
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
r
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Reaction of inflation to a supply shock 0.25
0.00
-0.25
-0.50
-0.75H
-i.ooH -1.25
n
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1-
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
70
Chapter 2 Keynesian and Monetarist Views
Table 2,6: Forecast Error Variance Decomposition in the "Money as a Monetary Phenomenon" Phillips Curve Model: Contribution of Demand Shocks Period 0 1 6 12 18 24 36 48 96
Unemployment
Inflation
32.30 32.05 36.67 31.14 28.41 26.72 25.14 24.43 23.58
61.23 59.19 60.38 63.86 71.30 78.32 86.38 90.25 95.38
restricted not to have a permanent effect on inflation. But this shock reduces the unemployment rate permanently by a sizeable amount, even though by less than is the case in the "natural rate" model. Table 2.6 shows the forecast error variance decomposition for this monetarist Phillips curve model. It is apparent that demand shocks account for about onethird of the variance in unemployment at short horizons. With the forecast horizon becoming longer the role of demand shocks becomes smaller, but at the business cycle frequency they still account for approximately one-quarter of the variance in unemployment and in the long run they have a share of 20 percent. For inflation, the picture is reversed. Initially, demand shocks are behind 60 percent of the variance in inflation, with the share becoming larger as the forecast horizon is extended. The identifying restriction imposed on this model ensures that for an infinite forecast horizon demand shocks account for 100 percent of the variance in inflation. In sum, this version of the monetarist model can be interpreted as a compromise between the two models we considered previously. In this model, demand conditions are allowed to have a moderate effect on unemployment. At the business cycle frequency this is consistent with monetarist thinking, since it is a key plank of the monetarist argument that discretionary monetary policy actions are an important cause of business cycle fluctuations. Hence, the "inflation as a monetary phenomenon" model captures an important element of monetarist business cycle theory that is not present in the "natural rate" model. However, in the monetarist model considered here, demand conditions also have some—^though limited—influence on unemployment in the long run, which is clearly inconsistent with monetarist theory, since the long-run neutrality (and supemeutrality) of monetary policy is another key implication of this theory. Regarding the comparison with the Keynesian model, it is useful to recall that monetarists do not dispute the Keynesian assertion that demand management policies can have
2.2 The Long-Run Phillips Curve
71
powerful short-run effects on real variables like unemployment, but they disagree strongly with Keynesians on the monetary transmission mechanism leading to the real effectiveness of monetary policy. In particular, monetarists argue that unexpected inflation plays a key role in the monetary transmission mechanism, and that monetary policy actions ultimately have strong inflationary effects. Hence, the main difference between the "inflation as a monetary phenomenon" and the Keynesian model is that the inflation response to a demand shock is much stronger in the former, and this mitigates the effect of the demand shock on unemployment. It would be useful to determine which of the three models is the relative "best" in the sense that it is most realistic in describing the inflation-unemployment relationship in Germany. Since all three models are just-identified, we cannot test directly the parameter that differentiates them, A^^. Hence, below we are going to evaluate the realism of the models using a more informal standard; in particular, we are going to investigate how the models explain several important business cycle episodes in Germany in the past 25 years and compare this with views on these episodes in the business cycle literature. However, before we do this, we conclude our discussion of supemeutrality tests by comparing our results with those found by other authors in the literature. 2.2.2.5
Other Results on Supemeutrality Tests
King and Watson (1994) employ the same approach we use in this paper to U.S. data. In general, for U.S. data the estimated long-run trade-off between inflation and unemployment tends to be somewhat smaller than the comparable estimate for Germany. Interestingly, while it is not surprising that King and Watson find a large long-run trade-off for the Keynesian Phillips curve, they also find a small but significant trade-off for the monetarist Phillips curves. In this respect the results for Germany and the United States are surprisingly similar in that they both reject the supemeutrality hypothesis for an identification scheme that would otherwise favor this hypothesis.^ ^^ Regarding the Keynesian Phillips curve. King and Watson estimate for the United States a long-run trade-off of-0.71 for the full sample period from 1954 until 1992, while we estimate for Germany a value of-1.61 for the period from 1970 until 1998. Since the sample periods are quite different, the two variables are not directly comparable. Regarding the subsample period from 1954 until 1969, King and Watson report a value of-1.30. For this sample period the Keynesian Phillips curve model for Germany yields a value of-1.82. ConsiderThe identification of the monetarist model using the "natural rate" hypothesis corresponds to King and Watson's RBC identification scheme. Since both schemes impose the supemeutrality restriction on the data, they do not differ in this respect. Interestingly, the resulting impulse responses are fairly similar.
72
Chapter 2 Keynesian and Monetarist Views
ing the large uncertainty in estimating the inflation and unemployment response to a demand shock, these values are relatively close to each other. For the second subsample period covering the time from 1970 until 1992, which is comparable to the sample period used in this study. King and Watson report a considerably smaller value for the long-run trade-off of-0.57. This decrease in the long-run trade-off coincides with an increase in the median inflation rate from 1.67 percent in the earlier period to 4.82 percent in the latter period. King and Watson point out that the increase in trend inflation was accompanied by the inflation process becoming more persistent. In terms of (2.22) this means that the sum of coefficients in the inflation process became larger. Since Lucas and Sargent have shown that an increase in the persistence of the inflation process tends to reduce the trade-off between inflation and unemployment one would find in a Keynesian type of Phillips curve estimate, the increase in persistence would account for the long-run trade-off becoming smaller in the Keynesian Phillips curve model. Interestingly, a comparable increase in the median inflation rate did not occur in Germany (the median inflation rate in the earlier period is 2.29 percent and 3.23 percent in the latter period). Thus, to the extent that this implies that the inflation process in Germany did not become more persistent, the unchanged inflation process would explain why the long-run trade-off in Germany remained relatively high in the 1970s and 1980s. Also, it is likely that the increase in the trend inflation rate in the United States reflected at least to some degree an attempt by monetary policy makers "to ride the Phillips curve," meaning they tried to reduce high unemployment by stimulating the economy. If the resulting increase in inflation led to an increase in the persistence of inflation, this implies that the very attempt "to ride the Phillips curve" led to the partial disappearance of the Phillips curve, making monetary policy less effective. This confirms the prediction of monetarists that the Phillips curve trade-off cannot be exploited in the long run. Monetary policy makers in Germany, on the other hand, did not try as aggressively to exploit the Phillips curve, and, thus, the Phillips curve trade-off did not disappear from the data. Regarding the monetarist Phillips curve. King and Watson report for the United States a significant but steep long-run Phillips curve.^^^ For Germany, we find the same result for the "inflation as a monetary phenomenon" Phillips curve. Moreover, Bullard and Keating (1995) investigate a similar model using the same identifying restriction and find for German data too that a permanent increase in inflation is associated with a positive, permanent, and statistically significant increase in the level of output. In addition, they find for a number of 111 For the sample period 1954-1992 they report a long-run trade-off of-0.29. For the
subsample period 1954-1969 they estimate a long-run trade-off of-0.47 and for the period 1970-1992 the corresponding value is -0.23. For Germany, we find for the period 1970-1998 a long-run trade-off of -0.44 for the monetarist Phillips curve based on the "inflation as a monetary phenomenon" identification. See also King and Watson (1997: 95).
2.2 The Long-Run Phillips Curve
73
low-inflation countries that supemeutrality does not hold. BuUard and Keating (1995: 478) write, "We note, more generally, that our estimated long-run response [of output] tends to be positive for low-inflation countries and lower or negative for countries with higher average inflation rates over the sample period. These results are consistent with theories which predict Mundell-Tobin effects at low steady state inflation rates, but where the effect dissipates at higher steady state inflation rates." This is conflrmed by BuUard (1999: 74), who finds in a recent survey on supemeutrality tests that for low-inflation countries the available evidence suggests that permanently higher money growth or inflation is associated with permanently higher output and permanently lower real interest rates. Thus, even though our finding of a small but significant long-run trade-off for a monetarist Phillips curve specification is likely to be controversial, it is nevertheless well established in the literature. A closely related approach to the one used in this paper is the testing procedure proposed by King and Watson (1992, 1997), which we discussed earlier. These authors investigate neutrality/supemeutrality properties of a bivariate model by considering a wide range of identifying assumptions for Ay^n, A^y, Yym -> a^d Yyny. In summarizing their results for U.S. data. King and Watson (1997: 95) write: "We conclude that the data contain little evidence against the long-run neutrality of money and suggest a very steep long-run Phillips curve." The latter finding implies that the long-run Phillips curve is not exactly vertical, meaning the supemeutrality hypothesis does not hold, but deviations from supemeutrality are likely to be small. This result is consistent with our result for the monetarist Phillips curve using the "inflation as a monetary phenomenon," where we also find a steep long-mn Phillips curve. King and Watson investigate also the supemeutrality of money in a bivariate model containing the differences of money growth and output. They find that it is possible to find evidence against supemeutrality, but these rejections tend to be marginal and are not robust against variations of lag length and sample periods. Thus, the jury is still out on this type of model. Weber (1994) applies the King and Watson (1992, 1997) methodology to German data. Like those authors he tests the supemeutrality of money in a bivariate system containing differenced time series of money growth and output. Weber (1994: 19) finds that "it is fairly easy to find evidence against the supemeutrality of money in German data." Regarding the long-mn Phillips curve he writes that "except for very extreme values of /i;2i^(>6.37) [in our notation this is X^^^\ and /?j^;^.(<-0.06) [A^^], the hypothesis of a long-mn vertical Phillips curve (YJJ^ = 0 [YuAp = ^1) cannot be rejected at the five-percent level. ... In the case with reverse causation, ..., it is easy to find evidence against the long-mn neutrality hypothesis /;a, = 0 [y^^ = 0 ] ..." (Weber 1994: 20). Our results do not replicate his results exactly, since our "inflation as a monetary phenomenon" identification implies a value of-0.0295 for y^^ and we do find for this value a small but nevertheless significant long-mn trade-off, whereas he finds that
74
Chapter 2 Keynesian and Monetarist Views
supemeutrality cannot be rejected if A^^^ is larger than -0.06, which would include our estimate of this parameter. These differences are probably due to differences in the sample period and the data set. However, it should be noted that a value of-0.07 for A^/^p^forexample, hardly seems "very extreme" since it implies only a very small contemporaneous response of the unemployment rate to a nominal shock and also happens to be the value used by King and Watson (1994) to identify their monetarist Phillips curve model. Hence, even on the basis of Weber's results supemeutrality cannot be ruled out, since defensible values for Xu^ give rise to a nonvertical long-run Phillips curve. Moreover, it should be noted that King and Watson (1997: 92ff) show that Weber's "reverse causation" identification corresponds to the traditional Keynesian identification of the Phillips curve. Hence, his finding that the long-run neutrality restriction y^u = ^ can easily be rejected implies that in Keynesian Phillips curve models the longrun Phillips curve is not vertical. Even though we could not reject the hypothesis of a vertical Phillips curve in our Keynesian Phillips curve model because of very wide confidence intervals, Weber apparently finds strong evidence against this hypothesis, which is encouraging from a traditional Keynesian viewpoint. In sum, Weber's results are broadly consistent with the result's we have found in this study. So far, the literature on neutrality and supemeutrality tests has considered largely bivariate models. The advantage of these models is that their small size requires only few identifying restrictions and that they are highly tractable. However, the drawback is that they provide at best a stylized presentation of the macroeconomy. In addition, limiting the model to only two classes of stmctural disturbances could also lead to an identification problem, because this implies that all disturbances buffeting the economy are classified as belonging either to the class of demand or supply disturbances. It is not clear that this is possible for all disturbances; an exchange rate disturbance, for example, affects both the demand and supply side of the economy. Even an oil price disturbance, which is the classic example for a supply side disturbance, has effects on the demand side of the economy by transferring income to oil producing countries.^ ^^ The obvious remedy to these problems would be to conduct the supemeutrality tests in larger models. This raises, however, another serious identification problem: this approach requires a considerably larger number of identifying restrictions, because the number of necessary identifying restrictions increases with the square of the variables in the model. This is a serious problem, since the number of sound theoretical restrictions is very small, as Ganova (1994: 122) pointed out. This problem becomes particularly severe when some of the variables are co^^^ Gottschalk and Van Zandweghe (2001) investigate for German data whether the small size of bivariate models adversely affects the reliability of these models. These authors find that the small size is indeed somewhat a problem, but more so for the identification of demand disturbances than for supply disturbances.
2.2 The Long-Run Phillips Curve
75
integrated. For illustration, we consider a model with five variables and two cointegration vectors. Modeling the cointegration vectors requires one identifying restriction each. In addition, the existence of two cointegration vectors implies the presence of three so-called common trends—disturbances with permanent effects—and two disturbances with transitory effects. In addition to the commonly used orthogonality restrictions, identification of these five disturbances requires another four identifying restrictions; three for the identification of the common trends and one for the identification of the transitory disturbances (Carstensen and Gottschalk 2001: 10). The problem is that identification of the common trends requires long-run restrictions, and economic theory offers only very few of these restrictions that are widely accepted. In fact, commonly used long-run restrictions in this context are neutrality restrictions. However, if one aims to test neutrality, this rules out this source of long-run restrictions, and not many alternatives are available. ^ ^ ^ There is a large body of VAR literature that takes cointegration into account by including level variables in the VAR, but imposes no reduced rank restriction on the model. That is, these models allow for long-run relations between the variables by not differencing the variables, but make no effort in modeling the cointegration variables explicitly. The structural disturbances are then identified using only short-run restrictions. Since theoretically motivated short-run restrictions are also in somewhat short supply, often a Choleski-type decomposition is used, which imposes a triangular structure on the model without offering a theoretical motivation for this particular structure. An example for a VAR model with level variables that is used for testing long-run neutrality is Bemanke and Mihov (1998a).^^'* These authors employ a seven-variable VAR using U.S. data and identify a monetary policy disturbance with restrictions derived from a theoretical model of the market for federal fiinds.^^^ They conclude that monetary policy disturbances have no significant long-run effect on output, but this reflects partly a very imprecise long-run estimate; the point-estimate continues to be positive even after seven years after the disturbance occurred. The problem with this approach is, however, that Phillips (1998) has shown that impulse response functions from unrestricted VARs are inconsistent at long horizons. In contrast, reduced rank regressions produce impulse responses that are consistent and predictions that are asymptotically optimal. Moreover, simulations show that these findings are relevant in finite samples in VARs with some unit roots and cointegration. In sum, Phillips' results suggest that if one uses large VARs to test supemeutrality, it would be useful to model cointegration relationships explicitly, but in this case one has to confront the problem that only ^ ^^ For a recent example of a common trend analysis for Germany, see Carstensen and Gottschalk (2001). See footnote 8 for a discussion of the use of level variables. ^ ^^ Nonmonetary shocks are identified using Choleski-type restrictions.
76
Chapter 2 Keynesian and Monetarist Views
few credible long-run restrictions are available to identify the common trends. The lack of these restrictions is the principal reason why bivariate models have proven so popular for testing neutrality. 2,2.2.6
The Source of Business Cycle Fluctuations
2.2.2.6.1 The Historical Decomposition Technique In this section we attribute the fluctuations in unemployment and inflation to demand and supply shocks buffeting the economy using the historical decomposition technique. The idea of this technique is best understood by considering the moving average representation of a structural model.^^^ In particular, consider the general model (2.43)
X,=C^(L)A+C(I)f,,
where the vector X represents the endogenous variables. The vector D contains the deterministic part of the model, with the term C^(L) representing a polynomial matrix giving the effects of D on the variables in X. The vector e contains the structural shocks. In the case of our Phillips curve model these are the demand and supply shocks. Finally, the matrix C{L) contains the estimated impulse response functions, showing how the endogenous variables respond to the structural shocks. Equation (2.43) states that the dynamics of the endogenous variables can be expressed as the sum of the deterministic and the stochastic component of the model. The latter is of particular interest. For expositional convenience, the deterministic part of the model is omitted in the following presentation of the historical decomposition technique. With this convention, for a particular period t-\- j , equation (2.43) can be rewritten as (2.44)
X,,j = 'tc,e,,j_, + t^s^t.j-s 5=0
S=j
with C denoting the impulse responses to a structural innovation. Equation (2.44) represents the historical decomposition of the variables in the vector ^ . It is apparent from (2.44) that the variable Xf+j is composed of two types of terms. The term on the far right contains the information that is available at time t. Based on this information the expected X^+j can be computed. This is the so-called "base projection" of X^+j, which contains also the effects of the deterministic part of the model. However, the base projection is unlikely to coincide with Xt+j, because in the time period from / + 1 to r + y "new" structural innovations hit the system. By their very nature these shocks are ^^^ See, e.g., Fackler and McMillin (1997) for a detailed description of the historical decomposition technique.
2.2 The Long-Run Phillips Curve
11
unexpected; hence, the first term on the right-hand side can be interpreted as the forecast error of X^^j. This is the most interesting part of the historical decomposition because it allows one to attribute the unexpected variation in X^^j to individual structural innovations buffeting the economy, which is useful for exploring the sources of fluctuations. Using the historical decomposition technique given by (2.44), there are essentially two ways to compute a time series of the forecast errors of X^^j. The first approach we use is to keep the forecast horizon fixed while the time index t moves from the beginning of the sample period to the end. The historical decomposition presented below is computed with the forecast horizon set to 7 = 24. We choose a forecast horizon of two years (24 months) because this horizon corresponds to a typical business cycle frequency. To illustrate the procedure, t is first set to 1970:1, the beginning of the effective sample period, and the forecast error of ^1970:1+24 = ^\9i2:\ is computed on the basis of the demand and supply shocks hitting the economy in the time period from 1970:2 until 1972:1. Next, t is set to 1970:2 and the forecast error of ^1972:2 is computed. This procedure is repeated until X^+24 reaches the end of the sample period. Thus, the historical decomposition computed in this way plots the variables in X^ as a function of the demand and supply shocks occurring in the time period from ^ to / - 23, thereby showing how these two structural shocks have led to the unexpected variation in the unemployment and inflation variables at the two-year horizon. The alternative approach to compute the forecast error is to set t to the beginning of the sample period and to increase the forecast horizon^ until the end of the sample period is reached. This approach has the disadvantage that the decomposition may not be very reliable for the early part of the sample period because only a limited number of shocks have been identified, meaning that the decomposition proceeds on a rather small basis.^^^ Still, this is not a major drawback as this period is presumably not of very much interest, while more recent developments are. To control for this shortcoming, we plot the historical decomposition of the unemployment and inflation variable below beginning in 1972:1. The strength of this approach is that it allows us to isolate the demand and the supply components in the time series. Consider, for example, the unemployment rate: by computing u^ as a function of all supply shocks occurring in the time period from 1970:1 until t we obtain the supply component of the unemployment rate in time t. Put another way, with this approach we can com117 To illustrate this problem, it is useful to consider the decomposition of unemployment in 1970:1, which is the first period for which estimates of the structural shocks are available. The change in unemployment in this month is attributed in full to the demand and supply shocks occurring in this month even though it is very likely that earlier shocks have had an influence as well. But the effects of these shocks cannot be identified here, because they lie outside the effective sample period.
78
Chapter 2 Keynesian and Monetarist Views
pute the unemployment rate that would have been obtained if there were no demand shocks, and vice versa. Also, defining the natural rate of unemployment as being determined by the deterministic component in the unemployment rate and its supply component, we can estimate the natural rate of unemployment implied by our three Phillips curve models. This way we can determine whether the secular increase in the German unemployment rate since the early 1970s is due to the natural rate increasing over time or whether it reflects progressively worsening demand conditions. 2.2.2.6.2 The Source of Business Cycle Business Fluctuations in the Keynesian Phillips Curve Model Figures 2.13 and 2.14 display the historical decomposition of the unemployment rate and the inflation rate for the Keynesian Phillips curve model. The inflation rate is computed here as the annual change in the price level, 100[ln(/J IPf-^)], and not as the monthly annualized inflation rate which we have used in the estimation of the Phillips curve models, because the latter series displays too much noise, which makes its interpretation difficult. The solid lines show the contribution of the supply shock (first panel) and the demand shock (second panel) to the fluctuations in unemployment and inflation at the business cycle frequency, while the dashed lines give the combined effect of the demand and the supply shock. It is apparent from the first panel that supply shocks practically play no role for the unemployment rate at the business cycle frequency, meaning that virtually all fluctuations in this variable are accounted for by demand shocks. On the one hand, this is very much in line with the traditional Keynesian perception that the unemployment rate is an indicator of aggregate demand conditions. On the other hand, this means also that all recessions, which are indicated by the shaded areas in Figures 2.13 and 2.14, have been caused by adverse demand shocks.^^^ However, it is widely believed that at least the large recessions in 1974/75 and 1980/81 were caused to some extent by the large oil price shocks preceding these recessions. Thus, the Keynesian identification seems to yield an interpretation of fluctuations in the unemployment rate, which puts an extreme emphasis on demand shocks. The fluctuations in inflation, on the other hand, are dominated by supply shocks. Even though the large demand-induced recessions are effective in reducing the inflation rate, their role is relatively small compared with those of the supply shocks. In Figure 2.15, we present the estimate of the natural rate of unemployment implied by the Keynesian Phillips curve model (dashed line) together with the ^^^ The recession dates are the same as those used in Figures 2.7 and 2.8. These have been computed for industrial production, which may explain why there is some discrepancy between the recession dates and the cyclical fluctuations in unemployment. In particular, it appears that the recession in 1995 had an effect on unemployment only in 1996 and the minor recessions in 1987 and 1998 were probably too small to have a noticeable effect on unemployment.
2.2 The Long-Run Phillips Curve
79
actual unemployment rate (solid line). It becomes apparent that even in the Keynesian model the secular increase in the German unemployment rate reflects an increase in the natural rate. Technically, this is due to the deterministic trend in the unemployment rate, which we estimate in the reduced form model of the Phillips curve. Since a deterministic time trend is not very informative on the causes of unemployment, we are facing here the limitations of the Phillips curve model, which, as a business cycle model, has not much to say about the trend component of unemployment.^^^ Nevertheless, this finding shows that even a Keynesian model of the business cycle does not give rise to the claim that the unemployment problem in Germany is entirely a demand problem. Still, the second panel in Figure 2.15 shows that, according to the Keynesian view, Germany experienced very high rates of cyclical unemployment in the past 30 years, particular so in the 1980s. This is in line with the assertion by many Keynesian economists that fiscal and monetary policies in Germany have been way too tight since the monetarist revolution in the 1970s. Figure 2.16 shows the historical decomposition of the inflation rate. The first panel shows that our reduced form model implies a deterministic downward trend in the inflation rate. This deterministic disinflation process reduces the inflation rate from approximately 3 percent in the early 1970s to about 1 percent in 1998. The fluctuations in the inflation rate around this deterministic trend are attributed to supply shocks (second panel) and demand shocks (third panel). The Keynesian view implies that the high inflation rates throughout the 1970s and the first half of the 1980s were attributable to adverse supply shocks. In light of the large oil price shocks in this period this is not implausible. Apparently a policy of tight demand throughout the 1980s tried to offset the inflationary pressures arising from these shocks, a policy which came with very high costs in terms of unemployment, as we have seen above. The increase in inflation in the early 1990s during the unification boom is equally attributable to demand and supply shocks.
^^^ In fact, there is an important strand in the literature which argues that cyclical fluctuations can affect the trend component of unemployment via so-called hysteresis effects. In hysteresis models, demand-induced unemployment can become permanent if, for example, the newly unemployed workers become disenfranchised from the workforce and wage setters make no effort to restrain wage growth in order to reintegrate them. In these models, there is no clear conceptual distinction between cyclical and trend unemployment. Even though the Keynesian Phillips curve we consider here is not based explicitly on hysteresis models, it nevertheless captures a key feature of these models by allowing demand shocks to have a permanent effect on unemployment. Still, Figure 2.15 shows that in spite of possible hysteresis effects the role of demand shocks for the natural rate of unemployment is relatively small. In Chapter 6 we will revisit this issue within a New Keynesian framework, using a larger model and employing multivariate cointegration analysis techniques. Hysteresis effects turn out be more important in this framework, but they nevertheless explain only part of the increase in trend unemployment in Germany over the past twenty years.
80
Chapter 2 Keynesian and Monetarist Views
Figure 2.13: Business Cycle Fluctuations in the Unemployment Rate: Keynesian Phillips Curve Model Effects of supply shocks 24-month ahead forecast errors 4.0 3.2 2.4-1 A
1.6 H
0.8-1
i? I 4
-0.0 -0.8
-1.6-1 -2.4 -3.2
II I
r'^"^'^i't^'T^''i'^j'' |>t-^vfHI
I
>i ^i \
1'
fi , 1/
-I—I—I—rn—rn—r—\—i—T—i—r—i—i—i—rn—i—i—i—i—f—rn—T—i—i—r 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98
Effects of demand shocks 24-month ahead forecast errors
-i—I—I—I •-i - 'I'* I—I—I—I—Y''''"'V'''''''('''''' I—I—I—r'^—I—I—I—I—f—rn—T—f—i—r* 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98
2.2 The Long-Run Phillips Curve Figure 2.14: Business Cycle Fluctuations in the Inflation Variable: Keynesian Phillips Curve Model Effects of supply shocks 24-month ahead forecast errors
-\—I—I—I
70
72
i
74
I
T—I—I—I—f—rh—T—f—I—r
I—1—I—r
76
78
80
88
82
90
92
94
92
94
96
98
Effects of demand shocks 24-month ahead forecast errors
I
70
72
74
76
78
80
82
84
86
88
90
I
96
I
I
98
81
82
Chapter 2 Keynesian and Monetarist Views
Figure 2.15:
Historical Decomposition of the Unemployment Rate: Keynesian Phillips Curve Model The natural rate of unemployment and actual unemployment
0 - "
1 — I — I — I — I — \ — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — \ — r
72
74
76
78
80
82
84
86
88
90
92
94
96
98
Cyclical unemployment Unemployment due to demand conditions
~ T — I — I — I — I — I — I — I — I — I — I — I — I — I — I — \ — I — I — I — I — \ — I — I — I — I — I — r -
72
74
76
78
80
82
84
86
88
90
92
94
96
98
2,2 The Long-Run Phillips Curve
83
Figure 2.16: Historical Decomposition of the Inflation Rate: Keynesian Phillips Curve Model Inflation and its trend component
Effects of supply shocks
72" '74'
76'
78'
80" 82'
84' 86'
88'
QO' 92'
94
96'
98
Effects of demand stiocks
72
74
76
78
80
82
84
86
88
90
92
94
96
98
84
Chapter 2 Keynesian and Monetarist Views
2.2.2.6.3 The Source of Business Cycle Fluctuations in the ^'Natural Rate" Phillips Curve Model Figures 2.17 and 2.18 show the source of business cycle fluctuations in the unemployment and inflation rate implied by the monetarist "natural rate" model. This identification seems to yield exactly the opposite implications as the Keynesian model. This is useful to illustrate the sharp clash between the two schools of thought, which continues to persist in the public debate up to the present time. Whereas the Keynesian view attributes all fluctuations in the unemployment rate at the business cycle frequency to demand shocks, the "natural rate" model attributes all of these fluctuations to supply shocks. In fact. Figure 2.17 reveals again the RBC characteristics of our "natural rate" identification, since it is a central tenet of RBC models that real variables like unemployment are a function only of real shocks. However, monetarist models in general do allow for nominal shocks to have temporary effects on real variables. In particular, monetarists argue that recessions in many instances are due to monetary policy actions. That is, they view discretionary monetary policy as an important source of business cycle fluctuations. Consequently, even monetarists are likely to disagree with Figure 2.17, where every recession is entirely due to supply shocks. Since we found earlier that the monetarist model is rejected by the data when the "natural rate" restriction is imposed together with the "money as a monetary phenomenon" restriction, the extreme implications of the "natural rate" restriction visible in Figure 2.17 suggest that it is this restriction that is at odds with the data. Regarding Figure 2.18, business cycle fluctuations in the inflation rate are attributed almost entirely to demand shocks. While this is in line with monetarist thinking, it is somewhat implausible that the two large oil price shocks in the 1970s did not have a noticeable effect on inflation. Figure 2.19 shows the natural rate of unemployment implied by the "natural rate" restriction. It is apparent that practically all changes in the unemployment rate reflect changes in the natural rate whereas the role of demand shocks is negligible. Figure 2.20 shows the historical decomposition of the inflation rate. A comparison with Figure 2.16 is striking: the fluctuations in inflation that the Keynesian model attributes to supply shocks are attributed by the "natural rate" model to demand shocks, and vice versa. In the "natural rate" interpretation of inflation fluctuations, the high inflation rates observed in the 1970s and 1980s were the consequence of expansionary demand policies, reflecting presumably an inflationary bias of policy makers. Supply shocks had a dampening effect on inflation. Since under the "natural rate" restriction the impulse response function for the inflation variable shows that an adverse supply shock tends to lower inflation in the long run (Figure 2.1 lb), the dampening effect of supply shocks on inflation visible in Figure 2.20 is due to adverse supply shocks. However, this
2.2 The Long-Run Phillips Curve Figure 2.17: Business Cycle Fluctuations in the Unemployment Rate: "Natural Rate" Identification Effects of supply shocks 24-month ahead forecast errors
-3.6
—'
1 — I — I — I
70
'•^••'••••f'' I — I — I — I — ^ ' • • • ' • ' ^ • • • • ' Y
72
74
76
78
80
82
84
86
88
90
92
94
96
98
Effects of demand shocks 24-month ahead forecast errors AH—, 1
\1
3.2-
iiiiiiii
I 1
2.4-
t
1.60.8-
^M
1 1 1 1 1
\
.Lr
-0.0
^ ' It
f
•'1
-0.8-
1
1
I,
^ ^
t<(\
!',
^ ^
ijj.
' iVi^ JiwiSiiiii / N ^ ^ „ ^ ;p4rsL^ 1 i\
1 1
-1.6-
1 1 /
III
---^^ .
' i l Thi]
-2.4-
;'\ '
I
i i
M
' "T
M
n
1
V
n
1
:1
" i'
1 '
\\
II :
'
7 9
70
72
1
74
1
76
78
i i i 1 1 1 1 80 82 84 86
88
90
92
I
94
1
96
9i J
85
86
Chapter 2 Keynesian and Monetarist Views
Figure 2.18:
Business Cycle Fluctuations in the Inflation Rate: "Natural Rate" Identification Effects of supply shocks 24-month ahead forecast errors
70
72
74
76
78
80
82
84
88
90
92
94
96
98
92
94
96
98
Effects of demand shocks 24'month ahead forecast errors
88
90
2.2 The Long-Run Phillips Curve Figure 2.19: Historical Decomposition of the Unemployment Rate: "Natural Rate" Identification The natural rate of unemployment (--) and actual unemployment
-i—I—I—I—I—I—I—I—I—I—I—I—I—I—I—i—I—I—I—I—I—I—I—\—I
72
74
76
78
80
82
84
86
88
90
92
94
I
96
i~
98
Cyclical unemployment Unemployment due to demand conditions
" T — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — r -
72
74
76
78
80
82
84 86
88 90
92
94
.
96 98
(~)
87
88
Chapter 2 Keynesian and Monetarist Views
Figure 2.20: Historical Decomposition of the Inflation Rate: "Natural Rate" Identification Inflation and its trend component
Effects of supply sfiocks
-2.0-i
WV 72
74
76
78
80
82
84
86
88
90
92
94
96
98
Effects of demand sfiocks
jijkik til I 72
74
76
—1
78
1
1
80
r-
82
84
86
88
90
92
94
96
98
2.2 The Long-Run Phillips Curve
89
notion is hard to reconcile with the implications of standard models about the effects of such shocks. 2.2,2.6.4 The Source of Business Cycle Fluctuations in the ^^Inflation As a Monetary Phenomenon'' Phillips Curve Model The "inflation as a monetary phenomenon" identification provides a more balanced view of the source of business cycle fluctuations than any of the two preceding identification schemes. Figure 2.21 shows that most fluctuations in the unemployment rate at the business cycle frequency are due to supply shocks, but demand shocks also play a noticeable role. According to this view, the recessions following the two oil price shocks are largely, but not entirely, due to adverse supply shocks, while the recession following the unification boom in 1992/93 is largely the consequence of adverse demand shocks. Since the latter recession followed a tight policy by the Bundesbank to cool the German economy down, this appears to be a plausible characterization of this episode. In general, demand shocks lead to fluctuations in the unemployment rate of about one percentage point in either direction. Regarding inflation. Figure 2.22 shows that fluctuations in the inflation rate are dominated by demand shocks. But supply shocks also play a noticeable role. In particular, the two oil price shocks are clearly visible in the decomposition of the inflation series. Nevertheless, the high inflation rates in the 1970s are, in general, the product of demand shocks. All in all, this seems to be a characterization of business cycle fluctuations that many economists in Germany would find plausible. Figure 2.23 shows the natural rate of unemployment implied by this model. It is apparent that over most of the sample period the natural rate of unemployment was higher than the actual unemployment rate, which is consistent with the perception of many monetarists that policy makers constantly try to push unemployment below the natural rate. This holds in particular for the 1970s and early 1980s, when the cyclical component in the unemployment rate is strongly negative. The other episode where demand shocks push the unemployment rate by a considerable amount below the natural rate is the period in the late 1980s and early 1990s, following unification. More generally, comparing Figure 2.23 with Figure 2.15 shows that monetarists have a completely different view of demand conditions in Germany than Keynesian economists. While the latter think that in the past 30 years demand conditions in Germany were almost always depressed, the former believe that Germany suffered over most of this time from excess demand.
90
Chapter 2 Keynesian and Monetarist Views
Figure 2.21: Business Cycle Fluctuations in the Unemployment Rate: "Inflation as a Monetary Phenomenon" Identification Effects of supply shocks 24-month ahead forecast errors
Effects of demand shocks 24-month ahead forecast errors
-\—I—I—rn—rn—i—i—i—T—i—i—i—i—i—rn—i—i—i—i—f—rn—T—f—i—n 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98
2.2 The Long-Run Phillips Curve Figure 2.22: Business Cycle Fluctuations in the Inflation Rate: "Inflation as a Monetary Phenomenon" Identification Effects of supply shocks 24-month ahead forecast errors
-1—I—I—r-n—r
70
~T
72 74
T
I 1
I
82
84
80
I
T"^
I
86
88 90
I r~
Tni—T—f—I—n
92
94
96 98
92
94
96
Effects of demand shocks 24-month ahead forecast errors
~T
70
I
I
72
I
I
74
I
I
76
I
I
78
I
T
80
r~~i
1
82
1
84
I
n
88
90
98
91
92
Chapter 2 Keynesian and Monetarist Views
Figure 2.23: Historical Decomposition of the Unemployment Rate: "Inflation as a Monetary Phenomenon" Identification The natural rate of unemployment (--) and actual unemployment (-)
Cyclical unemployment Unemployment due to demand conditions 1.00 0.50 0.00 -0.50 -1.00 -1.50 -2.00 72 74 76 78 80 82 84 86 88 90 92
94 96 98
2.2 The Long-Run Phillips Curve
Figure 2.24: Historical Decomposition of the Inflation Rate: "Inflation as a Monetary Phenomenon" Inflation and its trend component
72
'74
76
78
80
82
84
86
88
90
92
94" 96" 98
Effects of supply shocks
^.5-\ 1.0-
0.5 H 0.0-0.5-1.0-1.5-2.0-
'Af'^Y**^ 72
74
76
78
80
82
84
86
88
90
92
94
m^
96
98
96
98
Effects of demand shocks
72
74
'76 "78 '80 "82" "84 '86 "88 "90" "92' 94
93
94
Chapter 2 Keynesian and Monetarist Views
Figure 2.24 shows that in the monetarist model demand shocks account for most of the inflationary episodes. In this context it is important to recall that in the "inflation is always and everywhere a monetary phenomenon" model demand shocks are interpreted as monetary policy shocks. From this follows that the episodes of high inflation reflect a tendency by monetary policy makers to increase the inflation rate, presumably in order to push the unemployment rate below the natural rate. In this sense, Figure 2.24 reveals the inflationary bias of monetary policy makers which so often is deplored by monetarist economists in Germany, confirming that this identification captures an important aspect of monetarist thinking. Besides demand shocks, supply shocks also play a role for inflation dynamics in this Phillips curve model, even though they cannot have a permanent effect on inflation. Important supply shocks include the two oil price shocks in the 1970s and the sharp decline in oil prices in 1985. Interestingly, the unification boom in 1990 also had a noticeable positive supply component.
2.3
Conclusion
Keynesians and monetarists have been debating each other in Germany for more than 20 years, essentially exchanging always the same arguments. This stalemate in the public discussion of important policy issues like the appropriate monetary policy stance is due to the fact that both sides base their arguments on fundamentally different models. When two theories disagree sharply on one subject, economists usually attempt to determine on empirical grounds which of the two theories is right and which is wrong. In the present case it has become apparent in this chapter that this cannot be done in a straightforward manner. The key parameter, which determines whether a model has Keynesian or monetarist characteristics, is the slope of the long-run Phillips curve. However, estimating this parameter is complicated by the fact that this parameter is a structural parameter since it derives from the structural wage/price setting relation of the underlying theoretical model. From this follows that in order to test whether the long-run Phillips curve is vertical or not it is not sufficient to consider the correlation between the inflation and unemployment time series and to test the significance of the resulting correlation coefficient. Rather, for estimating the slope coefficient it is necessary to identify the Phillips curve model first. At this stage the empirical researcher has to decide whether he imposes a Keynesian or monetarist structure on the model, which, of course, predetermines the long-run slope of the Phillips curve. Thus, it is not possible to test the slope of the long-run Phillips curve in a "theory-free" manner since Keynesian and monetarist Phillips curve models are observationally equivalent as long as no overidentifying restrictions are imposed on the model.
2.3 Conclusion
95
Nevertheless, it is possible to check whether the resulting models yield plausible results. In this regard this chapter finds that most economists would probably find the monetarist model identified under the assumption that inflation is in the long run a monetary phenomenon the most convincing model considered here. But since this model implies that there is a significant long run trade-off between inflation and unemployment, this does not represent an unambiguous triumph of the monetarist position, even though the long-run trade-off is quantitatively small. In particular, if a vertical long-run Phillips curve is imposed on the model, the resulting "natural rate" model displays the characteristics of a RBC model and therefore is implausible from a monetarist viewpoint. Finally, it should be noted that even though most economists are unlikely to find the Keynesian Phillips curve model very plausible, this does not represent compelling evidence against this model. What makes this model implausible is that it implies that virtually all recessions in the past 30 years were entirely due to adverse demand shocks. Although most economists would think that adverse supply shocks played a role too, the notion that business cycle fluctuations reflect fluctuations in aggregate demand is entirely consistent with the traditional Keynesian position and therefore Keynesians may simply choose to disagree with the majority position on this issue. In sum, this chapter does not produce evidence which decisively refiites either the Keynesian or the monetarist position, but it shows what exactly these positions imply for the long-run Phillips curve and for the source of business cycle fluctuations, thereby hoping to clarify the debate. The current stalemate in the public discussion is nevertheless unsatisfying. One possible avenue to resolve this impasse is to consider what developments in modem macroeconomics have to add to the debate. These include the rational expectations revolution starting in the 1970s, which shattered on theoretical grounds much of the foundations traditional Keynesian theory has been built on. But Keynesian economists responded by launching in the 1980s and 1990s a research agenda to incorporate rational expectations into Keynesian economics. In the late 1990s this led to a widely accepted new strand of macroeconomic modeling called "New Keynesian economics" which, despite its label, comprises elements of both traditional Keynesian and monetarist models. The public debate on the German unemployment problem would probably benefit greatly if the insights of this new paradigm were to enter the debate. In the remainder of this study, we are going to follow this avenue and discuss both the rational expectations revolution and New Keynesian economics in more detail.
The Rational Expectations Revolution
The preceding chapter has reviewed the debate between Keynesians and monetarists, which underlies much of the pubHc debate in Germany. However, macroeconomic theory has evolved considerably, with potentially far-reaching implications for this debate. A large impetus into the way macroeconomic models changed was the introduction of rational expectations into macroeconomic modeling. This was pioneered by New Classical models, and later refined by Real Business Cycle models. In the former, expected monetary policy actions have neither short- nor long-run effects on output, and in the latter monetary policy does not matter at all. These results undermine any case for activist demand management policies, thereby putting a large question mark behind the Keynesian line of argument. This chapter provides a short introduction into these two models. This is followed by an overview of the response by so-called New Keynesian economists, who provide micro-foundations to much of the Keynesian argument and show that monetary policy can be effective even in the presence of rational expectations.
3.1
New Classical Economics
In the 1970s the principles of macroeconomic modeling of the 1950s and 1960s were challenged by economists like Lucas, Sargent, Wallace, and others. Their research program became known as New Classical economics. In a sense this research program represented the logical conclusion of the monetarist line of enquiry: While monetarists reintroduced some classical principles into macroeconomic models by rejecting nominal rigidities and assuming instead flexible prices. New Classical economists adopted the classical paradigm in full and applied it in an innovative way to business cycle research. Their starting point is the classical assumption that individuals and firms make the decisions that maximize their well-being subject to their budget and technological constraints (Espinosa-Vega and Russell 1997: 18). That is, in New Classical models the behavior of agents is derived from microeconomic principles. The emphasis on microeconomic principles separates New Classical models fi"om traditional Keynesian and monetarist macroeconomic models because the latter were not built on micro-foundations but were based on assumptions about the behavior of
3.1 New Classical Economics
97
consumption, investment etc. on the aggregate level. ^^^ Moreover, in New Classical models the principle of optimization is extended to intertemporal decisions. With intertemporal optimization New Classical models took a new approach to dynamic analysis and went beyond the comparative-static analysis common in traditional Keynesian and monetarist models. The New Classical approach to modeling economic fluctuations as resulting from decisions of intertemporal optimizing agents implies that the process of expectation formation plays an important role in the dynamic analysis of economic models. Intertemporal optimization means that current choices do not depend only on current and past conditions, but also on future conditions. Since future conditions cannot be known with certainty, agents have to form expectations. New Classical economists argued that adaptive expectation formation, which was favored by monetarists, is hard to reconcile with rationally acting agents, because adaptive expectations only use some of the available information. Since the resulting expectation errors have large real consequences, it is likely that rational agents would choose to form their expectations in a more sophisticated manner to avoid these disturbances. Moreover, adaptive expectations imply that agents do not learn fiilly from their earlier mistakes. For example, in monetarist models an entirely predictable policy of monotonically increasing the growth rate of the money supply is sufficient to fool workers again and again into working more hours even though this decreases their welfare. Since New Classical economists found the implications of adaptive expectations to be implausible they chose instead to assume that the expectations of households and firms are formulated in the most accurate possible manner, given the information available to them (Espinosa-Vega and Russell 1997: 19). This assumption is called rational expectations. An important implication of rational expectations is that agents form expectations about the behavior of policy makers. If the government changes its policy, agents may not recognize this immediately, but they will learn the new policy rule eventually and adjust their behavior accordingly. Technically, rational expectations imply that the mean expectation of agents with respect to some phenomena, say the price level, is equal to the prediction that would be made by the relevant economic theory (Buiter 1980: 35). Thus, the agents in the model do not make systematic expectation errors. The relevant economic theory is, of course, the theory underlying the model in question. In other words, the agents in the model are assumed to know the structure of the model. New Classical economists conduct their investigations in general equilibrium settings (Espinosa-Vega and Russell 1997: 18). In accordance with the classical paradigm they assume perfect price flexibility, implying that the economy is in 120 Principally, monetarists used the same modeling framework as Keynesians but put more emphasis on price flexibility and on the role of expectation formation in the dynamic analysis of these models.
98
Chapter 3 The Rational Expectations Revolution
continuous market-clearing equilibrium. Hence, in contrast to Keynesians, New Classical economists do not believe that nominal rigidities matter. The sources of economic fluctuations are unexpected shocks buffeting the economy. That is, New Classical models are stochastic models. They postulate that agents respond to these shocks in a rational way, basing their decisions on intertemporal optimization and rational expectations, and the resulting adjustment process leads to the economic fluctuations, which are commonly called business cycles. An important implication of New Classical models is that systematic monetary policy has no real effects. This is also called the policy ineffectiveness proposition. ^^^ The reason for the ineffectiveness of systematic policy is that agents are assumed to know the policy rule (rational expectations), therefore they are not surprised by systematic policy actions and adjust their prices immediately to the new situation. In other words, the assumption of rational expectations together with the assumption of perfect price flexibility implies that agents neutralize the effects of systematic monetary policy immediately by changing their prices accordingly. Since the economy is initially in equilibrium, the immediate price adjustment prevents the monetary impulse from disturbing this equilibrium. Monetary policy can have real effects in New Classical models only by surprising the agents. In this case imperfect information regarding the monetary policy course prevents agents from neutralizing the effects of the monetary impulse immediately. Mankiw (1990: 18) summarizes the transmission mechanism in New Classical models as follows: "Individuals were assumed to be more aware of the prices of the goods they produce than they are of the prices they purchase. They therefore tend to confiise movements in the overall price level (which should not matter) with movements in relative prices (which should matter). An unanticipated inflation leads individuals to infer that the relative price of the goods they produce are temporarily high, which induces them to increase the quantity supplied. This story thus implies that output depends on the deviation of inflation from expected inflation. In this way, the assumption of imperfect information was used to generate the expectations-augmented Phillips curve of Friedman and Phelps." New Classical models have strong policy implications: Since systematic policy is ineffective, there is no rationale for monetary policy to try to stabilize the economy in a systematic fashion. Unexpected policy has real effects, meaning that policy makers in general could affect output using this channel of transmission. But if the monetary authority has no more information than the public, a monetary policy based on random decisions is unlikely to improve welfare, because it would only add noise to the economy, thereby decreasing the allocative efficiency of the price system (Blanchard 1990: 797). If policy makers have more information than the public, in principle policy shocks could be used to offset other shocks and improve welfare, but the same outcome could be achieved by ^^^ For a detailed discussion of this proposition see Buiter (1980) and Gordon (1982).
3.2 Real Business Cycle Models
99
making the information available to the public. Thus, in New Classical models there is no role for monetary policy in stabilizing the economy. During the course of the 1980s the popularity of New Classical economics declined considerably (Mankiw 1990: 18ff.). An important reason was that the empirical evidence has generally been unfavorable. Particular attention has been paid to the hypothesis that anticipated monetary policy has no real effects. While the early empirical work of New Classical economists like Barro (1977) provided favorable evidence for the policy ineffectiveness proposition, these findings could not be substantiated by later work. Buiter (1983) shows that most of the earlier work suffered from serious identification problems. Mishkin (1982) develops an econometric methodology for analyzing rational-expectations models and finds that anticipated monetary policy has real effects, even if they are smaller than the effects of unanticipated policy. ^^^ Another reason for the lack of general acceptance of New Classical models is that for many observers it seemed implausible that misperceptions about the monetary policy course can have large output effects, since monetary data is widely available (McCallum 1989: 187ff). McCallum (1989: 188) summarizes the modem view on New Classical economics as follows: "Most economists today, then, doubt the relevance of the Lucas model to current business cycle fluctuations. Monetary misperceptions may have been important in the prewar U.S. or U.K. economies, but they are probably not in the 1980s." Even though New Classical positions are not relevant anymore for today's policy discussions, this research program has nevertheless made an important contribution to the field of macroeconomic theory by imposing "more rigorous scientific discipline on macroeconomic theorizing" (Espinosa-Vega and Russell 1997: 22). The emphasis of New Classical economists on micro-foundations of macroeconomic models and the assumption of rational expectations has had a lasting effect on the field of macroeconomics, since any modem macroeconomic model shares these features with New Classical models.
3.2
Real Business Cycle Models
Real business cycle (RBC) models are the direct successor of New Classical models. They were first introduced in the early 1980s and continued to command widespread attention until the middle of the 1990s.^2^ Like New Classical ^^^ Regarding evidence for Germany, Scheide (1984) finds evidence in favor of New Classical models using Granger noncausality tests. However, Leamer (1985) forcefully argues that Granger noncausality tests are silent on causation in an economic sense, and Hansen (1989) shows that Scheide's results are not robust with respect to specification. ^^•^ For an introduction into RBC models see Plosser (1987).
100
Chapter 3 The Rational Expectations Revolution
models, RBC models are based on intertemporal optimization, rational expectations, and continuous market-clearing. The difference is that RBC models do not aim to explain business cycle fluctuations as the result of monetary shocks, but see "real" shocks like changes in technology or tastes or shocks to government spending as the source of those fluctuations. ^^"^ Regarding the origins of RBC models, it appears that many proponents of New Classical models became convinced in the early 1980s that monetary policy shocks are indeed too small to account for a sizeable part of business cycle fluctuations and turned their attention to other sources of shocks while maintaining the general approach to macroeconomic modeling introduced by the New Classical research program (Blanchard 1990: 801). McCallum (1989: 195) notes in this regard: "In fact, the basic RBC model can be viewed as a more fully worked-out version of Lucas's model together with two crucial assumptions: that production function shocks are important and that individuals do possess information concerning current money stock magnitudes." Besides production function shocks (also called productivity or technology shocks), which refer to random fluctuations in the rate of technological change, the "real" shocks in RBC models are comprised of shocks to preferences, opportunities, resources, and endowments (Plosser 1989: 57). Later versions of these models also introduced government spending shocks. But the type of shock that usually receives most attention are the productivity shocks. Since these shocks are central for economic growth theories, RBC models offer a unified explanation for economic growth and economic fluctuations. The highly parsimonious framework offered by RBC models is part of the attraction of these models, particularly so because these models are, at the same time, rigorously founded on microeconomic principles. Consequently the effects of productivity shocks on the economy are investigated within real general dynamic equilibrium models. Regarding the core elements of RBC models, Goodfriend and King (1997: 242) write: "One key element is the intertemporal optimization approach to consumption and labor supply. Another is the similar intertemporal analysis of investment and labor demand, arising from the profit-maximizing decisions of firms. Plans of households and firms are then combined into a general equilibrium, in which quantities and prices are simultaneously determined." Changes in the technological capability of the economy lead in this framework to changes in relative prices, which induce households to rationally adjust their consumption and labor supply plans to the new environment. The same holds for firms. When the adjustment process is completed, the economy reaches a new steady state. One could argue that the different steady states determine the underlying trend growth of the economy, whereas the process of reaching the steady states represents the ^^^ Mankiw (1990: 19) writes on RBC models: "The business cycle is, according to this theory, the natural and efficient response of households and firms to changes in the available production technology."
3.2 Real Business Cycle Models
101
business cycle fluctuations. But it should be emphasized that trend growth and business cycle fluctuations have the same source in form of productivity shocks. RBC models do not offer any rationale for stabilization policy. Since money is completely ineffective in these models, monetary policy makers are powerless. In any case, they have no reason even to try to stabilize the economy. Mankiw (1989: 83) notes: "Since real business cycle theory describes economic fluctuations as a changing Walrasian equilibrium, it implies that these fluctuations are efficient. Given the tastes of individuals and the technological possibilities facing society, the levels of employment, output, and consumption cannot be improved. Attempts by the government to alter the allocations of the private market, such as policies to stabilize employment, at best are ineffective and at worst can do harm by impeding the 'invisible hand'." The assumptions that money does not matter and the inherent efficiency of economic fluctuations have made RBC models always very controversial. In particular the claim that large fluctuations in employment over the course of a business cycle reflect changes in the amount people want to work seemed incredible to many observers. In addition, there is disagreement about the nature of technological shocks. Critics find large technological changes, and in particular technological regress, implausible and argue that technological progress occurs gradually, which raises the question of what exactly is behind booms and recessions in RBC models (Mankiw 1990: 20). Moreover, the empirical evidence offered by RBC researchers, which usually involved the calibration of their models, was rejected by many observers on methodological grounds. In sum, most economists remained unconvinced on the implications of RBC models regarding the source of business cycle fluctuations and the notion that all fluctuations are efficient. But the RBC research program has nevertheless put its mark on modem macroeconomics. First, it has contributed greatly to advances in dynamic general equilibrium modeling. In particular, RBC models provide the underpinnings of most modem New Keynesian models. ^^^ Second, they have directed attention to the possibility that a substantial part of cyclical variability may be explained by real shocks of a technological nature (McCallum 1989: 195ff). Even if most economists are not prepared to believe that these shocks account for all economic fluctuations, it is hard to deny that they may account for some fluctuations. ^^^ Thus, RBC models have enriched the analysis of business cycle fluctuations considerably. ^^^ See Goodfriend and King (1997) for a comprehensive discussion of this issue. Blanchard (1990: 801) notes that given the complexity of models with intertemporal optimization, the focus on real business cycles may be justified as a tractable and necessary first step towards a richer macroeconomic model. ^^^ Empirical evidence from SVAR models to this effect is provided by Gottschalk and Van Zandweghe (2001).
102
3.3
Chapter 3 The Rational Expectations Revolution
The New Keynesian Research Program
While most economists in the early 1980s concurred with the view that macroeconomic models should feature rational expectations, many of them remained nevertheless convinced that systematic monetary policy has real effects. To overcome this dilemma, the New Keynesian research program tried to reconcile the effectiveness of monetary policy with the assumption of rational expectations. It soon became clear that the crucial assumption leading to the policy ineffectiveness proposition was not the rational expectations assumption, but the assumption of perfect price flexibility. Consequently New Keynesians faced the challenge of showing that price stickiness can arise in a model with optimizing agents with rational expectations. The remainder of this section reviews the empirical evidence on the effectiveness of systematic policy and discusses the ineffectiveness proposition from a New Keynesian viewpoint. Having outlined the basis for the New Keynesian approach, this section continues by giving an overview of the building blocks of New Keynesian models which provide the microfoundations for price stickiness.
3.3.1
Empirical Evidence on the Effects of Systematic Policy
There is a widespread perception that systematic and, hence, anticipated monetary policy matters. Otherwise, for instance, the substantial literature on the benefits of competing monetary policy rules like nominal GNP targeting, the famous Taylor (1993) rule or the rule proposed by McCallum (1987) would be misplaced, since these rules are evaluated on their ability to reduce the variance of output. If systematic monetary policy has no output effects, there would be no reason to expect monetary policy rules to be effective in reducing the variance of output in the first place. Many economists believe that monetary policy in its systematic pursuit of price level stability has played a significant role in causing many of the recessions in past decades.^^^ In this respect the work by Friedman and Schwartz (1963) on the monetary history of the United States has been particularly influential. Another case in point was the recession engineered by Federal Reserve Chairman Volcker. Ball and Mankiw (1994a: 129) write on this episode: "Monetary policy tightened in 1979 because Volcker was more committed to the goal of low inflation than was his predecessor, William Miller. It is easy to explain the deep recession that accompanied the disinflation of the early 1980s if one believes that monetary policy affects output."
12'7 See, for example, Fuhrer and Schuh (1998: 4).
3.3 The New Keynesian Research Program
103
However, providing direct econometric evidence on the real effects of systematic monetary policy actions is a highly challenging undertaking, since this requires dealing with a formidable identification problem. ^^^ Systematic policy responds itself to developments in the real sphere; therefore, determining the output effects of such a policy action requires one to separate the output movements attributable to policy from those the central bank responded to in the first place. ^^^ The seminal contribution in this field is Romer and Romer's (1989) work "Does Monetary Policy Matter? A New Test in the Spirit of Friedman and Schwartz." The two authors employ the so-called "narrative approach," which is based on careful reading of the minutes of the meetings of the Federal Reserve's Open Market Committee. Using these documents the authors attempt to identify times "when the Federal Reserve specifically intended to use the tools it had available to attempt to create a recession to cure inflation," and proceed to investigate whether the following policy actions, which where announced in the minutes and thus did not come as a surprise to the public, had significant output effects (Romer and Romer 1989: 134). Romer and Romer justify this focus on these particular episodes by pointing out that policy decisions to reduce inflation come as close as practically possible to being independent of other factors that affect real activity. They (ibid.) write: "In other words, we do not believe that the Federal Reserve states an intent to cause a recession to lower inflation only at times when a recession would occur in any event." Also, since the shift in the policy stance was announced, the effects cannot be attributed to a surprise monetary policy action. They find evidence for substantial falls of output and a rise of unemployment following a shift of monetary policy to an anti-inflationary stance. Comparable evidence for other countries is, however, in short supply. Nevertheless, from an empirical perspective the hypothesis that anticipated monetary policy has real effects appears to be justified if not proven.
3.3.2
Revisiting the Policy Ineffectiveness Proposition
In an influential paper, Gordon (1982: 1088) summarizes the "policy ineffectiveness" proposition developed by Robert E. Lucas, Thomas J. Sargent and Neil ^^° A number of New Classical economists have attempted to provide evidence that anticipated money growth has no real effects, see for example Barro (1977). A critical review of this work can be found in Buiter (1983) and Mishkin (1982). The latter author attempts to develop a more reliable methodology and finds that anticipated monetary policy does seem to matter. ^^^ For a survey of the methodological challenges in this regard and available empirical evidence see for example Friedman (1995). Cochrane (1998) provides evidence on the effects of anticipated monetary policy using the S VAR methodology for US data. Gottschalk and Hoppner (2001) extend and apply his methodology to euro area data.
104
Chapter 3 The Rational Expectations Revolution
Wallace as follows: "The LSW [Lucas-Sargent-Wallace] proposition, as it may also be designated, is based on the three theoretical assumptions of rational expectations, perfect market clearing, and a one-period aggregate information lag. It holds that real output responds only to unanticipated changes in the money supply, with no response of output to anticipated monetary changes such as those that would be associated with a systematic feedback-type monetary rule. The corollary of the LSW proposition is that the inflation rate responds contemporaneously and proportionally to any such anticipated change in money, and it is the validity of this corollary that depends on the outcome of empirical research concerning the speed of adjustment of inflation." It is important to emphasize that the debate about the validity of the policy ineffectiveness proposition is not a debate about the long-run responses of real activity to monetary policy actions. The long-run neutrality of money or, equivalently, the natural rate hypothesis has become an integral part of New Keynesian models. ^^^ Rather, the debate is about the question whether prices are sticky. And price stickiness depends crucially on factors like adjustment costs, long-term contracts or the decentralization of decision making, which prevent prices from jumping instantaneously in response to a nominal disturbance. Gordon (1982: 1090) concludes: "Thus the real issue separating proponents from critics of the LSW proposition is the importance of inertia in price adjustment; for LSW to be true, there can be no inertia, whereas inertia is the essence of the alternative NRH-GAP approach."^^^ An implication of the preceding discussion is that the assumption of rational expectations alone does not lead to the policy ineffectiveness proposition, since it is the degree of instantaneous price flexibility that is the central issue in the debate between the approaches. Consequently, Gordon notes that it is misleading to label the LSW proposition the "rational expectations approach," as is sometimes done.^^^ In a world characterized by price inertia in response to an anticipated nominal disturbance, agents with rational expectations will take this inertia into account when forming their price expectations, so rational expectations and price inertia are in principle compatible with each other.^^^ In other words, the assumption of rational expectations does not automatically imply that prices have ^^^ See, for example, Clarida et al. (1999). For this reason, Ball and Mankiw (1994a: 132) remark that "new Keynesians" could just as easily be called "new monetarists." The implications of the acceptance of the natural rate hypothesis will be discussed in the next chapter in more detail. ^^1 Gordon (1982: 1089) labels this approach with the acronym NRH-GAP, which stands for the combination of the long-run Natural Rate Hypothesis with the shortrun Gradual Adjustment of Prices. ^^^ For a discussion of the role of rational expectations in modem macroeconomics see also McCallum (1999: 3). He also points out that the strong association of the hypothesis of rational expectations with the policy ineffectiveness proposition was a widespread misconception in the 1970s and early 1980s. ^^^ For a simple, formal illustration of this point, see Buiter (1980: 40ff).
3.3 The New Keynesian Research Program
105
to be flexible. Rather, as McCallum (1999) points out, the hypothesis of rational expectations presumes only that agents form expectations so as to avoid systematic expectations errors. To do so, the agents have to behave as if they knew the structure of the actual economy. This implies that their expectations will agree with the theoretical model they "inhabit," because this model is intended to represent the true structure of the economy. Consequently, when the theoretical model does not specify prices to be instantaneously flexible, the agents in his model will not believe in instantaneously flexible prices either. Thus, it is the assumption of perfect market clearing or, more precisely, perfect price flexibility, not rational expectations, that is central for the policy ineffectiveness proposition.134 Regarding the validity of the market-clearing assumption, Tobin (1980) remarks that "the market-clearing assumption is just that, an assumption. It is not justified by any new direct evidence that a Walrasian auctioneer process generates the prices observed from day to day or month to month or year to year, or by any new theory telling how separate Marshallian markets or administered prices yield Walrasian results." Tobin goes on to note that in accordance with "the methodology of positive economics" this assumption should be empirically tested to help resolve the debate. There is indeed a wide body of literature devoted to this subject, including the aforementioned paper by Gordon, who finds on the basis of long time-series data for the USA strong evidence for his view of a gradual adjustment process of prices. Regarding more recent work on this subject, Ball and Mankiw (1994a) conclude from their survey of evidence from microeconomic studies of prices that the finding of substantial stickiness is universal. However, there is no consensus on this question in the literature yet, since, for example, McCallum (1999) disagrees on this point. Still, even though McCallum (1999: 28) finds the microeconomic evidence regarding the stickiness of prices noncompelling, he notes: "More influential, I believe, has been the perception that sharp major changes in monetary policy conditions (e.g., in the United States during 1981) have in fact had major real effects in the same direction, together with the belief that price stickiness provides the most satisfactory means of rationalizing the fact." However, even if there is empirical evidence in favor of price stickiness. New Classical economists argued that one should not give up the perfect marketclearing assumption easily, even if it does not hold exactly in the real world. After all, economic models always represent a simplification of the real world. Moreover, the alternative of sluggish price adjustment appears to collide with a fundamental principle of economics, namely that economic agents always strife to maximize their utility. This argument can be illustrated with the help of a ^^^ The third assumption regarding the one-period aggregate information lag is crucial for unexpected monetary poUcy shocks to have real effects, but this is not the issue here.
106
Chapter 3 The Rational Expectations Revolution
thought experiment where output is initially at its natural level until the government accelerates the growth rate of the money supply. In a sticky prices world this nominal disturbance induces agents to produce more goods and services than they would have in equilibrium. They can return to their original demand and supply schedules only after they have managed to adjust their prices to offset the nominal impulse in fiill. Given that the economy is initially in equilibrium and output at its natural level, the increase in real activity is clearly welfare-reducing. Hence, the question arises why agents fail to adjust their prices immediately to avoid this welfare loss. Put another way, fi"om this viewpoint it appears to be contradictory that on the one hand economic theory postulates optimizing behavior, but on the other hand here is a situation where economic agents clearly fail to act in their own self-interest by not adjusting their prices promptly. Or, in Lucas's famous quip, traditional models assume that people leave US$500 bills on the side walk. ^^^ This behavior of not adjusting all prices promptly becomes even more puzzling if one considers that an easy solution is available in the form of full indexation of prices or wages. ^^^ Early models proposed by Fischer (1977) and Taylor (1979) to counter the policy ineffectiveness proposition showed that if firms and workers fix nominal wages using long-term contracts, anticipated monetary policy can have real effects in spite of rational expectations. However, these models provide only an incomplete response to the New Classical position, since both workers and firms would benefit fi-om indexation, thereby eliminating the nominal rigidity inherent in the long-term contracts. In other words, the assumption of inflexible long-term contracts appears to be at odds with the notion that optimizing agents would not enter contracts that are unfavorable to them, particularly so because the lack of nominal flexibility in these contracts prevents them from optimally responding to aggregate demand fluctuations. This suggests that the perfect market-clearing assumption has some logical appeal even if it is empirically at best a rough approximation of the real world. However, this viewpoint risks ignoring that New Keynesian economics have made substantial progress in the last twenty years to incorporate price inertia into a fiilly optimizing modeling framework.
3.3.3
The Building Blocks of New Keynesian Economics
The label "New Keynesian economics" denotes the research efforts aimed at providing a theoretical framework where optimizing agents choose to create ^^^ Barro (1979) puts this more technically by noting that not all feasible trades that are to the perceived mutual advantage of the exchanging parties have been exhausted in this situation. 1^^ See Gordon (1990: 1139ff.) on the indexation puzzle.
3.3 The New Keynesian Research Program
107
nominal rigidities. ^^^ This research program is modest in the sense that it does not seek to formulate a new theory of fluctuations, as Ball et al. (1988) write, but instead attempts to strengthen the foundations of the traditional Keynesian view that fluctuations in output arise largely from fluctuations in nominal aggregate demand. ^^^ They write: "In particular, its goal is to answer the theoretical question of how nominal rigidities arise from optimizing behavior, since the absence of an answer in the 1970s was largely responsible for the decline of Keynesian economics" (Ball et al. 1988: 4). The central thesis is that nominal rigidities, and hence the real effects of changes in nominal demand, can be large even if the frictions preventing full price flexibility are small. Thus, seemingly minor aspects like the costs of price adjustment can account for large nonneutralities. The explanation of large effects of nominal rigidities rests on four foundations: imperfect competition, small "menu" costs of price adjustment, real rigidities, and staggered price adjustment. The remainder of this section provides a short introduction into the particular role assigned to the individual building blocks. ^^^ 3.3.3.1
Imperfect Competition
The assumption of imperfect competition is central for New Keynesian theories for a number of reasons. To begin with, under perfect competition firms are price takers, not price setters. In other words, under perfect competition the question under which conditions a firm chooses to keep its price fixed in response to a nominal disturbance is not useful, since firms do not choose their prices in the first place. The framework of imperfect competition is therefore a natural starting point for New Keynesian models. ^^^ Sometimes this label is also used for the type of models associated for instance with authors like Barro and Grossman (1976) or Malinvaud (1977), where prices are assumed to be initially fixed. These models emphasize that economic agents face quantity restrictions on some markets following a disturbance, since lack of price flexibility implies that markets do not always clear. This section does not refer to this research direction, since these models assume price stickiness without providing the micro-foundations for this feature. 138 While NeYv^ Keynesian economics primarily explain why changes in nominal demand have real effects due to lack of full price flexibility, this approach also helps to account for the output effects of real demand shocks like changes in goVemment spending. In this context it is helpful to note that the effect of a change in money supply on output is usually modeled via its effect on real money balances, which enter the aggregate demand function. If one interprets the money term in the aggregate demand equation as a shift term, it becomes clear that a change in real demand, which shifts aggregate demand too, works through the same transmission channels as a change in money. For a more detailed discussion of this point see Ball etal. (1988: 17). ^^^ For a more detailed discussion of the building blocks of New Keynesian models see Ball et al. (1988). This section draws very much on their work and in addition on the survey by Ball and Mankiw (1994a).
108
Chapter 3 The Rational Expectations Revolution
Second, Mankiw (1985) and Akerlof and Yellen (1985) have shown that small costs of price adjustment and imperfect competition are not only separate building blocks of a New Keynesian model, but are also highly complementary. They point out that under imperfect competition the profit loss of a firm due to nonadjustment of prices following a change in nominal demand is only of second order. This implies that the cost of price rigidity to the firm is small. In contrast, the macroeconomic effects of price rigidity can be of first order. To illustrate, it is useful to consider an aggregate demand function where output is a function of real balances; in this case, a change in money supply will lead to a proportional change in output, which means it has a first-order effect on output. Therefore, the macroeconomic effects are likely to be much larger than the costs of nonadjustment an individual firm faces. This results helps to resolve the aforementioned puzzle why optimizing agents fail to adjust their prices in response to a change in nominal demand, even though price stickiness leads to unwanted fluctuations of activity and thus reduces their welfare: An individual firm does not adjust its price because with imperfect competition it finds that the gains of price flexibility are smaller than the costs associated with price adjustment. But this holds only on the individual firm level, whereas on the aggregate level the gains of price flexibility would outweigh the costs by a wide margin. An alternative interpretation of this result is provided by Blanchard and Kiyotaki (1987), who show that the social costs of price rigidity are likely to exceed the private costs incurred by firms, because imperfect competition creates aggregate demand externalities. For instance, if the money stock falls and prices do not adjust, the lower real money stock reduces total spending in the economy and the demand curve each firm faces shifts inward, leading to a fall of the firm's profits. If a single firm adjusts its price, this has no effect on the position of its demand curve. Changing prices for the individual firm means only that it moves to a new point on the curve, which yields a second-order profit gain by optimally dividing the losses from recession between reduced sales and a lower price. However, if all firms adjusted their prices to the contraction in money supply, the lower aggregate price level would return real money balances to their original level and the demand curve would shift back out again. The gains in profit would be large, since the recession would end. The externality arises because an individual firm does not take this effect into account. Each firm believes that, as a small part of the economy, it cannot end the recession. As a consequence, it may not bother because of small price adjustment costs to make price adjustments that, taken together, would make everyone better off. Third, the assumption of imperfect competition implies that the effects of nominal rigidity on welfare are also of first order. Under imperfect competition, the price determined by profit maximization is socially suboptimal. More specifically, the price is too high, while output is too low. This implies that welfare would be higher if prices fell below the profit-maximizing price. In case of a contraction of the money supply, nonadjustment of prices means that the actual
3.3 The New Keynesian Research Program
109
price is kept above the price compatible with profit maximization, which leads to a first-order welfare loss. An increase in nominal demand, on the other hand, can lead to a first-order welfare gain if prices are kept fixed, since in this case the profit-maximizing price is higher than the price chosen by the firm. In other words, booms raise welfare. This is in line with the public perception that booms represent good times, but stands in stark contrast to the implications of perfect competition models, where all fluctuations are welfare-reducing. In this context, it is interesting to notice that in the latter models half the welfare loss of a business cycle occurs during upswings and booms when workers are required to work more than they supposedly want to. Even though the presence of aggregate demand externalities means changes in aggregate demand can have first-order welfare effects, it would be premature to conclude that this in itself implies that stabilization policy is desirable. The reason for this is that if changes in aggregate demand are symmetrically distributed, recessions will lower welfare and booms will raise welfare, but on average the welfare effects will cancel each other out. In fact, it is a standard assumption in New Keynesian models that output fluctuates symmetrically around potential output. That is, since in this regard New Keynesian models have monetarist characteristics, stabilization policy only affects the variance of output but not its mean, thereby ruling out first-order effects of stabilization policy. However, this result could change if the aggregate supply curve were nonlinear, so that decreases in demand would have large output effects, whereas increases in demand would have large price responses and only small output effects. Such an asymmetry would strengthen the case for an active stabilization policy, since stabilization of demand could raise the average level of output as well as reduce the variance of output and inflation. This scenario corresponds well with traditional Keynesian thinking about business cycle fluctuations, where it is often assumed that prices are stickier downwards than upwards, which leads to the nonlinearity of supply discussed here.^"^^ Another possibility is that output fluctuations are symmetric around potential output, but the welfare effects of recessions are larger than those of booms. Both possibilities will be discussed in the next chapter in more detail. Fourth, the assumption of imperfect competition implies that output is demand-determined. From the Keynesian perspective on the nature of the business cycle this is an appealing feature; particularly so because this feature is not obtained by the assumption of price stickiness alone. To the contrary, when prices are rigid it is more natural to assume that quantity equals the smaller of demand and supply. In case of a recession the demand side would determine For a more detailed discussion of sources of a nonlinear aggregate supply curve see Ball and Mankiw (1994a: 145ff). However, Ball and Mankiw (1994b: 248) provide a counterexample where this kind of asymmetry does not provide a rationale for demand stabilization.
110
Chapter 3 The Rational Expectations Revolution
output, in line with the Keynesian perspective. But in a boom prices are below their market-clearing level and thus there would be no supply response to the demand pull. This implies that in a boom output is determined by supply conditions, not by demand. With imperfect competition, however, firms would meet the expanded demand even when prices do not rise, since they have set their initial price above marginal costs. Thus, a change in demand conditions would always cause output to move into the same direction. 3.3.3.2
Menu Costs
Regarding the second building block of New Keynesian models, the so-called menu costs of price adjustment, the key question is what these costs are. Literally speaking, the term "menu costs" refers to the costs of printing new menus, catalogs or to the costs of changing price tags, etc. However, as Ball and Mankiw (1994a) notice, this term should be interpreted more as a metaphor, like the term "shoe leather costs" is a metaphor for the costs of inflation. In this broader sense it captures also the costs associated with gathering the relevant information and the time and attention required of managers to make and implement decisions. To minimize these costs, firms may decide to review their prices only at fixed intervals, leading to infi'equent price adjustment as long as the private costs of nonadjustment are small. More generally. Ball and Mankiw point out that this metaphor is similar to the parable of the Walrasian auctioneer, who ensures that prices always move instantaneously to equilibrate supply and demand. Just like models of perfect competition do not offer a literal account of the mechanism behind instantaneous perfect price flexibility, it is not necessary to identify exactly sources of menu costs in actual economies in order to study models with sticky prices. ^'^^ 3.3.3.3
Real Rigidities
The two building blocks discussed so far, imperfect competition and "menu costs," establish that nominal rigidities can be far larger than the frictions that cause them. However, as shown by Ball and Romer (1990: 184), they are not sufficient to explain nonneutralities of the size observed in actual economies: "For plausible parameter values, small nominal frictions produce only small rigidities. Thus Mankiw's and Akerlof and Yellen's argument, by itself, is not successful in providing foundations for the Keynesian assumption of nominal rigidity." Ball and Romer proceed to show that a high degree of real rigidity in combination with small nominal frictions can lead to large nonneutralities. They ^^^ As regards this argument, Ball and Mankiw (1994a: 143) write: "It is no more appropriate to insist on an exact identification of menu costs than it is to demand the social security number of the Walrasian auctioneer."
3.3 The New Keynes ian Research Program
111
define real rigidity as a small response of real wages and real prices to changes in real demand. Real prices refer to the ratio of a firm's price to the aggregate price level. It is important to notice that real rigidities alone are no impediment to full price flexibility. Therefore they do not imply nonneutrality by themselves, since the economy-wide adjustment to a change in nominal demand does not require a change in real prices. Instead, real rigidities increase the nominal rigidity arising from a given small cost of price adjustment. In this sense they serve as an amplifier in the transmission process from small costs of price adjustment to substantial nominal rigidity. An example for a source of real rigidities relevant in this context is firms paying efficiency wages. To provide some intuition why the assumption of efficiency wages can have the effect of greatly increasing the non-neutrality inherent in a New Keynesian model, it is useful first to consider an economy with imperfect competition and menu costs but no real rigidity. In this case a change in nominal demand leads to an increase in aggregate demand, which in turn triggers a rise in demand for labor. It is a stylized fact of most economies that labor supply is quite inelastic, which implies that the shift in labor demand leads to a large rise of real wages. Facing a sizeable increase of labor costs a firm has every incentive to raise prices to pass this cost increase on to customers. Consequently, nominal rigidity would not be an equihbrium response. However, if the firm would pay efficiency wages, nominal rigidity may turn out to be sustainable at small private costs for the firm. The assumption of efficiency wages implies that firms set wages initially above market-clearing level. Therefore, during times of rising aggregate demand the firm is able to find additional labor that is willing to work at the existing real wage level. That is, with this assumption real wages are not tied directly to the inelastic labor supply and therefore real wages are likely to be less procyclical. It is this feature that helps to reinforce nominal rigidities. With acyclical real wages, shifts in aggregate demand have little effect on marginal costs, and so the desire of firms to change prices is small. ^"^^ The introduction of real rigidities also implies that a hybrid world, in which some prices are sticky and others are flexible, is likely to be more accurately described by a sticky-price model than by a model with perfect price flexibility. The definition of real rigidity implies that firms do not wish to change their real price in response to a change in aggregate demand; in other words, they desire to keep their price relatively close to those set by the other firms in the economy. Consequently, a flexible-price firm does not adjust its nominal prices substantially if other firms in the economy do not do so, since proceeding unilaterally with price adjustment causes the real price of the firm to change markedly, which it seeks to avoid according to the real rigidity assumption. Therefore, flexible-
^^^ See also Jeanne (1998) for a dynamic general equilibrium model where real rigidities in the labor market amplify nominal rigidities in the goods markets.
112
Chapter 3 The Rational Expectations Revolution
price firms "inherit" sluggish price adjustment from thefixed-pricefirms,as Ball and Mankiw put it. 3.3.3.4
Staggered Price Adjustment
The model outlined so far still cannot account for the persistence of the real effects of changes in nominal demand. Once all prices have adjusted, the nominal rigidity is eliminated and output returns to its equilibrium value. However, business cyclefluctuationscan last for several years, while prices are unlikely to be fixed for such a long time. To illustrate this point, it is assumed in the following example that all firms choose to adjust their prices only once a year, for instance on January 1. If the central bank chooses to contract nominal demand and to engineer a recession on January 2, the real output effects will last only until January 1 the following year, when all firms adjust their prices downwards in proportion to the fall in money supply. ^"^^ In this scenario a recession can last at most for one year. It is the task of the fourth building block in New Keynesian models, staggered price adjustment, to explain the persistence of output effects in response to changes in nominal demand. Price staggering means that allfirmsdo not change their prices simultaneously, but adjust their prices at different dates. ^"^"^ With synchronized price adjustment, all firms adjust fiilly to a nominal disturbance as soon as their next adjustment date arrives. With staggering prices, however, some firms have to make the first step and thus have to change their prices while all other firms in the economy maintain fixed prices. This implies that their real price changes, which they deem to be undesirable under the assumption that real rigidities prevail. Therefore, these firms will change their prices only slightly. As a consequence it will take many rounds before fiiU adjustment to the nominal disturbance is completed. This helps to explain the persistence of the real effects of a change in nominal demand, since fiill adjustment can take much longer than the period for which each price is fixed. To summarize, the four building blocks imperfect competition, menu costs, real rigidity, and price staggering are mutually reinforcing and provide a framework where optimizing agents choose to create substantial nominal rigidity, even though this is likely to lead to unwanted economic fluctuations. Hence, this ^^^ Hence the real money balances retum to their original level, the aggregate demand curve shifts back outward again, and the recession ends. ^^"^ In the literature two forms of price staggering are discussed. With "time-contingent" price adjustment a firm adjusts prices at intervals of fixed length, while with "state-contingent" adjustment it does so whenever the state of the economy warrants it in the sense that the deviation between the actual price and the optimal price given the state of the economy makes it worthwhile to pay the "menu costs" and to adjust the price. Taylor (1979) shows for "time-contingent" adjustment that staggering produces considerable inertia of the price level. For a discussion of "statecontingent" adjustment see Ball and Mankiw (1994a: 140ff.).
3.3 The New Keynes ian Research Program
113
framework provides a theoretical justification for the Keynesian (and monetarist) assumption that systematic and thus anticipated monetary policy has real effects, which is also bolstered by substantial empirical evidence.
Monetary Policy in the New Keynesian Model
Chapter 2 concluded that it is unlikely that the differences between Keynesians and monetarists can be resolved on empirical grounds. However, spurred by the rational expectations revolution macroeconomic theory has come a long way since the heyday of the controversy between the Keynesian and monetarist camps. In particular, in the late 1990s a convergence between RBC and New Keynesian models emerged, which Goodfriend and King (1997: 255) called the New Neoclassical Synthesis: "The New Neoclassical Synthesis is defined by two central elements. Building on new classical and RBC analysis, it incorporates intertemporal optimization and rational expectations into dynamic macroeconomic models. Building on New Keynesian economics, it incorporates imperfect competition and costly price adjustment." This modeling approach is often also called New Keynesian, which is the label we will adopt in the remainder of this study, but it could also be called with equal justification New monetarist. ^"^^ Foreshadowing the main results of this chapter, this type of model features a Keynesian transmission mechanism, but many of its policy implications are similar to monetarist policy prescriptions. In a log-linearized version, the model typically is comprised of an expectational Phillips curve, a forward-looking IS curve, and an interest rate equation describing the policy rule of the central bank.^"^^ In the first section of this chapter, these equations are going to be derived, with special emphasis placed on providing the intuition behind the New Keynesian model. Next, Section 4.2 simulates a standard New Keynesian model to investigate the monetary transmission mechanism and the source of business cyclefluctuationsin the New Keynesian framework. Based on these results, Section 4.3 is going to explore the scope for stabilization policy in New Keynesian models, and discuss the implications for the macroeconomic policy debate in Germany. It will become clear in this chapter that the New Keynesian monetarist policy implications are, to some extent, due to the fact that the standard New Keynesian model is strictly linear, whereas Chapter 2 has shown that traditional Keynesian models have strong nonlinear features. Hence, the next chapter is going to extend ^^^ See Ball and Mankiw (1994a: 132) and the discussion in De Long (2000). ^^^ According to McCallum (2001a), this type of model represents the standard model used for macroeconomic analysis. For a nontechnical review, see King (2000). An extensive derivation and discussion is provided in Woodford (2002). The seminal contribution on the analysis of monetary policy in New Keynesian models is Claridaetal. (1999).
4.1 Deriving the Core Equations of the New Keynesian Model
115
the New Keynesian framework by introducing nonlinearities and discuss the implications for stabilization policy. Moreover, the final chapter is going to revisit the natural rate hypothesis, which is another cornerstone of the New Keynesian paradigm.
4.1
Deriving the Core Equations of the New Keynesian Model
The standard version of the New Keynesian model is comprised of three equations. These are the New Keynesian Phillips curve determining aggregate supply, aggregate demand is determined by the New IS curve, and the model is closed by the interest rate rule describing the behavior of the central bank.
4.1.1
The New Keynesian Phillips Curve
The starting point of the analysis is the assumption of monopolistic competition. ^"^^ There is a continuum of firms indexed by ie. [0,l], each producing a differentiated good Y^ (i) that it sells at a nominal price /J (/). The aggregate output and price levels are denoted as Y^ and P^, respectively. Monopolistic competition implies that each firm faces a demand curve for its product given by
(4.1)
YXi)--
Ml
y..
P. y where £ denotes the price elasticity of demand. For the production function a Cobb-Douglas type technology is assumed, which abstracts from endogenous accumulation of capital. This is customary in New Keynesian models, partly because of the observation that at the business cycle frequency movements in the capital stock and aggregate output are only weakly correlated, and partly because models with and without an endogenous capital stock can be calibrated to predict very similar output and inflation dynamics in response to the same kind of monetary policy shock. ^^^ This suggests that many policy-relevant issues can be
^'^'7 This discussion draws on Gali et al. (2001), King (2000), and Mankiw (2001). ^^^ For a discussion on the link between the capital stock and aggregate output see McCallum and Nelson (1997). They argue that to a large part the correlation is low because a typical year's investment is very small in relation to the existing stock of capital. Regarding the second point, see Woodford (2002: Section 4.5). However, Woodford also notes that the transmission mechanism behind the similar output
116
Chapter 4 Monetary Policy in the New Keynesian Model
analyzed in the less complicated model without explicit consideration of the capital stock. Hence, we assume the following production function: (4.2)
Y{i),=A,N,{i)'-\
where A^,(/) is labor input and A^ and a are technological factors common to all firms. ^^^ If prices were perfectly flexible, firms would always set prices as a constant markup over nominal marginal costs: (4.3)
P:(i) = ^MC7(i\
Here, P* (/) denotes the desired price of firm /, the markup is denoted as // and is equal to ju = e/{e-\), and MC"{i) denotes the nominal marginal costs of firm /. However, New Keynesian models are based on the notion that small costs of price adjustment, the so-called menu costs, prevent instantaneous price adjustment. In addition, price-staggering is assumed. A widely used approach to model price-staggering is the Calvo (1983) approach: Calvo proposes a stochastic price adjustment model, in which each firm has a constant probability of being able to adjust its price every period. That is, the probability for each firm to reset its price is only (l - ^), which is independent from the time period that has elapsed since the last price adjustment, and also independent from what the current price may be. This price-setting process may appear to be unrealistic, but it does capture the behavior of individual firms to adjust prices discretely at irregular intervals, and it simplifies the analytical treatment of modeling price adjustment by making the timing of the firm's price decision independent fi-om history. Moreover, at the aggregate level it is observationally equivalent to the quadraticcost-of-price-adjustment model. In this model, firms minimize the costs of changing prices, weighted against the costs of being away from the price the firm would choose in the absence of adjustment or menu costs. ^^^ This model represents a realistic approach to modeling price adjustment, but it is also more complicated, which is why many researchers prefer the Calvo model.
and inflation dynamics is quite different, owing to significant effects of the endogenous capital accumulation. ^^^ It is also possible to derive the New Keynesian Phillips curve using a CES function, which may be more appropriate for German data. For the theoretical derivation and empirical results for Germany see Carstensen (2002). 150 pQj. ^ discussion of this and other New Keynesian Phillips curve models, see Roberts (1995).
4.1 Deriving the Core Equations of the New Keynesian Model
111
With price-staggering, some of the prices will always have been set in the past, while others are newly adjusted. For the Calvo model, the following loglinear specification describes the aggregate price level:^^^ (4.4)
;. = (1 - d)YdJpij
= dp,_, + (1 - e)p:.
The variable p] denotes the logarithm of the newly chosen price. Since there are no firm-specific state variables, all firms that change prices in period t choose the same price. An important implication of the price-staggering mechanism can be illustrated by rewriting the second equality as a partial adjustment mechanism, Pj - p^_j = (l - 6)\p] - Pf_^ ]. This shows that if an expansion in aggregate demand pushes p* above p^.^, the price level will adjust only gradually, with the speed of adjustment being governed by the microeconomic probability of price adjustment, 0, This parameter determines also the expected time period a price remains fixed: l/(l - 0), Thus, in the Calvo model the degree of nominal price rigidity is completely described by 0. The fact that in the future a firm may be unable to change its price makes it necessary for the firm to consider the effects of a price chosen today on its profitability tomorrow. In fact, the probability of being stuck in period t + J with the price set in period t is 0^. Consequently, when the firm has the opportunity to change its price it is going to choose the new price P* (/) such as to maximize current and future profits: ^,X7=o(y^^y[^*(0^/+y(0-C(r,+y(0)]» where P is the discount factor and C(7^+^ (/)) denotes the cost fUnction of firm / (Carstensen 2002: 3). It can be shown that intertemporal profit maximization leads to following log-linearized price-setting rule:^^^
(4.5)
p:=\ogti^{\-P0)f^{P0yE\mclX
where mcl^j is the logarithm of nominal marginal cost in period / + y of a firm that last reset its price in period t. Intuitively, price equation (4.5) implies that firms set prices as a markup on a weighted average of current and expected nominal marginal costs. Expected marginal costs further out in the future are given less weight, partly because of the conventional discount factor P^, and partly because of the declining probability given by 0^ that the firm will be stuck with the price set in period t in period t-\- j . Another way to interpret (4.5) is to rewrite it as (4.6)
p] = log// + (1 - P0)mc: + 0PE,PI,
.
^^^ Small letters denote logarithms. ^^2 See Woodford (2002: Section 3.2) for the details.
118
Chapter 4 Monetary Policy in the New Keynesian Model
According to (4.6), a firm adjusting its price in period t will choose its new price as a weighted average of today's desired price as a markup over current nominal marginal costs and next period's expected adjustment price. In the log-linearized form nominal marginal costs are defined as mc" = mCf + p^, where mc^ is real marginal costs and p^ is the aggregate price level. Given the choice of the production function, real marginal costs are given by (4.7)
mc\ ={w,-p,)- {y^ - «J - log(l - a),
where w, is the nominal wage per unit of labor input, n^. Hence, with this specification price dynamics depend crucially on real unit labor costs. In this sense, the New Keynesian aggregate supply function incorporates a firmly Keynesian transmission mechanism, since traditional Keynesian models also emphasized the role of wage costs for price-setting decisions. However, once the New Keynesian model is put together, it will become clear that ultimately inflation is determined by monetary policy, as postulated by monetarists. Another central assumption in New Keynesian models is that real marginal cost is positively related to the output gap by (4.8)
mc,=h{y,-y,).
Here, y^ is natural rate of output, and {yt -y^) is the output gap.^^^ The relation given by (4.8) is an approximation, which holds under certain conditions. ^^"^ An increase in economic activity would lead to an increase in marginal costs if the aggregate production function had some fixed factors, or if firms had to pay higher real wages to induce workers to work additional hours. After combining equations (4.4), (4.5) and (4.8) and further transformations, one obtains the standard aggregate supply curve in the New Keynesian framework: (4.9)
Ap=j3EMH^
The parameter K is defined as K = h{l-0){l-J30)/0. It describes the effects of a change in aggregate demand, which leads to a change in the output gap, on inflation. The strength of this effect depends on two parameters, 0 and h. The larger 6, the larger the degree of nominal rigidity in the economy and the smaller the effect of a change in the output gap on inflation. The parameter h can be interpreted as measuring the degree of real rigidity in the economy. ^^^ As ^^^ The natural rate of output is defined as the level of output one would obtain if prices were completely flexible. ^ ^4 For a discussion see Rotemberg and Woodford (1997). ^^^ See also the discussion in Mankiw (2001).
4.1 Deriving the Core Equations of the New Keynes ian Model
119
discussed in Chapter 3, a high degree of real rigidity means that firms desire to keep their price relatively close to those set by the other firms in the economy. That is, in response to a change in real demand, which corresponds to a change in the output gap, a firm that has the opportunity to change its price will do so only slightly, in order to avoid a marked deviation fi'om the aggregate price level. If one substitutes (4.8) into (4.5), it becomes apparent that a small value for h impHes a small response of the firm's adjustment price p* to current and expected output gaps. Hence, h measures the responsiveness of a firm's relative price to changes in real demand, thereby capturing the degree of real rigidity in the economy. Chapter 3 pointed to the possibility that features like efficiency wages in the labor markets can lead to a high degree of real rigidity. However, New Keynesian modelers typically avoid explicit modeling of the labor market and other features giving rise to a high degree of real rigidity and proceed by simply assuming small values for h to introduce real rigidity into the model. ^^^ For explaining the linkages between monetary policy, output, and inflation this shortcut is often sufficient. The aggregate supply fiinction (4.9) has gained widespread acceptance in modem macroeconomic analysis. In fact, Mankiw (2001) notes that this model has become the workhorse for much recent research on monetary policy, while McCallum (1997) observes that it is "the closest thing there is to a standard specification." Equation (4.9) is often also referred to as the New Keynesian Phillips curve, because it models the inflation rate today as a fiinction of the inflation rate expected to prevail in the next period and of the output gap. This specification closely resembles the traditional expectations-augmented Phillips curve in which infiation is a function of expected current inflation and of the output gap. The main differences to its traditional counterpart are that the New Keynesian Phillips curve is clearly forward-looking, that it uses rational expectations instead of adaptive expectations, and the fact that it is firmly based on micro-foundations. It is interesting to notice that the triangle model of inflation, which has been developed by Keynesian economists in the second half of the 1970s as an empirical model of inflation and which has continued to be refined up to the present day, is broadly consistent with the New Keynesian Phillips curve. The primary source of inflation in the triangle model is excess demand, which corresponds to the output gap in (4.9), and the triangle model incorporates the process of expectations formations by including numerous lags. The broad correspondence between the two models strengthens the theoretical underpinnings of the triangle model, while at the same time the plausibility of the New Keynesian Phillips curve benefits from the empirical success of the triangle model.
^^^ For a discussion of the importance of real rigidities for New Keynesian models, see also Farmer (1999).
120
Chapter 4 Monetary Policy in the New Keynesian Model
For the policy debate between Keynesians and monetarists, a central issue is whether the New Keynesian Phillips curve embraces the monetarist natural rate hypothesis, or whether monetary policy can have long-run effects, an argument championed by Keynesians. In fact, the New Keynesian Phillips curve implies that money is both neutral and supemeutral. Beginning with the former, rewriting (4.9) as (4.10)
prPt-x = J3{E,p,,, - A ) + K{y, - y,)
shows that if the price level is constant at all dates, that is E^p^^^ - Pt = Pt-\ = P^ then output is at its natural level, >' - J^ = 0. Hence, a policy that changes the price level permanently has no long-run effects on output once the economy has reached its new steady state. Regarding supemeutrality, the New Keynesian Phillips curve implies that the steady-state inflation rate A/?, = E^Ap^^^ = Ap is related to output by (4.11)
y,=y,-^^-^Ap,
The parameter {\-P)IK gives the long-run slope of the Phillips curve. This slope measures the responsiveness of output after the inflation rate has moved from one steady state to the other. The central parameter here is the discount factor p. Typically, it is specified to be very close to unity. McCallum (2001a), for example, uses for the calibration of his New Keynesian model the value y5 = 0.99. Another example is Clarida et al. (1999), who impose the condition >5 = 1 on the New Keynesian Phillips curve. With this specification there is practically no link between the steady-state inflation rate and the output gap, and, consequently, a policy that permanently changes the inflation rate will have no effect on output. Using McCallum's specification of P = 0.99 and K - 0.03, and assuming a steady-state inflation rate of 1.5 percent, (4.11) implies that increasing the steady-state inflation rate by one percentage point increases output in the long run only by 0.125 percent, which is negligible from an economic point of view.^^^ King (2000: 51) observes that experiments with fiilly articulated models that lead to price adjustment equations like (4.9) also suggest a negligible longrun trade-off at moderate inflation rates. He writes: "The fully articulated models provide this quantitative result because (i) firms do not allow sustained inflation to have much effect on their monopoly profits and (ii) households do not allow sustained inflation to have much effect on their factor supply" (King 2000: 69). Thus, for all practical purposes supemeutrality holds in New Keynesian models. This is a key feature of New Keynesian models, which is responsible for many of the monetarist policy implications of these models discussed below.
^^' Notice that McCallum uses nonannualized interest and inflation rates in his model.
4.1 Deriving the Core Equations of the New Keynesian Model
121
We have seen in Chapter 2 that the supemeutrality assumption is somewhat at odds with Keynesian and monetarist Phillips curve models for German data; in Chapter 6 we will revisit this issue in a New Keynesian framework. Until then, we follow the convention in New Keynesian economics and assume that superneutrality holds.
4.1.2
The New IS Curve
The starting point for the derivation of the New IS curve is the assumption that households maximize their utility over time.^^^ That is, each household seeks to maximize the time-separable utility function Z7=o>^^^(Q+;'^/+y)' where P is again the discount factor. The household's consumption is denoted as Q , and M; is the stock of real money at the beginning of the period. The latter variable is included to capture the transaction services provided by money. Households consume a bundle of goods, whose aggregate is represented by Q , but they specialize in production, producing a single good according to the production function 7, = / ( A ^ J , where Y^ and A^^ are again output and labor input. As before, we abstract from the exogenous capital stock. Each household is assumed to inelastically supply one unit of labor each period to the labor market. In this market, households as producers of goods can purchase a unit of labor at the real wage rate Wf, To introduce an interest-bearing asset, a market for one-period government bonds is assumed, which are denoted B^. The real rate of interest on those bonds is r^, and the real purchase price for a bond that is redeemed in the next period for one unit of output in the next period is (l + r)~^. The government is also assumed to levy a lump-sum tax V^ on each household. These assumptions imply that each household faces a budget constraint of the form (4.12)
f{Nyw:{N,-\)-V,=C,^[{\
+
^p^Ml,-M:V
^ B,.,-B, 1+n
In (4.12), the term W[{N^ -1) denotes the real wages paid out by a household to its employees minus its own labor income, while the last two terms in square brackets on the right-hand side are the changes in real money and bond holdings, respectively. ^^^ With this budget constraint, the Lagrangian resulting from the intertemporal maximization of utility is: ^^^ This sections draws on McCallum and Nelson (1997). ^^^ Note that the term (l + Ap,)M;^., simplifies to M^^JP^, where M^^j denotes the nominal money stock in period ^ +1.
122
Chapter 4 Monetary Policy in the New Keynesian Model
(4.13a)
L=^PJ U[C,,J,MUJ)+AA y=0
-[{i +
f{N,J-W,lj{N,,j-l)-V,,j t+J -C,^t+j
^..M,Hj-M!:J-
•^i+uj-^i+j
,1 + ';^,
To derive thefirst-orderconditions it will be useful to write out (4.13a): (4.13b) i = t/(C„M;)+y5f/(C„„M,;,)+... + A,
f{N,)-Wr{N,-i)-v,-C,
-[(I + 4 P , K ' ; , - M ; ] -
1 BM-B, l+K
f{NM)-wUN,,,-\)-v,^, -c,„ -[(I+4P,.,)M,;, -M;,,] 1 •^<+2-^<+i l + r. Since the variables M; and B, are predetermined, the choice variables of the household in each period are therefore consumption C„ labor input into its production N„ real money A/,*;,, and bond holdings at the end of the period 5,+,. Maximizing L over these choice variables in response to the paths of real wages, the real interest rate, the inflation rate, and the lump-sum tax yields the following first-order conditions, which have to hold in all periods: (4.14) (4.15)
U^{C„M:)-A,=0
f,{N,)-W[=0
(4.16)
y5t/^(c„„M,;,)-/l,(l + A p , ) + A . . = 0
(4.17)
-/l,(l + 0 - ' + A . i =0.160
To determine equilibrium, the government budget constraint has to be observed: (4.18)
- K, = (1 + Ap, )M,;, - M ; + (1 + r,)"' B,,, - B,,
^"^ The notation g,() denotes the partial derivation of g with respect to its /th argument.
4.1 Deriving the Core Equations of the New Keynes ian Model (4.18)
123
- F , = ( l + A p j M ; , - M ; + ( l + r,)-'5,,,-5,,
and the market-clearing conditions for the labor and the money markets have to hold: (4.19)
N,=l
(4.20) M ; = ^ . Here, M, denotes the nominal money supply. Taking together, the budget constraints (4.12) and (4.18), the first-order conditions (4.14)-(4.17) and the market-clearing conditions (4.19)-(4.20) determine the path of the household choice variables [C^,N^,M'_^,^,B^^^) and the price variables \fV',r^,Pj in response to the paths of the government choice variables nominal money supply (M, ) and the lump-sum tax [Vf). McCallum and Nelson (1997) show that the system given by (4.12)-(4.20) can be used to derive a relation that represents behavior of the sort described by the IS relation in traditional Keynesian models. To that end (4.17) is substituted into (4.14), yielding^^^ (4.21)
C/,(c„M;)=t/,(c,,„M;J^(l + rJ.162
This equation implies that households seek to equalize the marginal benefit of consumption today with the discounted marginal benefit of consumption in the next period times the real rate of return on savings. Next, it is assumed that the functional form of the utility function U[Cf,M') is separable. In particular, McCallum and Nelson assume that the utility function is of the form
(4.22)
^(c,,M;) = 0c7(^-irc("-^)/- + (l-0)<^(M;).
Here, 0 defines the weights of consumption and real money balances in the utility function, a represents the elasticity of substitution of consumption at different dates, and W\^t) specifies the utility of real money balances. According to this specification, the marginal utility of consumption is (4.23)
t/,=0Cr^/-.
Inserting this result into (4.21) gives
(4.24)
0Cr^/-=^C-V->5(l + rJ.
1 ^ 1 Note that (4.14) implies /l,+, = U, (c,+i, M;^I ). ^^^ Again, this relation has to hold in all periods.
124
Chapter 4 Monetary Policy in the New Keynesian Model
It is important to emphasize that (4.24) is a behavioral equation which represents the choice of a household of today's consumption in response to the real interest rate and expectations concerning tomorrow's consumption, and not the choice of tomorrow's consumption as a function of lagged values of consumption and the real interest rate. After all, in this model the choice variable is C, and not C,^,. Solving (4.24) for C, yields (4.25)
C,=C,,,L5(l + r j r . l 6 3
Upon taking natural logarithms, we have (4.26)
c, = c,,, - a log(l + r j - a log y5.
Using the common approximation log(l •¥x) = x for small values of x and assuming that households form rational expectations about fiiture consumption, we obtain the following consumption equation: (4.27)
c,=E,c,,,-a{r,-r),
where r is defined as r = (l - 0)1 p. For the latter term we use the approximation -logj3 = {l-j3)/j3, which holds for values of J3 close to unity.^^"^ For reasons that will become apparent below, F can be interpreted as the steady state natural rate of interest. ^^^ The relation given by (4.27) shows that current consumption depends on expected consumption. Intuitively, this result arises because households wish to smooth consumption. Hence, an expectation of higher consumption in the next period leads them to want to consume more today. The negative effect of the real interest rate on current consumption reflects the intertemporal substitution of consumption that arises when a higher real interest rate makes saving today more attractive, thereby shifting consumption into the future. ^^^ The final step to obtain the New IS curve is replacing consumption with output in (4.27). Since the standard Keynesian model abstracts from endogenous capital accumulation for reasons outlined above, the market-clearing condition implies Y^ =0^-^-0^, where G^ is government consumption. From this follows 163 PQJ. ^Y^Q interpretation of crit is useful to notice that (4.25) can be rewritten as ^t+i/^t =L^(l + ^/)r.The inverse of crdefines the relative risk aversion of households. The specific functional form chosen here implies that this parameter is constant. See also the discussion in Romer (1996: 40, 324). ^^^ As discussed in the previous section, a value arbitrarily close to unity is typically chosen for the discount factor j8. ^"^ To keep the notation simple, we assume in the remainder of this study that the steady state refers to an economy that is not growing. Relaxing this assumption would lead to the inclusion of additional constants into the expression for the steady state interest rate, but would not change the results qualitatively. ^^^ See also the discussion in Clarida et al. (1999) on the New IS curve.
4.1 Deriving the Core Equations of the New Keynesian Model
125
that private consumption can be expressed as Q = [ 1 - ( G ^ / 7 j 7 j . In logarithms, this yields Cf=y^-e^, with e^ defined as e, = - l o g [ l - ( G , / y ; ) ] . Inserting this relation into (4.27), we obtain: (4.28)
y, -e, =E,{y,,, -e,,,]-a{r,
-r).167
Rewriting (4.28), we finally have the New IS curve: (4.29)
y,=E,y,,,-(7{r,-r)^g,,
where g^ =£'^{-A^,^,}. This term can be interpreted as a shock to aggregate demand, which mainly reflects changes in government consumption. This relation has a strong similarity to the traditional IS curve, since both postulate that an increase in the real interest rate lowers aggregate demand. Hence, relation (4.29) is commonly referred to as the New IS curve. However, the transmission mechanism is different: In the New IS curve a higher real interest rate leads to lower consumption today because of larger incentives to save income, while in the traditional IS curve the transmission channel via lower investment demand is emphasized. Another significant difference is that the New IS curve is explicitly forwardlooking. That is, expected output is an important determinant of output demanded today. Technically, this arises because in modem consumption theory efficient consumption growth is positively related to the real interest rate: ^r+i/c, = L^(l + ^ j r .^^^ The traditional IS curve, on the other hand, postulates a link between the level of current output and the real interest rate. The traditional IS curve is consequently not inherently forward-looking. However, the forwardlooking component of the New IS curve is not incompatible with the investment behavior underlying the traditional IS curve, since firms are likely to take in their investment decisions expectations concerning future output into account. In fact, the omission of the forward-looking term in the traditional IS curve may explain the difficulties in isolating the effects of the interest rate on aggregate demand in empirical investigations of this relation (King 2000: 72ff). The forward-looking nature of the New IS curve has important implications for the transmission mechanism. By forward iterating (4.29), it becomes apparent that current output is a fimction of the current and of the future path of the real interest rate:
167 For a more explicit treatment of government consumption in the New Keynesian
model, see McCallum and Nelson (1997: 25). For an open-economy extension of the model see McCallum and Nelson (2001). For a model with an endogenous capital stock see Casares and McCallum (2000). 168 See also Romer (1996: 324) and the discussion in King and Kerr (1996: 55).
126
(4.30)
Chapter 4 Monetary Policy in the New Keynesian Model
y, =E,Y,{-CT[r,,j -r^gt.X y=o
Hence, to the extent that monetary policy has leverage over the short-term real interest rate, (4.30) suggests that monetary policy has real effects via its current and its expected policy actions (Clarida et al. 1999). Woodford (2002) argues that this result is of considerable importance for the theory of monetary policy. He writes: "It implies that a central bank's primary impact upon the economy comes about not through the level at which it sets current overnight interest rates, but rather through the way it affects private sector expectations about the XiktXy future path of overnight rates. This in turn implies that the credibility of policy commitments must be a paramount concern, that discretionary optimization will almost surely lead to a suboptimal outcome, and that interest rate smoothing is desirable" (Woodford 2002: 9). Another way of interpreting (4.30) is that if the expectations hypothesis of the term structure holds it is not a short-term but a long-term real interest rate that determines that aggregate demand in this model. The New IS curve has also implications for the natural rate of interest. King (2000) observes that if the economy is operating at its capacity level of output, then there is a particular level of the real interest rate which one may call the natural rate of interest, r^}^^ Inserting the corresponding values of output into the New IS curve and rearranging, we obtain:
(4.31)
^=-[^J,.i-5^,+gJ+r. (7
This equation implies that the natural rate of interest increases when the capacity level of output is expected to grow more rapidly, and when there is a positive shock to aggregate demand. In fact, this holds more generally for the relationship between the real interest rate and output: (4.32)
r,^-[Etyt^^ -yt+gt]+r. G
This relation has important implications for the cyclical co-movement between the real interest rate and cyclical fluctuations in output. In particular, if the economy is in a recession, but a recovery is expected, this would be associated with a high real interest rate. On the other hand, if the economy is in a temporary boom, the New IS curve implies one would observe a low real interest rate. In steady state, with y^^y^^ E^y^^^ = y and no aggregate demand shocks, the natural rate of interest becomes ^^^ See King (2000: 74). Here we equate the natural rate of output with the capacity level of output.
4.1 Deriving the Core Equations of the New Keynesian Model (4.33)
127
F, = F ,
which is the steady state natural rate of interest in the New IS curve. From a monetarist perspective, it might be surprising that the New IS curve does not include any role for real money balances to affect aggregate demand. After all, the importance for money balances in the monetary transmission mechanism has been an important part of the monetarist research agenda. In the model considered here, the exclusion of real money balances resultsfi-omthe assumption of a utilityfiinctionseparable in consumption and real money balances. McCallum and Nelson (1997: 19) motivate this assumption as follows: "We do not claim that separability is theoretically an appropriate assumption. But we believe that for many purposes an approximation that neglects interaction effects will be satisfactory. Such approximations are certainly quite common in the literature." In fact, neglecting the role of real money balances in the New IS curve is well justified on empirical grounds. Ireland (2001) generalizes the model above by allowing for a household's utility fiinction that is nonseparable across consumption and real balances. In this model, real money balances enter either both the New IS curve and the New Keynesian Phillips curve, or none of the two relations. Ireland (2001: 16) proceeds to estimate the model using maximum likelihood methods, and finds that the null hypothesis that real money balances fail to enter the IS and Phillips curves cannot be rejected. He concludes that "changes in real balances appear to be unimportant in the model's IS and Phillips curves. Evidently, previous studies are justified in their minimal treatment of money's role in the monetary business cycle" (Ireland 2001: 4). McCallum (2001b) and Woodford (2002: Section 4.3.2) simulate extended New Keynesian models which relax the assumption of the separability of the utilityfiinction,and both find that the responses of none of the variables in the model are very different when real balance effects are considered relative to the baseline model without those effects. A final note concerns the fact that the New IS curve has been derived under the assumption of perfect price flexibility while the New Keynesian model assumes sticky prices. However, introducing sticky prices into the model discussed in this section simply requires dropping the labor market clearing condition (4.19), which determines aggregate supply in this model, and replacing it with the aggregate supply fiinction derived in the previous section. This is exactly what we are going to do in Section 4.2, where we assemble the core equations of the New Keynesian model and proceed to simulate the resulting model.
128
4.1.3
Chapter 4 Monetary Policy in the New Keynesian Model
The Interest Rate Rule
In traditional Keynesian models aggregate demand is modeled by the IS curve and the LM curve, where the latter represents a money demand relationship. Regarding the money demand relationship, McCallum and Nelson (1997) show that the same model that is used to derive the New IS curve can also be used to derive a money demand function, where the demand for real money balances depends on consumption spending and the nominal interest rate. Hence, the resulting money demand function is very similar to the one used in traditional Keynesian models. All that would be needed to close the model is a policy rule specifying the money supply set by the central bank. However, most New Keynesian modelers choose a different route: They close the model by specifying an interest rate rule to represent the monetary policy reaction function of the central bank. That is, in New Keynesian models it is typically assumed that the central bank uses its control over the money supply to steer the short-term interest rate, its policy instrument, into the desired direction, thereby influencing aggregate demand. By specifying the path of the interest rate directly, there is no need to model the money market explicitly. ^^^ Regarding the choice of the nominal interest rate Rf as the prime monetary policy instrument, McCallum (1999: 24) observes: "In the case of the second aspect, that R^ is specified as the instrument variable, the rationale is almost entirely empirical. The fact is that actual central banks in industrial countries conduct monetary policy in a manner that is much more accurately depicted by writing R^ rather than Mf (even if interpreted as the monetary base) as the instrument or operating-target variable. Thus, such policy rules are studied even by economists who might be regarded as possessing 'monetarist' tendencies and possibly even believing that policy might be improved if central banks used M^ as their instrument." One might argue that Germany is a special case since the Bundesbank consistently claimed that it was committed to pursuing a money growth target. However, there is a substantial body of empirical evidence showing that money did not play a prominent role either in its operating procedures or as a final objective of policy. For instance, Clarida and Gertler (1997) provide evidence that the Bundesbank was accommodating money demand shocks, thereby smoothing the short-term interest rate, which is not in accordance with a strict monetary targeting regime. A more formal test whether the Bundesbank was indeed targeting a monetary aggregate is presented by Clarida et al. (1998). They estimate a forward looking version of the well-known Taylor rule for interest rate setting and find that this interest rate rule describes the behavior of the Bundesbank relatively well. This suggests that the interest rate is a reasonable 170 For this reason Romer (2000) argues that the LM curve can be dropped from modem macroeconomic models.
4.1 Deriving the Core Equations of the New Keynes ian Model
129
indicator of Bundesbank policy. In order to test the role of monetary aggregates as an objective of Bundesbank policy they include in the reaction function a money variable which they define as the gap between the actual money stock and the official Bundesbank target. The empirical estimates of this extended reaction fiinction show that "our baseline interest rate reaction function clearly wins. The monetary target just does not matter, while the other parameter estimates are largely unchanged" (Clarida et al. 1998: 1046). Bemanke and Mihov (1998b) model the operating procedures of the Bundesbank and find that short-term interest rates played a dominant role in the implementation of policy, whereas a model of operating procedures based on a narrow monetary aggregate is clearly rejected. Like Clarida et al., they also investigate the role of money as a final objective of Bundesbank policy. To this end they test empirically whether for a given forecast of inflation changes in forecasted money growth affected Bundesbank policy. They find that this was not the case and conclude that the Bundesbank is better described as an inflation targeter than as a money targeter. Regarding the latter point, Svensson (1999) comes to a similar result. He shows on theoretical grounds that in the medium term there will often be a conflict between stabilizing inflation around the inflation target and stabilizing money growth around the monetary target. He notes that the inflation record of the Bundesbank has been unprecedented while it has missed its money growth targets about half the time and concludes that the Bundesbank has given priority to the inflation target and disregarded the monetary target whenever a conflict between the two arose.^^^ In sum, it appears that monetary aggregates did not play the special role claimed by the Bundesbank. In most New Keynesian models the behavior of the central bank is described using some form of the interest rate setting rule popularized by Taylor (1993): (4.33)
R,=^p,+r+(l>,{y^-y^)
+ (l>,{l^^-7i)+ef,
According to the Taylor rule, the central bank sets the nominal short-term interest rate R^ as a function of inflation, the steady state natural rate of interest F, and economic conditions. ^^^ The latter are represented by the output gap and the deviation of inflation from the inflation target W, The parameters ^ and ^ determine the strength of the policy response to these disequilibria. The variable e^ represents a monetary policy shock; that is, a policy action unrelated to the determinants of systematic monetary policy. The unit coefficient on inflation implies that the central bank varies the real interest rate in response to economic conditions. Due to nominal rigidities in the New Keynesian model, a change in the nominal interest rate does not lead immediately to a change in the inflation rate, which implies that the central bank has leverage over the real interest rate. ^'^ Forftirtherliterature supporting this view, see Svensson (1999: 89ff). The inflation rate Taylor uses is actually the rate over the previous year.
130
Chapter 4 Monetary Policy in the New^ Keynesian Model
And as the discussion in connection with (4.30) has shown, this gives the central bank leverage over aggregate demand conditions. If the economy is in steady state with yt=yt=y and A/?, = Ap, the central bank sets the real interest rate equal to the level of the steady state natural rate of interest, F. This is consistent with the New IS curve being in steady state, as shown in (4.33). Taylor (1993) assumes values for the response parameters ^ and ^ of 0.5 each, and of 2 percent each for the inflation target and the steady state natural rate of interest, and finds that the resulting policy rule describes the actual policy of the Federal Reserve Bank fairly well. The Taylor rule also turned out to provide a reasonable fit of the actual policy performance of other central banks. Even the Deutsche Bundesbank (1999: 52fif.) concedes that a conventional Taylor rule gives a good approximation of the actual path of its policy instrument. Additional evidence for the relevance of the Taylor rule in central bank practice is provided by Clarida et al. (1998), who estimate a forward-looking variant ofthe Taylor rule: (4.34a) R:=R-^
j3{EM.i - ^) + ^ (^.-i>^. " >^,) + ^^
(4.34b) R,={\- S)R* + ^,.1 + V,. Here, the variable R* represents the target for the nominal short-term interest rate of the central bank, and R is the long-run equilibrium nominal rate defined as the sum ofthe steady state natural rate of interest and the inflation target. The parameter j3 gives the response ofthe target nominal interest rate to a change in expected inflation; it is related to the parameter ^ in (4.33) by >5 = 1 + 02 • The second equation represents the tendencies of central banks to smooth interest rate adjustments. Clarida et al. estimate the system given by (4.34a) and (4.34b) for the United States, Germany, and Japan. Regarding the choice of the sample period, they argue that the way monetary policy was conducted had fundamentally shifted around 1979, when all three central banks began a concerted effort to reign in inflation. For the post-1979 period they find that the forward-looking Taylor rule does a good job of characterizing monetary policy for all three countries. In fact, the estimated coefficients turn out to be remarkably similar. Clarida et al. (1998:1035) summarize the estimation results as follows: "The kind of rule that emerges is what one might call 'soft-hearted' inflation targeting: In response to a rise in expected inflation relative to target, each central bank raises nominal rates sufficiently enough to push up real rates. This behavior is statistically significant and quantitatively important for each country. The estimated rules thus imply a clear focus on controlling inflation. At the same time, however, there is a modest pure stabilization component to each rule: Holding constant expected inflation, each central bank adjusts rates in response to the state of output." The Taylor-type rules are not only popular because they appear to describe the actual behavior of central banks fairly well, but also because they are con-
4.1 Deriving the Core Equations of the New Keynesian Model
131
sistent with a number of principles of optimal policy emerging from the New Keynesian framework. The following two subsections are going to provide a short introduction into those principles. ^ ^^ 4,1.3.1
Optimal Monetary Policy under Discretion
Monetary policy can operate either under discretion or under commitment. Under discretion monetary policy makers reoptimize in each period. That is, in each period the policy makers decide anew what the optimal policy response to the present situation is, without being bound by policy decisions they made in the past. Hence, policy makers do not commit themselves to any kind of policy rule. Since in practice no major central bank makes any kind of binding commitment over its future policy course, this is a realistic starting point to explore optimal monetary policy in the New Keynesian framework. To determine optimal monetary policy, the central bank objective function has to be specified. To simplify notation, we define the output gap as x^ =(j;^-5;J. In addition, we introduce the variable n^, which denotes the deviation of inflation from the inflation target. ^^^ Typically, a loss function of the form
(4.35)
mm^E,\±p\nlj
+A{x,^j-kf\
is assumed. This loss function implies that the central bank seeks to minimize the deviation of inflation from the target, and of output from natural output. The parameter k represents the desire of the central bank to increase output above the natural rate of output. As discussed in the previous chapter, the assumption of imperfect competition implies that the natural rate of output is inefficiently low, and the central bank may try to raise output to a more efficient level. However, since supemeutrality holds in the New Keynesian model, the central bank is powerless to push output permanently above the natural rate level. Since the assumption of rational expectations implies that central bankers and private sector agents understand the limitations of monetary policy, it is reasonable to assume that the former will not attempt to do the impossible. ^^^ Hence, we follow here Clarida et al. (1999) and assume A: = 0. ^^^ Both subsections draw on Clarida et al. (1999). ^'^ In principle, one also can analyze price level targets in the New Keynesian framework. However, since all major central banks define price level stability as being achieved when the inflation rate is somewhere between one and three percent, we assume that the central bank pursues a low inflation target. ^^^ Put another way, the assumption of rational expectations implies that the private sector understands that the central bank is free to reoptimize every period and takes
132
Chapter 4 Monetary Policy in the New Keynesian Model
Another motivation for the assumption A: = 0 is that the combination of discretionary policy with k>() would lead to the famous time-inconsistency problem, implying an inflationary bias of the central bank. This bias has been blamed for persistently high inflation in the 1970s, but since the 1980s inflation has been brought under control, suggesting that the value of k substantially declined when central bankers launched their concerted efforts to reign in inflation in the late 1970s. For the following analysis we assume that the central bank aims to minimize the loss function
(4.36) mini£,|Xy54<. ^KL where A denotes the value the central bank assigns to output stabilization. This loss function is not only widely used in monetary policy analysis, but also attractive on the grounds that it is consistent with welfare maximization because it can be regarded as an approximation to the utility function of the household in an economy with monopolistic competition and nominal price rigidity. Before proceeding to analyze optimal monetary policy, we need to extend the New Keynesian Phillips curve by adding a cost-push shock e^: (4.37)
n,=pE,n,,,+K{x,)+e[.
The cost-push shock is included to allow the model to generate variation in inflation that arises independently from excess demand. Hence, it captures all factors other than excess demand that might affect real marginal costs. The inclusion of the cost-push shock implies that we relax the assumption that real marginal costs always move proportionally with the output gap, since cost-push shocks affect marginal costs independently from the output gap.^^^ A prominent example for a cost-push shock is an oil price shock that pushes up prices by increasing real marginal costs without increasing the output gap. Finally, in order to simplify the optimization problem we rewrite the New IS curve in terms of the output gap: (4.38)
X, = E,x,,, - a{R, - E,n,,, - r) + g,,
where g^ is now defined as g^ = Ef{Ay^^^ ~^^/+i} and the real interest rate is expressed as r^=R^- E^n^^y. this into account in its expectation formation process. In the rational expectations equilibrium the central bank has therefore no incentive to change its behavior in an unexpected way. In this sense the policy that emerges in equilibrium is timeconsistent. See Clarida et al. (1999) for this line of argument. 176 Technically, equation (4.8) needs to be expanded to allow for a cost-push shock.
4.1 Deriving the Core Equations of the New Keynesian Model In this framework the central bank faces the optimization problem of minimizing its loss function (4.36) over n^, x^, and R^ subject to the constraints given by the New Keynesian Phillips curve (4.37) and the New IS curve (4.38). This can be construed as a two-stage problem where the central bank determines first the optimal level of the output gap and then computes the level of the real interest rate to support this level of output. To characterize optimal policy it will suffice to focus on the first stage of the problem. Under discretion, the central bank reoptimizes each period, which implies that it does not specify the path for the real interest it intends to pursue in the future. According to (4.30) this means that future output and inflation are independent from current policy decisions. Since the central bank does not make any commitment, it also cannot influence expectations. Taken together, this has the effect to reduce the central bank's optimization problem to a static problem where the central bank takes future output and inflation as given. The resulting Lagrangian is (4.39)
^ = | k ' ^Xx]\^w,Xn, - PE.n.^.-Kx^^w^Xx,
-E,x,^, ^a[r, - r ) ] .
By optimizing over n^, x^, and R^ we obtain the following first-order conditions: (4.40)
7r,+w^,=0
(4.41)
>ijc^-w,,/r + W2^ = 0
(4.42)
^2,^7?, = 0 .
Equation (4.40) implies that Wj^ = -TT^, and from (4.42) follows that ^2^ = 0. Inserting both results into (4.41) leads to the following optimality condition: (4.43)
^.=-^^..
Clarida et al. (1999) interpret this condition as implying that the central bank should pursue a "lean against the wind" policy: Whenever inflation is above target, the central bank should contract demand below capacity; and vice versa when it is below target. The strength of the central bank response to an inflationary threat depends on the responsiveness of inflation to reduced aggregate demand given by the parameter K and inversely on the relative weight the central bank places on stabilizing output, l/A. In case of a cost-push shock, the optimality condition (4.43) implies that the central bank faces a short-run trade-off between stabilizing inflation and output: A cost-push shock which increases inflation requires pushing output below the natural rate of output to bring inflation back on target. The policy trade-off the
133
134
Chapter 4 Monetary Policy in the New Keynesian Model
central bank faces is therefore not characterized by a Phillips curve type relationship between inflation and unemployment, but by a trade-off between the variability of inflation and the output gap. The particular trade-off chosen by the central bank depends on the central bank preference parameter / I : As /I rises, indicating a greater preference of the central bank for output stabilization, the optimal policy will engineer a lower standard deviation of the output gap, but this will come at the cost of a higher standard deviation of inflation. ^^^ However, this trade-off arises only in the case of a cost-push shock. If an aggregate demand shock leads to a positive output gap, the optimal policy response of the central bank would be to contract aggregate demand. Thereby it achieves simultaneously the stabilization of output and inflation. The same holds for an increase in the natural rate of output, since without a stimulation of aggregate demand the output gap would become negative and inflation would tend to undershoot the target. Stabilizing both the output gap and inflation requires in this case the central bank to ease its policy stance. In both cases there is no trade-off between the output and inflation stabilization objectives. If cost-push shocks drive inflation, Clarida et al. show that optimal policy implies a gradual return of the inflation to its target. They write: "The optimal poHcy incorporates inflation targeting in the sense that it requires to aim for convergence of inflation to its target over time. Extreme inflation targeting, however, i.e., adjusting policy to immediately reach an inflation target is optimal only under one of two circumstances: (1) cost push inflation is absent; or (2) there is no concern for output deviations" (Clarida etal. 1999: 1673). Consequently, even with optimal policy there may be sustained departures from the inflation target as a result of cost-push shocks. Alternatively, this result can be interpreted as implying that the inflation target is a function of cost-push shocks and is, therefore, flexible. ^^^ Finally, it can be shown that in response to an increase in inflation the central bank needs to raise the nominal interest rate sufficiently to increase the real interest rate. That is, in the Taylor rule the coefficient ^2 needs to be larger than zero. Otherwise a policy rule with a weak response to inflation may imply indeterminacy of the rational expectations equilibrium. ^^^ Put another way, the strong response to inflation is required to guarantee that the economy has a nominal anchor.
^^^ Clarida et al. (1999) show that one can construct an efficiency policy frontier which is a locus of points that characterize how the standard deviations of the output gap and inflation under the optimal policy, a^ and cr^, vary with central bank preferences, defined by i . ^^^ For this interpretation, see King (2000: 55). ^^^ For an extensive discussion of conditions for determinacy of equilibrium, see Woodford (2002: Section 4.2).
4.1 Deriving the Core Equations of the New Keynesian Model
135
Moreover, the fact that the central bank provides the nominal anchor to the economy also means that monetary policy ultimately determines the inflation rate. In this sense inflation is a monetary phenomenon in New Keynesian models. To see this, it is assumed that the economy is in equilibrium, with Ap, = E^Ap^^^ = Ap and yt =yt = ^tyt+i = >^- To satisfy the constraint imposed by the New IS curve, the central bank has to ensure that r^ =r , Inserting these conditions into (4.33) shows that in equilibrium Ap^n, Hence, the equilibrium inflation rate is determined by the central bank's choice of the target inflation rate.l^^ 4.13.2
Optimal Monetary Policy under Commitment
In this section we assume that the central bank is willing to commit itself to some kind of policy rule. In the context of the time-inconsistency problem it can be shown that such a commitment can overcome the inflationary bias that otherwise would be present in monetary policy, thereby achieving a lower inflation rate in equilibrium. However, in the previous section we assumed on a priori reasons that the inflationary bias is not a major issue under discretionary policy. Nevertheless, even without the time-inconsistency problem a policy commitment has sizeable advantages in the New Keynesian framework. By committing itself to a policy rule the central bank can anchor expectations regarding its future policy, which enhances the effectiveness of monetary policy because in the New IS curve aggregate demand depends on expectations concerning future policy actions. Under commitment, the central bank's optimization problem becomes dynamic, because current monetary policy actions now affect also future output and inflation. Otherwise, the problem is similar to that in the previous section. In particular, optimizing over R^ again yields the result that the Lagrange multiplier associated with the IS relation is zero. Hence, we can simplify the Lagrangian as follows: (4.44)
L = i £ , | i ; 5 > ( [ ; r / , , + A ^ , J+w,,,,, k , . - y9£,;r„,,,. - / r x , , J ) | .
Minimizing (4.44) over the current output gap and inflation, x^ and ;r^, yields the same first-order condition as before. However, under commitment the central bank minimizes the Lagrangian also over all future output gaps and inflation, x^+, and n^^.^ with / = 1,...,<^ . This yields the following first-order conditions: (4.45) (4.46)
P^,,,-PKW,,,,=^
y5;r,,,+M..,-M..M=0.
1^^ See also the discussion in McCallum (2001b: 146).
136
Chapter 4 Monetary Policy in the New Keynesian Model
These conditions have to hold for all / = 1,.-,°°. The crucial difference to the outcome of the static optimization problem is that the first-order condition for inflation includes now two Lagrangian multipliers, Wj^^. and >v^+,_i. The latter arises from the fact that the New Keynesian Phillips curve is forward-looking and agents consequently form expectations over the inflation rate in the next period. In the static optimization problem the central bank took those expectations as given. Under commitment, however, the central bank can influence expectations and therefore has to take the term w^E^TTf^^ into account when determining optimal policy for the period / + 1 . That is, under commitment optimal policy is history-dependent. To simplify the first-order conditions, we eliminate ^ from (4.45) and (4.46) and, next, solve (4.46) for Wj ^^.. This yields w^^^. = Wi^^._i -TT^^. . Inserting this into (4.45) gives (4.47)
/Ix,^. - /avi,^,_, + KTT,^. = 0.
From optimizing (4.44) over x^+y_i, we have Wj^+^.i =(/l//r)x^+-_i. Inserting this into (4.47) leads to the following optimality condition for monetary policy under commitment: (4.48)
x,^.-x,^._,=-j7r,^^.
The difference to optimal policy under discretion is that under commitment the central bank will not adjust the level but the change in the output gap to inflation. ^^^ If a cost-push shock raises inflation above target, under discretion the central bank would initially lower output below the natural rate, but as the inflation rate begins to fall, the central bank would allow output to gradually return to the natural rate until both variables are back on target. Under commitment, however, the central bank would continue to lower output as long as the inflation rate is above target. The credible threat of contracting output in the future has the immediate effect of dampening current inflation, since current inflation depends on expected future output gaps. Consequently monetary policy is more effective under commitment because of its management of expectations. Since this means the short-run trade-off between inflation and the output gap is more favorable, this shows commitment pays off in the New Keynesian framework even in the absence of the time-inconsistency problem.
^°^ Under commitment, only in the initial period does the central bank adjust the level of the output gap.
4.1 Deriving the Core Equations of the New Keynes ian Model
4.1.3.3
137
Taylor Rules and Optimal Monetary Policy
As mentioned above, part of the reason for the popularity of the Taylor rule is that this rule is consistent with the main principles of optimal policy in New Keynesian models. An important aspect in this regard is that by following a monetary policy rule, the central bank is in a powerful position to shape expectations, thereby making monetary policy more effective. Regarding cost-push shocks, the Taylor rule implies that the central bank contracts demand conditions when a cost-push shock pushes inflation above target, and thus pursues the "leaning against the wind" policy which is optimal in New Keynesian models. Also, the parameter ^ is significantly larger than zero, so that the central bank raises the real interest rate when inflation increases. This rules out indeterminacy of the rational expectations equilibrium. Moreover, the Taylor rule ensures a gradual return of the inflation rate back to target, and not an immediate adjustment. Again this is in line with optimal policy. If an aggregate demand shock occurs, the Taylor rule calls for a strong countercyclical response to stabilize both output and inflation. The fact that the Taylor rule is written in terms of the output gap and not the level of output also ensures an appropriate response to an increase in the natural rate of output: Since this leads to a negative output gap, the central bank will stimulate aggregate demand, thereby accommodating this particular type of shock. Both responses are consistent with optimal policy. There is, however, an important difference between the Taylor rule and the principles of optimal policy derived above. Empirical estimates show that interest rate smoothing plays an important role in the way central banks conduct monetary policy in practice. This behavior can be captured by specifying an additional equation for the interest rate adjustment process like (4.34b), or by including a lagged interest in the policy rule.^^^ Clarida et al. (1999) observe that theoretically it is an important unresolved issue why central banks choose a smoother path for the interest rate than predicted by theory. One way to motivate this behavior is that model uncertainty poses a formidable problem to central banks. Uncertainty about the exact structure of the model and about parameter values may persuade policy makers to act cautiously, leading to a smoother interest rate path. Another interpretation is that a gradual adjustment could give the central bank more leverage over the long-term interest rate, which, according to the expectations hypothesis, is the sum of expected short-term interest rates over the same horizon. According to the New IS curve this would give the central bank also more leverage over aggregate demand conditions. With gradual adjustment more modest movements in the short-term interest rate than otherwise required would suffice to achieve its stabilization goals, which is desirable to the extent that the central bank wishes to avoid excessive volatility in the short-term interest rate. ^^^ Both approaches are equivalent to each other.
138
Chapter 4 Monetary Policy in the New Keynesian Model
4.2
Simulating the New Keynesian Model
4.2.1
The Standard New Keynesian Model
In this section we put the three core equations together and simulate the New Keynesian model using the Solvek algorithm by Paul Klein (2000) to solve for the rational expectations solution. ^^^ The three core equations are the New Keynesian Phillips curve, the New IS curve, and a Taylor rule specification for the interest rate. The first two equations have been derived in the previous section. ^^"^ The Taylor rule is derived from (4.34a) and (4.34b), with the latter inserted into the former. Taken together, we obtain the following New Keynesian model: (4.49)
n,=PE,n,,,^K{y,-y,)
+ s[
(4.50)
y, = E^y,,, - CJ{R, - E,n,,,
(4.51)
R,={\-S)[r^^p,+(t\{E,_,y,-y,)
-r^g, +
(|>,{EM.^-^)h3R,^^^
This model is the same as the one used by McCallum (2001a: 258) to investigate monetary policy in New Keynesian models. He chooses this particular model because it represents the "considerable agreement about the general, broad structure of the macroeconomic model to be used." To simulate the model, he chooses the values P = 0.99 and K = 0.03 for the parameters in the New Keynesian Phillips curve. The model is parameterized for quarterly data. For the New IS curve he chooses cr = 0.4 . McCallum motivates this choice by arguing that a value of cr = 0.2 would be more appropriate if (4.50) were to capture only consumption behavior, but needs to be increased to reflect the investment spending that is not explicit in the model structure (4.49)-(4.51). For the Taylor rule, he follows Taylor (1993) and sets ^ and 02 to 0.5 each. The interest rate smoothing parameter is set to cJ = 0.8 in order to introduce a realistic degree of interest rate smoothing into the model. The steady state natural rate of interest F and the inflation target W are modeled as constants in the model. Since constants play no role in the solution to the model, they are set to zero. The exogenous variables in this model are the three exogenous shocks s^, g^, and 8^ and the natural rate of output, y^. All four variables are assumed to be AR(1) processes with AR parameters 0.0, 0.0, 0.0, and 0.95. That is, the three shocks follow a
^^^ I am grateful to Bennett McCallum to make this algorithm and a number of example files available to me. Running this algorithm requires MATLAB. All programs used in this paper are available from the author upon request. ^^^ See equations (4.37) and (4.29).
4.2 Simulating the New Keynesian Model
139
white noise process, whereas the natural rate of output is a near random walk process. With this specification, the model can be simulated. To illustrate its dynamics we plot the impulse response functions of the endogenous variables to the three shocks above and to a shock to the natural rate of output. The resulting plots can be interpreted as showing the deviation of the endogenous variables from steady state in response to shocks to the system. That is, the zero line represents the steady state. The results are shown in Figure 4.1. In addition to the endogenous variables Figure 4.1 also plots the response of the natural rate of output. The first row shows the response of the system to a unit shock to the monetary policy instrument. The monetary policy shock raises the short-term interest rate by one percentage point. ^^^ This can be interpreted as a "surprise" tightening of the policy stance. Since this policy action is unrelated to any endogenous policy response of the central bank to developments within the economy, the subsequent movements of output and inflation are entirely due to the monetary policy shock. This is useful to deal with the issue of reverse causation, which otherwise would raise the problem that observed co-movements between the policy instrument and private sector variables could reflect the endogenous response of monetary policy to changing economic conditions. In this context it is interesting to notice that the analysis of the monetary transmission mechanism in SVAR models is based on the same principle: In SVAR models an exogenous monetary policy shock is identified, and then the impulse response functions for the endogenous variables in the system to this shock are computed. ^^^ This procedure allows SVAR models to isolate those comovements between the policy instrument and output and inflation which are caused only by monetary policy actions. In the simulation of the New Keynesian model, the monetary policy shock is exogenous by definition, which allows us to compute the dynamic responses of output and inflation to an exogenous change in monetary policy. Since the approach to analyzing the transmission mechanism is similar, the resulting impulse response functions from SVAR models are comparable to those obtained from the simulation of the New Keynesian model, and, hence, provide some benchmark to judge whether the New Keynesian model captures the salient features of business cycle dynamics. It is apparent from Figure 4.1 that the increase in the interest rate leads on impact to a strong contraction in output, reflecting the increase in the current and future real interest rates triggered by the monetary tightening. The contraction in output corresponds to a negative output gap, since monetary policy has no effect
^^^ The interest rate and the inflation rate plotted in this and the following figures are not annualized. ^^" See also the discussion of the role of monetary policy shocks in SVAR models by Bagliano and Favero (1998: 1074).
140
Chapter 4 Monetary Policy in the New Keynesian Model
Figure 4.1: Impulse Response Functions for the Standard New Keynesian Model y response
ybar response
dp response
R response
0.5 monetary ° policy -05 shock -1 -1.5
IS shock 0.5 0
on the natural rate of output. Regarding the future real interest rates, it is important to notice that the interest rate smoothing parameter implies that the monetary policy shock leads to a sustained tightening of policy, since the central bank will return the interest rate to the baseline only gradually. This is also apparent in the plot of the interest rate response, which shows that it takes more than ten quarters before the initial tightening has been reversed. The interest rate smoothing therefore plays an important role in amplifying the monetary transmission mechanism. The deep contraction in output leads to an immediate fall in the inflation rate. It is noticeable that in this model monetary policy has its peak effect on impact. Unfortunately, evidence from SVAR models points to a delayed impact of monetary policy. This is also consistent with the conventional wisdom on long lags in the monetary transmission mechanism. Hence, the standard New Keynesian model fails to replicate an important aspect of business cycle dynamics. To remedy this, it will be necessary to extend the New Keynesian model. But before doing so, we consider the impulse response functions to the remaining shocks which will prove useful for gaining a better understanding why this result arises in this model.
4.2 Simulating the New Keynesian Model
141
The response to an IS shock is shown in the second row. This shock increases output on impact by one percent, but then returns immediately to the baseline. The reason for the effects of the shock being so short-lived is that the New IS curve has no inherent persistence mechanism. This lack of persistence is also the reason why monetary policy shocks have their peak effect on impact. Since the Taylor rule is specified in terms of E^_^yf, the central bank is surprised by the IS shock and does not respond immediately. This prevents the persistence inherent in the Taylor rule from making the effects of the IS shock more persistent. Without any persistence, the inflationary effects of the IS shock are negligible. The effects of the cost-push shock are shown in the third row. This shock raises the inflation rate on impact by one percentage point, but this shock has no persistent effects either. Since the Taylor rule responds to expected inflation, there is again no immediate interest response. There is also no immediate output response, since the real interest rate r^=Rf- E^n^^^ remains constant. The lack of persistence in the New Keynesian Phillips curve poses a substantial problem. In fact, the standard New Keynesian Phillips curve has been criticized in the literature on a number of grounds. First, it is at odds with the inflation persistence observed in the data, which has been first pointed out by Fuhrer and Moore (1995).^^^ They showed for US data that the standard New Keynesian Phillips curve has difficukies generating a realistic degree of inflation persistence. ^^^ Regarding inflation persistence in Germany, the autocorrelation coefficient for the first lag is approximately 0.6.^^^ The simulation of the standard New Keynesian model, on the other hand, implies an autocorrelation coefficient of only 0.10.1 ^^ Second, the standard New Keynesian Phillips curve has been criticized because it implies that a fiilly credible disinflation would lead to a boom, which many observers find incredible.^^^ The reason for the boom is that agents would anticipate the disinflation and begin to lower prices well before the central bank begins to tighten policy to lower the inflation rate. Given the structure of the New Keynesian Phillips curve, this behavior is optimal because otherwise firms might find themselves stuck with a price which is too high if nominal rigidity prevents price adjustment after the disinflation has begun. The preemptive lowering of prices implied by the standard New Keynesian Phillips curve induces a boom. 1^^ See also the discussion in Mankiw (2001). 1^8 See also the discussion in Roberts (1997) of the Fuhrer-Moore result. 189 The autocorrelation coefficient has been estimated for quarterly data for West Germany for the sample period 1962:2-1999:4. The time series for West German inflation is seasonally adjusted and has been obtained from DATASTREAM (code: WGCP....E). 1^^ A standard deviation of one for all shocks has been assumed. The stochastic simulation of the model has been replicated 500 times. 1^1 See also the discussion in Ball (1991).
142
Chapter 4 Monetary Policy in the New Keynesian Model
whereas in reality a disinflation is typically accompanied by a recession. ^^^ The recession may reflect a lack of credibility when central banks announce their intention to disinflate the economy, but Mankiw (2001) uses impulse response analysis to show that even fully credible disinflations go along with a contraction in output. Third, the standard New Keynesian Phillips curve implies that the current inflation rate is negatively related to the lagged output gap.^^^ To see this, we simplify the New Keynesian Phillips curve by setting /? = 1 and rearrange the resulting relation by setting the time index one period back and solving for n^: (4.52)
n = n,_, - K{y,_, - y,_,)+w,,
where u^ =n^ ~^t-i^t ~^f • This, however, is contradicted by the data. Figure 4.2 plots the correlation coefficient for inflation and the lagged output gap for West German data.^^"* The output gap has been computed with the band pass filter procedure proposed by Baxter and King (1999), using the Bums-Mitchell specification that isolates frequency components of between 6 and 32 quarters of the West German output series. Figure 4.2 shows that the lagged output gap is clearly positively correlated with the current inflation rate. This is in accordance with conventional wisdom that a positive output gap in the last period is likely to lead to inflationary pressures in the current period. While this traditional transmission mechanism is obviously consistent with the data, the New Keynesian Phillips curve, on the other hand, does not allow for past output gaps to affect current inflation. By ruling out backward-looking components, the New Keynesian Phillips curve unfortunately imposes a "perverse" correlation between inflation and the output gap on the data. This problem is, of course, closely related to the second problem of disinflations being correlated with booms. Estrella and Fuhrer (1998) show that all three problems are related to the fact that inflation in this version of the New Keynesians model is a jump variable that adjusts instantaneously to changing economic conditions. The standard New Keynesian Phillips curve ensures only that prices are sticky, but it imposes no such restriction on inflation. Mankiw (2001) draws an analogy to the standard growth model where the capital stock is a state variable that adjusts slowly, but investment—^the change in the capital stock—can jump quickly in response to changing conditions. Regarding inflation, such a behavior obviously contradicts the gradual adjustment of inflation found in the data. In the next section we are
^^^ For evidence on the costs of disinflation, see Ball (1996). ^^^ See also GaH et al. (2001: 1242). ^^^ The inflation is the same used for the estimation for the autocorrelation coefficient. Regarding the time series for West German real GDP, it is seasonally adjusted and has been obtained from DATASTREAM (code: WGGDP...D). The sample period is 1962:2-1998:4.
4.2 Simulating the New Keynesian Model
143
Figure 4.2: Cross Correlation between Inflation and the Lagged Output Gap in Germany
-0.1
-0.2
going to employ the specification of the New Keynesian Phillips curve proposed by Fuhrer and Moore (1995) to remedy this problem. Before turning to the extended New Keynesian model, we briefly review the effects of a shock that increases the natural rate of output in the standard model. This shock can be interpreted as a technology shock. The results are shown in the fourth row of Figure 4.1. This shock is the only one that has an effect on the natural rate of output in the model. In contrast to the other shocks in the model this shock has a very persistent effect because of the assumed near random walk behavior of the natural rate of output. ^^^ Actual output increases initially by less than the natural rate of output, inducing a substantial negative output gap. This leads to a fall in the inflation rate and to a fall in the interest rate as the central bank accommodates the increase in the supply potential of the economy by easing policy.
195
The fact that the persistence of the technology shock has to be assumed is, of course, a major shortcoming of the model, since it reveals that the economic processes that could lead to the persistence of a technological innovation are not well understood. In fact, many observers remain unconvinced that technological progress is adequately modeled by random shocks, because this implies that technology changes suddenly and that there could be technological regress. See also our discussion of RBC models in Chapter 3.
144 4.2.2
Chapter 4 Monetary Policy in the New Keynes ian Model The Extended New Keynesian Model
In this section we extend the New Keynesian models in two aspects. The preceding analysis has shown that both the New Keynesian Phillips curve and the New IS curve lack in persistence. To remedy these problems we are going to modify both relations. 4.2.2,1
Alternative Specifications of the New Keynesian Phillips Curve
Beginning with the New Keynesian Phillips curve, the previous section has shown that the central problem with this specification of the inflation process is that the inflation rate jumps in response to shocks, instead of the gradual adjustment observed in the data. Estrella and Fuhrer (1998: 15ff) show that one way to overcome this problem is to difference the inflation variable in the New Keynesian Phillips curve. To demonstrate their approach, we rewrite the New Keynesian Phillips curve as follows: (4.53)
n,^^-n,=^-K{xye[.
For simplicity, we have ignored expectation viewpoint dates and approximated the discount factor with P = \. Expressing the New Keynesian Phillips curve this way shows that a change in aggregate demand or a cost-push shock will lead to an immediate jump in the inflation rate. This "jump" behavior was also apparent in Figure 4.1. Estrella and Fuhrer's suggestion is to difference the inflation variable [n^^^ -n^) in (4.53) which has the effect of displacing the "jump" behavior to the second difference in inflation: (4.54)
{n,^^-n,)-{n,-7t,_,)
=
-2K{x,_,)-2e[.
This relation can also be expressed as follows: (4.55)
7t^ = 0.5E^7^^^^ + 0.5;r,_, + fc{x^_^ )-^£f,
which is closely related to the specification of the New Keynesian Phillips curve proposed by Fuhrer and Moore (1995). While the relation (4.53) corresponds to a sticky-price model, the relation (4.54) can be interpreted as a sticky-inflation model, because the elimination of the "jump" behavior ensures that the inflation rate will adjust only gradually to disturbances. Fuhrer and Moore also emphasize that costless disinflation is impossible with this specification of the inflation process. It is also apparent from (4.55) that with this specification inflation is positively correlated with the lagged output gap, and not negatively as is the case with the sticky price New Keynesian Phillips curve. Consequently, the adoption of (4.55) as the inflation model would solve the aforementioned problems that arise with the sticky-price Phillips curve.
4.2 Simulating the New Keynesian Model
145
Since it would contradict the modeling principles of New Keynesian models to simply assume a functional form of the Phillips curve because it fits the data, it is necessary to provide some theoretical underpinnings for the Fuhrer-Moore inflation model. Unfortunately, it is not based on microeconomic foundations as compelling as the Calvo model described earlier. Instead, their model is a variant of the staggered wage contracts model proposed by Taylor (1980).^^^ The sources of nominal rigidities in the Taylor model are long-term wage contracts. To simplify the exposition, we assume that wages are set for only two periods. Hence, the average wage w, afirmpays in the current period is (4.56)
w, = {cw^ + cw,_,)/ 2 ,
where cw^ denotes the contract wage negotiated in period t and which the firm is going to pay in the periods / and f+ 1. Workers are assumed to set the expected real wage over the contract period as a function of aggregate demand conditions, which we proxy here with the output gap x,. Hence, the labor supply curve is given by (4.57)
cw, - {p^ + E,p,,,
)/2 = vx, + e^ .
Here, v denotes the responsiveness of real wage contract to aggregate demand conditions, and ej- represents a labor supply shock. Finally, it is assumed that firms set prices as a markup over wages. For simplicity, the markup is set to zero: (4.58)
p,=w,.
It can be shown that the equations (4.56)-(4.58) can be combined to yield (Roberts 1997: 175): (4.59)
Ap, = E,^p,,, + 2v{x, + x,_,) + [sf + e^,)+;/,,
where rj^ denotes an expectational error, rj^ =E^_yp^ -p^. Since the relationship given by (4.59) has essentially the same structure as the New Keynesian Phillips curve based on the Calvo price setting mechanism, the Taylor model would give rise to the same problems as the New Keynesian Phillips curve discussed in the previous section. ^ ^^ Fuhrer and Moore's contribution is to modify the wage contract equation (4.57) by assuming that wage negotiations do not only take aggregate demand conditions into account, but also the real wages which have been negotiated in ^^" The derivation of the Fuhrer-Moore model presented here draws on Roberts (1997). ^^^ See also the discussion in Roberts (1995).
146
Chapter 4 Monetary Policy in the New Keynes ian Model
the last period and those which are expected to be negotiated in the next period. That is, workers are assumed to negotiate real wages with reference to the real contract wages expected to prevail over the length of the contract. Hence, Fuhrer and Moore replace (4.57) with the following relation: (4.60)
cw, -p,=E,[{cw,_,
-p^_,)+{cw,,, -p,J]/2
+
v'x,^e;^.
The real contract wage {cw^ -Pt) is defined here as the difference between the nominal contract wage and the current price index. Fuhrer and Moore choose this approximation to the correct price deflator {p^ -{-E^p^^^) to simplify the analysis. To help comparison with the Taylor model, it is useful to rewrite (4.60) as (4.61)
Acw^ - (Ap, + ^/A^r+i)/ 2 = v/' A:, + f/-.
This equation shows that the Fuhrer-Moore specification essentially differences the term on the left-hand side of (4.57), which represents the Taylor specification of the wage contracting process. The Fuhrer-Moore specification implies that the change in the contract wage depends on expected changes in prices over the contract period and on the level of economic conditions. By combining (4.60) with (4.56) and (4.58), we obtain the Fuhrer-Moore Phillips curve: (4.62)
A'p,=EA'p,,,
^vix,
^x,_,)^2{e^
+^.-,)+^..
This relationship can be rewritten as: (4.63)
Ap,=0,5EM.i
+0.5Ap,_, +v/'(x, +x,_J/2 + (£,^ +^,^_J+;7,/2.
This relationship has generally the same structure as the inflation model given by (4.55). McCallum (2001a) approximates the term capturing the term for economic conditions with the current output gap, while Mankiw (2001) chooses the difference between the current unemployment rate and the natural rate of unemployment. In (4.55) this term is approximated with the lagged output gap, because this ensures that the resulting inflation equation implies a positive correlation between the current inflation rate and the lagged output gap, as implied by the data. This is also consistent with the specification of the New Keynesian Phillips curve proposed by Svensson (1997), which is shown by Estrella and Fuhrer (1998) to yield plausible impulse response functions. To complete the discussion of possible modifications to the New Keynesian Phillips curve, it should be noted that as an alternative to the differencing of the inflation variable in (4.53) it is also possible to assume that all variables relevant for the determination of inflation are subject to an earlier expectation viewpoint. This is essentially the path taken by Mankiw and Reis (2001). They propose a
4.2 Simulating the New Keynes ian Model sticky-information model in which every firm sets its price every period, but firms gather information and recompute optimal prices slowly over time. Mankiw and Reis use a Calvo process to model the price updating process by assuming that in each period a fraction (l ~ 0) of firms obtains new information about the state of the economy and computes a new path of optimal prices. Regarding the transmission mechanism, the sticky-information model has farreaching implications, since it is in essence an imperfect-information model in the tradition of New Classical models. Nevertheless, if one broadens the definition of "menu costs" to include also the costs of gathering and processing information, this is just another way to introduce nominal rigidity into the price setting process. Mankiw and Reis show that their model leads eventually to the following specification of the New Keynesian Phillips curve: (4.64)
Ap, = [f4-0)/0]y,
^{l-0)f^d^E,_,_j{Ap,^KAy,). y=o
Here, inflation depends on output, expectations of inflation, and expectations of output growth. It needs to be emphasized that the expectation terms are past expectations of current economic conditions. Mankiw and Reis show that this Phillips curve avoids the problems of the sticky-price New Keynesian Phillips curve discussed in the preceding section. Another alternative is to construct a Phillips curve based on real marginal costs. Gali et al. (2001) show that the common approximation of marginal costs in the price setting equation (4.5) with the output gap is inappropriate if labor market frictions are present, because in this case real marginal costs depend not only on the output gap, but also on the wage markup. This opens up another source of inertia. In fact, since real marginal costs display considerable persistence, the resulting inflation model is likely to overcome the problems discussed in the preceding section. ^^^ In sum, the issue of the appropriate specification of the New Keynesian Phillips curve has not yet been settled. A number of promising approaches have been proposed in the literature, but considerable research remains to be conducted before it will become clear which of these models will emerge as the preferred approach. Here, we will follow McCallum (2001a) and choose the FuhrerMoore approach because it is computationally easy to implement and yields plausible impulse response functions.
^^^ For an empirical application of this approach to German data, see Carstensen (2002).
147
148 4.2.2.2
Chapter 4 Monetary Policy in the New Keynesian Model The New IS Curve with Habit Persistence
In this section we are going to modify the New IS curve to introduce more persistence into this relation. To this end we are going to assume that the consumption behavior of private sector agents displays habit persistence. ^^^ That is, we assume that the desired level of consumption in the current period depends on the level of consumption in the last period. This implies that we have to relax the assumption that the utility function of the representative household is timeseparable with respect to consumption. Instead, it is assumed that the household seeks to maximize the following utility function:
(4.65)
E,±P^C,,JX,,J_,,M:^X j=0
However, we continue to assume that the utility function is separable across consumption and real money balances. In particular, following McCallum and Nelson (1999) we use the specific functional form of the utility function to derive the New IS curve: (4.66)
t/(C„C,.„Mr) = exp(v,)(a/(cT-l))(C,/C,'L,f-""' + (l-rrM;<"-''>.
Here, v^ is a preference shock, and y is the elasticity of marginal utility of real money balances. The parameter he [0,l] introduces habit persistence into the utility function; the larger h is, the more current consumption depends on past consumption. The parameters a and h determine together the elasticity of marginal utility of consumption. Optimizing the resulting Lagrangian, which is similar to the one used in Section 4.1.2 with respect to consumption yields the following first-order condition:
(4.67)
u, (c,, M; )-^j3u, [c,,,, M;,, )- /I, = 0,
where A^ is again the Lagrangian multiplier. Given the functional form of the utility function, (4.67) is equivalent to: (4.68)
exp(v, )(1/C/L, f-""^C,""- - /3hE, exp(v,„ )c^>-'"-y-cl-;^)'-
-A,=0.
Log-linearizing this condition and neglecting constants yields (McCallum and Nelson 1999: 564): (4.69)
log/l, = {ij3h^a + fiha - /3h^ - l)/(o-[l - J3h])}c, - h{{a - l)/{a[l - fih])}c,_, - Ph{{a -\)l{a[\ - ^h])}E,c,,,
+{\-Phy-{\-php^)v,. ^^^ This section draws on McCallum and Nelson (1999).
4.2 Simulating the New Keynes ian Model
149
Here, p^ defines the AR(1) parameter in the stochastic process assumed for the preference shock, v, = p^v,_^ + ej. The second relation required to derive the New IS curve with habit persistence is relation (4.17). Taking logarithms we obtain: (4.70)
log;i, = E, log A,,, ^R,-
EM.I •
By combining (4.69) and (4.70) we obtain the following expectational difference equation for the change in consumption: (4.71)
j3g,EAc,,, +g2^,Ac,,, -g,Ac, = g,{R, - ^ , A p , , J + g,v,.
The parameters in (4.71) are defined as follows: gi={h- ah), go = (l + J3h^ - (Tj3h^ -aj3h), g^= cr(l - J3h), and ^4 = -a{\ + >9, - ^ h p ^ + ^hp^). Equation (4.71) represents the New IS curve with habit persistence. In the case of A = 0, it is apparent that this relation reduces to (4.27), the consumption equation underlying the New IS curve without habit persistence. In the following simulation we are going to employ the relation given by (4.71) as the IS relation in the extended New Keynesian model. 4.2.2.3
Simulating the Extended New Keynesian Model
In this section we are going to represent the simulation results for the extended New Keynesian model. This model is comprised of (4.55) for the New Keynesian Phillips curve, (4.71) for the New IS curve, and (4.51) for the policy rule. Since the standard New Keynesian model does not yield plausible impulse response functions, McCallum (2001a) uses this model for monetary policy analysis.^^^ Regarding the New IS curve with habit persistence, he sets the parameter /? to 0.8. The AR(1) parameter for the preference shock is set to zero. The results of the simulation are shown in Figure 4.3. The first row displays again the response of the economy to a monetary policy shock. The peak effect of the shock on output occurs now with a delay, and the recession is less severe than in the previous model. But the output contraction lasts longer, which amplifies the effect of the monetary policy shock on inflation considerably. It also takes now about a year for the peak effect on inflation to materialize. With a more protracted recession and a larger fall in inflation, the central bank returns the interest rate more quickly to the base line. All in all, the impulse response functions for the monetary policy shock resulting from this model appear to be more consistent with the conventional view on the effects of monetary policy. ^^^ The only difference to his model is the Fuhrer-Moore New Keynesian Phillips curve, where McCallum uses the current output gap as proxy for economic conditions, while here the lagged output gap is used for reasons outlined above.
150
Chapter 4 Monetary Policy in the New Keynesian Model
Figure 4,3: Impulse Response Functions for the Extended New Keynesian Model y response 0.5,
monetary policy shock
cost-push shock
technology shock
R response
dp response
ybar response 1 0.5 r
-0.5
-11
Qg
20
0
10
20
0
10
20
0
The second row shows the effect of an IS shock. Without habit persistence this shock would have raised output on impact by one percent, but with habit persistence households seek to smooth changes in consumption and output increases initially by only 0.5 percent. But due to habit persistence it takes longer for output to return to the baseline. Hence, the modification of the New IS curve has the desired effect of introducing some degree of persistence into this relation. Compared to the previous model the output expansion induced by the IS shock has now a stronger effect on the inflation rate and the nominal interest rate, but the effects on these two variables remain quantitatively small. The extension of the New Keynesian model has changed the response of the system to a cost-push shock fundamentally. To begin with, the cost-push shock increases inflation on impact by more than one percentage point. This reflects the effect of higher expected inflation on current inflation via the forward-looking component of the Fuhrer-Moore Phillips curve. The backward-looking component of the Phillips curve has the effect of making the inflation response persistent, thereby keeping the inflation rate high for a sustained period of time. The increase in the inflation rate forces the central bank to tighten policy. Because of the persistence in the inflation rate, the central bank has to respond forcefully by
4.2 Simulating the New Keynes ian Model
151
raising the interest rate substantially and keeping it high for a long time. This triggers a deep and protracted recession. This recession is essential to reign in inflationary pressures, but it also demonstrates the short-run trade-off the central bank faces in stabilizing either inflation or the output gap in response to a costpush shock. Interestingly, this result shows that oil price shocks could lead to substantial output contractions engineered by the central bank in response to the inflationary pressures resultingfromthe increase in oil prices. The fourth row shows the response to a technology shock. The results are qualitatively similar to those from the previous model, but the habit persistence in the IS curve implies that it takes longer for actual output to catch up with the higher natural rate of output. Hence, the output gap is deeper, which leads to a more pronounced fall in the inflation rate. Consequently the central bank eases monetary policy by more than in the previous model in its attempt to stabilize the economy.
4.2.3
The Sources of Business Cycle Fluctuations in the New Keynesian Model
The analysis of New Keynesian models in the literature typically ends with the presentation of the implied impulse response fimctions of the model. In this study, we intend to extend the analysis to investigate a number of issues that are central to the policy debate in Germany and for applied macroeconomic analysis in general. A particular important but unresolved issue is the source of business cycle fluctuations. As discussed in Chapter 2, in the monetarist view of the business cycle the well-intended but somewhat futile efforts of policy makers to stabilize the economy or to push output above the natural rate of output are a prime source of business cycle fluctuations. That is, monetarists believe the private sector is inherently stable and attempts by policy makers to improve upon the market outcome will only disturb the economy. Monetary policy therefore should commit itself to following a policy rule and avoid discretionary policy. Keynesians, on the other hand, take a more benign view of the ability of monetary policy to stabilize the economy. In their view the economy is subject to frequent nonmonetary shocks and, hence, stabilizing the economy is an important objective of monetary policy. In this section we are going to use the technique of variance decomposition analysis to determine the role of the different shocks in the New Keynesian model forfluctuationsin output and inflation. Applying this technique to the analysis of New Keynesian models is a novel approach to investigate the relative importance of monetary policy and nonpolicy shocks for
152
Chapter 4 Monetary Policy in the New Keynesian Model
business cycle fluctuations which may turn out to be quite useful for the question at hand.201 The variance decomposition technique has already been introduced in Chapter 2. It should be noted that this technique is frequently employed in empirical S VAR analysis. Since the computation of the variance decomposition requires only the impulse response functions and the standard deviations of the shocks as input, it is in principle straightforward to employ this technique also in the analysis of theoretical models. However, specifying the standard deviations of the shocks can pose a challenge. One option we have is to employ the standard deviations chosen by McCallum (2001a). He sets the standard deviations of the monetary policy shock to 0.0017, and the corresponding values for the IS shock, the cost-push shocks, and the technology shocks are 0.03, 0.002, and 0.007. It should be noted, though, that this particular specification implies that the IS shock is approximately 18 times larger than the monetary policy shock. This in itself will virtually guarantee that the IS shock will dominate the variance decomposition. For this reason we also consider an alternative specification where we set the standard deviation for all shocks to one.^^^ We will refer to this as the baseline specification, because by avoiding taking a stand on the relative size of the shocks this specification is more neutral. The difficulties in specifying the standard deviations point, of course, to the inherent limitations of a purely theoretical analysis. Instead of assuming plausible parameter values for the simulation of the model it would be preferable to estimate the model, using, for example, maximum likelihood methods.^^^ This is, however, beyond the scope of the present study and left for future research. The results for the variance decomposition using the specification of McCallum (2001a) for the standard deviation of the shocks are shown in Table 4.1. Not surprisingly, given the large standard deviation assigned to the IS shock, this shock dominates the variance decomposition of output. However, already at the oneyear horizon technology shocks also become a quantitatively important source of business cycle fluctuations. At the three-year horizon both shocks are approximately equally important. Hence, with this specification business cycle fluctuations are entirely due to IS and technology shocks, with the former dominating in the short run while the latter dominate in the long run. The variability in inflation, however, is dominated by cost-push shocks. In spite of their large size. ^^^ The present author is only aware of the paper by Ireland (1997) that also employs the variance decomposition technique in a similar context. However, his model does not allow for IS or cost-push shocks. ^^^ This may appear to be a very large value relative to the choice of McCallum (2001a), but it should be noted that it is the relative size of the shocks that matters for the variance decomposition. 203 See Ireland (2001) for an example.
4.2 Simulating the New Keynes ian Model
153
Table 4.1: Variance Decomposition Using the McCallum Specification of Shock Variances Variance decomposition of OUTPUT Forecast horizon ~l 2 3 4 5 6 7 8 12 16 20 40
Monetary shock
IS shock
062 1.17 1.53 1.60 1.50 1.38 1.27 1.20 1.08 1.00 0.95 0.88
97.10 91.93 84.59 76.74 69.79 64.20 59.84 56.40 48.11 44.31 42.24 38.97
Variance decomposition of E>JFLATION
Cost-push Technology Monetary shock shock shock 0.23 0.90 1.98 3.10 3.92 4.34 4.45 4.37 3.79 3.52 3.56 3.10
2.06 6.00 11.91 18.56 24.79 30.08 34.45 38.03 47.02 51.17 53.45 57.05
0.36 0.94 1.64 2.36 3.01 3.52 3.84 4.01 4.00 4.00 3.99 3.97
IS shock 8.14 21.00 28.63 32.24 33.45 33.48 33.12 32.83 33.15 33.31 33.21 33.01
Cost-push Technology shock shock 89.61 73.18 62.28 55.85 52.32 50.56 49.79 49.46 48.85 48.56 48.42 48.11
1.89 4.88 7.45 9.55 11.22 12.44 13.25 13.71 14.00 14.13 14.38 14.90
IS shocks do not explain more than one-third of the variation in inflation at any horizon. Over time, technology shocks also gain in importance. The contribution of monetary policy shocks, on the other hand, is negligible. But it would be premature to conclude that monetary policy does not matter for inflation. To the contrary, as discussed above, it is monetary policy that determines the steady state inflation rate. Hence, the finding here only implies that monetary policy is not an important source forfluctuationseither in output or inflation. The preceding analysis might be biased by some extent by the large relative size assigned to the IS shock. To control for this factor, we present in Table 4.2 the results for the baseline specification where all shocks have the same size. This table shows that reducing the relative size of the IS shock reduces the role of this shock for business cycle fluctuations to almost negligible levels. Now monetary policy shocks dominate output fluctuations at very short horizons. However, already at the one-year horizon their contribution has fallen to one-third. That is, monetary policy shocks play an important role for high frequency noise of output, but less so for business cyclefluctuations.Instead, at the business cycle frequency between one and three years it is the cost-push shock that matters most. As before, with an increasing forecast horizon technology shocks also become relatively more important. In fact, at the business cycle frequency they typically outweigh monetary policy shocks. Regarding inflation, cost-push shocks dominate again, with monetary policy shocks gaining importance at longer horizons. Both specifications agree on one important aspect: Business cycle fluctuations are caused mostly by nonmonetary shocks. This is also in accordance with evidence from SVAR models. Sims (1998: 933) observes in this context that SVAR analysis consistently shows that the real effects of monetary policy shocks are
154
Chapter 4 Monetary Policy in the New Keynesian Model
Table 4.2: Variance Decomposition Using the Baseline Specification of Shock Variances Variance decomposition of OUTPUT Forecast horizon 1 2 3 4 5 6 7 8 12 16 20 40
Monetary shock
IS shock
50.75 47.44 38.84 30.92 25.05 21.20 18.90 17.63 15.98 14.94 14.32 13.33
25.62 11.97 6.92 4.75 3.72 3.18 2.87 2.67 2.29 2.12 2.03 1.89
Variance decomposition of INFLATION
Cost-push Technology Monetary shock shock shock 13.65 26.24 36.36 43.20 46.97 48.29 47.92 46.60 40.63 37.90 36.36 33.85
9.97 14.36 17.88 21.12 24.26 27.34 30.31 33.09 41.10 45.03 47.29 50.92
0.56 1.74 3.47 5.44 7.24 8.60 9.44 9.86 9.95 9.98 9.99 9.99
IS shock 0.04 0.12 0.19 0.24 0.26 0.26 0.26 0.26 0.26 0.27 0.27 0.27
Cost-push Technology shock shock 99.23 97.61 95.40 93.03 90.92 89.34 88.38 88.00 87.74 87.67 87.61 87.53
0.17 0.53 0.93 1.30 1.59 1.79 1.92 1.99 2.05 2.08 2.12 2.21
relatively small. Regarding the debate on the sources of business cycle fluctuations he writes: "There is a view, which Milton Friedman used to restate regularly some years ago, that erratic variation in monetary policy is the primary source of business cycle fluctuations, with each postwar U.S. business cycle largely explainable via the pattern of monetary policy variations preceding it. Friedman used to defend this view via statistical analysis that took the time path of a monetary aggregate as a sufficient statistic for the time path of monetary policy. The recent VAR literature decisively undercuts this way at looking at history, and as far as I know there are no attacks on the VAR literature, including this one, that explicitly put forth a quantitative model that contradicts the VAR literature on this score" (Sims 1998: 934). The result that at horizons longer than one year monetary policy shocks in New Keynesian models are relatively unimportant reflects, of course, the fact that monetary policy in these models behaves very much as recommended by monetarists. After all, monetary policy in New Keynesian models is modeled via a policy rule, which means policy makers try to avoid discretionary policy actions. Nevertheless, measurement errors caused by lags in the collection of data and frequent data revisions imply that policy makers cannot avoid making policy errors due to faulty data.^^"* These policy errors are likely to be an important source of monetary policy shocks in the New Keynesian model, but they are unlikely to be either large or persistent enough to become an important source of business cycle fluctuations. Put another way, the relative unimportance of monetary policy shocks is not necessarily a contradiction of the monetarist view of ^^^ The economic interpretation of monetary policy shocks is also an important issue in SVAR models. See Bemanke and Mihov (1996) for a discussion.
4.2 Simulating the New Keynesian Model
155
Table 4,3: Variance Decomposition for the Baseline Specification with p = 0.6 Variance decomposition of OUTPUT Forecast horizon
~12 3 4 5 6 7 8 12 16 20 40
Monetary shock
IS shock
15M 11.71 7.87 5.58 4.32 3.65 3.30 3.09 2.69 2.46 2.33 2.14
35.08 15.36 8.34 5.56 4.30 3.67 3.30 3.07 2.61 2.39 2.26 2.07
Variance decomposition of INFLATION
Cost-push Technology Monetary shock shock shock 30.50 48.39 56.04 58.30 57.83 56.02 53.63 51.15 43.82 40.13 38.05 34.91
18.56 24.54 27.74 30.56 33.54 36.66 39.77 42.68 50.89 55.02 57.36 60.88
0.07 0.21 0.41 0.77 0.89 0.95 0.98 1.00 1.00 1.00 1.00 1.00
IS shock 0.04 0.13 0.21 0.26 0.29 0.31 0.31 0.32 0.31 0.31 0.31 0.31
Cost-push Technology shock shock 99.74 99.20 98.58 98.00 97.52 97.16 96.91 96.75 96.47 96.33 96.24 96.07
0.15 0.46 0.80 1.14 1.42 1.65 1.82 1.95 2.21 2.35 2.45 2.63
business cycle fluctuations but could be interpreted as a measure of the widespread acceptance of monetarist thinking both in central bank practice and in theoretical modeling. The variance decomposition technique is also useful to explore the monetary transmission mechanism in more detail. To this end we investigate the sensitivity of the results to the choice of the monetary policy parameters. This analysis shows that changing the parameter (/\, which determines the responsiveness of the policy instrument to the output gap in the Taylor rule, hardly affects the results of the variance decomposition at all. This probably reflects the fact that output responds relatively quickly to changing economic conditions—in spite of the introduction of habit persistence into the New IS curve—-which leaves little room for stabilization policy. Inflation, on the other hand, is more persistent and, consequently, the variance decomposition results are more sensitive to the choice of the inflation parameter ^ in the Taylor rule. Increasing this parameter implies that the central bank responds more aggressively in particular to cost-push shocks. This amplifies the effects of this shock on output and thereby leads to a relatively larger role of cost-push shocks in the variance decomposition of output. However, the most important parameter in the Taylor rule turns out to be the smoothing parameter p. For example, reducing this parameter only slightly from 0.8 in the baseline specification to a value of 0.6 has already a substantial effect on the variance decomposition. The resuhs in Table 4.3 show that with this specification the relative importance of monetary policy shocks drops dramatically; in fact, at the one-year horizon the importance of policy shocks is now negligible. This shows the paramount importance of interest smoothing for the effectiveness of monetary policy.
156
Chapter 4 Monetary Policy in the New Keynesian Model
The lessons which emerge from the sensitivity analysis are twofold: First, the scope for stabilization policy depends crucially on the inherent persistent in output and inflation. In a sense, this is a variation of the old controversy between Keynesians and monetarists. For instance, the Keynesian assertion that the private sector is inherently instable is consistent with nonmonetary shocks having persistent effects on output and inflation, which also implies that there is ample scope for stabilization policy to be effective. In contrast, in the monetarist view the effects of nonmonetary shocks are short-lived, which makes policy interventions in general unnecessary. The second lesson that emerges is that for monetary policy to be effective it is not so important to raise or lower the interest rate substantially, but to sustain the new policy stance for a long period of time.
4.2.4
The Effects of Systematic Policy
In this section we are going to investigate the effects of systematic policy actions on output. As discussed in Chapter 3, the effectiveness of systematic policy is the center of another long-running controversy in macroeconomics. In this debate, Keynesians and monetarists actually agree that monetary policy has powerful effects on the economy, whereas New Classical economists believe that only unexpected monetary policy actions have real effects. Since private sector agents form expectations about systematic policy, in New Classical models it is therefore ineffective. However, it was a key objective of the New Keynesian research agenda to show that the New Classical policy ineffectiveness proposition depends crucially on the perfect price flexibility assumption in New Classical models, while rational expectations and optimizing behavior are compatible with real effects of systematic policy. The discussion in the preceding section has shown that in New Keynesian models systematic policy is clearly effective. However, the key question that up to now remains unanswered is how effective exactly systematic policy is. In the literature, this issue is typically addressed by simulating New Keynesians models with different specifications for the Taylor rule. The ability of these rules to stabilize output and inflation is then evaluated by comparing the resulting standard deviations for the variables of interest. However, this procedure does not answer what the output effects of systematic policy actions themselves are. That is, we have no quantitative measure yet of the size of the output effects that result from changes in the policy stance due to the systematic response of the central bank to a nonmonetary shock. This is an important omission in previous analysis because for central banks it is of paramount importance to understand what the real effects of their policy actions are. In fact, understanding the effects of systematic policy actions is arguably more important than those of monetary policy shocks, because the former ac-
4.2 Simulating the New Keynesian Model count for most policy actions.^^^ In this section, we try to construct such a measure. It needs to be emphasized that, contrary to widely held beliefs, the preceding impulse response analysis is largely silent on this issue. In particular, one might be tempted to use the output response to the monetary policy shock as a proxy for the real effects of systematic policy. However, this would be highly misleading, because a monetary policy shock is precisely the type of unexpected monetary policy action which also would have real effects in New Classical models. In New Keynesian models expected monetary policy is effective because nominal rigidities prevent instantaneous adjustment of prices, but prices are not completely rigid either, implying that expected policy is less effective than an unexpected monetary policy shock. Moreover, the focus on shocks in the impulse response analysis is very useful for investigating the monetary transmission mechanism by ensuring that the causality runs only from monetary policy to the other endogenous variables, which is why this type of analysis is widely used both in the simulation of theoretical models and in empirical SVAR analysis. However, since it is the very point of this approach to rule out that co-movements between the policy instrument and other variables are due to an endogenous response of monetary policy to changing economic conditions—^which would reverse the direction of causality—it is consequently difficult to investigate the effects of systematic policy with this approach. Nevertheless, the output response to the monetary policy shocks provides at least qualitatively a clue on the importance of systematic policy. In this context, it is important to notice that the output response plotted in Figure 4.3 is conditional on the entire interest rate path given by the impulse response function for the policy instrument. The interest rate impulse response function shows that a monetary policy shock leads to an interest rate hike of one percentage point lasting for one quarter, which represents the direct interest rate effect of the shock, and triggers an endogenous policy response in it that keeps the interest rate above the baseline for approximately one and a half years. In fact, the subsequent period of tight monetary policy, which represents the systematic policy response to the initial shock, appears to be almost the mirror image of the output response. This raises the possibility that the protracted recession following the policy shock is largely the product of systematic policy, while the direct effects of a policy shock could be small. In fact, empirical analysis by Cochrane (1998) and Gottschalk and Hoppner (2001) confirm this conclusion.
^^^ Sims (1998: 933) observes in this context that this is afrequentfinding in the SVAR literature. He writes, "Most variation in monetary policy instruments is accounted for by responses of policy to the state of the economy, not by random disturbances to policy behavior."
157
158
Chapter 4 Monetary Policy in the New Keynesian Model
To isolate the direct effects of a monetary policy shock, Cochrane (1998) investigates the effects of a policy shock that is not followed by a systematic policy response and presents results for U.S. data; Gottschalk and Hoppner (2001) apply his methodology to euro area data. Cochrane (1998: 278) stresses that impulse response functions capture history, as he puts it, in the sense that they give the average path of output and the interest rate following a monetary policy shock. Cochrane continues to ask "What does this history tell us about the effects of monetary policy? What does it tell us, for example, about the course of events we should expect if there is a monetary shock not followed by the customary further expansion of money?" (ibid.). To answer this question Cochrane develops an algorithm for SVAR analysis that isolates the output effects attributable to the direct effects of the monetary policy shock from the indirect effects arising from the systematic policy response to the shock. That is, he computes the effects on output of an unanticipated increase in the policy instrument by one percentage point that lasts only one period, which he calls an "unanticipated blip." His method requires as input an assumption concerning the relative effectiveness of anticipated policy versus unanticipated shocks. In the case where there is no distinction between anticipated and unanticipated policy he shows that the output effects of a one period "blip" in the policy instrument turn out to be small and fairly short-lived. Gottschalk and Hoppner find similar results for euro area data. These empirical results point to two conclusions: First, the direct effects of a monetary policy shock (an unanticipated "blip") on output are indeed small. Consequently, the large output response seen in the impulse response analysis is due to the indirect effect of a monetary policy shock; that is, it is the systematic policy response to the shock which accounts for most of the output response to a policy shock. Second, since the output effects of a one-period innovation in the policy instrument are fairly small—regardless whether they are anticipated or not—it follows that monetary policy has to sustain a given policy stance for a considerable period of time to have a significant output effect. This supports the earlier result on the importance of interest rate smoothing in the variance decomposition analysis. If systematic monetary policy is important, it is also likely to play an important role in the transmission of nonmonetary shocks. This is likely to be particularly true for the cost-push shock, since monetary policy tightens considerably in response to this shock. Measuring the output effects of a systematic policy response requires determining to what extent policy tightens or eases in response to a shock. This, in turn, requires determining what the corresponding neutral policy stance would have been. Here, we follow common practice in applied business recycle research where policy is considered to be neutral if the real interest rate is equal to the steady state natural rate of interest. In other words, maintaining a neutral policy stance requires a central bank to respond to changes in economic conditions only to the extent necessary to keep the real interest rate at its steady
4.2 Simulating the New Keynesian Model
159
State level. With this policy monetary policy would still manage aggregate demand conditions, but this is a responsibility it cannot escape because aggregate demand depends crucially on current and fUture real interest rates, which in turn are always determined by monetary policy. But by keeping the real interest rate at its steady state level the central bank ensures that aggregate demand conditions will remain neutral. Technically, in the following simulation the neutral policy stance will be determined by the Fisher equation: (4.72)
R, =1.01-^,Ap,^, +r-\-ef.
That is, we will insert this equation into the extended New Keynesian model in place of the Taylor rule. A comparison of (4.72) and (4.51) shows that the essential difference between the two policy rules is that in the former the parameters ^ , ^ , and /?, which typically characterize monetary policy, are set practically to zero. The parameter ^ is not set to exactly zero but to 0.01 in order to ensure that the rational expectations equilibrium remains uniquely determined. Simulating the model with the Fisher equation will yield the output and inflation responses to the shocks in the model under the assumption that monetary policy always maintains a neutral stance. Comparing the simulation results with those obtained in the previous section will provide some insight into the effects of a more activist policy. The results are shown in Figure 4.4. The solid line represents the effects obtained with a neutral policy, while the dotted line shows the results the model yields with a conventional Taylor rule.^^^ To isolate the effects of systematic policy, in a second step we subtract the impulse response functions generated with the neutral policy stance from those generated with the Taylor rule. The resulting impulse response functions for the systematic component of monetary policy are shown in Figure 4.5. Since the real interest rate is of paramount importance for the transmission mechanism of systematic policy, it is placed here in the first row. A change in the real rate indicates a change in the stance of systematic policy, and the remaining rows show the effects on output, the output gap, and inflation. In addition, the response of the nominal interest rate is shown. The first column in Figure 4.4 shows the effects of a monetary policy shock. A shock to the Fisher equation is going to be reversed after one period, since there is no persistence mechanism. This shock raises both the nominal and real interest rate by one percentage point for only one quarter. This policy experiment corresponds exactly to the "unanticipated blip" discussed by Cochrane (1998). The results here are consistent with his empirical work, since they also point to ^^" The results for each shock are shown in the columns of Figure 4.4, whereas the rows show the response of the individual variables. Here, y denotes output, y bar is the natural rate of output, y gap is the output gap, dp is inflation, R is the nominal interest rate, and r is the real interest rate.
160
Chapter 4 Monetary Policy in the New Keynesian Model
Figure 4.4: Simulating the New Keynesian Model with a Neutral Policy Rule Monetary policy shock 0.5
1
0 y
0.5
-0.5
n\
-1 I
0.2
y bar
o
) 0 2^ 0 -0?
10
Technology shock
Cost-push shock
IS shock 0 -0.5 -1 -1.5
) 2 °0.2' 0 -0?
1 0.5
\.y
0 10
20 1 0.5
0
very small and short-lived effects. The results show once again that if a policy stance is not maintained over some period of time, it practically has no effects. On the other hand, Figure 4.5 shows that the sustained tightening of policy that follows the shock has considerable effects on inflation and output. Hence, systematic monetary policy is potentially very effective. The second column displays the effect of an IS shock. Both the output and inflation responses show that relative to the neutral policy stance the Taylor rule is effective in stabilizing the economy. However, this holds more for the inflation rate than for output, since there is not much of a difference between the output responses in the models with the Taylor rule and the neutral policy stance. This result is not entirely unexpected, since already the results from the variance decomposition analysis suggested that the scope of stabilization policy for output is limited. Interestingly, with a neutral policy stance the nominal interest rate increases by more than with the Taylor rule. This reflects to some extent that with neutral policy the inflation rate increases by more, meaning the nominal interest rate has to increase too to keep the real interest rate constant. But this
4.2 Simulating the New Keynes ian Model Figure 4.5: The Effects of Systematic Policy Monetary policy shock
IS shock
Cost-push shock
Technology shock
ygap -0.5
dp
also reflects the interest rate smoothing behavior present in the Taylor rule which prevents the interest rate from responding immediately to the IS shock in a forceful manner. In fact, with the Taylor rule the real rate initially falls. After one year the real interest rate increases above the baseline and remains high for another one and a half years. Figure 4.5 shows that this implies that systematic policy has its peak effect on economic conditions well before the central bank policy has completed its tightening of policy. This suggests that the expectation of an eventual tightening has a powerful dampening effect on the output and inflation response, which underlines the importance of managing expectations for a successful stabilization policy. The third column shows the effects of a cost-push shock. A comparison of the results from the models with the Taylor rule and the Fisher equation illustrates the short-run trade-off the central bank faces when a cost-push shock occurs: If the central bank wants to reign in inflation more quickly, it needs to engineer a larger output contraction. This is exactly what the central bank does when it follows the Taylor rule. With this rule the central bank chooses to impose a deep recession on the economy, thereby bringing inflation back to the baseline within
161
162
Chapter 4 Monetary Policy in the New Keynes ian Model
two years, while the same task with a neutral policy course would take approximately five years. Figure 4.5 quantifies the output losses resulting from the systematic tightening of policy: At its peak, output is lower by approximately 0.5 percent. In spite of the less ambitious approach to stabilization, it is with the neutral policy stance that the nominal interest rate increases initially most. Again, this reflects the effect of the interest rate smoothing parameter in the Taylor rule. As with the IS shock, the real rate initially falls and again it takes approximately one year before it increases above the baseline. The final column shows the effects of the technology shock. Here, stabilization policy requires an easing of the policy stance to allow actual output to quickly catch up with the higher natural rate of output. Hence, with the Taylor rule the output gap closes faster than it does with a neutral policy stance. The Taylor rule is particularly effective in keeping the inflation rate close to the baseline. While a decline in the real interest would have been desirable to stimulate the economy, the real interest rate increases initially—interest rate smoothing prevents the nominal interest rate from falling sufficiently to offset the decline in inflation— but after one year the real interest rate begins to fall. Figure 4.5 shows that the variation in the real interest rate is fairly small, but systematic policy has nevertheless quantitatively significant effects on output and inflation. An important result that emerges from Figures 4.4 and 4.5 is that if the policy stance is measured by comparing the level of the real interest rate to the steady state natural rate, as is frequently done in applied business cycle research, it would often appear that monetary policy is significantly "behind the curve," in the sense that the central bank acts only with considerable delay decisively to economic developments. But this actually reflects the desire of central banks to smooth interest rates, and it has been shown previously that this is a very important tool to enhance the effectiveness of monetary policy. Another interesting result is that the relationship between the interest rate, the output gap, and inflation seems to depend on the source of the shock that hits the economy. For example, comparing the effects of the IS and the cost-push shocks, it becomes apparent that with the IS shock stabilization policy has hardly any effect on the output gap, but a significant effect on the inflation rate, while with the cost-push shock the effectiveness regarding inflation seems to be much smaller. Interestingly, this is consistent with the monetarist dictum on the variability of lags in the transmission mechanism and uncertain magnitude of the effects of monetary policy. It also means that applied business cycle analysis faces a challenging task since forecasting the effects of monetary policy requires both correctly identifying the shocks that hit the economy and predicting the response of the central bank to these shocks over time. Another noteworthy result is that even if the central bank follows the Taylor rule it actually does not change the real interest by very much. For example, in the case of the cost-push shock the initial fall in the real interest rate is almost completely offset by the later tightening. In fact, computing the cumulative sum of the real interest rate over the 20 quarters con-
4.3 New Keynesian Economics and the Policy Debate in Germany
163
sidered here shows that the real interest rate has been raised in this period by a total of only 0.4 percentage points. It is hard to believe that this rather small increase in the real interest rate alone is responsible for the substantial output contraction engineered by systematic policy. This shows that the commitment of monetary policy to the Taylor rule anchors the expectations of private sector agents in an effective way and that this is an important factor in the monetary transmission mechanism.
4.3
New Keynesian Economics and the Policy Debate in Germany
The discussion in Chapter 2 has shown that Keynesians and monetarists disagree fundamentally on the need for active demand management policies. This is also a constant issue in the public debate in Germany. The preceding discussion in this chapter has shown that in this controversy New Keynesian economics come down firmly on the side of the monetarists.^^^ The monetarist policy implications of New Keynesian models arise mainly because these models fully embrace the monetarist natural rate hypothesis. From this follows that output fluctuates symmetrically around the natural rate of output and the best that stabilization policy can hope to accomplish is reducing the variance of fluctuations in output and inflation. Moreover, New Keynesians clearly recognize the limitations of monetary policy arising from the natural rate hypothesis for the analysis of optimal monetary policy in New Keynesian models. This is, after all, why the loss function of the central bank typically specifies that monetary policy should seek to minimize the deviation of output from the natural rate of output and to keep inflation close to target. Consequently, in New Keynesian models even a superbly executed stabilization policy has only second-order effects on welfare. This stands in stark contrast to the traditional Keynesian view postulating that stabilization policy has the potential to manage demand conditions in such a way that the economy operates at a higher level of activity than would be achieved without policy intervention, thereby having first-order effects on welfare. The inefficient low level of output in traditional Keynesian models is due to the prevalence of monopoly power of firms in these models. This is, in fact, an assumption both traditional and New Keynesian models share, since the latter also assume that a modem market economy is characterized by imperfect competition, and consequently output is on average inefficiently low in New Keynesian models too. But what differentiates New Keynesian models from their traditional counterparts is that the former have embraced the natural rate hypothesis while ^^^ See also the discussion in De Long (2000).
164
Chapter 4 Monetary Policy in the New Keynes ian Model
the latter have not. It needs to be emphasized here that in New Keynesian models the natural rate of output itself is inefficiently low. After all, the natural rate of output is the level of output that is obtained when prices are perfectly flexible, and since with imperfect competition firms set prices at a socially suboptimal high level, the resulting output level is inefficiently low. In this situation, traditional Keynesians would argue that demand management policies could improve the performance of the economy by "filling in the troughs without shaving off the peaks," as we put it in Chapter 2. However, for a New Keynesian this is an impossible task since the natural rate hypothesis implies that any attempt to increase permanently the level of output above the natural rate level would be prohibitively expensive in terms of inflation. Consequently, a New Keynesian poHcy maker would not engage himself in trying to increase the average level of output, but would pursue the more modest task of stabilizing output around its natural rate level. The adoption of the natural rate hypothesis has also strong implications for the debate on the appropriate policy assignment in Germany. The discussion in Chapter 2 has shown that monetarists believe that monetary policy should focus solely on its goal of maintaining price level stability, while it is the responsibility of trade unions and firms to achieve and maintain full employment by setting wages accordingly. Keynesians, on the other hand, believe that a policy of wage moderation by trade unions can only be effective in increasing employment if it is accompanied by expansionary demand policies. As shown above, this controversy is central to the policy debate in Germany, and has been going on for two decades. In this debate, the embrace of the natural rate hypothesis by New Keynesians means again that they are coming down on the side of monetarists, since this hypothesis implies that the long-run aggregate supply curve is vertical. Hence, in New Keynesian models, a policy of wage moderation will unambiguously shift the aggregate supply curve to the left, and employment will increase. However, there is also a Keynesian element in the transmission mechanism, since wage moderation has the effect to increase the supply potential of the economy, and the resulting negative output gap will induce the central bank to ease policy. Thus, monetary policy accommodates the wage moderation policy of trade unions by stimulating aggregate demand. However, this is not part of a concerted action of trade unions and the central bank to lower unemployment, as demanded by Keynesians, but follows from the systematic response of the central bank to economic conditions, as specified in the Taylor rule. Moreover, the simulation of the extended New Keynesian model shows that the central bank response to an increase in the supply potential of the economy is quite limited. In this model, the effects of wage moderation are similar to that of a technology shock, and Figure 4.3 shows that the interest rate response is relatively small. In fact. Figure 4.4 shows that a supply response to a policy of wage moderation would also be forthcoming if the central bank would not ease policy but pursue a neutral policy course throughout. This illustrates that in New Keynesian models aggregate
4.3 New Keynesian Economics and the Policy Debate in Germany
165
supply tends to create its own demand, which is a cornerstone of monetarist thinking. Another aspect where New Keynesians have adopted an important plank of monetarist thinking is that they prefer to analyze optimal policy in terms of policy rules, instead of analyzing each business cycle episode as requiring a unique and idiosyncratic policy response.^^^ Monetarists argue that a commitment to a policy rule would be beneficial because it would help in anchoring expectations. New Keynesians advocate the use of policy rules for exactly the same reason, which results from the incorporation of rational expectations into their models. After all, with rational expectations the management of expectations has become a central element of the monetary transmission mechanism in New Keynesian models. The importance of policy rules in New Keynesian economics has also significant implications for applied business cycle research, since most business cycle reports analyze case by case what the optimal monetary policy ought to be. That is, they take the past as given, and determine optimal policy each period by reoptimizing their models. This is exactly the discretionary approach to monetary policy that New Keynesian models reject in favor of policy rules. A more appropriate approach to policy analysis would be to determine first what type of policy rule would be optimal in general and then to discuss the implications of the resulting policy rule for the present situation, taking interest rate smoothing behavior and therefore the role of past conditions for current policy decisions into account. Recent empirical evidence on the significance of the Taylor rule in central bank practice also tends to undermine a key argument of Keynesians in the policy debate in Germany. In their view, the macroeconomic performance in the United States in the past two decades has been more satisfactory than in Germany because the Federal Reserve Bank pursued a more active stabilization policy, which reflects the U.S. central bank's twin goals of stabilizing employment and prices. The Bundesbank, on the other hand, was only committed to stabilizing the price level, and, according to the Keynesian argument, pursued a generally tight policy in its endeavor to lower the inflation rate further and further. As discussed in Chapter 2, Keynesians believe this is a key reason behind the unsatisfactory high unemployment rate in Germany. However, evidence provided by Clarida et al. (1998) on monetary policy rules in practice shows that the estimated monetary policy reaction functions for the Federal Reserve Bank and the Bundesbank are strikingly similar. Both conform to the forward-looking Taylor rule discussed above. For the Federal Reserve Bank they report following result:^^^
208 See also De Long (2000: 84). 209 The sample is 1979:10-1994:12. See Clarida et al. (1998: 1049).
166 (4.73)
Chapter 4 Monetary Policy in the New Keynesian Model R, = (l~0.92)[r+^-0.07(£,_,>;, -y,)+\.19{EAp,,^
-n)]
Here, S^ and S2 are the coefficients for a second-order partial adjustment process, with ^1+^2= ^-92. For the Bundesbank they find the following result:^^^ (4.74)
R,={l-0.9l)[r+W-0,25{E,_,y,-y,)^l3l{EAp,,,-^)] + 0.9lR,_^+e^.
A comparison of both reaction functions shows that the Bundesbank, if anything, is less aggressive in its response to inflationary pressures and more willing to make use of its policy instrument to stabilize output. Hence, the claim that the Bundesbank is more "hawkish" than its American counterpart is not substantiated by the available empirical evidence. In fact, already the original policy rule proposed by Taylor (1993) provides a reasonably good fit for Bundesbank policy in the past two decades. In Figure 4.6, we plot the Taylor rule for Germany together with the actual path of the shortterm interest rate, the Bundesbank policy instrument.^ ^^ For computing the Taylor rule for Germany, we follow Taylor (1993) and set the parameters (/\ and ^ to 0.5, and compute the inflation rate Ap^ as the rate over the previous year. For the output gap, we employ the band pass filter using the Bums-Mitchell specification. We also use the band pass filter to isolate the trend component of the real short-term interest rate, using a high pass specification. The resulting trend estimate is our proxy for the steady state natural rate of interest F in (4.33). Like Clarida et al. (1998) we focus on the post-1979 period. As can be seen from Figure 4.6, the resulting estimate for the Taylor interest rate tracks the actual interest path quite closely. As mentioned above, even the Bundesbank itself acknowledges that the Taylor rule provides a good fit for its policy. Since the Taylor rule is broadly consistent with the principles of optimal policy in New Keynesian models, this suggests that from a New Keynesian perspective the Bundesbank actually did a good job in the past two decades. Another area where New Keynesians have adopted the monetarist line of argument is the debate on the benefits of "fine-tuning" the economy. Monetarists argue that monetary policy should abstain from "fine-tuning," because information lags and long and variable lags in the transmission mechanism mean that an activist policy is likely to become itself a significant source of disturbances. Even though some monetarists might reject the Taylor rule because of the role of the 210 The sample is 1979:3-1993:12. See Clarida et al. (1998: 1045). 211 Following the estimation of the Taylor rule in Deutsche Bundesbank (1999), we use West German data. The time series for real GDP and inflation are the same as those used in Figure 4.2. For the short-term interest rate we use a three-month interest rate provided by DATASTREAM (code: BD3MTH..R).
4.3 New Keynesian Economics and the Policy Debate in Germany Figi4re4.6: The Taylor Rule and the Short-Term Interest Rate for Germany
' • I •''
1979
I ' •' I
1981
1983
1985
1987
Short-term interest rate
1989
1991
1993
— Taylor rate
output gap in this rule, the Taylor rule actually does not represent an attempt at fine-tuning the economy, because the interest rate smoothing behavior inherent in this rule prevents the central bank from responding in an overly activist manner to economic disturbances. That is, in New Keynesian models monetary policy does not seek to return output immediately to the natural rate, but does so gradually over time. Part of the reason for the gradual response is uncertainty concerning the exact structure of the appropriate economic model and parameter values. In this way, New Keynesian models have incorporated monetarist concerns regarding information lags and other uncertainties into policy behavior. The emphasis in New Keynesian models on monetary policy as the prime tool of stabilization policy instead of fiscal policy is another area where monetarist thinking has had a profound influence. After all, in traditional Keynesian models fiscal policy was the first choice for stabilizing the economy. However, both the monetarist research agenda demonstrating the effectiveness of monetary policy and the fact that persistent fiscal imbalances since the second half of the 1970s largely preclude aggressive use of this instrument have helped monetary policy taking the driver seat. In sum, monetarist thinking has had a pervasive influence on economic thinking. However, this does not hold not for a particular strand of monetarism that De Long (2000) dubs "Political Monetarism." He characterizes Political
167
168
Chapter 4 Monetary Policy in the New Keynesian Model
Monetarism as follows: "Political Monetarism argued not that velocity could be made stable if monetary shocks were avoided, but that velocity was stable. Thus, the money stock became a sufficient statistic for forecasting nominal demand, and central bankers could close their eyes to all economic statistics save monetary aggregates alone. Political Monetarism argued not that institutional reforms were needed to give the central bank the power to control the money supply tightly, but that the central bank already did control shifts in the money supply. The central bank was the source of all monetary forces, either in its actions or in its failure to neutralize private actions. Everything that went wrong in the macroeconomy had a single, simple cause: the central bank had failed to make the money supply grow at the appropriate rate" (De Long 2000: 91). New Keynesian economics disagree with practically every point of Political Monetarism. Regarding the stability of velocity, monetary targeting has lost substantially in significance in central bank practice precisely because of the instability of velocity. Even though it is possible to find a stable money demand function for some countries, including Germany, this is typically the case only for broadly defined monetary aggregates. Hence, circumventing the problem of instability in velocity for high-powered monetary aggregates by focusing on broad money comes at a high price, since the central bank will find it very hard to control the supply of broad money effectively. In practice, the central bank will try to control broad money via manipulation of the short-term interest rate. The resulting transmission mechanism is fairly indirect, since it runs from the interest rate to output and finally to broad money via the money demand function.^ ^^ Thus, the lack of full control over broad money means neither is the money stock a sufficient statistic for the monetary policy stance, let alone for nominal demand, nor is the central bank the source of all changes in this monetary aggregate.^^^ Regarding the issue of central bank policy being the source of all that goes wrong in the macroeconomy, the discussion in this chapter has shown that in New Keynesian models, monetary policy has a stabilizing influence on economic conditions, and it is definitely not a major source of fluctuations in the economy. The latter is also confirmed by ample empirical evidence from SVAR models. However, since Political Monetarism represents at best a stripped down version of monetarist theory that includes "substantial proportions of misrepresentation and overstatement," as De Long (2000: 91) observes, its demise does not represent a significant setback to monetarism. ^^^ For the euro area, this transmission mechanism has been investigated in Gottschalk and Stolz (2001). The resulting dynamics tum out to be very complex, implying that the resulting information and transmission lags would make it very difficult for the central bank to exercise effective control over broad money. ^^^ For an investigation of the leading indicator qualities of monetary aggregates for economic conditions in the euro area, see Gottschalk et al. (2000). These authors find that monetary aggregates contain some information on economic conditions, but they are definitely not a sufficient statistic to forecast nominal demand.
4.3 New Keynesian Economics and the Policy Debate in Germany
169
The fact that New Keynesian models generally have strong monetarist characteristics may give rise to the question why the literature refers to them as "New Keynesian" instead of "New Monetarist." While the latter label would be appropriate too, the Keynesian label captures the fact that the transmission mechanism in these models is clearly Keynesian in character. After all, monetary policy in New Keynesian models has real effects because of nominal rigidities in the economy and not because of expectational errors, as postulated by monetarists or New Classical economists.^^"* In particular, monetary policy affects inflation in New Keynesian models by managing aggregate demand conditions. Aggregate demand, in turn, affects real marginal costs of firms because workers demand higher wages or because firms have fixed factors of production. In either case, firms will raise prices to pass on the cost increases to their customers. Thus, this transmission mechanism is very similar to that in traditional Keynesian models. In fact, the New Keynesian Phillips curve is much more closely related to the Keynesian formulation of the expectations-augmented Phillips curve (2.4b) than it is to the monetarist formulation given by (2.6). In addition, money balances are central to the monetary transmission mechanism in monetarist models, but they have at best a secondary role in New Keynesian models. One may ask why the policy implications of New Keynesian models are so different from traditional Keynesian models if the transmission mechanisms are so similar. A key factor here is that New Keynesian models analyze policy in an explicit, stochastic framework, which incorporates optimizing behavior of agents and rational expectations. In this framework, it emerges clearly that monetary policy is unlikely to have long-run effects on real variables. Given the structure of New Keynesian models, such long-run effects could emerge only if a nominal demand stimulus would persuade workers to increase permanently the supply of labor they offer, or if firms would accept a permanent reduction in their monopoly profits. Both outcomes would increase the natural rate of output, but they appear to be highly implausible.^ ^^ However, is also should be borne in mind that this result reflects to some extent the relatively simple structure of New Keynesian models. That is, since it is the main purpose of New Keynesian models to explain fluctuations in output and inflation lasting at most a limited number of years, it often suffices to model the supply side of the economy in a rudimentary way. For this reason, it is customary in New Keynesian models to abstract from the accumulation of capital ^^^ However, the sticky-information New Keynesian Phillips curve proposed by Mankiw and Reis (2001) bears some resemblance to earlier monetarist models of inflation with adaptive expectations. ^^^ Put another way, the discussion in Chapter 2 has shown that the long-run effects of demand policies emerge in traditional Keynesian models because the traditional Phillips curve was falsely specified in terms of nominal wages instead of real wages. New Keynesian models correct this shortcoming, and as a consequence, the long-run effects disappear.
170
Chapter 4 Monetary Policy in the New Keynesian Model
or to avoid modeling the labor market by assuming that real marginal costs are a function of the output gap. But this also closes off a number of transmission channels through which monetary policy could affect the supply side of the economy.^ ^^ For example, since monetary policy has the leverage over the real interest rate, it also affects the user costs of capital and, hence, the rate of capital accumulation. Andersen (1998) shows that the interactions between nominal rigidities and capital accumulation can give rise to a situation where monetary policy has permanent effects on the capital stock and, thus, on output. Another possibility is that monetary policy via its management of aggregate demand conditions can affect the entry and exit of firms into the market. Again, monetary policy might have long-run effects via this supply side channel. A third channel is the so-called hysteresis effect, which we will discuss in more detail below. This list of possible supply side effects of demand management policies is not complete, but it shows that the issue of the long-run effects of monetary policy has not yet been theoretically settled. Nevertheless, the fact that these channels are typically ignored in New Keynesian models reflects the conviction of most economists that the natural rate hypothesis represents a reasonable approximation of the real world. Since the validity of the natural rate hypothesis is central for the long-run properties of New Keynesian models, this study is going to revisit this issue below and present a test of this hypothesis within a New Keynesian framework.
^^^ For a discussion of these channels, see Lindbeck and Snower (1994).
Introducing Nonlinearities into the New Keynesian Model
The preceding section has shown that the monetarist policy implications of New Keynesian models are mainly due to its embrace of the natural rate hypothesis. In particular, this hypothesis is a key reason why stabilization policy in New Keynesian models has only second-order effects on output. A contributing factor, however, is that these models are also inherently linear. To assess the importance of the latter assumption, we are now going to introduce some nonlinearities into the New Keynesian model and proceed to reevaluate the benefits of stabilization policy. Since nonlinearities in the model raise the possibility that stabilization policy may havefirst-ordereffects on welfare even if the natural rate hypothesis holds, demand management by the central bank becomes potentially more important for the welfare of the economy, which may lead to policy prescription more in line with Keynesian thinking. To explore this possibility, we are first going to consider nonlinearities in the aggregate supply function. Next, we are going to allow for nonlinearities in the welfare function, which provides another avenue for stabilization policy to have potentially large effects. This section will also present empirical evidence on the welfare costs of business cycle fluctuations in Germany. After all, a rationale for an activist demand management policy can arise only if the welfare costs of business cyclefluctuationsare sizable.
5.1
Nonlinearities in the Aggregate Supply Curve
To illustrate the effects of introducing a nonlinear aggregate supply curve into the New Keynesian model, we plot in Figure 5.1 a conventional linear short-run aggregate supply curve (SRAS I) together with a convex short-run aggregate supply curve (SRAS II). In the long run, we assume that the natural rate hypothesis holds and therefore the corresponding long-run aggregate supply curve (LRAS) is vertical. Let us consider first a typical business cycle under the assumption that the short-run supply curve is linear: According to Figure 5.1, in equilibrium output and inflation are equal to y and W, while booms and recessions are assumed to lead to realizations of output and inflation given by yi°°'^, n^°'''^ and yrecession^ j^recession JQ simplify thc cxpositlou, wc assumc that a boom is caused by a nominal demand expansion engineered by the central bank, while a recession is caused by a nominal demand contraction of similar size. With shocks of
172
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
Figure 5.1: A Convex Short-Run Aggregate Supply Curve Inflation LRAS SRASII
SRASI
Output
similar size but opposite signs, output and inflation fluctuate symmetrically around their equilibrium values. However, this ceases to be the case if we assume a convex short-run supply curve. The convexity implies that a nominal demand expansion triggers a larger price response, and the corresponding output effects become smaller. Hence, if we assume that the central bank engineers boom and recession phases leading to the same inflation fluctuations as before, the output contraction will be of similar magnitude as in the linear case, but the output expansion will be much smaller, with output increasing only to y^"""" instead of j;^*^^'". While the fluctuations in inflation continue to be symmetric, the output fluctuations are now asymmetric with a larger weight on the recession phase. This also implies that the average level of output becomes smaller. That is, in equilibrium, output is still at its natural rate of output, but if the economy spends equal amounts of time being in boom and recession phases, the average level of output will be smaller than the natural rate of output. Thus, the introduction of a nonlinear element into the short-run supply curve drives a wedge between the natural rate of output and the average level of output. This raises the prospect that an active stabilization policy, which manages to reduce the fluctuations in output, could increase the average level of output, because the reduction in the depth of recessions will
5.1 Nonlinearities in the Aggregate Supply Curve
173
more than offset the reduction in the strength of booms. From this follows that stabilization policy can have first order effects on output, thereby giving the New Keynesian model a more traditional Keynesian flavor. At the same time, the natural rate hypothesis still holds in the sense that policy is powerless to increase output permanently above the natural rate.
5.1.1
Nonlinearities in the Supply Curve and Credit Market Imperfections
The assumption of a convex short-run supply curve can be justified both on theoretical and empirical grounds. Theoretically, it can be shown that credit market imperfections could give rise to such a relationship.^^^ These imperfections arise because of asymmetric information between borrowers and lenders. This leads to an adverse selection problem, meaning the credit market becomes suboptimal small, and borrowers will have to pay an external finance premium. A central factor for the size of this premium is the net worth of borrowers, because it determines the collateral they can put up. Moreover, the net worth is also an important factor for moral hazard problems; a reduction in the net worth of a firm, for example, reduces the owners' equity stake in their firm, giving them more incentives to engage in risky investment projects. With credit market imperfections, monetary policy affects the quantity and price of credit in the economy in essentially two ways: First, monetary policy has some degree of control over equity prices in the economy and therefore over the net worth of firms. The ability of monetary policy to influence equity prices is actually an important part of the monetarist view of the monetary transmission mechanism, which emphasizes that monetary policy affects not only one relative asset price, the interest rate, but also a universe of relative asset prices and real wealth. By having an effect on the net worth of firms, the central bank has some leverage over the prevalence of the adverse selection and moral hazard problems and therefore also over the price and availability of credit in the credit market. Second, since the traditional Keynesian transmission mechanism implies that monetary policy is an important determinant of aggregate demand conditions, monetary policy also affects the cash flow available to firms. This tends to reinforce the effects from the adverse selection and moral hazard problems. To illustrate, if monetary policy tightens aggregate demand, the reduction in cash flows makes firms particular dependent on credit markets while at the same time banks are reluctant to provide external finance because of the effect of the downturn on firms' net worth. The resulting credit crunch means that firms are ^^' The role of credit market imperfections for business cycle fluctuations is closely related to the so-called credit channel of the monetary transmission mechanism. For a survey, see Bemanke and Gertler (1995).
174
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
likely to curtail their spending plans to preserve as much free cash as possible, and real activity slumps even more. This transmission mechanism of monetary policy is referred to as credit channel. Since its main role is to amplify the real effects of the traditional Keynesian and monetarist transmission mechanisms, it is also called "financial accelerator." Interestingly, this view of the transmission mechanism is very similar to the traditional Keynesian perception of the way monetary policy works. As discussed in Chapter 2, Keynesians believed that monetary policy works primarily by affecting the availability of financial intermediary credit, which is particularly important for small firms and individuals. They were reluctant to make full use of this instrument because it worked by a distortion of sorts. In fact, characterizing the monetary policy transmission mechanism as working via "a distortion of sorts" would also describe the modem version of the credit channel quite well. What makes this transmission mechanism special in the present context is that it implies that the real effects of a given monetary policy easing are likely to be stronger in a recession than in a boom, which is exactly what is implied by the convex short-run supply curve depicted in Figure 5.1, too. In a boom, the balance sheets of firms tend to be strong and their net worth high. In this situation, the external finance premium is unlikely to be very sensitive to monetary policy actions. Moreover, firms do not depend much on credit markets in the first place because of large cash flows. Hence, a further easing would not improve credit market conditions by much, and a monetary stimulus would fail to stimulate activity significantly. Instead, it would lead to a large price response. In a recession, however, firms are much more sensitive to credit market conditions because of their dependence on external finance and because their low net worth means credit is either expensive or not available to them at all. In this situation, a monetary policy stimulus is therefore much more likely to be effective in raising output; both by improving the cash flow of firms and by raising their net worth. Interestingly, in both phases of the business cycle the central bank will find it easier to contract real activity than to stimulate it, since monetary policy gains in effectiveness once credit market conditions have begun to deteriorate. Hence, in this model monetary policy has the character of a string on which the central bank can pull but not push.^^^
^^^ Friedman (1989) notes that the characterization of monetary policy as a string is consistent with Romer and Romer's (1989) approach to measuring the effects of monetary policy and with the pre-Friedman-Schwartz view of monetary policy.
5.1 Nonlinearities in the Aggregate Supply Curve
5.1.2
175
Nonlinearities in the Supply Curve and Downward Nominal Rigidities
A second class of models that give rise to a convex shaped short-run supply curve are based on downward nominal rigidities. The classic example is, of course, the case of downward rigidity of nominal wages, which underlies both the kinked supply curve shown in many macroeconomic textbooks to illustrate the Keynesian view of the business cycle and the convex shape of the traditional Phillips curve. A more recent example of a model with downward nominal rigidity is provided by Ball and Mankiw (1994b). They show that a menu cost model of price adjustment very similar to the one used in this chapter to derive the New Keynesian Phillips curve can give rise to a convex short-run supply curve if one allows for positive trend inflation. The intuition behind their result is that trend inflation causes firms' relative prices to decline automatically between adjustments. Hence, when afirmwants a lower relative price, it need not pay the menu cost, because inflation does much of the work. A positive shock to its desired relative price, on the other hand, means its desired relative price rises while at the same time inflation increases the general price level and therefore decreases the firm's actual relative price, leading to a large gap between its desired and its actual price. Thus, in this situation a firm has much stronger incentives to pay the menu costs to adjust its price. As a result. Ball and Mankiw observe that positive shocks are more likely than negative shocks to induce price adjustment, and the positive adjustments that occur are larger than the negative adjustments. From this they conclude, "Our model implies that shifts in aggregate demand have asymmetric effects on output. Since prices are sticky downward, a fall in aggregated demand reduces output substantially. A rise in demand has a smaller absolute effect on output, because prices adjust more quickly. We thus provide a theoretical rationale for the empirical finding that monetary shocks have asymmetric effects. The model also implies that, with a symmetric distribution of demand shocks, the distribution of output is skewed to the left" (Ball and Mankiw 1994b: 248). These asymmetric effects of monetary policy are consistent with the convex shape of the short-run aggregate supply curve shown in Figure 5.1. Moreover, since in a boom trend inflation tends to be high, the real effects of a monetary easing would be limited, while in a recession monetary policy would be more effective in stimulating output, because trend inflation would be lower. Hence, this model would have implications similar to those of the model with credit market imperfections discussed above.
176 5.1.3
Chapter 5 Introducing Nonlinearities into the New Keynesian Model Empirical Evidence on Nonlinearities in the Supply Curve
The observation by Ball and Mankiw (1994b) that their model implies a skewed distribution of output points towards a simple empirical test to check whether the nonlinearities discussed in this chapter are empirically relevant for Germany. To this end, we are going to employ two different methodologies to estimate the output gap for Germany and then compute the corresponding histograms to investigate their distribution. For the estimate of the first output gap we use the band pass filter methodology employed before for this purpose. The second output gap is obtained from a segmented trend model, where we model the natural rate of output as a function of a deterministic trend.^^^ To allow for the fact that the trend growth rate probably changed in the 1970s, we allow for an endogenous break in the time trend. The breakpoint is determined using the Perron (1997) procedure, which suggests that such a break occurred in 1972:3. The estimation results imply that in the 1960s and early 1970s the German economy grew by approximately 4 percent per year, but after 1972 the trend growth rate declined to about 2.2 percent per year. The resulting histograms for the two output gaps are shown in Figure 5.2 and 5.3. Both histograms show clearly that the distribution is skewed to the left. This is exactly what one would expect to occur if the economy were characterized by a convex short-run supply curve. More formal evidence for asymmetries in the German business cycle is provided by Kakes (2000) and Peersman and Smets (2001). Both papers seek to test whether monetary policy is more effective in recessions than in booms. To this end, they use a Markov switching model to identify boom and recession regimes and then proceed to estimate the effects of a monetary tightening in the two regimes. As argued above, the finding that monetary policy is more effective in recessions would be consistent with the presence of a credit channel in the monetary transmission mechanism or with a convex short-run supply curve arising from downward nominal rigidities. The results in both papers point clearly to asymmetric effects of monetary policy. Peersman and Smets (2001: 13) apply their methodology to a number of European countries and summarize their results as follows: "In a recession the effect [of a monetary tightening] varies from -0.60 in the Netherlands to -1.44 in Germany and (with the exception of the Netherlands) is always significant. ... The effect on output during downturns is significantly larger in Germany than in other countries. In an expansion, the effect ranges from -0.21 in France to -0.76 in Austria." In sum, empirically the presence of nonlinearities in the short-run supply curve cannot be easily dismissed.
^^^ The time series for West German real GDP in both cases is the same as the one used in Figure 4.2.
5.1 Nonlinearities in the Aggregate Supply Curve Figure 5.2: Distribution of the Output Gap Using the Band Pass Fiher
Series: GAP BP Sample 197? :1 1998:4 Observations 112 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis
0.075453 -0.066643 3.051550 -3.216442 1.407926 0.480150 2.979236
Jarque-Bera Probability
4.305504 0.116164
Figure 5.3: Distribution of the Output Gap Using a Segmented Trend Model
Series: GAP SEGTREND Sample 1971:1 1998:4 Observations 112
• 4 - 2
0
Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis
-0.001854 -0.189579 6.712477 -5.147536 2:579285 0.551432 2.930855
Jarque-Bera Probability
5.698418 0.057890
177
178 5.1.4
Chapter 5 Introducing Nonlinearities into the New Keynesian Model Policy Implications
From a policy standpoint of view we have already discussed above that these nonlinearities raise the prospect that stabilization policy can have first order effects. Hence, a New Keynesian model with a nonlinear short-run supply curve becomes somewhat more Keynesian in its policy implications. In fact, comparing Figure 5.1 with Figure 2.4 in Chapter 2 shows that the combination of a convex short-run supply curve with a vertical long-run supply curve captures very much the spirit of early NAIRU models. In particular, the model discussed here is consistent with the assertion of Modigliani and Papdemos, who proposed the NAIRU concept in 1975, that due to nominal rigidities the economy spends most of its time in a state below the natural rate of output. However, it needs to be emphasized that the convexity of the short-run supply curve does not mean that the central bank should relentlessly try to stimulate aggregate demand. Rather, the objective of stabilization policy in this framework would be to reduce the magnitude of business cycle fluctuations and to keep output as close as possible to the natural rate. In fact, the convexity of the supply curve imposes a strong constraint on the ability of policy makers to stimulate the economy, since any attempt to raise output above the natural rate would trigger a much stronger inflation response than would result from a linear supply curve. Moreover, if such an attempt were to lead to a permanent increase in the trend inflation rate, lowering inflation again would become very expensive in output terms. This is shown in Figure 5.4: The initial increase in the inflation rate would correspond to the movement from A to B. Once inflation expectations adjust to this higher inflation rate, implying a permanent increase in the trend inflation rate, the economy would move from B to C. Bringing the trend inflation down again to its initial value would require bringing the economy from C to D. Figure 5.4 clearly shows that the output costs of the resuhing disinflation would be much larger than the output gains from the initial boom. Hence, with a convex short-run supply curve there is a premium on avoiding a permanent increase in the trend inflation rate in the first place. The discussion in this section has shown that a convex short-run supply curve can imply that stabilization policy has the potential to increase the average level of output, but it needs to be emphasized that this is neither a necessary nor a sufficient condition for this to be the case. For example, the model outlined by Ball and Mankiw (1994b) implies a convex short-run supply curve, but the average level of output in their model is nevertheless independent from the variability of demand conditions and always zero, ruling out first-order effects of stabilization policy. Consequently, Ball and Mankiw conclude that because average output is invariant to the distribution of demand in their model, it provides a counterexample to a conjecture offered by De Long and Summers (1988). These authors argue on the basis of empirical evidence on asymmetric effects of monetary policy that reducing fluctuations in aggregate demand would raise average output.
5.1 Nonlinearities in the Aggregate Supply Curve
179
Figure 5.4: Disinflation in a Model with a Convex Short-Run Aggregate Supply Curve Inflation SRASII
SRASI
Output Ball and Mankiw point out that their invariance result follows from the assumption that firms minimize a quadratic loss function. In fact, the loss function they use is very similar to the one used in the quadratic cost of price adjustment model which is observationally equivalent to the Calvo price adjustment model we used earlier to derive the New Keynesian Phillips curve. That is, their result is likely to hold for a wide range of frequently used models. Intuitively, in this type of model firms set their price equal to the average optimal price over the period in which the price is expected to be in effect. With a positive rate of trend inflation and a high variability in demand conditions, firms realize that if a positive demand shock occurs, they are likely to change their price very soon. In contrast, with a negative shock their initial price is likely to stay in effect for a longer period of time. Hence, it becomes optimal for them to set their initial prices lower than they would in the absence of demand fluctuations. After all, this ensures that in the case of a negative demand shock their actual price will be closer to the desired price, while in the case of a positive shock they are going to adjust their price in any case. The lower initial price raises the level of output in the absence of shocks, which exactly offsets the lower average output from asymmetric responses to shocks. As a consequence, average output is invariant to the variability of demand and equal to the natural rate of output.
180
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
In sum, even though allowing for nonlinearities in the short-run supply curve can have the effect of making stabilization policy more powerful, it is necessary to specify the exact transmission mechanism behind such nonlinearities before fielding them as an argument in the policy debate.
5.2
Nonlinearities in the Welfare Function
In this section, we investigate the welfare effects of business cycle fluctuations. To this end, we employ an approach recently proposed by Gali et al. (2002a). These authors show that even if output fluctuates symmetrically around the natural rate of output, this can result in quantitatively important effects on welfare, because the welfare function is inherently nonlinear. That is, even if the short-run supply curve is linear and average output is always equal to the natural rate of output, strong business cycle fluctuations would still negatively affect welfare. This would stand in contrast to our previous analysis of (linear) New Keynesian models in Chapter 3, where we argued that on average the welfarereducing effects of recessions would be cancelled out by the welfare-enhancing effects of booms. The notion that the welfare effects of business cycle fluctuations are small is also supported by an influential analysis by Lucas (1987). Hence, a finding that the welfare effects of business cycle fluctuations are sizable would overturn a widely accepted tenet of macroeconomics and would have potentially far-reaching policy implications, since an active stabilization policy that seeks to moderate business cycle fluctuations would be beneficial by increasing the average level of welfare. Following Gali et al. (2002a), we illustrate the welfare effects of business cycle fluctuations with the help of Figure 5.5. This figure depicts the situation in the labor market, showing labor demand and labor supply, «, as a function of real wages, w- p. With perfect competition, labor demand is equal to the marginal rate of productivity of labor, mpn, and labor supply is equal to the marginal rate of substitution between consumption and labor, mrs. In steady state, the economy is at PC. With imperfect competition, however, firms demand a price markup in the goods market, and workers demand a wage markup in the labor market. In Figure 5.5, we denote the steady state price and wage markups as//^ and //'*', respectively. Those markups have the effect to shift both the labor demand and labor supply functions inwards to mpn- JLLP and mrs-\- fX^, respectively, implying that in steady state the economy is at SS. Comparing SS to PC shows clearly that relative to perfect competition the economy operates under imperfect competition at a less efficient level, since the natural rate of employment under im-
5.2 Nonlinearities in the Aggregate Supply Curve
181
Figure 5.5: The Business Cycle and Wage and Price Markups w-p
nR
riss
riB
ripc
Source: Figure 1 in Gali et al. (2000a). perfect competition, n^s, is significantly lower than the natural rate of employment under perfect competition, w^^ ?^^ An alternative measure for the inefficiency arising from imperfect competition is the vertical distance between the perfectly competitive labor supply and demand curves at the new steady state, given by line dc in Figure 5.5. This measure, which Gali et al. refer to as the inefficiency gap, is proportional to the employment gap given by rip^ -n^s, and it has the advantage that it captures the source of the inefficiency, namely the size of the price and wage markups demanded by firms and workers. Moreover, Gali et al. show that it is possible to compute the welfare costs of business cycle fluctuations associated with a given inefficiency gap. In Figure 5.5, we measure the welfare effects of business cycle fluctuations under the assumption that economic activity fluctuates symmetrically around the steady state SS, with booms denoted by B and recessions by R. In a recession, the welfare losses due to foregone rents by firms and workers relative to the steady state are equivalent to the area given by abed. In a boom, the corresponding welfare gains are given by the area cdef Clearly, the welfare losses of a 220 Whether the real wage that workers receive is higher or lower under imperfect competition depends on the relative size of wage and price markups.
182
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
recession outweigh the welfare gains of a boom, even if the employment gains and losses cancel each other out on average. In sum, considering the welfare implications of business cycle fluctuations offers another avenue to justify the importance of stabilization policy, thereby helping to make the New Keynesian model more Keynesian. In the remainder of this section, we are going to construct a measure of the inefficiency gap for West German data and discuss its role for business cycle fluctuations. This will set the stage to compare this measure to conventional measures of business cycle fluctuation. Having evaluated its usefulness, we proceed to estimate the welfare effects of business cycle fluctuations. The last step will allow us to evaluate the importance and effectiveness of stabilization policy in Germany.
5.2.1
The Inefficiency Gap and Business Cycle Fluctuations
As discussed above, the inefficiency gap is defined as the vertical distance between the perfectly competitive labor supply and demand curves, evaluated at the current level of employment :^^^ (5.1)
gap^ =mrs^ -mpn^,
where gap^ denotes the inefficiency gap and mrs^ and mpn^ are the marginal rate of substitution between consumption and labor and the marginal product of labor, respectively. All three variables are expressed in logarithms. With imperfect competition, it can be shown that the inefficiency gap can also be expressed as a combination of the price and wage markups. Beginning with the price markup, imperfect competition implies that firms set prices as a markup over nominal marginal costs. Assuming that firms are wage takers and there are no labor adjustment costs, nominal marginal costs can be expressed as (5.2)
mc" = w^ - mpn^,
where w, is the (log) compensation per unit of labor input. Accordingly, the price markup can be defined as (5.3a)
lii^ =p,-
(5.3b)
lu^
(w, - mpn^), or
=mpn,-{w^-pX
As before, p^ is the log of the aggregate price level. 221 This section draws on Gali et al. (2002a: 3ff.).
5.2 Nonlinearities in the Aggregate Supply Curve
183
Next, the aggregate wage markup corresponds to the difference between the wage and the marginal disutility of work, both expressed in terms of consumption. That is, the wage markup is defined as follows: (5.4)
//; =(w,-;?,)-wr^,.
Gali et al. (2002a) emphasize that the wage markup should be understood in a broad sense, including also the wedge created by payroll taxes paid by firms and labor income taxes paid by workers (Gali et al. 2002a: 4). To formalize the link between the inefficiency gap and the markups, we rewrite (5.1) as (5.5)
gap,=-{[mpn,-{w^
- A)] + [(>v, - j^,) - mr^ J }.
Combining (5.3b), (5.4) and (5.5) yields: (5.6)
gap,=-{juf+jurl
Hence, the inefficiency gap can be expressed as the sum of the price and wage markups, with the sign reversed so that the inefficiency gap is negative. The larger the inefficiency gap becomes in absolute terms, the deeper the economy moves into a recession. Vice versa, a small inefficiency gap in absolute terms means the economy is in a boom phase. In steady state, the inefficiency gap is equal to (5.7)
gap = -(juP+ju'')<0,
which corresponds to the distance de in Figure 5.5. Moreover, it is natural to assume that at all times juf > 0 and ju^ > 0, implying that gap^ < 0 for all t. In this case, the level of economic activity is always inefficiently low, but in a boom the distortions become smaller and the economy moves closer to the perfectly competitive allocation. In fact, this view of business cycle fluctuations is very similar to the traditional Keynesian view of business cycle fluctuations, which holds that the economy typically operates at an inefficiently low level of economic activity, and only reaches its potential in boom phases. In Chapter 2, we illustrated this view with the help of Figure 2.2. The potential level of output shown in Figure 2.2 would correspond in Figure 5.5 to the perfectly competitive state of the economy. However, in the framework outlined here the natural rate of output is below the potential given by the perfect competitive allocation, and output cannot deviate from the natural rate permanently. Gali et al. (2002a) emphasize that a variety offi*ictions,and in particular wage and price rigidities, may induce countercyclical fluctuations in the markups. They write, "It is in this respect that these fi-ictions are associated with inefficient
184
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
cyclical fluctuations, or more precisely, with variations in the aggregate level of (in)efficiency" (Gali et al. 2002a: 4). Put another way, the ultimate source of business cycle fluctuations are still exogenous shocks like those discussed in the simulation of the New Keynesian model, but wage and price rigidities can induce fluctuations in the markups that would amplify the effects of these shocks on the business cycle. In fact, this amplifying mechanism is closely related to our discussion of the underlying structure of New Keynesian models in Chapter 3. There, we argued that real wage rigidities stemming from efficiency wages would amplify nominal rigidities, which makes it possible for nominal demand fluctuations to have significant real effects. To illustrate the role of price and wage markups for business cycle fluctuations, we consider a contraction in nominal demand. The nominal rigidities inherent in New Keynesian models prevent prices fi'om falling to offset the contraction in nominal demand, meaning that the price markup increases. In a frictionless labor market, the resulting increase in unemployment would be mitigated by a fall in real wages, which would help to stabilize the economy. Sticky real wages due to efficiency wages, on the other hand, prevent the real wage adjustment and limit the scope for any price adjustment, since real marginal costs remain high. Moreover, the increase in unemployment tends to reduce aggregate demand even fiirther, thereby deepening the recession. With real wages being sticky in the face of falling employment, the wage markup increases. Hence, this example shows that the countercyclical behavior of both price and wage markups plays an important role in the transmission mechanism of business cycle fluctuations. Also, since we have here a situation where deflcient labor and product demand reinforce each other, this is another instance where the resulting transmission mechanism closely resembles the traditional Keynesian view of business cycle fluctuations discussed in Chapter 2. Next, we are going to present empirical evidence on the cyclical behavior of wage and price markups and discuss the relationship of these markups and the inefficiency gap to business cycle fluctuations. 5.2.1.1
Estimating the Wage Markup
Estimating the wage markup requires quantifying the marginal rate of substitution between consumption and labor. To this end, we have to extend the utility function used to derive the New Keynesian Phillips curve in Section 4.1.2 to include the (dis)utility that results from supplying additional units of labor.^^^ Hence, we assume now that the utility function of the representative household is given by Y^T^aP^^i^f^X where U{Cf,Nf) is separable in consumption and
^^^ In Section 4.1.2 we simply assumed that each household supplies one unit of labor. Hence, labor supply was inelastic.
5.2 Nonlinearities in the Aggregate Supply Curve
185
labor. Solving the intertemporal optimization problem leads to the following relationship between the real wage and household preferences: (5.8)
w U ^ = -^//r223 ^t
^
C.t
Next, we assume that the utility function is of the form (5.9)
U{C„N,) = ^x^[e,)-^
^ .
This functional form is similar to the one we used in Section 4.1.2. However, to remain consistent with the notation in Gali et al. (2002a), the parameter a denotes now the relative risk aversion of households.^^^ The parameter S gives the marginal disutility of labor supply, which defines the curvature of the labor supply function. In addition, Gali et al. include the variable e^ to capture lowfrequency shifts in preferences over consumption and leisure. They argue that these preference shifts should be interpreted broadly to include institutional or demographic changes that affect the labor market. With this utility function, the marginal utilities of consumption and labor supply are given by (5.10a) (5.10b)
L^c,/ =exp(f;)C-^, and U,^,=-Nf,
The marginal rate of substitution between consumption and labor is defined as MRS^=-Uf^JUc^t. Here, we obtain MRS^=NfC{'Qxp{-£,). In logarithms, this yields mrs^^CTc^-^Sn^-ef. After log-linearizing (5.8) and inserting our result for mrs^, we have (5.11)
w^-p^
=ac^-{-Sn^-£j-\-iu^,
where small letters again denote logarithms. Solving this for the (logarithm) of the wage markup yields:
(5.12)
/^,-=(w,-;7,)-K+(y«J + ^,225
22^ See the discussion in Gali et al. (2001: 126Iff). Taking logarithms, and noting that the marginal rate of substitution between consumption and labor is defined as -Uj^j lUc^t^ this relation is equivalent to (5.4). 22"* In Section 4.1.2 the relative risk aversion was given by \la. 22^ This relation corresponds to (5.4) derived in the previous section, with the marginal rate of substitution between consumption and labor resulting from our utility function inserted.
186
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
To quantify the wage markup, we use data for West Germany obtained from the DIW Statfinder database. The variable w, represents the compensation per labor unit defined as hours worked. We construct the corresponding time series by dividing the gross wage income by the total sum of hours worked.^^^ The variable p^ is the aggregate price level, c^ is consumption per capita, and n^ is hours worked per capita.^^^ We follow Gali et al. (2002a) and set the parameter S = 5. This corresponds to a wage elasticity of labor supply of 0.2, which is consistent with evidence from micro data. Regarding the relative risk aversion of households, we are going to present results for (7 = 1 and <J = 5. The first parameter choice is consistent with a balanced growth path, while the second choice better reflects the results from microeconometric studies on this parameter.^^^ Finally, we need to identify the low-frequency shifter e^. The starting point is the observable component of the wage markup, given by ju^ = {wf-pt) - {aCf + Sn^). From this follows that
(5,13)
jur=Mr-^r
This presentation suggests that ju^ is the cyclical component of ju^ and e^ is (minus) the trend component. To identify the cyclical component of /2^, Gali et al. (2002a) employ the band pass filter using the high-pass specification, which discards fluctuations outside a frequency range between 2 and 60 quarters. We follow their approach, and the resulting time series for the wage markup in Germany is presented below in Figure 5.7. 5.2.1.2
Estimating the Price Markup
For estimating the price markup, we need to make an assumption about the production technology. If we were to assume a Cobb-Douglas-type production function, as suggested by Gali et al. (2002a), the marginal product of labor (up to an additive constant) would simply be
^^^ The code for the gross wage income series for West Germany is in the DIW Statfinder database WH20011B. The series for total hours worked is obtained by multiplying the number of employees with the series for daily hours worked (code WH1105B) with the series for the days worked per quarter (code WH1104). The time series for the number of employees is based on an annual time series obtained from the Sachverstandigenrat (1998) that has been interpolated using the quadratic match function in EViews. ^^^ For the price level we employ the GDP deflator (code WH3116ZB), consumption per capita is constructed by dividing private consumption in 1991 prices (code WH3201B) by the population number (code WHIOO), and hours worked per capita is obtained by dividing total hours worked by the population number. 228 YoY the discussion on microeconometric evidence on these two parameters see Gali et al. (2002a: 6ff.).
5.2 Nonlinearities in the Aggregate Supply Curve (5.14)
mpn,
187
=y,-n,,
where y^ denotes output per capita and n^ is again hours per capita. Inserting this result into (5.3b) would yield the following estimate of the price markup:
(5.15)
//;=U-«J-(W,-A)^-W/C,.
Hence, Gali et al. (2002a) observe that with this specification the price markup can be measured (up to an additive constant) as minus (log) real unit labor costs, denoted by ulc^. However, Carstensen (2002) shows that the Cobb-Douglas production function provides only a poor fit for German data, whereas the CES production function is much more successful in this regard. Hence, in the following we are going to base the approach of Gali et al. (2002a) to measuring the price markup on a CES production function. This function is given by (5.16)
Y,=Ayc;^+{l-^)L-'l'"\
where Y^ denotes output and K^ and L^ are the capital and labor input, respectively.^^^ The parameter ^ is a distribution parameter defining the tilt of the isovalue line in the capital and labor input space, v is the homogeneity parameter, A is the efficiency parameter, and 0 defines the substitution elasticity cp according to ^ = 1 /(l + d). The substitution elasticity defines the curvature of the isovalue line; a larger value for the substitution elasticity implies that it is relatively easier to substitute production factors for each other. The CES production function implies that the marginal productivity of labor is given by (5.17)
MPN, =
VA-''''Y}'^'^'{1-0)L-^'''K
Taking logarithms, and using output per capita and hours per capita as output and labor input variables, we obtain: (5.18)
mpn,=\og{v)-0/vlog{A)-\-[{0/v)
+
\]y,-¥\og{l-(/>)-{0-^l)n,,
To quantify the parameters in this relation, we employ an estimate of the Deutsche Bundesbank (1995) of the CES production function for West German data using quarterly data over the time period 1970 until 1994: (5.19)
y; = 1392.4-eO-^7'[0.64A:-o-24 +0.3670-24 ]-iii/o-24
^^^ For an extensive discussion of the CES production function see Hansen (1993).
188
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
This estimate implies that the distribution parameter is ^ = 0.64, the homogeneity parameter is close to unity, and the implied substitution elasticity is ^ = (l - 0.24)/ 0.24 = 0.81. In fact, the finding of the substitution elasticity being smaller than one is consistent with the finding of Carstensen (2002: 14). In addition, technical progress is modeled via the trend term e^"^^' where t represents a deterministic time trend. However, this specification does not allow for a trend break in the underlying growth rate to reflect the productivity slowdown beginning sometime in the early 1970s, and the implied annual trend growth rate seems to be unrealistically high. Hence, we are going to disregard the Bundesbank trend estimate and use the same band pass filter procedure we used for the wage markup to identify the cyclical component of the price markup. Using the Bundesbank estimate for v, 6, and 0, the observable component of (5.18) is given by (5.20)
mpn^ = log(l.ll)+[(0.24/1.1 l)+lly,+log(l-0.64)-(0.24 + 1 ^ .
For the output per capita series we employ the real GDP series fi-om the DIW Statfinder database and divide it by the population number.^^^ For the hours worked per capita series we employ the same series we constructed for the estimation of the wage markup. With these assumptions we can express the observable component of the price markup as (5.21)
Jlj' =fnpn,-{w,-pX
From this follows that we can write the observable component of the price markup as (5.22)
//;=//;-^(0,
where A{t) denotes the trend component in the production function attributable to the unobservable technical progress. We interpret juf again as the cyclical component of p^l' and identify it using the high-pass specification of the band pass filter. Having constructed a time series for both the wage and price markup, we can now proceed to discuss the resuhing estimate for the inefficiency gap for West Germany. 5.2.1.3
The Inefficiency Gap and Its Components
In Figure 5.6, we present the results for the inefficiency gaps for <7 = 1 and <j = 5. A positive realization of the inefficiency gap implies the economy is in a boom phase, and a negative realization means the economy is in a recession. The band pass filter methodology used in the construction of the inefficiency gaps ^^^ The corresponding code for real GDP is WH1212FB.
5.2 Nonlinearities in the Aggregate Supply Curve
189
Figure 5.6: The Inefficiency Gap Inefficiency gaps for different values of sigma
-Sigma = 1
- Sigma = 5
ensures that the gaps are on average zero. That is, we present a demeaned inefficiency gap, gap^ = gap^ -gap. Put another way, in Figure 5.6 we normalize the steady state markup to zero when the economy is at its natural rate of output. Thus, in terms of Figure 5.5 the inefficiency gaps presented here show the fluctuations in the markups around the steady state SS, and not in reference to the perfect competition outcome PC. The choice of SS as the reference point helps to facilitate the analysis of business cycle fluctuations, since economic activity in our model fluctuates around SS and not PC. Figure 5.6 shows that the fluctuations of the markups around zero are broadly symmetric. An exception are the two deep recessions occurring in the late 1960s and middle of the 1970s, which are not accompanied by equally strong booms. As shown in Section 5.1, this slight asymmetry reflects the fact that the band pass filter allows to some extent for nonsymmetric fluctuations. It is also apparent fi'om Figure 5.6 that the fluctuations in the inefficiency gap are considerably larger when we choose cr = 5 instead of cr = 1. This result arises because a larger relative risk aversion implies that households are less willing to substitute consumption between different dates, and consequently labor supply becomes less responsive to changes in the real wage rate. Since Figure 5.5 shows that a steeper labor supply curve implies a larger inefficiency gap, the fluctuations in the gap increase in size when we increase the relative risk aversion parameter.
190
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
Figure 5.7: The Inefficiency Gap and Its Components The inefficiency gap Higli-pass specification
1961
1963 1965 1967 1969 1971
1973 1975 1977 1979 1981
1983 1985 1987
Wage marl
1961
I"'' I'M ' 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981
1983 1985 1987 1989 1991
1993
1983 1985 1987 1989 1991
1993
Price markup component
1961 1963 1965 1967 1969 1971
1973 1975 1977 1979 1981
In Figure 5.7, we plot the inefficiency gap for G = \ together with its wage and price markup components. To faciUtate the analysis of the role of the wage and price markups for business cycle fluctuations, we shade periods when the economy was in recession. Like in Chapter 2, the recession dates are obtained from Artis et al. (1997), who define a recession as the time period between a peak and the following trough. The correspondence between the inefficiency gap and the independently determined recession dates is striking: the beginning of a recession according to the Artis et al. methodology coincides practically always with the peak of a boom according to our measure, and the same holds for the
5.2 Nonlinearities in the Aggregate Supply Curve
191
Table 5.1: Cross Correlations between the Inefficiency Gap and Its Components for Various Lags (/) ^_^ Wage markup component Price markup component
/^O 0.98 0.21
l^ 0.86 -0.04
/^2 0.79 -0.24
/=3 0.65 -0.36
end of recessions. This close correspondence suggests that our inefficiency gap captures the salient features of business cycle fluctuations. We return to this issue below, when we compare the inefficiency gap to conventional measures of the output gap. Visual inspection of the components of the inefficiency gap shows that the magnitude of cyclical fluctuations in the price markup is much smaller than those of the wage markup. Moreover, it appears that changes in the inefficiency gap are mainly driven by the wage markup component, whereas the price markup tends to move into the opposite direction. This is confirmed by the corresponding cross correlations shown in Table 5.1. The contemporaneous correlation between the inefficiency gap and the wage markup component is almost one, while the corresponding correlation with the price markup component is only about 0.2. Within two quarters, however, the correlation between the inefficiency gap and the price markup component becomes negative. Interestingly, Gali et al. (2002a) find a very similar result for US data. They report a contemporaneous correlation coefficient for the relationship between the inefficiency gap and the wage markup component of 0.92, while the correlation coefficient for the price markup component is -0.22. Regarding the wage and price markup components, it is important to remember that these are defined as - ju^ and -//f, respectively. Hence, the results in Table 5.1 imply that the fluctuations in the wage markup /n^ are strongly countercyclical, while those in the price markup juf are moderately procyclical. It is apparent from Figure 5.7 that the wage markup increases considerably when the economy moves into a recession. This is consistent with real wage rigidity preventing a reduction in real wages to offset the effects of a fall in aggregate demand on the labor market. In contrast, prices turn out to be more flexible, since the price markup declines soon after the beginning of the recession. However, the procyclical movements in the price markup are not nearly large enough to compensate for the countercyclical behavior of the wage markup. This is not surprising, since we aheady pointed out that real wage rigidity limits the extent of downward price adjustment. In sum, our analysis points to an important role of real wage rigidities for the transmission of business cycle fluctuations.^^ ^ In principle, one could also appeal to nominal wage rigidity to explain the countercyclical behavior of the wage markup. In fact, traditional Keynesian economics
192 5.2.1.4
Chapter 5 Introducing Nonlinearities into the New Keynesian Model The Relation of the Inefficiency Gap to Output Gap Measures
Gali et al. (2002b) show that the output gap is proportional to the inefficiency gap.^^2 Since business cycle fluctuations are typically measured using output gap estimates, comparing our inefficiency gap to different output gap estimates provides another avenue to evaluate the usefulness of the inefficiency gap as a measure for business cycle fluctuations. To derive the relationship between the output gap and the inefficiency gap, Gali et al. restrict the reduced form aggregate production to (5.23)
y,=a'n,+z,,
where z^ is exogenous. They interpret z^ as including both technology and capital, where capital is treated as exogenous on the grounds that the percent fluctuations in capital at the business cycle fi-equency are relatively small.^^^ With this production function, the inefficiency gap becomes (5.24)
gap, = mrs, - mpn, ={oc,-^3^,-£,)-
{y, - « J .
Solving (5.23) for n, and inserting into (5.24) yields (5.25)
gap,^''-''^^^
.1 + ^
Z,
-8,
The corresponding steady state inefficiency gap is given by (5.26)
gap = I — ^ ^ \y, -\-oc,-
\+S
where y, and c, denote the natural rate level of output and consumption, respectively. To obtain a relation between the output gap x,=y,- y, and our demeaned inefficiency gap gap, = gap, - gap, which we represented in Figures 5.6 and 5.7, we first combine the relations given by (5.25) and (5.26) to express gap, as follows: emphasized downward rigid nominal wages as an important part of the transmission mechanism of business cycle fluctuations. However, the combination of (moderately) flexible prices with sticky nominal wages implies that real wages move countercyclical. Since empirical evidence tends to reject the hypothesis of a countercyclical behavior of real wages, this implication is an important reason why New Keynesian economics abandoned the assumption of sticky nominal wages in favor of sticky prices. See also the discussion in Mankiw (2001) on this issue. ^•^^ I am grateftil to Mark Gertler for making the revised manuscript of Gali et al. (2002a) available to me. 233 PQJ. ^Q same reason we abstracted from capital in the derivation of the New Keynesian IS curve. Gali et al. (2002a) also emphasize that this specification of the production function allows the possibility of variable capital utilization.
5.2 Nonlinearities in the Aggregate Supply Curve
(5.27)
gap, = [ ~^J
193
k + c^,,
where c, = c,-c,. Next, we express the consumption gap, c,, as a time-varying proportion of the output gap: (5.28)
c,=r},x,.
Inserting (5.28) into (5.27) and solving for the output gap yields the following relation between the output gap and our inefficiency gap: (5.29)
X, =
ti+^^rK-i)r^-
Gali et al. argue that a reasonable range for T], is 0.6 to 1. Here, we assume rj, = 0.8. As before, we set S = 5, and follow the suggestion by Gali et al. to set a to unity. In Figures 5.8a and 5.8b we plot the implied output gap of our inefficiency gaps together with two output gap measures which we used before in this chapter, the band pass filter estimate and the segmented trend model of output. In general, our inefficiency gaps track the conventional output gap measures very well, in particular for the early part of the sample period lasting until the early 1980s. This close resemblance is even more remarkable if one considers that we employ a more complex production function for the construction of the inefficiency gaps than is assumed in (5.23), and therefore (5.29) represents only an approximation of the relationship between our gap measure and the output gap.^^"^ It is apparent from Figure 5.8a that with cr = l, the peaks of our implied output gap series are noticeably smaller than those of the conventional output gap measures. However, with a = 5 the peaks and troughs of the implied and actual output gaps match quite well, which suggests that this specification for our inefficiency gap might be preferable. This is also consistent with the fact that (7 = 5 can be better justified on microeconometric grounds than cr = 1. There is, however, one business cycle episode where our measure deviates significantly from those of the conventional output gap measures: in the second half of the 1980s, both the band pass filter estimate of the output gap and the segmented trend model agree on that the West German economy was in a protracted recession. According to the latter, the output contraction in this period was so deep and so long that it almost could be described as a depression. In ^•^^ Taking logarithms of the CES production function (5.16) and using a Kmenta approximation yields logY, = log^ + v^logJ^, + v(l -^)logL^ -O(v0(l -^)/2)(log4 -logK^y for our production function. The main difference between this fimction and (5.23) is the quadratic term. For the derivation of the logarithmic form of the CES function, see Hansen (1993: 23).
194
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
Figure 5.8a: The Implied Output Gap of the Inefficiency Gap: The Band Pass Filter Estimate Comparing the implied output gap of the inefficiency gap to the band pass filter estimate of the output gap
Implied output gap sigma = 1
Band pass filter output gap
Implied output gap sigma = 5
Band pass filter output gap
5.2 Nonlinearities in the Aggregate Supply Curve Figure 5.8b: The Implied Output Gap of the Inefficiency Gap: The Segmented Trend Model Estimate Comparing the Implied output gap of the inefficiency gap to the segmented trend model estimate of the output gap
Implied output gap sigma = 1
Output gap of the segmented trend model
Implied output gap sigma = 5
Output gap of the segmented trend model
195
196
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
Figure 5,9: The Price Markup Estimate Observable component of the price markup and the cyclical component 15.0% T
Observable component
Cyclical component
contrast, our measure suggests that the German economy enjoyed a moderate expansion in this period. In fact, the Council of Economic Experts observes in his annual report for 1989/90 that the economy in the past seven years did not experience any pronounced cyclical fluctuations (Sachverstandigenrat 1989: 116). Since this independent characterization of the cyclical situation in the second half of the 1980s is more consistent with our measure than with the two other output gap measures, it is reasonable to conclude that our inefficiency gap provides a plausible characterization of business cycle fluctuations in Germany. The observable component of the price markup provides some clue where the disagreement on the cyclical situation in the second half of the 1980s might be coming from. In Figure 5.9 we plot the observable component of the price markup, juf, together with the cyclical component, juj". It becomes apparent that the price markup is characterized by a strong trend increase beginning in the early 1980s and lasting until the end of the sample period. For the construction of the inefficiency gap, we only consider the cyclical component of the price markup and discard this trend component. However, in terms of Figure 5.5 the underlying trend increase in the price markup implies that the steady state SS shifted to the left. That is, the efficiency level of the economy decreased, and the natural rate of output shifted to a lower level. The conventional output gap measures may fail to recognize this change in the natural rate, and attribute the lower level of economic activity to a cyclical downturn.
5.2 Nonlinearities in the Aggregate Supply Curve 5.2.2 5.2.2.1
197
The Welfare Effects of the Inefficiency Gap The Welfare Function^^^
For deriving a function giving the welfare effects of the inefficiency gap we follow Gali et al. (2002b) and again restrict the production technology to (5.30)
Y,=Z,N,,
In contrast to (5.23) here we write the production function in levels and set a = 1. Next, we let W{Nf) be the utility value of output in period t, net of the utility cost of working, and conditional on employment level N^, With this notation, the utility gain or loss from reallocating employment from the natural rate of employment N^ to the level N^ is given by (5.31)
\=W{N^)-W{NX
As in the previous section, we assume that U{Cf,N^) represents the utility function of the representative household. The marginal utility of consumption and the marginal (dis)utility of working are given by C/c./ ^^^ ^N,t > respectively. Our production function implies that the marginal product of labor is MPNf = Z,. Hence, the gross utility gain from working an additional hour is equal to the marginal utility of consumption times the marginal product of labor, i.e., U^^tZ^. The cost is given by L^^, < 0, the disutility of work. The net welfare effect is therefore given by W{N,) = UC,Z, +U^,. To obtain an expression for the utility gap, A^, Gali et al. argue that if the percentage deviation between N^ and N^ is not large, it is reasonable to approximate W{N^ ) with a second-order Taylor expansion about 1V{N,). Assuming that utility is separable in consumption and leisure, i.e., t/^iv = ^»they find that A^ can be approximated as (5.32)
A, = [Uc,Z,
+U^JN,-N,)+MUCC,,
^Z,+U,,,
df,
\N,-N,J,
where U^ denotes Uf[Cf,Nj. To quantify this expression, we assume that the utility function is of the form (5.33)
U(a,N,)=:-^
^5--^—,
^^^ The derivation of the welfare fiinction in Gali et al. (2002a) contains a mistake, which is why this section is based on Gali et al. (2002b).
198
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
which is practically the same functional form we used in the preceding section, but here we abstract from the term modeling the low-frequency shifts in preferences over consumption and leisure. Gali et al. show that with this specification of the utility fimction the utility gap A^ can be expressed as the following quadratic fimction of the percent deviation of employment from its natural rate value, «, = log(A^^ / A^J:
(5.34)
A, ^ ^ 1 ^ ^ ^ ^
where ^^r./ = ^^t / ^ ^ X ^ ' ^ ^ J ^^ the elasticity of the natural rate of consumption with respect to the natural rate of output, and /u is the steady state markup. For simplicity, we follow Gali et al. and assume that rfcy^t -1 • They emphasize that the following results are not sensitive to reasonable variations in this parameter. The final hurdle we need to overcome is that we have no direct measure for the variable n^, since the natural rate of employment is not observable. However, it is possible to derive a relationship between n^ and our measure of the inefficiency gap, gap^. Given the production fimction (5.30), it follows that n^ = x^, where x^ represents again the output gap. Using our analysis in the previous section, and noting that here we have set a = \ and ff^Y,t = ^ = 1 > it follows from (5.29) that n^ is linked to gap^ by:
By combining equations (5.34) and (5.35) we finally obtain an expression for A, in terms of our inefficiency gap: (5.36)
A, = U(.,,Y,\\{gap,), where
(5.37)
H
If,
d
2
[X + Hla + S)
The fimction y^i,gap^) describes the welfare loss or gain that arises from fluctuations in the economy around its steady state as measured by the inefficiency gap variable. These changes in welfare_areexpressed as a percent of the natural rate of output Y^, since m^gap^) = A^ / ( ( / ^ ^ r j . Gali et al. (2002: 17) interpret y\{gap^) as follows, "The first term in brackets, the linear term, reflects the symmetric costs and benefits from the gap moving below and above the steady state, due to the positive steady state markup /u. The second term, the quadratic term, captures the asymmetric effect of gap fluctuations on welfare. In particular, a reduction in the gap below the steady state results in an efficiency loss that exceeds the gain stemming from a commensurate increase in the gap above the steady state. Under the (weak) assumption that ju{(j-\)l{(J-\-S)> -\,
5.2 Nonlinearities in the Aggregate Supply Curve
199
w is a concave function of the gap, implying that the welfare losses from gap contractions are less than made up for by the welfare gains from symmetric gap expansions." In Figure 5.10 we plot Ms^t) as afiinctionfor different values of the steady state markup ju and for our two values for the relative risk aversion of households, a = 1 and cr = 5. For the marginal disutility of labor supply, S, we assume again S = 5. The nonlinear welfare effects of fluctuations in the inefficiency gap are clearly visible in Figure 5.10. Moreover, the two plots in Figure 5.10 show that a higher steady state markup leads to larger welfare effects of a given inefficiency gap. Intuitively, in terms of Figure 5.5 this result arises because a higher steady state markup implies that the steady state SS shifts to the left, and, consequently, the areas between the perfectly competitive labor demand and supply curves given by the areas cdef and abed, which represent the welfare effects of booms and recessions, become larger. An increase in the relative risk aversion parameter from cr = l to cr = 5, on the other hand, has the effect of decreasing the welfare effects of a given gap. A larger relative risk aversion means that labor supply is less responsive to real wages, which implies that for a given inefficiency gap the distance between actual employment and the natural rate of employment, «,, becomes smaller, thereby limiting the corresponding welfare effects. Hence, even though we observe in Figure 5.6 that an increase in a leads to largerfluctuationsin the inefficiency gap, the effects on welfare are nevertheless ambiguous. 5.2.2.2
The Welfare Effects of the Inefficiency Gap
Gali et al. observe that in the literature it is customary to express welfare losses in termsjof an equivalent loss in consumption. Hence, they suggest dividing A^ by UcjCj to make the metric the percent of the natural rate of consumption. Defining K = Y IC as the steady state output/consumption ratio, we can express the welfare effects as a percent of C, as follows:
(5.38)
j^^-^w{gap,)^fC'w{gapX
where the second approximation holds under the assumption that rfcy^t ~1- For West German data, we find that /r = 1.83. In Figure 5.11 we plot the resulting welfare effects of our inefficiency gaps for a = \ and (7 = 5. For the steady state markup we assume a value of 25 percent. Both plots show clearly that the welfare effects of downturns typically outweigh the effects of expansions. However, with the exception of the two deep recessions in the late 1960s and middle of 1970s, the welfare effects of business cyclefluctuationsare generally small and typically fall within a band of +/-0.5 percent of consumption. This result is robust with respect to the choice of the relative risk aversion parameter.
200
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
Figure 5.10: Welfare and the Inefficiency Gap Welfare as a function of the inefficiency gap (sigma = 1) for different values of the steady state markup
-20% -18% -16% -14% -12% -10% -8%
0%
2%
4%
6%
8%
10% 12% 14% 16% 18% 20%
Welfare function for sigma = 5
- • - s t e a d y state markup 15%
— s t e a d y state markup 25%
-at-steady state markup 40%
5.2 Nonlinearities in the Aggregate Supply Curve Figure 5.11:
Welfare Effects of Business Cycle Fluctuations Welfare effects of the inefficiency gap (sigma = 1) High-pass specification
Welfare effects of the inefficiency gap (sigma = 5)
201
202
Chapter 5 Introducing Nonlinearities into the New Keynesian Model
To obtain a measure of the average welfare cost over time, we take the unconditional expectation of (5.38) to obtain:
(5.39)
E\j^\ =Uc,C,\ {\ + fila + 6)
(-^]™'(-'
where var(gap,) denotes the variance of the inefficiency gap. As a result of the concavity of the welfare function vJ^ap^), the expected welfare effects of business cycle fluctuations are negative, i.e., these fluctuations imply losses in expected welfare. These losses could be potentially large, depending on the magnitude of the variance of the inefficiency gap. However, for both inefficiency gaps estimated here the average welfare costs turn out to be very small: for <j = 1 we find that these costs are equivalent to only 0.06 percent of consumption, while for cr = 5 the corresponding costs are 0.11 percent. Even if we choose relatively high values for cr and S, which would lead to a steeper labor supply curve and therefore higher welfare costs of business cycle fluctuations, the magnitude of average welfare costs remain small. For example, for a = 10 and ^ = 10, we find that the average welfare costs do not exceed 0.17 percent of consumption. The welfare costs of business cycle fluctuations in the United States are somewhat larger, but of a similar overall magnitude. For example, for S = G-5 and a steady state markup of 25 percent, Gali et al. estimate the average welfare costs to be approximately 0.41 percent of consumption. These costs are four times as large as those we find for Germany, but in absolute terms, they are still relatively small. The larger size of the welfare costs of U.S. business cycles reflects the fact the magnitude of the peaks and troughs of the inefficiency gap for U.S. data is approximately twice the size of those in Germany, which means the variance of the U.S. gap is four times as large. Gali et al. observe that any measure of the average cost of business cycles obscures the fact that individual recessionary episodes may be costly. Since these episodes are fairly infrequent, their effect on the average welfare costs may be small. To investigate the welfare costs of major business cycle episodes, we consider the four episodes in our sample where the economy experienced a large boom followed by a deep recession. We follow Gali et al. and measure the boom in each instance as the period where the gap variable climbs above zero up to the point where it returns to zero. The recession is the period that follows, covering the time where the gap turns negative and returns to steady state. In Table 5.2, we report the welfare gains from the booms and the costs from the recession, and the net loss of each episode. The welfare gains and losses are measured as a percent of one year's consumption. The calculations are based on <J = 1, 5 = 5, and ju = 0.25. Table 5.2 shows that the first two major business cycle episodes have indeed been costly in terms of welfare. The welfare losses of these episodes correspond to approximately 1.2 percent of one year's consumption in each case.
5.2 Nonlinearities in the Aggregate Supply Curve
203
Table 5.2: Welfare Costs (-) and Benefits (+) of Boom/Recession Episodes Start
Turning point
End
Boom
Recession
Net
1964:111 1972:1 1979:11 1991:1
1967:1 1974:111 1982:11 1993:11
1969:IV 1978:1 1985:11 1994:4
1.0 0.7 1.0 0.8
-2.2 -1.9 -1.1 -0.5
-1.2 -1.2 -0.1 0.2
However, since the late 1970s, the magnitude of business cycle fluctuations has decreased considerably, with the effect that the welfare effects of the boom and recession periods in the early 1980s are canceling each other almost out. Moreover, in the remainder of the 1980s, a boom and bust cycle was avoided completely. The welfare costs of the last major episode in our sample period appear also to be small, but a final judgment is still outstanding since the economy was still in a recession at the end of our sample period. Our finding that the welfare effects of business cycle fluctuations in Germany generally have been small, suggests two possible conclusions. On the one hand, these results are consistent, for example, with the assertion by Lucas (1987) that in a representative-agent setting, the potential welfare gains from stabilizing consumption around its mean are small. That is, our results support his finding that social welfare is not sufficiently nonlinear in output for the stabilization of output to yield a significant gain in welfare.^^^ On the other hand, it is equally well possible that the welfare costs of business cycle fluctuations turn out to be small precisely because policy makers have been very successful in stabilizing economic activity and smoothing out fluctuations. This interpretation is supported by the fact that business cycle fluctuations became more moderate in the 1980s and 1990s, which coincides with the period when the Bundesbank followed a Taylor type rule in its policy making process. Since the Taylor rule implies a commitment to stabilizing output and, moreover, has optimality properties, it is possible that the adoption of this rule by the Bundesbank in the late 1970s has been very effective in stabilizing output. Both of these interpretations are not very comforting from a traditional Keynesian standpoint of view, since they imply either that stabilization policy does not matter in the first place or that the Bundesbank did an excellent job in stabilizing output, at least in the past twenty years. The latter interpretation in particular would undermine the Keynesian line of argument that the Bundesbank contributed to the German unemployment problem by pursuing an overly tight monetary policy, thereby failing to stabilize output adequately.^^^ ^^^ See also the discussion of Lucas' finding in Romer (1996: 414ff). 237 We ^^Qoutlined outlinedthe thecor controversy on Bundesbank policy between Keynesians and monetarists in Chapter 2.
Revisiting the Natural Rate Hypothesis
In the preceding chapters, we have assumed that the natural rate hypothesis holds when we analyzed the New Keynesian model. Our empirical analysis in Chapter 2 using Keynesian and monetarist identification schemes has shed, however, some doubt on the relevance of this hypothesis for German data. In this chapter we are going to revisit this issue and test the natural rate hypothesis within a New Keynesian framework. To this end we employ a methodology recently developed by Farmer (2000) and Beyer and Farmer (2002). These authors use multivariate cointegration analysis to test the long-run implications of the New Keynesian model. For the United States they find that the data reject the natural rate hypothesis and propose an alternative aggregate supply function that would allow for a nonvertical long-run Phillips curve. In this section, we are going to apply their framework to data which refer to West Germany as in Chapter 2. Before we commence with the analysis, we are going to take a preliminary look at the data. In the second subsection we will outline the framework proposed by Beyer and Farmer. In Section 6.3, we proceed to present the results of the cointegration analysis. We find evidence for a structural break in the macroeconomic relations occurring in 1979, and we find the second sample period is characterized by a negative long-run correlation between unemployment and inflation. Even though such a long-run relation is inconsistent with the natural rate hypothesis, in Section 6.4 we show that it is nevertheless consistent with a number of recent approaches in modem macroeconomics. In the final subsection, we modify the New Keynesian model to incorporate one of those approaches and investigate the implications for the effectiveness of monetary policy. We find that this modification changes the policy implications of the New Keynesian model substantially. While this is only an explorative investigation, it does suggest that the standard New Keynesian model needs some extensions to fit the long-run properties of German data better. Before we proceed, it is useful to introduce some additional notation. In this section, we are going to investigate the relationship between the interest rate, the inflation rate, and the unemployment rate. We denote the logarithm of the unemployment rate as u^. Moreover, we assume that unemployment is inversely related to output through an Okun's law type relationship, which allows us to rewrite the standard New Keynesian model as follows: (6.1)
u, =E,u,,, +b,{R, -EM.^
- ^ ) + v;,
(6.2)
^p, = PEM.x + «i (". - «,) + v^
6.1 A Preliminary Look at the Data
(6.3)
205
/e, = ( 1 ~ / / ) [ F + 4P, + ^ " ( 4 P , -n) + (l>^{u,-u,)]^fiR,_,^vl
The variable w, represents the logarithm of the natural rate of unemployment, and we assume that a^,^ < 0.
6.1
A Preliminary Look at the Data
The New Keynesian model implies that even though there is a negative relationship between inflation and unemployment at the business cycle frequency, there should be no such relationship in the long run. In Figure 6.1, we plot the relation between five-year averages of both variables for West Germany. The five-year period has been chosen since it corresponds approximately to the typical length of business cycles. One would expect that over the course of a business cycle, those periods where the unemployment rate is above the natural rate are balanced by periods where the unemployment rate is below the natural rate. Since the natural rate hypothesis implies that a given natural rate is compatible with any rate of inflation, there should be no discernible relationship between the two variables. This is, after all, the essence of the natural rate hypothesis. Figure 6.1 shows that over the entire sample period from 1965 until 1999 there is indeed not much of a relationship. However, a closer look reveals that over the period from 1980 until 1999 there is a strong negative relationship between the two variables, as suggested by the traditional Phillips curve. The longrun Phillips curve in this period appears to be fairly steep, but not vertical. It also appears to be relatively stable. Interestingly, already our analysis in Chapter 2 of the correlation between the trend components of unemployment and inflation pointed towards a strong negative relationship in the period from 1980 until 1995; Table 2.1 in Chapter 2 reports a correlation coefficient of-0.89 for this period. In the remainder of this section, we use the technique of multivariate cointegration analysis to investigate more formally whether there is a significant relationship between the trend components of inflation and unemployment. More importantly, this approach allows us also to investigate whether such a relationship can be reconciled with the New Keynesian model.
6.2
A Framework for Cointegration Analysis
In this subsection, we outline the framework developed by Farmer (2000) and Beyer and Farmer (2002) to test the natural rate hypothesis before we apply it in the next section to West German data. These authors argue that if the unemploy-
206
Chapter 6 Revisiting the Natural Rate Hypothesis
Figure 6.1: The Relationship between Inflation and Unemployment in Germany, 1965-1999 and 1980-1999 70-74 •
i
^^,i)eriod: 1965-1999
^ ^
y = -0.3125x +5.0942 R^ = 0.3758
80-84
75-79
period: 1980-1999
, , ^
65-69
90-94
^
^
1 y = .l.0446x +11.347 R^ = 0.7932
^^"""'^^^ifc.^V
85-89
1
^ ^
^
95.gg
X^
Average Unemployment Rate (5 Years)
ment rate, interest rate, and inflation rate are nonstationary but cointegrated, a vector error correction model (VECM) can be used to study the relationship between them: (6.4)
AJC^
= ^(L)A^,_I + nx^_,^ ^z^-\-z.
Here, x^ is a vector containing the variables R^, A/?^, and u^?'^^ ^ ( L ) is a polynomial in the lag operator and models the short-run dynamics between the variables.^^^ The matrix 77 is of special interest. It can be factorized so that 77 = ap; if the variables are cointegrated, 77 has reduced rank r, with r representing the number of cointegration vectors. The term >5'x^_^ contains the cointegration relationships, while the matrix a determines to what extent each variable adjusts to a given disequilibrium in the long-run relations. Finally, the vector z^ contains stationary disturbance terms (z^ --1(0)), and z collects the constants in the system. To render the New Keynesian model suitable for cointegration analysis, Beyer and Farmer (2002) show that the model can be written as follows: (6.5a)
A^E, [x,^, ] + A^x, + A^ {L)X^_^ - V = V, ,
^^° As before, with the exception of the interest rate all variables in x^ are expressed in logarithms. ^•^^ The lag polynomial is defined as A{L)xf = AQX^ + A^Xf.^ + A2Xf_2 +....
6.2 AFrameworkforCointegration Analysis
(6.5b)
^ , k J = 0,
(6.5c)
EXV,,,V\,,] = Z,
207
where A2 is a matrix that describes the influence of future expectations, A^ describes the contemporaneous links, and A^{L) is a polynomial in the lag operator. The vector v contains the constants of the model, and v, collects the structural disturbances, which are assumed to be uncorrelated.^^^ In a more compact form, this model can be written as
(6.5d)
A{L)EXX,,,VV^V,,
However, Beyer and Farmer argue that if all the disturbances were stationary, the model could not account for the nonstationarity of the variables reported below. To illustrate this, it is useful to consider the moving average presentation of(6.5d),
(6.5e)
x,,,=A{Ly{v,^v),
where we assume for simplicity perfect foresight of agents. The matrix A in New Keynesian models is always chosen to ensure that the resulting model is stable, in order to rule out explosive processes and to make sure that the rational expectations equilibrium is uniquely determined. This choice of A implies that if all disturbances are stationary, the variables in x^ are stationary, too.^"*^ Hence, New Keynesian models are stationary structural models. In fact, in steady state, when x^ = x^^^ = x^_^ = x and v, = 0, the model converges to x = y4(l)~^ v . This solution pins down the long-run mean of the variables in the model and rules out any stochastic trends. To introduce a source of nonstationarity into the New Keynesian model, Beyer and Farmer assume that one of the disturbances in the New Keynesian model is a random walk. In this case, the structural model given by (6.5) can be rewritten as a VECM. By differencing the equation with the nonstationary disturbance and rewriting the other two equations in differences and levels, one arrives at the following VECM representation of the New Keynesian model: (6.6a)
^2^/^/+i "•" A^t
+ A {^)^t-\ ••• ^P'^t-k - w = w/.
^^^ Hence, the covariance matrix I is diagonal. ^^^ The stationarity of the variables in x^ does not mean that New Keynesian models always abstract from the trend growth rate of the economy. In fact, New Keynesian models can accommodate a trend growth in the level of these variables, but to be able to solve the model, the variables are transformed such as to obtain a stationary model.
208
Chapter 6 Revisiting the Natural Rate Hypothesis
By appropriate ordering of the equations one can always choose the nonstationary disturbance to be in the third equation. In model (6.6), the vector of errors w^ is stationary with variance-covariance matrix U. The disturbance vectors w^ and v^ are related by the expression v;
'w;' (6.6b)
2
2
V,
—
^t 3
W,
t
3 3 V/ - V , , I
t—\
This formulation of the New Keynesian model implies that the random walk process v] leads to a nonstationary behavior of x^. This raises the possibility that some or all of the variables in jc, are cointegrated. In the VECM formulation of the model, these cointegration relationships are captured by the term 5y9'x^_^, where a represents the structural loading matrix and P' the matrix of structural cointegrating vectors. As a final step, we need to supplement model (6.6) with a description of the process how expectations are formed. To this end, Beyer and Farmer (2002: 21) assume that expectations are rational in a very weak sense by requiring only that there should be no systematic long-run biases in the mechanism generating expectations.
6.2.1
The Aggregate Demand Equation in the VECM
In the VECM form of the New Keynesian model, the aggregate demand equation can be written as (6.7a)
£,[Z.f(i)A«,„]+3«(i?,-Ap,-F)-v« = v/'.
The fact that differences of unemployment instead of the level enter this equation follows from the fact that in the forward-looking IS curve the coefficients on future and current unemployment are the same (see equation (6.1). By including lags of the differenced unemployment variable, this model is more) general than the purely forward-looking IS curve in (6.1). The specification in (6.7) would arise, for example, if habit formation is present in the utility function of agents. Hence, (6.7) is consistent with the New IS curve that we used in the simulation of the extended New Keynesian model. For the cointegration analysis presented below, it is important to notice that if the disturbance term in (6.7) is stationary, the aggregate demand relation would give rise to a cointegration vector linking the interest rate to the inflation rate with coefficients (1; -1). This relation is also called the Fisher relation.
6.2 A Frameworkfor Cointegration Analysis
209
Beyer and Farmer (2002) observe that the Fisher relation is a strong assumption to impose on the data, since there are a variety of alternative models that impose a weaker long-run restriction. To allow for this class of models, they also consider the following aggregate demand function (6.7b)
^Jfef (L)At/,,J+a^(/?, -Ap, - F - y g > J - v ^ = vf,
where both the level and the differences of unemployment appear in the equation. This relation implies a cointegration vector of the form R-Ap- P^u - F = 0. Such a relation is consistent with the traditional IS curve, which postulates that there is an upward-sloping relationship between the unemployment rate and the real interest rate. Moreover, Beyer and Farmer note that it is possible to derive a similar long-run relationship in overlapping generations models or in representative-agent models with tax distortions that allow the real interest to vary with policy. In these models, the Fisher relation is a special case of the IS curve where the IS curve is horizontal.
6.2.2
The Aggregate Supply Equation
The New Keynesian Phillips curve in model (6.6) can be written as: (6.8a)
E[bi^[L)A^p,,,]^a^{u, - « J - v ^ = vf.
This equation can be interpreted as the VECM representation of the following version of the New Keynesian Phillips curve (Farmer 2000: 9): (6.8b)
Ap, =^{L)Ap,_, +EX{\-?^{L))Ap,,,]-a'{u, - w j + v^ +vf.
By including lags of the inflation rate, (6.8) has a richer specification than (6.2) because it adds backward-looking elements to the price adjustment process. In fact, this specification is very similar to the Fuhrer and Moore specification of the New Keynesian Phillips curve we used in the extended version of the New Keynesian model. The specification given by (6.8) is consistent with the natural rate hypothesis since all coefficients on the lags of inflation sum to zero. That is, we impose >5 = 1 on the New Keynesian model. As we have seen previously, this rules out any long-run relationship between the inflation rate and the unemployment rate. Technically, the natural rate hypothesis is imposed on the VECM form of the model by letting only differences of the inflation rate enter the Phillips curve. With this specification, in steady state a given unemployment rate (w, =Wr) is consistent with any constant inflation rate.
210
Chapter 6 Revisiting the Natural Rate Hypothesis
The natural rate of unemployment is, of course, an unobservable variable. For the empirical analysis, Beyer and Farmer start out by approximating this variable with a constant, u . If this approximation were nearly correct, we would expect the unemployment rate u^ to be stationary around a constant, provided the disturbance term wf is stationary. In this case, the unemployment rate would form one of the cointegration vectors in our empirical model. The resulting model would have the form (6.8c)
E\bi^{L)^^p,,,]^a\
- v ^ = vf,
where u is part of the constants collected in v ^. However, the pronounced upward drift in the unemployment strongly suggests that the hypothesis of a stationary unemployment rate is unlikely to hold. In fact, this drift is consistent with the monetarist assertion that the natural rate of unemployment has been drifting over time due to structural changes in the labor market. Hence, it appears to be more appropriate to model the natural rate as a unit root process. To introduce this hypothesis into our empirical model, Beyer and Farmer assume in a second step that the natural rate follows the process (6.8d)
S^(w,-w,_i)=wf+ w ^
where wf is an l(o) variable, w^ is a drift parameter, and a^ is the structural loading factor in the supply equation. That is, the natural rate of unemployment is modeled here as a random walk with drift. Assuming fiirthermore that there is no other shock hitting the aggregate supply equation so that vf is identically zero and abstracting from the constants in v^, we can rewrite our VECM specification of the New Keynesian Phillips curve as (6.8e)
E\bi^{L)^^p,,,]+a^u,
= a%.
The right-hand side of (6.8e), which would constitute the observable part of our empirical model of aggregate supply, is clearly imbalanced because of the relegation of the unobservable natural rate of unemployment to the error term. Consequently, since a^u^ is nonstationary, we would not expect to find a cointegration relationship associated with the aggregate supply relation. Hence, our vector error correction model would have a reduced rank. With a nonstationary natural rate of unemployment, the only way to arrive at an aggregate supply fiinction with a stationary error term is taking differences of this relationship. In differences, (6.8e) becomes (6.8f)
E\^bi^{L)^^p,,,]^a'^u,
= wf + w^.
It should be noted that by imposing a reduced rank restriction on our empirical VECM model, we eliminate the level of unemployment from the ag-
6.2 A Frameworkfor Cointegration Analysis
111
gregate supply equation and model this relation entirely in differences, consistent with (6.8f). Finally, with a view towards the empirical results presented below, it needs to be emphasized here that neither (6.8c) nor (6.8e) imply a cointegration relationship between the unemployment rate and inflation.
6.2.3
The Policy Rule
The policy rule in model (6.6) is given by (6.9a)
EXb^^{L)^R,,,]^a^[R,-P[^^p, +,g/(w, -w,)-F]+vf + v ^
According to Farmer (2000: 9), this equation is equivalent to (6.9b)
R,=d{L)R,.,^[\-S{L)tp[,^p,
+A'{ut -iTj + rJ+vf + v ^
Here, 5{L) is a polynomial that jiodels the interest rate smoothing behavior of the central bank. The parameter /?^ dves the long-run response of the central bank to the inflation rate, equivalent to (1 + ^") in (6.3), while P^ gives the response to the unemployment gap, which is equivalent to ^2" • The vector collecting the constants, v ^, also includes the inflation target, n. Since the natural rate of unemployment is unobservable, we face a similar problem as in the preceding section. If approximating the natural rate with a constant proves to b^adequate, the policy rule will give rise to a cointegration vector of the form R - P^^ + P^u - ;^ = 0, where / is a constant encompassing both the steady state natural rate of interest, F, and the constant natural rate of unemployment, u. On the other hand, if the natural rate of unemployment is better described as a unit root process, the policy rule will become (6.9c)
EXb'M^t.MSc^k
-K^t
+ AT". -r]-y'
= ^'P^^t + vf.
Similar to the aggregate supply equation (6.8e), the observable part of the policy rule will again be imbalanced, and we will find no cointegration relationship because the error term on the right-hand side, a^P^u^ +vf, is clearly nonstationary. Hence, in this case our New Keynesian model would yield only one cointegration vector, namely the Fisher relation resulting from the aggregate demand relationship. However, precisely because of the unobservability of the natural rate of unemployment, it is also conceivable that the central bank would not respond to the unemployment gap, u^-u^, but only to the actual unemployment rate, w^. If this were the case, we would find a cointegration vector of the form
212
Chapter 6 Revisiting the Natural Rate Hypothesis
R - P[pl^ + P^u - ;^ = 0, even though the natural rate of unemployment is nonstationary. Interestingly, the latter scenario raises the possibility that the stochastic trend in the natural rate of unemployment is transmitted to the inflation rate. In fact, this transmission channel is emphasized by Orphanides (2000) in his explanation of the increase in the trend inflation rate during the 1970s. He argues that in the 1970s many economists did not realize that the natural rate of unemployment had increased, and substantiates this by looking at real time estimates of potential output. He finds that these estimates were much more optimistic than were subsequent revisions of the same series. Hence, it is likely that the Federal Reserve Board concluded from the increase in the actual unemployment rate that the economy suffered from a severe shortfall in demand, even though the increase in unemployment stemmed from the increase in the natural rate of unemployment. The attempt of the central bank to stimulate the economy led consequently to significant inflationary pressures. In sum, by having monetary policy respond to Uj instead of the correctly specified unemployment gap, u^-u^, this explanation accounts simultaneously for the trend increase in the unemployment rate and the inflation rate by linking both to the stochastic drift in the natural rate. However, it is hard to believe that over the long run, the central bank would fail to recognize that the natural rate of unemployment had increased, which means this explanation might be valid for the 1970s, but probably not for the 1980s or 1990s. Finally, we need to consider the possibility that the inflation target of the central bank follows a stochastic trend, W^, Like the natural rate of unemployment, this variable is unobservable and would consequently be included in the error term. Substituting Wj for W in equation (6.3), and assuming for simplicity that the natural rate of unemployment is constant, would yield
(6.9d)
EXb'AL)^t.MSc^[Rt-P[p^Pt^k{u,
-uyA-v^
As before, a stochastic trend in the inflation target would lead to an imbalance in the observable part of the policy rule, thereby leading to a reduced rank of our vector error correction model. To summarize, if all disturbances in the New Keynesian model were stationary, ruling out a nonstationary natural rate of unemployment and a stochastic inflation target, and given the stability of the dynamics in this model, the variables in the model will converge to means satisfying
(6.10a) R-^ (6.10b)
= 0, or,
u-u=0.
R-Ap-P^^u-r=0,
6.3 Results of a Multivariate Cointegration Analysis for Germany (6.10c)
R-P[^^p^p^^u-Y
213
= 0.
However, if one of the disturbances is nonstationary, the system will have a vector error correction presentation with at most two cointegration vectors, which would correspond either to (6.10a), (6.10b), and/or (6.10c). The preliminary evidence suggests that the disturbance term in the aggregate supply equation is nonstationary, reflecting a unit root process in the natural rate of unemployment. In this case, we would expect to find only one cointegration relationship, which would correspond to (6.10a). However, if the central bank responds to the actual unemployment rate because it cannot observe the nonstationary natural rate, we might find in the data an additional cointegration relationship corresponding to (6.10c). On the other hand, a stochastic trend in the inflation target may lead to instability in (6.10c) and, consequently, to only one cointegration relationship. The next section will perform a multivariate cointegration analysis for West German data, test the rank of the system, and determine whether the resulting cointegration vectors are consistent with those derivedfi*omthe New Keynesian model.
6.3
Results of a Multivariate Cointegration Analysis for Germany
In a first step, we estimate a vector autoregression (VAR) model for the period fi*om 1965 until 1998 and use Chow breakpoint tests to test for a structural break in the model. The preliminary evidence on the long-run Phillips curve suggests that such a break has occurred in the late 1970s or early 1980s. Since a stable long-run Phillips curve appears to be present only in the latter sample period, finding formal evidence for a structural break around this time is crucial for the argument that the natural rate hypothesis may not hold for Germany in the past twenty years. In a second step, we are using univariate unit root tests to determine whether the unemployment rate, the interest rate, and inflation in West Germany are nonstationary.^^^ In a third step, we present the results of the cointegration analysis for Germany.
242
Since a structural break in the time series may lead unit root tests to conclude that the time series are nonstationary, we compute first the structural break tests using a VAR model that is robust with respect to the stationary properties of the time series. For testing the lag length, we consider the Akaike, the Hannan-Quinn, and the Schwarz criteria.
214 6.3.1
Chapter 6 Revisiting the Natural Rate Hypothesis Testing for a Structural Break
To test for structural breaks, we estimate a VAR model for quarterly data for the full sample period from 1965:2 until 1998:4. It consists of the 3-month interest rate, the West German unemployment rate, and the inflation rate, computed on the basis of the West German consumer price index.^"^^ On the basis of information criteria we choose a lag length of two.^^^ Table 6.1 shows that this model displays severe signs of misspecification; there is evidence for a structural break in the interest rate equation, and there are signs of autocorrelation, nonnormality, and heteroscedasticity. Figure A3 a in the Appendix shows the result for a recursive Chow 1-step ahead forecast test.^"*^ Beginning in 1980, the break statistic is significant at the 5% for several years. This confirms the impression from Figure 6.1 that the relationship between the three variables began to change around this time.^^^ In the following, we assume that the break occurred in the fourth quarter of 1979. The choice of this breakpoint is motivated by the observation of Clarida et al. (1998) that policy rules in the G3 countries changed after 1979. These authors note that after nearly a decade of high inflation, a number of important central banks, including the Bundesbank, began in 1979 a concerted effort to reign in inflation (Clarida et al. 1998: 1034). As a result, after 1979 they raised interest rates sufficiently to increase the real interest rate in response to the inflationary pressure emanating from the second oil price shock, while before 1979 they allowed the real interest rate to decline following an increase in inflation. This change in policy is also visible in Figure 6.2, which shows the annualized real short-term interest rate in Germany. Consistent with a shift towards a more aggressive policy in fighting inflation, the real short-term interest increased markedly after 1979 and remained high throughout the 1980s. A break in the policy fimction of the Bundesbank is also consistent with the results from the Hansen stability test, which shows that the interest rate equation in the VAR is instable. Assuming a break in 1979, Table 6.1 shows that the resulting VAR models for the subsample periods are far better specified than the model estimated for the ^^^ All time series are obtained from Datastream. The corresponding Datastream codes are BD3MTH..R, WGTOTUN%E, and WGCP....E. The sample period ends in 1998:4, since from 1999 onwards the Bundesbank ceased to set monetary policy for Germany. ^^^ The empirical analysis has been conducted using MALCOLM, CATS for RATS, andPcGive 10. '^^^ The recursive estimation is initialized using the first 20 quarters of the sample period. ^^^ There are also signs of a structural break in the first half of the 1970s. But since the break statistic is significant at only two points in time in this period, these appear to be outliers. This is also confirmed by the Hansen stability test, which shows no signs of instability in the early sample period.
6.3 Results of a Multivariate Cointegration Analysis for Germany
215
entire period; neither the stabiHty tests nor the residual tests show serious signs of misspecification for the subsample models. Figure 6.2: The Real Short-Term Interest Rate and Its Mean in Germany
Table 6.1: VAR Specification Statistics Sample period
Equation
1965:2 1998:4
/
1965:2 1979:3
1979:4 1998:4
u Ap System i u Ap System i u Ap System
Lag length
Hansen stability test
2
2.5* 0.8 1.9
1.9 0.5 1.6 1.4*
2
1.2 1.2 1.2
3
2.6 1.7 1.4
0.9 [0.49] 2.6* [0.04] 0.6 [0.73] 1.7* [0.02] [0.40] 1.0 [0.67] 0.6 0.2 [0.97] 1.3 [0.10]
ARl-5 [0.10] [0.78] [0.17] [0.04]
Normality 36.6** [0.00] 0.4 [0.80] 6.2* [0.05] 46.5** [0.00] [0.66] 0.8 [0.28] 2.6 3.6 [0.16] 9.8 [0.13] 6.5* [0.04] 0.4 [0.83] 2.7 [0.26] 11.0 [0.09]
Heteroscedasticity 3.1** 1.8 1.6 1.5* 1.5 2.2* 0.9 1.1 3.1** 0.4 1.2 1.1
[0.00] [0.05] [0.10] [0.01] [0.18] [0.03] [0.59] [0.29] [0.00] [0.97] [0.29] [0.20]
* = significant at the 5% level; ** = significant at the 1% level. Note: The numbers in the square brackets denote the p-values. The stability test gives the joint stability test statistic based on Hansen (1992). The critical values of this test depend on the lag length. The AR 1-5 statistic gives the resuh of an LM test for autocorrelated residuals up to fifth order. The test for normality is a Jarque-Bera normality test. The heteroscedasticity test is based on White (1980).
216
Chapter 6 Revisiting the Natural Rate Hypothesis
Below, we will show that we find stable cointegration vectors in both subsample periods. This allows us to employ multivariate cointegration analysis to investigate whether the natural rate hypothesis holds. Cointegration analysis presents a valuable extension of our analysis in Chapter 2, where we tested this hypothesis using bivariate models comprised of differenced variables. These models showed no signs of instability over the sample period from 1970 to 1998, but when we considered a possible cointegration relationship the recursive statistic for the trace test showed severe signs of instability. Hence, we abandoned this approach for the bivariate models. Here, on the other hand, we have extended the information set by including the interest rate variable, and this has the effect of making cointegration analysis feasible if one allows for a break in the sample period.
6.3.2
Univariate Unit Root Tests
In this section, we employ conventional ADF tests to test the null hypothesis that the time series have a unit root. We compute the tests for the two subsample periods, since the structural break in the full sample period could be mistaken by the unit root tests as a sign of nonstationarity. The lag length is chosen based on a LM test for autocorrelation of order 12, and the results are shown in Table 6.2. The ADF tests indicate that all variables are integrated of order one, with the possible exception of the inflation rate in the early sample period. The multivariate unit root tests computed in the next section will confirm that all variables are 1(1).
6.3.3
Results of the Multivariate Cointegration Analysis for the Period 1965-1979
In a first step, we test the cointegration rank of the model using the maximum likelihood procedure suggested by Johansen (1988).^'*^ Table 6.3 reports the values of the X-trace statistic testing the null hypothesis of no cointegration relationship, at most one and at most two cointegration relationships. At the five percent significance level, there is evidence for one cointegration relationship. Consequently, we impose the restriction r = 1 on the system. Next, we test whether the cointegration vector results from one of the variables in the model being stationary. The results of this multivariate unit root test are shown in the right part of Table 6.3. The null hypothesis of stationarity is rejected for all variables at the five percent significance level, confirming the results from the univariate unit root tests. The existence of one cointegration vector implies that two of the long-run relationships resulting from the New Keynesian model have nonstationary disturbances. ^^' For the specification and misspecification tests, see Table 6.1.
6.3 Results of a Multivariate Cointegration Analysis for Germany
217
Table 6.2: Results from ADF Tests Sample period
Variable
1965:2 1979:3
/ u Ap
1979:4 1998:4
z u Ap
ADF t-statistic
Order of integration
l;c;t 0;c;t
-2.9 -2.9 -4.0*
1(1) 1(1) borderline
12; c;t l;c;t l;c',t
-2.8 -3.0 -3.1
1(1) 1(1) 1(1)
Specification
* = significant at the 5% level. Note: A time trend (t) is included in the regression if the time series appears to be trending over time, otherwise only a constant (c) is allowed for. Table 6.3: Cointegration Statistics for the Period 1965-1979 Rank test r<0 r
Trace test 30.9* 8.0 1.0
P'WaluQ
0.04 0.47 0.33
Multivariate unit root test / u Ap
X^ test
/7-value
6.9* 19.5** 17.4**
0.03 0.00 0.00
* = significant at the 5% level; ** = significant at the 1% level. Note: A constant is included in the cointegration relationships. The test statistics have been computed using PcGive 10. The/>-values are based on the approximations to the asymptotic distributions derived by Doomik (1998). The cointegration vector resulting from the empirical model has the following form: (6.11)
/?-0.75A^ + 0.43w = 0.
This cointegration vector is consistent with the policy rule (6.10c). This suggests that both the aggregate demand and the aggregate supply equations have nonstationary disturbances. The nonstationarity of the aggregate supply equation in particular does not come as a surprise, since already Figure 6.1 showed that there is no long-run correlation between the unemployment rate and inflation. Moreover, Figure A4 in the Appendix shows that the unemployment rate increased over time in the first sample period, which points to a stochastic trend in the natural rate of unemployment. Above, we argued that in the case where the
218
Chapter 6 Revisiting the Natural Rate Hypothesis
natural rate hypothesis holds, but the natural rate is nonstationary, we would not expect to find a cointegration relationship associated with the aggregate supply relation. Consequently, our finding of a reduced rank of our empirical model supports the natural rate hypothesis. Regarding the nonstationarity of the aggregate demand relation, this may be related to the fact that the demise of the Bretton Woods system led to a large real appreciation of the German currency, which caused foreign demand for German goods to decline considerably. This regime shift may have induced a nonstationary behavior of aggregate demand. The interpretation of (6.11) as a policy rule is supported by the fact that the estimated coefficients have the expected signs and are of plausible magnitude: according to (6.11) the Bundesbank responded to an increase in the unemployment rate by lowering the short-term interest, thereby seeking to stabilize the economy. In response to an increase in inflation, the Bundesbank increased the interest rate, which is consistent with an attempt to contain inflationary pressures, but the estimated coefficient is smaller than one. Thus, the Bundesbank allowed the real short-term interest to decline when inflation increased. This result confirms the observation in Clarida et al. (1998) that G3 central banks before 1979 did not respond strongly to inflationary pressures. Moreover^ our previous discussion of the New Keynesian model has shown that with P[p < 1 the rational expectations equilibrium is not uniquely determined. Hence, monetary policy is unable to ensure that inflation converges in the long run to its inflation target, and the inflation rate may increase permanently. The resulting trend increase in inflation set the stage for a more aggressive response of central banks in the late 1970s to the second oil price shock, thereby trying to avoid past mistakes and reverse inflationary pressures. The results from the cointegration analysis suggest also that Orphanides' (2000) explanation of the simultaneous increase in the unemployment rate and the inflation rate due to a misjudgment of the central bank on the supply potential may be relevant not only for the United States but also for Germany. After all, our findings that the natural rate of unemployment followed a unit root process and that the Bundesbank responded to the actual unemployment rate instead of the unemployment gap are consistent with this view.^^^ Moreover, taking into account that the natural rate of unemployment was fairly stable throughout the 1960s, it is indeed conceivable that the Bundesbank did not realize that the natural rate increased permanently in the 1970s. If the Bundesbank mistakenly assumed that the natural rate remained constant, it would have interpreted the increase in the unemployment rate as indicating a large unemployment gap, Uf-u>0, and eased policy in an ultimately unsuccessfiil attempt to restore fiiU employment. This easing would have slowed down the adjustment of the un^^^ It may be useful to recall here that if the Bundesbank had responded to the unemployment gap, the nonstationarity of the natural rate would have meant that no stable cointegration vector corresponding to the policy rule would exist.
6.3 Results of a Multivariate Cointegration Analysis for Germany
219
employment rate to the natural rate, but at the cost of permanently increasing inflation. Hence, the increase in the natural rate would have led to a simultaneous increase in the trend rates of inflation and unemployment.
6.3.4
Results of the Multivariate Cointegration Analysis for the Period 1979-^1998
The results for the rank test for the second subsample period are displayed in Table 6.4. At the five percent significance level, the model appears to have full rank, which would imply that all three variables are stationary around a constant. However, visual inspection of Figure A4 in the Appendix shows that all three variables display a trend in this period, making the stationarity assumption highly unlikely. Moreover, this would contradict the results from the univariate unit root tests. Hence, a rank of two appears to be more plausible. This is also consistent with the results fi'om the trace test at the one percent significance level. The lower part of Table 6.4 displays the result for the multivariate unit root tests. At the five percent significance level, the null of stationarity is rejected for all three variables, confirming the results of the univariate unit root tests. With two cointegration vectors, it is necessary to impose one identifying restriction on each vector to obtain estimates of just identified cointegration vectors. Following Beyer and Farmer (2002), we impose the following two zero restrictions in Table 6.5, where ^^ and y^j represent freely estimated parameters. This yields the following two cointegration vectors: (6.12a)
R-l,95Ap
=0
(6.12b) w + 1.14Ap = 0. The existence of two cointegration vectors implies that one of the disturbances in the New Keynesian model is nonstationary. If either the aggregate demand disturbance or the policy rule disturbance were nonstationary, one of the stationary long-run relationships implied by the New Keynesian model would be the long-run relationship resulting from the New Keynesian Phillips curve, equation (6.10b). According to this equation, the unemployment rate would be stationary. Since this is clearly rejected by the data, it follows that it is the aggregate supply disturbance term which is nonstationary. The analysis so far suggests that the natural rate of unemployment followed a random walk in both subsample periods. While the natural rate hypothesis is consistent with the empirical facts of the first subsample period, we still need to determine whether this is also the case for the second period. In particular, it is still an open question whether the estimated cointegration vectors given by (6.12)
220
Chapter 6 Revisiting the Natural Rate Hypothesis
Table 6.4: Cointegration Statistics for the Period 1979--1998 Rank test
Trace test
/7-value
45.8** 20.6** 16.5*
0.00 0.00 0.01
r<0 r
Multivariate unit root test / u Ap
X^ test
/?-value
7.5** 5.7* 6.6*
0.01 0.02 0.01
* = significant at the 5% level; ** = significant at the 1% level. Note: A constant is included in the cointegration relationships. The test statistics have been computed using PcGive 10. The/?-values are based on the approximations to the asymptotic distributions derived by Doomik (1998) Table 6.5: Restrictions on the Cointegration Vectors Vector 1 Vector 2
/
u
Ap
1 0
0 1
A A
are consistent with the long-run relations resulting from the aggregate demand equation, (6.10a), and the policy rule, (6.10c). If the strong form of the aggregate demand equation holds, (6.10a) and (6.10c) would imply the following two cointegration vectors (neglecting constants): (6.13a)
R-Ap
=0
(6.13b) w + - ^ A p = 0. Beginning with (6.13a), this relation shows that in New Keynesian models the Fisher relation holds. However, when we test whether the Fisher relation is one of the cointegration vectors in (6.12), this is clearly rejected by the data at the five percent significance level. Regarding (6.13b), since monetary policy responded after 1979 strongly to an increase in inflation, the parameter P[p in the policy rule is likely to be greater than one.^"*^ Since P^ is^ greater than zero, this means the New Keynesian model predicts the term {\-P[p)lPu to be smaller ^^^ Clarida et al. (1998: 1045) estimate the parameters in the policy rule of the Bundesbank after 1979 and find that the parameter a^ is approximately 1.3, while a2 is approximately 0.25.
6.3 Results of a Multivariate Cointegration Analysis for Germany than zero. However, in (6.12b) this coefficient is positive. Hence, this version of the New Keynesian model does not fit the data. As an alternative, we consider the weaker form of the aggregate demand equation, which allows for a long-run relationship between the real interest rate and the unemployment rate. In this case, the New Keynesian model would yield the following cointegration vectors:
(6.13c) ^ - - ^ | 7 ^ £ V = 0 (6.13d) "
^
V
= 0.
With P[p, P^, and P^ all larger than zero, the estimated cointegration vector (6.12a) is now consistent with (6.13c). However, (6.13d) stillj:annot account for the positive coefficient on the inflation variable in (6.12b) if P^ > 1. It follows that even the weaker version of the New Keynesian model does not provide an adequate description of the long-run relations in the German data. In sum, the difficulties to reconcile the New Keynesian Phillips curve with our estimated cointegration vectors stem from the fact that one of the estimated vectors contains a negative long-run relationship between inflation and the unemployment rate. We have shown above that the New Keynesian Phillips curve specifically rules out any long-run relationship between these two variables. The other two equations in the model also do not give rise to such a relation, because empirical estimates of the Taylor rule by Clarida et al. (1998) suggest that P^ typically takes a value of approximately 1.5. Inserting this into (6.13d) shows that this model gives at best rise to a weak positive long-run relationship between unemployment and inflation, but not to a strong negative relationship that we observe in the data. Even if the New Keynesian model were consistent with the estimated cointegration vectors, it would still be difficult to explain with this model why the unemployment rate increased over most of the second subsample period, while simultaneously the inflation rate declined. For the first subsample period, we showed that the New Keynesian model could account for a simultaneous increase in both variables, but in the second period, they have been moving in opposite directions. It is, of course, possible that the natural rate of unemployment has continued to drift upwards, while at the same time the Bundesbank may have chosen to disinflate the economy, for reasons unrelated to the trend increase in unemployment. For example, the Bundesbank might have chosen to reverse the increase in trend inflation it had brought about in the 1970s. This view of events probably represents the main stream view, but it is nevertheless based on the somewhat unattractive assumption that the correlation in the trend components
221
222
Chapter 6 Revisiting the Natural Rate Hypothesis
we observe in the data is nothing but a coincidence. In addition, this explanation would correspond to the case where the inflation target in the policy rule is not constant but follows a stochastic trend. As shown above, in this case we would not expect to find a cointegration relationship corresponding to the policy rule. That is, with two independent drifts in the unemployment rate and the inflation rate, we would expect to find only one cointegration vector, which would represent the aggregate demand relation. However, this interpretation of events in the 1980s is contradicted by our finding of two cointegration vectors.
6.3.5
A Long-Run Phillips Curve
In this section, we adopt a proposal by Beyer and Farmer (2002) and replace the natural rate hypothesis (6.10b) with the following long-run relation:
(6.14a) u-u-fil^Ap
= 0.
These two authors find that the natural rate hypothesis does not hold for U.S. data either, owing to a positive correlation between the trend components of inflation and unemployment, and propose as an alternative the aggregate supply equation given by (6.14a) with a positively sloped long-run Phillips curve, P^>0. Like our results for Germany, they find evidence for a structural break in 1979 in the policy equation. For the time period from 1980 until 1999, they find two cointegration vectors, and conclude that one of those vectors corresponds to the upward-sloping long-run Phillips curve (6.14a) and the other to the policy equation. Hence, the nonstationarity in this model is induced by a nonstationary disturbance term in the aggregate demand equation. In general, our results for Germany are similar to those of Beyer and Farmer; but in contrast to the United States, the correlation between the trend components of unemployment and inflation is negative in Germany and not positive. Hence, we modify (6.14a) as follows: (6.14b) u-u-^Pl^p
=0.
In this model, the long-run Phillips curve has a negative slope, just like the traditional Phillips curve. In the next section, we are going to offer some theoretical motivation for (6.14b). But before we explore the theoretical reasoning behind such a relation, we need to show that it is consistent with the data. Like Beyer and Farmer, we assume that the disturbance term in the aggregate demand equation is nonstationary.^^^ Combining the policy equation (6.10c) 250 ^ g ^igQ considered the case where the disturbance term in the policy equation is nonstationary, but this turned out to be inconsistent with the data.
6.3 Results of a Multivariate Cointegration Analysis for Germany
223
with (6.14b) yields the following long-run relationships implied by the modified New Keynesian model:
(6.14c)
R'{p^+fi:fiiyp=o
(6.14d) M + y5^Ap = 0. In this case, the cointegration vector (6.12b) can be interpreted as an estimate of the long-run Phillips curve (6.14d), yielding a jlopejparameter of-1.14. Moreover, the cointegration vector (6.12a) implies;5^+y5//?^ 0^=1.95. Inserting in this equation our estimate for >&^, and assuming that j3^ is approximately 1.3, we obtain a value of approximately 0.6 for J3^. This value is close to the one we found in the estimation of the policy rule for the first subsample period. Hence, this model appears to be consistent with the data. Importantly, this finding implies that the natural rate hypothesis has to be abandoned to obtain a version of the New Keynesian model that is consistent with the long-run trends in German data. If the natural rate hypothesis does not hold, this raises the possibility that demand conditions have a lasting effect on the German unemployment rate. In particular, our estimate of the long-run Phillips curve suggests that the reduction in the inflation rate in the 1980s was accompanied by a permanent increase in the unemployment rate. Average inflation decreased from approximately 5 percent in the 1970s to approximately 3 percent in the 1980s and to 2.5 percent in the 1990s. Assuming that this reduction in trend inflation is the result of the Bundesbank's determination to lower average inflation, our estimate of the long-run Phillips curve implies that in the 1980s this would have been accompanied by a permanent increase in the unemployment rate of 2.3 percentage points, and a further increase of 0.6 percentage points in the 1990s. This would explain about half of the increase in average unemployment from 3 percent in the 1970s to 8 percent in the 1980s and to 9 percent in the 1990s. However, it needs to be emphasized that this estimate represents the upper bound for the role of macroeconomic conditions in explaining the trend increase in German unemployment. Splitting the sample period in 1979 implies that the second period covering the 1980s and the 1990s contains very few strong supply side disturbances that lead to a positive relationship between the unemployment and inflation rates and weaken the negative long-run relationship present in this part of the sample. From this perspective, it is not surprising that the bivariate models considered in Chapter 2 find a smaller role for aggregate demand shocks in explaining the path of unemployment, since the sample period covers also the 1970s with its oil price and wage cost shocks. However, since we find strong evidence for a structural break in the extended information set considered in this chapter, our choice to split the sample period is justified on empirical grounds.
224
Chapter 6 Revisiting the Natural Rate Hypothesis
Nevertheless, one should be aware that this has the effect of magnifying the negative long-run relationship between the two variables. Since our finding that weak macroeconomic conditions play a role for the trend increase in unemployment contradicts conventional wisdom, we try to bolster our case with additional evidence. To this end, we plot in Figure 6.3 the relationship between the vacancy and the unemployment rates for West Germany, the so-called Beveridge curve.^^^ At any moment, the Beveridge curve is a downward-sloping curve, since it is easier to fill a vacancy when there are more unemployed workers to choose from. The upper left area can be described as a fast growing economy with many employment opportunities whereas the lower right area reflects a recession state with few employment opportunities and high unemployment. In a frictionless labor market, the Beveridge curve would coincide with the axes of the diagram.^^^ The more frictions there are in the labor market, the more the Beveridge curve shifts outward. Since an increase in structural unemployment typically means that the labor market has become less efficient, one would expect that an increase in the structural unemployment rate coincides with an outward shift in the Beveridge curve.^^^ However, Figure 6.3 shows that the Beveridge curve in Germany has been remarkable stable in the period fi-om 1970 to the early 1980s, which is exactly the period when the unemployment rate increased from 1 percent to 9 percent. Solow (2000: 5) summarizes the evidence on the Beveridge curve in Germany and France as follows: "The main message transmitted by the Beveridge curves for France and Germany goes squarely against the cliche that high and persistent unemployment is entirely or mainly a matter of worsening functioning of the labor market. It is precisely in France and Germany that there is no sign of a major unfavorable shift of the Beveridge curve during the period of rising unemployment. To the extent that the location of the Beveridge curve is a reasonable summary of the degree of labormarket rigidity, the large continental economies do not seem to have suffered from noticeable more rigid labor markets during the high-unemployment 1980s than they did in the low unemployment 1970s." To summarize, our empirical findings suggest that the disinflation in the first half of the 1980s is likely to have contributed to the permanent increase in the unemployment rate that occurred in this time period. However, the further increases in trend unemployment in the remainder of the 1980s and 1990s are probably unrelated to demand conditions, since the trend inflation rate changed ^^^ The analysis of the Beveridge curve draws on joint work with Ulrich Fritsche from the German Institute of Economic Research (DIW). ^^^ In a frictionless labor market, there would be no unemployed workers if vacancies were available, and there would be no vacancies if unemployed workers were available to fill these positions. ^^^ See also Bleakley and Fuhrer (1997) on the factors determining the Beveridge curve.
6.4 Explaining the Long-Run Phillips Curve
225
Figure 6.3: The Relation between the Vacancy Rate and the Unemployment Rate in Germany Beveridge curve (Germany 1962-1997) Vacancy Rate
6.0%
Unemployment rate
little in this period. Instead, the strong outward shifts in the Beveridge curve in this period suggest that structural factors are responsible. Put another way, the simultaneous decrease in inflation and increase in unemployment in the first half of the 1980s can be interpreted as a move on a long-run Phillips curve, whereas the increase in unemployment in the following years at an unchanged inflation rate is consistent with a shift of the Phillips curve due to structural factors.
6.4
Explaining the Long-Run Phillips Curve
We have shown in Chapter 2 that the traditional Phillips curve of the 1960s has been thoroughly discredited in the economic literature. In this section^^^, we do not propose to return to this concept, but aim to show that there are a number of ^^^ This section draws on joint work with Uli Fritsche. The latter author contributed to the expositions on asymmetric information and the nonlinear Phillips curve models.
226
Chapter 6 Revisiting the Natural Rate Hypothesis
modem macroeconomic models that could give rise to the long-run Phillips curve we observe in the data. However, before we do so, we will clarify one issue relating to a nonvertical Phillips curve on the outset. It is often thought that the existence of a traditional Phillips curve in the data implies that there is a long-run trade-off between inflation and unemployment that can be exploited by monetary policy makers. Such a conclusion would be premature, since the effectiveness of monetary policy depends on the exact type of model that gives rise to the long-run relation between inflation and unemployment. We are going to explore the consequences of our findings for monetary policy in more detail below. In any case, it is worth noting that we probably only find a traditional Phillips curve in the data precisely because the Bundesbank did not try to exploit this relationship in the past twenty years.
6.4.1
Asymmetric Information Models
One possible explanation of the long-run relation between unemployment and inflation we observe in the data draws on what Greenwald and Stiglitz (1993) call the "second strand of New Keynesian literature." The key ingredients of these models are risk averse firms, a credit allocation mechanism with risk-averse banks, the existence of asymmetric information, and real wage rigidity in the labor market. In fact, this type of model is closely related to the models with credit market imperfections discussed in the context of a nonlinear short-run aggregate supply curve. However, in contrast to the credit channel model, the model discussed here can give rise to very persistent effects of demand conditions on unemployment, with aggregate supply ultimately becoming dependent on aggregate demand. To illustrate the transmission mechanism in this type of New Keynesian model, we consider a tightening in aggregate demand conditions. If an adverse aggregate demand shock occurs, or if the Bundesbank tightens its policy stance to reduce inflation, the resulting recession will reduce the profits and cash flow of firms, and, hence, in order to keep up production firms will have to increase their borrowing. In addition, the fall in inflation pushes up the real value of the flrms' debt, increasing the risk of bankruptcy. In this situation, risk-averse firms may choose not to reduce prices to maintain demand for their products, but to reduce instead the production level, thereby conserving cash reserves in order to reduce the risk of bankruptcy. As Greenwald and Stiglitz put it, the riskiness of production has increased, and firm's willingness and ability to bear that risk has decreased. This means that for a given price firms reduce the supply of their goods. From this follows that the inward shift of the aggregate demand curve leads to an inward shift of the aggregate supply curve. In addition, with firms reducing their production levels, their demand for investment may shift down
6.4 Explaining the Long-Run Phillips Curve
227
markedly, reinforcing the weak demand conditions. Consequently, the economy has little tendency to move out of the recession. This effect is reinforced if banks are risk-averse. Since the recession has lowered the cash flow of firms, which reduces their ability to service their debt, and has lowered their net worth, making them less credit-worthy, banks find that the riskiness of their lending activity has increased. Since raising interest rates to compensate for the higher credit risk may lead in a world of asymmetric information to the adverse selection effect of chasing away credit-worthy borrowers, banks may choose instead to ration the credit supply, shifting the aggregate supply curve even fiirther inwards. Together, these ingredients can explain how the effects of an adverse demand shock or a tightening in monetary policy are amplified and their persistence greatly increased. With real activity remaining depressed, inflation is going to remain subdued too. Hence, we would observe a co-movement between the trend components of inflation and output. However, a low level of trend output is only translated into a permanently higher unemployment rate if real wages are sticky and therefore fail to clear the labor market. Thus, if a reduction in the inflation rate is going to be accompanied by a lasting increase in the unemployment rate, it is necessary to invoke insider-outsider or efficiency-wage theories to introduce considerable real wage rigidity into the model. In sum, if one puts all these ingredients together, the "second strand" of New Keynesian model can explain how the German economy shifted from a situation of buoyant demand and over-employment in the 1960s and first half of the 1970s to a situation of weak demand and high unemployment in the 1980s and 1990s. According to this view, in the first period monetary policy was committed to maintaining favorable demand conditions, but allowed the inflation rate to drift upwards. In the second period, when the natural rate hypothesis had gained almost universal acceptance, monetary policy committed itself solely to reducing inflation and keeping it low. If the natural rate hypothesis had been true, this disinflation would have had no lasting effect on the unemployment rate. However, if the model described here were true, the economy would find itself stuck in a high unemployment situation. After all, due to an economy-wide market failure, the private sector would have no tendency to return to its previous equilibrium, monetary policy makers would not act because the inflation rate was at its desired level, and fiscal policy would lack the resources to reflate the economy.
6.4.2
Nonlinearities in the Long-Run Phillips Curve
An alternative explanation for our empirical finding is offered by Akerlof et al. (2000). Based on microeconometric evidence these authors argue that the long-
228
Chapter 6 Revisiting the Natural Rate Hypothesis
run Phillips curve may be nonlinear. They build a macroeconomic model in which agents at low rates of inflation display near-rationality, meaning that in the wage-setting process they either ignore inflation entirely, or they fail to appreciate that inflation increases the nominal demand for their services, and consequently demanding higher wages would not reduce their competitiveness. Hence, they are prepared to accept lower wage increases than they otherwise would. In this case, at low rates of inflation wages are set lower relative to nominal demand than predicted in models with fully rational agents, and the economy can operate at a higher level of real activity. This means that at low rates of inflation, the unemployment rate will be below its natural rate deflned as the unemployment rate resulting from an environment with fully rational agents. However, if inflation approaches zero, the near-rational effect disappears, and the unemployment rate returns to the natural rate, which is also the case when inflation increases. Near-rationality arises in this model because the costs of collecting and processing information on inflation outweigh the private costs of not taking this information fully into account. While these private costs are likely to be small, the resulting macroeconomic effects may still be large. In fact, since in New Keynesian models a similar discrepancy between private and social costs explains significant nominal rigidities in the macroeconomy resulting from small costs of changing prices (menu costs), the concept of near-rationality is fully compatible with the philosophy of New Keynesian models. If the rate of inflation increases, the costs of ignoring inflation increases too and more and more agents will switch to fully rational behavior. Consequently, the unemployment rate begins to return to its natural rate level. Likewise, when inflation falls and reaches zero inflation, any misperception about inflation is eliminated and the unemployment rate also returns to its natural level. Taken together, this yields a nonlinear long-run Phillips curve, which is plotted in Figure 6.4. Here, ;r* denotes the low but positive inflation rate at which an unemployment rate below the natural rate can be maintained. Wyplosz (2001) estimates such a nonlinear Phillips curve for several European countries. For Germany, he finds that n* is approximately 6.5 percent. When inflation falls to about 2 percent, Wyplosz results suggest that the unemployment rate increases by about 3.5 percentage points. This raises the possibility that the disinflation in the early 1980s led to a permanent increase in the unemployment rate as the economy moved from n* towards a suboptimal low inflation rate. However, since the German economy experienced in the 1960s a long period of both very low inflation rates and low unemployment rates, this model would have to be extended to allow for a changing optimal inflation rate to explain the negative long-run correlation between both variables we observe in the data.
6.4 Explaining the Long-Run Phillips Curve
229
Figure 6.4: A Nonlinear Long-Run Phillips Curve
^Natural
6.4.3
Unemployment rate
Disinflation and Hysteresis Effects
Ball (1999) offers another explanation for the link between disinflation and higher unemployment. Like in asymmetric information models, in Ball's model aggregate demand conditions can have long-run effects on the unemployment rate. He argues that these effects arise due to hysteresis effects.^^^ In his model, the response of monetary policy to a recession and the accompanying disinflation is decisive for the path of unemployment following the recession. He shows empirically for the recessions in the early 1980s that countries like the United States which have been successfiil in maintaining low unemployment have eased monetary policy in a recession and reflated the economy once the recession has ended, bringing the unemployment rate back to its pre-recession levels. Other countries like Germany, for example, have maintained a tight monetary policy stance during the recession and refUsed to reflate the economy after the recession 255 Hysteresis as an explanation for persistently high European unemployment has been introduced by Blanchard and Summers (1986).
230
Chapter 6 Revisiting the Natural Rate Hypothesis
Figure 6.5: The Length of Disinflation and Unemployment in Germany and the United States Germany Percent
United States Percent
6 0 6 5 7 0
75
Unemployment
8 0 8 5 9 0 9 5 Inflation
Percent
Percent
60
65
70
75
80
Unemployment
85
90
95
Inflation
in order to disinflate the economy even further. However, by keeping the unemployment rate high for a long period of time, Ball argues that this made it possible for hysteresis effects to take hold, causing the natural rate of unemployment to increase. This effect is due to the long-term unemployed becoming increasingly unemployable in the labor market, either because their human capital deteriorates, or because employers view them suspiciously, or because they loose attachment to the labor force. In sum, by drawing out the disinflation over a long period of time, countries like Germany had to pay a high price for a lower inflation rate by incurring a permanently higher unemployment rate. Supportive evidence for his hypothesis is provided in Figure 6.5, which shows that disinflation periods—the shaded areas—coincide with rising unemployment rates. While such a negative short-run correlation in itself would not be surprising, since it is predicted by any short-run Phillips curve, it is noteworthy in Figure 6.5 that the disinflation periods in Germany turn out to be about double as long as those in the United States. Moreover, they are followed by a permanent increase in the unemployment rate while unemployment falls sharply in the United States once the disinflation is over. This is consistent with Ball's hypothesis that a gradual approach to disinflation can lead to a permanent increase in the unemployment rate. Ball's model implies that as time passes, tight monetary policy becomes less effective in reducing inflation, because the long-term unemployed become less of a threat to other workers in the competition for jobs, and therefore exert less downward pressure on wages. This suggests that a gradual approach to disinfla-
6.4 Explaining the Long-Run Phillips Curve
231
tion is not only costly, but also inefficient. Nordhaus (1999: 245) summarizes the lessons from Ball's model for disinflation as follows: "I would label his approach the Powell-Ball doctrine for economic stabilization: Use massive and overwhelmingly recessionary force to overwhelm the inflationary enemy. Conduct a short and vicious war. ... Stun workers but do not maim them. They should return to the negotiating table bloodied by the recent memory. Above all, avoid a European-style war of attrition in which you keep long-term unemployment high for extended periods."
6.4.4
Using Monetary Policy to Lower the Unemployment Rate Permanently
This chapter has argued that monetary policy might have contributed to the trend increase in German unemployment; the issue that remains to be resolved is whether monetary policy can also be used to permanently lower unemployment in countries like Germany. It needs to be emphasized here that the empirical evidence presented in this study suggests that to the extent that tight monetary conditions did lead to a lasting increase in unemployment, this happened almost entirely in the 1980s. This result arises mainly, because the task of reducing the trend inflation rate to acceptable levels was essentially completed by the mid1980s. Thus, a negatively sloped long-run Phillips curve cannot account for the increase in trend unemployment in the second half of the 1980s or in the 1990s, since the reduction in trend inflation in this period was marginal. Also, our bivariate Phillips curve estimates using the Keynesian identification show that high unemployment due to tight demand conditions was prevalent in the 1980s, but this ceased to be the case in the 1990s. Moreover, given the currently low levels of inflation, the unemployment costs of disinflation are unlikely to play a significant role in the future either. Hence, the issue is not so much how to engineer a disinflation without incurring high costs in terms of permanent unemployment, because Germany went through this phase aheady almost twenty years ago; rather, the issue is whether monetary policy can contribute in some way to the permanent reduction in unemployment once unemployment has shifted upwards. An important implication of the preceding theoretical discussion is that simply pursuing an expansionary policy to increase the trend rate of inflation is unlikely to lead to a permanent reduction in unemployment, because in two of the three models discussed here a low inflation rate in itself is not the cause of high unemployment.^^^ In particular, in the asymmetric information models and
In the model with the nonlinear long-run Phillips curve, the problem is indeed that the inflation rate may have become suboptimal low, and in this case, it may be useful to revisit the choice of the optimal inflation target. However, we have argued
232
Chapter 6 Revisiting the Natural Rate Hypothesis
the hysteresis model a traditional Phillips curve relation would not arise in the data, because there is an inherent trade-off between unemployment and inflation, but because a poorly conducted monetary policy can have negative long-run real effects. As argued in Chapter 2, the long-run aggregate supply curve may be vertical, but its location is endogenous to macroeconomic policy, and sustained tight demand conditions may shift this curve inwards.^^^ In these models, to be successfiil in reducing unemployment permanently, monetary policy has to reflate the economy without triggering inflationary pressures, since otherwise higher inflation would force the central bank eventually to change its course and deflate the economy again, thereby reversing previous employment gains again. If the expansionary stance cannot be sustained for a long period of time, there is no hope that firms will shift their supply curve outwards or that hysteresis will work in reverse. Regarding the hysteresis approach. Ball (1999) provides empirical and theoretical evidence that monetary policy can be successfiil in raising employment permanently with only modest inflationary costs. From a theoretical point of view, it is essential that inflation expectations have a backward-looking component for this to happen.^^^ In this case, an expansionary policy does not lead to an immediate upward revision of inflation expectations, and monetary policy may be able to reduce unemployment over a sustained period of time without triggering strong inflationary pressures. With hysteresis at work, the higher employment level resulting from the monetary stimulus may become permanent. Since this increases the productive capacity of the economy, this tends to dampen the inflationary pressures resulting from the expansionary policy, and a permanent increase in employment can be achieved at modest inflationary costs. In the next section, we are going to investigate the effectiveness of monetary policy in a model with hysteresis in more detail.
6.5
A New Keynesian Model with Hysteresis
Ball (1999) introduces hysteresis into his model by distinguishing between the effects of short- and long-run unemployment on inflation. He defines short-term unemployment, S, as workers in their first period of unemployment. Employment is defined as E, and long-term unemployment is \-E-S. He interprets a "period" as a year, since applied work usually defines long-term unemployment as unemployment beyond one year. above that this model faces the problem to explain the coexistence of low inflation and low unemployment in the 1960s. 257 See also Solow (1999: 11). 25^ For a formal exposition, see Buiter (1987).
6.5 A New Keynesian Model with Hysteresis
233
Regarding the job-matching process, Ball assumes that if E increases from its level in the previous period, E^ - E^_^ new jobs are created, with workers hired from the unemployment pool. If employment falls, then E^ - E^,^ jobs are destroyed, and the laid-off workers become unemployed. Besides job creation and destruction. Ball assumes a fixed rate of breakups of employer-employee matches in existing jobs, with the breakup rate denoted as b. Since the number of jobs continuing from the previous period is min(£',,£'^_i), the number of matches that break up is bmm{E^,E^_^). To reflect the fact that finding new jobs takes time, it is assumed that laid-off workers cannot find a new job in the same period. Thus, their jobs are filled from the previous period's unemployed. According to these assumptions, short-term unemployment is defined as follows: (6.15a)
S, = bE,_^
(6.15b) S, = £,_! - (l - b)E,
if E, > E,_^, and if E, < E,_^.
If employment increases, the only workers in their first period of unemployment are those whose matches break up. On the other hand, if employment decreases, the short-term unemployed are those whose jobs are destroyed [E^-E^_^), plus those who are separated from the remaining jobs {bEX In steady state, we have E^ = Ef_^ = E, which implies S = bE. So far, the model outlined here corresponds to a conventional search model of the labor market. Hysteresis effects in a macroeconomic model arise, because Ball assumes that the price-setting equation in this model can be described as a conventional expectations-augmented Phillips curve, except that only short-term unemployment enters this relation: (6.16)
Ap,=/S4?,_,-a{S/E-b),
with a>0. According to this equation, inflation is constant when the short-term unemployment rate, S/E, is at its steady state level, b. What differentiates (6.16) from conventional Phillips curve specifications is the assumption that the long-term unemployed do not put pressures on wages, for reasons which we outlined above. This model has interesting dynamics; to illustrate the effects of a disinflation policy, we assume a breakup rate of b = 0.05, and set a = 0.36 ?^^ In the initial steady state, the short-term unemployment rate is 5 percent, and we assume that the long-term unemployment rate is also 5 percent. In an effort to lower the ^^^ Ball finds that b = 0.05 corresponds to typical values for the steady state shortterm unemployment rate in OECD countries, while the choice of a = 0.36 is consistent with the findings in Roberts (1995) of the effects of unemployment on inflation using annual data.
234
Chapter 6 Revisiting the Natural Rate Hypothesis
inflation rate, we assume that the central bank engineers a demand contraction, and increases the short-term unemployment rate to 7 percent. The initial impact on the long-term unemployment rate is small, with this rate increasing only to 5.2 percent, while inflation decreases by 0.73 percent. If the central bank refuses to expand demand again in order to keep inflation at this lower level, the short-term unemployment rate returns to 5 percent, since it is pinned down by the breakup rate. However, the long-term unemployment rate increases to 7.2 percent and remains at this level. Hence, the reduction in the inflation rate comes at the cost of a signiflcant increase in long-term unemployment. If the central bank expands demand again after the initial recession, both the short-term and long-term unemployment rate return to their initial values of 5 percent. The permanent reduction in inflation is now 0.70 percent. Consequently, maintaining tight demand conditions indefinitely yields only small gains in terms of lower inflation. This result arises because if employment stays low after the initial recession, the short-term unemployed turn into long-term unemployed and stop putting pressure on wages. In fact, with ^7 = 0.05, then 95 percent of the inflation reduction fi-om a permanent employment fall is achieved by the temporary increase in short-term unemployment. The previous simulations assume that the central bank has perfect control over aggregate demand conditions, and use a Phillips curve specification based on adaptive expectations. Hence, the lack of an adequate specification of the aggregate demand block and the omission of rational expectations suggest that it would be usefiil to extend this analysis to a fiilly specified New Keynesian model, which incorporates a hysteresis mechanism. However, since (6.15) is inherently nonlinear, this poses the problem that no algorithm is yet readily available that would allow us to solve for the rational expectations equilibrium of this particular model. Therefore, in the following we are going to return to the extended New Keynesian model we simulated previously, and to introduce hysteresis into this model, we follow a suggestion by Mankiw (2001) and specify the equation for potential output as follows: (6.17)
37^ = 0.85J;,_i + 0. \y^ + ff-^ .260
We will use this specification in place of y^ = 0.95>'^_i + ef""^ used in the simulation of the New Keynesian model without hysteresis. In (6.17), we preserve the near-random walk specification of potential output common in New Keynesian models, but add a small hysteresis effect by including past actual output as a determinant of potential output. This way, potential output tends to ad260 Mankiw (2001) introduces hysteresis into a Phillips curve model with unemployment by specifying the process for the natural rate of unemployment as
6.5 A New Keynesian Model with Hysteresis just towards the level of actual output. This specification represents a short cut to modeling hysteresis, since we omit the microfoundations that would give rise to hysteresis effects, but it captures nevertheless the essential feature of these models to make the natural rate of output dependent on the actual level of output. Moreover, this specification has the advantage that it preserves the linear structure of the New Keynesian model. Finally, it should be noted that in (6.17) we keep the hysteresis parameter small in size in order to show that already a small modification of the standard New Keynesian model can have major implications for the conduct of monetary policy. In Figure 6.6, we plot the impulse response functions of the extended New Keynesian model together with the results for the hysteretic specification of this model (dotted lines). Regarding the monetary policy shock. Figure 6.6 shows clearly that adding hysteresis does not change much the properties of the New Keynesian model. From this follows that even if hysteresis is present, an expansionary monetary policy in itself would not be effective in reducing unemployment permanently, because the boom created by a stimulating monetary policy shock would not be persistent enough to allow large hysteresis effects to set in. Like monetary policy shocks, neither IS nor technology shocks would be effective in permanently reducing unemployment, since the output response in both cases is again not persistent enough for hysteresis to have significant effects. It needs to be emphasized here that we obtain these results even though the model used here includes already all the elements typically used in New Keynesian models to enhance the persistence of variables. However, our simulation exercise shows that the results for the price shock in the model with hysteresis differ substantially from those found in the nonhysteretic model. In particular, in the case of the price shock, the recession induced by the sustained monetary policy tightening in response to the increase in inflation is deep and long enough for significant hysteresis effects to take hold. Figure 6.6 shows that after five years about one-third of the peak effect of the monetary tightening on output is still present in the output series.^^^ This result is consistent with Ball's hypothesis that a disinflation drawn out over a long period of time can have significant adverse effects on real variables if hysteresis is present. These results suggest that an opportunistic monetary policy, which stimulates the economy in the presence of a negative price shock, could be effective in lowering the unemployment rate permanently. A negative price shock lowers the inflation rate for a relatively long time, which offers monetary policy the opportunity to pursue a sustained expansionary stance without triggering inflationary pressures, thereby being able to engineer a boom long enough for hysteresis to work in reverse. However, the response to a positive price shock, which leads to ^"^ Since our model continues to have a stationary structure, the effect of the price shock on output dissipates eventually. However, this takes so long that one can characterize these effects as nearly permanent.
235
236
Chapter 6 Revisiting the Natural Rate Hypothesis
Figure 6.6: Impulse Response Functions for the New Keynesian Model y response
ybar response
Rresponse
dp response 1
monetary o policy -0.5 shock
0.5
0
\>--s=^;---—'
pnce shock
technology shock
an increase in inflation, would have to be asymmetric. That is, monetary policy would have to respond either with a sharp but short tightening of policy to reign in the inflationary pressures without causing a long recession, or it would have to respond to a positive price shock in a much weaker manner than to a negative shock, thereby avoiding a deep recession in the first place. As long as the commitment of the central bank to the inflation target is credible, such a response would not lead to a permanently higher inflation rate following the price shock. This asymmetric response is essential for monetary policy to have a permanent effect on output, because if the distribution of price shocks is symmetric in the sense that over time as many negative and as positive shocks occur, a symmetric policy response implies that the positive and negative long-run effects of monetary policy actions would cancel each other out. However, even though these results point to some potential of monetary policy to contribute to the objective of lowering unemployment in Germany, it is worth noting that the New Keynesian model with hysteresis would not give rise to the negative long-run relationship between inflation and unemployment which we observe in the data. The reason for this is that in this model only price shocks
6.5 A New Keynesian Model with Hysteresis lead to persistent effects of monetary policy, and these shocks push unemployment and inflation into the same direction, thereby giving rise to a positive and not a negative long-run relationship between these two variables. To obtain a negative long-run relationship, the effects of aggregate demand disturbances would have to be considerably more persistent than they are in the present model. Since we have already included habit persistence in the IS curve to make the effects of IS and monetary policy shocks more persistent, additional mechanisms inducing even more persistence would be needed. Including capital accumulation into the model might lead to some additional persistence, but this is an area for further research. In sum, in this section we showed that the New Keynesian model has difficulties accounting for the long-run correlations that we observe in the German data. In particular, we find that the natural rate hypothesis central to New Keynesian models is inconsistent with the negative long-run correlation between inflation and unemployment that is clearly present in the 1980s. There are, however, a number of approaches in modem macroeconomics which could give rise to such a correlation. Since in all these models nonlinearities play an important role, they deviate from the New Keynesian model in a significant way, since the latter is inherently linear. In fact, the discussion in the preceding section has shown that nonlinearities may also play an important role for the short-run dynamics of the New Keynesian model. Interestingly, the inclusion of nonlinearities represents also a return to the past, since ahready the earliest Keynesian models included such asymmetries in the form of downward but not upward rigid nominal wages. This suggests the possibility that present-day New Keynesian models may be missing an important aspect of earlier Keynesian models that may be crucial for explaining the German experience. Even though these asymmetries are difficult to model, it might be nevertheless worthwhile to pursue this avenue to gain a better understanding of the limits and potential of monetary policy in European economies that sufferfi-ompersistently high unemployment.
237
Concluding Remarks
This study has shown that the debate between Keynesians and monetarists is inextricable linked to the validity of the natural rate hypothesis. Empirically, on balance the evidence presented here shows that the natural rate hypothesis does not present an adequate description of the German data, at least not in an exact sense. Whether the deviations from the natural rate hypothesis are economically significant is, however, a matter of debate. It turns out that the cointegration analysis in this study establishes an upper bound for the effects of macroeconomic conditions on unemployment, suggesting that up to three percentage points of present unemployment in West Germany could be due to effects of tight demand conditions. According to this analysis, most of this reflects a permanent increase in unemployment in the 1980s when the Bundesbank tightened demand to lower the average inflation rate. Nevertheless, even if one accepts this estimate, and given that average unemployment in West Germany was approximately 9 percent in the 1990s, the monetarist view that unemployment in Germany has mostly structural causes remains essentially intact. Moreover, different approaches to testing the natural rate hypothesis or a different sample period would all lead to smaller estimates of the role of aggregate demand for the trend rate of unemployment. Still, this does not mean that the effects of demand conditions on unemployment are negligible, and the debate on the contribution of monetary policy to the German unemployment problem is certainly legitimate. Hence, the evidence presented here tends to rule out "extremist" positions claiming that unemployment is either entirely an aggregate demand problem or only due to structural causes, from which follows there remains a large middle ground which is open to debate. From a theoretical perspective, this study has reviewed the contribution of New Keynesian economics to the policy debate in Germany. The New Keynesian model has gained widespread acceptance in recent years, because it embodies elements of several of its predecessors. These include a Keynesian transmission mechanism, rational expectations as in New Classical models, an intertemporal optimizingframeworkcommon in RBC models, and a vertical long-run Phillips curve consistent with the natural rate hypothesis championed by monetarists. Since New Keynesian models are widely used in the academic literature for the analysis of monetary policy, they are eminently relevant for the policy debate in Germany. In spite of their Keynesian transmission mechanism, the discussion in this study has shown that these models have strong monetarist policy implications.
Chapter? Concluding Remarks
239
Nevertheless, the monetarist policy implications of the New Keynesian model follow to a significant extent from its embrace of the natural rate hypothesis and the fact that the model is inherently linear. This study has not only shown that the natural rate hypothesis is inconsistent with the long-run trends in German data, but also that there are a number of alternative modeling approaches which might be more successful in this regard. That is, it is too early to declare the policy debate settled on theoretical grounds, since there is still considerable scope for both monetarists and Keynesians to develop the New Keynesian model further in order to fit it better their respective research agendas. Indeed, if monetarists and Keynesians were willing to embrace the principles of economic modeling embodied in New Keynesian economics, thereby giving their analysis a modem macroeconomic fundament, both would have a clear research agenda ahead of them. For monetarists, it would be very useful to extend the New Keynesian model by including a more refined specification of the labor market. Since monetarists emphasize the role of real wages for the German unemployment problem, a modeling of the wage-setting process is indispensable for an insightful discussion of this issue. This would also allow pinpointing the institutional characteristics of the German labor market which prevent real wages from clearing the labor market, thereby leading to concise policy recommendations. An added benefit is that modeling nominal and real wage rigidities in the labor market would lead to a better understanding of business cycle fluctuations, since these are central to the transmission mechanism in New Keynesian models. Keynesians face a somewhat more challenging task, since they would have to extend the New Keynesian model so that aggregate demand disturbances can have permanent effects on output, and, second, they would have to introduce a significant source of nonlinearities into the model. With this combination, they probably could make a theoretical case that the Bundesbank did contribute to the German unemployment problem.^^^ To obtain permanent effects of aggregate demand disturbances on output and employment, Lindbeck and Snower (1994) show that this requires aggregate demand conditions to have an effect on the supply side of the economy. This could be achieved, for example, by introducing capital accumulation into the New Keynesian model, or by modeling the rate of entry and exit of firms into the economy. The second task is more challenging, since the presence of nonlinearities in the model makes it more awkward to solve for the rational expectations equilibrium. However, without some source of nonlinearity it will be difficult to argue that monetary policy contributed in a meaningful way to the unemployment problem, since in a linear world the effects of positive and negative shocks ^"^ An alternative may lie in considering models in which the equilibrium is indeterminate. See Farmer (1999) for a discussion of the relation between these models and New Keynesian models.
240
Chapter 7 Concluding Remarks
tend to cancel each other out on average. Presumably, the monetary policy reaction function would be an important source of nonlinearity in the Keynesian version of the New Keynesian model. It should be noted, though, that making a convincing empirical case for a nonlinear reaction function will be nontrivial, since the linear Taylor function is already very successful in describing monetary policy in Germany. Looking ahead, if monetarists and Keynesians were to accept the challenge of modernizing their macroeconomic analysis and base it on a New Keynesian framework, the dialogue might become more constructive. Theoretically, the two sides would still be differentiated by different modeling choices, and presumably by differences on the empirical relevance of particular model features, but since this debate could take place within an accepted framework, the resulting discussion could actually help to advance the state of the art of applied economics in Germany. Regarding policy recommendations, both camps might also move closer together. By incorporating supply side channels into the monetary transmission mechanism, Keynesians might become more appreciative of supply side policies to raise output. Monetarists, on the other hand, would find it hard to deny that the optimal monetary policy response to labor market reforms which increase the supply potential of the economy is an easing of the policy stance to close the resulting output gap. This follows clearly from the analysis of optimal monetary policy in a New Keynesian framework. Hence, Keynesians could count on monetary policy to accommodate labor market reforms, which would allow the debate to focus on the question which particular reforms are likely to be most effective.
Appendix
A.l
Appendix for Chapter 2
Fig^reAl: Estimating the Phillips Curve: The Time Series (in percentage points) Change in the unemployment rate
-0.3
Change in the annualized monthly inflation rate
70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
242
Appendix
Figure A2: Stability of the Reduced-Form Phillips Curve Relationship
Table Al: Misspecification Tests Test AR(1-13) Jarque-Bera White
Testing the system 1.15 31.95** 1.07
Testing the single equations Aw 0.50 1.37 1.13
A^p 2.59** 32.71** 0.99
Note: The asterisks indicate a rejection of the null hypothesis at the 1% (**) level. The AR (1-13) statistic gives the result of an LM test for autocorrelated residuals up to order 13. For single equations this test statistic has a F(13, 308) distribution, in the multivariate case F(52, 588). Jarque-Bera is a normality test with a chi-square (4) distribution in the multivariate and a chi-square (2) in the univariate case. The White statistic is the test statistic of a test for heteroscedasticity. The respective distributions are F(52, 268) and F( 156, 798).
A.2 Appendix for Chapter 6
A.2
Appendix for Chapter 6
Figure A3a: Structural Break Test: Full Sample Period 1.75
1.50
0.75
0.50
0.25 \r
1970
1975
1980
1990
1985
2000
1995
Figure A3b: Structural Break Test: 1965-1979
0.50
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
243
244
Appendix
Figure A3c: Structural Break Test: 1979-1998
1985
1995
1990
Figure A4: The Time Series and Their Trend Components 3-month interest rate
1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997
unemployment rate
1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997
inflation rate
1965
1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999
2000
A. 3 An Introduction into the SVAR Methodology
A.3
An Introduction into the SVAR Methodology
A.3.1
Introduction
245
Structural vector autoregression (SVAR) models have become a popular tool in recent years in the analysis of the monetary transmission mechanism and sources of business cycle fluctuations.^^^ The SVAR methodology is now also widely implemented in standard econometric software packages like EViews or RATS, which makes it possible to make use of this methodology in relatively simple and straightforward ways.^^^ This paper aims to provide a nontechnical introduction into the SVAR analysis. Since many applied macroeconomists are familiar with the use and estimation of traditional structural models like dynamic siniultaneous equation models, this study takes this class of models as a starting point. A crucial issue in the estimation of a structural model is always the identification of the empirical model. For this reason, Section 2 begins with a review of the identification problem and illustrates the identification of a dynamic simultaneous equation model using a simple example. In Section 3 the SVAR methodology is introduced. The identification problem is the same as that in a dynamic simultaneous equation model, but SVAR models take another approach to achieve identification by focusing on the role of shocks for the dynamics of the model. This approach avoids some of the difficulties inherent in the traditional approach to identification, but it also implies that SVAR models cannot perform the same tasks as dynamic simultaneous equation models. In the field of monetary economics, for example, SVAR models are not well suited for policy simulations, which is a strength of the dynamic simultaneous equation models, but have instead an advantage in the analysis of the monetary transmission mechanism. The SVAR methodology has not remained without criticism. In Section 4 a number of objections to SVAR models are reviewed. These include doubts regarding the interpretation and importance of shocks, reservations about the undisciplined use of informal restrictions, and skepticism whether the assumptions that the identified shocks are uncorrelated can be justified. The final section offers a brief conclusion.
263 For a survey on the use of SVAR models in the monetary transmission mechanism
see Christiano et al. (1999). The seminal paper popularizing the use of SVAR models in the analysis of the source of business cyclefluctuationsis Blanchard and Quah(1989). 264 For RATS the software package MALCOLM is available, which is dedicated to SVAR analysis.
246
Appendix
A.3.2
Identification in Macroeconometric Models: A Traditional Perspective
A.3.2J
A Review of the Identification ProblenP-^^
Since dynamic simultaneous equation models and SVAR models mostly differ in their approach to identification, we review first the identification problem all empirical macroeconomic models have to confront in the estimation of structural parameters.^^^ The identification problem can be illustrated with the help of the following structural model, which is assumed to represent the "true" structure of the economy. (A.l)
rY,=BX^-¥e^ > t
where Y^ is a («xl) vector of the endogenous variables, X^ contains the exogenous and lagged endogenous variables, and I =E{ee') gives the variancecovariance matrix of the structural innovations.^^' The coefficients in F and B are the parameters of interest. The fundamental problem in the estimation of structural models is that one cannot directly estimate (A.l) and derive the "true" values of F and B. The sampling information in the data is not sufficient for this to be feasible without further identifying restrictions. There is an infinite set of different values for F and B which all imply exactly the same probability distribution for the observed data, which makes it impossible to infer from the data alone what the true values for F and B are; hence, these parameters are said to be "unidentified." To demonstrate this problem, the reduced form of model (A.l) is derived, which summarizes the sampling information in the data set. The reduced form expresses each endogenous variable solely as a function of predetermined variables (Hamilton 1994: 245): (A.2)
Y,=B*X,^u
/' with B* = F~^B and u^ = F'^e^; the variance-covariance matrix of the reduced form is given by Z^ = E{uu'). Next, we consider a different structural model. This model is obtained by premultiplying the model (A.l) by a full rank matrix Q, which leads to the new model (A.3):
^^^ The following discussion draws heavily on Faust (1998), Bagliano and Favero (1998), and Leeper et al. (1996). 266 Yox 2i discussion of the different approaches to identification proposed in the literature see Favero (2001). ^^' All variables are written in logarithms.
A.3 An Introduction into the SVAR Methodology (A.3) (A.4)
247
QrY,=QBX,+Qe,, rQY,=BQX,+eQ^,
with rQ=Qr,BQ=
QB and CQ^ = Qe,.
The reduced form of model (A.3) is given by (A.5)
Y, = PQ'BQX, + Te'ee, = r-'Q-'QBX, + F-'Q-'Qe, = P-'BX, + T-'e,.
In other words, the reduced form of model (A.3) is equal to (A.6)
y;=5*X,+w,,
which coincides with the reduced form of model (A.l). This implies that both models are observationally equivalent. This is the identification problem: Without additional assumptions, so-called identifying restrictions, no conclusions regarding the structural parameters of the "true" model can be drawn from the data, because different structural models give rise to the same reduced form. A.3.2,2 Identification in Dynamic Simultaneous Equation Models^^^ To provide some background on the origins of the structural vector autoregression approach, we show first how a dynamic simultaneous equation model is identified using the traditional approach to identification and then discuss the potential problems arising from this approach. Since the SVAR methodology was developed in response to these problems, it is helpful to have an understanding of the difficulties inherent in the traditional approach to identification. The identification of F and B requires a set of restrictions that rule out all but one Q, The matrix Q has n'^ elements that need to be pinned down by the identifying restrictions. Of those n'^ restrictions, n restrictions are simply normalizations that pick the units of the coefficients. In the traditional approach to identification the other [n-\)n identifying restrictions are obtained by imposing linear restrictions on the elements of the matrices F and B ?^^ Often exclusion restrictions are used for this purpose. Note that in the traditional approach to identification the variance-covariance matrix of the structural disturbances E^ is usually left unrestricted: In particular, it is not assumed that the structural disturbances are orthogonal. This is the crucial difference with identification in SVAR models. 268 PQJ. ^ j^Qj.g detailed discussion of simultaneous equation models see Hansen (1991: 339ff). These models are also called "Cowles Commission Models." See Favero (2001: 88ff.). ^^^ Moreover, the identifying restrictions have to fulfill the rank and order conditions for identification. For a discussion see Greene (1997: 724ff).
248
Appendix
In the remainder of this section we demonstrate how a dynamic simultaneous equation model is identified with the help of a simple bivariate model consisting of an output {y^) and a money stock variable (w,). The first variable is intended to represent a nonpolicy macroeconomic variable while the second variable represents the monetary policy instrument. The structural model is assumed to have the form (A.7)
y, = Y,m, + B^ {L)y, + B^^ (L)m, + e^,
(A.8)
m, = r,y, + B^^iL)y, + B^JL)m, + e^,,,
where B{L) denotes polynomials in the lag operator L, and Z^ is again the variance-covariance matrix of the structural disturbances.^^^ The first equation shows the impact of the monetary policy instrument on real activity. This equation is interpreted as an aggregate demand relation parsimoniously specified. An equation like (A.7) is often used to obtain estimates of the so-called dynamic multipliers of monetary policy which describe the impact of the monetary policy instrument on output. The dynamic multipliers are useful, for example, to determine the value to be assigned to m^ to achieve a given path for the macroeconomic variable y^ (Bagliano and Favero 1998: 107Iff). The second equation can be interpreted as a money supply function. Here, we assume that the central bank sets the money supply according to a feedback mechanism involving current output and the history of both variables, while discretionary policy actions are captured by the money supply shock e^^. As discussed in the preceding section, there is no way to obtain estimates of the structural parameters of interest without some identifying restrictions. The reduced form of (A.7) and (A.8) is given by the following set of equations: (A.9) (A.10)
y,=B'^(L)y,
+B;^{L)m,^u,,
m,=Bl^{L)y,^B*^^{L)y,^u^,^,,
where B* = P-^B and u = F'^e as before. Assuming a uniform lag length of ^ it is apparent that the reduced form represented by (A.9) and (A. 10) has Ak coefficients while the structural model represented by (A.7) and (A.8) has (4A: + 2) coefficients, so one identifying restriction for each equation is needed to obtain estimates of the structural parameters from the data. As noted above, identification in simultaneous equation models is typically achieved by imposing exclusion restrictions on the elements of the matrices F and B. These restrictions are imposed on the model on a priori grounds and cannot be tested. For this reason they should be based on a firm theoretical foundation. ^'70 The lag polynomial B{L) takes the general form B{L) = bxL + b2l} +... + Z>„L" .
A. 3 An Introduction into the SVAR Methodology
249
Regarding restrictions on F, one could argue that due to lags in the collection of statistics on economic activity monetary policy makers cannot observe output within the period, and, therefore, cannot respond contemporaneously to the output variable. This would suggest restricting the parameter fi ^^ ^^^^- ^^^ could also argue that monetary policy affects output only with a delay due to lags in the transmission mechanism. According to this argument, the parameter Y\ could be set to zero. With these two restrictions the matrix F becomes the identity matrix and the reduced form given by (A.9) and (A. 10) actually represents a structural model of the economy. For the moment, we will not pursue restrictions on the simultaneous relationships between the variables further, but return to this issue in the context of the SVAR analysis where this type of restriction is very popular. The model can also be identified by imposing restrictions on the elements of the matrix B, The matrix B describes the effects of the lagged endogenous variables on output and money. That is, this matrix describes the dynamic relationships between the variables in the model. The lagged endogenous variables are predetermined, meaning that they do not correlate with the contemporaneous or future realizations of the structural shocks. Variables that are predetermined can be treated, at least asymptotically, as if they were exogenous (Greene 1997: 714). Even though this makes these variables easy to handle empirically, restrictions on lagged endogenous variables are difficult to justify fi-om a theoretical perspective, since economic theory usually does not say much regarding the dynamic relationships between variables, and for this reason it is preferable to let these coefficients be determined by the data.^^^ In SVAR models, no restrictions are imposed on the elements of B. Another approach is to search for exogenous variables to help with identification.^^^ A variable is defined as strongly exogenous if it does not correlate with the contemporaneous, future or past realizations of the structural shock in the equation (Hansen 1991: 340). This is a stronger condition than that holding for predetermined variables, but fi-om the standpoint of identification both types of variables can be treated in a similar manner (Greene 1997: 714ff; Favero 2001: 88ff). Since the use of exogenous variables for identification is specific to dynamic simultaneous equation models in the sense that SVAR models consist only of endogenous variables, we concentrate in the following on the role of exogenous variables in the identification of our small simultaneous equation models. This will prove useful in bringing out the fundamental difference in identification between dynamic simultaneous equation models and SVAR models. As regards the structural model considered here, we need at least two exogenous variables to achieve identification. One of those two variables should ^^^ For a discussion see also Amisano and Giannini (1997: 22ff.). ^'^ Inclusion of exogenous variables increases the chances for the model to be identified. See Favero (2001: 88ff).
250
Appendix
be highly correlated with the aggregate demand variable but not with the policy instrument, whereas the opposite should hold for the other variable. In the following two subsections we illustrate how exogenous variables which fulfill these requirements can help with the identification of the money supply and the aggregate demand relations. A.3.2.2.1 Identification of the Money Supply Schedule To illustrate the identification principle for the money supply relation, we make the reasonable assumption that fiscal policy, which is exogenous to our model, is a major determinant of aggregate demand conditions, but is not a factor in the setting of the monetary policy course. That is, we assume that this variable can be restricted on a priori grounds to be irrelevant for the determination of money supply. Setting the coefficient for this variable to zero in the money supply equation provides the identifying restriction needed to estimate the structural parameters in this equation. The identification principle is illustrated with the help of Figure A5. Figure A5: Identifying the Money Supply Schedule
Figure A5 plots the money supply schedule MS and the aggregate demand schedule AD. Initially, the system is at point A. Next, fiscal policy is assumed to become expansionary, which is denoted by dG^. According to the identifying restriction this change in the fiscal policy stance only shifts the aggregate demand schedule, but not the money supply schedule. As regards this point, recall that the fiscal policy coefficients in the money supply function have been set to zero, so that there is no direct response of the money supply to the fiscal policy stance. This restriction ensures that the money supply schedule is pinned down in
A. 3 An Introduction into the SVAR Methodology
251
Figure A5 with respect to the fiscal policy stance. Following the fiscal impulse, the system reaches a new equilibrium in B. Next, fiscal policy is assumed to become restrictive {dG2\ moving the system to C. To see how this procedure identifies the money supply equation, it is useful to notice that the points A, B, and C provide a good description of the money supply schedule MS. In other words, changes in the fiscal policy stance are an exogenous source of shifts in the aggregate demand schedule and help to trace out the MS schedule, which is being pinned down by the identifying restriction. With the help of the fiscal policy variable and the accompanying identifying restriction it is also possible to use regression analysis methods like the two-stage least square method to obtain consistent estimates of the structural parameters in the money supply equation (Hamilton 1994: 238ff). Using an instrumental variables approach like two-stage least squares, the fiscal policy variable serves in the estimation of (A.8) as an instrument variable for the contemporaneous output variable. For the discussion of this approach it is useful to reformulate the identification problem: If one estimates (A.8) using ordinary least squares (OLS), this would lead to an inconsistent estimate of the parameter Yi > because the resulting estimate would represent an average of the structural parameters j^jand Y2 -> with weights depending on the sizes of the variances of the structural disturbances e^ and e^^. This is known as simultaneous equation bias (Hamilton 1994: 234). Technically, this bias arises because for the contemporaneous output variable in (A.8) the condition is violated that the determining variable needs to be independent of the disturbance term if the OLS estimator is to be consistent (Favero 2001: 107). The source of the problem is that the contemporaneous output variable is an endogenous variable and, therefore, it is correlated with the disturbance term e^^^. In other words, the OLS estimate of y^ is biased because output and money in our model are simultaneously determined and, hence, the output variable is a function of the disturbance term of the money supply equation. The intuition behind the instrumental variables approach is that by using for the endogenous determining variable an instrument which is uncorrelated with the disturbance term this approach reestablishes the orthogonality between the determining variable and the disturbance term, thereby obtaining a consistent estimator.^^-^ In our case the instrumental variables approach requires a variable that is highly correlated with the contemporaneous output variable, but uncorrelated with e^^^. The fiscal policy variable is such an instrument. On the one hand, this variable is likely to be highly correlated with output because it is an important factor for aggregate demand conditions. On the other hand, it is uncorrelated with the disturbance term e^^ ^, because fiscal policy is assumed to be an exogenous
^^^ For a detailed exposition of the instrumental variables estimator, see Favero (2001: lOSff.).
252
Appendix
variable and, therefore, it is not a function of the money supply variable.^^"^ Finally, according to our identifying restriction fiscal policy is not a determining variable in the money supply equation. If it were, it could not simultaneously serve as an instrument for another determining variable in this equation. In other words, the fiscal policy variable would not add a new source of information to our estimation problem in this case. But our identifying restriction rules this case out, thereby ensuring that the fiscal policy variable is a valid instrument. A.3.2.2.2 Identification of the Aggregate Demand Schedule For the estimation of the structural parameters in the aggregate demand relation an instrument is needed that is correlated with the money supply variable but not with the disturbance term e^^. Moreover, this variable should not be a factor in determining aggregate demand. Finding such a variable poses a considerable challenge. One candidate is the term spread. This variable is correlated with money supply if monetary policy makers accommodate shifts in money demand due to portfolio reallocations, which are due to exogenous changes in the term spread.^^^ In addition, one has to assume that the term spread is exogenous with respect to output, to ensure that it is not correlated with the disturbance term e^. That is, it is assumed that the term spread is not influenced by aggregate demand conditions. This is harder to justify; for instance, in an economic upswing the demand for long-term capital typically rises, leading to higher long-term interest rates and thereby increasing the term spread.^^^ Finally, one has to assume that the term spread has no direct effect on aggregate demand, which represents our identifying restriction. This assumption is also hard to justify if agents are forward-looking. We will return to this issue below. If all three assumptions hold, movements in the term spread shift the money supply function and thus help to trace out the aggregate demand schedule, which remains fixed. Another common assumption for the estimation of the aggregate demand relation is that the money variable in (A.7) is not an endogenous but an exogenous variable.^^^ With this assumption no identification problem arises in the first ^'^ If the exogeneity assumption does not hold, the fiscal variable would be just another endogenous variable like output. In this case the model given by (A.7) and (A. 8) should be extended by an additional equation modeling the fiscal policy stance as a function of the contemporaneous monetary policy stance. ^'^ The term spread is often used to model the opportunity costs of holding money. Changes in this variable lead therefore to changes in money demand. For an empirical model of money demand with this specification, see for example Coenen and Vega (1999). ^^^ For a discussion of the determinants of the yield spread, see Berk and Van Bergeijk (2000: 5ff). ^^^ For a discussion, see Bagliano and Favero (1998: 107Iff) and Leeper et al. (1996: 6ff).
A. 3 An Introduction into the SVAR Methodology
253
place. This allows us to estimate (A.7) in a straightforward way using ordinary least squares, because the problem of endogenous money is not an issue anymore. In terms of Figure A5 the money supply schedule is vertical. This assumption would hold, for example, if the central bank sets the money supply according to some predetermined schedule (for example a k% rule). This assumption has an interesting but often unnoticed implication for the variance-covariance matrix of the structural disturbances, 2"^: Since money is exogenous with respect to output, the coefficients in YJ and By^{L) in the money supply equation are zero and, moreover, the money variable is uncorrelated with the aggregate demand disturbance e^. From this follows that the structural disturbances e^ and e^^ are orthogonal.^^^ This result will be of some significance in the comparison of identification in dynamic simultaneous equation models and SVAR models. A.3.2.3 Objections to the Traditional Approach to Identification in Dynamic Simultaneous Equation Models What, if any, are the problems with this approach to identification ? A forceful critique comes from Sims (1980) who argues that truly exogenous variables are hard to come by. He notes that many exogenous variables in large macroeconomic models are treated as exogenous by default rather than as a result of there being a good reason to believe them to be strictly exogenous (Sims 1980: 5). Regarding policy variables, he points out that these typically have a substantial endogenous component, which precludes treating them as exogenous.^^^ Moreover, Sims (1980: 4) argues that there are only a few powerfiil a priori identifying restrictions. This holds in particular when one allows for agents forming their decisions on the basis of rational expectations and intertemporal optimization. The textbook paradigm for identification is a simultaneous equation model for the supply and demand of an agricultural product. In this example, a weather variable is used as an instrument to identify the demand schedule. That is, the identifying restriction is imposed on the model that weather does not affect the demand for the agricultural good directly. Sims (1980: 6) argues that even this assumption is undermined if one allows for expectations: "However certain we are that the tastes of consumers in the U.S. are unaffected by the temperature in Brazil, we must admit that it is possible that U.S. consumers, upon reading of a frost in Brazil in the newspapers, might attempt to stockpile coffee in anticipation of the frost's effect on price. Thus variables known to affect supply enter the demand equation, and vice versa, through terms in expected price." The fact that identifying restrictions are often controversial can also be illustrated with the restrictions that have been imposed on the small structural model considered here. Beginning with the identification of the money supply relation. ^^^ See also the discussion in Leeper et al. (1996: 6ff.). 2'^^ See Sims (1980: 6). For a similar argument see Bagliano and Favero (1998: 1072).
254
Appendix
it has been argued that the direct effect of fiscal policy on money supply can be restricted to zero on a priori grounds. Barro (1977) disagrees: In an influential paper he argues that due to the seigniorage to be gained from expanding the money supply there is an incentive for the government to fall back on this source of revenue when fiscal expenditure rises above trend. Accordingly he models the money supply in his model as a function of a fiscal policy proxy, while the effect of this variable on his aggregate demand variable is restricted to zero. Thus, Barro uses exactly the opposite identifying restriction than the one used here, where fiscal policy was assumed to be an important factor for demand fluctuations, but not for the monetary policy stance. The identifying restriction involving the term spread is also open to challenge. For the identification of the aggregate demand relation we assumed that the spread does not enter this relation as a determining variable. However, in New Keynesian models it is typically assumed that current real spending depends on the expected future level of real spending.^^^ Since the term spread is often used as a predictor of future economic activity, one would expect this variable to have a direct effect on current aggregate demand, thereby invalidating the identifying restriction.^^^ Since the identifying restrictions used so far are vulnerable to criticism, this would suggest searching for another set of exogenous variables to help with the identification of the aggregate demand and the money supply relations, but the challenge to find a new set of exogenous variables returns the discussion to the first point stressed by Sims, namely that there are not so many credible exogenous variables to begin with. This example illustrates that it is quite hard to find suitable instruments for identification in the traditional dynamic simultaneous equation approach.
A.3.3
The SVAR Methodology
A.3.3.1
The SVAR Model
The preceding discussion of the traditional approach to identification provides a useful background for the SVAR methodology. The bivariate structural model introduced in the last section is used here as well to demonstrate the SVAR approach to identification. But before we can discuss this issue, we need to introduce the SVAR model itself For this purpose it is useful to rewrite the structural model given by (A.7) and (A.8) in matrix form, which leads to (A.11)
rY,=B(L)Y,-^e,,
280 PQJ. ^ discussion of the forward-looking IS equation, see King (2001: 50). ^^^ See the discussion in Berk and Van Bergeijk (2000).
A.3 An Introduction into the SVAR Methodology with
Y.=
y, m,
r=
255
and -Yi
^dms
£ = dms
ms J
where a"J gives the variance of the demand innovations, O"^^ denotes the variance of the money supply innovations, and o^^^ is the respective covariance. The starting point of the SVAR analysis is the reduced form of (A.l 1), which in matrix notation is given by
(A.12) y; = r-^B(L)Y, + r-^e,, or (A.13)
Y,=B\L)Y,+u„
where, as before, B* = P-^B and u^ = P-^e^. The variance-covariance matrix of the reduced form can be written as I^ = r~^Z^r-^\ Model (A.13) is a convenient point of departure, because this system can be estimated together with Z^ in a straightforward way as a vector autoregression (VAR) model. A VAR is a system where each variable is regressed on a constant (and a deterministic time trend if necessary) and on k of its own lags as well as on k lags of the other variables. In other words, each equation in the VAR contains the same set of determining variables. This allows estimating the VAR using ordinary least squares. Next, the moving average (MA) representation of (A.13) is computed, meaning that the system is reparameterized to express the endogenous variables in Yf as a function of current and past reduced-form innovations, w,. The MA form can be obtained by rearranging (A.13), leading to
(A.14) (A.15)
Y,={I-B\L)ru,,ov r,=C(L)w,,
with C(L) = (/-5*(L))"^282 A comparison of the MA representation (A.15) with the conventional autoregressive (AR) representation (A.13) shows that in the AR representation the output variable is expressed as a function of past values of output and money, whereas in the MA representation output is expressed as a function of current and past innovations in u^ and u^^. The same holds for the money variable. Even though both forms appear to be very different from each other , they are nevertheless nothing but different representations of the same system.
282 It is assumed here that the polynomial (I -B
(L)) is invertible.
256
Appendix
For a better understanding of the MA representation it may help to write (A. 15) out, (A.16)
^dd,2
yt
m,tj
\}^ms,t J
.c
c
\J^ms,t-l
y^-'msd,!
^dms,2
^d,t-l
+ ... .
msms,l J
To demonstrate the interpretation of the matrix polynomial C{l) in (A.16), we use the coefficient Q^2 ^s an example: Since this coefficient can be expressed as dy^^2l^d,t -^dd,i'> ^^ Allows that Q^2 represents the response of output in period / + 2 to a unit innovation in the disturbance term u^ occurring in period t, holding all other innovations at all other dates constant.^^^ Accordingly, a plot of Q^^ as a ftinction ois gives the response of output over time to a unit innovation in u^^. The resulting plot is called the impulse response function of output to a unit innovation in u^^. To illustrate the concept of the impulse response function. Figure A6 plots the time path of the disturbance term u^ for this simulation experiment in the upper panel and the path of the output variable in the lower panel. In the time period prior to period t, there are no disturbances (both u^ and u^^ are set to zero) and output is at its natural level, which in this simulation experiment is set to zero. In period t, a unit innovation in u^ occurs. Afterwards, no further disturbances follow.^^"* Due to the unit innovation in w^,, output increases in period / by one unit. The response of output in the following periods shows how long it takes for output to return to its natural level if it does so at all. The system given by (A. 15) is not yet identified. In the discussion of the general identification problem it was shown that identification boils down to restricting the elements in the matrix Q so that a unique structural model can be retrieved from the data set. In the case of model (A. 11) the matrix Q has four elements. Two restrictions can be obtained from a suitable normalization of the model, which leaves two identifying restrictions to be imposed on the model. Since these restrictions have not yet been imposed on the model, it follows that the impulse response functions given by C do not have any economic meaning. In other words, even though they show the response of the economy to the reduced form disturbances u^ and u^^, this is not particularly interesting, because these disturbances are devoid of economic content, since they only represent a linear combination of the underlying structural innovations e^ and e^^, given by u^ = F'^e^. For the interpretation of the impulse response functions it would be far more interesting to decompose the system (A. 15) into
^^^ See also the discussion in Hamilton (1994: 318ff). ^^^ The disturbance term u^^ is set to zero throughout the experiment.
A.3 An Introduction into the SVAR Methodology
257
Figure A6: The Impulse Response Function of Output in Response to an Impulse in u^ Ud
-X
t-2
t-1
X-
t-\
t-\
(A.17)
7,=C(L)r-i/w,,or
(A.18)
r, = r(L)e,,
t+\
t^l
/+1
/+2
with C*(L) = C(L)r~^ containing the impulse response functions of the output and money variable to the structural innovations e^ and e^^. The difference to system (A. 15) is that the innovations in e have an economic interpretation and,
258
Appendix
therefore, the impulse response functions given by C* can be interpreted in a meaningful way. For example, C^^^ would give the response of output to a monetary policy shock, which is useful to understand the transmission mechanism of monetary policy. However, the matrix F needs to be known in order to compute C*, which returns the discussion to the familiar identification problem. A.3.3.2 Identification in the SVAR Model A.3.3.2.1 The Orthogonality Restriction The identifying restriction that distinguishes the SVAR methodology from the traditional dynamic simultaneous equation approach is the assumption in SVAR models that the structural innovations are orthogonal, that is, the innovations e^ and e^^ are uncorrelated. Formally, this requires the variance-covariance matrix 1, to have the form
^ .e =
{0}
lo
0^ <^lsj
In other words, the covariance G^^^ is restricted to zero. Since the reduced form disturbance is linked to the structural innovation by /w = e, the reduced form and the structural variance-covariance matrix are related to each other by FE^P-E^. From this follows that the orthogonality restriction imposed on E^ leads to one nonlinear restriction on F, thereby providing one of the two identifying restrictions needed here (Faust 1998: 6ff). To explain the intuition behind the orthogonality restriction in SVAR models, Bemanke (1986: 52) writes that he thinks of the structural innovations "as 'primitive' exogenous forces, not directly observed by the econometrician, which buffet the system and cause oscillations. Because these shocks are primitive, i.e., they do not have common causes, it is natural to treat them as approximately uncorrelated." Bemanke continues to point out that this does not imply that there is no contemporaneous correlation between the variables in the structural model: "However one would not want to restrict individual w' s [structural shocks in his notation] to entering one and only one structural equation, in general; thus the matrix A [here: F ] is allowed to have arbitrary off-diagonal elements. Under this interpretation, then, the stochastic parts of individual structural equations are allowed to be contemporaneously correlated in an arbitrary way; however, the correlation between any two equations arises explicitly because the equations are influenced by one or more of the same fundamental shocks u^ [here: e^\^ This discussion shows that the structural innovations occupy a central place in the SVAR approach, because they represent the driving force behind the stochastic dynamics of the variables in the model.
A. 3 An Introduction into the SVAR Methodology
259
In the dynamic simultaneous equation approach to identification the structural variance-covariance matrix 2"^ usually remains unrestricted, because the structural innovations have a fundamentally different role: They are interpreted as errors in equations, reflecting minor influences on the determined variables by nonessential factors omitted from the determining variables of the equations.^^^ That is, these errors merely represent the aggregate effects of a large number of individually unimportant variables, and hence lack economic significance (Qin and Gilbert 2001: 425). Of course, from this standpoint of view it appears odd to use the variance-covariance matrix of the structural innovations as a source of identifying restrictions. However, in Section 2 we saw that making assumptions about the exogeneity of variables can also imply orthogonality restrictions,^^^ suggesting that the differences between these two approaches may not be as pronounced as it appears on first glance.^^^ A.3.3.2.2 The Normalization of the SVAR Model Before discussing the second identifying restriction, the normalization of the SVAR model needs to be clarified. In dynamic simultaneous equation models, the structural model is expressed in AR form, and the empirical analysis seeks to obtain estimates of the parameter matrices F and B. In this framework it is convenient to normalize the model by setting the diagonal elements of F to one, yielding
In contrast to dynamic simultaneous equation models, SVAR models are based on the MA representation of the structural model, and the empirical analysis seeks to estimate the impulse response functions given by the matrix C*(L). The impulse response functions are usually computed to show the response of the model to a standard deviation shock to the structural innovations. This makes it convenient to normalize the SVAR model by setting the variances a] and cr^^ to one, because the standard deviation shocks, with this normalization, correspond to unit innovations in e^ and e^^, respectively. From this follows that the variance-covariance matrix of the structural innovations is assumed to have the form
2^^ For a detailed discussion see Qin and Gilbert (2001: 430ff). ^^" The assumption of an exogenous money supply in our bivariate structural model implies that the two structural innovations are orthogonal. ^^' For a detailed discussion of this point see Leeper et al. (1996: 9ff.).
260
Appendix
2* =
^
0 0 1
or, in brief, 2'^ = / . It needs to be emphasized that the normalization is only about the scaling of the system and nothing of substance is altered here. Technically speaking, with the structural innovations related to the reduced form disturbances by e = /w, the matrix F is normalized so that ri^P=I^=I is obtained. In dynamic simultaneous equation models the diagonal elements of F are set to one, which happens to be just another transformation of F. A.3.3.2,3 Restrictions on the Matrix F Having normalized the model, the discussion now returns to the identification issue. By imposing the orthogonality restriction and the normalization, we have restricted the variance-covariance matrix of the structural innovation to the form 2*^ = / . Since the reduced-form variance-covariance matrix is given by I^ = F-^I^F-^\ this simplifies now to I^ = F-^F-^\ There are three distinct elements in X^, which have been estimated in the first step of the SVAR procedure. The matrix F-^F~^' has four elements, so we require one more restriction to identify the model. Exclusion restrictions are imposed on the matrix F for this purpose, just as is done in traditional dynamic simultaneous equations models. But there is a subtle difference in the interpretation of these restrictions in the context of SVAR models, because the matrix F has a different role. In dynamic simultaneous equations models this matrix models the contemporaneous relationships between the variables in the model, whereas in SVAR models it models the contemporaneous relationship between reduced-form disturbances. The reason for the reinterpretation of F is that SVAR models aim to identify the structural innovations e in order to trace out the dynamic responses of the model to these shocks, which yields the impulse response functions. To this end the SVAR model focuses on the relation /w^ = e^, and identifies the structural innovations by imposing suitable restrictions on F .\n other words, in SVAR models the dynamic relationships in the economy are modeled as a relationship between shocks. To show how the "shock view" characteristic for SVAR models is related to the conventional AR representation of the structural model, we take the structural model given by (A. 11) as a starting point.^^^ Imposing the orthogonality restriction on (A.l 1) yields the following model (A. 19)
FY,=B{L)Y,^e,,
^^^ The following presentation is based on Clarida and Gertler (1997: 380ff.).
A. 3 An Introduction into the SVAR Methodology
261
where the vector e contains the structural shocks and the variance-covariance matrix has the form 2'^ = / . Next, we subtract from each side of (A. 19) the expected value of Yt implied by the model, conditional on the information available at time / - I , E^^J^. Beginning with the term on the left-hand side, according to (A. 13) the information on Y^ available at time / - I is summarized in the term B*(L)Yf, implying that the forecast error Y^ -Et_J^ is equal to the reduced-form error u^. Regarding the right-hand side of (A. 19), the term B{L)Y^ contains only variables known at time t-\ and therefore drops out, leaving only the structural innovations e^ which cannot be forecasted. This yields the familiar relationship (A.20)
ru, = e,.
To summarize, the "shock view" is obtained by removing all those components from the structural model that are expected at t-\. By focusing on the relation given by (A.20), SVAR models concern themselves only with modeling the unexpected changes in Y^. This represents a considerable departure from the traditional modeling practice, because dynamic simultaneous equation models do not make a distinction between expected and unexpected changes in Y^ in the first place.2^^ To show the implications of the "shock view" for the interpretation of the restrictions imposed on the matrix F, we consider the identification of a monetary policy shock. There are essentially two sets of restrictions that are widely used in the SVAR literature to identify the monetary policy shock.^^^ One approach is based on the assumption that the central bank cannot respond instantaneously to developments in the real economy.^^^ Imposing this restriction on (A.20) yields ^y,t
(A.21) .0
Y21.
^ms,t)
^d.t 0
ms,t J
It is apparent from (A.21) that this restriction imposes a recursive order on the reduced-form disturbances; contemporaneous causality is restricted to run from the money disturbance u^^ to the output disturbance Uy but not into the other direction.^^2 This implies that an aggregate demand shock, which corresponds to 2^^ See also Bagliano and Favero (1998: lOTlff). 2^^ See also the discussion in Bemanke and Blinder (1992: 902). ^^^ As argued in Section 2, this assumption is motivated by lags in the collection and publication of statistics for many macroeconomic variables, which make it impossible for the central bank to observe these variables within the period. This assumption, of course, is only plausible for models based on monthly or quarterly data, but is not suitable for models using annual data. ^^^ The other approach proposes just the other direction of causality by assuming that real activity variables only respond with a lag to a policy innovation. For our bivariate model this means that output does not respond instantaneously to a mone-
262
Appendix
an innovation in e^,, leads within the period to a forecast error in the output variable, but not in the money supply variable, because the central bank does not realize that this shock occurs and, therefore, fails to adjust the policy instrument accordingly. When we discussed the identification of dynamic simultaneous equation models with the help of exclusion restrictions on the matrix F, we considered a similar restriction {YI^^)Writing the model given by (A.7) and (A.8) in matrix form and restricting the parameter Yi ^^ ^^^^ we obtain y,
(A.22) vO 1
'y.^ \^ms,t J
The matrices F in (A.21) and (A.22) are practically identical.^^^ Nevertheless, they differ in their interpretation. In the simultaneous equation model the restriction on F implies that a change in the output variable, regardless whether it is expected or not, does not affect the money supply within the period. This is a considerably stronger assumption than that imposed on the SVAR model. Put another way, in the simultaneous equation model the equation for the money variable is interpreted as a central bank reaction function, showing how the central bank sets the money supply in response to current and past output, without making a distinction between expected or unexpected changes in output. The equation for the money variable in the SVAR model can also be interpreted as a reaction function of the central bank, albeit as a "reaction function in surprises," as Clarida (2000) puts it. This equation models unexpected changes in the policy stance, u^^^, as a function of unexpected changes in output, Uy^, and of unexpected discretionary policy actions, which are represented by the monetary policy shock e^^^. Up to now we have discussed only exclusion restrictions on the matrix F. In our bivariate model an exclusion restriction on F automatically imposes a recursive order on the system. This is called a Choleski decomposition. In applied work the Choleski decomposition is fairly popular, because it is easy to handle econometrically (Enders 1995: 302ff.). Nevertheless, the Choleski decomposition represents just one possible strategy for the identification of a SVAR model and should only be employed when the recursive ordering implied by this identification scheme is firmly supported by theoretical considerations. Alternatives include nonrecursive restrictions on the matrix F .^^^ Besides the restrictions on tary policy shock. For the SVAR model, this approach suggests to restrict the parameter Yn to zero. In the simultaneous equation model discussed in Section 2 this is equivalent to restricting the parameter Y\ to zero. ^^^ The elements on the diagonal of F differs, but this reflects only the different normalizations of the two models. ^^^ These have been introduced by Bemanke (1986). For another application see Blanchard(1989).
A. 3 An Introduction into the SVAR Methodology
263
contemporaneous interactions it is also possible to impose long-run restrictions on the effects of structural shocks.^^^ Finally, it is also possible to combine contemporaneous and long-run restrictions.^^^ With the help of econometric programs like MALCOLM or EViews all these identification schemes can be implemented fairly easily.^^^ A.3.3.2.4 Identification in SVAR Models Compared to the Traditional Approach to Identification The approach to identification in SVAR models is designed to avoid the problems in dynamic simultaneous equation models which often lead to "incredible" identifying restrictions, as Sims (1980) puts it. One of the major problems in the traditional approach to-identification is the difficulty of finding truly exogenous variables that can be used as instruments. This is particularly so in the field of monetary economics, because practically every variable in the monetary/financial sector is to some extent endogenously determined given well established financial markets and rational expectations. Moreover, for the same reasons it is hard to justify on a priori grounds that a given variable has no influence on another variable. That is, there are hardly any compelling identifying restrictions. In response to these difficulties, SVAR models treat all variables as endogenous. The sampling information in the data is modeled with the help of VAR models, which model each variable as a function of all other variables. Regarding the identifying restrictions, SVAR models first decompose all variables into their expected and unexpected parts. The identifying restrictions are then imposed only on the unexpected part, where plausible identifying restrictions are easier to find. With respect to monetary policy, the SVAR approach recognizes that the policy instrument is for the most part endogenously determined, which precludes treating this variable as exogenous. Having modeled the reduced form of the model with the help of a VAR system, the SVAR analysis proceeds to identify the model. To this end a "reaction function in surprises" is modeled, which expresses unexpected changes in the policy instrument as a function of unexpected changes in the nonpolicy variable and of monetary policy shocks. The objective is to identify the monetary policy shocks from this relation, which represent the discretionary component of policy, or, according to Bagliano and Favero (1998: 1074), the deviation of policy from the rule. The two authors (ibid.) justify the focus on shocks in SVAR models as follows: "the focus is not on rules but on deviations from rules, since only when central banks deviate from their rules it ^^^ The seminal article in this context is Blanchard and Quah (1989). 296 This has been introduced by Gali (1992). 29^ See Keating (1992) for a discussion on the different modeling strategies within the SVAR framework.
264
Appendix
becomes possible to collect interesting information on the response of macroeconomic variables to monetary policy impulses, to be compared with the predictions of the alternative theoretical models." To identify the monetary policy shocks in our example, we imposed the restriction that monetary policy makers cannot observe unexpected changes in output within the period. Since this restriction is based on the observation that there is a lag in the collection of statistics, this assumption is fairly unrestrictive. It is also much more plausible than the corresponding restriction in dynamic simultaneous equation models stating that monetary policy makers do not respond to output movements within the period regardless whether they expect this movement or not. However, these advantages come with a price. First, even though the restrictions imposed on the matrix F may not be particularly restrictive, the SVAR methodology requires, in contrast to simultaneous equation models, the structural innovations to be orthogonal, which is a fairly restrictive assumption, as we will see below. Second, even though the "shock view" of the SVAR approach is well suited to investigate the dynamics of a system by subjecting it to an unexpected shock, the question how the system responds to an expected change in a variable remains unanswered. This issue is taken up in the following section in more detail. A.3,3,3 Dynamic Multipliers Versus Impulse Response Functions In Section 2 we discussed modeling the effect of monetary policy on output using a dynamic simultaneous equation model. Based on estimates of the parameters Yx, Byy{L), and By^{L) this approach allows us to compute the dynamic multipliers of output which describe the impact of the policy instrument on output. Alternatively, we can investigate the effects of monetary policy using a SVAR model, and obtain an impulse response function showing how output responds to a monetary policy shock. It is tempting to interpret impulse response functions in a similar manner as dynamic multipliers.^^^ In particular, we may be tempted to use impulse response analysis to shed some light on the issue of how long it takes until a change in the monetary policy stance reaches its full effect on output, which is an important issue in applied business cycle analysis. But impulse response analysis is unlikely to be helpful in this regard, because most monetary policy actions represent a systematic response of the central bank to the state of the economy and do not come as surprises. That is, most monetary policy actions are not monetary policy shocks. It is therefore important for applied business cycle research to know what the output effects of systematic monetary policy are, while the output effects of unanticipated, discretionary monetary policy are only of secondary interest. But impulse response analysis only says something about ^^^ For a detailed discussion of this issue see Cochrane (1998).
A. 3 An Introduction into the SVAR Methodology
265
the latter aspects, and remains largely silent on the output effects of systematic and hence anticipated monetary policy. Dynamic multipliers, on the other hand, are useful in investigating the output effects of a change in the policy stance even when the new policy stance has been widely expected, because dynamic multipliers give the impact of the policy instrument on output without distinguishing between expected and unexpected monetary policy (Bagliano and Favero 1998: 107Iff). This means that dynamic multipliers can be employed, for example, to determine the values to be assigned to the policy instrument to achieve a given output path. The difference between dynamic multipliers and impulse response functions is also a reflection of the fact that dynamic simultaneous equation models and SVAR models are designed for different tasks.^^^ In the field of monetary economics dynamic simultaneous equation models are primarily used for policy simulation, whereas SVAR models are used for the analysis of the monetary transmission mechanism. The shock analysis conducted in SVAR models is the closest approximation of a controlled experiment available in empirical economics. Once the monetary policy shock is identified, one can see the monetary transmission mechanism unfold by observing the response of the non-policy variables to this monetary impulse. The issue of reverse causality which usually plagues the analysis of dynamic relationships is not an issue in SVAR models, because by tracing out the dynamics of the system to an unexpected shock the causality is pinned down and runs unambiguously from the monetary policy shock to the other variables in the model. This kind of structural inference is not possible using the conventional reduced-form analysis of the lead/lag structure, which is often employed as an ahemative tool to investigate the transmission mechanism. For example, a cross correlogram may show that money leads output in time, but one cannot conclude from this finding that money is causal for output.^^^ The reason for this is that it is very possible that the monetary authority anticipates future movements in output and sets the contemporaneous money supply accordingly. In this case causality actually runs from output to money, even though money leads output in time.^^^ The results from the SVAR analysis are more reliable in this respect, because the simulation experiment is designed to rule out this problem.
^^^ This point is emphasized by Bagliano and Favero (1998: 1072). ^^^ The classic example to illustrate the fallacy of interpreting correlation as proof of causality is that of sales of anti-freeze fluid and winter. For a discussion of this issue see Hamilton (1994: 305ff.). ^^^ Proponents of the Real Business Cycle school use this line of argument to explain the stylized fact that money leads output in time, while maintaining that output movements are due to real shocks and not to monetary policy actions. More precisely, with cash-in-advance constraints producers have to accumulate money balances first before they can expand production in response to a (positive) real
266
Appendix
Another important advantage of S VAR models in the analysis of the monetary transmission mechanism is that the identifying restrictions imposed on these models are in many instances quite general and therefore are compatible with a wide spectrum of alternative theories (Bagliano and Favero 1998: 1074). For instance, identifying restrictions are often based on relative uncontroversial assumptions about the minimum lag of the responses of macro variables to monetary impulses, or they are derived from the institutional context. An example of the latter is the restriction employed in the preceding sections that the central bank cannot observe contemporaneous output due to lags in the collection of the relevant statistics. The use of restrictions compatible with a large number of theories allows to employ the SVAR methodology to discriminate between competing theories.^^^ To summarize, impulse response functions are a useful tool for the analysis of the monetary transmission mechanism, but they are less suited for the analysis of the effects of systematic policy or for policy simulation. In principle, SVAR models can also be employed for the latter task, but this requires modifications to the conventional impulse response analysis which are not yet standard in econometric software programs like Malcolm or EViews.^^^
A.3.4
Objections to the SVAR Methodology
The SVAR methodology has become a popular but controversial tool for the analysis of the monetary transmission mechanism and business cycle fluctuations. This section reviews the main challenges to the SVAR approach. These can be grouped into three categories: First, many observers have doubts on the role of shocks in SVAR models. Particularly in monetary economics it is questionable whether the estimated monetary policy shocks are truly measuring a relevant part of central bank behavior. Second, there is concern that the widespread use of informal restrictions in SVAR models may give rise to undisciplined data mining. This raises the broader question of what can be learned from these models if they reflect, due to the informal restrictions, largely the prejudice of the modeler. Third, the orthogonality restriction is a major source of concern.
302 303
shock. This leads to the observed correlation between money and output, even though monetary policy plays only a passive role. For an application see, for example, Sims (1992). For the analysis of systematic monetary policy using SVAR models see Cochrane (1998), Bemanke et al. (1997), Sims (1999), and Gottschalk and Hoppner (2001).
A. 3 An Introduction into the SVAR Methodology A.3.4.1
267
What Do the Shocks Mean?
The SVAR approach to analyzing the monetary transmission mechanism is often criticized on the grounds that it supposedly suggests that central banks operate as "random number generators."^^"* Since hardly any monetary authority wishes to randomize its decisions, any error is likely to be quickly reversed. This raises the question of how the monetary policy shocks in SVAR models are related to central bank behavior and how they could be large enough to matter. Regarding the second issue, it should be noted that SVAR models use monetary policy shocks to trace out the dynamics of the model and, for this purpose, the shocks need neither be large nor persistent. Nevertheless, the economic interpretation of these shocks remains an open question. Bemanke and Mihov (1996: 34) argue that "policy shocks can be generated from two realistic sources: (a) imperfect information on the part of the central bank about the current economy, and (b) changes in the relative weights put by the central bank on moderating fluctuations in output and inflation." The first source of monetary policy shocks refers to measurement errors caused by lags in the collection of data and frequent data revisions. The central bank can observe the true state of the economy and reverse policy actions due to measurement errors only after final data have become available. These policy errors due to measurement error can be identified by estimating the equation for the policy instrument in the VAR, which represents the policy rule, with revised data, that is, data that were not known contemporaneously to the monetary authority. With the policy rule based on revised data all policy actions due to misperceptions of the true state of the economy show up in the SVAR model as deviations from the policy rule, which are then interpreted as monetary policy shocks.^^^ The second source of shocks refers to the decision-making process within the central bank. The members of the central bank committee in charge of setting the money supply are likely to have different preferences regarding the relative weights to be put on the stabilizing output or on the adherence to the inflation target. As a consequence, the decision-making process itself may follow a random process, depending on shifts within the committee. In this case the random part of the reaction fiinction corresponds to the random fluctuations in central bank preferences. Thus, these random fluctuations become a usefiil source of monetary policy shocks that can be used to identify the effects of monetary surprises on macro variables. If monetary shocks are mainly due to measurement error or to the random component in the decision-making process, this suggests that they are unlikely to ^^^ On this issue, see the discussion in Bemanke and Mihov (1996) . 305 PQJ. ^ critical view of the role of measurement error as a source for policy shocks see Rudebusch (1998: 918ff).
268
Appendix
be an important source of business cycle fluctuations. Bemanke and Mihov (1998b: 872) write: "The emphasis of the VAR-based approach on policy innovations arises not because shocks to policy are intrinsically important, but because tracing the dynamic response of the economy to a monetary policy innovation provides a means of observing the effects of policy changes under minimal identifying assumptions." A.3.4.2 Do the SVAR Measures of Monetary Policy Shocks Make Sense? Closely related to the issue of the meaning of shocks is a provocative question raised by Rudebusch (1998): "Do the VAR interest rate shocks make sense?" He argues that the estimates of the impulse response functions are only reliable if the VAR measure of the policy shocks are accurate proxies of the "true" policy shocks. To shed some light on this, he computes a series of unanticipated policy shocks based on forward-looking financial-market time series as a benchmark for the VAR measure of the policy shocks. He finds the Federal fimds futurecontract series to be an unbiased predictor of the Federal funds rate. His measure of the unanticipated policy shocks is the forecast error of this financial-market series with respect to the actual Federal funds rate. Assuming that the financial markets accurately measure policy shocks, Rudebusch proceeds to show that movements in the "true" shocks account for only about 10 to 20 percent of the variation in a monetary policy shock series obtained from a standard SVAR model. In addition he shows that monetary policy shocks obtained fi'om different SVARs are only weakly correlated. Following Rudebusch's logic these results cast a dim light on the reliability of impulse response functions obtained from SVAR models. This line of reasoning has not remained unchallenged. Sims (1998: 937) points out that it is a main point of the VAR literature that "there is no reason in principle to assume that unforecastable changes in the federal funds rate are policy shocks." This puts a question mark behind the claim by Rudebusch that his forecast error series based on future contracts is an adequate measure of the "true" monetary policy shocks. In the SVAR literature the reduced form disturbances to the Federal funds rate equation correspond to forecast errors, but, as pointed out by Sims, these are not the policy shocks used as instruments in the SVAR methodology. After all, obtaining the policy shocks from the reducedform errors is exactly what identification is about. This suggests that Rudebusch's measure remains silent on one of the most important issues in the SVAR approach, namely the identification of shocks. His series is comparable with the reduced-form shocks but not with the policy shocks of interest. In this context it is also not particularly surprising that different identification schemes yield different histories of the policy innovations, so that the correlation between policy shocks derived from SVAR models is rather low.
A. 3 An Introduction into the SVAR Methodology
269
This goes some way to answer the criticism of Rudebusch, but an important issue remains unresolved: He shows that the reduced-form errors of the VAR interest rate equation are also only weakly correlated with his measure, which suggests a poor forecast performance of the VAR compared to the future rates that are probably quite close to being efficient predictors. As Rudebusch (1998: 920) notes, "it is hard to imagine that one could get the unanticipated shocks wrong [the reduced form disturbances], but still get the exogenous unanticipated shocks [the structural shocks] right." There are essentially three counter-arguments. First, Sims (1998) notes that forecast errors for the monetary policy instrument are due to two sources, namely on the one hand to surprises in private sector variables relevant for central bank behavior and on the other hand to the monetary policy innovation. The VAR literature seeks to identify the latter. If the financial markets are really good at forecasting monetary policy behavior, then the forecast error of future contracts embodies mainly the first source, which would make them worse measures of the "true" monetary policy shocks than the VAR errors, which contain both sources. Second, Kuttner and Evans (1998) show that quantitatively small deviations from perfect futures-market efficiency create a significant downward bias in the correlation metric employed by Rudebusch. They conclude that the correlation between VAR residuals and futures-market shocks is probably a poor measure of the VAR's performance. Third, Bagliano and Favero (1998) compare the monetary policy shocks derived from a VAR with three alternative measures obtained from direct observation of financial market behavior. The authors apply the same identification scheme to all four series, which allows them to compute the impulse response functions for the different policy shock measures. Bagliano and Favero (1998: 1111) find that "despite of the not very high correlation between the benchmark VAR and the alternative measures of monetary policy shocks, the descriptions of the monetary transmission mechanism obtained by impulse response fiinctions estimated are not substantially different from each other." To summarize, while Rudebusch initiated a fhiitful discussion, it appears that the SVAR approach withstands this criticism so far.^^^
^^^ Besides raising the question whether the VAR's policy shocks make sense Rudebusch also questions whether the VAR interest rate equations are reasonable. However, the issues he discusses like the choice of a time-invariant, linear structure, the scope of the information set or the long distributed lags are not particular to VAR models; any reasonably specified empirical model should pay attention to these issues. For a discussion in the VAR context see again Sims (1998) or Bagliano and Favero (1998).
270 A.3.4.3
Appendix The Use of Informal Restrictions in the Identification of Shocks
Another objection to the SVAR approach concerns the use of informal restrictions. These are indeed widespread; most researchers will have some idea how the impulse response functions to a given structural innovation should look like. For instance, with regard to the monetary policy shock a widely held view is that an increase in the money supply should lead to a temporary decrease in the shortterm interest rate, in addition this shock should trigger a positive but temporary output response followed by a sluggish but lasting increase in the price level. Having imposed the formal identifying restrictions, many SVAR modelers check in a next step whether the estimated impulse response functions are in accordance with their a priori views. If they find implausible responses, usually the researcher returns to the specification of his model and examines whether it is possible to come up with a more plausible model. This kind of procedure leads to the charge that SVAR analysis is prone to undisciplined data mining. Leeper et al. (1996: 5ff) respond to this by pointing out that the use of informal restrictions "differs from the standard practice of empirical researchers in economics only in being less apologetic. Economists adjust their models until they both fit the data and give 'reasonable' results. There is nothing unscientific or dishonest about this. It would be unscientific or dishonest to hide results for models that fit much better than the one presented (even if the hidden model seems unreasonable), or for models that fit about as well as the one reported and support other interpretations of the data that some readers might regard as reasonable." Nevertheless, since informal restrictions are often not made explicit some care is warranted when interpreting impulse response functions. Uhlig (1999) argues that otherwise some degree of circularity may arise in the way conclusions are drawn from the SVAR literature. For instance, consider the fi*equent finding in the SVAR literature that there are no long-run effects of monetary policy shocks on output. It is tempting to conclude that this proves conclusively the notion that money is neutral in the long run. However, this line of reasoning is likely to suffer from circularity, because the long-run neutrality of money is exactly of one of those restrictions that is frequently used either formally or informally to specify the SVAR model in the first place. Related to the issue of informal restrictions is the question of whether the SVAR methodology is a suitable tool to establish stylized facts in order to discriminate between different theoretical models. Even though the formal identifying restrictions may be weak enough to be compatible with a number of theories, the presence of informal restrictions makes it almost unavoidable that the impulse response functions reflect at least to some degree the preconceived ideas of the modeler about the dynamics of the system.^^^ This puts some doubt ^^^ Uhlig (1999) proposes a procedure which formalizes common informal restrictions for the shape of impulse response functions, which is a useftil step to enhance the transparence and to investigate the robustness of SVAR results.
A. 3 An Introduction into the SVAR Methodology
211
on the claim that impulse response functions are as impartial as the more traditional cross-correlation statistics when it comes to establishing stylized facts. A.3.4.4
What Are SVAR Models Good For?
The preceding discussion may raise the question of what impulse response functions are actually good for when they reflect as much the prejudices of the modeler as the sampling information in the data. As regards this point, it needs to be emphasized that SVAR models are structural models—after all, this is what the S stands for. Therefore, they are intended to represent a "true" model of the economy. Since the sampling information alone does not reveal what the "truth" is, some a priori held views have to be imposed to identify the empirical model. This holds for every structural macroeconometric model. That is, any structural model, be it an SVAR or a simultaneous equation model, reflects the prejudice of the modeler to some degree. Structural modeling always means that one has to take a stand on the way the economy works. From this point of view the identifying restrictions are derived, and finally the corresponding empirical model is estimated. Having done this, one can test overidentifying restrictions to investigate those aspects of the theoretical model that have not been imposed a priori on the empirical model. This modeling strategy is, for instance, neatly summarized by the title chosen by Gali (1992) for his seminal paper "How Well Does the IS-LM Model Fit Postwar US Data?". In this paper Gali takes the IS-LM model as the starting point, imposes the corresponding identifying restrictions on the data, and proceeds to check whether the unrestricted aspects of the empirical model conform with the underlying theoretical model. He finds that his model fits the data quite well, which, of course, falls well short of claiming that his model is the "true" model, because nothing is said about the ability of competing models to fit the data. They might do so as well or even better. The modeling strategy implemented by Gali shows that it is a strength of the SVAR framework that it allows it to explore what exactly a given theoretical view implies for the dynamic linkages in an empirical model which has been identified on this basis. The dynamic linkages are represented in the form of impulse response functions, which are easy to interpret. In addition it is possible to quantify the role of the individual structural shocks for the variability of the variables in the model. For instance, Gali presents a historical decomposition of the output series, which links different business cycle episodes to specific shocks hitting the economy. To summarize, the SVAR approach is useful to explore what a given theoretical view implies for the dynamic behavior of the variables of interest. Or, as Breitung (1998: 389) puts it, SVAR models are useful to take a theory-guided look at the data.
272
Appendix
A.3.4.5 The Orthogonality Restriction A major objection to the SVAR methodology concerns the orthogonality restriction for the structural shocks. As has become apparent, this restriction is central for the SVAR identification approach. To illustrate the potential problems with the orthogonality assumption, we consider the bivariate model comprised of the unemployment rate and the growth rate of output. This model has been popularized by Blanchard and Quah (1989), who identify a demand and a supply shock with the help of the restriction that a demand shock cannot have long-run effects on the level of output. This model has become a standard tool in the analysis of the sources of business cycle fluctuations. The problem with the model proposed by Blanchard and Quah is that even though it is in accordance with simple textbook versions of the macroeconomy, the system's low dimension proves to be highly restrictive when seen in the context of the more elaborate theoretical models where there are more than two shocks. Blanchard and Quah recognized this potential weakness and derived the conditions under which this approach may still lead to meaningful results. The starting point of their analysis is the assumption that the economy is driven by m shocks, but each shock is either a supply or a demand shock. This is still quite restrictive, because it implies that all shocks can be classified as belonging either to the one group or to the other. It also implies that all supply disturbances have permanent output effects, while all demand disturbances have only a transitory effect on output. The two authors demonstrate that this additional assumption is not sufficient to prevent the commingling of shocks, i.e., the identified shocks are likely to be a mixture of both underlying shocks. In their final step, they proceed to prove that the commingling of shocks is avoided when the dynamic relationship between output and unemployment remains the same across different supply disturbances, with the same result holding for all demand disturbances. The authors note that this is highly plausible for demand disturbances, but not for supply disturbances. This analysis has recently been extended by Faust and Leeper (1997). In addition to the issue of the commingling of shocks, Faust and Leeper ask under what conditions the timing of shocks will not be distorted. They point out, for instance, that even when the identified aggregate demand shock involves only the "true" demand shocks, the SVAR identification procedure may still fail to preserve the timing of the shocks in the sense that the "true" dynamic response of the economy to any particular demand shock will differ from the estimated response of the economy to the identified aggregate demand shock. To put it differently, since the average response of output to demand disturbances is not particularly informative for a number of purposes, it is well worth asking under what conditions the estimated output response corresponds exactly to the effects
A. 3 An Introduction into the SVAR Methodology
273
of the "true" demand shocks.^^^ Faust and Leeper (1997: 349) show that preserving both the categories of the shocks and the timing of the responses requires "that each underlying shock of a given type affects the economy in the same way up to a scale factor." The intuition behind this result is simple: Since the empirical analysis yields only one output impulse response function to a demand disturbance, this one demand response could have preserved the timing of the different "true" demand disturbances only if those shocks all affect output in essentially the same way.^^^ The two authors point out that this is implausible in most cases. The problem with the low dimension of the bivariate models becomes even more serious when one does not believe that there are only two groups of fundamental shocks. A shock to the nominal exchange rate, for example, has effects both on the supply and demand side of the economy; therefore, this shock is not easily classified as belonging only to one or to the other group, but should be modeled as a distinct shock. Seen from this standpoint, the orthogonality restriction, which is based on the assumption that there are only two fundamental sources of shocks, becomes rather difficult to justify.-^ ^^ Given that it is impossible to identify three structural shocks using a bivariate model, this would suggest to turn to larger systems. However, there are limits to this, because the number of restrictions required for identification increases rapidly with the size of the system. Garratt et al. (1998), for example, consider an eight-variable model, which implies the need of 28 restrictions to exactly identify the impulse response functions. In this context, they note that "it is not clear how these restrictions could be obtained, let alone motivated from an appropriate economic theory perspective." Also, the number of underlying structural disturbances in their theoretical model is considerably larger than the number of reduced-form disturbances, which alone precludes the orthogonalization of the variance-covariance matrix. Instead they compute so-called "Generalised Impulse Responses," which give the time profile of the effects of a unit shock to a particular equation on all the endogenous variables. The advantage of this procedure is that it does not require the orthogonalization of shocks. The disadvantage is that no economic interpretation is given to the shock. Rather, these 308 PQJ. instance, the estimated output response to an aggregate demand response is of little help when the effects of a foreign demand shock are of interest. The problem is that under the conditions outlined by Blanchard and Quah to avoid the commingling of shocks the estimated aggregated demand response represents the average of the output responses to diverse demand shocks and there is no way of disentangling the responses of output to the foreign demand shock, which is of interest here. ^^^ The scaling does not affect the shape of the impulse response function. ^^^ If there are indeed three types of fiindamental shocks, the two structural shocks identified in the bivariate framework are likely to represent linear combinations of these three shocks and there is no reason to expect them to be orthogonal.
274
Appendix
shocks are thought of as representing those typically observed in the past, but this vagueness makes the interpretation of the "Generalised Impulse Responses" quite hard. This discussion suggests that the orthogonality restriction is likely to be a very restrictive assumption in most cases. However, the SVAR methodology is not alone with this problem, because the assumption of an exogenous money supply in the traditional approach to identification was shown in Section 2 to imply also the assumption that the structural innovations are uncorrelated.^^^ This usually remains unnoticed, because in our example it was sufficient to estimate only the output equation to identify the parameters in the aggregate demand relation. In a SVAR model, on the other hand, both the output and money equations are estimated. The imposition of the orthogonality restriction leads in the SVAR methodology to an explicit restriction on F so that this matrix fulfills the condition FE^r'^E^. This is not the case in the traditional approach, because there the reduced-form variance-covariance matrix E^ does not enter the considerations in the first place. Leeper et al. (1996: 9) notice in this context: "In practice, traditional SE [simultaneous equation] approaches often focus on the equations and treat the rest of the stochastic structure casually." Moreover, they point out that the correlation among disturbances is a serious embarrassment when a model is used for policy analysis, as is often the case with dynamic simultaneous equation models. Leeper et al. (1996: 9) write: "If disturbances to the monetary policy reaction function are strongly correlated with private sector disturbances, how can one use the system to simulate the effects of variations in monetary policy? In practice, the usual answer is that simulations of the effects of the paths of policy variables or of hypothetical policy rules are conducted under the assumption that such policy changes can be made without producing any change in the disturbance term in other equations, even if the estimated covariance matrix of disturbances shows strong correlations." Seen in this light it is an advantage of the SVAR methodology that it treats the stochastic structure of the model explicitly.
A.3.5
Conclusion
The discussion in this part of the Appendix has shown that SVAR models are a useful tool for analyzing the dynamics of a model by subjecting it to an unexpected shock. Since the identifying restrictions are often compatible with a wide spectrum of alternative theories, the SVAR methodology is frequently employed to investigate the monetary transmission mechanism. However, since informal restrictions play an important role in the practice of SVAR modeling, ^ ^ ^ See also the discussion in Leeper et al. (1996: 9ff.).
A. 3 An Introduction into the SVAR Methodology
21S
this methodology is less capable to discriminate sharply between competing theories, but rather allows a theory-guided look at the data. Another application includes the analysis of the sources of business cycle fluctuations. The ability of SVAR models to attribute a specific business cycle episode to the occurrence of demand or supply (or other) shocks is presumably of considerable value for applied business cycle research. The discussion in the preceding section has also shown, however, that the orthogonality restriction, which is fundamental to identification, is likely to be a fairly restrictive assumption due to the low dimension of many SVAR models. As a consequence, the commingling of shocks is an issue. This means that an identified demand shock, for example, is comprised of "true" demand shocks and other underlying shocks. This puts a question mark behind the reliability of the results of SVAR models. Nevertheless, even though this suggests characterizing this methodology as useful but not particular reliable, this puts the SVAR models into good company, because a similar judgment is likely to hold for most econometric methods, particularly for dynamic simultaneous equation models.
References
Akerlof, G.A., and J.L. Yellen (1985). A Near-Rational Model of the Business Cycle, with Wage and Price Inertia. Quarterly Journal of Economics 100 (402): 25-50. Akeriof, G.A., W.T. Dickens, and G.L. Perry (2000). Near-Rational Wage and Price Setting and the Long-Run Phillips Curve. Brookings Papers on Economic Activity (1): 1-60. Altimari, N.S. (2001). Does Money Lead Inflation in the Euro Area? ECB Working Paper 63. ECB, Frankfurt am Main. Amisano, G., and C. Giannini (1997). Topics in Structural VAR Econometrics. Berlin: Springer. Andersen, T.M. (1998). Staggered Wage-Setting and Output Persistence. Working Paper 14. Department of Economics, University of Aarhus, Aarhus. Artis, M.J., Z.G. Kontolemis, and D.R. Osbom (1997). Business Cycles for G7 and European Countries. Journal of Business 70 (2): 249-279. Bagliano, F.C., and C.A. Favero (1998). Measuring Monetary Policy with VAR Models: An Evaluation. European Economic Review 42 (6): 1069-1112. Ball, L. (1991). The Genesis of Inflation and the Costs of Disinflation. Journal of Money, Credit and Banking 23 (3): 439-461. Ball, L. (1996). Disinflation and the NAIRU. NBER Working Paper 5520. NBER, Cambridge, Mass. Ball, L. (1999). Aggregate Demand and Long-Run Unemployment. Brookings Papers on Economic Activity (2): 189-251. Ball, L., and N.G. Mankiw (1994a). A Sticky-Price Manifesto. Carnegie-Rochester Conference Series on Public Policy 41: 127-151. Ball, L., and N.G. Mankiw (1994b). Asymmetric Price Adjustment and Economic Fluctuations. Economic Journal 104 (1): 247-261. Ball, L., and D. Romer (1990). Real Rigidities and the Non-Neutrality of Money. Review of Economic Studies 57 (2): 183-203. Ball, L., N.G. Mankiw, and D. Romer (1988). The New Keynesian Economics and the Output-Inflation Trade-Off Brookings Papers on Economic Activity (1): 1-82. Barro, R.J. (1977). Unanticipated Money Growth and Unemployment in the United States. American Economic Review, Papers and Proceedings 67 (2): 101-115.
References
277
Barro, R.J. (1979). Second Thoughts on Keynesian Economics. American Economic Review 69 (2): 54-59. Barro, R.J., and H. Grossman (1976). Money, Employment and Inflation. Cambridge: Cambridge University Press. Baxter, M., and R.G. King (1995). Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series. NBER Working Paper 5022. NBER, Cambridge, Mass. Baxter, M., and R.G. King (1999). Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series. Review of Economics and Statistics 81 (4): 575-593. Bean, C.R. (1994). European Unemployment: A Survey. Journal of Economic Literature 32 (2): 5?3-619. Berk, J.M., and P. Van Bergeijk (2000). Is the Yield Curve a Useful Information Variable for the Eurosystem? ECB Working Paper 11. ECB, Frankfurt am Main. Bemanke, B.S. (1986). Alternative Explanations of the Money-Income Correlation. Carnegie-Rochester Conference Series on Public Policy 25: 49-100. Bemanke, B.S., and A.S. Blinder (1992). The Federal Funds Rate and the Channels of Monetary Transmission. American Economic Review 82 (4): 901-921. Bemanke, B.S., and M. Gertler (1995). Inside the Black Box: The Credit Channel of Monetary Policy Transmission. Journal ofEconomic Perspectives 9 (4): 27-48. Bemanke, B.S., and I. Mihov (1996). What Does the Bundesbank Target? NBER Working Paper 5764. NBER, Cambridge, Mass. Bemanke, B.S., and I. Mihov (1998a). The Liquidity Effect and Long-Run Neutrality. NBER Working Paper 6608. NBER, Cambridge, Mass. Bemanke, B.S., and I. Mihov (1998b). Measuring Monetary Policy. Quarterly Journal ofEconomics 113 (3): 869-902. Bemanke, B.S., M. Gertler, and M. Watson (1997). Systematic Monetary Policy and the Effects of Oil Price Shocks. Brookings Papers on Economic Activity (1): 91-157. Beyer, A., and R.E.A. Farmer (2002). Natural Rate Doubts. ECB Working Paper 121. ECB, Frankfurt am Main. Blanchard, O.J. (1989). A Traditional Interpretation of Macroeconomic Fluctuations. American Economic Review 79 (5): 1146-1164. Blanchard, O.J. (1990). Why Does Money Affect Output? A Survey. In B.M. Friedman and F.H. Hahn (eds.). Handbook of Monetary Economics. Vol. II. Amsterdam: Elsevier. Blanchard, O.J., and N. Kiyotaki (1987). Monopolistic Competition and the Effects of Aggregate Demand. American Economic Review 11 (4): 647-666. Blanchard, O.J., and D. Quah (1989). The Dynamic Effects of Aggregate Demand and Supply Disturbances. American Economic Review 79 (4): 655-73.
278
References
Blanchard, O.J., and L.H. Summers (1986). Hysteresis and the European Unemployment Problem. NBER Macroeconomics Annual 1: 15-78. Bleakley, H., and J.C. Fuhrer (1997). Shifts in the Beveridge Curve, Job Matching and Labor Market Dynamics. New England Economic Review (September/October): 3-19. Breitung, J. (1998). Neuere Eritwicklungen auf dem Gebiet okonometrischer Strukturmodelle: Strukturelle Vektorautoregressionen. ifo Studien 44 (4): 371-392. Buiter, W.H. (1980). The Macroeconomics of Dr. Pangloss. Economic Journal 90 (1): 34-50. Buiter, W.H. (1983). Real Effects of Anticipated and Unanticipated Money—Some Problems of Estimation and Hypothesis Testing. Journal of Monetary Economics 11 (2): 208-224. Buiter, W.H. (1988). The Right Combination of Demand and Supply Policies: The Case for a Two-Handed Approach. In H. Giersch (ed.), Macro- and Micro-Policies for More Growth and Employment. Tiibingen: Mohr. Bullard, J. (1999). Testing Long-Run Monetary Neutrality Propositions: Lessons from the Recent Research. Federal Reserve Bank of St. Louis Review 81 (6): 57-77. Bullard, J., and J.W. Keating (1995). The Long-Run Relationship between Inflation and Output in Postwar Economies. Journal of Monetary Economics 36 (3): 477-496. Burda, M., and C. Wyplosz (1997). Macroeconomics—A European Text. Oxford: Oxford University Press. Calvo, G.A. (1983). Staggered Prices in a Utility-Maximizing Framework. Journal of Monetary Economics 12 (3): 383-398. Canova, F. (1994). Testing Long-Run Neutrality: Empirical Evidence for G7-Countries with Special Emphasis on Germany. A Comment. Carnegie-Rochester Conference Series on Public Policy 41 (December): 119-125. Carstensen, K. (2002). Estimating a Generalized New Phillips Curve for Germany. Mimeo. Institute of Statistics and Econometrics at the University of Kiel, Kiel. Carstensen, K., and J. Gottschalk (2001). Inflationary Shocks in a Small Monetary Model of Germany. Working Paper 151/01. Institute of Statistics and Econometrics at the University of Kiel, Kiel. Casares, M., and B.T. McCallum (2000). An Optimizing IS-LM Framework with Endogenous Investment. NBER Working Paper 7908. NBER, Cambridge, Mass. Christiano, L.J., M. Eichenbaum, and C.L. Evans (1999). Monetary Policy Shocks: What Have We Learned and to What End? In J.B. Taylor and M. Woodford (eds.). Handbook of Macroeconomics. Amsterdam: Elsevier. Clarida, R.H. (2000). The Empirics of Monetary Policy Rules in Open Economies. Mimeo. Columbia University, New York.
References
279
Clarida, R.H., and M.L. Gertler (1997). How the Bundesbank Conducts Monetary Policy. In CD. Romer and D.H. Romer (eds.), Reducing Inflation: Motivation and Strategy. NBER Studies of Business Cycles 30. Chicago: University of Chicago Press. Clarida, R.H., J. Gali, and M.L. Gertler (1998). Monetary Policy Rules in Practice: Some International Evidence. European Economic Review 42 (6): 1033-1067. Clarida, R.H., J. Gali, and M.L. Gertler (1999). The Science of Monetary Policy: A New Keynesian Perspective. Journal ofEconomic Literature 37 (4): 1661-1707. Cochrane, J.H. (1998). What Do the VARs Mean? Measuring the Output Effects of Monetary Policy. Journal of Monetary Economics 41 (2): 277-300. Coenen, G., and J.-L. Vega (1999). The Demand for M3 in the Euro Area. ECB Working Paper 6. ECB, Frankfiirt am Main. De Long, J.B. (2000). The Triumph of Monetarism? Journal of Economic Perspectives 14(1): 83-94. De Long, J.B., and L.H. Summers (1988). How Does Macroeconomic Policy Affect Output? Brookings Papers on Economic Activity (2): 433-480. Deutsche Bundesbank (1995). Monatsbericht. August. Frankfurt am Main. Deutsche Bundesbank (1999). Monatsbericht. April. Frankfurt am Main. Dolado, J.J., J.D. Lopez-Salido, and J.-L. Vega (1997). Spanish Unemployment and Inflation Persistence: Are There Phillips Trade-Offs? Documento de Trabajo 9712. Banco de Espana, Servicio de Estudios, Madrid. Doomik, J.A. (1998). Approximations to the Asymptotic Distributions of Cointegration Tests. Journal ofEconomic Surveys 12 (5): 573-593. Dopke, J. (1999). Predicting Germany's Recessions with Leading Indicators—Evidence fi*om Probit Models. Kiel Working Paper 944. Kiel Institute for World Economics, Kiel. Elliott, G., T.J. Rothenberg, and J.H. Stock (1996). Efficient Tests for an Autoregressive Unit Root. Econometrica 64 (4): 813-836. Elmeskov, J. (1993). High and Persistent Unemployment: Assessment of the Problem and Its Causes. OECD Economic Department Working Paper 132. OECD, Paris. Elmeskov, J. (1998). The Unemployment Problem in Europe: Lessons from Implementing the OECD Jobs Strategy. Cahiers BEJ 3(1): 29-54. Elmeskov, J., and M. MacFarlan (1993). Unemployment Persistence. OECD Economic Studies 21. Paris: OECD. Enders, W. (1995). Applied Econometric Time Series. New York: Wiley. Espinosa-Vega, M.A. (1998). How Powerful Is Monetary Policy in the Long Run? Federal Reserve Bank ofAtlanta Economic Review 83 (3): 12-31. Espinosa-Vega, M.A., and S. Russell (1997). History and Theory of the NAIRU: A Critical Review. Federal Reserve Bank ofAtlanta Economic Review 82 (2): 4-25.
280
References
Estrella, A., and J.C. Fuhrer (1998). Dynamic Inconsistencies: Counterfactual Implications of a Class of Rational Expectations Models. Working Paper 98-5. Federal Reserve Bank of Boston, Boston. Fabiani, S., and R. Mestre (2000). Alternative Measures of the NAIRU in the Euro Area: Estimates and Assessment. ECB Working Paper 17. ECB, Frankfurt am Main. Fackler, J.S., and W.D. McMillin (1997): Historical Decomposition of Aggregate Demand and Supply Shocks in a Small Macro Model. Southern Economic Journal 64 (3): 648-664. Farmer, R.E.A. (1999). Two New Keynesian Theories of Sticky Prices. EUI Working Paper ECO 99/33. European University Institute, San Domenico. Farmer, R.E.A. (2000). Natural Rate Doubts. CEPR Discussion Paper 2426. CEPR, London. Faust, J. (1998). The Robustness of Identified VAR Conclusions about Money. Carnegie-Rochester Conference Series on Public Policy 49: 207-244. Faust, J., and E.M. Leeper (1997). When Do Long-Run Identifying Restrictions Give Reliable Results? Journal ofBusiness and Economic Statistics 15 (3): 345-353. Favero, C.A. (2001). Applied Macroeconometrics. Oxford: Oxford University Press. Fischer, S. (1977). Long-Term Contracts, Rational Expectations, and the Optimal Money Supply Rule. Journal ofPolitical Economy 85 (1): 191-205. Fisher, M.E., and J.J. Seater (1993). Long-Run Neutrality and Supemeutrality in an ARIMA Framework. American Economic Review, Papers and Proceedings 83 (2): 402-415. Franz, W. (2000). Neues von der NAIRU? ZEW Discussion Paper 00-41. ZEW, Mannheim. Friedman, B.M. (1989). Comment. NBER Macroeconomics Annual 4: 177-183. Friedman, B.M. (1995). Does Monetary Policy Affect Real Economic Activity? Why Do We Still Ask This Question? NBER Working Paper 5212. NBER, Cambridge, Mass. Friedman, M. (1968). The Role of Monetary Policy. American Economic Review 58 (1): 1-17. Friedman, M., and A.J. Schwartz (1963). A Monetary History of the United States, 1867-1960. Princeton: Princeton University Press. Fuhrer, J.C, and G. Moore (1995). Inflation Persistence. Quarterly Journal of Economics WO {\):. 127-160. Fuhrer, J.C, and S. Schuh (1998). Beyond Shocks: What Causes Business Cycles? An Overview. New England Economic Review 29 (6): 3-23. Gali, J. (1992). How Well Does the IS-LM Model Fit Postwar US Data? Quarterly Journal of Economics 107 (2): 709-738.
References
281
Gali, J., M. Gertler, and J.D. Lopez-Salido (2001). European Inflation Dynamics. European Economic Review A5 (7): 1237-1270. Gali, J., M. Gertler, and J.D. Lopez-Salido (2002a). Markups, Gaps, and the Welfare Costs of Business Cycle Fluctuations. NBER Working Paper 8850. NBER, Cambridge, Mass. Gali, J., M. Gertler, and J.D. Lopez-Salido (2002b). Markups, Gaps, and the Welfare Costs of Business Cycle Fluctuations. Revised draft (June 2002). Garratt, A., K. Lee, M.H. Pesaran, and Y. Shin (1998). A Structural Cointegrating VAR Approach to Macroeconometric Modeling. Mimeo. University of Cambridge, Cambridge. Greene, W.H. (1997). Econometric Analysis. New Jersey: Prentice Hall. Goodfriend, M., and R.G. King (1997). The New Neoclassical Synthesis and the Role of Monetary Policy. NBER Macroeconomics Annual 12: 231-283. Gordon, R.J. (1970). The Recent Acceleration of Inflation and Its Lessons for the Future. Brookings Papers on Economic Activity (1): 8-41. Gordon, R.J. (1982). Price Inertia and Policy Ineffectiveness in the United States, 18901980. Journal of Political Economy 90 (6): 1087-1117. Gordon, R.J. (1990). What Is New-Keynesian Economics? Journal of Economic Literature 2% (3): 1115-1171. Gordon, R.J. (1997). The Time-Varying NAIRU and Its Implications for Economic VoWcy. Journal of Economic Perspectives 11 (1): 11-32. Gottschalk, J., and F. Hoppner (2001). Measuring the Effects of Monetary Policy in the Euro Area: The Role of Anticipated Policy. Kiel Working Paper 1074. Kiel Institute for World Economics, Kiel. Gottschalk, J., and S. Stolz (2001). The Link of the Monetary Indicator to Future Inflation in the Euro-Area: A Simulation Experiment. Vierteljahreshefte zur Wirtschaftsforschung 70 (3): 416-433. Gottschalk, J., and W. Van Zandweghe (2001). Do Bivariate SVAR Models with LongRun Identifying Restrictions Yield Reliable Results? The Case of Germany. Kiel Working Paper 1068. Kiel Institute for World Economics, Kiel. Gottschalk, J., F.M. Rico, and W. Van Zandweghe (2000). Money as an Indicator in the Euro Area. Kiel Working Paper 984. Kiel Institute for World Economics, Kiel. Greenwald, B.C., and J.E. Stiglitz (1993). New and Old Keynesians. Journal of Economic Perspectives 7 (1): 23-44. Hamilton, J.D. (1994). Time Series Analysis. Princeton: Princeton University Press. Hansen, B.E. (1992). Testing for Parameter Instability in Linear Models. Journal of Policy Modeling 14 (4): 517-533. Hansen, G. (1989). Testing for Money Neutrality. European Journal of Political Economy 5 (\): 89-112.
282
References
Hansen, G. (1991). Neuere Entwicklungen auf dem Gebiet der Okonometrie. Zeitschrift jur Wirtschafts- undSozialwissenschaften 111 (3): 337-399. Hansen, G. (1993). Quantitative Wirtschaftsforschung. Munchen: Franz Vahlen. Ireland, P.N. (1997). A Small, Structural, Quarterly Model for Monetary Policy Evaluation. Carnegie-Rochester Conference Series on Public Policy 47: 83-108. Ireland, P.N. (2001). Money's Role in the Monetary Business Cycle. NBER Working Paper 8115. NBER, Cambridge, Mass. Jarchow, H.-J. (1998). Theorie und Politik des Geldes. Band I: Geldtheorie. Gottingen: Vandenhoeck und Ruprecht. Jeanne, O. (1998). Generating Real Persistent Effects of Monetary Shocks: How Much Nominal Rigidity Do We Really Need? European Economic Review 42 (6): 1009-1032. Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control 12 (2-3): 231-254. Kakes, J. (2000). Monetary Policy and Business Cycle Asymmetry in Germany. Kredit undKapital 33 (2): 182-197. Keating, J.W. (1992). Structural Approaches to Vector Autoregressions. Federal Reserve Bank of St. Louis Review 74 (5): 37-57. King, R.G. (2000). The New IS-LM Model: Language, Logic, and Limits. Federal Reserve Bank of Richmond Economic Quarterly 86 (3): 45-103. King, R.G., and W. Kerr (1996). Limits on Interest Rate Rules in the IS Model. Federal Reserve Bank of Richmond Economic Quarterly 82 (2): 47-75. King, R.G., and M.W. Watson (1992). Testing Long-Run Neutrality. NBER Working Paper 4156. NBER, Cambridge, Mass. King, R.G., and M.W. Watson (1994). The Post-War U.S. Phillips Curve: A Revisionist Econometric History. Working Paper Series Macroeconomic Issues 94-14. Federal Reserve Bank of Chicago, Chicago. King, R.G., and M.W. Watson (1997). Testing Long-Run Neutrality. Federal Reserve Bank of Richmond Economic Quarterly 83 (3): 69-101. King, R.G., J.H. Stock, and M.W. Watson (1995). Temporal Instability of the Unemployment-Inflation Relationship. Economic Perspectives 19 (3): 2-13. Klein, P. (2000). Using the Generalized Schur Form to Solve a Multivariate Linear Rational Expectations Model. Journal of Economic Dynamics and Control 24 (10): 1405-1423. Kuttner, K.N., and C.L. Evans (1998). Can VARs Describe Monetary Policy? In Topics in Monetary Policy Modeling. BIS Conference Papers 6. Basle: Bank for International Settlements.
References
283
Kwiatkowski, D., P.C.B. Phillips, P. Schmidt, and Y. Shin (1992). Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root. Journal of Econometrics 54 (1-3): 159-178. Learner, E.E. (1985). Vector Autoregressions for Causal Inference? Carnegie-Rochester Conference Series on Public Policy 22: 255-304. Leeper, E.M., C.A. Sims, and T. Zha (1996). What Does Monetary Policy Do? Brookings Papers on Economic Activity (2): 1-63. Lindbeck, A., and D.J. Snower (1994). How Are Product Demand Changes Transmitted to the Labour Market? Economic Journal 104 (March): 386-398. Lucas, R.E., Jr. (1972). Econometric Testing of the Natural Rate Hypothesis. In O. Eckstein (ed.). The Econometrics of Price Determination. Washington, D.C. Lucas, R.E., Jr. (1981). Tobin and Monetarism: A Review Article. Journal of Economic Literature 19 (2): 558-567. Lucas, R.E., Jr. (1987). Models of Business Cycles. Oxford: Basil Blackwell. Lucas, R.E., Jr., and T.J. Sargent (1978). After Keynesian Macroeconomics. In After the Phillips Curve: Persistence of High Inflation and High Unemployment. Boston: Federal Reserve Bank of Boston. Malinvaud, E. (1977). The Theory of Unemployment Reconsidered. New York: Halsted Press. Mankiw, N.G. (1985). Small Menu Costs and Large Business Cycles: A Macroeconomic Model of Monopoly. Quarterly Journal of Economy 100 (400): 529-537. Mankiw, N.G. (1989). Real Business Cycles: A New Keynesian Perspective. Journal of Economic Perspectives 3 (3): 79-90. Mankiw, N.G. (1990). A Quick Refresher Course in Macroeconomics. NBER Working Paper 3256. NBER, Cambridge, Mass. Mankiw, N.G. (2001). The Inexorable and Mysterious Tradeoff between Inflation and Unemployment. Economic Journal 111 (May): 45-61. Mankiw, N.G., and R. Reis (2001). Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve. NBER Working Paper 8290. NBER, Cambridge, Mass. McCallum, B.T. (1987). The Case for Rules in the Conduct of Monetary Policy: A Concrete Example. Weltwirtschaftliches Archiv 123 (3): 415-429. McCallum, B.T. (1989). Monetary Economics—Theory and Policy. New York: Macmillan. McCallum, B.T. (1997). Comment. NBER Macroeconomics Annual 12: 355-359. McCallum, B.T. (1999). Recent Developments in Monetary Policy Analysis: The Roles of Theory and Evidence. NBER Working Paper 7088. NBER, Cambridge, Mass. McCallum, B.T. (2001a). Should Monetary Policy Respond Strongly to Output Gaps? American Economic Review, Papers and Proceedings 91 (2): 258-262.
284
References
McCallum, B.T. (2001b). Monetary Policy Analysis in Models without Money. Federal Reserve Bank of St. Louis Review 83 (4): 145-160. McCallum, B.T., and E. Nelson (1997). An Optimizing IS-LM Specification for Monetary Policy and Business Cycle Analysis. NBER Working Paper 5875. NBER, Cambridge, Mass. McCallum, B.T., and E. Nelson (1999). Nominal Income Targeting in an Open-Economy Optimizing Model. Journal of Monetary Economics 43 (3): 553-578. McCallum, B.T., and E. Nelson (2001). Monetary Policy for an Open Economy: An Alternative Framework with Optimizing Agents and Sticky Prices. NBER Working Paper 8175. NBER, Cambridge, Mass. Mishkin, F.S. (1982). Does Anticipated Monetary Policy Matter? An Econometric Investigation. Journal of Political Economy 90 (1): 22-51. Nordhaus, W.D. (1999). Comment on Laurence Ball's Aggregate Demand and LongRun Unemployment. Brookings Papers on Economic Activity (2): 241-245. OECD (2000). Economic Outlook. Volume 68. Paris: OECD. Orphanides, A. (2000). The Quest for Prosperity without Inflation. ECB Working Paper 15. ECB, Frankfurt am Main. Paque, K.-H. (1999). Structural Unemployment and Real Wage Rigidity in Germany. Tiibingen: Mohr Siebeck. Peersman, G., and F. Smets (2001). Are the Effects of Monetary Policy in the Euro Area Greater in Recessions Than in Booms? ECB Working Paper 52. ECB, Frankfurt am Main. Perron, P. (1997). Further Evidence on Breaking Trend Functions in Macroeconomic Variables. Journal of Econometrics 80 (2): 355-385. Phillips, A.W. (1958). The Relationship between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957. Economica 25 (November): 283-299. Phillips, P.C.B. (1998). Impulse Responses and Forecast Error Variance Asymptotics in Nonstationary VARs. Journal of Econometrics 83 (1-2): 21-56. Plosser, C.I. (1989). Understanding Real Business Cycles. Journal of Economic Perspectives 3 (3): 51-77. Qin, D., and C.L. Gilbert (2001). The Error Term in the History of Time Series Econometrics. Econometric Theory 17 (2): 424-450. Roberts, J.M. (1993). The Sources of Business Cycles: A Monetarist Interpretation. International Economic Review 34 (4): 923-934. Roberts, J.M. (1995). New Keynesian Economics and the Phillips Curve. Journal of Money, Credit and Banking 27 (4): 975-984. Roberts, J.M. (1997). Is Inflation Sticky? Journal of Monetary Economics 39 (2): 173196.
References
285
Romer, CD., and D.H. Romer (1989). Does Monetary Policy Matter? A New Test in the Spirit of Friedman and Schwartz. NBER Macroeconomics Annual 4: 121-170. Romer, D. (1993). The New Keynesian Synthesis. Journal of Economic Perspectives 1 (1): 5-22. Romer, D. (1996). Advanced Macroeconomics. New York: McGraw-Hill. Romer, D. (2000). Keynesian Macroeconomics without the LM Curve. NBER Working Paper 7461. NBER, Cambridge, Mass. Rotemberg, J.J., and M. Woodford (1997). An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy. NBER Macroeconomics Annual 12: 297-346. Rudebusch, G.D. (1998). Do Measures of Policy in a VAR Make Sense? International Economic Review 3*9 (4): 907-931. Sachs, J.D. (1986). High Unemployment in Europe: Diagnosis and Policy Implications. NBER Working Paper 1830. NBER, Cambridge, Mass. Sachverstandigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung (1975). Jahresgutachten 1975/76 des Sachverstdndigenrates. Bonn: Deutscher Bundestag Drucksache 7/4326. Sachverstandigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung (1977). Mehr Wachstum—Mehr Beschdftigung. Jahresgutachten 1977/78 des Sachverstandigenrates. Stuttgart: Kohlhammer. Sachverstandigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung (1989). Weichenstellungen fur die neunziger Jahre. Jahresgutachten 1989/90 des Sachverstandigenrates. Stuttgart: Metzler-Poeschel. Sachverstandigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung (1998). Vor weitreichenden Entscheidungen. Jahresgutachten 1998/99 des Sachverstandigenrates. Stuttgart: Metzler-Poeschel. Sargent, T.J. (1971). A Note on the "Accelerationist" Controversy. Journal of Money, Credit and Banking 3 (3): 721-725. Sargent, T.J. and U. Soderstrom (2000). The Conquest of American Inflation: A Summary. Sveriges Riksbank Economic Review (3): 12^4. Scheide, J. (1984). Geldpolitik, Konjunktur und rationale Erwartungen. Tiibingen: Mohr Siebeck. Siebert, H. (1998). Arbeitslos ohne Ende? Strategien fur mehr Beschdftigung. Frankftirt am Main: Frankfurter Allgemeine Zeitung. Sims, C.A. (1980). Macroeconomics and Reality. Econometrica 48 (1): 1-48. Sims, C.A. (1992). Interpreting the Macroeconomic Time Series Facts: The Effects of Monetary Policy. European Economic Review 36 (5): 975-1000. Sims, C.A. (1998). Comment on Glen Rudebusch's "Do Measures of Monetary Policy in a VAR Make Sense?" International Economic Review 39 (4): 933-941.
286
References
Sims, C.A. (1999). The Role of Interest Rate Policy in the Generation and Propagation of Business Cycles: What Has Changed Since the '30s? In J.C. Fuhrer and S. Schuh (eds.), Beyond Shocks: What Causes Business Cycles? Conference Series 42. Boston: Federal Reserve Bank of Boston. Snower, D. (1997). Evaluating Unemployment Policies: What Do the Underlying Theories Tell Us? In D.J. Snower and G. de la Dehesa (eds.), Unemployment Policy: Government Options for the Labor Market. Cambridge: Cambridge University Press. Solow, R.M. (1970). Discussion of Gordon. Brookings Papers on Economic Activity (1): 42-44. Solow, R.M. (1999). How Cautious Must the Fed Be? In R.M. Solow and J.B. Taylor (eds.). Inflation, Unemployment and Monetary Policy. Cambridge: MIT Press. Solow, Robert (2000). The European Unemployment Problem. CESifo forum 1 (1): 3 20. Staiger, D., J.H. Stock, and M.W. Watson (1996). How Precise Are Estimates of the Natural Rate of Unemployment? NBER Working Paper 5477. NBER, Cambridge, Mass. Stiglitz, J. (1997). Reflections on the Natural Rate Hypothesis. Journal of Economic Perspectives 11 (1): 3-10. Stock, J.H., and M.W. Watson (1999). Forecasting Inflation. NBER Working Paper 7023. NBER, Cambridge, Mass. Svensson, L.E.O. (1997) Inflation Targeting: Some Extensions. NBER Working Paper 5962. NBER, Cambridge, Mass. Svensson, L.E.O. (1999). Monetary Policy Issues for the Eurosystem. CarnegieRochester Conference Series on Public Policy 51: 79-136. Taylor, J.B. (1979). Staggered Wage Setting in a Macro Model. American Economic Review, Papers and Proceedings 69 (2): 108-13. Taylor, J.B. (1980). Aggregate Dynamics and Staggered Contracts. Journal of Political Economy SS (I): 1-24. Taylor, J.B. (1993). Discretion versus Policy Rules in Practice. Carnegie-Rochester Conference Series on Public Policy 39: 195-214. Taylor, J.B. (2001). An Interview with Milton Friedman. Macroeconomic Dynamics 5 (1): 101-131. Tobin, J. (1980). Are New Classical Models Plausible Enough to Guide Policy? Journal of Money, Credit and Banking 12 (4): 788-799. Tobin, J. (1993). Price Flexibility and Output Stability: An Old Keynesian View. Journal of Economic Perspectives 7(1): 45-65. Tobin, J. (1996). Interview with James Tobin. The Region (December). Federal Reserve Bank of Minneapolis.
References
287
Uhlig, H. (1999). What Are the Effects of Monetary Policy on Output? Results from an Agnostic Identification Procedure. CEPR Discussion Paper 2137. CEPR, London. Weber, A.A. (1994). Testing Long-Run Neutrality: Empirical Evidence for G7 Countries with Special Emphasis on Germany. CEPR Discussion Paper 1042. CEPR, London. White, H. (1980). A Heteroskedastic-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica 48 (4): 817-838. Woodford, M. (2002). Interest and Prices. Mimeo. Available from . Wyplosz, C. (2001). Do We Know How Low Inflation Should Be? In A. Garcia Herrero (ed.). Why Price Stability? Frankfurt: ECB.