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.).
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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).
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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
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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.
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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).
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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
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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^ 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, = tiXt-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 (' - 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.
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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.
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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 •^^. " >^,) + ^^
(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£,|Xy54ijc^-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,...,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.
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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).
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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; -\,
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 r0, 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 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.
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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.
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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^
