Handbook of Macroeconomics, Volume 1B

INTRODUCTION

TO THE SERIES

The aim of the Handbooks in Economics series is to produce Handbooks for various branches of economics, each of which is a definitive source, reference, and teaching supplement for use by professional researchers and advanced graduate students. Each Handbook provides self-contained surveys of the current state of a branch of economics in the form of chapters prepared by leading specialists on various aspects of this branch o f economics. These surveys summarize not only received results but also newer developments, from recent journal articles and discussion papers. Some original material is also included, but the main goal is to provide comprehensive and accessible surveys. The Handbooks are intended to provide not only useful reference volumes for professional collections but also possible supplementary readings for advanced courses for graduate students in economics. KENNETH J. ARROW and MICHAEL D. 1NTRILIGATOR

PUBLISHER'S

NOTE

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

CONTENTS O F T H E HANDBOOK

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

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

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

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

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

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

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

Chapter 7 Learning Dynamics GEORGE W. EVANS mad SEPPO HONKAPOHJA

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

vii

Contents of the Handbook

viii PART 3 - MODELS

OF ECONOMIC

GROWTH

Chapter 9 Neoclassical Growth Theory ROBERT M. SOLOW

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

1B

PART 4 - CONSUMPTION

AND INVESTMENT

Chapter 11 Consumption ORAZIO E ATTANASIO

Chapter 12 Aggregate Investment RICARDO J. CABALLERO

Chapter 13 Inventories VALERIE A. RAMEY and KENNETH D. WEST PART 5 - M O D E L S

OF ECONOMIC

FLUCTUATIONS

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

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

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

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

Chapter 18 Job Reallocation, Employment Fluctuations and Unemployment DALE T. MORTENSEN and CHRISTOPHER A. PISSAR/DES

Contents of the Handbook

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

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

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

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

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

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

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

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

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

ix

PREFACE TO THE HANDBOOK

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

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

xi

xii

Preface

The extent to which the field has changed over the past decade is considerable, and we think that there is a great need for the survey of the current state ofmacroeconomics that we and the other contributors to this book have attempted here. We hope that the Handbook of Macroeconomics will be useful as a teaching supplement in graduate courses in the field, and also as a reference that will assist researchers in one area of macroeconomics to become better acquainted with developments in other branches of the field. Overview The Handbook of Macroeconomics includes 26 chapters, arranged into seven parts. Part 1 reviews evidence on the Empirical and Historical Performance of the aggregate economy, to provide factual background for the modeling efforts and policy discussion of the remaining chapters. It includes evidence on the character of business fluctuations, on long-run economic growth and the persistence of crosscountry differences in income levels, and on economic performance under alternative policy regimes. Part 2 on Methods of Dynamic Analysis treats several technical issues that arise in the study of economic models which are dynamic and in which agents' expectations about the future are critical to equilibrium determination. These include methods for the calibration and computation of models with intertemporal equilibria, the analysis of the determinacy of equilibria, and the use of "learning" dynamics to consider the stability of such equilibria. These topics are important for economic theory in general, and some are also treated in the Handbook of Mathematical Economics, The Handbook of Econometrics, and the Handbook of Computational Economics, for example, from a somewhat different perspective. Here we emphasize results - such as the problems associated with the calibration of general equilibrium models using microeconomic studies - that have particular application to macroeconomic models. The Handbook then tunas to a review of theoretical models of macroeconomic phenomena. Part 3 reviews Models of Economic Growth, including both the determinants of long-run levels of income per capita and the sources of cross-country income differences. Both "neoclassical" and "endogenous" theories of growth are discussed. Part 4 treats models of Consumption and Investment demand, from the point o f view of intertemporal optimization. Part 5 covers Models of Economic Fluctuations. In the chapters in this part we see a common approach to model formulation and testing, emphasizing intertemporal optimization, quantitative general equilibrium modeling, and the systematic comparison of model predictions with economic time series. This common approach allows for consideration of a variety of views about the ultimate sources of economic fluctuations and of the efficiency of the market mechanisms that amplify and propagate them. Part 6 treats Financial Markets and the Macroeconomy. The chapters in this part consider the relation between financial market developments and aggregate economic

Preface

xiii

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

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

John B. Taylor Michael Woodford

Chapter 11

CONSUMPTION

*

ORAZIO P. ATTANASIO

University College London, Institute for Fiscal Studies and NBER

Contents

Abstract Keywords 1. Introduction 2. Stylised facts 2.1. Aggregate time series data

742 742 743 745 746

2.2. Household consumption expenditure

750

2.2.1. Nature of the data sets and their comparability with the National Account data 2.2.2. Life cycle profiles

3. The life cycle model 3.1. The simple textbook model 3.2. Quadratic preferences, certainty equivalence and the permanent income model 3.3. The Euler equation approach 3.4. Precautionary motives for saving 3.5. Borrowing restrictions 3.6. Taking into account demographics, labour supply and unobserved heterogeneity 3.7. Bequest motives

4. Aggregation issues 4.1. Aggregation across consumers 4.2. Aggregation across commodities

5. Econometric issues and empirical evidence 5.1. Aggregate time series studies 5.2. Micro data: some econometric problems

751 752 760 761 762 765 770 772 777 780

781 781 782 783 784 785

5.2.1. Consistency of estimators derived from Euler equations

785

5.2.2. Average cohort techniques

787

* A preliminary draft of this chapter was presented at a conference at the New York Fed., February 27-28 1997, where I received useful comments from my discussant, Chris Carroll and several participants. Tullio JappeUi provided many careful and insightful comments for which I am very grateful. I would like to thank Margherita Borella for research assistance and James Sefton for providing me with the UK National Accounts Data. Material from the FES made available by the ONS through the ESRC Data Archive has been used by permission of the Controller of HMSO. Neither the ONS nor the ESRC Data Archive bear any responsibility for the analysis or interpretation of the data reported here.

Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor and M. Woodford © 1999 Elsevier Science B.V. All rights reserved 741

742 5.2.3. Conditional second (and higher) moments 5.3. Micro data: some evidence 6. Where does the life cycle model stand? 7. Insurance and inequality 8. Intertemporal non-separability 8.1. Durables 8.2. Habit formation 9. Conclusions References

O.P. Attanasio 788 789 791 795 798 799 802 804 805

Abstract Consumption is the largest component of GDP. Since the 1950s, the life cycle and the permanent income models have constituted the main analytical tools to the study of consumption behaviour, both at the micro and at the aggregate level. Since the late 1970s the literature has focused on versions of the model that incorporate the hypothesis of Rational Expectations and a rigorous treatment of uncertainty. In this chapter, 1 survey the most recent contribution and assess where the life cycle model stands. My reading of the evidence and of recent developments leads me to stress two points: (i) the model can only be tested and estimated using a flexible specification of preferences and individual level data; (ii) it is possible to construct versions of the model that are not rejected by the data. One of the main problems of the approach used in the literature to estimate preferences is the lack of a 'consumption function'. A challenge for future research is to use preference parameter estimates to construct such functions.

Keywords consumption, life cycle model, household behaviour JEL classification: E2

Ch. 11:

Consumption

743

1. Introduction

In most developed economies, consumption accounts for about two thirds of GDP. Moreover, it is from consumption that, in all likelihood, utility and welfare are in large part determined. It is therefore natural that macroeconomists have devoted a considerable amount of research effort to its study. In modern macroeconomics, consumption is typically viewed as part of a dynamic decision problem. There is therefore another sense in which an tmderstanding of consumption is central for macroeconomics. Consumption decisions are also saving decisions from which the funds available for capital accumulation and investment arise. Therefore, consumers attitudes to saving, risk bearing and uncertainty are crucial to understand the behaviour of capital markets, the process of investment and growth and development. It is not by chance that modern consumption theory is also used to characterise asset prices equilibrium conditions. The desire consumers might have to smooth fluctuations over time determines the need for particular financial instruments or institutions. Understanding recent trends in consumption and saving is crucial to the study, both positive and normative, of the development of financial markets, of the institutions that provide social safety nets, of the systems through which retirement income is provided and so on. One of the main themes of this chapter is that consumption decisions cannot be studied in isolation. Exactly because consumption and saving decisions are part of a dynamic optimisation problem, they are determined jointly with a number of other choices, ranging from labour supply to household formation and fertility decisions, to planned bequests. While modelling all aspects of human economic behaviour simultaneously is probably impossible, it is important to recognise that choices are taken simultaneously and to control for the effects that various aspects of the economic environment in which consumers live might have on any particular choice. This is particularly true if one wants to estimate the parameters that characterise individual preferences. Implicit in this argument is another of the main themes of this chapter: consumption decisions should be modelled within a well specified and coherent optimisation model. Such a model should be flexible and allow for a variety of factors. Indeed, I think it is crucial that the model should be interpreted as an approximation of reality and should allow for a component of behaviour that we are not able to explain. However, such a model is crucial to organise our thinking and our understanding of the data. Without a structural model it is not possible to make any statement about observed behaviour or to evaluate the effect of any proposed change in economic policy. This, however, is not a call for a blind faith in structural models. Inferences should always be conditional on the particular identification restrictions used and on the particular structural model used. Such models should also be as flexible as possible and incorporate as much information about individual behaviour as is available. It should be recognised, however, that without such models we cannot provide more than a statistical description of the data.

744

0.17. Attanasio

The other main theme of the analysis in this chapter is that to understand aggregate trends it is necessary to conduct, in most situations, a detailed analysis of individual behaviour. In other words, aggregation problems are too important to be ignored. This obviously does not mean that the analysis of aggregate time series data is not useful. Indeed, I start the chapter with a brief summary of the main time series properties of consumption. Estimation of structural models of economic behaviour, however, cannot be performed using aggregate data only. This chapter is not an exhaustive survey of the literature on consumption: such a literature has grown so much that it would be hard even to list it, let alone summarise all the contributions. What I offer, instead, is a discussion of the current status of our knowledge, with an eye to what I think are the most interesting directions for future research. In the process of doing so, however, I discuss several of the most important and influential contributions. Omissions and exclusions are unavoidable and should not be read as indicating a negative judgement on a particular contribution. At times, I simply chose, among several contributions, those that most suited my arguments and helped me the most to make a given point. Moreover, notwithstanding the length of the chapter, not every sub-fields and interesting topic has been covered. But a line had to be drawn at some point. There are four fields that I did not included in the chapter and over which I have agonised considerably. The first is asset pricing: while much of the theoretical material I present has direct implications for asset prices, I decided to omit a discussion of these implications as there is an entire chapter of this Handbook devoted to these issues. The second is the axiomatisations of behaviour under uncertainty alternative to expected utility. There are several interesting developments, including some that have been used in consumption and asset pricing theory, such as the KrepsPorteus axiomatisation used by Epstein and Zin (1989, 1991) in some fascinating papers. The third is the consideration of within-household allocation of resources. There is some exciting research being developed in this area, but I decided to draw the line of 'macro' at the level of the individual household. Finally, I do not discuss theories of consumption and saving behaviour that do not assume optimising and fully rational behaviour. Again, there is some exciting work in the area of social norms, mental accounting, time varying preferences, herd behaviour and so on. In the end, however, I decided that it would not fit with the rest of the chapter and rather than giving just a nod to this growing part of the literature I decided to leave it out completely. The chapter is organised as follows. In Section 2, I start with a brief description of some stylised facts about consumption. These include both facts derived from aggregate time series data and from household level data. Throughout the section, I use in parallel data from two countries: the USA and the UK. In Section 3, I discuss at length what I think is the most important model of consumption behaviour we have, the life cycle model. In that section, I take a wide view of what I mean by the life cycle model: definitely not the simple textbook version according to which the main motivation for saving is the accumulation of resources to provide for retirement. Instead, I favour a flexible version of the model where demographics, labour supply, uncertainty and precautionary saving and possibly

Ch. 11: Consumption

745

bequests play an important role. In other words, I consider the life cycle model as a model in which consumption decisions are determined within an intertemporal optimisation framework. What elements of this model turn out ot be more important is largely an empirical matter. Indeed, even the presence of liquidity constraints, or borrowing restrictions, can and should be incorporated within this framework. In Section 4, I discuss aggregation problems. In particular, I focus on two different kinds of aggregation: that across consumers and that across commodities. The aim of this section is not just to give lip service to the aggregation issues and proceed to sweep them under the carpet. With the development of computing and storage capability and with the availability of increasing large number of micro data sets, it is important to stress that scientific research on consumption behaviour cannot afford to ignore aggregation issues. In Section 5, I consider the empirical evidence on the life cycle model and discuss both evidence from aggregate time series data and evidence from micro data. In this section I also address a number of econometric problems with the analysis of Euler equations for consumption. In Section 6, I take stock on what I think is the status of the life cycle model, given the evidence presented in Section 5. In Section 7, I address the issues of insurance and inequality. In particular, I present some of the tests of the presence of perfect insurance and discuss the little evidence there is on the evolution o f consumption inequality and its relationship to earning inequality. Most of the models considered up to this point assume time separability of preferences. While such a hypothesis is greatly convenient from an analytical point of view, it is easy to think of situations in which it is violated. In Section 8, I discuss to forms of time dependence: that induced by the durability of commodities and habit formation. Section 9 concludes the chapter.

2. Stylised facts In this section, I document the main stylised facts about consumption behaviour using both aggregate and individual data. I consider two components of consumption expenditure: on non-durable and services and on durables. In addition I also consider disposable income. While most of the facts presented here are quite well established, the evidence in this section constitute the background against which one should set the theoretical model considered in the rest of the chapter. The data used come from two western countries: the United States and the United Kingdom. I have deliberately excluded from the analysis developing or less developed countries as they involve an additional set of issues which are not part of the present discussion. Among the developed countries I have chosen the USA and the UK both because data from these two countries have been among the most widely studied and because the two countries have the best micro data on household consumption. For

O.P. Attanasio

746

4000

UK USA - disposable income and consumption ~------150000 100000

2000

-

disposable income and consumption

50000

J J

97.1

2319 55

6's

75

as

&

65

75

85

95

Fig. 1. Disposable income (top curve) consumption, divided into durables (bottom curve) and nondurables (middle curve).

the UK, in particular, the Family Expenditure Survey runs for 25 consecutive years, giving the possibility of performing interesting exercises. 2.1. Aggregate time series data In this section, I present some of the time series properties of consumption expenditure and of disposable income. While the models considered in the following sections refer to household behaviour, typically the consumption aggregates considered in the National Account statistics include outlays of a sector that, together with households, includes other entities, such as charities, whose behaviour is unlikely to be determined by utility maximisation. While this issue is certainly important, especially for structural tests of theoretical models of household behaviour, in the analysis that follows I ignore it and, instead of isolating the part of total expenditure to be attributed to households, I present the time series properties of National Account consumption. Seslnick (1994) has recently stressed the importance of these issues. In Figure 1, I plot household (log) disposable income along with consumption divided into durables and non-durables and services for the UK and the USA. The series have quarterly frequency and run from 1959:1 to 1996:3 for the USA and from 1965:1 to 1996:2 for the UK. The data are at constant prices and are seasonally adjusted. From the figure, it is evident that non-durable consumption is smoother than disposable income. Durable consumption, on the other hand, which over the sample accounts, on average, for 13% of total consumption in the USA and around 14% in the UK, is by far the most volatile of the three time series. This is even more evident in Figure 2 where I plot the annual rate of changes for the three variables. In Table 1, I report the mean and standard deviation of the three variables. These figures confirm and quantify the differences in the variability of the three variables considered. In Tables 2 and 3, I consider two alternative ways of summarising the time series properties of the three series I analyse for both countries. In Table 2, 1 report the estimates of the coefficient of an MA(12) model for the same series. The advantage of such an un-parsimonious model is that it avoids the sometimes difficult choice among competing ARMA representations. Furthermore, its impulse response function

Ch. 11:

747

Consumption

USA- disposable income and consumption rates of growth

UK- disposable income and consumptionrates of growth

0.2

0.2

0.1

0.1

0

0

-0.1

-0.1

-0.2

-0.2

55

65

75

85

95

65

75

85

95

Fig. 2. Annual rates of change for the variables of Figure 1. Table 1 Mean and standard deviations (annual rates of growth) US

Disposable income Nondurable consumption Durable expenditure

UK

Mean

St. dev.

Mean

St. dev.

0.032 0.023 0.048

0.025 0.018 0.069

0.026 0.017 0.043

0.026 0.021 0.112

can be easily read from the estimated coefficients. I also purposely decided to be agnostic about the presence o f random walks in the time series consumption or income, even though this has implications for the so called 'excess smoothness' puzzle briefly discussed below. In Table 3, instead, I report the M a x i m u m Likelihood estimates o f a parsimonious A R M A m o d e l for the first differences o f the log o f the three variables. While in some cases there were alternative specifications that fitted the data as well as those reported in the table, the latter all pass several diagnostic tests. The Q-statistics reported in the table indicates that the representations chosen capture adequately the dynamic behaviour o f the series over the period considered. The time series properties o f the rate o f growth o f the three variables are remarkably different. Notice, in particular, the fact that both in the U K and in the USA, the sum o f the M A coefficients for non-durable consumption is positive, while that for durables is negative. The time series properties o f non-durable consumption differ remarkably: in Table 2 the sum o f the first 12 M A coefficient is much larger in the U K than in the USA. Furthermore, while the US data are well represented by an M A ( 3 ) (with the first and third lag large and very strongly significant), the U K require an AR(2) model 1.

I The presence of an MA(3) effect in the non-durable series for the USA is evident even in the MA(12) representation but it is not very robust. If one truncates the sample to 1990 or dummies out the few quarters corresponding to the 1990-91 recession, 03 is estimated non-significantly different from zero

748

O.P Attanasio

Table 2 MA(12) representation a US

0i

01 02 03 04 05 06 07 08 09 010 011 012

~ ) 2 I 0i

UK

Disposable income

Non-durable consumption

Durable consumption

Disposable income

Non-durable consumption

Durable consumption

-0.30 (0.091) 0.15 (0.094) 0.092 (0.094) -0.092 (0.088) -0.15 (0.087) 0.11 (0.088) -0.13 (0.087) -0.17 (0.088) 0.38 (0.088) 0.20 (0.095) -0.06 (0.096) -0.27 (0.091) -0.25

0.41 (0.096) 0.18 (0.103) 0.43 (0.104) 0.12 (0.110) -0.057 (0.108) 0.100 (0.108) 0.11 (0.107) -0.20 (0.107) 0.05 (0.109) -0.03 (0.100) 0.05 (0.099) 0.08 (0.092) 1.23

-0.092 (0.088) -0.035 (0.089) 0.063 (0.089) 0.084 (0.086) -0.16 (0.085) 0.15 (0.077) -0.45 (0.077) -0.021 (0.085) -0.23 (0.085) -0.03 (0.088) 0.005 (0.087) -0.23 (0.086) -0.95

-0.10 (0.094) 0.12 (0.095) -0.06 (0.092) -0.18 (0.088) -0.19 (0.089) 0.22 (0.088) 0.21 (0.088) 0.14 (0.087) -0.14 (0.086) -0.20 (0.087) 0.05 (0.088) -0.05 (0.086) -0.18

0.005 (0.094) 0.20 (0.093) 0.004 (0.093) 0.28 (0.092) 0.19 (0.093) 0.19 (0.094) 0.09 (0.094) 0.22 (0.092) -0.11 (0.090) 0.23 (0.091) 0.18 (0.091) 0.03 (0.093) 1.51

-0.29 (0.094) -0.14 (0.096) 0.24 (0.097) -0.45 (0.099) 0.15 (0.106) 0.05 (0.107) -0.07 (0.106) -0.18 (0.104) -0.08 (0.098) 0.02 (0.095) -0.20 (0.094) -0.02 (0.089) -0.97

a Standard errors are given in parentheses. The sum o f the M A coefficients for disposable income in both countries is quite small in absolute value, but is positive in the U S A and negative for the UK. As far as a 'parsimonious' specification is concerned, in the U S A I chose an MA(1) for the first differences, even though its coefficient is not very large and is statistically insignificant. This model was almost indistinguishable from an AR(1) model. In the UK, the best model for disposable income is an ARMA(1,1). The richer dynamics o f the U K series is also evident in the pattern o f the M A coefficients in Table 2.

both in the MA(12) and in the MA(3) model. The same result is obtained if one excludes services from this series.

Ch. 11:

749

Consumption

Table 3 ARMA representation a Variable

US Disposable income

'[Pl

--

--

'10 2

--

_

01

-0.19 (0.088)

0 2

--

03

-

UK

Non-durable D u r a b l e Disposable Non-durable Durable consumption consumption income consumption consumption -0.103 (0.089)

-0.77 (0.293) -

0.684 (0.339)

0.38 (0.083) 0.18

0.015 (0.087) 0.28 (0.087) -

-1.09 (0.098) -0.45 (0.082) 0.85 (0.077)

-

0.85 (0.077) 7.22 (0.30)

(0.088)

Q-stat (p-value)

13.40 (0.10)

0.39 (0.082) 7.35 (0.28)

-

10.09 (0.26)

0.684 (0.339) 11.79 (0.11)

11.49 (0.12)

a Sample 1965:3-1996:3 (125 observations). Standard errors are given in brackets. The properties of durable consumption are particularly interesting. The fact that the time series properties are inconsistent with a simple model which adds durability to the standard random walk property derived from some version o f the permanent income has been noticed by Mankiw (1982). Such a model would imply an MA(1) model for the changes in expenditure with a coefficient that would differ from minus one by an amount equivalent to the depreciation rate. As can be seen from Table 2, the US series' best representation is indeed an MA(1) with a negative coefficient; but that coefficient is far from minus one 2. Caballero (1990b) has interpreted this and the fact that, as reported in Table 3 :for b0th~eountries, the sum o f the 12 M A coeflici~fits is negative and much larger in absolute value, as an indication o f the presence of inertial behaviour that 'slows down' the process o f adjustment o f durables. Having characterised the main time series properties o f consumption and income, the next step would be the estimation of a multivariate time series model that would stress the correlations among the variables considered at various leads and lags. Indeed, some of the studies I cite below, such as Flavin (1981), do exactly this with the purpose of testing some of the implications o f the life cycle-permanent income hypothesis. For the sake of brevity, I omit the characterisation o f the multivariate time series process o f consumption and other macro variables. One of the reasons for this omission is the belief, discussed below, that aggregation problems make it very difficult to give

2 For durable consumption in the UK, the best model is an ARMA(2,1), by far the most complex model I fitted to these data.

750

0.17 Attanasio

structural interpretation to this type of results. This does not mean, however, that aggregate time series studies are not useful. The careful specification of a flexible time series model for consumption and other variables can be quite informative, especially if the dynamic specification allows for the type of dynamic effects implied by the microeconomic behaviour. Several of the studies by David Hendry and his collaborators are in this spirit; one of the most widely cited examples of this literature is the paper by Davidson et al. (1978). The approach taken in these papers, which received a further motivation by the development of cointegration techniques, is to estimate a stable error correction model which relates consumption to other variables. The statistical model then allows to identify both short run and long run relationships between consumption and its determinants. While the theory can be informative on the choice of the relevant variables and even on the construction of the data series, it does not provide explicit and tight restrictions on the parameters of the model. A good example of a creative and informative use of this type of techniques is Blinder and Deaton (1985). While it is difficult to relate this type of models to structural models and therefore they cannot be directly used for evaluating economic policy, they constitute useful instruments for summarising the main features of the data and, if used carefully, for forecasting. Often the lack of micro economic data makes the use of aggregate time series data a necessity. The only caveat is that these studies cannot be used to identify structural parameters.

2.2. Household consumption expenditure In this section, I use two large microeconomic data set to document the main stylised facts about consumption. The two data sets used are the US Consumption Expenditure Survey (CEX) and the UK Family Expenditure Survey (FES). Both data sets are run on a continuous basis to gather information for the construction of the weights for the CPI (RPI in the UK). They have, however, been extensively used by researchers and have now become an essential tool to study household consumption and saving behaviour. The focus of the analysis is going to be the household. No attempt will be made to attribute consumption to the single household members, even though some (limited) information on this does exist 3. Most of the descriptive analysis presented below attempts at describing the main features of the life cycle profile for consumption expenditure and some other variables.

3 Both data sets contain very detailed information on the expenditure on individual commodities. Some of this information can be used to attribute some items to some household members. For many items, however, such attribution is difficult both in practice and conceptually. Browning (1987) has imputed expenditure on alcoholand tobaccoto the adults to checkwhether predictedchangesin householdincome and composition(such as the arrival of children with consequent- at least temporary- withdrawal from the labour force of the wife) cause changes in consumption. Gokhale, Kotlikoffand Sabelhaus (1996) in their study of saving behaviourhave attempted to impute all of consumptionto the individual household members.

Ch. 11: Consumption

751

This approach reflects the fact that the theoretical discussion in the next sections will be focused around the life cycle model.

2.2.1. Nature of the data sets and their comparability with the National Account data The FES is now available for 25 consecutive years. Each year around 7000 households are interviewed and supply information on their consumption patterns as well as their demographic characteristics and several other economic variables such as employment status, income, education and so on. Each household stays in the sample for two weeks, during which it fills a diary in which all expenditure items are reported. At the end o f the two week period an interviewer collects the diaries and asks additional information on durables acquired during the previous three months and on all major expenditure items reported in the diary and periodic expenditures such as utilities. The CEX is available on a continuous and roughly homogeneous basis since 1980. Each year about 7000 different households are interviewed for 4 subsequent interviews, with quarterly frequency 4. Each month new households enter the survey to replace those that have completed their cycle o f interviews. During each interview the household is asked to report expenditure on about 500 consumption categories during each o f the three months preceding the interview 5. The panel dimension of the CEX is unfortunately very short: because each household is only interviewed four times, seasonal variability is likely to dominate life cycle and business cycle movements. In what follows, I do not exploit the panel dimension o f the survey. There have been several discussions about the quality o f survey data and the importance o f measurement error and about their ability to reproduce movements in aggregate consumption. Several studies, both in the U S A and the UK, have addressed the issue 6. It should be stressed that the aggregated individual data and the National Account aggregate should be expected to differ for several reasons. First o f all, for many consumption categories, the definitions used in the surveys and in the National Accounts are quite different. Housing, for instance, includes imputed rents in the National Accounts data but does not in the surveys. In the CEX, health expenditure

4 In total there are data for over 20000 interviews per year. Each household is in fact interviewed five times. However, the Bureau for Labor Statistics does not release information on the first (contact interview). The Bureau of Labor Statistics also rtms a separate survey based on diaries which collects information on food consumption and 'frequently purchased items'. s Unfortunately,the monthly decomposition of the quarterly expenditure is not very reliable. For several commodities and for many households, the quarterly figure is simply divided by three. Given the rotating nature of the sample, the 'quarters' of expenditure do not coincide perfectly. For instance, somebody interviewed in December will report consumption in September, October and November, while somebody interviewed in November will report consumption in August, September and October. 6 See, for instance, Seslnick (1992) and Paulin et al. (1990) for comparisons between the aggregate Personal Consumption Expenditure and the CEX in the USA and the papers in Banks and Johnson (1997) for comparisons on the FES and the UK National Accounts.

752

O.P. Attanasio

measures only out-of-pocket expenditures, while~ the National Accounts definition includes all health expenditures regardless o f the payee. Furthermore, the populations of reference are quite different. Surveys, for instance, do not include institutionalised individuals, while the National Accounts do. Finally, National Account data arc not exempt from measurement error that, for some items, can be quite substantial. Should major difference emerge, it is not obvious that the National Account data should be considered as being closer to the 'truth'. The issues that arise are different for the two data sets. Overall, the degree o f correspondence between the aggregated individual data and the National Account data seems to be higher in the UK. For most consumption components, aggregating the FES data, one obtains about 90% o f the corresponding National Accounts figure, while the same ratio is about 65% for the CEX in the 1980s. This is probably due to the use o f diaries rather than recall interviews. The latter, perhaps not surprisingly, tend to underestimate consumption. In both surveys, however, because o f the consistent methodology used over time, there is no major trend in the ratio o f the aggregated individual data to the corresponding National Accounts aggregates 7. Furthermore, the dynamics o f consumption and income growth and o f saving in both the aggregated CEX and FES data do not track the corresponding macroeconomic aggregates badly. The data are therefore not only useful to characterise individual behaviour and its shifts over time, but also to make inferences, based on individual behaviour, about possible explanations o f the observed macroeconomic trends.

2.2.2. Life cycle profiles In the second part o f the chapter, in which I discuss the main theoretical model o f consumption behaviour, a substantial amount o f attention is devoted to the life cycle model in its several incarnations. In this section, I present life cycle profiles for consumption, its components and various other variables in the USA and the UK. In this sense, the life cycle model is the conceptual framework that I use to organise the presentation of the microeconomic data. As the data sets I use are not panels, to estimate age profiles, I am forced to use grouping techniques. These techniques were first used within life cycle models by Browning, Deaton and Irish (1985)8. The idea is quite simple. Rather than following the same individual over time, one can follow tile average behaviour o f a group of

7 There are substantial differences in this ratio between the early CEX surveys (1960-61 and 1972-73) and those of the 1980s, probably due to the differences in the methodology employed. In the FES the one commodity for which a (downward) trend in the ratio is apparent is tobacco. 8 Ghez and Becker (1975) use observations on individual of different ages to study life cycle behaviour. However, as they use a single cross section, they do not control for cohort effects as Browning et al. (1985) do. Deaton (1985) and, more recently, Moffitt (1993) have studied some of the econometric problems connected with the use of average cohort techniques. Heck~manand Robb (1987), MaCurdy and Mroz (1989) and Attanasio (1994) discuss identification issues.

Ch. 11:

Consumption

753

individuals as they age. Groups can be defined in different ways, as long as the membership o f the group is constant over time 9. Within the life cycle framework, the natural group to consider is a 'cohort', that is individuals (household heads) born in the same period. Therefore, to compute the life cycle profile o f a given variable, say log consumption, one splits the households interviewed in each individual cross section in groups defined on the basis o f the household head's year o f birth. This involves, for instance, considering all the individuals aged between 20 and 24 in 1980, those aged between 21 and 25 in 1981 and so on to form the first cohort; those aged between 25 and 29 in 1980, between 26 and 30 in 1981 and so on to form the second cohort, etc. Having formed these groups in each year in which the survey is available, one can average log consumption and therefore form pseudo panels: the resulting data will have dimension Q x T, where Q is the number o f groups (cohorts) formed and T is the number o f time periods m. Even if the individuals used to compute the means in each year are not the same, they belong to the same group (however defined) and one can therefore study the dynamic behaviour o f the average variables. Notice that non-linear transformations o f the variables do not constitute a problem as they can be computed before averaging. The resulting age profiles will not cover the entire life cycle o f a given cohort, unless the available sample period is longer than any o f the micro data set commonly used. Each cohort will be observed over a (different) portion o f its life cycle. These techniques can be and have been used both for descriptive analysis and for estimating structural models. Their big advantage is that they allow to study the dynamic behaviour o f the variables o f interest even in the absence o f panel data. Indeed, in many respects, their use might be superior to that o f panel data ~1. Furthermore, as non-linear transformations o f the data can be handled directly when forming the group means, they allow one to solve various aggregation problems that plague the study o f structural models with aggregate time series data. In what follows, I define groups on the basis o f the year o f birth and educational attainment o f the household head. The length o f the interval that defines a birth

9 Group membership should be fixed over time so that the sample is drawn from the same population and the sample mean is a consistent estimator of the mean of the same population. Attanasio and Hoynes (1995) discuss the implications of differential mortality for the use of average cohort techniques. Other possible problems arise, at the beginning of the life cycle, from the possible endogeneity of household formation and, more generally, from migration. ~0 Here I am implicitly assuming that the pseudo panel is a balanced one. This is not always the case as each group might be observed for a different number of time periods. Suppose, for instance, to have data from 1968 to 1994. One might want to follow the cohort born between 1965 and 1970 only from the late 1980s or the early 1990. On the other hand, at some point during the 1980s one might want to drop the cohort born between 1906 and 1910. l~ Time series of cross sections are probably less affected by non-random attrition than panel data. Furthermore, in many situation, averaging across the individuals belonging to a group can eliminate measurement error and purely idiosyncratic factors which are not necessarily of interest. As most grouping techniques, average cohort analysis has an Instrumental Variable interpretation.

O.P. Attanasio

754 Table 4 Cohort definition and cell size Cohort

Year of birth

Cell size US Average size

Years in sample

Averagesize

UK Years in sample

1

1895-1999

-

-

338

1968-1977

2

1900-1904

-

-

459

1968-1982 1968-1987

3

1905-1909

-

-

526

4

1910-1914

232

1980-1992

560

1968-1992

5

1915-1919

390

1980-1992

519

1968-1992

6

1920-1924

333

1980-1992

653

1968-1992

7

1925-1929

325

1980-1992

572

1968-1992

8

1930-1934

317

1980-1992

546

1968-1992

9

1935-1939

345

1980-1992

562

1968-1992

10

1940-1944

420

1980-1992

594

1968-1992

11

1945-1949

566

1980-1992

652

1968-1992

12

1950-1954

657

1980-1992

547

1971-1992

13

1955-1959

734

1980-1992

508

1976-1992

14

1960-1964

-

-

463

1981-1992

15

1965 1969

-

-

334

1986-1992

cohort is chosen taking into account the trade-off between cell size and within-cell homogeneity. Table 4 contains the definition o f the cohorts and the average sample size for both surveys. We start, in Figures 3 and 4, with the life cycle profile of (log) consumption and disposable income at constant prices for both countries. The units o f measurement for income and consumption are chosen so that the two graphs would be roughly in the same scale, enabling to stress the differences in the shape of the age profile. In the figures, I plot the average cohort (log) consumption at each point in time, against the median age o f the household head. Each connected segment represent the behaviour o f a cohort, observed as it ages, at different points in time. As each cohort is defined by a five year interval, and both surveys cover a period longer than five years, at most ages we observe more than one cohort, obviously in different years. It might be tempting to attribute the differences between adjacent cohorts observed at the same age, to 'cohort effects'. It should be remembered, however, that these observations refer to different time periods and might therefore be reflecting business cycle effects. The plotted profiles reflect age, time and cohort effects 12 that, without

12 As well as measurement error and small sample variability.

755

Ch. 11." Consumption USA - disposableincome

UK - disposable income

25000

~'250 200

20000 150 15000

O

lOO 8 50

10000 20

40

Age

60

70

20

40

Age

60

70

60

70

Fig. 3. USA - total consumption 25000

~

20000

UK - total consumption 250

~

~2o0 "~150

~o

o

&loo

15000

05

8

10000

0 20

40

Age

60

70

50 20

40

Age

Fig. 4. an arbitrary normalisation or additional information from a structural model, cannot be disentangled. Several considerations are in order. First of all, both consumption and income age profiles present a characteristic 'hump'. They both peak in the mid 40s and decline afterwards. The picture seems, at first glance, to contradict the implications of the life cycle model as stressed in the typical textbook picture which draws a 'hump shaped' income profile and a flat consumption profile. For total disposable income, the decline around retirement age is faster in the UK than in the USA, but approximately of the same magnitude. This probably reflects the more synehronised retirement of British individuals. The consumption profiles, however, present some strong differences. The most notable is the fact that UK consumption declines much more at retirement than US consumption. Total consumption at age 70 is roughly 35% of the peak in the UK and above 50% in the USA. I discuss the decline of consumption at retirement below. In the UK consumption profile, the consumption boom of the late 1980s, followed by the bust of the early 1990s, is quite apparent. Notice, in particular, the fact that the aggregate consumption boom is accounted for mainly by the youngest cohorts. I have discussed elsewhere how to interpret that episode. It is worth stressing, however, that the analysis of the cross sectional variability of consumption can be useful to shed some light on the nature of episodes that the analysis of the time series data cannot

0.17. Attanasio

756 Table 5 Variability of consumption and income Standard error (%)

Variable

Total consumption Total consumption per adult equivalent Non-durable consumption Non-durable consumption per adult equivalent Durable consumption Non-durable consumption (from levels) Income

USA (CEX)

UK (FES); age < 81

UK (FES); 10 cohorts, year < 86

2.94 2.39 2.60 1.95 15.79 2.58 3.68

2.46

2.65

2.62 2.30 2.49 9.54

2.64 1.88 2.05 8.54

2.31 3.05

1.86 3.60

explain. Information about which groups in the populations where mainly responsible for a determinate episode can be informative about alternative hypotheses 13 It is not obvious how to assess the time series volatility o f (log) consumption and income. The main reason for this is that a large part o f the variation o f consumption over the life cycle is very predictable and can be explained by age and cohort effects. Furthermore, given the limited size o f our samples, the year to year variation in the average cohort data reflects both genuine time series variation and the measurement error induced by sample variation. As Deaton (1985) has stressed, some information about the size o f the measurement error can be gained using the within-cell variability o f the variables used. Using this information, one might correct for that part o f variability accounted for by sampling variation and attempt to isolate the genuine time variation. In an attempt to isolate this component, I run a regression o f log consumption and income on a fifth order polynomial in age and cohort dummies and consider the deviations o f the observed profiles from such a profile. The standard deviation o f the changes in these deviations, corrected for that part which can be attributed to sampling error, is my measure o f time variability 54. These estimates o f volatility for (log) income and consumption are reported in Table 5 along with those for the other variables considered. The first column refers to the USA, while the second and third columns are computed using the U K data. The former includes the whole sample,

i3 See Attanasio and Weber (1994). Groups do not need to be formed on the basis of age. In Attanasio and Banks (1997) that analysis is extended considering not only the variability across cohorts but also across regions. 14 The sample mean • is distributed around the population mean as a random variable with variance given by o2/N, where N is the cell size and cr is the within-cell variance. The latter can be estimated from the available micro data. These estimates can be used to correct our estimates of volatility.

Ch. 11:

Consumption

757 UK - non-durable consumption per household and per adult equivalent

USA - non-durable consumption per household and per adult equivalent ~"

15000

200-

10000 100E

8

5000 20

40

Age

60

70

5020

40

Age

60

70

Fig. 5.

while the latter truncates it to 1986 to remove the effect of the consumption 'boom and bust' of the last part of the sample. As in the case of aggregate time series, total consumption appears less volatile than disposable income, both in the UK and in the USA. In particular, the standard deviation of changes in total disposable income at the cohort level is above 3% in both countries. That of total consumption is between 0.6% and 0.95% less. It may be argued that the differences in the consumption profiles for the two countries are due to the differences in the definitions used in the two surveys. For this reason, I next focus on a narrower definition of consumption which excludes a number of items which might be recorded in different fashion in the two countries. In particular, in Figure 5 I plot (log) expenditure on non-durables and services against age. This definition excludes from total consumption durables, housing, health and education expenditure. The other advantage of considering consumption of non-durables and services, is that I avoid the issue of durability and the more complicated dynamics that is linked to durables. The main features of the two profiles, however, including the larger decline observed in the UK, are largely unaffected. In Table 5, the volatility of non-durable consumption is considerably less than that of total consumption, especially in the UK when data up to 1986 are used. An important possible explanation for the life cycle variation of consumption over the life cycle (and between the two countries considered), is the variation in needs linked to changes in family size and composition. To control for this possibility, I have deflated total household expenditure by the number of adult equivalents in the household. For such a purpose, I use the OECD adult equivalence scale 15. The most evident result is that the life cycle profile of consumption looks much flatter now. In this sense, we can say that a large proportion of the variability of consumption over the life cycle is accounted for by changes in needs. This result is perhaps not surprising

15 No adult equivalence scale is perfect. Different alternatives, however, do not make much difference for the point I want to make here. The OECD scale gives weight 1 to the first adult, 0.67 to the following adults and weight 0.43 to each child below 19.

O.P. Attanasio

758 USA - durables

UK - durables

5000-

4000-

looo-

30002000

8

1000-

~0

4o

6o

~0

Age

~0

40

6'o

8S

1;0

Age

Fig. 6. if one considers that the life cycle profile of the number of adult equivalents (or of family size) is also 'hump-shaped'. It may be argued that changes in needs are, to a large extent, predictable. In terms o f the measure o f volatility in Table 5, it is greatly reduced for the USA, while is slightly increased for the UK. While the profile for non-durable consumption per adult equivalent is quite flat in the first part of the life cycle, a marked decline is still noticeable in the last part. It seems that the decline corresponds roughly to the time of retirement. In the UK, where retirement is much more synchronised than in the USA, the decline is much more rapid. The fact that per adult equivalent consumption declines with retirement suggests that this might be due to a link between labour market status and consumption. A possibility, for instance, is that some components of consumption are linked to labour market participation. More generally, it is possible that consumption and leisure are non-separable and, therefore, need to be analysed jointly. These issues have been recently discussed by Banks et al. (1998). Finally, it is of some interest to consider the life cycle profile of expenditure on durables. The life cycle profiles for durables are plotted in Figure 6. Consistently with the findings in aggregate time series data, the life cycle profiles for durable expenditure are much more volatile than those for non-durables and services. The measure in Table 5 for durables is 5 times as large as that o f total consumption for the USA and almost 4 times as large for the U K 16. Several variables are likely to be important determinants of, or determined jointly with consumption. I have already stressed the important role which is likely to be played by demographics and retirement behaviour in shaping the life cycle profiles o f consumption. Similar considerations can be made for other labour supply variables

16 Because durable expenditure can be zero at the individual level I do not compute the average of the log. Therefore, the deviations from the life cycle profiles are not percentage deviations, but are measured in constant dollars. Because of this, in Table 5, in the row corresponding to durables I report the coefficient of variation, rather than the standard deviation. For comparison, I adopt the same procedure for non-durable consumption, in the following row.

Ch. 11:

Consumption

759

such as the participation rate of females to the labour market and the total number of hours of work. A characterisation of the life cycle patterns of these variables and their differences between the U K and the USA would go beyond the scope of this section 17. However, it is important to stress that, as I argue in Section 5 and 6 below, one cannot test any model of consumption without controlling for these factors, that, for the most part, can only be analysed using household level data. In Table 5, I only report the variability of the various components of consumption and of disposable income. As with the aggregate time series data, it would be interesting to characterise the autocorrelation properties of these variables and their covariances. This analysis could be quite informative about the plausibility of alternative structural models 18. One of the implications of the textbook version of the life cycle model I discuss in Section 3, is that consumption and current income should not be related. And yet, comparing Figures 3 and 4, one cannot help noticing the similarity in the shape of the two life cycle profiles. This similarity was interpreted as a failure of the life cycle model by Thurow (1969) and reinterpreted in terms of non-separability of consumption and leisure by Heckman (1974). To pursue this issue, in Figure 7, I plot the life cycle profile of (log) disposable income and non-durable consumption for four education groups in the USA defined on the basis of the educational attainment of the household head: high school dropouts, high school graduates, some college and college graduates. An interesting feature of this figure is that the differences across groups in the shape of the income profiles are mirrored in differences in the consumption profiles. In particular, notice that both income and consumption profile of better educated individuals present a more pronounced hump; not only are their income and consumption higher, but the profiles are also much steeper in the first part of the life cycle. These differences where interpreted within a life cycle model by Ghez and Becker (1975), but have interpreted as a failure of the model by Carroll and Summers (1991) in an influential paper. An interesting question, addressed below, is whether a version of the life cycle model I discuss could generate these profile and account for the differences across education groups. In Table 6, I compute the variability of income, consumption and its components as in Table 5, but splitting the sample by education. The most interesting feature of this table is the fact that the only large difference in volatility among the groups is in durable consumption. Expenditures on durables by high school dropouts is twice as variable as that of college graduates, while the figure for high school graduates is in the middle. 17 Interested readers can find the life cycle profiles for several variables in Attanasio (1994), Banks, Blundell and Preston (1994) and Attanasio and Banks (1997). a8 MaCurdy (1983) and Abowd and Card (1989) perform analyses of these kinds for earnings and hours of work and use the results to assess the plausibility of different structural model. No similar analysis exists for consumption and/or its components.

O.P. Attanasio

760 log i n c o m e a n d n o n d u r a b l e c o n s u m p t i o n by e d u c a t i o n high school graduates

high school dropouts

40000l 30000

20000

-°°°°l 10000

3--~

5459.04

I

i

some college

i

i

college graduates

30000

20000

10000

5459,04

q

20

910

410

50

age

Fig. 7. Table 6 Variability of consumption and income by educational group Variable

Standard error (%) High school dropouts High school graduates Morethan high school

Total consumption Non-durable consumption Durable consumption Income

2.88 2.40 22.85 5.98

2.74 2.93 16.58 6.53

2.88 2.25 9.66 5.17

3. The life cycle model In this and in the next few sections, I will sketch what 1 think is the most important model of intertemporal consumption behaviour: the life cycle-permanent income model. In doing so, I take a fairly wide definition of the model: I consider a very general framework in which consumption (and saving) decisions are taken as a part of an intertemporal decision process. This general definition includes both the initial formulations of the life cycle and permanent income models and more recent and sophisticated developments, such as the precautionary saving model or the bequest motive. While the emphasis given to various aspects of the problem is different in the various incarnations of the general model I will consider, they have in common the hypothesis that consumption decisions are taken by a decision unit that

Ch. 11: Consumption

761

maximises utility over time. The various versions of the model will then differ for their assumptions about optimisation horizon, uncertainty, curvature of the utility function, assumptions about separability and so on. Which of these various versions is the most relevant is in part a matter of taste and, above all, an empirical matter. 3.1. The simple textbook model

The main attractiveness of the life cycle-permanent income model, developed during the 1950s in a number o f seminal contributions 19, is the fact that consumption decisions are treated as part of an intertemporal allocation problem. The allocation of consumption over time is treated in a fashion similar to the allocation of total expenditure among different commodities in demand analysis. The model recognises, therefore, that intertemporal prices and the total amount of resources available to an individual are bound to be important determinants of consumption. This approach immediately gives the study of consumption solid microfoundations and constitutes a discontinuous jump with respect to the Keynesian consumption function which assumed consumption to be a simple function of current disposable income. The main difference between the life cycle and the permanent income model in their original formulation lies in the time horizon considered. The life cycle model is, almost by definition, a finite horizon model, while in the permanent income model the horizon is infinite. In both cases, however, consumers decide how much to consume keeping in mind their future prospects. If no uncertainty is introduced in the model, its predictions are quite straightforward: concavity of the utility function implies a desire to smooth consumption over time; the main motivation for saving is to smooth out fluctuations in income; consumption increases with current income only if that increase is a permanent one. In the case of the life cycle model, the explicit consideration of retirement, that is a period in which income declines considerably, generates the main motivation for saving: households accumulate wealth to provide for their consumption during retirement. An interesting implication of the life cycle model in its simplest incarnation is the way in which aggregate saving is generated. It is quite obvious that in a stationary life cycle economy with no growth aggregate saving is zero: the younger generations will be accumulating wealth, while the older ones will be decumulating it. Aggregate saving, however, can be generated in the presence of growth. I f the amount of resources available over the life cycle to younger generations is larger than that available to older ones, it is possible that the amount accumulated at a point in time exceeds the amount that is decumulated. This introduces a relationship between aggregate saving and growth that Modigliani has stressed in several studies. It should be stressed, however, that such a relationship depends on a number of factors including the life

19 Modiglianiand Brumberg(1954) contains the first formulation of the life cycle model. The permanent income model was sketched in Milton Friedman's 1957 volume [Friedman (1957)].

762

O.P. Attanasio

cycle profile, the way in which growth is generated and who benefits from it and so on.

The life cycle-permanent income models were developed to provide an answer to several needs. First, by framing consumption decision within an intertemporal problem, immediately introduces dynamics into the picture. This gives the possibility of fitting some of the empirical facts that seemed at odd with the Keynesian consumption function 20, such as the difference between average and marginal propensity to consume in the short and long run. In addition, the introduction of dynamics is obtained in a theoretically consistent fashion which is appealing to economists. The model gives an obvious explanation of the smoothness of consumption relative to disposable income linked to some well defined preference parameter (the concavity of the utility function). Obviously, the first empirical applications of the model were quite different from the studies of the last 20 years, mainly for the much more sophisticated treatment of uncertainty which I discuss below 21. The model, however, seemed to score a number of empirical successes. I have already mentioned the fact that the model accounts for differences between short run and long run responses of aggregate consumption to disposable income (or other variables). More generally, it was clear that the model was able to generate very rich dynamic patterns for aggregate consumption and its response to disposable income. It could also explain the relationship between consumption and wealth and provide a rationale for the relationship between wealth-income ratios and growth. Indeed, as Modigliani has pointed out, the simplest version of the model is capable to generate an aggregate wealth to income ratio of 5 which is close to what this number is for the USA. Furthermore, the model also seemed able to explain some of the regularities observed in cross sectional data. Just to mention one, Friedman showed how the permanent income model can explain the fact that black households seem to save, at each level of income, a larger fraction of their income than white households 22.

3.2. Quadratic preferences, certainty equivalence and the permanent income model One of the problems with the life cycle-permanent income model is that the dynamic problems that consumers are assumed to solve can be quite complex. As a

20 Carroll and Kimball (1996) provide quotes from Keynes' General Theory in which he suggested a concave consumptionfimction. 21 Friedman(1957) essentially approximatedpermanent income with a distributed lag of current income. Modigliani and Ando (1963) stressed the role played by wealth (in addition to disposable income) in aggregate consumptionequations. Both the Modigliani and Ando paper and Friedman's book contained interesting discussions of the aggregationproblems that were absent, for a long time, from subsequent empirical studies. 22 This fact is still true: data from the Consumer Expenditure Surveyfrom 1980 to 1992 confirm that the saving rates of household headed by a black are systematicallyhigher, for any interval of income, than those of household headed by a non-black.

Ch. 11:

Consumption

763

consequence, if one considers an uncertain environment, unless strong assumptions about the nature of uncertainty and preferences are made it is not possible to obtain a closed form solution for consumption. A popular parametrization of the model which can yield an analytical solution is that of intertemporally separable and quadratic preferences. Indeed, a large part of the profession has come to identify the 'permanent income model' with such a parametrization of preferences with the additional assumptions of infinite horizon, constant interest rates and stochastic labour income. The analysis of the model is greatly simplified by the linearity of the marginal utility of consumption. This, and the fact that the only uncertainty comes from labour income, allows the derivation of an analytical solution for consumption which depends only on the first moment of future labour income. In particular, under the assumptions listed in the previous paragraph, consumption at time t can be expressed as a simple fimction of 'permanent income': Ct = kY p,

(1)

where k= 1 if the (fixed) interest rate equals the subjective discount factor, and permanent income YP is defined as

j=0 (1 +r)J where r is the fixed interest rate, ;~=r/(1 +r), At is the value of current wealth, and y is disposable labour income. The main attraction of Equations (1) and (2) is that they provide a straightforward relationship between the stochastic process that generates income and consumption. These relationship give rise to a number of testable implications that have been studied at length in the literature. Flavin (1981) and Sargent (1978) were the first studies to exploit the fact that Equations (1) and (2), together with the hypothesis that expectations about future labour income are rational, imply cross equation restrictions on the bivariate VAR representation of consumption and disposable income. Flavin (1981), in particular, estimated such a system using US time series data and rejected the restrictions implied by Equations (1) and (2). Flavin finds some evidence of excess sensitivity of consumption to income. Campbell (1987) proposes a slightly different interpretation of Flavin's results. From Equations (1) and (2) it is possible to obtain the following expression for saving 23: OO

st = )~ ~ j-0

EtYt+j -Yt (1 + r)J

(3)

23 s on the left-hand side of Equation (9) coincideswith saving (i.e. income minus consumption),only when k in Equation (7) is equal to 1. Otherwise,s = y - c/k.

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The restrictions implied by Equation (3) are the same as those implied by Equations (1) and (2). The nice thing about Equation (3), however, is its interpretation. The fact that consumers smooth consumption over time is reflected in Equation (3) in the fact that saving anticipates expected decline in disposable income. It is for this reason that Equation (3) has been dubbed as the 'saving for a rainy day' equation. Formally, the implication of Equation (3) can be written as saying that actual saving should equal the best forecast of labour income declines. Consistently with Flavin's findings, Campbell (1987) rejects the implications of the model. Campbell, however, finds that the time series pattern of actual saving is not far from that implied by the model. He claims that excess sensitivity of consumption to income within this framework "is more naturally interpreted as insufficient variability of saving than as a correlation between changes in consumption and lagged changes in income" (p. 1272). Related to the tests of excess sensitivity discussed above, and using the same framework, are those papers discussing the issue of 'excess smoothness' of consumption. Campbell and Deaton (1989) were the first to stress that, because Equations (1) and (2) can be used to derive the relationship between changes in consumption and innovations to the process generating income, the relationship between the volatility of consumption (or permanent income) and that of current income depends on the stochastic properties of the process generating the latter. In particular, if labour income is difference stationary (rather than trend stationary), permanent income, and therefore consumption, will be more volatile than current income. Intuitively, this result follows the fact that if labour income is not stationary, current innovations are persistent and will therefore imply a permanent revision to permanent income. Therefore the observation that consumption growth is less volatile than current disposable income growth contradicts the permanent income hypothesis 24. This result is ironic as one of the original motivations for the development of the permanent income model was, indeed, the observation that consumption is smoother than income. The most problematic issue with this branch of the literature is the well known difficulty in distinguishing between trend stationary and difference stationary models 25. The version of the model with quadratic preferences has also been used to introduce further refinements to the model. Goodfriend (1992) and Pischke (1995), for instance, consider the implications of the lack of complete information on contemporaneous aggregate variables. Pischke, in particular, explains the excess sensitivity results typically obtained with aggregate data with this type of phenomena 26. In a recent paper, Blundell and Preston (1998) use the assumption of quadratic preferences to devise a clever way of decomposing transitory and permanent components of income shocks. The idea is quite simple: under the permanent income

24 For a clear discussion of these issues see chapters 3 and 4 in Deaton (1992). 25 See, for instance, Christiano and Eichenbaum(1990) 26 Deaton(1992) also discusses the possibilitythat the informationset used by individual agents differs from that available to the econometrician.

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model, consumption should react to innovations to permanent income and not to transitory income. Consumption variability can therefore be used to isolate that part of the observed volatility of income which is to be attributed to permanent shocks.

3.3. The Euler equation approach Without the assumption of quadratic utility (and of uncertainty confined to the exogenous income process), one is left with the problem that it is not possible to derive an analytical solution for the level of consumption. The most important theoretical development since the development of the life cyclepermanent income model is the rigorous treatment o f uncertainty introduced in the late 1970s, after the rational expectations revolution in macroeconomics. In a famous paper, Hall (1978) used what is the main implication of the intertemporal optimisation problem faced by a generic consumer to derive empirically testable restrictions that have been at the centre of much of the empirical analysis in the last 20 years. The idea is simple and elegant: in a situation in which consumers maximise expected utility under uncertainty, they act so to keep the expected (discounted) marginal utility of consumption constant. This condition is equivalent to the equalisation of the marginal rate of substitution to relative prices in consumer demand. The beauty of the approach lies in the way in which the difficulties associated with the presence of uncertainty are circumvented. The effect of future variables on consumption at a given point in time is summarised by the multiplier associated to the budget constraint: the marginal utility of wealth. This object is eliminated by considering the equations for two different periods and considering the optimal pattern for the evolution of the multipliers. It is now time to introduce a bit of notation and formalise what said so far. Suppose a consumer maximises expected life time utility subject to an intertemporal budget constraint. She consumes a homogeneous consumption good C, receives labour income y and has the possibility of investing in N different assets A i that pay a rate of return R I at the end of period t. Both rates of returns and labour income are uncertain. This setup is formalised in the following equation: T-t

max Et ~

fiJ U(Ct~j, zt+j, vt+j)

j-0

(4) N

subject to Z i-1

N

A~+j+, = Z AI+J(1 + RJ+t)+Yt+i-Ct+J ' i=l

where I allow the instantaneous utility function U to depend on a vector of observable variables z, and an unobservable variable v. The operator Et denotes expectations conditional on the information available at time t. I omit an index for the individual for notational simplicity. Implicit in Equation (4) are a number of simplifying assumptions of various nature that will be relaxed in the following sections. It is useful to list some of them along with ways in which they can be rationalised.

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(i)

Equation (4) assumes that utility is separable over time. This is a strong assumption and rules out at least two important phenomena: habit formation and durable commodities. The marginal utility o f consumption in any given time period does not depend on consumption expenditure in any other period. We also assume that expenditure coincides with consumption. One obvious possibility to rationalise this model without excluding the existence o f durables is to assume that the instantaneous utility function is additively separable in non-durables and in the services provided by durables. In this case, a term for expenditure on durables should be added to the intertemporal budget constraint. (ii) Utility is derived from an homogeneous consumption good. The conditions under which intertemporal choices can be summarised by a single price index are seldom discussed. The two situations that are treatable are the absence o f changes in relative prices, so that one can construct a Hicks composite commodity, or that preferences take the Gorman polar form. These issues are discussed below. (iii) Labour income is exogenous. No labour supply choices are considered. One can reconcile a situation in which labour supply is endogenous with the model discussed above, assuming that the instantaneous utility function is additively separable in leisure and consumption. In this case, one should modify only the budget constraint o f the problem (4) above. (iv) The duration o f life is certain. This assumption is easily relaxed to assume an uncertain life time. Davies (1981) has shown that this equivalent to assuming a discount factor fi that varies with age as a consequence of a varying probability o f survival. Utility at future ages is discounted not only because it accrues in the future but also because its accrual is uncertain. I will not discuss this issue any further, except when I discuss some o f the issues relevant for the analysis of consumption based on numerical methods. (v) The rate o f return on assets does not depend on the net position on that asset or on the total level o f wealth held by the consumer. The model, however, can easily accommodate a situation in which several assets are subject to various kinds of constraints, as long as there is at least one asset in which is possible to borrow and lend at the same rate 27 (vi) For simplicity, I have not considered explicitly the presence o f inflation. Obviously the presence of (uncertain) absolute price changes is simply accommodated in the model above by changing appropriately the budget constraint and the definition o f interest rates. Under these assumptions it is possible to derive an extremely useful first-order condition for the intertemporal maximisation problem described above. I f we denote

27 This is the condition under which the first-order condition derived below holds. If the rate of return on a given asset changes with the net position in that asset in a continuous and differentiable fashion, that is if the intertemporal budget constraint is concave and does not present kinks, the first-order condition derived below can be easily modified. More complicated is the situation in which there are discontinuities and kinks for all assets at some level of net worth (for instance zero).

Ch. 11: Consumption

767

with )~t the multiplier associated to the intertemporal budget constraint at time t, it can be shown that two of the first-order conditions for the problem in Equation (4) are

OU(Ct, zt, 03 OCt

(5)

-- i~t,

)~t = Et D~t+x/3(1 +R~+,)] ,

i= l,...,m.

(6)

Equation (6) holds for the m (m ~
i = 1,...,m,

(7)

where Uc is the derivative of the instantaneous utility function with respect to consumption. It is Equation (7) that Hall (1978) used to derive his famous 'random walk' property of consumption. These can be derived for the level of consumption if utility is assumed to be quadratic, or, under some distributional assumptions, for its log if utility is isoelastic. Notice that I have allowed instantaneous utility to depend on a number of observable variables (the vector z) for which I have not specified any property. Such variables could in principle be choice variables determined in the same intertemporal maximisation problem. Indeed, the variables z constitute the vehicle through which I introduce a number of factors such as the effect of demographics or of labour supply. As long as we control for their effect on the marginal utility of consumption (and treat them as endogenous at the estimation level), I do not need to model them explicitly. It should be stressed that Equation (7) is not a consumption function, but only an equilibrium relationship that can be used (and has been used) to estimate structural (behavioural) parameters and/or to test some of the implications of the model. The big advantage of Equation (7) is the elimination of the term that represents the marginal utility of wealth and therefore the necessity of explicitly modelling the way in which the distribution of future variables influences consumption choices. The price of this simplification, however, is not a small one: we lose the ability to say anything about the levels of consumption. While it is true that given the level of current consumption, we can use Equation (7) to forecast the expected level of future consumption, we do not

28 MaCurdy (1981) uses this frameworkto construct his 'A-constant' labour supply function.

0.17. Attanasio

768

know how consumption reacts to unexpected changes in the economic environment. These include changes to taxes or any other policy instruments that might affect consumption decisions. The elimination of the tmobservable marginal utility of wealth is similar to the elimination by quasi differencing of fixed effects in econometrics. The problem here is that the 'fixed effect' that is differenced out is one of great importance. Hall (1978) used quadratic utility to derive his famous 'random walk' result. After his paper, several studies developed and used the Euler equation approach with different assumptions about preferences. Hansen and Singleton (1982), for example, used isoelastic preferences to derive an expression whose parameters they estimated by GMM on aggregate time series data for consumption and several rates of return. In particular, Equation (7) with isoelastic preferences (and neglecting the z and v variables) implies c t-Y+l

The assumption of rational expectations and the fact that expectations in Equation (8) are conditional to the information available at time t can be used to find valid instruments to identify the structural parameters of Equation (8), which, once again, can be considered for several rates of returns. If we denote with q the dimension of the vector of parameters [in Equation (8), q = 2], with m the assets for which (8) holds and with k the number of instruments considered, Equation (8) yields m k - q overidentifying restrictions that can be used to test the model. The results obtained by Hansen and Singleton on aggregate data indicate that the model is strongly rejected whenever several returns are considered simultaneously. On the other hand, when one asset is considered in isolation, the overidentifying restrictions are not violated, but the preference parameters are estimated at somewhat implausible values. Hansen and Singleton (1983) considered a log-linear version of Equation (8). If one assumes that the rate of returns and consumption growth are joint log-normal, from Equation (8) one can derive the following expression: Alog(Ct+l) = 1 [log/3 + g2vart(Alog(Ct+l )) + vart (log(1 + Rit+l)) (9) +2Cov(Alog(Ct+l), log(1 +R)+I))] +

log(1 +Rt+l) ) + et+l,

where et+l is an expectational error uncorrelated with all the information available at time t. The advantages of Equation (9) are that it is (log) linear and some of its coefficients, as the one on the interest rate, have a natural and interesting interpretation. When the utility function in Equation (4) is isoelastic, its curvature parameter y plays a double rote. On the one hand it is equal to the coefficient of relative risk aversion and therefore summarises consumer's attitude towards risk. On the other,

Ch. 11:

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its reciprocal is equal to the elasticity o f intertemporal substitution and therefore measures as consumption growth changes when the relative price o f present and future consumption changes 29. The linearity of Equation (9) allowed a number o f researchers to estimate it by linear instrumental variables methods. Valid instruments include, as before, any information available to consumers at time t - 1. Hall (1988), however, noted that if the frequency with which consumption decisions are taken is higher than the frequency o f observations, the residuals o f equations will not be uncorrelated over time, as implied by the assumption o f rational expectations, but have, under certain assumptions, an MA(1) structure with a positive coefficient. If this is the case, valid instruments will be any variable dated t - 2 or earlier. The choice of lagged two instruments has become the common practice for the studies who estimate versions o f Equation (9) using aggregate time series data 3°. Most empirical applications that used a version o f Equation (9), including Hansen and Singleton (1983), typically assume that the conditional second moments that appear on its right hand side are constant over time so that they can be estimated as an intercept term. I discuss the role o f the conditional variances in Section 5. For the time being it will suffice to notice that assumption o f constant second moments can be relaxed to the weaker one that the innovations to the second moments in Equation (9) are uncorrelated with the instruments used in estimating the equation. Having found the instruments that allow the (over) identification o f the parameters o f Equation (9), it is possible to estimate its parameters and test the model. Alternatively, it is possible to test for the significance of additional variables that might be o f particular interest and that, according to the simplest versions o f the model, should not appear in the equation. A test which has received considerable attention is the addition o f the expected value o f current labour income growth. One o f the main examples o f this approach, is a series o f papers by Campbell and Mankiw (1989, 1991) who have estimated on aggregate time series data an equation like the following: Alog(Ct+l) = a + ort+l + )~Alog(yt+l) + et+l,

(10)

where y is labour income and r an interest rate. Both o f the variables on the right hand side are instrumented. According to the model the parameter )~ should be zero and the residual term should be orthogonal to the information available at time t. Equations (8) and (9) illustrate one of the main advantages o f the Euler equation approach. Even if it is not possible to obtain a closed form solution for consumption, it

29 For a discussion of the interpretation of such a parameter and the links between intertemporal substitution and risk aversion see Hall (1988), Attanasio and Weber (1989) and Epstein and Zin (1989, 1991). 3o Carroll et al. (1994) argue for the explicit consideration of the MA(1) process that would allow the use of the orthogonality conditions with instruments dated t - 1 and therefore yield more precise estimates and more powerful tests.

770

O.P.Attanasio

is possible to consider equilibrium relationships that can be used to estimate structural parameters. While these, as I discuss below, are not sufficient to answer many important policy questions, they constitute a basic ingredient of any answer. Furthermore, the orthogonality restrictions implied by the equations (and the assumption of rational expectations) can be used to test the validity of the model. Finally, the model can encompass a number of features that make it quite realistic without loosing its empirical tractability. In particular, it is possible to consider the effects that variables such as durables, labour supply, children and so on have on the marginal utility of non-durable consumption without having to model explicitly these variables. Having said this, however, one should also stress that the empirical implementation of the Euler equation is not without problems. First of all, data requirements can be quite formidable. Furthermore, a number of subtle econometric problems needs to be considered. I discuss these problems and some o f the available empirical evidence in Section 5.

3.4. Precautionary motives for saoing The assumption of quadratic preferences, which makes it possible to derive a closed form solution for consumption, is not very appealing. In addition to various shortcomings of quadratic preferences, many would find certainty equivalence, i.e. what makes the model easy to handle, questionable. It is therefore not surprising that a large literature has developed in the attempt to go beyond quadratic preferences. The first paper to consider explicitly the effects of non-linear marginal utility is Dreze and Modigliani (1972). While the Dreze and Modigliani contribution focuses on a two period problem, it contains many of the insights of the precautionary saving literature, such as the fact that the importance of the precautionary motive for saving depends on the third derivative of the utility function. Kimball (1990) discusses within a rigorous framework the conditions under which one can expect to observe precautionary savings. In particular, he proves that precautionary saving will occur when the utility function exhibits 'prudence', that is when the 3rd derivative of the utility function is positive. Under a CRRA utility function this will always be the case. To see this it is sufficient to consider Equation (6) above, that is the log-linearization of the Euler equation under the assumption of lognormally distributed random variables 31. Notice that, keeping the other variables constant, an increase in the conditional variance of consumption increases, at time t, the expected rate of growth of consumption between t and t + 1. This can be achieved by decreasing consumption at t, that is increasing saving at t. It is this that is usually referred to as precautionary

31 Alternatively, an equation similar to Equation (6) can be obtained by a Taylor expansion of the marginal rate of substitution, as in Dynan (1993). Banks, Blundell and Brugiavini (1997) use an approximation of the Euler equation developedby Blundell and Stoker (1999).

Ch. 11:

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771

motive for saving. As Browning and Lusardi (1996) stress, the fact that the effect that the conditional variance has on the rate of growth of consumption is scaled by the coefficient of relative risk aversion is an artefact of the CRRA utility function in which a single parameter controls both risk aversion and prudence (as well as the elasticity of intertemporal substitution). More generally, Carroll and Kimball (1996) have proved the concavity of the consumption function under precautionary saving. It should be noticed that the variance of consumption is not an exogenous variable. While it is likely to depend on the overall uncertainty facing the consumer, it is not obvious how it reacts to the arrival of new information or how it is related to uncertainty in income and interest rates. To evaluate this relationship it would be necessary to solve for the level of consumption and establish how consumption at t+l reacts to changes in the economic environment which, under CRRA preferences, is not possible. Caballero (1990a,b, 1991) using the exponential utility function as a parametrization of within-period utility obtains, with some additional assumptions, a closed form solution for consumption. In an interesting example, he expresses consumption as a function of permanent income (as in the case of certainty equivalence), minus a term which summarises the effect of the precautionary motive. He then goes on to evaluate the effect that precautionary saving is likely to have in reality. While the results obtained with the exponential utility give useful insights about the potential importance of the precautionary motive, such a parametrization of the utility function is not exempt from criticism. It is therefore important to evaluate the importance of precautionary saving using more general functional forms for the utility function. Unfortunately, when one uses different utility functions is not possible to obtain a closed form solution for consumption. It is therefore necessary to use numerical methods to obtain solutions and additional assumptions about the nature of the problem faced by consumers. This is the approach taken in a number of studies, such as those of Skinner (1988), Zeldes (1989b), Deaton (1991), Carroll (1994) and Hubbard, Skinner and Zeldes (1994, 1995). A disturbing feature of these studies is that the quantitative importance of the precautionary motive depends crucially on the properties of the distribution of the income process in the left tail. Bounding away the income process from zero (or from arbitrarily small realisations) greatly reduces the precautionary motive. While the reason for this is clear (consumers will want to insure themselves against disastrous events), the realism of such a mechanism is questionable. It might be worth investigating how the precautionary motive would change in the presence of insurance mechanisms other than self insurance (such as a safety net supplied either by society or by family and relations). Carroll (1994, 1997a) has strongly advocated the precautionary saving motive (or 'buffer stock saving') as an explanation of most empirical puzzles in consumption, including the tracking of expected consumption and income. I discuss the empirical findings on the precautionary motive and more generally on the Euler equation in Section 5. From a theoretical point of view, however, it should be stressed that while the

772

O.P Attanasio

precautionary motive is likely to be important for impatient consumers and especially in the early part of the life cycle, it is also clear that if retirement savings become, at some point during the life cycle, important, they can be used to buffer unexpected fluctuations to income. This effect, however, can be limited if most retirement wealth is held in the form of claims to future benefit or in other illiquid assets (such as special retirement accounts, housing, social security etc.). The relevance of the precautionary saving motive is ultimately an empirical matter, as it depends on preference parameters, on the features of the individual income process and on the availability of safety nets and insurance mechanisms. An attractive possibility to test the relevance of the precautionary motive for saving is to relate observed saving behaviour to perceived uncertainty. Guiso, Jappelli and Terlizzese (1992) is the only paper that uses direct observations on the perceived variance of the income process to assess the importance of precautionary savings. They use a unique data set (the Bank of Italy Survey of Household Income and Wealth) in which individuals are asked not only about their income expectations, but about the complete probability distribution of future income 32. This allows the authors to compute individual variances, which they then relate to individual savings, finding some mild evidence of precautionary savings. One obvious problem with this approach is the possibility that the individuals who have selected themselves into riskier occupation are less risk averse and, maybe, less 'prudent'. A similar argument was used by Skinner (1988) to justify his finding that self-employed individuals seem to save less than the average. More recently, Guiso, Jappelti and Terlizzese (1996) have studied the implications of the precautionary motive for portfolio composition. They show that, in the presence of different and unrelated sources of risk, individuals with higher and undiversifiable earning uncertainty will tend to invest in relatively 'safer' portfolios. 3.5. Borrowing restrictions

Related to the issue of precautionary saving is that of the presence of borrowing constraints. The standard model sketched above assumes that individuals can borrow against future labour income to finance current consumption at the same rate at which they can lend. Of course, if this is not the case, the basic model has to be amended in that the maximisation problem in Equation (4) has to take into account the additional constraint. It has now become customary to interpret evidence of 'excess sensitivity' of consumption growth to labour income as an indication of 'liquidity constraints', by which it is usually meant the presence of some imperfection in financial markets that prevents people from borrowing. However, there is no reason to believe that liquidity constrained individuals consume their disposable income. Only when the constraints are actually binding will this

32 Individuals are asked to divide 100 probabilitypoints over several intervals of income growth.

Ch. 11:

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773

occur. Therefore, excess sensitivity tests and, more generally, Euler equations are not the best way to identify the presence o f liquidity constraints. Furthermore, as we discuss below, there are several reasons why predicted income and consmnption might be related that have nothing to do with the presence of liquidity constraints. With these considerations, I do not want to dismiss the possibility of liquidity constraints as unimportant or unrealistic 33. Especially for some groups in the populations, they might be quite relevant and have an important effect on aggregate consumption. Early contributions to the literature on the policy implications of the permanent income-life cycle models, such as the papers by Flemming (1973) and Tobin and Dolde (1971), were quite aware of the importance o f liquidity constraints. It is crucial, however, that the presence o f liquidity constraints is incorporated in the optimising framework sketched above. The definition o f liquidity constraints I use in what follows appeal to partial equilibrium considerations: the interest rate schedule is taken as given. General equilibrium considerations, however, even though they are rarely made, can be quite important. In a world o f identical consumers, the possibility o f smoothing consumption over time will be constrained by the technology available to transfer resources over time. In equilibrium, interest rates and asset prices will adjust depending on the demand for borrowing (saving) and on the available technology. In such a situation, nobody is liquidity constrained at the current interest rates. With heterogeneous consumers, it is possible that some will want to borrow and others will be saving. The equilibrium interest rates will then reflect these factors. While the focus o f most o f the considerations in this section is on the partial equilibrium effects, it is worth keeping in mind that aggregate fluctuations, for instance a recession, might have effects on asset prices that reduce the demand for loans relative to what would be observed under constant interest rates. The first step in the integration of borrowing restrictions in the model above must be their exact definition. There are several possibilities. The first and most general alternative is to allow the interest rate paid on assets to depend on the net asset position. As a simple example o f this alternative, consider the possibility o f a difference between borrowing and lending rate. Such a wedge induces a kink in the intertemporal budget constraint. One can then consider Euler equations for individuals who are net borrower and net savers: the interest rate relevant for the two groups will be different, but the Euler equation still holds as an equality. For the individuals that will cluster at zero net assets, however, the Euler equation (with either interest rate) holds as an inequality.

33 As Hayashi (1996) stresses, most specifications of preference implicitly imply a form of borrowing restrictions. If the marginal utility of consumption is infinite a zero consumption, consumers will not want to borrow more than the present discounted value of the minimum realisation of income, even though the probability of this event is very low. This is because they want to avoid the possibility of zero consumption even with a very small probability.

O.P. Attanasio

774

It is also possible that the interest rate varies continuously with the quantity borrowed or saved. I f that is the case, at any point in which the function is differentiable, it is still possible to write down an Euler equation which, relative to Equation (8), contains an additional term referring to the derivative of the interest rate with respect to the asset position 34:

OAf ,'/3

(l +

Et

= 1

(al)

At those points of the intertemporal budget constraint where the interest rate changes discontinuously (such as zero), Equation (11) will be replaced by an inequality. An alternative to the consideration of interest rates varying with the amount borrowed (or saved) is the assumption that individuals face a limit to the amount they can borrow (which can be zero). Obviously this can be interpreted as a case o f the previous situation, with the borrowing rate being infinite at the limit. Even in this case, however, there are several alternatives. It is possible, for instance, that the limit an individual can borrow is not fixed but a function of some variables which, in turn, can be endogenous 35. Finally, it is possible to consider the existence of collateralizable loans. When liquidity constraints take the form of a limit to borrowing, it is still possible to write the Euler equation for consumption, as long as the constraint is not binding. When it is binding, instead, the Euler equation will hold as an inequality, or as an equality with the addition of a slack variable (a Kuhn-Tucker multiplier). Equation (8) becomes E,

[ C'+Yl(1

]

= 1 +~tt,

(12)

where #t is an unobservable Kuhn-Tucker multiplier associated to the borrowing restriction. If instead of considering a homogeneous consumption good, one considers several commodities explicitly, assuming that none of them is durable or can be used as a collateral, for each of these commodities it is possible to obtain an equation of the following form: OU( ) _ ,~,p~ + ~,,

where At is the marginal utility of wealth and Pl is the relative price of commodity i. Notice that gt appears in the first-order conditions for all commodities, so that any

34 A paper which contains this type of analysis is Pissarides (1978). 35 Alessie et al, (1989) and Weber (1993) consider the possibility that the limit to borrowing is a function of earnings.

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two of these equations can be used to eliminate it. This implies that the intratemporal first-order conditions hold regardless of the presence of liquidity. Meghir and Weber (1996) used this intuition to distinguish between liquidity constraints and intertemporal dependence in preferences. They consider three different non-durable commodities and stress that the presence of dynamic effects in the Euler equation can be rationalised with intertemporal non-separabilities only if the same dynamic effects are found in the intratemporal first-order conditions. On the contrary, if one finds that the intratemporal conditions do not show any sign of dynamic effects while these appear in the Euler equations, one should interpret this evidence as a sign of binding liquidity constraints. Some studies have explored the possibility that some commodities, such as durables, can be used as collateral to relax the severity of borrowing restrictions. Because durables can be used as collateral, when liquidity constraints are binding, they become relatively more attractive than non-durables. This fact has implications for the withinperiod allocation of resources between durables and non-durable consumption. In the absence of liquidity constraints, this would depend only on the relative price and on their marginal rate of substitution (where the relevant price for durables would be their user cost). In the presence of liquidity constraints, however, an additional term has to be added to the first-order condition to reflect the fact that it is possible to use durables to borrow against future resources. Therefore, as Chah, Ramey and Starr (1995), Brugiavini and Weber (1994) and Alessie, Devereux and Weber (1997) have noted, the possibility of using durables as collateral and the presence of liquidity constraints distorts the intratemporal allocation of resources between durables and nondurables. At several points in the discussion so far ! have stressed that even when liquidity constraints are present, if they are not binding, the Euler Equation (8) will hold. Therefore, such an equation and the mis-specification tests conducted on it (such as tests of 'excess sensitivity') are likely to be a poor tool to identify the presence of borrowing restrictions. In addition to the power considerations just made, in what follows I also stress that evidence on excess sensitivity can often be interpreted as evidence of non-separability between consumption and leisure. The fact that the Euler Equation (8) holds whenever the borrowing restrictions are not binding does not mean that these constraints have no effect on the level of consumption. Indeed, as discussed clearly by Hayashi (1987), the presence of potential liquidity constraints has the same effect as that of a shortening of the horizon relevant for current choices. Alternatively, one can interpret the presence of liquidity constraints (when they are not binding) as an increase in the discount factor. From a policy perspective, liquidity constraints are important because of their effect on the level of consumption, rather than on its changes. In other words, what matters is how consumption reacts to unexpected changes in the economic environment (including policy changes). Euler equations are not informative about this. Deaton (1991) provides one of the first analysis of the effect of liquidity constraints on the level of consumption. By solving the Euler equation numerically, he shows that the behaviour induced by the presence of liquidity constraints is similar to that

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associated with a precautionary motive for saving. As in the precautionary motive for saving, people will accumulate a buffer stock to avoid the possibility of needing a loan that they cannot obtain. Furthermore, the liquidity constraint will be binding only occasionally as during most periods, individuals avoid, by their optimal behaviour, to find themselves constrained. For liquidity constraints (or precautionary saving) to be relevant for individual behaviour, it is necessary that the households concerned want to borrow, that is they face an increasing income path and are impatient enough to -want to bring resources from the future to the present. Even in such a situation, however, it is not necessary that the Euler equation restrictions are violated. If one rules out the possibility of dying in debt and considers finite lives and a marginal utility of consumption that goes to infinity when consumption goes to zero, it is possible that 'liquidity constraints' are generated endogenously by the model. In particular, to avoid the possibility of having zero resources (and therefore zero consumption) in the last period of life, individuals will not want to borrow any amount in excess of what they can repay with probability one. Notice that in such a situation, consumption in any two periods satisfies the Euler

equation 36. From a theoretical point of view, the considerations above indicate that a profitable research strategy is one which aims at characterising the response of consumption to various news when liquidity constraints are relevant (regardless of whether they are binding). Deaton (1991) constitutes a first important step in this direction. On a more specific level, the analysis in Hubbard, Skinner and Zeldes (1994, 1995) constitutes another good example of how a consistent theoretical model incorporating borrowing restrictions can be used and be informative about important policy issues 37 Several other interesting problems remain to be modelled and understood. If labour supply choices are endogenous, the presence of liquidity constraints might induce female labour force participation. These effects might be strengthened if the ability to borrow is linked to earnings 38. All these issues are examples of the need to be able to use the model to make statements about consumption levels that I discuss again below. Identifying the presence and the relevance of borrowing restrictions is not easy. One possibility is to use direct questions on the matter. Jappelli (1990) used this strategy and analysed the answers to some questions contained in the Survey of Consumer Finances in the USA. The households interviewed in 1983 were asked whether they were denied credit or whether they did not applied because they felt they would be denied. The main problem with this research strategy is that very few household surveys contain questions similar to those analysed by Jappelli.

36 This point was also noted in Hayashi (1987). 37 Jappelli and Pagano (1994) eharaeterisethe link between liquidityconstraints, saving and growth. 38 See O'Brien and Hawley(1986).

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The presence of (binding) liquidity constraints has some direct implications for the demand for loans. Its analysis constitute therefore an interesting possibility for the identification of borrowing restriction and for evaluating their importance. If consumers are subject to binding borrowing restrictions they will be at a kink (or in a relatively steep section) of an intertemporal budget constraint. Their demand for loans, therefore, will not be much affected by changes in the interest rate. On the contrary, if consulners are not at a corner (or in a relatively fiat part of the budget constraint) their demand for loans will be elastic to the interest rate. The effects of maturity, however, should be opposite. A consumer who is not affected by borrowing restrictions will be indifferent to changes in maturity. On the other hand, a constrained consumer, for whom an increase in maturity will effectively increase his ability to borrow by reducing the size of the payments to maturity, will increase its demand for loan. Juster and Shay (1964) were the first to use this intuition using semi-experimental data. They asked a sample of consumers whether they would finance the hypothetical purchase of an automobile when faced with different packages of interest rates and maturity. The packages of interest rate and maturity were randomised to the individuals in the sample so to enable the estimation of the interest rate and maturity elasticity of the demand for loans. In a recent paper, Attanasio and Goldberg (1997) develop the work of Attanasio (1995b) and perform a similar exercise but on a sample of households who actually purchased (and occasionally financed) automobiles. The main advantage of the Attanasio and Goldberg exercise is that their data refer to actual choices. The main disadvantage relative to the work of Juster and Shay (1964) is that for the households that decided not to finance their car purchases neither interest rates nor maturity are observed. This poses a number of econometric problems that are similar to those that labour economists deal with when analysing participation choices and labour supply.

3.6. Taking into account demographics, labour supply and unobseroed heterogeneity In the previous sections, for the sake of expositional simplicity, I have neglected the vector of observable variables z and the unobserved component v in Equation (4). Their exclusion, however, especially if one wants to estimate or test the model, would be unrealistic. It is quite obvious, for instance, that family size and composition affect the marginal utility of a given amount of consumption expenditure. It is also likely that labour supply behaviour, and in particular female labour supply, will also affect the utility derived from expenditure. Working often implies bearing a certain number of costs that range from transport, to eating out, to clothing. Furthermore, if both spouses work, a number of services that would be produced at home by the partner not participating in the labour force would have to be purchased on the market and would be counted as consumption. More generally, it is plausible that consumption and leisure are not separable in the utility function and that consumption, saving and labour supply choices are taken simultaneously.

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Given these considerations, it is important, especially if one wants to bring the model to the data, to consider a specification that allows for these factors. While it is true, as shown in Section 2, that consumption life cycle profiles often mirror income profiles, it is not obvious that one should interpret this as evidence of the empirical failure of the model without considering explicitly the possibility of important demographic effects and that consumption and leisure are not separable. These are not new arguments and I discuss them at length in Section 5, where I interpret the available evidence. The point of this section, however, is to stress that the consideration of these factor is not only important, but also relatively simple. If one does not want to model explicitly these variables, controlling for them does not jeopardise the empirical tractability of the model illustrated by Equations (8) and (9). I re-write a slight modification of Equation (4) for convenience: T-t

max Et Z [3J U(Ct+j, nd zt+j, vt+j), j=o

(4')

where the superscript nd indicates that I am now modelling explicitly only non-durable consumption. As before, the vector of observable variables z indicates variables that are relevant for the intertemporal optimisation problem. The variable u is unobservable to the econometrician. The latter variable is sometimes referred to as 'taste shift'. More generally, it represents all the unobservable factors that affect consumption choices and that we do not model or control for. The variables included in the vector z may range from demographic variables, to labour supply variable, to other components of consumption (such as services from durables). Notice that these variables may be either exogenous to the choice problem (age is a good example), or chosen simultaneously with non-durable consumption (such as labour supply). Even if one does not wish to model these latter variables explicitly, it is possible to identify, using Equation (4I), conditional preferences and the associated parameters under very mild conditions 39. If the z variables in Equation (4 ~) enter the utility function in an additive separable fashion there is no need to consider them. If, on the other hand, they affect the marginal utility of non-durable consumption, they will enter the corresponding Euler equation. As an example, let us consider the following parametrization: U ( C t d, zt, ot) -

(cpd)l-7 exp(O'zt + 1-y

ut).

(13)

A possible interpretation of Equation (13) is that the discount factor varies with variables z and v. Such an interpretation is particularly attractive for demographic variables. In this case, the vector of parameters 0 implicitly represents an equivalence scale.

39 See the discussion in Browningand Meghir (1991) on demand systemsconditionalon labour supply.

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Consumption

Under the parametrization used in Equation (13), the Euler equation for non-durable consumption will be

E, [ \ ~ - j

[(,q,+a)

(1 + R ~ + , ) / 3 e x p [ O ' ( z t + l - z , ) +

v t + x - vt]

l

= 1.

(14)

It should be stressed that Equation (14) holds even if some of the variables included in z are endogenous choice variable, regardless of the way in which they are determined. Modelling labour supply or durable consumption, for example, can be quite difficult because of corner solutions, intertemporal (non)-separability and transaction costs. These problems do not need to be tackled explicitly and Equation (14) can be considered as an equilibrium relationship that holds at the optimal values of the endogenous z, regardless of how these are obtained. Equation (14) can be linearised in the same fashion as Equation (8) to obtain a log-linear expression similar to Equation (9). Neglecting the second moments, that I incorporate into the constant of the equation, we have: Alog(C~dl) = const. + oR~+1 + OtAZt+ 1 + Avt+l + et+l.

(15)

Notice that because of the presence of the term representing unobserved heterogeneity and taste shocks, the residual of equation has now two components, one which represents an expectational error and, by the assumption of rational expectations, is likely to be uncorrelated over time, and another that has an MA(1) structure if taste shocks are i.i.d, over time. If the unobserved heterogeneity term v has a time invariant component which is individual specific, it will be eliminated in the first differences. On the other hand, it is possible that such a term is persistent (rather than white noise) but not fixed and/or that the 'pure' discount factor/3 is individual specific. In the former case the term Av in Equation (15) would have a structure more complex than a simple MA(1), while in the latter, Equation (15) would have a fixed effect. In Section 5, I discuss these econometric problems. The particular parametrization considered in Equation (13) is just an example. More complex structures may be and have been considered. It is possible, for instance, to allow some of the variables in the vector z to affect the curvature of the utility function as well as the rate at which utility is discounted. Blundell, Browning and Meghir (1994) and Attanasio and Browning (1995) have used this approach and found significant deviations of estimated differences from the simple isoelastic case. The issue is particularly important in that preferences of this kind can allow for systematic differences in the elasticity of intertemporal substitution across consumers. Attanasio and Browning (1995) also stress the fact that to estimate an Euler equation and its parameters, it is not necessary to specify explicitly the within-period utility function. It is possible and analytically convenient to start from a flexible specification

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for the marginal utility of consumption and, if needed, obtain the corresponding utility function by integration 4°.

3.7. Bequest motives

According to the simplest version of the life cycle model sketched at the beginning of the section, the main motivation for individual saving is to provide resources during the last part of the life cycle, when, following retirement, income is low. In such a situation aggregate wealth can be generated by and associated with productivity growth, if the generations that save (the young) are relatively wealthier than those that dis-save (the old). I f the bequest motive is operative, on the other hand, the mechanism through which aggregate wealth is accumulated is quite different. A lively exchange on whether a large or small proportion of aggregate wealth in the USA is accounted for by bequeathed wealth or retirement saving wealth developed in the 1980s between Kotlikoff and Summers [Kotlikoff and Summers (1981), Kotlikoff (1988)] on one side and Modigliani (1988) on the other. The result of that debate remained somewhat ambiguous, as the answer seems to depend mainly on whether one considers the interests earned on bequeathed wealth as originating from bequests or not. A bequest motive can be simply added to the basic model (1) by considering a term which is a function of the bequest left. As it is obvious such a term does not affect the Euler equation for consumption in subsequent periods. It will, however, affect the level of consumption (and saving). One of the implications of the simplest version of the life cycle model is that wealth is decumulated in the last part of the life cycle. While the rate at which wealth is decumulated depends on the parameters of the model and in particular about beliefs about longevity, the result that wealth should decline seems to be robust. The evidence on this point is mixed, in that several studies do not find strong evidence of decumulation of wealth by the elderly 41. When bequests motives are operative, from a theoretical point of view, the wealth age profile can take different shapes in the last part of the life cycle. In an important paper Hurd (1989) has characterised several of these profiles. Hurd also showed that for several realistic sets of parameters, the wealth age profile under bequests is also declining in the last part of the life cycle. From an empirical point of view, Hurd (1989) stresses the importance of conditioning on the labour force status of the individuals in the sample. In particular, whether individuals are retired or not seems to be crucial for the decumulation of their wealth.

40 If one follows such a procedure, one should check the integrability conditions. 41 JappeUiand Modigliani (1997) have forcefully argued that pension benefits should be considered as decumulation of pension wealth.

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4. Aggregation issues The models considered in Section 3 refer to the dynamic optimisation problem faced by an individual consumer (or household). The early contributors to the life cyclepermanent income model were quite aware of the aggregation issues involved with the empirical implementation of the theory of intertemporal optimisation. These issues, however, were largely ignored by the literature of the late seventies and early eighties which focused mainly on the rigorous introduction of uncertainty in the model. Aggregation problems, however, cannot be ignored when the model is tested and when is estimated to evaluate structural parameters. In this section, I consider briefly two problems: the aggregation across consumers and that across commodities. 4.1. Aggregation across consumers

The Euler equations for (non-durable) consumption that can be derived from the problem in Equation (1) are, for most specifications of preferences, non-linear. As they refer to individual households, their aggregation is problematic. A number of papers have shown that the dynamics of aggregate consumption implied by the Euler equation for individual consumption cannot be described simply by the first moments of the cross-sectional distribution of consumption. Attanasio and Weber (1993), Blnndell, Pashardes and Weber (1993b) and Blundell, Browning and Meghir (1994) have shown that higher order moments can play an important role. Attanasio and Weber (1993), in particular, have stressed that the use of aggregate data to estimate an Euler equation is equivalent to omit high moments of the cross sectional distribution of consumption and might cause systematic biases in the estimation of structural parameters and lead to rejections of the over-identifying restrictions 42. These contributions will be discussed when I evaluate the empirical evidence, at this point I only wanted to stress that exact aggregation is in general impossible when considering the Euler equation for consumption. This implies that aggregate data cannot be used to estimate structural preference parameters and/or to test the model. Individual panel data on consumption might be very difficult to obtain. Partly because of this, many of the papers I discuss in Section 5 use the average cohort data that I have used in Section 2 to describe the individual data. The use of grouped data allows one to use time series of repeated cross section to study dynamic models. In this sense, average (or synthetic) cohort data are particularly useful to study life cycle models. It is important to stress, however, that synthetic cohort data are aggregate data; the difference relative to National Accounts data is that the aggregation process is controlled directly. As a cohort ages, the researcher can follow the evolution of the variables of interest, that range from consumption to income, to family size and

42 Blundell, Pashardes and Weber (1993b) make a similar point for a demand system. Similar results were obtained in an asset pricing frameworkby Constantinides and Duffle (1996).

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composition, to labour supply behaviour. The presence ofnon-linearities in the relevant equations (as long as they are linear in the parameters) does not constitute a problem, as one can compute the relevant non-linear transformations before averaging the data. Unlike in the aggregate data, therefore, time series of the average of any non-linear transformations of the variables of interest is readily available. In addition to the standard aggregation problems caused by the non-linearity of the Euler equations, there is another sense in which aggregation across consumers can be problematic. As discussed above, it is likely that demographic variables are likely to be important for the determination of consumption. If one does not want to make arbitrary assumptions about the effects that these demographic variables have on the utility function, it might be necessary to consider individual data explicitly 43. In the aggregate, demographic variables move quite slowly so that, even neglecting nonlinearities, their effect cannot be estimated precisely from those data. On the contrary, differences across cohorts, observed over different parts of their life cycle, can be profitably be exploited to identify these effects. Finally, because repeated cross sections are much more common than long panels, one can estimate the structural parameters using a relatively long time period. The importance of a 'large T' in getting consistent estimates is discussed in section 5. The use of average cohort data is not without problems. Probably the most important is that of the presence of measurement error and sample variation. Particular care has to be devoted to evaluating the quality of the data and to use the appropriate econometric techniques. 4.2. Aggregation across commodities

Another important aspect which is often neglected in the literature on the Euler equation is the aggregation of expenditure on different commodities. In principle, one should consider simultaneously the allocation of total expenditure across time periods and the allocation within each period across different commodities. I f one had detailed enough data on expenditure on individual commodities and was willing to specify the form of the direct utility function, the problem could be addressed in a straightforward manner. One could consider the Euler equation defined in terms of the marginal utility of each individual commodity. The issue, however, is to determine under what conditions one can consider the within-period utility function defined in terms of total consumption and assume that the allocation of expenditure over time can be determined with the help of a single price index. One obvious and not particularly interesting answer is when relative prices do not change so that it is possible to construct a Hicks composite commodity. Gorman (1959) was the first to provide a more interesting answer in that he derived

43 Estimation of the effects of demographic variables can be interpreted as the estimation of adult equivalent scales and is therefore important for a variety of reasons.

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the conditions that the utility function has to satisfy so that it is possible to consider a single commodity 44. In particular, it is necessary that preferences take the generalised Gorman Polar form, that is, i f X is the K x 1 vector of commodities andp the vector of corresponding prices, the indirect utility function has to take the form

V(X, p) = F(X/b(p), a(p)),

(16)

where b(p) and a(p) are functions homogeneous of degree 1 and degree 0 respectively and depend on within-period preferences. From the specification in Equation (16) one can derive an Euler equation for total consumption expenditure: two-stage budgeting can be used to separate the intertemporal from the within-period allocation. To implement Equation (16) it is necessary, however, to estimate the price functions a(p) and b(p), which requires the specification and estimation of a within-period demand system. In an important paper, Blundell, Browning and Meghir (1994) estimate a demand system and use the resulting price indexes to estimate the Euler equation for total consumption expenditure. A remarkable result they obtain is that a Stone price index (which does not require the knowledge of preference parameters) constitutes a good approximation to the price indexes in Equation (16). This result is important because points to a simple way to implement Euler equations for non-durable consumption without estimating the entire demand system. The results in Blundell, Browning and Meghir are generalised to a demand system with quadratic Engel curves by Banks, Blundell and Preston (1994). Attanasio and Weber (1995) with a different parametrization of the indirect utility function find a statistically significant role for the zero-homogeneous price index a(p) on US data. If one is willing to specify a utility function defined over several commodities, one can derive an Euler equation for each of these commodities. Under the assumption of additive separability, each of these Euler equation depends only on expenditure on that commodity, nominal interest rates, changes in the commodity-specific price index and on the relevant controls. On the other hand, when additive separability does not hold, the individual commodity Euler equation depends also on the consumption of other commodities. This is an important point in that creates problems for the use of data sources which contain information only on some components of total expenditure, such as the US PSID which gives only information on food consumption. Attanasio and Weber (1995) show that the consideration of food consumption in isolation can yield very misleading results. 5. Econometric issues and empirical evidence

I now move to consider the empirical evidence on the life cycle-permanent income model. In the process of doing so, I also discuss some of the econometric problems 44 See Deaton and Muellbauer (1980) for a clear discussion of these issues.

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relevant for theanalysis. As I want to have a rigorous treatment of uncertainty, I only consider the contributions that followed the Hall (1978) paper. I start with a discussion of studies based on aggregate data and then discuss some based on individual data. As ! focus mainly on studies based on Euler equations, I do not discuss a large empirical literature, which has estimated flexible error correction models for aggregate consumption that I have mentioned in Section 2. 5.1. Aggregate time series studies

Because of the aggregation problems discussed in Section 4.1, it is my opinion that aggregate time series data cannot be used to estimate structural preference parameters and test the life-cycle model. Indeed, some papers, such as Attanasio and Weber (1993, 1995), have shown that aggregation issues can easily explain some of the rejections of the model found in the literature. Nonetheless, the papers that have tested the life cycle-permanent income model using aggregate time series data are many and almost impossible to list. Many of the most influential papers in the literature on consumption, such as those by Hall (1978, 1988), Hansen and Singleton (1982, 1983) and Flavin (1981), have been useful conceptual exercises that have brought to the attention of the profession many important issues. Among the most influential and most widely cited studies of aggregate time series papers are those of Campbell and Mankiw (1989, 1991). In these papers the authors consider a simple version of the Euler Equation (5) and estimate it on aggregate data with the addition of income growth on the right hand side. The justification they use for such a specification is that there is a fraction )~ of consumers behaving according to the permanent income-life cycle model while the remaining follow a 'ruleof-thumb' which consists in setting their consumption equal to their disposable income. Several scholars have since interpreted the coefficient ( 1 - ) 0 estimated by Campbell and Mankiw as the fraction of consumers that are 'liquidity constrained'. Campbell and Mankiw estimate their equation by instrumental variables 45 and obtain a coefficient ( 1 - ) 0 of 0.4. There is no reason to believe that the 'excess sensitivity' of consumption to income, as summarised in such a coefficient, represents the fraction of consumers that behave according to Campbell and Mankiw's rule of thumb. First of all, one would have to assume that, if the consumers behaving according to such a rule were the same, the fraction of income (and consumption) accruing to them was constant over time. Second, one would have to believe that the non-linearities in the Euler equation have no effect and could not generate such a result. Finally, to exclude that income and consumption are unrelated under the life cycle model, one would have to believe that consumption and leisure are separable in the utility function.

45 Because they worry about time aggregation, Campbell and Mankiw use instruments dated t - 2 and earlier.

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More recently, in the spirit of the Campbell and Mankiw studies, several papers have studied the time series properties of aggregate consumption and have tried to interpret its relation to a number of other variables in terms of the life cycle-permanent income model or as alternative deviations from it. Carroll et al. (1994), for instance, relate consumption to the index of consumer confidence and provide some interpretation of the high predictive power that such a variable has. Ludvigson (1997), on the other hand, relates consumption to consumer credit and finds that 'excess sensitivity' of consumption to such a variable is even more marked than that to labour income. In the past, some of the papers that used aggregate time series data have also tried to incorporate in the model the possibility that consumption and leisure are not separable in the utility function. Bean (1986), Eichenbaum and Hansen (1988) and Mankiw, Rotemberg and Summers (1985) are examples of these attempts. The presence of corner solutions in labour supply, such as those observed in the case a spouse does not participate to the labour force or in the case of retirement, make the aggregation issues even more complicated.

5.2. Micro data: some econometric problems The analysis of household data on consumption presents a variety of problems that range from the availability and reliability of individual consumption data, to some subtle econometric problems. Of the many problems that is worth stressing three in particular are relevant for the discussion at hand. The first relates to the way in which consistent estimates are achieved from the orthogonality conditions implied by an Euler equation for consumption. The second concerns instead estimation and inference with average cohort data instead of genuine panels. The last point is about the presence of conditional second moments in the (log) linearised Euler equation.

5.2.1. Consistency of estimators derived from EuIer equations The first issue was pointed out by Chamberlain (1984) and subsequently discussed by Itayashi (1987), Altug and Miller (1990) and Deaton (1992) among others. The Euler equation for consumption for a generic individual i can be written as follows: i i Et [h(xt+l,x t, 0)] = 0,

(17)

where 0 is a vector of parameters and x a vector of observable and unobservable variables. Equation (17) states that a function of parameters and variables is orthogonal to information available at time t. If the unobservables are i.i.d, innovations to stationary processes, we can, without loss of generality, restrict the vector x to be made of observable variables. In such a situation one can identify a vector of instruments wt that, if its size is greater than the dimension of the parameter vector, can be used to identify it. The problem arises if one tries to exploit the cross sectional dimension rather than the time dimension to construct the sample equivalent of Equation (17). Equation (17)

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implicitly defines expectational errors, which by rational expectations are orthogonal with lagged information, o f which, typically, the instruments are part. There is no reason to believe, however, that expectational errors average to zero in a cross section, at a given point in time. Analogously, there is no reason to believe that the cross sectional covariance o f h in Equation (17) with the vector o f instruments w equals zero. The addition o f time dummies, therefore, is not a solution for the problem at hand: each orthogonality condition one considers would imply the inclusion o f a vector of dummy variables. The only condition under which one can use the cross sectional equivalent of Equation (17) under which introducing a vector o f time dummies can solve the problem is when the expectational errors at a point in time are known to be exactly the same across individuals. But this is equivalent to assume complete markets. This is the option chosen, for instance, by Altug and Miller (1990) and by Atkeson and Ogaki (1996). If one is not willing to assume complete markets, the only alternative is to have a sample covering a long time horizon. This is necessary so that expectation errors average out to zero. Notice that the 'large T' refers to the total length o f the sample period over which individuals (or groups of individuals) are observed and not to the length over which a single individual is observed 46. The necessity of a 'large T' to obtain consistent estimates of the parameters o f an Euler equation follows from the nature o f the residuals of such an equation which incorporate expectational errors. The same argument does not apply to the residuals o f intratemporal (within-period) first-order conditions. Indeed, if expectational errors are the only component o f the residuals, such equations should have a perfect fit. It is for this reason that the consideration o f unobserved heterogeneity is crucial in the specification o f preferences [see Equation (13) above]. As mentioned in Section 3.6, the presence o f unobserved heterogeneity has implications on the nature o f the residuals of the Euler equation. The specification of preferences in Equation (13) implies that in Equation (9 ~) unobserved heterogeneity enters in first differences, so that, depending on the time series properties o f v~, the properties of the Euler equation residuals will be different. If the unobserved heterogeneity term v I has a time invariant component which is individual specific, it is differenced. If v I has a unit root, its differences would be white noise. I f the deviation o f v~ from a constant component are white noise, the residuals of the Euler equation are an MA(1) process. This has implications for the choice o f instruments and the computation o f the standard errors. The situation is more complicated if the deviations o f v I from its fixed component are persistent (rather than white noise) and/or if the 'pure' discount factor /3 is

46 A problem similar to the one just discussed is the issue of the presence of individual fixed effects in the Euler equation for consumption. These could arise, for instance, if the discount factors contain an individual specific component. In this case, the use of weakly exogenous instrument would be invalid. For a discussion of the issues related to this problem see Keane and Runkle (1992) and the comments to that paper in the Journal of Business and Economic Statistics.

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individual specific. In the former case the term Ao in Equation (9 ~) would have a structure more complex than a simple MA(1), while in the latter, Equation (9 ~) would have a fixed effect. In such a situation the choice of instruments is not trivial, in that lagged individual variables are, in principle, correlated with the residuals of the Euler equation. The problem might be less severe if one uses average cohort data: grouping the individuals belonging to a given cohort averages out the individual fixed effects and leaves only the cohort specific ones. Here the availability of a long time period is once again crucial: it is possible to estimate cohort specific fixed effects (say in discount factors) by introducing cohort dummies in the Euler equation. The necessity of a 'large T' to obtain consistent estimates of the parameters of an Euler equation follows from the nature of the residuals of such an equation which incorporate expectational errors. The same argument does not apply to the residuals of intratemporal (within-period) first-order conditions. Indeed, if expectational errors are the only component of the residuals, such equations should have a perfect fit. It is for this reason that the consideration of unobserved heterogeneity is crucial in the specification of preferences (see Equation 13 above).

5.2.2. Average cohort techniques The lack of true panel data has often forced researchers to use the synthetic cohort data, which I have used in Section 2 for descriptive purposes, to estimate and test dynamic models, such as the Euler equation for consumption. The use of these techniques, pioneered by Browning, Deaton and Irish (1985) and discussed by Deaton (1985) and more recently by Moffitt (1993), has several advantages over real panels 47. Nonrandom attrition, for instance, is much less of an issue. On the other hand, one should be careful about the econometric problems induced by these data. In particular, because the size of the cell one uses to compute averages of the variables of interest is less than infinite, one should consider explicitly the presence of sampling error in the data one uses. Furthermore, because the averages are computed on the levels of variables and one is typically interested in the first differences of variables, the presence of sampling error induces an MA(1) structure on the residuals of the Euler equation estimated on synthetic cohort data. The presence of MA(1) residuals obviously has implications for the choice of the instruments and the computation of standard errors. The fact that synthetic cohort data are typically constructed out of independent repeated cross section, however, suggests simple valid instruments: by lagging the instruments an extra period should guarantee consistency of the IV estimator 48.

47 Average cohort techniques can be interpreted as an example of an estimator using complementary data sources of the kind discussed in Arellano and Meghir (1992). 48 The Consumer Expenditure Survey used, for instance, in Attanasio and Weber (1995) is a rotating panel so that the construction of valid instruments is more complicated.

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The structure of the errors is even more complicated when one considers more cohorts simultaneously. In this case, one has to keep into account the possibility that the residuals of different cohorts in the same time period are correlated. The variance covariance matrix of the residuals is therefore quite complex. Its computation is, however, important to make correct inferences 49. Besides adjusting the estimated standard errors for the presence of an MA(1) error and the correlation among the expectationat errors of different cohorts, it is also possible to use a GLS type of scheme to improve the efficiency of the estimator. One should be careful, however, in filtering the data so to avoid the inconsistency caused by the correlation of lagged expectational errors with the instruments 5o. 5.2.3. Conditional second (and higher) moments

In Equation (9~), as in Equation (10), I have neglected the presence of conditional second (and, if the log-normality assumption does not hold, higher) moments that follows from the log-linearization of the Euler equation in (6). In theory, this is not quite correct in that these variables are likely to vary as new information is made available to the individual consumer. This is particularly true for the conditional variance of consumption which is endogenously determined by the model (consumption is a choice variable). Incorporating these variables in the constant is equivalent to assuming that innovations to the conditional second (or higher) moments of consumption and interest rates are uncorrelated with the variables typically used as instruments. Assessing the plausibility of this assumption is very difficult, especially because the answer is likely to depend on the time series properties (and in particular on the heteroscedasticity) of the determinants of consumption levels (income, wages and so on). In a recent paper, Ludvigson and Paxson (1997) have used numerical methods to compare the consumption function obtained from a log-linearised Euler equation to the 'true' one. Their method, however, does not provide estimates for the bias introduced in Euler equation estimation. Carroll (1997b) also uses numerical techniques to simulate log-linearised Euler equations, but focuses on the cross sectional rather than time series dimension, which, given the considerations in 5.2.1 is the relevant one. An interesting and novel approach to this problem is the one used by Banks, Blundell and Brugiavini (1997) in a recent paper. These authors use an approximation to the consumption fimction derived by Blundell and Stoker (1999) which implies weighting the conditional second moments by the ratio of income to wealth at a given point in time. Banks et al. (1997) also try to identify separately the effect of aggregate and cohort specific shocks. The main findings of the exercise are two. First, conditional

49 A technical problem arises from the fact that is not easy to guarantee that the estimated variance covariance matrix is positive definite in finite samples. 50 See Hayashi and Sims (1983).

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second moments are significant in the Euler equation; and second, the estimate of some important structural parameters, such as the elasticity of intertemporal substitution, is not much affected by the introduction of the conditional second moments. Yet another alternative to the log-linearization procedure is the one proposed in Attanasio and Browning (1995) who start with a flexible functional form for the (log) marginal utility of consumption so to avoid the necessity of approximating an Euler equation. Should one be interested in the utility function that generates such a function, one can obtain it by integration. Not only does this method avoid dealing with the issue of linearization, but gives the possibility of estimating much more flexible functional forms than the isoelastic one. This is not to say that precautionary motives are unimportant, but that their relevance is going to depend on the curvature of the marginal utility of consumption and is, in the end, an empirical matter. The alternative of estimating a non-linearised Euler equation (such as Equation 8) is particularly unappealing because it would imply assuming away measurement error and would, in any case, make the use of average cohort techniques much harder, if not impossible. 5.3. Micro data: some evidence

In this section, I do not discuss in detail all the papers that have estimated and tested Euler equations for consumption using micro data. Rather, I summarise some of the main contributions with an eye to the overall evaluation of the evidence which I give in the next sub-section. One of the first papers to consider the implications of the permanent incomelife cycle models with micro data is Hall and Mishkin (1982) in which the authors used PSID data to test and reject the implication that consumption changes were uncorrelated with lagged values of current income. Hall and Mishkin (1982) evidence was later criticised by Altonji and Siow (1987) because it did not allow for measurement error. Hall and Mishkin (1982) focused on the permanent income hypothesis and did not consider explicitly the Euler equation that one can get from the consumer intertemporal optimisation problem. One of the first, and probably the most influential article to take such an equation to the data, was the paper by Zeldes (1989a), who implemented ideas very similar to those in Runkle (1991). In both articles, the Euler equation is fitted to observations on food consumption from the PSID. In both articles, the authors consider explicitly the possibility of liquidity constraints and the possibility that these constraints affect different group in the population differently. Effectively, Zeldes (1989a) and Runkle (1991) estimated versions of Equation (12) for different groups of the populations that had, on the basis of an observable variable, different probabilities of having/tt = 0. The results they get, however, are quite different. Zeldes (1989a), in particular, splits the sample according to the wealth held and finds that the rate of growth of consumption is related with the lagged level of income for the low wealth sample. The

790

O.P. Attanasio

same result does not hold for the high wealth sample. Zeldes interprets this results as evidence of binding liquidity constraints for a large fraction of the population. Runkle (1991), who uses a different extract of the PSID, and different econometric techniques, obtains different results 51. Since Zeldes (1989a) and Runkle (1991), many papers, including Hayashi (1985a,b), Garcia, Lusardi and Ng (1997), Lusardi (1996), Mankiw and Zeldes (1994) and Shea (1995), have used PSID data, either alone or in conjunction with other data, to estimate and test various versions of the model. Shea (1995), in particular, identifies a subsample of PSID households for whom he can track their union wage contracts and therefore construct a good measure of their expected wage growth. As many others, Shea (1995) tests (and marginally rejects) the hypothesis that consumption growth is not related to wage growth. Shea (1995), however, also notices that liquidity constraints imply an asymmetry between households who expect a decline and a rise in wages, because the former should be saving rather than borrowing. As he fails to identify these effects, his results cast doubts about the plausibility of liquidity constraints as an explanation of the excess sensitivity of consumption growth to income or wage growth. One of the main problems with the PSID is that the measure of consumption that is included in the survey refers only to food consumption. I have stressed above the theoretical problems with such a measure. Attanasio and Weber (1995) show how the use of such a measure of consumption can lead to misleading results. In that paper, my co-author and I use average cohort data constructed from the CEX for the period 1980-1992 to show that some of the excess sensitivity results obtained on micro data can be accounted for by the non-separability of food and other consumption. The other two issues on which Attanasio and Weber (1995) focuses are the effects of aggregation over consumers and over commodities. As far as the aggregation over commodities is concerned, Attanasio and Weber (1995) find significant effects of the zero-homogeneous price index in Equation (14) that, however, are not quantitatively important. This evidence is consistent with that for the UK FES reported in Blundell, Browning and Meghir (1994) and Banks, Blundell and Preston (1994). About the aggregation over individuals, Attanasio and Weber (1995) report evidence which shows that the effect of the non-linearities in the Euler equation can be quite important. This is consistent with the evidence reported in Attanasio and Weber (1993) on FES data. In the latter paper, my co-author and I show that aggregating the individual data so to obtain an aggregate conceptually similar to the National Accounts statistics (i.e. taking the log of the arithmetic mean of consumption) one obtains results that are quite similar to those obtained with aggregate times series data. In particular, it is possible to obtain excess sensitivity to predicted income, a low estimated elasticity of intertemporal substitution and rejection of the overidentifying

51 Keane and Rtmkle (1992) have recently re-estimated Zeldes' equations on his data but using different econometrictechniques. Jappelli, Pischke and Souleles (1997) match SCF data, which contain information on self reported 'liquidity constrained' status with PSID data.

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restrictions. The results obtained aggregating the data in the proper way (i.e. taking the average of log consumption), however, are much more consistent with the theoretical model. In particular, there is no rejection of the overidentifying restrictions. The difference between the log of the average and the average of the log is a measure of inequality which varies over the business cycle and is likely to be correlated with the instruments used in estimating the Euler equation. The last group of papers I have cited [Attanasio and Weber (1993, 1995), Blundell, Browning and Meghir (1994), Banks, Blundell and Preston (1994), Attanasio and Browning (1995)] all stress the importance of controlling for demographic factors and for labour supply effects. These papers, which use average cohort data for the UK and the USA (the data presented in Section 2) show that once one controls for the influence that demographics and labour supply might have on the marginal utility of consumption, there is no evidence of excess sensitivity of consumption to income or rejection o f the overidentifying restrictions. Female labour force participation and family size seem to be particularly important in this respect 52. If one believes that the estimation of the Euler equations discussed in this section yields consistent estimates, the parameter on the real interest rate can be interpreted as the elasticity of intertemporal substitution. Such a parameter is of some importance for a number of policy issues and its size has been discussed at length. Hall (1988) in particular, claims that the use of the correct instruments delivers very low estimates of this elasticity. However, the evidence that emerges from the micro studies which use an isoelastic specification of preferences [such as Attanasio and Weber (1993, 1995), and Blundell, Browning and Meghir (1994)], is that, both in the UK and in the USA, the elasticity of intertemporal substitution of consumption (EIS) is just below 153. From the discussion above, it is clear that in addition to the EIS, a number of other parameters, measuring the effect of leisure, that of demographics or other variables affecting the marginal utility of consumption are likely to be extremely important in determining the level of consumption. Their interpretation, however, is not easy without a solution for the level of consumption.

6. Where does the life cycle model stand?

It is now time to take stock on the empirical relevance of the models discussed so far. My reading of the evidence briefly presented in Section 5 is that the life cycle model, enriched to account for the effect of demographic and labour supply variables, is not rejected by the available data. Alternatively, and perhaps more accurately, one could

52 Demographicvariablesmight be capturing the effect of the conditional second (and higher) moments ignored in the log linearization procedure. Lusardi (1996) criticises the use of income data in the CEX as they might be affected by measurement error. 53 As mentioned above, the use of aggregate rather than individual data and aggregation problems can explain part of the differences in the size of the estimatesof the elasticity of intertemporal substitution.

792

0.t?. Attanasio

say that the life cycle model can be made complex enough not to be inconsistent with the available data. This view is not widely accepted in the profession so that it deserves some discussion. Before discussing these issues, however, a number of caveats are in order. First, the model has been fitted with success only to households in the middle of their life cycle. While these account for a large fraction of aggregate consumption, additional work is needed to understand the behaviour of young and elderly households. The behaviour of retirees in particular, can be quite difficult to model. I f leisure and consumption are non-separable in the utility- function, a radical change in labour supply could be linked to a change in consumption. Furthermore, a number of other important factors, ranging from family size, to health status, to the probability of death, changes dramatically in the years after retirement. In section 2, we have seen that both in the USA and especially in the UK, consumption drops substantially at retirement. This could be related to insufficient savings and a misperception about the amount of (public and private) pension benefits. Alternatively, the drop in consumption could be explained within the optimisation framework of the life cycle model if considered together with all the changes mentioned above. This important topic is studied in a recent paper by Banks, Blundell and Tanner (1998) who find that, even ignoring health status and mortality issues, two thirds o f the drop in consumption observed around retirement can be rationalised by an optimisation model. Second, while the endogeneity of labour supply choices can be controlled for in the empirical analysis, the joint modelling of consumption and of labour supply is extremely valuable and is still at the beginning 54. Similarly, expenditure on durables, which is an important component of total expenditure, needs to be modelled in a different way, as discussed in Section 8. Third, the fact that a particular specification of preferences fits the data reasonably well and that one can obtain consistent estimates of the structural parameters, does not mean that borrowing restrictions and liquidity constraints are unimportant. The Euler equation can be a very poor tool for identifying the presence of such phenomena, as the equation holds whenever the constraints are not binding. For the notion of liquidity constraints to be useful, however, it is necessary to model the behaviour of constrained individual explicitly and determine what the aggregate implications of these constraints might be. A literal interpretation of the papers mentioned in the last part of Section 5 is that a flexible version of the life cycle model, which allows for demographic and labour supply effects in the utility function, cannot be rejected by the data. Neither excess sensitivity tests, nor tests of overidentifying restrictions reject the null. The strength

54 Surprisinglyfew studies analyse consumption and labour supply choicesjointly. An almost exhaustive list includes MaCurdy (1983), Browning, Deaton and Irish (1985), Hotz et al. (1988), Altug and Miller (1990), Blundell, Meghir and Neves (1993a) and Attanasio and MaCurdy (1997). Of these only the last two papers consider female and male labour supply jointly.

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of a result that does not reject the null, however, obviously depends on the power of the test used. The power of the tests of overidentifying restrictions or of the excess sensitivity tests that fail to reject within a sufficiently complex version of the model might be questioned. If an Euler equation is saturated with demographic and labour supply variables, it might be hard to measure precisely the coefficient on expected income or, more generally, reject overidentifying restrictions. This problem might be particularly serious if some of these variables, such as labour supply, are correlated with expected income. In this sense, this criticism is equivalent to state the difficulty in distinguishing hypotheses about preferences from hypotheses on budget constraints. A possible response to this kind of criticism is to check whether the preferences parameters of the model that is not rejected by the data are sensible and, most importantly, whether the model is able to explain facts other than those that have been used to fit it. An example will make this argument clear. In Attanasio et al. (1996), my co-authors and I consider a relatively simple version of the life cycle model where the within-period utility function includes demographic variables and whose parameters are assumed to be the same across education groups. Such a specification of the model is estimated on US average cohort data and it is not rejected by the data. The elasticity of intertemporal substitution is estimated to be just below 1. Given some hypotheses about the stochastic process that generates income, interest rates and demographic variables, and given an assumption on terminal conditions, one can solve numerically for the consumption function at each age. We do so and then simulate the model for income and demographic profiles calibrated on different education groups. With this technique we are able to reproduce some of the main feature observed in the data, that is, that the consumption profiles are steeper for the groups that have a steeped income profiles. This feature of the data has been interpreted as a failure of the life cycle model by Carroll and Summers (1991). Our exercise, however, shows that a flexible version of the life cycle model incorporating some realistic features, such as the effect of family composition on utility, can explain it. The result is remarkable because there is nothing, at the estimation level, that fits the particular feature of the data (differences in consumption age profiles by education groups) that the estimated preferences (assumed to be the same across groups) and the differences in demographic profiles are able to explain. In this sense the exercise constitute a genuine 'out-ofsample' verification of the ability of the model to fit the data. As the utility function is of the CRRA type, the model also incorporates the precautionary motive linked to income uncertainty which Carroll (1997a) has recently advocated as the most likely explanation of the relationship between the shape of consumption profiles and that of income profiles. The simulations show, however, that this effect is quantitatively less important than that generated by differences in demographic profiles. Indeed, most of the 'tracking' of consumption and income profiles is generated by corresponding similarities in demographics. This argument

794

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is also consistent with the evidence presented in Section 2 where consumption 'per adult equivalent' profiles are quite flat over the life cycle 55. The simulation techniques used in Attanasio et al. (1996) are similar to those used by Deaton (1991) and by Hubbard, Skinner and Zeldes (1994), among others, to obtain a closed form solution for consumption. These techniques are the only way, if one is not willing to assume quadratic utility or CARA utility [as in Caballero (1990a)] 56, to obtain a consumption function in the presence of uncertainty. They are quite expensive as they are numerically intensive for any problem which goes beyond the simplest assumptions and require the researcher to take a stand on any detail of the optimisation problem (from the terminal condition to the nature of the income process). The payoff one can obtain can, however, be quite large. The Euler equation approach, first used by Hall (1978) in the consumption literature, was a major innovation. It allowed the rigorous consideration of uncertainty in a complicated dynamic decision problem while preserving the empirical tractability of the model. The beauty of the approach consists in the fact that exploits the main implication of the life cycle-permanent income model, that is that an optimising consumer keeps the discounted expected value of the marginal utility of consumption constant, to eliminate the unobservable 'fixed effect', the marginal utility of wealth, which incorporates the influence of expectations and all the variables that are relevant for the consumer optimisation problem. The price that one pays by differencing out the marginal utility of wealth is, however, non-negligible. While it is true that one can use the Euler equation to estimate structural parameters, one looses the ability of saying anything about the l e v e l of consumption. This implies that without additional information and structure, it is not possible to answer a number of extremely important questions. In other words, the Euler equation for consumption is n o t a consumption function and therefore it does not tell us anything about how consumption reacts to news about the economic environment in which economic agents operate. The symptom of this unsatisfactory state of affairs are apparent in the literature. If one reads, for instance, the literature on saving, which in recent years has dealt with a number of interesting issues that range from the decline in personal saving rates in the USA to the effects of tax incentives on personal and national saving, one rarely finds a systematic use of Euler equation estimates or even references to the Euler equation literature. Indeed, the use of structural models of consumption behaviour is quite rare. On the other hand, the same literature suffers from a number of identification problems that arise from the inability or unwillingness to put more structure onto the descriptive analysis. A good example is the debate on the effectiveness of fiscal incentives to retirement saving.

55 It can be argued that the demographics in the Euler equation for consumption are picking up the effect of the omitted conditional higher moments. 56 Both in the case of quadratic and CARA utility a number of additional assumptions about interest rates are necessary.

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It seems that, 40 years after the publication o f Friedman's book, we still have not been able to construct a 'consumption function' which incorporates the main features of the dynamic optimisation model without loosing analytical and empirical tractability. The development o f the numerical solution techniques referred to above is one possible avenue. The main problem with these techniques, however, is that they require a complete specification of the economic environment (including terminal conditions) in which the agent lives. Therefore, to make the problem treatable, even with the use o f powerful computation methods, very strong assumptions are needed. Furthermore, we cannot use the conditioning arguments which simplify the estimation o f an Euler equation. While at the estimation level variables such as durables and labour supply can be rigorously treated as endogenous without modelling them explicitly, at the level o f numerical solutions, they cannot be ignored.

7. Insurance and inequality One o f the main implications of the life cycle model sketched in Section 3, is the fact that households attempt to smooth consumption over time. I f one sees an individual household in isolation, this can be achieved only through the accumulation of buffer stock saving or through borrowing. However, if one considers the interaction of many households, one realises that if individual shocks are not perfectly correlated, there is scope for the diversification o f idiosyncratic risk and for welfare improving contracts that allow the individual households to share part o f the risk they face. The essence o f a risk sharing situation, as formalised, for instance, by Townsend (1994), is well described by one of the characters in Shipping News, the novel by Anne Proulx set in Newfoundland. Describing life in one of the small islands off the coast, he declares "... it was never easy ... on Gaze Island, but they had the cows and a bit of hay, and the berries, the fish and the potato patches, and they'd get their flour and bacon in the fall from the merchant over at Killiek-Claw, and if it was hard times, they shared, they helped their neighbor. No they didn't have any money, the sea was dangerous and men were lost, but it was a satisfying life in a way people today do not understand. There was a joinery of lives all worked together, smooth in places, or lumpy, but joined." (pp. 16~169) Social and economic interactions in modern western societies are probably much more complex than those that prevailed on Gaze Island. It is however an interesting question to establish to what extent institutions of various kinds are used to smooth consumption across households and to diversify idiosyncratic risk. In other words, it might be interesting to establish the extent to which implicit or explicit contracts, family networks, social safety nets and so on can approximate the intertemporal allocation that would prevail under complete contingent markets o f the kind described in an Arrow-Debreu equilibrium. Furthermore, it might be interesting to establish what are the welfare costs implied by the lack o f complete contingent markets, given the nature of the observed idiosyncratic shocks.

796

O.P Attanasio

From a theoretical point of view, the basic proposition can be derived if one considers the allocation problem faced by a central planner who maximises, given a set of Pareto weights, the average of individual utilities given the resource constraint. This framework is particularly useful because it can be used to control easily for a number of factors and in particular for the presence of multiple commodities, non-separable leisure and so on. The basic implication is that the rate of change of the marginal utility of consumption (which might depend on leisure and other commodities) is equalised across individuals. Townsend (1994) was one of the first to consider the empirical implications of complete market, that is that under certain conditions "... individual consumptions are determined by aggregate consumption, no matter what the date and history of shocks, and so individuals' consumption will move together" (p. 540) 57. While Townsend (1994) considered data from India, other studies, such as Mace (1991), Cochrane (1991) and Hayashi et al. (1996), performed similar exercises using US data, that is either the CEX or the PSID. Both Cochrane (1991) and Hayashi et al. (1996) reject the implications of the risk sharing hypothesis. Cochrane (1991) finds that food consumption changes in the P SID are related to changes in health and employment status. Hayashi et al. (1996) use the same data but control for the possibility that the relationship between changes in wages and consumption is generated by the non-separability of leisure and consumption in the utility function. By following spin-offs in the PS1D, they also test (and reject) the hypothesis that risk is shared among families. Attanasio and Davis (1996) have matched data from the Current Population Survey and the CEX to test the hypothesis that movements in relative wages are reflected into movements in relative consumption or, to be precise, in marginal utilities of consumption. Attanasio and Davis consider education and year of birth cohorts. Most of the variability in relative wages comes from the shifts in the wage distribution across education groups that occurred during the 1980s. They find that such movements were mirrored in movements in the consumption distribution, indicating a 'spectacular failure' of the perfect insurance hypothesis 58. The analysis of Attanasio and Davis is particularly damning for the perfect insurance paradigm because it focuses on economy wide, well observed shifts, and therefore the relationship between consumption and income cannot be explained with models which consider private information such as those in Phelan and Townsend (1991). Attanasio and Davis (1996) also try to evaluate the welfare cost of the lack of an institutional framework that allows for the diversification of idiosyncratic risk. The evaluation of such a cost obviously depends on preference parameters and on

57 Townsend (1994) credits Diamond (1967) and Wilson (1968) with the first versions of this proposition. 58 As Hayashi et al. (1996), Attanasio and Davis (1996) use lead as well as lags of wages as instruments. Both studies consider short and long tun shocks.

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the nature o f the shocks considered. Attanasio and Davis (1996) under a set of plausible assumptions and a coefficient o f relative risk aversion of two, evaluate the cost of the lack of insurance to 'group specific shocks' at 2.5% of consumption. This estimate is considerably larger than the cost of business cycle fluctuations evaluated by Lucas (1987) and is more in line with the results reported by Imrohoroglu (1989). It should also be stressed that Attanasio and Davis (1996) estimate completely ignores 'within-groups' shocks and focuses mainly on relative low (rather than business cycle) frequencies. Whilst the analysis of Attanasio and Davis (1996) can be framed in terms of a test of the perfect insurance hypothesis, it can also be interpreted as documenting the evolution in inequality in consumption and wages in the USA during the 1980s. The increase in inequality in wages in the USA has been analysed in many studies by labour economists. On the other hand, the evolution o f inequality in consumption has not received much attention until quite recently. Little is known about the evolution of consumption inequality over the business cycle and over different stages of the process of economic growth. In addition to Attanasio and Davis (1996), Cutler and Katz (1991) analyse the evolution of inequality in consumption during the 1980s using CEX data. Goodman, Johnson and Webb (1997) provide an exhaustive analysis of the recent trends in both income and expenditure inequality in the UK. The lack of evidence on consumption inequality is somewhat disconcerting, especially if one compares it to the amount of evidence on wage and income inequality. From a theoretical point of view, it is not completely obvious which of the two measures of inequality is more interesting. Blundell and Preston (1998) discuss the advantages and drawbacks of both: consumption inequality is more likely to reflect the cross sectional variability of permanent income, while income inequality is more affected by temporary shocks. The relationship between the two, however, depends on a number of factors that range from the specification of preferences to the nature of the income shocks, to the institutions and instruments available to households to (self) insure against idiosyncratic shocks. More generally, a theoretically consistent analysis of consumption inequality cannot avoid the discussion of the implications of different preference specifications and market institutions. Suppose, for instance, that individual households are prevented from borrowing. If labour supply behaviour is considered exogenous, these households will engage in precautionary saving to avoid the effects of extremely negative shocks to income. On the other hand, if one models labour supply choices and in particular female participation in the labour market, it is quite possible that the role of precautionary saving is taken by labour supply. That is to say, it is possible that households, rather than consuming less goods, decide to consume less leisure. Another important element, which has been only recently analysed, is the availability of means tested safety nets. Hubbard, Skinner and Zeldes (1994) consider the effect that liquidity constraints and means tested safety nets have on the pattern of consumption using numerical techniques to solve the consumption function.

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Browning and Crossley (1997) have recently considered another potentially important channel that some households might use to smooth the marginal utility of consumption over time: what they call small durables. The idea is intuitive: individuals that have no access to savings or loans to smooth out fluctuations in income, might postpone the replacement of small durables. The features that characterise the 'small durables' in Browning and Crossley's problem are the durability and the irreversibility (due to the lack of a second hand market) of such items, as well as the fact that scrappage decisions are not only determined by the physical depreciation but also by the economic situation faced by the agent. Browning and Crossley (1997) present both some theoretical results and some empirical evidence on a sample of Canadian unemployed supporting the importance of this type of smoothing behaviour. The evidence I presented in Table 6, about the relative variability of durable expenditure for groups of households with different levels of education is consistent with the idea that poorer individuals might use durables to smooth out fluctuations in income. Browning and Crossley (1997) focus on items that cannot be used as collateral (such as clothes or small appliances) to obtain loans. It would be interesting to consider the implications of the same ideas for the replacement of items for which reasonably efficient second hand markets exists and which are collateralizable such as automobiles and, to a certain extent, 'white goods'. Greenspan and Cohen (1996) have stressed the important role that scrappage of old cars plays in forecasting expenditure on automobiles which, in turn, is a very important indicator of the status of the business cycle. A few studies, recently, have started to study the evolution of inequality over the life cycle. The idea is quite simple: if consumption follows a random walk, the cross sectional distribution of individual consumption should 'fan out' over the life cycle. That is, the cross sectional variance of individual consumption should be increasing, on average, over long periods of time. This idea was first exploited by Deaton and Paxson (1994) who analysed average cohort profiles for the variance of (log) nondurable consumption in three different countries, the USA, the UK and Taiwan.

8. Intertemporal non-separability In the discussion so far, I have assumed that preferences are separable over time. While this is an extremely convenient assumption, it is easy to think of situations in which it is violated. In this section I consider the implications of the fact that current expenditure might have lasting effects. After sketching the general problem, I discuss in detail two particular examples of time non-separability of some importance: that of durability and of habit formation. As is clear from the discussion, the complication implied by time dependence of preferences is only one of the things that make the treatment of these phenomena extremely hard. The general problems can be stated in reasonably simple terms if one states the problem in terms of a flow of services derived from a 'stock' and assumes that there

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are no costs in changing the 'stock'. The simple problem in Section 3, can therefore be re-written as: T-t

max

Et v(s,+j) j=0

IAt+j+l~l+rt+j)At+j+Yt+j-st+j,

subject to [St+j = Z

(18)

= 1

k=0

where St is the 'stock' from which utility is derived, st is expenditure and the coefficients ak define the type of time dependency. As we see below, such a model can easily incorporate durability as well as habit formation. It is also straightforward to consider the case in which S is a vector whose components have different degrees of durability 59. A rational individual, in choosing the level of expenditure s will take into account the effect that this has on the level of the 'stock' in the current as well as in the future period. It is straightforward to verify that the first-order condition for such a problem is going to be

Etmt = Et[3(1 + rt+l) mr+l, T

(19)

t

where m t = ~-~'~k=0~ku1(St+k) ak" Notice that if the ak s are different from zero, mt is not a variable known at time t as it depends on the future marginal utility of the stock S. In general, therefore, it will not be possible to express Equation (19) in terms of the rate o f growth of mt as is usually done [see, for instance, Equation (8)]. Notice also that the marginal utility of expenditure mt depends on a potentially very large number of terms. To make an equation such as (19) operational it will be necessary to simplify it by some algebraic manipulation whose nature depends, once again, on the pattern of the coefficients ak. The two models of non-separability I consider below (durables and habits) differ on the nature of the time dependence. In the first case we have substitutability, while in the latter we have complementarity of expenditure over time.

8.1. Durables As illustrated in Section 2, expenditure on durables, both at the aggregate level and at the cohort level, is by far the most volatile component of consumption. In addition, the dynamic of durable expenditure seems much more complex of that of the other components o f consumption. A simple model of durable consumption can be obtained

59 See, for instance, Eichenbaum and Hansen (1990).

O.P Attanasio

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from the system in Equation (18) if it is assumed that ak = (1 - 6) k. In this case S can be interpreted as the value of the stock of durables, and 6 as the depreciation rate, and the third equation in system (18) becomes St = (1 - 6)St_1 +st.

(20)

Assuming quadratic utility, Mankiw (1982) generalised Hall's random walk model to durable expenditure. In particular, he showed that under these circumstances the model implies that changes in expenditure should follow an MA(1) process with coefficient equal to ( 1 - 6). This implication is strongly rejected by the aggregate data, as shown, for instance, in Section 2. Dunn and Singleton (1986) have used a more attractive preference specification and considered the Euler equation for durable consmnption and its implications for asset pricing. The most comprehensive treatment of durability and of the Euler equations associated with a variety of preferences is found in Eichenbaum and Hansen (1990) who use a Gorman-Lancaster technology that converts expenditure into stocks and stocks into services over which utility is defined. The aggregation issues I discussed in Section 4 are obviously relevant for durables as well. The aggregation problems are actually even more complicated because of the possibility of corner solutions, i.e. households that decide not to own a durable (a car for instance), that can be safely ruled out for non-durables under the assumption that the marginal utility goes to infinity at zero or low levels of consumption 6°. A possibility for the deviations of the dynamics of aggregate durable expenditure from that implied by the simple model is that of the existence of adjustment costs. It seems natural to assume that adjusting the stock of durables involves costs, motivated both by the existence of imperfections in the second hand market and by 'pure' adjustment costs (such as search costs, taxes and similar). The literature first studied convex (typically quadratic) costs of adjustment. A typical example is Bernanke (1984, 1985), who estimated models with quadratic costs both with aggregate and individual data. Eichenbaum and Hansen (1990) also incorporate the possibility of adjustment costs in their technology. Such attempts, however, have turned out to be unsuccessful. The main reason for this is that convex adjustment costs predict a smooth adjustment towards an equilibrium. To avoid increasing costs households will adjust their stock of durables often and by small amounts. Even casual observation suggests that this is not a very accurate description of household behaviour. The next step is then to consider non-convex costs of adjustment; that is either fix or proportional costs. The characterisation of optimal behaviour under this type of costs is obviously much harder because for many households in many periods the optimal policy involves no adjustment. The first paper to characterise the optimal

6o Bernanke (1984) and Hayashi (1985a,b) are among the few studies that have used individual data to analyse durable expenditure.

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adjustment policy under non-convex costs was Grossman and Laroque (1990) who studied a problem of a consumer deriving utility from a single durable and solving a dynamic optimisation problem involving the choice of the optimal size for the durable and the optimal portfolio investment for her financial wealth. Grossman and Laroque (1990) proved that the optimal strategy involves an (S, s) rule of the kind considered in the optimal inventory literature of the 1950s. Specifically, they proved that the value function associated to the consumer problem is a function of a single state variable, the ratio of the value of the durable to financial wealth, and that the durable is adjusted to a 'target' level when the state variable crosses a lower or an upper bound. When the state variable is within the two bounds the optimal policy is not to adjust the durable. In addition, Grossman and Laroque (1990) characterised the size of the inaction band as a function of the parameters of the problem, as well as the optimal portfolio strategy. One of the problems of the Grossman-Laroque model is that a solution can be obtained only if the problem can be expressed as a function of a single state variable. This precludes, for instance, the consideration of labour income. More recently, Eberly (1994) and Beaulieu (1993) have extended the Grossman-Laroque model in various directions. Eberly (1994), has showed that changes in the durable stock between periods in which an adjustment is performed obey to an Euler equation. Beaulieu (1993) has reformulated the Grossman-Laroque model and expressed the (S, s) rule in terms of the ratio of durables to non-durables. The attractiveness of the (S,s) model of adjustment lies in its implications that, in most periods, consumers do not adjust their stock of durables and when they do adjust, they usually make substantial adjustments. These features (large and infrequent adjustments), that can be generated by the (S, s) model, are the exact contrary of those of the quadratic adjustment model which yields small and frequent adjustments. The consideration of large and infrequent adjustments poses an entire new category of aggregation problems. Caplin (1985) was the first to consider them. Caplin and Spulber (1987), in the context of a model of price adjustment, provided (stringent) conditions under which lumpy individual adjustment could result in a smooth aggregate adjustment. Bertola and Caballero (1990) analysed the implications of the (S,s) type of adjustment for the dynamics of aggregate durable expenditure and stressed that the assumptions needed to generate the type of neutrality results obtained by Caplin and Spulber are indeed very fragile. (S, s) models can generate very rich and complicate dynamics that seem not to be inconsistent with the observed autocorrelation of durable expenditure. Caballero (1990a,b, 1993), in particular, has stressed how (S,s) models can generate patterns of MA coefficients that are similar to those I reported in Section 2. Caballero and Engel (1991) have studied more generally the aggregate properties of (S, s) economies. Caballero (1993) has tried to estimate the parameters of the (S, s) model by fitting the highly non-linear model resulting from the aggregation of a simple (S, s) rule to aggregate time series data. The estimation of (S, s) models with individual data is not an easy task for several reasons. First of all, the data requirements can be quite formidable: information on the value of the stock of durables before and after the adjustment is necessary. It is

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also desirable to follow households over some time to bound the range of inaction by the households that are observed not to adjust. In addition, the numerical problems in estimation can be quite formidable. The first attempt at estimating such a model with individual data was by Lam (1991) who estimated by maximum likelihood an (S, s) rule defined in terms of the ratio of the stock of automobiles over permanent income. Eberly (1994), also estimated the width of the (S, s) rule for the subset of consumers who were observed to adjust the stock of their automobiles in her sample 6~. B eaulieu (1992) also uses individual observations but follows a different approach. He considers a single cross section and computes the ergodic cross sectional distribution to which the economy would converge in the absence of aggregate shocks. The parameters of this distribution will depend on the parameters of the (S, s) rule. He can then estimate them from the parameters of the observed cross sectional distribution which is assumed to coincide with the ergodic distribution. Like Lain (1991), I have estimated the parameters of the (S,s) rule by maximum likelihood on individual data in Attanasio (1995a). However, I formulate the (S, s) rule in terms of the ratio of the stock of automobiles to non-durable consumption, allow for observed and unobserved heterogeneity in both the target and the band width and consider a more flexible stochastic specification. The consideration of unobserved heterogeneity in both the target level and the band width makes the model equivalent to a recent formulation of lumpy adjustment by Caballero and Engel (1991) who consider, rather than a strict (S, s) rule, a 'hazard function' which gives the probability of adjusting as a function of the difference between the current stock and its target level. While substantial progress in the understanding of the behaviour of models with lumpy adjustment has been made (not only in consumption but also in investment and labour demand), a lot of research is still necessary to establish the empirical relevance of these models and to quantify their parameters. The aggregate dynamics of an (S, s) system depends crucially on the properties of several stochastic processes about which we still have little or no information. These include the process by which the state variable changes when no adjustment occurs, the process by which the target level changes, the degree of heterogeneity in target levels and band width, the degree of persistence of individual shocks to band width (cost of adjustment) and the correlations among these variables.

8.2. Habit formation A form of intertemporal persistence of preferences alternative to durability is that of habits. As said above, habits can be obtained using a specific patterns for the 61 Eberly (1994) also splits the samplebetween consumers who are likelyto be liquidity constrained and those that are liquid. In doing so she uses both the procedure used by Zeldes (1989a) and a switching regression model.

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coefficients a in Equation (18). For instance, Heaton (1995) and Constantinides (1990) use the following specification: O<3

St = ct - a(1 - 0) ~

OJet a~;

O~a~l,

0~0~1.

(21)

j-0 The term (1 - 0) ~ ) ~ 00Jct-l-j is referred to as the 'stock of habits', which depreciates according to the parameter 0. A particularly simple specification is obtained when 0 = 0, in which case the stock of habits is simply given by last period consumption. As with the cases considered above, the marginal utility of time t expenditure is a function of both present and future variables, so that it is now known at time t. The habit formation model has a long history, dating back at least to Gorman (1967), Pollak (1970) and Houthakker and Taylor (1970) 62. Spynnewin (1981) presents an ingenious reparametrization of the optimisation problem which, by an appropriate redefinition of prices and quantities, allows the maximisation of an intertemporally additive function. However, it is only in the 1980s that habits models are coupled with the hypothesis of rational expectations and preferences incorporating temporal persistence are used to derive Euler equations analogous to Equation (19) above. Examples of this practice include Eichenbaum and Hansen (1988) (for a model with habit forming consumption and leisure), Eichenbaum and Hansen (1990), Novales (1990) and Constantinides (1990), while Hotz, Kydland and Sedlacek (1988) and Kennan (1988) consider habit formation in leisure. Browning (1991) uses a dual approach to derive the equivalent of 'Frisch' consumption functions in the presence of intertemporal non-separability 63. More recently, Heaton (1993, 1995) has considered the interplay between time aggregation and habit formation. His argument is that at high frequency consumption seems to exhibit substitutability, while at lower frequencies, there is evidence of complementarities. Heaton argues that the local substitutability of consumption could be explained by time aggregation. In general, he presents preferences that are flexible enough to accommodate the 'slow' formation of habits. Most of the work on habit models so far has been done on aggregate time series data. One of the reasons for this is the fact that very few panel data contain information on consumption. The CEX, which I used in Section 2, contains only up to four quarterly observations per households. The average cohort analysis that is used in the study of dynamic models of consumption, cannot be used in the analysis of habit formation, because these models involve the covariance of subsequent consumption observations f o r the s a m e household. In other words, we cannot aggregate the product C th C th k over the household index h, unless we have observations for times t and t - k for the same households. 62 Browning (1991), however, has citations from Marshall and Haavelmo. 63 Browning's simple structatre can encompass both substitutability and complementarities over time. The main problem with his approach is that he can only introduce uncertainty by considering points expectations about the future.

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The only paper that studies time dependence in preferences using micro data is, to the best of my knowledge, Meghir and Weber (1996), that I discussed in the section on liquidity constraints. Another novelty of that paper is that it considers different components of consumption and allows for different levels of persistence depending on the commodity considered. The interesting evidence is that, when durable commodities are controlled for, there is no evidence of persistence in the 3 equations demand system that Meghir and Weber (1996) consider.

9. Conclusions

Rather than summarising the various sections that compose the chapter I prefer to conclude the chapter comparing the status of our knowledge and understanding of consumption behaviour to that of twenty years ago. It is fair to say that substantial progress has been made. In the last twenty years we have learned how to deal with uncertainty in a rigorous fashion and have recognised the importance that this may have for consumption and saving decision. Indeed an entire branch of the literature, that on precautionary saving, has developed to deal with these issues. While the emphasis given to the proper treatment of uncertainty and the lack of appropriate data sources has meant that many studies have focused on aggregate data, it has now become clear that it is very hard, if not impossible, to estimate preference parameters from aggregate time series data. Aggregation issues are important in many dimensions. In addition to the standard aggregation problems created by the non-linearity of the relevant theoretical relationships, there are other ways in which aggregation issues become important. Corner solutions and participation decisions (in labour and financial markets), inertial behaviour and transaction costs, all add a new dimension of complexity and make the cross sectional distribution of the variables under study relevant for the dynamics of the aggregate. The Euler equation has been the main instrument to analyse consumption both in micro and macro data, to estimate preference parameters and to test the overidentifying restrictions implied by the consumers' optimisation problem. In the process we have learned a lot about the econometric problems of estimating Euler equations. In particular, we have learned what are the identifying assumptions that one needs to make to get consistent estimates from the available data. The Euler equation is a powerful tool in that it allows the consideration of complex and flexible preference specifications without loosing the empirical tractability. As long as the variable over which one is optimising can be adjusted without cost and is not at a corner, one can derive an Euler equation which, even if it includes the values of other endogenous variables, delivers orthogonality restrictions that can be used to estimate preference parameters. The empirical research has used Euler equations for non-durable consumption and its components that have become, in the attempt to fit the observable data, increasingly complicated. This level of complexity is probably unavoidable if one is serious about taking the model to the data.

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As I stressed several times during the chapter, the price one pays in dealing with Euler equations is not negligible: one loses the ability of saying anything about the level of consumption. The empirical tractability of the Euler equation is obtained differencing out the marginal utility of wealth, and therefore one of the main determinants of consumption levels. The challenge for future research is to construct a consumption function that incorporates the insights of the Euler equation and yet allows us to say something about the levels o f consumption and about how consumption reacts to changes in the economic environment. Such a consumption function is necessary to make predictions about future consumption, about saving behaviour, and about the effects of alternative policy measures. One possibility that is being explored is the use of numerical techniques. They have proved to be useful both to improve our understanding of the dynamic optimization problems typically postulated and to characterise the implications of different preference structures and economic environments on consumption and saving behaviour. They can also be used to validate, indirectly, the preference specifications implied by the Euler equation estimates that best fit the consumption growth data. Their main limitation, however, is an important one: they can only be used to analyse extremely simplified models and they require the full characterisation of the agents' economic environment. Several other areas of research are important and exciting. I will just mention two. Our understanding of consumption smoothing and of the evolution of inequality is still at the beginning. The development of this understanding and of the importance that different institutional frameworks and financial instruments have for these issues is an extremely important research agenda both from a positive and from a normative point of view. Related to this is also the issue of the time series properties of individual consumption: unlike for earnings and hours of work, next to nothing is known about this. Our understanding of durable expenditure is still very limited and yet it is an extremely important issue, both because durables are the most volatile component of consumption and because they have a number of features (the fact that they can be used as collateral, transaction costs, the durability itself) that make them difficult to model.

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Hayashi, E, J. Altonji and L. Kotlikoff (1996), "Risk-sharing between and within families", Econometrica 64:261~94. Heaton, J. (1993), "The interaction between time-nonseparable preferences and time aggregation", Econometrica 61:353-386. Heaton, J. (1995), "An empirical investigation of asset pricing with temporally dependent preferences", Econometrica 63:681 718. Heckman, J.J. (1974), "Life-cycle consumption and labour supply: an exploration of the relationship between income and consumption over the life cycle", American Economic Review 64:188-194. Heckman, J.J., and R. Robb (1987), "Using longitudinal data to estimate age period and cohort effects in earnings equations", in: W.M. Mason and S.E. Fienberg, eds., Cohort Analysis in Social Research (Springer, Berlin). Hotz, V.J., EE. Kydland and G.J. Sedlacek (1988), "Intertemporal preferences and labor supply", Econometrica 56:335-360. Houthakker, H.S., and L.D. Taylor (1970), Consumer Demand in the United States: Analyses and Projections, 2rid edition (Harvard University Press, Cambridge, MA). Hubbard, R.G., J.S. Skinner and S.P. Zeldes (1994), "The importance of precautionary motives in explaining individual and aggregate saving", Carnegie-Rochester Conference Series on Public Policy 40:59-125. Hubbard, R.G., J.S. Skinner and S.P. Zeldes (1995), "Precautionary saving and social insurance", Journal of Political Economy 103:360-399. Hurd, M.D. (1989), "Mortality risk and bequests", Econometrica 57:779-813. Imrohoroglu, A. (1989), "Cost of business cycle with indivisibilities and liquidity constraints", Journal of Political Economy 100:118-142. Jappelli, T. (1990), "Who is credit constrained in the US economy?", Quarterly Journal of Economics 105:219-234. Jappelli, T., and E Modigliani (1997), "Is the age-saving profile consistent with the life cycle hypothesis?", mimeograph (MIT). Jappelli, T., and M. Pagano (1994), "Saving, growth and liquidity constraints", Quarterly Journal of Economics 109:83-110. Jappelli, T., J.-S. Pischke and N. Souleles (1997), "Testing for liquidity constraints using complementary data sources", Review of Economics and Statistics, forthcoming. Juster, ET., and R.P. Shay (1964), "Consumer sensitivity to finance rates: an empirical and analytical investigation", NBER Occasional Paper No. 88. Keane, M.P., and D. Rankle (1992), "On the estimation of panel-data models with serial correlation when instruments are not strictly exogenous", Journal of Business and Economic Statistics 10:1 9. Kennan, J. (1988), "An econometric analysis of fluctuations in aggregate labor supply and demand", Econometrica 56:317-334. Kimball, M.S. (1990), "Precautionary saving in the small and in the large", Econometrica 58:53-73. Kotlikoff, L.J. (1988), "Intergenerational transfers and savings", Journal of Economic Perspectives 2:41-58. Kotlikoff, L.J., and L.H. Summers (1981), "The role of intergenerational transfers in aggregate capital accumulation", Journal of Political Economy 89:706-732. Lam, P.S. (1991), "Permanent income, liquidity and adjustment of automobile stocks: evidence from panel data", Quarterly Journal of Economics 106:203-230. Lucas Jr, R.E. (1987), Models of Business Cycles (Blackwell, New York). Ludvigson, S. (1997), "Consumption and credit: a model of time-varying liquidity constraints", mimeograph (Federal Reserve Bank of New York). Ludvigson, S., and C. Paxson (1997), "Approximation bias in linearized Euler equations", mimeograph (Princeton University). Lusardi, A. (1996), "Permanent income, current income and consumption: evidence from two panel data sets", Journal of Business Economics and Statistics 14:81-90.

Ch. 11:

Consumption

811

Mace, B.J. (1991), "Full insurance in the presence of aggregate uncertainty", Journal of Political Economy 99:928-956. MaCurdy, T.E. (1981), "An intertemporal model of portfolio choice and human capital accumulation under uncertainty with extensions incorporating taxes, consumer durables, imperfections in capital markets and non separable preferences", Working Paper E-81-18 (Hoover Institution). MaCurdy, T.E. (1983), "A simple scheme for estimating an intertemporal model of labor supply and consumption in the presence of taxes and uncertainty", International Economic Review 24:265-289. MaCurdy, T.E., and T.A. Mroz (1989), "Measuring macroeconomic shifts in wages from cohort specifications", mimeograph (Stanford University). Manldw, N.G. (1982), "Hall's consumption hypothesis and durable goods", Journal of Monetary Economics 10:417-425. Mankiw, N.G., and S.P. Zeldes (1994), "The consumption of stock owners and the consumption of non stock owners", Journal of Financial Economics. Manldw, N.G., J.J. Rotemberg and L.H. Summers (1985), "Intertemporal substitution in macroeconomics", Quarterly Journal of Economics 100:225-253. Meghir, C., and G. Weber (1996), "Intertemporal non-separability or borrowing restrictions? A disaggregated analysis using a U.S. consumption panel", Econometrica 64:1151 1181. Modigliani, E (1988), "The role of international transfers and life cycle saving in the accumulation of wealth", Journal of Economic Perspectives 2:15-40. Modigliani, E, and A. Ando (1963), "The life cycle hypothesis of saving: aggregate implications and tests", American Economic Review 53:55-84. Modigliani, E, and R. Brumberg (1954), "Utility analysis and the consumption function: an interpretation of cross-section data", in: K.K. Kufihara, ed., Post-Keynesian Economics (Rutgers University Press, New Brunswick, NJ) 128-197. Moffitt, R. (1993), "Identification and estimation of dynamic models with a time series of repeated cross-sections", Journal of Econometrics 59:99-124. Novales, A. (1990), "Solving nonlinear rational expectations models: a stochastic equilibrium model of interest rates", Econometrica 58:93-111. O'Brien, A.M., and C.B. Hawley (1986), "The labor force participation behavior of married women under conditions of constraints on borrowing", Journal of Human Resources 21:267-278. Paulin, G., M. Boyle, R. Branch and R. Cage (1990), "Comparison of 1987-1988 CE integrated survey and PCE annual estimates", mimeograph (BLS). Phelan, C., and R.M. Townsend (1991), "Computing multi-period information constrained optima", Review of Economic Studies 58:853-881. Pischke, J.-S. (1995), "Individual income, incomplete information, and aggregate consumption", Econometrica 63(4, July):805-840. Pissarides, C.A. (1978), "Liquidity considerations in the theory of consumption", Quarterly Journal of Economics 92:279-296. Pollak, R.A. (1970), "Habit formation and dynamic demand functions", Journal of Political Economy, 78:745-763. Runlde, D.E. (1991), "Liquidity constraints and the pernaanent-income hypothesis: evidence from panel data", Journal of Monetary Economics 27:73-98. Sargent, T.J. (1978), "Rational expectations, econometric exogeneity and consumption", Journal of Political Economy 86:673-700. Seslnick, D. (1992), "Aggregate consumption and saving in the postwar United States", Review of Economics and Statistics 585-597. Seslnick, D. (1994), "Are our data relevant to the theory? The case of aggregate consumption", mimeograph (Rice University). Shea, J. (1995), "Union contracts and the life-cycle/permanent- income hypothesis", American Economic Review 85:186-200.

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Skinner, J.S. (1988), "Risky income. Life cycle consumption and precautionary savings", Journal of Monetary Economics 22:237-255. Spynnewin, E (1981), "Rational habit formation", European Economic Review 15:91-109. Thurow, L. (1969), "The optimum lifetime distribution of consumption expenditures", American Economic Review 59:371-396. Tobin, J., and W.C. Dolde (1971), "Wealth, liquidity and consumption", Reserve Bank of Boston, Monetary Conference Series No. 5. Townsend, R.M. (1994), "Risk and insurance in village India", Econometrica 62:539-592. Weber, G. (1993), "Earnings related borrowing restrictions: empirical evidence from a pseudo panel for the UK", Annales d'Economie et de Statistique 29:157-173. Wilson, R. (1968), "The theory of syndicates", Econometrica 36:119-132. Zeldes, S.P. (1989a), "Consumption and liquidity constraints: an empirical analysis", Journal of Political Economy 97:305-346. Zeldes, S.E (1989b), "Optimal consumption with stochastic income", Quarterly Journal of Economics 104:275-298.

Chapter 12

AGGREGATE INVESTMENT

*

RICARDO J. CABALLERO MIT and NBER

Contents Abstract Keywords 1. Introduction 2. Basic investment t h e o r y and findings 2.1. Pre 1990s: Dismay 2.2. "Econometrics": Cost of capital and q matter 2.2.1. Long-run 2.2.2. Short-run 3. L u m p y and irreversible investment 3.1. Plant/firm level 3.1.1. Microeconomic adjustment: characterization 3.1.2. "Representative" problem 3.1.3. A detour: q-theory and infrequent investment 3.1.3.1. On the fragility of marginal q 3.1.3.2. When does q-theory work? 3.1.3.3. Taking stock 3.1.4. Another detour: Several misconceptions about irreversible investment 3.1.5. Adjustment hazard 3.2. Aggregation 3.3. Empirical evidence . . . . . 3.3.1. Microeconnmic data 3.3.2. Aggregate data 3.3.3. Pent-up demand 3.4. Equilibrium 4.

814 814 815 816 816 818 820 821 822 822 823 824 828 828 830 832 832 835 837 838 838 839 841 842

Entry, exit and scrapping

844

4.1. Competitive entry and irreversibility 4.2. Technological heterogeneity and scrapping

844 847

* I am grateful to Andrew Abel, Steve Bergantino, Olivier Blanchard, Jason Cummins, Esther Duffio, Eduardo Engel, Austan Goolsbee, Luigi Guiso, Kevin Hassett, Glenn Hubbard, John Leahy, Kenneth West, and Michael Woodford for many useful comments. I thank the NSF for financial support. Handbook of Macroeconomics, Volume 1, Edited by JB. Taylor and M. WoodJbrd~ © 1999 Elsevier Science B.V. All rights reserved

813

814 5. Inefficient investment 5.1. Informationalproblems 5.2. Specificityand opportunism 5.2.1. Genericimplications 5.2.2. Credit constraints 6. Conclusion and outlook References

R.J. Caballero 848 849 851 854 856 857 858

Abstract

The 1990s have witnessed a revival in economists' interest and hope of explaining aggregate and microeconomic investment behavior. New theories, better econometric procedures, and more detailed panel data sets are behind this movement. Much of the progress has occurred at the level of microeconomic theories and evidence; however, progress in aggregation and general equilibrium aspects of the investment problem also has been significant. The concept of sunk costs is at the center of modern theories. The implications of these costs for investment go well beyond the neoclassical response to the irreversible-technological friction they represent, for they can also lead to firstorder inefficiencies when interacting with informational and contractual problems.

Keywords sunk costs, irreversible investment, (S, s) models, adjustment hazard, aggregation, non-linearities, private information, incomplete contracts, pent-up investment

JEL classification: E22, D21, D23, E32

Ch. 12: Aggregate Investment

815

1. Introduction

Aggregate investment is an important topic. Cotmtries and firms are often judged by their performance along this dimension, since investment is viewed as providing hope for future prosperity. It is not surprising, therefore, that much has been written about investment. It is even less surprising that many surveys, and surveys of surveys, already exist ~. Rather than surveying the surveys of surveys, as one would expect from a handbook chapter, I have chosen to focus most of my discussion on that which is relatively new. The cost of this, of course, is that most of the theories I will discuss have not yet passed the test of time and are often only half the distance toward full development. Most, but not all, of the subjects I plan to discuss relate directly to investment in equipment and structures. Investing means trading the present for the future; as is the case, for example, when a firm purchases equipment, builds structures, trains its workers, restructures production, spends resources on R&D, hoards labor during a recession; or when a worker leaves a job to search for another one, invests in human capital; or when a country undergoes a structural adjustment, a trade liberalization or a fiscal reform. The more theoretical sections of this survey apply to most of these examples. Further, except for specific empirical results, a large part of the discussion about equipment and structures also applies to other forms of investment. The style of this review article is mostly empirical in early sections and mostly theoretical in later ones. This ordering is highly correlated with the chronology of research on investment. It follows that I am implicitly advocating for more empirical work on the newest theories. The layout of the chapter is as follows. Section 2 is rather traditional in content. It describes the basic investment theory and findings, taking the view that the pre 1990s empirical literature was in disarray with respect to finding a role for the cost of capital in investment equations. During the 1990s, however, we have learned from long run relationships and "natural experiments" that the cost of capital does indeed have significant effects on investment, although it is probably not the most important explanatory variable. Neither, I should add, is measured q. Section 3 describes what has been well known but largely ignored until recently: that microeconomic investment is lumpy and mostly sunk. It turns out that changes in the degree of coordination of lumpy actions play an important role in shaping the dynamic behavior of aggregate investment. The old concept of pent-up demand is back. This section contains a more detailed description of models and techniques than the others. It also attempts to clarify several misconceptions about the implications of these models. Section 4 is about equilibrium interactions and scrapping. It describes the consequences of free entry and different assumptions about the elasticity of the supply 1 See, for example, Chirinko (1993), Hassett and Hubbard (1996b), for excellent surveys of traditional investment equations.

816

R.J. Caballero

of capita~'~.for equilibrium investment anti, scrapping, :Vimage and putty-clay models are briefly mentioned as a natural environment in which to address the economic obsolescence issue. This concept is particularly relevant for understanding capital accumulation during episodes of rapid growth and after substantial shocks to the price of intermediate inputs. Section 5 discusses inefficient investment. The first part of the section deals with informational problems. Discontinuous action due to irreversibility and fixed costs are compounded by the presence of private information and create a powerful drag on investment. Inaction is a natural information trap, small information flows lead naturally to further inaction, and the feedback process goes on. Aggregate investment will appear too sluggish given the ex-post information of an econometrician, and it will probably be too slow in responding to new conditions relative to first and second best scenarios. The second part of this section describes how the sunk nature of investment, when combined with contractual incompleteness, can lead to underinvestment and, through general equilibrium, to a series of distortions in the scrapping margin and in the response of investment to aggregate shocks. Financial constraints are discussed within this context. The concept of rationing, the effects of underinvestment on complementary factors (and vice versa) and the relation between excessive capital/tabor substitution and investment are also part of this section. The issue of property rights and investment also fits very naturally here. Section 6 concludes.

2. Basic investment theory and findings 2.1. Pre 1990s: Dismay

Since very early on, economists have attempted to explain investment behavior using both scale and relative price variables, and since very early on, the former have been more successful than the latter. One of the first "theories" of investment was the accelerator model [Clark (1917)]. Scarcely a theory, the accelerator model is derived by inverting a simple fixed proportion production function and taking first differences. Unable to account for the serial correlation of investment beyond that o f output growth, this model was soon transformed into the flexible accelerator model [Clark (1944), Koyck (1954)]: n

I, = Z/3~AKT-r'

(2.1)

"~-0

where I denotes investment, the/3r's are distributed lag parameters, and K* is the desired, as opposed to actual, level of capital. In the simple fixed proportions world, K* can be written as a linear function of the output level, Y: K* = a Y

where a is a parameter.

Ch. 12: AggregateInvestment

817

The absence of prices (the cost o f capital, in particular) from the right-hand side of the flexible accelerator equation has earned it disrespect despite its empirical success. Jorgenson's (1963) neoclassical theory o f investment intended to remedy this situation. Starting from the optimization problem o f a perfectly competitive firm facing no adjustment costs, myopic expectations, and constant returns Cobb-Douglas technology, Jorgenson obtained the standard static first-order condition:

K = aY/Ck, where Ck stands for the cost of capital and a is now the share o f capital in a simple Cobb-Douglas production function. As with the accelerator model, this model was unable to account for the serial correlation o f investment, and so gave way to the flexible neoclassical model o f Hall and Jorgenson (1967), where

K* = aY/Ck,

(2.2)

was now used in Equation (2.1). Soon it was shown, however, that by constraining the coefficient o f the cost o f capital to be the same as the coefficient of out-put, this model imposed rather than found a role for the cost o f capital in the investment function. Eisner (1969) estimated a modified Hall and Jorgenson model which allowed for different coefficients on output and the cost o f capital and found no independent role for the cost o f capital. The cost o f capital's rise and fall from grace was not an unknown experience, however. Several decades before, authors such as Tinbergen (1939) and Meyer and Kuh (1957) had pointed out the dominance o f liquidity variables over interest rates for short run investment 2. None o f these are full theories of investment, rather they are theories conditional on the level o f output 3. The famous q-theory o f Tobin (1969) and Brainard and Tobin (1968) went one step further. They argued that investment should be an increasing function o f the ratio o f the value of the firm to the cost o f purchasing the firm's equipment and structures in their respective markets. This ratio, known as average q4, summarizes most information about future actions and shocks that are of relevance for investment 5. Indeed, average q would later be shown to be a sufficient statistic for investment in a wide variety o f scenarios. Thus, the new canonical investment equation became I = yq, where • is a strictly positive parameter. 2 See Chirinko (1993) for a more thorough review of the history of the debate over the role of the cost of capital, profits and output in investment decisions. 3 Things are even worse for the basic frictionless neoclassical model; it is ill defined as a full model because firm level output is not determined under constant reta.trns and perfect competition. 4 It is also often referred to as Tobin's q. 5 This includes the optimal path of output.

818

R.J. Caballero

The elegant theoretical contributions o f Abel (1979) and Hayashi (1982) connected the existing theories and partial theories. They showed that the neoclassical model with convex adjustment costs yields a q-model. This q, known as marginal q, should be interpreted as the marginal value o f an installed unit o f capital, which corresponds to the shadow value o f a trait o f capital in the firm's optimization problem. Further, Hayashi showed that (for price-taking firms) when the production function and adjustment cost function are linearly homogeneous in capital and labor, marginal and average q are equal. This is an important result from an empirical standpoint because marginal q is unobservable to the econometrician whereas average q is, in principle, observable to the econometrician 6. Soon, however, the q-model, along with expanded and ad-hoc "flexible-q" models (i.e. with additional lags o f q on the right-hand side), joined models based on the cost o f capital in their lack o f empirical success. Scale variables such as cash-flows always seemed to matter more in investment equations than q which, in principle, should have been a sufficient statistic 7. Figure 2.1, which reproduces figures 1 and 3 o f Hassett and Hubbard (1996b), helps us understand the statistical reasons for the problem. The bottom line is clear: In aggregate US data (which is probably representative o f many other data sets for this purpose) the unconditional correlation between cost o f capital and investment is low, and so is that between average q and investment. On the other hand, cash flows and sales's growth closely track aggregate investment. The 1980s discontent with respect to investment equations is probably well captured in Blanchard's (1986) discussion o f Shapiro's (1986) investment paper at Brookings: "... it is well known that to get the user cost to appear at all in the investment equation, one has to display more than the usual amount of econometric ingenuity, resorting most of the time to choosing a specification that simply forces the effect to be there ..." [my emphasis] Today, the first emphasized statement still holds, but the second one probably does not. This takes me to the next subsection. 2.2. "Econometrics": Cost o f capital a n d q matter

Econometric "ingenuity" eventually pays off, although this often means isolating that part o f the relationship which conforms with the theory, rather than explaining a 6 I have mixed feelings about this equivalence result, however. Not about its theoretical derivation, which is elegant and useful; rather about its abuse in empirical work. Too often, it is used to justify substituting average for marginal q on the right-hand side of investment equations, even though the assumptions required for the equivalence between the two are not nearly satisfied in the industry or firms studied (e.g. Compustat). This does not mean that average q should not be used, but it says that we should not pretend that the foundation for its use is beyond the basic intuition provided by Tobin (1969), and that the additional properties that hold for marginal q are to be expected from average q (e.g. sufficiency). 7 Fazzari et al. (1988) started a large literature documenting the role of these variables, even after conditioning for average q. I will return to the interpretation of these regressions later in the survey.

Ch. 12: Aggregate Investment o

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substantial fraction of the movements of the left-hand side variable, or even relating a significant fraction of the volatility of the right-hand side variables to that of the left-hand side variable. In my view, this is the type of payoff obtained from the recent incarnations of the "traditional" line. Still, it is progress. Going from less to more ambitious, there are two generic developments I wish to discuss. First, ignoring high and medium frequency variations, we have come to the realization that the low frequency aspects of the data are not inconsistent with theories that assign an important role to the cost o f capital in determining the rate of capital accumulation. Second, there are distinctive episodes during which changes in the cost of capital are sufficiently dramatic that it becomes possible to demonstrate the importance of the cost of capital at higher frequencies as well. Other recent developments within the traditional line include the use of Euler equation procedures. In my view, and unlike the case in basic finance and consumption applications, these procedures are a form of morphine rather than a remedy: their lack of statistical power allows us to sometimes not see the problem. Since my goal is to discuss progress, I will skip results obtained with these procedures s. 2.2.1. L o n g - r u n

Many of the problems with investment equations have to do with the presence of complex and not well understood dynamic issues (more on this in the next sections). From early on, researchers have found it useful to think about investment in two steps: first, derive some simple expression for a "target" stock of capital, which I have called K* here; and second, model dynamics as a, possibly complex, function of contemporaneous and lagged changes in K*. It seems sensible, therefore, to start by asking whether the first step resembles what we expect before going into the difficult issues of timing. Taking logs on each side of Equation (2.2), disregarding constants, and relaxing the unit elasticity constraint on the cost of capital, yields k* - y

= yck,

(2.3)

where lower case letters denote logarithms and y is the parameter of interest. This expression cannot be estimated, of course, because k* is not observed. There is a simple argument based on cointegration, or a close small sample "cousin," which allows us to get around this observability problem, however. The whole purpose of deriving k* is to then model k as trying to keep pace with it. Thus, differences between these two variables should only be transitory (up to constants). I f k* and k are

See Oliner, Rudebusch and Sichel (1995) for a damaging evaluation of the statistical properties of these procedures.

Ch. 12: Aggregate Investment

821

sufficiently volatile (ideally with unit roots, in large samples), then we can "ignore" the discrepancy between these two variables in estimating y. Let k = k* + e, with c a stationary residual that captures transitory discrepancies between the two variables due to adjustment costs. Substituting this expression into Equation (2.3) yields an equation that can be estimated: k - y = yck + c.

(2.4)

Estimating this equation by OLS (the simplest o f the cointegration procedures) yields, for aggregate US data, an estimate o f y o f -0.4; significantly different from zero 9. We can do better, however. In any small sample, the cointegration argument will not take its full bite, and the estimates o f ~/will be affected by the correlation between regressors and e. Caballero (1994a) argues that this is particularly serious and systematic in models with slow adjustment (e.g. due to adjustment costs). The intuition behind this idea is simple. A partial adjustment mechanism implies that, in any finite sample, the variance o f K/Y ought to be less than the variance o f K * / Y , which means the lefthand side o f Equation (2.4) ought to be less volatile than the right-hand side of Equation (2.3), or yck lo. However, by the normal equations o f OLS, the estimated counterparts o f yck and e on the right-hand side o f Equation (2.4) must be orthogonal, so that the variance o f k - y is greater than the variance o f )ck, which is equal to the variance o f the estimated £'* - y . Since this inequality is in contradiction with what is implied by adjustment cost mechanisms, we conclude that the estimate o f y is biased toward zero. Using Monte Carlo simulations, I showed in that paper that this bias can be substantial, and then proceeded to correct it using Stock and Watson's (1993) procedure. I obtained an estimate o f ~/close to minus one, very near the neoclassical benchmark 11. 2.2.2. Short-run

Demonstrating a relationship between capital accumulation and the cost of capital at higher frequencies has required two changes in approach: first, a change in emphasis from aggregate to microeconomic data; and second, the use of natural

9 This estimate of g was obtained using US quarterly NIPA data for the period 1957:1-1987:4. Capital corresponds to equipment capital and cost of capital is constructed as in Auerbach and Hassett (1992). l0 Note that if adjustment costs are non-convex it is possible, at the microeconomic level, and in a sufficiently short sample, to have these relative volatilities reversed. This is not an issue for the aggregate data results discussed here. See the next section for more on non-convex adjustment cost models. 11 Similar estimates were obtained by Bertola and Caballero (1994) and Caballero, Engel and Haltiwanger (1995) with different data sets.

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R.J Caballero

experiments, such as periods of tax reform, which present the econometrician with more accurate measures of (often substantial) changes in the cost of capital and q. Measures of q, for example, are not only very noisy because of the substitution of average q for marginal q, but also because there may be substantial "non-fundamental" movements in the value of firms, making average q mismeasured as well. However, there are certain episodes (e.g., periods of tax reform) when the movements in q are likely to be large, in a predictable direction, and for the "right reasons". As with cointegration, during those episodes problems with the residual can be more or less disregarded. The movement from aggregate to microeconomic data, by itself, has not done much to improve affairs. Although microeconomic data has improved precision, coefficients on the cost of capital and q in investment equations have remained embarrassingly small. Combined with the use of natural experiments, however, emphasis on microeconomic data has had much higher payoffs. The work of Cummins, Hassett and Hubbard (1994, 1996a) is salient in this regard. They isolate periods with important tax reforms and find that the coefficient on q is much larger in those episodes. Most recently, using firm level data for 14 developed countries, they find that while using standard instrumental variable procedures yields coefficients on q which range from 0.03 to 0.1, when contemporaneous tax reforms are included among the instruments, the estimates jump to a range between 0.09 to 0.8, with median and mean not very far from 0.5. In the USA, for example, the estimate of the coefficient on q jumps from 0.048 to 0.6512 Although these empirical results represent significant progress, there is still plenty of work needed to retrace the steps back to the aggregate and we must not forget that a substantial component of the variation in aggregate and microeconomic investment remains unexplained. The next sections describe progress on both fronts.

3. Lumpy and irreversible investment Investment is a flow variable, and as such it is very sensitive to obstacles. Investment is the by-product of the process by which the capital stock catches up with its desired level; but there are many paths leading the former to the latter. In this section I begin discussing some of these obstacles, emphasizing those that have had prominence in the recent literature. 3.1. Plant~firm level

The most basic form of friction occurs at the level of microeconomic units, and goes under the general heading of adjustment costs.

12 See Caballero (1994b) for a discussion of their results, interpretations and procedures.

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3.1.1. Microeconomic adjustment: characterization

There are essentially three basic types o f adjustments observed at the establishment level: (a) ongoing frictionless flow (maintenance); (b) gradual adjustments (e.g. refinements and training dependent improvements); (c) major and infrequent adjustments 13 The structural literature o f the 1980s and before, based explicitly or implicitly on convex adjustment cost models (the quadratic adjustment cost model, in particular) dealt with (a) and (b). The implicit "hope" was that the smoothness brought about by aggregation would make disregarding the importance o f infrequent adjustments for individual units, unimportant for aggregate phenomena. Instead, the idea was to derive aggregate investment equations as coming from the solution to the optimization problem of a fictitious agent facing adjustment costs which only led to smooth adjustments o f type (a) and (b). Many authors disagreed with this strategy [e.g. Rothschild (1971)]; but for most the relative simplicity of the quadratic model was too enticing to resist. A combination of factors eventually led economists to revisit and reevaluate some o f the shortcuts which were in widespread use by the end o f the 1980S 14. First, there was frustration with the disappointing empirical results described above. Second, techniques which could handle models of lumpy investment became part of the modern economist's tool kit. And third, microeconomic data made the obvious even more apparent: microeconomic investment is extremely lumpy, and this lumpiness is unlikely to fully "wash out" at the aggregate level. The work o f Doms and Dunne (1993) was instrumental in stressing the last point. They documented investment patterns o f 12 000 plants in US manufacturing over the 17 year period, 1972-1989. Their findings are many, of which I have chosen to emphasize those that are most closely related to the purpose o f this survey. For each establishment, Doms and Dunne constructed a series o f the proportion o f the total equipment investment o f the establishment (over the 17-year period) made in each year. They found that on average the largest investment episode accounts for more than 25 percent o f the 17 year investment o f an establishment and that more than half o f the establishments exhibited capital growth close to 50 percent in a single year. They also note that the second largest investment spike often came next to the largest investment spike (right before or right after) suggesting that both spikes correspond to a single investment episode. 15 Combining the two primary spikes, they find that nearly

~3 Which may, in turn, have a time to build aspect. 14 Chronologies are never exact, of course. For example, Nickell had already discussed irreversible investment and many of its implications in 1978; but the mode did not move until much later. 15 All investment project may not be fully counted within one year since not all projects start on January 1, and certainly may take more than a few days to implement. One should not confuse "time to build" with the standard convex adjustment costs. Time to build is the optimal scheduling of a given lumpy project, while in the standard convex adjustment costs model the firm changes this project continuously and smoothly [see Caballero and Leahy (1996)].

R.J Caballero

824

40 percent of the sample investment of the median establishment probably corresponds to a single investment episode 16. Moreover, this is likely to be a lower bound on the lumpiness of investment since these numbers correspond to establishments that remained in the sample during the entire 17-year period. Adding entry and exit would undoubtedly make the evidence on microeconomic lumpiness even more apparent. As for evidence on the macroeconomic relevance of microeconomic lumpiness, Doms and Dunne offer several hints. First, using data on about 360 000 establishments for Census years 1977 and 1987, they document that about 18 percent of aggregate investment is accounted for by the top 100 projects. As a metric, only 6 percent of employment is in the top 100 employers, and less than 10 percent of production occurs in the top 100 producers. More importantly, they show that the time series correlation between aggregate investment and a Herfindahl index of microeconomic investments is very high (close to 0.45). They also constructed a series with the number of firms undergoing their primary investment spike during each year. They show that this measure, rather than the average size of these spikes, closely tracked aggregate investment 17. The subsections that follow describe models which are broadly consistent with these findings, and reviews structural evidence based on these models which lends further support to the view that microeconomic lumpiness is very important for aggregate investment dynamics.

3.1.2. "'Representative" problem There is by now a vast literature (and surveys of it) describing microeconomic models able to capture the essence of the lumpy and discontinuous adjustment highlighted by the evidence described above. Rather than giving a thorough presentation of the canonical model, I refer the interested reader to one of these surveys 18. Instead, I will only sketch the problem, mostly to characterize the nature of the solution and to develop notation which will prove useful later. Let actions and realizations of shocks evolve in discrete time, with time intervals, At. Having optimized over all inputs but capital during the period, a firm with stock of capital K and facing conditions 0, has a flow of profits net of rental cost of capital:

II(K, O)At = (KYO- rK)At

0 < ~ < 1,

(3.1)

where K is the firm's stock of capital; 0 is a profitability index that combines demand, productivity and wage shocks; r is the discount rate; and 7 represents the elasticity 16 Cooper, Haltiwanger and Power (1994) go one step further in characterizing infrequent lumpiness. Using a data set similar to that of Doms and Dtmne, they show that the probabilityof a firm experiencing a major investment spike is increasing in the time since the last major spike. This feature of the data is highly consistent with the implications of the models reviewed later in this section. 17 Where aggregate investmentcorrespondsto the investmentof all the establishmentsin their sample. 18 Dixit (1993) provides an excellent discussion of the basic problem and the mathematicaltechniques needed to solve it.

Ch. 12: AggregateInvestment

825

o f gross profits with respect to capital. It is less than one as long as the firm exhibits some degree o f decreasing returns or market power, which ! assume to be the case. For convenience, capital does not depreciate. It will also facilitate things to assume that increments in the logarithm o f 0 are i.i.d., and that time and the sample paths of 0 are "ahnost" continuous (i.e. At is small and changes in the value of 0 over an interval o f time At are small). I make these assumptions so I can, informally, use all the convenience o f Ito's lemma and Brownian motions. I choose to depart from strict continuous time, on the other hand, because discrete time will allow me to present this section in a more ratified manner. As in the previous section, we can find an expression for the static optimum of the stock o f capital, or "desired" capital: I I-y

K* = argmaxxH(K, 0) =

.

(3.2)

It is apparent from this expression that K* inherits the stochastic properties of 0, so it also follows a geometric random walk. Moreover, the measure o f capital "imbalance": Z=

K K*

'

also inherits the geometric random walk process, for any given K. Substituting this expression into Equation (3.1) and using Equation (3.2) to solve for 0 yields

H(Z,K*) = 7r (ZY - 7Z) K*

0 < 7 < 1.

(3.3)

In order to generate infrequent actions, the cost of adjusting the stock o f capital must increase sharply around the point of no adjustment. A cost proportional to the size of adjustment is enough to do so. Lumpiness requires a little more, for there must be an advantage in bunching adjustment; increasing returns in the adjustment technology is the standard recipe, o f which a fixed cost is the simplest. Let C(rI, K*) denote the cost o f adjusting the capital stock by K ' t / :

C(rI, K . ) = { A K ~ e O } K .

(cf+c~rl

/ cf-Cprl

if if

t/>0, t/<0,

(3.4)

where the K* term ensures that the relative importance of adjustment costs remains unchanged over time 19. Figure 3.1 illustrates an example of C(., .)/K*.

19 This goal would also be accomplished by K, but K* yields slightly simpler mathematical expressions at a low cost in terms of substantive issues. Also, I have allowed proportional costs to differ with respect to upward and downward adjustments in order to talk later about the irreversible investment case; for this purpose, I could have done it equally well through asymmetric fixed costs. Allowing for both forms of asymmetries simultaneously is a trivial but uninteresting extension.

826

R.J. Caballero

\ J Cf

<

)rl

Fig. 3.1. Adjustment costs.

The problem of the firm can be characterized in terms of two functions of Z and K*: V(Z,K*) and ~'(Z, K*). The function V(Z,K*) represents the value of a firm with imbalance Z and desired capital K* if it does not adjust in this period, and V(Z,K*) is the value of the firm which can choose whether or not to adjust. Thus, v ( z , , I,:?) = rt(z,, I
(3.5)

~'(Zt,K[)=max {V(Zt,K[),m~x {V(Zt + rI,K[)-CQI, K[)} }.

(3.6)

and:

The nature of the solution of this problem is now intuitive. Given the function

V(Z, K*), Equation (3.6) provides most of what is needed to characterize the solution. First, since C is positive even for small adjustments, it is apparent that when Z is near that value for which V(Z,K*) is maximized, the first term on the right-hand side of Equation (3.6) is larger than the second term; that is, there is a range of inaction. Second, since both adjustment costs and the profit function are homogeneous of degree one with respect to K*, so are V and ~'. Thus, it is possible to fully characterize the solution in the space of imbalances, Z. Among other things, this implies that the range of inaction described before, is fixed in the space of Z. Let L denote the minimum value of Z for which there is no investment, and U the maximum value for which there is no disinvestment; thus the range of inaction is (L, U). Third, conditional on adjustment, changes must not only be large enough to justify incurring the fixed cost, but also the (invariant) target points must satisfy Vz(/) = Cp

(3.7)

and

Vz(u) = -Cp, where Vz is the derivative of

(3.8)

V with respect to Z, while 1 and u denote the target points from the left and right of the inaction range, respectively. These first-order

827

Ch. 12." AggregateInoestment "-.. ............."..... '...........

el

I ..../........

V ( z, K*) / K*

i" <

> L

1

u

U

Fig. 3.2. Value fimction. conditions are known as "smooth pasting conditions," and simply say that, conditional on adjustment taking place, it must cease when the value of an extra unit of investment (or disinvestment) is equal to the additional cost incurred by that action. There are two additional smooth pasting conditions:

Vz(L) = Cp

(3.9)

and v z ( u ) = -Cp,

(3.10)

which ensure no expected advantage from delaying or advancing adjustment by one At around the trigger points. These smooth pasting conditions are enough to find the optimal (L, l, u, U) rule, given the value function. In order to find the latter, however, we need to go back to Equation (3.5). Standard steps reduce this equation, in the interior of the inaction range, to a second-order differential equation. The two boundary conditions required to find V are obtained from equalizing the two terms on the right-hand side of Equation (3.6):

V(L,K*) = V ( I , K * ) - (cy + c p ( l - L ) ) K*,

(3.11)

V(U,K*) = V ( u , K * ) - (of + cp(U - u)) K*,

(3.12)

which simply say that since the investment rule (optimal or not[) dictates that once a trigger point is reached, adjustment must occur at once, the only difference in the value of being at trigger and target points must be the adjustment cost of moving from the former to the latter. Figure 3.2 illustrates the value function. Smooth pasting says that the tangents at L and l have slope Cp, while those at U and u have slope -Cp. Value matching says

828

R.J. Caballero

that the value function evaluated at the target minus the value function evaluated at the trigger point is equal to the variable cost paid at adjustment plus the fixed cost (all these normalized by K* in the figure). There are a few particular cases which are worth highlighting because they appear often in the literature: (1) If there is no variable cost of investment, once the adjustment decision has been taken, adjustment from both sides is complete since the marginal cost of adjustment is zero. Thus, the (L, l, u, U) rule reduces to an (L, c, U) rule, where c is the common target for investment as well as disinvestment, and is that value which maximizes V(Z, K*) for any K* 2o. (2) If there are variable costs but no fixed cost, there is no reason for adjustment to be lumpy, for there are no increasing returns in the adjustment technology 21. Once the boundaries of the inaction range, L and U, are reached, the firm adjusts just enough to avoid crossing outside the inaction range; that is L and U become reflecting barriers. (3) If there is a large (not necessarily infinite) cost to disinvestment, then investment becomes irreversible. In the absence of investment costs, the investment rule reduces to a single reflecting barrier L, which is to the left of one (reluctance to invest). This is the standard irreversible investment case.

3.1.3. A detour." q-theory and infrequent investment One of the main manifestations of the empirical failure o f previous investment theories, has been the difficulty in finding either a significant and sizable role for q, or evidence that it is a sufficient statistic for investment. Do the theories studied in this section help explain these empirical failures? I see two reasons to believe so. The first one is rather negative, q-theory is no longer robust in our setting, so there :are many scenarios where we should not expect it to work. The second one is more positive. In the subclass o f models where it does work, the functional form relating q and investment is likely to be highly non-linear, thus quite different from the standard linear regressions leading to the rejection o f q-theory.

3.1.3.1. On the fragility of marginal q. It is apparent from the lack of global concavity o f the value function in Figure 3.2, that traditional q-theory is not likely to work in the presence o f jumps. Caballero and Leahy (1996) develop the argument in detail, which I summarize below.

20 Note that in general c ~ 1. That is, the optimal dynamic target is generally different from the static one. 21 And we have already assumed that shocks are "small" in any given At.

829

Ch. 12." Aggregate Inoestment

(a)

lqw...-....-..---.---.....~ J ~ ~ q m 1+ C+p S

qm(z)

il-c<

L

1

u

U

(b) qm

1 + C+p

1 - c-p

>

<

U=u

L=I

Fig. 3.3. Marginalq. The value of the firm is equal to K + V, thus marginal q is 22 qM(Z) = 1 + Vx = 1 + K~.

(3.13)

Figure 3.3a plots qM against the imbalance m e a s u r e Z 23. Smooth pasting implies that qM must be the same at trigger and target points (because Vz must be the same at trigger and target points); if there are jumps, these are points very far apart in state

22 Recallthat P was definedas the presentvalueof profitsnet of adjustmentcosts and interestpayments on capital. 23 See, for example, Dixit (1993) for a characterizationof the (L, l, u, U) solutionin terms of a similar diagram.

830

R.J. Caballero

space. Two points with the same value of qM lead to very different levels of investment (zero and large). Moreover, since the value function becomes linear outside the inaction range, all points outside the inaction range (on the same side) have the same q~t, and all of them lead to different levels of investment. It is apparent, therefore, that the function mapping qM into investment no longer exists. Worse, in between trigger and target points, the relation between qM and Z is not even monotonic. What is happening? Marginal q is the expected present value of the marginal profitability o f capital. Far from an adjustment point, it behaves as usual with respect to the state o f the firm: if conditions improve, future marginal profitability of capital rises, and so does q~. Close to the investment point, on the other hand, the effect of a change in the state of the firm over the probability o f a large amount of investment in the near future dominates. An abrupt increase in the stock of capital brings about an abrupt decline in the marginal profitability o f capital as long as the profit function is concave with respect to capital 24. Thus, an improvement in the state of the firm makes it very likely that it invests in the near future, reducing the expected marginal profitability o f capital in the near future, thus lowering the value of an extra unit of installed capital. Caballero and Leahy (1996) show that adding a convex adjustment cost to the problem does not change the basic intuition of the mechanism described above. They also show, somewhat paradoxically, that average q, which is often thought o f as a convenient albeit inappropriate proxy for marginal q, turns out to be a good predictor of investment even in the presence of fixed costs, although it is no longer a sufficient statistic, except for very special assumptions about the stochastic nature of driving forces. 3.1.3.2. When does q-theory work?. The failure o f q-theory described above is rooted in the presence of increasing returns in the adjustment cost function (3.4). This feature of the adjustment technology is responsible for the loss of global concavity of the value function, which is behind the non-monotonicity o f marginal q 25. Monotonicity of qM inside the inaction range is recovered by dropping the fixed cost from Equation (3.4), as was done in cases 2 and 3 in Section 3.1.2. Figure 3.3b portrays this scenario. Adjustment at the trigger points no longer involves large projects, thus proximity to these triggers no longer signal the sharp changes in future marginal profitability of capital which were responsible for the "anomalous" behavior of qM 26 There is still the issue that in the (very) rare event that a firm finds itself outside the inaction range it will adjust immediately to the trigger, at a constant marginal cost, so

24 Which I take to be the standard case. z5 Indeed, value functions for (S, s) models are often only K-concave. 26 Of course, once at the trigger, large projects may result from the accumulated and - more or less continuous response to a sequence of shocks with the same sign. But this does not give rise to a sharp change in profitability since investment occurs only in response and to offset new, as opposed to accumulated, changes in profitability.

Ch. 12: AggregateInvestment

831

different levels of investment are consistent with the same value o f qM. This is easily remedied by adding a convex component to the adjustment cost function27:

c(.,K*) =

0tK* {c l,I +c l.I

> 1.

(3.14)

This is essentially what Abel and Eberly (1994) do 28. Absent the advantage of lumping adjustment brought about by the presence o f fixed costs, standard q-theory is recovered whenever the firm invests. Provided adjustment takes place, the firm equalizes the marginal benefit of adjustment and the marginal cost o f investing, which is now an increasing function o f adjustment: qM = 1 + sgn(r/)

(Cp +/3Cqlr/l~-l) ,

for t / ~ 0. By setting ~ to zero, we can obtain the boundaries o f inaction in qM_space. Indeed, investment will not occur if

1-cp
27 Which, at the same time, makes transitions outside the inaction range less rare. 28 Needless to say, it is trivial to add asymmetries to the adjustment cost function. But that is beside the point of this section. 29 Alternatively, if one assumes perfect competition and constant returns to scale, the profit function becomes linear with respect to capital (if the other factors of production can be adjusted at will), so changes in investment do not feed back into q. In this extreme case, the modified (i.e. with an inaction range) q-theory works well even in the presence of traditional fixed costs.

832

R.J Caballero

range relevant for different types of investments could explain the negative BarnettSakellaris finding. 3.1.3.3. Taking stock. One may be inclined to conclude from this section that before going ahead with q-theory one should check whether investment literally exhibits jumps or not. This is not the lesson I draw, however. For once, this is not right. It is not difficult to add a time to build mechanism such that a lumpy project is decomposed into a fairly smooth flow, without altering the argument of why marginal q fails in the presence of fixed costs. But more importantly, I suspect the main lesson is one of modesty. I doubt that researchers will often find the required data and/or patience to determine whether one scenario or the other holds. In this case, we might as well acknowledge that the relationship between marginal q and investment is not robust, and that average q is unlikely to be a sufficient statistic for investment. Of course it is important to include variables that capture knowledge of the future on the right-hand side of investment equations, but we should avoid reading "too much" from these regressions. 3.1.4. Another detour." Several misconceptions about irreuersible investment As I mentioned before, when describing the special case of irreversible investment, the regulation barrier, L, is to the left of one. That is, investment occurs only when the stock of capital is substantially below the frictionless stock of capital. Alternatively, investment occurs when the marginal profitability of capital is substantially above the cost of capital. This is the famous "reluctance to invest" result. There are several misconceptions about the implications of this "reluctance" result. I will mention three of them. It is often said that, (a) reluctance implies that, in the presence of irreversibility, the firm accumulates less capital; (b) since reluctance rises with uncertainty (the regulation point moves further to the left), more uncertainty implies less capital; and (c) standard present value techniques are inappropriate because reluctance reflects the value of the "option to wait" for more information before irreversibly sinking resources and this is not taken into account by the standard formulae. In order to show the fallacious nature of the first statement, it is useful to go back to our canonical problem and simulate the path o f the (log of) stock of capital of a firm facing no irreversibility constraint. Panel (a) in Figure 3.4 does so for a random realization of the path of 0. Panel (b) in the figure shows the corresponding path of the marginal profitability of capital, which is equal to the constant - frictionless - cost of capital, r 3°. Imagine now imposing an irreversibility constraint on the firm, but assume that the firm does not modify its "frictionless" investment rule whenever it can invest. This is

3o These figures are from Caballero (1993a).

833

Ch. 12: Aggregate Investment (a)

(b)

[I

~r

~L IlL o;

~L ~o s

lo

rs

20

~

~o

~

40

4S

l

~0

l

l

l

l

l

,

t~ne

l

l

P~E~ ]

l

tlme

(c)

(d)

I~rg. Prof.

~o

;

;

;

g

,;

~

io ,',

~

r

i

i

i

tlme

'i

| .............

i Is

t

I

i ............ I?'--

t Io

r

(f)

Al

i ~

i

tlme

(e)

o

i

i zo

r zls

time

i ao

l

i ~

- -

/

In Kf

- - -

In K d

--

InK i 4o

tl 4s

c --

/

c+h

Mar'g. so

:

,_

.:

,

,

5

I0

m

~o

J 2'~

time

Fig. 3.4. Reluctance and its counterpart.

t ~

~

~ 4o

Prof i 45

"

J

so

834

R.J Caballero

portrayed in panel (c) of the figure. The solid and dashed lines represent the actual and frictionless stocks o f capital, respectively. It is apparent that the firm would, on average, have too much capital, for it would have the same stock o f capital in good times, but too much in bad times. The counterpart o f this is in panel (d), which shows that on average the marginal profitability of capital is below the cost o f capital. Reluctance to invest in good times is an optimal response attempting to offset the natural tendency to over-accumulate capital induced by the irreversibility constraint. Panel (e) illustrates this point. The solid and dashed lines represent the same variables as in panel (c), while the dotted line illustrates the target stock of capital when the firm behaves optimally. The counterpart o f the negative value of ln(Ka/Kf ) is a positive constant h in the marginal profitability o f capital required for investment to take place (panel f). It is apparent that whether the stock o f capital is on average higher or lower than without the irreversibility constraint is unclear; the firm has too little capital during good times but too much during very bad times. A precise answer depends on things about which we know little, and which may turn out to yield only secondorder effects 31. It is now easy to see the fallacious nature of the second statement. More uncertainty raises reluctance precisely because it raises the need to reduce the extent o f excessive capital during the now deeper recessions. Without raising reluctance, an increase in uncertainty would raise the average stock o f capital in the presence of irreversibility constraints. This occurs because there would now be greater capital accumulation during extremely good times which would not be offset by large disinvestment during extremely bad times 32. The third misunderstanding is o f a different nature. In my view, it is the result of insightful but, unfortunately, abused language. First, what is right: there is nothing mysterious about irreversibility constraints as a mathematical problem. Dynamic programing works, in the same way it does with other, more traditional, adjustment frictions. This means that present value formulae, using the correct calculation of future marginal profitability of capital also work. O f course such calculations must be performed along the optimal investment path, constraints included! What is wrong: the standard analysis must be modified to consider the value of the "option to wait".

3a See Bertola (1992), Caballero (1993a), Bertola and Caballero (1994) for early discussions of this issue and of the related uncertainty-investment misconception. More recently, Abel and Eberly (1996b) have formalized these claims and made them more precise. 32 This does not mean that one cannot construct scenarios where an increase in uncertainty reduces investment. For example, if there is an increase in perceived future uncertainty, the investment threshold may jump today - i.e., before the variance of shocks does - resulting in an unambiguous decline in investment. Also, one should not confuse changes in uncertainty with changes in the probability of a bad event. The latter links increases in uncertainty to a reduction in expected value, an entirely different and more straightforward effect on investment. One can find traces of this confusion in the (informal) credibility literature.

Ch. 12: Aggregate Investment

835

As we have seen, there is no need to do so. However, one may choose to follow an alternative path, in which one starts by evaluating the future marginal profitability o f capital without considering the effect o f future optimal investment decisions on marginal profitability. This "mistake" can then be "corrected" with a term that has an option representation. This alternative way o f doing things is akin to the arbitrage approach in finance, and it was nicely portrayed in Pindyck (1988). The confusion arises, in my view, from mixing the language in the two approaches 33. A related claim exists for a once and for all project (as opposed to incremental investment). It is said that the simple positive net present value rule used in business schools to decide whether a project should be implemented does not hold because it does not consider the option to wait and decide tomorrow, when more information is available. Since I have never taught at a business school I cannot argue directly against that claim. However, if the issue is whether to invest today or tomorrow, the right criterion has never been invest if NPV is positive - at least that is what we teach economics undergraduates. This is a case of mutually exclusive projects, thus the fight criterion has always been to compare their net present value and take that with the highest NPV, provided it is positive. If investment is irreversible, the project invest tomorrow has a lower bound at zero (because investment will not occur if N P V looks negative tomorrow), which the project invest today does not. Thus, other things equal, irreversibility necessarily makes investing tomorrow more attractive than investing today. 3.1.5. Adjustment hazard

At a qualitative level, the (L, l, u, U) models described above capture well the nonlinear nature o f microeconomic adjustment. Maintenance expenditures aside, investment is mostly sporadic and often lumpy; scarcely reacting to small changes in the environment but abruptly undoing accumulated imbalances when they become sufficiently large, and with possibly significant asymmetries between investment and disinvestment. At an empirical level, however, these characterizations are too stark. For reasons, some o f which we understand and most of which we do not, firms respond differently to similar imbalances over time and across firms. Caballero and Engel (1999) propose a probabilistic instead o f a deterministic adjustment rule. Rather than having a clear demarcation between regions o f adjustment and inaction, they model a situation where large imbalances are more likely to trigger adjustment than small ones 34.

33 See Bertola (1988) for one of the first discussions of this issue in the economics literatme. There is also a related discussion in applied mathematics; see, for example, E1 Karoui and Karatzas (1991). Abel et al. (1996) have recently revisited and expanded the discussion on the relation between the two approaches. 34 Another advantage of this approach is that it nests linear models as the probability of adjustment becomes independent of Z.

R.J. Caballero

836

There are many formal motivations for such an assumption. A particularly simple one, pursued by Caballero and Engel (1999), is to assume that cf in the adjustment cost fimction (3:4) is an i.i.d, random variable, both across firms and time. Although technically more complex, the nature of the problem is not too different from that of the simpler (L, l, u, U) model. Let ~o denote the random fixed cost, and G(w) its time invariant distribution. It is possible to characterize the problem of the firm in terms of two functions similar to those used before: V(Z, K*) and ~'(Z, K*, w), the value of a firm with imbalance Z, desired capital K*, and realization of fixed adjustment cost w. In particular, V(Z,K*) is the value o f the firm provided it does not adjust, while [/(Z,K*, w) is the value o f the firm when it is left free to choose whether or not to adjust. Thus,

V(Zt, 1£7) = H(Zt, K t )At + (1 - rAt)Et [V(Zt+At,K~+At,Wt+At,)],

•

V(Zt,K; ,~o)-max

{ V(Zt,K[),max {V(Zt+ tl, K[)-C(tI, K[,wt)}

}

(3.15)

.

(3.16)

Not surprisingly, the nature of the solution is not too different from that o f the (L, l, u, U) case. Indeed, conditional on c~ it is an (L, l, u, U) rule, although there are additional intertemporal considerations, since the firm weighs the likelihood of drawing higher or lower adjustment costs in the future. Without conditioning on ~o, it is a probabilistic rule in the space of imbalances. In order to simplify the exposition, I will suppress the proportional costs. Thus, conditional on adjustment, the target point is the same regardless of whether the firm is adding or subtracting to its stock of capital (i.e. l = u = c). Moreover, let me define a new imbalance index centered around zero: x - In (Z/c). The probability of adjustment rises with the absolute value of x because there are more realizations of adjustment costs which justify adjustment. This is the sense in which the (S, s) nature of the simpler models is preserved. Let A(x) denote the function describing the probability of adjustment given x, and call it the adjustment hazard function [see Caballero and Engel (1999)]. Given an imbalance x, it is no longer possible to say with certainty whether or not the firm will adjust, but the expected investment by the firm is given by E

11, ]

K/t x = (e ~ -

1)A(x) ~ - x A ( x ) ,

(3.17)

which is simply the product of the adjustment if it occurs, and the probability that adjustment occurs 35. Aggregation is now only a step away. 35 Caballero and Engel (1999) refer to A(x) as the "effective hazard" to capture the idea that, through a normalization, it also captures scenarios where adjustment, if it occurs, is only a fraction of the imbalance X.

Ch. 12: AggregateInvestment

837

3.2. Aggregation Unlike microeconomic data, aggregate investment series look fairly smooth. Large microeconomic adjustments are far from being perfectly synchronized. The question arises, and this was the maintained hypothesis during the 1980s, as to whether aggregation eliminates all traces of lumpy microeconomic adjustment. The answer is a clear no. Doms and Dunne's evidence on the role of synchronization of primary spikes in accounting for aggregate investment, and on the high time series correlation between aggregate investment and a Herfindahl index of microeconomic investments, as well as the more structural empirical evidence reviewed in the next section, support this conclusion, With the setup at hand, aggregation proceeds in two easy steps. To simplify things further, I will define the aggregate as the behavior of the average, rather than the weighted average 36. Both steps rely on having a large number of establishments, so that laws of large numbers can be applied. In the first step, one takes as the average investment rate (i.e. the ratio of investment to capital) of establishments with more or less the same imbalance of capital, x, the conditional expectation of this ratio given in Equation (3.17):

It ,~x = -xA(x),

(3.18)

g)

where the superscript x denotes the aggregate for plants with imbalance x. The second step just requires averaging across all x. Let f(x, t) denote the cross sectional density of establishments' capital imbalances just before investment takes place at time t. Then the aggregate investment rate at time t, (It/Kt) A, is

( It ~A = - f xA(x)f(x,t)dx.

g)

(3.19)

This is an interesting equation, with macroeconomic data on the left and microeconomic data on the right-hand side. An example serves to illustrate this aspect of the investment equation: If the adjustment hazard is quadratic,

A(x) = )~o+ ;qx + )~2x2, Equation (3.19) reduces to I, ~A = __~r~,-(1)__~lXt(2) g)

_ •2X(3),

(3.20)

where Xt(1), Xt(2) and Xt(3) denote, respectively, the first, second and third moments of the distribution of establishments' imbalances. 36 Using microeconomicdata, Caballero, Engel and Haltiwanger (1995) show that in US manufacturing this approximationis. See Caballero and Engel (1999) for a detailed discussion of the issue.

838

R.J. Caballero

If t l l = ,~2 = 0, the model only has aggregate variables, both on the right and left• hand side. Indeed this case corresponds to the celebrated partial adjustment model, and it also coincides with the equation obtained from a quadratic adjustment cost model with a representative agent [e.g. Rotemberg (1987) and Caballero and Engel (1999)]. If either )!.1 or/~2 is different from zero, however, information about the cross sectional distribution o f imbalances is needed on the right-hand side. All the microeconomic models discussed in this section yield situations where higher moments o f the cross sectional distribution play a role. 3.3. Empirical evidence There are two polar empirical strategies used to estimate Equation (3.19), with a continuum o f possibilities in between. At one extreme, one can use microeconomic data to construct all the elements on the right-hand side; in particular one can construct the path o f the cross sectional distribution and estimate the adjustment hazard as an accounting identity, or estimate a parametric version o f it. At the other extreme, one can attempt to learn about the adjustment hazard from aggregate data only, by putting enough structure on the stochastic processes faced by firms and by starting with a guess on the initial cross sectional distribution. Both avenues have been explored, with similar results along dimensions they can be compared. 3.3.1. Microeconomic data Caballero, Engel and Haltiwanger (1995) use information on approximately seven thousand US manufacturing plants from 1972 to 1988 to empirically recreate the steps described in the previous section 37. The figures below were constructed with data from that paper 3s. The procedure used by Caballero, Engel and Haltiwanger is essentially accounting, except for the first step, which requires estimating a series of frictionless capital for each establishment, and, from this, a m e a s u r e ofxit (an index of the capital imbalance o f firm i at date t). The series o f frictionless capital were constructed using a procedure similar to that described in Section 2, but cointegration regressions were run at the individual establishment level 39. The average estimate of the long run elasticity of capital with

37 As in Doms and Dunne (1993), we used data from the Longitudinal Research Datafile (LRD). The LRD was created by longitudinally linking the establishment-level data from the Annual Survey of Manufacturing. The data used in that paper is a subset of the LRD, representing all large, continuously operating plants over the sample. The data sets include information on both investment and retirement of equipment (i.e. the gross value of assets sold, retired, scrapped, etc. 38 Warning: x in that paper corresponds to ~ in this survey. 39 The results reported there constrained the coefficient on the elasticity of capital with respect to its cost to be equal across two-digit sectors, but all principal results were robust to different constraints and specifications.

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0.4

0.3

0.2

0.1

I -2

-1

0

1

o.o

Fig. 3.5. Adjustment hazard.

respect to its cost was close to minus one, with substantial heterogeneity across sectors. The measures ofxit, up to a constant, correspond to the difference between actual and estimated frictionless capital4°. There are two results from that paper which seem particularly relevant for this section of the survey. One on the shape o f the adjustment hazard, and the other on the consequences o f this shape for aggregate dynamics. I discuss the former here and the latter after the next subsection. Figure 3.5 reports the average adjustment hazard constructed from simply averaging the investment rates o f establishments in a small neighborhood o f each x, divided by minus the corresponding x. The hazard is clearly increasing for positive adjustment (i.e. expected investment rises more than proportionally with the shortage o f capital), as one would expect from the nonlinearities implied by (L, 1, u, U) type models, and unlike the linear models which imply a constant hazard. The estimated hazard is also very low for negative changes, suggesting irreversibility 41 . Following a similar procedure, Goolsbee and Gross (1997) have studied very detailed and high quality microeconomic data on capital stock decisions in the US airline industry. They found clear evidence of behavior consistent with non-convex adjustment costs.

3.3.2. Aggregate data I f only aggregate data are available, one needs to make some inference about the path o f the cross sectional distribution of capital imbalances, f ( x , t), from these data. This is possible if enough structure is placed on the stochastic processes faced by firms.

40 The establishment specific constants were estimated as the average gap between their respective kit and k/t for the five points with investment closest to their median (broadly interpreted as maintenance investment). 41 Retirements include assets sold, scrapped or retired. It is possible that observations are very noisy on this side. The right-hand side of the figure should therefore be viewed with some caution.

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The basic operations affecting the evolution o f f ( x , t) are quite simple. Given the density, or histogram, at time t - 1, there are three basic operations in its transformation into f ( x , t). First, aggregate shocks and common depreciation shift everybody's x in the same direction; second, given the adjustment hazard, the density at each x is split into those that stay there and those that adjust and move to some other position in the state space (in the simplest case, they move to x = 0, but this is not necessary); and third, idiosyncratic shocks hit, which amounts to a convolution o f the density resulting from the second step and that o f idiosyncratic shocks. Making distributional assumptions about idiosyncratic shocks and the initial cross sectional distribution, is enough, therefore, to keep track o f the evolution o f the cross sectional density, conditional on aggregate shocks and for a given adjustment hazard. In continuous time, and assuming Brownian motions for aggregate and idiosyncratic shocks, Bertola and Caballero (1994) estimated the irreversible investment model, and Caballero (1993b) did so for the (L,/, u, U) model. 42 In discrete time but continuous state space, Caballero and Engel (1999), estimated the more general adjustment hazard model described in the previous sections, assuming that both idiosyncratic and aggregate shocks were generated by log-normal processes. We did so for US manufacturing investment in equipment and structures (separately) for the 1947-1992 period 43. The results were largely consistent with those found with microeconomic data by Caballero, Engel and Haltiwanger (1995). There is clear evidence o f an increasing hazard model; that is, the expected adjustment o f a firm grows more than proportionally with its imbalance 44. An important point to note is that since only aggregate data were used, these microeconomic nonlinearities must matter at the aggregate level, for otherwise they would not be identified. The improvement in the likelihood function from estimating this non-linear model rather than a simple linear model (including the quadratic adjustment cost model) was highly significant, and so was the improvement in the out-of-sample forecasting accuracy 45.

42 See Bertola and Caballero (1990) for a discrete time and space model and estimation procedure. 43 Another important difference between this and the previous papers is that estimation was done by a single step maximum likelihood procedure, which did not require estimating frictionless capital separately. 44 We did not allow for asymmetries between ups and downs but this turned out not to matter much because given the strong drift induced by depreciation and the small value we found for the hazard in an interval around zero, the model effectively behaves as if investment is irreversible (i.e. It is very asymmetric around the median value of x and with a very small hazard for values of x much higher than that.). 45 For within sample criteria, we ran Vuong's [Rivers and Vuong (1991)] test for non-nested models, and we rejected strongly the hypothesis that both models (linear and non-linear) are equally close to the true model against the hypothesis that the structural (non-linear) model is better. For out-of-sample criteria, we dropped the last ten percent of the observations and evaluated the Mean Squared Error of the one step ahead forecasts for these observations [see Caballero and Engel (1999)].

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Ch. 12." Aggregate Investment 3.3.3. Pent-up demand

What is the aspect of the data that makes these models better than linear ones at explaining aggregate investment dynamics? The simplest answer comes from an example. Suppose that a history of mostly positive aggregate shocks displaces the cross sectional distribution of imbalances toward the high part of the hazard. Such a sequence of events will not only lead to more investment along the path but also to more pent-up investment demand; indeed, the cross sectional distribution represents unfulfilled investment plans. But as unfulfilled demand "climbs" the hazard, more units are involved in responding to new shocks; incremental investment demand is more easily boosted by further positive aggregate shocks, or depressed by a turnabout of events. This time-varying/history-dependent aggregate elasticity plays a very important role for aggregate investment dynamics. It captures the aggregate impact of changes in the degree of synchronization of large adjustments; already an important explanatory variable in Doms and Dunne's less structural study. In particular, their observation that the Herfindahl of investment rises during episodes of large aggregate investment matches well this mechanism. Using the path of cross sectional distributions and hazards described at the beginning of this subsection, Caballero, Engel and Haltiwanger (1995) found an important role for the mechanism described above. Figure 3.6 depicts the relative contribution of the time-varying aggregate elasticity for aggregate investment dynamics. A positive value reflects an amplification effect (micro-nonlinearities exacerbate the economy's response to aggregate shocks), while a negative value reflects an offsetting effect. The impact of the time-varying elasticity appears to be especially large after the tax-reform of 1986 (when tax-incentives for investment were removed). The decline in investment was 20 percent greater than it would have been under a linear model.

Fraction 0.15 0.10 / 0.05 0 - 0.05

-0.10 -0.15 I

1976

1978

I

1980

I

I

1982

1984

1986

Fig. 3.6. Relative contributionof time-varyingmarginal response, 1974-1988.

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R.J. Caballero d CD

d

A

LO 0

d

o

V

[___

c)

Fig. 3.7. Equipment-mean-difference. The importance of the time-varying elasticity is confirmed by Caballero and Engel (1999), this time using only aggregate data. As before, it is the flexible cyclical elasticity o f the increasing hazard model which allows it to better capture the high skewness and kurtosis imprinted on aggregate data by brisk investment recoveries 46. The solid line in Figure 3.7 plots the difference between the path o f the US manufacturing equipment investment-capital ratio and the predictions o f a linear model (partial adjustment) fed with the shocks estimated for the increasing-hazard model; the dashed line portrays the path o f the aggregate investment-capital ratio around its mean. It is apparent from these figures that the linear model makes its largest errors at times o f large investment changes. 3.4. Equilibrium The literature described in the previous section only considers exogenous aggregate shocks. What the econometric procedures identified as aggregate shocks are in all likelihood a combination o f " d e e p " aggregate shocks and the feedback and constraints brought about by factor markets, goods markets, and intertemporal preferences, among other things. Bottlenecks may certainly limit the extent o f synchronized investment. Equilibrium constraints not only affect the response of aggregate investment to deep aggregate shocks, but also affect the nature o f the stochastic processes faced

46 Note that just allowing for skewness and kurtosis in shocks, although it improves the performance of linear models, is not nearly enough to make the linear model as good as the non-linear one. In Caballero and Engel (1999) we compared the structural model with normal shocks (to the rate of growth of desired capital) with a linear model which flexibly combined normal and log-normal shocks (which allows for skewness and kurtosis). We found that Vuong's test still favored the non-linear model very clearly. Moreover, in Caballero, Engel and Haltiwanger (1995) we found no evidence that would allow us to reject the hypothesis that shocks have a normal distribution.

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by firms and the dimension of the state space. It is this last observation which has inhibited progress in constructing general equilibrium versions of these models. In principle, the entire cross sectional distribution is needed to forecast future prices faced by any particular firm, which means that actions today, and therefore equilibrium determination, depend on these complex forecasts, and so on. We are, however, beginning to see progress along this dimension. Much of this has occurred in models with active extensive margins, and will be discussed in the next sections, together with the reasons why the presence o f an extensive margin (entry and/or exit) may facilitate rather than complicate the solution of the model. However, there has also been recent progress along the lines of the intensive margin models discussed up to now. Krieger (1997) embeds the heterogeneous agents irreversible investment model of Bertola and Caballero (1994) into a more or less standard Real Business Cycle model. He deals with the curse of dimensionality by arguing that, except for very high frequency aspects of the data, expectations can be well approximated by keeping track of a finite (and not too large) number of statistics of the Fourier representation of the cross sectional distribution. I suspect that the quality of this approximation is facilitated by the fact that, in Krieger's model, aggregate shocks occur only infrequently. Nonetheless, I view his as an important step forward. At this stage, the primary effect of general equilibrium is not surprising. It brings important sources of aggregate convexity into the problem, smoothing further the response of aggregate investment to aggregate shocks. How important are aggregate sources of convexity? I suspect that, together with time to build considerations, they are among the main sources of convexity in the short run. On one hand, we have already presented substantial evidence on microeconomic lumpiness, which is largely inconsistent with a dominant role for generalized convexity at the microeconomic level. On the other, not only is it well known that estimated partial adjustment coefficients grow with the degree of disaggregation of the data, but we also have direct evidence on the importance of bottlenecks. Goolsbee (1995a) provides interesting evidence on the latter. He exploits the variation across time and assets (capital) in investment tax incentives, as instruments for short-run investment demand. He shows that the price of assets is highly responsive to ITCs: A 10 percent increase in ITCs leads to an average increase in the price of capital goods of about 6 percent. This price effect slowly vanishes over the following three years 47. Equilibrium considerations will play a central role in the sections that follow. In particular, the issue of the elasticity of the supply of capital, generally interpreted, as well as that of other bottlenecks will be revisited often.

47 In further work, Goolsbee (1997) concludes that an important fraction of the increase in short rnn marginal cost is due to an increase in the wages of workers who produce capital goods. In the last part of Section 5 I will discuss the connection between sunk investment and payments to complementary factors. Questioning the robustness of Goolsbee's(1995a) findings, Hassett and Hubbard (1996a), find evidence of a positive effect of tax credits on prices of capital goods before 1975 but not after that.

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4. Entry, exit and scrapping Changes in the aggregate stock of capital are not only due to the expansion of existing establishments and projects, but also result from the entry (creation) decisions of existing and new entrepreneurs, the exit decisions of some incumbents, and the restructuring of possibly outdated forms of production. There is a very extensive and interesting industrial organization literature on these issues which I will not discuss here. Instead, I will focus on issues that directly relate to our current discussion: the impact of sunk costs on aggregate investment and the feedback of equilibrium considerations into individual decisions about lumpy actions. This section contains three main messages: First, by truncating the distribution of perceived future returns, free entry acts as if each competitive investor internalized the negative effect of its entry decision on expected future industry prices. Second, equilibrium scrapping and creation are closely connected: if industry wide creation costs are linear, scrapping will be less responsive to aggregate shocks than if these costs are convex (i.e. if there is an upward sloping short-rtm supply of (newly) installed capital). Among other things, this is important for capital accumulation and the patterns of its mismeasurement. And third, in equilibrium, shocks to the scrapping margin can lead to investment booms, and to double-counting problems in the measurement of capital 48.

4.1. Competitive entry and irreversibility Dixit (1989), Leahy (1993), and Caballero and Pindyck (1996), among others, have provided simple models of competitive equilibrium investment in which the only meaningful investment decision of firms is whether or not to enter into and, in some cases, exit from the industry 49. Below, I sketch a representative model of this type. Investment is sunk upon entry in the sense that selling the firm's capital does not change its productivity. The flow accruing to a firm i at time t is summarized by the product of an idiosyncratic productivity level, Sit > 0 and the industry price, Pt. The idiosyncratic productivity level is such that industry output, Yt, is

Yt =

/o

Sit d i = N~,

(4.1)

where Nt is the measure of firms at time t. Given Art, the industry price is determined from the demand equation:

Pt

= V t Y t -1/~1 =

VtNt 1/~,

(4.2)

48 See Greenspan and Cohen (1996), for a discussion of the importance of considering endogenous scrappage to forecast sales of new motor vehicles in the USA. 49 See Hopenhayn (1992) for an elegant characterization of the steady state properties of a competitive equilibrium model of entry and exit.

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where Vt is an aggregate demand shock that follows a geometric Brownian motion with drift/~ > 0 and standard deviation a, and t/ is the elasticity of demand with respect to price 50. Let there be an infinite supply of potential entrants, whose initial productivity upon entry is drama from the distribution of productivities of existing firms. There is an entry cost F and no depreciation or higher productivity alternative use (issues of exit will be discussed in the next subsection). Free entry implies:

F >~Ei { Et [f ~ PsSi,e-r(" Odsl } .

(4.3)

Using Fubini's Theorem (i.e. moving the expectation with respect to the idiosyncratic shocks inside the integral) allows us to remove the idiosyncratic component from Equation (4.3), yielding

F>~Etlft°°P,.er(St)dsJ.

(4.4)

Given Nt, the industry price is exclusively driven by the aggregate demand shock. Thus, absent entry, the right-hand side of Equation (4.4) is an increasing function of Pt, call it j~(P). Entry, however, cannot always be absent, for that would occasionally violate the free entry condition. Indeed, as soon as J~(P) > F, there would be infinite entry which, in turn, would lower the equilibrium price instantly. There is only one price, call it/5o, such that the free entry condition holds with equality. Once this price is reached, enough entry will occur to ensure that the price does not cross this upper bound; but, to be justified, entry must not occur below that bound either. Entry, therefore, changes the stochastic process of the equilibrium price from a Brownian Motion to a regulated Brownian Motion. This change in the price process, however, means that.]~ is no longer the right description of the expression on the right-hand side of Equation (4.4). There is a new function, Ji(P), which is still monotonic in the price, but which satisfies Ji(P) < J~(P) for all P because of the role of entry in preventing the realization of high prices. This, in turn, implies a new reservation/entry price P1 > P0, which leads to a new function )~(P), such that j~ > y~ > Ji, which leads to a new regulation point in between the previous ones, and so on until convergence to some equilibrium, ~(p),p)51. Thus, through competitive equilibrium, we have arrived at a solution like that of the irreversible investment problem at the individual level, but now for the industry as a whole. Periods of inaction are followed by regulated investment (through entry) during favorable times. The constructive argument used to illustrate the solution isolates

50 Adding an aggregate productivity shock is straightforward. The Brownian Motion assumption is not needed, but it simplifiesthe calculations. 51 Needless to say, this iterative procedure is not needed to obtain the solution of this problem.

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the feedback of equilibrium on individual decisions. Potential entrants (investors) know that if market conditions worsen they will have to absorb losses (this is where irreversibility kicks in), while if market conditions improve, entry will occur, limiting the potential gains (since the price will never be higher than/5). As a result, they delay entry because the expected value of future market prices is necessarily lower than the current/entry price. There is a methodological angle in this literature. Entry (and exit) is a very powerful mechanism. With the "appropriate" assumptions about potential entrants, entry often simplifies the computation of equilibrium in models with heterogeneity and sunk costs. Essentially, the methodological "trick" is that the degree of complexity of the computational problem in cases where both extensive and intensive margins are present is often largely determined by the nature of the distribution of potential entrants, which can be made much simpler than the endogenous evolution of the cross sectional distributions discussed in the previous section. Of course, in reality there is substantial inbreeding, so the distribution of potential entrants is in all likelihood related to that of incumbents. Nonetheless, the current set of models are convenient machines that allow us to cut the chain of endogeneity before it gets too forbidding, but after the first stage, where there are no endogenous interactions. This methodological advantage has allowed researchers to explore some of the equilibrium issues left open in Section 3. Caballero and Hammour (1994) have explored in more detail the consequences of different assumptions on the supply of capital for the pattern of aggregate investment (job creation) and scrapping (job destruction). The latter is a very important, and often disregarded, aspect of the timing of capital accumulation. I will return to the scrapping issue in the next sections, but for now I just want to interpret it as an incumbent's decision (as opposed to a potential entrants' decision). The issue at hand is how does the entry pattern affect the response of incumbents to aggregate shocks. A scrapping margin can easily be added to the entry model discussed above by, for example, allowing Si to take negative values (e.g. due to the increase in the price of an intermediate input). Imagine, however, that the drift in the aggregate shock (and/or the failure rate of incumbents) is strong enough so there is continuous entry. Since the supply of capital faced by the industry is fully elastic (the entry cost is constant), continuous entry implies that the industry price is constant and equal to/5 (corrected for the exit possibility). That is, aggregate shocks are accommodated by the flow of investment by new entrants; fully insulating insiders from aggregate shocks. Insiders go about their scrapping decisions only considering their idiosyncratic shocks; adding a standard intensive margin does not change the basic insight [see Campbell and Fisher (1996)]. Caballero and Hammour (1994) refer to this result as perfect insulation. From a technical point of view, the simplicity of the computation of equilibrium in the perfect insulation case carries through to situations where the cost of investment fluctuates exogenously, although in that case perfect insulation breaks down. If the industry faces an upward sloping supply of capital, a sensible assumption at least in the

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short run (remember Goolsbee's evidence), we return to a scenario in which the "curse of dimensionality" appears. Caballero and Hammour (1994, 1996a) have dealt with this case in scenarios where aggregate shocks follow deterministic cycles 52. Besides the specific issues addressed in those papers, the main implication for the purpose of this survey is that investment by potential entrants becomes less responsive to aggregate shocks, which also means a break down of perfect insulation and therefore a more volatile response of the scrapping and intensive margins. Krieger (1997) also discusses equilibrium interactions between creation and destruction margins, although he obtains positive rather than negative comovement between investment and scrapping. In his model, a permanent technology shock leads to a short term increase in interest rates which squeezes low productivity units relative to high productivity ones. The ensuing increase in scrapping frees resources for new higherproductivity investment. Similarly, Campbell (1997) studies the equilibrium response of entry and exit to technology shocks embodied in new production units. He argues that the increase in exit generated by positive technological shocks is an important source of resources for the creation of new production sites. 4.2. Technological heterogeneity and scrapping Scrapping is an important aspect of the process of capital accumulation. Understanding it is essential for constructing informative measures of the quantity and quality of capital at each point in time. Nonetheless, the scrapping margin is seldom emphasized, I suspect, mostly because of the difficulties associated with obtaining reliable data53. As a result, many time series comparisons of capital accumulation and productivity growth (especially across countries) are polluted by inadequate accounting of scrapping. Effective capital depreciation must surely be higher in countries tmdergoing rapid modernization processes. Partly to address these issues, vintage capital and putty-clay models have regained popularity lately. Benhabib and Rustichini (1993), for example, describe the investment cycles that follow scrapping cycles in a vintage capital model. While Atkeson and Kehoe (1997) argue that putty-clay models outperform standard putty-putty models with adjustment costs in describing the cross sectional response of investment and output to energy shocks. Gilchrist and Williams (1996), on the other hand, embody the putty-clay model in an otherwise standard RBC model and document a substantial gain over the standard RBC model in accounting for the forecastable comovements of economic aggregates. And Cooley et al. (1997) describe the medium/low frequency

52 In work in progress [Caballero and Hammour (1997b)], we have obtained an approximate solution for the stochastic case, in a context where the sources of convexity are malfimctioninglabor and credit markets. 53 See Greenspan and Cohen (1996) for sources of scrapping data for US motor vehicles.

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aspects of a multisectoral vintage capital economy, and show how tax policy can have significant effects on the age distribution of the capital stock 54. The technological embodiment aspect of these models captures well the creativedestruction component of capital accumulation and technological progress 55. Salter's (1960) careful documentation of the technological status of narrowly defined US and UK industries is very revealing with respect to the simultaneous use of different techniques of production and the negative correlation between productivity ranking and the technological age of the plant 56. For example, his table 5 shows the evolution of methods in use in the US blast furnace industry from 1911 to 1926. At the beginning of the sample, the "best practice" plants produced 0.32 gross tons of pigiron per man-hour, while the industry average was 0.14. By the end of the sample, best practice plants productivity was 0.57 while the industry average was 0.30. While at the beginning of the sample about half of the plants used hand-charged methods of production, only six percent did at the end of the sample. As mentioned above, obsolescence and scrapping are not only driven by slowly moving technological trends, but also by sudden changes in the economic environment. Goolsbee (1995b) documents the large impact ofoil shocks on the scrapping of old and fuel-inefficient planes. For example, he estimates that the probability of retirement of a Boeing 707 (relatively inefficient in terms of fuel) more than doubled after the second oil shock. This increase was more pronounced among older planes. Once more, the endogenous nature of the scrapping dimension must be an important omitted factor in our accounting of capital accumulation and microeconomie as well as macroeconomic performance. The sunk nature of technological embodiment is a source of lumpy and discontinuous actions at the microeconomic level. The (S, s) apparatus, with its implications for aggregates, is well suited for studying many aspects of vintage and putty-clay models. In particular, episodes of large investment which leave their technological fingerprints, and remain in the economy, reverberating over time.

5. Inefficient investment

Fixed costs, irreversibilities and their implied pattern of action/inaction, have microeconomic and aggregate implications beyond the mostly technological (and neoclassical) ones emphasized above. Indeed, they seed the ground for powerful inefficiencies. This section describes new research on the consequences o f two of

54 Jovanovic(1997) studies the equilibriuminteractionof the cross sectionalheterogeneityimplied by vintage capital and putty-claymodels with heterogeneityin labor skills. 55 Besides obsolescence and scrapping, these models are also useful for studying the issues of "mothballing" and capital utilization. 56 This correlation is less clear in modern data; perhaps because retooling occurs within given structures.

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the most important sources of inefficiency in aggregate investment: informational and contractual problems. 5.1. Informational problems

Information seldom arrives uniformly and comprehensively to every potential investor. Each investor probably holds part of a truth which would be more easily seen if all investors could (or would) pool their information. Actions by others are a partial substitute for information pooling, for they reveal, perhaps noisily, the information of those that have taken actions. If, however, investment is irreversible, it may pay to wait for others to act and reveal their information before investing. Moreover, if lumpiness leads to periods of no or little action, information may remain trapped for extended periods of time, and when agents finally act, an avalanche may occur because accumulated private information is suddenly aggregated. These issues form the crux of a very interesting new literature, summarized in Gale (1995) under the heading of "social learning." There are two themes emerging from this literature which are of particular importance for this survey. The first is the existence of episodes of gradualism, during which industry investment can occur at an excessively slow pace, or even collapse altogether. The second is an exacerbation of the aggregate nonlinearities implied by the presence of fixed costs; aggregation of information coincides with the synchronization of actions, further synchronizing actions. Caplin and Leahy (1993, 1994) cleanly isolate the issues I have chosen to stress here. Caplin and Leahy (1993) describe a model very similar to the free entry model reviewed in Section 4.1, except that their model has neither aggregate nor idiosyncratic shocks. Instead there is a flow marginal cost of producing which is only known to industry insiders. Insiders have the option to produce one unit of output or none and they will produce if price is above marginal cost. This generates an information externality. If all incumbents are producing, potential investors know that marginal cost is below the current equilibrium price; if not, the industry's marginal cost is revealed to be equal to the current price. Whenever a new establishment is created, equilibrium price either declines or stays constant, improving the precision of potential investors' assessment of the industry's marginal cost. In a second best solution, investment occurs very quickly up to a point at which, even if marginal cost has not yet been reached, no further investment takes place because it is very unlikely that the present value of future social surpluses is enough to cover the investment costs. The industry equilibrium outcome has the same critical point at which investment stops, but unlike the second best outcome, it yields a much slower pace of industry investment. A potential entrant must weigh the value of coming early into the industry (expected profits are higher than they will be later), not only against the cost of capital (as in the second best solution) but also against the probability o f learning in the next second from the investment decisions of others that it was not worth entering

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the industry. Caplin and Leahy show that the price process x(t) obeys the following differential equation:

where F is the fixed entry cost paid by the firm and r is the real interest rate. This equation has a natural interpretation which captures the idea that competitive firms are indifferent between entry today and entry tomorrow. The left-hand side represents the loss in current revenue incurred by a firm which delays entry for a brief instant beyond t s7. The right-hand side captures the expected gain from this delay. The term rF reflects the gain due to the postponement of the entry cost, while the last term represents the saving due to the possibility that delay will reveal the true industry's marginal cost, aborting a wasteful investment sS. In equilibrium, entry is delayed and price declines slowly; "gradualism" maintains prices high enough for sufficiently long so as to offset (in expectation) the risk incurred by investors who act early rather than wait and free-ride off of others' actions s9. Caplin and Leahy (1994) characterize the opposite extreme, one of delayed exit. The key connection with the previous sections is that the problem of information revelation arises from the fact that, as we have seen, fixed costs of actions make it optimal not to act most of the time. Thus, information that could be revealed by actions remains trapped. Their model is one of time-to-build. Many identical firms simultaneously start projects which have an uncertain common return several periods later (e.g. a real estate boom). Along the investment path, firms must continue their investment and receive private signals on the expected return. The nature of technology is such that required investment is always the same if the firm chooses to continue in the project. The firm has the option to continue investing ("business as usual"), to terminate the project, or to suspend momentarily, but the cost of restarting the project after a suspension is very large. Project suspension reveals (to others) negative idiosyncratic information; if nobody suspends, it is good news. However, the costly nature of suspension delays it, and therefore information revelation is also delayed. Bad news may be accumulating but nobody suspends, because everybody is waiting for a confirmation of their bad signals by the suspension of other people. Eventually, some firms will receive enough bad signals to suspend in spite of the potential cost of doing so (i.e., if they are wrong

57 At the time when the industry starts, potential investors' priors are that the price is distributed uniformly on [0, I]. As entry occurs and the price declines, the priors are updated. If convergence has not happened at time t, marginal cost is assumed uniformly distributed on [0,x(t)]. The expected cost of waiting is, therefore, equal to the price minus the expected marginal cost, ½x(t). 58 Here ~ d t is the probabilitythat price hits marginal cost during the next dt units of time. 59 Even though entrants make zero profits in expectation, ex-post, early entrants earn positive profits, while late entrants lose money.

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in their negative assessment o f market conditions). Since the number of firms in their model is large, the number of firms that suspend for the first time fully reveals future demand: if demand is low, everybody exits; if it is high, all those that suspended restart. If it were not for the interplay between inaction (investment as usual) and private information, the fate of the market would be decided correctly after the first round of signals. Information aggregation does not take place until much later, however. Thus, substantial investment may turn out to be wasted because the discrete nature of actions inhibits information transmission. The title of their paper beautifully captures the expost feeling: Wisdom after the fact. The "classic" paper from the literature on information and investment is due to Chamley and Gale (1994). In their model all (private) information arrives at time zero; the multiple agent game that ensues may yield many different aggregate investment paths, including suboptimal investment collapses. In reviewing the literature, Gale (1995) illustrates the robustness of the possibility of an inefficient investment collapse (or substantial slowdown and delay). He notices that in order for there to be any value to waiting to see what others do before taking an action (investing for example) it must be the case that the actions of others are meaningful. That is, the action taken in the second period by somebody who chose to wait in the first period must depend in a non trivial way on the actions of others at the first date. If a firm chooses to wait this period, possibly despite having a positive signal, it will only invest next period if enough other firms invest this period. It must therefore be possible for every firm to decide not to invest next period because no one has invested this period, even though each firm may have received a positive signal this period, in which case, investment collapses. This is a very interesting area of research for those concerned with investment issues and is wanting for empirical developments. 5.2. Specificity and opportunism

The quintessential problem of investment is that it is almost always sunk, possibly along many dimensions. That is, the number of possible uses of resources is reduced dramatically once they have been committed or tailored to a specific project or use. Every model I discussed in the previous sections, at some stage hinges in a fundamental way on this feature of investment. To invest, often means opening a vulnerable flank. Funds which were ex-ante protected against certain realizations of firm or industry specific shocks, for example, are no longer so. In equilibrium, investment must also allow the investor to exploit opportunities which would not be available without the investment. If the project is well conceived, the weight of good and bad scenarios is such that the expected return is reasonable. Indeed, this is precisely the way I characterized the standard irreversible investment problem early on. The problem is far more serious, and more harmful for investment, when the probability of occurrence of the bad events along the exposed flanks are largely

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controlled by economic agents with the will and freedom to behave opportunistically. In a sense, this is a property rights problem, and as such it must have a first-order effect in explaining the amount and type o f capital accumulation and, especially, differences in these variables across countries. Thus, the window for opportunism arises when part o f the investment is specific to an economic relationship, in the sense that if the relationship breaks up, the potential rewards to that investment are irreversibly lost. Further, such opportunism is almost unavoidable when this "fundamental transformation" from uncommitted to specialized capital is not fully protected by contract [Williamson (1979, 1985)] 60 Specificity, that is, the fact that factors o f production and assets may be worth more inside a specific relationship than outside o f it, may have a technological or an institutional origin. Transactions in labor, capital and goods markets are frequently characterized by some degree o f specificity. The creation of a job often involves specific investment by the firm and the worker. Institutional factors, such as labor regulations or unionization also build specificities. There is a very extensive and interesting microeconomic literature on the impact of unprotected specificity on the design o f institutions, organizations and control rights. Hart (1995) reviews many o f the arguments and insights. For the purpose o f this survey, however, the fundamental insight is in Simons (1944), who clearly understood that hold-up problems lead to underinvestment: ... the bias against new investment inherent in labor organizations is important .... Investors now face ... the prospect that labor organizations will appropriate most or all of the earnings .... Indeed, every new, long-term commitment of capital is now a matter of giving hostages to organized sellers of complementary services. More recently, Grout (1984) formalized and generalized Simons' insight, and Caballero and Hammour (1998a) studied, at a general level, the aggregate consequences o f opportunism 61. Here, I borrow the basic model and arguments from that paper to discuss those aspects o f the problem which are most relevant for aggregate investment. Everything happens in a single period 62. There is one consumption good, used as a numeraire, and two active factors o f production, 1 and 2 63. Ownership o f factors 1 and 2 is specialized in the sense that nobody owns more than one type of factor.

60 This is known as the hold-up problem. 61 For specific applications which relate to investment see Kiyotaki and Moore (1997) [credit constraints]; Caballero and Hammour (1996a, 1998b) and Ramey and Watson (1996) [turnover and unemployment]; Caballero and Hammour (1996b), Blanchard and Kremer (1996) [transition economies and structural adjustments]; Caballero and Hammour (1997b) [interactions between labor market and credit market oppor~nism]; Acemoglu (1996) [human capital investment]. 62 Many of the insights discussed here can and have been made in dynamic, but more specialized contexts. I am confident, therefore, that this section's discussion is fairly robust to generalizations along this dimension. 63 Also, there is a passive third factor which earns the rents of decreasing returns sectors.

Ch. 12: Aggregate Investment

8 5 3

There are two modes o f production. The first is joint production, which requires, in fixed proportions, xl and x2 units of factors 1 and 2, respectively, to produce y units o f output. Let E denote the number of joint production units, so Ei = x i E represents employment o f factor i in joint production. The other form o f production is autarky where each factor produces separately, with decreasing returns technologies Fi(Ui), and where Ui denotes the employment of factor i in autarky, such that Ei + Ui = 1. The autarky sectors are competitive, with factor payments, pi: Pi = F;(Ui).

(5.2)

For now, there are no existing units. At the beginning of the period there is mass one o f each factor o f production. There are no matching frictions so that, in the efficient/complete contracts economy, units move into joint production (assuming corners away) until y-p~xl

+p2x2,

(5.3)

where asterisks are used to denote efficient quantities and prices. Specificity is captured by assuming that a fraction q~i of each factor of production cannot be retrieved from a relationship once they have agreed to work together. I f the relationship breaks up, (1 Oi)xi units of factor i can return to autarky, where it produces for the period, while ¢)ixi is irreversibly wasted. In the simple deterministicsingle-period model discussed here, specificity plays no role in the efficient economy, where there are no separations. Contracts are needed because investment occurs before actual production and factor participation. There are myriad reasons why contracts are seldom complete. An extreme assumption which takes us to the main issues most directly, is the assumption that there are no enforceable contracts. It turns out that, in equilibrium, the incomplete contracts economy has no separations either; but unlike the efficient economy, the mere possibility o f separations alters equilibrium in many ways. Generically, equilibrium rewards in joint production will have ex-post opportunity cost and rent-sharing components. For simplicity, let us assume that factors split their joint surplus 50/50. Thus, the total payment to the xi units of factor i in a unit of joint production is 64 -

wixi = (1

1

-

~)i) xiPi -1- ~S,

(5.4)

where s denotes the (ex-post) quasi-rents of a production unit: s ~- y - (1

- q}l)plXl

- (1 - q}2)p2x2.

64 Factors bargain as coalitions within the production unit.

(5.5)

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R.J. Caballero

For a factor of production to willingly participate in joint production it must hold that WiXi ~ pixi.

(5.6)

Substituting Equations (5.4) and (5.5) into Equation (5.6), transforms factor i's participation condition into y ~ p l x t +p2x2 + Ai,

(5.7)

Z~i ~ ~)iPiXi -- ~ j p j x j ,

(5.8)

with

which measures the net sunk component of the relationship for factor i. In other words, it is a measure of the "exposure" of factor i to factor j. When Ai is positive, part of factor i's contribution to production is being appropriated by factor j 65. 5.2.1. Generic implications

Figure 5.1 characterizes equilibrium in both efficient and incomplete contract economies. The two dashed curves represent the right-hand side of condition (5.7) for factors 1 and 2. They are increasing in the number of production units because the opportunity cost of factors of production (the pis) rise as resources are attracted away from autarky. The thick dashed curve corresponds to that factor of production (here factor 1) whose return in autarky is tess responsive to quantity changes 66. If one thinks of capital and labor, arguably capital is this factor; which is a maintained assumption through most of this section. The horizontal solid line is a constant equal to y, which corresponds to the left-hand side of condition (5.7). Equilibrium in the incomplete contracts economy corresponds to the intersection of this line with the highest (at the point of intersection) of the two dashed lines. In the figure, the binding constraint is that of capital. An efficient equilibrium, on the other hand, corresponds to the intersection of the horizontal solid line with the solid line labeled Eft. The latter is just the sum of the exante opportunity costs of factors of production [the right-hand side of Equation (5.3)]. This equilibrium coincides with that of the incomplete contracts economy only when both dashed lines intersect; that is, when net appropriation is z e r o (A i = - A j = 0). There are several features of equilibrium which are important for investment (or capital accumulation). First, there is underinvestment; equilibrium point A is to the left of the efficient point A*. Because it is being appropriated, capital withdraws into autarky (e.g. consumption, investment abroad, or investment in less socially-valuable

65 It should be apparent that A i = -Aj. 66 That is, autarky exhibitsrelativelyless decreasingreturns for this factor.

855

Ch. 12: Aggregate Investment

(2) Eft. B ~ y , ~ (1) ~ l /

.'i//

//

///

U. / / /

~.

E

Fig. 5.1. Opportunism in general equilib-

rium.

activities) 67. Second, the withdrawal of capital constrains the availability of jobs and segments the labor market 68. In equilibrium, not only are there fewer joint production units, but also the right-hand side of condition (5.7) for labor is less than y, reflecting the net appropriation of capital; outside labor cannot arbitrage away this gap because its promises are not enforceable. Third, investment is more volatile than it would be in the efficient economy 69. Changes in y translate into changes in the number of joint production units through capital's entry condition (thick dashes), which is clearly more elastic (at their respective equilibria) than the efficient entry condition ("Eft" line). If profitability in joint production is high enough, equilibrium is to the right of the balanced specificity point, B. In that region, it is the labor entry condition which binds. In principle, problems are more easily solved in this region through contracts and bonding. I f not solved completely, however, there are a few additional conclusions o f interest for an investment survey. First, there is underinvestment since the complementary factor, labor, withdraws (relative to the first best outcome) from joint production. Second, capital is now rationed, so privately profitable investment projects do not materialize. Third, investment is now less volatile than in the efficient economy. Changes in y translate into changes in the number of joint production units through labor's entry condition (thin dashes), which is clearly less elastic than the efficient entry condition ("Eft" line).

67 See Fallick and Hassett (1996) for evidence on the negative effect of union certification on firm level investment. 68 This holds even in the extreme case where capital and labor are perfect substitutes in production. See Caballero and Hammour (1998a). 69 In a dynamic model, this translates into a statement about net capital accumulation rather than, necessarily, investment. The reason for the distinction is that the excessive response of the scrapping margins and intertemporal substitution effects on the creation side may end up dampening actual investment. See Caballero and Hammour (1996a).

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The equilibrium implications of incomplete contracts also affect the scrapping decisions of firms. The easiest way to see this is to examine an existing production unit and ask how low its profitability would have to be for it to scrap itself and seek other opportunities. Moreover, assume that neither factor suffers from specificity in this production unit, so that the efficient rule is scrap whenever profitability is less than y. Two, apparently contradictory, features characterize the incomplete contracts economy. First, because the opportunity cost of factors of production is depressed by the excessive allocation to autarky, there is sclerosis; that is, there are units with profitability below y which are not scrapped because the opportunities in autarky are depressed. Second, given the depressed level of investment, there is excessive destruction. Since the appropriating factor earns rents in joint production, some of them leave socially valuable production units in order to improve their chances of earning these excess returns. Caballero and Hammour (1998a,b) argue that, over the long run, capital/labor substitution takes place. If capital is being appropriated, it will seek to exclude labor from joint production by choosing a capital intensive technology. This effect goes beyond purely neoclassical substitution, as it also seeks to reduce the appropriability problem 70. At a general level, of course, unenforceability of contracts results from the absence of well defined property rights. There is plenty of evidence on the deleterious consequences of such problems for investment. Two recent examples in the literature are Besley (1995) and Hall and Jones (1996). The former provides a careful description of land rights in different regions of Ghana. He documents that an "extra right" over a piece of land increases investment in that land by up to 9 percent in Anloga and up to 28 percent in Wassa 71. Hall and Jones (1996) use a large cross section of countries to show, among other things, that capital/labor ratios are strongly negatively related to "divertment activities." 5.2.2. Credit constraints

There is by now a large body of evidence supporting the view that credit constraints have substantial effects on firm level investment. Although there are a number of qualifications to specific papers in the literature, the cumulative evidence seems overwhelmingly in favor of the claim that investment is more easily financed with internal than external funds 72. I will not review this important literature here because there are already several good surveys 73.

70 We argue that this is a plausible factor behind the large increase in capital/labor ratios in Europe relative to the USA. 71 Rights to sell, to rent, to bequeath, to pledge, to mortgage, etc. 72 For a dissenting view, see e.g. Kaplan and Zingales (1997) and Cummins, Hassett and Oliner (1996b). 73 See e.g. Bernanke et al. (1996, 1999) and Hubbard (1995) for recent ones.

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While there are extensive empirical and theoretical microeconomic literatures, the macroeconomics literature on credit constraints is less developed. Notable exceptions are: Bernanke and Gertler (1989, 1990), Kiyotaki and Moore (1997) and Greenwald and Stiglitz (1993)74. Although the exact mechanisms are not always the same, many of the aggregate insights of this literature can be described in terms of the results in the preceding subsections. Changing slightly the interpretation of factor 2, from labor to entrepreneurs, allows us to use Figure 5.1 to characterize credit constraints. Rationing in the labor market becomes rationing of credit available to projects. To the left of point B, which is the region analyzed in the literature, net investment is too responsive to shocks; there is more credit rationing as the state of the economy declines; and there is underinvestment in general. Internal funds and collateralizable assets reduce the extent of the appropriability problem by playing the role of a bond, and introduce heterogeneity and therefore ranking of entrepreneurs. Since the value of collateral is likely to decline during a recession, there is an additional amplification effect due to the decline in the feasibility of remedial "bonding" 75.

6. Conclusion and outlook

This survey started by arguing that the long run relationship between aggregate capital, output and the cost of capital is not very far from what is implied by the basic neoclassical model: in the US, the elasticity of the capital-output ratio with respect to permanent changes in the cost of capital is close to minus one. In the short run things are more complex. Natural-experiments have shown that, in the cross section, the elasticity of investment with respect to changes in investment tax credits is much larger than we once suspected. How to go from these microeconomic estimates to aggregates, and to the response of investment to other types of shocks is not fully resolved. We do know, however, that these estimates represent expected values of what seems to be a very skewed distribution of adjustments. A substantial fraction of a firm's investment is bunched into infrequent and lumpy episodes. Aggregate investment is heavily influenced by the degree of synchronization of microeconomic investment spikes. For US manufacturing, the short run (annual) elasticity of investment with respect to changes in the cost of capital is less than one tenth the long run response when the economy has had a depressed immediate history, while this elasticity can rise by over 50 percent when the economy is undergoing a sustained expansion.

74 Also see Gross (1994) for empirical evidence and a model integrating financial constraints and irreversibility. 75 See e.g. Kiyotaki and Moore (1997).

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Still, the mapping from microeconomics to aggregate investment dynamics especially equilibrium aggregate investment dynamics - is probably more complex than just the direct aggregation o f very non-linear investment patterns. Informational problems lead to a series o f strategic delays which feed into and feed off o f the natural inaction o f lumpy adjustment models. This process has the potential to exacerbate significantly the time varying n a c r e o f the elasticity o f aggregate investment with respect to aggregate shocks. Moreover, sunk costs provide fertile ground for opportunistic behavior. In the absence o f complete contracts, aggregate net investment is likely to become excessively volatile. The lack o f response o f equilibrium payments to complementary - and otherwise inelastic - factors (e.g. workers), exacerbates the effects o f shocks experienced b y firms. Also, the withdrawal o f financiers' support during recessions further reduces investment. Thus, capital investment seems to be hurt at both ends: workers that do not share fairly during downturns, and financiers that want to limit their exposure to potential appropriations from entrepreneurs which cannot credibly commit not to do so during the recovery. The last two themes, equilibrium outcomes with informational problems and opportunism, are wanting for empirical work. I therefore suspect that we will see plenty o f research filling this void in the near future.

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Simons, H.C. (1944), "Some reflections on syndicalism", Journal of Political Economy 52:125. Stock, J.H., and M.W Watson (1993), "A simple MLE of cointegrating vectors in higher order integrated systems", Econometrica 61(4, July):783-820. Tinbergen, J. (1939), "A method and its application to investment activity", in: Statistical Testing of Business Cycle Theories, vol. 1 (Economic Intelligence Service, Agathon Press, New York). Tobin, J. (1969), "A general equilibrium approach to monetary theory", Journal of Money, Credit and Banking 1:15-29. Williamson, O.E. (1979), "Transaction-cost economics: the governance of contractual relations", Journal of Law and Economics 22(2, October):233-261. Williamson, O.E. (1985), The Economic Institutions of Capitalism (Free Press, New York).

Chapter 13

INVENTORIES * VALERIE A. RAMEY

University of California - San Diego KENNETH D. WEST

University of Wisconsin

Contents Abstract Keywords Introduction 1. Sectoral and secular behavior of inventories 2. Two stylized facts about inventory behavior 2.1. Procyclical inventory movements 2.1.1. Illustrative evidence 2.1.2. A survey of results 2.2. Persistent movements in the inventory-sales relationship 2.2.1. Illustrative evidence 2.2.2. A survey of results

3. Linear quadratic models 3.1. Introduction 3.2. A model 3.3. A first-order condition 3.4. Whose inventories?

4. Decision rule 4.1. Introduction 4.2. Derivation of decision rule 4.3. Persistence in the inventory-sales relationship 4.4. Summary on persistence in the inventory-sales relationship

5. The flexible accelerator model

864 864 865 868 872 873 873 875 877 877 880 882 882 882 885 887 887 887 888 891 892 893

* We thank the National Science Foundation and the Abe Foundation for financial support; Clive Granger, Donald Hester, James Kahn, Anil Kashyap, Linda Kole, Spencer Krane, Scott Schuh, Michael Woodford and a seminar audience at the University of Wisconsin for helpful comments and discussions; and James Hueng and especially Stanislav Anatolyev for excellent research assistance. Email to: kdwest @ facstaff, wisc. edu; vrameyOweber, ucsd. edu.

Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor and M. Woodford © 1999 Elsevier Science B.V. All rights reserued 863

864 6. Dynamic responses 7. Empirical evidence 7.1. Introduction 7.2. Magnitude of cost parameters 7.3. Shocks 7.4. Interpretation 8. Directions for future research 8.1. Introduction 8.2. Inventories in production and revenue functions 8.3. Models with fixed costs 8.4. The value of more data 9. Conclusions Appendix A. Data Appendix Appendix B. Technical Appendix B.1. Solution of the model B.2. Computation of E(Q2 - S2) B.3. Estimation of B.4. Social planning derivation of the model's first-order conditions References

V.A. Ramey and K.D. West

894 902 902 903 906 906 909 909 909 910 911 912 913 914 914 919 919 919 920

Abstract We review and interpret recent work on inventories, emphasizing empirical and business cycle aspects. We begin by documenting two empirical regularities about inventories. The first is the well-known one that inventories move procyclically. The second is that inventory movements are quite persistent, even conditional on sales. To consider explanations for the two facts, we present a linear-quadratic model. The model can rationalize the two facts in a number o f ways, but two stylized explanations have the virtue o f relative simplicity and support from a number o f papers. Both assume that there are persistent shocks to demand for the good in question, and that marginal production cost slopes up. The first explanation assumes as well that there are highly persistent shocks to the cost o f production. The second assumes that there are strong costs of adjusting production and a strong accelerator motive. Research to date, however, has not reached a consensus on whether one of these two, or some third, alternative provides a satisfactory explanation o f inventory behavior. We suggest several directions for future research that promise to improve our understanding o f inventory behavior and thus o f business cycles.

Keywords J E L classification: E22, E32

Ch. 13:

Inventories

865

Introduction In developed countries, inventory investment typically averages less than one-half of one percent of GDP, whereas fixed investment averages 15% of GDP and consumption two-thirds. Perhaps with these fractions in mind, macroeconomists have concentrated more on the study of consumption and fixed investment than on inventories. Inventories generally do not appear as separate variables in dynamic general equilibrium models, nor in exactly identified vector autoregressive models. It has long been known, however, that other ways o f measuring the importance of inventories suggest that inventories should receive more attention, especially in business cycle research. Half a century ago, Abramowitz (1950) established that US recessions prior to World War II tended to be periods of inventory liquidations. Recent experience in the G7 countries indicates this regularity continues to hold, and not just for the USA. In six of the seven G7 countries (Japan is the exception), real GDP fell in at least one recent year. Line 2 of Table 1 shows that in five of those six countries (the United Kingdom is now the exception), inventory investment also declined during the period of declining GDP, accounting in an arithmetical sense for anywhere 12-71% of the fall in GDE And Table 1 's use of annual data may understate the inventory contribution: Table 2 indicates that for quarterly US data, the share is 49 rather than 12% for the 1990-1991 recession, with 49 a typical figure for a post-War US recession. Such arithmetical accounting of course does not imply a causal relationship. But it does suggest that inventory movements contain valuable information about cyclical fluctuations. In this chapter, we survey and interpret recent research on inventories, emphasizing empirical and business cycle aspects. Among other points, we hope to convince the reader that inventories are a useful resource in business cycle analysis. They may be effective in identifying both the mechanisms of business cycle propagation and the sources o f business cycle shocks. Our chapter begins by documenting two facts about inventories. The first is the well-known one that inventories move procyclically. They tend to be built up in expansions, drawn down in contractions. The second, and not as widely appreciated, fact is that inventory movements are quite persistent, even conditional on sales. In many data sets, inventories and sales do not appear to be cointegrated, and the firstorder autocorrelations of supposedly stationary linear combinations of inventories and sales are often around 0.9, even in annual data. To consider explanations for the two facts, we use a linear quadratic/flexible accelerator model, which is the workhorse for empirical research on inventories. In our model, one source of persistence is from shocks to demand for the good being put in inventory - "demand" shocks. ("Demand" is in quotes because we, and the literature more generally, do not attempt to trace the ultimate source of such shocks; for example, for an intermediate good, the shocks might be driven mainly by shocks to the technology of the industry that uses the good in production.) But even if this shock has a unit root, our model yields a stationary linear combination of inventories

V.A. Ramey and K.D. West

866

Table 1 Arithmetical importance of inventory change in recessions of the 1990s (annual data)a Country

Canada France

(1) Peak year trough year b (2) Peak-~ough change in inventory change as percentage ofpeak-to-~oughfallin GDP c

West Italy Japan Germany

UK

USA

1989 1991

1992 1993

1992 1993

1992 1993

n.a.

1990 1992

1990 1991

50

71

19

30

n.a.

-0.

12

a The figures are based on annual real data. The inventory change series is computed by deflating the annual nominal change in inventories in the National Income and Product Accounts by the GDP deflator; see the Data Appendix. b The trough year was found by working backwards from the present to the last year of negative real GDP growth in the 1990s. There were no such years in Japan. The peak year is the last preceding year of positive real GDP growth. c Computed by multiplying the following ratio by 100: inventory change in trough year-inventory change in peak year GDP in trough year- GDP in peak year By construction, the denominator of this ratio is negative. A positive entry indicates that the numerator (the change in the inventory change) was also negative. The negative entry for the United Kingdom indicates that the change in the inventory change was positive.

Table 2 Arithmetical importance of inventory changes in post-war US recessions (quarterly data) a Peak quarter-trough quarter

Peak-to-trough inventory change as a percentage of peak-to-trough fall in GDP

1948:4-1949:2

130

1953:2-1954:2

41

1957:1-1958:1

21

1960:1-1960:4

122

1969:3-1970:1

127

1973:4-1975:1

59

1980:1-1980:3

45

1981:3-1982:3

29

1990:2-1991:1 b

49

a The figures are based on quarterly real data. See the notes to Table 1 for additional discussion. b The figure for the 1990-1991 recession differs from that for the USA in Table 1 mainly because quarterly data were used. It also differs because in this table the inventory change is measured in chain weighted 1992 dollars, whereas Table 1 uses the nominal inventory change deflated by the GDP deflator.

Ch. 13: Inventories

867

and sales. This stationary linear combination can be considered a linear version of the inventory-sales ratio. We call it the inventory-sales relationship. And our second inventory fact is that there is persistence in this relationship. While the model is rich enough that there are many ways to make it explain the two facts, we focus on two stylized explanations that have the virtue of relative simplicity, as well as empirical support from a number of papers. Both explanations assume a upward sloping marginal production cost (a convex cost function). The first explanation also assumes that fluctuations are substantially affected by highly persistent shocks to the cost of production. Cost shocks will cause procyclical movement because times of low cost are good times to produce and build up inventory, and conversely for times of high cost. As well, when these shocks are highly persistent a cost shock that perturbs the inventory-sales relationship will take many periods to die off, and its persistence will be transmitted to the inventory-sales relationship. The second explanation assumes that there are strong costs of adjusting production and a strong accelerator motive. The accelerator motive links today's inventories to tomorrow's expected sales, perhaps because of concerns about stockouts. Since sales are positively serially correlated, this will tend to cause inventories to grow and shrink with sales and the cycle, a point first recognized by Metzler (1941). As well, with strong costs of adjusting production, if a shock perturbs the inventory-sales relationship, return to equilibrium will be slow because firms will adjust production only very gradually. Both explanations have some empirical support. But as is often the case in empirical work, the evidence is mixed and ambiguous. For example, the cost shock explanation works best when the shocks are modelled as unobservable; observable cost shifters, such as real wages and interest rates, seem not to affect inventories. And the literature is not unanimous on the magnitude of adjustment costs. While the literature has not reached a consensus, it has identified mechanisms and forces that can explain basic characteristics of inventory behavior and thus of the business cycle. We are optimistic that progress can continue to be made by building on results to date. Suggested directions for future research include alternative ways of capturing the revenue effects of inventories (replacements for the accelerator), alternative cost structures and the use of price and disaggregate data. The chapter is organized as follows. Section 1 presents some overview information on the level and distribution of inventories, using data from the G7 countries, and focussing on the USA. We supply this information largely for completeness and to provide a frame of reference; the results in this section are referenced only briefly in the sequel. Section 2 introduces the main theme of our chapter (business cycle behavior of inventories) by discussing empirical evidence on our two facts about inventories. Procyclical movement is considered in Section 2.1, persistence in the inventory-sales relationship in Section 2.2. In these sections, we use annual data from the G7 countries and quarterly US data for illustration, and also summarize results from the literature.

868

V.A. Ramey and K.D. West

Sections 3 - 7 develop and apply our linear quadratic/flexible accelerator model. Sections 3-5 present the model. Much o f the analysis in these three sections relates to the process followed by the inventory-sales relationship, because this process has not received much direct attention in existing literature. The discussion focuses on analytical derivations, for the most part deferring intuitive discussion about how the model works to Section 6. That section aims to develop intuition by presenting impulse responses for various configurations o f parameters. Section 7 reviews empirical evidence from studies using the model. In Section 8, we discuss extensions and alternative approaches, including models that put inventories directly in production and profit functions, models with fixed costs, and the use o f different data. Section 9 concludes. A Data Appendix describes data sources, and a Technical Appendix contains some technical details.

I. Seetoral and secular behavior of inventories In this section we use basic national income and product account data from the G7 countries, and some detailed additional data from the USA, to provide a frame of reference for the discussion to come. As just noted, for the most part this is background information that will not loom large in the sequel. Lines 1(a) and 1(b) of Table 3 present the m e a n and standard deviation of the real annual change in economy wide inventory stocks in the G7 countries, over the last 40 years. These were computed from the national income and product account data on Table 3 Basic inventory statistics Canada

France

West Germany

Italy

Japan

UK

USA

(1) Annual NIPA change in inventories, 1956 1995a,b (a) Mean

2.32

37.4

12.3

12.3

2.41

1.81

23.6

(b) Standard deviation

3.91

40.1

12.7

9.8

1.44

3.04

21.6

(2) Reference: 1995 GDP c (3) 1995 Inventory leveld

721 131

6882 n.a.

2608 411

1351 n.a.

453 71

584 104

6066 971

a The inventory change series is computed by deflating the annual nominal change in inventories in the National Income and Product accounts by the GDP deflator; see the Data Appendix. Units for all entries are billions (trillions, for Italy and Japan) of units of own currency, in 1990 prices. b Sample periods are 1957-1994 for West Germany and 1960-1994 for Italy, not 1956-1995. c GDP entries for Italy and Germany are for 1994, not 1995. d The "level" entries for Canada, West Germany, Japan and the UK are computed by deflating the nominal end of year value by the GDP deflator; see the Data Appendix. The entry for the US is the Department of Commerce constant (chained 1992) dollar value for non-farm inventories, rescaled to a 1990 from a 1992 base with the GDP deflator.

869

Ch. 13." Inventories

Table 4 Sectoral distribution of US non-farm inventories a,b (1) Percent of total level, 1995

(2) Mean (s.d.) of change

(3) Mean (s.d.) of growth

100

21.4 (22.5)

3.5 (3.5)

37

7.0 (11.6)

2.8 (4.2)

Finished goods

13

2.5 (4.4)

3.0 (4.8)

Work in process

12

2.3 (5.9)

2.8 (6.0)

Raw materials

12

2.2 (5.4)

2.6 (6.2)

52

12.2 (13.4)

4.4 (4.5)

Retail

26

5.9 (10.3)

4.2 (6.7)

Wholesale

26

6.2 (7.3)

4.5 (4.8)

11

2.2 (5.1)

3.1 (5.8)

Total Manufacturing

Trade

Other

a Data are in billions of chained 1992 dollars, 1959:I-1996:IV. b The inventory change differs from the US data on changes in Tables 1 7 in coverage (Tables 1-3 include changes in farm inventories), in sample period (195%1996 here, 1956-I995 in Table 3) and in base year (1992 here and Table 2, 1990 in Tables 1 and 3). the change in aggregate inventories. See the notes to the table and the Data Appendix for details. Upon comparing line 1(a) to line 2, we see that in all seven countries, the average change in inventories is small, about one percent o f recent GDP in Italy, well less than that in other countries. Inventory changes are, however, reasonably volatile, with the standard deviation roughly as large as the mean in all seven countries. We have less complete data on the level (as opposed to the change) o f inventory stocks. Line 3 o f Table 3 indicates that in the countries for which we have been able to obtain data, total inventories are about one-sixth o f GDP. This implies a monthly inventory-sales ratio o f about 2, a value that will be familiar to those familiar with monthly US data. Table 4 has a breakdown o f US non-farm inventories by sector. We see in column 1 that about h a l f o f non-farm inventories are held by retailers and wholesalers (including

V.A. Ramey and K.D. West

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I

I

I

I

I

,I

I

I

I

I

06

o6

.9

~

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h

A

4

.8

,7

,'\ ,..,,,,',,,",

,,.

.6 "t " ~ ""

""~

•

'

chained 1992 dollars

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56

6b

66

76

year

ob

Fig. 1. Quarterly ratio of nonfarm inventories to final sales.

non-merchant wholesalers who are associated with particular manufacturers), whereas somewhat over a third are held by manufacturers. The remaining "other" category reflects holdings by a number of industries, including utilities, construction, and service companies. Like the aggregates in Table 3, investment in each of the components is positive on average, and has standard deviations about the same size as means. This applies whether one looks at arithmetic changes (column 2) or growth rates (column 3). For future reference, it will be useful to note that manufacturers' inventories of finished goods, which have received a fair amount of attention in the inventory literature, are only 13% of total inventories, and are not particularly volatile. Figure 1 plots the ratio of total non-farm inventories to final sales of domestic product. The dashed line uses real data (ratio of real inventories to real sales), the solid line nominal data. In the real data, the inventory series matches that in line 1 of Table 4, but over the longer sample 1947:I-1996:IV (Table 4 uses the 1959-1996 subsample because the disaggregate breakdown is not available 1947-1958.) The real ratio shows a run-up in the late 1960s and early 1970s, followed by a period of slight secular decline. At present, the ratio is modestly above its value at the start of our sample (0.63 vs. 0.56). It will be useful to note another fact for future reference. The figure suggests considerable persistence in the inventory-sales ratio, an impression borne out by estimates of first-order autocorrelations. These are 0.98 for the sample as whole, 0.93 if the autocorrelation is computed allowing for a different mean inventory-sales ratio for the 1947:I-1973:IV and 1974:I-1996:IV subsamples.

871

Ch. 13: Inuentories I 1096.7

I

I

I

I

-

.pi

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I

E

20t.8 3513

'

17A3.97

final sales of domestic business

Fig. 2. Quarterly inventories and sales, 1947:1-1996:4, in billions of chained 1992 dollars.

Readers familiar with the monthly inventory-sales ratios commonly reported in the US business press may be surprised at the absence of a downward secular movement. Such monthly ratios typically rely on nominal data. The solid line in Figure 1 shows that the ratio of nominal non-farm inventories to nominal sales of domestic product indeed shows a secular decline. Evidently, the implied deflator inventories has not been rising as fast as that for final sales. We do not attempt to explain the differences between the nominal and real series. We do note, however, the nominal ratio shows persistence comparable to that of the real ratio. The estimate of the firstorder autocorrelation of the ratio is 0.97 whether or not we allow a different mean inventory-sales ratio for the 1947:I-1973:IV and 1974:I-1996:IV subsamples. To return to the secular behavior of the real series: we see from column 3 in Table 4 that the rough constancy of the overall ratio hides some heterogeneity in underlying components. In particular, raw materials, and to a lesser extent, work in progress, have been growing more slowly than the aggregate, implying a declining ratio to final sales. This fact was earlier documented by Hester (1994), who noted that possible explanations include just-in-time inventory management, outbasing of early stages of manufacturing to foreign countries, and a transitory response to transitory movements in costs. In the sequel we do not attempt to explain secular patterns in inventory-sales ratios; see Hester (1994) for a discussion of US data, for retail as well as manufacturing, West (1992a) and Allen (1995) for discussions of Japanese data. Instead we hope that the reader will take the message away from these tables that inventories and sales are positively related in the long run: they tend to rise together. This is illustrated quite

872

V.A. Ramey and K.D. West

strikingly in Figure 2, which is a scatterplot o f the inventory and sales data. A second message in the tables and the autocorrelations reported above is that while inventory movements are small relative to GDP, they are volatile and persistent. Characterizing and explaining the stochastic, and especially business cycle, behavior o f inventories is the subject o f the rest o f this chapter.

2. Two stylized facts about inventory behavior Our essay focuses on the business cycle aspects o f inventory behavior, and is oriented around two stylized facts: (1) inventory movements areprocyclicaL (2) the inventorysales relationship is highly persistent (the inventory-sales relationship is our term for a linear version o f the inventory-sales ratio). These facts serve two purposes. First, they demonstrate the potential role o f inventories in understanding economic fluctuations. Second, they serve as a measure by which we j u d g e inventory models and, more generally, theories o f the business cycle. For each o f the two "facts", we present illustrative evidence from annual, postWorld War II data, for the G7 countries, as well as from quarterly post-War US data. We then review estimates from the literature. For the first o f our stylized facts (procyclical movements), Section 2.1.1 below presents estimates, Section 2.1.2 presents the review. Sections 2.2.1 and 2.2.2 do the same for the second o f our facts (persistence in the inventory-sales relationship). The remainder o f this introductory subsection describes the data used in both 2.1 and 2.2. For the G7 countries, we continue to use the aggregate (nation-wide) change in inventory stocks used in previous sections, and construct a time series o f inventory levels b y summing the change 1. We measure production as GDP and sales as final sales. The quarterly US inventory data are that used in the previous section, total non-farm inventory and final sales o f domestic product in chained 1992 dollars, and with sales measured at quarterly rates 2.

1 When we summed the AH t series, we initialized with H 0 _: 0. Given the tinearity of our procedures, the results would be identical if we instead used the AH t series to work forwards and backwards from the 1995 levels reported in Table 3. The reader should be aware that when prices are not constant, a series constructed by our procedure of summing changes typically will differ from one that values the entire level of stock at current prices. Those with access to US sources can get a feel for the differences by comparing the inventory change that figures into GDP (used in the G7 data, and in NIPA Tables 5.10 and 5.11) and the one implied by differencing the series for the level of the stock (used in our quarterly US data and NIPA Tables 5.12 and 5.13). 2 We repeated some of our quarterly calculations using final sales of goods and structures, which differs from total final sales because it excludes final sales of services. There were no substantive changes in results.

Ch. 13: Inventories

873

All of these measures are linked by the identity production = sales + (inventory investment), or

Qt = st +AHt,

(2.1)

where Qt is production, St are sales, and Ht is end of period t inventories. This relationship holds by construction, with St being final sales.

2.1. Procyclical inventory movements 2.1.1. Illustrative evidence Procyclicality o f inventory movements can be documented in several ways. A simple indication that inventories move procyclically is a positive correlation between inventory investment and final sales. Consider the evidence in Table 5. In column 1 we see that all the point estimates of the correlation are positive, with a typical value being 0.1-0.2. The correlation between sales and inventory investment is related to the relative variances of production and sales. As in Table 5, let "var" denote variance, "cov" covariance. Since (2.1) implies var(Q) = var(S) + var(AH) + 2 cov(S, AH), it follows from the positive correlation in column 1 that var(Q)> var(S) (column 2). Other indications of procyclical behavior include two variance ratios robust to the possible presence of unit autoregressive roots. The column 3 estimates indicate that var(AQt)/var(ASt)> 1, the column 4 estimates that E(Q2-S2t)>O. [E(Q~-S~) is essentially an estimate of var(Q)-var(S) robust to the presence of unit autoregressive roots; see the Technical Appendix.] To illustrate the pattern of correlation over different short-run horizons, we present impulse response functions. The responses are based on a bivariate VAR in the level of inventories and sales for the quarterly US data, including eight quarterly lags, a time trend, and breaks in the constant and trend at 1974. In accordance with this section's aim of presenting relatively unstructured evidence, we present responses to a one standard deviation shock to the VAR disturbances themselves, and not to orthogonalized shocks. Figure 3 shows the responses of inventories and sales to a disturbance to the sales equation, Figure 4 the responses to a disturbance to the inventory equation. To prevent confusion, we note that on the horizontal axis, we plot the pre-shock (period - 1 ) values of the variables; the shock occurs in period 0. Figures 3 and 4 both show a positive comovement of inventories and sales. In Figure 3, by construction the contemporaneous (period 0) response of inventories is zero. But the 7 billion (approximately) dollar rise in sales in period 0 is followed in the next quarter by a 1.5 billion dollar increase in inventories. Inventories continue to rise for the next five quarters, even after sales turn down. Both series smoothly decline together. Figure 4 shows that after a 3 billion dollar shock to inventories, sales rise by nearly 2 billion dollars. Both inventories and sales subsequently show some wiggles.

874

V.A. Ramey and K.D. West

Table 5 Relative variability of output and final sales a-e Country

Period

(1) corr(S, AH)

(2) var(Q)/var(S)

(3) var(AQ)/ var(AS)

(4) 1 + [E(Q 2 - S 2)/ var(AS)]

Canada

1956 1995 1974-1995 1956 1995 1974-1995 1957-1994 1974-1994 1960-1994 1974-1994 1956-1995

0.14 0.17 0.17 0.32 0.12 0.13 0.13 0.11 0.23

1.16 1.21 1.36 1.63 1.10 1.08 1.30 1.27 1.07

1.53 1.55 1.65 2.09 1.36 1.27 1.81 1.83 1.10

1.41 1.24 1.68 1.41 1.01 1.03 1.12 1.08 1.30

1974-1995 1956-1995 1974-1995 1956-1995 1974-1995 1947:I-1996:IV 1974:I-1996:IV

0.51 0.28 0.26 0.26 0.25 0.30 0.14

1.15 1.21 1.17 1.19 1.21 1.26 1.13

1.08 1.52 1.38 1.48 1.50 1.39 1.40

1.12 1.10 1.04 1.12 0.98 1.41 1.48

France West Germany Italy Japan UK USA USA

a "var" denotes variance, "corr" correlation, Q = output, S = final sales, A H - change in inventories. The variables are linked by the identity Q = S + AH. b In all but the last row, data are annual and real (1990 prices), with Q=real GDP, S=real final sales, AH=real change in aggregate inventories. In the last row the data are quarterly and real (1992 prices), with S=final sales of domestic business goods and structures, AH=ehange in non-farm inventories, and Q _=S + AH. See the text and Data Appendix for sources. c In colmnns 1 and 2, Q and S were linearly detrended, with the full sample estimates allowing a shift in the constant and trend term in 1974 (1974:I in the last row); AH was defined as the difference between detrended Q and S. In columns 3 and 4, AQ and AS were simply demeaned, again with the full sample estimates allowing a shift in the mean in 1974 (1974:I). d In column 4, the term E(Q 2 - S 2) essentially is the difference between the variance of Q and the variance of S, computed in a fashion that allows for unit autoregressive roots in Q and S. See the Technical Appendix for further details. e The post-1973 sample, as well as the post-1973 shifts in the full sample estimates, were included to allow for the general slowdown in economic activity.

This s h o c k a p p e a r s to h a v e m o r e p e r s i s t e n t e f f e c t s t h a n does the sales s h o c k , w i t h i n v e n t o r i e s still over 2 b i l l i o n dollars a b o v e t h e i r initial level after six years. T h e i m p o r t a n t p o i n t is t h a t b o t h sets o f i m p u l s e r e s p o n s e f u n c t i o n s offer t h e s a m e p i c t u r e o f p r o c y c l i c a l i n v e n t o r i e s as t h e statistics i n Table 5. T h u s , i n v e n t o r i e s s e e m to a m p l i f y r a t h e r t h a n m u t e m o v e m e n t s i n p r o d u c t i o n .

Ch. 13. Inventories

875 I

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2b

2~

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lg

2b

2a

8.7077

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/ o

~

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/

,--4

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~

o

~

~

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5.01083

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f_

(7} 01

d

~

quarter

Fig. 4. Response to inventory equation shock, quarterly VAR. 2.1.2. A survey o f results

As many readers no doubt are aware, similar findings have been reported for many though not all data sets. A brief summary of estimates o f variance inequalities in studies using aggregate data: Fukuda and Teruyama (1988) report comparable results

876

V.A. Ramey and K.D. West

for industrialized countries, but also conclude that by contrast in less developed countries GDP tends to be smoother than final sales 3. Beaulieu and Miron (1992) report that in manufacturing in some industrialized countries, seasonals in production are no less variable than those in sales. For US quarterly economy-wide or monthly two-digit manufacturing data, the pattern is as pronounced as in Table 5. This applies first of all to demeaned or detrended data such as is reported in Table 5. For example, Blinder (1986a) reports var(Q)/var(S) > 1 for 18-20 two-digit manufacturing industries. It also applies to deterministic seasonals [West (1986), Miron and Zeldes (1988), Cecchetti et al. (1997)]: in US manufacturing, seasonal variation in production tends to be larger than seasonal variation in sales 4. Finally, for both deterministic and stochastic terms, studies that have taken sampling error into account sometimes but not always find it quite unlikely that sampling error alone accounts for the lack o f evidence production smoothing [West (1986, 1990b)]. Does aggregation substantially account for the lack of production smoothing evident in these studies, either because o f measurement error in aggregate data sets, or heterogeneity across firms? Probably not. It has been argued persuasively that disaggregate data measured in physical units are more accurate than the aggregate data used in most studies [see Fair (1989), Krane and Braun (1991), and Ramey (1991)] 5 But as summarized below, studies with disaggregate data still find production more variable than sales in many cases. For evaluation of the effects o f firm heterogeneity, analytical arguments are not particularly helpful. I f var(Q) > var(S) for a single firm, the inequality may be shown analytically to apply to an aggregate o f firms if each individual firm solves a linear quadratic problem such as the one presented below with identical parameters, regardless o f the correlation o f demand shocks across firms [West (1983)]. But if the cost functions are different for different firms, analytical results appear not to be available. Lai (1991) and Krane (1994) show by example that aggregate variance ratios might differ substantially from individual firm ratios. And even if we assume identical parameters across firms, which as just noted implies that var(Q)/var(S)<~ 1 in the aggregate, this aggregate ratio may be larger (or smaller) than that o f individual firms, with the direction o f the bias depending on the correlation across firms of demand shocks. So to consider possible biases from aggregation we must turn from analytical to empirical studies of data disaggregated to the firm or perhaps physical product level.

3 So far as we know, there have been no systematic attempts to explain this finding. It is possible that measurement error plays a large role. 4 Carpenter and Levy (1998) report a related finding: for manufacturing, the spectra of inventory investment and production show very high coherence at seasonal frequencies. 5 And the G7 data that we use for illustration are among the worst measured. In some countries, the change in inventories apparently is constructed at least initially as the difference between product and income estimates of GDP, and thus includes the statistical discrepancy. See West (1990a).

Ch. 13." Inventories

877

The disaggregate picture is broadly similar though less striking than the aggregate one, at least in the relatively well-studied USA. Production smoothing is markedly absent in the automobile industry [Blanchard (1983), Kashyap and Wilcox (1993)]. But Krane and Braun (1991) found production is less variable than sales in about two thirds of a set of 38 physical products. Finally, Schuh (1996) found deseasonalized production less variable than deseasonalized sales in only one fourth of 700 manufacturing firms; deterministic seasonals in production were less variable than those in sales in about half the firms. For the deseasonalized data, Schuh reports that the median ratio of production to sales variance was about 1.1, which is consistent with the US figure reported in column 2 of Table 5. 2.2. Persistent movements in the inventory-sales relationship Our second stylized fact is that the inventory-sales relationship is highly persistent. While there may be a steady state linear relationship between inventories and sales, movement towards that steady state is very slow. This characteristic may be more recognizable to inventory experts if it is stated as a "slow speed of adjustment"; a link between persistence in the inventory-sales relationship and the speed of adjustment is demonstrated formally in Sections 4 and 5 below. Section 2.2.1 illustrates this with the annual G7 and quarterly US data used above, Section 2.2.2 documents it with citations to various papers. 2.2.1. Illustrative evidence To illustrate persistence, we use a standard technique described in the Technical Appendix to attempt to find a stationary relationship between the levels of inventories and sales. This yields Ht - ~OSt for a parameter 0 estimated from the data. Those familiar with the literature on cointegration will recognize Ht - OSt as the (estimated) error-correction term if inventories and sales have unit autoregressive roots and are cointegrated. We refer to H t - OSt as the inventory-sales relationship, sinee it is a generalized linear version of the inventory-sales ratio. More precise terminology for this variable is "deviation from the long-run inventory-sales relationship." In our view, the disadvantages of the length of this term outweigh the advantages of being more precise. After obtaining 0, we estimate the first two autocorrelations in the putatively stationary variable Ht - "OSt, to gauge the extent of persistence in the relationship. We emphasize that our aim is merely to document quickly evidence of high persistence, not to work towards a complete time series model, nor even to endorse the use of unit roots as a modeling device; among other tasks, the latter would require testing for unit roots in Ht and St, perhaps allowing for a one-time shift in mean in 1974, and so on. Rather, this is a way of organizing facts and theories about inventories that has some rough plausibility for a wide range of data.

878

V..A. Ramey and K.D. West

Table 6 Persistence in stationary linear combinations of inventories and sales a,b Country

Period

(1) Estimate of cointegrating parameter 0

(2) First two autocorrelations of H t - OSt

Canada

1956-1995

0.16

0.92

0.82

France

1956-1995

0.31

0.95

0.89

West Germany

1957 1994

0.27

0.93

0.82

Italy

1960 1994

0.45

0.88

0.80

Japan

1956-1995

0.22

0.97

0.91

UK

1956-1995

0.20

0.95

0.87

USA

1956-1995

0.24

0.88

0.82

USA

1947:I-1996:IV

0.68

0.94

0.88

USA

1947:~1996:IV, H and S in logs

1.12

0.95

0.90

a See notes to Table 5 for description of data and variable definitions. b In the inventory-sales relationship H t - O S t , the estimate 0 is obtained with the Stock and Watson (1993) procedure to estimate a cointegrating vector. Details are in the Technical Appendix. If the inventory and sales series have unit autoregressive roots, the adjective "stationary" used in the title to this table applies only if the inventory and sales series in fact are cointegrated, and then only asymptotically.

Table 6 p r e s e n t s results. T h e T e c h n i c a l A p p e n d i x d e s c r i b e s c o m p u t a t i o n a l details. C o l u m n s 1 a n d 2 p r e s e n t the e s t i m a t e s o f 0 a n d t h e first two a u t o c o r r e l a t i o n s o f H t - OSt. I n c o l u m n 1, the e s t i m a t e s o f 0 are all p o s i t i v e , s u g g e s t i n g t h a t i n v e n t o r i e s a n d sales m o v e t o g e t h e r p o s i t i v e l y in t h e l o n g r u n 6. B u t e v e n i f this is the case, the result t h a t w e w i s h to e m p h a s i z e is in c o l u m n 2: all o f the first-order a u t o c o r r e l a t i o n s are a b o v e 0.8. T h e r e is o f c o u r s e a d o w n w a r d b i a s i n e s t i m a t e s o f a u t o c o r r e l a t i o n s n e a r 1, a n d a n a d d i t i o n a l b i a s i m p a r t e d b y t i m e a g g r e g a t i o n (recall t h a t t h e d a t a are a n n u a l or q u a r t e r l y r a t h e r t h a n m o n t h l y ) . T h e c o l u m n 2 e s t i m a t e s t h u s s u g g e s t that m e a n r e v e r s i o n takes p l a c e quite s l o w l y 7.

6 The technique used is not invariant to normalization. For the annual data, we re-estimated with S t on the left instead of H t. Positive estimates of (1/0) resulted. On the other hand, if time trends are

included, negative estimates of 0 result for 4 of the 7 annual data sets. 7 Consistent with the high autocorrelation, the null of no cointegration cannot be rejected at the 5% level in three of the seven annual data sets (Canada, Japan, USA), nor in the quarterly US data. This suggests that for these three countries an appropriate model might be one in which there is no steady-state linear relation between inventories and sales. As we shall see, the model to be presented rationalizes such lack of a steady state with unit root cost shocks. When we quickly investigated the extent to which a onetime change in regime in 1974 could account for the persistence, we got mixed results. With post-1974 annual data, the autocorrelations fell; what is perhaps notable is that in one case (the USA) the fall was dramatic, to 0.28 (vs. the 0.88 reported in Table 6). Next, using the quarterly data, we re-estimated using

Ch. 13: Inventories

879

I

I

I

I

I

I

I

P-_ B.7077

B.7077 P-_ I/ -4.58753

inventory-sales relationship

V' quapteP Fig. 5. Response to sales equation shock, quarterly VAR.

We note that this g e n e r a l i z a t i o n applies w h e n we use logs instead o f levels o f inventories and sales (last r o w o f the table). We noted above that the i n v e n t o r y - s a l e s ratio displays h i g h autocorrelations. The upshot o f the last row is that transforming to logs, and a l l o w i n g 0 ¢ 1 - that is, considering not log(Hi~St) but log(Ht/S °) for a freely estimated 0 - still suggests considerable persistence 8. To illustrate the persistence f r o m a different perspective, Figures 5 and 6 depict the response o f sales and the i n v e n t o r y - s a l e s relationship to shocks, u s i n g the same V A R estimated for Figures 3 and 4. The sales responses are identical to those in Figures

the whole sample but allowing for different means in the 1947:I-1973:IV and 1974:I-1996:IV sample. This reduced the estimate only slightly, to 0.89 and 0.94 (vs. the 0.94 and 0.95 values in Table 6). Rossana (1998) carefully investigates the question of stability in two-digit US data. He finds evidence of instability, and lack of cointegration within subsamples. s Now seems an appropriate time to comment on the use of logs versus levels of the data, in response to comments by two of the readers of an earlier version of this paper. Much empirical work in inventories, and a distinct majority of work using intertemporal dynamic models, has relied on levels rather than logarithms of the variables in question. We follow that convention in most of this paper. Working in levels has the advantage of preserving the identity that links inventories, production and sales [see Equation (2.1)]. In addition, inventory investment, as reported by the National Income and Product Accounts, is defined as the change in the level of inventories, and is frequently negative, which further discourages the use of logarithms. In a few cases, such as in the last row of Table 6, we do use logarithms. That little turns on levels versus logs is suggested by the similarity of the results in the last two rows in Table 6, and, more generally of the review of the literature that we are about to present: flexible accelerator studies typically use data in logs, while linear quadratic studies typically use levels. Both find great persistence.

V.A. Ramey and K.D. West

880 I

3.74996

~ . ,,'~'~

I

I

I

I

I

~

~4 "0 t~ t~ O~ ~4

0

quapter, Fig. 6. Response to inventoryequation shock, quarterlyVAR. 3 and 4. The inventory-sales relationship is computed using the estimated value of = 0.68 from Table 6 to form a linear combination of the impulse response functions for sales and inventories. In response to a positive one standard deviation shock to the sales equation, inventories rise, but less rapidly than do sales (see Figure 3). This induces the fall in the inventory-sales relationship depicted in Figure 5. Eventually, inventories build up more rapidly, leading to overshooting and an increase relative to the initial position. Since both inventories and sales are close to their pre-shock values after six years (see Figure 3), the inventory relationship returns as well, as Figure 5 shows. By contrast, a shock to the inventory equation leads to a complicated pattern displaying more persistence. The inventory-sales relationship rises initially by construction, and then declines erratically for eight quarters before briefly rising again and then slowly decaying. At the end of six years, a return to the pre-shock value is not evident: these unrestricted VAR estimates suggest great persistence in the inventory-sales relationship. 2.2.2. A suruey o f results

Table 6 and Figures 5 and 6 suggest that there is little mean reversion in economywide inventory-sales relationships. Congruent evidence comes from two sources, unstructured tests such as in Table 6, and structural estimates of what is called a "speed of adjustment". Consider first the unstructured tests. Using quarterly economy-wide data, West (1990b, 1992b) cannot reject the null of no cointegration for the USA and for

Ch. 13: Inventories

881

Japan. Using monthly US data, Granger and Lee (1989) find only mild evidence for cointegration in monthly two-digit manufacturing and trade series; fewer than a third of their 27 data sets reject the null of no cointegration at the 5% level, and the median first-order autocorrelation of the putatively stationary linear combination of inventories and sales is about 0.99. Rossana (1993, 1998) uses similar data and allows a vector of cost variables W t to enter the cointegrating relationship. He uses regression techniques to search for a combination H t - OSt - otI W t that is stationary. Wt is defined to include real wages, real materials prices, nominal interest rates and inflation. In the end, however, he finds mixed evidence of cointegration across H t , St and Wt. (He does not report autocorrelations o f stationary linear combinations.) In addition, a large literature has used structural inventory models to estimate the "speed of adjustment". We shall describe such models below. For the moment, what is relevant is that under conditions described below, a slow speed of adjustment is equivalent to persistence in the inventory-sales relationship. Let p be the largest autoregressive in H t - OSt, or H t - OSt - ct~Wt, with the latter variable the relevant one if, as in the Rossana (1993, 1998) papers cited above, a vector of cost variables is entered into the cointegrating relationship. The large empirical literature has estimated inventory equations, with results implying that ~ is near 1. A typical value in quarterly data is around 0.8-0.95. The following are some examples. Using quarterly economy-wide data for some industrialized countries, Wilkinson (1989) found ~ - 0.75-1.0, with W t including one or more of: sales shocks, inflation, wages, raw materials prices and capacity utilization. Similar results have repeatedly been found using monthly or quarterly US manufacturing data. Examples include Maccini and Rossana (1981), Blinder (1986b), and Haltiwanger and Maccini (1989). In these papers, Wt included one or more of: factor prices such as wages, raw materials prices and real and nominal interest rates, other factors of production such as labor, and sales expectational errors. Does aggregation across heterogeneous firms substantially account for this high serial correlation? We are not aware of analytical arguments establishing genera] conditions under which aggregate estimates of p will be higher than typical firmspecific estimates, though no doubt such arguments could be constructed. Simulations in Lovell (1993) and a limited amount of empirical evidence suggests that aggregation does impart a bias. Schuh (1996) reports that for monthly data for 700 manufacturing firms, the median estimate of p is about 0.6 (Wt includes a real interest rate); for quarterly data for some publicly owned firms, and with Wt including measures of credit conditions, ~ is reported to be about 0.6-0.8 by Carpenter et al. (1994, 1998), although a somewhat higher value of about 0.9 is found by Kashyap et al. (1994)10 9 The autocorrelation was computed from the Durbin-Watson statistic reported in the last column of Table II in Granger and Lee, using 2(1 -~) = d.w. 10 A small literature has discussed how estimation ofp is affected when the decision interval for firms is smaller than the sampling interval of the data [Christiano and Eichenbaum (1989), Jorda (1997)]. Such time aggregation does not appear capable of explaining the high persistence.

882

V.A. Ramey and K.D. West

Of course, tests for cointegration have notoriously low power. And there is heterogeneity of estimates o f p implied by the flexible accelerator literature. But these results suggest that there is little evidence that mean reversion of Ht - OSt towards its mean takes place rapidly, and considerable evidence of persistence. To interpret such persistence, as well as the procyclical behavior discussed in the previous section, we now present a standard inventory model.

3. Linear quadratic models 3.1. Introduction

The linear quadratic inventory model dates back to Holt et al. (1960). Although this book is written in an operations research style that suggests that its main aim was to provide practical advice to managers, it may still be profitably reviewed by economists interested in inventory behavior. In fact, Holt et al. (1960) develop models more general than those in many of the applications we review here: they allow for stockout costs, order backlogs, and stochastic variation in costs. Early uses of a linear quadratic model to interpret macro data include Childs (1967) and Belsley (1969). Tools developed in the 1970s and 1980s to estimate and interpret decision rules and first-order conditions from rational expectations models [e.g., Hansen and Sargent (1980), Hansen and Singleton (1982)] were subsequently used by many authors to estimate one or another version of the model. Some papers used aggregate data (sometimes economy wide, sometimes at the two-digit level); some used data at the level of individual firms or physical products. It is this more recent literature that we review in this and the next four sections. The focus of this literature, and of our discussion, is on how production parameters and constraints influence the intertemporal interaction between production, sales and inventories. While different papers of course vary in the details of the model, there is sufficient commonality that the model presented in Section 3.2 may fairly be described as representative. Section 3.3 derives a first-order condition. Section 3.4 discusses whether the model is applicable to a wide range of inventories. Table 7 lists notation, and may be a useful reference in this and subsequent sections. 3.2. A model

We assume that a firm maximizes the present value of future cash flows. In macro applications this will be a representative firm. In the formal statement of the model about to be given, we omit constant, linear and trend terms for notational simplicity. Earlier work provides tediously detailed treatment o f such terms, allowing for trends that are either arithmetic [West (1983)] or geometric [working paper versions of West (1988, 1990b)].

Ch. 13:

Inventories

883 Table 7 Variable and parameter definitions a

A. Definitions of basic variables H t

inventories at end of period t

H t -H i

stationary linear combination o f l i t , S t and W t when Udt and W t have unit autoregressive roots, but Uct does not; H t - H i = H t - ( OS t + aI W t )

H t -- OS t

inventory-sales relationship

Qt

production in period t

St

sales in period t

Uct

cost shifters, Uct = ~ W t + uct

uct

cost shock, unobservable to the economist

Udt

demand shock, unobservable to the economist

Wt

vector of observable cost shifters

B. Definitions of basic parameters

Mnemonic

Description

a0

cost o f changing production

Section b 3.2

a1

cost o f production

3.2

a2

inventory holding cost

3.2

a3

accelerator term for inventories

3.2

b

discount factor

3.2

g

inverse of slope o f demand curve

4.2

a

a = - ( b a 2 ) ~(1- b ) a , coefficient vector on W t in H ;

3.3

coefficient vector on W t in Uct

3.2

0c

AR(1) coefficient of Uct , uct = 0cUct_l + ect

4.2

0d

AR(1) coefficient of Udt, Udt =0dUdt-I +edt

4.2

qSw

AR(1) matrix o f coefficients of W t , Wt = ~ w Wt 1 + ewt

4.2

0

= a 3 [al(1-b)/ba2] , coefficient on S t in H i

3.3

:~H

an autoregressive root in H t - H i when a 0 - 0

4.2

:v t, :v2

two autoregressive roots in H a H T when a 0 ~ 0

4.3

a All variables and parameters are scalars, with the exceptions of ewt, W t , a, ~t and q~w. The variables in panel A are introduced in Section 3.2. b Section where parameter is introduced.

W e u s e t h e f o l l o w i n g n o t a t i o n : P t is real p r i c e (say, r a t i o o f o u t p u t p r i c e to t h e w a g e ) , St

real sales, Q t real p r o d u c t i o n , H t

real e n d o f p e r i o d i n v e n t o r i e s , Ca real p e r i o d

c o s t s , b a d i s c o u n t f a c t o r , 0 ~< b < 1, a n d E t m a t h e m a t i c a l e x p e c t a t i o n s c o n d i t i o n a l o n

V.A. Ramey and K.D. West

884

information known at time t, assumed equivalent to linear projections. The objective function is T

max l i m r ~

Et Z

bj(Pt +ySt +j - Ct +j)

j-o subject

(3.1)

to ~ Ct = 0.5a0AQ 2 + 0.5alQ 2 + 0.5a2(Ht-i - a3St) 2 + U c t Q t ,

( Qt = St + He -

He 1.

The scalar Uct is a cost shock, and, as discussed below, may depend on both observable and unobservable variables. The term Pt +jSt +j is revenue. The analysis in this section does not depend on specification of demand or market structure, so we defer discussion o f P t + j S t +j until the next section.

The cost function Ct allows two possible roles for inventories. One is a production smoothing role, in which inventories facilitate intertemporal allocation of production. (N.B.: in much of the inventory literature, the phrase "production smoothing" references smoothing from demand shocks; we use it to reference smoothing from cost shocks as well.) This role is reflected in the terms in AQ 2 and Q2. The second role is a revenue role, in which inventories allow a firm to satisfy demand that cannot be backlogged. This role is reflected in the " a 3 S t " term in (Ht-1 - a3St)2; (He 1 - a 3 S t ) 2 induces an accelerator motive. In our discussion o f these terms, we assume for the moment that a~ and a2 are positive, ao and a3 nonnegative. The first production smoothing term, aoAQ2t, captures increasing costs of changing production and of production. This represents, for example, hiring and firing costs. Not all authors include this term, and, as discussed in Section 7, some empirical tests find estimates of ao insignificantly different from zero. The second production smoothing term, a~Q 2, reflects costs of production. It can be interpreted as the second order term in a quadratic approximation to an arbitrary convex cost function associated with a decreasing returns to scale technology. In data with trends, this approximation would likely be around a growth path. (Recall that constant and trend terms are omitted for notational simplicity.) The accelerator term a 2 ( n t - 1 - a 3 S t ) 2 embodies inventory holding and backlog costs. Consider first when a3 = 0, so that the term becomes a2H2t 1. Then this can be interpreted as the second order term in a quadratic approximation to an arbitrary convex inventory holding cost function. When a3 ~ 0, the term is intended to reflect backlog (stockout) and batch as well as inventory holding costs, and thus captures a revenue-related motive for holding inventories. Stockout costs arise when sales exceed the stock on hand, perhaps entailing lost sales, perhaps entailing delayed payment if orders instead are backlogged. Batch costs vary inversely with the stock of inventories, since fewer production runs and larger lot sizes imply larger inventory levels on average. Ceteris paribus, the higher the stock of inventories, the less likely is a stockout and the lower are stockout costs. As well, higher stocks result when the number of batches

Ch. 13: Inventories

885

falls, since lot sizes rise. On the other hand, higher stocks entail higher inventory holding costs. This quadratic term approximates the tradeoff between the two costs, with a3 rising as stockout costs rise relative to backlog costs. Holt et al.'s (1960) formal derivation o f this time invariant approximation to this inherently nonlinear, and timevarying, cost is presented in Section 8. Note in any case that in many applications, inventories are strictly positive and large relative to sales in all time periods, perhaps in some data sets because o f aggregation over heterogeneous firms. So in such data, careful treatment of nonlinearity may have limited empirical payoff. Section 8 below discusses alternative approaches. The final term in the cost function is UotQt. This captures exogenous stochastic variation in costs. (We omit terms o f the form cost shock x A Q t and cost shock × H t to avoid needless algebraic complications.) In some applications Uct = 0 and this shock is absent [West (1986)]; in others it is not observed by the economist and follows an exogenous process [Eichenbaum (1989)]; in still others it has both observable and unobservable components [Ramey (1991)]. To cover all three cases, we write Uct = a' W t + Uct.

(3.2)

In (3.2), Wt is a vector o f observable components; uot is unobservable to the economist and follows an exogenous process. In one or another paper, Wt includes variables such as real wages, materials prices and real and nominal interest rates. If there are no such components, W t - 0; if cost shocks are entirely absent, Uct =- 0 as well. For convenience we refer to uct as a "shock", even though it may be serially correlated and partially or fully observable. 3.3. A first-order condition

A n optimizing firm will not expect to increase cash flow by producing one more unit this period, putting the unit in inventory, and decreasing production by one unit next period, all the while holding revenue constant. Formally, upon differentiating the objective function (3.1) with respect to H t we obtain 11 E t [a0(AQ, - 2bAQt +1 + b 2zxQt+2) + a l (Qt - bQt+ l) + ba2 (Ht - a3S,+ 1) + Uct

b Uct+i ] = O.

(3.3) For discussion of the second o f our stylized facts (persistence in the inventory-sales relationship), it will be helpful to note a low frequency implication o f Equation (3.3), namely, that inventories and sales are cointegrated if St is I(1) and Uct is I(0). [Here,

11 The first-order condition derived assuming that [O(pt+jSt+j)/OHt]- O. This assumption is not particularly appealing, since a 3 > 0 is motivated in part by stockout costs, and presumably increases in H t will decrease stockouts and increase revenues (increase p,St). As noted above, our modeling of stockout costs is crude but given data constraints in some applications the gains from more sophisticated treatments perhaps are small. See Section 8 below for alternative treatments.

EA. Ramey and K.D. West

886

we use standard time series notation: a variable that is integrated o f order 0 - I(0), for short - is one that is covariance stationary, with a spectrum that is finite and strictly positive at all frequencies. An "integrated" variable - I(1), for short - is one whose arithmetic difference is I(0). I(1) variables are sometimes called "difference stationary", or as having unit autoregressive roots (a term that we used in Section 2).] To see the cointegration result, write the term in brackets in Equation (3.3) as xt+2, so that (3.3) is Etxt+2 = 0. If we replace expectations with realizations, we can write (3.4)

Xt+2 = ~ t + 2 , tlt+2 ~ (Xt+2 -- Etxt+2) ~ I(0).

Note that even if some or all o f the variables that comprise xt+2 are integrated, ~t+2 will still be stationary. Kashyap and Wilcox (1993) observe that xt+2 may be rewritten Xt+2 =

ao( AQt - 2bAQt+l + b2 AQt+2) - b a l ( A H t + l

+

Agt+l) + all'r-It

- a2a3ASt+l - ba2OASt+l + ba2(Ht - OSt) + Uct - bEtUct+b

(3.5)

al(1 - b ) O~a

3

ba2

Suppose U c t ~ I ( O ) but H t , S t ~ I ( 1 ) . Then A H t ~ I ( O ) and A Q t ~ I ( O ) , and Equainventories and sales are tion (3.4) (stationarity o f xt+2) requires H t - O S t - I ( O ) : cointegrated with cointegrating parameter 0. We focus on St ~ I ( 1 ) for concreteness and empirical relevance, but it is worth noting that 0 is still economically interpretable in other cases. I f St and Uct are both I(0), then O = E H t / E S t is the inventory sales ratio evaluated at steady state values o f St and Hr. (Recall that we have omitted deterministic terms for notational simplicity.) I f St and H t have deterministic drift ( E A S t ~ 0) - which is consistent with Uct either I(0) or I(1), and St either I(1) or I(0) around trend 12 _ then O = E A H t / E A S t . Suppose there are observable cost shifters. I f Uct = ~ l W t + u c t with W t ~ I ( O ) or W t ~ I ( 1 ) [see Equation (3.2)] then from similar logic Uct~[(O) ~ H t - O S t + (ba2) 1(1 - b ) ' a I W t z H t - O S t - o f f W t =- H t - H t ~ I(0): after controlling for possibly nonstationary observable cost shifters, inventories and sales are cointegrated. (Once again, OSt + a ~W t remains economically interpretable under other conditions on presence or absence o f unit roots.) We summarize the preceding two paragraphs as follows: if St HI(l), H t - H t ~ I(0), Uot ~ I(O) Uct ~ I(O)

~ =~

H t = OSt, Ht -

1-b

O = a3 - al - ba2 '

OSt + a ' W t ,

a =_

(3.6)

l-b_

--a. ba2

Observe that this result does not require parametrization of the demand curve, or specification o f market structure. Rossana (1995, 1998) assumes exogenous revenue 12 A variable xt is 1(0) around trend if Ext = m o + m lt for some m l ~ 0 and xt -Ex~ = I(0). Such variables are sometimes called trend stationary.

Ch. 13: Inventories

887

and uses the resulting decision rule to provide a complementary proof that Uct ~ I(O) [Uct ~I(0)] implies cointegration between H t and St (between H t , St and Wt). 3.4. Whose inoentories?

The preceding description o f the model suggests that manufacturers' inventories o f finished goods are a natural area for applying the model. Indeed, a large fraction of the inventory literature focuses on manufacturers' finished goods inventories, often in six two-digit industries that are known as "production to stock". 13 To some, in fact, the model is not a particularly attractive one for studying any other types of inventories [e.g., Blinder and Maccini (1991)]. In connection with our discussion of Table 4's sectoral breakdown o f US inventories, however, we noted that manufacturers' inventories of finished goods are a small and not particularly volatile component of total inventories. If, indeed, the model is applicable only to finished goods inventories, then it has limited relevance for aggregate inventory fluctuations. We conclude this section by briefly noting that this arguably constitutes an unadvisedly narrow reading of the model. First, works in progress inventories apparently function as a buffer in many industries, particularly ones that are production to order [West (1988)], and thus fit naturally into the model. More importantly, however, it is possible that an invisible hand causes a large aggregate to solve an optimization problem such as (3.1), using transactions not explicitly modeled in Equation (3.1) to do so. This point was first made by Blanchard (1983), who combined data from the production and retail sectors of the auto industry, modelling explicitly the transactions between the two sectors, and showed that the industry as a whole solved an optimization problem such as (3.1). This is an illustration of the equivalence between a social planning and a decentralized equilibrium, which is well known to occur under general circumstances. We are therefore sympathetic to the view that there has been too strong a focus on manufacturers' inventories o f finished goods. But we feel the implication may be not that the model is of limited relevance, but that it, or related models that capture similar forces, should be applied more widely.

4. Decision rule 4.1. Introduction

Section 4.2 briefly reviews alternative treatments of demand, and solves for a decision rule under a simple specification. Section 4.3 derives the process followed by the

13 "Production to stock" industries are ones that typically sell finished goods off the shelf. By contrast, "production to order" industries are ones that maintain order backlogs, often deferring final assembly until orders are in hand. See Abramowitz (1950) and Belsley (1969).

888

V.A. Ramey and K.D. West

inventory-sales relationship, and may be skipped without loss of continuity. Section 4.4 summarizes the implications of Section 4.3 for persistence in the inventory-sales relationship. We present a detailed treatment o f the inventory-sales relationship because this process has not received much direct attention in existing literature. Discussions o f procyclicality in subsequent sections will cite analytical results in existing literature. 4.2. Derioation o f decision rule

Derivation o f a decision rule requires specification o f revenue because current and expected sales and output appear in the first-order conditions. We begin by reviewing some alternatives. We then work through in detail a specification that is relatively tractable. In some applications, sales is taken as exogenous, with cost minimization (i.e., m i n E t }--~/~0 bJCt+j) the objective 14. Examples include Holt et al. (1960), Belsley (1969) and Blanchard (1983). The use o f this assumption in industry-wide data is valid only if the demand curve facing the industry is vertical. In other applications, an industry equilibrium is analyzed, and a linear demand curve is specified [e.g., Eichenbaum (1984)]. We write such a demand curve in inverse form as

Pt = - g S t + g [ f dt ~ -gSt + Udt.

(4.1)

In (4.1), Udt and Udt are stochastic. The demand curve is written in this form so that exogenous sales is a special case of Equation (4.1), implemented by letting the parameter g --+ oo and specifying ~rdt as exogenous; with g ---+ oo, St = Udt. In practice, one needs to allow for serial correlation in Udt. In principle one might want to rationalize such serial correlation with (say) costs of adjustment on the part of purchasers, or with observable shifters o f the demand curve [West (1992b)]. But since the model focuses on production, and, moreover, is typically not used to study the effects of a hypothetical intervention or change in regime, taking such serial correlation as exogenous is a useful simplification that will be maintained here. Finally, Christiano and Eichenbaum (1989) and West (1990b), building on Sargent (1979, ch. XVI) derive the linear demand curve (4.1) in general equilibrium. Both papers assume a representative consumer whose per period utility is quadratic in St and linear in leisure. The disturbance Udt is a shock to the consumer's utility. There is no capital; the only means o f storage is inventories. See the cited papers for detail.

14 TO prevent confusion, we note that the first-order condition (3.3) also results if one assumes cost minimization. So if one aims to use condition (3.3) to estimate model parameters, one can motivate the equation by reference to cost minimization without taking a stand on the how revenue is determined (apart from the caveat stated in Footnote 11).

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Here, we do not derive Equation (4.1) in general equilibrium but take (4.1) as given. We do not attempt to trace the demand shock back to preferences or other primitive sources. We therefore caution the reader that despite the label "demand", Udt should not be thought of as literally a nominal or monetary shock, since it (like all our variables) is real. As well, one can imagine scenarios in which Udt reflects forces typically thought of as supply side. If the good in question is an intermediate one, for example, one can imagine that shocks to the technology of the industry that produces the good dominate the movement of Uat. Whatever the interpretation of Udt, we derive an industry equilibrium assuming a representative firm. Even so, to obtain a decision rule, we must be specific about market structure and the structure of the demand and cost shocks. We assume here that the market is perfectly competitive, and normalize the number of firms to one. If the firm is a monopolist, the reduced form is identical, but with a certain parameter being the slope of the marginal revenue curve rather than the slope of the demand curve. We assume that Wt, Udt and Uct follow exogenous AR processes, possibly with unit autoregressive roots. By "exogenous" we mean "predictions of Wt, Udt and uot conditional on lagged Ws, Uas and uos are identical to those conditional on lagged Ws, Uds, uos, and industry-wide H s and Ss: Wt, Uat and uot are not Granger-caused by industry-wide Ht or St". (Of course in general equilibrium, such exogeneity of Wt is doubtful.) Finally, for notational simplicity, and to make contact with the literature on the "speed of adjustment" (see the next section), we tentatively assume that a0 = 0.

(4.2)

This assumption is arguably not a good one empirically, and we will relax it below. Under the assumption of perfect competition, there are two equivalent methods for deriving the decision rules for inventories and sales. The first method, which studies the decentralized optimization problem, derives the individual firm's first-order conditions and then incorporates those into the industry equilibrium. The second method, which uses a social planning approach, derives the first-order conditions for the social planner problem and obtains decision rules for those. Both methods yield identical answers. We exposit here the decentralized method, and present in the Technical Appendix the social planner approach. With a0 = O, the first-order condition for sales St for the representative firm is Pt - Et[alQt - a2a3(Ht-i - a3St) + Uct] = O.

(4.3)

In the absence of inventories, this would simply tell our competitive firm to set marginal revenue Pt equal to marginal cost a l Q t + U c t . The additional term aaa3(Ht 1 - a3St) is the effect on inventory holding costs of an additional unit produced for sale. Upon using Pt = - g S t + Udt in Equation (4.3) and Qt =St + A H t in Equation (4.3) and the inventory first-order condition (3.3), we obtain a pair of linear stochastic

V.A. Ramey and K.D. West

890

difference equations in Ht and St. This two equation system is solved in the Technical Appendix. The resulting decision rule is Ht = YgHHt-1 + distributed lag on uct, Udt and Wt,

(4.4a)

St = ~sHt 1 + a different distributed lag on uct, Udt and Wt.

(4.4b)

In (4.4a), srH is the root to a certain quadratic equation, ]~H[ < 1. Both ~ / a n d ~s depend on b, g, al, a2 and a3. (Note two differences from the relatively well-understood case of exogenous sales. Even when as, a2 > 0, i f g < oc: (a) it is in principle possible to have :v~ ~<0, and (b) the accelerator coefficient a3 affects ~/t.) The distributed lag coefficients on Uct, Udt and Wt depend on b, g, al, a2 and a3 as well as the autoregressive parameters governing the evolution of the uct, Udt and Wt. In the empirically relevant case of z~H > 0, ~H increases with marginal production costs al and decreases with marginal inventory holding costs a2. The signs of OJvH/Oa3 and OYfH/Og a r e ambiguous. The solution when revenue is exogenous (g --+ c~) is obtained by replac~g Udt with gUdt [see Equation (4.1)] and letting g ~ c~. In this case, :Vs =0, St = Udt and the solution (4.4) may be written in the familiar form H t = ~HHt I + distributed lag on St and on measures of cost,

(4.5a)

St N exogenous autoregressive process.

(4.5b)

On the other hand, when revenue is endogenous, :rs ~ 0 and we see in Equation (4.4b) that inventories Granger-cause sales. The intuition is that forward looking firms adjust inventories in part in response to expected future conditions. Thus industry-wide stocks signal future market conditions, including sales. This signalling ability is reflected in Equation (4.4b). These same results can be obtained directly from the social planner problem that maximizes consumer surplus plus producer surplus, which is equal to the area between the inverse demand and supply curves. See the Technical Appendix. In empirical application, matching the data might require allowing shocks with rich dynamics. Such dynamics may even be required to identify all the parameters of the model. Blanchard (1983), for example, assumes that the demand shock follows an AR(4). For expositional ease, however, we assume through the remainder of this section that all exogenous variables - Udt, uct, Wt - follow first-order autoregressive processes (possibly with unit roots). Specifically, assume that Et-1 Wt = (I-)wWt 1,

Wt = CrAwWt-1 + ewt,

Et_lewt = O,

I I - ~wZl = 0 ~ Izl/> 1, Et l Uct = q~cuct-1, Et-1 Udt = ~ d U d t - 1 ,

Uct = q~cUct-1 + ect,

Udt = ~JdUdt-1 + edt,

Et-leot = 0, Et ledt = O,

[q~c[ ~< 1,

]•d[

~< 1. (4.6)

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Inventories

891

(Given the growth in the number of symbols, it may help to remind the reader that Table 7 summarizes notation.) The Technical Appendix shows that the distributed lags in Equation (4.4) are all first order, and Equation (4.4) is H t = YfHHt-1 +f~/w W t + f HcUct + f HdUdt,

(4.7a)

St = ~sgt-I

(4.7b)

+ f t s w W t + f scUct + f sdUdt.

See the Technical Appendix for explicit formulas for the ')¢"s in terms of b, g, al, a2, a3, qJw, q~c and q~d. Of course, if ~ = 0 so that Uct =uct, thenfHw = f s w =0. 4.3. Persistence in the inventory-sales relationship

To analyze the second of our stylized facts (persistence in the inventory-sales relationship), we now further assume that the demand shock and the observable cost shifters follow random walks: (bd = 1, Udt = Udt 1 + edt, qDw = I , W t = Wt-1 + ewt.

(4.8)

Recall that if Uct is stationary, H t - OSt is stationary as well, where the cointegrating parameter 0 is defined in Equation (3.5). When there are no observable cost shifters (~ = 0 ~ fHw = f s w = 0), tedious manipulation o f Equation (4.7) yields H t - H t =~ H t - OSt = ~ H ( H t - l

- OSt-1) + mocuct -t- mlcUct l + modedt,

(4.9)

where moo, ml~ and m0d depend on O, f H o , f H d , f S c and f S d (see the Technical Appendix). Let "L" be the lag operator. Since ( 1 - ~ c L ) u c t = e c t , it follows from Equation (4.8) that (1 - ~,vL)(1 - (bcL)(Ht - H t ) = vt, vt = mocect + m~cect-i + mOdedt -- ~)cmOdedt-1 ~ MA(1).

(4.10)

Thus, H t - H t ~ ARMA(2, 1) with autoregressive roots Jr/4 and ~bc. (This presumes that the moving average root in vt does not cancel an autoregressive root in H t - H i, which generally will not happen.) Note that the innovation edt, rather than the shock Udt, appears in Equation (4.9) and thus in Equation (4.10). With q~d ~ 1, however, the right hand side of Equation (4.10) would include a linear combination of Udt and Udt-I that would not reduce to a linear function of edt, and ~d would also be one of the autoregressive roots of H t - H i . In this case, if ~d ~ 1, then Ht - H i would also have a moving average root that would approximately cancel the autoregressive root of ~bd. Similarly, when there are observable cost shifters (a ~ 0), it may be shown that Equations (4.6) and (4.7) imply H t - H i = H t - OSt - ¢TIWt = :rH(Ht-i - OSt-1 - a1Wt-1) + disturbance,

disturbance

= m~owewt + mocUct + mlcUct-i + mOdedt.

(4.11) Once again, persistence in H t - H 2 is induced by ;r,q and q~c.

892

V.A. Ramey and K.D. West

We close this subsection by re-introducing costs of adjusting production a0. Suppose a0 ~ 0.

(4.12)

It is well known that when revenue is exogenous (g ---+ oc), costs of adjusting production put additional persistence in inventories [Belsley (1969), Blanchard (1983)]: in this case Equation (4.5a) becomes H t = Y g H I H t I + J~H2Ht 2 q- distributed lag on S t and on measures of cost,

(4.13) with Y~H2~ 0. Unsurprisingly, inventory decisions now depend on Qt-1 =St-1 +Ht-1 H t - 2 and thus on Ht-2, even after taking into account Ht-t and the sales process. As one might expect, the presence of costs of adjusting production has a similar effect even when sales and revenue are endogenous, and on the inventory-sales relationship as well as inventories. The Technical Appendix shows that a0 ~ 0 puts an additional autoregressive root in Ht - H t , which now follows an ARMA(3, 2) process. One autoregressive root is Oc. We let Jrl and Y~2 denote the two additional (possibly complex) roots. These are functions of b, a0, al, a2, a3 and g. Intuition, which is supported by the simulation results reported below, suggests that increases in a0 increase the magnitude of these roots.

4.4. S u m m a r y

on persistence

in t h e i n v e n t o r y - s a l e s

relationship

We summarize the preceding subsection as follows: assume the shocks follow the AR(1) processes given in Equation (4.6), with the additional restriction (4.8) that the demand shock and observable cost shifters follow random walks. Then ao = 0 ~

H t - H t = H t - OSt - ct ~W t ~ ARMA(2, 1),

with AR roots : r t / a n d 0c.

(4.14)

The root ~H is a function of b, g and the ai, but not the autoregressive parameters of the shocks, and is increasing in the marginal production costs at. In addition, ao ~ 0 ~

Ht - Ht

=-- H t - OSt - a t W t ~

with AR roots ~1, ~2 and ¢c; if

0c=0,

Ht-H

ARMA(3, 2), (4.15)

t~ARMA(2,1)

with AR roots Z~l and z~2. The roots ,TgI and JL"2 are functions of b, g and the ai, but not the autoregressive parameters of the shocks; both analytical manipulations of the formulas in the

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893

Technical Appendix and simulations reported in Section 6 indicate that the modulus o f the larger o f the roots increases with a0 and al 15 Thus the persistence documented in Section 2.2 above follows i f there are sharply increasing production costs (a0 and/or al are sufficiently large) and/or serially correlated cost shocks. In addition, it is important to observe that qualitatively similar reduced forms are implied b y the following two scenarios: (1) serially correlated cost shocks with no costs o f adjusting production, and (2) serially uncorrelated cost shocks and sharply increasing costs o f adjusting production. We shall return to this point below. O f course persistence m a y also follow if we put different dynamics into the shocks Wt, Uct and Udt.

5. The flexible accelerator model We now derive (4.10)-(4.11) from another optimization problem. This optimization problem is one that underlies empirical work motivated by the flexible accelerator model. In this model, pioneered by Lovell (1961), firms solve a static one period problem, balancing costs o f adjusting inventories against costs o f having inventories deviate from their ffictionless target level H i. Specifically, the firm chooses H t to minimize 0.5(Ht - H~) 2 + 0 . 5 v ( H t - Ht-l)2 + utHt.

(5.1)

In (5.1), v > 0 is the weight o f the second cost relative to the first, and ut is an exogenous unobservable disturbance 16. The first-order condition is then Ht-Ht-1

= [1/(1 + v ) ] ( H ; - H t - 1 ) -

[1/(1 + v)]ut.

(5.2)

The coefficient 1/(1 + v) is the fraction o f the gap between target and initial inventories closed within a period. I f v is big (cost o f adjusting inventories is big), the fraction o f

~5 Under the present set of assumptions, then, the parameter called "p" in Section 2.2 is max{~H, $c} if a 0 = 0, max{l~ l I, 1~2I,Oc} if a 0 ¢ 0. 16 Ht and St are sometimes measured in logs [e.g., Maccini and Rossana (1981, 1984)], and the variable ut is sometimes split into a component linearly dependent on the period t surprise in sales and a component unobservable to the economist [e.g., Lovell (1961), Blinder (1986b)]. We slur over differences between regressions in levels and logs, which in practice are small (see Footnote 8), and omit a sales surprise term in the inventory regression, which in practice has little effect on the coefficients that are central to our discussion.

V.A. Ramey and K.D. West

894

the gap expected to be closed is, on average, small. To make this equation operational, target inventories H~ must be specified. Let (5.3)

H t = OS, + a ' W t .

Here, Wt is a vector of observable cost shifters [as in Section 2.2.2 and Equation (3.2)]. Notation has been chosen because of link about to be established with 0 and a ~W t as defined earlier. Suppose S t = St-1 + edt,

W t = W t - 1 + ewt,

(5.4)

= 0. (In practice, Et-lSt is usually approximated as a linear function of a number of lags of S, the actual number dependent on the data, and similarly for Wt [e.g., Maccini and Rossana (1984)]. The single lag assumed here is again for simplicity.) Then with straightforward algebra, the first-order condition (5.2) implies

Et-1 edt = O, Et l ewt

H t - OSt - a ' W t = :rH(Ht 1 - OSt-1 - a~Wt_l) + disturbance,

:vH = [v/(1 + v)],

disturbance = [1/(1 + v)](Oed, + a'ew, -- ut),

(5.5)

which is in the same form as Equation (4.11). We have thus established that in the simple parameterization of this section, in which sales follows an exogenous random walk, high serial correlation in a stationary linear combination of inventories and sales is the same phenomenon as slow speed of adjustment of inventories towards a target level.

6. Dynamic responses To develop intuition about how the model works, and what the two stylized facts suggest about model parameters and sources of shocks, this section presents some impulse responses. Specifically, we present the industry equilibrium response of (1) H t , St and Qt, or (2) H t , St and H t - OSt, to a shock to Udt or Uct, for various parameter sets, with no observable cost shifters (a = Wt = 0). While the parameter values we use are at least broadly consistent with one or another study, we choose them not because we view one or more of them as particularly compelling, but because they are useful in expositing the model. Table 8 lists the parameter sets. It may be shown that the solution depends only on relative values o f g, ao, al and a2; multiplying these 4 parameters by any nonzero constant leaves the solution unchanged. [This is evident from the first-order conditions (3.3), (B.4) and (B.5): doubling all these parameters leaves the first-order conditions unchanged, apart from a rescaling of the shocks.] Our choice of a2 = 1 is simply a normalization. We fix g = 1 in part because some of the properties documented below can be shown either to be invariant to g [see West (1986, 1990b) on procyclicality of inventories] in part because a small amount of

Ch. 13:

895

Inventories

Table 8 Parameter sets a (1) Mnemonic

(2) g

(3) a0

(4) a1

(5) a2

(6) a3

(7) ~c

(8) ~d

A

1

0

1

1

0

n.a. b

0.7

B

1

0

1

1

1

n.a.

0.7 0.7

C

1

0

-0.1

1

0

n.a.

AI

1

0

1

1

0

n.a.

1

An

1

0

1

1

0

0.7

n.a.

D

1

3

1

1

0

n.a.

1

E

1

3

1

1

1

n.a.

1

a See Table 7 for parameter definitions. The behavior of the model depends only on the scale of the parameters g, a0, a~ and a2; doubling all these leaves behavior unchanged. The discount factor b is set to 0.99 in all experiments. b "n.a." means that the autoregressive parameter is irrelevant for the impulse responses plotted in Figures 7-13: the response is for a shock to the other variable, whose AR(1) parameter is given. e x p e r i m e n t a t i o n indicated little sensitivity to g. To p r e v e n t possible confusion, we note explicitly that the p a r a m e t e r a3 is identified in absolute terms and not just relative to other parameters. Throughout, w e set the discount factor b = 0.99, and interpret the t i m e p e r i o d as quarterly. To facilitate discussion, in the graphs we set vertical tick marks labelled " - 1 " , " 1 " , "2", and so on, but this (or any other) choice o f traits to measure the response is arbitrary. [In actual application, the units u s e d w o u l d o f course be m o n e t a r y (e.g., billions o f 1992 dollars in the impulse responses in Section 2 above)]. The p r o d u c t i o n s m o o t h i n g aspect o f the m o d e l is m o s t clearly e v i d e n t w h e n shocks are m e a n reverting. We therefore begin with three p a r a m e t e r sets illustrating the response to an innovation in a stationary A R ( 1 ) d e m a n d shock Ud~, w i t h A R parameter ~d = 0 . 7 . Since q~d = 0 . 7 is probably far e n o u g h f r o m unity to m a k e the notion o f cointegration b e t w e e n H t and St unappealing, we plot the responses o f Qt, St and H t but not those o f H t - O S t 17. Parameter set A illustrates the production s m o o t h i n g model. F i g u r e 7 presents the response to a d e m a n d shock. A s may be seen, w h e n there is a , p o s i t i v e innovation to demand, sales o f course rise. But part o f the increase in sales is m e t by drawing d o w n inventories, thereby b u f f e r i n g production f r o m the d e m a n d shock. A s sales return to

17 Naturally, even though we do not include the plots here we did examine them ourselves. As it turned out, H t - O S t showed persistence. From Equation (B.11) in the Technical Appendix, we see that H t - OSt has an autoregressive root of Od that is cancelled by a moving average root only when 0d --4 1. This autoregressive root apparently explains the persistence. In our view such persistence is not particularly interesting: in a stationary model, 0 = a3 - [al (1 - b)/ba 2 ] is not the parameter corresponding to a projection o f H t onto St, and thus H t - OS t does not correspond to the quantity displaying persistence in, for example, Table 6.

896

V.A. Ramey and K.D. West I

I

I

I

I

5 43-

"-1

2.t-

O-

~,

inventories quarter

Fig. 7. Response to a stationary demand shock; parameter set A.

the steady state, inventories are gradually built back up. It may be seen in the graph that production is smooth relative to sales. The intuition is straightforward: given increasing marginal costs (al >0), it is cheaper to produce at a steady rate than to produce sometimes at a high rate, sometimes at a low rate. So the increased demand is met partly with inventories, and production is smoothed relative to sales. (Note that this logic applies even for a competitive firm that can sell as much as it wants at the prevailing market price.) Inventory movements are countercyclical, in the sense that they covary negatively with sales. It may be shown analytically that such cotmtercyclical behavior will obtain when a l > 0, a3 = 0 and there are no cost shocks [West (1986) for a stationary model, working paper version o f West (1990b) for a model with unit roots]. One can obtain procyclical movements when costs are convex if the accelerator term is operative (a3 > 0) and is sufficiently strong to offset the production smoothing motive. In Figure 8, which shows results when a3 = 1 rather than a3 = 0, inventories initially rise along with sales when there is a positive innovation to the stationary demand shock. So production rises even more than does sales, and is more variable. All three variables then fall smoothly back towards the steady state. Some algebra may help with intuition: if ao=a] =0, and Uct=O, the firstorder condition for Equation (3.1) is simply Ht=a3EtSt+l. Thus inventories will covary positively with expected sales, and thus with sales themselves since St is positively serially correlated in equilibrium. With a0 ¢ 0, al ~ 0, inventory movements will reflect a balance of accelerator and production smoothing motives. I f the

Ch. 13." Inventories

897 I

4

I

I

I

I

A

-t-I e-

1

0 I

o

I

2

I

quarter

a

Fig. 8. Response to a stationary demand shock; parameter set B.

accelerator motive dominates, as it does in this parameter set, inventories will move procyclically IS. Another way to obtain procyclical movements in response to demand shocks, is with nonconvex production costs [Ramey (1991)]. Parameter set C captures this with a small negative value for al. [The linear quadratic problem will still be well-posed, and lead to an internal solution, as long as the nonconvexity is not too marked; in the present context, this essentially demands that a2 and g be sufficiently large relative to ]al I. See Ramey (1991).] We see in Figure 9 that a positive innovation to demand causes inventories to rise (though by a small amount - an artifact o f our choice o f parameters): with al < 0 it is cheaper to bunch rather than smooth production. Thus, firms build up inventories when sales are high. If there is a cost o f changing production (a0 ~ 0), marginal production costs are (1 +b)ao +al. Ramey (1991) has noted that al < 0 may induce a tendency to bunch production even if (1 + b)ao + a~ > 0 [see West (1990b) for a particular set o f parameters for which this happens]. We now turn to parameter sets with a unit root in the demand shock (q~d= 1). Figure 10 plots the response o f inventories, sales and the inventory-sales relationship

18 Recall that the accelerator term is motivated in part by stockout costs. Kahn (1987) rigorously shows that when nonnegativity constraints are imposed, demand uncertainty (which implies uncertainty about whether a stockout will occur) will lead to procyclical movements if demand is serially correlated.

898

V.A. Ramey and K.D. West I

[

I

I

I

6

8

~.2 10 8

E

6

4 2 0

~

2_

_'~-~_ 2 _

I

0

_"-2"~-_ _ - _ ' _

_ _-_,_

I

2

_ ~ =

-

-

I

4 quartsr

I

Fig. 9. Response to a stationary demand shock; parameter set C.

H t - O S t , with the technology parameters matching those in parameter setA. As with a stationary shock, firms draw down inventory stocks when demand increases (though the fall is slight in our figure). They will replenish stocks in response to a negative shock (not depicted). Thus inventories buffer production. With our choice of parameters, the transition to the new steady state is quite rapid 19. In parameter sets B and C, a demand shock with a unit root leads to procyclical inventory movements (not depicted): with or without a unit root in the demand shock, inventories buffer production. Figure 10 also plots the response o f the inventory sales relationship H t - OSt. To understand the pattern it exhibits, some mechanics may be helpful. Since a3 = 0, 0 < 0 and ( - 0 ) > 0 [see Equation (3.5)]. In Figure 10 we see that the response o f Ht is negative but small in absolute value, that of St positive and relatively large; in the end, the net response of (-O)St > 0 is greater than that o f Ht < 0, and Ht - OSt increases in response to a demand shock. The inventory-sales relationship has little persistence, however; it has a first-order autocorrelation coefficient o f a little under 0.3. When we computed impulse responses for parameter sets B and C with a unit root demand shock (not depicted), the sign o f the initial response of l i t - OSt happened to be negative for parameter set B, positive for parameter set C: the sign o f the initial response to a demand shock is sensitive to exact parameter values. A characteristic

19 To prevent confusion: sales and revenue are endogenous in this experiment (g<ec). Although St looks like a random walk in the figure, in fact ASt does have a little bit of serial correlation, and is Granger-caused by inventories.

Ch. 13. Inventories

899 I

I

I

I

I

5

4

sales

3 e-

2

1

0

] inventory-sales relationship / J_¢/

inventories

quarter Fig. 10. Response to a unit root demand shock; parameter set A ~.

of all three parameter sets, however, was rapid mean reversion in H t - OSt. The autoregressive root x~/ [see Equation (4.9)] was 0.270 (parameter set A), 0.269 (B) and -0.148 (C). The negative sign of xH in parameter set C perhaps deserves a word of mention. Recall that al < 0 in this parameter set, and that downward sloping marginal costs induces production bunching. So bunching generates a negative autocorrelation, since high activity in one period tends to be followed by low activity in the next. In parameter set A", we continue to use the same technology parameters, but now plot responses to a cost rather than demand shock. The cost shock is stationary, with an AR parameter of q~o= 0.7. We see in Figure 11 that inventories move procyclically in response to a negative cost shock: the shock causes both inventories and sales to rise, and makes production (not depicted) more variable than sales. (Recall that we are studying industry equilibrium, and sales of course change as costs change.) The intuition once again is straightforward: a firm with a convex cost function will use periods of low cost to produce a lot and to build up inventory stocks (as in the figure), and use periods of high cost (not depicted) to produce little and instead sell out of inventory stocks that have already been built up. In this case, inventories serve to buffer production from cost shocks. (Reminder: the phrase "production smoothing" is conventionally used only to describe smoothing from demand shocks but not, as in the present paragraph, smoothing from cost shocks.) Inventory movements are procyclical. It may be shown analytically that such procyclical behavior will obtain when al > 0,

900

V.A. Ramey and K.D. West I

I

I

I

!

6

8

4 sales

3

=~1 r-

2

I

0

1

2

I

4 quarter

I

Fig. 1i. Response to stationary cost shock; parameter set A". a3 = 0 and there are no demand shocks [see the working paper version o f West (1990b)]. We see that there is now persistence in H t - OSt 2o. We showed above that when a0 = 0 , persistence in H t - OSt results even in the absence o f cost shocks i f production costs a l are sufficiently large relative to inventory costs a2. W h e n sales are exogenous (g ~ oe), it is straightforward to establish analytically that persistence also increases as ao increases relative to al and a2. We use the final two parameter sets to document via simulation that large values o f ao also cause persistence when sales are endogenous. Parameter set D varies from A ~ only by introducing a0 = 3 instead o f a0 = 0. Figure 12 plots responses o f H i , S t and H t - OSt to a positive innovation in a unit root demand disturbance. From the perspective o f buffering, there are no new results: sales increase and inventories are drawn down to buffer production. But now there is persistence in the inventory-sales relationship H t - OSt, which has an autocorrelation a little above 0.7. The intuition is that i f costs o f adjusting production are large, and i f there is a (say) jump in demand, firms only very gradually increase production to build the stock up. Finally, parameter set E varies from D by allowing the accelerator motive, setting a3 = 1 (as in parameter set B). In Figure 13 we see that inventories now move procyclically in response to demand shocks, and that there continues to be persistence in the inventory-sales relationship.

20 Of course, for the computed response of H t - OSt to give us insight into the empirical behavior of H t - OSt, there must be unit roots or near unit roots in H t and St, and hence this experiment and parameter set cannot provide the whole explanation for the two stylized facts.

Ch. 13:

901

Inventories I 5

I

I

I

I

-

43-

B .H t--

2~.-

~--i

n_7_nt_°_r_Y- sa~e_s_5 e1.ati° nshi P

O-

....

inventories I

I

0

I

2

4

quarter Fig. 12. Response to a unit root demand shock; parameter set D.

I

I

I

I

5 4

/ ~

inventories

3 2 i -I

0

/ -2

-3

X

\//

/

inventory-sales relationehlp

I

I

0

2

[

4

I

6

quarter Fig. 13. Response to a unit root demand shock; parameter set E.

Table 9 s u m m a r i z e s the discussion in this section. Evidently, we m u s t consider e m p i r i c a l e v i d e n c e on: the accelerator motive, the relative values o f a0, al and a2, and cost shocks.

902

V.A. Ramey and K.D. West

Table 9 Possible explanations of stylized facts a Inventories procyclically

Persistence in inventory sales relationship b

no

yes

yes yes

i"10

yes

yes

Inove

In response to demand shocks:

(1) Marginal production costs rise very rapidly relative to marginal inventory holding costs (a2 small relative to al and/or ao) (2) Declining marginal production costs ° (al < 0) (3) Strong accelerator motive (aza3 large relative to a 0 and a a )

no

In response to cost shocks;

(4) Increasing marginal production costs

a The parameters are defined in Table 7. b The implications for persistence in the inventory-sales relationship apply if there is a unit root in the demand shock [explanations (1) (3)] and persistence in the cost shock [explanation (4)]. c The reference to "declining marginal production costs" abstracts from costs of changing production (from ao). With a0 * 0, marginal production cost is a0(1 + b) + a I. But even if a0(1 + b) + at > 0, inventory movements may be procyclical if a 1 < 0.

7. Empirical evidence 7.1. I n t r o d u c t i o n

The analytical results in West (1986, 1990b) and Section 4 and the simulations in Section 6 suggest at least two different ways o f rationalizing the procyclicality o f inventory movements and the persistence o f the inventory-sales relationship. One is a demand-driven model with rapidly increasing marginal production costs (marginal production costs a0 and/or al are large relative to marginal inventory holding costs a2), together with a strong accelerator motive (a2a3 large relative to a0 and a 0 . The second is a cost-driven model, with increasing marginal production costs; such a model may or may not have a role for the accelerator. For simplicity we somewhat loosely refer to these as our d e m a n d - d r i v e n and our c o s t - d r i v e n explanations. We do so with some reservations: please recall that our demand shock Udt may in some data basically reflect supply side forces. These two do not exhaust the possibilities, and many economists (including us) would expect both cost and demand shocks to be important over samples o f reasonable length. Our own work, for example, has emphasized the possibility o f declining marginal production costs [Ramey (1991)]. In combination with highly persistent cost shocks, both procyclicality o f inventories and persistence o f the inventory-sales relationship m a y result. A n d West (1990b) finds both stylized facts explicable with a model with strong costs o f adjusting production and a substantial role for both cost and demand shocks, but with no accelerator.

Ch. 13: Inventories

903

But our demand-driven and cost-driven explanations have the virtue of simplicity, and both have support from a number of papers: as summarized in this section and the next, most aggregate studies, and the limited microeconomic evidence available, do not point to declining marginal cost, and do find a role for the accelerator. In citing such support we do not cast a wide net but instead selectively cite representative papers. In addition, after some introductory remarks on papers using the flexible accelerator model (Section 7.2), we focus on papers that explicitly use the linear quadratic model, for ease of exposition. Section 7.2 reviews parameter estimates from the linear quadratic literature, Section 7.3 discusses sources of shocks, and Section 7.4 provides an interpretation. We remind the reader that the behavior of inventories depends only on the relative values of g, a0, al and a2. All statements referencing "large" values of one of these parameters should be understood to mean "large relative to another parameter or linear combination of parameters". The normalization involved will be clear from the context.

7.2. Magnitude of cost parameters Our discussion will focus on estimates of the linear quadratic model. We begin, however, with a brief discussion of results from less structured studies, including those using the flexible accelerator. We record two results. The first is that in flexible accelerator studies, actual or expected sales is generally found to be an important determinant of inventory movements, with a positive relationship between the two series. See, for example, Maccini and Rossana (1981, 1984) or Blinder (1986b). In terms of the model in Section 5, a positive relationship may be interpreted as 0 > 0, where 0 is the coefficient on sales in the expression for target inventories [see Equation (5.3)]. As well, in direct estimation of a cointegrating parameter, Granger and Lee (1989) do obtain 0 > 0 in all 27 of their US two-digit manufacturing and trade series. To interpret this with the linear quadratic model, recall that under certain conditions, the decision rule from the flexible accelerator model (5.1) can be mapped into that of the linear quadratic model (3.1). Under those conditions, 0 = a3 - [al (1 - b)/(ba2)] [see Equations (3.5), (4.11) and (5.5)]. Thus a3 > 0 is necessary for the cointegrating parameter 0 to be positive, as noted by Kashyap and Wilcox (1993). [This holds even when Uct is present (although cointegration requires Uct-I(0)).] Thus here and in linear quadratic studies (see below) there is support for a nontrivial role for the accelerator motive - a result that may be unsurprising or reassuring to some, but in any event is not particularly helpful in discriminating between our two candidate explanations. The second result from the flexible accelerator literature concerns the structure of production costs. As discussed in Section 2, this literature has found large autoregressive roots in H t - H i, which implies slow adjustment of Ht towards H i. In quarterly data, a typical estimate of the root is around 0.8-0.9, implying that about

904

V.A. Ramey and K.D. West

10-20% o f the gap between actual and target inventories is closed in a quarter. Ever since Carlson and Wehrs (1974) and Feldstein and Auerbach (1976), many observers have found such estimated speeds puzzling and perhaps not well-rationalized by the flexible accelerator model. One reason is that even the largest quarterly movements in inventories amount to only a few days production. This suggests to Feldstein and Auerbaeh (1976, p. 376) and others that costs o f adjusting inventories [v, in the notation o f Equation (5.1)] cannot be very large 21 . To interpret this second result with the linear quadratic model, recall that we set a0-= 0 when we established a mapping from the flexible accelerator to the linear quadratic model (3.1). With a0-= 0, an arbitrarily slow speed o f adjustment results when al is arbitrarily large. It is not clear to us how large a value o f al is implausibly large. But we take from the flexible accelerator literature the message that many find this simplest version o f the model unappealing [see Blinder and Maccini (1991) for a recent statement]. Accordingly we consider the other sources o f persistence isolated above: costs of adjustment (discussed in this subsection), and serial correlated cost variables (discussed in the next subsection). To focus the discussion o f costs of adjustment, we highlight estimates from some recent linear quadratic studies using two-digit manufacturing data from the USA. Different studies present estimates o f a0, al and a2 relative to different parameters or linear combinations o f parameters. To display results from various studies in consistent form, we restate published estimates of ao, a~ and a2 relative to a c o m m o n linear combination o f the published estimates of those parameters. This linear combination is c ~ (1 + 4 b + b 2 ) a o + ( 1 + b ) a l +ba2,

(7.:)

with b ~ 0.99. Here, "c" is the second derivative o f the objective function (3.1) with respect to Ht; the Legendre-Clebsch condition states that e > 0 is a necessary condition for an optimal solution. [See Stengel (1986, p. 213) or Kollintzas (1989, p. 11).] Note that the estimates we discuss will therefore not be comparable to those used in the simulations in the previous section and in Table 8, and often are not as easily interpreted as those expressed relative to a single parameter. We nonetheless use this normalization since studies sometimes report negative estimates o f a0, al or a2, which can make interpretation o f estimates relative to one o f those parameters problematic. Most authors examine more than one specification. Table 10 presents results for a specification that seemed to be preferred by the author(s). For the preferred specification, columns 2-6 present the median point estimate o f ao/c, a l/c, [(1 + b)ao + a l ]/c

21 The logic apparently is that it should be easy to make inventory movements rapid if firms are beginning from a starting point in which current movements are small relative to production. But small inventory movements seem to be exactly what one would associate with slow adjustment speeds, if costs of adjustment determine both the size of movements and the adjustment speeds; if, instead, the slow adjustment speeds were accompanied by large movements in inventories, there would be a puzzling contrast between regression results and basic data characteristics.

Ch. 13:

905

Inventories

Table 10 Median point estimates of model parameters a-d

(1) Reference e

(2) ao/C

(3) al/c

(4) [(1 +b)a 0 +al]/ c

a2/c

(5)

(6) a3

(7) Number of industries

5

Models with serially correlated cost variables:

(1) Durlauf and Maccini (1995)

0.

0.43

0.43

0.15

0.55

(2) Eichenbaum (1989)

0.

0.21

0.21

0.58

1.15

7

-0.16

0.83

0.64

-0.09

1.14

6

0.15

-0.63

-0.43

1.69

0.40

6

(3) Kollintzas (1995) (4) Ramey (1991)

Models without serially correlated cost variables:

(5) Fuhrer, Moore and Schuh (1995)

0.13

0.12

0.38

0.00

0.67

1

(6) West (1986)

0.05

0.34

0.44

0.01

1.12

10

a In the column definitions, e -- (1 + 4b + b2) a 0 + (1 + b) a 1 + ba2, b =- 0.995. Note that the magnitudes in columns 2-4 are therefore not comparable to those in columns 4-6 in Table 8. b Different papers expressed point estimates relative to different linear combinations of parameters. For each paper, the reported point estimates were restated relative to c. The Legendre-Clebsch condition states that c > 0 is a necessary condition for an interior solution of the optimization problem. The table reports the median of the restated estimates. When a0 = 0 (lines 1 and 2), or when there is only one industry (line 5), the column 4 entry for marginal production cost is by construction equal to: (1 +b) times column 2, plus column 3. c All the studies used two-digit manufacturing data from the USA. The exact data, sample period, specification and estimation technique vary from paper to paper. d Most papers present more than one set &results. We chose the specification that seemed to be favored by the author(s). e Sources by reference: (1) Table 7 (p. 85), entries labelled "Table 3"; (2) Table 2 (p. 861); (3) Tables 1 6 (pp. 77-80), columns labelled "random walk"; (4) Table 1 (p. 323), excluding autos; (5) Table 4 (p. 128), entry labelled "FIML-endogenous sales"; (6) Table 4 (p. 391). ( = m a r g i n a l production cost, taking into account costs o f adjusting production), a 2 / c a n d a3. The m e d i a n is c o m p u t e d across the datasets considered b y the author; the n u m b e r o f datasets is given i n c o l u m n 7. A skim o f the table suggests a broad consensus on a3 ( c o l u m n 6). A s well, there is relatively little d i s a g r e e m e n t on the sign o f the slope o f marginal production costs ( c o l u m n 4); with the exception o f R a m e y (1991), the studies find a n upward slope to m a r g i n a l production cost. There is, however, some variation in the extent to which the cost o f adjustment a0 contributes to this upward slope. Consistent with the d e m a n d driven explanation, F u h r e r et al. ( t 9 9 5 ) (line 5) and to a lesser extent West (1986) (line 6) find that a0 contributes to the upward slope. Some studies with other datasets have found an even stronger role for the cost o f adjustment a0, with a0 positive and significant but with estimates o f the production cost al negative [consistent with R a m e y (1991)], or e c o n o m i c a l l y or statistically

906

V.A. Ramey and K.D. West

indistinguishable from zero. For example, Kashyap and Wilcox's (1993) study of the automobile industry in the 1920s and 1930s yielded median estimates of parameters as follows: ao/c al/c [(1 + b)ao + al]/c a2/c a3 (7.2) 0.20 -0.11 0.29 0.03 0.72" Similar results are reported for the modern automobile industry by Blanchard (1983) and Ramey (1991), and for US aggregate inventories by West (1990b). On the other hand, we see in lines 1 and 2 that the preferred specifications in the Eichenbaum (1989) and Durlauf and Maccini (1995) set the cost of adjustment to zero. In these two papers, the estimates of al tended to be positive but perhaps not so large as to imply a speed of adjustment that Feldstein and Auerbach (1976) would find implausibly slow. In part these papers set a0 to zero - because in a setup similar to that of Kollintzas (1995) in line 3, negative and insignificant point estimates of a0 tended to result. Rounding out the cost-driven story requires finding substantial persistence from stochastic variation in costs. This is discussed in the next subsection. 7.3. Shocks There is much circumstantial evidence that serially correlated cost shifters have important effects on inventory behavior. In particular, the data often seem happy with specifications in which the unobservable disturbance uct is highly autocorrelated [e.g., Eichenbaum (1989), West (1990b), Ramey (1991)]. One's confidence that this unobservable disturbance really reflects stochastic variation in production costs would be increased if inventories could be shown to respond aggressively to observable measures of costs. Unfortunately, this appears not to be so. In practice, factor prices and interest rates usually are insignificant (in both economic and statistical terms), and sometimes have effects opposite of the theoretical predictions. For statistical significance, Table 11 shows a selection of results using cost variables, from studies of two-digit manufacturing in the USA, and now including flexible accelerator as well as linear quadratic studies. It may be seen in columns 1-4 that a finding of a statistically significant effect of observable measures of costs is rare: only 2 entries are "y"s, indicating that in only two of the 21 studies did significance at the 5% level characterize at least three-fourths of the coefficients estimated in a given study. 11 entries are "n"s, indicating that in these 11 studies fewer than one-fourth of the coefficients were significant. On the other hand, in column 5 it may be seen that for the unobservable disturbance, three of the 6 entries are "y"s, and that two of these "y"s are for studies that also included some observable measures of costs (lines 6 and 8); none of the 6 entries are "n"s. 7.4. Interpretation We showed in Section 4 that the demand-driven and cost-driven explanations put two large autoregressive roots in the inventory sales relationship H t - O S t ; in fact,

Ch. 13: Inventories

907 Table 11 Statistical significance of cost variables ~c

Reference d

Wage

Materials prices

(1) Blinder (1986b)

?

?

(2) Durlauf and Maccini (1995)

?

n

Energy prices

Interest rate

Unobservable shock

n

?

n

(3) Eichenbaum (1989)

y

(4) Kollintzas (1995)

?

(5) Maccini and Rossana (1981)

y

?

n

?

(6) Maccini and Rossana (1984)

n

y

n

y

(7) Miron and Zeldes (1988)

n

?

n

(8) Ramey (1991)

n

?

n

(9) Rossana (1990)

?

?

n y ?

a This table is an updated version of a table in West (1995). b All the studies used two-digit manufacturing data from the USA. The exact data, sample period, specification and estimation technique vary from paper to paper. c A "y" entry indicates that the coefficient on the variable in a given column was significantly different from zero at the 5% level in at least three-fourths of the datasets in a given study, a "n" that it was significant in at most one-fourth of the datasets, a "?" that it was significant in more than one-fourth but fewer than three-fourths of the datasets. A blank indicates that the variable was not examined. d Sources by reference: (1) Table 1 (pp. 360 61); (2) Table 3, inst. set. 4; (3) Table 2 (p. 861); (4) Tables 1-6 (pp. 77-80), columns labelled "HP filter" and "quadratic trend"; (5) Table 1 (p. 20); (6) Table 3 (p. 231) and discussion on p. 227; (7) Table I1 (p. 892); (8) Table 1 (p. 323); (9) Tables 3 and 4 (pp. 26-27), with the cost of capital variable "ce" and "cp" interpreted as interest rate variables.

u n d e r certain conditions, b o t h i m p l y A R M A ( 2 , 1) p r o c e s s e s o f l i t - OSt. Specifically, this happens w h e n q~c= 0 in the d e m a n d - d r i v e n explanation [see E q u a t i o n s (4.14) and (4.15)1. That the similar A R M A structures might allow both m o d e l s to fit a g i v e n b o d y o f data is illustrated by Kollintzas (1995). Kollintzas' results in line 3 o f Table 10 were for a specification w i t h a r a n d o m w a l k (q~c= 1) cost shock (i.e., Kollintzas differenced the first-order condition b e f o r e estimating). A m o n g other specifications, Kollintzas allowed for an i.i.d, u n o b s e r v a b l e cost shock. In the specification with i.i.d, cost shocks, the m e d i a n estimates o f the p a r a m e t e r s were:

ao/c

al/c

0.03

0.42

[(1 + b)ao + al]/C 0.47

a2/c

a3

0.01

2.51'

(7.3)

W h i l e the estimate o f m a r g i n a l production costs was n o t wildly different (0.47 with i.i.d, shocks vs. 0.64 w i t h r a n d o m walk shocks [line 3, c o l u m n 4 o f Table 10)], the

908

V.A. Ramey and K.D. West

median estimate of a0 was higher. In fact, the estimate o f a0 was higher in 5 o f the 6 datasets 22. An interpretation is that a model that fits his data would imply two autoregressive roots. When serial correlation in the cost shock was suppressed, the positive values for a0 rationalized a second autoregressive root; when serial correlation in the cost shock was imposed, large (or even positive) values o f a0 would imply an autoregressive structure too elaborate for the data, and accordingly the regression yielded diminished values o f a0. Discriminating between the two explanations thus means distinguishing between costs o f adjustment [when a0 ¢ 0 and the serial correlation of the cost shock is zero (~bc= 0)] and exogenous serial correlation (when a0 = 0 and q~c is near one). In principle this may be done, using either cross-equation restrictions, or additional variables such those in the Wt vector. But in both inventory and non-inventory contexts this has proved difficult [e.g., Blinder (1986b), McManus et al. (1994), Surekha and Ghali (1997)]. And in any case, our discussion so far perhaps has understated the extent o f conflict across empirical results. There is a range of estimates of most parameters (including some wrong-signed or otherwise implausible ones), and we have pushed papers into one o f just two camps in the interest o f summarizing a complex set o f results: while in principle it may be possible to pin down important macroeconomic parameters and sources o f shocks by simply estimating linear inventory models with aggregate data, this tantalizing idea has not proved true in practice so far. The conflict across papers, or the range o f estimates, may be no worse than in empirical work in other areas. For example, those familiar with the real business cycle literature will probably not be surprised that it is difficult to find observable counterparts to unobservable cost shocks. And Lovell (1994) shows that the estimated speed o f adjustment o f Ht towards H~ is in fact no slower than those o f some other variables. As well, part o f the conflict across papers no doubt results from econometric problems related to sample size or estimation technique [West and Wilcox (1994, 1996), Fuhrer et al. (1995)]. Finally, it may be that careful analysis would reveal that seemingly disparate conclusions in fact result mainly from the use o f different sample periods, datasets, and observable cost shiflers ("Wt", in the notation o f the previous sections). But pointing out (perhaps unfairly!) that other literatures have similar problems will not advance our knowledge about inventories. Nor, most likely, will sharp estimates be produced by even the most refined econometric technique, at least when applied to familiar data. We therefore suggest some alternative approaches.

22 Such statements potentially are sensitive to how the parameters are expressed (relative to "c", as in Table 10, or some other linear combination of parameters). But in this case the statement applies not only with respect to the normalization we have used, but also with respect to the normalization used by Kollintzas, which was relative to a0(1 + b)+ a l.

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909

8. Directions for future research

8.1. Introduction

In this section we offer what we believe to be fruitful directions for future research. Sections 8.2 and 8.3 describe alternative modelling strategies. Some of our suggestions are based on alternatives to the basic linear quadratic production smoothing model; others extend the basic model. All build on the insights delivered by the basic model: that procyclical movements result when inventories facilitate sales (a force captured in the basic model with the accelerator term), and that the shape of production costs influences both the character of cyclical movements and the persistence of the inventory-sales relationship. In addition, all seem intuitively capable of helping explain either or both of our stylized facts (procyclicality of inventories, persistence o f the inventory-sales relationship), although, of course, research to date involving these suggestions has its share of blemishes (e.g., wrong-signed parameter estimates). Finally, Section 8.4 describes how the use of different data may help understand inventory behavior. 8.2. Inventories in production and revenue functions

The potential importance of the accelerator term (a3) in explaining both the business cycle and long-run behavior of inventories suggests that the relationship between inventories and sales deserves more study. Consider first Holt et al.'s (1960) original motivation for this formulation as az(Ht-a3St+l) 2. As discussed on pp. 56-57 of their book, their initial model of optimal inventory holdings used lot-size formulas, where the optimal batch size, the number of batches and optimal inventory levels all increase with the square root o f the sales rate. They used two approximations to capture the costs and benefits associated with inventory holdings. First, they approximated the square-root relationship with a linear relationship between inventories and sales (e.g., H 7 =a3St+l). Second, they approximated all costs and benefits associated with inventories with a quadratic in which costs rise with the square of the deviation of inventories from the optimal level. This generates the accelerator term a 2 ( H t - H t ) 2. While this tractable formulation provides a plausible mechanism for procyclical inventory movements, there are two potential problems with it. First, the approximations may be inadequate. As we will discuss below, the approximations used imply that the cost of a marginal reduction in inventories is linear in the stock of inventories, whereas at least one paper found significant convexities. Second, inventories may directly affect revenue in a way that is not well captured by including the accelerator term in the cost function. One alternative strand of the literature has modelled inventories as factors of production, or considered interrelationships between inventories and other factors of production. Christiano (1988), Ramey (1989), Galeotti et al. (1997) and Humphreys et al. (1997) are examples. Ramey (1989) argues that since inventories at all stages

910

V.A. Ramey and K.D. West

of production facilitate production and shipments, they should be considered factors of production. She includes three stages of inventories in the production function, and estimates factor demand relationships. This approach obviously has the potential to make inventories move procyclically, since factor usage fluctuates with output. The results from the linear quadratic model suggest if costs of adjustment are allowed, persistence would result as well. A second line of research has considered the revenue role of inventories. Kahn (1987, 1992) develops a theory of a stockout avoidance motive for holding inventories and tests some of its implications using automobile industry data. Kahn argues that demand uncertainty and a nonnegativity constraint on inventories can explain several important patterns in the data. Bils and Kahn (1996) extend this line of research by assuming that the demand function is a (nonlinear) function of the stock of goods available for sale. They apply the model to two-digit manufacturing data with mixed success. Rotemberg and Saloner (1989) offer another potential role for inventories in revenue, arguing that inventories may be accumulated to deter deviations from an implicitly collusive arrangement between firms. The nature of the equilibrium implies that inventories will be high when demand is high. They show empirically that the correlation between inventories and sales is higher in concentrated industries, as predicted by their model. A third line of research studies uses more general functional forms for the relationship between inventories and sales. [The work by Kahn (1992) and Bils and Kahn (1996) also fits into this category.] Pindyck (1994) studies the convenience yield of inventories for three commodities. Augmenting the usual production, sales and inventory data with futures prices, he provides evidence that the marginal convenience yield is very convex, increasing sharply as inventories approach zero. This indicates that the approximation embodied in the basic Holt et al. (1960) model may miss some important aspects of inventory behavior.

8.3. Models with fixed costs

We next consider arguments and evidence that a key shortcoming of the linear quadratic model is that it fails to account for fixed costs facing firms. Blinder (1981), Caplin (1985), Mosser (1988), Blinder and Maccini (1991), and Fisher and Hornstein (1996) all argue that fixed costs of ordering may be very important for understanding the behavior of retail and wholesale inventories as well as manufacturers' materials and supplies. In some environments the aggregation argument presented in Section 3.4 will not apply, and research to date has shown that under certain conditions such fixed costs may lead to (S, s) type of decision rules. In their review article, Blinder and Maccini (1991) recommend that future inventory research concentrate on the (S, s) model. This will require resolution of difficult problems of aggregation, perhaps partly through the use of simulations [Lovell (1996)]. While the results look suggestive at the level of a single-product firm, the implications for a multi-product firm, let alone for an

Ch. 13: Inventories

911

industry or economy, have been harder to obtain because of difficulties of aggregating (S, s) rules. The studies by Bresnahan and Ramey (1994) and Hall (1996) show that fixed costs are an important determinant of production costs in the automobile industry. Bresnahan and Ramey follow some fifty assembly plants on a weekly basis from 1972 to 1983, and uncover important lumpiness in the margins for varying production. Hall studies fourteen assembly plants from 1990 to 1994. Both studies isolate two important methods for varying production, which appear to involve some sort of nonconvex costs. First, they find that complete shut-down of a plant for a week at a time is an important method for temporarily decreasing output rates. Second, the adding and dropping of extra shifts (each of which doubles or halves production) are an important source of output variability, and appear to involve fixed costs and lumpiness of production levels. Thus, costs in the automobile industry deviate from the linear quadratic production smoothing model in two important ways. First, there appear to be fixed costs of adjusting production, not convex costs as postulated in the production smoothing model. Second, the lumpiness of the margins, accompanied by the fixed costs, leads to a nonconvex cost function. It is important to point out that the nonconvexity is due not to declining marginal costs [as Ramey (1991) originally posited], but rather to the existence of large fixed costs at key points in the cost curve. Thus, both the (S, s) literature and the limited amount of factory evidence available suggests that fixed costs may be very important. Furthermore, the types of fixed costs highlighted can potentially explain both the procyclicality of inventories and the persistence of the inventory-sales relationship. For example, the lumpiness of the shifts margin in the automobile industry can explain why an increase in sales might lead to a more than proportional increase in production. Also, the importance o f fixed adjustment costs can explain why significant deviations in the inventory-sales relationship are allowed to occur before production responds. It is not yet clear, however, how general are the results from the automobile industry. And more generally it is not well understood how and whether fixed costs at the plant or firm level translate into industry- or economy-wide behavior. Thus, the role of these types of fixed costs in explain aggregate inventory fluctuations remains an important topic for future study. 8.4. The value o f more data

Finally, we discuss how the addition of more data may help narrow the estimates obtained from the linear quadratic model, as well as shed light on the unobserved cost shocks. We will argue that there are several available sources of data that have the potential to clear up ambiguities. One possible explanation for the range of estimates obtained from the production smoothing model is the data are not sufficient for distinguishing the relative values of the parameters. One way to glean more information from macroeconomic data is to use information contained in prices, something done in a handful of papers

912

V.A. Ramey and K.D. West

including Eichenbanm (1984), Blanchard and Melino (1986) and Bils and Kahn (1996). Pindyck's (1994) results using futures prices provides additional evidence of the information contained in prices. A second possible use of new data is to measure the stochastic variation in cost. As Table 11 indicates, a number of authors have experimented with several observable cost shifters, but generally do not find effects. Another possible source of cost shocks that has been studied in a few papers is credit conditions. We remarked in Section 2.2 that Kashyap et al. (1994) and Carpenter et al. (1994, 1998) still find persistence in the inventory-sales relationship after including measures of credit conditions. But they also regularly find that credit conditions affect inventory holding behavior of small firms, across various specifications. If these credit conditions are serially correlated (which they are likely to be), and if small firms are important enough to substantially affect industry- and economy-wide aggregates, credit conditions may ultimately help explain our two stylized facts. Finally, we advocate more plant and firm-level studies, although gathering such data requires substantial work. Schuh (1996), for example, uses panel data from the M3LRD to calibrate biases from aggregation. And consider Holt et al.'s (1960) study o f six firms ranging from a paint producer to an ice cream maker and Kashyap and Wilcox (1993) and Bresnahan and Ramey's (1994) studies of the automobile industry. They use not only firm-level data on production, inventories and sales, but also company reports and industry press, which provide valuable insights into the cost structure facing firms. For example, Bresnahan and Ramey (1994) were able to categorize the cause of every plant shutdown using information from Automobile News, which chronicled drops in demand and cost shocks such as strikes and model year change-overs.

9. Conclusions

We conclude by briefly reiterating several points we have made in this chapter. We began by asserting that inventories are a useful resource in business cycle research. The theoretical dependence of the comovements o f sales, production, and inventories on important parameters such as the slope of marginal costs, and on the nature of the underlying shocks, indicates that inventory models can in principle be used to identify these important macroeconomic features. The two stylized facts we highlight - the procyclicality of inventories and the persistence of the inventory-sales relationship are intimately linked to other aspects of business cycle fluctuations. Thus, inventory movements have valuable business cycle information. To consider explanations for the two facts, we presented a linear quadratic model. We showed that the model can rationalize the two facts in a number of ways, but focused on two stylized explanations have the virtue of relative simplicity and support from a number of papers. Both assume that there are persistent shocks to demand for the good in question, and that marginal production cost slopes up. The first explanation assumes as well that there are highly persistent shocks to the cost of production. The second

Ch. 13: Inventories

913

assumes that there are strong costs of adjusting production and a strong accelerator motive. Our review o f the empirical evidence, however, indicates that the range of estimates of key parameters and of the relative importance of cost versus demand shocks is too wide to allow us to endorse one of the two or some third explanation. But while the literature has not reached a consensus, it has identified mechanisms and forces that can explain basic characteristics of inventory behavior. We believe that several research strategies, and use of different data, promise to continue to improve our understanding of inventory movements and therefore of business cycle fluctuations.

Appendix A. Data Appendix Data sources for annual G7 data: all data on inventory changes were obtained from International Financial Statistics, mostly from the 1996 CD-ROM. From the CD-ROM, we obtained nominal and real GDP and the nominal change in aggregate inventories. The GDP deflator was used to convert the inventory change from nominal to real. For the Canada, France, the UK and the USA, 1955 data were available to compute AQ and AS in 1956. For all other countries an observation was lost in computing the initial AQ and AS. Additional sources were used for West Germany and Italy. West Germany: (a) 1957-1978: the IFS data used in West (1990a), rebenchmarked to a 1990 from a 1980 base, and output measured with GNP instead of GDR (b) 19791994: in both the CD-ROM and in recent hardcopy versions of IFS, the figures on the annual change looked suspicious: they were uniformly positive and large relative to 1957-1958, bore no obvious connection to the figures on the levels reported in the Statisches Bundesamt publication cited below, and in recent years bore no obvious connection to the average of the reported quarterly figures. So for 1979-1990, we used the annual change reported in the hardcopy IFS, obtaining a given year's data from the April issue three years later (e.g., the 1990 figure came from the April 1993 issue of IFS). (For 1980 we used the May 1983 issue, because the April 1983 issue was missing.) For 1991-1994, we used the average of the quarterly figures from the April 1995 hardcopy version of IFS. Italy: 1993 and 1994 real GDP came from OECD Economic Surveys, Italy, 1996, rebenchmarked to a 1990 from a 1985 base. We checked the US data against the Department of Commerce's 1992 chain-weighted NIPA data, and while there were notable differences, overall the two perhaps were tolerably close: the correlation between inventory investment as constructed here and the Department of Commerce measure was 0.96. Data sources for non-US data on inventory levels: Canada: private communication from Statistics Canada gave a nominal 1995:IV inventory figure for all nonfmancial industries of 140.8 billion Canadian dollars, which we deflated with the GDP deflator. West Germany: Statisches Bundesamt, Volkswirtschafiliche Gesamtrechnungen,

914

V.A. Ramey and K.D. West

Table 3.2.9. Agriculture (line 2) was subtracted from total (line 1), and the result was deflated by the GDP deflator. Japan: Economic Planning Agency, Annual Report on National Accounts, 1997, table on "Closing Stocks". The nominal figure for total stocks was deflated by the GDP deflator. United Kingdom: Office for National Statistics, United Kingdom National Accounts: The Blue Book, 1996, Table 15.1. Agriculture (series DHIE) and government (AAAD) were subtracted from total (DHHY), and the result was deflated by the GDP deflator. Data sources for sectoral distribution of US inventories: broad sectoral categories were obtained from Citibase, and manufacturing inventories by stage of processing were obtained from the BEA. The stage of processing inventories were converted from monthly to quarterly data by sampling the last month of the quarter.

Appendix B. Technical Appendix This appendix discusses the following: (1) solution of the model 23; (2) Computation of E(Q 2 - S 2) in Table 4; (3) Estimation of 0 in Table 5; (4) the social planning approach to derivation of the first-order conditions. B. 1. Solution o f the model

We assume throughout that al, a2, g > 0 and a0, a3/> 0. See Ramey (1991) for solutions when al < 0. We begin by working through in detail the solution discussed in Section 4, when a0 = 0 and the forcing variables follow first-order autoregressions. For simplicity, for the most part we set ~ ---- 0 as well. Thus Uot =Uct [see Equation (3.2)], Et-luct =(&u~t-l and Et 1Udt = (9,JUdt-l. To insure a unique stable solution, we assume that either (B.la) or (B.lb) holds: g > a2a3(1 - a3), a2a3(1 - a3) > g >

(B.la) 2(1 + b 1)ala2(a3 - 0.5)(a3 - b(1 + b) -1) a2 +2al(1 + b 1)

(B.lb)

Note that the right-hand inequality in (B. l b) follows if a3 falls outside (b(1 + b) -I , 0.5), a narrow range when b ~ 1. There will also be a stable solution when a2a3(1 - a 3 ) = g . But to allow us to divide by g - a2a3(1 - a 3 ) at certain stages in the derivation, we rule this out for conciseness.

23 We thank StanislavAnatolyevfor assistancein the preparationof this part of the TechnicalAppendix.

915

Ch. 13.. Inventories

When a0 = 0, differentiating the objective function (3.1) with respect to St gives Pt - Et[al Qt - a2a3(Ht-1 - a3St) + Uct] = 0.

Use P t = - g S t + U d t , (B.2) becomes

(B.2)

and our tentative assumption that Uct=Uot.

Qt=St+AHt,

- a l H t - (al + a2a~ + g ) S t + (al + a2a3)Ht-1 - Uct + Udt = 0.

(B.3)

al St = - ~ H t

(B.4)

al + a2a3 . + ~ - - H t

1

l-~Uct+

1 ~Udt'

d ---- (al + a2a~ + g).

Use (B.4) and (B.4) led one period to substitute out for St and St+l in H t ' s first-order condition (3.3) (with a0 =- 0). After some rearrangement, the result may be written 0 = bEtHt+i - (1 + b + m ) H t + H t 1 + gtlcuct + grid

Udt

bEtHt+À - ~lHt + H t - I + gHcUct + gHdUdt, m=

a2[b(al + g) + ala3(1 - b)] a l [ g +a2a3(a3 - 1)]

'

(B.5)

g + a2a 2 - bOc[g + a2a3(a3 - 1)] gHc =-

grid --

al [g + a2a3(a3 - 1)]

al - bq~d(al + a2a3) a l [ g + a2a3(a3 - 1)]'

It can be shown that inequality (B. 1) guarantees that there is exactly one root less than one to the polynomial bx 2 - t/x + 1 = 0.

(B.6)

Call this root ~H, where /2]

if

~/>0,

0 . 5 b - 1 [ ~ l + ( t 1 2 - 4 b ) 1/2]

if

~/<0.

=0.5b-l[r]-(r]2-4b) ~z4

(B.7)

Using techniques from Hansen and Sargent (1980) it follows that the solution to problem (B.5) is H t = ~ H H t - 1 + f HcUct + f Hd Udt, f Hc =-- [YgH/(1 --b~14Oc)]gHc,

f Hd =~ [~H/(1 --bYgHOd)]gHd.

(B.8)

Upon substituting Equation (B.8) into Equation (B.4) and rearranging, we obtain St = ~ s H t - I + f scUct + f sdUdt, fSc =

1 + alfHc 2 ' al + a2a 3 + g

~S =~

al(1 - ~ H ) + a2a3 al + a2a 2 + g

(B.9)

1 -- a l f H d f S d =-

al + a2a~ + g

•

916

V.A. Ramey and K.D. West

Let L be the lag operator, "adj" the adjoint of a matrix. From Equations (B.7) and (B.8), a representation for the bivariate (Ht, H t - O S t f =-- Y t process is Yt = AYt-I +BUt,

Jr. A ----

¢C14 - 0¢Cs

0

fH BI ~

0 '

Yt = (I-AL)-IBUt

-

file--

c0 f Sc

fHd f Hd -- O f sd

adj ( I - A L ) ~ . ~

(B.lO)

t~t-/t

1I - A L l Yt : a d j ( I - A L ) B U t .

This m a y be used to solve for the univariate process for H t - OSt, which is (1 - ¢CHL)(Ht - OSt) = ( f Hc - O f so) uct + O ( : V H f Sc -- Y f S f Hc)Uct-1

03.11)

+ ( f H d -- O f s d ) Udt + O(¢gHfSd -- ~ S f H o ) U d t - 1 .

Suppose that Udt follows a random walk, so that Cd = 1 and ( f H d - O f s d ) U d t = ( f H d -- O f s d ) ( U d t 1 + edt). Upon using the definition of 0 in Equation (3.5), and in light o f the quadratic equation used to obtain ZrH, tedious manipulations reveal that ( f Hd -- O f sd) + O ( : r H f Sd -- : r S f HO) = 0. It follows that Od = 1

:=k

(1 -- : r H L ) ( H t - OSt) = ( f n c - O f sc) uct + O(¢~mf Sc -- ¢ ~ S f Hc) Uc,-I + ( f e o -- O f sd) edt =- mocUct + mlcUct-i + mOdedt

(1 -

:rilL)(1 - (bcL)(Ht - OSt) = v¢ - moce~t + m1~e~t-1 + m0dedt - OcmOdedt 1 ~ MA(1).

(B.12) Thus, when Od = 1, H¢ - OSt N ARMA(2, 1) with autoregressive roots eVIl and 0c. Now suppose that a ¢ 0, so that Uct = "aIWt + Uct, with E t a Wt = q)wWt 1. Algebra similar to that used above may be used to conclude that the first-order condition (B.5) and the decision rules (B.8) and (B.9) become /

0 = E t ( b H t + l - r]Ht + H t - t + g , w W t +gHeUct + gmdUdt), H t = Z~HHt 1 + f ~ w W t

+ f HcUct + f HdUdt,

S t = YgsHt-1 + f s w W t + f scuct + f Sd Udt, gHw ~

(B.13)

( g + a 2 a 2 ) I -- b [ g + a2a3(a3 - 1)]q~/w ~, al [ g + aza3(a3 - 1)]

f H w ----:rH(I -- bZCHq)/w)-1 gHw,

f S w --

"a + a l f i-lw 2

al + a2a 3 + g

Ch. 13:

Inventories

917

with the other parameters unchanged. It follows that when ~bd= 1 (1 - ~ , L ) ( H t - OSt) = ( f g w -- O f s w f W t + O(~HfSw -- Y ~ S f H w f W t 1 + (fI4c -- Ofsc)Uct + O ( ~ g f S c -- YgSfHc)Uct-I + (fHd -- Ofsd)edt.

(1 - :vHL)(Ht - OSt - a' Wt) = (fh'w - Ofsw - a ) ' W t + [O(gHfsw - arsfHw) + YgHa]'Wt-1 + ( f i l e -- Ofsc) Uct + O(~14fSc -- ~ S f H c ) Uct t + OCHd -- Ofsd) __

edt

!

= mow Wt + [ O ( ~ H f s w - arsf14w) + :rHa]'Wt_l + mo~uct + ml~Uct i + modedt. (B.14) When q~w = I and Wt = Wt 1 +ewt, it may be shown that mow + O ( : r H f S w - - : r S f , w)+ ZCHa = 0. Then (B.14) implies (1

-

x14L)(Ht-OSt

--

a ' W t ) - --

(B.15)

m o' w e w t + mocUct + m l c U c t - 1 + mOdedt.

Now allow ao ~ 0, as well as arbitrary autoregressive processes for Wt, Uct, and Udt. When a0 ~ 0, the first-order condition for St (B.2) becomes -gSt

+ Udt -

Et[(aoAQt - baoAQt+l ) +

alQt

- a2a3(Ht-l

- a 3 S t ) + U c t ] = O,

(B.16) where Pt = - g S t + Udt has been used to substitute out for Pt. The solution is most concisely derived if one uses St = Q t - A t t t to remove the St from the first-order condition (equivalently, if one makes Qt and H t rather than St and H t the choice variables). After so doing, Equations (B.16) and (3.3) may be written Et[bAtlXt+l + A o X t +A1Xt-1 +BoUt +BlUr+l] = O, X t = (Ht, Q t f .

(B.17)

The (2×1) vector Ut is (Udt, U c t f . The matrices A1, Ao and Bo and B1 are (2 × 2), with

Ao =A 1 =--

(1 + b)g + a2a~ + ba2(1 - a3) 2 - ( g + a2a 2)

I

-[g-a2a3(1-a3)] [ g - a2a3(1 -

0

~' 0

Vt~CVt.

--a0

Bo =

B1 =

1

--

'

I°:l 0

" (B.18) Suppose that Vt ~ (uet, Udt, W~) f N AR(p) (possibly with unit autoregressive roots), Et 1Vt =q)lVt l + ' " . + ~ p V t ~ . (There may be many zeros in the q)i if there is lots more dynamics in say Wt than in either uct or Ud¢). Note for the future that Ut = 10 01

a3)]

- ( g + a2a23) g + a~ + a2 a2 + (1 + b)ao '

(B.19)

918

V.A. Ramey and K.D. West

Guess a solution of the form Xt

=

(B.20)

R Y t - l -]- GoVt + ' . . + Gp 1Vt~+l =- RXt_~ + G(L)Vt.

In Equation (B.20), the Gi are 2 × (2 + dimension o f Wt). In Equation (A.17), use (B.20) led once to substitute out for EtXt+l, and then substitute out for X t using (B.20). For condition (B.17) to hold, we must have (bAil R2 + AoR + A l ) X t - l = 0,

(B.21a)

bA'1 { R G ( L ) V t + [EtG(L)Vt+I]} + AoG(L)Vt + B o C V t + B~ CEt Vt+l = O.

(B.Zlb) Equation (B.21a) requires bA'l R2 +AoR+A1 =0. Given model parameters, and thus knowledge o f A1 and A0, this equation may be used to solve for a stable matrix R. (The matrix equation will have multiple solutions, just as does the scalar quadratic Equation (B.5). Restrictions similar to those in (B. 1) will insure that there is a unique stable solution.) It may help to note that the solution matches the earlier one if we reimpose the assumption that there are no costs o f adjusting production. With a0 = 0, the second column o f A1 is zero, from which it follows that the second column o f R is zero. Further, R(1, 1) ~ rl 1 = JrH, r21 = JrH + ;rs - 1 for JrH and ;rs defined in Equations (B.7) and (B.9). Whether or not a0 = 0, once R is recovered from Equation (B.21 a), Equation (B.2 lb) may then be used to solve for the Gi. For example, suppose that Wt and the shocks are first-order autoregressive, so that p = l : q~l is block diagonal with ~bc in its (1, 1) element, Cd in its (2, 2) element and q~w in the block in its lower right hand corner. Then Equation (B.21b) implies bA'I (RGo + Goq~l) + AoGo + BoC + B1C ~ I = 0,

(B.22)

which can be used to solve linearly for Go in terms o f the model parameters and q~l. Return to the solution (B.20). Let R = [r/j]. Transform from a solution in (Ht, Qt)' to one in (Ht, St)' =- Zt, using Qt = St + A H t . The result is Zt = 111Zt-I + H2Zt-2 + Fo Vt + • " • + Fp 1Vt p+l,

//1 =

rll +r12 1 +r22+r21 - ( r l l +r12)

Fi = MGi,

M =

lO 1 1

r12 r22-r12

112 = '

-r12 -(r22-r12 )

0 0 '

"

(B.23) Thus St 2 does not appear in the reduced form, and the first column o f / / 2 is the negative o f the second column o f H~. To repeat an earlier point: if ao = 0, then rl2=r22 =0, rl~ = ~ H , and 1 + r 2 ~ - r l l = ~ s . Finally, suppose we use Equation (B.23) to derive the autoregressive process for (Ht, H t - OSt)', and then solve for the univariate process for H t - OSt, using the method

Ch. 13.

919

Inventories

that led to Equation (B.11). When a0 s 0 , the relevant determinant [the analogue of ] I - A L I in Equation (B.10)] is a second-order polynomial in the lag operator. Specifically, for/'/1 defined in Equation (B.23), let II1 = [~/j]. Then this second order lag polynomial is 1 - (Jr11 + 3g12)L+ (3"gl13"g22-}-,7112 -- gg213"gi2)L 2.

(B.24)

The roots to this polynomial are called ~l and :r2. Equation (B.22) may be used to show that the moving average component of H t - OSt is first order when q)c = 0 and Od = 1.

B.2. Computation of E(Q 2 - S 2) The computation of E ( Q 2 - S 2) follows West (1988). In the stationary case, and ignoring deterministic terms, E(Q 2 - S ] ) v a r ( A H t ) = 2EStAHt = 2cov(S, AHt) = 2 cov[(ASt + ASt-1 + ASt 2 - t - ' ' '), z~LIt] = 2[cov(ASt, AHt) + cov(ASt_l, AHt) + - . . ] . It may be shown that even in the case S~I(1): (1) under regularity conditions, Y'~-o cov(ASt4, AHt) is finite and may be consistently estimated; (2) the implications of the model for the sign of E(Q 2 - S 2) are the same as those for var(Q)-var(S) when St (and Ht) are I(0) [see the working paper version of West (1990b)]. Let "~j be an estimate of cov(ASt_j, AHt), which we computed as ~j = T -t ~ t r=j +1 Ast-jAht, where As and Ah are residuals produced by demeaning or detrending. When St ~I(1), consistent nonparametric estimation of ~ 0 cov(ASt_j, AHt) involves computing }-~ii' ~j and letting m ~ oo as T ~ ec. In the computations in Table 4, we let the number of lags m be 5 for the full samples, 4 for post-1973 samples.

B.3. Estimation of~O The cointegrating parameters were estimated using dynamic OLS, as advocated by Stock and Watson (1993). We regressed inventories on a constant and sales (with no deterministic trend), and included current plus up to two years (or eight quarters) of leads and lags of the change in sales. We successively eliminated variables with t-statistics less than 1.65 in absolute value. Heteroskedasticity and autocorrelation consistent standard errors were computed using a Bartlett kernel with two years (or eight quarters) of lags.

B. 4. Social planning derivation of the model's first-order conditions The area under the inverse demand curve is just the integral of the inverse demand (4.1), and is given by

fo

CX~(udt gXt) dXt -

-

UdtS, - 0.5gS~.

(B.25)

The area under the supply curve is equal to the cost function presented as part of Equation (3.1). Thus, the competitive equilibrium solution is equivalent to the solution

920

V..A. Ramey and K.D. West

to the following social planner problem that maximizes the difference between these two functions: MaxH,s V = E, ~_~ b j IUdt+jSt+j - 0.5gSet+j j-O O.5aoAQ2±/ - O.5al Q~+j - O.5a2 (Ht +j-i - a3St +j)2 - U c t +jQt +j] 03.26) subject to the inventory identity that Qt +j = St +j + A H t +j. The first-order c o n d i t i o n for inventories is identical to the one o b t a i n e d from the firm-level problem. The first-order c o n d i t i o n for sales is identical to the one obtained w h e n the industry d e m a n d curve is substituted into the firm-level first-order c o n d i t i o n for sales.

References Abramowitz, M. (1950), Inventories and Business Cycles (National Bureau of Economic Research, New York). Allen, D.S. (1995), "Changes in inventory management and the business cycle", Federal Reserve Bank of St. Louis Review 77:17-26. Beaulieu, J.J., and J.A. Miron (1992), "A cross country comparison of seasonal cycles and business cycles", The Economic Journal 102:772-788. Belsley, D. (1969), Industry Production Behavior: The Order-Stock Distinction (North-Holland, Amsterdam). Bils, M., and J.A. Kalm (1996), "What inventory behavior tells us about business cycles", manuscript (University of Rochester). Blanchard, O.J. (1983), "The production and inventory behavior of the American automobile industry", Journal of Political Economy 91:365-400. Blanchard, O.J., and A. Melino (1986), "The cyclical behavior of prices and quantifies: the case of the automobile market", Journal of Monetary Economics 17:379-408. Blinder, A.S. (1981), "Retail inventory behavior and business fluctuations", Brookings Papers on Economic Activity 1981(2):443-505. Blinder, A.S. (1986a), "Can the production smoothing model of inventory behavior be saved?", Quarterly Journal of Economics 101:431-453. Blinder, A.S. (1986b), "More on the speed of adjustment in inventory models", Journal of Money, Credit and Banking 18:355-365. Blinder, A.S, and L.J. Maccini (1991), "Taking stock: a critical assessment of recent research on inventories", Journal of Economic Perspectives 5:73-96. Bresnahan, T.E, and V.A. Ramey (1994), "Output fluctuations at the plant level", Quarterly Journal of Economics 109:593-624. Caplin, A.S. (1985), "The variability of aggregate demand with (S, s) inventory policies", Eeonometrica 53:1395-1409. Carlson, J.A., and W. Wehrs (1974), "Aggregate inventory behavior", in: G. Horwich and E Samuelson, eds., Trade, Stability and Growth: Essays in Honor of Lloyd A. Metzler (Academic Press, New York). Carpenter, R.E., and D. Levy (1998), "Seasonal cycles, business cycles and the comovement of inventory", Journal of Money, Credit and Banking 30:331 346.

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Carpenter, R.E., S.M. Fazzari and B.C. Petersen (1994), "Inventory investment, internal-finance fluctuations, and the business cycle", Brookings Papers on Economic Activity 1994(2):75-138. Carpenter, R.E., S.M. Fazzari and B.C. Petersen (1998), "Financing constraints and inventory investment: a comparative study using high frequency data", Review of Economics and Statistics 80:513-519. Cecchetti, S.G., A.K. Kashyap and D.W Wilcox (1997), "Interactions between the seasonal and business cycles in production and inventories", American Economic Review 87:884-892. Childs, G.D. (1967), Inventories and Unfilled Orders (North-Holland, Amsterdam). Christiano, L.J. (1988), "Why does inventory investment fluctuate so much?", Journal of Monetary Economics 21:247-280. Christiano, L.J., and M.S. Eichenbaum (1989), "Temporal aggregation and the stock adjustment model of inventories", in: T. Kollintzas, ed., The Rational Expectations Inventory Model (Springer-Verlag, New York) 70-109. Durlauf, S.N., and L.J. Maccini (1995), "Measuring noise in inventory models", Journal of Monetary Economics 36:65-90. Eichenbaum, M. (1984), "Rational expectations and the smoothing properties of finished goods", Journal of Monetary Economics 14:71-96. Eichenbaum, M. (1989), "Some empirical evidence on the production level and production cost smoothing models of inventory investment", American Economic Review 79:853-864. Fair, R.C. (1989), "The production smoothing model is alive and well", Journal of Monetary Economics 24:353070. Feldstein, M.S., and A.J. Auerbach (1976), "Inventory behavior in durable goods manufacturing: the target adjustment model", Brookings Papers on Economic Activity 1976(2):351-396. Fisher, J.D.M., and A. Hornstein (1996), "(S, s) inventory policies in general equilibrium", working paper WP-96-24 (Federal Reserve Bank of Chicago). Fuhrer, J.C., G.R. Moore and S. Schuh (1995), "Estimating the linear-quadratic inventory model: maximum likelihood versus generalized method of moments", Journal of Monetary Economics 35: 115-157. Fukuda, S.-i., and H. Ternyama (1988), "Some international evidence on inventory fluctuations", Economics Letters 28:225-230. Galeotti, M., L. Guiso, B. Sack and E Schiantarelli (1997), "hwentories, production smoothing and the shape of the cost function", manuscript (Universit~t degli Studi di Bergamo). Granger, C.WJ., and T.H. Lee (1989), "Investigation of production, sales and inventory relationships using multicointegration and non-symmetric error correction models", Journal of Applied Econometrics 4:S145-S159. Hall, G. (1996), "Non-convex costs and capital utilization: a study of production and inventories at automobile assembly plants", manuscript (Federal Reserve Bank of Chicago). Haltiwanger, J.C., and L.J. Maccini (1989), "Inventories, orders, temporary and permanent layoffs: an econometric analysis", Carnegie-Rochester Series on Public Policy 30:301-366. Hansen, L.P, and T.J. Sargent (1980), "Formulating and estimating dynamic linear rational expectations models", Journal of Economic Dynamics and Control 2:7-46. Hansen, L.E, and K.J. Singleton (1982), "Generalized instrumental variables estimation of nonlinear rational expectations models", Econometrica 50:1269-1286. Hester, D.A. (1994), "Changing relations between inventories and bank loans", in: R. Fiorito, ed., Inventory Cycles and Monetary Policy (Springer-Verlag, Berlin) 125-147. Holt, C.C., E Modigliani, J.E Muth and H.A. Simon (1960), Planning Production, Inventories and Work Force, (Prentice Hall, Englewood Cliffs, NJ). Humphreys, B.R., L.J. Maccim and S. Schuh (1997), "Input and output inventories", manuscript (Federal Reserve Bank of Boston). Jorda, O. (1997), "Random-time aggregation in partial adjustment models", manuscript (University of California at Davis).

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Kahn, J.A. (1987), "Inventories and the volatility of production", American Economic Review 77: 667-680. Kahn, J.A. (1992), "Why is production more volatile than sales? Theory and evidence on the stockoutavoidance motive for inventory holding", Quarterly Journal of Economics CVII:481-510. Kashyap, A.K., and D.W Wilcox (1993), "Production and inventory control at the General Motors Corporation during the 1920s and 1930s", American Economic Review 83:383-401. Kashyap, A.K., O.A. Lamont and J.C. Stein (1994), "Credit conditions and the cyclical behavior of inventories", Quarterly Journal of Economics CIX:565-592. Kollintzas, T. (1989), "The linear rational expectations equilibrium inventory model: an introduction", in: T. Kollintzas, ed., The Rational Expectations Equilibrium Inventory Model (Springer-Verlag, New York) 1-32. Kollintzas, T. (1995), "A generalized variance bounds test with an application to the Holt et al. inventory model", Journal of Economic Dynamics and Control 19:59-89. Krane, S.D. (1994), "The distinction between inventory holding and stockout costs: implications for target inventories, asymmetric adjustment, and the effect of aggregation on production smoothing", International Economic Review 35:117-136. Krane, S.D., and S.N. Braun (1991), "Production smoothing evidence from physical product data", Journal of Political Economy 99:558-581. Lai, K.S. (1991), "Aggregation and testing of the production smoothing hypothesis", International Economic Review 32:391-403. Lovell, M.C. (1961), "Manufacturers' inventories, sales expectations, and the acceleration principle", Econometrica 29:293-314. Lovell, M.C. (1993), "Simulating the inventory cycle", Journal of Economic Behavior and Organization 21:147-179. Lovell, M.C. (1994), "Researching inventories: why haven't we learned more?", International Journal of Production Economics 35:33-41. Lovell, M.C. (1996), "Macroeconomic implications of S, s versus accelerator finished goods inventory strategies", International Journal of Production Economics 45:55-64. Maccini, L.J., and R.J. Rossana (1981), "Investment in finished goods inventories: an analysis of adjustment speeds", American Economic Review 71:17-22. Maccini, L.J., and RJ. Rossana (1984), "Joint production, quasi-fixed factors of production, and investment in finished goods inventories", Journal of Money, Credit and Banking 16:218-236. McManus, D.A., J.C. Nankervis and N.E. Savin (1994), "Multiple optima and asymptotic approximations in the partial adjustment model", Journal of Econometrics 62:91-128. Metzler, L.A. (1941), "The nature and stability of inventory cycles", The Review of Economics and Statistics XXIII:113-129. Miron, J.A., and S.P. Zeldes (1988), "Seasonality, cost shocks and the production smoothing model of inventories", Econometrica 56:877-908. Mosser, P.C. (1988), "Empirical tests of the (S, s) model for merchant wholesalers", in: A. Chikan and M. Lovell, eds., The Economics of Inventory Management (Elsevier, Amsterdam) 261-284. Pindyck, R.S. (1994), "Inventories and the short-rtm dynamics of commodity prices", The RAND Journal of Economics 25:141-159. Ramey, V.A. (1989), "Inventories as factors of production and economic fluctuations", American Economic Review 79:338-354. Ramey, V.A. (1991), "Nonconvex costs and the behavior of inventories", Journal of Political Economy 99:306-334. Rossana, R.J. (1990), "Interrelated demands for buffer stocks and productive inputs: estimation for two digit manufacturing industries", Review of Economics and Statistics 72:19-29. Rossana, R.J. (1993), "The long-run implications of the production smoothing model of inventories: an empirical test", Journal of Applied Econometrics 8:295-306.

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Rossana, R.J. (1995), "Technology shocks and cointegration in quadratic models of the firm", International Economic Review 36:5-17. Rossana, R.J. (1998), "Structural instability and the production smoothing model of inventories", Journal of Business and Economic Statistics 16:206-215. Rotemberg, J.J., and G. Saloner (1989), "The cyclical behavior of strategic inventories", Quarterly Journal of Economics 104:73-98. Sargent, T.J. (1979), Macroeconomic Theory (Academic Press, New York). Schuh, S. (1996), "Evidence on the link between firm-level and aggregate inventory behavior", Finance and Economics Discussion Paper No. 1996-46 (Federal Reserve Board of Governors). Stengel, R.E (1986), Stochastic Optimal Control: Theory and Applications (Wiley, New York). Stock, J.H., and M.W. Watson (1993), "A simple estimator of cointegrating vectors in higher order integrated systems", Econometrica 61:783-820. Surekha, K., and M. Ghali (1997), "The speed of adjustment and production smoothing", manuscript (Western Washington University). West, K.D. (1983), "Inventory models and backlog costs", Ph.D. Thesis (Massachusetts Institute of Technology). West, K.D. (1986), "A variance bounds test of the linear quadratic inventory model", Journal of Political Economy 94:374401. West, K.D. (1988), "Order backlogs and production smoothing", in: A. Chikan and M. Lovell, eds., The Economics of Inventory Management (Elsevier, Amsterdam)305-318. West, K.D. (1990a), "Evidence from seven countries on whether inventories smooth aggregate out-put", Engineering Costs and Production Economics 19:85-90. West, K.D. (1990b), "The sources of fluctuations in aggregate inventories and GNP", Quarterly Journal of Economics CV:939 972. West, K.D. (1992a), "A comparison of the behavior of US and Japanese inventories", International Journal of Production Economics 26:115-222. West, K.D. (1992b), "Sources of cycles in Japan, 1975 1987", Journal of the Japanese and International Economies 6:71-98. West, K.D. (1995), "Inventory models", in: M. Pesaran and M. Wickens, eds., Handbook of Applied Econometrics, vol. I, Macroeconometrics (Basil Blackwell, Oxford) 188-220. West, K.D., and D.W. Wilcox (1994), "Some evidence on the finite sample behavior of an instrumental variables estimator of the linear quadratic inventory model", in: R. Fiorito, ed., Inventory Cycles and Monetary Policy, (Springer-Verlag, Berlin) 253-82. West, K.D., and D.W Wilcox (1996), "A comparison of alternative instrumental variables estimators of a dynamic linear model", Journal of Business and Economic Statistics 14:281-293. Wilkinson, M. (1989), "Aggregate inventory behavior in large European economies", European Economic Review 33:181-194.

Chapter 14

RESUSCITATING REAL BUSINESS CYCLES * ROBERT G. KING University of Virginia and NBER SERGIO T. REBELO Northwestern University and NBER

Contents Abstract Keywords 1. Introduction 2. Stylized facts o f a g g r e g a t e activity 2.1. Measuring business cycles with the HP filter 2.2. Some stylized facts of US business cycles 2.3. Some stylized facts of economic growth 2.4. Implications of stylized facts 3. The basic neoclassical m o d e l 3.1. The structure 3.2. Steady-state growth and transforming the economy 3.3. Optimal capital accumulation 3.4. The nature of the steady state 3.5. Transitional dynamics 3.6. The (Un)importance of capital formation 3.7. Constructing dynamic stochastic models 4. The Real Business C y c l e s h o c k 4.1. The driving process 4.2. Calibrating and solving the model 4.3. Business cycle moments 4.3.1. Simulations of US business cycles 4.4. The importance of capital accumulation 4.5. Early successes and criticisms

928 928 929 931 932 934 941 941 942 942 944 946 947 948 950 951 952 952 953 956 958 960 960

* We benefited from the comments of the editors as well as from those of Rui Albuquerque, Robert Barro, Marianne Baxter, Satyajit Chatterjee, Aubhik Khan, Daniele Coen Pirani, Henry Siu, Julia Thomas, and Michelle Zaharchuk. Dorsey Farr provided detailed comments and excellent research assistance. Support from the National Science Foundation is gratefully acknowledged. Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor and M. Woodford © 1999 Elsevier Science B.V. All rights reserved 927

928 5. The central role o f productivity shocks 5.1. Productivity shocks must be large and persistent 5.2. The influence of productivity persistence 5.3. Why not other shocks? 6. Extensions o f the basic neoclassical model 6.1. The supply of labor 6.1.1. Estimated and assumed labor supply elasticities 6.1.2. Implications of varying the aggregate labor supply elasticity 6.1.3. Modeling the extensive margin 6.2. Capacity utilization 7. Remeasuring productivity shocks 8. Business cycles in a high substitution economy 8.1. Specification and calibration 8.2. Simulating the high substitution economy 8.3. How does the high substitution economy work? 8.4. What are the properties of the shocks? 8.5. How sensitive are the results? 9. Conclusions Appendix A. Dynamic theory A.1. Assumptions on preferences and technology A.2. The dynamic social planning problem A.3. A dynamic competitive equilibrium interpretation A.4. The welfare theorems References

R.G. King and S.T. Rebelo

963 963 969 973 974 974 975 975 976 980 982 984 984 986 986 988 990 993 995 995 997 999 1001 1002

Abstract The Real Business Cycle (RBC) research program has grown spectacularly over the last decade, as its concepts and methods have diffused into mainstream macroeconomics. Yet, there is increasing skepticism that technology shocks are a major source o f business fluctuations. This chapter exposits the basic RBC model and shows that it requires large technology shocks to produce realistic business cycles. While Solow residuals are sufficiently volatile, these imply frequent technological regress. Productivity studies permitting unobserved factor variation find much smaller technology shocks, suggesting the imminent demise o f real business cycles. However, we show that greater factor variation also dramatically amplifies shocks: a RBC model with varying capital utilization yields realistic business cycles from small, nounegative changes in technology.

Keywords macroeconomics, business cycles JEL class~cation: El0, E32

Ch. 14:

Resuscitating Real Business Cycles

929

1. Introduction

Business cycle research studies the causes and consequences of the recurrent expansions and contractions in aggregate economic activity that occur in most industrialized countries. Over the last century, exploration of real business cycles the idea that economic fluctuations are caused primarily by real factors - has itself undergone periods of intense activity and relative dormancy. In the 1920s, real theories played a leading role: economists sought to use new microeconomic tools to learn about the aggregate consequences of shifts in demand and supply of goods and productive factors. However, the Great Depression of the 1930s had a dramatic effect on business cycle research. Economists began to believe that microeconomic theory was an inadequate basis for understanding business cycles. Real factors came to be less stressed, with greater weight given to monetary conditions and the psychology of households and firms. Government management of the economy came to be seen as not only desirable but essential. The rise of Keynesian macroeconomics to a position of orthodoxy in aggregate economics meant that it took half a century for a revival of interest in equilibrium business cycle models. The breakdown in the performance of macroeconometric models in the 1970s and the associated rational expectations revolution pioneered by Lucas (1976) set the stage for a vigorous recovery, since the logic of rational expectations ultimately required general equilibrium analysis 1. Kydland and Prescott (1982) and Long and Plosser (1983) first strikingly illustrated the promise of this approach, suggesting that one could build a successful business cycle model that involved market clearing, no monetary factors and no rationale for macroeconomic management. It is now perhaps hard to recall that this idea was met with surprise and disbelief. By the end of the 1980s there was a central and controversial finding of real business cycle (RBC) research, as this line of work came to be called. Simple equilibrium models, when driven by shifts in total factor productivity measured using Solow's (1957) growth accounting approach, could generate time series with the same complex patterns of persistence, comovement and volatility as those o f actual economies. Writing a survey of RBC research at that time, it was difficult to find sufficient material so we settled for expositing the basic model and forecasting future developments 2. A decade later, our task in this chapter is substantially different: it is time to take stock of a decade of research, to assess criticisms, and to evaluate the health of the research program. The first observation is that it has been a decade of spectacular growth: so many theoretical and empirical articles use the RBC approach that a full bibliography would

Sargent (1982). 2 King,Plosserand Rebelo (1988a,b) surveyedthis area when a single conferenceprogram could include most participants in the RBC research program.

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R.G. King and S.T. Rebelo

likely exhaust the generous page constraint on our contribution to this volume. 3 Real business cycle analysis now occupies a major position in the core curriculum of nearly every graduate program. 4 At a recent NBER conference, a prominent Cambridge economist of the New Keynesian school described the RBC approach as the new orthodoxy of macroeconomics, without raising a challenge from the audience. Continuing on the positive side of the ledger, the methods of the RBC research program are now commonly applied, being used in work in monetary economics, international economics, public finance, labor economics, asset pricing and so on. In contrast to early RBC studies, many of these model economies involve substantial market failure, so that government intervention is desirable. In others the business cycle is driven by shocks to the monetary sector or by exogenous shifts in beliefs. The dynamic stochastic general equilibrium model is firmly established as the laboratory in which modern macroeconomic analysis is conducted. At the same time, there has been increasing concern about the mechanism at the core of standard RBC models: the idea that business cycles are driven mainly by large and cyclically volatile shocks to productivity, which in turn are well represented by Solow residuals as in the provocative study of Prescott (1986). A key difficulty is that typical estimates of Solow residuals imply a probability of technical regress on the order of 40%, which seems implausible to most economists. Recent studies have corrected the Solow residual for mismeasurement of inputs - notably, unobserved effort and capacity utilization - and inappropriate assumptions about market structure. These remeasurements have produced technology shocks with more plausible properties: notably, productivity growth is much less likely to be negative. In effect, these studies have caused productivity shocks to grow smaller and less cyclically volatile by introducing elements which respond sympathetically to economic activity [see, for example, Burnside, Eichenbaum and Rebelo (1996)]. Since the standard RBC model requires large and volatile productivity shocks, this remeasurement research is typically interpreted as indicating that our chapter should be a first draft of the obituary of the RBC research program. In fact, most of our survey does read like a chronicle of the life and death of RBC models. We begin in Section 2 by discussing the measurement of the business cycle as well as reviewing facts about growth and business cycles that have motivated the construction of aggregate models. We next turn in Section 3 to the basic neoclassical model of capital accumulation, as initially developed by Solow (1956) and others for the purpose of studying economic growth but now used more widely in the study of aggregate economic activity. We then celebrate the early victories of the RBC program in Section 4 and discuss early criticisms.

3 One valuable monitor of this ever-expanding literature is provided by Christian Zimmermann's web page (http : //ideas. uqam. ca/QMRBC/index, html). 4 One manifestation of the breadth of this intellectual impact is that Hall (1999) cites Berkeley's David Romer (1996) and Harvard's John Campbell (1994) for authoritative presentations of the basic RBC model.

Ch. 14: Resuscitating Real Business Cycles

931

There has been a substantial amomlt of research on real business cycles, but we organize our discussion around three main points in the next three sections. The central role of large and persistent productivity shocks in the basic model is discussed in Section 5. Important improvements to the basic RBC framework are highlighted in Section 6. The remeasurement of productivity shocks, which has fostered concern about the health of real business cycles, is reviewed in Section 7. In Section 8 we argue that the incipient demise o f the real business cycle is hardly as likely as suggested by conventional wisdom. In fact, rather than weaken the case for a real theory of the cycle, our view is that the recent remeasurement of productivity actually strengthens it. To make this point, Section 8 describes a very simple variant of the basic RBC model, but one that is different on two key dimensions. The economy has indivisible labor, which is one of the key improvements reviewed in Section 6, and has costly variation in capital utilization, which is one of the structural features that makes the standard Solow residual depart from productivity. There is a substantial remeasurement of productivity shocks mandated by this economy: when we do the necessary correction, the standard deviation of productivity growth drops to less than one-fifth of the standard deviation of the growth rate of the Solow residual. Productivity regress occurs in less than 1% of the postwar quarterly observations, even though the measured Solow residual shrinks 37% of the time. Yet these small shocks can generate empirically reasonable business cycles because our model features substantial amplification o f productivity shocks: readily variable capital utilization and a highly elastic labor supply lead small changes in productivity to have major effects on macroeconomic activity. When we drive our model with such small measured productivity shocks, there is a remarkable coincidence between actual US business cycles and simulated time paths of output, consumption, investment, and labor input. The same structural features that lead the Solow residual to dramatically overstate productivity fluctuations also lead the economy to greatly amplify productivity shocks.

2. Stylized facts of aggregate activity In the 1930s, Burns and Mitchell began to document the existence of a remarkable set of business cycle regularities. This research program culminated in their 1946 treatise on Measuring Business Cycles. Burns and Mitchell's arcane methodology led many economists to view their findings with skepticism [see e.g. Koopmans (1947)] and their methods fell into disuse 5. But when Hodrick and Prescott (1980) employed modern time series tools to re-examine the empirical regularities of the business cycle, they

s However,there is some recent interest in these methods. Watson (1994) uses the Burns and Mitchell methodology to contrast inter-war and post-war US business cycles. Simkins (1994) and King and Plosser (1994) show that RBC models produce artificial data that the Burns and Mitchell methods would recognize as having similar characteristics to US data.

932

R. (7. King and S.T. Rebeto

found the Burns-Mitchell facts intact, lurking underneath almost half a century of accumulated dust. As stressed by Lucas (1977), the finding that "business cycles are all alike" suggested that the nature o f macroeconomic fluctuations does not hinge on institutional factors or country-specific idiosyncrasies, so that one can hope to construct a unified theory of the business cycle. 2.1. M e a s u r i n g business cycles with the H P f i l t e r

Most real quantities, such as US real national output in the top panel o f Figure 1, grow through time. Hence, the statistical measurement o f business cycles necessarily involves some way o f making the series stationary, which is most commonly done by the removal o f a secular trend. In their study o f quarterly post-war US data, Hodrick and Prescott (1980) detrended their variables using a procedure now widely known as the HP filter. In essence, this method involves defining cyclical output y~ as current output Yt less a measure o f trend output yg, with trend output being a weighted average o f past, current and future observations: J Y; = Yt - Yg = Yt - Z ajyt4. j=-j

(2.1)

Figure 1 displays how cyclical output is constructed. In the first panel, the logarithm o f current output is the more variable series and trend output is the smoother series. The HP cyclical component o f output is the dotted line in the second panel, defined from the elements o f the first panel as y~ = Yt - Y t g except that we have multiplied by 100 so that cyclical output is a percentage 6. Aggregate output displays business cycles in that there are alternating periods o f high and low output, but these episodes are of unequal duration and amplitude. To see how the cyclical output measure produced by the HP filter compares with those from other detrending methods, we can look at the second and third panels of

6 The HP filter is derived by solving the following minimization problem: min

{(Yt _yg)2 + it [(yg+, yg)_ (yg _ygl)]2}. t=l g oc

{y, },=0 For quarterly data, the standard value chosen for the smoothing parameter it is 1600. When it = oo the solution to this problem is a linear trend, while with it = 0 the trend coincides with the original series. In a finite sample context, the weights aj in Equation (2.1) depend on the length of the sample, so that the text expression is a simplification. King and Rebelo (1993) discuss additional properties of this detrending procedure, including derivation of filter weights and frequency response fimctions for the case in which the sample is infinitely large. They establish that the HP filter has strong detrending properties, in the sense that it can make stationary series up through four orders of integration.

Ch. 14: Resuscitating Real Business Cycles 8.8 -

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934

R.G. King and S.T. Rebelo

Figure 1. First, if we simply subtract a linear trend from the log o f output, the resulting business cycle component would be the solid line in the third panel o f Figure 1. This alternative measure o f cyclical output is much more persistent than the HP measure: for example, output is high relative to its linear trend during most o f the 1960s and 1970s. The dashed line in the third panel is the gap between the HP trend and a linear trend, thus indicating that the HP filter extracts much more low frequency information than a simple linear trend. It is also useful to compare the HP cyclical component with the business cycle measures resulting from the band-pass (BP) filter procedure developed by Baxter and King (1995), since such measures are presented by Stock and Watson (1999) in their extensive compilation o f business cycle facts elsewhere in this volume 7. In the second panel o f Figure 1, the HP measure o f cyclical output is accompanied by a BP measure o f cyclical output: this procedure makes the cyclical component mainly those parts o f output with periodicities between 6 and 32 quarters. For series like output, which contain relatively little high frequency variation, Figure 1 shows that there is a minor difference between these alternative cyclical measures. There has been some controversy about the suitability of the HP filter for business cycle research. Prescott (1986) notes that the HP filter resembles an approximate highpass filter designed to eliminate stochastic components with periodicities greater than thirty-two quarters. Adopting that perspective, we are simply defining the business cycle in a fairly conventional way: it is those fluctuations in economic time series that have periodicity o f eight years or less s. At the same time, the third panel o f Figure 1 reminds us that there are slow-moving stochastic components o f economic time series omitted by this definition, which may have substantial positive and normative significance.

2.2. Some stylized facts of US business cycles Making some selections from the data set that Stock and Watson (1999) investigate more extensively, we apply the HP filter to produce cyclical components for key US macroeconomic variables 9. Figures 2, 3 and 4 provide graphs of the HP business cycle components o f major US aggregates. We use the cyclical component of output as a reference variable, placing it in each panel of each figure, so as to allow the reader to

7 Since an exact bandpass filter contains an infinite number of moving average terms, a practical bandpass filter cannot be produced exactly but involves approximations. Baxter and King (1995) derive the relevant formulas, imposing the constraint that the sum of the filterweights must be zero; they also compare the BP filter to several other detrending methods including the HP filter. 8 Eightyears corresponds to the longest reference cycle that Burns and Mitchell (1946) tmcoveredusing very different methods. Stock and Watson (1999) adopt an alternative view of the interesting business cycle periodicities (six to twenty four quarters), but this is a difference of degree rather than kind. 9 This data set covers the period 1947 (first quarter) to 1996 (fourth quarter).

Ch. 14: Resuscitating Real Business Cycles

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Spending

and Output

i~

50

k,v:'li i

m-1O

,g

'71

-5-

,l

-

,jv'i ~

,~/.-..-~

""','
v

" ; ':'

,.~A/.~

I

-254 -25

Output -- -- - - Gov't Spending

!~

-15 : '

:

I

;

-vv ,.;.--,'w-v

. . . . . . .

; ; 52

:

:

', ; 57

;

;

: : 62

:

:

; ; 57

;

;

: : 72

:

:

: : 77

:

:

: : 82

:

:

: : 87

:

:

: : 92

:

:

-

Date

Fig. 2. Cyclical components of US expenditures. Sample period is 1947:1-1996:4. All variables are detrended using the Hodrick-Prescott filter.

R.G. King and S.T. Rebelo

936 6

Total Hours

and Output

4.

2.

"<

!f

-..

'!d

-; ;--~ °2',,?'.o°~

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-6-8,

:

:

:

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:

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:

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:

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: : 72

:

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:

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:

:

: : 87

:

:

: : 92

:

:

Date

Capital

6

:t

p

i~ ~!

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~

i

!

I

"

:

.

and Output

V

!

i

i:

"

A

i t

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i '

, :.,:

V

lJ

i

:

:

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: ', 52

;

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:

:

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:

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: : 67

I

I

I I 72

v

!, i

i/

V

I

i

i I 77

I

I

/ ............. pu,

:

~I

..........

I I 82

I

I

I I 87

i

I

I I 92

I

I

Date

Capital

10-

Utilization

and Output

5-

J',~

:'~,,~

! ~' t;i

t I

~'4

;I

t'l

~

I

"~1

-lO -15,

fl, h

i,!

:%2

it "v'~e

VI

.D

/jl

\,-/

4

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-

h

f

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I ,

57

62

67

72

-" "

~V'

~ I

~,I

~l

52

m ....

'~ .t

:,

"~,..d u '~ u

"

Out ut - - -- - - Capital UtilizaSon

77

82

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92

Date

i

!4

Productivity

I

1.',J

i

|

~

v

J. ~-

47

"~/

~/

[J

it

.o

(Solow

,t

"

residual)

'(.,'~Lt

/b/

7

?!

~

52

57

and Output

a

~,

~

62

67

72

I*:

'~/

;

.............o=°,

~"

77

82

- - - - - - Productivity

87

92

Date

Fig. 3. Cyclical component of US factors of production. Sample period is 1947:1-1996:4. All variables are detrended using the Hodrick-Prescott filter.

Ch. 14." Resuscitating Real Business Cycles

937

Hours per Worker and Output

it

o ~

~

P

~t

~.i<

~,

I

._,~,,i.~

~"

iv;

[

.,

t I ~

'~

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tY

i,

s

,

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"

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,.A!,,,x.<,~

~ . ~ ^ ]

;~"

I

i/

~,

I >

t;

,1

~

\ f ........................ Output - - - - - - Hoursper Worker

\

Date

Employment and Ouput

,~',

:-

-4

V~

-6

!

.

.

v

47

i. 7 '

52

(;

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kV'

","

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ij

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o.o., Employment

----

82

87

92

Average Product and Output

, ,,

,:,

P.

h,,>, ,2,~v.,~," ~l\w.

A

/

.D ,j,,],k{"~ .,w), t~ ,.~,h:

t /

,

~

i l;~ .ACd~,..."~_,

:

i, ii

- -

h~..- .,

-

A,e,.g. P,odoot

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I

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:

:

:

52

;

:

;

;

~

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;

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I

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J

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67

I

I

I

I

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I

I

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I

I

I

I

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82

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I

I

I

I

92

Real Wages and Output

6•

V'UI ~"," W" ~.-2. 4-

I

i"'"v',d'".'hv '-'v"

i! t 7 / i I}

•,

t/ {/ I'

. 47 . . . . . . 52 . . . . . . 57. . . . . 62

'..~; '4,;',41 "i'/

ti

t~

6]i 7I

~/ / ) 7 V

712 . . . . 77 . . .

~

v.>.-/'- ~.~'>,",-./" /

i " ~ \,J

," .4 ......... Output -- - - - Rea Wages

812111817

I

I

I 912111

Date

Fig. 4. Cyclical component of US labor market measures. Sample period is 1947:1-1996:4. All variables are detrended using the Hodrick-Prescott filter.

R.G. King and S.T. Rebelo

938 Table 1 Business cycle statistics for the US Economy Standard deviation

Relative standard deviation

First-order autocorrelation

Contemporaneous correlation with output

Y

1.81

1.00

0.84

1.00

C

1.35

0.74

0.80

0.88

I

5.30

2.93

0.87

0.80

N

1.79

0.99

0.88

0.88

Y/N

1.02

0.56

0.74

0.55

w

0.68

0.38

0.66

0.12

r

0.30

0.16

0.60

-0.35

A

0.98

0.54

0.74

0.78

a All variables are in logarithms (with the exception of the real interest rate) and have been detrended with the HP filter. Data sources are described in Stock and Watson (1999), who created the real rate using VAR inflation expectations. Our notation in this table corresponds to that in the text, so that Y is per capita output, C is per capita consumption, I is per capita investment, N is per capita hours, w is the real wage (compensation per hour), r is the real interest rate, and A is total factor productivity.

easily gauge the relative volatility o f the series i n question and its c o m o v e m e n t with output. S u m m a r y statistics for selected series are provided in Table 1 10 Volatility: Economists have long b e e n interested in understanding the e c o n o m i c m e c h a n i s m s that underlie the different volatilities o f key m a c r o e c o n o m i c aggregates. The facts are as follows, working sequentially w i t h i n each figure and using the notation panel 2-1 to denote panel 1 o f Figure 2 and so forth: • C o n s u m p t i o n o f non-durables is less volatile t h a n output ( p a n e l 2-1); • C o n s u m e r durables purchases are m o r e volatile t h a n output ( p a n e l 2-2); • I n v e s t m e n t is three times more volatile than o u t p u t ( p a n e l 2-3); • G o v e r n m e n t expenditures are less volatile than output ( p a n e l 2-4); • Total hours worked has about the same volatility as output ( p a n e l 3-1); • Capital is m u c h less volatile than output, b u t capital utilization in m a n u f a c t u r i n g is more volatile than output ( p a n e l s 3-2 and 3-3)11; • E m p l o y m e n t is as volatile as output, while hours per worker are m u c h less volatile than output (panels 4-1 and 4-2), so that most o f the cyclical variation in total hours worked stems from changes in employment; • Labor productivity (output per m a n - h o u r ) is less volatile than output ( p a n e l 4-3);

10 For a discussion of open economy stylized facts see Baxter and Stockman (1989), Back-us and Kehoe (1992) and Baxter (1995). 1~ This measure of capacity utilization, constructed by the Federal Reserve System, is subject to substantial measurement errol, see Shapiro (1989).

Ch. 14.. Resuscitating Real Business Cycles

939

• The real wage rate is much less volatile than output (panel 4-4). Comovement: Figures 2 through 4 show that most macroeconomic series are procyclical, that is, they exhibit a positive contemporaneous correlation with output. The high degree of comovement between total hours worked and aggregate output, displayed in panel 3-1, is particularly striking. Three series are essentially acyclical wages, government expenditures, and the capital stock - in the sense that their correlation with output is close to zero 12. Persistence: All macroeconomic aggregates display substantial persistence; the firstorder serial correlation for most detrended quarterly variables is on the order of 0.9. This high serial correlation is the reason why there is some predictability to the business cycle. In presenting these business cycle facts, we are focusing on a small number of empirical features that have been extensively discussed in recent work on real business cycles. For example, in the interest of brevity, we have not discussed the lead-lag relations between our variables. In choosing the series to study, we have also left out nominal variables, whose cyclical behavior is at the heart of m a n y controversies over the nature o f business cycles 13. However, we do report the cyclical behavior of a measure of the expected real rate of interest from Stock and Watson (1999) in Table 1. This real interest rate is constructed by subtracting a forecast o f inflation from the nominal interest rate on US treasury bills. There is a negative correlation of the real interest rate with real output contemporaneously and, indeed, this negative relationship is even stronger between real output and lagged real interest rates. Many modern macroeconomic models, including real business cycle models, have difficulty matching this feature of business cycles ~4

12 The observation that the real wage is not tightly related to the business cycle goes back to Dunlop (1938) and Tarshis (1939) who stressed that this was at odds with Keynesian models. This finding is somewhat dependent on precisely how the real wage is constructed,depending on whether the numerator (the wage) includes various compensation items and on the index in the denominator (the price level). Two particular features of wage measurement that affect its cyclical behavior are as follows. First, firms pay for overtimehours in an expansion and layoffregular hours in a recession. Second, there is a cyclical composition bias in the labor force lowerquality workers are hired in expansions - which suggests that the real wage per efficiencyunit of labor effort is procyclical. 13 See Stock and Watson (1999, Sections 3.4, 3.6, and 4.1) for a discussion of literature and empirical results. 14 King and Watson (1996) find this negative "leading indicator" relationship between the real interest rate and real activity, using BP filtered data. They also show that a number of modem macroeconomic models, including the basic RBC model, are unable to match this fact even when driven by complicated forcing processes that allow them to match most other features of the business cycle. However, while this result is provocative, it is important to stress that the behavior of this real interest rate involves assuming that the inflation forecasting equation is temporallystable and that agents know this forecasting structure in advance.

R.G. King and S.T. Rebelo

940 0.6.

L a b o r ' s Share of O u t p u t

0.575. s', / t k/ '. / ~j/ ,,~

0.65 •

0.525-

~i•

> ?

"W

<'j

i~ ;

=~" j

i l t!j

b!

.... 4 7

"2

'

D

. . 62 . . .

7~

67

'

"

'

'2

'

"

'

92 '

'

Date

0.25 -

Investment - Output Ratio

0.2-

0.15 -

0.1-

0.o5 -

oi

'

47

'

52

D

'

"~

'

D

'

"2

'

7,

'

"2

'

6',

72

'

Daia

6>75

Consumption - Output Ratio

0.7 \J'lt.

0.65

J

,,.#

J

0.6 0.55

o%

,

. 52

. . .

57

'2

'

D

'

' 72

'

7,

. . .82 .

"2

87

Date

11oo

Hours per Person / i~

j~

/

1000

~J

l

<ji

660

2

\/

000

850 . . . . .

47

,

52

.

,

,

62

,

.

,

,

,

72 Date

77

,

.

,

,

,

67

Fig. 5. Growth facts: great ratios and hours per person.

.

,

'

Ch. 14: ResuscitatingReal Business Cycles

941

2.3. Some stylized facts of economic growth While the US time series for many aggregates grow overtime, there are many '~great ratios" that appear to be relatively constant, suggesting that there are a small number of common forces which give rise :to trend growth. As with the systematic patterns of business cycles, this finding :is also consistent across many countries and .time periods, suggesting that there may be a coherent theoretical explanation of its origin. These stylized facts of economic growth were uncovered as applied researchers such as Kuznets (1973)assembled long time series on economic growth. 'They are sometimes called the "Kaldor facts" of growth because Kaldor (1957) drew attention to them: in addition to the constancy o f great ratios, he stressed that the growth-process seemed to involve growth rates and interest rates that were stationary'even'though the'level of economic aggregates were not. The great ratios. Panels 1-3 of Figure 5 illustrate that the .process ,of:sustained growth appears to leave many of the shares of income components and output components relatively unaffected 15. The ratios of investment to output and labor income to output appear to fluctuate around constant means. The ratio of consumption to output does increase from 1952 onwards, but there is nothing like the 'large trend that we saw in output in Figure 1. Stability of the great ratios implies that most ~series have a similar rate o f growth, .so that there is no deterministic trend in the ratios, and that factors causing permanent changes in the 'level of economic activity do so in a way that makes their effects proportional across series. Labor and growth. During long-term economic growth, which most economists believe occurs mainly due to population growth and technical progress, measures 'of labor input per person are also relatively constant asdocumented inpanel 4 of Figure 5. This relative constancy of hours per capita is remarkable given the rise in real wages that accompanies economic growth. Over our sample period, the real wage measure previously studied in panel 4 of Figure 4 grew at 1.76% per year, but there is little evidence of a trend in hours worked per person.

2.4. Implications of stylized facts Some of the facts just described have been influential .in shaping the views of economists about of how the economy operates. In terms of the business cycle facts, the high volatility of investment no doubt underlies Keynes' famous assertion that investors have "animal spirits". At the same time, the low cyclical volatility of capital is often taken to imply that one can safely abstract from movements in capital in constructing a theory of economic fluctuations. The remarkably high correlation

15 Klein and Kosobud (1961) produced an early test of the stability of the "great ratios" in the USA. More recently, King, Plosser, Stock and Watson (1991) drew attention to how the constancy of these great ratios was a cointegration implication about the logarithms of the variables, which they tested for the USA. Evidence on cointegration for other OECD countries is contained in Neusser (1991).

R.G. King and S.T. Rebelo

942

between hours worked and aggregate output has led some economists to believe that understanding the labor market is key to understanding business fluctuations. Finally, the relatively small variability of real wages and the lack of a close correspondence of wages with aggregate output, has led some economists to conclude that the wage rate is not an important allocative signal in the business cycle. The growth facts suggest the importance of building models that feature a common trend in most real aggregates.

3. The basic neoclassical model

In the 1950s and 1960s, aggregate economic activity was analyzed with two very different types of dynamic macroeconomic models. The trend components of aggregate economic activity were studied with "growth models" that stressed three sources of dynamics: population growth, productivity growth and capital formation. The business-cycle components were studied with Keynesian macroeconomic models, which stressed the interaction of consumption and investment but downplayed the importance of capital accumulation and productivity growth. While there were attempts to synthesize these developments towards the end of this period, the study of growth and business cycles most frequently involved very disparate models. Relative to this traditional macroeconomic approach, the real business cycle literature took a very different point of view. Its core is a neoclassical growth model of the form developed by Solow (1956), Cass (1965) and Koopmans (1965). It then follows Brock and Mirman (1972) in making this growth model stochastic, by positing that the production technology is buffeted by random aggregate shocks to productivity. Our introduction to RBC analysis thus naturally begins by reviewing the "basic neoclassical model", which has implications for both growth and business cycles. In this section, we focus on the structure of the model, trace some of its implications for capital accumulation, and discuss Solow's work on productivity measurement. In the next section, we discuss its business cycle properties.

3.1. The structure The basic neoclassical model is built on assumptions about preferences, endowments and technology that are designed to capture key features of growth and business cycles, while building a model economy that is readily amenable to economic analysis. Preferences: The economy is populated by a large number of infinitely lived agents whose expected utility is defined as O<3

Eo ~

btu(Ct, Lt),

b > 0,

(3.1)

t=O

where b denotes the discount factor, Ct represents consumption and Lt leisure. The symbol E0 denotes the expectation of future values of C and L based on the information

Ch. 14: Resuscitating Real Business Cycles

943

available at time zero 16. The infinite horizon assumption, which greatly simplifies the mathematical analysis o f economic growth and business cycles, is usually justified by appealing to the presence o f altruistic links across generations [Barro (1974)]. However, it can be viewed as an approximation to an economy with many long-lived agents 17. In our exposition o f this model, we treat the population as constant for simplicity, although we discuss the consequences of relaxing this assumption at various points below. The momentary utility function u(Ct, Lt) in Equation (3.1) is assumed concave and obeys regularity conditions discussed in the Appendix. It implies a preference for smooth profiles o f consumption and leisure. It also implies a willingness to substitute across time if interest rates and wage rates imply differing costs of consumption and leisure at different dates. Thus, the neoclassical model imbeds a form of the permanent income hypothesis of Friedman (1957). Endowments: The fundamental endowment that individuals have is their time, which can be split between work (Nt) and leisure activities (Lt). Normalizing the total amount o f time in each period to one, the time constraint is:

Nt + Lt = 1.

(3.2)

We abstract from other endowments of resources since the production from unimproved land and from nonrenewable resources is a small fraction o f output in most developed countries. Technology: The output o f the economy is assumed to depend on a production function that combines labor and capital inputs. To capture the upward trend in output per capita that is shown in Figure 1, the basic neoclassical model incorporates secular improvement in factor productivity. In particular, output (lit) depends on the amounts o f capital (Kt) and labor (Nt) according to a constant returns to scale production function which satisfies regularity conditions discussed in the Appendix.

Yt = AtF(Kt, NtXt),

(3.3)

where At is a random "productivity shock" variable, whose law of motion will be described further below, and Xt represents the deterministic component o f productivity. This latter component of productivity is assumed to expand at a constant rate, Xt+ 1 = yXt,

y > 1.

(3.4)

16 TO simplify, we adopt a dating convention that does not distinguish between "planning time" for the individual and "calendar time" for the economy. Alternative presentations that emphasize this distinction would write the objective as E t }-~)~obJu(Ct+j,Lt+j), where t is calendar time andj is planning time. 17 Rios-Rull (1994) finds that an overlapping generations model calibrated to the age structure of the US population has business cycle properties that are similar to an infinite horizon model.

R.G. King and S.T. Rebelo

944

The output o f the e c o n o m y c a n be used for consumption or investment (It) so that an additional resource constraint is:

(3.5)

I1, = c , + 1,1

This equation corresponds to the basic national i n c o m e accounting identity for a closed economy with no government. The stock of capital evolves according to: Kt+ l = It + (1 - 6)Kt,

(3.6)

where 6 is the rate o f depreciation. This formula coincides with the one used in practice to estimate the stock o f capital according to the "perpetual inventory method ''18. The form o f the production function (3.3) is motivated by the growth facts and was widely employed in growth models after Phelps (1966) showed that steady-state growth - a situation in which all variables grow at a constant rate - required that the deterministic component o f technology be expressible in labor augmenting form in economies with Equations (3.5) and (3.6) 19~ In fact, in the feasible steady states of this model consumption, investment, output and capital all grow at the same rate - the rate o f trend technical progress - so that the great ratios are stationary. Initial conditions: The economy starts out with a capital stock K0 > 0. It also begins with a level o f the technology trend X0 > 0, which we set equal to unity for convenience, and an initial productivity shock A0 > 0.

3.2. Steady-state growth and transforming the economy Our assumptions on the production side o f the. model ensure that a steady-state path is feasible in the face o f the trend productivity expansion in X~. However, additional assumptions are necessary to make such a steady state desirable. In the standard fixed labor version o f the basic neoclassical model momentary utility has to take the form 1

u(C) = ~-L-~[C

1-o

- 1],

(3.7)

where cr > 0. This utility function insures that the marginal rate o f substitution between consumption at dates t and t + 1 depends only on the growth rate o f consumption. 18 In practice the perpetual inventory method allows the depreciation rate to vary through time according to empirical measures of economic depreciation schedules. Ambler and Paquet (1994) study a RBC model with depreciation shocks. 19 Three types of technical progress frequently discussed in the literature can be represented in a general production function:

Yt = X y F (KtXK, NtX,). The variable X'tH represents total factor augmenting (Hicks-neutral) technical, progress, YtK capital augmenting technical progress, and Xt labor augmenting (Harrod-neutral) technical progress,. When the production fimction is Cobb-Douglas these different forms of technical progress are interchangeable and, hence, they are all consistent with balanced growth. For all other production functions, the only form of technical progress consistent with steady-state growth is labor augmenting,

Ch. 14:

Resuscitating Real Business Cycles

945

In the basic neoclassical model of growth and business cycles, which features endogenous labor supply, a steady state also requires that hours per person be invariant to the level of productivity. King, Plosser and Rebelo (1988a,b) show that the momentary utility function must be expressible as b/(C, L) = ~

{ [ C v ( L ) ] 1-g _ 1},

(3.8)

which also implies exactly offsetting income and substitution effects of wage changes on labor supply 2°. The function v(.) satisfies regularity conditions discussed in the Appendix. When these restrictions are imposed, it is possible to transform the economy - so that steady-state growth is eliminated - by scaling all of the trending variables by the initial level of X: Using lower case letters to denote these ratios, for example yt = Yt/Xt, we can then write the optimal growth problem as maximizing the transformed utility fimction: C~

(3.9/

~-~/3tu(ct,Lt) t=0

with/3 = by 1-~ being a modified discount factor satisfying 0 < /3 < 1. Utility is maximized subject to the transformed constraints: Nt

= 1 - Lt,

(3.1 O)

Yt

= AtF(kt,Nt),

(3.11)

Yt

= Ct + it,

(3,12)

ykt+ l = it ÷ (1 - 6)kt.

(3.13)

Relative to an economy in which there is no growth due to X, this transformed economy involves an altered discount factor and a slight modification of the capital accumulation equation. Given this close correspondence, RBC analyses sometimes omit growth all together or simply start with the transformed economy 21.

20 That is, suppose that Equation (3.8) is maximized subject tothe static budget constraint C <~ w(1 -L). The equality of the real wage with the marginal rate of substitution between leisure and consumption implies CDv(L) _ [w(1-L)]Dv(L) W

=

v(L)

v(L)

'

with the latter equality following from eliminating consumption using the budget constraint. Changes in w have no effect on the optimal level of leisure and labor supply. 21 By leaving out population growth, we have essentially proceeded in this manner. However, since productivity is labor-augrnenting~ we can reinterpret the stationary transformation as.one that involves dividing through by both the population and the productivity of labor. Under this interpretation, ~' is the growth rate of population and productivity.

946

R.G. King and S.T. Rebelo

Constraints (3.11), (3.12), and (3.13) can be summarized by the equation ct + ykt + ~ = A t F ( k t , N t ) + (1 - 6)kt.

(3.14)

3.3. Optimal capital accumulation

The optimal path of capital accumulation can be obtained by choosing sequences for consumption {ct}~0, leisure {Lt}~0, labor {Nt}~-0 and the capital stock {kt+ l}~0 to maximize Equation (3.9) subject to conditions (3.10) and (3.14). For this purpose, we form the "Lagrangian" O<3

L = Z

fitu(ct'Lt)

t=O

+ ~ffXt[AtF(kt,Nt)

+ (1 - b)kt - ct - 7kt+ 1]

t=O oG

t=O

The first-order conditions include ct

: DlU(Ct,Lt) = L ,

Lt

: D2u(ct,Lt) = cot,

Aft

: L A t D 2 F ( k t , N t ) = cot,

kt+l : [3)~t+l[At+lD1F(kt+l,Nt+l)+ 1 - 6 ] = yAt,

(3.15) (3.16) (3.17) (3.18)

where we use the notation Diu(c, L) to denote the partial derivative of the function u(c,L) with respect to its ith argument. The first pair of these efficiency conditions dictate that the marginal utility of consumption be set equal to its shadow price [associated with the constraint (3.14)] and that the marginal utility of leisure be set equal to its shadow price (associated with the time constraint Nt + Lt = 1). The second pair of efficiency conditions dictate that the utility value of goods produced with a marginal unit of work (the marginal value product &tAtD2F(kt, Nt)) equal its utility denominated cost (cot) and that the present value of the future product of capital ([~t+ 1[At+ 1DlF(kt+ 1,Nt+ 1) + 1 - 6]) equal its current utility cost (T),t). An optimal consumption, leisure, work and capital plan - sequences {ct}~0, {Lt}~0, {Nt}~0, and {kt}~ 0 - satisfies these first-order conditions, the original constraints, the initial condition requirement on kt and the transversality condition, l i m t ~ fit,~tkt +j = O. Optimal capital accumulation in the basic neoclassical model is a "general equilibrium" phenomenon in three ways. First, the choices of consumption, labor and capital accumulation are interdependent at each point in time and across time:

Ch. 14: ResuscitatingReal Business Cycles

947

a solution for optimal capital accumulation involves specifying sequences for all three of these variables. Second, the requirement that the optimal decisions must respect the resource constraints of the economy is signalled by the shadow prices (cot and )~t). An optimal capital accumulation plan thus also involves specification of sequences of these prices. Third, if these shadow prices were market prices for individual households, then they would similarly signal these agents to supply and demand the optimal quantities. That is, there is an equivalence between the optimal quantities chosen by the social planner and those in a dynamic competitive general equilibrium in the basic neoclassical model. We will thus move between optimal and market outcomes in our discussion of the basic model as it seems useful in the next several sections. We will return later to discuss how work on real business cycles relates to other developments in dynamic stochastic general equilibrium modeling.

3.4. The nature of the steady state There is a unique stationary state that occurs in the transformed economy when At = A for all t. The first-order conditions can be used to describe this stationary state in a recursive manner. First, the capital accumulation efficiency condition implies that

AD1F(k, N) = (r + 6),

(3.19)

where r = ~ - 1 is the stationary state real interest rate and r + 0 is the stationary state rental price of capital. Given that the production function is constant returnsto-scale, the marginal product of capital depends on the capital-labor ratio k rather than on the levels of the factors. Accordingly, Equation (3.19) determines the capitallabor ratio as a function of productivity and the rental rate. Second, given this capitallabor ratio and the level of A, the marginal product of labor is also determined, since ADzF(k, N) = ADzF(~, 1). Thus, there is a real wage rate w = co/;. that is determined independently o f the total quantity of labor:

w=~=AD2F(k,1). Third, there are unique levels of work, consumption and the shadow price of consumption that satisfy the remaining equations. We know that the variables in the original, untransformed economy are related to those of the transformed economy by a simple scaling procedure, Yt = ytXt, etc. Hence, if the transformed economy is in a stationary state, then the original economy will be in a steady state with many variables - including, consumption, capital output and real wages - growing at the same rate. Other variables will be constant, notably work effort and the real interest rate.

R.G. King and S, T. Rebelo

948

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Fig. 6. Transitional dynamics: Basic RBC model (stars); fixed labor model (circles); dashes in mid left-hand panel represent labor response.

3.5. Transitional dynamics Transitional dynamics arise whenever the intitial capital stock is different from its steady-state value 22. For stationary versions of the fixed labor model, Cass (1965) and Koopmans (1965) established that it is always optimal for the economy's capital stock to move monotonically toward the stationary level from any positive initial level o f

22 In the transformed economy, this is the movement from an initial level of capital k0 to the stationary level k.

Ch. 14: Resuscitating Real Business Cycles

949

capital. Working to establish this stability theorem, Cass and Koopmans were hampered by the absence of an explicit solution to the model, which stemmed from the presence of many interdependent choices for consumption and capital at different dates. Thus, they were able to establish the stability property, rather than ascertaining how the pace of the transition process depended on the underlying preferences and technology. More precise descriptions required the detailed specification of preferences and technology, with near steady-state linear approximations sometimes being used to evaluate the nature of the global transitional dynamics. Figure 6 illustrates the nature of these local transitional dynamics of capital, as well as the related movements in output, investment and consumption. There are two sets of paths in each of the panels: the ' o ' path describes the fixed-labor model used by Cass and Koopmans and the ' . ' path describes the variable-labor model used in RBC analysis. In these panels, all variables are displayed as percentage deviations from their corresponding stationary values. For both models, the economy is assumed to start off with a capital stock that is one percent lower than its stationary value, so that both of the paths in the upper left panel have an entry o f - 1 at the first date. Looking first at the 'o' paths that describe the transitional dynamics of the CassKoopmans model, we see that capital accumulates through time toward its stationary level, i.e., the (negative) deviation from the stationary level becomes smaller in magnitude through time. Since capital is low relative to the steady state, the second panel shows that output is also low relative to the stationary state. Capital is built up through time by individuals postponing consumption. In a market economy, a high real rate of return is the allocative signal that makes the postponement of consumption occur, with the rate of return given by rt = [ A D 1 F ( k t + I , N ) - 6] in the fixed labor economy. Using the preference specification (3.7), in fact, one can show that the growth rate of consumption is given by l o g \( O ct r + ' j) -- - ~1 log ( ~ t l )

~ -1~ [ r t - r ] ,

(3.20)

so that a high real interest rate fosters consumption growth along the transition path 23. The initial level of consumption is set by the wealth o f individuals or, equivalently, so that the efficient path of consumption will ultimately be at the stationary level. In general, as the economy saves to accumulate the new higher stationary level of capital, net investment it - 6kt is positive along the transition path. In this figure gross investment is also higher than its stationary level during the process of capital accumulation. 23 In fact, the value of cr used in constructing Figure 6 is one, so that consumption growth and the rate of return are equal. The time unit of these graphs is a quarter of a year, however, and the interest rate is expressed at an annual rate, so that the slope of the consumption path is one fourth of the annualized interest rate shown in the next to last panel. A basis point is one hundredth of a percentage point, so that an annual interest rate that is 0.10 percentage points above the steady-state level causes consumption to grow from about -0.600 to about -0.575 in the second panel.

R.G. King and S.T. Rebelo

950

When work effort is endogenous, as in the ' , ' path of Figure 6, these transitional dynamics change significantly, although there is still a period of capital accumulation toward the stationary level. The extra margin matters for the speed of the transition. When capital is initially low individuals work harder and produce more output that is used for capital accumulation. This extra effort occurs despite the fact that the real wage (wt = AD~F(kt,Nt)) is low relative to its stationary level. Again, the allocative signal is a high rate of return that makes it desirable to forgo leisure (as well as consumption) during the transition process. In fact, there is a subtle general equilibrium channel that enhances the magnitude of the effect on the rate of return. With more future effort anticipated, the rate of return rt = [ADtF(kt+I, Nt+ 1) - 6] is higher than in the fixed labor case, because additional effort raises the marginal product of capital. Further, this higher rate of return stimulates current work effort. On net, variable effort raises the speed of transition and mitigates the effects of initially low capital on output and consumption, while enhancing the investment response. 3.6. The (Un)importance o f capital formation

The capital accumulation mechanism at the heart of the basic neoclassical model is sometimes viewed as relatively unimportant for growth and business cycles. In the growth area, Solow followed his (fixed saving rate) growth model (1956) with a celebrated demonstration that productivity was much more important to economic growth than was capital formation. It is easiest to exposit this result if we assume that the production function is Cobb-Douglas: Yt = AtK~t-a(NtXt) a,

(3.21)

with the parameter a being measurable as labor's share of national output (an idea which we discuss more below) and thus being constrained to be between zero and one 24. Then, using time series for output, labor and capital, we can compute the Solow residual as: logSRt = log Yt - a logNt - (1 - a) log Kt.

(3.22)

Abstracting from measurement error in outputs or inputs, the Solow residual can be used to uncover the economy's underlying productivity process, log SRt = log(At) + a log(Xt).

(3.23)

To evaluate the importance of capital accumulation to economic growth, Solow (1957) looked at how the average growth rate of output per unit of labor input 24 Our depiction of Solow's (1957) procedure is impressionistic rather than literal. Solow worked in changes rather than levels and incorporated time varying, rather than constant factor shares. Moreover, in ways which anticipate recent developments, he also sought to correct for changes in the utilization of capital.

Ch. 14: Resuscitating Real Business Cycles

951

(the average of log(Yt/Nt) - log(Yt 1/Nt-l)) was divided between growth in productivity (the average of log(SRt) - log(SRt_l)) and growth in capital per unit of labor input (the average of log(KJNt) - log(Kt i/Nt 1)). The result was a surprising one and must also have been disappointing in view of his just completed work on the dynamics of capital accumulation [Solow (1956)]: capital accumulation accounted for only one eighth of the total, with the remainder attributable to growth in productivity. Thus, the transitional dynamics of capital formation turned out to be not too important for understanding economic growth. Moreover, the transitional dynamics of Figure 6 do not display the positive comovement o f output, consumption, investment and work effort that take place during business cycles. Labor and investment are higher than in the steady state when capital is low while consumption and output are below the steady state. Further, consumption is much more responsive to a low capital stock than either labor or output, which is inconsistent with the evidence on relative volatilities reviewed earlier. Sometimes these results are interpreted as indicating that one should construct macroeconomic models which abstract from capital and growth, since the introduction of these features complicates the analysis without helping to understand business cycle dynamics. However, real business cycle analysis suggests that this conclusion is unwarranted: the process of investment and capital accumulation can be very important for how the economy responds to shocks. 3.7. Constructing dynamic stochastic models

In this section, we have concentrated on describing the steady state and the transitional dynamics of the basic neoclassical model, as an example of the type of dynamic general equilibrium model now used in RBC analysis and other areas of macroeconomics. There is now a rich tool kit for studying the theoretical properties of stochastic equilibrium in these models, such as the advances described by Stokey, Lucas and Prescott (1989). A systematic analysis of the Brock and Mirman (1972) stochastic growth model, modified to include variable labor supply as above, calls for the application of these methods. We review these developments in the Appendix, using the basic RBC framework to highlight two important issues. First, we characterize the optimal decision rules for consumption, capital, output, investment and labor using dynamic programming. Second, we demonstrate that the outcomes of the optimal growth model are the same as the outcomes of a dynamic stochastic general equilibrium model, in which firms and workers trade goods and factors in competitive markets. This equivalence requires that firms and workers have rational expectations about future economic conditions. Another notable result for this stochastic model, first established by Brock and Mirman (1972), is that the stationary state is replaced by a stationary distribution, in which the economy fluctuates in response to shocks. We have also discussed the local transitional dynamics of the basic neoclassical model illustrated in Figure 6. The development of real business cycle models and dynamic stochastic general equilibrium theory has also heightened interest in methods

952

R.G. King and S.T. Rebelo

for solving and simulating dynamic equilibrium models. In this survey, we rely on now-standard loglinear approximation methods for solving the various real business cycle models that we construct 25. These methods have been shown to be highly accurate for the basic RBC model 26. The application of these methods contains essentially two steps. First, it is necessary for us to specify the utility function, the production fixnction, the depreciation rate and so forth so that we can solve for the steady state of the model economy, working much as we did in Section 3A. Second, we take loglinear approximations to the resource constraints (3.10)-(3.13) and the efficiency conditions (3.15)-(3.18). We then assume that these approximate equations hold in expected value - a certainty equivalence assumption - and solve the resulting expectational linear difference equation system. This yields a system of linear difference equations forced by random shocks, f r o m which moments and simulations can b e easily computed.

4. The Real Business Cycle shock The stark simplicity of the analysis of Prescott (1986) provided a dramatic demonstration of the empirical power of RBC models. His results were surprising because the neoclassical model - even with stochastic productivity - was widely viewed as suitable for long-run analysis, but not for the study of business cycles. In particular, Prescott (1986) showed that a simulated version of the basic neoclassical model could generate business cycle statistics like those in Table 1 when driven by productivity shocks. To make these shocks "realistic", Prescott required that they have the same statistical properties as the actual residuals from an aggregate production function computed using the method of Solow (1957). Building on this idea, Plosser (1989) showed that empirical Solow residuals constructed from post-war US data produced model time series for macroeconomic activity that appeared visually close to the actual business cycle fluctuations on a period-by-period basis. In this section, we display these moment and time-path results as an introduction to real business cycles. 4.1. The drioing process

The crucial assumption in RBC analysis is that the stochastic component of productivity can be extracted from the empirical Solow residual using Equation (3.23), log(SRt) = log(At) + a log(Xt). Then, assuming that log(At) follows an AR(1) process, log(At) = p log(At-O + et,

(4.1)

and exploiting the fact that log(Xt) = log(Xt_l)+ log(y), it is possible to estimate the stochastic process for productivity and, in particular, the persistence parameter p and 25 There are versions of the basic RBC model that can be solved analytically but require restrictive assumptions on preferencesand technology. See, e.g., Radner (1966), Long and Plosser (1983), Devereux, Gregory and Smith (1992), and Rebelo and Xie (1999). 26 See, e.g., Danthine, Donaldson and Mehra(1989), Christiano (1990), and Dotsey and Mao (1992).

Ch. 14: ResuscitatingReal Business Cycles

953

the standard deviation of the innovation et. Todo this, one fits a linear trend to logSRt in order to compute y. Then, one uses the residuals from this regression to estimate p and standard deviation of~t. For our quarterly data set, the resulting point estimates are 0.979 for p and .0072 for the Standard deviation o f et. The high estimated value of p reflects the substantial serial correlation in panel 4 o f Figure 3, where the variable described as productivity is the Solow residual.

4.2. :Calibrating and solving the model The work of Kydland and Prescott (1982) and Long and Plosser (1983) illustrated the value of exploring the workings of stochastic dynamic models by using a "reasonable" set of parameter values. Following the methodological recommendations of Lucas (1980) in his influential "Methods and Problems in Business Cycle Theory," Kydland and Prescott relied on microeconomic empirical studies and on the long-run properties of the economy to choose parameter values. To explore the operation of their multiple sector business cycle model, Long and Plosser (1983) drew parameters from inputoutput tables for the US economy. This new approach, which came to be known as "calibration" has at times been controversial. This partly reflects the fact that most research in macroeconomics followed one of two other routes prior to the rational expectations revolution 27. First, many authors explored qualitative features of theoretical models and compared them informally with empirical evidence. Second, many researchers formally estimated and tested models. To see how the calibration approach works, let us apply it to our basic neoclassical model. There are broadly two parts of calibration. One must begin by choosing functional forms which imply that certain parameters are important and then one must assign parameter values. The great ratios in the steady state: From our discussion in Section 3.4 above, we know that the production side of the model determines nearly everything about the steady State. We choose the discount factor so that the steady-state real interest rate coincides with the average return to capital in the economy. This is 6.5% per annum, if we equate it with the average return on the Standard and Poor 500 Index over the period 1948-1986. Since we are interested in a quarterly model, we choose the discount factor b so that the quarterly real interest rate is 0.065/4. In the Cobb-Douglas production function (3.21), there are three parameters a , X and A. We set a equal to

27 This calibration approach is commonlyassociated solelywith the RBC program, but it was also used in the early 1980s by researchers studying the effects of nominal contracting on economicfluctuation, such as Blanchard and Taylor. The calibration approach had been previously used in other areas of economics, such as public finance and international trade, which employedcomplicated, though static, general equilibrium models. Calibration is now routine in a wide range of macroeconomicareas, although it was controversial in the late 1980s because of Kydland and Prescott's (1991) insistence that it should be used instead of standard econometricmethodology.A nontechnical review of the interaction between the quantitative theory approach and econometricsis provided by King (1995).

R.G. King and S.T. Rebelo

954

two-thirds which is a standard value for the long run US labor income share 28. Both X0 (the initial level o f technical progress) and the m e a n value o f A are parameters which affect only the scale o f the economy, and hence can be normalized to one. The growth rate o f technical progress is chosen to coincide with the average growth rate o f p e r capita output in the U S A during the post war period (1.6% per annum), which implies a quarterly gross growth rate o f technical progress o f 7 = 1.004 29. The rate o f depreciation is chosen to be 10% p e r annum (6 = 0.025) 3°. Taking all o f this information together, we can solve for the capital-labor ratio k/N, using the requirement that r + 6 = A D 1 F ( k , N ) . In the C o b b - D o u g l a s case we obtain: k

N

_

[ r+6

]

"

In turn, this implies that the steady-state value o f the capital-output ratio is k/y = ( k / N ) / ( y / N ) since the average product o f labor y / N = A ( k / N ) l-a. We also thus compute the steady-state ratios i/y = ( y - 1 + 6 ) ( k / y ) and c/y = 1 - (i/y), as well as the steady-state real wage rate w = aA(k/N) l-a. P a r a m e t e r i z i n g utility: The constant elasticity class o f utility functions (3.8) is motivated b y having steady-state growth in productivity lead to steady-state growth in consumption and a constant average level o f hours per person. In our discussion o f this basic model, we use the momentary utility function u ( c t , L t ) = log(ct)+ _1- ~ 0 (L~- r l - 1),

(4.2)

Once we specify the parameter which governs the labor supply elasticity (r/) we choose 0 to match steady state N , which is about 20% o f the available time in the U S A in the postwar period 31 . The studies o f Prescott (1986) and Plosser (1989) used the " l o g - l o g " case, which makes utility u(Ct, Lt) = l o g ( C t ) + 0 log(Ll), motivating this form b y arguing that a range o f microeconomic and asset-pricing evidence suggests a coefficient o f risk aversion o f ~r = 132. We begin with this case (in which ~/= 1) and then consider some alternative values in Section 6 below. 28 This is higher than the value of a = 0.58 used in King, Plosser and Rebelo (1988a,b). This number is somewhat sensitive to the treatment of the government sector and of proprietor's income. See Cooley and Prescott (1995) for a discussion. 29 Many calibration studies ignore growth all together, as we ignore growth in population. Incorporating population growth would raise the appropriate value of 7 to 1.008. 30 Here we use a conventional value for 6, but there is some evidence that it should be lower. The ratio of capital consumption allowances to the capital stock (excluding consumer durables and government capital) for the USA in the post war period takes values of the order of 6 percent [see Stokey and Rebelo (1995, Appendix B)]. The average investment share is very sensitive to y and 6, but the near steady-state dynamics are not. c which can be solved for 0. 3~ That is, the condition w = D2u(c,L) Dlu(c.r) = ~Oc implies that a = - ~ - ~ON;, 32 There is substantial uncertainty about ~r, which tends to be estimated with a very large standard error, see Koeherlakota (1996).

955

Ch. 14: Resuscitating Real Business Cycles Table 2 Calibration of baseline model ~r

b

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1

0.984

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Collecting these results, we have Table 2 listing the parameters that are used in the baseline model in the remainder o f this section. Loglinearizing the model economy: The next step in solving the model is to approximate its various equations, which is most frequently done so as to produce log-linear relations. Sometimes, as with the utility specification (4.2), it happens that the relations o f interest are exactly log-linear to start. For example, the consumption efficiency condition (3.15) is At = DlU(Ct,Lt) = (ct) -I and the leisure efficiency condition (3.16) is cot = ~twt = D2u(ct,Lt) = L t ~, so that: -ct

= •,

-t/Lt = (~t + ~t).

(4.3) (4.4)

In these expressions, a circumflex ("hat") over a variable represents proportionate deviations o f that variable from its steady-state level, ~t = log(ct/c), etc. The C o b b - D o u g l a s production function also implies that the efficiency condition (3.17) - which can be rewritten as an equality between the real wage rate and the marginal product o f labor - is exactly loglinear, wt = At + (1 - a ) ( L - N t ) ,

(4.5)

i.e., the real wage is raised by productivity and by increases in the capital labor ratio. Other equations o f the m o d e l are not exactly log-linear and so must be approximated. The time constraint is Nt + Lt = 1 so that small changes in labor and leisure satisfy dNt dNt + dLt = 0 and thus ~" ) v d N ' + L @ = 1. Since log(-~) ~ ~ - , we conclude33: N (N)Nt + (L)Lt = 0.

(4.6)

33 An alternative derivation of this and other results involves assuming that the behavioral equation depends on A/t = log(Nt/N) etc. and then taking a linear approximation in the hatted variables. For example, the time constraint is N exp()~,)+ L exp(I,t) = 1, so tha~t is approximately Equation (4.6), given that a first-order Taylor series approximation to exp(~t) about Nt = 0 is Nt.

956

R.G. King and S.T. Rebelo

A 1.(1 a)~'t 7tra so that a Since the constraint on uses of goods takes the form ct + it = ~t'~t mixture of the two methods used above yields (4.7) Other equations such as (3.6) and (3.18), which contain variables at different dates, can be similarly approximated. The result is a loglinear dynamic system that can be solved numerically. Interpreting aspects o f the model economy: One benefit of this solution strategy is that the researcher maybe able to interpret certain aspects of the model economy prior to obtaining its numerical solution. For one example; Equation (4.5) can be interpreted as a description of "labOr demand", so as to discuss the influence of productivity, the real wage rate and the stock of capital on the quantity of labor. For another, combining Equations (4.4) and (4.6), we arrive at a "labor supply schedule" that relates the quantity of labor to the real wage and the shadow price of goods, Le., L

so that a higher value of r/ lowers the labor supply elasticity. Individually, these equations describing "labor supply" and "labor demand" can be used to evaluate the consistency of the macroeconomic model with microeconomic evidence. Taken together, they provide an explanation of how the quantity of labor and the real wage rate respond to variations in productivity, the capital stock, and the shadow price. 4.3. Business cycle moments

One way of evaluating the predictions of the basic RBC model is to compare moments that summarize the actual experience of an economy with similar moments from the model. On the basis of such a moment comparison, Prescott (1986) argued that the basic RBC model predicts the observed "large fluctuations in output and employment" and, more specifically, that "standard theory.., correctly predicts the amplitude o f . . . fluctuations, their serial correlation properties, and the fact that investment is about six times as volatile as consumption." Table 3 reports summary statistics on HP cyclical components of key variables for simulations of the basic neoclassical model driven by productivity shocks. These statistics are comparable to those reported in Table 1 for the US economy. Volatility o f output and its components: Productivity shocks produce a model economy that is nearly as volatile as the actual US economy. More specifically, comparing the ratio of model and empirical standard deviations, Kydland and Prescott (1991) have argued that the real business cycle model explains the dominant part

Ch. 14: Resuscitating Real Business Cycles

957

Table 3 Business cycle statistics for basic RBC model a,b Standard deviation

Relative standard deviation

First-order autocorrelation

Contemporaneous correlation with output

Y C I

1.39 0.61 4.09

1.00 0:44 2.95

0.72 0.79 0.71

1.00 0.94 0.99

N Y/N w r A

0.67 0.75 0.75 0,05 0.94

0.48 0.54 0.54 0.04 0.68

0.71 0.76 0.76 0.71 0.72

0.97 0.98 0.98 0.95 1.00

All variables have been logged (with the exception of the real interest rate) and detrended with the HP tilter. b The moments in this table are population moments computed from the solution of the model. Prescott (1986) produced multiple simulations, each with the same number of observations available in the data, and reported the average HP-filtered moments across these simulations. a

o f business cycles 34. For the numbers in Tables 1 and 3, the Kydland-Prescott variance ratio is 0.77 = (1.39/1.81) 2, suggesting that the RBC model explains 77% o f business fluctuations. Using a variation on the basic m o d e l which introduces costs o f moving labor out o f the business sector, Kydland and Prescott (1991) argued that "technology shocks account for 70 percent o f business cycle fluctuations". Using a slightly different version o f the model Prescott (1986) h a d previously attributed 75% o f output fluctuations to productivity shocks. The real business cycle m o d e l is consistent with the observed large variability o f investment relative to output, as indicated by the relative standard deviations reported in the second columns o f Tables 1 and 3. In particular, investment is about three times more volatile than output in both the actual economy (where the ratio o f standard deviations is 5.30/1.81=2.93) and the model economy (where the ratio o f standard deviations is 2.95). Consumption is substantially smoother than output in both the model and actual economies. In our basic model, however, consumption is only about one-third as volatile as output while it is over two thirds as volatile as output in the US economy. We return to discussion o f this feature o f the economy in Section 6 below. Persistence and comovement with output. Business cycles are persistently high or low levels o f economic activity: one measure o f this persistence is the first-order serial correlation coefficient. Table 3 shows that the persistence generated by the basic model

34 See Eichenbaum (1991) for a criticism of this interpretation of the variance ratio.

958

R.G. King and S.T. Rebelo

is high, but weaker than in the data (see Table 1). The relative standard deviations also provide a measure of the limited extent to which the basic RBC model amplifies productivity shocks: in terms of its business cycle behavior, output is 1.48 times as volatile as productivity. Business cycles also involve substantial comovement of aggregate output with inputs (such as labor) and the components of output (such as consumption and investment). Accordingly, Table 3 reports the contemporaneous correlation of output with the other four measures. All of these correlations are quite high, indicating the basic RBC model captures the general pattern of comovement in the data. However, the empirical correlations of output with labor, investment and productivity are substantially smaller than their model counterparts. From this battery of statistics, we can see that the RBC model produces a surprisingly good account of US economic activity. However, there are also evident discrepancies. Notably, consumption and labor input in the basic model are each much less volatile than in the data. Further, the basic RBC model produces a strongly procyclical real wage and real interest rate, which does not accord well with the US experience summarized in Table 1. 4.3.1. Simulations o f US business cycles

Figure 7 depicts US data together time series generated by simulating the model with the innovations to the actual US Solow residual. On the basis of results similar to those in this figure, Plosser (1989) argued that "the simple (RBC) model appears to replicate a significant portion of the behavior of the economy during recessions and during other periods" 35. Indeed, looking at the first panel of Figure 7, it is clear that the basic RBC model gives quite a good account of the quarter-to-quarter variation in the output time series. The correlation between these series is 0.79; the model also works well in all major recession and expansion episodes. Turning to the individual components of output, the performance of the RBC model is also surprisingly good for such a simple model. Consumption in the model and the data are strongly positively associated (the contemporaneous correlation is 0.76), although the model's series in the bottom panel of Figure 7 is much less volatile than the actual experience, as suggested by the previous discussion of moments above. Investment in the model and the data also move together in the third panel of Figure 7, although model investment appears to lead actual investment by one to two quarters. One measure of this lead is that the contemporaneous correlation of model and actual investment is 0.63 and the correlation between actual investment and past model investment is 0.73 at one lag and 0.69 at two lags. While the volatility of labor is

35 This section uses a model that is essentially the same as that in Plosser (1989), but our simulated time series are slightly different due to (i) differences in data; and (ii) differences in filtering. Plosser's use of the first-differencefilter emphasizes higher frequency components of time series relative to our use of the HP filter.

Ch. 14." Resuscitating Real Business Cycles

959

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R.G. King and S.T. Rebelo

960

broadly similar in the data and in the model, there is much less of a period-to-period correspondence between labor and output in the simulations in the second panel of Figure 7 than there is in the US economy. 4.4. The importance of capital accumulation The process of capital accumulation is central to business cycles in the RBC framework. To highlight this importance, consider the effect of a positive productivity shock under the assumption that investment is zero at all dates. Then, higher productivity would raise the level of the production function and the marginal product of labor schedule, with each increasing proportionately. From the standpoint o f the representative individual, this would work just like a secular rise in the real wage rate, with exactly offsetting wealth and substitution effects on labor. Thus, hours per worker would be invariant to productivity, with consumption moving one-for-one with output 36. By contrast, in the RBC framework, investment increases in response to a positive productivity shock, i.e., the representative household optimally saves some fraction of the higher current output. Thus, it is also efficient to lower consumption and raise work effort relative to the fixed investment case, producing the cyclical comovements that we see in the actual economy. However, the introduction of capital as a factor of production in the basic model tends to make it difficult to match the behavior of output and labor input that we saw in the first panel of Figure 3, where labor is nearly as volatile as output. Fundamentally, this reflects the fact that capital is not particularly variable over the business cycle (see the second^panelof Figure 3). More specifically, the Solow decomposition indicates that 33t At + aNt + (1 a)tct, so that we expect a one percent change in labor to produce an a = ~ per cent change in output. It also works to mitigate the volatility of labor input, since it makes the marginal product of labor decline with the quantity of labor, given that the capital stock is essentially fixed over the business cycle. That is, despite substantial business cycle changes in investment, these do not have a large effect on the capital stock. =

4.5. Early successes and criticisms The results of Table 3 and Figure 7 illustrate why the last decade has witnessed an explosion of research on real business cycles. The basic RBC model holds the promise of being a coherent framework that integrates growth and business cycles. At the same time, there were clear areas in which the model needed to be improved, so that there

36 With a total factor productivity shock, this exact offset requires that there be a Cobb-Douglas production function, although it holds for any production function if the shock is labor augmenting. While it clearly holds if there is no capital, it also holds if capital is present, as may readily be verified using the line of argument in footnote 20. A key part of this more general result is that capital income increases with the productivity shock.

Ch. 14: Resuscitating Real Business Cycles

961

clearly was important additional work to done. Prescott (1986) summarizes moment implications as indicating that "the match between theory and observation is excellent, but far from perfect". Plosser ('1989) summarizes the model simulations as indicating that "the whole idea that such a simple model with no government, no market failures of any kind, rational expectations, no adjustment costs could replicate actual experience this well is very surprising". Rogoff (1986) warns of the potential power of the RBC model: " T h e . . . real business cycle results.., are certainly productive. It has been said that a brilliant theory is one which at first seems ridiculous and later seems obvious. There are many that feel that (RBC) research has passed the first test. But they should recognize the definite possibility that it may someday pass the second test as well." One notable part of the RBC program is its insistence on the construction of dynamic stochastic general equilibrium models, which is now the accepted approach to macroeconomic analysis across a wide range of research areas and perspectives. Even those who are skeptical o f the central role of productivity shocks have accepted the idea that "the basic methodological approach ... (is) ... relevant to models in which monetary disturbances play a greater role" as Rogoff (1986) forecasted that they would. But it is the other component of the RBC approach that was immediately controversial and remains so to this day: that technology shocks are the dominant source of fluctuations. The striking performance of the basic RBC model drew a strong critical reaction from macroeconomists working in the Keynesian tradition [Summers (1986), Mankiw (1989)]. Their criticisms focused on three main points. First, they questioned some of the parameter values used in the calibration of the model. In particular, they stressed that the model's performance required an empirically unreasonable degree of intertemporal substitution in labor supply. Second, they emphasized the model's counterfactual implications for some relative and absolute prices. The critics observed that the strongly procyclical character of the model's real wage rate was inconsistent with the findings of numerous empirical studies. They also pointed to Mehra and Prescott's (1985) earlier finding that standard preferences, such as Equation (4.2), are incompatible with the equity premium, i.e. the difference between the average rate of return to equities and the risk free rate. 37 In addition, t h e y suggested that a productivity shock theory of the cycle should imply a strongly countercyclical price level. Third, they argued that the use of the Solow residual was highly problematic, leading to excessively volatile productivity shocks. In retrospect, the first two criticisms of RBC analysis had a small impact on the RBC program. Rather than being fragile, the model's performance is surprisingly resilient to variations in its parameters. Much of the model's performance is anchored on three single ingredients: a highly persistent technology shock that is sufficiently volatile, a sufficiently elastic labor supply, and empirically reasonable steady-state shares of

37 See John Campbell (1999) for a detailed discussion.

962

R.G. King and S. T Rebelo

consumption and investment in output 38. The RBC model does not need to rely on a high degree of intertemporal substitution in labor choice. In fact some RBC models [e.g. Greenwood, Hercowitz and Huffman (1988)] assume that this elasticity is zero. However, either intertemporal or intratemporal substitution must be strong enough to produce realistic labor movements, a point to which we will return in Section 6 below. RBC researchers have produced a battery of models that lead to a relatively high elasticity of labor supply. The model's predictions for the real wage can be improved if we step away from the assumption of spot labor markets and incorporate contracts between firms and workers that allow for wage smoothing [Gomme and Greenwood (1995), Boldrin and Horvath (1995)] or other forms of labor contracts [Danthine and Donaldson (1995)]. It is hardly surprising that the assumption of spot labor markets produces unreasonable implications for the real wage. And while research on the equity premium puzzle continues, we now have models that are consistent with some aspects of the equity premium while maintaining the business cycle performance of the basic model 39. Lastly, the studies of Kydland and Prescott (1990) and Cooley and Ohanian (1991) have concluded that the price level is indeed strongly countercyclical during most time periods. It is the final criticism - that the Solow residual is a problematic measure of technology shocks - t h a t has remained the Achilles heel of the RBC literature. The key issues in this area involve quantitative rather than qualitative disagreements. With the exception of the two oil shocks, it is hard to identify the macro shocks that produce the productivity variations suggested by the Solow residual. If these shocks are large and important why can't we read about them in the Wall Street Journal? Also, the Solow residual often declines suggesting that recessions are caused by technological regress. Finally there are several measurement problems that can make the Solow residual a bad measure of productivity at cyclical frequencies. Summers and Mankiw emphasized the importance of labor hoarding, that is, unmeasured variation in labor effort over the business cycle. Perhaps even more important than labor hoarding is the cyclical variability in capital utilization. Solow-residual based measures of technology shocks that do not account for unmeasured variations in labor and capital will tend to be more volatile and procyclical than true shocks to technology. These difficulties arose as well in the earlier literature on growth accounting, where the Solow residual had its origins. The stated goal of that literature was to measure the long run evolution of disembodied technical progress, not the short run behavior of productivity. Its hidden agenda was to make the Solow residual negligible, that is, to measure production inputs well enough that all growth in output could be accounted for by movements in factors of production. For this reason the residual was often referred 38 Given the high correlation between investment and output it is not surprising that the model cannot display enough investment volatility if its share is unreasonably high. As the steady-state investmentoutput ratio increases the volatility of investment has to converge to that of output. 39 See Boldrin, Christiano and Fisher (1995) and Christiano and Fisher (1995). These models employ a two-sector structure and use preferencesthat feature habit formation.

Ch. 14: Resuscitating Real Business Cycles

963

to as a "measure of our ignorance". Growth accountants were horrified when they saw the measure of their ignorance recast as the main impulse to the business cycle. For now we will put the problems associated with the Solow residual as a measure of technology shocks on the back burner. But we return to them in Sections 7 and 8.

5. The central role of productivity shocks

In the standard RBC model, productivity shocks are central to the nature of business cycles. In this section, we will discuss three major aspects o f this relationship. First, we explain that the standard RBC model requires large and persistent productivity shocks, by considering how the comparative dynamics of the model change as productivity persistence is altered. Second, we show how the assumption that agents have rational expectations matters to the nature of real business cycles. Third, we discuss why other shocks cannot easily generate real business cycles in the standard model.

5.1. Productivity shocks must be large and persistent The simple driving process for productivity used by Prescott (1986) and Plosser (1989) provides a natural basis for discussing the volatility and persistence of productivity. These authors modeled the stochastic component of productivity as a first-order autoregressive process, log(At) = plog(At 1) + et. Under this specification, the statistical behavior of the productivity process is influenced by the serial correlation parameter p and the standard deviation of the zero mean "innovations" et. A standard result from time series textbooks [e.g., Hamilton (1994)] is that the autocovariance of log(At) with its own value lagged by j periods is /-" ,,J var(et) l _ p 2 • This autocovariance expression reveals that increases in the variability of the innovations directly raise the variability of productivity. Increases in the parameter p also increase the variability of the time series, since the variance of log(At) is var(Et) 1_p2 • However, an increase in p produces this additional variability by raising the persistence of the productivity series, since the jth-order correlation of log(At) is pJ. Thus, when we say that the standard RBC model requires that there must be large and persistent variations in productivity, we are making several related statements. Mathematically, these can be summarized by saying that the model requires large values of var(et) and o f p . Why does the standard model require large shocks? When we say that the model requires large shocks, we mean that there must be considerable variability in productivity. This statement is based on understanding how output, consumption, and other variables respond to shifts in e in the basic model. In all of the models that we study in this section, for example, output responds to a one percent increase in productivity by rising by no more than two percent: there is not much amplification of the productivity shock by the model. To illustrate the effect of smaller productivity shocks, we recomputed the simulation of the basic RBC model using an alternative series of productivity shocks, which have

964

R.G. King and S.T. Rebelo

an innovation standard deviation that is 0.0012 or about ~ times as large as the Solow residual. The result of this is shown in panels 1 and 2 of Figure 8: real business cycles explain a very small fraction of output and labor volatility. Since the standard RBC model is approximately linear, changes in the standard deviation of the innovations, std(e), simply work to rescale the model's fluctuations. We will return later to discuss more of the details of the computation of these alternative shocks, but at present it is sufficient to note that they were not chosen arbitrarily. Rather, they arise from correcting the Solow residual for the effects of varying capital utilization in ways that we will discuss further in Sections 6-8 below. Why does the standard model require persistent shocks? By saying that the variations in productivity must be persistent, we mean that the series generated from the standard RBC model will display autocorrelation similar to the US data only if p is near one. To discuss this, we consider in detail how the standard RBC model's implications depend on the extent of serial correlation in productivity. We begin by discussing the response of the economy to a serially uncorrelated productivity shock, i.e., the solution of the model when p = 0. While the dynamic responses to this shock shown in Figure 9 are the result of a complex set of factors - the preferences of households for consumption and labor supply, the production function and the mechanism for accumulating capital, and the interaction of households and firms in general equilibrium - the key mechanisms can be easily described. Productivity is assumed to increase by one percent (e = 1) in the initial period (date 1). Given the rise in the marginal product of labor resulting from the increase in productivity, the representative household faces an unusually high opportunity cost of taking leisure in this initial period. While there are offsetting income and substitution effects, the model's preferences were chosen so that a permanent increase in the real wage (such as the one associated with the trend in technical progress) generates exactly offsetting income and substitution effects so that labor and leisure are left unchanged. An implication of this result is that N has to rise in response to a temporary productivity increase. With a temporary shock, there is a much smaller income effect and there is greater incentive to substitute intertemporally, since the current wage is high relative to expected future wages. On net, the positive labor response amplifies the productivity shock: the impact effect on output in Figure 9 is 2%. Half of this response is due to the direct effect of the productivity shock and half due to the increase in labor. The representative agent must choose what the economy will do with all this additional output. One possibility is to consume it all in period one 40. However, this would be inefficient given that the marginal utility of consumption is decreasing, thus inducing a preference for smooth consumption paths. It is optimal to increase consumption both today and in the future. In fact, given that there are many future

40 Our figures make the impact date of the shock period 1, while the earlier theoretical analysis made the initial period zero. The discussion in the text follows the dating conventionin the figures.

Ch. 14." Resuscitating Real Business Cycles

965

Output with small A shocks

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Fig. 8. Consequences of smaller shocks and smaller labor elasticity. Sample period is 1947:2-1996:4. All variables are detrended using the Hodrick-Prescott filter.

King and S.T. Rebelo

R.G.

966 1.2-

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Fig. 9. Comparative dynamics to purely temporary productivity shock.

Ch. 14: ResuscitatingReal Business Cycles

967

periods, only a small fraction of the output windfall will be consumed at time 1; most of it will be invested. Thus investment rises by 8% in response to a 2% increase in output. It is interesting to note that the high volatility of investment, which Keynes ascribed to "animal spirits", arises naturally in this economy as the flip side of consumption smoothing. In the future, which begins with period 2 in Figure 9, productivity retums to its original benchmark level. The only difference relative to period zero is that the economy has accumulated some capital and only a relatively small amount since the productivity shock lasted just for one period. In line with the transitional dynamics that we discussed in Section 3 above, the optimal policy for the economy is to gradually reduce this excess capital by enjoying higher levels of consumption and leisure. The real interest rate again signals individuals to adopt these consumption and leisure paths: with a purely temporary change in productivity, the real interest rate falls in the impact period and in all future periods, making it desirable for individuals to choose consumption profiles that decline through time toward the steady-state level. The impulse response makes it clear that there will be no tendency for a period of high output and work effort to be followed by another period which has similarly high output. That is: the basic neoclassical model does not produce substantial internal propagation of temporary productivity shocks, a point which has been stressed by Cogley and Nason (1995). The effects of the one-time shock are propagated over time: the large investment in period 1 leads to high values of the capital stock that keep output above its steady-state level in the following periods. But this propagation mechanism is very weak. This weakness, together with the fact that Solow residuals display substantial persistence led most RBC studies to focus on specifications in which the persistence is inherited from the shock process. What happens with serial correlation in productivity consistent with Solow residuals? The solid line in Figure 10 depicts the effect of a serially correlated productivity shock using the estimate discussed in Section 3 above ( p = 0.979). In this case, the different series exhibit realistic persistence, which is inherited from the shock. The same mechanisms are at work as in the case of a purely temporary shock, but these effects are now drawn out over time. We now have an extended interval in which productivity is above normal. During this interval, workers respond by increasing their labor supply and most of the additional output is invested. Interestingly, high productivity is now initially associated with a high real interest rate, since the marginal product of capital schedule [At+ iD1F(kt+l,Nt+ 1) - 6] is shifted upwards by the productivity shock and by a higher level of future labor input, with capital responding only gradually via the accumulation of investment. However, later in the impulse responses, the rate of return is below its steady-state level because the capital stock has been built up while the stimulative effects of the productivity shock and labor input have dissipated. This leads consumption to initially grow through time and then subsequently to decline back toward the stationary level. Later in the impulse responses, as productivity converges slowly to its normal level, labor supply actually drops below the steady-state level as the economy enters a phase that resembles the

R.G. King and S.T. Rebelo

968 Productivity

1.2

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Ch. 14: ResuscitatingReal Business Cycles

969

transitional dynamics discussed above. Investment also eventually drops below the steady state, as the economy runs down the capital that was accumulated during the initial expansion. As with the case of the purely temporary shock discussed above, the early part of the impulse responses is dominated by the fact that the productivity shock raises the desirability of work effort, production, investment and consumption; the latter part of the impulse response function is dominated by the transitional dynamics, i.e., reduction o f capital back toward its stationary level. These impulse responses govern the autocovariances of productivity, output and other variables. With many periods of high output, there will be positive correlation between output and its past values: expansions and recessions will persist for many periods. Since the HP filter is so widely used in the real business cycle literature, it is worthwhile investigating its effects on the impulse response function, as an indication o f the effects that it has on the moments of the different variables: In Figure 10, the HPfiltered impulse responses are given by the generally lower paths that are highlighted with the 'o' symbol. One notable feature of this filtered impulse response is that there is less tendency for series to remain above or below their normal levels, i.e., filtering reduces the persistence of the various series: This effect is particularly noticeable for output and for productivity. Filtering also flattens the response of consumption and the real wage, at the same time that it makes the capital stock largely acylical.

5.2. The influence of productivity persistence In the basic RBC model~ the persistence parameter governing the productivity process has an important influence on the effects of shocks. For example, if we compare the responses of output in the two figures that we just looked at, that there is a larger initial output response in Figure 9 (where p = 0) than in Figure I0 (where p = 0.979). In particular, the additional persistence lowers the impact effect on output from about 2 when p = 0 to about 1.5 when p = 0.979. Similarly, the impact effect on work effort is smaller and the impact effect consumption is larger in Figure 10 than it is in Figure 9. When the productivity is very persistent, in the sense that the coefficient p is near unity, there are very dramatic effectS of small changes in the value of p. In this subsection, to exposit these effects, we focus on the consequences of assuming that productivity is a random walk. Economically, this involves the plausible assumption that changes in technology are permanent and there is some empirical support for the idea that productivity contains a unit root [e.g., Nelson and Plosser (1982)]. Mathematically, this amounts to setting p = 1 and implies that all shocks to productivity are expected to have an equal effect on current and expected future productivity. Impulse response analysis: Figure 11 shows that the impulse responses of all variables are substantially affected by changing the driving process parameter p from 0.979 to 1. Part of this difference involves the fact that a permanent productivity shock

R.G. King and S.T. Rebelo

970 Productivity

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Ch. 14: ResuscitatingReal Business Cycles

971

leads to an identical, proportional, long-run increase in consumption, investment and output, while the stationary shock has no long-run effect. There are also important differences in how the economy responds in the short-run depending on the value o f p . For example, in the impact period of the shock (t = 1), there is a much smaller response of labor and output to a permanent shock (the ' . ' path) than the standard shock (the ' o ' path). The date t = 1 shock is assumed to be 1% in both cases so that labor rises by 0.7% with productivity when p = 0.979 and by 0.5% when p = 1.0. Conversely, the impact effect on consumption is larger when p = 1 than it is when p = 0.979. After the impact period of the shock, the differences between the unit root case and the base case involve a combination of the differing direct effects of the shocks as well as the differing responses to permanent and temporary shocks. For example, one year after the productivity shock, the stationary model implies that 0.919 = p4 of the initial one percent impulse to productivity is (expected to be) present when p = 0.979 and the unit root model implies that there is a one percent higher productivity level. Explaining the influence of persistence: We previously used our intuition to explain the general shape of impulse response patterns, as in our discussion o f Figures 9 and 10 above. We described how the consumption and labor supply plan of the representative household are affected by shocks that affect wealth and the time path of wages. However, in the standard RBC model, there are general equilibrium effects that are subtle to think through. Consumption and labor supply decisions also depend on the time path of interest rates as well as wages. At the same time the time path of wages is influenced by labor supply decisions. To understand the channels of effect by which increased persistence affects the impulse responses, we adopt a version of Hick's celebrated demand decomposition that is suitable for dynamic models. 41 To exposit this decomposition, let us focus on the determination of the increase in consumption and leisure at the initial date t = 0. When a productivity shock occurs, the representative household understands that there is a higher amount of wealth as a result of this shock. I f wages and interest rates are unchanged, then this wealth effect would be used to finance a permanently higher level o f consumption and a permanently lower level of work effort. These effects are shown in Figure 12 for the persistent shock ( p = 0.979) and the fully permanent shock ( p = 1). There are two notable aspects of these wealth effects, which are computed in Hicksian fashion by finding the constant increments to the consumption and leisure paths that yield the same utility change as arises in the general equilibrium of the model. First, the wealth effects are the same for consumption and leisure in proportionate terms, which reflects the fact that the preference specification [u(ct,Lt) = log(&)+ Olog(Lt)] makes the wealth elasticities equal across goods. Second, the wealth effects are much larger when p = 1 as they are when p = 0.979. The representative household knows the path of wages which will arise as a result of the shock to productivity. Taking into account just the change in the wage path, we can

41 This decompositionis developed in King (1991).

R.G. King and S.T. Rebelo

972

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.~"~]'+"

-0.6 -0.8 -1

"+ m m + m + + + , z - , ~ . m

,

m

,

51

o+.~am

+.14 .p/ -0.++,

m ram+ram+++ 71s

,

loo

o,+I

1

,

++

,

+

,

7+

,

1oo

Quarl~

Fig. 12. Substitution and w e a l t h effects o f persistent and p e r m a n e n t shocks: stars, p e r m a n e n t s h o c k s ; squares, p e r s i s t e n t , s h o c k s .

Ch. 14: Resuscitating Real Business Cycles

973

determine the consequences for consumption and leisure at date O, which we call the wage effect. This effect is analogous to the Hicksian effect of the wage on consumption and leisure, in that it holds utility fixed, tracing out a substitution response. However, in our general equilibrium model, the productivity shock implies that wages change in all periods, {wt}t-0. Thus, the wage effect in Figure 12 takes into account the entire change in the time path of wages, combining static and intertemporal substitutions. When p = 0.979, the representative household correctly understands that productivity will raise the path of wages at date 0 and in many future periods, but that the long-run level of the wage will be unchanged. Accordingly, the household plans to consume more at date 0. Leisure hardly changes at all because the current period is about "average"; this conclusion depends on the particular p value. However, this pattern is sharply altered when p = 1, for then the household recognizes that the current wage is below the long-run wage and leisure rises due to the wage effects that stem from a positive productivity shock 42. In the general equilibrium of our RBC model, there is one additional channel: interest rate effects that induce intertemporal substitutions of consumption and leisure. In general, these intertemporal price effects are a powerful influence, but one that is not much discussed in informal expositions of the comparative dynamics of RBC models. In particular, permanent increases in productivity lead to high real interest rates and these induce individuals to substitute away from date 0 consumption and leisure as shown in Figure 12. We are now in a position to describe why a permanent shift in productivity (arising when p = 1) has a smaller effect on labor than a persistent but ultimately temporary shock ( p = 0.979). When the shock is temporary, there is a small wealth effect that depresses labor supply but temporarily high wages and real interest rates induce individuals to work hard. When the shock is permanent, there are much larger wealth effects and the pattern of intertemporal substitution in response to wages is reversed since future wages are high relative to current wages. However, labor still rises in this case in response to productivity shocks due to very large intertemporal substitution effects of interest rates. 5.3. Why not other shocks?

We have just seen that the basic real business cycle model driven by persistent technology shocks can produce realistic business cycle variation in real quantities. Do these same patterns emerge when the economy is buffeted by other disturbances? Shocks to fiscal and monetary policy have been long standing suspects in the search

42 The wage effect on consumptionis constant acrosstime in each case because the separablemomentary utility function implies that efficient consumption plans do not depend on the amount of work. Equivalently, with this utility function, there is a general substitution effect on consumption at all dates that works much like a wealth effect.

974

R.G. King and S.T. Rebelo

for the causes o f business cycles. It is thus natural to ask what are the effects o f these shocks in the standard RBC model. Shocks to government spending cannot, by themselves, produce realistic patterns o f comovement among macroeconomic variables 43. This result stems from the fact that an increase in government expenditures (financed with lump sum taxes) gives rise to a negative wealth effect that induces consumption to fall at the same time that labor and output rise. Thus, if government spending were the only shock in the model, consumption would be countercyclica144. Changes in labor and capital income taxes have effects that are similar to productivity shocks. However, these taxes change infrequently making them poor candidates for sources o f business cycles fluctuations. Monetary policy shocks have small effects in this class o f models both in versions in which money is introduced via a cash-in-advance constraint [Cooley and Hansen (1989)] and in models that stress limited participation [Fuerst (1992), Christiano and Eichenbaum (1992b)]. Many researchers are also currently investigating the nature of business cycles in models that start with the core structure of an RBC framework but also incorporate nominal rigidities o f various forms 45. This research has not yet produced a business cycle model that performs at the same level as the RBC workhorse described in Section 4.

6. Extensions of the basic neoclassical model

Since the basic RBC model contains explicit microeconomic foundations, part o f the literature has tried to improve its predictions for individual behavior. Other researchers have sought to improve the fit between model and data, focusing on moments and sample paths o f macroeconomic time series. In this section, we discuss two strands of this research: work on labor supply and on capital utilization. 6.1. The supply of labor There is a substantial body of work that focuses on the labor supply and, more generally, on the labor market in RBC models. This research is motivated by four difficulties encountered by the basic model on micro and macro dimensions. In most

43 There is a large literature that investigates the effects of fiscal policy in an RBC context. References include Wyrme (1987), Christiano and Eichenbaum (1992a), Rotemberg and Woodford (1992), Baxter and King (1993), Braun (1994), McGrattan (1994), and Cooley and Ohanian (1997). 44 For an early discussion of this difficulty, see Barro and King (1984). There is actually some evidence that in historical periods dominated by large shocks to government expenditures consumption was countercyclical, see Correia, Neves and Rebelo (1992) and Wynne (1987). 45 Examples include Cho and Cooley (1995), Dotsey, King and Wolman (1996), and Chari, Kehoe and McGrattan (1996).

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RBC models the implied labor supply elasticity to wage changes is very large, relative to micro studies. All of the variation in aggregate hours in the model arise due to movements in hours-per-worker, while the US experience is that most of the action comes from movements of individuals in and out of employment. Labor in the model lacks a close correspondence to labor in data (see Figure 6). Finally, labor input and its average product are very highly correlated in the model, but not in the data.

6.1.1. Estimated and assumed labor supply elasticities Labor economists have long been interested in estimating the response of the labor supply to a change in the real wage rate. In the standard static model, an increase in the real wage produces a substitution effect which leads to an increase in N and C as well as a wealth effect which leads to a decline in N and an increase in C. While the effect of a wage increase on consumption is unambiguous, the effect on the labor supply involves conflicting substitution and wealth effects. In a dynamic model, the effect of a wage change is complicated by the fact that the size of the wealth effect depends on the anticipated duration of the wage change: temporary wage changes have a small wealth effect and permanent ones have a large wealth effect. In a dynamic setting, the key equation that determines the supply of labor is the requirement that the marginal utility of leisure equal its cost along the intertemporal budget constraint. Many empirical studies of dynamic labor supply [e.g., MaCurdy (1981)], suppose that the utility function has the separable form (4.2), that we introduced in our discussion o f the approximation of the RBC model in Section 5 above and for which we showed that 1-N ^ = ~-(w + ,~).

(6.1)

In this expression, the term ~~-N - is the )~-constant elasticity of labor supply. To isolate the substitution effect, labor economists often estimate a )t-constant elasticity of labor supply and we organize our discussion of labor supply issues around this elasticity. In the basic RBC model, with its assumption of log utility (77 = 1) and a steadystate fraction of time spent working o f N = 0.2, it follows that the implied labor supply elasticity is four: a one percent change in the wage rate calls forth a four percent change in hours worked if there is little wealth effect ()~ constant), as with a temporary wage change. Yet, the microeconomic evidence on variations in hours worked is sharply at odds with the elasticity built into the RBC model. While estimates of this elasticity vary across different gender and race groups, they are typically much lower than unity [e.g. Pencavel (1986)].

6.1.2. Implications of varying the aggregate labor supply elasticity To show the consequences of adopting a labor supply elasticity in line with microeconomic estimates, the third and fourth panels of Figure 8 show the effect of

R.G. King and S.T. Rebelo

976

choosing 1-N 1 which is the upper bound suggested by Pencavel's estimates, rather than ~-N = 4 as in the model of Section 4. There is an important reduction in the volatility of output in the third panel of Figure 8. However, the model loses most of its ability to produce fluctuations in labor (see the fourth panel of Figure 8). In terms of moments, the standard deviation of output falls from 1.39 to 1.16 with the smaller labor supply elasticity and the standard deviation o f labor falls from 0.67 to 0.33. =

6.1.3. Modeling the extensive margin RBC researchers have investigated ways of enhancing the aggregate labor supply response by focusing on' the extensive margin. Figure 4 shows that most fluctuations in total labor input occur as households substitute between employment and nonemployment (the extensive margin) rather than between a greater or smaller number of per capita hours worked (the intensive margin). Explaing these facts seems to require that there are fixed costs of going to work or other attributes of the technology that lead to nonconvexifies in the individual's opporttmity set. There are two strategies for incorporating the extensive margin into business cycle analysis. The first is to assume that households are heterogeneous with respect to their reservation values of work, probably due to differences in fixed costs of working such as travel time to the job. This is a conventional approach in labor economics [see, e.g., Rosen (1986)] that has been introduced into a business cycle model by Cho and Rogerson (1988) and Cho and Cooley (1994). In order to make such a model tractable, it is necessary to view individual agents as efficiently sharing the resulting employment risks 46. An alternative approach, developed by Rogerson (1988) and applied to business cycles by G.D. Hansen (1985), assumes that households are identical but agree on an efficient contract which allocates some individuals to work in each period while leaving the remaining idle. A remarkable feature of both approaches is that there is a stand-in representative agent whose preferences generally involve more intertemporal substitution in work than displayed by the underlying individual agents. For simplicity and congruence with the literature, we focus our discussion on the economies with indivisible labor and lotteries, following Rogerson (1988). Each individual in the economy has to choose between working a fixed shift of H hours and not working at all. Suppose that preferences are such that individuals would ideally like to supply a number of hours N < H. This arrangement is not possible because the choice set is not convex, it includes N = 0 (with zero labor income) and N = H (with labor income wH) but no linear combinations of these two points. In this set up agents can be made better off by the introduction of lotteries which convexify their

46 In actual economies,variationsin aggregate hours reflect changes at both the intensive and extensive margins. In a model where workers have different fixed costs of going to work, Cho and Cooley (1994) have captured both of these responses. Such a framework appears necessary to explain the differing cyclical patterns of employmentand hours-per-workerin the USA and Europe that are documented by Hansen and Wright (1992).

Ch. 14: Resuscitating Real Business Cycles

977

choice set. By entering a lottery an agent can choose to work a fraction p of his days remaining unemployed a fraction (1 - p ) of his time. Let us use the subscript 1 to denote those agents who are assigned to work by the random lottery draw and the subscript 2 to refer to the unemployed agents. The expected utility of an individual prior to the lottery draw is p u ( c l , 1 - H ) + (1 - p)u(c2, 1),

(6.2)

where p is the fraction of the population assigned to work. Feasible allocations of consumption across the employed and unemployed agents must obey p c l + (1 - p ) c 2 = c,

(6.3)

where c is per-capita consumption. Maximizing Equation (6.2) subject to condition (6.3), we find that marginal utility of consumption must be equated across types, i.e., DlU(Cl, 1 - H ) = DlU(C2, 1),

(6.4)

which is an efficient risk-sharing condition in this situation of employment lotteries as in many other contexts. The standard indivisible labor model. The typical treatment of the indivisible labor model, as in Rogerson (1988) and Hansen (1985), involves assuming separable utility. Within the general class of utility functions (3.8), this corresponds to a = 1 so that u(c, L) = log(c) + log(o(L)). In this case, efficient risk-sharing implies that the employed and unemployed share the same level of consumption (c~ = c2). Using this fact, expected utility can be written as u(c, L) = log(c) + (1 - L) ~1 log(V~ \ 02//"] + log(v2),

(6.5)

where L = 1 - p H is the average number of hours of leisure in the economy and where vl = v(1 - H ) and v2 = v(1). There are three notable features of this economy. First, even though each individual agent has a finite elasticity of labor supply, the macroeconomy acts as if it were populated by agents with a more elastic supply of labor. In particular, the standin representative agent for this economy has preferences that are linear in leisure, implying a infinite )>constant elasticity of labor supply [see Equation (6.1) with t / = 0], a feature whose consequences we explore further below. Second, contrary to conventional wisdom, this is an economy in which it is optimal to have unemployment. Finally, agents actually choose to bear uncertainty by entering the lottery arrangement instead of working a fixed number of hours in every period. It is interesting to explore further why the individual elasticity of labor supply differs from that of the economy as a whole and the consequences of this difference for the

978

R.G. King and S.T. Rebelo

determination of output and labor. The individual elasticity of labor supply answers the question "how many more hours would you work in response to a 1% raise in salary?". But the answer to this question is irrelevant because the number o f hours worked is not flexible, it is either H or zero. In other words, the intensive margin is not operative and hence its elasticity of response is irrelevant. Proceeding to the consequences for the determination of labor, the preferences o f the stand-in representative agent (6.5) imply that small changes in wages and prices can lead to very large effects on quantities. To see this, consider an isolated individual maximizing

[3tIl°g(ct)+(1-Lt)ll°gQ~ ) + log(v2) 1 t=0

Along the relevant intertemporal budget constraint, suppose that the discounted cost of a unit o f leisure is [3t)~twt. Then, for the individual to work part of the time (0 < Lt < 1) But, if this condition is in each period, it must be the case that )~twt = 1 1og(vl/V2)47. satisfied, the individual is indifferent across all sequences of leisure which imply the same level of ~ _ 0 /3t [(1 - Lt ) ~ log(vl/v2 )]: there is an infinite intertemporal elasticity of substitution in work. One implication of this labor supply behavior is that it is the demand side o f the labor market which determines the quantity o f employment and work effort in the equilibrium o f the indivisible labor model. From this perspective, firms choose the quantity o f labor that equates its marginal product to the real wage, with the position of the demand schedule being shifted by the level o f productivity and the capital stock. Since the capital stock and the multiplier )~t are endogenously determined, this labor market equilibrium picture is incomplete, but it is a useful partial equilibrium description. The indivisible labor model with more general preferences: When the indivisible labor model is generalized, as in Rogerson and Wright (1988), there are interesting new conclusions. To develop these, we use the utility function (3.8), with a ¢ 1. Efficient risk-sharing condition implies that consumption allocations must satisfy

Cl ~C2

(6.6)

According to this specification, if a > 1 there will be more consumption allocated to the employed (group 1) than to the unemployed (group 2) 48. Thus, as more individuals are allocated to the market (higherp) aggregate consumption will rise even

47 If AtW~ < 1 1og(v~/O2), our agent spends all available time at t in leisure (L = 1). If ,~twt > log(vl/V2), our agent devotes no time to leisure (L = 0). 4s This conclusion makes use of the fact that v2 = v(l) > vI = v(1 -H), which follows from the fact that v is an increasing function.

979

Ch. 14." Resuscitating Real Business Cycles

if consumption o f employed individuals and unemployed individuals stays relatively constant. Further, using this consumption rule along with the expected utility objective, there is a stand-in representative agent whose preferences are 49 1

u(c,r) =

{cl-av*(L) l - a -

1}

(6.7)

where o

v*(L)=

v1~ +

1-

v ~-) i ~ .

There are two points about this expression. First, the stand-in's utility function inherits the long-run invariance o f hours to trend changes in productivity from the underlying utility function (3.8). Second, the stand-in's utility function inherits the original utility function's properties with respect to effects of changes in leisure on the marginal utility of consumption. In particular, when a > 1, the marginal utility of consumption is decreasing in leisure. Let us again think about an isolated individual maximizing lifetime utility, ~ _ o f i t u ( c t , L t ) , but with the new momentary utility function (6.7). As with our discussion of the representative worker in Section 4 and as with our previous discussion in this section, the stand-in agent equates the marginal utility of consumption and the marginal utility o f leisure to the shadow values along the economy's resource constraint (Dlu(ct,Lt) = )~t and Dzu(ct, Lt) = ~twt = ),tAtDzF(kt,Nt)). These conditions must always hold if there is an interior optimum for work effort, i.e., 0 < Lt < 1 in each period. Taking loglinear approximations to this pair of conditions, we find - a ~ t + (1 - a)xL,

q

-

where Ic economy 50.

= ~t,

LDo* (L)

v*(r)

L

=

(6.8)

+

(6.9)

is pinned down by information on the steady state of the

49 There are two steps to this demonstration. First, one shows that efficient risk-sharing implies that expected utility is proportional to:

1 {

1-a

[ (1 a)

ct a [ pol~

( ]-o'~]0 } +(l-P)V2°'J-1 if a ¢ l ,

and then one substitutes in for leisure using L = 1 -pH. 50 That is, tc- LDo*(L) - v*(L)

) - Lw - L (wN/y) -LD2u(c,L CDlu(c,L) c N (c/y)"

R.G. King and S.T. Rebelo

980

This set of equations reveals that there is infinitely elastic labor supply even when the preference specification is not separable. That is, the pair of equations implies that 0 = ~, + a~, which is the statement that the stand-in will supply any amount of work at a particular real wage. But because preferences are nonseparable, variations in work require variations in consumption. When a > 1, in particular, workers require more consumption than nonworkers and aggregate consumption is negatively related to leisure, i.e.,

Thus, this model involves a modified form of the permanent income hypothesis, which includes the effects of changes in work effort on the marginal utility of consumption. Baxter and Jermann (1999) have argued that this type of preference nonseparability will arise in any model with household production; they have also stressed that this specification can make consumption more cyclically volatile. 6.2. Capacity utilization

In the standard version of the neoclassical model, there is a dramatic contrast between the short run and long run elasticities of capital supply. The short run elasticity of capital supply is zero: there is no way for the economy to increase the capital stock inherited from the previous period. In contrast, the long run elasticity of capital supply is infinity: there is only one real interest rate consistent with the steady state o f the economy. This difference between short run and long run elasticities stems from the assumption that capital services are proportional to the stock of capital. This is an assumption we make every time we write a production function as Y = F ( K , N ) . While this assumption may be suitable for some purposes, it is clearly problematic for business cycle analysis. The third panel of Figure 3 suggests that capacity utilization displays pronounced cyclical variability. The fact that equipment and machinery are used more intensively in booms than in recessions is corroborated by the procyclical character of electricity consumption in manufacturing industries [Burnside, Eichenbaum and Rebelo (1995)] and by the fact that expansions are accompanied by the use of two and three shifts in manufacturing industries [Shapiro (1993)]. All this evidence suggests that the flow of capital services is high in expansions. In contrast, recessions are times when capital tends to lie idle, thus producing a small service flow. Several authors have extended the basic RBC model to incorporate variable capital utilization. Kydland and Prescott (1988) showed that introducing time-varying capital utilization enhanced the amplification capability o f their 1982 model. Greenwood, Hercowitz and Huffman (1988) introduced variable utilization in a model that features

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shocks to the productivity o f new investment goods 51. Finn (1991) used a similar framework to study the interaction between capital utilization and energy costs. In her model, more intensive capital use accelerates the depreciation o f capital and raises marginal electricity consumption. Burnside and Eichenbaum (1996) explored a model with both capital utilization and labor hoarding. They showed that these two features significantly enhance the ability of the model to propagate shocks through time 52. Modeling variable utilization. Most studies o f variable utilization assume that depreciation is an increasing function of the utilization rate 53. The benefits from variable capital utilization can be incorporated into the production function as follows: Yt = AtF(ztKt,NtXt) = At(ztKt) l a(NtXt)a. where zt denotes the utilization rate 54. The costs o f variable capital utilization are imbedded in the following law o f motion for the capital stock: K t + 1 : ~ + [1 - b ( z , ) ] K t ,

where 6(.) is a convex, increasing function o f the utilization rate 55. To determine its optimal rate o f utilization, a firm maximizes its profits holding fixed its future capital stock. The marginal benefit of a higher utilization rate is additional output (AtDiF(ztKt, NtXt)Kt) and the marginal cost is higher (replacement) investment (dIt = Db(zt)Kt). Equating these and using the Cobb-Douglas production function, we find that efficient utilization implies (1 - a)At(zt)-a(Kt)~-a(NtXt) a = Dr(zt)Kt,

(6.10)

which is the requirement that the marginal benefit in terms o f additional output produced be equated to the marginal cost in terms o f additional units o f capital being worn out. The consequences o f variable utilization. To explore how efficient variation in the utilization rate affects the linkages in the economy, we linearize Equation (6.10) to

51 These shocks tend to make consumption and investment move in opposite directions. Introducing capital utilization eliminates this counterfactual correlation between consumption and investment. 52 Their model is also capable of producing a humped shape response of investment to technology shocks - a feature that is common in empirical impulse response functions estimated using VAR techniques. 53 An exception is Kydland and Prescott (1988). 54 For simplicity, we use the Cobb-Douglas form throughout our discussion of capital utilization. 55 Thus, it has a positive first derivative Dr(.) and a positive second derivative De6(.).

R.G. King and S.T. Rebelo

982

obtain an expression for ~t and substitute this result into the linearized production function: 33t = 3t + a-~t + (1 - a)(]c~ + ~t) = A t + (1 - a)/ct + aNt + ~1 - a ( A t - a ] c t + a N t )

(6.11)

In this expression ~ represents the elasticity o f Db(zt), which is positive if there is increasing marginal depreciation cost of higher utilization 56. The model without utilization occurs as a special case in which ~ is driven to infinity, since in that case the quantity o f capital services does not respond to changes in the marginal product of these services. At the other extreme, as ~ is driven toward zero, the response of output becomes )t = FAt 1 ^ + Nt. ^ For this reason, time-varying capital utilization is sometimes described as leading to a short-run production fimction that is nearly linear in labor. Variable utilization makes the marginal product o f labor - the real wage rate - less responsive to changes in labor input. The comparable log-linear expression for the real wage rate is

~t:(f:,-Nt):3t+(1-a)[ct+(a-1)Nt+

1-a

(At-alct+aNt)

(6.12)

and, as ~ is driven toward zero, the response o f the real wage approaches wt = FAt.1 ^ In other words, the labor demand schedule drawn in (w,N) space "flattens" as depreciation becomes less costly on the margin (~ falls). When ~ is driven to zero, the labor demand curve becomes completely flat.

7. Remeasuring productivity shocks We have seen that productivity shocks are an essential ingredient of real business cycle models. In the absence of measurement error in labor and capital services, these shocks coincide with the Solow residual. Prescott (1986) used the Solow residual as a measure of technology shocks to conclude that these shocks "account for more than half the fluctuations in the postwar period with a best point estimate near 75%". There are three reasons to distrust the standard Solow residual as a measure of technology shocks. First, Hall (1988) has shown that the Solow residual can be forecasted using variables such as military spending, which are unlikely to cause changes in total factor productivity. Similarly, Evans (1992) showed that lagged values o f various monetary aggregates also help forecast the Solow residual. Second, the conventional Solow residual implies probabilities of technological regress that are implausibly large. Burnside, Eiehenbaum and Rebelo (1996) estimate that the

56 It can be shown that ~ = z(D26)/D6 > O.

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983

probability o f technological regress associated with the conventional Solow residual is 37% in US manufacturing. Finally, cyclical variations in labor effort ("labor hoarding") and capital utilization can significantly contaminate the Solow residual. There are two strategies for dealing with these extra, hard-to-measure sources o f factor variation. The first strategy is to use an observable indicator to proxy for the unobserved margin. For example, since individuals working harder may have more accidents in an industrial setting, the frequency o f worker accidents could be used as an indicator o f unobserved effort 57. More commonly, electricity consumption in manufacturing industries is taken as an indicator o f capacity utilization. The second strategy is to use implications o f the model to solve out for the unobserved factor variation and then to examine other implications o f the m o d e l economy. We discuss application o f each o f these strategies to measuring capacity utilization in the remainder o f this section. Capital utilization proxies: Burnside, Eichenbaum and Rebelo (1996) employ electricity use as a proxy for capacity utilization. In particular, assuming that the utilization rate is proportional to electricity utilization, they can use the Solow decomposition in modified form, log SR[ = log Yt - a log Art - (1 - a)[log Kt + log(z[)],

(7.1)

where log(z/) is the log o f electricity use. They find that when electricity use is employed as a proxy for capital services the character o f the Solow residual associated with the manufacturing sector changes dramatically: (i) there is a 70% drop in the volatility o f the growth rate o f productivity shocks relative to output, implying that a successful model must display much stronger amplification than the basic RBC model; (ii) the hypothesis that the growth rate o f productivity is uncorrelated with the growth rate o f output cannot be rejected; and (iii) the probability o f technological regress assumes much more plausible values, dropping to 10% in quarterly data and to 0% in annual data. These corrections to the Solow residual significantly reduce the fraction o f output variability that can be explained as emanating from shocks to technology 58. Using the model to measure capacity utilization: A n alternative strategy is to use the model's implications for efficient utilization to solve for the unobserved

57 Several variants of this proxy strategy have been used to shed indirect light on the presence of labor hoarding. Bils and Cho (1994) use time and motion studies to document the presence of variability in effort. Shea (1992) uses data on on-the-job accidents to construct an indirect measure of labor hoarding. Burnside, Eichenbaum and Rebelo (1993), Sbordone (1997), and Basu and Kimball (1997) postulated a model of labor hoarding that they proceeded to use to purge the Solow residual of variations in the level of effort. s8 Aiyagari (1994) proposed a method to compute a lower bound on the contribution of technology shocks to output volatility. His procedure relies on knowledge of two moments in the data: the variability of hours relative to the variability of output and the correlation between hours worked and labor productivity (which is essentially zero in the data). Unfortunately, his method is not robust to the presence of labor hoarding or capacity utilization.

984

R.G. King and S.T. Rebelo

utilization decision, i.e., zt. In essence, this empirical strategy corresponds to our theoretical method in the previous section, when we solved out for zt in order to derive Equation (6.11), which describe how output responds to changes in labor, capital and productivity when utilization is efficiently varied. One possibility would be to exactly follow this strategy, substituting observed variations in labor and capital into Equation (6.11) to compute the productivity residual, but we use a more "reduced form" approach that we describe more fully in the next section.

8. Business cycles in a high substitution economy Motivated by the vanishing productivity shock, we now construct an economy in which small variations in productivity can have large effects on macroeconomic activity, i.e., an RBC model in which there is substantial amplification of shocks. There are two central ingredients to this model. First, as in Section 6.1, we assume that there is indivisible labor. This makes the supply o f aggregate hours strongly responsive to changes in wages and intertemporal prices. Second, as in Section 6.2, we assume that there is variable capacity utilization. This makes the supply o f capital services strongly responsive to changes in the level o f aggregate hours. Taken together, these ingredients mean that the economy has high substitution in all factors o f production. Further, the Solow residual is a very poor measure o f technology shocks in our model economy. However, the very same structural feature that makes the Solow residual a bad measure o f technology shocks (unmeasured variation in capital services) also provides a powerful amplification mechanism that allows our model to account for the observed output variation with much smaller shocks. Finally, our model provides a means o f implicitly measuring the smaller shocks that occur, which can be viewed as a variant o f Solow's approach 59. 8.1. Specification and calibration

The specification and calibration o f the model follows the same general approach that we used in Section 4, but with some relatively minor modifications. Restrictions on the steady state: First, we know that the production side o f the basic model determines most aspects o f the steady state and that continues to be true with variable capital utilization. The efficiency condition for utilization in the steady state determines a steady-state utilization rate such that r + b(z) = D6(z), with the remainder o f the steady-state relative prices and great ratios then adjusted to reflect the fact that the flow o f capital services is z K rather than K.

59 The approach was suggested by Mario Crucini in unpublished research many years ago, so perhaps we should call these "Crucini residuals". Another application is contained in Burnside, Eichenbaum and Rebelo's (1993) study of unobserved effort (labor hoarding). Ingram, Kocherlakota and Savin (1997) use a similar procedure to infer information on observed shocks to the home production sector.

Ch. 14: Resuscitating Real Business Cycles

985

Table 4 Calibration of high substitution economy ~r

b

y

a

~

~

P

(Ye

3

0.984

1.004

0.667

0.025

0.1

0.9892

0.0012

Second, since we are assuming an indivisible labor model, there is a different calibration of the preference side of the model. Evidence from asset pricing studies suggests that a is larger than the unit value used in the basic model; this means that our model will have the realistic implication that more consumption is allocated to working individuals than to nonworking individuals. Drawing on Kocherlakota's (1996) review, we use o = 3. We assume that 60% of the population is employed in the steady state and that employed individuals work 40 hours. This implies that an average individual's hours are N = 0.214, i.e., 24 hours out of a weekly 112 hours o f nonsleeping time. Then, this information (including the assumed value of a ) determines the ratio v(1)/v(1 - H ) which dictates the ratio of consumptions o f the two types o f individuals. It turns out that the ratio CJCe is 3.31 so that workers have substantially higher consumption than nonworkers. Table 4 summarizes our parameter assumptions. Unless otherwise discussed, the parameters are the same as in Table 2. Measuring technology shocks: We use the implications of our model as discussed in the last section to produce a series on technology shocks which is consistent with unobserved variation in capacity utilization 6°. In particular, we start by assuming a value for the persistence and volatility of technology shocks and solve the model. The decision rule for output can be written as

Yt = : ykkt + ZyAA,. Using this decision rule together.with data for output and capital (which we logged and linearly detrended), we can compute an initial guess about the time series for technology shocks 61: 1

_ ,ryk

60 There is no unique way of computing this shock process, but rather any of the model's decision rules could be used in this way or these rules could be combined with other relationships in the model. For example, one could exploit the decision rule for utilization as in Burnside, Eichenbaum and Rebelo's (1993) analysis of labor hoarding, ~t = JVyklct+ ~yA~lt, and combine this with the modified Solow decomposition(7.1). This alternativemethod would produce a different shock process, which lead to broadly similar, but somewhat less dramatic results. The difference between these two productivity measures lies in whether labor in Equation (7.1) is taken from the data or from the model. 61 We should not use the empirical capital stock series since these are flawed in the eyes of the model: they are computed assuming constant rates of depreciation. This can be circumventedby using a second decision rule to compute the "true" capital stock series. In practice this has little impact on the results.

986

R.G. King and S.T. Rebelo

This guess is not exactly fight because the serial correlation coefficient (p) for this zit series need not match that used to solve the model and to construct the Jr coefficients. Therefore, once we obtain a time series for zit, we compute its persistence (p) and use this new value to solve the model again. Using the new decision rule, we recompute ~it and once again its calculate its persistence. We continue this process until the new and old estimates for the serial correlation of~it are the same. This iterative procedure yielded an estimate of 0.9892 for the first-order serial correlation and 0.0012 for the standard deviation of the et. 8.2. Simulating the high substitution economy With a series of productivity shocks in hand, we simulated our model economy's response to these shocks just as we previously did for the standard RBC model. Figure 13 displays the results, which we think are dramatic. Panel 1 shows the model and actual paths for output, which are virtually identical. In part, this is an artifact of our procedure for constructing the technology shock, which is a weighted average of output and capital as we just discussed. For this reason, we think that the performance of the model should not be evaluated along this dimension. Instead, the model has to be judged by its predictions for other variables of interest. The remaining panels of Figure 13 display the model's implications for total hours worked, consumption and investment, with all of these series detrended with the HP filter. The correlation between the empirical and the simulated series is 0.89 for labor, 0.74 for consumption and 0.79 for investment! This remarkable correspondence leads to three sets of questions, similar to those which arose in the analysis of the standard RBC model. First, how do small variations in productivity have such dramatic effects? Second, what are the properties of the technology shocks? Third, how sensitive are the results? 8.3. How does the high substitution economy work? The high substitution economy contains four mechanisms that substantially amplify productivity shocks and lead to strong comovements of output, labor, consumption and investment. To begin, variable capacity utilization makes output respond more elastically to productivity shocks in Equation (6.11), which we repeat here for the reader's convenience:

Since utilization of capital increases when there is a positive productivity shock, there is a direct effect which is part of the amplification mechanism. In the limiting case of = 0 for example, a labor's share of a = 2 implies that the productivity shock raises output by ~1 or 3 times its direct effect. We use a value of ~ = 0.1 in constructing our simulations, so that the effect with a = 2 is 1 + ~l-a = 1+°33 ~_~ = 1.43. Thus, variable utilization helps create amplification, but only in a modest manner.

Ch. 14." Resuscitating Real Business Cycles

987

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Fig. 13. Capacity utilization model: simulated business cycles. Sample period is 1947:2-1996:4. All variables are detrended using the Hodrick-Prescott filter.

R.G. King and S.T. Rebelo

988

Relative to the standard RBC model that we discussed in Section 4, most of the increased amplification in the model of this section comes from greater elasticity of the labor demand and labor supply schedules. Highly elastic labor supply is due to indivisible labor: work effort is highly responsive to small changes in its rewards. In fact, we have previously argued that it is the demand side which approximately determines this quantity in indivisible labor economies. Variable capacity utilization makes the labor demand more elastic. As discussed above, labor demand is implicit in the equation:

~t = ( ) t _ ~ t ) = ~ t + ( l _ a ) ~ + ( a _

1)~t + 1 - a

(At-aict+aNt)

In the model without variable utilization (or with ~ = c~), a one percent increase in labor quantity causes the real wage to fall by 0.333 percent when a = 2, since the coefficient on Nt is (a - 1). At the other extreme, as ~ is driven toward zero, the response of the real wage to a productivity shock approaches ~t = FAt, 1 ^ i.e., the labor demand schedule becomes more elastic until it is completely elastic in the limit. With variable utilization, the combined coefficient on labor is (a - 1) + ~1-a a . Using a = ~ and ~ = 0.10, as in our simulations, we find that the combined coefficient is (0.67 - 1) + 0.33 n 67 = -0.043: a one percent change in labor requires a decline in the 0.77 .... wage that is an order of magnitude smaller than in the standard model. With indivisible labor and variable utilization, a small productivity shock shifts up labor demand and calls forth a large increase in labor supply. In order to determine the exact size o f this change, however, it is essential that we simultaneously determine the path of capital (kt) and the multiplier ()~t). The final structural feature that is important for the simulated time series is the nonseparable form of the utility function. In the standard Hansen-Rogerson case of log utility, most of the model's change in output goes into investment rather than consumption. However, since the efficient plan calls for the allocation of more consumption to employed individuals when ~r > 1, the high substitution economy displayed in Figure 13 involves more volatile consumption that corresponds closer to the data. We return to a discussion of this feature in the context of impulse responses later in this section.

8.4. What are the properties of the shocks? Is this remarkable coherence between data and model achieved by using an empirically unpalatable productivity shock as a driving force? Figure 14 answers this question. The first panel depicts the level of the productivity, which involves a combination of the deterministic trend and stochastic component (i.e., AtXta). It increases through time smoothly in the manner that many economists believe is appropriate for the level of technology. The second panel of Figure 14 shows the growth rate of productivity in our economy. This graph shows that the average rate of technical progress is large

989

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Fig. 14. Capacity utilization model: productivityand the Solow residual. enough that a measured technological regress occurs only very rarely, given the low variability of technology shocks. The third panel of Figure 14 graphs business cycle variation in the conventional Solow residual and the productivity shock used in our model, using the HP filter to create these components. Figure 14 illustrates that it

990

R.G. King and S. T. Rebelo

Table 5 Sensitivity analysis to different ~ values value

ec 1 l 1 I 1

7 11o

Standard deviations I N A

Y

c

1.36 1.39 1.40 1.40 1.41 1.41 1.42

1.01 0.94 0.92 0.91 0.91 0.90 0.89

2.62 2.86 2.94 2.99 3.05 3.09 3.15

0.90 1.07 1.13 1.16 1.20 1.23 1.26

0.79 0.45 0.34 0.28 0.22 0.19 0.15

e

Persistence parameter (p)

Likelihood of technical regress

0.0061 0.0034 0.0026 0.0021 0.0017 0.0014 0.0012

0.9783 0.9798 0.9822 0.9841 0.9866 0.9880 0.9892

0.1859 0.1106 0.0653 0.0352 0.0101 0.0050 0.0050

is possible to explain the variability o f US macroeconomic activity with productivity shocks that are much smaller than those conventionally used in the literature. 8.5. H o w sensitive are the results?

We next discuss the sensitivity o f our results to the choice of parameters and to the measurement o f output. Sensitivity to parameterization. The value chosen for the parameter ~ is a key ingredient in the results. This is not surprising since we know that when ~ equals infinity the model with capital utilization reduces essentially to the standard model. Table 5 shows how some key model statistics change with different values for ~. For every value of ~ we used the iterative process described above to ensure that the stochastic process assumed for A~ is in fact consistent with the properties o f the technology shock implied by the model. In every case we report the persistence of the shock ( p ) and the standard deviation of the innovation (e) as well as the implied probability o f technological regress. Low probabilities o f technological regress can be 1 obtained for values o f ~ that are lower than 3" As an alternative check on the sensitivity o f the model to ~, Figure 15 depicts the impulse response for this model for three values o f ~: oe, I and 1 . To simplify the comparison between these impulse responses we did not adjust the stochastic process for the technology shock. All three responses were computed with the same standard deviation o f innovation (a~, = 0.0072) and same persistence ( p = 0.979). The three impulse response functions depicted in this figure have similar dynamic properties, but vary mostly in the degree of amplification. The solid line is a fixed capital utilization model (~ = oc) like the basic RBC model of Section 4, but with indivisible labor. In this model, a productivity shock has a larger effect on output than in the standard RBC model: when there is a one percent productivity shock, output rises by just less than two percent on impact with fixed utilization (~ = ec). However, the

Resuscitating Real Business Cycles

Ch. 14:

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R.G. King and S.T. Rebelo

992

increase in amplification is small relative to what happens when indivisible labor and capacity utilization are introduced simultaneously. A one percent productivity shock has an impact effect on output o f 8 percent when ~ = 0.2 and o f 13 percent when = 0.1. From various experiments with this model economy, it is clear that values of ~ less than one are important to obtain substantial amplification. For example, if there is a value of ~ = 1 then there continues to be on average a regress in the level of productivity every ten quarters (see Table 5 above). It is important that econometric evidence be produced on the cost o f varying capital utilization, so as to determine the extent to which this high substitution economy is realistic 62. One specific feature o f the impulse response in Figure 15 is worth some additional discussion. In all o f the cases, the real interest rate increases in response to a positive productivity shock, at least for the first twenty quarters shown in the graph. In all cases, the level o f consumption broadly resembles the level o f output and the growth rate of consumption is negative, even though the real interest rate is high by comparison to its steady-state level. This behavior o f consumption reflects the fact that aggregate consumption is the sum o f consumptions by individuals that are working and those who are not. Since working agents have more consumption, an increase in the fraction o f individuals working makes aggregate consumption rise and fall with aggregate employment 63. Sensitivity to the measurement o f output. We have seen that variable utilization and indivisible labor produce an economy in which (i) small productivity shocks have large effects on output; (ii) the standard Solow residual is substantially mismeasured; and (iii) labor and output move together on an approximately one-for-one basis. In this economy, however, there is an important sense in which output is mismeasured. There is a standard line o f intuition which suggests that "intermediate" activities such as utilization should not be too important for economic activity and, in this case, suggests that the large effects o f productivity on output and the strong eomovement o f output and labor are simply artifacts of output mismeasurement. To explore these ideas, output net o f depreciation can be defined as Ot = Yt - 6(zt)kt = AtF(ztkt, Nt) - 6(zt)k~

(8.1)

and this expression can be used to make four important points. First, output is also mismeasured in the standard neoclassical model, i.e., even in the absence of a variable depreciation rate. Second, with efficient utilization, changes in net output are dot = F(ztkt, Nt) dA, + AtO2F(ztkt, Nt) dN, +AtDlF(ztkt, Nt)(kt dzt + zt dkt) - D6(zt) ]~tdzt --

(~(Zt)

dkt

= F(ztkt, Aft) dAt + AtO2F(ztkt, Nt) dNt + AtOlF(ztkt, Nt) zt dkt - 6(zt) dkt, 62 Basu and Kimball (1997) provide an estimate of a parameter that is essentially our ~. Their point estimate is about unity, but the parameter is very imprecisely estimated. 63 Baxter and Jermann (1999) stress that equilibrittm models with nonseparable preferences can generate apparent excess sensitivity of consumption to income, working in a model where labor supply variation is on the intensive rather than extensive margin.

Ch. 14: Resuscitating Real Business Cycles

993

where the latter equality follows from AtD2F(ztkt, Nt) kt dzt - D6(zt) ktdzt = 0 when utilization is efficient. Thus, there is a sense in which the standard intuition is correct because net output does not respond to utilization. Third, near the steady state, the Solow decomposition for net output is (8.2)

where m = ~ = [1 @]-l. This modification takes into account the fact that the net production function :is more labor intensive and the fact that productivity shocks affect gross output but not depreciation. Thus, for example, if depreciation investment is 10% of output, then m = 1.11. Thus, if output is measured as net of depreciationindependent of whether capacity utilization affects depreciation - then this will tend to strengthen the magnitude o f labor's effect on output. Fourth, most importantly for our purposes, the net production function qSt = AtF(Nt, ztkt) - 6(zt)kt has the same marginal product schedule for labor, A t D I F ( N t , ztkt) as does the standard production function. Thus, our analysis of the "labor demand" consequences of efficient utilization are unaffected by whether depreciation costs are deducted from output or whether they are not. Returning to Equations (6.11) and (6.12), we can thus see that a "net output" measurement requires that we replace Equation (6.12) with the modified growth accounting expression (8.2), but that we need not change the labor demand schedule (6.11) at all. Further, it is a highly elastic labor demand that is the key force behind the great amplification present in our high substitution economy. -

9. Conclusions

This chapter provides a perspective on developments in the literature on real business cycles over the last decade. We discussed the structure of these models, their successes and their deficiencies. We also argued that three main criticisms levied against first-generation real business cycle models have been largely overcome. First, the performance of the basic RBC model has proved to be remarkably resilient to alternative parameterizations, including versions in which the elasticity of labor supply is small at an individual level but large in the aggregate economy. Second, the model has been usefully extended to accommodate more realistic price behavior. Finally, we showed by example that there are RBC models which can provide enough amplification so that the underlying technology shocks can be small and involve a low probability of technological regress 64. Our example made clear that major

64 Just as this first round of problems is set to rest, new challenges arise for the RBC model regarding the comovement between productivity and economic activity. In a recent paper, Gali (1996) argues, using VAR techniques, that technology shocks actually reduce input usage in the aggregate economy.

994

R.G. King and S.T. Rebelo

amplification o f productivity shocks requires highly elastic labor supply and readily variable capital utilization 65. Although we have concentrated on the one sector neoclassical model, which has been the central laboratory for most work on real business cycles, the next stages o f RBC research will likely use richer frameworks, as we discuss next. However, we believe that the exploration o f these richer frameworks will require consideration of the structural features that we have stressed in this chapter. One exciting research direction is the exploration o f models with multiple sectors, i.e., a long overdue continuation o f the trail scouted by Long and Plosser (1983). Interesting recent work on these models retains most o f the assumptions on preferences and production opportunities commonly incorporated in the one-sector RBC model [Horvath (1997), Dupor (1998)]. The one-to-one movement between hours and output observed in aggregate data also holds at a sectoral level. To us, this suggests the importance o f introducing variable capacity utilization into sectoral production structures. Another promising direction is work on models with heterogeneous agents [Krusell and Smith (1998), den Haan (1993)]. This work seems particularly important for enriching labor market dynamics and modeling unemployment 66. Fleshing out labor market dynamics is important on its own terms. But this work may also provide us with an alternative way o f obtaining a highly elastic aggregate labor supply which appears necessary for RBC modeling. A third interesting research direction seeks to tmderstand the industry dynamics that seem intimately related to the business cycle [Hopenhayn and Rogerson (1993), J.R. Campbell (1998)]. Finally, there are many aspects o f microeconomic activity in addition to employment in which discrete choice seems very important. It has frequently been suggested, for example, that the volatility o f investment is related to the fact that much o f firm investment is lumpy in character label and Eberly (1995), Caballero and Engel (1994)]. The incorporation o f lumpy investment decisions into the RBC model and its implications for aggregate dynamics is an exciting new direction o f research on which some initial progress has been made [Veracierto (1996), Thomas (1997)]. The interaction o f lumpy investment with costly capacity utilization seems a particular important topic o f investigation. All four of

This finding receives indirect support from two sources that do not rely on the VAR methodology: Burnside, Eichenbaum and Rebelo (1996) document that a sectoral capital-utilization adjusted measure of technology shocks is essentially tmcorrelated with production in 2-digit SIC manufacturing industries. Basu, Fernald and Kimball (1997) show that, for this same set of industries, input usage is negatively correlated with technology shocks. One interpretation of these facts is that they reflect the presence of nominal rigidities that keep nominal aggregate demand fixed and lead inputs to contract in response to a productivity increase [Gali (1996)]. An alternative flexible-price explanation for these same facts involves a multisector model in which goods are complements so that a technology shock to an individual sector does not necessarily warrant an expansion of input usage in that sector. 65 All interesting and open question is whether these same mechanisms can amplify other shocks besides productivity shocks sufficiently that these can produce realistic business cycles. 66 Some recent examples include Andolfatto (1996), Merz (1995), Gomes, Greenwood and Rebelo (1997) and den Haan, Ramey and Watson (1997).

Ch. 14: Resuscitating Real Business Cycles

995

these lines o f inquiry involve enriching the RBC model in ways that seemed virtually impossible a decade ago. While we think that economists may have prematurely dismissed the idea that the business cycle m a y originate from real causes, we also think that m a n y o f the lessons drawn from current and future RBC research are likely to be independent o f the main source o f business fluctuations. This is one important reason why the RBC literature has been a positive technology shock to macroeconomics.

Appendix A. Dynamic theory This Appendix discusses some theoretical aspects that underlie the construction o f Real Business Cycle Models.

A. 1. Assumptions on preferences and technology The specific forms o f the momentary utility and production functions used in RBC models may seen arbitrary, but they are typically chosen on the basis o f economic theory and empirical observation. Preferences: In order for preferences to be consistent with steady-state growth in a deterministic version o f the basic RBC model they must have two properties: (i) households must be willing to expand their consumption at a constant rate when the real interest rate is constant; and (ii) it must be optimal for households to supply a constant number o f hours when the real interest rate is constant and the real wage rate grows at a constant rate. King, Plosser and Rebelo [1988a] study the admissible utility specifications when utility depends on "pure leisure" (L)67. These two requirements imply that momentary utility must have the form

j_d[Cv(L)]1-G

l l-or

if

o > 0,

if

o = 1.

cr ~e 1, (A.1)

u(C,L) =

log(C) + log v(L)

It is easy to verify two properties o f these specifications. First, i f agents have a budget constraint for goods and leisure o f the form e + wL <. w, where w is the real wage rate and 1 is the time endowment, then there is invariance o f L to the level o f w 68.

67 Another possibility is that utility depends on leisure in efficiency units, i.e., on leisure augmented by technological progress (L~Xt). In this case it is sufficient to assume that u(C, LX) is homogeneous, of class C2, and concave. The dependency of utility on leisure measured in efficiency units can be justified by introducing home production into the model. See Greenwood, Rogerson and Wright (1995, pp. 161-162) for a discussion. 68 This invariance extends to a setting where the budget constraint includes nonwage income which grows at the same rate as the real wage.

R.G. King and S.T. Rebelo

996

Second, u s i n g U H o p i t a l ' s rule, the s e c o n d case is the limiting expression o f the first as a --+ 1. We require that utility be sufficiently differentiable as well as c o n c a v e and increasing in c o n s u m p t i o n and leisure; this implies restrictions that m u s t be p l a c e d on v w h i c h d e p e n d on the value o f a 69. Differentiability allows us to characterize efficient allocations u s i n g variational methods. W h e n c o m b i n e d w i t h convexity o f the constraint set, c o n c a v i t y o f preferences insures that the s o l u t i o n to the planner's p r o b l e m is unique, w h e n e v e r lifetime utility ( U ) is finite 7°. Since, as we will see shortly, the c o m p e t i t i v e e q u i l i b r i u m under rational expectations c o i n c i d e s with the solution to the planner's p r o b l e m , this guarantees that the c o m p e t i t i v e equilibrium is also unique. T e c h n o l o g y : The p r o d u c t i o n function F ( . ) is also t w i c e continuously differentiable, concave and h o m o g e n e o u s o f degree one. Constant returns to scale implies that the n u m b e r o f firms in the competitive e q u i l i b r i u m is undetermined. W i t h increasing returns to scale a competitive e q u i l i b r i u m does not exist because it w o u l d entail negative profits for all firms 71. In contrast, with d e c r e a s i n g returns to scale we w o u l d see an infinite n u m b e r o f infinitesimal firms w h o s e total output w o u l d be infinite 72. Alternatively, firms w o u l d earn e c o n o m i c profits if, for some reason, entry were limited. We a s s u m e that F ( . ) satisfies the f o l l o w i n g l i m i t i n g conditions, often referred to as Inada conditions 73: lim DIF(K,N)

K --~ c,o

= 0,

lim DtF(K,N)

K-+O

= cxz.

These c o n d i t i o n s ensure the existence o f a steady state in which the level o f capital is strictly positive. One can also show that they i m p l y that labor is essential in production: F ( K , O) = O.

69 More specifically, we assume that the fimctions vi are twice continuously differentiable. If a - 1, then concavity requires that the function log(v) must be increasing and concave. If a is not equal to 1, then v 1-a must be increasing and concave if a < 1 and decreasing and convex if a > 1. In addition we need - a v ( L ) v"(L) > (1 - 2a)[v'(L)] 2 to assure the overall concavity of u. 70 Whenever there is one path that yields infinite utility it is always possible to construct other paths (in fact a continuum of paths) that also yield infinite utility. Thus, to ensure that there is only one solution to the planner's problem we need to constrain the discount factor so that life-time utility, U, is finite. The requirement (by I a < 1) involves the interaction of preferences and technology. See Alvarez and Stokey (1999) for a discussion of this type of conditions. 71 See Hornstein (1993), Rotemberg and Woodford (1995), and Chatterjee and Cooper (1993) for a discussion of models that move away from perfect competition and incorporate increasing returns to scale. 72 Suppose, for example, that the production function is Cobb-Douglas and that there is a stock of capital K and a number of labor hours N which will be divided equally among n fu-ms. Total production will be given by Y = nA(K/n) a~(N/n) a2 - AKa~Na2n 1 a~ a2. With decreasing returns to scale a I + a 2 < 1 and lim, _~~ Y = 0<~. 73 As ill the main text we use the notation DiF(.) to refer to the partial derivative of F(-) with respect to its ith argument. We use DF(.) to refer to the total derivative of a fimction of a single variable.

Ch. 14: Resuscitating Real Business Cycles

997

A.2. The dynamic social p l a n n i n g problem

Let us consider first the case in which allocation decisions are made by a benevolent planner who maximizes the welfare of the representative agent. The solution to this problem will be a symmetric Pareto-optimum in which all agents receive the same consumption and leisure allocations. The stationary economy: In the steady state of a deterministic version of this economy Y, C, I, and K all grow at rate ~, i.e., the model captures the Kaldor growth facts. This suggests that it is useful to write the planner's problem for this economy in terms of variables that are constant in the steady state: y = Y/X, c = C/X, i = I / X , k = K/X. Using these stationary variables the planner's problem is given by oo

max Eo ~

f l u ( c , 1 - Nt)

(A.2)

t-0

subject to: Yt

= AtF(k,,Nt),

(A.3)

Yt

= ct + it,

(A.4)

~/kt + 1 = it + (1 - b)k,,

(A.5)

k0

(A.6)

> 0,

where fi =_ b y ~-°. In a deterministic environment the solution to the problem of maximizing Equation (A.2) subject to conditions (A.3)-(A.5) would be a sequence of consumption, labor supply and capital accumulation decisions: {ct}t=0,°~ {N~}t=0,ooand {]~t}t~l.~ These decisions could be made at time zero, since no relevant information is revealed later on. In contrast, in a stochastic economy agents learn over time the realizations of the random shocks that affect their environment. It would be inefficient to ignore this information that will be available later on and cast in stone the consumption and leisure decisions at time zero. For this reason, the solution to the utility maximization problem is a set of contingency rules, which specify how much to consume and work at each point in time as a function of the state of the economy in that period. Since the state of the economy can be, at any point in time summarized by two variables, the value of At, which influences current output and helps predict future productivity, and the value of the stock of capital. Thus contingency rules take the form c = c ( k , A ) and N = N(k,A). D y n a m i c programming: To use this approach, we write the planner's problem in

recursive form as V ( k , A ) = max{u(c, 1 - N ) + f l E V ( k ' , A ' ) } ,

(A.7)

c,N,k I

subject to:

c + y k ' - (1 - 6)k = A F ( k , N ) .

(A.8)

where we use primes ( ) to denote the value of a variable in the next period. The value function V ( k , A ) represents the expected life-time utility of the representative

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agent of an economy with a capital stock equal to k and a level of productivity equal to A. Equation (A.7) decomposes this life-time utility into two parts: the utility flow that accrues in the current period, u(e, L), and the expected utility that results from starting tomorrow with a stock of capital k' and a shock A' and proceeding optimally from then on. The planner will decide today on the value of U, so this variable is known with certainty at time t. However, the value of A' will only be known in the next period, so we have to compute the expectation of fiV(U,A') with respect to A': [3EV(U,A') = [3 f V(U,A')H(dA',A). Bellman's Principle of Optimality guarantees that the solution to the problem (A.2)-(A.5) coincides with the solution to the recursive problem (A.7)-(A.8) [see Stokey, Lucas and Prescott (1989), Section 9.1]. The efficiency conditions for the planning problem can be computed forming a Lagrangian in which Equation (A.7) is the objective and Equation (A.8) the constraint. The optimal value of c is dictated by DI u(c, 1 - N) = )~,

(A.9)

where X is the multiplier associated with the constraint (A.8). The optimal value of N, which we assume has an interior solution (0 < N < 1), is given by D2u(c, 1 - N) = )~ADzF(k, N).

(A. 10)

The optimal U is given by )~y = flED1 V(k',A') This condition involves the expectation of the term DI V(U,A'), which is unknown, since we do not know the form of the value function. Information about D1V(k,A) can, however, be obtained differentiating the Lagrangian with respect to k: D 1 V ( k , A ) = )~ [ADIF(k,N) + (1 - 6)] + [)~ADzF(k, N) - D2u(c, 1 - N)]

+

V(k',A')-

dN

d~-

dk' dk"

Using the same logic as in the derivation of the "envelope theorem" in demand theory, this equation can be greatly simplified by using the first-order conditions (A.9) and (A.10) to set the two bracketed terms equal to zero. Intuitively, given that the values of N and U were optimally chosen, there are zero net benefits from the adjustments in these quantities that will arise from a change k. Thus D~ V(k,A) can be simplified to D1V(k',A') = )~ [A'D1F(U,N') + (1 - 6)].

(A.11)

Finding the decision rules: Conditions (A.9) and (A. 10) can be used to solve for c and N as a function of )t, k and A. These functions are not quite the decision rules for

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999

consumption and labor, since they depend on ,~ which we have not yet determined. We specify the resulting functions as N = N(k, ).,A) and c = ~(k, )~,A). To find the decision rule for capital, we proceed as follows. Using N = N(k, )~,A) and c = ~(k, X, A), we can express the optimization conditions as a first-order system o f nonlinear stochastic difference equations in ;. and k:

)~7

= flEX' [A'D1F(k',N(k',)(,A')) + (1 - 6)],

(A.12)

A F [ k , N ( k , )~,A)] = O(k, )~,A) + yk' - (1 - 6)k. The solution to this system is a pair of decision rules U = h(k,A)and )~ = )t(k,A). In turn, these imply decision rules for consumption and labor N = N ( k , A ) and c = c(k, A). Taking these decision rules for c,N,;~,U, we have a complete description of how quantities in the real economy will efficiently evolve through time. The steady state of the optimal economy: The stationary distribution of A is given by the function G(A) such that: G(A') = f H ( A ' , A ) G ( d A ) . Given this stationary distribution the mean value o f A can be computed as A* = f AG(dA). If we ignore, for the moment, the stochastic nature of A and set it equal to its mean, A = A*, the model reduces to a variant of the Cass-Koopmans neoclassical model. It is well known that this deterministic model has a unique non-trivial steady state which is globally stable [Stokey, Lucas and Prescott (1989), Section 6.1]. Replacing A and A ~ by A* in Equations (A.8)-(A.11) we obtain the system of equations that characterize the steady state:

A*DIF(k*,N*)+(1-6) = 7/3, A*D2F(k*, N*)D1 u(c*, 1 - N*) = D2u(c*, 1 - N*),

(A.13)

7k*

(A.15)

= A * F ( k * , N * ) - c* + (1 - 6 ) k * .

(A.14)

We use an asterisk to denote the steady-state values o f the different variables. This system of equations is recursive. Equation (A.13) determines the value of k*/N*; recall that F is homogeneous o f degree one and thus D1F is homogeneous of degree zero implying that DlF(k*, N*) = D1F(k*/N*, 1). Equations (A.14) and (A. 15)jointly determine c* and N*. We will return below to discussing the nature of the steady state in the competitive economy.

A.3. A dynamic competitive equilibrium interpretation Our theoretical discussion so far has focused on a planning problem. However, the stylized facts described in Section 2 pertain to market economies where economic decisions are made in a decentralized manner. For this reason we now turn our attention to this economy's competitive equilibrium under rational expectations. There are several ways of decentralizing the basic R B C model economy. Here we will focus on a sequential competitive equilibrium in which households own the firms

R.G. King and S.T. Rebelo

1000

and the stock of capital and make three inter-related decisions: how much labor to supply (Ns), how much capital to accumulate (k~), and how much to consume (c). In this decentralization scheme, households have to take into account the law of motion for the wage rate (w) and for the rental price of capital (R). Both of these prices are a function of the state of the economy, as summarized by the productivity level A and the aggregate capital stock k: w = w(k,A),

(A.16)

R = R(k,A).

(A.17)

To forecast these prices, agents have to know the functions w and R and the law of motion for A and k. The variable A evolves according to H ( A ' , A ) , while the law of motion for the aggregate capital stock will be described as k'=g(k,A). The H o u s e h o l d Problem. With these preliminaries in place we can now write the

household problem as: v(k~;A, k) = max {u(c, 1 - N~) + fiEv(k~;A', k')}, c,N~,k~

subject to: c + yk~ = w(k,A)N~. + (1 + R ( k , A ) - b)k~ + zc.

(A.18)

where v is the value function of the household and :v denotes the firms' profits, which, as we will see in a moment, are always equal to zero. It is useful to define the real interest rate as the rental price of capital net of depreciation: r ( k , A ) = R ( k , A ) - 6.

The solution to the household problem is described by the following contingent rules: k~ = ks(ks, k , A ) , c

= c(ks, k,A),

Ns = N(ks, k,A).

These rules must satisfy the following set of efficiency conditions: D2u(c, 1 - Ns) = Dl u(e, 1 - Ns) w ( k , A),

(A.19)

g D l u ( e , 1 - Ns) = f l E D l u ( c , 1 - Ns)[R(k' c Y ) + (1 - 6)].

(A.20)

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Resuscitating Real Business Cycles

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The Firm "s Problem. The firms in this economy solve a static problem. They have to decide how much capital and labor to hire in the spot competitive markets for both of these factors:

max

k,t , Nd

Jr =

AF(kd, Nd)

-

wNd

-

Rkd.

The familiar optimization conditions for this problem are: ADtF(kd, Nd) = R(k, A),

(A.21)

ADzF(kd, Nd) = w(k, A).

(A.22)

Given that the production function exhibits constant returns to scale, profits will always be equal to zero: = AF(kd, Nd) - AD2F(kd, Nd)Nd -- ADIF(kd, Nd)kd = O. Market Clearing. There are three markets in this economy: spot markets for capital, labor and output. By Walras's law if two of these markets are in equilibrium the third market will also have to be in equilibrium. Thus we can state the equilibrium conditions limiting ourselves to the factor markets:

kd =k,=k,

Nd=Ns.

To ensure that this is a competitive equilibrium under rational expectations, the law of motion conjectured by households for the competitive equilibrium has to coincide with the actual aggregate law of motion for this variable: ks(k, k , A ) = g(k,A). The steady state in the market economy: If we treat N as fixed for the moment, we can interpret Equation (A. 13) as equating the long run demand and supply for capital. The real rate of return to capital in a decentralized version of this economy is given by r = A D 1 F ( k , N ) - 6. This can be seen as a demand schedule; given the value of r (and the value of N) it tells us the value of k that the economy would choose. The long run supply of capital is given by r = y/fi - 1 and is thus perfectly elastic: the capital stock of the economy always adjusts so that the steady-state real interest rate is r = y / f i - 1 . A.4. The welfare theorems

To show heuristically the connection between the competitive equilibrium and the Pareto Optimum we can now compare the first-order conditions of the competitive equilibrium with those of the planner's problem to show that they coincide. Replacing

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R.G. King and S.T. Rebelo

Equations (A.21) and (A.22) in (A. 18) and exploring the fact that F(.) is homogeneous of degree one, we obtain a resource constraint that is equivalent to the one implied by Equations (A.3)-(A.5). Making use of Equations (A.21) and (A.22) it can also be readily shown that (A.19)-(A.20) are equivalent to (A.9)-(A.11). Notice that the assumption o f rational expectations is crucial for this comparison. The equivalence between the conditions that characterize the two problems underlies the two welfare theorems that apply to this economy: the competitive equilibrium is Pareto Optimal and a Pareto Optimal allocation can be decentralized as a competitive equilibrium. The fact that the competitive equilibrium can be solved as a solution to a planning problem has important technical implications. Since the planners problem involves maximizing a continuous function defined over a compact set we know that a solution to the problem exists. Furthermore, since the planner's problem is strictly concave, its solution is unique. Thus, the existence and uniqueness o f the competitive equilibrium can then be established by exploring its equivalence to the planner's problem. There are many instances in which we may want to explore economies where the first welfare theorem does not hold. Examples include economies with distortionary taxes, externalities, or monopolistic competition. Rarely can the competitive equilibrium for these economies be mapped into a concave planning problem TM. We can still linearize the system o f equations that characterizes the competitive equilibrium to explore some of its properties. However, we no longer have the guarantee that the equilibrium exists or that it is unique. This is the reason why the multiple equilibrium literature discussed in Farmer (1993) focuses on economies in which the competitive equilibrium is suboptimal.

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74 See Danthine and Donaldson (1985) for an exception.

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Rogoff, K. (1986), "Theory ahead of business-cycle measurement: a comment", Carnegie-Rochester Conference Series on Public Policy 25:45~48. Romer, D. (1996), Advanced Macroeconomics (McGraw-Hill, New York). Rosen, S. (1986), "The theory of equalizing differences", in: O. Ashenfelter and R. Layard, eds., Handbook of Labor Economics, vol. 1 (North-Holland, Amsterdam) 641 692. Rotemberg, J.J., and M. Woodford (1992), "Oligopolistic pricing and the effects of aggregate demand on economic activity", Journal of Political Economy 100:1153 1207. Rotemberg, J.J., and M. Woodford (1995), "Dynamic general equilibrium models with imperfectly competitive product markets", in: T.E Cooley, ed., Frontiers of Business Cycle Research (Princeton University Press, Princeton, NJ) 243-293. Sargent, T. (1982), "Beyond demand and supply curves in macroeconomics", American Economic Review 72:382-389. Sbordone, A. (1997), "Interpreting the procyclical productivity of manufacturing sectors: external effects or labor hoarding?", Journal of Money, Credit and Banking 29:26-45. Shapiro, M. (1989), "Assessing the Federal Reserve's measures of capacity utilization", Brookings Papers on Economic Activity 1989(1): 181-225. Shapiro, M. (1993), "Capital utilization and the premium for working at night", Working Paper (University of Michigan). Shea, J. (1992), "Accident rates, labor effort and the business cycle", Working Paper (University of Maryland). Simkins, S. (1994), "Do real business cycle models exhibit business cycle behavior", Journal of Monetary Economics 33:381-404. Solow, R.M. (1956), "A contribution to the theory of economic growth", Quarterly Journal of Economics 70:65-94. Solow, R.M. (1957), "Technical change and the aggregate production function", Review of Economic Studies 39:312-320. Stock, J.H., and M.W Watson (1999), "Business cycle fluctuations in US macroeconomic time series", ch. 1, this Handbook. Stokey, N.L., and S.T. Rebelo (1995), "Growth effects of flat-rate taxes", Journal of Political Economy 103:519-550. Stokey, N.L., R.E. Lucas and E.C. Prescott (1989), Recursive Methods in Economic Dynamics (Harvard University Press, Cambridge, MA). Surmaaers, L.H. (1986), "Some skeptical observations on real business cycle theory", Federal Reserve Bank of Minneapolis Quarterly Review 10:23-27. Tarshis, L. (1939), "Changes in real and money wage rates", Economic Journal 49:150-154. Thomas, J. (1997), "Lumpy investment, partial adjustment, and the business cycle", manuscript (University of Virginia, November). Veracierto, M. (1996), "Plant level irreversible investment and equilibrium business cycles", Working Paper (Cornell University). Watson, M.W. (1994), "Business cycle durations and postwar stabilization of the U.S. economy", American Economic Review 84:24M6. Wynne, M. (1987), "The effects of government spending in a perfect foresight model", Working Paper (University of Rochester).

Chapter 15

STAGGERED PRICE A N D WAGE SETTING IN MACROECONOMICS * JOHN B. TAYLOR Stanford University

Contents Abstract Keywords 1. Introduction 2. A n empirical guide to price and wage setting in m a r k e t e c o n o m i e s 2.1. General observations about wage and price setting 2.1.1. Wage setting 2.1.2. Price setting 2.2. Individual firm and worker evidence 2.2.1. Direct evidence on wage setting 2.2.2. Indirect evidence on wage setting 2.2.3. Direct evidence on price setting 2.3. Summary of findings about price and wage setting 3. Market-clearing and expected-market-clearing approaches 3.1. Market-clearing models 3.1.1. Empirical tests 3.2. Expected-market-clearing models 4. Staggered contracts m o d e l s 4.1. A simple price setting model 4.2. More general staggered wage- and price-setting models 4.2.1. Fixed duration models 4.2.2. Random duration models 4.2.3. State-dependent duration models 5. Bolstering the theoretical foundations o f staggered contracts m o d e l s 5.1. Deriving the optimal price: the role of market power 5.2. Towards dynamic optimizing models of staggered price and wage setting 5.3. Staggered price and wage setting in general equilibrium models

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* This research was supported by the Center for Economic Policy Research at Stanford University. I wish to thank VV Chari, Christopher Erceg, Robert Hall, Ellen McGrattan, Akila Weerapana, and Michael Woodford for useful comments and assistance. Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor and M. Woodford © 1999 Elsevier Science B.V. All rights reserved 1009

1010 5.4. Explanationsof why price and wage setting is staggered 5.5. Indexingand optimal contractlength 6. Persistence puzzles and possible resolutions 6.1. Inflationpersistence 6.2. Real output persistence 6.3. Changes in stabilityand nominal rigidity over time 7. Concluding remarks on policy applications and future research References

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Abstract

This chapter reviews the role of temporary price and wage rigidities in explaining of the dynamic relationship between money, real output, and inflation. The key properties to be explained are that monetary shocks have persistent, but not permanent, effects on real output, and that the correlation between current output and inflation is positive for leads of inflation and negative for lags of inflation. The paper begins with a short empirical guide to price- and wage-setting behavior in market economies. It then compares alternative price- and wage-setting theories and argues that staggered contracts models continue to provide the most satisfactory match with the key macroeconomic facts. It then examines the microeconomic foundations of staggered contracts models and reviews some of their extensions and applications. Research in this area has been very active in the 1990s with a remarkable number of studies using, estimating , or testing models o f staggered price and wage setting. A new generation of econometric models incorporating staggered price and wage setting with rational expectations has been built. Researchers have begun to incorporate staggered wage and price setting into real business cycle models. Close links have been discovered between the parameters of people's utility functions and the parameters of staggered price- and wage-setting equations. There is now a debate about whether standard calibrations of utility functions prevent staggered price models, at least those with frequent price changes, from explaining long persistence of real output. A theme of the paper is that the advent of rational expectations in the 1970s led to models of price and wage rigidities which were more amenable to empirical testing than earlier models, and this is one reason for the recent controversies and debates. There is much to be discovered from these debates and from the future research they stimulate. Keywords staggered price and wage setting, staggered contracts model, contract multiplier, money, monetary policy, monopolistic competition, market clearing, expected market clearing, time-dependent pricing, state-dependent pricing JEL classification: E32, El0

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1. Introduction

Why does a change in the money supply cause real output and employment to change in the short run, but not in the long run? This is one of the oldest questions in macroeconomics, yet it persists as both the most difficult and the most practical of all. From David Hume in the 18th century to Milton Friedman in the 20th, economists have had a common answer: there are temporary price and wage rigidities in the economy. In other words, in the short run, price and/or wage levels do not change as much as the money supply changes. Thus, if the money supply increases, then real money balances rise, stimulating production and employment. As described by David Hume more than 200 years ago, "by degree the price rises, first of one commodity, then of another", or as stated more recently by Milton Friedman "prices are sticky" [see Rotwein (1955, p. 38) and Friedman (1982, p. 64)]. Except in unusual circumstances, it takes time for price and wage levels to fully adjust; as prices and wages gradually rise, real money balances return to their original level and in the long run the real economy is unaffected. The purpose of this chapter is to review the current state of knowledge about the nature of price and wage rigidities and their ability to explain the dynamic relationship between money, real output, and inflation. I survey recent research, classify the major facts and models, and draw some conclusions and suggestions for future research. Because both price rigidities and wage rigidities are important for macroeconomic dynamics, both types of rigidities are reviewed. The dynamic stochastic properties of money, output, and inflation that we would like the theories to explain have been carefully documented using modern time series techniques in the chapters by Stock and Watson (1999) and by Christiano, Eichenbaum and Evans (1999) in this Handbook. In addition to the property that money shocks have a short-run impact on output and a long-run impact on inflation, three other important properties of the money, real output, and inflation relation have attracted attention. These properties are (1) that a monetary shock has a persistent effect on real output a propagation effect that lasts well beyond the initial impact effect of a monetary shock, (2) that there is a positive correlation between real output and future inflation, and (3) that there is a negative correlation between inflation and future real output. [See Stock and Watson (1999), Table 2, lines 41 and 54, and Christiano, Eichenbaum and Evans (1999), Figures 2 and 3, which compare the impact of alternative measures of money shocks.] Properties (2) and (3) can also be characterized using vector autoregressions and the concept of Granger-causality: property (2) is that real output Granger-causes inflation positively and property (3) is that inflation Granger-causes real output negatively. This "reverse dynamic" cross correlation was shown to hold in the USA and other countries in Taylor (1980a, 1986). The ability to explain such robust findings represents an important measure of success for any theory of price and wage rigidities. It was in the early 1970s that the rational expectations revolution in macroeconomics first began to take hold. Of course, price and wage rigidities were a big part of

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macroeconomics before the early 1970s; indeed, they were central to both Keynesian and monetarist ideas. However, by forcing macroeconomists to think in economywide (general equilibrium) terms, the rational expectations revolution fundamentally changed how economists model price and wage rigidities. It was at this time that the staggered contracts model was first proposed. This model emphasizes the overlapping of individual prices and wages due to staggered price and wage setting. It could explain not only why changes in money impact real output, but also why the other properties mentioned above are found to hold in many countries. Fron~ the start the staggered contract model was explicit enough that testable hypotheses could be formulated and, as a result, the model underwent extensive empirical and theoretical scrutiny, generating much debate. This explicimess was necessitated, in my view, by the discipline of the rational expectations approach to modeling. During the 1980s, researchers extended and modified models of staggered price and wage setting, fitted them to data from many different countries, and began to give them a more specific theoretical footing. Models of staggered price and wage setting were frequently used as a source of monetary nonneutrality in rational expectations policy studies of monetary policy rules. By using these theories of price and wage rigidities for policy analysis and by confronting them with practical tests using real world data both microeconomic and macroeconomic - much has been learned about the process of wage and price formation in market economies. In the 1990s research on staggered price and wage setting has shown no signs of slowing down. Modifications motivated by a need to explain inflation dynamics more accurately or to reduce model complexity have been introduced and used in econometric models. A new generation of econometric models incorporating price and wage rigidities with rational expectations has been put in place for policy analysis at many central banks including the Federal Reserve Board. Perhaps even more exciting, researchers have begun to incorporate theories of staggered wage and price setting into what would otherwise be real business cycle models. This research has uncovered close links between the parameters of people's utility functions or firm's production functions and the parameters of staggered price and wage setting equations. The research has also uncovered a puzzle: in some models, standard calibration of utility function parameters indicates substantially less persistence of real output than had been found in earlier estimates of staggered contract models that had not made this formal link to individual utility maximization. Several ways to resolve this puzzle have been proposed and are discussed here. On balance, the staggered wage and price setting models still seem to be consistent with the broad features o f the data, but there is much to be discovered in future research. With the price and wage setting theories so amenable to empirical testing, it is not surprising that controversies and debates about price and wage rigidities continue. I begin the chapter with a short guide to price and wage setting behavior in market economies based on direct and indirect observations. I then review alternative price and wage setting models and show how models based on staggered price and wage setting match the facts mentioned above, a match that explains, in my view, why

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the models have proved useful to macroeconomists doing applied econometrics and policy work. I then go on to explore the microeconomic foundations for these models, discussing several intriguing puzzles and their possible resolutions. Finally, I discuss several historical and policy applications of econometric models based on staggered price and wage setting. As research on staggered price and wage setting has developed, several surveys of research on price and wage rigidities have appeared, including Taylor (1985), Btanchard (1990), Roberts (1995), and Goodfriend and King (1997), as well as several good graduate textbook treatments including Blanchard and Fischer (1989, Chapter 8) and Romer (1996, Chapter 6). In this survey I try to focus on topics that are either more recent or that have not been emphasized in these other surveys and reviews. I also try to trace out the gradual evolution of the staggered contracts model over time.

2. An empirical guide to price and wage setting in market economies Hume's theoretical idea - that slow price adjustment provides an explanation for the short run impact of changes in money on production - was based on his observations of price changes in the market economy in which he lived. Thanks to research in recent years we now have much more quantitative information about the timing, frequency, and determinants of price and wage changes. 2.1. General observations about wage and price setting

Before discussing this quantitative evidence, I think it is useful to first review some general observations about wage and price setting which are simply part of our everyday experience as participants in market economies. One might criticize these types of observations as arbitrary and subjective, but in fact such informal case studies have informed the theoretical research in this area much as David Hume's casual observations informed his theory. 2.1.1. Wage setting

One observes a great variety of ways in which wages are determined through the interaction of workers and firms in a market economy. These mechanisms evolve over time especially when there are large changes in the economic environment such as a change in the tax law or a rise in the average rate of inflation. There are, however, some important common features of these wage setting arrangements. For most workers employed in medium to large sized firms, wages (including benefits) are normally adjusted at rather long discrete intervals, most commonly once per year. The wage adjustment is typically associated with an extensive performance and salary review. A large fraction of the wage payment is usually stated in a fixed amount of dollars (or other currency) per unit of time (hour, week or month), but

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overtime pay, bonuses, profit sharing, piece rates, and other incentive arrangements are not uncommon for part of workers' pay. Indexing of wages to macroeconomic variables, such as the inflation rate, occurs, but is rare in wage setting arrangements of one year or less. It is important to emphasize that setting nominal wages at a fixed level for more than several quarters and usually for as long as a year appears to be just as prevalent for workers who are not in unions, or who do not have formal employment contracts, as for union workers with employment contracts. It is a mistake to limit studies o f how wages are set to formal employment contracts. As we will see below there is more quantitative information about indexing and contract length for workers and firms in the union sectors, but in the USA only a relatively small fraction of workers are in unions, so the evidence is less relevant. Throughout the economy wage setting is not usually synchronized in any one period. Rather wage adjustments occur at different times for different firms throughout the year, much as the dates for firms' fiscal years vary throughout the year. There are exceptions to this nonsynchronization. In Japan, for example, there has been a Shunto, or spring offensive, during which wages at most large firms are set. Wage decisions are clearly influenced by wages paid to other workers in a community or in similar occupations. When hiring new engineers or business school graduates, firms must consider the prevailing wage in the market for similarly educated workers when designing a wage package. Pattern bargaining among labor unions where the wage set at one union becomes a strong influence at another union is common. 2.1.2. Price setting There are even greater varieties of price setting than of wage setting. Prices change continuously in auction markets for commodities and financial instruments. The idea of price rigidities seems ludicrous when applied to such markets. On the other hand, prices change infrequently in posted-price customer markets for goods and services. [Okun (1981) used the term "customer markets" to distinguish these types of markets from "auction markets".] Prices of final goods in customer markets seem to be more responsive to changes in the costs of intermediate inputs to production than they are to changes in demand. In other words, changes in markups seem less of a source of price change than changes in costs. But even within socalled customer markets, prices - and markups of prices over costs - can and do change rapidly. For example, the price of airline tickets changes on a day to day basis depending on estimates of demand. Some airline tickets are now even auctioned on the Internet. Like wages, the prices of goods and services appear to be staggered over time and set taking the prevailing price of competing producers (or monopolistically competing producers) into account. News accounts suggest, for example, that a decision to change the price of Big Macs is closely watched by Burger King and other fast food companies. Case studies of pricing at large supermarket chains by Levy, Dutta, Bergen

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and Venable (1998) show that obtaining information about the prices of competitors is the first step in deciding on how much to change prices; they find that "people are sent on a weekly basis to competitors" stores to gather and record (usually by hand) their price ... ". Clearly some degree of non-synchronized or staggered price setting is necessary if such surveys of competitors' prices are to be useful. The policy o f matching a competitor's price is common among discount stores. The prevailing price is even an important consideration in price setting in auction markets. For example, knowing the price of recently auctioned items influences the reservation price of buyers and the minimum price of sellers in auctions for art and other rare goods. Because surveys of competitors and other steps in the process of changing prices (such as changing and verifying tag changes) are costly to undertake, Levy, Bergen, Dutta and Venable (1997) find that the costs to a retail store of changing prices are quite large. Examining several large US supermarket chains, they find that the fixed cost is about $0.52 per price change; such costs are "fixed" in the sense that they do not depend on the size of the price change. (Because the cost of changing a menu also does not depend on the size of the price change, such costs are usually called "menu costs".) Using a different methodology Slade (1996) finds the fixed costs of a retail price change to be even larger. 2.2. Individual f i r m and worker evidence

One of the great accomplishments of research on wage and price rigidities in the 1980s and 1990s is the bolstering of these case studies and casual impressions by quantitative evidence from thousands of observations of price and wage setting collected at the firm, worker, or union level. By carefully studying these data one can learn much about the nature of wage and price rigidities in the USA and other countries. Some of the conclusions I draw from these data are summarized in Section 2.3 below, but it is worthwhile to consider in detail several of the individual research studies. 2.2.1. Direct evidence on wage setting

Most quantitative microeconomic information on wage setting comes from government data collected on the union sector. For example, Taylor (1983) and Cecchetti (1984) use data from major union contracts in the USA to get some quantitative measures for wage rigidities. Unfortunately, the large labor union sector represents only about 10 percent of US employment. More than half of the wage agreements in the union sector last for more than one year, with the remaining being either one-year or two-year contracts. Slightly over 50 percent of the multiyear contracts in this sector are indexed. The data reported by Taylor (1983) demonstrate how the wage setting is highly nonsynchronized. In any one quarter only about 15 percent of the workers are adjusting their contracts. In any one year only about 40 percent are adjusting their contracts. For example, aerospace, trucking, and automobile workers contracts are generally renegotiated in different quarters.

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Cecchetti (1984) computed a time series of average duration of wages in the USA for the large union sector. He found that the average period between wage changes was slightly less than 2 years (7 quarters) in the 1950s and 1960s when inflation was low, but then fell to about one year (four quarters) in the 1970s during the high-inflation period. Hence, there is some evidence that the length of the period between wage changes is sensitive to the underlying inflation rate. However, even in the years of the great inflation wages were set at fixed nominal levels for one year on average. Cecchetti (1984) also found evidence that the amount of indexing increased as the inflation rate rose from the 1960s to the 1970s. Of course, quantitative observations on wage setting at the microeconomic level is not confined to the USA. For example, Fregert and Jonung (1986) provide evidence from Sweden. Their data show that contract length decreased in Sweden as inflation and monetary uncertainty rose. However, average contract length never dropped below one year. They also found that wage setting showed little synchronization until the 1950s when centralized wage bargaining was introduced. Recall that Japan is another country where much union wage setting occurs at the same time each year. Lebow, Stockton and Wascher (1995), McLaughlin (1994), and Card and Hyslop (1997) provide evidence about wage rigidity in the USA using individual wage data from the Panel Study of Income Dynamics. Because these studies, which reach similar conclusions, are not restricted to union workers, they are an important addition to the earlier studies on unions. However, because the wage is only sampled once per year, these studies do not provide information about whether the average duration of fixed wages is less than one year. Card and Hyslop (1997), who also examine data from the US Current Population Survey form 1979 to 1993, report that between 6 and 15 percent of workers (among those who do not change jobs) have their nominal wages unchanged from one year to the next, suggesting a relatively small number of workers whose wages change less frequently than once per year. Card and Hyslop (1997) also report that the frequency of wage adjustment increases with inflation: during the highinflation period of the late 1970s, only 6 to 10 percent of workers with the same job had unchanged wages from one year to the next, while during the lower-inflation period of the 1980s the fraction of workers with unchanged wages was close to 15 percent. This confirms the results observed by Cecchetti (1984) using union wage data in the USA and Fregert and Jonung (1986) for Sweden. Card and Hyslop (1997) also report information on downward wage rigidity (again for annual wage changes) and find that a significant fraction of workers (15 to 20 percent) experience nominal wage reductions from one year to the next. This suggests that downward wage rigidities are no more significant for macroeconomics than upward wage rigidities. In fact, few of the models of price and wage rigidities used empirically in macroeconomic models make use of the distinction between upward and downward rigidity - in particular asymmetric rigidities have little relevance for the key empirical correlations mentioned in the introduction.

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2.2.2. Indirect eoidence on wage setting

The microeconomic evidence on wage setting procedures can be supplemented with more indirect evidence based on macroeconomic data. I f some structural assumptions about the general form of wage setting are made, it is possible to extract information about individual wage setting mechanisms from the autocorrelation functions of aggregate time series data. The indirect method is similar to estimating the parameters of utility functions or production functions from data on consumption and investment. The duration o f fixed nominal wages - and the distribution of the different durations in the economy - has implications for the aggregate time series; from the time series data one can back out estimates of the wage duration distribution. Examples of these indirect methods are Benabou and Bismut (1987), Levin ( 1991 ), Taylor ( 1979b, 1993 a), Montgomery (1983), Christiano (1985), and Backus (1984). Benabou and Bismut (1987), Levin (1991), and Taylor (1993a) examine the distribution of workers by length of wage setting interval in the USA. There are similarities in the results even though different data sets are used. Benabou and Bismut (1987) find that the average length of time between wage adjustments is about 1½ years with a mode length of one year; the distribution of workers by contract length is not geometric: there are fewer workers with one-quarter wage setting intervals than fourquarter intervals. Levin (1991) also reports estimates of a cross sectional distribution of wage changes in the USA. He finds that about 10 percent of wages are adjusted in one quarter, 25 percent in two quarters, and 65 percent in four quarters. Levin uses quarterly data on aggregate wages to obtain these estimates.Using a less flexible geometric/exponential distribution assumption and focussing on Canada, Backus (1984) used exchange rate data to infer a median contract length slightly over a year, ranging from 5.4 quarters to 8.4 quarters. Estimates reported in Taylor (1993a) also indicate that annual contracts are the most common length of wage setting interval. Aggregate time series for wages in the USA imply that about 80 percent of workers have annual contracts; the fraction is somewhat smaller in Canada and Germany. Estimates of time-varying cross-section distributions are also reported in Taylor (1993a) to accommodate some synchronization as in the case of the Shunto mechanism in Japan. (The distribution of wage changes can not be the same in each quarter in Japan because more workers have their wages adjusted in the Spring quarter.) But, even in the Japanese economy, not all workers have wage adjustments in the second quarter. Some annual wage changes occur in the summer quarter and not all annual wage contracts are adjusted as part of the Shunto. Moreover, wages for some workers change more frequently than once per year. According to the estimates in Taylor (1993a), aggregate wages behave as if 88 percent of wage contracts in Japan are annual, 12 percent are adjusted every quarter, and a negligible amount are adjusted every two quarters. Of the 88 percent, 42 percent of workers have their wages changed in the spring quarter, 26 percent in the summer quarter, 16 percent in the fall quarter and 3 percent in the winter quarter.

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Some empirical researchers have also endeavored to determine whether wages are set relative to the prevailing wages as the casual observations mentioned above indicated. They use auxiliary structural assumptions about the wage process to derive spillover effects from aggregate data. Montgomery (1983) and Benabou and Bismut (1987) report little evidence of such spillovers, but these estimates require strong auxiliary assumptions. In sum, these empirical studies suggest that the most common wage setting interval for the USA is about one year and that wage setting dates are staggered. However, a potential problem with these indirect estimates is their dependence on time aggregation of the quarterly data employed. Using continuous time econometric methodology, Christiano (1985) examined whether any wage setting intervals were shorter than the minimum quarterly interval in the aggregate wage data, and found evidence that there were some that short. These disadvantages of the use of the indirect methods point to the great value of better data on wage setting in the economy as a whole. 2.2.3. Direct evidence on price setting

Carlton (1986, 1989), using actual transactions price data that originated with Stigler and Kindahl (1970), has documented in great detail the extent of price rigidity for a wide variety of products in the USA. [Carlton (1989) also provides a useful summary of studies of price rigidity prior to Stigler and Kindahl (1970). One of the most interesting early findings, attributed to EC. Mills, is that the empirical frequency distribution of price change is U-shaped: goods with low-frequency and high-frequency price changes are more common than goods with medium-frequency price changes]. For most product groups, Carlton (1989) found that the time between adjustment of transactions prices seems remarkably long: ranging from about 1½ years for steel, cement, and chemicals to about g1 year for plywood and nonferrous metals. Carlton found little evidence for a fixed cost of adjusting prices, but observed a positive correlation between industry concentration and price rigidity. Cecchetti (1986) collected data on US magazine prices and also found price changes to be remarkably infrequent. In the 1950s the average length of time between price changes was 7 years; in the high-inflation years in the 1970s the time between price change was much lower at 3 years, but still remarkably infrequent given the changes in demand and costs during such long periods. Similarly, Kashyap (1995) found that mailorder companies keep their catalog prices fixed for periods ranging from six months to two years. Surveys of pricing policies at firms by Blinder (1994) and by Blinder et al. (1998) confirm the findings of Carlton and Cecchetti. Blinder (1994) found the mode frequency of price adjustment for firms in the survey to be one year. About 40 percent of firms tend to change their prices once per year, while only 10 percent change prices more frequently than once per year; the remaining 50 percent leave their prices unchanged for more than a year. Blinder (1994) also reports that the mean lagged response of price changes to changes in demand or costs is about three months and is

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invariant to whether the change is positive or negative, supporting Carlton's (1989) result. In another study of survey data, Buckle and Carlson (1995) found that the average duration of prices at small business was about 8 months in the USA during the 1980s and 1990s and about 7 months in New Zealand during the early 1990s. These durations are only slightly smaller than Blinder's findings. Buckle and Carlson also found that the average duration between price changes was shorter in periods of higher inflation. Until very recently few of the studies of price setting have examined directly the degree to which prices are set in a staggered or synchronized fashion. Domberger and Fiebig (1993) look at the amount of staggering by examining the skewness of the distribution of price changes. They look at prices in 80 disaggregated industry groups in the UK. They find a significant lack of symmetry, indicating that many prices are not changed in a given quarter. Moreover, the sign of the skewness is related to the sign of the average price change. An increasing average price causes a rightward skew, and a decreasing average price causes a leftward skew. Using a data set on retail store prices, Lach and Tsiddon (1992, 1996) find that the prices at retail stores are staggered across different price-setters. Eden (1994a), Levy et al. (1997), Warner and Barsky (1995) also examine the patterns of individual price changes at the retail level. The data used by Lach and Tsiddon consist of the prices of different meat products and wines at retail stores in Israel. They find that in any given month only a fraction of stores are changing the price of a given meat product or wine. The monthly fractions of stores changing prices are usually in the 30 to 40 percent range. Interestingly they find that price changes for different products within a store are highly synchronized. When stores change prices they seem to change the price for most of their products at the same time: within-store synchronization. But most stores make these adjustment at different times: across-store staggering. Dutta, Bergen and Levy (1997) provide evidence of much more frequent price change at the retail level than would be expected from the work of Carlton (1986), Cecchetti (1986), and Blinder (1994). Dutta, Bergen and Levy (1997) examine retail and wholesale prices of several types of frozen and refrigerated orange juice in the Midwestern USA. They find that orange juice prices at supermarkets change very frequently: about every 2 weeks, much more frequently than the price change observed by earlier researchers. Dutta, Bergen and Levy (1997) argue that the frequent price adjustment in their study reflects the highly competitive nature of the supermarket business in the Midwest. Such rapid price adjustment may also reflect weekly, monthly, or seasonal discounting - the price could simply fluctuate between a rigid "regular" price and another "rigid" sale price, and not reflect any true price flexibility. In fact, Dutta, Bergen and Levy (1997) find the adjustment of retail orange juice prices to changes in costs to be somewhat slower than the average duration of prices about three to six weeks - in comparison to the twelve to sixteen weeks reported by Blinder (1994).

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2.3. Summary o f findings about price and wage setting It is difficult to summarize briefly the large amount of microeconomic evidence on wage and price setting discussed above. And we still have much to learn from this evidence. But I would emphasize the following general features of price and wage setting in a market economy based on this research: (1) While casual observation may suggest that wage rigidity is greater than price rigidity, the detailed studies do not provide evidence that one form of rigidity is more significant than the other: the studies suggest that price changes and wage changes have about the same average frequency - about one year. It would be inaccurate and misleading to build a model in which the average frequency of price or wage adjustment is longer than one year. Price and wage rigidities are temporary. But one should also feel comfortable with a model that assumes that prices and wages do not all change instantaneously and simultaneously, as if determined on a spot market with full information. And there is no empirical reason - aside from the need for a simplifying assumption or the desire to illustrate a key point - to build a model in which wages are perfectly flexible (determined on a spot market with full information) while prices are temporarily rigid, or vice versa. Except for the findings of Blinder (1994) and Dutta et al. (1997) on the effect of changes in costs on prices, this review of wage and price rigidities has said little about the connection between prices and wages, a subject taken up in the chapter by Rotemberg and Woodford (1999) in this Handbook. There is a long history of thought on the behavior of real wages, or product wages, over the business cycle, leaving the impression that there is little correlation, either positive or negative, between real wages and the business cycle. Domowitz, Hubbard and Petersen (1986) and Carlton (1989) review the empirical literature on the relationship between price rigidities and wage rigidities. There is little agreement among empirical researchers about whether the mark-up of price over costs is procyclical or countercyclical. Of course there is a strong correlation between the growth of real wages and long-term productivity growth, as the slowdown in productivity and real wage growth in the t970s illustrates. But this is a correlation between long-term trends, not a business cycle phenomenon related to the effects of money on the economy. (2) There is a great deal o f heterogeneity in wage and price setting. In fact, the data suggest that there is as much a difference between the average lengths of different types of price setting arrangements, or between the average lengths of different types of wage setting arrangements, as there is between wage setting and price setting. Grocery prices change much more frequently than magazine prices frozen orange juice prices change every two weeks, while magazine prices change every three years! Wages in some industries change once per year on average, while others change once per quarter and others once every two years. One might hope that a model with homogeneous "representative" price or wage setting would

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be a good approximation to this more complex world, but most likely some degree of heterogeneity will be required to describe reality accurately. It is worth noting that the aggregate time series studies of Christiano, Eichenbaum and Evans (1999) and Stock and Watson (1999) also show considerable heterogeneity in price and wage setting: for example, commodity prices seem to respond more quickly to money shocks than general price indices or than wages. (3) Neither price setting nor wage setting is synchronized. Except for cases of national union bargaining, wage setting is staggered through time, whether one looks at union or non-union workers. Price setting is also staggered through time. These facts, which are apparent in casual observation, are confirmed in studies of wages, retail prices, and industrial prices. (4) The frequency of wage and price changes depends on the average rate of inflation. Data from union workers and non-union workers in different countries show that the frequency of wage setting increases with the average rate of inflation. Similarly, prices at small businesses, industrial prices, and even the prices of products like magazines are adjusted more quickly when the rate of inflation is higher. This dependency of price and wage setting on events in the economy is one of the more robust empirical findings in the studies reviewed here. However, it should be emphasized that for the range of inflation rates observed in the developed economies in the 1970s the average duration of wages and prices remained high. Moreover, we have no empirical evidence that anything other than a change in the inflation rate would change the frequency of price and wage adjustment, though one would expect legal or technological changes that increase the cost of changing prices would reduce price adjustment frequency. For a given average inflation rate, constant frequencies of price adjustment may not be a bad assumption to make in an empirical or policy model.

3. Market-clearing and expected-market-clearing approaches Having examined the nature of price and wage setting at the microeconomic level, I now turn to a discussion of how price and wage rigidities can explain the impact of money on the economy. I focus on explanations of the impact effect of money on real output in this section, considering both market-clearing and expected-market-clearing approaches. In general I assume that expectations are endogenous and described by the assumption of rational expectations. The rational-expectations assumption rules out the possibility that biased or adaptive expectations are a source of monetary nonneutralities, though I briefly discuss learning models which can temporarily result in such biases. 3.1. Market-clearing models Market clearing models assume that prices and wages can adjust instantaneously to satisfy equilibrium conditions. In order for such models to explain the slow adjustment

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of prices and thereby explain the impact of a change in money on the economy a la Hume and Friedman, it is necessary to posit some lack of information by people which slows down the adjustment of prices endogenously. Imperfect information about whether a change in the money supply or some other factor is the source of the shift in a firm's demand curve, for example, may cause prices to change by less than they would if the firms were fully informed. Thus, prices become temporarily rigid or sticky in an otherwise perfectly flexible price model. Robert Lucas's (1972) path-breaking "expectations and the neutrality of money" paper - which introduced rational expectations and dynamic optimization into economy-wide monetary models - takes this approach. McCallum (1984) provides a good review of this model and Lucas (1996) provides a recent survey of the general imperfect-information approach in comparison with other approaches. The Lucas (1972) model is an overlapping-generations model with rational expectations in which trading takes place in decentralized markets. The overlapping-generations model assumption is used to create an endogenous demand for money. The old, who are neither able to store goods they produce when young nor produce goods when old, use money to pay the young for the goods. When the old exchange money for goods a price is determined. Under certain uniqueness assumptions, a single equilibrium price level can be found in each period. If the money supply is constant, and distributed evenly to the old, then the price level will be a constant. When everyone is perfectly informed, the price level will be proportional to the money supply. Thus, with perfect information there are no price rigidities as defined here: a once and for all increase in the money supply will lead to a proportional increase in the price level and employment and production will be tmchanged. Price rigidities arise as a result of limits on information that prevent a realization of the money stock from being revealed to both the young and the old. The mechanism for limiting information is that trading takes place in two distinct markets. Then an increase in the price in one of the markets can signal either (1) that the money stock has increased, in which case there is a general increase in all prices and no need to change production, or (2) that there are fewer suppliers in the market and that the relative price has increased, in which case it makes sense to increase production. Hence, with limited information about the source of the price rise, suppliers must solve a signal extraction problem; the solution to the problem is to increase supply when the price rises, but by an amount that is less than the increase in the money supply. The response of prices to the increase in the money supply depends on the relative variability of money supply changes and market specific shocks. Thus, in this case there is a price rigidity: the price level rises by less than the increase in the money supply and production increases. 3.1.1. Empirical tests"

Lucas (1973) provided the first test of this model; he looked at the price-output behavior in several countries and found evidence that an increase in the variability of the general price level tended to raise the response of prices to changes in aggregate

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demand as predicted by the theory. Later, Ball, Mankiw and Romer (1988) provided further support. For example, in a sample of 43 countries Ball, Mankiw and Romer (1988) find a significant negative relationship between the response coefficient of real output to aggregate nominal demand shocks (a more general measure of demand than the money supply) and the variability of nominal demand. Soon after the Lucas model appeared, Barro (1977) endeavored to test the theory by empirically distinguishing between unanticipated and anticipated changes in money, finding that the effects of unanticipated money were larger, as predicted by the theory. Barro's study triggered an enormous amount of research and debate about whether anticipated money had any effect at all. Because his tests could not completely distinguish between limited information models and other models with rational expectations (such as the ones discussed later in this paper) that also predicted a difference between expected and unexpected money, questions were raised about the relationship between his test and the Lucas theory. See Mishkin (1982) for a good summary and econometric assessment of this debate. Three types of empirical results, however, raised questions about market clearing models with imperfect information as an explanation of the impact of money on the economy. First, contrary to the theory, actual measures of mis-perceived changes in money had little impact on production; Barro and Hercowitz (1980), for example, provided evidence for this by comparing preliminary and revised data on the money supply in the USA; the difference between the preliminary and the revised data was taken as a measure of mis-perceived money. One can question the Barro-Hercowitz method as taking the Lucas model too literally - clearly many people are unaware of the money supply even after it is revised. Perhaps a better test of the spirit of the model would use a more general measure of aggregate demand as in Ball, Mankiw and Romer (1988). Nevertheless, the information limitations assumed in the Lucas model do seem strong without direct evidence for their existence. A second empirical result that raised questions about the market-clearing approach with limited information, is that unanticipated changes in prices seem to explain only a small fraction of the changes in production over the business cycle, again contrary to the causal mechanism of the model when taken literally. Sargent (1976), for example, showed that unanticipated changes in prices had little effect on production using data for the USA. However, like the Barro-Hercowitz tests, these tests may focus too much on the details of the Lucas model and not enough on its more general implications. For example, in models with sequential purchase restrictions [such as Lucas and Woodford (1994) and Eden (1994b)], an unanticipated increase in demand causes an increase in sales without an immediate increase in prices to signal more production. A third empirical shortcoming relates to the persistent effects of a money shock on real output. In market-clearing limited information models, the duration of the effect of a money shock on real output is no longer than the time it takes to resolve the uncertainty about the source of the shock. It is unlikely that such information would take longer than a few months let alone longer than a year to obtain. Hence, without adding other sources of persistence the market-clearing models with limited

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information have difficulty explaining a key fact about the money, real output, inflation relationship. To be sure, it is possible to add in such persistence effects through adjustment costs or inventories, but doing so leaves other aspects of the business cycle - such as the reverse dynamic cross correlations between inflation and output discussed in the introduction - unexplained. It is because of these difficulties in explaining persistence, in my view, that most estimated economy-wide monetary models do not utilize the perfectly flexible-price, market-clearing, assumption, even with limited information. In any case, there has been relatively little research in recent years on imperfect information as a source of price rigidities in models with perfectly flexible prices. However, for reasons discussed below it is likely that a complete theory of price rigidities will eventually involve elements of the limited information theory, though perhaps in conjunction with the staggered wage and price setting formulations discussed below. One rationale for infrequent price changes stems from the information value that a stable price conveys to customers. Moreover, as discussed below, the microeconomic foundations of the staggered contracts models - and in particular why staggering even exists - involves imperfect information about whether a shock is temporary or permanent or local or economy-wide.

3.2. Expected-market-clearing models Soon after the Lucas (1972) model appeared, several researchers began to try to incorporate some form of sticky price or wage formation directly into rational expectations macro models, as an alternative to the imperfect information approach. This research originally had two objectives. The first objective was to develop new econometric models that could be used for monetary policy evaluation. That existing econometric models with adaptive expectations and arbitrary lag structures were inadequate for this purpose was shown clearly in the Lucas (1972) paper and even more transparently in Lucas's (1976) critique paper, which showed, using the example of the output-inflation tradeoff, the pitfalls of doing monetary policy evaluation without paying careful attention to expectations and the reactions of agents in the model. In order to overcome these pitfalls it was clear that a model with rational expectations was needed. If one had doubts about the ability of the imperfect information theory to explain fully the impact of monetary policy on the economy, then a sticky price formulation was a good alternative. Its long tradition in macroeconomics (among both monetarists and Keynesians) and the hope that it could help explain the persistence effects of monetary shocks as well as the impulse effects made it attractive. The second objective was to respond to the work of Sargent and Wallace (1975) which showed that, under Lucas's (1972) imperfect-information assumption with perfectly flexible prices, monetary policy had no effect - the so called "policy ineffectiveness proposition". Thus, the second objective of the research on sticky prices was to demonstrate that this proposition was due to the flexible price assumption rather than to the rational expectations assumption. Another approach to explaining

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the real effects of money in rational expectation models with perfectly flexible prices assumes that people must learn about monetary policy during a "transition" to rational expectations [Taylor (1975), Brunner, Cukierman and Meltzer (1980)]. Models with learning have developed considerably in the 1980s and 1990s as discussed in the chapter by Evans and Honkapohja (1999) in this Handbook. Incorporating sticky prices or wages directly into an economy-wide rational expectations model meant assuming that prices or wages are set in advance of the market period when they apply and then are fixed at that level during the market period. For example, automobile firms might set their price pt for the quarter t at the start of quarter t - 1 and then keep the price at that value throughout the market period. Or firms might set the wage wt for year t at the start of period t - 1 and set the wage Wt+l for the year t + 1 at the start of period t, and so on. To make this model operational in an internally consistent rational-expectations model of the economy, one might assume that prices or wages are set in such a way that markets are expected to clear during the period in which the price or wage applies. If we let St(pt) represent supply in period t and Dt(pt) represent demand in period t, then expected market clearing simply means that the price pt which is set in period t - j is chosen so that Etq(St(pt)) = Et-j(Dt(pt)),

(3.1)

where Et_j is the conditional expectation given information through periods t - j . This is the approach taken by Fischer (1977), Gray (1976) and Phelps and Taylor (t977) to incorporate price and wage rigidities into economy-wide models. In applying this approach Phelps and Taylor (1977) focussed on the aggregate price level; they assumed that firms set prices one period in advance so that expected aggregate demand for goods (a negative function of the price level) equals expected aggregate supply. Fischer (1977) and Gray (1976) assumed that wages were set in advance in an analogous fashion with the price level perfectly flexible. They assumed that the wage was set so that the expected quantity of labor supplied equaled the expected quantity of labor demanded. In other words, in the Fischer and Gray models the wage is set in advance and D and S refer to the economy-wide labor market during the period when the wage applies, while in the Phelps and Taylor (1977) model prices are set in advance and D and S refer to the aggregate goods market during the period when the price applies. This is also the approach taken in more recent work by Cho (1993), Cho and Cooley (1995), and Rankin (1998) to incorporate price or wage rigidities into real business cycle models, though the D and S functions in these models are far more complex than in the relatively simple macro models in which price and wage rigidities were inserted in the mid-1970s. When setting prices or wages, agents in the model are assumed to make forecasts of supply and demand conditions in the future. Because the forecasts of supply and demand depend on the price in the next period, it is possible to find a price so that the expected quantity supplied equals the expected quantity demanded as shown in Equation (3.1). This price is the expected equilibrium price level; it is this value

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which is assumed to be set in advance of the market period and then not changed. Actual supply and demand conditions will differ from these expected values because of unforeseen shocks. But because the price is fixed, the actual quantity demanded will not equal the actual quantity supplied - hence there is an excess demand or excess supply. The convention is then simply to assume that the quantity demanded determines the supply. For example, firms are assumed to supply whatever is demanded at the fixed price for that period. In the meantime the price is set for the next period and the model proceeds through time. Of course, this expected-market-clearing mechanism describing how the price is determined is not necessarily a realistic description of how firms actually set prices, no more than the standard market-clearing assumption in perfectly flexible-price models is meant to be a realistic description of how firms actually set prices. In the equilibrium models, it is hoped that the market-clearing approach gives good predictions and so it is with the "expected equilibrium" models. One advantage of this approach to sticky prices or wages is that the longrun neutrality of monetary policy is always preserved, a point first emphasized by McCallum (1982) in an earlier survey. However, there is a serious disadvantage: the expected-market-clearing approach provides no explanation of the persistence of monetary shocks. The persistence caused by this type of sticky wage or price mechanism could last no longer than the longest lead time for wage and price setting. Recall that the review of the studies of wage and price setting in the previous section showed that the average duration of nominal wages and prices was no longer than one year. Yet the persistence of money shocks lasts well beyond one year. In other words, the expected-market-clearing approach has the same empirical shortcoming as the market-clearing approach, and trying to remedy these shortcomings by introducing other sources of persistence leads to a counterfactual implication for the inflation and output dynamics. It was in trying to apply the expected-market-clearing approach in constructing an estimated econometric model that I realized how serious this disadvantage was. The empirical problem with such a formulation was that real output jumped back to the full employment level much too quickly and sharply after a money shock. I found that in building an empirical model I could not use the expected-market-clearing formulations that had proved useful in building the simple theoretical models of Phelps and Taylor (1977), Gray (1976), or Fischer (1977). It is interesting that Yun (1994, Chapter 2) had a similar experience when endeavoring to introduce sticky prices into an empirical real business cycle model; he found that setting a price for a single market period in advance could lead to no longer persistence than the length of the longest lead time in price setting, and for this reason he eventually adapted to an alternative approach used prior to the development of real business cycles - a version of the staggeredprice-setting approach described in the next section. In retrospect, it is interesting to observe that the persistence problems of the expected-market-clearing models with prices or wages set in advance are similar to those of the market-clearing model with perfectly flexible prices and limited

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information. The persistence of a shock to money would not last beyond the length of the longest lead time for price setting or beyond the longest time for learning the source of an observed shock to aggregate demand.

4. Staggered contracts models The staggered price and wage setting approach focuses on the nature of the price or wage decision itself, asking what would be a reasonable way to describe how prices and wages are set in different circumstances. Many of the general observations about real world price and wage setting described in Section 2 guide the formulation. These general observations include: (1) Wage and price setting appears to be staggered or unsynchronized; not everyone sets prices or wages in the same period. (2) Wages and prices are set at fixed values for fairly long periods of time (frequently called a "contract" period) and are frequently, though not always, non-contingent on events that occur during the contract period. Wage changes occur annually for many workers but the length of time varies and is not a fixed time length in many instances. Because price or wage setting is staggered these contract periods overlap with each other - hence, the term "staggered contracts". (3) When setting prices or wages, firms find that other prices and wages in the economy, or at least in closely related markets, are relevant for their decisions; this is true both for competitive markets and for markets where price setters have a degree of market power. 4.1. A simple price setting model

The staggered contract model developed in Taylor (1979a, 1980a) was explicitly designed to have these features; it is a simple model of price or wage setting designed to highlight certain key properties of real-world price and wage setting. The equations are essentially the same for wage setting and price setting. Consider the case of price setting. In the basic model prices are set for a fixed number (N > 1) of periods and are not changed during the length of this N-period "contract period". Each period, 1/N of the firms change their "contract prices". At any moment of time, the prevailing price would be an average of the N outstanding contract prices determined in the current and the last N - 1 periods. When setting the current price, firms would take account of both future and past price decisions of other firms because these would be part of the prevailing price. Thus the equations have both forward-looking and backwardlooking terms which are implied automatically from elementary considerations about how prices are set. These staggered contract equations had the feature that there is no long-run trade off between inflation and unemployment: regardless of the steadystate inflation rate the unemployment rate would equal the natural rate, although this property requires that future prices are not discounted when setting today's price, a property that may be a good approximation for short contracts of one year or less.

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To be concrete, suppose that N = 2, and that Pt is the log of the average price prevailing in period t, xt is the log of the price set in period t to apply to period t and t + 1, and Yt is the log of aggregate real output. Then, the basic staggered price setting model is Pt = 0.5(xt +xt-1),

(4.1)

xt = 0.5(pt + Etp~+l) + ]/Yt + yEtYt+l + et,

(4.2)

where et is a shock to price setting. The first equation states that the current price is the average of the two outstanding "contract prices". Equation (4.2) posits that this contract price will depend on prices prevailing during the contract period and on a measure of total demand in the economy during the two-period contract length. In Taylor (1979a, 1980a) I viewed the role of Yt in this equation as representative of excess demand in the markets during the periods when xt applied, but as discussed below this is only one interpretation. The model can be closed by assuming a simple demand-for-money function such as (rot - P t ) = Yt, where mt is the log of the money supply, and by specifying a stochastic process for the money supply. Suppose for example that mt = rot-1 + th, where t/t and et are serially uncorrelated random variables. Then, by substituting for Yt in Equation (4.2) using the demand for money and then substituting for pt using Equation (4.1) one can easily derive an autoregressive moving average process for Yt in which the autoregressive parameter (the coefficient onyt_~) is a = e - (e 2 - 1)-J , where c = (1 + ]/)(1 - •)-1 and the moving average terms depend on the shocks to money and the price-setting equation. The autoregressive parameter a is inversely related to the parameter y. For small y, the parameter a will be large and there will be a lot of persistence. Hence, 7 is a key parameter. The autoregressive part of the process for Yt arises because the price xt set by one firm partly depends on the price xt-1 set at other firms - as can be seen by substituting Equation (4.1) into (4.2). Because of the autoregression, a shock to the money supply has a long drawn out effect on output and the price level. The autoregressive term is analogous to a dynamic multiplier and for this reason I used the term "contract multiplier" to describe this persistence effect. This autoregressive component is why the effect on output lasts much longer than the length of the longest contract (2 periods here). West (1988) and Phaneuf (1990) showed with more detailed models and data from the USA and other countries, that the persistence could be large enough to explain the near unit-root behavior that had been associated with real business cycle models. In other words they showed that near unit-root behavior was consistent with a monetary theory of the business cycle with relatively short-lived staggered prices and wages. Moreover, as I showed in Taylor (1980b), there is also a pattern of reverse dynamic cross correlations implied by this model in which a higher level of real output is followed by a higher price level, while a higher price level is followed by a lower level of real output - in other words real output Granger-causes the price level (positively)

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while the price level Granger-causes real output (negatively). This reverse correlation is found in the data from many countries as reported in Taylor (1980b) and mentioned in the introduction to this chapter. Hence, even this highly stylized model is capable of explaining key facts of the dynamic relation between money, output, and the price level. Note, however, that these facts pertain to the behavior of the price level rather than the rate of inflation, an important issue to which I will return in the discussion o f inflation persistence below.

4.2. More general staggered wage- and price-setting models Given the heterogeneity of wage- and price-setting structures summarized in Section 2, it is likely that the simple uniform-length staggered contract structure in Equation (4.1) would have to be generalized for empirical work to describe a world with a multiplicity of contracts of different lengths. For example, rather than have all prices or wages change every N periods, one could have a range of contracts of lengths N I , N2, N3 . . . . . representing different types of price- or wage-setting arrangements. Thus some prices would be set for a relatively long period of time while others would usually change more frequently. One way to represent such a model is to generalize Equation (4.1) as

Pt = Z

~,xt-,,

(4.3)

s=0

which is drawn from Taylor (1979b); Equation (4.2) can also be generalized in an analogous fashion with ~ weights replacing 1/N or 1 in the case o f N = 2. In the special case where ar0=a~ =0.5 and the rest of the a~'s are zero, Equation (4.3) reduces to Equation (4.1), the two-period price-setting case. Alternatively, if there were an equal number of prices with durations of one through four quarters, then the a~ weights would decline linearly. In the next several sections, I consider versions of Equation (4.3) that have proved useful in research.

4.2.1. Fixed duration models In a series of empirical studies [Taylor (1979b, 1983, 1993a)] I used the general formulation (4.3) in several different ways, none of which restricted the parameters to any special stylized case such as Equation (4.1). This allowed for a general frequency distribution of different contract lengths: some workers and firms would set their price or wage each quarter, others every two quarters, others every year and so on. In Taylor (1979b) I estimated the ~ weights using aggregate wage data for the USA. I assumed a flexible functional form for the pattern of the Jr weights in order to reduce the number of parameters - the functional form allowed the frequency of contract length to increase, reach a peak, and then decrease. By estimating the parameters of that distribution, I was able to infer the distribution of contract lengths in the USA. In Taylor

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(1983) I calibrated the ~ weights using union wage data in the USA; the observed contract distribution varied in length from 4 quarters to 12 quarters. The resulting model was then used to simulate different disinflation paths for the USA to follow to bring the inflation rate down from the high levels of the late 1970s and early 1980s. Finally, in an estimated multicountry model [Taylor (1993a)] I estimated implied distributions of contract length for the largest seven industrialized countries, with the allowance of more synchronization in Japan, where observation of the wage setting process suggested there would be synchronization. (These estimates were discussed in the section on indirect observations of wage setting above.) Blanchard (1983, 1987) significantly extended the idea of unsynchronized price and wage setting to a complete stage-of-process model in which the price of inputs affects the price of outputs which then affects the price of an input to another firm and so on. The process of passing through price changes at each stage of production generates staggered price setting with the dynamics depending on the input-output structure of the economy. Hence, this provides another way to calibrate, or at least interpret, staggered price- and wage-setting models. Gordon (1981) also places great emphasis on stage-of-process effects in models of aggregate price dynamics. Christiano's (1985) extension of the staggered price and wage setting model also proved useful. He allowed for adjustment of contracts more frequent than the time interval for data collection and estimation. For example, Christiano's generalization could be used to estimate a model in which some contracts last only one quarter, but the data are annual. Using this approach Christiano was able to improve the goodness of fit of the simple staggered contract model. Buiter and Jewitt (1981) generalized the staggered contract model to allow wage setters to take the real wages of other workers into account rather than nominal wages. They showed that this change preserved many of the dynamic properties of the basic model, but allowed for additional effects because different price indices might be relevant for workers and firms. This is especially relevant in international economics where distinguishing between consumer and producer prices allows one to consider the important implications of exchange-rate pass-through. 4.2.2. Random duration models

Calvo (1982, 1983) developed a simple, but useful, version of Equation (4.3) by assuming that the Jr weights had a simple geometric form: Jr~. = a ~' for a < 1. Calvo's original suggestion was to convert the staggered contract model to continuous time and thus assume an exponential distribution. Moreover, Calvo (1982) provided a stochastic interpretation of the staggered contracts model: in his words "we basically adopt the same assumptions [as the standard staggered contracts model] except, to simplify the mathematics, we suppose that contract length is stochastic and independent and identically distributed across contracts" rather than described by a fixed distribution of contracts of different lengths. Calvo (1982) suggested that the equations could be interpreted as implying that the contracts ended randomly according to a geometric (or

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exponential) distribution, thereby leading to a random duration version of staggered wage setting. To complete the geometric version of the staggered price-setting model, Calvo generalized Equation (4.2) as in Taylor (1979b). Levin (1989, 1991) proposed a more general version of the random duration model in which the frequency distribution of contracts is not necessarily exponential. He estimated the distribution for the USA and found it to be significantly different than geometric with one-year wage setting intervals more common than shorter intervals. The stochastic interpretation implies that firms or workers will randomly change prices, which might seem less realistic than the assumption that the price changes occur at a typical time each year, such as in the spring. Backus (1984) and Chadha (1987) found the geometric assumption useful in discrete time empirical formulations, but Levin (1991) and Benabou and Bismut (1987) found that the distribution of contracts is not generally geometric. Hence, the simple geometric assumption should probably be used with caution in empirical work. 4.2.3. State-dependent duration models

The exogeneity of the price- and wage-change intervals in both the fixed and random-duration staggered price-setting models has been one of their most criticized assumptions. Making the price change or contract termination decision endogenous is important for policy or empirical work, especially if exogeneity is a poor approximation. Fortunately, a number of recent studies have begun to develop models in which the duration of price and wage decisions depends on the state of the economy; this approach is called state-dependentpricing. In contrast the simple staggered priceand wage-setting model is called time-dependentpricing because prices change at fixed or randomly selected times. Caplin and Spulber (1987) developed a widely-discussed model in which all prices are completely state dependent; that is, there is no explicit dependence on time as in the staggered contract models. With state-dependent pricing each firm is faced with fixed costs of price adjustment and uses an (S, s) policy to determine whether the price will change and by how much [see Sheshinski and Weiss (1988) for more on (S, s) policies in price adjustment]. Because not every firm will change its price in every period the resulting pattern of price adjustment looks just like staggered timedependent pricing. However, Caplin and Spulber (1987) find the switch from pure time-dependent pricing to pure state-dependent pricing greatly reduces the effects of staggered wage and price setting on the macroeconomy. In particular they find that money can be completely neutral in such a model. The reason is that if all price setters are following a (S, s) policy, with a wide enough band, then they can all change prices by the full amount of a monetary shock as soon as the shock appears. In contrast with the time-dependent pricing in the staggered price-setting model discussed above, some firms will not change their price so that the aggregate price level adjusts slowly. Tsiddon (1991, 1993) shows that slow aggregate price adjustment and the nonneutrality of money reappear if the changes in the money supply are highly persistent or

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have large swings. In such cases the size of the firm's price change is reduced leading to smaller changes in the aggregate price than the money supply. Conlon and Liu (1997) show that if firms change prices in response to other things than price misalignment (a product upgrade, a new model or a new product mix), then the nonneutrality of money reappears. Essentially this change results in a mixture of time-dependent and state-dependent pricing, a situation which probably better reflects reality than either extreme. An important recent application of state-dependent pricing is found in a general equilibrium model developed by Dotsey, King and Wolman (1996), who modified the geometric staggered contract framework of Calvo (1982) to allow for state-dependent pricing. In the Dotsey, King and Wolman (1996) model the fraction of firms that are changing their prices in any one period increases when the inflation rate rises. This prediction of the model is supported by many of the papers surveyed in Section 2. An important advantage of the Dotsey, King and Wolman (1996) paper is that they embed state-dependent pricing into an economy-wide model and preserve some degree of time dependence. They find that the money, output, and price dynamics resulting from their state-dependent model are not too dissimilar from the dynamics of the purely time-dependent model discussed above. Another example of state-dependent pricing is the model of Caballero and Engel (1993). Like the Caplin and Spulber (1987) model, only a fraction of prices will be adjusted each period in the Caballero and Engel model. Thus staggered price setting emerges. However, Caballero and Engel (1993) assume that the probability that an individual price will adjust depends on both the size and the sign of the deviation of the price from some desired price. Caballero and Engel (1993) look at the implications of their model for time-series behavior of the aggregate price level focussing on the producer price index. The detrended log of the index itself is described by a second-order vector autoregression with coefficients of 1.68 and -0.76. The Caballero and Engel (1993) model with its emphasis on first-order adjustment has difficulty mimicking this humped-shape behavior implicit in a second-order process, but at least the model generates the persistence or stickiness of the aggregate price levels found in the pure time-dependent staggered contract model.

5. Bolstering the theoretical foundations of staggered contracts models

As described above in Section 4.1, the basic staggered contract model was constructed to be consistent both with certain observed features of price- and wage-setting behavior and with basic microeconomic principles about the operation of competitive or imperfectly competitive markets. In particular, the idea that the price and wage decisions of firms depend on the prevailing prices and wages - and thus on the price and wage decisions at other firms - is an essential characteristic of staggered wage- and price-setting equations. In a sense these equations endeavor to describe a price discovery process in markets with posted prices, much like the equilibrium

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of supply and demand equations is a description of price discovery in spot markets. Davis and Holt (1997) have noted the development of price rigidities in experimental markets with posted prices and it is likely that experimental economics will help improve on current formulations of staggered wage and price setting. Nevertheless, the price- and wage-setting mechanism in the original staggered contract models was not derived from an explicit maximization problem, and this lack of a formal optimization underpinning is a potential disadvantage that many researchers have pointed out. Fortunately, many studies over the years have provided a more solid microfoundation for these equations. 5.1. Deriving the optimal price: the role of market power Most formal derivations of price determination take as given either (1) the cost of adjusting price, or (2) the fixed (or possibly random) interval for setting the price. Subject to this constraint an optimal value of the price to maximize profits can be found. Arrow (1959) first pointed out the need for some degree of market power to make the price decision of a firm meaningful. He outlined a possible framework in which even competitive firms had a temporary degree of market power at the time of the price decisions. Prescott (1975) also outlined a model of price setting in which firms had some degree of market power, but the market is essentially competitive in that the efficiency conditions of competition hold. Models in which firms have market power - due usually to a monopolistic competition assumption - so that an optimal price can be calculated are used frequently in studies of price and wage rigidity. In an early paper on this subject, Rotemberg (1982) assumed that firms face an explicit cost of adjusting prices, a cost that depends on the size of the price change. He also assumed that each firm faces a downwardsloping demand curve. These assumptions enabled him to derive a price-setting rule in which the actual price level adjusts slowly toward the optimal monopoly price. Rotemberg (1982) originally used this approach as an alternative to staggered price setting, but Rotemberg (1987) and Roberts (1995) show that the cost of price-level adjustment model leads to very similar equations as staggered contract models. In two influential papers, Svensson (1986) and Blanchard and Kiyotaki (1987) developed complete macroeconomic models in which monopolistic competition plays a role in determining the optimal price for firms. These models incorporate money formally and can be used to show the impact of a change in aggregate demand rising from changes in the money supply. In their original form, the Svensson (1986) and Blanchard and Kiyotaki (1987) models were static and were not addressed to the problems of persistence or dynamic cross correlations that are the main subject of this review. 5.2. Towards dynamic optimizing models of staggered price and wage setting Blanchard and Fischer (1989) developed a dynamic model that could address such issues. The model combines monopolistic competition with staggered price setting.

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The combination is achieved in two steps. The first step is to find the optimal price from a monopolistically competitive model without staggered price setting, such as Svensson (1986) or Blanchard and Kiyotaki (1987). For example, a typical optimal pricing rule would say that the price should depend on the average of other monopolistically competitive firms prices (p) and on a constant times aggregate output (y), which would represent a demand shift. A linear version of such a rule would look like x = p + yy,

(5.1)

where x is the firm's price, p is the average of other firms prices, and y is aggregate output. Now, suppose that pricing is staggered with 2 period contracts so that the price xt must last for two periods: t and t + 1. Then it seems reasonable that firms would set their price to be the average of the optimal price during the two periods during which the price applies. This reasoning leads to the second step which sets xt = 0.5(pt + YYt) + 0.5(Et lPt+l + ]/Et-lYt+l).

(5.2)

Note that Equation (5.2) is identical in functional form (ignoring the random shock) to Equation (4.2). Hence, pricing under monopolistic competition gives a more formal underpinning of the staggered price setting model. However, now the role of y is to shift firms' demand functions rather than to serve as a measure of (excess) demand pressure in the market. Blanchard and Fischer then went on to describe various persistence properties when Equation (5.2) is imbedded in a model. Because Equation (5.2) is identical to Equation (4.2), the properties are identical to those I discussed above. Romer (1996) presents a very useful textbook treatment of this type of derivation of the staggered price setting equation, providing useful details of the derivations and fin'ther discussion. Rotemberg's (1987) derivation of a staggered price setting mentioned above is similar to the one of Blanchard and Fischer (1989) described here, except that rather than using the example in Equation (4.2) he uses the version of Equation (4.2) with geometric declining weights on future p's and y's as in Calvo's (1982) geometric version of the staggered contracts model [see the discussion following Equation (4.3)]. Although the above derivation of the staggered price setting equations provides a helpful microeconomic interpretation, it is still not a fully optimizing treatment. In work that began in the mid-1980s, Akerlof and Yellen (1991) developed a dynamic model in which Equation (4.2) or (5.2) emerged directly from a monopolistic competition model without the two steps described above. They showed how the simple staggered contract equations could be derived from a maximization problem in which monopolistically competitive firms interact. Consider a simple two-firm model in which each firm faces a downward-sloping demand curve and thus has a degree of market power. The demand curve depends on real income in the economy, its own price, and the price charged by its rival. (The

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process determining real income is left unspecified, but is eventually related to the money supply as in other models.) One firm sets prices in even periods and the other firm sets prices in odd periods. The prices are fixed at the same nominal value for two periods. The rival firm can be thought of as a monopolistic competitor that sets a constant nominal price every other period. Akerlof and Yellen (1991) show that if each firm chooses a price to maximize expected profits taking as given (1) the price set by the rival firm (a Bertrand price setter) and (2) income in the economy, then the optimal price is given by the simple staggered price setting model in Equations (4.1) and (4.2). To get linearity in the decision rule, Akerlof and Yellen (1991) approximate the profit function by a quadratic. 5.3. Staggered price and wage setting in general equilibrium models

Although Akerlof and Yellen (1991) derived staggered price- and wage-setting equations from first principles, they did not endeavor to embed the equations in a fully optimizing model of the economy - that is, a model that includes utility functions for representative households. During the late 1980s and 1990s there has been a great amount of research aimed at doing just that. Nelson (1997) provides an excellent review of the most recent part of this research, but some discussion of earlier work is useful too. In one of the earliest studies along these lines, Deborah Lucas (1985, 1986) developed a full optimizing model in which some prices are determined in spot markets and some are determined in contract markets. The prices in spot markets are determined in the usual market-clearing way. The wage contracts are assumed to last two periods; 50 percent of the contracts are set in odd periods and the other 50 percent are set in even periods. The contract specifies a fixed nominal wage for two periods: the current period and the next period. Interestingly, Lucas (1985, 1986) developed a wage-setting mechanism for the contracts in competitive markets, so that the results do not depend on the market power of firms. The terms of the contract are determined in a market-clearing fashion. As stated by Lucas (1986), "In the process of competing for the N workers available to a given sector, the economy equilibrates so that the marginal utility gained from the wages paid over the contract period equals the marginal disutility of labor over the contract period". Note that this approach to modeling wage determination in the contracts is analogous to that used in the optimal contract literature [see Azariadis (1975)]; it is different from both the monopolistic competition assumption and the expected-market-clearing approach mentioned above. Deborah Lucas (1985, 1986) used a cash-in-advance approach to money demand and has prices set for two periods, with decisions being made every other period. Simulations demonstrated the effect of the nominal rigidities on the effect of monetary policy. In her model, the amplitude of cycles was proportional to the fraction of markets with wage contracts compared with spot pricing. Levin (1989, Chapter 2 and 1990) also developed an optimizing model in which wages are set in a staggered manner and determined optimally. Levin also obtained estimation and policy results. He estimated the model using maximum likelihood

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methods and US data. He then stochastically simulated the model to derive optimal feedback rules for monetary policy, and calculated the tradeoff between output stability and price stability. Because the parameters of Levin's model were estimated he could obtain quantitative estimates of the policy rule and the policy tradeoff. Yun (1994, 1996) developed a general equilibrium model with staggered price setting, both with a fixed and random duration. Because Yun uses monopolistic competition, his analysis of staggered price setting has similarities to that of Blanchard and Fischer (1989) above, but it is not a two-step approach. Staggered pricirrg equations of the form (5.2) emerge from the optimization problem without requiring that one first find the optimal price without staggering and then inserting that price into the basic staggered price-setting equations. A difference in the resulting equations is that prices in furore periods are discounted relative to current prices; that is (pt + Yyt) would get a larger weight than (Et lPt+1 + yEt lYt+l) in Equation (5.2) because the firms' profits in the second period would be discounted. Yun's approach shows explicitly how the single price in a staggered price-setting model must balance out profits in different periods because the price cannot be at different levels in different periods. Kimball (1995) discusses several results that emerge when he places formally derived staggered price-setting equations in a general equilibrium model. Kimball (1995) noted that the parameters of the resulting equations may give less persistence than earlier estimated staggered price-setting models (for reasons similar to those mention in my discussion of Blanchard and Fischer) and discussed several factors that could lengthen persistence that have proved useful in later work. In commenting on Kimball (1995), Woodford (1995) gives a nice comparison of the Yun (1994, 1996) and Kimball (1995) models. Compared to other research in this area, the work by King and Wolman (1996) focusses more explicitly on policy analysis. King and Wolman (1996) develop a utility maximization model with price and wage rigidities. Like Deborah Lucas (1985, 1986), Levin (1989), and Yun (1994) they add price rigidities to the model, using a staggered price-setting model. Money enters their model through a transactions technology device in which monetary services allow for higher levels of consumption. As with Levin (1989) and Deborah Lucas (1985, 1986), money has a real effect in the model because of the nominal rigidities. King and Wolman (1996) examine inflation targeting procedures and other important issues in the design of monetary policy rules. By the mid-1990s there were also a number of papers that added other forms of price and/or wage rigidities to a general equilibrium model. Hairault and Portier (1993), Kim (1995), and Ireland (1997) used a quadratic cost of price adjustment approach as suggested by Rotemberg (1982), while Cho and Cooley (1995) assumed that prices were set in advance in such a way that the overlapping features of staggered price setting would not play a role in producing persistence. Other work in this general area has been motivated by various policy, empirical, and methodological issues and includes Leeper and Sims (1994), Bernanke, Gertler and Gilchrist (1999), Ohanian and Stockman (1994), Chari, Kehoe and McGrattan (1998), and others. The paper by Chari, Kehoe and McGrattan (1998) raised some puzzles about the ability of staggered

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price and wage equations to deliver persistent dynamics and is taken up along with several responses later in this chapter.

5.4. Explanations of why price and wage setting is staggered

Although based on empirical observations, the staggering of wage and price setting is simply assumed in all the models discussed thus far in this chapter, from Taylor (1979b) through Chaff, Kehoe and McGrattan (1998). Why is price and wage setting staggered? This question has been pursued by many researchers in the 1980s and 1990s and is still the subject of debate. The question goes to the heart of the price discovery process in a market economy and well beyond macroeconomics. Fethke and Policano (1984, 1986) develop a model in which wages must be set several periods in advance and then are fixed without contingencies. The question is whether in such a world the wage settings should be staggered or all occur at one time. Fethke and Policano (1984) proved that staggering is a good way for the economy to adjust to sector-specific shocks. When disturbances are primarily due to relative, as distinct from aggregate, shocks, staggering of decisions is optimal because adjustments of some prices enable the sectors that are locked into fixed wages or prices to partially adjust. Parkin (1986) also shows that the degree of staggering depends on the relative size of aggregate shocks versus sector specific shocks. The analysis of monetary policy in this type of model is considered in Fethke and Policano (1987). They derive a Nash equilibrium where timing of monetary policy intervention and synchronization of contracts are simultaneously decided upon. An entirely different explanation for the existence of staggering comes from informational considerations. Ball and Cecchetti (1988) show that staggering allows firms to obtain information about what is going on in other markets. By observing the price in other markets firms are able to extract information about whether shocks are aggregate or relative. In addition, Ball and Romer (1989) find that there is a more rapid adjustment to sector (idiosyncratic) shocks with staggering. As shown by Ball (1987), these microeconomic advantages are offset, at least in part, by macroeconomic disadvantages of slow aggregate price adjustment, a concept he refers to as "externalities from contract length". Sheshinski and Weiss (1988) consider the question of staggering in oligopolies where timing is endogenous. Lau (1996, 1997) explores the strategic issues between price setters in an oligopoly game. The strategic rationale for staggering was explored by Matsukawa (1986) in the case of wage setting. In a recent paper, Bhaskar (1998) derives endogenous price staggering in a model with heterogeneous firms. Firms within an industry have stronger strategic complementarities than firms in different industries. This results in an equilibrium in which there is synchronization within industries but not across the economy. De Fraja (1993) also utilizes such strategic considerations in a model in which staggered price setting can be endogenous.

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5.5. Indexing and optimal contract length A major puzzle in the area of wage and price rigidities is why contracts are fixed in nominal terms for so long. Gray (1978) provided at least part of the answer in a paper on the optimal degree of indexing. In a model in which there are both nominal and real shocks, Gray (1978) showed that it is not optimal to fully index a wage contract to a single variable like the price level. A still unsettled issue is why contracts would not be indexed to all relevant information. Complexity, asymmetric information, and measurement problems must all be part of the answer.

6. Persistence puzzles and possible resolutions A general theme of this chapter is that the assumption of rational expectations and the need for economy-wide modeling has led to more specific models of wage and price rigidity than before the rational-expectations revolution. This greater specificity has led to the formulation of many statistical tests of the price- and wage-rigidity models. Several years ago, Blinder (1994) noted that models of price and wage rigidity have not been tested, saying, "Try to think of even a single case in which a theory of sticky prices has been rejected econometrically". But, while this criticism may apply to prerational-expectations theories, it certainly does not apply to the price- and wage-rigidity models that have arisen since the 1970s. Indeed, the simple representative staggered contract model described in Equation (4.1) is an example of a theory of sticky prices that - at least in that stylized form - was rejected econometrically as early as 1982. In a 1985 survey paper I stated that "Empirical tests of the sticky-price models have not yet been as extensive as the information-based models." [see Taylor (1985)], but they had already begun. Because of the extensive testing of staggered price-setting and other sticky-price models in recent years, it would not be accurate to make that 1985 statement today. Recall first that staggered price- and wage-setting models do explain in broad terms the observations summarized in the introduction of this chapter. For example, many of the serial correlation properties of the aggregate data - including the reverse dynamic cross correlation, the persistent effect of monetary shocks on real output, and the permanent effect of monetary shocks on prices - are all explained by the simple staggered contracts model. More generally, simulations of the impact of monetary policy shocks, summarized in Taylor (1993a), look much like vector autoregressions reported by Christiano, Eichenbaum and Evans (1999). However, when one looks more closely at the properties of the serial correlation, one starts to see discrepancies, which raise interesting puzzles. Most of these discrepancies are related to the ability of the models to explain persistent movements of real output or inflation. In an early paper on testing the staggered price and wage setting model, Ashenfelter and Card (1982) found that the simple staggered contract model was inconsistent with the serial correlation of wages. Levin (1991) has shown, however, that the more general formulations of these

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models such as Equation (4.3) above do pass goodness of fit tests like those proposed by Ashenfelter and Card (1982). Another empirical criticism of the staggered contract model is found in Dezhbakhsh et al. (1984). They argued that the statistical Phillips curve correlations reported in Taylor (1980b) arose after supply shocks, not demand shocks, and that correlations were actually based on forward looking derivatives (differences). While the point about the supply shocks is correct, the more typical statistical Phillips curve correlations would arise if demand shocks were correlated. A related point was made by Phaneuf (1987a,b). He pointed out that uncorrelated demand shocks showed a negative effect after the length of the longest contract. This property can be avoided with serially correlated demand shocks. 6.1. Inflation persistence

A widely discussed econometric problem with the staggered contract model is its apparent inability, without serial correlation or other sources of dynamics, to generate the persistence (or inertia) of inflation observed in the data. For example, Ball (1994) showed how it was possible to reduce inflation without recession - indeed with the right policy to have a boom! Phelps (1978), Taylor (1983), and Abraham (1987) also examined costless disinflations with rational expectations, but they did not relate this finding to empirical defects with the model. Though the inconsistency between these results and the observed costly disinflations can be easily explained by learning or by lack of credibility, the inconsistency raises some doubts about the ability of staggered contracts models with rational expectation to generate inflation persistence. The apparent inconsistency has led some empirical researchers to use a modification, proposed by Fuhrer and Moore (1995a,b), of the staggered contracts model. Fuhrer and Moore (1995a,b) present autocorrelation plots that nicely document some of the difficulties with the ability of the staggered contract model to produce inflation persistence. They show that the cross autocorrelation functions based on actual inflation and output data were not closely matched with the simulations of the basic staggered contract model. Note that the tests reported in Taylor (1980b) mentioned in Section 4 above compared price levels rather than rates of inflation; hence, the reason for one test passing and the other failing. To remedy this problem Fuhrer and Moore (1995a,b) modified the staggered contract model. Rather than current price levels being based on expected future price levels as in the standard staggered contract models, their modified model has current price inflation being based on expected future price inflation. The replacement of levels by rates of change generated a model with inflation persistence rather than simply pricelevel persistence. However, the theoretical foundations of the staggered contract model are based on levels not rates of change [recall the discussion of the derivation by Akerlof and Yellen (1991) above]. To be sure, Fuhrer and Moore motivated their alternative formulation by restating the price decision in "real" terms. To see this most simply, set 7 = et = 0 and replace

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rational expectations by perfect foresight in Equation (4.2). Note that after substitution from Equation (4.1) we get xt = 0.5(x,_l +xt+l),

(6.1)

which illustrates how the current contract price depends on future and lagged contract prices. Now suppose that rather than using xt in Equation (6.1) we formulate the price decision in terms of xt - P t , which looks like a "real" price: the current (log) contract price is deflated by the (log) aggregate price. Replacing xt+~ with Xt+s-Pt+s for s = 0, 1 and -1, in Equation (6.1), we get (after some algebraic manipulation) Axt = 0.5(Axt_l + Axt+l),

(6.2)

where Axt = x t - x t 1. Thus, all the properties stated above in terms of price levels are now restated in terms of the inflation rate. However, this definition of the real price effectively deflates by a price that does not apply to the full period (t and t + 1) of the contract price; that is, pt applies to only 1 of the period that xt applies to. Replacing xt in Equation (6.2) with x t - 0.5(pt +Pt+1) may seem to result in a more appropriate real price. Thus, while the Fuhrer-Moore formulation may work in macroeconomic empirical applications, it leaves puzzles about the microfoundations. Rotemberg (1997), in commenting on Fuhrer (1997), argues that there is nothing wrong with appealing to other sources of persistence of inflation within the staggered contracting approach. It is possible, of course, that inflation persistence could be due to serial correlation of money, but since one of the aims of these models is to explain persistence, leaving all the persistence of inflation to exogenous serial correlation is not a completely satisfactory conclusion either. In a recent paper Roberts (1997) re-examines Fuhrer and Moore's (1995a,b) findings. By exploring alternative expectations-formation mechanisms, Roberts (1997) demonstrates that a small amount of"imperfect information" about the determinants of inflation when combined with staggered price setting is enough to explain the observed serial correlation of inflation. In my view, Roberts' (1997) results indicate why it is likely that a full understanding of price and wage rigidities will eventually involve both imperfect information and staggered contracts of some form. Gertler (1981, 1982) developed a model of wage rigidities and wage inertia that is based on imperfect information. Rudin (1987) developed a formal model of staggered price setting in which there are diverse expectations on the part of firms giving rise to a situation where firms' expectations depend on other firms' expectations, and so on. 6.2. Real output persistence

The recent study by Chari, Kehoe and McGrattan (1998) emphasizes another potential persistence problem with the staggered price- and wage-setting model. Their study and the responses it has stimulated nicely illustrate the potential benefits of using dynamic

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optimizing models to study wage and price stickiness. As mentioned above, Chari, Kehoe, and McGrattan (1996) place a staggered contracts mechanism into an optimizing model in which price-setting rules are derived assuming monopolistic competition; they assume that money is in the utility function. They then examine the dynamic properties of the model and compare the properties with the staggered contract mechanism when placed in a model with less formal optimization; that is, with Equations (4.1) and (4.2) above. Through a pairwise comparison of the models, they find that, with reasonable parameter values calibrating the optimizing model, they cannot get coefficients on the staggered price setting equations that are large enough to generate empirically realistic serial correlation; they find virtually no persistence beyond the length of the longest contract. In terms of Equation (4.2), the value of 7 they get from their calibration exercise is much too large. Hence, the persistence is much shorter than the kind of persistence that West (1988), Blanchard (1990), and Phaneuf (1990) have found with the staggered contract model. Ascari (1998) develops an optimizing model of staggered wage setting which also implies that the y parameter is way too large. Several interesting papers have already been written in reaction to the findings of Chari, Kehoe and McGrattan (1998). Gust (1997) shows that restricting capital mobility between sectors can increase persistence in the Chari, Kehoe and McGrattan (1998) model. Kiley (1997) and Jeanne (1997) show that increasing the size of real rigidities [in the sense of Ball and Romer (1990)] can increase persistence in the model. A common theme of these papers is that there needs to be some neighborhood effects between price setters, so that one firm pays close attention to the price decision of the next firm and the most recent firm, thereby linking the price decision of one firm to another and causing the persistence effects. Gust's (1997) model illustrates this by tracing out in detail the effects of shocks with and without capital mobility; in his model capital plays a role in affecting the linkage between price decisions in different markets. The Chari, Kehoe and McGrattan (1998) model assumes complete wage flexibility. Alternatively, Erceg (1997) shows how including staggered wage setting along with staggered price setting increases persistence and enables a calibrated optimizing model with staggered contracts to generate the persistence observed in the data. Bergen and Feenstra (1998) introduce a more general functional form for the demand curve facing the monopolistic competitors, which leads to a lower value for 7. The effect of the constant elasticity demand functions on persistence is also noted by Kimball (1995). It is also important to note that Rotemberg and Woodford (1999) and King and Wolman (1998) in a similar type of modeling framework find long persistence of monetary shocks with relatively short price contracts. Rotemberg and Woodford (1999) assume price-setting equations which are geometric after a time delay, thereby coming close to the microeconomic empirical estimates discussed in Section 2 where the most common length of price contracts seems to be about three or four quarters. Rotemberg and Woodford (1999) conclude that their model generates realistic macroeconomic persistence of money shocks. King and Wolman (1998) assume two-period contracts and also generate realistic macroeconomic persistence.

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Another possible resolution of the Chari, Kehoe and McGrattan persistence puzzle is that the monopolistic competition model used to derive the price adjustment equation may not be adequate. Recall that Deborah Lucas (1985, 1986) used a competitive contracting mechanism to derive the price rule (actually a wage rule), and found that the impacts of shocks were quite persistent. The inconsistency pointed out in the Chari, Kehoe and McGrattan (1998) study raises issues about monopolistically competitive pricing that need to be investigated further. As Arrow (1959) argued, the market power a firm has when setting its price is temporary and may be quite different thar~ the market power in a full monopolistic competition model. If so, then it is a mistake to tie the price adjustment parameter • to demand-elasticity parameters. As mentioned in the discussion following Equation (4.1) above, prices may be responding to excess demand and not simply be moving along a demand curve as is assumed in the monopolistic model of price setting. Thus, the findings of Chari, Kehoe and McGrattan (1998) may indicate that the monopolistic competition (stationary market power) model may not be sufficient as a microeconomic foundation. 6.3. Changes in stability and nominal rigidity over time

One of the great historical puzzles in monetary economics is why economic fluctuations are smaller now than they were before the World War II. Part of the explanation has been that economic shocks are smaller, perhaps because of better monetary and fiscal policy or perhaps because of other changes in the economy such as dividend policy at firms. Using the staggered contracts model in Equations (4.1) and (4.2), DeLong and Summers (1986) argued that the improved economic performance was the result of a greater degree of price and wage rigidity in the economy. On the other hand, Taylor (1985) argued just the opposite using the same model, but calibrating the average size of the price shocks compared to the average size of the demand shocks: if price shocks are large enough, then greater price and wage rigidity would increase instability because it takes larger swings in real output and employment to offset price shocks. Other explanations for the increased economic stability - such as dividend policy or monetary policy changes - would therefore be needed. As shown in Driskill and Sheffrin (1986) the different views do in fact boil down to whether demand shocks or price shocks are more important. They show analytically that if price shocks are more important, then less rigidity of prices would lead to greater output stability.

7. Concluding remarks on policy applications and future research One of the most important reasons to develop detailed models of wage and price rigidities that explain the effects of money on the economy is to conduct monetary

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policy evaluation research. Such policy applications are an appropriate place to conclude this survey for they suggest where future research may be going. Econometric evaluation of monetary policy is now well-established and increasingly used in policy research. The most common strategy is to build and estimate a dynamic econometric model of the economy and then simulate that model with alternative feedback rules for monetary policy. Among the alternative rules, the policy which leads to the best, or at least a reasonably good, outcome is the optimal policy, and presumably the one recommended to policymakers. The general approach was developed by Lucas (1976) building on work by Marschak (1953) and others at the Cowles Commission where the need for structural econometric models for policy was a major motivation for the development of simultaneous equation methods. Improvements in rationalexpectations solution algorithms and estimation techniques have made it possible to perform such policy evaluations in large scale non-linear systems, in which stochastic simulations are essential. Without these newly developed algorithms, the large number of required replications would not be feasible. Examples of the use of econometric models for policy evaluation include Taylor (1979a) and McCallum (1988) which have focussed on small models. In Taylor (1979a) I derived an optimal feedback rule for the money supply in a rational expectations model with staggered price setting. McCallum (1988) simulated policy rules for several different models, including nonstructural models. This research is summarized in the chapter by McCallum (1999) in this H a n d b o o k . More recently it has been possible to carry out such policy simulation exercises in large scale open economy models. These international models incorporate uncovered interest-rate parity assumptions as in the Mundell and Fleming framework as well as staggered price and wage setting, following the lead of Dornbusch (1982). For example, in Taylor (1993a) a multicountry model with rational expectations and staggered wage setting was used to search for good interest rate and/or exchange rate policy rules. Comparative simulations of several other large scale models - many within the rational-expectations, staggered price- and wage-setting framework - are presented in Bryant, Hooper and Mann (1993). Using these results ! suggested a policy rule for monetary policy [Taylor (1993b)], which has been useful for practical monetary policy discussions, illustrating the usefulness of this whole approach to policy. The Federal Reserve Board has developed and started using a new econometric model which incorporates both rational expectations and a form of staggered wage and price setting. As described by Brayton, Levin, Tryon and Williams (1997) the model is used mostly for policy evaluation, including the evaluation of monetary policy rules. More recently researchers such as Rotemberg and Woodford (1997) and King and Wolman (1998) have begun to use estimated or calibrated general equilibrium optimizing models with staggered price setting to evaluate alternative monetary policy rules. Further developments along these lines are bound to be interesting and useful in policy work. For example, what are the policy implications of combining time-dependent pricing with state-dependent pricing as in Dotsey, King and Wolman (1996)?

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A n important advantage o f the newer models that include both utility maximization and staggered price setting is that monetary policy can be evaluated using the standard tools o f public finance. Welfare measures such as compensating variations or equivalent variations thus replace cruder quadratic loss functions in terms o f aggregate output or inflation. Rotemberg and Woodford (1999) evaluate the effect o f different monetary policy rules using the welfare function o f the representative agents in their model. They find that the parameters o f the staggered price-setting equations in their model have a significant effect on their welfare calculations. In sum, the form, interpretation, and parameter values o f staggered price and wage setting models are highly relevant not only for explaining the impact o f monetary policy, but also for evaluating its welfare consequences. Understanding these models more thoroughly takes one well beyond macroeconomics into the heart o f the price discovery and adjustment process in competitive and imperfectly competitive markets. Further research on the empirical robustness and microeconomic accuracy o f staggered contracts models is thus both interesting and practically important.

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Bah'o, R.J., and Z. Hercowitz (1980), "Money stock revisions and unanticipated money growth", Journal of Monetary Economics 6:257-267. Benabou, R., and C. Bismut (1987), "Wage bargaining and staggered contracts: theory and estimation", Discussion Paper No. 8810 (CEPREMAP, Paris, France). Bergen, ER., and R.C. Feenstra (1998), "Staggered price setting and endogenous persistence", Working Paper No. 6429 (NBER). Bernanke, B.S., M. Gertler and S. Gilchrist (1999), "The financial accelerator in a quantitative business cycle framework", ch. 21, this Handbook. Bhaskar, V. (1998), "On endogenously staggered prices", University of St. Andrews Discussion Paper Series, No. 9806 (St. Andrews, Scotland). Blanchard, O.J. (1983), "Price asynchronization and price level inertia", in: R. Dornbush and M. Simonsen, eds., Inflation, Debt, and Indexation (MIT Press, Cambridge, MA) 3-24. Blanchard, O.J. (1987), "Aggregate and individual price adjustment", Brookings Papers on Economic Activity 1987(1):57-122. Blanchard, O.J. (1990), "Why does money affect output? A survey", in: B. Friedman and E Hahn, eds., Handbook of Monetary Economics (North-Holland, Amsterdam) 779-835. Blanchard, O.J., and S. Fischer (1989), Lectures on Macroeconomics (MIT Press, Cambridge, MA). Blanchard, O.J., and N. Kiyotaki (1987), "Monopolistic competition and the effects of aggregate demand", American Economic Review 77:647-666. Blinder, A. (1994), "On sticky prices: academic theories meet the real world", in: N.G. Mankiw, ed., Monetary Policy (University of Chicago Press, Chicago, IL) 117-150. Blinder, A.S., E.D. Canetti, D.E. Lebow and J.B. Rudd (1998), Asking About Prices: a new approach to understanding price stickiness (Russell Sage Foundation, New York). Brayton, E, A. Levin, R. Tryon and J.C. Williams (1997), "The evolution of macro models at the Federal Reserve Board", in: B.T. McCallum and C.I. Plosser, eds., Carnegie-Rochester Conference Series on Public Policy 47:43 81. Brunner, K., A. Cukierman and A.H. Meltzer (1980), "Stagflation, persistent unemployment, and the permanence of shocks", Journal of Monetary Economics 6:467-492. Bryant, R.C., E Hooper and C.L. Mann (1993), Evaluating Policy Regimes: New Research in Empirical Macroeconomics (Brookings Institution, Washington, DC). Buckle, R.A., and J.A. Carlson (1995), "Price duration with two-sided pricing rules", in: K.H. Oppenlander and G. Poser, eds., Business Cycle Surveys: Forecasting Issues and Methodological Aspects (Avebury, Aldershot) 99-118. Buiter, W., and I. Jewitt (1981), "Staggered wage setting with real wage relatives: variations on a theme of Taylor", The Manchester School 49:211-228. Caballero, R.J., and E. Engel (1993), "Microeconomic rigidities and aggregate price dynamics", European Economic Review 37:691-711. Calvo, G.A. (1982), "Staggered contracts and exchange rate policy", in: J.A. Frankel, ed., Exchange Rates and International Macroeconomics (University of Chicago Press, Chicago, IL). Calvo, G.A. (1983), "Staggered prices in a utility maximizing framework", Journal of Monetary Economics 12:3-398. Caplin, A.S., and D. Spulber (1987), "Menu costs and the neutrality of money", Quarterly Journal of Economics 102:703-725. Card, D., and D. Hyslop (1997), "Does inflation 'grease the wheels of the labor market'?", in: C. Romer and D. Romer, eds., Reducing Inflation (University of Chicago Press, Chicago, IL) 71-114. Carlton, D.W (1986), "The rigidity of prices", American Economic Review 76:637~558. Carlton, D.W. (1989), "The theory and the facts of how markets clear: is industrial organization valuable for understanding macroeconomics?", in: R. Schmalensee and R.D. Willig, eds., Handbook of Industrial Organization, vol. 1 (North-Holland, Amsterdam) 909-946. Cecchetti, S.G. (1984), "Indexation and incomes policy: a study of wage adjustment in unionized manufacturing", Journal of Labor Economics, 5:391-412.

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Cecchetti, S.G. (1986), "The frequency of price adjustment: a study of newsstand prices of magazines", Journal of Econometrics 31:255-274. Chadha, B. (1987), "Is increased price inflexibility stabilizing?", Journal of Money, Credit and Banking 21:481-497. Chaff, VV, EJ. Kehoe and E.R. McGrattan (1998), "Sticky price models of the business cycle: can the contract multiplier solve the persistence problem?", Research Department Staff Report No. 217 (Federal Reserve Bank of Minneapolis) revised April 1998. Cho, J.O. (1993), "Money and business cycles with one period nominal contracts", Canadian Journal of Economics 26:638 659. Cho, J.O., and T.E Cooley (1995), "The business cycle with nominal contracts", Economic Theory 6:13-33. Christiano, L.J. (1985), "A method for estimating the timing interval in a linear econometric model, with application to Taylor's model of staggered contracts", Journal of Economic Dynamics and Control 9:363-404. Christiano, L.J., M. Eichenbaum and C.L. Evans (1999), "Monetary policy shocks: What have we learned and to what end?", ch. 2, this Handbook. Conlon, J.R., and C.Y. Liu (1997), "Can more frequent price changes lead to price inertia? Nonneutralities in a state-dependent pricing context", International Economic Review 38:893-914. Davis, D., and C.A. Holt (1997), "Price rigidities and institutional variation in markets with posted prices", Economic Theory 9:63-80. De Fraja, G. (1993), "Staggered versus synchronized wage setting in oligopoly", European Economic Review 37:1507-1522. DeLong, J.B., and L.H. Summers (1986), "Is increased price flexibility stabilizing?", American Economic Review 78:1031-1044. Dezhbakhsh, H., A.A. Haug, J.H. McCulloch, G.S. Poonia and L.-T. Wang (1984), "The statistical Phillips Curve in Taylor's staggered contracts model", unpublished paper. Domberger, S., and D.G. Fiebig (1993), "The distribution of price changes in oligopoly", The Journal of Industrial Economics 41:295-313. Domowitz, I., R.G. Hubbard and B.C. Petersen (1986), "Business cycles and the relationship between concentration and price-cost margins", Rand Journal of Economics 17:1-17. Dornbusch, R. (1982), "PPP exchange rate rules and macroeconomic stability", Journal of Political Economy 90:158-165. Dotsey, M., R.G. King and A.L. Wolman (1996), "State dependent pricing and the dynamics of business cycles", unpublished paper. Driskill, R.A., and S.M. Sheffrin (1986), "Is price flexibility destabilizing?", American Economic Review 76:802 807. Durra, S., M. Bergen and D. Levy (1997), "Price flexibility in channels of distribution: evidence from scanner data", unpublished paper ( Emory University, September 14). Eden, B. (1994a), "Time rigidities in the adjustment of price to monetary shocks: an analysis of micro data", Discussion paper No 94.16 (Bank of Israel). Eden, B. (1994b), "The adjustment of prices to monetary shocks when trade is uncertain and sequential", Journal of Political Economy 102:493-409. Erceg, C. (1997), "Nominal wage rigidities and the propagation of monetary disturbances", unpublished paper (Federal Reserve Board). Evans, G.W, and S. Honkapohja (1999), "Learning dynamics", oh. 7, this Handbook. Fethke, G., and A. Policano (1984), "Wage contingencies, the patterns of negotiation and aggregate implications of alternative contract structures", Journal of Monetary Economics 14:151-170. Fethke, G., and A. Policano (1986), "Will wage setters ever stagger decisions?", Quarterly Journal of Economics 101:867-877. Fethke, G., and A. Policano (1987), "Monetary policy and the timing of wage negotiations", Journal of Monetary Economics 19:87-105.

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Fischer, S. (1977), "Long-term contracts, rational expectations, and the optimal money supply rule", Journal of Political Economy 85:191~05. Fregert, K., and L. Jonung ( 1986), "Monetary regimes and file length of wage contracts", paper presented at the 1986 Konstanz Conference. Friedman, M. (1982), Column, p. 64, Newsweek, July 12. Fuhrer, J.C. (1997), "Towards a compact, empirically-verified rational expectations model for monetary policy analysis", in: B. McCallum and C. Plosser, eds., Carnegie-Rochester Conference on Public Policy 47:197-231. Fuhrer, J.C., and G.R. Moore (1995a), "Monetary policy tradeoffs and the correlation between nominal interest rates and real output", American Economic Review 85:219-239. Fuhr'er, J.C., and G.R. Moore (1995b), "Inflation persistence", Quarterly Journal of Economics 110: 127-159. Gertler, M. (1981), "Long-term contracts, imperfect information, and monetary policy", Journal of Economic Dynamics and Control 3:197-216. Gertler, M. (1982), "Imperfect information and wage inertia in the business cycle", Journal of Political Economy 90:967-987. Goodfriend, M., and R.G. King (1997), "The new neoclassical synthesis and the role of monetary policy", in: B.S. Bernanke and J.J. Rotemberg, eds., NBER Macroeconomics Annual (MIT Press, Cambridge, MA) 493 530. Gordon, R. (1981), "Output fluctuations and gradual price adjustment", Journal of Economic Literature 19:493-530. Gray, J.A. (1976), "Wage indexation: a macroeconomic approach", Journal of Monetary Economics 2:221~35. Gray, J.A. (1978), "On indexation and contract length", Journal of Political Economy 86:1-18. Gust, C. (1997), "Staggered price contracts and factor immobilities: the persistence problem revisited", unpublished paper (Northwestern University). Hairault, J.-O., and E Portier (1993), "Money, new Keynesian macroeconomics, and the business cycle", European Economic Review 37:1533 1568. Ireland, EN. (1997), "A small structural quarterly model for monetary policy evaluation", CarnegieRochester Conference Series on Public Policy 47:83-108. Jeanne, O. (1997), "Generating real persistent effects of monetary shocks: how much nominal rigidity do we really need?", Working Paper No. 6258 (NBER). Kashyap, A.K. (1995), "Sticky prices: new evidence from retail catalogues", Quarterly Journal of Economics 110:245-274. Kiley, M.T. (1997), "Staggered price setting, partial adjustment, real rigidities, and sunspots", unpublished paper (Federal Reserve Board). Kim, J. (1995), "Monetary policy in a stochastic equilibrium model with real and nominal rigidities", unpublished paper (Yale University). Kimball, M.S. (1995), "The quantitative analysis of the basic neomonetarist model", Journal of Money Credit and Banking 27:1241-1277. King, R.G., and A.L. Wolman (1996), "Inflation targeting in a St. Louis model of the 21st century", Federal Reserve Bank of St. Louis Review 78:93-107. King, R.G., and A.L. Wolman (1998), "What should the monetary authority do when prices are sticky", in: J.B. Taylor, ed., Monetary Policy Rules (University of Chicago Press, Chicago, IL). Lach, S., and D. Tsiddon (1992), "The behavior of prices and inflation: an empirical analysis of disaggregated data", Journal of Political Economy 100:349-389. Lach, S., and D. Tsiddon (1996), "Staggering and synchronization in price-setting: evidence from multiproduct firms", American Economic Review 86(December): 1175 1196. Lau, S.H.E (1996), "Aggregate pattern of time-dependent adjustment rules I: a game-theoretic analysis of staggered versus synchronized wage setting", Economic Journal 106:1645-1658.

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Lau, S.H.R (1997), "Aggregate pattern of time-dependent adjustment rules II: strategic complementary and endogenous nonsynchronization", Working Papers in Economics and Econometrics, No. 317 (The Australian National University, January). Lebow, D.E., D.J. Stockton and W. Wascher (1995), "Inflation, nominal wage rigidity and the efficiency of labor markets", unpublished paper (Federal Reserve Board). Leeper, E.M., and C.A. Sims (1994), "Toward a modern macroeconomic model usable for policy analysis", in: S. Fischer and J.J. Rotemberg, eds., NBER Macroeconomics Annual (MIT Press, Cambridge, MA) 81-118. Levin, A. (1989), "The theoretical and empirical relevance of staggered wage contract models", Ph.D. Dissertation (Stanford University). Levin, A. (1990), "Monetary stabilization policy in a general equilibrium model with wage contracts", Working Paper No. 90-hyphen;43 (University of California at San Diego, December). Levin, A. (1991), "The macroeconnmic significance of nominal wage contract duration", Working Paper No. 91-08 (University of California at San Diego, February). Levy, D., M. Bergen, S. Dutta and R. Venable (1997), "The magnitude of menu costs: direct evidence from large U.S. supermarket chains", Quarterly Journal of Economics 114:791-825. Levy, D., S. Dutta, M. Bergen and R. Venable (1998), "Price adjustment at multiproduct retailers", Managerial and Decision Economics, forthcoming. Lucas, D.J. (1985), "Price and interest rate dynamics induced by multiperiod contracts", Working Paper (Northwestern University). Lucas, D.J. (1986), "Rigid wages as a transmission mechanism for monetary shocks", Working Paper (Northwestern University). Lucas Jr, R.E. (1972), "Expectations and the neutrality of money", Journal of Economic Theory 4: 103-124. Lucas J1; R.E. (1973), "Some international evidence on output inflation tradeoffs", American Economic Review 63:326-334. Lucas Jr, R.E. (1976), "Econometric policy evaluation: a critique", Carnegie-Rochester Conference Series on Public Policy 1:19-46. Lucas Jr, R.E. (1996), "Nobel lecture: monetary neutrality", Journal of Political Economy 104:661 682. Lucas Jr, R.E., and M. Woodford (1994), "Real effects of monetary shocks in an economy with sequential purchases", Working Paper No. 4250 (NBER). Marschak, J. (1953), Economic Measurement for Policy and Prediction, Studies in econometric method, CoMes Commission for Research in Economics, Monograph No. 14 (Yale University Press, New Haven, CT). Matsukawa, S. (1986), "The equilibrium distribution of wage settlements and economic stability", International Economic Review 27:415-437. McCallum, B.T. (1982), "Macroeconomics after a decade of rational expectations: some critical issues", Federal Reserve Bank of Richmond Economic Review 68:3-12. McCallum, B.T. (1984), "A linearized version of Lucas's neutrality model", Canadian Journal of Economics 17:138-145. McCallum, B.T. (1988), "Robustness properties of a rule for monetary policy", Carnegie-Rochester Conference Series on Public Policy 29:173-203. McCallum, B.T. (1999), "Issues in the design of monetary policy rules", ch. 23, this Handbook. McLaughlin, K.J. (1994), "Rigid wages?", Journal of Monetary Economics 34:383-414. Mishkin, F.S. (1982), "Does anticipated monetary policy matter? an econometric investigation", Journal of Political Economy 90:22-51. Montgomery, E. (1983), "A note on aggregate dynamics and staggered contracts: a test of the importance of spillover effects", Working paper 82-6 (Carnegie Mellon School of Urban and Public Affairs). Nelson, E. (1997), "A framework for analyzing alternative models of nominal rigidities", unpublished paper (Carnegie Mellon University).

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Ohanian, L.E., and A.C. Stockman (1994), "Short run effects of money when some prices are sticky", Federal Reserve Bank of Richmond Economic Review 80:1~3. Okun, A.M. (1981), Prices and Quantities: A Macroeeonnmic Analysis (Brookings Institution, Washington, DC). Parkin, M. (1986), "The output-inflation tradeoff when prices are costly to change", Journal of Political Economy 94:200-224. Phaneuf, L. (1987a), "Can contract-based models explain business cycles?", working paper (University of Montreal). Phaneuf, L. (1987b), "Propri6t6s dynamiques des modules du cycle/t contrats echelonn6s", Canadian Journal of Economics 20:123-139. Phaneuf, L. (1990), "Wage contracts and the unit root hypothesis", Canadian Journal of Economics 23:580-592. Phelps, E. (1978), Disinflation without recession: adaptive guideposts and monetary policy, Weltwirtschaftliches Archiv 114:783 809. Phelps, E., and J.B. Taylor (1977), "Stabilizing powers of monetary policy under rational expectations", Journal of Political Economy 85:163-190. Prescott, E.C. (1975), "Efficiency of the natural rate", Journal of Political Economy 83:1229 1236. Rankin, N. (1998), "Nominal rigidity and monetary uncertainty", European Economic Review 42: 185-199. Roberts, J.M. (1995), "New Keynesian economics and the Phillips curve", Journal of Money, Credit and Banking 27:975 984. Roberts, J.M. (1997), "Is inflation sticky?", Journal of Monetary Economics 39:173-196. Romer, D. (1996), Advanced Macroeconomics (McGraw-Hill, New York). Rotemberg, J.J. (1982), "Sticky prices in the United States", Journal of Political Economy 90:1187-1211. Rotemberg, J.J. (1987), "The new Keynesian foundations", in: S. Fischer, ed., NBER Macroeconomics Annual 1987 (MIT Press, Cambridge, MA) 69 104. Rotemberg, J.J. (1997), "A comment", Carnegie-Rochester Conference Series on Public Policy 47: 231-243. Rotemberg, J.J., and M. Woodford (1997), "An optimization-based econometric framework for the evaluation of monetary policy", in: B.S. Bernanke and J.J. Rotemberg, eds., NBER Macroeconomics Annual (MIT Press, Cambridge, MA). Rotemberg, J.J., and M. Woodford (1999), "The cyclical behavior of prices and costs", ch. 16, this Handbook. Rotwein, E., ed. (1955), David Hume's Writings on Economics (University of Wisconsin Press, Madison, WI). Rudin, J. (1987), "Diverse expectations in an empirical model: an extension of the staggered contracts model", Chapter 2 of "Diverse expectations: policy and empirical implications", Ph.D. Dissertation (Stanford University). Sargent, T.J. (1976), "A classical maeroeconomic model for the United States", Journal of Political Economy 84:207-237. Sargent, T.J., and N. Wallace (1975), "'Rational' expectations, the optimal monetary instrument, and the optimal money supply rule", Journal of Political Economy 83:241-254. Sheshinski, E., and Y. Weiss (1988), "Staggered and synchronized price polices and multiproduct monopolies", Working paper No. 24-78 (Foerder Institute for Economic Research, Tel-Aviv, July). Slade, M.E. (1996), "Optimal pricing with costly adjustment: evidence from retail-grocery prices", unpublished paper (University of British Columbia). Stigler, G., and J. Kindahl (1970), The Behavior of Industrial Prices, NBER General Series, No. 90 (Columbia University Press, New York). Stock, J.H., and M.W. Watson (1999), "Business cycle fluctuations in US macroeconomic time series", ch. 1, this Handbook.

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Svensson, L.E.O. (1986), "Sticky goods prices, flexible asset prices, monopolistic competition, and monetary policy", Review of Economic Studies 52:385~405. Taylor, J.B. (1975), "Monetary policy during a transition to rational expectations", Journal of Political Economy 83:1009-1021. Taylor, J.B. (1979a), "Estimation and control of an econometric model with rational expectations", Econometrica 47:1267 1286. Taylor, J.B. (1979b), "An econometric business cycle model with rational expectations: some estimation results", unpublished paper (Columbia University); condensed version reprinted in chapter 2 of Taylor (1993a). . Taylor, J.B. (1980a), "Aggregate dynamics and staggered contracts", Journal of Political Economy 88:1-22. Taylor, J.B. (1980b), "Output and price stability: an international comparison", Journal of Economic Dynamics and Control 2:109-132. Taylor, J.B. (1983), "Union wage settlements during a disinflation", American Economic Review 73: 981-993. Taylor, J.B. (1985), "Rational expectations models in macroeconomics", in: K. Arrow and S. Honkapohja, eds., Frontiers of Economics (Basil Blackwell, Oxford). Taylol, J.B. (1986), "Improvements in macroeconomie stability: the role of wages and prices", in: R.J. Gordon, ed., The American Business Cycle. Continuity and Change (University of Chicago Press, Chicago, IL). Taylor, J.B. (1993a), Macroeeonomic Policy in the World Economy: From Econometric Design to Practical Operation (W.W. Norton, New York). Taylor, J.B. (1993b), "Discretion versus policy rules in practice", Carnegie-Rochester Conference Series in Public Policy 39:195-214. Tsiddon, D. (1991), "On the stubborness of sticky prices", International Economic Review 32:69-75. Tsiddon, D. (1993), "The (mis)behavior of the aggregate price level", Review of Economic Studies 60:889-902, Warner, E.J., and R. Barsky (1995), "The timing and magnitude of retail store markdowns: evidence from weekends and holidays", Quarterly Journal of Economics 110:321-352. West, K.D. (1988), "On the interpretation of near random-walk behavior in GNP", American Economic Review 78:202-209. Woodford, M. (1995), "Comment on the quantitative analysis of the basic neomonetarist model", Journal of Money, Credit and Banking 27:1277-1284. Yun, T. (1994), "Monetary policy, nominal price rigidity and business cycles", Ph.D. Dissertation (Department of Economics, University of Chicago). Yun, T. (1996), "Nominal price rigidity, money supply endogeneity, and business cycles", Journal of Monetary Economics 37:345-70.

Chapter 16

T H E C Y C L I C A L B E H A V I O R OF P R I C E S A N D C O S T S JULIO J. ROTEMBERG Harvard Business School MICHAEL WOODFORD Princeton University

Contents

Abstract Keywords 1. Introduction: Markups and the Business Cycle 2. The cyclical behavior of markups 2.1. Cyclical behavior of the labor share 2.2. Corrections to the labor-share measure of real marginal cost 2.2.1. A non-Cobb-Douglas production function 2.2.2. Overhead labor 2.2.3. Marginal wage not equal to the average 2.2.4. Costs of adjusting the labor input 2.2.5. Labor hoarding 2.2.6. Variable utilization of capital 2.3. Alternative measures of real marginal cost 2.3.1. Intermediate inputs 2.3.2. Inventory fluctuations 2.3.3. Variation in the capital stock 2.4. The response of factor prices to aggregate shocks 2.5. Cross-sectional differences in markup variation

3. Implications of markup variations for business fluctuations 3.1. Explaining cyclical variation in productivity and profits 3.1.1. Cyclical productivity 3.1.2. Cyclical profits 3.2. Identifying the output fluctuations due to markup variation

4. Models of variable markups 4.1. Sticky prices 4.2. Variations in desired markups 4.2.1. Varying elasticity of demand 4.2.2. Customer markets Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor and M. Woodford © 1999 Elsevier Science B.V All rights reserved 1051

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4.2.3. Implicit collusion 4.2.4. Variableentry 4.3. Interactionsbetween nominal rigidities and desired markup variations 5. Conclusions Acknowledgment References

1123 1125 1126 1129 1131 1131

Abstract

Because inputs are scarce, marginal cost is an increasing function of output. Diminishing returns, costs of increasing employment as well as the increasing marginal disutility of working when hours worked and effort rise all contribute to make this function steep. Without changes in this function relating marginal cost to output, aggregate output can vary if and only if the markup of price to marginal cost (the inverse of real marginal cost for typical filmS) varies. We first study whether, empirically, real marginal cost does rise in cyclical expansions. Average real labor cost is not very procyclical but, for several reasons, marginal labor cost is more procyclical than average labor cost. These include the presence of overhead labor and adjustment costs as well as differences between the marginal and the average wage. These corrections results in procyclical measures o f real marginal cost. Measures of marginal costs based on materials costs and inventories also appear procyclical. We show that these procyclical movements in marginal cost may, depending on how costs are modeled, account for a substantial fraction of cyclical output movements. Finally, we survey models of variable markups. These include both models of sticky prices (in which markups vary because firms cannot all costlessly charge the markup they desire) and models in which firms' desired markup varies over time. This set of models allows a rich set of variables to affect output even if these variables do not shift the marginal cost schedule.

Keywords JEL classification: E3, D4, D3

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1. Introduction: Markups and the Business Cycle In this chapter, we consider the role of variations in the relationship between the prices at which goods are supplied and the marginal cost o f supplying them in accounting for observed fluctuations in economic activity and employment. We shall argue that there exists a great deal of evidence in support of the view that marginal costs rise more than prices in economic expansions, especially late in expansions. Thus real marginal cost (MC/P) rises, for the typical firm; and alternatively, the markup of price over marginal cost (which we shall define as the ratio P/MC 1) declines for the typical firm. These two ways of describing the feature of business cycles with which we are concerned are equivalent in the case of a symmetric equilibrium (in which the costs, output and prices of all goods move exactly together), though they are not equivalent propositions regarding an individual firm or industry in the asymmetric case (since the firm's or industry's relative price may vary). Because of our concern with the explanation of fluctuations in aggregate activity, and because such aggregate fluctuations are characterized by a striking degree of comovement among sectors, we will mainly conduct our analysis in terms of a symmetric (aggregative) model, and treat procyclical movements in real marginal cost as equivalent to countercyclical markup variations. Discussion of the cyclicality of real marginal cost is most natural when one is discussing measurement (since the crucial measurement issue is to infer the level of marginal costs), and so this is how the issue is framed in many empirical studies [such as Bils (1987) and Bils and Kahn (1996)]. But when we turn to theoretical explanation, it is most useful to describe the phenomenon in terms of variation in firms' markups, because the crucial decisions responsible for the phenomenon are firms' decisions about the prices at which they are willing to supply their products. In fact, in a broad class of models discussed below, the cyclicality of real marginal costs in equilibrium turns not upon the nature o f the production technology or the conditions under which firms can obtain factors of production, but upon the nature of the competition among firms in their product markets; and so, from an analytical point of view, it seems most important to emphasize variation in markups. The observation that costs rise more than do prices, at least late in expansions, is not a new one. It was emphasized in the work of Wesley Clair Mitchell, for example, who writes (1941, p. 52) that as activity expands, "equipment of less than standard efficiency is brought back into use; the price of labor rises while its efficiency falls; the cost of materials, supplies and wares for resale advances faster than selling prices; discount rates go up at an especially rapid pace, and all the little wastes incidental to the conduct of business enterprises grow steadily larger." That real marginal costs should rise for such reasons is, of course, a simple consequence of the fact that factors of production are not in unlimited supply. But, as Mitchell notes, from the point of view of

1 Many authors instead define the "markup" or "price-cost margin" as (P- MC)/P. The two quantities are obviouslymonotonic transformations of one another.

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JJ Rotembergand M. WoodJord

theory "a problem still remains: Why cannot businessmen defend their profit margins against the threatened encroachment of costs by marking up their selling prices?" As we shall see, a variety of theories of imperfectly competitive behavior by firms explain why they may choose not to do so. Such imperfectly competitive behavior thus plays an important role in accounting for the character of aggregate fluctuations. Fluctuations in markups are an important factor, in our view, for a reason somewhat different than that emphasized by Mitchell. In Mitchell's analysis, the squeezing of profit margins late in booms is what brings the boom to an end, as reduced profitability dampens investment demand and hence sales. This suggests that an improvement in firms' power to set prices above marginal cost would extend the boom. But this neglects the fact that firms cannot all raise their relative prices. Let the marginal cost of each firm i be given by Pc(yi), where Yi is the quantity supplied and P is the general price level. (Marginal costs are proportional to the general price level because the variable factors of production are supplied at relative prices that depend upon the quantity demanded of those factors.) Let us suppose furthermore that c(y) is an increasing fimction, for the sort of reasons cited by Mitchell. Then an increase in the quantity supplied by industry i, if not associated with any shift in the marginal cost schedule, wilt be associated with an increase in marginal cost. In the case of an individual firm or industry, this need not be associated with any change in markups; it might simply be associated with an increase in the relative price P i / P 2. But if we consider a uniform increase in the quantity produced by each sector, all relative prices Pi/P would have to increase by the same amount and this is not possible. In fact, in a symmetric equilibrium, one must have

1 -

c(Y),

(1.1)

where Y is the common (and hence aggregate) level of output, and/~ the common (and hence average) markup. It follows from Equation (1.1) that an increase in output Y is possible only insofar as either the real marginal cost schedule c shifts, or the markup falls. If firms allow their markups to decline, this will mean a higher level of equilibrium output than would otherwise be possible, given the current real marginal cost schedule. Thus if markups decline in the later stages of economic expansions, as Mitchell argues, this is not something that brings the expansion to an end; rather, it makes the expansion stronger (and possibly more prolonged) than is justified by cost conditions alone 3. Equation (1.1) suggests that a useful question about fluctuations in aggregate activity is to ask to what extent they result from variations in average markups, as opposed 2 For example, in the case of a competitive industry, the industry supply curve is simply given by Pi - Pc(Fi). An increase in industry demand results in a movement up this curve, to a higher relative

price as well as higher output. 3 This view of the role of markup variations in accounting for aggregate fluctuations is also one with a long history; two early proponents were Robinson (1932) and Kalecki (1938).

Ch. 16:

The Cyclical Behavior o f Prices and Costs

1055

to shifts in the real marginal cost schedule of the typical firm. A related question that has received more attention in the literature is the extent to which the historical record actually suggests that markups were indeed low when output was high. This question is related to the first because, if the data suggested that markups were constant (or procyclical), independent movements in markups could not possibly account for a significant portion o f output fluctuations. Thus, our survey o f empirical evidence starts in Section 2 with the simpler question of the extent to which measured markups are countercyclical. Since marginal cost cannot be measured directly, all o f these measures are indirect and rely on theories o f the cost function facing individual firms. Once one has made these assumptions, however, one need only make a few additional suppositions to obtain an estimate o f the derivative of the function c with respect to Y. This then allows one to infer the output fluctuations induced by changes in measured markups. The result is that one obtains a decomposition of output in terms o f output movements due to markup changes and output movements due to shifts in the marginal cost schedule. We consider this decomposition in Section 3. Section 4 is devoted to a brief survey o f models o f variable markups 4. The above decomposition makes it clear that these models can serve two separate purposes. First, they can affect the extent to which shifts in the marginal cost schedule affect output. If, for example, reductions in marginal cost lower markups, their effect on output is magnified. What is perhaps more interesting still is that these theories allow shocks other than shocks to the marginal cost schedule to affect output as long as these shocks affect markups. In particular, allowing for endogenous markup variations adds a channel through which demand disturbances may affect output and employment. This does not mean that the part of output variations that is due to shifts in the real MC schedule is due to "supply shocks", and the part due to markup variations with the part due to "demand shocks". There are various ways in which demand disturbances might, in principle, shift the real MC schedule 5. Similarly, as we have already mentioned, the models of endogenous markup variation discussed below imply that "supply shocks" as well as "demand shocks" may cause markups to vary. For example, in Rotemberg and Woodford (1996b) it is shown how an endogenous increase in markups following an oil price increase can increase the contractionary impact o f such a shock, even though the oil shock would also contract output (by shifting up the real MC schedule) to a lesser extent in a perfectly competitive model.

4 See Rotemberg and Woodfurd (1995) for further discussion of several of the leading models, with greater attention to the structure of general equilibrium models incorporating these mechanisms, and to issues such as calibration and numerical solution of such models. 5 Well-knownproposals include nominal wage rigidity, as in Keynes (1936), as a result of which inflation lowers the real wage and hence real marginal cost; and variations in the household labor supply schedule due to wealth effects and intertemporal substitution effects, as in Barro's (1981) analysis of the effects of government purchases. Evaluation of their importance is beyond the scope of this survey, though it is important to remember that these proposals require that real wages fall (by as much as the marginal product of labor) for output to expand.

1056

J.J. Rotemberg and M. WoodJbrd

An objection to the usefulness of this decomposition might be that the validity of Equation (1.1) does not itself imply that output variations are usefully "explained" by the markup variations that occur at the same time. One might view the markup as simply the ratio of two quantities (P and M C ) that are each determined by other (and relatively independent) factors, including output, the causal determination of which must be understood in other ways. Such a view is possible if one views prices as evolving without reference to marginal costs (perhaps according a "Phillips curve" relation that makes the rate of price change a function of the level of real activity), and output as determined by demand given the current level of prices. In this case, markups might covary systematically with output [because of Equation (1.1)], but this would be irrelevant for output determination. Such a crude view, however, is difficult to take seriously. While we believe that nominal price stickiness plays a role, at least in short-run fluctuations in activity - and this is one of the reasons for markup variation taken up in Section 4 below - it is not plausible that the level of marginal costs should not be a crucial determinant of the evolution of prices. If a firm's price is expected to remain fixed for a period of time, then the price chosen will depend not solely upon the current level of marginal cost, but upon (loosely speaking) the average of the expected levels of marginal cost over the entire period for which the price will be fixed. As a consequence, the rate of inflation (and expectations regarding future inflation) will be one of its determinants, as is explained further in Section 4.1 below. In such a model, the connection between inflation and real activity (i.e., the aggregate supply relation) can be usefully understood as resulting from the relation between inflation and the average markup, onthe one hand, and the relationship between the markup and output determination indicated by Equation (1.1) 6. Furthermore, it does not seem that nominal rigidities alone can account for all markup variations. First, some of these variations appear not to be related to inflation in the way that can be accounted for by the simple hypothesis of prices remaining fixed for a time. For example, Rotemberg and Woodford (1996b) find that markups rise following an oil shock; but such shocks have also been associated with increases rather than decreases in inflation, so that slowness of prices to adjust to changes in nominal marginal costs might be expected to shrink markups, rather than raising them. And second, the very slowness of prices to adjust to changes in marginal costs (following, say, a loosening of monetary policy) is more easily explained if one posits that decreases in desired markups (i.e., the ratio between price and marginal cost that would be chosen in the absence of the nominal price rigidity) coincide with declines in the ratio of actual to desired prices (due to slow price adjustment). If desired markups decline endogenously at times of temporarily high output, this "real rigidity" will amplify the effects of nominal rigidities, so that nominal disturbances have both larger and more persistent real effects. For both reasons, it would seem that

6 The crucial role of markup variations in explainingthe real effects of purely nominal disturbances is stressed in particular by Kimball (1995).

Ch. 16:

The Cyclical Behavior o f Prices and Costs

1057

variations in desired markups - and not simply variations in markups resulting from a discrepancy between actual and desired prices - are of some importance in accounting for aggregate fluctuations. A consideration of the determinants of desired markups is therefore required. Our survey proceeds as follows. In the next section, we discuss the evidence on cyclical variation in markups. Most of the evidence reviewed relates the slightly procyclical behavior of real wages to cyclical movements in the marginal product o f labor. The key issue in Sections 2.1 and 2.2 is whether, as a result of technical progress, the marginal product of labor is as procyclical as real wages. While the marginal product of labor cannot be measured directly, we provide a number of reasons to believe that it is substantially more countercyclical than the relevant real wage so that, indeed, markups are countercyclical. In Section 2.3 we consider measures of markup variation that are not based on wage variations; these involve cyclical variations in the use of intermediate inputs and in inventory accumulation. We then proceed to study responses of markups to particular shocks. Insofar as we are able to identify nontechnological disturbances, the analysis of markup changes is considerably simplified because we do not have to worry about the effect of technical progress on the real marginal cost schedule. Section 2 closes with an analysis of the differences in markup variations across industries. Section 3 then turns to the consequences of markup variations for macroeconomic variables of interest. First we deal with the effect of markup changes on productivity and profits. We show that, under a variety of circumstances, increases in output that are caused by reductions in markups are associated with increases in profits and measured productivity. Since both productivity and profits are known to be procyclical, this is important in making sure that it is not implausible for changes in markups to be behind movements in output. Section 3 concludes with a method for decomposing output movements into those caused by shifts in the marginal cost schedule and movements due to markup changes (which induce movements along particular marginal cost curves). Section 4 is devoted to a survey of theories of markup variation, and Section 5 concludes.

2. The cyclical behavior of markups In this section, we discuss empirical evidence regarding variation in markups over the business cycle. The main challenge in constructing measures of markup variation is to find suitable measures of marginal cost; and for this reason, it will often be useful to think, equivalently, of how one should measure cyclical variations in real marginal cost 7. It is not easy to obtain measures of marginal cost of which one can be certain.

7 Note, however,that the studies of individual industries discussed in Section 2.4 do attemptto measure industry markups, rather than levels of real marginal cost.

1058

J.J. Rotemberg and M. Woodford

Nonetheless, a variety o f considerations may be offered, several o f which provide support for the view that real marginal costs are procyclical, and hence that markups are countercyclical in the typical sector. I f so, this implies that markup variations play a role in causing or at least amplifying cyclical fluctuations in economic activity.

2.1. Cyclical behavior o f the labor share The most common measures o f marginal cost in the literature consider the cost o f increasing output through an increase in the labor input, holding fixed other inputs. (Measures o f marginal cost deriving from variation o f production decisions along other margins are considered in Section 2.7 below. Note that if firms are minimizing cost, the measure o f marginal cost obtained by considering each possible margin should be the same, so that it suffices to consider one.) If output is a differentiable function o f the labor input, and firms are wage-takers, then marginal cost is equal to the wage divided by the marginal product o f labor. If we assume an aggregate production function o f the form

Y = F ( K , zH),

(2.1)

where K is the capital stock, H the number o f hours worked, and z an index o f laboraugmenting technical progress, then the markup o f price over marginal cost # is given by 8

PZFH(K, zH) /~ -

W

(2.2)

This equation provides an approach to the measurement of markup (or real marginal cost) variations. It also highlights two reasons for the real marginal cost schedule referred to in Section 1 to be upward-sloping. The first is that, holding constant other determinants o f labor supply, the real wage must presumably rise to induce more people to work. The second is that, if one makes the standard assumption that the production function F is concave and one fixes both the capital stock and the state of technology z, the marginal product FH is a decreasing function o f the labor input. Whether or not typical increases in employment are in fact associated with markup declines depends, however, upon whether they are associated with increases in K or z, or decreases in the real wage W/P, sufficient to offset the effects o f the increase in the labor input on FH. In general, real wages do not move countercyclically, and in fact, there is clearlyprocyelical variation in the real wages received by individuals, once one corrects for cyclical variation in the composition o f the workforce 9. This is the famous

8 Here and below, we use the notation FH to mean the partial derivative ofF with respect to its second argument, the effective labor input zH, rather than with respect to H. 9 Kydland and Prescott (1988); Solon et al. (1994). This is not true of all industry wages, however. See Chirinko (1980), Rotemberg and Saloner (1986) and Solon et al. (1994). For a review of this issue, see Abraham and Haltiwanger (1995).

Ch. 16:

The Cyclical Behavior o f Prices and Costs

1059

criticism raised by Dunlop (1938) and Tarshis (1939) against the theory of aggregate supply of Keynes (1936), which is essentially just Equation (2.2), under the assumption of constant technology and a markup equal to one. Keynes (1939) recognized the appeal of a hypothesis of countercyclical markup variation as a resolution of the puzzle, which is the interpretation that we propose. An alternative explanation, of course, is that real wages are procyclical because fluctuations in activity are caused by variations in technical progress. [Real business cycle models are sometimes criticized for predicting real wage movements that are t o o procyclical, so that Kydland and Prescott (1988) take their findings as support for the technology-shock hypothesis.] The need to correct for possible variations in the rate of technical progress means that one needs to measure the variation in both the labor input and in the quantity produced. The required calculation is especially simple if, following Bils (1987), we specialize the production function (2.1) to the case Y = g ( K ) ( z H ) a,

(2.3)

where g is a positive increasing function, and a > 0. Marginal cost is then W H / a Y , so that the markup is given by kt = a S H l ,

(2.4)

where SH is the labor share W H / P Y . Under these assumptions, markup variations are simply the inverse of the variations observed in the labor share. In the case of a Cobb-Douglas production function (or the slightly more general form assumed above), marginal cost is proportional to average labor cost so that a valid measure of markup variations is given by fluctuations in the ratio of price to "unit labor cost" W H / Y - a measure of variations in price-cost margins often referred to in empirical studies of business cycles such as those of Moore (1983)10. We first consider the evidence regarding cyclical variation in this simple measure. The price P with which firms are concerned is the price they receive for their products. This means that the relevant labor share is not the ratio of labor compensation to the value of output conventionally measured in national income accounts, but rather the ratio to the revenue received by firms, which equals the value of output minus indirect taxes 11. We consider cyclical variation in three different measures of this labor share, for the whole economy, the corporate sector and the nonfinancial corporate sector respectively. The first of these measures is less satisfactory than the others for two reasons. First, it includes the government, many of whose services are not sold in markets. Second, it includes income of proprietors in the denominator, and this

10 The ratio of price to unit labor cost is also used as an empirical proxy for the markup in studies such as Phelps (1994). 11 The denominator is thus obtained by adding depreciation (the difference between GNP and NNP) to the conventional concept of "national income".

1060

J.J Rotemberg and M. Woodford

0.68

l

La

0.66

Nonfinancial

/~ v\/~ A

c°rpirate,

0.64 0.62

- 0.78

Overall

/[~j/!^<2~i ~

'

-I~,

k4,

~2 -C "4

,~

- 0.76

~ A.

~-~J'-~.~,

~

,:7

"

%,/j

,'.',

,, ~

v"

v.,'

v~',

-

0,74

- 0~72

0.60

- 0.70

0.58

- 0.68 Corporate

0.56

- 0.66 50

55

60

65

70

75

80

85

90

Fig. 1. The evolution of various labor shares. contains an element of compensation as well. The use of the narrower measures of the labor share eliminates both of these problems. Nonetheless, we include some statistics relating to the overall labor share as well, for comparability with other studies. Figure 1 plots these three series for the period 1947:1 to 1993:1 12. For future reference, the figure also plots the Hodrick-Prescott trend in the labor share for the nonfinancial corporate sector. The figure reveals that the labor share in the corporate sector is essentially identical to the labor share in the nonfinancial segment. On the other hand, the overall labor share deviates from the other two shares in the early 1960s and remains above them from then on. All three series show large increases in the late 1960s. Particularly for the labor share corresponding to the whole economy, this appears to represent a structural break that cannot be regarded as an example of business-cycle variation in the series. Hence in considering the cyclical behavior of the series, we also considered a sample that begins only in 1970. We next wish to relate the movements in one or another of these labor shares to those of a variable that measures the business cycle. One attempt to do so is provided in Figure 2, which plots the labor share in the nonfinancial corporate business sector against the NBER recessions. For each of these recessions, the first line in Figure 2 represents a business cycle peak while the second represents the trough. At first glance, this picture might suggest that the labor share is countercyclical because the labor share series tends to have a local maximum between peaks and troughs. But, it is important

t2 Our sample stops in 1993 because, at the time these calculations were made, the pre-1960 data were not comparable to the more recent revised NIPA data. The results from 1970 onwards were the same for the two data sets, however.

Ch. 16:

The Cyclical Behauior o f Prices and Costs 0.78-

0.76 -

1061

,,-7

,,

-~

E

,:

ii i i

i i

~

i

[ ]

i

~

i

i i I i i I

!!

i i i i i

i i

li r '

i

j

i

'

''

i i 1 L i i

II

i I i

i

i

:III i i '11

,I

-0.8

I

i 1

i

0.74 i

1.0

q

,,,, i!

i

i

-0.6

i' 0.72 i r i

0.70 -

0.68

i ~ i

ii i i

i 1

i i

i i

i i

1

0.66

ii ii ii ii ii ii

i ~i i I ]

ii ii ii ii

i i 1

i i I I ii Ii ii ii ~1

1

I

I

i

1 i

i i

-0.4

-0,2

-0.0

50

55

60

65

70

75

80

85

F i g . 2. L a b o r s h a r e i n n o n f i n a n c i a l c o r p o r a t e s e c t o r a n d N B E R

90 recessions.

to remember that, for the labor share to be perfectly procyclical, its peaks ought to be aligned with the business cycle peaks themselves. The labor share ought then to decline between peak and trough and then increase during the recovery that takes place after the trough. It is this latest implication of a procyclical labor share that is closest to being true, as the labor share increases in the recoveries after the 1954, 1974 and 1982 recessions. The actual correlation between the change in the labor share and a dummy variable that takes the value of one between peaks and troughs and a value of zero otherwise is 0.17, which suggests, albeit very weakly, that the labor share rises when output is declining. However, the correlation between the labor share and the two quarter lagged value of this dummy variable is -0.28. Thus, as the plot itself suggests, the labor share tends to rise late in expansions and to fall late in recessions. This basic pattern: a weak slightly negative relation between the labor share and contemporaneous cyclical indicators and a much stronger positive relation between the labor share and slightly lagged indicators of cyclical activity is what comes out of a more formal analysis as well. For this slightly more formal statistical analysis, we considered four indicators of the business cycle. A popular indicator of this sort is obtained by detrending real GDP using the Hodrick-Prescott filter and then using this detrended series to be a measure of the business cycle. This is, however, a rather arbitrary procedure (since there is no obvious reason to choose one value rather than another of the weighting parameter that

1062

J J Rotemberg and M. Woodford

determines the degree to which the trend is smoothed) 13. An alternative that we find appealing is to follow Beveridge and Nelson (1981) and equate the "cyclical" level of GDP at time t with the expected decline in GDP from time t onwards. This captures the intuitive idea that cyclical movements are temporary, so that a cyclically low level of output corresponds to a high expected rate of growth of output. The difficulty with this approach is that it only becomes meaningful when one specifies an information set that can be used to forecast GDP growth. Following on the steps of an extensive literature, Rotemberg and Woodford (1996a) show that the linearly detrended level of hours spent working in nonagricultural establishments and the ratio of consumer expenditures on nondurables and services to GDP are particularly useful in this respect. A simpler cyclical indicator is the linearly detrended level of hours worked. We prefer to linearly detrend hours rather than GDR since once a trend is included in the regression, the Dickey-Fuller test strongly rejects the hypothesis that the logarithm of hours worked in non-agricultural establishments has a unit root. This measure of detrended hours is in fact one of the main components of the Rotemberg-Woodford measure of forecastable output movements; low levels of hours worked (which are closely related to high unemployment), imply that output can be expected to grow and are thus a good indicator of recessions. For purposes of comparison, we also consider an hours series that has been detrended using the Hodrick-Prescott filter. The first three rows of Table 1 report correlations of our three measures of the labor share with the various cyclical indicators, over the sample period 1947:1 through 1993:1. The first column shows correlations with the predicted declines in output over 12 quarters considered in Rotemberg and Woodford (1996a), the second column shows the correlations with the Hodrick-Prescott filtered level of output, the third column uses linearly detrended hours while the last uses the hours series detrended using the H - P filter. Except the correlations with linearly detrended hours (which are small and positive), the other correlations are small and negative; suggesting weak countercyclical movements in the labor share. These results are consistent with Boldrin and Horvath (1995), Gomme and Greenwood (1995) and Ambler and Cardia (1998) who also report negative correlations of the labor share with output. The correlations they report are larger in absolute magnitude because they use the H - P filter to detrend the labor share as well as to detrend output. Using the H - P filter to detrend the labor share seems problematic, however, because the large movements at relatively high frequencies of the resulting "trend" displayed in Figure 1 are difficult to interpret 14. The last twelve rows of Table 1 report the correlations of the labor share in the nonfinancial corporate sector with leads and lags of the four cyclical indicators. The correlations with the lags are uniformly positive and attain their biggest value when the

13 For further discussion of the properties of this filter, see King and Rebelo (1993). 14 We also considered labor shares detrended with a linear trend. This had only a negligible effect on our results.

Ch. 16:

The Cyclical Behavior of Prices and Costs

1063

Table 1 Correlations of selected variables with cyclical indicators a Predicted declines in GDP

H-P filtered GDP

Linearly detrended hours

H-P filtered hours

Share of compensation in after indirect tax gross product

Long sample Overall

-0.070

0.095

0.055

-0.023

Corporate

-0.080

-0.188

0.031

-0.044

Nonf. Corp.

-0.014

-0.158

0.072

-0.014

Private

-0.009

-0.192

0.178

-0.192

-0.015

Sample: 1969:1-1993:1 Overall

-0.230

-0.403

-0.189

Corporate

-0.077

-0.273

-0.010

0.064

0.066

-0.169

0.103

0.184

-0.334

-0.466

-0.293

-0.156

Nonf. Corp. Private

Correlation of private labor share with leads and lags of cyclical indicator Lead six quarters

-0.437

-0.108

-0.218

-0.136

Lead five quarters

-0.521

Lead four quarters

-0.579

-0.176

-0.312

-0.211

-0.270

-0.406

Lead three quarters

-0.276

-0.5828

-0.360

-0.461

-0.314

Lead two quarters

-0.564

-0.429

-0.454

-0.304

Lead one quarters

-0.509

-0.477

-0.407

-0.256

Lagged one quarter

-0.157

-0.283

-0.100

0.015

Lagged two quarters

0.026

0.110

0.063

0.162

Lagged three quarters

0.075

0.023

0.180

0.270

Lagged four quarters

0.149

0.138

0.258

0.346

Lagged five quarters

0.177

0.194

0.303

0.388

Lagged six quarters

0.213

0.222

0.317

0.406

aThe long sample for all correlations except those involving either the labor share in the private sector or predicted declines in private GDP is 1947:1 to 1993:1. The sample for the correlations involving the labor share in the private sector starts in 1952:1. That for the correlations of predicted output declines with the other labor share starts in 1948:3 because these predicted declines are drawn from Rotemberg and Woodford (1996a). The correlations with leads and lags of output are based on data from 1969:1 to 1993:1.

1064

J.J. Rotemberg and M. Woodford

cyclical indicator is lagged four quarters. Thus a high level of activity is associated with subsequent increases in the labor share. Interestingly, this result also extends to the case where we study the cross-correlogram of H-P filtered output and the H-P filtered labor share. The correlations of the labor share with the leads of our cyclical indicators are uniformly negative. This means that the labor share peaks before the peak in hours. 2.2. Corrections to the labor-share measure o f real marginal cost While the labor share (or equivalently, the ratio of price to unit labor cost) is a familiar and easily interpretable statistic, it represents a valid measure of markup variations only under relatively special assumptions. In this section, we briefly discuss a number of corrections to this measure that would arguably be required to obtain a more realistic measure of real marginal cost. As we shall see, several of these corrections imply that real marginal cost is more procyclical than the labor share. For any of several reasons, then, the measurements discussed above may understate the degree to which cyclical variations in output and employment are due to markup variations as opposed to shifts in the real marginal cost schedule. We take the possible corrections up in sequence. 2.2.1. A non-Cobb-Douglas production function Suppose that the aggregate production function is of the general form (2.1), but that F is not necessarily of the Cobb-Douglas form [or, more precisely, isoelastic in the labor input, as in Equation (2.3)]. Equation (2.2) can still equivalently be written # = t/Hs~1,

(2.5)

where t/H --= zHFH(K, zH)/F(K, zH) is the elasticity of output with respect to the (effective) labor input. [Equation (2.5) reduces to (2.4) in the case of a constant elasticity.] The effect of the additional variable factor in Equation (2.5) depends upon the nature of cyclical variations, if any, in the elasticity of output with respect to the labor input. In the case that F exhibits constant returns to scale, the elasticity t/H can be expressed as a function of the effective labor-to-capital ratio, zH/K, or equivalently as a function of the output-to-capital ratio: t/~q = t/H(y),

(2.6)

where y - Y/K. In the case that the elasticity of substitution between capital and (effective) labor inputs is less than one, the function t/H(y) is monotonically decreasing. This would seem the most likely direction of deviation from the CobbDouglas case (a constant elasticity of substitution exactly equal to one), as the CobbDouglas specification is widely regarded as a reasonable representation of long-run substitution opportunities, whereas short-run factor substitutability (which is relevant

Ch. 16." The Cyclical Behavior o f Prices and Costs

1065

for the present calculation) might well be less (for example, because technology is "putty-clay"). In this case, because y is a procyclical variable (this follows directly from the fact that the capital stock evolves slowly relative to the length of business-cycle fluctuations), Equation (2.6) implies that the additional factor t/H in Equation (2.5) imparts additional countercyclical variation to the implied markup series, roughly coincident with the cyclical component of output or hours. A correction of this kind thus leads to the conclusion that markups fall more in booms than is suggested by the simple labor share measure, and that markup declines coincide more closely in time with increases in output and hours. The size of this correction can be quantified as follows. Assuming constant returns to scale, the elasticity of t/H with respect to y is given by a - (1 - e K 1 ) ( r ] H 1 - - 1), where c ~ is the (Hicks-Allen) elasticity of substitution between capital and labor inputs. A log-linear approximation to the markup series implied by Equation (2.5) is then given

by = @ - s~4,

(2.7)

where hats denote deviations of the logarithm of a stationary variable from its average value. A quantitative estimate of the elasticity a requires values for exH and for the average value of OH (i.e., the value of this elasticity in the case of the "steady-state" factor ratio arotmd which one considers perturbations). Using Equation (2.5), the latter parameter may be calibrated from the average labor share, given an estimate of the average markup, resulting in a = (1 - e~q)(l~-lsTi 1 - 1). (In this last expression, all symbols refer to the average or steady-state values of the variables.) With a markup kt near one, a labor share of 0.7 and an elasticity o f substitution eK~ of 0.5, this formula gives a value of a equal to -0.4. Table 2 reports the resulting correlations between fi and predicted declines in GDP for markups based on both the nonfinancial corporate and the private labor shares. Not surprisingly, markups are now much more cotmtercyclical. However, the contemporaneous correlation of the markup with detrended output is still smaller in absolute value than the correlation with lagged output. Also, as in the case where we do not adjust the labor share, the correlations with leads of output are greater than the contemporaneous correlation. These are actually positive for output led more than 3 quarters 15. 2.2.2.

Overhead

labor

In deriving Equations (2.5)-(2.7), we assume constant returns to scale. An important reason why this may be inaccurate is the presence of overhead costs. Particularly relevant to the above calculations would be the existence of overhead labor. Suppose

15 As is true of all the results of Table 2, similar results obtain when we use detrended hours as our cyclical indicator.

JJ. Rotembergand M. Woodford

1066

Table 2 Correlation of markup based on private labor share with leads and lags of expected declines in GDP a a = -0.4, b,c:0

b - -0.4, a,c=0

c = 4, a,b=0

c = 8, a,b=0

Lead six quarters

0.355

0.370

0.136

-0.058

Lead five quarters

0.323

0.342

0.067

-0.169

Lead four quarters

0.256

0.289

0.048

-0.316

Lead three quarters

0.135

0.189

-0.203

-0.478

Lead two quarters

-0.001

0.075

-0.321

-0.594

Lead one quarters

-0.163

-0.050

-0.418

-0.670

Contemporaneous

-0.402

-0.212

-0.372

-0.542

Lagged one quarter

-0.504

-0.312

-0.235

-0.319

Lagged two quarters

-0.522

-0.344

-0.162

-0.181

Lagged three quarters

-0.503

-0.337

-0.124

-0.095

Lagged four quarters

-0.451

-0.301

-0.066

-0.001

Lagged five quarters

-0.355

-0.226

-0.003

0.079

Lagged six quarters

-0.278

-0.164

0.011

0.110

a Markup is based on Equations (2.14) and (2.15) and uses the labor share in the nonfinancial corporate business sector. that e a c h f i r m ' s p r o d u c t i o n f u n c t i o n 16 is o f t h e f o r m Y = F(K, z ( H - / z / ) ) , w h e r e F is h o m o g e n e o u s o f d e g r e e o n e as b e f o r e , a n d f / ~> 0 r e p r e s e n t s " o v e r h e a d l a b o r " that m u s t b e h i r e d r e g a r d l e s s o f the q u a n t i t y o f o u t p u t that is p r o d u c e d . N o t e that a n o v e r h e a d l a b o r r e q u i r e m e n t i m p l i e s i n c r e a s i n g r e t u r n s ( a v e r a g e cost e x c e e d i n g m a r g i n a l cost), a l t h o u g h m a r g i n a l cost r e m a i n s i n d e p e n d e n t o f scale 17.

16 Once we depart from the assumption of constant returns to scale, it is important to distinguish between firm production functions and the relation that exists between aggregate inputs and outputs. We now assume that each firm is the sole producer of a differentiated good, so that the overhead costs cannot be reduced by simply concentrating all production in a single firm. In a symmetric equilibrium, where the same quantity is produced of each good using the same factor inputs, then this equation also indicates the relation that exists among aggregate output and aggregate factor demands. 17 There are other ways of modeling increasing returns. In particular, one might suppose that marginal cost declines with output; an econometric specification of this kind is estimated, for example, by Chirinko and Fazzari (1994). The notion that marginal cost declines with output is problematic, however. For many firms, increasing output involves an increase in either the number of machines that are employed or an increase in the number of hours for which a given number of machines are used. Both of these seem inconsistent with declining marginal cost since more efficient machines would presumably be used first. More generally, firms whose technology has a declining marginal cost over some range would benefit by bunching production so that their plants are idle some of the time, and output, when positive, is always at a level sufficiently large that marginal cost is not declining in output.

Ch. 16:

The Cyclical Behavior of Prices and Costs

1067

Replacing Equation (2.1) by this, implies that Equation (2.5) should become instead

where t;H now refers to the elasticity of output with respect to the effective nonoverhead labor input. Under this definition, ~,/ is again constant in the case that F takes the Cobb-Douglas form, and countercyclical if the elasticity o f substitution between capital and labor is less than one. The new factor in Equation (2.8), H--~' is a monotonically decreasing function of H i f / 7 / > 018. Allowing for overhead labor thus provides a further reason to regard markups as more countercyclical than is indicated by the labor share alone. A similar conclusion is reached if one assumes fixed costs in production that do not take the form of overhead labor alone, e.g., if one assumes a production function o f the form Y= F(K, zH)

45,

where q5 > 0 represents the fixed costs of operation. The consequences of this correction can be quantified as follows. The elasticity o f the factor ~ with respect to H is given by b - -so~(1 - So), where So is the average or steady-state value o f H / H , the share o f overhead labor in the total labor input. Equation (2.7) may then be generalized to yield fi = @ + b / 2 / - s ~ .

(2.9)

The elasticity b is obviously non-positive. Its size depends on the average fraction o f labor which constitutes overhead labor. A useful bound on this can be obtained by relating So to the degree o f returns to scale. Let the index o f returns to scale p be defined as the ratio of average cost to marginal cost o f production. Measured at the steady-state factor inputs, one obtains p = 1 + t//4 so that instead o f calibrating So, one may equivalently calibrate p. In terms of this parameter, we obtain t/H = #sH -- (p -- 1) for the steady-state elasticity o f output with respect to non-overhead labor, and b = - ( / 9 - 1)/[#SH -- (p -- 1)]. It is easily seen that one must have p ~< #, in order for there to exist non-negative profits in the steady state. This allows one to bound the possible size o f the elasticity

18 Here we assume that the overhead labor requirement is acyclical. This depends upon an assumption that entry of either firms or plants is slow, as in Rotemberg and Woodford (1995) and Ambler and Cardia (1998), and so can be neglected at business cycle frequencies. The consequences of variable entry are considered further below, in Section 3.

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J J Rotemberg and M. Woodford

b, given an estimate o f the average markup. On the other hand, the same consideration provides a reason for supposing that overhead costs are non-negligible, if one believes that prices do exceed marginal cost on average. For with constant returns to scale, prices higher than marginal cost would imply the existence of pure profits (in addition to the competitive return to capital); for example, a markup o f 25% (bt = 1.25) would imply that pure profits should make up 20% o f total revenues. This is rather large given the scant evidence for the existence o f pure profits in US industry. Indeed, Hall (1988) finds (using stock market re~rns to construct a user cost for capital) that pure profits in US industry are close to zero. It furthermore makes sense that profits should be zero in the steady state, due to entry, which one should expect to eliminate persistent profits in the long run, even if entry does not respond quickly enough to eliminate cyclical fluctuations in profits. If we assume this, we can impose p =/~, so that there is only a single parameter to calibrate, that describes both the degree o f returns to scale and the degree o f market power. With # = 1.25 and a labor share o f 0.7, the parameter b is then -0.4. Table 2 shows that, even letting a equal zero, such a value o f b leads to markups that are strongly countercyclical though the correlations with lagged output remain higher in absolute value 19. The significance that one attaches to such findings obviously depends upon the size of the average markup (or degree o f returns to scale) that one is willing to assume. Here it is worth remarking that a value of ~ equal to 1.6 need not mean that any individual firm marks up its costs by 60%. The reason for this is that firms do not just mark up their labor costs but also their materials cost. To see what this implies about the markup, suppose that, as in Rotemberg and Woodford (1995), materials are a fixed proportion SM o f aggregate output while value added constitutes only a fraction (1 - S M ) o f total costs. The marginal cost o f producing one unit o f gross output is then (1 - sM) W

zFH

q- SM,

and the markup o f the price o f gross output over total marginal cost ktc ° is given by 1

btGO

- (1

1 --SM)~ +SM,

(2.10)

where tt vA is the "value-added markup" that satisfies Equation (2.2). If the materials share equals 0.6 (as is typical of US manufacturing), then a/~vA o f 1.6 [the "baseline 19 Rotemberg and Woodford (1991) use a variant of this method to construct series for markup changes using aggregate US data. Assuming an average markup of 1.6 and an elasticity of substitution equal to 1 (their baseline case), they find that markups fall by about 1% when hours increase by 1%. The constructed markup series is also strongly negatively correlated with fluctuations in aggregate hours worked. Portier (1995) uses the same method on French data, and assumes an average markup of 1.373 and an elasticity of substitution equal to 1. His estimates imply that a 1% increase in GDP is associated with about a 1.5% reduction in markups. Thus markups would appear to be more countercycliealfor France (a finding that is especially striking given the lower assumed returns to scale).

Ch. 16: The Cyclical Behavior of Prices and Costs

1069

case" o f Rotemberg and Woodford (1991)] requires that the typicalfirm "s price be only 18% higher than its marginal cost. A related correction would assume, instead o f overhead labor, a "setup cost" for each employee, as is considered in Basu and Kimball (1997). Suppose that the production function is Y = F ( K , z(h - h)N)), where now N represents the number of employees and h the number of hours worked by each. We again assume that F is homogeneous o f degree one; the "set-up cost" h > 0 represents a sort o f per-employee fixed cost. (The observed preference for full-time employees observed in many lines o f work makes the existence o f such costs plausible 20.) If we consider the marginal cost of increasing output solely on the employment margin (holding fixed hours per week), we again obtain Equation (2.8), but with H and { / r e p l a c e d by h and h in the first factor. We correspondingly again obtain Equation (2.9), but with if/replaced by h. Since hours per employee are also a strongly procyclical variable, the first factor in Equation (2.8) is again a source of further countercyclical movement in implied markups. Basu and Kimball suggest that So = 0.25 should be an upper bound on the importance of such set-up costs (as full-time wage premia should otherwise be larger); but this value would still allow the elasticity in Equation (2.9) to be as large as b = -0.3. 2.2.3. Marginal wage not equal to the average

Thus far, we have assumed wage-taking behavior on the part o f firms, meaning that they regard themselves as being able to hire additional hours o f work, at the margin, at a wage which is also the wage paid for each o f the hours that they do hire - so that the relevant marginal wage is also the average wage that is paid. Suppose, however, that this is not true, and that the firm's wage bill is W ( H ) , a function that is increasing, but not necessarily linear in H 2~. In this case, marginal cost depends upon the marginal wage, W t ( H ) , so that Equation (2.5) becomes # = 09-1 tlHS~i1,

(2.1 1)

where o) = H W t ( H ) / W ( H ) is the ratio o f the marginal wage to the average wage. This might vary cyclically for several reasons. One reason might be monopsony power in the labor market. Suppose that each firm faces an upward-sloping firm-specific labor supply curve, and takes this into account in its hiring and production decisions. (The wage that the firm must pay may also

20 One might ask, if such costs exist, why finns do not minimize costs by hiring all of the time of those employees that they hire at all. The answer must be that finns face a wage schedule that is not simply linear in the number of hours worked by a given employee, as discussed below. Note that this hypothesis about individual wages is of no consequence for the marginal cost calculation considered in this paragraph. 21 A marginal wage that is increasing in the number of hours hired is, for example, allowed for in such studies as Abel (1978), Shapiro (1986), Bils (1987), and Basu and Kimball (1997).

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J.J Rotembergand M. Woodford

depend upon other variables such as the overall level of employment in the economy, but these factors are taken as given by the individual firm, and can simply be treated as time-variation in the location of the firm-specific labor supply curve.) If w(H) is the wage that the firm must pay if it hires H hours of work, then W(H) = Hw(H), and -l where CHw is the elasticity of the firm-specific labor supply curve. This co = 1 +CHw, might be either increasing or decreasing with increases in hours hired by the firm. The most plausible assumption, however, would probably be that the elasticity of labor supply decreases as the hours hired by the firm increase (it is hard to induce people to work more than a certain number of hours, even at very high wages, while on the other hand the opportunity cost of their time tends not to fall below a certain level even when the number of hours worked is small). Under this assumption, the factor m is an increasing function of H , and Equation (2.9) again holds, with b < 0. This would imply that real marginal costs would actually be more procyclical (and markups more countercyclical) than would be suggested by consideration only of the terms in Equation (2.5). Alternatively, one might imagine that firms first hire a certain number of employees, and that they initially contract with them about a wage schedule which determines the wage as a function of hours worked. Subsequently, perhaps after receiving additional information about current demand conditions, the firms determine the hours of work. If all employees are asked to work the same number of hours at this stage, we may interpret W(H) in Equation (2.11) as the wage schedule negotiated with each employee. Now if the number of employees is chosen ex ante so as to minimize the cost of the number of hours that the firm expects to use, then ex ante expected hours per worker will be the level H* that minimizes the average wage W ( H ) / H 22. At this point, the marginal wage should equal the average wage, and (assuming a unique minimum) in the case of small fluctuations in H around the value H*, co should be increasing in H. Again this would imply markups more countercyclical than would be suggested by Equation (2.5). Most observed wage contracts do not involve wages that increase continuously with the number of hours that the employee is asked to work. On the other hand, if one supposes that contractual wages are not the true shadow price of additional labor to a firm, because of the presence of implicit contracts of the kind assumed, for example, by Hall (1980), then one might suppose that the true cost to the firm rises in proportion to the employee's disutility of working, even if the wages that are paid in the current period do not. This would be a reason to expect the effective wage schedule W(H) to be convex, so that the above analysis would apply. Bils (1987) observes that in many industries, a higher wage is paid for overtime hours (i.e., hours in excess of 40 hours per week). He thus proposes to quantify the extent to which the marginal wage rises as firms ask their employees to work longer

22 This conclusion depends upon an assumption that only person-hours enter the production ftmction, rather than employmentor hours per employeemattering separately.

Ch. 16: The Cyclical Behavior of Prices and Costs

1071

hours, by measuring the extent to which the average number o f overtime hours per employee, V, rises with increases in the total number o f hours worked per employee H , and then assuming that W ( H ) = wo[H + p V ( H ) ] , where w0 is the straight-time wage a n d p is the overtime p r e m i u m (0.5 according to the US statutory requirement)23. For example, he finds that when average hours per employee rise from 40 hours p e r week to 41 hours, the average number o f overtime hours worked per employee rises b y nearly 0.4 hours, while when they rise from 41 to 42 hours per week, overtime hours rise by another 0.5 hours. This increase in the fraction o f hours that are overtime hours as average hours increase means not only that the marginal wage exceeds the average wage, but that the ratio o f the marginal wage to the average wage rises as hours increase. A s s u m i n g p = 0.5, Bils finds that an increase in average hours from 40 to 41 hours increases the average wage b y about 0.5%, but increases the marginal wage by 4.6%. O n average, he finds that the factor co in Equation (2.11) has an elasticity o f 1.4 with respect to variations in average hours a4. Thus a loglinear approximation to Equation (2.11) is again o f the form (2.9), where in Bils' w o r k / 2 / r e f e r s to fluctuations in average hours per worker 25, and b = -1.4. Since average hours worked in US manufacturing are strongly procyclical, taking into account this factor m a k e s the implied markup significantly more countercyclical. Indeed, when Bils regresses his constructed markup series [using Equation (2.9)] on a measure o f cyclical employment 26, he finds that markups decline, on average, by 0.33% for each one-percent increase in employment. O f this cyclical variation, a 0.12% decline is implied by the increase in the labor share (which is mildly procyclical in his sample), while the remaining 0.21% decline comes from the increase in the ratio o f the marginal wage to the average wage. One may question whether the statutory premium p a i d for overtime hours represents a true cost to the firm; some argue, for example, that the opportunity to work overtime is in fact dispensed as a reward for exemplary behavior at other times. Bils answers

23 The fact that V(H) is modeled as a fraction that rises continuously with H, rather than being zero for all H ~<40 hours per week and one for all H > 40 hours per week requires that not all employees work the same number of hours. The nature and consequences of this heterogeneity are not explicitly modeled. 24 This average elasticity is slightly smaller than the elasticity of 1.6 indicated by the figures given in the text relating to an increase from 40 to 41 hours per week. 25 Bils studies the variations of production-worker hours in manufacturing, and computes the marginal cost of increasing output through an increase in production-worker hours only, holding other inputs fixed, including non-production-worker hours. Thus in Equation (2.9), s~4 refers to fluctuations in the share of production-worker wages. Because he assumes a production function which is isoelastic in production-worker hours, holding fixed the other inputs, a = 0 in his calculations. 26 His cyclical indicator is the difference between current production-worker employment and a moving average of that series. Note that Bils does not assume, as in the simple analysis above, that employment is fixed in advance and that all short-run variation in hours occurs on the hours-per-employee margin. In fact, in his "second method" of computing the cyclical variability of the marginal wage, he explicitly considers substitution between the employment and hours-per-employee margins.

1072

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this objection by pointing out that if one assumes that because of sophisticated implicit contracts, the true cost to the firm is proportional to the worker's disutility of working o(H), then one might well obtain estimates of the degree of procyclical movement in the ratio of the marginal wage to the average that are as large as those obtained using his method. Under the assumption suggested above about the steady-state level of hours, the coefficient b in Equation (2.9) would in that case equal -o"/1t*ol, or -C,w, where eHw is now the Frisch (or intertemporal) elasticity of labor supply by a wage-taking household in a competitive spot market. A value of b less negative than Bils' value of -1.4 would then be obtained only if one assumed preferences implying an elasticity of labor supply greater than 0.7, whereas many microeconomic studies of labor supply estimate a lower elasticity than that.

2.2.4. Costs of adjusting the labor input An additional reason why marginal hours may be more expensive in booms is the presence o f adjustment costs. It is simplest to illustrate this point if we assume, as, for example, in Pindyck and Rotemberg (1983), that there are convex costs of changing the labor input H. Suppose that, in addition to the direct wage costs wtHt of hiring Ht hours in period t, there is an adjustment cost of lctHt(~(Ht/Ht_l). Here tot represents a price index in period t for the inputs that must be purchased as part of the adjustment process; we shall assume that the (logarithms of the) factor prices tc and w are co-integrated, even if each is only difference-stationary. (More specifically, we shall assume that tc/w is stationary.) The factor HtO(Ht/Ht_l) represents the physical quantity of inputs that must be expended in order to adjust the labor input; note that adjustment costs increase in proportion to the quantity of labor used by a given firm. This specification implies that adjustment costs remain of the same magnitude relative to direct labor costs, even if both H and w exhibit (deterministic or stochastic) trend growth. The exposition is simplest if we treat the adjustment costs as "external", in the sense that the additional inputs that must be purchased are something other than additional labor, so that both the production function (2.1) and the formula for the labor share can still be written as before in terms o f a single state variable " H ''27. Finally, we assume that ~b is a convex function, with q~(1) = Ct(1) = 0; thus adjustment costs are non-negative, and minimized (equal to zero) in the case of no change in the labor input. We can then compute the marginal cost associated with an increase in output at date t, assuming that production is increased solely through an increase in the labor input at date t, with no change in the inputs used in production at other dates, except

27 This assumption is more appealing in the case that H is interpreted to refer solely to productionworker hours, as in Bils's (1987) work, rather than total hours.

Ch. 16:

The Cyclical Behavior o f Prices and Costs

1073

for the necessary changes in the inputs used in the adjustment process at both dates t and t + 1. In this case, Equation (2.5) becomes 28 /x = g2 1 r#HSTs1,

(2.12)

where £2t =

1 + K't {[O(rHt) + Wt

rHtOt(]lHt)]

-- E t [ R t , t + l

2 10, (]/Ht+l)] }, 'Y1ct+l]/~/t+

(2.13)

in which in turn Ym - H t / H t 1, Yrt = tot~tot-1 29, and Rt,t+l is the stochastic discount factor by which firms discount random income at date t + 1 back to date t. [Here we have written Equation (2. t 3) solely in terms o f variables that we expect to be stationary, even i f there are unit roots in both H and w, to indicate that we expect Y2 to be a stationary random variable. I f ~b is strictly convex (i.e., i f there are non-zero adjustment costs), the cyclical variation in the factor g2 changes the nature o f implied markup fluctuations. Because ~ is positive when the labor input is rising and negative when it is falling, 12 should be a procyclical factor, though with a less exact coincidence with standard business cycle indicators than the cyclical correction factors discussed thus far. I f we take a log-linear approximation to Equation (2.13), near a steady-state in which the variables H , to~w, yx, and R are constant over time, we obtain D, =

~[~'H, -/3E~9~,+,],

(2.14)

where here the coefficient c > 0 denotes q~"(1) times the steady state value o f to~w, and fl denotes the steady-state value o f Ryr, the discount factor for income streams measured in units o f the adjustment-cost input. This can then be substituted into the log-linear approximation to Equation (2.12), = a ~ - s 7 4 - {2,

(2.15)

to obtain a formula to be used in computing markup variations. Equation (2.14) makes it clear that the cyclical variations in the labor input are the main determinant o f the cyclical variations in f2. The factor Y2 will tend to be high when hours are temporarily high (both because they have risen relative to the past and because they are expected

28 In this equation, sH refers to wH/PY as before. In order for this to correspond to labor compensation as a share of value added, one must assume that the adjustment-cost inputs are not purchased from outside the sector of the economy to which the labor-share data apply. However, to a first-order approximation, it does not matter whether the adjustment costs are internal or external, as discussed below. 29 More generally, we shall use the notation Yxtto denote the growth rate xt/xt_l, for any state variable x.

1074

J.J Rotemberg and M. WoodJbrd

to fall in the future), and correspondingly low when they are temporarily low. Thus, it tends to increase the degree to which implied markups are countercyclica130. More precisely, the factor g2 tends to introduce a greater negative correlation between measured markups and future hours. Consider, as a simple example, the case in which hours follow a stationary AR(1) process given by ~It = p~It l -}- ~t,

where 0 < p < 1, and c is a white-noise process. Then ~2t is a positive multiple of f / t - )~/~t-l, where )~ ~ (1 -fl(1 - p ) ) - l , and cov(g2t, Art+j)is of the form C(1 -)~p)pJ for all j ~> 0, where C > 0, while it is of the form C(1 - ) , p 1)p4 for all j < 0. One observes (since p < )~ < 1/p) that the correlation is positive for all leads j ~> 0, but negative for all lags j < 0. Thus this correction would make the implied markup series more negatively correlated with leads of hours, but less negatively correlated with lags of hours. The intuition for this result is that high lagged levels of hours imply that the current cost of producing an additional unit is relatively low (because adjustment costs are low) so that current markups must be relatively high. Since, as we showed earlier, the labor share is more positively correlated with lags of hours (and more negatively correlated with leads of hours) this correction tends to make computed markup fluctuations more nearly coincident with fluctuations in hours. To put this differently, consider the peak of the business cycle where hours are still rising but expected future hours are low. This correction suggests that marginal cost are particularly high at this time because there is little future benefit from the hours that are currently being added. The last two columns of Table 2 show the effect of this correction for c equal to 4 and 8 while fi is equal to 0.99. To carry out this analysis, we need an estimate of Et~m+l. We obtained this estimate by using one of the regressions used to compute expected output growth in Rotemberg and Woodford (1996a). In particular, the expectation at t of Ht+l is the fitted value of a regression of/~/t+i on the values at t and t - 1 of/~/, the rate of growth of private value added and the ratio of consumption of nondurables and services to GDE Subtracting the actual value of/~/t from this fitted value, we obtain Et)'m+l. This correction makes the markup strongly countercyclical and ensures that the correlation of the markup with the contemporaneous value of the cyclical indicator is larger in absolute value than the correlation with lagged values of this indicator. On the other hand, the correlation with leads of the indicator is both negative and larger still in absolute value, particularly when c is equal to 8. The same calculations apply, to a log-linear approximation, in the case that the adjustment costs take the form of less output from a given quantity of labor inputs.

30 Even though they allow for costs of changing employment, Askildsen and Nilsen (1997) do not find any industries with countercyclicalmarkups in their study of Norwegian manufacturing industries. However, their adjustment-cost parameter is often estimated to have the wrong sign and one would expect the markups computed on the basis of these estimates to be procyclical.

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The Cyclical Behavior of Prices and Costs

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Suppose that in the above description o f production costs, H refers to the hours that are used for production purposes in a given period, while Hq~ indicates the number o f hours that employees must work on tasks that are created by a firm's variation o f its labor input over time. (In this case, t¢ =_ w.) Equations (2.12) and (2.13) continue to apply, as long as one recalls that H and sH now refer solely to hours used directly in production. Total hours worked equal AH instead, and the total labor share equals AsH, where A = 1 + q~(yu). But in the log-linear approximation, we obtain zi = 0, and so Equations (2.14) and (2.15) still apply, even if )/t and s~r refer to fluctuations in the total labor inputs hired by firms. A more realistic specification of adjustment costs would assume costs of adjusting employment, rather than costs of adjusting the total labor input as above 31. Indeed, theoretical discussions that assume convex costs o f adjusting the labor input, as above, generally motivate such a model by assuming that the hours worked per employee cannot be varied, so that the adjustment costs are in fact costs o f varying employment. In the data, however, employment variations and variations in total person-hours are not the same, even if they are highly correlated at business-cycle frequencies. This leads us to suppose that firms can vary both employment N and hours per employee h, with output given by F(K, zhN), and that costs o f adjusting employment in period t are given by lftNtO(Nt/Nt 1)- If, however, there are no costs o f adjusting hours, and wage costs are linear in the number o f person-hours hired Nh, firms will have no need ever to change their number o f employees (which is clearly not the case). If, then, one is not to assume costs o f adjusting hours per employee 32, one needs to assume some other motive for smoothing hours per employee, such as the sort o f non-linear wage schedule discussed above. We thus assume that a firm's wage costs are equal to W(h)N, where W(h) is an increasing, convex function as above. One can then again compute the marginal cost o f increased output at some date, assuming that it is achieved through an increase in employment at that date only, holding fixed the number o f hours per employee h at all dates, as well as other inputs. One again obtains Equation (2.12), except that the definition o f g2 in Equation (2.13) must be modified to replace YH by YN, the growth rate of employment, throughout. [In the modified Equation (2.13), w now refers to the average wage, W(h)/h.] Correspondingly, Equation (2.15) is unchanged, while Equation (2.14) becomes ~'~t = C[YNt -- ~Et YNt+l ],

(2.16)

31 Bils and Cho (1994) assume a convex cost of adjusting the employee-to-capital ratio, interpreting this as a cost of changing the organization of production, rather than a cost of hiring and firing employees. Because most variations in the employment-to-capital ratio at business-cycle frequencies are due to variations in employment, the consequences of such a specification are similar to those of the more familiar assumption of convex costs of changing the number of employees. 32 Studies that estimate separate adjustment costs for variations in employment and in the number of hours worked per employee, such as Shapiro (1986), tend to find insignificant adjustment costs for hours.

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J.J Rotemberg and M~ Woodford

Thus one obtains, as in the simpler case above, a correction to Equation (2.5) that results in the implied markup series being more countercyclical (since employment is strongly procyclical, just as with the total labor input). Alternatively, one could compute the marginal cost o f increased output, assuming that it is achieved solely through an increase in hours per employee, with no change in employment or in other inputs. In this case, one obtains again Equation (2.11), but with H everywhere replaced by h in the first factor on the right-hand side. There is no contradiction between these two conclusions. For the right-hand sides o f Equations (2.11) and (2.12) should be equal at all times; cost-minimization requires that W'(ht) = wt+tCt[~)(Ymt)+ YNtO'(YNt)] -Et[Rt,t+l~:t+lY~t+l¢ 2 , (YNt+l)]},

(2.17)

which implies that g2 = ~o. Condition (2.17) is in fact the Euler equation that Bils (1987) estimates in his "second method" of determining the cyclicality of the marginal wage; he uses data on employment and hours variations to estimate the parameters o f this equation, including the parameters of the wage schedule W(h)33. An equivalent method for determining the cyclicality o f markups would thus be to determine the importance o f employment adjustment costs from estimation o f Equation (2.17), and compute the implied markup variations using Equations (2.15) and (2.16). Insofar as the specification (2.17) is consistent with the data, both approaches should yield the same implied markup series. It follows that Bils' results using his second method give an indication o f the size o f the correction that would result from taking account o f adjustment costs for employment, if these are o f the size that he estimated. His estimate of these adjustment costs imply an elasticity o f 12 even greater than the value o f 1.4 discussed above. 2.2.5. Labor hoarding Suppose now that not all employees on a firm's payroll are used to produce current output at each point in time. For example, suppose that o f the H hours paid for by the firm at a given time, Hm are used in some other way (let us say, maintenance o f the firm's capital), while the remaining H - H m are used to produce the firm's product. Output is then given by Y = F ( K , z ( H - H m ) ) rather than Equation (2.1). We can again

33 Bils is able to estimate this equation by assuming parametric ftmctional forms for the functions W~(h) and O(YN), and assuming that t¢t is a constant multiple of the straight-time wage. He also notes that the term wt should refer not simply to the average hourly wage, but to total per-employee costs divided by hours per employee; the numerator thus includes the costs of other expenses proportional to employment but independent of the number of hours worked per employee, such as payments for unemployment insurance. In fact, identification of the parameters in Equation (2.17) is possible only because wt is assamed not to be given by a time-invariant fimction W(ht)/ht, but rather by (W(ht) + Ft)/ht, where the shift term F t representing additional per-employment costs is time-varying in a way that is not a function of h t.

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compute the marginal cost o f increasing output by hiring additional hours, holding Hm fixed (along with other inputs). One then obtains instead of Equation (2.5) Iz = u ) l tlHS741,

(2.1 8)

where UH ---- ( H - H m ) / H is the fraction of the labor input that is utilized in production. Note that this conclusion is quite independent o f how we specify the value to the firm o f the alternative use to which the hours Hm may be put. It suffices that we believe that the firm is profit-maximizing, in its decision to allocate the hours that it purchases in this way, as in its other input decisions, so that the marginal cost of increasing production by shifting labor inputs away from maintenance work is the same as the cost o f increasing production by hiring additional labor. The fraction uH is often argued to be procyclical, insofar as firms are said to "hoard labor" during downturns in production, failing to reduce payrolls to the extent o f the decline in the labor needed to produce their output, so as not to have to increase employment by as much as the firms' labor needs increase when output increases again. For example, the survey by Fay and Medoff (1985) finds that when output falls by 1%, labor hours used in production actually fall by 1.17%, but hours paid for fall only by 0.82% 34, Insofar as this is true, it provides a further reason why markups are more countercyclical than would be indicated by Equation (2.5) alone 35. I f the Fay and Medoff numbers are correct, and we assume furthermore that nearly all hours paid for are used in production except during business downturns, they suggest that UH falls when output falls, with an elasticity o f 0.35 (or an elasticity of about 0.4 with respect to declines in reported hours). Thus this factor alone would justify setting b = - 0 . 4 in Equation (2.9). A related idea is the hypothesis that effective labor inputs vary procyclically more than do reported hours because ofprocyclical variation in work effort. We may suppose in this case that output is given by Y = F ( K , zeH), where e denotes the level o f effort exerted. If, however, the cost o f a marginal hour (which would represent e units o f effective labor) is given by the reported hourly wage W, then Equation (2.5) continues to apply. Here the presence o f time-variation in the factor e has effects that are no different than those o f time-variation in the factor z, both of which represent changes in the productivity o f hours worked; the fact that e may be a choice variable of the

34 Of the remaining hours paid for, according to survey respondents, about two-thirds represent an increase in employee time devoted to non-production tasks, while the other third represents an increase in employee time that is not used at all. Fair (1985) offers corroborating evidence. 35 Models in which output fluctuations result from changes in firms' desired markups can also explain why labor hoarding should be counter-cyclical, as is discussed further in Section 2.3. At least some models in which fluctuations in output result from shifts in the real marginal cost schedule have the opposite implication: periods of low labor costs should induce increases both in the labor force employed in current production and in the labor force employed in maintenance tasks.

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firm while z is not has no effect upon this calculation. Note that this result implies that variations in the relation between measured hours of work and the true labor input to the production due to "labor hoarding" are not equivalent in all respects to variations in effort, despite the fact that the two phenomena are sometimes treated as interchangeable 3 6. I f we allow for variation in the degree to which the measured labor input provides inputs to current production (either due to labor hoarding or to effort variations), one could also, in principle, measure marginal cost by considering the cost of increasing output along that margin, holding fixed the measured labor input. Consideration of this issue would require modeling the cost of higher utilization of the labor input for production purposes. One case in which this does not involve factors other than those already considered here is if higher effort requires that labor be better compensated, owing to the existence of an effort-wage schedule w(e) of the kind assumed by Sbordone (1996). In this case the marginal cost of increasing output by demanding increased effort results in an expression of the form (2.11), where now co =_ ew'(e)/w(e). If, at least in the steady state, the number of hours hired are such that the required level of effort is cost-minimizing, and that cost-minimizing effort level is unique, then (just as in our discussion above of a schedule specifying the wage as a function of hours per employee) the elasticity co will be an increasing function of e, at least near the steady-state level of effort. The existence of procyclical effort variations would then, under this theory, mean that implied markup variations are more countercyclical than one would conclude if the effort variations were not taken into account. This does not contradict the conclusion of the paragraph before last. For in a model like Sbordone's, effort variations should never be used by a firm, in the absence of adjustment costs for hours or employment (or some other reason for increasing marginal costs associated with increases in the measured labor input, such as monopsony power). In the presence, say, of adjustment costs, consideration of the marginal cost of increasing output through an increase in the labor input leads to Equation (2.12), rather than to Equation (2.5); this is consistent with the above analysis, since a cost-minimizing choice of the level of effort to demand requires that co(e) = f2

(2.19)

at all times. It is true (as argued two paragraphs ago) that variable effort requires no change in the derivation of Equation (2.12). But observation of procyclical effort variations could provide indirect evidence of the existence of adjustment costs, and hence of procyclical variation in the factor Q. A further complication arises if the cost to the firm of demanding greater effort does not consist of higher current wages. Bils and Kahn (1996), for example, assume

36 For example, models of variable effort are sometimes referred to as models of "labor hoarding", as in Burnside et al. (1993).

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that there exists a schedule w(e) indicating the effective cost to the firm of demanding different possible effort levels, but that the wage that is actually paid is independent of the current choice of e, due to the existence of an implicit contract between firm and worker o f the form considered in Hall (1980). They thus suppose that the current wage equals w(e*), where e* is the "normal" (or steady-state) level of effort. In this case, Equation (2.12) should actually be 1

w(e*)

t~ = ~2 ~OHSH w(e)

(2.20)

I f effort variations are procyclical, the factor w(e)/w(e*) is procyclical, and so this additional correction makes implied real marginal costs even more procyclical. In their empirical work Bils and Kahn (1996) relate w(e)/w(e*) to variations in the energy consumption per unit of capital and show that this correction makes marginal cost significantly procyclical in four of the six industries they study. Interestingly, these four industries have countercyclical marginal costs when they ignore variations in the cost of labor that result from variations in effort.

2.2.6. Variable utilization o f capital It is sometimes argued that the degree of utilization of firms' capital stock is procyclical as well, and that the production function is therefore properly a function of"effective" capital inputs that do not coincide with the measured value of firms' capital stocks. If by this one means that firms can produce more from given machines when more labor is used along with them, then it is not clear that "variable utilization" means anything that is not already reflected in a production function of the form (2.1). Suppose, however, that it is possible for a firm to vary the degree of utilization of its capital stock other than by simply increasing its labor-to-capital ratio, and that the production function is actually of the form Y = F(uKK, zH), where uK measures the degree of utilization of the capital stock K. Even So, the derivation of Equation (2.5) is unaffected [and the same is true of subsequent variations on that equation, such as (2.8), (2.11), (2.12) and (2.18)]. The reason is that variation in capital utilization has no consequences for those calculations different from the consequences of timevariation in the capital stock itself. It is simply necessary to define y in Equation (2.6) by y/uK. In the case of an isoelastic production function (2.3), the methods of calculating implied markup variations we discussed above do not need to be modified at all. Variable capital utilization matters in a more subtle way if one assumes that capital utilization depends upon aspects of the firm's labor input decisions other than the total labor input H . For example, Bils and Cho (1994) argue that capital utilization should be an increasing function of the number of hours worked per employee; the idea being that if workers remain on the shop floor for a longer number of hours each week, the capital stock is used for more hours as well (increasing the effective capital inputs

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used in production), whereas a mere increase in the number o f employees, with no change in the length o f their work-week, does not change the effective capital inputs used in production 37. Under this hypothesis, the aggregate production function is given by Y = F(ux(h)K, zhN). This modification again has no effect upon the validity o f the derivation o f Equation (2.12) from a consideration of the cost o f increasing output by varying employment, holding hours per employee fixed [except, again, for the modification o f Equation (2.6)]. Thus Equation (2.15) becomes (2.2t) where ~ is the elasticity o f u~ with respect to h, while Equation (2.16) is unchanged. If one assumes a = 0 [as Bils (1987) does], this would mean no change in the implied markup variations obtained using this method (which, as we have argued, is equivalent to Bils' "second method") 38. Assuming that uK depends upon h does affect our calculation o f the cost o f increasing output by increasing hours per employee. In particular, Equation (2.11) must instead be replaced by

= ~o-l(nH +zox)~h ~,

(2.22)

where OK is the elasticity o f output with respect to the effective capital input. However, while the presence o f ~ > 0 in Equation (2.20) is o f considerable importance for one's estimate o f the average level o f the markup (it increases it), it has less dramatic consequences for implied markup fluctuations. In the Cobb-Douglas case, r/H and r/K are both constants, and implied percentage variations in markups are independent of the assumed size o f )~. Thus this issue has no effect upon the computations o f Bils (1987). If we maintain the assumption o f constant returns but depart from the Cobb-Douglas case by supposing that ~//t is countercyclical (because eKH < 1), then allowance for 0 < 3~ ~< 1 makes the factor ~//~+ )o/K less countercyclical. This occurs for two reasons; first, the factor z/H + )~r/K decreases less with decreases in ~/H (and in the limit of ~, = 1, it becomes a constant), and second, the factor y/uK (upon which 0/4 depends) is again less procyclical. Nonetheless, even if we assume that all countercyclical

37 They provide evidence of a statistical correlation between hours per worker and other proxies for capital utilization. Their econometric results are consistent with an assumption that capital utilization is proportional to hours per employee, a result that also has a simple interpretation in terms of a common work-week for all inputs. On the other hand, as Basu and Kimball (1997) note, this correlation need not indicate that firms are forced to vary the two quantities together. 38 More generally, belief that ~. should take a significant positive value, perhaps on the order of 1, reduces the significance of variations in r/n as a contribution to implied markup variations, since both y and h are strongly procyclical. It is not plausible, however, to suppose that ~. should be large enough to make ~ - ,b~ a significantly countercyclicalfactor.

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variation in this factor is eliminated, implied markup variations will still be as strongly countercyclical as they would be with a Cobb-Douglas production function. To sum up, there are a number of reasons why the simple ratio of price to unit labor cost is likely to give an imprecise measure of cyclical variations in the markup. As it happens, many of the more obvious corrections to this measure tend to make implied markups more countercyclical than is that simple measure. Once at least some of these corrections are taken account of, one may easily conclude that markups vary countercyclically, as is found by Bils (1987) and Rotemberg and Woodford (1991). 2.3. Alternative measures o f real marginal cost

Our discussion in Sections 2.1 and 2.2 has considered for the most part a single approach to measuring real marginal cost (or equivalently, the markup), which considers the cost of increasing output through an increase in the labor input. However, as we have noted, if firms are minimizing cost, the measures of real marginal cost that one would obtain from consideration of each of the margins along which it is possible to increase output should move together; thus each may provide, at least in principle, an independent measure of cyclical variations in markups. While cyclical variation in the labor input is clearly important, cyclical variations in other aspects of firms' production processes are observed as well. We turn now to the implications of some of these for the behavior o f real marginal cost. 2.3.1. Intermediate inputs

Intermediate input use (energy and materials) is also highly cyclical. Insofar as the production technology does not require these to be used in fixed proportions with primary inputs [and Basu (1995) presents evidence that in US manufacturing industries it does not], this margin may be used to compute an alternative measure of real marginal cost. Consideration of this margin is especially attractive insofar as these inputs are not plausibly subject to the kind of adjustment costs involved in varying the labor input [Basu and Kimball (1997)], so that at least some of the measurement problems taken up in Section 2.2 can be avoided. Suppose again that gross output Q is given by a production function Q(V,M), where V is an aggregate o f primary inputs, and M represents materials inputs. Then, considering the marginal cost of increasing output by increasing materials inputs alone yields the measure -

PQM(V,M)

PM

(2.23)

by analogy with Equation (2.2). [Note that in Equation (2.23),/~ refers to the "grossoutput" markup which we called/~c in Equation (2.10). Also note that P now refers to the price of the firm's product, and not a value-added price index as before.] Under

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the assumption that Q exhibits constant returns to scale 39, QMis a decreasing function o f M / V , or equivalently of the materials ratio m = M/Q. In this case, log-linearization of Equation (2.23) yields =fr~ -/3v,

(2.24)

where f < 0 is the elasticity of QM with respect to m, and/3~ indicates percentage fluctuations in the relative price of materials pM =-- PM/P. Both terms on the right-hand side of Equation (2.24) provide evidence that markups vary counter-cyclically. Basu (1995) shows that intermediate inputs (energy and materials) rise relative to the value of output in expansions, at least when these are not due to technology shocks 4°. Basu furthermore assumes thatpM is equal to one because he views materials inputs as indistinguishable from final output. Under this assumption, the increase of m in booms immediately implies that markups are countercyclical. In fact, however, goods can be ranked to some extent by "stage of processing"; all goods are not used as both final goods and intermediate inputs of other sectors to the same extent. And it has long been observed that the prices of raw materials rise relative to those of finished goods in business expansions, and fall relative to those of finished goods in contractions [e.g., Mills (1936), Means et al. (1939)]. Murphy, Shleifer and Vishny (1989) show that this pattern holds up consistently both when they consider broad categories of goods grouped by stage of processing, and when they consider particular commodities that are important inputs in the production of other particular goods. Hence it would seem that for the typical industry, PM is a procyclical variable. Because of Equation (2.24), this would itself be evidence of countercyclical markup variation, even if one regarded QM as acyclical. The combination of these two facts clearly supports the view that real marginal costs are procyclical, and hence that markups are countercyclical. Note that in the case that the production function Q ( V , M ) is isoelastic in M, Equation (2.23) implies that/~ should be inversely proportional to the share of materials costs in the value of gross output, Sm = pMm. Thus in this case the materials share would directly provide a suitable proxy for variations in real marginal cost, just as in our previous discussion of the labor share. However, this specification (implying a unit elasticity of substitution between intermediate and primary inputs) is hardly plausible. Rotemberg and Woodford (1996b) estimate elasticities of substitution for 20 two-digit manufacturing sectors, and find an average elasticity less than 0.7. Basu's

39 This assumption allows for increasing returns, but requires that they take the form of increasing returns in the value-addedproduction function V(K, zH). 40 This is shown in the fourth row of his Table 5. He regresses the percentage change in m on the percentage change in Q, for each of 21 two-digit US manufacturing industries. He instruments output growth using the Ramey-Hall instntments for non-technological aggregatedisturbances. He also shows that intermediate inputs rise more than does a cost-weightedaverage of primaryinputs (labor and capital), using the same instruments; as one should expect, the regression coefficientin this case is much larger.

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(1995) estimate of the response o f m to changes in the relative price o f primary and intermediate inputs suggests an elasticity o f substitution half that size 41. Thus it seems most likely that i n s t e a d f < - 1 in Equation (2.24). If the materials ratio rn is procyclical as found by Basu, it follows that real marginal costs are actually more procyclical than is indicated b y the materials share alone. A related measure is used by Domowitz, Hubbard and Petersen (1986), who measure "price-cost margins" defined as the ratio o f price to "average variable cost". They measure this as a the ratio o f industry revenues to the sum o f labor and materials costs, which is to say, as the reciprocal o f the sum o f the labor and materials shares. This should correspond to the markup as we have defined it only under relatively special circumstances. I f the production function is isoelastic in both labor inputs and materials inputs, then real marginal cost is proportional to the labor share (as explained in Section 2.1), and also proportional to the materials share (as explained in the previous paragraph). It then follows that these two shares should move in exact proportion to one another, and hence that their s u m is a multiple o f real marginal cost as well. Domowitz et al. report that this sum is somewhat countercyclical for most industries, and as a result they conclude that p r i c e - c o s t margins are generally procyclical. However, the conditions under which this measure should correspond to variations in the markup o f price over marginal cost are quite restrictive, since they include all o f the conditions required for the labor share to be a valid measure o f real marginal cost, a n d all o f those required for the materials share to be a valid measure. We have reviewed in Section 2.2 a number o f reasons why the labor share is probably less procyclical than is real marginal costs. Similar considerations apply in the case o f the materials share, although the likely quantitative importance o f the various corrections is different in the two cases; in the case o f materials, the elasticity o f substitution below unity is probably a more important correction, while adjustment costs are probably much less important. Nonetheless, one must conclude, as with our previous discussion o f the labor share alone, that real marginal cost is likely to be significantly more procyclical than is indicated by the Domowitz et al. measure o f "average variable cost" 42.

41 The last line of his Table 5 indicates an increase in rn of only 0.12% for each 1% increase in the relative price of primary and intermediate inputs. His estimates of the cyclicality of materials input use indicate three times as large an elasticity for M/V as for M/Q (comparing lines 2 and 4 of that table), though the estimated elasticity of M/V is reduced when labor hoarding is controlled for. This would suggest an increase in M/V of at most 0.36% for each percent increase in the relative price of inputs. 42 Similar issues arise with the study of Felli and Tria (1996) who use the price divided by overall average cost as a measure of the markup. They compute this by dividing total revenue by total cost including an imputed cost of capital (which depends on a measure of the real interest rate). Leaving aside the difficulties involved in measuring the cost of capital, it is hard to imagine that adding together the shares of labor, materials and capital is appropriate for computing markups unless each share in isolation is appropriate as well. In addition, the existence of adjustment costs of capital probably make the marginal cost that results from producing an additional unit by adding capital considerably more procyclical than average capital cost. These adjustment costs may also rationalize the dynamic relation they find between their ratio of average cost to output and output itself.

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2.3.2. Inventory fluctuations Another margin along which firms may increase the quantity of goods available for sale in a given period is by drawing down inventories of finished goods. For a costminimizing firm, the marginal cost of drawing down inventories must at all times equal the marginal cost of additional production, and thus measurement of the costs of reduced inventories provides another potential (indirect) measure of the behavior of marginal cost. The following simple framework will clarify what is involved in such an analysis. Inventories at the end of period t, It+l, equal It + Qt - S t , where Qt is production at t and St are sales at t. It is thus possible for a firm to keep its path of sales (and hence revenues) unchanged, increasing production and inventories at time t by one unit while reducing production by one unit at time t + 1. If the firm's production and inventoryholding plan is optimal, such a marginal deviation should not affect the present value of its profits. For the typical firm, the proposed deviation raises nominal costs by the marginal cost of production at t, ct, while lowering them by the present value o f the marginal cost of production at t + 1, and also raising profits by the marginal benefit of having an additional unit of inventory at the end of t. Denoting the real value o f this latter marginal benefit by b(It, Zt), where Zt denotes other state variables at date t that may affect this benefit, we have Ptb(It, Zt) + Et {Rt,t+~ct+l } = ct as a first-order condition for optimal inventory accumulation by the firm, where Pt is the general price level at date t (not necessarily the price of the firm's output), and Rt,t+l is a stochastic discount factor for nominal income streams. This may equivalently be written Ct

~

Ct+l

b(It, Zt) = Ptt - LtPt,t+l Pt+----l'

(2.25)

where now Pt,t+~ is the corresponding discount factor for real income streams. Given an assumption about the form of the marginal benefit function b(I, Z), observed inventory accumulation then provides evidence about real marginal costs in an industry - more precisely, about the expected rate o f change in real marginal costs. The early studies in this literature [e.g., Eichenbaum (1989), Ramey (t991)] have tended to conclude that real marginal cost is countercyclical. The reason is that they assume that the marginal benefit of additional inventories should be decreasing in the level of inventories (or equivalently, that the marginal cost of holding additional inventories is increasing); the finding that inventories are relatively high in booms then implies that b is low, from which the authors conclude that real marginal costs

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must be temporarily low 43. Eichenbaum interprets the countercyclical variation in real marginal costs as indicating that output fluctuations are driven by cost shocks, while Ramey stresses the possibility that increasing returns to scale could be so pervasive that marginal cost could actually be lower in booms. Regardless o f the explanation, if the finding o f countercyclical real marginal costs is true for the typical sector, it would follow that markups in the typical sector must be procyclical. This is indeed the conclusion reached by Kollman (1996). Bils and Kahn (1996) argue, instead, that real marginal cost is procyclical in each o f the six production-for-stock industries that they investigate. The differing conclusion hinges upon a different conclusion about cyclical variation in the marginal benefits of additional inventories. They begin by observing that inventory-to-sales ratios do not vary secularly. This suggests that the function b is homogeneous o f degree zero in inventories and sales; specifically, they propose that b is a decreasing function, not o f I alone, but o f I/S 44. A similar conclusion follows from noticing that inventory-to-sales ratios are fairly constant across different models o f automobiles at a given point in time, even though these models differ dramatically in the volume o f their sales. But this implies that b is actually higher in booms. The reason is that, as Bils and Kahn show, the ratio o f inventories to sales is strongly countercyclical; while inventories rise in booms, they rise by less than do sales. Thus, the marginal value o f inventories must be high in booms and, as a result, booms are periods where real marginal costs are temporarily high. This conclusion is consistent both with the traditional view that diminishing returns result in increasing marginal costs, and with the view that business cycles are not primarily due to shifts in industry cost curves. As noted earlier, Bils and Kahn also show that their inventory-based measures of real marginal cost covary reasonably closely with a wage-based measure of the kind discussed above, once one corrects the labor cost measure for the existence ofprocyclical work effort as in Equation (2.20). If their conclusion holds for the typical industry, and not just the six that they consider, it would have to imply countercyclical markup variations 45.

43 This aspect of inventory behavior has been much discussed as an embarrassment to the "production smoothing" model of inventory demand, which implies that inventories should be drawn down in booms [e.g., Blinder (1986)]. That prediction is obtained by adjoining to Equation (2.25) the assumptions that b is decreasing in I and that real marginal cost is increasing in the level of production Q. 44 A theoretical rationale for this is provided in terms of a model of the stockout-avoidance demand for inventories. 45 The price data for the particular industries considered by Bils and Kahn are ambiguous in this regard; they find that (given their measures of variations in marginal cost) markups are countercyclical in some industries but procyclical in others. This means that certain of their sectors have strongly procyclical relative prices for their products - something that cannot be true of industries in general.

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2.3.3. Variation in the capital stock

A final way in which output can be increased is by increasing the stock o f capital 46. Thus t~ -

PFK(K, z H ) E(r) '

(2.26)

where E ( r ) is the expected cost o f increasing the capital stock at t by one unit while leaving future levels o f the capital stock unchanged. Assuming that the capital stock at t can actually be changed at t but also letting there be adjustment costs, rt equals PK,t + CI,t - Rt,t+l(1 - 6)(PK,t+I + cI,t+l)

where PK,t is the purchase price o f capital at t, c~,t is the adjustment cost associated with increasing the capital stock at t by one unit, 6 is the depreciation rate. It then becomes possible to measure changes in/~ by differentiating Equation (2.26). This is somewhat more complicated than the computation o f marginal cost using either labor or materials because the rental rate o f capital r cannot be observed directly; it must be inferred from a parametric specification for c~. A related exercise is carried out by Galeotti and Schiantarelli (1998). After specifying a functional form for Cl and making a homogeneity assumption regarding F, they estimate Equation (2.26) by allowing/~ to be a linear function of both the level of output and o f expected changes in output. Their conclusion is that markups fall when the level of output is unusually high and when the expected change in output is unusually low. As we discuss further in Section 3, this second implication is consistent with certain models o f implicit collusion. 2.4. The response o f Jhctor prices to aggregate shocks

Thus far we have discussed only the overall pattern o f cyclical fluctuations in markups. Here we take up instead the degree to which markup variations play a role in the observed response o f the economy to particular categories of aggregate shocks. We are especially interested in shocks that can be identified in the data, that are known to be non-technological in character and that are thus presumptively statistically independent of variations in the rate o f technical progress 47. These cases are o f particular interest

46 We have considered separately each of these different ways in which firms can increase their output and their associated marginal cost. An alternative is to postulate a relatively general production (or cost) function, estimate its parameters by assuming that firms minimize costs, and thereby obtain estimates of marginal cost that relate to many inputs at once. One could then compare this "average" estimate of marginal cost to the price that is actually charged. Morrison (1992) and Chirinko and Fazzari (1997) follow a related approach. 47 In taking this view, of course, we assume that variations in technical progress are essentially exogenous, at least at business-cycle frequencies.

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because we can then exclude the hypothesis o f shifts in supply costs due to changes in technology as an explanation for the observed response o f output and employment. This allows us to make judgments about the nature o f markup variations in response to such shocks that are less dependent upon special assumptions about the form of the production function than has been true above (where such assumptions were necessary in order to control for variable growth in technology). In particular, in the case o f a variation in economic activity as a result of a nontechnological disturbance, if markups do not vary, then real wages should move countercyclically. In our basic model, this is a direct implication o f Equation (2.2), under the assumption o f a diminishing marginal product of labor 48. For in the short run, the capital stock is a predetermined state variable, and so increases in output can occur if and only if hours worked increase, as a result o f which the marginal product of labor must decrease; this then requires a corresponding decrease in the real wage, in order to satisfy Equation (2.2). In the case o f such a shock, then, the absence o f countercyclical real wage movement is itself evidence of countercyclical markup variation. Before turning to the evidence, it is worth noting that the inference that procyclical (or even acyclical) real wages in response to these shocks imply countercyclical markups is robust to a number o f types of extension o f the simple model that leads to Equation (2.2). For example, the presence of overhead labor makes no (qualitative) difference for our conclusion, since the marginal product o f labor should still be decreasing in the number o f hours worked. A marginal wage not equal to the average wage also leads to essentially the same conclusion. If, in particular, we assume that the firm's wage bill is a nonlinear function o f the form W(H) = woo(H), where the function o(H) is time-invariant though the scale factor w0 may be time-varying 49, then w(H), the ratio of the marginal to the average wage, is a time-invariant function. Since the denominator of Equation (2.2) should actually be the marginal wage, when the two differ, our reasoning above actually implies that/~o must be countercyclical. But as we have explained above, w(H) is likely to be an increasing function (if it is not constant), so that/~ should vary even more countercyclically than does the product/too (which equals the ratio o f the marginal product o f labor to the average wage). If there are convex costs of adjusting the labor input, one similarly concludes that #f2 must be countercyclical. But since the factor (2 [defined in Equation (2.13)] will generally

48 Note that the latter assumption is necessary for equilibrium, if we assume that markups do not vary because product markets are perfectly competitive. In the case of market power but a constant markup (as in a model of monopolistic competition with Dixit-Stiglitz preferences and perfectly flexible prices see below), a mildly increasing marginal product of labor schedule is theoretically possible, but does not seem to us appealing as an empirical hypothesis. 49 For example, Bils (1987) assumes a relationship of this kind, where w0 represents the time-varying straight-time wage, while the function v(H) reflects the nature of the overtime premium, which is timeinvariant in percentage terms.

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vary procyclically, this is again simply a reason to infer an even stronger degree of countercyclical variation in markups than is suggested by Equation (2.2). I f there is labor hoarding, it can still be inferred in the case of an increase in output due to a non-technological disturbance that H - H m must have increased; and then, if real wages do not fall, Equation (3.8) implies that markups must have declined. In the case of variable capital utilization, the situation is more complicated. Condition (2.2) generalizes to /~ =

PzFH(uI(K, zH) W

(2.27)

If we assume as above that F is homogeneous degree one, FH is a decreasing function of zH/uirK. But the mere fact that output and the labor input increase will not settle the question whether the ratio of labor inputs to effective capital inputs, zH/uirK, has increased or not. Hence it may not be clear that the marginal product of labor must decline in booms. Suppose, however, that the cost of higher capital utilization consists of a faster rate of depreciation of the capital stock. Let the rate of depreciation be given by 6(uir), and let V(K') denote the value to the firm of having an undepreciated capital stock of K ' at the end of the period. The usual assumption of diminishing returns makes it natural to suppose that 6 should be an increasing, convex function, while P should be an increasing, concave function s0. Then if we consider the marginal cost of increasing output solely by increasing the rate of utilization of the capital stock, we obtain the additional relation

F1((uxK, zH) # = V'((1 - 6(ux))K)6'(uir)"

(2.28)

Now if zH/uKK decreases when output expands, it follows that Fir declines. Furthermore, this requires an increase in uK, so that, under our convexity assumptions, both ~-/ and 6 ~ must increase. Thus Equation (2.28) unambiguously requires the markup to decrease. Alternatively, if zH/uirK increases, FH declines, and then, if there is no decline the real wage, Equation (2.27) requires a decline in the markup. Thus under either hypothesis, markup variations must be countereyclical, if real wages are not 51" We turn now to the question of whether expansions in economic activity associated with non-technological disturbances are accompanied by declines in real wages. There are three important examples of identified non-technological disturbances that are often used in the literature. These are variations in military purchases, variations in the world

so See Appendix 2 in Rotembergand Woodford (1991). 51 Which case is actually correct will depend upon the relative degrees of curvature of the various schedules that enter into the right-hand sides of Equations (2.27) and (2.28).

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oil price, and monetary policy shocks identified using "structural VAR" methods. At least in the USA, the level of real military purchases has exhibited noticeable variation over the post-World War II period (as a result of the Korean conflict, Vietnam, and the Reagan-era military build-up). The causes of these variations are known to have had to do with political events that have no obvious connection with technical progress. (We consider military purchases rather than a broader category of government purchases exactly because this claim of exogeneity is more easily defended in the case of military purchases.) Similarly, the world oil price has been far from stable over that period (the two major "oil shocks" of the 1970s being only the most dramatic examples of variation in the rate of increase in oil prices), and again the reasons for these variations, at least through the 1970s, are known to have been largely external to the US economy (and to have had much to do with political dynamics within the OPEC cartel)52. In the case of monetary policy shocks, the identification of a time series for exogenous disturbances is much less straightforward (since the Federal funds rate obviously responds to changes in economic conditions, including real activity and employment, as a result o f the kind of policies that the Federal Reserve implements). However, an extensive literature has addressed the issue of the econometric identification of exogenous changes in monetary policy 53, and we may therefore consider the estimated responses to these identified disturbances. In each of the three cases, the variable in question is found to be associated with variations in real activity, and these effects are (at least qualitatively) consistent with economic theory, so that it is not incredible to suppose that the observed correlation represents a genuine causal relation. We turn now to econometric studies of the responses to such shocks, using relatively unrestricted VAR models of the aggregate time series in question. Rotemberg and Woodford (1992) show that increases in real military purchases raise private value added, hours worked in private establishments and wages deflated by the relevant value added deflator. Ramey and Shapiro (1998) show that the effect on this real wage is different when revised NIPA data are used and that, with revised data, this real wage actually falls slightly. They argue that this response can be reconciled with a two-sector constant markup model. Whether a one-sector competitive model can be reconciled with their evidence remains an open question. Christiano, Eichenbaum and Evans (1996) show, using a structural VAR model to identify monetary policy shocks, that output and real wages both decline in response to the increases in interest rates that are associated with monetary tightening. This again suggests that the contraction in output is associated with an increase in markups. An increase in the federal funds rate by one percent that leads to a 0.4% reduction in output reduces real wages by about 0.1%. I f one supposes that hours fall by about the same percent as output, the effective increase in the markup is about 0.2%.

52 These first two series have been widely used as instruments for non-tectmologicalsources of variation in US economic activity, following the precedent of Hall (1988, 1990). 53 For a recent survey, see Leeper, Sims and Zha (1996).

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Rotemberg and Woodford (1996b) look instead at the response of the US economy to oil price increases. They show that during the pre-1980 OPEC period, such increases lowered private value added together with real wages. Specifically, a one percent unexpected increase in oil prices is shown to lead to a reduction of private value added by about a quarter of a percent after a year and a half, and to a reduction of the real wage (hourly earnings in manufacturing deflated by the private value-added deflator) by about 0.1%, with a similar time lag. This combination of responses again suggests that markups increase, especially during the second year following the sfiock. The inference is, however, less straightforward in this case; for one might think that an increase in oil prices should have an effect similar to that of a negative technology shock, even if it does not represent an actual change in technology. In fact, Rotemberg and Woodford show that this is not so. Let us assume again the sort of separable utility function used to derive Equation (2.23), but now interpret the intermediate input "M" as energy. In this case, consideration of the marginal cost of increasing output by increasing labor inputs yields /~ =

PQv(V,M) VH(K,zH) w

(2.29)

Comparison of Equation (2.29) with (2.23) allows us to write a relation similar in form to Equation (2.2),

PVH(K,zH) -

Vl

'

(2.30)

where the price index/5 is defined by /5 =

P Y - ~PMM V(K, zH)

(2.31)

Thus if we deflate the wage by the proper price index P, it is equally true of an energy price change that a decrease in labor demand must be associated with an increase in the real wage, unless the markup rises. [Note that the situation is quite different in the case of a true technology shock, since the relation (2.30) is shifted by a change in z.] Under the assumption of perfect competition (/~ = 1), the price index defined in Equation (2.31) is just the ideal (Divisia) value-added deflator. Thus a competitive model would require the value-added-deflated real wage to rise following an oil shock, if employment declines 54; and the observation that real wages (in this sense) decline would suffice to contradict the hypothesis of perfect competition. The results of Rotemberg and Woodford do not quite establish this; first, because their privatevalue-added deflator is not precisely the ideal deflator, but more importantly, because

54 This result is discussed extensively by Bruno and Sachs (1985), who use it to assert that the unemploymentfollowingthe oil shocks was due to real wage demands being too high.

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their measure of private value added includes the US energy sector, whereas the above calculations refer to the output of non-energy producers (that use energy as an input). Still, because the energy sector is small, even the latter correction is not too important quantitatively; and Rotemberg and Woodford show, by numerical solution of a calibrated model under the assumption of perfect competition, that while small simultaneous declines in their measure of output and of the real wage would be possible under competition, the implied declines are much smaller than the observed ones 55 Similar reasoning allows us to consider as well the consequences of changes in the relative price of intermediate inputs other than energy. We ignored materials inputs in our discussion above of the inferences that may be drawn from the response of real wages to identified shocks. As before, however, Equation (2.2) [and similarly (2.27)] can be interpreted as referring equally to a production technology in which materials inputs are used in fixed proportions with an aggregate of primary inputs, under the further assumption that the relative price of materials is always one, because materials and final goods are the same goods. But the relative prices of goods differing by "stage of processing" do vary, and so a more adequate analysis must take account of this. When one does so, however, one obtains Equation (2.30) instead of (2.2). It is still the case that the failure of real wages to rise in the case of a non-technological disturbance that contracts labor demand indicates that markups must rise, as long as the real wage in question is w/fL What, instead, if one observes only the behavior o f w/P? Then the failure of this real wage to rise might, in principle, be explained by a decline in P/P, consistent with a hypothesis of constant (or even procyclical) markups. However [referring again to Equation (2.29)], this would require a decline in Qv(V, M). Under the assumption that Q is homogeneous degree one, this in turn would require a decline in M/V, hence an increase in QM (V, M). I f markups are constant or actually decreasing, this would then require an increase in the relative price of materials, PM/P, by Equation (2.23). Thus we can extend our previous argument to state that if one observes that neither w/P nor PM/P increases in the case of a non-technological disturbance that leads to reduced labor demand, one can infer that markups must increase. In fact, Clark (1996) shows, in the case of a structural VAR identification of monetary policy disturbances similar to that of Christiano et al., that a monetary tightening is followed by increases in the price of final goods relative to intermediate goods and raw materials. This, combined with the evidence of Christiano et al. regarding real wage responses, suggests that a monetary tightening involves an increase in markups. A possible alternative explanation of declines in real wages and the relative price of materials inputs at the same time as a contraction of output and employment is an increase in some other component of finns' marginal supply cost. Christiano et al.

55 Finn (1999), however,finds larger declines in the case of a competitivemodel that allows for variable utilization of the capital stock.

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propose that an increase in financing costs may be the explanation o f their findings 56. As they show, in a model where firms require bank credit to finance their wage bill, the interest rate that must be paid on such loans also contributes to the marginal cost o f production; and it is possible to explain the effects o f a monetary tightening, without the hypothesis o f markup variation, as being due to an increase in marginal cost due to an increase in the cost o f credit. But while this is a theoretical possibility, it is unclear how large a contribution financing costs make to marginal costs o f production in reality 57. This matter deserves empirical study in order to allow a proper'quantitative evaluation o f this hypothesis. 2.5. Cross-sectional differences in markup variation In this subsection we survey the relatively scant literature that investigates whether markups are more countercyclical in industries where it is more plausible a priori that competition is imperfect. This issue is of some importance because countercyclical markups are less plausible in industries where there is little market power. For markups below one imply that the firm can increase its current profits by rationing consumers to the point at which marginal cost is no higher than the firm's price. But if markups never fall below one, there is little room for markup variation unless average markups are somewhat above one. In addition, the theoretical explanations we present for cotmtercyclical markups in section 3 all involve imperfect competition. A consideration of whether the measures o f markup variation that we have proposed imply that markup variation is associated with industries with market power is thus a check on the plausibility o f our interpretation o f these statistics. Quite apart from this, evidence on comparative markup variability across industries can shed light upon the adequacy of alternative models o f the sources o f markup variation. The most straightforward way o f addressing this issue is to compute markups for each sector using the methods discussed in section 2, and compare the resulting markup movements to output movements. In Rotemberg and Woodford (1991), we carry out this exercise for two-digit US data, treating each o f these sectors as having a different level o f average markups and using Hall's (1988) method for measuring the average markup in each sector 58. We show that the resulting markups are more negatively

56 The same explanation is offered by Clark for the behavior of the relative prices of goods at different stages of processing. 57 Interruptions of the supply of bank credit certainly can significantly affect the level of economic activity, but the most obvious channel through which this occurs is through the effects of financing costs upon aggregate demand. Financing costs are obviously important determinants of investment demand, the demand for consumer durables, and inventory accumulation; but a contraction of these components of aggregate demand can easily cause a reduction of equilibrium output, without the hypothesis of an increase in supply costs. 58 For a more elaborate analysis of the evolution of cyclical markups in four relatively narrowly defined (four digit) industries, see Binder (1995). He finds that these four industries do not have a common pattern of markup movements, though none of them has strongly countercyclical markups.

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correlated with GNP in sectors whose eight-digit SIC sector has a higher average four-firm concentration ratio. Thus, assuming this concentration is a good measure of market power, these results suggest that sectors with more imperfect competition tend to have more countercyclical markups. One source of this result is that, as shown earlier by Rotemberg and Saloner (1986), real product wages Wi/Pi are more positively correlated with GNP, and even with industry employment, in more concentrated industries. By itself, this is not sufficient to demonstrate that markups are more countercyclical since zFH could be more procyclical in these sectors. However, the analysis of Rotemberg and Woodford (1991) suggests that this is not the explanation for the more procyclical real product wages in more concentrated sectors. As we discussed earlier, Domowitz, Hubbard and Petersen (1986) measure markup changes by the ratio of the industry price relative to a measure of "average variable cost". They show that this ratio is more procyclical in industries where the average ratio of revenues to materials and labor costs is larger, and see this as suggesting that markups are actually more procyclical in less competitive industries. As we already mentioned, this method for measuring markup variation imparts a procyclical bias for a variety of reasons. This bias should be greater in industries with larger fixed (or overhead) costs [because of Equation (2.8)], and these are likely to be the more concentrated industries. In addition, the ratio of revenues to labor and materials costs is a poor proxy for the extent to which a sector departs from perfect competition, because this indicator is high in industries that are capital-intensive, regardless of the existence of market power in their product markets. Domowitz, Hubbard and Petersen (1987) use a different method for measuring industry markup variations and obtain rather different results. In particular, they run regressions of changes in an industry's price on changes in labor and materials cost as well as a measure of capacity utilization. Using this technique, they show that prices are more countercyclical, i.e., fall more when capacity utilization becomes low, in industries with higher average ratios of revenues to materials and labor costs. If the relation between capacity utilization and marginal cost were the same across industries, and if one accepted their method for deciding which industries are less competitive, their study would thus show that markups are more countercyclical in less competitive industries.

3. Implications of markup variations for business fluctuations In this section, we study whether it is empirically plausible to assign a large role on markup fluctuations in explaining business fluctuations. We first take up two related aspects of the observed cyclical variation in the relation between input costs and the value of output, that are sometimes taken to provide prima f a c i e evidence for the importance of cost shifts (as opposed to markup changes) as the source of fluctuations in activity. These are the well-known procyclical variation in productivity and in

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profits. We show that these procyclical variations contain very little information on the importance of markup changes because markup variations induce such procyclical responses. We next take up a more ambitious attempt at gauging the role of markup fluctuations in inducing cyclical fluctuations in economic activity. In particular, we study the extent to which the markup changes that we measured in Sections 2.1 and 2.2 lead to output fluctuations. Any change in output that differs from that which is being induced by changes in markups ought naturally to be viewed as being due to a shift in real marginal costs (for a given level of output). Thus, this approach allows us to decompose output changes into those due to markup changes and those due to shifts in the marginal cost curve. What makes this decomposition particularly revealing is that, under the hypothesis that markups are constant all output fluctuations are due to shifts in real marginal costs.

3.1. Explaining cyclical variation in productivity and profits 3.1.1. Cyclical productivity Standard measures of growth in total factor productivity (the "Solow residual" and variants) are highly positively correlated with growth in output and this fact is cited in the real business cycle literature [e.g., Plosser (1989)] as an important piece of evidence in favor of the hypothesis that business cycles are largely due to exogenous variations in the rate of technical progress. It might seem that variations in economic activity due to changes in firms' markups (in the absence of any shift in the determinants of the real marginal cost schedule) should not be associated with such variations in productivity growth, and that the close association of output variations with variations in productivity growth therefore leaves little role for markup variations in the explanation of aggregate fluctuations - or at least, little role for disturbances that affect economic activity primarily through their effect upon markups rather than through their effect on production costs. In fact, however, there are a number of reasons why variations in markups should be expected to produce fluctuations in measured total factor productivity growth, that are strongly and positively correlated with the associated fluctuations in output growth. Thus observation of procyclical productivity growth does not in itself provide any evidence that markup variations do not play a central role in accounting for observed aggregate fluctuations. (Of course, procyclical productivity is not in itself conclusive evidence of markup variation either, since other explanations remain possible. For this reason productivity variations are a less crucial statistic than those discussed in Sections 2.1 and 2.2.) One reason is simply that standard measures of total factor productivity growth may use incorrect measures of the elasticities of the production function with respect to factor inputs. If these elasticities are assigned values that are too small (in particular, the elasticity ~/H with respect to the labor input), then spurious procyclical variation in

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total factor productivity growth will be found. As Hall (1988) notes, the Solow residual involves a biased estimate of just this kind, if firms have market power. Consider a production function of the form (2.1), where F is not necessarily homogeneous of degree 1. Differentiation yields (3.1) As noted before, Equation (2.2) implies that r/,q = /~sH; similar reasoning (but considering the marginal cost of increasing output by increasing the quantity of capital used) implies that ~/K = #Sx. Thus under perfect competition (so that # = 1), the elasticities correspond simply to the factor shares, and a natural measure of technical progress is given by the Solow residual e s°l°w -

5'~ - s K p ~ -

s.5,..

More generally, however, substitution of Equation (3.1) (with the elasticities replaced by/* times the corresponding factor income share) yields eSolow = # - 1 Yr +sH#/> /Z

(3.2)

In the case of perfect competition, only the second term is present in Equation (3.2), and the Solow residual measures growth in the technology factor z. But in the presence of market power (# > 1), increases in output will result in positive Solow residuals (and decreases in output, negative Solow residuals), even in the absence of any change in technology. In particular, output fluctuations due to changes in the markup will result in fluctuations in the Solow residual, closely correlated with output growth. Hall (1990) points out that in the case that the production function exhibits constant returns to scale, this problem with the Solow residual can be eliminated by replacing the weights sK,sH by the shares of these factor costs in total costs, rather than their share in revenues. Thus he proposes a "cost-based productivity residual" C a l l -= ~?r - ~K ~?K - ~,v 9H,

where ~/~ = SH/(SK + sH), and sK = 1 - ~H. In terms of these factor shares, the production function elasticities are given by ~/H = p~H, ~/x = p~,v, where p = ~K + r/~/ is the index of returns to scale defined earlier. Similar manipulations as are used to derive Equation (3.2) then yield cHal I

=

p-

1^ . ^ Yr + s~/yz.

(3.3)

P Even if kt > 1, as long as p = 1, Hall's "cost-based" residual will measure the growth in z. One can show, in fact, that this measure of productivity growth is procyclical

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to essentially the same degree as is the Solow residual 59. But again this need not indicate true technical change. For if there are increasing returns to scale (p > 1), due for instance to the existence of overhead labor as discussed above, then increases in output will result in positive Solow residuals even without any change in technology. This explanation for the existence of procyclical productivity in the absence of cyclical changes in technology is closely related to the previous one, since we have already indicated that (given the absence of significant pure profits) it is plausible to assume that/~ and p are similar in magnitude. The quantitative significance of either of these mechanisms depends upon how large a value one believes it is plausible to assign to /~ or p. Hall (1988, 1990) argues that many US industries are characterized by quite large values o f these parameters. He obtains estimates of/~ that exceed 1.5 for 20 of the 26 industries for which he estimates this parameter. Within his 23 manufacturing industries, 17 have estimates of/~ above 1.5 while 16 have estimates of p that are in excess of 1.5. His evidence is simply that both productivity residuals are positively correlated with output movements, even those output movements that are associated with non-technological disturbances. In effect, he estimates the coefficients on the first terms on the righthand sides of Equations (3.2) and (3.3) by instrumental-variables regression in using military purchases, a dummy for the party of the US President, and the price of oil as instruments for non-technological disturbances that affect output growth. However, even assuming that the correlations with these instruments are not accidental, this merely establishes that some part of the procyclical productivity variations that are observed are not due to fluctuations in true technical progress; since explanations exist that do not depend upon large degrees of market power or increasing returns, one cannot regard this as proving that # and p are large. A second possible mechanism is substitution o f intermediate for primary inputs, as discussed by Basu (1995). Suppose that materials inputs are not used in fixed proportions, but instead that each firm's gross output Q is given by a production function Q = Q ( V , M ) , where M represents materials inputs and V is an index of primary input use (which we may call "economic value added"), and the function Q is differentiable, increasing, concave, and homogeneous of degree 1. As before, economic value added is given by a value-added production function V = F ( K , z H ) . Now consider a symmetric equilibrium in which the price of each firm's product is the same, and this common price is also the price of each firm's materials inputs (which are the products of other firms). Consideration of the marginal cost of increasing output by increasing materials inputs alone then yields t~ = Q M ( V , M ) .

(3.4)

59 Because, as Hall notes, pure profits are near zero for US industries, sK + SH has a value near one for a typical industry; hence the two types of factor shares, and the two types of productivity residuals, are quantitatively similar in most cases.

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Because of our homogeneity assumption, (3.4) can be solved for M/V = m(#),

where m is a decreasing function. Then defining accounting value added as Y - Q - M, one obtains Y / V = Q(1, m(g)) - m(/~).

(3.5)

Furthermore, as long as firms have some degree o f market power (~ > I), Equation (3.4) implies that QM > 1. Hence Q(1, m) - m will be increasing in m, and Equation (3.5) implies that Y / V , the ratio of measured value added to our index o f "economic value added", will be a decreasing function of g. This implies that a decline in markups would result in an increase in measured value added Y even without any change in primary input use (and hence any change in V). This occurs due to the reduction of an inefficiency in which the existence of market power in firms' input markets leads to an insufficiently indirect pattern of production (too great a reliance upon primary as opposed to intermediate inputs). I f one's measure of total factor productivity growth is based upon the growth in Y instead of V, then markup variations will result in variations in measured productivity growth that are unrelated to any change in technology. Since a markup decline should also increase the demand for primary factors of production such as labor, it will be associated with increases in employment, output, and total factor productivity - where the latter quantity increases because of the increase in Y / V even if the measurement problems stressed by Hall (relating to the accuracy of one's measure of the increase in V that can be attributed to the increase in primary factor use) are set aside. The quantitative importance of such an effect depends upon two factors, the elasticity of the function m and the elasticity of the function Q(1, m) - m. The first depends upon the degree to which intermediate inputs are substitutable for primary inputs. Basu (1995) establishes that materials inputs do not vary in exact proportion with an industry's gross output; in fact, he shows that output growth is associated with an increase in the relative use of intermediate inputs, just as Equation (3.4) would predict in the case of an output increase due to a reduction in markups. The second elasticity depends upon the degree of market power in the steady state (i.e., the value o f / t around which we consider perturbations), because as noted above, the derivative of Q(1, m) - m equals/t - 1. Thus while Basu's mechanism is quite independent of Hall's, it too can only be significant insofar as the typical industry possesses a non-trivial degree of market power. An alternative mechanism is "labor hoarding"; indeed, this is probably the most conventional explanation for procyclical productivity variations. I f only H - Hm hours are used for current production, but productivity growth is computed using total payroll hours H as a measure of the labor input, then a tendency of Hm to decline when H - Hm increases will result in spurious proeyclical variations in measured productivity

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growth. Furthermore, this is exactly what one should expect to happen, in the case o f fluctuations in activity due to markup variations. Suppose that the value to a firm (in units o f current real profits that it is willing to forego) of employing Hm hours on maintenance (or other non-production) tasks is given by a function v(Hm). It is natural to assume that this function is increasing but strictly concave. Then if the firm is a wage-taker, and there are no adjustment costs for varying total payroll hours H , the firm should choose to use labor for non-production tasks to the point at which (3.6)

v' (Hm) = w/P.

Let us suppose furthermore that the real wage faced by each firm depends upon aggregate labor demand, according to a wage-setting locus of the form (3.7)

w/P = v ( H ) ,

where v is an increasing function 6°. Since v' is a decreasing function while v is increasing, Equations (3.6) and (3.7) imply that H and Hm should move inversely with one another, assuming that the source of their changes is not a shift in either of the two schedules. Finally, allowing for labor allocated to non-production tasks requires us to rewrite Equation (2.2) as /~ =

PZFH (K, z ( H - Hm))

(3.8)

W

Substituting for Hm in the numerator the decreasing function of H just derived, and substituting for w in the denominator using Equation (3.7), the right-hand side o f Equation (3.8) may be written as a decreasing function of H. It follows that a reduction in the markup (not associated with any change in the state of technology, the value of non-production work, or the wage-setting locus) will increase equilibrium H and reduce equilibrium Hm. The result will be an increase in output accompanied by an increase in measured total factor productivity. If the firm faces a wage that increases with the total number of hours that it hires (due to monopsony power in the labor market, the overtime premium, or the like), then the resulting procyclical movements in measured productivity will be even greater. In this case, Equation (3.6) becomes instead J ( H m ) = og(H)w/P,

(3.9)

where ~o(H) is the ratio of the marginal to the average wage, as in Equation (2.11). We have earlier given several reasons why ~o(H) would likely be an increasing function, 60 If we imagine a competitive auction market for labor, then Equation (3.6) is just the inverse of the labor supply curve. But a schedule of the form (3.6) is also implied by a variety of non-Walrasian models of the labor market, including efficiency wage models, union bargaining models, and so on. See, e.g., Layard et al. (1991), Lindbeck (1993), and Phelps (1994) for examples of discussions of equilibrium employment determination using such a schedule.

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at least near the steady-state level of hours. Hence the specification (3.9) makes the right-hand side an even more sharply increasing function of H than in the case of (3.6). Similarly, if there are convex costs of adjusting the total number of hours hired by the firm, Equation (3.6) becomes instead ot (Hm) = g-2w/P,

(3.10)

where g2 is again the factor defined in Equation (2.13). Again, this alternative specification makes the right-hand side an even more procyclical quantity than in the case of (3.6). Thus either modification of the basic model with labor hoarding implies even more strongly countercyclical movements in Hm, and as a result even more procyclical variation in measured productivity. A related explanation for cyclical variation that results from markup variations in measured productivity is unmeasured variation in labor effort. If, as in the model of Sbordone (1996), the cost of increased effort is an increase in the wage w(e) that must be paid, and there are convex costs of varying hours, then the cost-minimizing level of effort for the firm is given by Equation (2.19). As discussed earlier, this implies that effort should co-vary positively with fluctuations in hours (albeit with a lead), since the factor £2 will be procyclical with a lead, while the function ~o(e) will be increasing in e. Furthermore, consideration of the marginal cost of increasing output by demanding increased effort implies that 61 PzFL,(K,zeH) -

(3.11)

w'(e)

Since wt(e) must be increasing in e (at least near the steady-state effort level, as a consequence of the second-order condition for minimization of the cost w/e of effective labor inputs), Equation (3.11) requires that a reduction in markups result in an increase in e H (to lower the numerator), an increase in e (to increase the denominator), or both. Since e and H should co-vary positively as a consequence of Equation (2.19), it follows that a temporary reduction of markups should be associated with temporary increases in effort, hours, and output. Countercyclical markup fluctuations would therefore give rise to procyclical variations in measured productivity. Another related explanation is marneasured variation in the degree of utilization of the capital stock. The argument in this case follows the same general lines. I f markups fall, firms must choose production plans that result in their operating at a point of higher real marginal costs (which quite generally means more output). Costminimization implies that real marginal costs increase apace along each of the margins available to the firm. Thus if it is possible to independently vary capital utilization, the real marginal cost of increasing output along this margin must increase; under standard

61 As noted earlier, this implies that Equation (2.11) holds with co replaced by co(e).

1100

JJ.. Rotemberg and M. WoodJord

assumptions, this will mean more intensive utilization o f the firm's capital. But the resulting procyclical variation in capital utilization will result in procyclical variation in measured productivity, even if there is no change in the rate o f technical progress. Similar conclusions are obtained when capital utilization is a function o f hours worked per employee. Consider again the case in which there is an interior solution for hours because the wage schedule W(h) is nonlinear in hours per employee, and in which hours per employee nonetheless vary because o f convex adjustment costs for employment. Then the cost-minimizing decision regarding hours per employee satisfies the first-order condition 62

O=~o(h)( ~/~ +nH)~/K ) "

(3.12)

If we assume both a Cobb-Douglas production function Y = ( u x K ) l - a ( z h N ) a and an isoelastic capital utilization function ux = h ~ with 0 < )~ <~ 1, the expression in parentheses is a constant, and Equation (3.12) implies that hours per employee h must covary positively with g2. This means that fluctuations in hours will accompany temporary fluctuations in employment (but with a lead). Furthermore, Equation (2.22) implies that

t~ =

[ a + ~,(1 - a)] P z a K l-a W,(h)hO_a)O_,~)Nl_ a •

Thus a decline in/~ must be accompanied by an increase in W'(h)h (l-a~(l-z) (hence an increase in h), an increase in N 1-a (hence an increase in N), or both. Since employment and hours must co-vary positively, there will be an increase in both. As a result, capital utilization will increase along with output and employment, again resulting in procyclical variation in measured productivity. 3.1.2. Cyclical profits

Business profits are also well-known to vary procyclically [e.g., Hultgren (1965)]; corporate profits after taxes have long been a component of the NBER's index o f coincident business cycle indicators. This is sometimes thought to make it implausible that business expansions are associated with declines in markups, since reduced markups should lower profits. Indeed, Christiano, Eichenbaum and Evans (1996) report calculations intended to show that a model in which expansions are due to markup declines will almost inevitably make the counterfactual prediction that profits must decline when output expands 63.

62 Note that this follows from the fact that both Equations (2.12) and (2.22) apply in this case. 63 They present their analysis as a criticism of sticky-price models of the effects of monetary policy; but in fact their criticism relates simply to the fact that the model is one in which output increases due to a reduction in markups.

Ch. 16:

The Cyclical Behaoior o f Prices and Costs

1101

This implication is, however, less direct than it might at first seem. There are a number of reasons why profits might well rise when markups fall. Many of these have been introduced above as reasons why the inverse of the labor share need not move countercyclically to the same extent as the markup. The connection between these two issues is simple. The cyclical variation in (real) profits is essentially determined by the cyclical variation in the amount by which the value of output exceeds the wage bill, Y - ( w / P ) H . (This is because the remaining deductions involved in the calculation of accounting profits, such as interest payments and depreciation allowances, are relatively less cyclical.) Now if the labor share w H / P Y is n o t procyclical, it follows that when output increases, w H / P increases no more than proportionally to output, which surely means l e s s in absolute magnitude, since labor compensation is on average only three-quarters of the value of output. Hence Y - ( w / P ) H will increase. Thus any model that does not predict a procyclical labor share will a f o r t i o r i not predict countercyclical profits. And indeed, parameter values that imply procyclical variation in profits in response to markup variations are not hard to find. Consider first our simplest model, in which firms pay the same wage regardless of the number of hours they hire, there are no adjustment costs, and the measured capital and labor inputs are all that matter for a firm's output. Then equilibrium output Y , hours t l , and real wage w / P are determined by Equations (2.1), (2.2), and (3.7), given the capital stock K, the state of technology z, and the markup #. Let us consider the effects of markup variations, holding fixed the other two parameters (and the functions F and v). If we neglect changes in interest and depreciation, the change in profits is given by d H = d(Y - v H ) = (ZFH - v) d H - H d v = (t~ - 1 - c , , ) v d H ,

(3.13)

where v = w / P is the real wage, and e~ - H v l / v is the elasticity of the wage-setting locus in Equation (3.7). It follows that profits increase along with employment and output if and only if kt > 1 + cv.

(3.14)

Now this is certainly possible; under the hypothesis of market power in the product market (which we require in order to suppose that markup variations are p o s s i b l e ) , /~ > 1, so it is simply necessary that e~ be small enough. This may not, however, seem empirically plausible; essentially, Christiano et al. argue that it would require a greater degree of market power than is plausible for most US industries. Their proposed value for e,, however (their "baseline" calculation assumes e~ = 1), is based not upon the observed degree of cyclicality of wages, but upon what they regard as a plausible specification of household preferences, given an interpretation of Equation (3.7) as the labor supply schedule of representative

J.J Rotemberg and M. WoodJbrd

1102

household. In fact, the average wage is observed to be relatively acyclical, and even i f this is a puzzle for the theory o f labor supply, there is no reason to assume a stronger real wage response to increases in labor d e m a n d in calculating the effect on profits o f an increase in output associated with a decline in markups. For example, Solon, Barsky and Parker (1994) find an elasticity o f the average real wage with respect to hours worked o f about 0.3 64; thus an average markup in excess o f 1.3 would suffice to account for procyclical profit variations. A n d again, this is the "value-added markup" that must exceed 1.3; for this, the typical supplier's markup need not be' much more than 10 percent. In any event, procyclical profits do not require even as large an average markup as this, i f we make the model more realistic, in any o f the several ways discussed above. Consider first the possibility that the marginal wage paid by a firm varies with the number o f hours that it hires, and not only with aggregate labor demand (as assumed above), due, for example, to m o n o p s o n y power in the labor market. Let us write the firm's wage bill as W(Hi;H), where H i represents hours hired b y firm i, and H represents aggregate hours hired. Then in a symmetric equilibrium, the average wage v is given by W(H; H)/H, and the ratio co o f the marginal wage to the average wage is given by HWI(H; H)/W(H; H). In this case, Equation (3.13) generalizes to dH = d(Y-

W ( H ; H ) ) = (zFi~ - W1 -

W2)dH

= (l~- 1 - W2/W1)W1 d H = (cot~ - 1 - e v ) v d H , so that Equation (3.14) becomes cog > 1 + ev.

(3.15)

Since, as explained earlier, there are a number o f reasons for co to be larger than one, the markup need not be as large as is required b y Equation (3.14) in order for profits to be procyclical. If, for example, we assume that co = 1.2, as Bils (1987) estimates 65, and c~ = 0.3, it suffices that/~ = 1.1 (which means a gross-output markup o f 4%).

64 Solon et al. find a considerably larger elasticity for the wage of individuals, once one controls for cyclical changes in the composition of the workforce. However, for purposes of the cyclical profits calculation, it is the elasticity of the average wage that matters; the fact that more hours are low-wage hours in booms helps to make profits more procyclical. 65 This is what Bils' estimates imply for the ratio of marginal wage to average wage when the margin in question is an increase in weekly hours per employee, and the derivative is evaluated at a baseline of 40 hours per week. (As noted above, Bils finds that this ratio rises as hours per employee increase.) In applying this ratio to Equation (3.15), we assume that the marginal cost of additional hours is the same whether they are obtained by increasing hours per employee or by increasing the number of employees, as must be true if firms are cost-minimizing.

Ch. 16:

1103

The Cyclical Behavior o f Prices and Costs

Alternatively, suppose that some labor is used for non-production purposes, as in our above discussion of "labor hoarding". Then Equation (3.13) becomes instead d H = d(Y -

vii) = zFH(dH - dHm) - v dH - H dv

= (0# - 1 - e~)v dH,

where 0 denotes the derivative of labor used in production total labor H . Thus Equation (3.14) becomes

H - Hm

O/z > 1 + cv.

with respect to

(3.16)

If labor hoarding is countercyclical, 0 > 1, and Equation (3.16) also requires a smaller markup than does Equation (3.14). The findings of Fay and Medoff (1985), discussed above, would suggest a value of 0 on the order of 1.4. This would be enough to satisfy Equation (3.16) regardless o f the size o f the markup. Similar results are obtained in the case of variable labor effort or variable capital utilization. The implied modification of Equation (3.14) is largest if the costs of higher effort or capital utilization do not show up in accounting measures of current profits. For example, suppose that effective capital inputs are given by u x K , where the utilization rate uK is an independent margin upon which the firm can vary its production process, and suppose that the cost of higher utilization is faster depreciation of the capital stock (but that this is not reflected in the depreciation allowance used to compute accounting profits). As explained above, we should expect a decline in markups to be associated with a simultaneous increase in real marginal costs along each margin, so that firms choose to increase ux at the same time that they choose to increase labor inputs per unit of capital. Let )~ denote the elasticity o f uK with respect to H as a result of this cost-minimization on the part o f firms 66. Then Equation (3.13) becomes instead d H = d(Y -

vii)

= zFHdH + KFK dux - v dH - H dv

= (#+ ~/Ks~- 1 - e~)vdH,

and Equation (3.14) again takes the form (3.16), where now 0 - (t/H + ,~K)/~7~I. If capital utilization and hours co-vary positively (as we have argued, and as is needed in order to interpret procyclical productivity variations as due to cyclical variation in capital utilization), then 0 > 1, and again a smaller markup than is indicated by Equation (3.14) will suffice for procyclical profits. If, for example, ;~ = 1, as argued

66 Note that we do not here assume a structural relation between the two variables.

1104

J J Rotemberg and M. Woodford

by Bils and Cho (1994), then 0 > 1:3, and Equation (3.16) is satisfied no matter how small the average markup may be. 3.2. Identifying the output fluctuations due to markup variation

We now describe the consequences of alternative measures of marginal costs for one's view of the sources of aggregate fluctuations. We propose to decompose the log of real GDP Yt as Yt = Y t +Yt~,

(3.17)

where the first term represents the level of output that is warranted by shifts in the real marginal cost curve introduced in Section 1 (for a constant markup), while the second is the effect on output of deviations of markups from their steady-state value, and hence represents a movement along the real marginal cost schedule. We then use this decomposition to investigate the extent to which changes in y are attributable to either term. Because there is no reason to suppose that changes in markups are independent of shifts in the real marginal cost curve, there is more than one way in which this question can be posed. First, one could ask how much of the fluctuations in aggregate activity can be attributed to the fact that markups vary, i.e., would not occur if technology and labor supply varied to the same extent but markups were constant (as would, for example, be true under perfect competition). Alternatively, one might ask how much of these fluctuations are due to markup variations that are not caused by shifts in the real marginal cost schedule, and thus cannot be attributed to shifts in technology or labor supply, either directly or indirectly (through the effects of such shocks on markups). The first way of posing the question is obviously the one that will attribute the greatest importance to markup variations. On the other hand, the second question is of particular interest, since, as we argued in Section 1, we cannot attribute much importance to "aggregate demand" shocks as sources of business fluctuations, unless there is a significant component of output variation at business-cycle frequencies that can be attributed to markup variations in the more restrictive sense. Mere measurement of the extent to which markup variations are correlated with the cycle - the focus of our discussion in Section 2, and the focus of most of the existing literature - does not provide very direct evidence on either question. I f we pose the first question, it is obviously necessary that significant markup variations exist, if they are to be responsible for significant variation in economic activity. But the relevant sense in which markup variations must be large is in terms of the size of variations in output that they imply. The size of the correlation of markup variations with output is thus of no direct relevance for this question. Moreover, markup variations could remain important for aggregate activity in this first sense even if markups were procyclical as a result of increasing whenever real marginal costs decline. In this case, markup variations would dampen the effects of shifts in real marginal costs.

Ch. 16." The Cyclical Behavior o f Prices and Costs

1105

If, instead, we ask about the extent to which markup variations contribute to output movements that are independent of changes in real marginal cost, the correlation of markups with output plays a more important role. The reason is that these orthogonal markup fluctuations lead output and markups to move in opposite directions and thus induce a negative correlation between output and markups. However, markups could be very important even without a perfect inverse correlation since, as we show below, the dynamic relationship between markup variations and the employment and output variations that they induce is fairly complex in the presence of adjustment costs. Furthermore, even neglecting this, a strong negative correlation between markups and activity would be neither necessary nor sufficient to establish the hypothesis that orthogonal movements in markups contribute a great deal to output fluctuations. The negative correlation might exist even though the business cycle is mainly caused by technology shocks, if those shocks induce countercyclical markup variations that further amplify their effects upon output and employment. And the negative correlation might be weak or non-existent even though shocks other than changes in real marginal cost are important, if some significant part of aggregate fluctuations is nonetheless due to these cost shocks, and these shocks induce procyclical markup variations (that damp, but do not entirely eliminate or reverse, their effects upon output). In this section, we try to settle these questions by carrying out decompositions of the sort specified in Equation (3.17) and analyzing the extent to which y*, ~ and the part o f ~ ~ that is orthogonal to y* contribute to movements in y. We do this for two different measurements of/Tt, which imply different movements in ~ . The first measurement of/Tt we consider is based on Equation (2.9) while the second is based on the existence of a cost of changing the level of hours worked. Because of space constraints, we are able to give only a cursory and illustrative analysis of these two cases. We start with the case where markups are given by Equation (2.9), for which we gave several interpretation above. To compute how much output rises when markups fall, we must make an assumption about the extent to which workers demand a higher wage when output rises. We thus assume that, in response to changes in markups, wages are given by ~t = t/w/2/,.

(3.18)

Thus, t/v/ represents the slope of the labor supply curve along which the economy moves when markups change. Obviously, this simple static representation is just a simplification. We again let t/H represent the elasticity of output with respect to hours when hours are being changed by markup movements. Using Equation (3.18) in (2.9) together with the assumption that changes in output induced by markup changes equal t/H times [/, it follows that =-

(1-b-~H(1-a) *Iw)~ ~H

F

~-H Y '

(3.19)

where the term in parentheses is positive because ~/H is smaller than one and a and b are nonpositive. This formula allows us to compute #~ once we have measured/~ as

1106

J.J. Rotemberg and M. Woodford

above. In other words, it allows us to go from the measurement of markups to the measurement of output movements implied by markups. Once we have obtained)3~ in this manner, we subtract this from y to obtain y*, as required by Equation (3.17). To do all this, we need three parameters, namely a and b (to construct the markup) and the expression in parentheses in Equation (3.19). Our illustrative calculation is based on setting a equal to zero, b equal to -0.4 (which we saw guarantees that the markup is quite countercyclical) and setting the expression in parentheses equal to 1/0.7. Given these values for a and b, this last parameter can be rationalized by supposing that ~/H = 0.7 and t/v/= 0.3. This elasticity of labor supply is broadly consistent with the estimates of Solon, Barsky and Parker (1994). I f we use these parameters and compute ~ in the way that we did in Section 2, however, the variance of ~ and, in particular, the movements in ~ that are orthogonal to movements in )3 are rather large. These orthogonal movements in )3~ must then be matched by equal and opposite movements in y*. One interpretation of this is that shifts in the marginal cost curve would lead to much larger output swings than those we actually observe if it weren't for procyclical markup movements that dampen these shifts. Another interpretation is that there are large errors in the measurement of the wage that lead the labor share to be measured with error. These random movements in the labor share then lead to offsetting movements in the two terms of Equation (3.17), )3# and y*. To deal with this possibility, we modify the analysis somewhat. Instead of using actual wages in computing ~, we use the projection of the ratio of per capita compensation to per capita output, ( w - y), onto the cyclical variables that we used in Rotemberg and Woodford (1996a). In other words, we make use of the regression equation w t - Yt = cI)wZt,

(3.20)

where Zt now represents the current and lagged values of the change in private value added, the ratio of nondurables and services consumption to output, and detrended hours worked in the private sector. To obtain the ratio of per capita compensation to per capita output that we use in Equation (3.20) we divided the labor share by the deviation of hours from their linear trend. Since this same deviation of hours is an element of the Zt vector, we would have obtained the same results if we had simply projected the labor share itself. For this included level of hours (and output) to be comparable to the labor share we use to construct (w - y ) , this labor share must refer to the private sector as a whole. We thus use only this particular labor share in this section. Because of the possibility that this labor share does not follow a single stationary process throughout our sample, we estimated Equation (3.20) only over the sample 1969:1 to 1993:1. Equation (3.20) allows us to express ( w - y) as a linear fimction of Z. Given that a is zero, the only other determinant of the markup in Equation (2.9) is the level of hours/2/, which is also an element of Z. Thus, our estimate of ~ is now a linear function of Z. Equation (3.19) then implies that fit~ is a linear function of Zt as well.

Ch. 16: The Cyclical Behavior of Prices and Costs

1107

It is not the case, however, that y[ is a linear function o f Zt. The reason for this is that Z includes only stationary variables and therefore does not include y. On other hand, the change in private value added, Ay, is an element of Z. This means that, armed with the stochastic process for Z that we estimated in Rotemberg and Woodford (1996a), Zt =AZt 1 +et,

(3.21)

we can construct the innovations in ~u and in y*. These are linear functions of the vector et which, given Equation (3.21), equals (Zt - A Z t - 1 ) so that these innovations depend only on the history of the Z's. Similarly, the vector (Zt - A Z t - l ) together with the matrix A in Equation (3.21) determines how the expectation of future values of Z is revised at t. This means that we can use Equation (3.21) to write down the revisions at t ^u and y*t+k as linear functions of the history of the Z's. in the expectations of Yt+k, Yt+k Finally, the variance covariance matrix of the c's (which can be obtained from A and the variance covariance matrix of the Z's) then implies variances and covariances for both the innovations and revisions in the y's, the ~U's and the y*'s. Table 3 focuses on some interesting aspects o f these induced variances and covariances. Its first row focuses on innovations so that it shows both the variance of the innovation in y* and in ~u as ratios of the innovation variance in y. The subsequent rows focus on revisions at various horizons. The second row, for example, gives the population variances of the revisions at t of y[+s and ~ut+5 as ratios to the variance of the revision of yt+s. All these revisions correspond to output changes one year after the effect of the corresponding et's is first felt. The next row looks at innovations two years after the innovations first affect output and so on. We see from Table 3 that this measure of the markup has only a very modest effect on one's account of the source of aggregate fluctuations in output. The variances of revisions in y* are almost equal to the corresponding variances of y for all the horizons we consider. The innovation variance of y* is actually bigger which implies that innovations in ~u that are negatively correlated with y* dampen the effect of these short-run movements of y* on y. The last column in Table 3 looks at the variances of the component o f ) u that is orthogonal to y*. This variance is equal to the variance of flu times (1 -/3 2) where p represents the correlation between flu and y* and where this correlation can easily be computed from Equation (3.21). To make the results clearer, we again present the variance of this orthogonal component of flu as a fraction of the corresponding variance of y. It is apparent from this column that this orthogonal component explains very little of the variance o f y at any of the horizons we consider. Thus, even though this measure of the markup is negatively correlated with our cyclical indicators, it induces movements in output that are much smaller than the actual ones. Overturning this finding appears to require implausible parameters. To make output more responsive to markup changes requires that the term in parenthesis in Equation (3.19) be smaller. We could achieve this by making r/r1 smaller or t/w bigger but, given the values that we have chosen, large changes of this sort would be unreasonable. An alternative way of lowering this coefficient is to make b smaller

J.J Rotemberg and M. Woodford

1108

Table 3 Fractions of the variance o f y accounted by fi~ and y* a

varAy* VarAy

varA))t~ VarAy

varAfig orthogonalto Ay*

Innovation variances

1.43

0.05

0.01

Revisions over 5 quarters

0.88

0.06

0.,06

Revisions over 9 quarters

0.86

0.08

0.08

Revisions over 13 quarters

0.90

0.07

0.07

Revisions over 17 quarters

0.90

0.05

0.05

Revisions over 21 quarters

0.91

0.05

0.05

Revisions over 25 quarters

0.91

0.04

0.04

Val'dy

b = -0.4, a , c = O

c=8, a , b - O Innovation variances

2.38

2.89

0.97

Revisions over 5 quarters

0.55

1.28

0.97

Revisions over 9 quarters

0.65

1.13

0.89

Revisions over 13 quarters

0.66

1.13

0.90

Revisions over 17 quarters

0.61

1.03

0.86

Revisions over 21 quarters

0.59

0.91

0.81

Revisions over 25 quarters

0.58

0.81

0.75

Revisions over 81 quarters

0.84

0.21

0.21

a Calculations based on projecting ( w - y ) on Z for period 1969:1 1993:1 and using properties of stochastic process in Equation (3.21) where this stochastic process is estimated from 1948:3 to 1993:1.

in absolute value. The problem is that, as we saw before, this makes the markup less cyclical. Thus, it does not help in making ~ track more of the cyclical movements in output. By the same token, setting a equal to a large negative number makes the markup more countercyclical but raises the term in parenthesis in Equation (3.19) thereby reducing the effect of the markup on 3~. We now turn to the case where adjustment costs imply that deviations of the markup from the steady state are given by Equation (2.15). We follow Sbordone (1996) in that we also let output vary with employee effort and this, as we saw, is consistent with Equation (2.15). Letting a be zero and using Equation (2.14), Equation (2.15) can be rewritten as (3.22) Allowing for variable effort is useful because it relaxes the restriction that the short run output movements induced by markup variations are perfectly correlated with changes

Ch. 16." The Cyclical Behavior o f Prices and Costs

1109

in hours. Thus, as in our earlier discussion of her model, we suppose that output is given by Y = F(K, zeH). As a result, we have f = t/H(/2/+ b).

(3.23)

We suppose as before that the wage bill is given by Hfvg(e), where ~ captures all the determinants of the wage that are external to the firm and g is an increasing ftmction. This leads once again to Equation (2.19) which, once linearized, can be written as et = c

[(f/t -/2L 1 ) -

Et(Iqt+l-/2/t)] •

(3.24)

Finally, we assume that average wages are given by #t = #or + Ow/2/t+ ~POt.

(3.25)

It is important to stress that the parameters ~ and ~p do not correspond to the elasticities of the average wage paid by an individualfirm with respect to the individual firm's hours and effort level. Rather, they are the elasticities of the economy-wide average wage with respect to aggregate changes in hours and average work effort. Note also that fVot is the exogenous component of the wage, i.e., the one that is not affected by changes in markups. Using Equations (3.23) and (3.25) to substitute for fit and #t respectively in Equation (3.22) and then using Equation (3.24) to substitute for ~t in the resulting expression we obtain c

2, + #or = (t/H-- 1-- t/W)/2/,+ (t/H -- ~P-- e o ) ~ [(/?/t - - / ) t - , ) - Et(H,+, - ~r)]. This difference equation in i2/can be written as

Et Lfi-(1-

- }~2L)/~, = -~(fi, -

i1L)(1

trot),

where L is the lag operator while ~.1 and ~.2 are the roots of /3/~,2 _ [l + / 3 +

013,+ 1 = 0

and 0--

1 + t/w - t/n e~o

~P+e~-t/H c'

~=

1

ca)

~P+e~o--t/H c

Noting that ~.1/3 is equal to 1/~.2 and letting ~. be the smaller root (which is also smaller than one as long as 1 + t/v/ > 0H and ~p + e,o > 0), the solution of this difference equation is OO

OO

I2It = -~ Z Z ~'k(/3~')JEt-k[fit+J k -- ¢Vot+jk]

(3.26)

k=0j-0

The deviations of hours from trend that are due to changes in markups,/~/~', can then be obtained by simply ignoring the movements in Wo in Equation (3.26). We can

J.J Rotemberg and M. Woodford

1110

then compute the deviations o f output from trend that are due to markup variations, ~ , by combining Equations (3.23) and (3.24) to yield

~t = I]1-!(~l~tt.q- C.~COI(~1~__/~t~1) _Et(~t~+l _

A~)]) .

(3.27)

This implies that, as before, )3~ is a linear function o f current and past values Zt. To see this, note first that Equation (3.22) implies that we can write/2t as a function of Zt. The reason for this is that (w - y) is a function o f Zt, Ht is part of Zt and, as a result o f Equation (3.21), Et/2/t+l is the corresponding element o f AZt. Therefore, using Equation (3.21) once again, the expectation at t o f future values of/~ must be a ftmction o f Zt. Past expectations of markups which were, at that point, in the future are therefore fimctions of past Z's. The result is that we can use Equation (3.26) to write ) ~ as a fimction of the history o f the Z's 67. Finally, we use Equation (3.27) to write the component of output that is due to markup changes as a function of the Z's. We require several parameter values to carry out this calculation. First, we set c equal to 8 to calculate ~t in Equation (3.22). To compute the connection between y~ and the Z's we need three more parameters. It is apparent from Equations (3.26) and (3.27) that this calculation is possible if one knows ~, ~ and cr~ in addition to c (which is needed to compute markups anyway). For illustrative purposes, we set these three parameters equal to 0.79, 0.13 and 3 respectively. The parameters ~ and ~ are not as easy to interpret as the underlying economic parameters we have used to develop the model. In addition to c and co) these include t/v, t/w, ~. Because the number o f these parameters is larger than the number o f parameters we need to compute .~, there is a one dimensional set of these economically meaningful parameters that rationalizes our construction of33~. In particular, while this construction is consistent with supposing that t/H, t/w, and ~0 equal 0.7, 0.25 and 0.1, respectively, it is also consistent with different values for these parameters 6s. We use our knowledge o f the relationship between ~ and the Z's for two purposes. As before, we compute the variances o f the innovations and revisions in )3~ as well as of y*. Second, we look at the resulting sample paths of)3~ and y*. The second part o f Table 3 contains the variances, which correspond to the ones we computed before. The results are quite different, however. In particular, the variance of the component of33 ~ that is orthogonal to y* now accounts for about 90% o f the variance of the revisions in output growth over the next two years. Thus, independent markup movements are very important in explaining output fluctuations over "cyclical" horizons. Moreover, if one

67 Because we later want to compute the sample values of~ ~ we truncate k so that it rtms only between zero and eighteen. Given that our ,~ equals 0.79, this truncation should not have a large effect on our results. 68 Note that we have made t/w, the elasticity of the wage with respect to hours along the aggregate labor supply curve, somewhat smaller than before because our use of a positive ~p implies that wages rise with output not only because hours rise but also because effort rises.

Ch. 16." The Cyclical Behavior o f Prices and Costs

1111

8.6 8.5 8.4 8.3 8.2 8.1

"~jl eli

8.0 Fig. 3. Constant-markupand actual output. takes the view that the movements o f y that are genuinely attributable to y* are those which are not due to the component offi ~ that is orthogonal to y*, the movements in y* account for only about 10% of the movements in y. Movements in y* have essentially no cyclical consequences. It is not that the revisions in the expectations of y* are constant. Rather, upwards revisions in y* over medium-term horizons are matched by increases in markups that essentially eliminate the effect of these revisions on y. This cannot be true over long horizons since the markup is assumed to be stationary so that flu is stationary as well. Thus, changes in y* that are predicted 20 years in advance account for about 80% of the revisions in output that are predicted 20 years in advance. An analysis of the sample path o f ~ ~ (and the corresponding path of y*) delivers similar results. Such sample paths can be constructed since ~ depends on the Z's which are observable. Admittedly, Equation (3.26) requires that the entire history of Z's be used. Data limitations thus force us to truncate k at 18 as explained in footnote 67. The result is that ~ depends on 18 lags of Z. To make sure that the lagged expectations of markups which enter Equation (3.26) are computed within the period where the labor share remains a constant stationary function Zt, we construct this sample path starting in 1973:2. The resulting values of y* and the log of output y are plotted in Figure 3. It is apparent from this figure that the episodes that are usually regarded as recessions (which show up in the Figure as periods where y is relatively low) are not reflected in movements of y*. Figure 4 plots instead y~ against the predicted declines of output over the next 12 quarters. These series are nearly identical so that, according to this measure of the markup, almost all cyclical movements in output since 1973

1112

J J Rotemberg and M, Woodford

0.06 Predicted decline f~

0.04 0.02

!"i

0.00

,

"-\/

i~, i_

-0.02 -0.04-

/

[.i /

/

/

-0.06 -

r

-0.08-0.10-

74

76

78

80

82

84

86

88

90

92

Fig. 4. Markup-induced output gap and predicted output declines. are attributable to markup variations. This second measure of markups is thus much more successful in accounting for cyclical output movements. This result is probably partly due to the fact that this method of estimating 33~' recognizes the possibility that, in booms, output expands more than is suggested by the labor input as a result of increases in effort 69.

4. M o d e l s o f variable m a r k u p s

We now briefly review theoretical models of markup variation. We give particular attention to models in which markups vary endogenously, and thus affect the way the economy responds to shocks. The shocks of interest include both disturbances that shift the marginal cost schedule and other sorts of shocks, where these other shocks would not have any effect on equilibrium output in the absence of an effect upon equilibrium markups. Before reviewing specific models, it is perhaps worth commenting upon the kind of theoretical relations between markups and other variables that are of interest to us. It is important to note that an explanation for countercyclical markups need not depend upon a theory that predicts that desired markups should be a decreasing function of the level of economic activity. If the real marginal cost schedule c(Y) is upward-sloping,

69 For another setting where inferences regarding markups are significantly affected by supposing that there are costs of adjusting labor, see Blanchard (1997).

Ch. 16: The Cyclical Behavior of Prices and Costs

1113

then any source of variations in the markup that are independent of variations in the marginal cost schedule itself will result in inverse variations in the level of output, and so a negative correlation between the markup and economic activity. Thus theories of why markups should vary as functions of interest rates or inflation (rather than of the current level of economic activity) might well be successful explanations of the cyclical correlations discussed in Section 2. In fact, a theory according to which the markup should be a function of the level of economic activity is, in some respects, the least interesting kind of theory of endogenous markup variation. This is because substitution of/~ =/~(Y) into Equation (1.1) still gives no reason for equilibrium output Y to vary, in the absence of shifts in the marginal cost schedule. (Such a theory, with /~ a decreasing function o f Y, could however serve to amplify the output effects of shifts in that schedule.) Care is also required in relating theories of pricing by a particular firm or industry, as a function of conditions specific to that firm or industry, to their implications for aggregate output determination. For example, a theory according to which a firm's desired markup is an increasing function of its relative output, /d = /t(yi/y) with /~ > 0, might be considered a theory of "procyclical markups". But in a symmetric equilibrium, in which all firms price according to this rule, relative prices and outputs never vary, and there will be no cyclical markup variation at all. If instead (as discussed in section 4.3 below) not all firms continuously adjust their prices, the fact that adjusting firms determine their desired markup in this way can reduce the speed of overall price adjustment; and this increase in price stickiness can increase the size of the countercyclieal markup variations caused by disturbances such as changes in monetary policy. The models we look at fall into two broad categories. In the first class are models where firms are unable to charge the price (markup) that they would like to charge because prices are sticky in nominal terms. Monetary shocks are then prime sources of discrepancies between the prices firms charge and the prices they would like to charge. This leads to changes in markups that change output even if desired markups do not change. In the second class of models, real factors determine variations in desired markups, even in the case of complete price flexibility. Finally, we briefly consider interactions between these two types of mechanisms. 4.1. Sticky prices

We do not provide a thorough survey of sticky price models since that is taken up in Taylor (1999). Rather, our aim is threefold. First, we want to show how price stickiness implies markup variations, and so may explain some of the findings summarized in our previous sections. Second, we want to argue that markup variations are the crucial link through which models with sticky prices lead to output variations as a result of monetary disturbances. In particular, such models imply a link between inflation and markups which is much more robust than the much-discussed link between inflation and output. Thus viewing these models as models of endogenous markup

J.J Rotembergand M. Woodford

1114

variation may help both in understanding their consequences and in measuring the empirical significance of the mechanisms they incorporate. Finally, we discuss why sticky prices alone do not suffice to explain all o f the evidence, so that other reasons for countercyclical markups also seem to be needed. It might seem at first peculiar to consider output variations as being determined by markup variations in a model where prices are sticky. For it might be supposed that if prices are rigid, output is simply equal to the quantity demanded at the predetermined prices, so that aggregate demand determines output directly. However, this' is true only in a model where prices are absolutely fixed. It is more reasonable to suppose that some prices adjust, even over the time periods relevant for business cycle analysis. The issue then becomes the extent to which prices and output adjust, and, as we shall see, this is usefully tmderstood in terms of the determinants of markup variation. We illustrate the nature of markup variations in sticky-price models by presenting a simple but canonical example, which represents a discrete-time variant of the model of staggered pricing of Calvo (1983), the implications of which are the same (up to our log-linear approximation) as those o f the Rotemberg (1982) model of convex costs of price adjustment. First, we introduce a price-setting decision by assuming monopolistic competition among a large number o f suppliers o f differentiated goods. Each firm i faces a downward-sloping demand curve for its product of the form

Y/=D(P~Yt, \PtJ

(4.1)

where Pj is the price of firm i at time t, Pt is an aggregate price index, I(t is an index o f aggregate sales at t, and D is a decreasing function. We suppose that each firm faces the same level of (nominal) marginal costs Ct in a given period 7°. Then neglecting fixed costs, profits of firm i at time t are given by

=

-

( e; ) r,. \PtJ

Following Calvo, we assume that in each period t, a fraction (1 - a) of firms are able to change their prices while the rest must keep their prices constant. A firm that changes its price chooses it in order to maximize

Et ~-" j~ .1-1i+j 2._., a ~xt,t+1Pt+j' j=0

where Rt,t+j is the stochastic discount factor for computing the present values at t of a random level of real income at date t +j. (The factor ctJ represents the probability 70 Note that we have discussed above reasons why this need not be so, for example when a firm's marginal wage differs from its average wage. As Kimball (1995) shows, deviations from this assumption may matter a great deal for the speed of aggregate price adjustment, but we confine our presentation to the simplest case here.

Ch. 16." The Cyclical Behavior o f Prices and Costs

1115

that this price will still apply j periods later.) Denoting by Xt the new price chosen at date t by any finns that choose then, the first-order condition for this optimization problem is

e,

aJe,,. j=o

O' t+J

X,

1

p~+j ~

1

eD(Xt/Pt+j)

C,./] Xt J = O,

(4.2)

where eD(x) =-- - x D ' ( x ) / D ( x ) is the elasticity of the demand curve (4.1). For now, we further simplify by assuming that the elasticity of demand is a positive constant [as would result from the kind of preferences over differentiated goods assumed by Dixit and Stiglitz (1977)]. This means that a firm's desired markup, in the case of flexible prices, would be a constant,/~* = eo/(eo - 1). In this way we restrict attention to markup variations due purely to delays in price adjustment. It is useful to take a log-linear approximation of the first-order condition (4.2) around a steady state in which all prices are constant over time and equal to one another, marginal cost is similarly constant, and the constant ratio of price to marginal cost equals g*. Letting xt, ~t and ct denote percentage deviations of the variables Xt/Pt, Pt/Pt i and Ct/Pt, respectively, from their steady-state values, Equation (4.2) becomes

(

j=0

, -

-

=

O,

(4.3)

k=l

where/3 < 1 is the steady-state discount factor. Here the factor J k-I

represents the relative price in period t + j of the firm that chooses new price Xt in period t, and so Equation (4.3) says, essentially, that the firm's price is expected to be proportional to its marginal cost of production on average, over the time that the price chosen at date t applies. This equation can be solved for the relative price ~t of firms that have just changed their price, as a function of expected future inflation and real marginal costs. The resulting relation can be quasi-differenced to yield 2ct = ot[3Etfrt+l + (1 - ot[3)~t + ot[3Et~t+b

(4.4)

We suppose that the price index Pt is a symmetric homogeneous degree one function of the prices of the individual goods. Then near the steady state, it can be approximated to first order by the geometric average of the prices. Since each period a fraction a

1116

JJ. Rotemberg and M. Woodford

of the prices remain unchanged, while the others all change to the common value Xt, the rate of increase of the index satisfies

in our log-linear approximation. Substituting this into Equation (4.4), we obtain f6 =/3Et}ct+, - tcftt,

(4.5)

where t¢ = (1 - a/3)(1 - a ) / a and fit = -ct denotes the percentage deviation of the average markup ktt =- Pt/Ct from its steady-state value of/~*. This equation relates the average markup at any date to current and expected future inflation. To obtain the behavior of equilibrium output, one must use Equation (1.1) along with this. If we log-linearize the real marginal cost schedule as ~t = z/c~¢t, where ~'t denotes the percentage deviation of output from trend, then Equation (1.1) implies - f t t = ~/~Yt. Substitution of this into Equation (4.5) then yields an aggregate supply relation of the form frt = OYt +/3Et~t+l,

(4.6)

where 0 -- t¢~c. This equation specifies an upward-sloping relation between inflation and output variations, for any given level of expected inflation. Roberts (1995), who specifies /3 = 1, calls this "the New Keynesian Phillips Curve," and provides econometric evidence that (when extended to allow for stochastic shifts in the real marginal cost schedule) US output and inflation data are consistent with a relation of this kind. Combined with a specification of the evolution of aggregate nominal spending [which is often taken, as for example in Rotemberg (1996), to be an exogenous process determined by monetary policy], Equation (4.6) allows us to solve for equilibrium fluctuations in output. Because variations in inflation must be associated with deviations of output from trend, monetary policy disturbances affect equilibrium output. It will be observed that the output fluctuations in response to such shocks are associated with countercyclical variations in the average markup. The endogenous markup variations affect the predicted response of output to other shocks as well. For example, technology shocks may be considered, by allowing for a stochastic shift term in the real marginal cost schedule. Such shocks may be associated with procyclical markup variations: a technological improvement lowers marginal cost, but because prices do not fall immediately in proportion to the decline in costs, markups rise, while (because prices do fall some) output increases. This is consistent with Equations (4.5) and (4.6) if prices fall faster immediately than they are expected to in the future. In such a case, the markup variation damp the output effects of the

Ch. 16:

The Cyclical Behavior of Prices and Costs

1117

technology shocks relative to what would happen under perfect competition; as a result, input demand may actually decline in response to a favorable technology shock 71 . We have seen that a sticky-price model of this kind involves endogenous variation in the average markup. But is it useful to think of the endogenous markup variations as central to the way that nominal variables have real effects in this model? We believe that there are several advantages to viewing the model in this way (in addition, of course, to the fact that it helps one in relating the predictions o f the sticky-price model to the kinds o f facts discussed in Sections 2 and 3). First, if one is willing (as seems reasonable) to abstract from the effects of monetary frictions upon the relations (labor supply, labor demand, and so on) that underlie the real marginal cost schedule, then the effects of monetary policy upon the determination o f real variables may be reduced entirely to its effects upon the average markup. A general equilibrium model of the effects o f monetary policy may then be usefully decomposed into three distinct parts, each derived from largely separate microeconomic foundations: (i) a theory of equilibrium output determination given the markup, essentially a more elaborate version of Equation (1.1); (ii) an equation relating the markup to inflation variations, Equation (4.5); and (iii) a theory of how monetary policy affects nominal aggregate demand. An advantage o f viewing the structure of one's macroeconomic model this way is that part (i) of the model involves no specifically monetary elements, and may (except for the allowance for a time-varying markup) be identical to the equations o f a real business cycle model, while part (iii) does not involve the specification o f aggregate supply relations, and so may be directly adapted from conventional Keynesian or monetarist models of the effects o f monetary policy on aggregate demand. The theory of endogenous markup variation thus provides the crucial link that allows the concerns o f real business cycle models and conventional monetary models to be synthesized 72. Second, understanding the markup variations that are associated with variations in real activity in a sticky-price model is important to understanding when and how those fluctuations in activity are inefficient, since the markup directly measures the extent to which a condition for efficient resource allocation fails to hold. This perspective can be a source o f important insights into the welfare losses from price-level instability and the nature of optimal monetary policy. And third, recognizing that Equation (4.5) is a more fundamental prediction of the model o f price-setting than is a relation such as (4.6), which also depends upon one's specification of wage-setting behavior and the like, may allow more accurate

71 This is what Gali (1999), Basu, Fernald and Kimball (1998) and Kiley (1996) find to be true in US data, using a variety of quite different methods. Shea (1998), who identifies productivity shocks from data on R&D spending and patents, does not find this contractionary effect upon input demand, though his identified shocks also have little impact on long run output. 72 See Kimball (1995) and Goodfriend and King (1997) for more detailed sketches of this program, which the latter authors term "the New Neoclassical Synthesis". Goodfriend (1997) also stresses the importance of markup variations in accounting for the real effects of monetary policy.

1118

J.J Rotemberg and M. Woodford

empirical estimation of the speed of aggregate price adjustment. Sbordone (1998) tests the accuracy of Equation (4.5) as a model of aggregate price dynamics in the USA by first estimating the evolution of unit labor cost (assumed to be proportional to marginal cost) using a VAR. Using this evolution of unit labor costs, she then computes the equilibrium path of the price index implied by Equation (4.5). She finds that this simple model accounts quite well for the evolution of the private GDP deflator in the USA, at the quarterly frequency, over the period 1960-1997. In the case of her best-fitting value for a 73, the variance of the discrepancy between the actual price aeries and the one that would be predicted on the basis of the unit labor cost process is reduced to only 12% of what it would be in the absence of price rigidity 74, while the variance of the discrepancy between the actual and predicted inflation series is reduced to only 4% of what it would be according to the flexible-price (constant-markup) model. It is especially striking that the model fits this well without any need for complications such as stochastic disturbances to the pricing equation; this suggests that Equation (4.5) is indeed more descriptive of the data than the aggregate supply relation (4.6). This would suggest that the stochastic disturbances to this aggregate supply relation, which require Roberts (1995) to add additional terms to his estimated equation and to estimate it using instrumental variables, represent mainly disturbances to the real marginal cost schedule, rather than disturbances to the pricing relation (4.5). Despite the impressive success of this simple model as an explanation of much of the cyclical variation in prices relative to labor costs, there is some reason to doubt that this model of markup variation is completely adequate. In particular, the implication that the output effect of supply shocks is muted in sticky-price models is problematic given that, as suggested by Hamilton (1983) economic activity has tended to fall in the aftermath of pre-1986 oil-price increases. If the principal effect of oil-price increases is to increase marginal costs, then a sticky-price model (by implying that prices should rise less than the increase in marginal costs, so that markups fall) will imply even less of a contraction of equilibrium output than one should expect in the case of a flexible-price model. However, the size of the observed contractionary effects of oil-price shocks on the US economy is already rather larger than makes sense under competitive pricing, owing to the relatively small share of energy costs in total marginal costs of production. For this reason, Rotemberg and Woodford (1996b) propose that oil price increases lead to increases in desired markups. With this motivation, we turn to a brief review of models where desired markups vary.

73 This value is about 0.75 for her quarterlymodel, which implies an averagetime betweenprice changes of approximately 14 months. This represents less frequent price adjustment than is observed in most sectors of the US economy, according to the survey evidence presented in Blinder et al. (1998). The coefficient I¢ estimated by Sbordone can be reconciled, however, with more frequent price adjustments if one hypothesizes variations in desired markups, as discussed in Section 4.3. 74 This means that the model of markup variation (4.5), combined with the simple measure (2.4) of marginal costs, can account for 88% of the observed variability of the log ratio of price to unit labor cost (or equivalently, of the log labor share) over this period.

Ch. 16: The Cyclical Behavior of Prices and Costs

1119

4.2. Variations in desired markups

For simplicity, in this section we assume completely flexible prices. We also simplify by making all firms fully symmetric so that, in equilibrium, they all charge the same price. A number of types of theories of this kind have been considered in the literature. 4.2.1. Varying elasticity o f demand

Probably the simplest and most familiar model of desired markup variations attributes them to changes in the elasticity of demand faced by the representative firm. There are two important ways in which one might allow for variations in the elasticity of demand at a symmetric equilibrium where all relative prices are equal to one. The first is to suppose that the utility and/or production functions that define buyers' preferences over differentiated goods are not homothetic, so that changes in aggregate purchases Yt change the elasticity of demand. This is not an entirely satisfactory assumption, however, because it is unappealing to assume that growth should lead to secular changes in the elasticity of demand and in markups. One may, however, avoid this implication by complicating the model, for example by assuming that growth is associated with an increase in the number of differentiated goods rather than any secular increase in the scale of production of any individual goods A more appealing way of obtaining changes in thi s elasticity is to follow Gali (1994) and Heijdra (1995) and assume that there are several different kinds of purchasers 75. Each of these purchases all of the goods that are produced, but the different types each have different preferences over differentiated goods. Suppose, for example, that two groups 1 and 2 each care only about the amount they obtain of a composite good defined by a symmetric, homogeneous degree 1 aggregate of all goods purchases, but that the aggregator functions H~ and H2 are different for the two groups. Then the demand for good i by groupj can be written as Yj,tDj(P[/pj,t), where Yj,t is the quantity purchased by group j of its composite good, and pj,t is the price of that composite good (a homogeneous degree 1 index of the individual goods prices). Total demand for good i is then

•

r/= D1 kPl,t ]

\P2,t J

y2,,

(4.7)

where Dj(1) = 1 for both groups. At a symmetric equilibrium, all prices are the same and the amount purchased of each good is the same, so that Yj,t is simply the

75 See Bils (1989) for a related idea.

1120

JJ. Rotemberg and M. Woodford

amount purchased of each good by group j. The elasticity of demand at a symmetric equilibrium is then found to be

ZtO11(1)+(1 -Zt)D~2(1)

where

Zt -

Yl,t

Yl,t + Y2,t"

Therefore, an increase in the share o f group 1 purchases in total purchases makes the overall elasticity of demand more similar to D~, the elasticity of the demand by group 1. An important feature of business cycles is that, as noted in Campbell (1987) and Cochrane and Sbordone (1988), the ratio of consumption to GDP is high in recessions and low in booms. Exactly the converse behavior applies to the ratio of investment to GDE Thus, as Gall (1994) points out, the assumption that firms have more elastic demands than consumers can provide one explanation for countercyclical markups. Moreover, an exogenous increase in the fraction of output demanded for investment purposes would increase yU. Another variable that varies more cyclically than GDP is the purchase of durables. This has led Bils (1989) and Parker (1996) to argue that increased purchases of durables in booms reduce markups in these periods. This idea is closely related to a proposal of Robinson (1932), who argued that people who purchased durables in downturns were predominantly replacing durables that had ceased functioning and that, as a result, demand in downturns was less elastic than demand in booms, which consisted largely of demand by new purchasers. To ensure that a story of this sort also leads to reduced markups when the government expands its own purchases of goods and services, as would be needed in order to account for the expansionary effects of government purchases other than through an effect on labor supply, one must assume that the government has a relatively elastic demand 76. The main disadvantage of this general type of explanation is that aggregate demand, as such, has no direct role in lowering markups and thereby increasing output. Rather, it is the composition of demand that affects aggregate output; increases in aggregate demand only raise output if they happen to shift demand towards sectors with more elastic demand. This means that at least some kinds of disturbances that increase some important component of current spending must be contractionary rather than expansionary (e.g., an increase in consumer demand, in Gali's model). It is hard to think of empirical support for this kind of prediction.

4.2.2. Customer markets An alternative class of models, that gives variations in aggregate demand a more direct role, is intertemporal models of markup variation, in which what matters is not the composition of demand at present, but rather how current sales compare to expected

76 See Heijdra (1995) for an analysis where government purchases may affect markups through this channel.

1121

Ch. 16: The Cyclical Behavior of Prices and Costs

future sales. Probably the best-known model of this type is the "customer market" model of Phelps and Winter (1970). The customer market model is a model of monopolistic competition, in that each firm maximizes profits with respect to its own price (markup) taking the price (markup) of all other firms as given. But it differs from the standard model of monopolistic competition [e.g., the model of Dixit and Stiglitz (1977)] in introducing a dynamic element into the response of demand to prices. A firm that lowers its current price not only sells more to its existing customers, but also expands its customer base. Having a larger customer base leads future sales to be higher at whatever price is charged then. One simple formulation that captures this idea involves writing the demand for firm i at time t as k t ~ t l mr

< 0,

t/(1) = 1,

(4.8)

where/~ is the markup of price over marginal cost implicit in the price charged by firm i at time t, and the "market share" m~ is the fraction of average demand Yt that goes to firm i if it charges the same price as all other firms. The market share depends on past pricing behavior according to the rule

mt+l = g \[At I m t

< 0,

g(1) = 1,

(4.9)

so that a temporary reduction in price raises firm i's market share permanently. Equations (4.8) and (4.9) are intended to capture the idea that customers have switching costs, in a manner analogous to the models of Gottfries (1986), Klemperer (1987), and Farrell and Shapiro (1988)77. A reduction in price attracts new customers who are then reluctant to change firms for fear of having to pay these switching costs. One obvious implication of Equations (4.8) and (4.9) is that the long-run elasticity of demand, i.e., the response of eventual demand to a permanent increase in price, is larger than the short-run elasticity of demand. In our case, a firm that charges a higher price than its competitors eventually loses all its customers, though this is not essential for our analysis. The firm's expected present discounted value of profits from period t onward is thus

j=O

-ff--+j/mHg z=O

77 For a survey of much of this theoretical literature and its applications, see Klemperer(1995).

1122

JJ. Rotemberg and M. Woodford

Firm i chooses/~ to maximize this expression, taking as given the stochastic processes {/~t} and {Yt} that define aggregate demand conditions. Therefore

(4.10) I r~t+y I

Fir

= O,

where subscripts denote partial derivatives. At a symmetric equilibrium where all firms charge the same price, each has a share mI = 1, and g equals 1 in all periods. So the expectation term in Equation (4.10) is equal to the common present discounted value of future profits, which we denote by Xt. Solving Equation (4.10) for the markup, we obtain /~t=/t

X ~ t ) ---

rf(1)

(4.11)

1 + ~/'(1) + g ' ( 1 ) ~

Because ~(1) and g~(1) are both negative, the derivative of/~ with respect to X / Y is negative 7s. An increase in X / Y means that profits from future customers are high relative to profits from current customers so that each firm lowers its price in order to increase its market share. Thus, in this model, expansionary fiscal policy (which raises real interest rates and thus lowers X/Y) raises markups and lowers output 79. On the other hand, this is a model that can potentially amplify the expansionary effects of loose monetary policy in the presence of sticky prices. The reason is that loose monetary policy lowers real interest rates if prices are rigid and this raises X / Y s0. A rather different view of the determinants of markups and output is obtained if the customer market model is combined with the assumption that financial markets are imperfect, as in Greenwald, Stiglitz and Weiss (1984) and Gottfries (1991). With imperfect capital markets, shocks that raise the shadow cost of funds by making it more difficult to borrow (such as reductions in asset values that lower the value of firm's collateral) can lower X / Y and thereby lower output. Chevalier and Scharfstein (1995, 1996) provide some evidence for this financeconstrained version of the customer market model. Chevalier and Scharfstein (1996) consider pricing by supermarkets and pay particular attention to the prices charged in states hit hard by the oil-price decline of 1986. They ask whether, within these

78 Felli and Tria (1996) argue that their proposed markup series is consistent with this implication. 79 Phelps (1994) emphasizes that this can be overturned in open economies under flexible exchange rates. Expansionary fiscal policies then tend to appreciate the exchange rate, thereby forcing domestic firms to lower their markups in order to compete effectivelywith foreign firms. 80 The model as expounded here and in the literature, however, involvesflexibleprices. The extension of the theory to allow for delays in price adjustment would seem a high priority for future research.

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oil states, supermarkets that belonged to national chains (and who thus could rely on externally provided cash to some extent) lowered their prices relative to those of local supermarkets, who were presumably more strapped for cash. They find that they do, suggesting that national supermarkets were more willing to invest in customers at this point, presumably because they had lower discount rates as a result of their access to cash. Chevalier and Scharfstein (1995) shows more generally that industries with a relatively large fraction of output produced by small firms tend to have more countercyclical markups if one controls for total concentration. The idea is that small firms have less access to capital markets and so should be more strapped for cash in recessions. This induces them to invest less in customers and raise their markups in recessions. Controlling for concentration creates problems of interpretation because, as discussed further below, highly concentrated sectors (in which large firms are clearly important) have more countercyclical markups. 4.2.3. Implicit collusion

An alternative intertemporal model, where the same variable X / Y again turns out to be the crucial determinant of the equilibrium markup, is the implicit collusion model presented in Rotemberg and Woodford (1992). We consider an economy with many industries, each of which consists of n firms. The n firms in each industry collude implicitly in the sense that there is no enforceable cartel contract, but only an implicit agreement that firms that deviate from the collusive understanding will be punished. On the other hand, the firms in each industry, even when acting in concert, take other industries' prices, the level of aggregate demand, and the level of marginal cost as given. Abusing the language somewhat, we can view industries as monopolistic competitors in the usual sense, while the firms within each industry collude implicitly. Keeping this distinction in mind, we write the demand for firm i in industry j as

The function

D i

is syrmnetric in its first n arguments except the ith, and the functions

D i (for i = 1 , . . . , n) are all the same after appropriate permutation of the arguments.

The resulting profits of firm i in industry j if all other firms in the economy charge a markup/h and it charges a markup #ij are

rt;

)= \

,I

\

j .

(4.13)

If the firm goes along with the collusive agreement at t and charges the same iJ markup as all other firms, it gets H~ (#t,/h) which we denote by H~(th)Yt. I f it deviates and the punishment is as strong as possible, it earns some higher profits at t

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but it can expect to earn a present value of zero thereafter. In this case, a deviating firm simply maximizes Equation (4.13) with respect to #y and its resulting profits are /-/ta(#t)Yt. It is easy to show that the difference Hta(/zt) - / ( f ( / ~ ) is increasing in #t. Intuitively, it should be clear that this difference is zero at the markup that corresponds to the equilibrium where each firm behaves like a monopolistic competitor and takes other firm's prices as given. If firms in the industry charge higher markups, deviating by cutting prices is more attractive. Because this difference is increasing in the markup, a profit-maximizing collusive oligopoly which is unable to sustain the monopoly outcome for the industry will agree upon a markup that keeps firms just indifferent between charging the collusive markup and deviating. Such a collusive optimum implies that

z/f(~t)-/V(~,)

- x,.

(4.14)

This equation can again be solved for an equilibrium markup function of the form ~t = # ( x # r t ) .

In Rotemberg and Woodford (1992) we give the conditions under which there exists an equilibrium where Equation (4.14) is binding near a deterministic steady state. Because the left-hand side of Equation (4.14) is increasing in the markup #t the equilibrium markup is increasing in X / Y . An increase in X, the expected present value of future collusive profits, makes firms want to go along with the collusive price so that this price can be higher. An increase in current output, by contrast, tends to reduce the markup that can be sustained without breaking the collusive agreement. The result is that tight fiscal policy, which raises real interest rates, raises markups and lowers output. Temporary oil-price increases also raise X relative to Y and thus also reduce output according to this model. Rotemberg and Woodford (1991) provide evidence that, if asset price data are used to compute X, markups are not just decreasing in Y but are also increasing in X. This fits well with the finding of Galeotti and Schiantarelli (1998) that markups fall when the expected rate of growth of output is high. Such a high rate of growth raises X since profits are procyclical and this should lead to an increase in markups according to this model. A striking confirmation that high levels of X raise current markups is provided by Borenstein and Shepard (1996) in their analysis of retail gasoline markets. Their analysis looks at retail gasoline prices in 59 cities over 72 months and takes advantage of the fact that the relationship between expected future demand and current demand varies across cities because they experience different seasonal cycles. Similarly, there are cross-city differences in expected future costs. Borenstein and Shepard show that, consistent with this model, high expected future demand and low expected future costs, both of which raise X, raise current markups. A similar finding, though the evidence in this ease is so weak that one cannot reject the hypothesis of no effect, is reported by Ellison (1994). He shows that a railroad cartel operating in the 1880s, the Joint

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Executive Committee, tended to have low prices when demand was low relative to expected future demand. The dependence of markups on X leads Bagwell and Staiger (1997) to conclude that this model actually implies procyclical markups. This conclusion follows from identifying booms with periods where the rate of growth of output is high and identifying recessions with periods where the rate of output growth is low. Given that the rate of growth of output is positively serially correlated, periods where output growth is high are actually periods where a crude computation of X/Y (one that only took note of the positive serial correlation of output growth) is high and the conclusion follows. As noted by several authors [see Evans and Reichlin (1994), Rotemberg and Woodford (1996a) and the papers cited therein] there are variables other than current output growth that are useful for forecasting future output growth. As Evans and Reichlin (1994) and Rotemberg and Woodford (1996a) show, once these other variables are taken into account when computing expected output growth, recessions as defined by the NBER are actually periods where expected output growth is high. Once this is recognized, the model does indeed predict that markups should be high in periods that are generally regarded as recessions. Because past output growth is nonetheless also somewhat useful in forecasting future output growth, it follows that expected output growth just after business-cycle troughs (when output has already started to increase) is higher than expected output growth just before these troughs. Thus, X / Y is higher just after business-cycle troughs than just before. The model is thus consistent with some interesting observations made by Baker and Woodward (1994). They compare the price charged by firms some time before an industry trough (the reference month) with the price charged after the trough in the first month in which output is no smaller than output in the reference month. They report that, for some industries, the latter price is much higher than the former. Moreover, the size of this price increase is larger in more concentrated industries. This suggests that concentrated industries, where this theory is more likely to apply, are ones where the markup is more likely to vary positively with X / Y . One open question about this model (and the customer market model) is whether they can explain the reduction in inputs that seems to accompany periods of genuine technical progress. What determines which of these two models can explain this fact is whether genuine technical progress raises or lowers X/Y. If the progress raises mainly output in the future, one might expect X to rise relative to Y except that this effect might be offset by an increase in the rate of interest (which reduces the present value X ) . I f X / Y nonetheless rises with technical progress, the implicit collusion would also imply that such shocks tend to raise markups and reduce output relative to what would occur under frictionless perfect competition. 4.2.4. Variable entry

A final theoretical reason for markups to vary with cyclical variables is that entry is procyclical. An advantage of this explanation is that it is undoubtedly true that

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more new firms incorporate in booms, as noted by Chatterjee, Cooper and Ravikumar (1993) for the USA, and documented by Portier (1995) for France. Moreover, as long as profits are procyclical, it makes sense that entry should be procyclical. As we saw in Section 3, such proeyclical profits are possible even if output fluctuations are entirely due to changes in markups, rather than to shifts in the real marginal cost schedule. Suppose that, as in Chatterjee, Cooper and Ravikumar (1993) or Pottier (1995) firms behave in Cournot fashion so that each industry contains several firms producing perfect substitutes and these firms take the output of all other firms as'given when deciding on their own level of output. In this model, the addition of new firms cause markups to fall 81. The biggest problem with this explanation for countercyclical markups is that technical progress would lead markups to fall both in the short run and in the long run. As long a technological progress does not increase the fixed cost q~, such long term progress increases the number of firms and thereby reduces markups. One way of avoiding this difficulty is to assume that entry simply leads to an increased number of goods being produced by monopolistically competitive firms, as in Devereux, Head and Lapham (1996) or Heijdra (1995). These authors assume that the monopolistically competitive finns produce intermediate goods that are purchased by firms which combine them into final goods by using a Dixit-Stiglitz (1977) aggregator. The result is that increased entry does not change the ratio of price to marginal cost. It does, however, reduce the price of final goods relative to the price of intermediate goods, because final goods can be produced more efficiently when there are more intermediate goods. This reduction in the price of final goods effectively raises real wages and, particularly if it is temporary, leads to an increase in labor supply. Thus, Devereux, Head and Lapham (1996) show that, in their model, an increase in government purchases raises output together with real wages. The increase in output comes about because the increased government purchases make people feel poorer and this promotes labor supply; this results in a shift out of the real marginal cost schedule. The real wage in terms of final goods then rises because of the increase in the number of intermediate goods firms. 4.3. Interactions between nominal rigidities and desired markup variations

Finally, we briefly consider the possibility that markups vary both because of delays in price adjustment and because of variations in desired markups, for one or another of the reasons just sketched. The possibility that both sources matter is worth mentioning, since interactions between the two mechanisms sometimes lead to effects that might not be anticipated from the analysis of either in isolation. For example, variations in desired markups may amplify the effects of nominal rigidities, making aggregate price adjustment even slower, and hence increasing the

81 Portier (1995) also considers a model where markups fall not only because entry occurs in booms but also because the threat of entry leads incumbentfirms to lower their prices.

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output effects of monetary policy, even if the model of desired markup variation would not imply any interesting effects of monetary policy in the case of flexible prices. To illustrate this, let us consider again the discrete-time Calvo model of Section 4.1, but now drop the assumption that the function D has a constant elasticity with respect to the relative price. In this case, log-linearization of Equation (4.2) yields

Et

j=0

-

[ ^ des

+ ct+j]

(4.t5)

= 0,

k=l

as a generalization of Equation (4.3), where /)des denotes the percentage deviation of the desired markup (-D,t

~,/des - -

CD,t -- 1 from its steady-state value. The elasticity CD, and hence the desired markup, is a function of the relative price of the given firm i, or equivalently of the firm's relative sales yi/y. Letting the elasticity of the desired markup with respect to relative sales be denoted ~, we obtain

t --

f'gt+k

-

[ ^ des

k=l

- c , +^j ,

= (1

(4.16)

k=l

as a consequence of which Equation (4.15) implies an equation of the same form as (4.3), but with the variable ct replaced by (1 + ~eD)-l~t each period. This in turn allows us to derive again an equation of the form (4.5), except that now 1 (1 - aft)(1 - a) t¢ ~_ - 1 +~eD a

(4.17)

A number of authors have proposed reasons why one might have ~ > 0, i.e., an elasticity of demand decreasing in the firm's relative price. Kimball (1995) shows how to construct aggregator functions that lead to arbitrary values of ~. Thus, this model can rationalize extreme price stickiness even when the fraction of firms that change prices is relatively high. Woglom (1982) and Ball and Romer (1990) suggest that search costs provide an alternative rationale for a positive ~. The idea is that search costs imply that relatively small price increases lead many customers to depart while small price reductions only attract relatively few customers. A smoothed version of this kinked demand curve gives the variable elasticity just hypothesized. Equation (4.17) implies that ~ > 0 makes t~ a smaller positive quantity, for any given assumed average frequency of price changes. This affects the quantitative form of the markup equation (4.5), and hence the aggregate supply curve (4.6), in the same

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JJ Rotemberg and M. Woodford

way as would a larger value of a 82. In particular, it implies that a given size permanent increase in nominal aggregate demand (due, for example, to a monetary policy shock) will result in both a larger and a more persistent increase in output. Thus allowing for variation in desired markups of this kind can increase the predicted real effects of monetary policy (including the size of the countercyclical markup variations caused by monetary shocks). To gain some intuition for this result, imagine an increase in aggregate demand which increases marginal cost by increasing the demand for labor by >firms whose prices are fixed. A firm which is free to change its prices would thus normally choose a price above that charged by other firms. If, however, having a price that is relatively high implies that demand is relatively elastic then such a firm would have a relatively low desired markup and would thus choose a relatively low price. The effect of this is that prices do not rise by as much on impact so that output increases by more. In subsequent periods, the same logic leads those firms who can change their prices to raise them to only a limited extent. Thus, the effects of the increase in nominal aggregate demand are drawn out. This occurs despite the fact that the hypothesis of a demand elasticity decreasing in a firm's relative price does not, in itself, provide any reason for monetary policy to have real effects. Indeed, under the hypothesis that all prices are perfectly flexible, it provides no reason for equilibrium markups to vary at all. For with flexible prices, we would expect a symmetric equilibrium in which all firms' prices are always the same, so that the elasticity of demand faced by a firm (and hence its desired markup) would never vary in equilibrium. Thus this hypothesis is much more interesting, both as an explanation of markup variations and as a channel for real effects of shocks other than cost shocks, when combined with the hypothesis of nominal price rigidity than it is on its own. It is also interesting to note that this hypothesis requires that desired markups be low when the firm's relative price is high, i.e., when its own sales are low relative to those of its competitors. Thus, its desired markups are positively correlated with its own output relative to that of its competitors. At the firm or industry level, one might well observe procyclical markups, if one measures the correlation with own output; yet as shown above, the hypothesis is one that can increase the size of the countercyclical markup variations at the aggregate level that occur as a result of aggregate demand variations. Inflation, search and markups are also linked in the work surveyed in Benabou (1992). The idea in this research is that price rigidity in the face of inflation leads to more price dispersion and this price dispersion makes search generally more valuable to consumers. This, in turn, makes demand more elastic for all producers and thus

82 Thus it may help to reconcile the estimate of t¢ by Sbordone (1998), based on the comovementof aggregate indices of prices and labor costs, with microeeonomic evidence on the frequency of price changes.

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exerts downwards pressure on markups. This theory implies that inflation ought to be generally negatively related to markups. As Benabou (1992) shows, this implication is confirmed in US data on the retail trade sector. Variations in desired markups that are uniform across goods (rather than depending on firms' relative demands) also interact in interesting ways with nominal rigidity. For example, Kiley (1997) develops a model which combines staggered price-setting with Gali's (1994) assumption of differential demand elasticities for consumption and investment purchases. Monetary expansions then increase investment disproportionately and this temporarily lowers desired markups for all firms. This means that firms that revise their prices do not raise them as much as they otherwise would (given the increase in marginal cost) so that output rises more. This mechanism increases the degree of strategic complementarity among different firms' pricing decisions. If other firms raise their prices less, a given change in nominal rates (or in the money supply) has a bigger effect on real rates of interest thereby affecting investment demand more. This, in turn, implies that any given firm wants to raise its price by less. The greater degree of strategic complementarity implies a slower adjustment of the aggregate price level and hence a more persistent effect of the monetary expansion. Thus, while Gali's (1994) model of markup variation does not directly imply that monetary shocks affect output, it increases both the size and the persistence of the output effects of monetary disturbances in the presence of sticky prices. These illustrations demonstrate that a combination of endogenous variation in desired markups and price stickiness can yield further channels through which disturbances other than cost shocks affect the level of economic activity. This relatively unexplored topic surely deserves further research.

5. Conclusions

The main benefit of allowing for markup variations is that it expands the range of types of disturbances that can affect aggregate economic activity s3. Without variable markups, output can only increase if real marginal cost falls, for example due to a change in the effective labor supply to firms, or as a result of technological progress. With variable markups, monetary and fiscal shocks can have effects other than those that result from changes in the real wages at which workers are willing to work. In addition, the output effects of certain supply shocks (like variations in the rate of technical progress) may be muted, while other supply shocks (such as oil-price increases) can lead to larger output movements.

83 In focusing on the effect of markup variations (rather than the effect of the average level of the markup) we are assigning to imperfect competitiona role in macroeconomicsthat is quite different from the one which Carlton (1996) argues is unimportant. For a discussion of the effect of the markup level, see also Rotemberg and Woodford (1995) and the references cited therein.

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This rich set of possibilities arises from consideration of a number of different models of variable markups. But it is not clear yet whether there is a single unified model that can make sense of the way all the major macroeconomic shocks affect output. Each of the models we have considered, on its own, seems unable to account for all the facts. In particular, as we have already suggested, the pure sticky price model cannot easily explain the strong effects of oil-price increases. The implicit collusion model, on its own, tends to imply that insofar as monetary contractions raise real rates of interest, they should raise rather than reduce output. The customer market model seems to require financial market imperfections to explain the expansionary effects of fiscal stimuli. And it is not clear even then whether it is able to explain the effect of oil and technology shocks on the economy. Thus, the task of constructing a unified model of variable markups that explains the effect of all the shocks we have considered remains to be carried out. Models that allow for interaction between sources of variation in desired markups with additional variation in actual markups due to delays in price adjustment would seem an important area for further study. Much research remains to be done on the measurement of markup variations as well. First, as we have seen, measurements of markup variations and of the extent to which output fluctuations can be attributed to them depend on the details of the production structure. For example, they are extremely sensitive to the presence of adjustment costs for employment. While the existence of such adjustment costs is probably not controversial, their exact form and precise magnitude is far from having been settled. One's estimate of markup variations also depends on aspects of labor markets about which we are less certain. In particular, we do not know precisely how compensation of existing employees varies when there is less work to do in recessions. Indeed, one of our better estimates of this derivative of compensation with respect to productive effort [due to Bils (1987)] is based upon an estimate of the cost of adjusting employees (together with the assumption that firms minimize costs so that the cost of an additional effective hour of effort is equalized across these two margins). But perhaps the hardest problem is that, particularly outside the USA, we are not sure to what extent firms can simply take the wage that they pay per unit of effort as a parameter outside their control and to what extent this wage is the result of bargaining between workers and employees. In this latter case, the connection between the real wage and the marginal product of labor depends also on the character of this bargaining, as emphasized by Blanchard (1997) in his discussion of markups in Europe. Thus, while we have treated the ratio of the marginal product of labor to the (marginal) wage as equal to the markup, this inference is not necessarily correct if workers and firms bargain over both the level and the terms of employment. Product market considerations of the sort we have emphasized would still play a role in such a setting, but measuring the effect of these product market distortions becomes much harder.

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Acknowledgment We w i s h to thank M a r k Bils, Susanto Basu, R o b e r t Chirinko, M i l e s Kimball, and A r g i a S b o r d o n e and J o h n Taylor for c o m m e n t s , and the N S F and the H a r v a r d Business School D i v i s i o n o f R e s e a r c h for research support.

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Kollman, R. (1996), "The cyclical behavior of markups in U.S. manufacturing and trade: new empirical evidence based on a model of optimal storage", mimeograph (University of Montreal). Kydland, EE., and E.C. Prescott (1988), "Cyclical movements of the labor input and its real wage", Working Paper 413 (Research Department, Federal Reserve Bank of Minneapolis). Layard, R., S. Nickell and R. Jackman (1991), Unemployment (Oxford University Press, Oxford). Leeper, E.M., C.A. Sims and T. Zha (1996), "What does monetary policy do?", Brooldngs Papers on Economic Activity 1996(2):1-63. Lindbeck, A. (1993), Unemployment and Macroeconomics (MIT Press, Cambridge, MA). Means, G.C., et al. (1939), The Structure of the American Economy (U.S. National Resource Committee, Washington, DC). Mills, E (1936), Prices in Recession and Recovery (National Bureau of Economic Research, New York). Mitchell, WC. (1941), Business Cycles and their Causes (University of California Press, Berkeley, CA). Moore, G.H. (1983), Business Cycles, Inflation and Forecasting, 2nd edition (Ballinger, Cambridge, MA). Morrison, C.J. (1992), "Markups in U.S. and Japanese manufacturing: a short-rnn econometric analysis", Journal of Business and Economic Statistics 10:51-63. Murphy, K.M., A. Shleifer and R.W Vishny (1989), "Building blocks of market clearing business cycle models", NBER Macroeconomics Annual, 24~86. Parker, J.A. (1996), "The timing of purchases, market power and economic fluctuations", mimeograph (Princeton University). Phelps, E.S. (1994), Structural Slumps: The Modern Equilibrium Theory of Unemployment, Interest, and Assets (Harvard University Press, Cambridge, MA). Phelps, E.S., and S.G. Winter (1970), "Optimal price policy under atomistic competition", in: E. Phelps, ed., Microeconomic Foundations of Employment and Inflation Theory (W.W. Norton and Co, New York) 309-337. Pindyck, R., and J.J. Rotemberg (1983), "Dynamic factor demands and the effects of energy price shocks", American Economic Review 73:1066-1079. Plosser, C.I. (1989), "Understanding real business cycles", Journal of Economic Perspectives 3:51-78. Portier, E (1995), "Business formation and cyclical markups in the french business cycle", Annales d'l~conomie et de Statistique 37:411-440. Ramey, VA. (1991), "Non-convex costs and the behavior of inventories", Journal of Political Economy 99:306-334. Ramey, V.A., and M.D. Shapiro (1998), "Costly capital reallocation and the effects of government spending", Carnegie-Rochester Conference Series on Public Policy 48:145-194. Roberts, J.M. (1995), "New Keynesian economics and the Phillips curve", Journal of Money, Credit and Banking 27:975-984. Robinson, J. (1932), The Economics of Imperfect Competition (Macmillan, London). Rotemberg, J.J. (1982), "Sticky prices in the United States", Journal of Political Economy 90:1187-1211. Rotemberg, J.J. (1996), "Prices, output, and hours: an empirical analysis based on a sticky price model", Journal of Monetary Economics 37:505-533. Rotemberg, J.J., and G. Saloner (1986), "A superganae-theoretic model of price wars during booms", American Economic Review 76:390-407. Rotemberg, J.J., and M. Woodford (1991), "Markups and the business cycle", NBER Macroeconomics Annual 63-129. Rotemberg, J.J., and M. Woodford (1992), "Oligopolistic pricing and the effects of aggregate demand on economic activity", Journal of Political Economy 100:1153-1207. Rotemberg, J.J., and M. Woodford (1995), "Dynamic general equilibrium models with imperfectly competitive product markets", in: T.E Cooley, ed., Frontiers of Business Cycle Research (Princeton University Press, Princeton, N J) 243-293.

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The Cyclical Behavior o f Prices and Costs

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Rotemberg, J.J., and M. Woodford (1996a), "Real business cycle models and the forecastable movements in output, hours and consumption", American Economics Review 86:71-89. Rotemberg, JJ., and M. Woodford (1996b), "Imperfect competition and the effects of energy price increases on economic activity", Journal of Money, Credit and Banking 28:549-577. Sbordone, A.M. (1996), "Cyclical productivity in a model of labor hoarding", Journal of Monetary Economics 38:331-362. Sbordone, A.M. (1998), "Prices and unit labor costs: a new test of price stickiness", IIES Seminar paper No. 653 (Stockholm University, October). Shapiro, M.D. (1986), "The dynamic demand for capital and labor", Quarterly Journal of Economics 101:513-542. Shea, J. (1998), "What do technology shocks do?", NBER Macroeconomics Annual, 275-310. Solon, G., R. Barsky and J.A. Parker (1994), "Measuring the cyclieality of real wages: how important is composition bias", Quarterly Journal of Economics 109:1-25. Tarshis, L. (1939), "Changes in real and money wage rates", Economic Journal 19:150-154. Taylor, J.B. (1999), "Staggered price and wage setting in macroeconomics", ch. 15, this Handbook. Woglom, G. (1982), "Underemployment equilibrium with rational expectation", Quarterly Journal of Economics 97:89-107.

Chapter 17

LABOR-MARKET FRICTIONS AND EMPLOYMENT FLUCTUATIONS ROBERT E. HALL Hoover Institution and Department of Economics, Stanford University National Bureau of Economic Research

Contents Abstract Keywords 1. Introduction 2. The baseline neoclassical model 2.1. Failure of amplification in the baseline neoclassical model 2.2. Evidence about technology impulses 2.3. Failureof the baseline neoclassical model to explain persistence 2.4. Absence of unemployment from the baseline neoclassical model 3. Amplification 3.1. Elastic conventionallabor supply 3.2, Empirical research 3,3. Unemployment 3.3.1. Mechanism design and labor contracts 3.3.2. The modem strategic view of the employmentrelationship 3,3,3. Efficiencywages 3.3.4. Job destruction 3.3.5. Reorganizationand reallocation 4. Persistence 4.1. Time-consumingmatching in the labor market 4.2. The importance of secondary job loss for persistence 5. Conclusion Acknowledgments References

Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor and M. Woodford © 1999 Elsevier Science B.V. All rights reserved 1137

1138 1138 1139 1140 1141 1141 1142 1143 1145 1145 1148 1150 1154 1157 1157 1158 1160 1162 1162 1163 1167 1167 1167

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Abstract The labor market occupies center stage in modern theories of fluctuations. The most important phenomenon to explain and understand in a recession is the sharp decline in employment and jump in unemployment. This chapter considers explanations based on frictions in the labor market. Earlier research within the real business cycle paradigm considered frictionless labor markets where fluctuations in the volume of work effort represented substitution by households between work in the market and activities at home. A preliminary section of the chapter discusses why frictionless models are incomplete - they fail to account for either the magnitude or persistence of fluctuations in employment. And the frictionless models fail completely to describe unemployment. The evidence suggests strongly that consideration of unemployment as a third use of time is critical for a realistic model. The two elements of a theory of unemployment are a mechanism for workers to lose or leave their jobs and an explanation for the time required from them to find new jobs. Theories o f mechanism design or of continuous re-bargaining of employment terms provide the first. The theory of job search together with efficiency wages and related issues provides the second. Modern macro models incorporating these features come much closer than their predecessors to realistic and rigorous explanations of the magnitude and persistence of fluctuations.

Keywords

JEL classification: E24

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Labor-Market Frictions and Employment Fluctuations

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1. Introduction

The bulk of modern fluctuations theory fits into the broad framework of impulsesamplification-persistence. In this framework, fluctuations begin with a random impulse. These can be shifts in technology or preferences, shifts in monetary or fiscal policy, or spontaneous movements in consumption, investment, or other components of spending. Most impulses of realistic size have small effects on employment in a standard neoclassical model. To explain the observed volatility of employment and other important aggregates, some form of amplification must occur. Modern thinking about sources of amplification has focused primarily on highly elastic labor supply. Labor supply is elastic because workers have economically valuable alternative uses of their time. Though non-market alternatives lie behind the standard view of labor supply and the view of labor supply in the original real business cycle model, the alternative that is most prominent in recent models is job search. In fact, more than anything else, this chapter is about the successful integration of unemployment theory into formal dynamic general-equilibrium models. Not only do the new general-equilibrium models comprehend the important phenomenon of unemployment, but it turns out that unemployment is key to amplification and persistence. Without consideration of unemployment, earlier dynamic general-equilibrium models explained persistence in employment largely through persistence in driving forces. The models themselves did not contain much in the way of persistence mechanisms. Where unemployment is considered explicitly, persistence arises naturally from the time-consuming process o f placing unemployed workers in jobs following an adverse impulse. This chapter does not consider the origins of impulses, nor the propagation of fluctuations across industries, though that propagation may interact with amplification and persistence. The chapter focuses on frictions in the labor market, some of which amplify impulses and others of which result in persistence, especially of unemployment. Most of the research I will consider here is developed within dynamic stochastic general equilibrium (DSGE) models. By placing amplification and persistence mechanisms in formal general equilibrium models, contributors to modern fluctuations research achieve a degree of clarity missing from earlier macroeconomics. Confusing notions from earlier work, such as "aggregate demand" and "supply shocks," are giving way to clearer general equilibrium counterparts, such as monetary and fiscal impulses and shifts in the terms of trade. Moreover, research in the impulses-amplificationpersistence mode has come close to eliminating the traditional polarization of macro researchers. Impulses come from technology, policy, and spontaneous shifts, a list broad enough to include almost any earlier idea about the sources of fluctuations. Old-fashioned Keynesian ideas such as wage rigidity, new Keynesian ideas such as efficiency wages, and ideas about imperfect information all compete on an equal footing to explain amplification, and are no longer assigned to warring schools of thought.

R.E. Hall

1140

2. The baseline neoclassical model

For several decades, a baseline neoclassical model has anchored macroeconomics. Because the baseline model is successful neither as a model of fluctuations nor of growth, both of the major branches of the field have explored alternatives to the baseline. For the purposes of this chapter, it is useful to lay out the baseline model and explain its failure as a model of fluctuations. Lack of amplification of impulses and lack of persistence of the resulting responses are the symptoms of the failure. In the baseline model, workers choose between two activities, work and leisure; there is no consideration of unemployment. The baseline model is so well known that it will suffice to describe it mainly verbally - see Campbell (1994) and Romer (1996, chapter 4) for more extensive discussions along this line. A single type of output is consumed or invested. It is produced by a Cobb-Douglas technology with constant returns to scale. Labor and capital are the inputs. Consumers' preferences are ordered by the time integral of log consumption plus weighted log leisure - that is, the intertemporal utility fimction is OQ

f e-/3t [log c(t) + )~log(~ -

n(t))] dt.

(2.1)

0

Log consumption insures that static labor supply has zero wage elasticity - models typically adopt this specification to match the positive trend in real wages to the zero trend in annual hours per worker 1. In principle, the baseline model could be driven by almost any kind of impulse shifts in technology or preferences, changes in policy regimes, or random elements of policy. Kydland and Prescott's (1982) pioneering exploration of fluctuations using the baseline model and alternatives focused on vibrations of the aggregate production function as the single driving force. Much o f the ensuing literature retained that focus, though changes in government purchases - an important topic before Kydland and Prescott's formalization of the baseline model - remain a second important driving force in that literature [see, for example, Aiyagari, Christiano and Eichenbanm (1992)]. Empirical measures of aggregate technology - generally obtained by calculating the Solow (1957) residual - suggest that changes in technology are quite persistent. In fact, a random walk is not a bad approximation to the stochastic properties of aggregate technology or for the technologies of particular industries. To put it differently, the year-to-year Solow residual, which measures the change in technology, is close to white noise. The custom has developed in the literature on DSGE models to model the stochastic process of aggregate technology as first-order autoregressive with a serial

J See King and Rebelo (1999) for further discussion of this point.

Ch. 17: Labor-MarketFrictions and Employment Fluctuations

1141

correlation parameter of 0.95. In that case, an innovation in technology in one period is followed by small movements in the opposite direction for many succeeding periods, as the level of technology gradually (at a rate of 5 percent per period) returns to normal. In this setting, a rough description of the perturbation in general equilibrium following, say, a negative shock to technology is the following: Immediately, employment falls. Output falls both because of the direct effect of the decline in productivity and because o f the decline in employment. Since the capital stock is unaffected, the marginal product of capital and thus the interest rate fall. Consumption rises and investment declines by more than the decline in output. There follows an extended period of gradual rises in the interest rate and real wage back to their normal levels. As a result, consumption - governed by its Euler equation - falls back to normal and, similarly, employment rises back to normal. 2.1. Failure of amplification in the baseline neoclassical model As I noted earlier, a central problem of fluctuations theory is that small impulses seem to result in large movements, especially those we call recessions. Can the baseline neoclassical model explain the actual magnitude of observed fluctuations based on the likely magnitude of technology shifts? From the starting point in Kydland and Prescott (1982), the answer has been no. Some form of amplification beyond what is found in the baseline model is needed. Campbell (1994) investigates this issue carefully. His Table 3 shows that a l-percent decline in technology that is reversed at 5 percent per quarter lowers employment by only 0.45 percent in the baseline model. In other words, to explain the 3-percent decline in employment typical of a recession, the model has to invoke a decline in technology of about 7 percent! The challenge to fluctuations theory is to change the baseline model in a reasonable way that overcomes this small response. The next section considers a number of attempts along this line. 2.2. Evidence about technology impulses Empirical work shows that the standard measure of technology shifts - the Solow residual - is correlated somewhat positively with employment and more positively with output. For example, in Hall (1997), the correlation of the Solow residual with hours of work at business-cycle frequencies is 0.32 while the correlation with real GDP is 0.75. The interpretation of the correlation is a disputed issue, however. A path of research whose origin was wholly apart from measuring macro impulses has suggested that the correlation is the result of the failure of assumptions underlying Solow's method. Hall (1988, 1990) observed that one form of the Solow residual could be used to test the assumption of competition in output markets and to measure the ratio of price to marginal cost. The resulting corrected Solow residual is hardly correlated with employment. Another form of the Solow residual can be used to test the assumption of constant returns to scale and to measure an index of increasing returns. Again, the

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R.E. Hall

Solow residual corrected for increasing returns is less correlated with output and is hardly correlated with employment. A substantial subsequent literature has questioned Hall's finding of high markups matched by equally high returns to scale. New work has substituted better measures of labor and capital input [Basu (1996), Burnside, Eichenbaum and Rebelo (1993)] and corrected aggregation bias [Basu and Fernald (1997)]. With all corrections in place, there is no remaining evidence of a correlation of the Solow residual with employment. Thus, there are two reasons to question the existence of teclinology shifts that are correlated with employment changes. First, what appears to be shifts in the simple Solow residual are actually artifacts of imperfect competition or increasing returns. Second, the correlation is the result of errors of measurement. Either finding is troublesome for the view that technology shocks are an important driving force. Hall (1997) investigates the role of the technology impulse in a semi-econometric general equilibrium framework. The model adopts the premise of the baseline model mentioned in the previous section - by making the kernel of utility depend on the log of consumption, the model excludes any direct effect of a technology shift on labor supply. A direct effect is one that occurs even in an economy without capital or other methods for shifting resources between time periods. The absence of direct effects occurs when the income and substitution effects in the corresponding static labor supply function offset each other. Hall observes that all of the effects of the technology impulse on employment must operate through the intertemporal channel, that is, through investment - a positive technology innovation sets off an investment boom. Hours of work rise, GDP rises, and consumption falls, as the economy moves quickly to take advantage of higher productivity. Hall examines the empirical relation between the investment/GDP ratio and the simple uncorrected Solow residual. He finds a robust positive relation a one-percent shift of the production function causes about a one-percent increase in the investment/GDP ratio. But the fraction of employment volatility explained by the technology impulse is essentially zero. Further, the use of a more refined version of the Solow residual would probably eliminate what little role the technology impulse is found to have.

2.3. Failure of the baseline neoclassical model to explain persistence Cogley and Nason (1995) observed that the pattern of movements of employment and output in the baseline neoclassical model is essentially that of its technology driving force. The point would apply to other driving forces as well. The neoclassical model cannot mimic the pattern of recession and recovery in response to a single shock, despite the common-sense impression that recessions often result from discrete shocks. In particular, after a one-year temporary decline in productivity, employment and output return to normal immediately in the neoclassical baseline model.

Ch. 17: Labor-MarketFrictions and EmploymentFluctuations

1143

2.4. Absence of unemployment from the baseline neoclassical model

The baseline model considers only two uses of time - employment and leisure. A strong consensus has emerged in macroeconomic thinking that a realistic model needs to consider a third use of time - job search or unemployment. Hall (1997) takes the following approach to demonstrating the need for explicit consideration of unemployment: He considers a neoclassical model without unemployment, but one where shifts in household preferences drive fluctuations along with shifts in technology and changes in government purchases. Because he considers three aggregate variables - output, consumption, and hours of work - he is able to solve for the values of the three impulses from the values of the three observed variables, based on standard values for the parameters of the neoclassical model. Almost all the explanatory power is assigned to the preference shift. Changes in government purchases have a small role because the observed changes are small and not generally associated with booms or recessions. Technology shifts also receive little weight because they operate solely through the intertemporal investment channel and because they should cause employment to change much more than consumption. Hall models the preference shift as a random variable that determines the marginal rate of substitution contemporaneously between consumption and leisure. Shifts in the variable cause employment and consumption to move in the same direction. Hall uses an empirical approach to determine the relative explanatory powers of the driving forces for employment fluctuations. Almost all the credit goes to the preference shift. But his conclusion is not that preference shifts are actually a major driving force. Rather, another use of time - unemployment - is left out of the model. Periods of higher unemployment are times when employment and consumption are both low. A better way to explain the positive correlation of employment and consumption at businesscycle frequencies is to bring unemployment explicitly into the model. Rotemberg and Woodford (1996) demonstrate the failure of the baseline model in a rather different way. They focus on the joint time-series properties of employment, output, and consumption. They show that the data contain a business cycle in the weak sense defined by Beveridge and Nelson (1981) - the data tend to return to a long-run trend whenever they deviate from that trend in the short run. The forecast of employment growth is unusually high, for example, if employment is below its trend because a recession occurred recently. In the baseline model driven by a technology shock that follows a strict random walk [not the AR(1) process with a serial correlation of 0.95 1 discussed earlier], employment and other variables lack almost any tendency to return to normal. They derive measures of that tendency from a 3-variable vector autoregression. When there is a tendency to return to normal, the VAR forecasts future values for the variables that are different from the current values. They measure this forecasting power at various horizons. Their findings are summarized in Table 1. In the baseline model, the current value of output is close to the best value of the forecast of future values at any horizon. There is a very slow-moving forecastable component in the baseline model, associated with capital accumulation, so the standard

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R.E. H a H

Table 1 Failure of the baseline modela Standard deviation of forecastable componentof output (percent)

Baseline model Actual data with VAR

8 quarters ahead

12 quarters ahead

24 quarters ahead

Infinitely ahead

0.17 2.95

0.23 3.22

0.36 3.05

0.53 3.06

a Data from Rotembergand Woodford (1996).

deviation o f the forecastable component rises as the horizon lengthens. In the actual data for the USA, there is a pronounced rebound from abnormal conditions in a year or two. The standard deviation of the change in output forecasted by the VAR is about 3 percent at all horizons. In addition to being much larger than the forecastable component in the baseline model, the time profile of the forecasting power is quite different in the actual US economy - the forecasted change occurs almost entirely in the first 8 quarters. In the baseline model, the forecasting power grows quite a bit after 8 quarters. Related failures of the baseline model are revealed in the correlations of the foreeastable components. In the baseline model, the forecasted change in work effort should have the opposite sign from the forecasted change in output. When a shock has caused the economy to be at a point below its steady-state capital stock, work effort will be above its steady state while output will be below. As capital is accumulated, output rises and work effort falls. In fact, forecasted movements in output and work effort are in the s a m e direction. After a recession, both hours of work and output rise more rapidly than normal. It appears that a reasonable explanation for the failure of the baseline model in Rotemberg and Woodford's work is the absence o f unemployment in the model. The forecastable rebound that occurs in the US economy following a recession occurs during the period when workers displaced during the recession are making their way back into long-term employment. In the baseline model, there is no burst of unemployment in the first place and no two-year period of rematching. Both anomalies reported by Rotemberg and Woodford are resolved by adding unemployment to the model - the augmented model has much more predictable recovery from bad (or good) shocks, and output and work effort move in the same direction during recoveries. Not only does consideration of unemployment provide a more sensible interpretation of correlations among key macro variables, but modern ideas about both amplification and persistence often involve job destruction and job search, key ideas in the modern theory of unemployment.

Ch. 17: Labor-Market Frictions and Employment Fluctuations

1145

3. Amplification Amplification occurs when the response of employment to a driving force is stronger than in the baseline neoclassical model. Macro research in the DSGE framework has recognized the need for amplification mechanisms since Kydland and Prescott's (1982) paper launched the framework. The mechanisms I discuss in this section all involve elastic labor supply, either in the conventional sense or in the sense that there is another activity - j o b search - that is a substitute for work.

3.1. Elastic conventional labor supply

The earliest amplification mechanisms invoked elastic labor supply in the standard setting where workers choose between work effort and leisure. I f labor supply is more elastic - for example, if the labor part of the kernel of the utility function is (~ - n) °s instead of log(~ - n) - the response of employment to a technology shock is almost twice as large; see Campbell (1994, Table 3). Then a favorable impulse to technology sets off the process that is the signature of the real business cycle model a burst of extra employment and a decline in consumption resulting in vigorous capital accumulation. In addition to the simple assertion of elastic labor supply, the literature proposing fluctuations theories based on that hypothesis has offered three supporting ideas. First was Kydland and Prescott's (1982) use of non-time-separable utility. Second was Rogerson's (1988) observation that workers facing a binary choice between not working and working full time may behave as if they had linear utility and perfectly elastic labor supply. Third was B enhabib, Rogerson and Wright's (1991) consideration of substitution between work in the market and work at home. Their paper marked the beginning of the investigation of margins other than labor-leisure within DSGE models. A convenient family of non-time-separable preferences follows suggestions of Sargent (1979, p. 371) and Kydland and Prescott (1982) [my discussion is taken from Hall (1991b)]. Let zt be the accumulated stock of current and past work effort, with persistence factor co: t

zt = (1 - co) ~

~oSnt_s.

(3.1)

s=0

My derivation will take nt to be weeks of work in period t and will assume (realistically) that variations in hours of work per week are small. The parameter ~o controls the memory of past work and leisure. If ~o is 0, there is no memory; only current work effort matters. I f ~o is large (close to its upper limit of 1), then zt depends on a long distributed lag of past work effort. As in my earlier discussion of the baseline

1146

R.E. H a l l

model, the worker orders work schedules with a utility function that is separable over time in the cumulation variable, z: (3.2) -

t-O

1~---1

"

Define effective leisure as ~ - zt and actual leisure as B - nt. The parameter o is both the intertemporal elasticity of substitution in effective leisure and the long-ruff elasticity of substitution in actual leisure (where the long run is enough time so that the distributed lag feature does not matter). In the short run, the elasticity of substitution in actual leisure is greater than a by an amount that is controlled by the memory parameter, ~o. The parameter ~ is the number of weeks physically available for work. A worker with a high cr will suffer little from a work schedule involving many weeks of work per year in one decade and few weeks per year in another decade, in comparison to putting in the same number of lifetime weeks with no variation from decade to decade. In a situation with free choice of weeks, such a worker will concentrate weeks disproportionately during the years of highest wages. On the other hand, a worker with low intertemporal substitution (low o) but high memory persistence, o) (that is, close to one), will tolerate short-term fluctuations in weeks of work but resist decade-to decade movements. Kydland and Prescott use preferences that are slightly more general - current work can have a role in the utility function beyond the role implicit in the variable zt. To illustrate the difference between the short-run and medium-run responses of labor supply to wage changes, consider the following question: let 2N be the number of periods considered to define the medium run, which might be 24 months. Suppose a worker increases weeks of work by 1 percent in periods t - N , . . . , t . . . . . t + N. By what percent does the supply price of a week of work in period t increase? The elasticity of labor supply over the 2N + 1-period run is the ratio of the two numbers. It is convenient to use the ~-constant or Frisch labor supply schedule to answer this question. Let ,~ be the Lagrangian multiplier associated with the worker's intertemporal budget constraint. The first-order condition associated with labor supply is O U (hi . . . . . n t , . . . , lilT)

Ont

= )~wt.

(3.3)

Here wt is the real wage in period t stated in period-0 prices, that is, in prices discounted to period 0. The Frisch inverse labor supply function is simply the marginal disamenity of work stated in wage units: 10U(nl

)~

.....

nt,. .. ,nT)

Ont

(3.4)

When U is additively separable in labor, this can be solved to give current labor supply as a fimction of the current wage. Absent separability, it states the supply price

Ch. 17." Labor-Market Frictions and Employment Fluctuations

1147

of work in one period as a function of the level o f work in that and other periods. Keeping & constant has two interpretations. First, Equation (3.4) gives the supply price of labor at different points in time along the same labor-supply trajectory. Under this interpretation, statements about the response of the supply price to different levels of work are comparisons of the supply price at different points in time; the change in the level o f work is fully anticipated. Second, the supply price conditional on ,~ has a comparative statics interpretation when the change has little or no effect on ,~. Under this interpretation, Equation (3.4) is very similar to (but not quite the same as) the compensated labor supply schedule. The Frisch labor supply function associated with the preferences considered here is Wt =

1 ~(1

T (3.5)

__ co) y ' ~ cos t (~__ Zs) 1/(7. S=t

Let x be the common increment to n t _ N , . . . , n t , . • • , rtt+N. For simplicity, assume that the horizon, T, is infinite and that nt and zt have the common value n in all periods. Then some manipulations show that the slope of the inverse labor supply schedule is dw _

dx

1 (~_n)_l/o_

1

1

~o

2coN+I)

.

(3.6)

l+co

The elasticity, e(N), of the labor supply schedule is ~-n e(N) = U

n

(

2coN+I) 1

T +~ J "

(3.7)

If there is no memory of past work (co = 0) or if the displacement of the work is lengthy (N is large), then the elasticity is just the intertemporal elasticity of substitution in leisure, o, multiplied by the ratio of non-work time to work time:

n-n /,/

e(oo) = a - -

(3.8)

The elasticity E(cxD) controls labor supply over the life cycle. A worker with an e(oo) of 1 will work twice as many weeks at age 40 as at age 20 if the wage at age 40 is double its level at age 20 (and this doubling was known to be in the offing at age 20). Life-cycle variations in weeks of work do not show an elasticity anywhere near 1 - the evidence appears to favor values of 0.1 to 0.2. If 7-, is 5/47 = 0.11 and the mediumn run elasticity of labor supply is 0.15, then ~r is 0.15/0.11 = 1.4. Here I am considering anticipated life-cycle changes in the wage or changes of short enough duration that feedback through & can be neglected.

R.E. Hall

1148

By contrast, the elasticity of labor supply in the context of a one-period displacement (N = 0) is ~ - n 1 +co e(0) = ~ . n 1-~o

(3.9)

If memory decays at a rate of 20 percent per period, as might be appropriate in a quarterly model, the very-short-run elasticity is 1.8/0.2 = 9 times as ,large as the medium-run elasticity. The specification is successful in delivering a high short-run elasticity of labor supply without relying on significant decade-to-decade elasticity of labor supply.

3.2. Empirical research There is a huge empirical literature on labor supply. Pencavel (1986) and Killingsworth and Heckman (1986) survey the direct evidence from panel data on individuals. MaCurdy (1981) is one of the leading studies they consider. The basic approach is the following: the elasticity of labor supply is the ratio of the change in work effort to the change change in wage that occurs as the result of a change in one or another instrumental variable. For example, as a worker moves from age 29 to age 30, the worker's wage typically rises more than normal because this is a steep part of the age-wage-rate profile. If hours of work also rise by more than trend from age 29 to age 30, there is a positive elasticity of intertemporal substitution. Pencavel's (1986) Table 1.22, p. 85, suggests that the elasticity estimated on this basis is somewhere between 0 and 0.45 for men. Card (1994) reviews subsequent research and concludes that Pencavel's earlier conclusion survives unaltered. Pencavel appropriately devotes considerable attention to the one group of shortrun exogenous events whose labor supply effects are well documented - the negative income tax experiments. Experimental subjects experienced a three-year reduction of 30, 50, or 70 percent in effective wages. Pencavel's survey reaches the conclusion that the elasticity of the response of labor supply to these wage reductions was in the fairly narrow range from 0.06 to 0.19 (Table 1.21, p. 80). This finding is the single most telling evidence against the view that intertemporal substitution is high in the short run. The negative income tax findings are less than definitive for the following reason. For good reasons relating to asymmetric information, workers delegate to their employers the determination of weeks of work. Workers shop among employers with different policies for setting weeks of work, but once the worker accepts a job, the weeks of work required on that job are largely out of the worker's control. In particular, if an event occurs that is personal to the worker, but not within the class of events (such as disability) contemplated by the employment arrangement, it is unlikely that the employer will agree to a reduction in weeks ad hoe. Employment arrangements with given, understood rules help control opportunistic behavior by both employers

Ch. 17:

1149

Labor-Market Frictions and Employment Fluctuations

Table 2 Seasonal averageddeviations from trenda Quarter Number of workers employed Weekly hours Total hours

1

2

3

4

-1.45 -0.87 -2.32

0.07 -0.14 -0.07

0.30 0.81 1.11

1.08 0.20 1.28

a Data from Barsky and Miron (1989, Table 2).

and workers. Workers could take extra weeks off by quitting one job and delaying taking another job, but that step dissipates the value o f job-specific capital. The finding of small reductions in weeks of work in the negative income tax experiments is not inconsistent with the hypothesis that much larger reductions can occur when the marginal revenue product o f labor declines in a downturn. One is unprecedented and unfamiliar, completely new to the environment under which employment arrangements have evolved; the other is exactly within the historical experience that shaped those arrangements. Another reason that panel studies, both survey and experimental, are not good evidence against elastic short-run supply is the amount of variability they reveal in annual work effort. According to MaCurdy (1981), the standard deviation of annual hours of work around the predictions of his labor supply function is several hundred hours, a significant fraction of the normal level of around 2000 hours. Most of this noise is variation over time around a worker's own normal level of work. I f the intertemporal elasticity of labor supply is as low as the numbers in Pencavel's survey, with respect to substitution between one year and the next, then the deadweight burden of the unexplained variability of work is extremely high. A more reasonable conclusion is that the low elasticities apply to life-cycle influences but that much higher elasticities operate at year-to-year frequencies. A low intertemporal elasticity of substitution in the short run should also make workers averse to predictable seasonal variations in their volume of work. Table 2, taken from Barsky and Miron (1989, Table 2), presents the seasonal averages in percent deviations from trend by quarter found for the private non-agricultural sector of the US economy. The United States has a recession every winter comparable to businesscycle recessions. There is a boom in the summer and fall. Although one might suppose that part of the seasonal movements in hours of work reflects seasonal variations in preferences for work and leisure, it is hard to see how that would result in more work in the summer, during the vacation season, and less work in the winter. If workers had a strong aversion to uneven work schedules, institutions would develop to smooth employment over the season. The seasonal data suggest reasonable amounts of intertemporat substitution among the quarters of the year.

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Mulligan (1995) surveys many studies of intertemporal substitution in labor supply, including some not considered in earlier surveys. He stresses novel tests, such as those occurring during exceptional events including wars, the construction of the Alaskan pipeline, and the Exxon Valdez cleanup. Unfortunately, he does not consider the negative income tax experiments explicitly but appears to believe that their results should be lumped with panel studies where there are no large exogenous changes in wages (the experiments are mentioned only in footnote 2 and in the summary of his paper). Evidence from the premiums needed to induce brief periods of 'extraordinary effort or acceptance of irregular work schedules yields higher values of the IES. Mulligan presents evidence on wage premiums in Alaska from the periods of high activity associated with the building of the Alaska pipeline and the Valdez cleanup; these range from 0.5 to 2.8. This type of evidence is not fully convincing, however, because if there is a distribution of the IES across workers, only those with the highest values will contribute observations. Mulligan makes an attempt to infer the elasticity of substitution from the experience of World War II, but, as he points out, this is a questionable exercise because, by most measures, real wages were lower during the war than at other times. Recall that the intertemporal elasticity of labor supply in the baseline neoclassical model is around 4, well above even most of Mulligan's findings. Much higher values than 4 are needed to achieve the degree of magnification required in a realistic macroeconomic model. Intertemporal substitution in labor supply can only be part of the story. Models that do not consider unemployment as a use of time alternative to work appear to be incapable of explaining observed employment volatility along neoclassical lines. Even with an infinite intertemporal elasticity of substitution, as Campbell (1994) shows, the elasticity of employment with respect to the technology shock is still below 1 unless the shock is highly transitory. 3.3. Unemployment

As I noted earlier, the most conspicuous shortcoming of the baseline model is its failure to understand unemployment. The mechanism by which workers lose jobs in response to adverse shocks is a promising area to find amplification, and the slow process of re-employment is surely part of the story of persistent periods of slack. The baseline neoclassical model fails to deal with unemployment in two ways. First, it assumes that the labor market clears instantaneously. Even if workers are leaving some jobs and taking others, the process takes no resources and no time. Second, the model recognizes no heterogeneity in workers or jobs. The model contains no ingredients that would suggest that workers should change jobs - that a worker is more productive in a new job than in the current one. Unemployment cannot be grafted on to the baseline model. A new model, unfortunately much more complicated, is needed to deal effectively with unemployment. New work on job destruction, job creation, and job search has made important advances in this area. Only recently have these ideas been incorporated in DSGE models. Newly developed models achieve employment

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Table 3 Alternative measures of quarterly rates of job loss a Source Permanent separations, UI system data CPS tenure survey, 1981 All separations, Current Population Survey Gross employment reductions, LRD Permanent layoffs, PSID, 1985 Displaced workers survey, all workers, 1991 1993 Displaced workers survey, workers on the job for at least 3 years, 1991-1993

Quarterly rate of job loss (%) t7.23 10.04 8.29 5.66 1.81 0.61 0.59

a For sources, see Hall (1995).

amplification by operating on the employment - unemployment margin rather than on the employment - leisure margin. In a sense, they consider labor supply to be elastic because events can cause significant movements o f workers between work and job search, even if they cause little movement along the market-nonmarket margin. Even in normal times, rates of job loss are astonishingly high in the US economy and in other economies like it. Hall (1995) presents data on a number of measures o f separation rates. First, the most comprehensive measure o f job separations comes from the unemployment insurance system, which includes even the briefest jobs lasting a day or two. Over a quarter, the ratio o f total separations to employment is about 17 percent. The same worker can contribute many separations in the same quarter, if engaged in day work, construction, or other high-turnover activities. Second, the tenure survey in the Current Population Survey asks workers how long ago they began their current jobs. Because the shortest category considered is 6 months, this measure does not include multiple separations within a 6-month period, and so, when stated as a quarterly rate, tenure is lower but still a substantial 10 percent per quarter. Third, the Current Population Survey measures separations implicitly, when the same person is reported as working in one month and working at a different job or not working the following month. The rate shown in Table 3 is adjusted for an upward bias that results from random errors in reporting labor-market status in the survey. The fourth line in Table 3 reports the rate o f gross employment reduction, from Davis, Haltiwanger and Schuh (1996). This rate is based on quarterly reductions in employment at the plant level. Because firms sometimes hire during a quarter when total employment falls, the change in employment understates the total separation rate. Their measure is properly called the job destruction rate rather than the separation rate. The remaining three lines in the table consider separations initiated by employers where the workers had held long-term jobs. These rates are much lower - around one

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percent per quarter. A large fraction of total job separations arise from temporary or short-term work. Rates of job loss rise dramatically at the onset of a recession. Davis and Haltiwanger's rate of job destruction in manufacturing reached peaks of 11 percent and 9 percent per quarter in the recessions of 1975 and 1982, from an average level of 5.7 percent [Davis, Haltiwanger and Schuh (1996)]. The magnitude of job loss when an adverse shock hits the economy is puzzling in some respects. The great majority of workers have been on the job for 5 years or more and expect to remain in the same job for many more years [Hall (1982)]. Higher-tenure workers may have accumulated substantial amounts of job-specific capital, measured as the difference in the expected present discounted value of earnings at their current jobs and the values conditional on departing. Evidence in Ruhm (1991) discussed in Hall (1995) suggests that the typical layoff of a high-tenure worker costs the victim about 1.2 years of earnings, in the form of multiple spells of unemployment and reduced hourly wages. I f the anticipated value of job-specific capital is divided evenly between worker and employer, then the typical level of the capital is 2.4 years of earnings, or around $100 000. It should take a substantial adverse shock to merit the dissipation of $100 000 of specific capital. Labor-market institutions should evolve to protect specific capital against shocks of all kinds, including aggregate ones. Of course, not every job has the typical amount of match capital. Workers with low tenure or in failing businesses may be close to the point where separation would be efficient - it would not lower the joint value of employers and worker. But the evidence at least creates the suspicion that many of the workers who lose their jobs in a recession do not fall into this category. As a general matter, it appears that firms tend to lay workers off despite opportunities to preserve still-valuable job-specific capital. A number of authors have taken this hypothesis as a point of departure for theories of amplification. In addition, recent work has considered the role of heterogeneity in the values of job matches - separations are most likely in the matches whose values are in the lower tail of the distribution, thanks to idiosyncratic factors. The basics of the theory of job termination are well developed in labor economics 2. A core question is the efficiency of terminations - efficiency, as usual, means the maximization of joint value. Figure 1 displays the analysis of efficient terminations. The horizontal axis shows earnings available from the next best job in the open market, net of search costs. The vertical axis shows the worker's marginal product at this employer. Separation should occur below the 45 ° line. Whether the separation is initiated by the worker as a quit or by the employer as a layoff depends on the details of the employment arrangement 3.

2 For example, Hashimoto and Yu (1980), Hall and Lazear (1984), and McLaughlin (1991). 3 See McLaughlin (1991).

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1153

Marginalproduct at firm

45 ° line

Workerstays, efficientlY~worke r departs, "Y

Wageat bestalternativejob

Fig. 1. Efficientseparation.

Efficient separations would be likely if the variables in Figure 1 were observed by the employer and the worker. For example, if the worker can locate the best possible outside wage offer costlessly, and the employer can verify the offer, then the employer will match the offer and retain the worker if the offer is below the worker's marginal product, and let the worker accept the offer otherwise. This arrangement does not require the marginal product to be observable 4. When neither party to the employment contract can verify the other's data, efficiency is more of a challenge. Any provision granting the employer the right to lower compensation after a worker has accepted employment and made job-specific investments will invite opportunistic wage cuts. Even when demand has truly fallen, and renegotiation of the terms of employment is appropriate to retain the worker efficiently, the worker will not be able to verify that the employer is not trying to deprive the worker of job-specific rents. Suppression of renegotiation may be an important feature of employment arrangements. Absent government prohibition of certain types of governance, one would expect the form of the employment relationship to evolve to maximize the joint value achieved by employers and workers. In principle, this proposition should apply even if either the employer or the employee, or both, have market power. Maximization of joint value will occur subject to the constraints of limited abilities to observe or verify key measures and the likelihood that many workers are unable to borrow as much as they would otherwise against future earnings. Most jobs have specific capital. Workers develop skills related to the employer's particular way of doing business. They develop personal relationships with their co-workers. They may choose places to live and particular houses based on their

4 Hall and Lilien (1979) discussed efficient employment arrangements with unilateral information private to employers.

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employer's location. Firms accumulate valuable knowledge about their workers' skills. More subtle employment practices may be needed to protect investments in specific capital. When the efficiency of the continuation of the match is a live issue, protection of specific investments becomes a serious challenge. In that case, some kind of joint or unilateral procedure is needed to determine if a match should continue or end. I f either party has the power to end the job (the worker to quit or the employer to terminate), the party can use that power to deprive the other party of the expected 'return to the investment. For example, an employer might attract a worker to make an expensive move by offering a high salary. A year later, the employer might approach the worker and say that the worker would be terminated unless the worker accepted a much lower salary. The worker would accept the salary reduction as long as the salary remained above the value of the next best job, which might involve another expensive move. An employment arrangement can include severance pay to limit this type of opportunistic behavior by employers. 3.3.1. Mechanism design and labor contracts"

The discussion of the design of the labor contract has been strongly influenced by the literature on mechanism design derived from Mirrlees's (1971) famous paper. A key idea in this literature is that contracts can only be contingent on measures that are verifiable - it is not enough that the measures be observable. Hart (1983) discusses the first round of thinking along these lines, where separation or other employment decisions are made unilaterally by worker or firm, subject to a contract determined in advance. A more recent elaboration of the theory of the employment relationship in the mechanism design framework is in the work of Charles Kahn and Gur Huberman (1988). In their model, the worker's productivity is observed only by the employer, but the productivity depends on an investment in specific capital observed only by the worker. Absent both of these information limitations, simple contracts would give the first-best outcome. If productivity were verifiable, then the wage would be contingent on actual productivity, and the worker would have the right incentive to make the investment. If the investment were itself observable, the employer would reward the worker for making the investment. With both unobservable, the following more complicated contract delivers the efficient outcome: The parties agree in advance on a wage to be paid after the investment is made. Upon observing the worker's productivity later, the employer can either keep the worker and pay the wage, or discharge the worker. The worker does in fact make the investment and is retained, which is the efficient outcome. Gilson and Mnookin (1990) argue that the up or out rule common in law firms is the result of suppression of renegotiation. In order to induce associates to make firmspecific investments, the firm promises not to offer the associate a salary just above the best outside salary. Instead, at a predetermined time, the firm chooses between offering partnership or terminating the associate.

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Although Kahn and Huberman do not stress the point, suppression of renegotiation is central to the success of their contract. After the worker has made the firm-specific investment, the employer could say, "If I have to pay you the wage we agreed upon, I won't keep you. But if you agree to a lower wage, I will keep you." There is no violation of the contract in this offer. But if the worker anticipates that the employer is free to make this offer, the worker will not make the investment and the scheme will fail. Considered as a game played only once, the Kahn-Huberman contract fails the test of credibility - it is not subgame perfect. Suppression of renegotiation requires the employer to commit not to take a step later that would be rational and permitted under the terms of the contract. The problem is the same as the one studied extensively by monetary economists (a central bank needs some way to commit not to create a monetary surprise later, when such a surprise would be rational later) and in public finance (the tax authorities need some way to commit not to levy a capital tax later, when such a tax is the ideal, neutral lump-sum tax later)5. Although in both the monetary and fiscal settings, there are no formal institutions to enforce commitments, experience - especially recently - suggests that something like the favorable equilibrium with commitment can be achieved anyway. Reputations of policymakers and institutions seem to be an important part of the story - see Barro and Gordon (1983) in the analogous context of monetary policy. Reputation may explain the credibility of the suppression of renegotiation as well. If an employer is expected to remain in business permanently, it will pay for it to develop a reputation for adhering to policies of not renegotiating. The concept of reputation can be explained in models of games of repeated play, or in other frameworks 6. Suppression of renegotiation seems to be an important part of the cultural norms of the labor market as well. The offer to retain an employee by departing from previously announced standards of compensation is seen as morally wrong. Standards of ethical conduct support up-or-out rules in universities and professional practices. It is wrong to extend a non-tenured faculty member's appointment after denial of tenure, even though both sides favor it. Truman Bewley's extensive field study of employment relationships in a depressed local labor market documents the absence of renegotiation 7. By far the most common reason given by employers and their advisers for not rewriting employment arrangements in order to preserve jobs is that lowering wages would destroy morale. In other words, workers see a departure from the established compensation patterns as a violation of the rules of the workplace. They think it is wrong to depart from the principle that employers unwilling to pay promised levels of compensation should discharge their workers. 5 See Fischer (1980). On the general issue of the value of commitment in games, see Fudenberg and Tirole (1991, pp. 74-77). 6 See Carmichael (1984). 7 Bewley (1994).

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Value at firm Inefficient 45 ° line i: qul•t / i i / Efficient

Efficient retention W

............. i ............................................

Inefficient layoff / /

/ /

J

i ! i

Efficient layoffquit

Effiaent i layoff

i

Contract value, w Value at best alternative job

Fig. 2. Wage contract with suppression of renegofiafion.

Suppression of renegotiation has some of the implications o f the types o f wage rigidity considered in macroeconomics. But it does not explain any failure of the labor market to clear. It puts no restriction on the terms under which new workers are hired; it is completely consistent with market clearing in the market for new hires. Figure 2 shows that suppression of renegotiation results in excess, inefficient separations. Suppose that the worker was hired with the understanding that the wage would be w. The firm has the right to terminate the worker if the wage falls below w and the worker has the right to quit if there is an alternative job paying more than w. The standard for efficiency remains as in Figure 1 and does not involve the contract wage. Figure 2 shows that a separation wilt always occur if the match has become inefficient. In the inefficient area below the 45 ° line, either a quit will occur (the triangle on the right) or a layoff will occur (the triangle at the lower left), or both a quit and a layoff will occur (the lower right quadrant). The suppression of renegotiation permits the destruction of efficient matches, however. When conditions are good in the outside market, relative to the contract wage, but conditions are even better at this employer (the triangle at the upper right), the worker quits even though the two parties could renegotiate to mutual advantage - there is a wage that will keep employment profitable for the employer but also exceed the worker's best alternative wage. At the left in Figure 2 is the case o f greatest interest in this chapter. An inefficient layoff occurs when conditions are bad at the firm but even worse in the outside market. The parties fail to renegotiate a wage reduction, even though a mutually beneficial one is available. Finally, the upper left quadrant describes a success for the contract; retention is efficient and it actually happens.

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3.3.2. The modern strategic view o f the employment relationship Modern thinking about the employment relationship, as reflected in Diamond (1982a, b), Mortensen (1982), Ramey and Watson (1997), Caballero and Harmrlour (1996, 1998), and many other papers, insists that strategic relationships, such as the employment relationship, satisfy the criterion of subgame perfection. Parties will not adhere to terms such as fixed wages that they can negotiate around later to their mutual benefit. An employment contract does not necessarily guide the relationship as stated, but only establishes the threat points for a subsequent bilateral bargaining problem. The Nash solution to that bargaining problem - where the parties split the joint surplus from their relationship - governs the outcome. For further discussion of the relation between the two branches, see Aghion, Dewatripont and Rey (1990) and Hall (1995, 1997) 8. 3.3.3. Efficiency wages The theory o f efficiency wages - Shapiro and Stiglitz (1984) and Akerlof and Yellen (1990) - has had an important role in macroeeonomics for more than a decade. At a minimum, the theory helps us understand why the natural or chronic level of unemployment is so high. Employers seek to create idiosyncratic value for their workers in their jobs, so that the threat to terminate deters misconduct such as shirking. Absent unemployment, employers wilt pay wage premiums to create the needed idiosyncratic value. Because it is impossible for every employer to pay a premium, there is unemployment in equilibrium. Note that unemployment from efficiency-wage factors is not a socially or privately valuable use of time directly - efficiency-wage models do not suggest that workers have elastic labor supply in the conventional sense. A number of writers have discussed the ways that efficiency wages contribute to amplification - see, for example, Danthine and Donaldson (1995), Picard (1993, Chapter 7), Phelps (1994) and D. Romer (1996, p. 220). Woodford's (1994b) discussion of Phelps reveals the benefits of a full DSGE treatment, as some of Phelps's proposed mechanisms may not work as he describes, once all feedbacks are considered. Woodford (1994a) shows that technology shocks have no more effect in a DSGE model with efficiency wages than in an otherwise similar one with a neoclassical labor market. MacLeod, Malcomson and Gomme (1994) develop a DSGE model where unemployment arises only because of efficiency wages. The model is able to match the volatility of output but falls short of matching the volatility of employment. The authors suggest that adding elastic labor supply as a second amplification mechanism would overcome this problem.

8 The recent literature on contracts in general has gone through a similar transformation see, for example, Segal and Whinston (1996, 1997).

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3.3.4. Job destruction Models with dynamic labor markets that incorporate job destruction, job search, and job creation have made important progress in explaining amplification. Job loss after an adverse shock seems a natural way to model employment reductions. As Mortensen and Pissarides (1994) point out, it is natural to assume the absence of adjustment costs for job destruction. As a result, there is an important asymmetry in the adjustment of employment. The level of employment can decline immediately when an ~idverse shock strikes, whereas the rate of increase is limited by the costs of hiring, which are convex in the hiring rate. Heterogeneity is essential to the story - if workers and jobs are homogeneous, there is no reason for matches to break up and no time required to put workers back in jobs. Wright (1986) appears the first to build a modern general equilibrium model where unemployment arises from heterogeneity and time-consuming matching. In Wright's model, as in a number of successors, separation is an exogenous event. Workers are thoughtful about selecting a new job from the heterogeneous set that is available. Search is time-consuming because workers find out about only one new job per period of search. Aggregate unemployment can jump upward because of an information limitation that can cause all searchers to make the inference that it is a good idea to wait for a better job to come along [the information setup is similar to the one in Lucas (1972)]. Mortensen and Pissarides (1994) is a leading example of current thought about job destruction and unemployment, although theirs is not a full DSGE model - product prices are taken as exogenous. The authors avoid dealing with a full model of the heterogeneity of job-worker matches through the assumption that the productivity of an existing match is drawn from the same distribution for all matches, not from a distribution that depends on the history of the match. Both job destruction and job creation are the result of rational economic behavior by employers and workers. Job destruction occurs at the moment that the joint surplus from the match passes through zero. A key concept in the theory is the option value of the employment relationship, which is an element of joint value. Merz (1995) and Andolfatto (1996) developed DSGE models with job search. To remain within the representative agent general-equilibrium framework - with huge resulting simplification - they presume that families or broader institutions insure individual workers against job loss. In these papers, jobs end at random, not in response to economic forces. But the levels of unemployment and employment fluctuate because of changes in the rate of job creation driven by aggregate conditions. These models achieve amplification, as discussed earlier, by opening up the employment-search margin. Because they do not permit jumps in job destruction along the lines suggested by Mortensen and Pissarides, the amount of amplification is limited. Caballero and Hammour (1996, 1998) have developed a model of endogenous job destruction. Caballero, Engel and Haltiwanger (1997) apply the ideas of that work empirically. A job is destroyed the moment that its match value crosses zero,

Ch. 17:

Labor-Market Frictions and Employment Fluctuations

Valueat f i r m

~

X

1159

X 45° line

Valueat best alternativejob

Fig. 3. Separations in the Ramey Watson model.

in accord with the efficiency condition discussed earlier. The value of each match begins at a positive level, reflecting match capital created by the worker's search effort and the employer's recruiting effort. Thereafter, it evolves as idiosyncratic and aggregate shocks perturb product demand, productivity, and the worker's alternative opportunities. In their general form, this type of model is hard to handle because the state of the economy at each moment includes the distribution of matches by current value, which has a dimension equal to the number o f matches. Gomes, Greenwood and Rebelo (1997) tackle the hard problem of studying a DSGE model without the simplifying assumptions of earlier authors. Their workers do not enjoy the perfect unemployment insurance assumed in earlier models. The value of a match evolves according to a stochastic process with memory, where every match is also influenced by an aggregate variable, so the distribution of workers by current match productivity cannot be simplified. Efficiency wages have been brought back into the picture in the DSGE framework by G. Ramey and Watson (1997). Figure 3 strips their model down to its bare essentials. Workers can enjoy a benefit, X, if they misbehave - for example, X might be the amount they could steal. Misbehavior is detected with certainty by the employer, but cannot be proven in court, so it cannot be a contingency in a contract. Unless workers have a personal value from continuing in the job of at least X, they will take X and then find another job. The zone of inefficient separations in the Ramey-Watson model is the area between the 45 ° line and the line that is X above the 45 ° line. A job could have substantial joint value, say at J in the figure. But a small shock could move that job below the upper line, causing a separation. The employment relationship is unnecessarily fragile (compared to its full-information version) because it breaks up whenever the joint value achieved by the match falls below X,, rather than surviving unless it falls to zero. In what sense is there amplification in the Ramey-Watson model? Jobs are at risk to small shocks even though they have positive amounts of joint job-specific

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value. In a world of homogeneous worker-employer matches, their model explains job destruction without requiring that all matches have little match value. On the other hand, with heterogeneous match values, as in Caballero and Hammour (1996) and related research, the contribution of efficiency wages to amplification is less clear. In those models, job destruction occurs when match values drift down to zero, under the influence of random idiosyncratic and aggregate influences. The Ramey-Watson setup changes the boundary point where job destruction occurs, but does not change the magnitude of the response to adverse aggregate' shocks in an obvious way. 3.3.5. Reorganization and reallocation Lilien (1982) began the literature suggesting that reorganization or reallocation could create aggregate effects on employment and unemployment. Impulses that have no net effect on aggregate productivity, for example, nonetheless raise unemployment during the period when they cause workers to move from one sector to another. Reorganization is an activity that is a close substitute for production [Hall (1991a)]. The most conspicuous form of reorganization is the movement of workers from unsuccessful productive units to new or growing units. Other forms of reorganization include relocation and re-employment of capital and the rearrangement of contractual relations among units. One can think of these activities as investment flows that form organizational capital. As in the case of the use of output either for consumption or capital formation, production and organizational capital formation are perfect substitutes. Perfect substitution is a natural source of amplification, just as is the perfect substitution between market work and time spent in other activities. Flows into reorganization occur out of jobs where the match value has just reached zero, possibly as the result of an aggregate impulse. Match value will fall either if workers' marginal contributions fall at their current jobs or if the likely value of employment elsewhere rises, net o f search costs. Thus three types of impulses are amplified in the reorganizational view: (1) Impulses that raise workers' contributions in some sectors and lower them in others, without affecting the efficiency of search, such as changes in the composition of product demand. (2) Impulses that lower productivity in all sectors but do not affect the efficiency of search, such as reductions in productivity in all sectors. (3) Impulses that do not affect productivity but raise the effÉciency of search, such as streamlining the labor market. Data on cyclical flows of labor are helpful in understanding reorganization. Flows out of various industries - measured either as gross job destruction [Davis, Haltiwanger and Schuh (1996)] or as net employment change - are highly correlated across industries. In particular, the abrupt shedding of workers during a recession occurs in most industries. Impulses that stimulate movements of workers from one sector to another cannot explain the most important facts about recessions.

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An exogenous improvement in the efficiency of job search relative to the productivity of employment would explain the burst of job separation and high volume of jobseeking in recessions. This explanation is a close relative to the one based on productivity at home rising relative to productivity in the market - workers are sucked out of employment because of the rising attractiveness of an alternative use of time. It shares the defects of that view discussed earlier. It does have the advantage of explaining - however implausibly - the sharp increase in unemployment in recessions, a phenomenon not considered in the existing home production models. Endogenous changes in job search costs are a more promising way to make reorganization a believable element in fluctuations theory. They arise in models of complementarity. Peter Diamond (1982b) began modern rigorous thinking on this topic. In his model, producer-consumers search for each other. Upon making a match, each can consume and then produce again. The presence of one search agent confers an external benefit on others by raising the probability of encountering a partner. This is a thick-market externality. In Diamond's model, two or more equilibria are possible. In one there are relatively few searchers ready to trade. Because it is difficult to trade, less production takes place. It is a decentralized equilibrium. In the superior equilibrium, more traders are in the market, so more production takes place. Again, this is a decentralized equilibrium. Diamond's model - like many successors based on complementarities - contains the ultimate form of amplification, indeterminacy. The tiniest impulse, including sunspots, could trigger a move from one equilibrium to another, with very different levels of output and employment. As stressed in a number o f places in this chapter, realistic fluctuations models need to consider unemployment seriously and explicitly. Most research on complementarities has concentrated on output rather than unemployment. Hall (1991a) makes an attempt to apply the logic of Diamond's model of search complementarities to unemployment over the business cycle. The paper offers a crude measure of endogenous increases in search efficiency when unemployment is higher. At one level, it must be true that it is better for one worker to search when many others are searching as well. Like most other economic activities, job search is concentrated during the daylight hours Monday through Friday. It is efficient to concentrate job-worker matching during a limited set of hours of the week. Many job markets - including the one for economists - are highly seasonal. Again, temporal concentration of matching activities is efficient. It is a leap from these observations, however, to the conclusion that recessions are good times to look for work in the same way that Tuesday at 3 pm and the first week in January are good times. Before rejecting the view that there are increasing returns to aggregate search, one should consider carefully the evidence developed by Davis, Haltiwanger and Schuh (1996) that the hiring rate (measured by gross job creation) reaches a startling peak immediately after the spike of job destruction that occurs during the initial contraction phase of a recession. The extended period o f high unemployment following

1162

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a contraction is a period of matching frenzy, with both job destruction and job creation at abnormally high levels. Evidence cited by Hall (1991a) on the cyclical behavior of job-finding rates is mixed. Blanchard and Diamond (1990) report that a recession that raises unemployment by two percentage points reduces the job-finding rate from a normal level of 24.0 percent per month to 21.8 percent per month. On the other hand, Hall reports a regression relating the Davis-Haltiwanger measure of the volume of job-worker matching to the level of unemployment. He finds an increasing margimll benefit from the stock of unemployment on the flow of new matches. Although the amplification mechanism based on endogenous improvements in search efficiency during recessions is on uncertain ground, the evidence just reviewed raises serious doubts about the opposite (and conventional) view that recessions are times when jobs become much harder to find. A reasonable intermediate view is that search efficiency is about the same at high and low unemployment. This disposes of a potential attenuation mechanism - job matches would be more stable in recessions than normal times if job search became more costly in recessions.

4. Persistence The time-series properties of the principal macro variables are reasonably well understood. Unemployment is stationary - it returns about one third of the way to its normal level each year after a shock displaces it 9. Output and employment have both cyclical and highly persistent - possibly integrated - components. The persistence mechanisms in a fluctuations model need to be able to explain the stationary but serially correlated movements of unemployment and the corresponding cyclical movements of output and employment. The highly persistent components of employment and output derive from slow-moving changes in preferences and technology and are not in the domain of the persistence mechanism of the fluctuations model. Although a number of authors have identified sources of persistence other than the mechanics of job search [such as Burnside and Eichenbaum (1996) and Saint-Paul (1996)], I will focus mainly on this single topic, which dominates current thinking about persistence. 4.1. Time-consuming matching in the labor market One of the most interesting and successful recent developments in the labor side of macroeconomics has been the development of modern models of job search. Diamond (1982b) and Mortensen (1982) are the starting points. Good summaries are

9 In the USA. In many other countries, unemploymentis close to a random walk.

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in Mortensen (1986), Pissarides (1990), and Romer (1996, chapter 10). My discussion will be brief because Mortensen's chapter in this volume covers this area in detail. In the standard matching model, a random meeting occurs between a job seeker and an employer. A match occurs if it increases the joint value of the two parties, in which case they divide the joint surplus. The simplest model has a constant probability that a job-seeker will be matched. The persistence parameter for aggregate unemployment the serial correlation coefficient - is controlled by the job-finding probability. The matching model provides a simple and elegant persistence mechanism for a general equilibrium macro model. From the start, it has been clear that it is an uphill battle to use the matching model to explain the actual persistence of unemployment in the USA. To see the relation between the job-matching rate and the serial correlation of unemployment, consider the following elementary model. Let dt be job destruction, nt be employment, ~ be the fixed supply of labor, ut = ~ - nt be unemployment, and f the per-period job-finding rate. Then employment this period consists of employment last period plus those among the unemployed who found new jobs less the number of jobs destroyed: nt =nt 1 + f u r - d r

(4.1)

ut = (1 - f ) u t

(4.2)

or

1 +dt.

Thus, if job destruction is white noise, unemployment follows an AR(1) process with serial correlation 1 - f . As I noted earlier, the average job-finding rate is about 24 percent per month. The monthly serial correlation of unemployment is 0.988, which would imply a job-finding rate of only 1.2 percent per month. There is a discrepancy of a factor of 20 between the time-series properties of unemployment and the job-finding rates experienced by individuals. Cole and Rogerson (1996) have studied this discrepancy and concluded, "Our main finding is that the [matching] model can account for the business cycle facts, but only if the average duration of a non-employment spell is relatively high - about nine months or longer." With an average job-finding rate of 24 percent per month, the average duration is actually much less. Something is missing from the simple model. 4.2. The importance o f secondary j o b loss f o r persistence

Hall (1995) suggests that the missing element is induced secondary job loss. The first job that a recently discharged worker finds may be an explicitly temporary job, or it may turn out to be a bad match once the worker joins the firm, or the match may break soon because, in its early stages, it has little job-specific capital. There is evidence of large amounts of secondary spells of unemployment following an initial impulse.

R.E. Hall

1164 12 10 8 6 o

4 2 0 72

73

74

75

76

77

78

79

80 81 Quarters

82

83

84

85

86

87

88

Fig. 4. Gross employment reduction rate in manufacturing.

Figure 4 shows quarterly data on gross employment reductions in manufacturing, taken from the work of Davis, Haltiwanger and Schuh. Gross employment reductions are measured at the level of individual plants. The series shows the total reduction in employment at plants where employment fell from one quarter to the next, as a percent of total employment. Gross employment reductions appear to be the best available measure of the immediate effect of adverse macroeconomic events on the labor market. In particular, as Figure 4 shows, recessions start off with large bursts of employment reductions. The flow of gross employment reductions is not persistent; during the extended slump after a sharp contraction, gross employment reductions are at normal levels 10. Persistence in unemployment and employment appear to come from other sources. Data on the flow of workers into unemployment provide another, quite different view of the dynamics of job loss. The best data for this purpose show the flow from permanent layoffs alone, separately from temporary layoffs, quits, new entrants, and re-entrants. Figure 5 shows these data since they became available in 197611. New permanent layoffs are much more persistent than gross job reductions. A burst of job reductions, as in 1982, is followed by several years of higher new permanent layoffs. The data have a strong distributed lag relationship - see Hall (1995). A number of factors enter the explanation of the lag from employment reductions to new unemployment. First, employment reductions are measured only in manufacturing,

10 As Davis, Haltiwanger and Schuh note, plant level employment is highly persistent; it is essentially a random walk. Hence the flow of reductions is close to white noise. tl The data come from the Current Population Survey and are published in Employment and Earnings. They refer to workers who became unemployed as a result o f permanent layoff, whose unemployment began within five weeks of the survey.

Ch. 17: Labor-Market Frictions and Employment Fluctuations

1165

3.5

2.5 2

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Fig. 5. New permanent layoff unemployment. Source: Bureau of Labor Statistics, Current Population Survey, permanent layoff unemployed less than 5 weeks.

whereas new unemployment is measured economy-wide 12. A systematic lag of nonmanufacturing behind manufacturing would explain some part of the lag. Second, many workers who lose their jobs do not become unemployed- they move immediately to other jobs or leave the labor force. During the period of slack labor markets following a burst of employment reductions, a larger fraction of job-losers become unemployed. Third, permanent job loss has important delayed effects. Many of the workers who move quickly to other jobs have taken temporary work, either jobs with predetermined short terms, or those with naturally high turnover. Those who left the labor force upon loss of a long-term job often re-enter the labor force. The micro and macro evidence suggests strongly that terminations beget later terminations. When an event breaks a set of long-term employment relationships, the workers released into the labor market will form new relationships. Many o f the new jobs will prove to be short-lived.. First, it.may make sense for an individual totake a temporary job while looking for a new permanent job. Second, a worker long out of the market may experiment with alternative types of work before finding a good longterm match. Third, employers may have explicit policies of hiring many candidates and keeping only the fraction who prove to be well matched. Fourth, immediately after being hired, the typical worker will be close to the margin for discharge, either by the standards o f the efficient separation model or the models of suppressed renegotiation or efficiency wages. Both the systematic accumulation of match-specific capital and the random accumulation o f rent will have had little time to occur. Low-tenure workers

t2 In principle, data on new permanent-layoffunemployment among workers previously employed in manufacturing could be tabulated from the Current Population Survey,but it would require processing all of the monthly CPS tapes. I do not believe this has yet been done.

1166

R.E. Hall

are the logical candidates for separation - last hired, first fired is the rational separation rule under broad conditions. A specific adverse event will create an immediate burst of terminations, followed by the second, third, and subsequent rounds of terminations. Induced subsequent job losses seem to be a promising explanation of persistence. Following a single adverse shock, employment will be depressed and unemployment elevated by subsequent rounds of adjustment in the labor market. A glance at the data show that a simple model of transitions between jobs and search cannot be faithful to even the most conspicuous features of the market's dynamics. Rates of separation from jobs decline sharply with tenure on the job, and job-finding rates fall with the duration of unemployment. Part of the duration dependence is genuine and part reflects the sorting of heterogeneous workers 13. Moreover, previous history appears to influence transition rates. For example, workers terminated from long-term jobs have lower job-finding rates than do other searchers, are more likely to lose subsequent jobs than are other short-tenure workers, and have lower job-finding rates in subsequent spells of unemployment. Some basic properties of job loss have emerged in this review of the evidence. Microeconomic studies of serious job loss show significant downstream effects on the subsequent experiences of individuals in the labor market. Loss of a long-term job leads to a period of episodic employment, periods of job search or time out of the labor market, and lower earnings when working. The effects extend for at least four years. In the macroeconomic evidence, bursts of gross employment reductions coincide with abnormal levels of serious job loss. The downstream effects visible in time series data for unemployment are similar to the effects found in micro data for individuals. The macro data show occasional sharp disruptions of employment followed by long periods of rebuilding of employment relationships. This rebuilding may be an important part of the propagation mechanism of the business cycle. The length of time that the economy takes to recover from an adverse shock has perplexed macroeconomists for many years. Rebuilding may help solve this puzzle of persistence. Den Haan, Ramey and Watson (1997) have developed a DSGE model with realistic persistence in which efficient job destruction interacts with capital formation. They provide an alternative explanation of induced secondary job loss. A key property of their model is that the idiosyncratic shock at the level of the plant or individual job match is unpredictable white noise. An aggregate shock results in a first rotmd of job destruction. There follows a period of high interest rates during which the threshold value for the idiosyncratic shock changes so as to increase the probability of job destruction. Until the aggregate shock wears off, job destruction continues at abnormally high levels. The model is successful in explaining the persistence of

13 See Heckmanand Singer (1985) and Devine and Kiefer (1991).

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job destruction and unemployment, without invoking unrealistically low rates o f job finding. On the other hand, it relies on highly persistent technology shocks (with a quarterly serial correlation of 0.95) in order to generate persistent changes in interest rates. The model's assumption that the idiosyncratic component of job match value is white noise is also intrinsic to the model's success in explaining persistence. Under the more realistic assumption o f a random walk for the idiosyncratic component, all of the job destruction triggered by an aggregate shift in technology would occur immediately and there would be no persistent subsequent job destruction.

5. Conclusion In the economies of the USA and other modem countries, large responses, especially recessions, seem to result from small impulses. Their effects on the economy must operate through an amplification mechanism. The fragility of the employment relationship seems to underlie that sensitivity. Despite substantial job-specific capital in the majority of jobs, millions of workers are released into the labor market during each contraction. The resulting unemployment is persistent. Not only does it take time for workers displaced by a recession to find new jobs, but the average one has to find several new jobs, a process that stretches over about four years. DSGE models have come a long way since Kydland and Prescott (1982) in incorporating labor-market frictions and giving correspondingly more realistic portrayals of the economy. Recognition of the heterogeneity of workers and jobs has been central to this improvement in macro modeling.

Acknowledgments This research was supported by the National Science Foundation under grant SBR9410039 and is part of the NBER's research program in Economic Fluctuations and Growth. I am grateful to the editors for helpful comments.

References Aghion, E, M. Dewatripont and P. Rey (1990), "On renegotiation design", European EconomicReview 34:322-329. Aiyagari, S.R., L.J. Christiano and M. Eichenbaum (1992), "The output, employment, and interest rate effects of government consumption", Journal of Monetary Economics 30:73-86. Akerlof, G.A., and J.L. Yellen (1990), "The fair wage-efforthypothesis and unemployment",Quarterly Journal of Economics 105:255-283. Andolfatto, D. (1996), "Business cycles and labor-market search", American Economic Review 86: 112-132. Barro, R.J., and D.B. Gordon (1983), "Rules, discretion, and reputation in a model of monetarypolicy", Journal of Monetary Economics 12:101-121.

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Barskry, R.B., and J.A. Miron (1989), "The seasonal cycle and the business cycle", Journal of Political Economy 97:503-534. Basu, S. (1996), "Procyclical productivity: increasing returns or cyclical utilization?", Quarterly Journal of Economics 111:719-751. Basu, S., and J.G. Fernald (1997), "Returns to scale in U.S. production: estimates and implications", Journal of Political Economy 105:249-283. Benhabib, J., R. Rogerson and R. Wright (1991), "Homework in macroeconomics: household production and aggregate fluctuations", Journal of Political Economy 99:1166-1187. Beveridge, S., and C.R. Nelson (1981), "A new approach to the decomposition of economic time series into permanent and transitory components with particular attention to the measurement of the 'business cycle'", Journal of Monetary Economics 7:151-174. Bewley, T. (1994), A Field Study on Downward Wage Rigidity (Yale University). Blanchard, O.J., and P.A. Diamond (1990), "The cyclical behavior of the gross flows of U.S. workers", Brookings Papers on Economic Activity 1990(2):85-155. Burnside, C., and M. Eichenbaum (1996), Factor hoarding and the propagation of business cycle shocks", American Economic Review 86:1154-1174. Burnside, C., M. Eichenbaum and S.T. Rebelo (1993), "Labor hoarding and the business cycle", Journal of Political Economy 101:245-273. Caballero, R.J., and M.L. Hammour (1996), "On the timing and efficiency of creative destruction", Quarterly Journal of Economics 111:805-852. Caballero, R.J., and M.L. Hammour (1998), "Jobless growth: appropriability, factor substitution, and unemployment", Carnegie-Rochester Conference Series on Public Policy 48(June):51 94. Caballero, R.J., E. Engel and J. Haltiwanger (1997), "Aggregate employment dynamics: building from microeconomic evidence", American Economic Review 87:115-137. Campbell, J.Y. (1994), "Inspecting the mechanism: an analytical approach to the stochastic growth model", Journal of Monetary Economics 33:463-506. Card, D. (1994), "Intertemporal labor supply", in: C.A. Sims, ed., Advances in Econometrics: Sixth World Congress of the Econometric Society, vol. II (Cambridge University Press) 49-78. Carmichael, H.L. (1984), "Reputations in the labor market", American Economic Review 74:713-725. Cogley, T., and J.M. Nason (1995), "Output dynamics in real-business-cycle models", American Economic Review 85:492-511. Cole, H.L., and R. Rogerson (1996), "Can the Mortensen-Pissarides matching model match the business cycle facts?", Staff Report 224 (Federal Reserve Bank of Minneapolis, Research Department, December). Danthine, J.-E, and J.B. Donaldson (1995), "Non-Walrasian economies", in: T.E Cooley, ed., Frontiers of Business Cycle Research (Princeton University Press, Princeton) 217-242. Davis, S.J., J.C. Haltiwanger and S. Schuh (1996), Job Creation and Destruction (MIT Press, Cambridge, MA). den Haan, W.J., G. Ramey and J. Watson (1997), Job Destruction and Propagation of Shocks (University of California, San Diego). Devine, T.J., and N.M. Kiefer (1991), Empirical Labor Economics: The Search Approach (Oxford University Press, New York). Diamond, P.A. (1982a), "Wage determination and efficiency in search equilibrium", Review of Economic Studies 29:217-227. Diamond, EA. (1982b), "Aggregate demand management in search equilibrium", Journal of Political Economy 90:881-894. Fischer, S. (1980), "Dynamic inconsistency, cooperation and the benevolent dissembling government", Journal of Economic Dynamics and Control 2:93-107. Fudenberg, D., and J. Tirole (1991), Game Theory (MIT Press, Cambridge, MA). Gilson, R.J., and R.H. Mnookin (1990), "The implicit contract for corporate law firm associates: ex post opportunism and ex ante bonding", in: M. Aoki, B. Gustafsson and O. Williamson, eds., The Firm

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as a Nexus of Treaties (Swedish Collegium for Advanced Study in Social Sciences Series, London) 209-236. Gomes, J., J. Greenwood and S.T. Rebelo (1997), Equilibrium Unemployment (University of Rochester, Rochester, NY). Hall, R.E. (1982), "The importance of lifetime jobs in the U.S. economy", American Economic Review 72:716-724. Hall, R.E. (1988), "The relation between price and marginal cost in U.S. industry", Journal of Political Economy 96:921-947. Hall, R.E. (1990), "Invariance properties of Solow's productivity residual", in: P. Diamond, ed., Growth/Productivity/Unemployment: Essays to Celebrate Robert Solow's Birthday (MIT Press, Cambridge, MA) 71-112. Hall, R.E. (1991a), "Labor demand, labor supply, and employment volatility", National Bureau of Economic Research Annual: 17-46. Hall, R.E. (1991b), "Substitution over time in consumption and work", in: L. McKenzie and S. Zamagni, eds., Value and Capital Fifty Years Later (MacMillan) 239-267. Hall, R.E. (1995), "Lost jobs", Brookings Papers on Economic Activity 1995(1):221-273. Hall, R.E. (1997), "Macroeconomic fluctuations and the allocation of time", Journal of Labor Economics 15 :$223-$250. Hall, R.E., and E.P. Lazear (1984), "The excess sensitivity of layoffs and quits to demand", Journal of Labor Economics 2:233-257. Hall, R.E., and D.M. Lilien (1979), "Efficient wage bargains under uncertain supply and demand", American Economic Review 69:868-879. Hart, O. (1983), "Optimal labour contracts under asymmetric information: an introduction", Review of Economic Studies 50:3-35. Hashimoto, M., and B. Yu (1980), "Specific capital, employment contracts, and wage rigidity", Bell Journal of Economics 11:536-549. Heckman, J.J., and B. Singer (1985), Longitudinal Analysis of Labor Market Data (Cambridge University Press, New York). Kahn, C., and G. Huberman (1988), "Two-sided uncertainty and 'up-or-out' contracts", Journal of Labor Economics 6:423-444. Killingsworth, M.R., and J.J. Heckman (1986), "Female labor supply: a survey", in: O. Ashenfelter and R. Layard, eds., Handbook of Labor Economics, vol. 1 (North-Holland, Amsterdam) ch. 2, 103-204. King, R.G., and S.T. Rebelo (1999), "Resuscitating real business cycles", ch. 14, this Handbook. Kydland, EE., and E.C. Prescott (1982), "Time to build and aggregate fluctuations", Econometrica 5:1345-1370. Lilien, D.M. (1982), "Sectoral shifts and cyclical unemployment", Journal of Political Economy 90: 777-793. Lucas, R.E. (1972), "Expectations and the neutrality of money", Journal of Economic Theory 4:103 124. MacLeod, W.B., J.M. Malcomson and P. Gomme (1994), "Labor turnover and the natural rate of unemployment: efficiency wage versus frictional unemployment", Journal of Labor Economics 12: 276 315. MaCurdy, T.E. (1981), "An empirical model of labor supply in a life cycle setting", Journal of Political Economy 89:1059-1085. McLaughlin, K.J. (1991), "A theory of quits and layoffs with efficient turnover", Journal of Political Economy 99:1-29. Merz, M. (1995), "Search in the labor market and the real business cycle", Journal of Monetary Economics 36:269-300. Mirrlees, J.A. (1971), "An exploration in the theory of optimum income taxation", Review of Economic Studies 38:175-208. Mortensen, D.T. (1982), "Property rights and efficiency in mating, racing, and related games", American Economic Review 72:968-979.

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Mortensen, D.T. (1986), "Job search and labor market analysis", in: O. Ashenfelter and R. Layard, eds., Handbook of Labor Economics (North-Holland, Amsterdam) 849-919. Mortensen, D.T., and C.A. Pissarides (1994), "Job creation and destruction in the theory of unemployment", Review of Economic Studies 61:397-415. Mulligan, C.B. (1995), "The intertemporal substitution of work - what does the evidence say", University of Chicago Population Research Center Discussion Paper 95-3. Pencavel, J. (1986), "Labor supply of men: a survey", in: O. Ashenfelter and R. Layard, eds., Handbook of Labor Economics (North-Holland, Amsterdam) 3-102. Phelps, E.S. (1994), Structural Slumps: The Modern Equilibrium Theory of Unemployment, Interest, and Assets (Harvard University Press, Cambridge, MA). Picard, P. (1993), Wages and Unemployment: A Study in Non-Walrasian Macroeconomics (Cambridge University Press, Cambridge, MA). Pissarides, C.A. (1990), Equilibrium Unemployment Theory (Blackwell, Oxford). Ramey, G., and J. Watson (1997), "Contractual fragility, job destruction, and business cycles", Quarterly Journal of Economics 112:873411. Rogerson, R. (1988), "Indivisible labor, lotteries, and equilibrium", Journal of Monetary Economics 21:3-16. Romer, D. (1996), Advanced Macroeconomics (McGraw-Hill, New York). Rotemberg, J.J., and M. Woodford (1996), "Real-business-cycle models and the forecastable movements in output, hours, and consumption", American Economic Review 86:71-89. Ruhm, C. (1991), "Are workers permanently scarred by job displacements?", American Economic Review 81:31%324. Saint-Paul, G. (1996), "Efficiency wages as a persistence mechanism", in: H.D. Dixon and N. Rankin, eds., The New Macroeconomics: Imperfect Markets and Policy Effectiveness (Cambridge University Press, Cambridge) 186-205. Sargent, T.J. (1979), Macroeconomic Theory (Academic Press, New York). Segal, I.B., and M.D. Whinston (1996), "Naked exclusive contracts and buyer coordination", Discussion Paper 1780 (Harvard Institute of Economic Research). Segal, I.B., and M.D. Whinston (1997), Exclusive Dealing and Specific Investments (Harvard University and University of California, Berkeley). Shapiro, C., and J.E. Stiglitz (1984), "Equilibrium unemployment as a worker discipline device", American Economic Review 74:433-444. Solow, R.M. (1957), "Technical change and the aggregate production function", Review of Economics and Statistics 39:312-320. Woodford, M. (1994a), "Notes on dynamic efficiency wage models". Unpublished. Woodford, M. (1994b), "Structural slumps", Journal of Economic Literature 32:1784-1815. Wright, R. (1986), "Job search and cyclical unemployment", Journal of Political Economy 94:38 55.

Chapter 18

JOB REALLOCATION, EMPLOYMENT FLUCTUATIONS AND UNEMPLOYMENT * DALE T. MORTENSEN Northwestern University CHRISTOPHER A. PISSARIDES London School of Economics

Contents Abstract Keywords Introduction 1. O E C D facts 2. The equilibrium rate o f unemployment 2.1. Job destruction and job creation conditions 2.2. Generalized Nash bargaining 2.3. Fundamental determinants of unemployment 3. Employment fluctuations 3.1. Stochastic equilibrium 3.2. The Beveridge curve 3.3. Job creation and job destruction flows 3.4. Quits and worker flows 4. Explaining the data 4.1. Explaining job flows data 4.2. Capital accumulation and shock propagation 5. Technological progress and job reallocation 5.1. Disembodied technology 5.2. Adoption through "creative destruction" 6. O E C D unemployment differences 6.1. 'Skill-biased' technology shocks 6.2. Mean-preserving shocks to idiosyncratic productivity

1172 1172 1173

1174 1183 1185 1188

1192 1194 1194 1196 1197 1198 1200 1201 1203 1207 1208 1210 1213 1215 1218

* Presented at the Federal Reserve Conference on "Recent Developments in Macroeconomics I", February 27-28, 1997, New York, NY. The authors acknowledge financial support from the US National Science Foundation, Northwestern University, and the Centre for Economic Performance at the London School of Economics. Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor and M. Woodford © 1999 Elsevier Science B.V. All rights reserved 1171

1172 6.3. Other influences 7. Concluding remarks Appendix A. Mathematical appendix A.1. Mean-preservingshifts in productivity A.2. Labor's bargaining strength References

D.T. Mortensen and C.A. Pissarides

1220 1223 1223 1223 1224 1225

Abstract The purpose of this chapter is twofold. First, it reviews the model of search and matching equilibrium and derives the properties of employment and unemployment equilibrium. Second, it applies the model to the study of employment fluctuations and to the explanation of differences in unemployment rates in industrialized countries. The search and matching model is built on the assumptions of a time-consuming matching technology that determines the rate of job creation given the unmatched number of workers and jobs; and on a stochastic arrival of idiosyncratic shocks that determines the rate of job destruction given the wage contract between matched firms and workers. The outcome is a model for the flow of new jobs and unemployed workers from inactivity to production (the 'job creation' flow) and one for the flow of workers from employment to unemployment and of jobs out of the market (the 'job destruction' flow). Steady-state equilibrium is at the point where the two flows are equal. The model is shown to explain well the employment fluctuations observed in the US economy, within the context of a real business cycle model. It is also shown that the large differences in unemployment rates observed in industrialized countries can be attributed to a large extent to differences in policy towards employment protection legislation (which increases the duration of unemployment and reduces the flow into unemployment) and the generosity of the welfare state (which reduces job creation). It is argued that on the whole European countries have been more generous in their unemployment support policies and in their employment protection legislation than the USA. The chapter also surveys other reasons given in the literature for the observed levels in unemployment, including mismatch and real interest rates.

Keywords J E L classification: J63, J64, J65, J68, E24, E32, J41

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1173

Introduction

Market economies experience large employment fluctuations and average unemployment rates that are often different from those experienced by apparently similar economies. The search and matching framework provides a convenient lens through which to view explanations of such differences. Our purpose in this chapter is twofold: first, to present the essential concepts that underlie the framework and, second, to use the framework to suggest answers to the questions posed by the data. Existing employment relationships command monopoly rents because of search and recruiting investments, hiring and firing costs, and other forms of match-specific human capital formation. The surplus that accrues is allocated between the parties to the employment relationship by a wage contract. Given a particular wage rule, employers provide jobs and recruit workers while workers search for employment. At the same time, an existing employer-worker match ends when sufficiently bad news arrives about their expected future. These job creation and job destruction decisions generate worker flows into and out of employment which depend on the current value of the employed stock. When the two flows differ, employment dynamics are set in motion which, under a reasonable set of conditions, lead to a unique steady-state employment level. These properties characterize the equilibrium model of job creation and job destruction applied in the chapter. The search and matching approach owes its origins to the pioneering works of Stigler (1962), Phelps (1968) and Friedman (1968) and was already at an advanced state when the Phelps et al. (1970) volume was published. The equilibrium analysis of the current vintage of models, however, did not start until the early 1980s, when models by Diamond (1982a,b), Mortensen (1982a,b) and Pissarides (1984a,b) explored the properties of two-sided search and characterized the nature and welfare properties of market equilibrium. Despite a flurry of activity since then, there are still many important questions that are unexplored. One such question is the dynamics of worker movement in and out of the labor force, of which, despite its empirical importance [Clark and Summers (1979), Blanchard and Diamond (1989)] and some attempts to model it by Burdett et al. (1984), Pissarides (1990, Chapter 6) and Andolfatto and Gomme (1996), our knowledge is still scant. Virtually all search equilibrium models assume an exogenous labor force, which is used to normalize all aggregate quantities, and model either the equilibrium employment or unemployment rate. It is simple enough to superimpose on this structure a neoclassical labor-supply decision, as is done, for example, by Andolfatto (1996) and Merz (1995), but still the worker flow from the labor force to out of the labor force is ignored. Given this restriction, we can interchangeably talk either about employment equilibrium or about unemployment equilibrium. In the latter case, the equilibrium is often referred to as a "natural rate" equilibrium, following Friedman's introduction of the term in 1968. Indeed, the equilibrium that we shall describe corresponds closely to the one advocated by Friedman (1968) and Phelps (1967, t968).

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We attribute the observed fluctuations in employment (or unemployment) to fluctuations in the natural rate, i.e., we ignore inflation and expectation errors. The driving force in the search and matching models that we describe is virtually without exception a real productivity or reatlocation shock [but see Howitt (1988) for an exception]. The reason for this is partly that models with real shocks calibrate the data fairly well but also, more importantly, that the search and matching approach is about the transmission and propagation mechanisms of shocks, not about their origins. It is then more convenient to take the simplest possible shock in this framework, which is a proportional productivity shock, as driving force and concentrate on the dynamics and steady states implied by the model - than dwell on debates of whether employment cycles are due to real or monetary shocks. Section 1 summarizes the aggregate data for OECD countries. Section 2 contains the core equilibrium matching model with a surplus sharing wage contract. The fundamental determinants of the natural rate o f unemployment are reviewed in this section. In Section 3 the model is embedded into a real business cycle model and its consistency with some recent facts on job flows is reviewed. In section 4 we review calibrations of the model and introduce capital accumulation. In section 5 we consider technological innovation and its employment effects. Finally, in Section 6, we return to OECD data and examine the model's implications for the facts noted in Section 1. How far can the model explain those facts and what remains to be done? We find that although a lot can be explained and the framework of search and matching models is a convenient device for studying those facts, a lot remains for future work.

1. O E C D facts

What are the main facts about employment and unemployment that the search and matching approach can help explain? In Figures 1 and 2, labor force and unemployment time series from 1960 to 1995 are illustrated for the USA, Japan and a weighted average of the four largest European economies, Germany, France, Italy and the United Kingdom. The four European countries are grouped together because their unemployment and labor force experiences have been sufficiently similar to each other. Comparable data can also be found for most of the other members of the European Union, in particular Spain, the Benelux, and Scandinavian countries. The experience of Spain and the Scandinavian countries, however, has been different from that of the big four, essentially for labor-market policy reasons. In Spain, excessive safeguarding of the rights of workers through the legal system created a sharp distinction between insiders and outsiders and led to low aggregate job creation. In the Scandinavian countries large-scale active labor market policies held unemployment artificially low until recently. Since we shall not address issues of labor market policy in any detail, we decided not to aggregate those countries with the four large economies. The experience

1175

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of the Benelux countries is sufficiently close to that of France and Germany, to the extent that data from them will not add to the information given here. Figure 1 shows the sharply contrasting participation experience of the USA on the one hand and Europe and Japan on the other. Whereas in the early 1960s the participation rates in Europe and the USA were essentially the same, since then participation in the USA has been on an upward trend and in Europe on a downward trend. The upward trend in the USA was driven largely by the female participation rate, whereas in Europe, where female participation rates have also increased, the downward trend was driven by early retirements among men and by later school leaving. In Japan the participation rate is uniformly above the European rate but its dynamic behavior since 1960 has been very similar to the European rate. The figure also shows some evidence of cyclical variations in the participation rate: it is these cyclical movements that the search and matching approach could in principle handle, but has so far ignored. The trend changes, in the USA in particular, are more likely the outcome of lifetime labor supply decisions that are independent of the labor market frictions that underlie the search and matching approach. In Europe, however, much of the decline in laborforce participation has been the result of policy incentives or of private responses to the rise in unemployment ("discouragement"). The policy to encourage early retirement was also largely in response to the rising unemployment, so the fall in participation can be partly attributed to the same factors that increased unemployment during this period. But exogenous labor supply changes have also played an important role, as comparison of Figures 1 and 2 shows. The trend decline in labor force participation

1176

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i

i

i

h

I

~

70

i

i

I

i

75

i

t

i

i - Y - F q ~ - i

80

i

85

i

i

90

i

i

i

95

Year Fig. 2. Standardizedunemploymentrates, 1960-1995. began before the unemployment rise and it was accompanied by a fall in annual hours of work for those that remained in the labor force. We shall briefly return to the question of participation changes in the final section. In the remainder of this section we look at the behavior of unemployment and at gross job creation and job destruction flows normalized by the labor force. The aim is to point out key features of the data ("stylized facts") that will guide the model presentation in the rest of the chapter. Figure 2 plots the unemployment rates for the three country groups, as far as possible adjusted to the same (US) definition. Table 1 gives data for more countries for two periods that were approximately in the same cyclical phase. The contrast is clear. Whereas in the USA and Japan unemployment is a cyclical variable without trend, in Europe the biggest changes in unemployment over the last thirty years were due to changes in the average level of unemployment across cycles. This latter feature of the European time series led most who analyzed this problem to conclude that the changes in European unemployment are changes in the "natural rate", not changes in its cyclical component [Layard et al. (1991), Phelps (1994), Blanchard and Katz (1997)]. The approach that we describe in this chapter is motivated by this observation and is especially suitable for the analysis of changes in the natural rate. Inflation, expectations errors and other nominal influences are ignored. The net changes in employment over the cycle conceal large movements in gross job creation and job destruction, as well as worker turnover for other reasons. Information on this feature of labor markets sheds light on the appropriate flow models that should be used to analyze aggregate labor market changes. This feature of labor markets has been emphasized by Davis and Haltiwanger (1992) in particular, but also by others

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

1177

Table 1 OECD unemployment,1974-79 to 1986~90a,b Country

Unemploymentrate 1974-1979

Percent change, 1974-79 to 1986-90

1.5

81.8

Europe Austria Belgium

6.3

41.1

Denmark

5.5

44.7

Finland

4.4

-2.3

France Germany

4.5 3.2

77.8 61.2

Ireland

7.6

75.7

Italy

4.6

51.5

Netherlands

5.1

54.5

Norway

1.8

66.5

Spain

5.3

126.1

Sweden

1.5

12.5

Switzerland

1.0

64.2

United Kingdom

5.1

54.5

6.7

-14.4

Others USA Cmlada

7.2

14.2

Australia

5.0

36.4

Japan

1.9

27.4

a Source: Layard et al. (1991), p. 398. b The table shows the average of annual unemploymentin 1974-1979 and the change in the log of this average from 1974-79 to 1986-90.

since then. Recently Contini et al. (1995) have assembled data on job reallocation for several countries. Their summary Table is shown in Table 2 and the results are also summarized in Figure 3. For most countries the job flow data are calculated from establishment level flows, though for some only firm-level data were available. Annual gross job creation reflects employment change only in the establishments or firms that are new entrants or that have experienced an increase in employment over the period. The job creation rate is defined as the sum o f the gross increase in employment expressed as a percentage of the total labor force. Similarly, gross job destruction includes only units that have experienced a decrease in employment and the j o b destruction rate is equal to the gross decrease in employment as a percentage of the employment level. By definition

1178

D.T. Mortensen and C.A. Pissarides

Table 2 Net and gross job flows, OECD, late 1980sa Country

Period

Japan UK Germany Finland Italy USA Canada France Sweden Denmark New Zealand

1985-1992 1985-1991 1983-1990 1986-1990 1984-1993 1984-1991 1983-1991 1984-1992 1985-1992 1983-1989 1987-1992

Job creation 8.64 8.70 9.00 10.40 11.90 13.00 14.50 13.90 14.50 16.00 15.70

Job destruction Net job creation 5.26 6.60 7.50 12.00 11.09 10.40 11.90 13.20 14.60 13.80 19.80

3.39 2.10 1.50 - 1.60 0.81 2.60 2.60 0.70 -0.10 2.20 -4.10

Gross reallocation 13.89 15.30 16.50 22.40 22.99 23.40 26.40 27.10 29.10 29.80 35.50

a Source: Contini et al. (1995), Table 3.1 [derived mainly from OECD Employment Outlook (1987, 1994)].

then, the net growth rate in employment is the difference between the job creation rate and the job destruction rate. International comparisons of data of this kind are fraught with difficulties and Contini et al. (1995, p. 18) warn that the numbers for Japan and the United Kingdom are probably understated and for France and New Zealand are overstated. So if anything, the small differences shown in Table 2 are likely to be overstated. Notwithstanding the statistical problems, the results show that Japan has low gross job creation and job destruction rates, despite high net job creation. The United Kingdom and Germany, also with positive net job creation, have low gross flows. But the rest of the countries have high gross job flows, comparable to those of the USA. There does not seem to be any relation between the volume of gross reallocation and the net employment change, and the USA does not appear unusually turbulent when compared to other countries. These findings are also illustrated in Figure 3. Some regularities emerge from the international comparison of job creation and job destruction rates. These findings apply to comparisons of economy-wide job creation and job destruction flows but are also consistent with the more detailed analysis of Davis et al. (1996) for US manufacturing flows. First, the flow data always exclude the public sector, where job reallocation is small. In some European countries the public sector employs a large fraction of the labor force (8% in Japan, 8.5% in the USA, 7.9% in Germany, 11% in the UK, 22.5% in Italy; the highest share in the European Union is in Denmark, 31%).

1179

Ch. 18. Job Reallocation, Employment Fluctuations and Unemployment

25

20

O

15

CA USA

i<

10 UK +GE//~ +FI / 5

1~0

15 ' 20, Job destruction rate (%)

25

Fig. 3. Job creation and job destructionrates, late 1980s, 11 countries.

Second, gross job reallocation is inversely correlated with capital intensity: service jobs create and destroy more jobs than manufacturing does. Third, smaller and younger establishments create and destroy more jobs than larger and older plants; about one-third of job creation and job destruction is due to plant entry and exit. So in international comparisons countries with a larger fraction of smaller firms (e.g. Italy) are likely to have a larger job reallocation rate than countries with larger firms (e.g. the USA). Fourth, at the individual level, the main cause of job turnover is idiosyncratic shocks, i.e. shocks that do not appear correlated with common economy-wide or sector-specific shocks, or with other common characteristics across firms. The implication of this fact is that the regularities listed above, as well as the business cycle, explain less than half the variance of gross job creation and job destruction across production units. Aggregate and cyclical shocks explain a small fraction of the variance, about 10 percent. Measurable firm characteristics, such as size and age, explain more, but still less than half. Fifth, although younger plants are more likely to create and destroy jobs, there is large persistence in job creation and job destruction. The idiosyncratic shocks that cause job reallocation do not reverse shortly after they occur. In both the USA and Italy (the only two countries with comparable data on this issue), about 70 percent of

1180

D.T. Mortensen and C.A. Pissarides

jobs created in one year are still active the next year and about 55 percent are active two years later. Persistence rates for job destruction are slightly higher. The cyclical properties of job flows, which is of primary concern in the analysis of employment fluctuations, are not clear-cut in the empirical data so far assembled. A fact that seems to be universal is that job creation and job destruction flows are negatively correlated with each other. Thus, recessions are times when job destruction rates rise and job creation rates fall, and vice versa for expansions. More controversial, but potentially more interesting, is the finding that job destruction is more "volatile", in the sense that even when abstracting from growth, the length of time when job destruction is the dominant flow is shorter than the length of time when job creation is the dominant flow. Since on average over the cycle job destruction and job creation rates must be equal, it follows that job destruction rates must peak at higher values than job creation rates, which are more flat. This asymmetry is consistent with the observation that recessions are on average of shorter duration than booms and has attracted a lot of attention in the empirical literature, where, following Davis and Haltiwanger (1990), it is often reported as a negative correlation between gross job reallocation and net job reallocation. However, the negative correlation, although a strong feature of the US manufacturing data, is not universal. The "asymmetry" of job creation and job destruction rates here is simply taken to mean that the difference between job destruction and job creation when positive is larger and of shorter duration than when it is negative. One final observation on the international comparison of job flows is of interest. There does not appear to be a significant correlation across countries either between the level of unemployment on the one hand and the gross job reallocation rate on the other or between labor productivity growth and the job reallocation rate. There does seem, however, to be a correlation between the gross job reallocation rate and the rate of long-term unemployment: countries with lower job reallocation rates seem to have, on average, longer unemployment durations [Garibaldi et al. 1997)]. Comparative data on worker flows are even less reliable than comparative data on job flows, even though the definition of worker flows can be a lot less ambiguous than the definition of job flows. The gross flow of workers in and out of employment, defined analogously to the gross flow of jobs, is necessarily larger than the job flow. The difference is, however, large. Contini et al. (1995, p. 108) report that in both the USA and the major European economies, the worker flow is about three times as big as the job flow. There is some evidence that worker flows are bigger for the USA than for the European countries or Japan, and also that in the USA there is more movement in and out o f unemployment and the labor force. The latter claim, however, may be based on the different kind of question that is often asked about participation in national surveys. Two interesting aggregate facts that have emerged from the study of worker flows, bearing in mind the paucity of the data, are that gross unemployment flows rise in recession and fall in the boom, whereas flows into employment are strongly procyclical and separations mildly pro-cyclical or neutral. Of course, because the stock of unemployment rises in recession as well, the average rate at which workers leave

1181

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment 2.5

CA +

USA

+

O

2.0 H+

I

DE+

0

1.5

Austria

0

NO +

AU+ +NZ

1.0

UK +

PO +

SW +

~D

o

GE + SP+ IT+

0.5

IR+~

GR +

SWI BE+ +

+JA

+

NE 0.0

I-

0

I

I

I

10 20 30 40 Outflow rate (outflows/unemployment)

50

Fig. 4. Unemploymentinflowand outflowrates, 1992.

unemployment goes down, even though the gross number of exits goes up. The finding about employment flows is explained by the fact that in the boom job creation is up and voluntary job-to-job quits are also up, leading to more inflows; whereas in recession quits are sufficiently down but job destruction up giving rise to conflicting influences on separations. Still, substantial systematic cross-country differences between unemployment inflow and outflow rates do exist, reflecting underlying differences in unemployment incidence and duration between Europe and the USA. In Figure 4, borrowed from Martin (1994), inflow-outflow rate combinations in 1992 are plotted for the OECD countries. These plots show that although the average length of unemployment spells (the inverse of the outflow rate) is much longer in the typical EU country than in the USA, the probability of job loss (to the extent reflected by the inflow rate) is much smaller. Hence, long spells of unemployment rather than more frequent spells is the reason for higher unemployment in the EU relative to the USA. The contrasting experience of unemployment in the USA and Europe is reflected in contrasting experience in wage growth. The fall in US real earnings at the bottom end of the wage distribution, in contrast to growth in Europe, has been documented by many writers and by the OECD in its official publications [see, e.g. OECD (1994), Chapter 5]. We show in our Figure 5 a feature of wage and unemployment behavior

1182

D.T. Mortensen and C.A. Pissarides

100 /-x

80

~ F R

NO

60 +

©

IT 40

UK

~ . AU +

.=~

+

JA

20

\--~ CA SW+ \ USA

-20 -20

-10

0

10

20

\

+

30

Increase in inequality (%) Fig. 5. Rise in unemploymentand wage inequality (late 1970s to late 1980s).

that should be explainable within the search and matching framework, though to our knowledge there are as yet no models that claim to explain it fully. We make an attempt to explain it in Section 5.1 [see also Mortensen and Pissarides [1999)]. Thus, for twelve OECD countries with comparable data on wage inequality, there appears to be a close correlation between the percentage change in wage inequality during the 1980s and the percentage rise in unemployment. Wage inequality is measured by the ratio of the earnings of the most educated group in the population to the least educated [usually, university graduates versus early school leavers; see OECD (1994), p. 160-1). Other measures of inequality, however, give similar results [e.g. OECD (1994), p. 3; the results in Galbraith (1996), are also consistent with our claim, despite his claim to the contrary, if one measures the change in inequality by the change in the Gini coefficient of the wage distribution]. Figure 5 shows that the USA, Canada and Sweden experienced the biggest rises in inequality and the smaller rises in unemployment (fall in the USA). Japan and Australia come next, with moderate rises in both, and the European countries follow, with small rises or falls in inequality but big rises in unemployment. The only country that does not conform to this rule is the United Kingdom, which experienced NorthAmerican style increase in inequality and European-style increase in unemployment over the sample of the chart. Recently, however, unemployment in the UK has fallen substantially, giving support to the view that the reforms of the 1980s moved the United

Ch. 18: Job Reallocation, EmploymentFluctuations and Unemployment

1183

Kingdom closer to a US style economy but had their impact first on inequality and only more recently on unemployment.

2. The equilibrium rate of unemployment Here we introduce the formalities of the search and matching approach and derive the equations that express the dynamics of the stock o f unemployment (or employment). This analysis will point to the variables that need to be explained in order to arrive at an equilibrium characterization of employment flows and unemployment levels. We shall talk explicitly about unemployment, with the solution for employment implied by the assumption of an exogenous labor force. The search and matching approach to aggregate labor market analysis is based on Pissarides' (1990) model of equilibrium unemployment as extended by Mortensen and Pissarides (1994) to allow for job destruction. The approach interprets unemployment as the consequence of the need to reallocate workers across activities and the fact that the process takes time. The model is founded on two constructs, a matching function that characterizes the search and recruiting process by which new job-worker matches are created and an idiosyncratic productivity shock that captures the reason for resource reallocation across alternative activities. Given these concepts, decisions about the creation of new jobs, about recruiting and search effort, and about the conditions that induce job-worker separations can be formalized 1. The job-worker matching process is similar to a production process, in which "employment" is produced as an intermediary production input. The output, the flow of new matches, is produced with search and recruiting efforts supplied by workers and employers respectively. As a simple description, the existence of a market matching function is invoked, an aggregate relation between matching output and the inputs. Under the simplifying assumption that all employers with a vacancy recruit with equal intensity and that only unemployed workers search, also at a given intensity, aggregate matching inputs can be represented simply by the numbers of job vacancies v and of unemployed workers u. Let the function m(v, u) represent the matching rate associated with every possible vacancy and unemployment pair. As in production theory, it is reasonable to suppose

t Of course, that at least some unemploymentis due to "frictional" factors has alwaysbeen recognized. Lilien (1982) was among the first to claim that even "cyclical"unemploymentwas of this kind. Although his results have been criticized, e.g. by Abraham and Katz (1986) and Blanchard and Diamond (1989), the modern approach to unemploymentgroups all kinds of unemploymentinto one, as we do here.

D.T. Mortensen and C.A. Pissarides

1184

that this function is increasing in both arguments but exhibits decreasing marginal products to each input. Constant returns, in the sense that

m(v,u)=m

(u) 1,-~ v = q(O) v

where

0-

O U

,

(2.1)

is a convenient additional assumption, one that is consistent with available evidence 2. The ratio of vacancies to unemployment, 0, market tightness, is an endogenous variable to be determined. On average, a job is filled by a worker at the rate re(o, u)/v = q(O) and workers find jobs at rate m(v, u)/u = Oq(O). By the assumption of a constant returns matching function, q(O) is decreasing and Oq(O) increasing in 0. Oq(O) represents what labor economists call the unemployment spell duration hazard 3. The duration of unemployment spells is a random exponential variable with expectation equal to the inverse o f the hazard, 1/Oq (0), a decreasing function of market tightness. Analogously, q(O) is the vacancy duration hazard and its inverse, 1/q(O) is the mean duration of vacancies. As noted above, the most important source of job-worker separations is job destruction attributable to an idiosyncratic shock to match productivity. Because initial decisions regarding location, technology, and/or product line choices embodied in a particular match are irreversible, subsequent innovations and taste changes, not known with certainty at the time of match formation, shock the market value of the product or service provided. For example, the initial decision might involve the choice o f locating a productive activity on one of many "islands". In future, island-specific conditions that affect total match productivity, say the weather, may change. If the news about future profitability implicit in the shock is bad enough, then continuation of the activity on that particular island is no longer profitable. In this case, the worker loses the job. To model this idea, we assume that the productivity of each job is the mathematical product of two components, p, which is common to all jobs, and x, which is idiosyncratic. The idiosyncratic component takes values in the range [0, 1], it is distributed according to the c.d.f. F(x) and new shocks arrive at the Poisson rate Z. Note that these assumptions satisfy the empirical properties of idiosyncratic job destruction, i.e. the shocks have persistence and they appear to hit the job independently of the aggregate state of the economy (here represented by p). Entrepreneurs are unconstrained with respect to initial location, technology and product choice and also have the same information about market conditions. Under the assumption that they know the product that commands the highest productivity, all will create jobs at the highest idiosyncratic productivity, x = 1. Given this property

2 See Pissarides (1986) and Blanchard and Diamond (1989). 3 As workers are generally happy when an unemployment spell ends, the unemploymenthazard seems an ironic label. This unfortunate term is borrowed from statistical duration analysis where the typical spell is that of a "life" that ends as a consequence of some "hazard", e.g. a heart attack or a failure.

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

1185

of the model and the assumption that future match product evolves according to a Markov process with persistence, all matches are equally productive initially, until a shock arrives 4. Under these assumptions, an existing match starts life with x = 1 but is eventually destroyed when a new value of x arrives below some reservation threshold, another endogenous variable denoted as R. Unemployment incidence 3.F(R), the average rate of transition from employment to unemployment, increases with the reservation threshold. As all workers are assumed to participate, the unemployed fraction evolves over time in response to the difference between the flow of workers who transit from employment to unemployment and the flow that transits in the opposite direction, i.e., /t = AF(R)(1 - u) - Oq(O) u,

(2.2)

where 1 - u represents both employment and the employment rate. The steady-state equilibrium unemployment rate is u=

)tF(R) )~F(R) + Oq(O)"

(2.3)

Equivalently, individual unemployment histories are described by a simple two-state Markov chain where the steady-state unemployment rate is also the fraction of time over the long run that the representative participant spends unemployed. It decreases with market tightness and increases with the reservation product, because the unemployment hazard Oq(O) and the employment hazard )~F(R) are both increasing functions. 2.1. Job destruction and j o b creation conditions

A formal equilibrium model of unemployment requires specification of preferences, expectations, and a wage determination mechanism. We assume that both workers and employers maximize wealth, defined as the expected present value o f future net income streams conditional on current information. Forward looking rational expectations are imposed. Several wage determination mechanisms are consistent with the matching approach. Following much of the literature, we shall assume bilateral bargaining as the baseline model. Given this specification, equilibrium market tightness satisfies the following job creation condition: the expected present value of the future return to hiring a worker equals the expected cost. The hiring decision is implicit in the act of posting a

4 Generalizing the model to realistically allow for productivity heterogeneity across vacancies and for the fact that a random sample of new job-worker matches initially improve in average productivity are still problems at the research frontier.

1186

D. 17 Mortensen and C.A. Pissarides

job vacancy and is taken by an employer. In contrast, the equilibrium reservation product, R, reflects the decisions o f both parties to continue an existing employment relationship. Individual rationality implies that separation occurs when the forwardlooking capital value o f continuing the match to either party is less than the capital value o f separation. For joint rationality, the sum o f the values o f continuing the match must be less than the sum o f the values o f separating, otherwise a redistribution o f the pair's future incomes can make both better off. Whether these job destruction conditions also satisfy the requirements o f joint optimality depends' on the wage mechanism assumed. For a given wage determination mechanism, a search equilibrium is a pair (R, 0) that simultaneously solves these job creation and job destruction conditions. For expositional purposes, we invoke the existence o f a wage mechanism general enough to accommodate the special cases o f interest. A wage contract, formally a pair (w0, w(x)), is composed o f a starting wage w0 E Re and a continuing wage function w : X --+ Re that obtains after any future shock to match specific productivity. Implicit in this specification is the idea that a worker and an employer negotiate an initial wage when they meet and then subsequently renegotiate in response to new information about the future value o f their match 5. A continuing match has specific productivity x and the worker is paid a wage w(x). Given that the match ends in the future if a new match specific shock z arrives which is less than some reservation threshold R, its capital value to an employer, J ( x ) , solves the following asset pricing equation r J ( x ) = p x - w(x) + ~

JR 1[J(z) -

J(x)] dF(z) + )~F(R)[ V - p T - d(x)],

(2.4)

where r represents the risk free interest rate, V is the value of a vacancy, a n d p T denotes a firing cost borne by the employer, represented as forgone output. We multiply the termination cost by p to show that it is generally more expensive to fire a more skilled worker than a less skilled one. The termination cost is assumed to be a pure tax and not a transfer payment to the worker and to be policy-determined. For example, it may represent the administrative cost o f applying for permission to fire, as is the case in many European countries. O f course, T ~> 0 and none o f the fundamental results are due to a strictly positive T. Condition (2.4), that the return on the capital value of an existing job-worker match to the employer is equal to current profit plus the expected capital gain or loss associated with the possible arrival of a productivity shock, is a continuous-time

5 Note that contracts of this form are instantly "renegotiated" on the arrival of a new idiosyncratic shock. MacLeod and Malcomson (1993) persuasively argue that the initial wage need not be adjusted until an event occurs that would otherwise yield an inefficient separation. Contracts of this form may well generate more realistic wage dynamics but job creation and job destruction decisions are the same under theirs and our specification. Hence, for the purpose at hand, there is no relevant difference.

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

1187

Bellman equation. A n analogous relationship implicitly defines the asset value o f the same match to the worker involved, W ( x ) . Namely, r W ( x ) = w ( x ) + ;~

fR [W(z) -

W(x)] dF(z) + , ~ F ( R ) [ U - W(x)],

(2.5)

where U is the capital value of unemployment. Given a match product shock z, the employer prefers separation if and only if its value V exceeds the value of continuation J (z). Similarly, the worker will opt for maemployment if and only if its value, U, exceeds W (z). Given that both J (z) and W (z) are increasing, separation occurs when a new value o f the shock arrives that falls below the reservation threshold R = max {Re, R w } ,

(2.6)

where J(Re) = V - p T and W ( R w ) = U. Because in the bilateral bargain wealth is transferable between worker and employer, the separation rule should be jointly optimal in the sense that it maximizes their total wealth. The necessary and sufficient condition for joint optimization is that R = Re = Rw where J ( R ) + W ( R ) = V - p T + U, a condition that holds only for an appropriately designed wage contract 6. Although the idiosyncratic component of a new job match is x = 1, the expected profit from a new match will generally be different from J(1), as defined in Equation (2.4), because o f the existence of a job creation cost. We therefore introduce the notation J0 for the expected profit o f a new match to the employer and write the asset pricing equation for the present value o f an unfilled vacancy, V, as r V = - p c + q( O)[Jo - V - p C ] ,

(2.7)

where p c is the recruiting cost flow per vacancy held, and p C is a fixed cost of hiring and training a new worker plus any other match-specific investment required. Here these costs are indexed by the aggregate productivity parameter to reflect the fact that the forgone output that these costs represent is larger when labor is more productive. The value of unemployment solves r U = b + Oq(O)[Wo - U],

(2.8)

where b represents unemployment-contingent income. Crucially for many o f the results that hold in matching equilibrium, unemployment-contingent income is independent o f employment income or o f the aggregate state o f the economy.

6 See Mortensen (1978) for an early analysis of this issue within the search equilibrium framework. For alternative approaches to the modeling of the job destruction flow, see Bertola and Caballero (1994), who model a firm with many employees moving between a high-employment and a low-employment state, and Caballero and Hammour (1994), who analyze the implications of sunk costs and appropriation.

1188

D.T. Mortensen and C.A. Pissarides

Given an initial wage equal to wo, the by now familiar asset pricing relations imply that the initial value o f a match to employer and worker respectively satisfy

// //

rJo = p - Wo + )~

and rWo = w0+,~

[J(z) - J0] d F ( z ) + )dZ(R)[ V - p T - J0l

[ W ( z ) - W0] d F ( z ) + ) ~ F ( R ) [ U - W0],

(2.9)

(2.10)

where J ( x ) and W(x) represent the values o f m a t c h continuation defined above. The j o b creation condition that we defined earlier is equivalent to a free entry condition for new vacancies. The exploitation o f all profitable opportunities from j o b creation requires that new vacancies are created until the capital value o f holding one open is driven to zero, i.e., V=0

e

¢:~ ~ + C qtv)

Jo

.

(2.11)

P

As the expected number o f periods required to fill a vacancy is 1/q(O), the condition equates the cost o f recruiting and hiring a worker to the anticipated discounted future profit stream. The fact that vacancy duration is increasing in market tightness guarantees that free entry will act to equate the two. 2.2. Generalized Nash bargaining

The generalized axiomatic Nash bilateral bargaining outcome with "threat point" equal to the option o f looking for an alternative match partner is the baseline wage specification assumption found in the literature on search equilibrium 7. Given that the existence o f market friction creates quasi-rents for any matched pair, bilateral bargaining after worker and employer meet is the natural starting point for an analysis 8.

7 See Diamond (1982b), Mortensen (1978, 1982a,b), and Pissarides (1985, 1990). s Binmore, Rubinstein and Wotinsky (1986), Rubinstein and Wolinsky (1985) and Wolinsky (1987) applied Rubinstein's strategic model in the search equilibrium framework. The analyses in these papers imply the following: If the worker searches and the employer recruits at the same intensities and if /3 is interpreted as the probability that the worker makes the wage demand (1 -/3 is the probability that the employer makes an offer) in each round of the bargaining, then the unique Markov perfect solution to the strategic wage bargaining is the assumed generalized Nash solution. If neither searches but there is a positive probability of an exogenous job destruction shock during negotiations, the solution is again the one assumed but with/3 = ½. However, if neither seeks an alternative partner while bargaining and there is zero probability of job destruction, the strategic solution divides the joint product of the match Jo - p C + Wo subject to the constraint that both receive at least the option value of searching and recruiting, U and V, rather than the net surplus, as we assumed. As these bargaining outcomes generate the same job creation and job destruction decisions, we consider only the former case with a /3 between 0 and 1.

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

1189

Given the notation introduced above, the starting wage determined by the generalized Nash bargain over the future joint income stream foreseen by worker and employer supports the outcome wo = arg max {[Wo - U]/3 [So -(Wo - U)] l-is } subject to the following definition of initial match surplus, So =- J o - p C -

(2.12)

V + Wo- U

In the language of axiomatic bargaining theory the parameter/3 represents the worker's relative "bargaining power." Analogously, the continuing wage contract supports the outcome w(x) = arg max { [ W ( x ) - U] t~ [S(x) - (W(x) - U)] l-Is},

where continuing match surplus is defined by S(x) = W ( x ) - U + J ( x ) -

(2.13)

V +pT.

The difference between the initial wage bargain and subsequent renegotiation arises for two reasons. First, hiring costs are "sunk" in the latter case but "on-the-table" in the former. Second, termination costs are not incurred if no match is formed initially but must be paid if an existing match is destroyed. The solution to these two different optimization problems satisfy the following firstorder conditions /3(Jo - V - p C )

= (1 - / 3 ) (w0 - u ) ~

w0 - u =/3SO

(2.14)

and /3(J(x) - V + p T ) = (1 - / 3 ) ( W ( x ) - U) ¢~ W ( x ) -

U =/3S(x).

(2.15)

As an immediate consequence of Equation (2.15), it follows that the reservation threshold R, defined by Equation (2.6) is jointly rational, i.e., it solves S ( R ) = J ( R ) - V + p T + W ( R ) - U = O.

As a preliminary step in solving for the match surplus function and the continuing wage contract that supports the bargaining solution, first rewrite Equations (2.4) and (2.5) as follows: (r + )0 (J(x) - V + p T ) = p x - w(x) - r ( V - p T ) 1

+ 2, ~ [J(z) - V + p T ] dE(z)

(2.16)

1190

D.T. Mortensen and C.A. Pissarides

and i" 1

(r + )0 (W(x) - U) = w(x) - r U + )~ JR [W(z) - U] dF(z).

(2. 17)

By summing these equations, one obtains the following functional equation which the surplus function must solve S(x)

p x - r ( U + V - p T ) + 3. f l S(z) dF(z)

(2.18)

r+J,

Because S(R) = 0 implies f~ S ( z ) d F ( z ) = f max(S(z), 0)dF(z), the right-hand side satisfies the Blackwell sufficient conditions for a contraction. Furthermore, the solution is linear in x. Hence, the solution can be written as S(x) = (x - R)/(r + )0 where R is the unique solution to pR+

~

p

(2.19)

(z-R)dF(z)=r(U+V-pT).

The reservation product, pR, plus the option value of continuing the match attributable to the possibility that match product will increase in the future, the left-hand side, equals the flow value of continuation to the pair, the right-hand side of the equation. As the left- and right-hand sides of Equation (2.16) multiplied by 1 -/3 respectively equal the left- and right-hand sides of Equation (2.17) when multiplied by /3 given (2.15), the continuing match product specific wage that supports the bargaining outcome is (2.20)

w(x) = rU +/3 [px - r(V - p T ) - rU].

Note that this result is the generalized Nash outcome in a continuous bargain over match output px given a "threat point" equal to the flow values of continuing the match, namely (r(V - p T ) , rU). Analogously, by summing equations (2.9) and (2.10), one obtains (r + )OSo = (r + X ) ( J o - V - p C + = p-r(U

Wo - U)

+ V)-(r + X)pC-lpT

+ ,~

S(z)dF(z)

(2.21)

= p(1 - R) - (r + )Op(C + T) = (r + X) (S(x) - p C - p T ) by virtue of Equations (2.12) and (2.19). Hence, the free entry conditions (2.11) and the initial surplus division rule (2.14) yield the following equilibrium relationship between market tightness and the reservation product: p c _ Jo - p C = (1 -/3) So q(O) = (1-[3)p(lrm+R-c-T).

(2.22)

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

1191

The logic of the derivation of the initial wage is similar to that used to obtain the continuing wage function. First, rewrite Equations (2.9) and (2.10) as (r + ~) (Jo - V - p C )

= p - wo - r V - (r + ) t ) p C - )tpT

+ 3,

[J(z) - V + p T ] dE(z)

and ( r + ) O ( W o - U) = wo - r U + ) ~

JR1[W(z)-

U] dF(z).

Second, multiply both sides of the first equation by 1 -/3, both sides of the second by /3, and then apply Equations (2.14) and (2.15) to obtain wo = r U +/3 [p - r ( V + U) - (r + ) O p C - )~pT].

(2.23)

Note that the initial wage equals the worker's share of the initial match flow surplus p - r ( V + U + p C ) less the sum of hiring and firing costs amortized over the initial period prior to the arrival of a subsequent match specific shock ){p(C + T). In short,

the worker share of both the quasi-rents and match specific investments required to both create and end the match is the market power parameter/3. To complete the derivation of the equilibrium conditions, we use the fact that the free entry condition (2.22), the surplus sharing rule (2.14), and the value of unemployment equation (2.8) imply that the flow value of unemployment is linear and increasing in market tightness. rU=b+/3Oq(O)So=b+(P--~/3)O.

By direct substitution into Equations (2.23) and (2.20), the equilibrium wage contract can be written as w0 =/3p [1 + cO - (r + )0 C - )~T] + (1 -/3) b

(2.24)

w(x) =/3p (x + cO + r T ) + (1 -/3) b.

(2.25)

and

Finally, the reservation threshold equation (2.19) becomes p

+ ~

(x-R)dF(x)

= r(g-pT)

(2.26) =b-rpT+(lfi~fi)pcO.

As the left-hand side is increasing in R, the equation implicitly defines a positive equilibrium relationship between the reservation product and market tightness, one that reflects the pressure on wages induced by greater market tightness.

1192 R

R*

D.T Mortensen and C.A. Pissarides

> C

~

D

D O*

0

Fig. 6. Equilibrium reservation product and market tightness

(R*, 0").

An equilibrium solution is any pair (R*, 0") that solves the job creation condition (2.22) and the job destruction condition (2.26). The associated starting wage w0, continuing wage function w(x), and steady-state unemployment rate u are those specified in Equations (2.24), (2.25), and (2.3). Because the relation defined by the job creation condition (2.22) is downward sloping, as illustrated by the line CC in Figure 6, while the job destruction condition (2.26) can be represented as the upward sloping line DD, there is a single equilibrium solution to the two equations 9. The equilibrium pair is strictly positive if the product of a new match, p, less the opportunity cost of employment, b, is sufficient to cover recruiting, hiring, and anticipated firing costs. 2.3. Fundamental determinants o f unemployment

Figure 6 provides insight into how the various parameters of the model affect the steady-state unemployment rate. For this purpose, it is useful to remember that the job creation line CC reflects the standard dynamic demand requirement that the cost of hiring and training a worker is equal to the expected present value of the future profit attributable to that worker over the life of the job. It is downward sloping because a higher reservation threshold implies a shorter expected life for any new match. The upward slope of the job destruction line DD reflects the sensitivity of the reservation product threshold to general wage pressure as reflected by market tightness. Now it is clear from Equation (2.22) that given R neither p nor b influence equilibrium 0. Thus, general productivity and the supply price of labor do not shift CC. By dividing Equation (2.26) byp, we find that b andp enter the equilibrium conditions as a ratio b/p. Hence, the influence of general productivity and the opportunity cost of employment is due entirely to the fact that the latter is independent of the former. If for whatever reason the opportunity cost of employment b was proportional to general productivity [as in the long-run equilibrium model of Phelps (1994), through wealth

9 Note in passing that the equilibrium pair is stationary even out of steady state because there is no feedback from currentemploymentto expectationsabout future match output. This fact is an implication of the linear specificationof both agent preferences and productiontechnologyand of the absence of memory in the idiosyncraticshock process. A change in any one of these specificationassumptions substantially complicatesbut enriches the model.

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

1193

accumulation], general productivity changes would not influence the equilibrium rate of unemployment. Given our specification and the interpretation of the two lines in Figure 6, an increase in the supply price of labor, b, or a fall in general productivity p, shifts the D D line up but has no direct effect on CC. As a consequence, the equilibrium value of the reservation threshold increases and the equilibrium value of market tightness falls with b/p. Hence, steady-state unemployment increases because both unemployment duration and incidence increase in response. The other parameters of the model have more complicated effects on equilibrium unemployment and at the analytical level we can only derive unambiguous results for unemployment duration and incidence, but not for the stock of unemployment. Inspection of equations (2.22) and (2.26) shows that the only other parameter that shifts only one of the lines is the job creation cost C. An increase in C shifts C C to the left and so implies lower R and 0: unemployment duration rises but incidence falls. The intuition behind the result is that higher job creation costs reduce job creation, increasing the duration of unemployment, but also reduce job destruction, to economize on the job creation costs that are incurred if the firm is to re-enter the market. The effect on unemployment is ambiguous. A similar ambiguity arises from changes in job termination costs. Higher T shifts the CC line to the left and the D D line to the right. Although the effect on 0 appears ambiguous, a formal differentiation of the equilibrium conditions yields a negative net effect on both R and 0. Once again, job destruction falls, because it is now more expensive to fire workers, implying less unemployment incidence. Job creation falls because over its lifetime the job will pay the termination cost with probability 1, implying a longer duration of unemployment. Other parameters of the model have even more complicated effects on unemployment duration and incidence. The rate of discount, r, and the rate of arrival of shocks, )~, both shift the job creation line down, because, in the case of r, future product is discounted more heavily and in the case of ;~, the expected life of the job falls. But the job destruction line also shifts. Differentiation of the two equilibrium conditions shows that both r and X reduce market tightness, and so increase the duration o f unemployment. The arrival rate of idiosyncratic shocks also reduces the reservation threshold, reducing the incidence of unemployment but the rate of discount has ambiguous effects on the threshold. Finally, an increase in the worker's share of match surplus as reflected in an increase in the "market power" parameter/3 shift CC downward but D D upward in Figure 6. The result is a negative effect on equilibrium market tightness but the sign of the resultant change in the reservation product is indeterminate. Differentiation of the equilibrium conditions shows that the effect of/3 on R has the sign of/3 - t/, where t/is the elasticity of the matching function with respect to unemployment. Interestingly, if/3 = t/ the search externalities are internalized by the wage bargain, and it is a useful benchmark case in simulations with search equilibrium models [Hosios (1990), Pissarides (1990)].

1194

D.T. Mortensen and C.A. Pissarides

3. Employment fluctuations The negative co-movement between aggregate measures of vacancies and unemployment, known as the Beveridge curve, has long been an empirical regularity of interest in the literature on labor market dynamics 10. Generally, high vacancies and low levels of unemployment characterize a "tight" labor market in which workers find jobs quickly and higher wage rates prevail. Time-series observations suggest that job vacancy movements lead unemployment changes both in the sense that drops ~n job vacancy rates herald downturns in employment and that employment recoveries follow jumps in vacancies. These observations also suggest that fluctuations in derived demand for labor, as reflected in vacancy movements, rather than labor supply shocks are the principal driving force behind cyclical unemployment dynamics. The empirical work of Davis and Haltiwanger (1990, 1992) and Davis, Haltiwanger and Schuh (1996) has stimulated general interest in the components & n e t employment change, which they call job creation and job destruction flows. As we saw in Section 1, the job creation and job destruction rates move in opposite directions over the business cycle but are always both large and positive at every level of industry and regional disaggregation. These facts suggest that employment reallocation across economic activities is a significant and continual process that accounts for a large measure of unemployment. Mortensen and Pissarides (1994), Mortensen (1994b), Cole and Rogerson (1996), and den Haan, Ramey and Watson (1997) claim that an extended version of the equilibriurn unemployment model, one that allows for an aggregate shock to labor productivity, can explain the stylized facts of the job creation and job destruction flows that we listed in Section 1. To recall, apart from the negative correlation between them just noted, job destruction is more volatile than job creation (which, at least for US manufacturing, shows up as negative correlation between the sum and difference of the job creation and job destruction flows) and quit rates are procyclical, i.e. there is a positive correlation between quit rates and the difference between job creation and job destruction. The purpose of this section is to present a version of the model that allows for employment fluctuations which can be used to illustrate these claims. 3.1. Stochastic equilibrium

The source of the underlying job reallocation process in the Mortensen-Pissarides model is an idiosyncratic shock which acts as match-specific "news" in the sense that it changes the profit prospect for an individual job on arrival. A general aggregate productivity shock which affects the output of every job by the same proportion is added here. Specifically, we let exogenous jumps in the common component of job

l0 For an interesting early treatment, see Hansen (1970). For more recent search-based analyses, see Pissarides (1986) and Blanchard and Diamond (1989).

Ch. 18: Job Reallocation, EmploymentFluctuations and Unemployment

1195

productivity p induce the cycle. On the argument that recruiting and hiring costs represent forgone output, we continue assuming as well that these costs are indexed by the productivity parameter p. According to real business cycle theory, economic fluctuations are induced by exogenous persistent shocks to aggregate labor productivity 11. Whether exogenous technical change is the cause or not, labor productivity is procyclical in fact and our model's implications for wage and employment responses are an implication of that fact whatever its cause. Given sufficient persistence, one would expect these shocks to induce cyclical effects on the market tightness and the reservation idiosyncratic product which are similar to those associated with a permanent change in the level of aggregate productivity. For the sake of a simple presentation, assume that aggregate productivity fluctuates between a high value Ph and a low value Pl, where the continuous time transition rate or frequency is t/. For this specification, the autocorrelation coefficient of the p-process given a short time interval of length A is 2e -r/a - 1. Indeed,

E{p(t + A) [p(t) =Pi} = e-~APi + (1 - e -hA) pj = (2e -~a - 1)pi + 2 (1 - e -*/a) E{p}, where 1 - e ,a is the probability of a change in state during the interval (t, t + A), and E { p } = (Ph +pt)/2 is the ergodic mean of this symmetric Markov chain. In the case of permanent aggregate productivity, i.e., ~/= 0, the equilibrium pair in state i, (Ri, Oi), solves Equations (2.22) and (2.26) given p = Pi. Consequently, Ph > Pt implies Oh > 0l and Rt < Rh in this case. This fact generalizes but only if the aggregate shock frequency t/is not too large. For ~ > 0, the equilibrium relationships are more complicated because forward looking agents knowing themselves to be in state i anticipate the effects and likelihood of transiting to statej in the future. Indeed, under generalized Nash bargaining in which the initial wage is set contingent on the aggregate state and the continuing wage is renegotiated in the event of either an aggregate or a match specific shock, the surplus value of a continuing match with idiosyncratic productivity x in aggregate state i, Si(x), and the surplus value of a new match in state i, SOi, satisfy the following generalization of Equations (2.18) and (2.21):

rSi(x) = p i x - r ( g ; + g i - p i T ) + ,1

['

[Si(z)-Si(x)] dF(x) + t/[Sj(x)- S/(x)],

d Ri

rSo; = p ; x o - r(U~ + Vi - p i T ) - (r + ,l + ~ ) p ; ( C + T )

+,1

[S;(z) - so;] dF(~) + n [SOj - So;], i

(3.1) 11 For example, see Kydland and Prescott (1982) and Lucas (1987).

D.T. Mortensen and C.A. Pissarides

1196

where the aggregate state contingent values o f a vacancy and unemployment solve rVi = q ( O i ) ( l -[~)Soi q- ~ (Vj - Vi) - p i c , rUi = b + Oiq ( Oi) flSoi + 71 ( Uj - Ui) .

(3.2)

An equilibrium now is a state contingent reservation threshold and market tightness pair (Ri, Oi), one for i = 1 and another for i = h, that satisfy the free entry job creation condition and job destruction condition in both states, i.e., V~=0

and

S~(R~)=0,

i E {I,h}.

Market tightness is procyclical and market tightness and the reservation product threshold move in opposite directions in response to aggregate shocks if the shock is sufficiently persistent. Formally, a unique equilibrium exists with the property that Ph > Pl

~

Rh < Rt f o r all ~ while a critical value cc > ~ > 0 exists such that

Oh > (<) 0t a s ~ < ( > ) ~ 12 Aggregate state contingent equilibrium market tightness is actually lower in the higher aggregate product state for sufficiently large values of the shock frequency because investment in job creation is relatively cheaper when productivity is low and because the present value of the retvxns to job creation investments are independent of the current aggregate state in the limit as ~ becomes large. In other words, job creation investment is larger when aggregate productivity is higher only if expected return given high current productivity offsets the cost advantage of investment in the low productivity state, a condition that requires sufficient persistence in the productivity shock. 3.2. The Beveridge curve

As just demonstrated, "boom" and "bust" in this simple model are synonymous with the prevalence of the "high" and "low" average labor productivity when the aggregate shock is persistent. Unemployment dynamics in each aggregate state are determined by the law of motion /t = )~F(R,)(1 - u) - Oiq(Oi) u.

(3.3)

Hence, the unemployment rate tends toward the lower of the two aggregate state contingent values, represented by . )tF(Ri) ui = )~F(Ri) + Oiq(Oi)'

i E {I, h},

(3.4)

during a boom and tends toward the higher value in a bust. 12 Formalderivationsof the value equations, those of(3.1) and (3.2), and proofscan be found in Burdett, Mortensen and Wright (1996).

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

uh Uz

1197

Oh

Oh

Ot

v;

0

- -

L

.2

.7

U

Fig. 7. The Beveridge curve.

The observation that actual vacancies and unemployment time series are negatively correlated is consistent with this model under appropriate conditions, a fact illustrated in Figure 7. In the figure, the two rays from the origin, labeled 0l and Oh, represent the vacancy-unemployment ratios in the two aggregate states when Oh > 0l. The negatively sloped curves represent the locus of points along which there is no change over time in the unemployment rate, one for each of the two states. Because the curve for aggregate state i is defined by vq(v/ui) - - tlF(Ri), 1 - ui Rh < Rl implies that uh < uz for every v as drawn in Figure 7. Finally, the two steadystate vacancy-unemployment pairs lie at the respective intersections of the appropriate curves, labeled L and H in the figure. Provided that the curve along which/l = 0 doesn't shift in too much when aggregate productivity increases, v~ > v~ as well as u~ < u~. However, sufficient persistence, in the form of a low transition frequency, is necessary here. Indeed, the points L and H lie on a common ray when persistence is at the critical value tl = ~ since 0l = Oh by definition. 3.3. Job creation and j o b destruction flows

In our simple model, the notion of a job is equivalent to that of an establishment, plant, or firm given the linear technology assumption. Consequently, the job creation flow, the employment changes summed across all new and expanding plants over a given period of observation, can be associated with the flow of new matches in the model. Analogously, job destruction, the absolute sum o f employment reductions across contracting and dying establishments, is equal to all matches that either experience an idiosyncratic shock that falls below the reservation threshold or were above the

D.T. Mortensen and C.A. Pissarides

1198

threshold last period but are below it this period. The fact that market tightness and the reservation product move in opposite directions in response to an aggregate productivity shock implies negative co-movements in the two series, as observed. Furthermore, a negative productivity shock induces immediate job destruction while a positive shock results in new job creation only with a lag. This property of the model is consistent with the fact that job destruction "spikes" are observed in the job destruction series for US manufacturing which are not matched by job creation "spurts" 13. As in the OECD data, cyclical job destruction at the onset of recession is completed faster than cyclical job creation at the onset of a boom.

3.4. Quits and worker flows As the model is constructed so far, aggregate hires are equivalent to job creation and separations equal job destruction. These identities no longer hold when some employed workers quit to take other jobs without intervening unemployment spells. As these so-called j o b to job flows constitute a significant component of both hires and separations, are procyclical, and represent a worker reallocation process across jobs, their incorporation in the model represents an important extension. Job to job worker flows can be viewed as the outcome of a decision by some workers to search for vacancies while employed, as in Mortensen (1994b). Given that Oq(O) represents the rate at which employed as well as unemployed workers find a vacant job, the quit flow representing job to job movement in aggregate state i E {l, h} is Qi = Oiq(Oi)(1 - ui)si, where s i is the fraction of the employed who search and Oi is now the ratio of vacancies to searching workers, i.e. 0i =

.

1)i

ui +si(1 - ui)" Once employed, workers have an incentive to move from lower to higher paying jobs. Suppose that employed workers can search only at an extra cost, ~, interpreted as foregone leisure, a reduction in b. As search is jointly optimal for the pair if and only if the expected return, equal to the product of the job-finding rate and the gain in

13 These points are discussed in more detail in Mortensen and Pissarides (1994) and Mortensen (1994b).

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

1199

match surplus realized, exceeds the cost, all workers employed at x equal to or less than some critical value, denoted as Qi, will search where 14 Oiq(Oi) [S/(1) - Si (Qi)] = a,

i c {l, h}.

(3.5)

Because idiosyncratic productivity is distributed F ( x ) - F ( R ) across jobs, it follows that the fraction of the employed workers who search in aggregate state i is given by (3.6)

si = F ( Q i ) - F(Ri).

Because a quit represents an employment transition for the worker and the loss of a filled job for the employer, the surplus value equation under joint wealth maximization is rSi(x) = p i x - o - r(Ui + Vi - T) + ~

[Si(z) - Si(x)] dF(x)

+ t/[Sj(x) - S i ( x ) ] + Oiq(Oi)(Si(1)-Si(x))

(3.7)

V x < Qi.

Because the worker does not search when x >7 Qi and this condition always holds when x = 1, Equations (3.1) continue to hold in this range. To the extent that market tightness is procyclical, Equation (3.5) implies Qh > Ql. Hence, the quit flow is procyclical for two separate reasons. First, because Q is higher and R is lower in the high aggregate productivity state, the fraction of employed workers who search is procyclical, i.e., sh > sl. Second, because Oh > 01 when the aggregate shock is sufficiently persistent, the rate at which searching workers meet vacancies Oq(O) is also larger in the high aggregate product state. Worker reallocation across different activities is represented by both the direct movement from one job to another via quits and by movements through unemployment induced by job destruction and subsequent new job creation. Davis, Haltiwanger and Schuh (1996) estimate that between 30% and 50% o f worker reallocation is attributable to the job destruction and creation process. Given the procyclicality of the quit flow and the flow of hires, the sum o f job creation and quits is highly procyclical, while the separation flow, the sum of job destruction and quits, is acyclical. Hence, the reallocation o f workers across activities is procyclical relative to the more countercyclical reallocation of jobs across activities both in fact and according to the model. The quit process also interacts with job creation and job destruction in more complicated ways that are not explicitly modeled here. For example, when a worker

14 Although the decision to maximize the sum of the pair's expected future discounted income by the appropriate choice of the worker's search effort is individually rational under an appropriate contract, both costless monitoring and enforcement of the contract is generally necessary to overcome problems of dynamic inconsistency. Indeed, otherwise the worker will search if and only if the personal gain exceeds cost, i.e., iff W/(1)- W/(x) =/~[Si(1)- Si(x)] > o" which would imply too few quits.

1200

D.T. Mortensen and C.A. Pissarides

quits an existing job to take a new one, the employer can c h o o s e to search for a replacement. If the decision is not to replace the worker, the quit has induced the destruction of a job with no net change in either the number o f jobs or unemployment. I f the decision is to declare the job vacant, a new job was created by the original match but there will be no net reduction.in unemployment unless the old job vacated is filled by an unemployed worker. O f course, if filled by an employed worker, the employer left by that worker must decide whether o r n o t to seek a replacement. This sequential replacement process by which a new vacancy leads to an ever/tual hire from the unemployment pool, known in the literature as a vacancy chain, propagates the effects o f job creation shocks on unemployment [see Contini and Revelli (1997) and Akerlof, Rose and Yellen (1998)]. Also, quit rates are high in the first several months after the formation of new matches and then decline significantly with match tenure, presumably as a consequence o f learning about the initially unknown "quality" o f the fit between worker and job 15. This source o f quits is o f significant magnitude and it represents the primary form o f quits to unemployment. Because this "job shopping" process implies that an unemployed worker typically tries out a sequence o f jobs before finding satisfaction, a job destruction shock is likely to be followed by a drawn-out period o f higher than normal flow into and out o f unemployment 16. Were the job shopping process incorporated in the model, job reallocation shock effects on worker flows would be prolonged and amplified, features that should also improve the model's fit to the data.

4. Explaining the data Besides the attempts to use the models that we have described to match the stylized facts o f job and worker flows 17, there have recently been some attempts to calibrate stochastic versions o f the models to explain the cyclical behavior o f the US economy. These attempts are partly motivated by the emergence o f the new data on job flows that need to be explained and partly by the apparent failure of competitive labor market models to match the business cycle facts in the data. In order to explain the business cycle facts the models need to be extended to include capital, an exercise that has attracted some attention recently 18

15 There is an extensive labor economics literature on this point initiated by the seminal theoretical development by Jovanovic (1979). See Farber (1994) for a recent analysis of the micro-data evidence on tenure effects on quit rates and the extent to which these are explained by the job shopping hypothesis. Pissarides (1994) explains these facts within a search model with learning on the job. J6 Hall (1995) argues that this effect is apparent in the lag relatioships between the time series aggregates. 17 For attempts to estimate structural forms of the matching model see Pissarides (1986) and Yashiv (1997). 18 When used to calibrate the business cycle facts the models are often offered as alternatives and compared with Hansen's (1985) indivisible labor model.

Ch. 18:

J o b Reallocation, E m p l o y m e n t Fluctuations and U n e m p l o y m e n t

1201

4.1. Explaining j o b f l o w s data

Cole and Rogerson (1996) conduct an analysis of the extent to which the rudimentary Mortensen-Pissarides model can explain characteristics of the time series observations on employment and job flows in US manufacturing. For this purpose, they construct the following stylized approximation to the continuous time formulation sketched above: Job creation in period t, ct, is equal to the matches that form during the observation period and survive to its end. As one can ignore the possibility that a job is both created and destroyed when the observation period is sufficiently short, approximate job creation in period t is ct = as, ~(1 - nt 1),

1-

(4.1)

a s t = e -O~tq(O~),

where nt-1 = 1 - ut-1 is employment at the beginning of the period, 1 - ai is the probability that the representative worker who is unemployed at the beginning o f the period is not matched with a job during the period given that aggregate state i prevails, Oiq(Oi) is the aggregate state contingent unemployment hazard rate, and st E {l, h} is the aggregate state that prevails during period t. Job destruction in period t has two components as already noted. First, the fraction of filled jobs that experience a shock less than the prevailing reservation threshold, which equals 1 - e -;~F(RI)given aggregate state i prevails, are destroyed. Second, the fraction of existing jobs that do not experience a shock but have match productivity less than the current reservation threshold are also destroyed. The latter is Gt I(Rt) where Gt-1 (x) is the fraction of jobs at the beginning of the period that have match productivity less than or equal to x. Although this distribution of jobs over productivity is not stationary but instead evolves in response to the history of aggregate shocks, between shock arrivals it converges toward an aggregate state contingent distribution equal to 0 for all x <~ R i obviously and F ( x ) - F ( R i ) / ( 1 - F ( R i ) ) for all values of Ri < x < 1. Given sufficient persistence in the aggregate shock (i.e., t/ small enough), Cole and Rogerson argue that these steady-state distributions can be used to approximate Gt-1. Because Rh < Rt implies that job destruction attributable to a change in the aggregate state only occurs when the transition is from high to low productivity, the following characterization of the job destruction flow holds as an approximation: dt = (b,, + Ot6o) nt-i

Ot =

where

1 ifst_l = h and st =l, 0 otherwise,

6i = 1 - e-zF(Ri), 6o = ~ (F(Rl) -

(4.2) F (Rh))

where 2"glh = 3"ghl = 375 =

1 - e -rl

is the probability of an aggregate state transition. Finally, the aggregate employment process {nt} is generated by the following stochastic difference equation defined by the employment adjustment identity r/t+1 ~-~ n t + ¢t+l -

dt+l = as, + (1 - as, - 6s,+, -

~t+160) nt

1202

D.T. Mortensen and C.A. Pissarides

given the Markov forcing process {st} defined on the state space {l,h} and characterized by the symmetric probability of transition Jr. Obviously, the employment, job creation, and job destruction processes are interrelated and fully characterized by the set of reduced form parameters {al, ah, 6t, 6h, 60, Jr}. The question asked by Cole and Rogerson (1996) is whether an appropriate choice of these parameters will replicate the salient features of the Davis-Haltiwanger-Schuh observations, which they summarize in the following useful way: (1) Volatility: Job creation is roughly four times as volatile as employment, and job destruction is more than six times as volatile. (2) Persistence: The series for job creation, job destruction and employment display strong positive autocorrelation, but the autocorrelation for employment, which is 0.9, is nearly twice that for the other two series. (3) Contemporaneous Correlations: Creation and destruction have a fairly large negative correlation. Destruction is (weakly) negatively correlated with employment, whereas creation is virtually uncorrelated with employment. (4) Dynamics: Creation is negatively correlated with lagged employment, and positively correlated with fuWxe employment. The opposite pattern holds for destruction. To answer their question, Cole and Rogerson simulate the model above for trial parameter values, compute the associated simulation statistics, and then adjust the parameter values to obtain a better match. They conclude that the model can replicate observations in their sense when the probability of finding a job is not too large. Specifically, the model simulation for the parameter set {al, ah, 6l, 6h, 6o, zc} = {0.21, 0.30, 0.069, 0.044, 0.01,0.2} generates their preferred results which are not only consistent with their qualitative characterization of the data but are quite close in quantitative terms as well. Given that the two job destruction rates 6l and 6h are set to match the average of 0.055 reported in the Davis-Haltiwanger-Schuh data, one potential problem which Cole and Rogerson emphasize and discuss are the low values of the probabilities of finding employment. To see the significance of the point, simply note that the two state contingent steadystate unemployment rates associated with this parameter set are

ul

-

-

-

6l+al-0"25'

uh

-

6h + ah

0 . 1 3 ,

two numbers that yield an average unemployment rate of 19%. Nonetheless, the authors argue that these numbers are reasonable given the following observations reported by Blanchard and Diamond (1990): First, although the simple model ignores nonparticipants, in fact the flow to employment from this stock is roughly equal to the flow from those officially categorized as unemployed. Second, the number of workers classified as out-of-the-labor-force who report they want jobs is also roughly equal to

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

1203

the number classified as unemployed. Including these individuals in the pool of the unemployed would rationalize the low average value of a, especially if these workers search at lower intensities. 4.2. Capital accumulation and shock propagation

Merz (1995) and Andolfatto (1996) each construct different but related syntheses of the neoclassical stochastic growth model and the Pissarides (1990) model of frictional unemployment. The contributions of these authors include a demonstration that the "technology shocks" responsible for business cycles in the real business cycle (RBC) model will also induce negative correlation between vacancies and unemployment, the Beveridge curve, and a positive correlation between flows into and out of unemployment in a version of the model with a labor market characterized by a matching process. However, like the earlier simpler RBC models, the amended models fail to propagate productivity shocks in the manner suggested by the observed persistence in actual output growth rates. Recently, den Haan, Ramey and Watson (1997) have constructed, calibrated, and simulated a synthesis of the Mortensen and Pissarides (1994) model of job creation and job destruction with the neoclassical stochastic capital accumulation model. As in the Merz and Andolfatto models, job creation is governed by a matching function whose inputs include vacancies and unemployed workers. In addition, a job destruction margin is introduced by supposing that existing job matches experience idiosyncratic productivity shocks orthogonal to the aggregate shock to match productivity as described above. They find that interaction between the household saving decision and the job destruction decision play a key role in propagating aggregate productivity shocks. As a consequence, their synthesis provides an explanation for the observed autocorrelation in output growth rates as well as the correlation patterns observed in job flows with themselves and employment, those matched by Cole and Rogerson (1996). Den Haan et al. (1997) explicitly formulated the model in discrete time with each period equal to one quarter. Following Merz (1995) and Andolfatto (1996), idiosyncratic variation in labor income attributable to unemployment spells is fully insured through income pooling. Hence, the existence of a representative household can be invoked; one assumed to have additively separable preferences over future consumption streams represented by ~ t ytu(Ct) where t is the time period index, y is the time discount factor, and u(C) is one period utility expressed as a concave function of consumption. A single consumable and durable asset, capital, exists which also serves as a productive input. The sequence of future market returns for holding the asset, denoted {rt}, is an endogenous stochastic process. Hence, the optimal consumption plan must satisfy the usual Euler equation u'(Ct) = gEt{u'(Ct+l)(1 - 6 + rt+l)},

(4.3)

where the expectation is taken with respect to information available in period t and 6 is the rate of physical capital depreciation.

D.T. Mortensen and C.A. Pissarides

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The surplus value of a new match is another endogenous stochastic process, denoted {S°+1}. When an unemployed worker and job vacancy meet at the beginning of period t + 1, Nash bargaining takes place. The outcome allocates the share fiS°t÷l to the worker and the remainder (1 -fl)S°÷l to the employer, where as above fi represents worker market power. The anticipated bargaining outcome motivates search and recruiting effort by unemployed workers and employers with vacancies during period t. The flow return to unemployed search is the sum of home production while unemployed, b, and the expected gain attributable to finding a match: '

b+Otq(Ot)[3Et{

•u ( t+l ~ )S?+1) .

(4.4)

The expected capital gain, the second term, is the product of the probability of finding a job and the expected value of the worker's share of match surplus given information available in period t appropriately discounted back to the present by a factor which accounts for any difference in the marginal utility of consumption in the next and the current period. Similarly, free entry of vacancies requires zero profit in the sense that recruiting cost per vacancy posted, ptc, equals expected return, the product of the probability that the employer finds a match and the employer's share of its expected discounted surplus value:

ptc = q(Ot)(1 -[3)Et{ Yu'(Ct~+~) t+l ]" S"

(4.5)

The aggregate productivity shock, the process {pt}, is Markov with the transition probability kemel assumed to be common knowledge. For simplicity, den Haan et al. (1997) assume that the match-specific process, represented by {xt}, is i.i.d, with c.d.f. F(x) 19. Still, the idiosyncratic shock is expected to persist for the duration of the current period. The output of an existing match in period t is ptxtf(kt) where kt is the amount of capital per worker rented during the period at rate rt, andf(k), normalized output per worker, is an increasing concave function. Because the option value of continuing the match is zero for the employer and equal to the flow value of search for the worker, b + [3ptcO/(1 -[3) from Equations (4.4) and (4.5), the joint match surplus conditional on idiosyncratic productivity xt is

St(xt) = mlax ~ t x t f (k) - rtk - b - ~lP~CflOt) + Et

{ yut(Ct+l)

u'(Ct~ max {St(Xt+l), O}

(4.6)

} ,

where the last term reflects appropriate discounting of next-period surplus and the option to destroy the match next period if need be. 19 Otherwise,the distributionof idiosyncraticproductivityacross existingmatchesis a decisionrelevant state variable.Theyclaimthatthe modelloses no essentialpropertyas a consequenceof this abstraction.

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By implication of the optimal capital choice, the current period demand for rented capital by an existing match characterized by idiosyncratic productivity xt = x is

k[(x)= { d ~p, 0

if

(4.7)

otherwise,

where d = (ft)-i is a decreasing function and Rt is the reservation value of the idiosyncratic shock. Obviously, the representation reflects the fact that an existing jobworker match is destroyed and no capital is rented if an idiosyncratic shock is realized below the reservation value. The capital rental rate rt is determined by the capital market clearing condition which can be written as

Kt=[fRid(~pt) dF(x)lNt,

(4.8)

where (Kt,Nt) is the given aggregate capital stock and employment pair as of the beginning of period t. As the current reservation value Rt solves St(R) = 0, Equation (4.6) implies

t~c (4.9) max{ptRtf(k)-rdQ+lZttr ]lbll(Ct+l) ~ max {St(xt+l), 0}} = b+ ~_fiw./3pt Given that xt ~ F(x), it follows that expected ex ante match surplus conditional on knowledge of (Pt,Rt) is --',

--

f max{St(x),O}dF(x)= fR~ {m~x {Ptf(k)-rtk}-mkax {ptRtf(k)-rtk} } dF(x) (4.10) by Equation (4.6). The fact that xt+1~ F(x) as well together with Equation (4.9) and (4.10) imply max {ptRf(k) k

- rtk}

/3ptc tl =b+~_flvt

- Et

ut(Ct)

t+l

(4.11)

(mU {p,+,xf(k) - max {Pt+,Rt+f(k) k

- rt+lk})dg(x) [ . J

Finally, because x = 1 for a new match, So = St(l). Hence, Equations (4.6) and (4.10) imply that Equation (4.5) can be written as

ptc = q(Ot)(1 -/3) }. x E f gU'(Ct+l)[n~x{pt+,f(k)-rt+,k}-m~x{pt+lRt+,f(k)-rt+lk}l (4.12)

D.T. Mortensenand C.A. Pissarides

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Note that Equations (4.11) and (4.12) are generalizations of the job destruction and job creation conditions. Indeed, in the non-stochastic case with linear utility and no capital, these equations are equivalent to Equations (2.26) and (2.22) since Equation (4.3) implies 7 = 1/(1 + rt) for all t and the discrete time specification and the assumption that the idiosyncratic shock persists for one period imply that the duration of any shock is unity, i.e., tt = 1. However, a complete characterization of general equilibrium also requires that the equilibrium conditions of the neoclassical stochastic growth model, Equations (4.3) and (4.8), and the laws of motion hold. The laws of motion for capital and employment are

t xf ( (g ~ gt+ 1 (1 - 6)Kt +Pt [~RRl =

dF(x) l Nt

(4.13)

- cptOtq(Ot)(1 - Art) - Ct and

Nt+1 Otq(Ot)(1 -- Aft) -- F(R¢) Nt =

(4.14)

respectively 2°. The first equation reflects the effects of job destruction and capital demand decisions made at the beginning of the period on output and the consumption decision while the second reflect the outcomes of current period job creation and destruction decisions. As the information relevant state of the economy is a triple composed of the capital stock, the employment level, and the aggregate shock, a dynamic stationary general equilibrium is a vector function that maps the state variable triple (N, K,p) to the four endogenous variables (C, r, R, 0); one that solves the Euler equation (4.3), the capital market clearing condition (4.8), the job destruction condition (4.11), and the job creation condition (4.12) under the laws of motion (4.13) and (4.14). Den Haan et al. (1997) derive the properties of the equilibrium by solving and simulating a particular parameterization of the model numerically. The qualitative properties they report are intuitively suggested by the known implications of the two models married in this synthesis. For example, a positive aggregate shock stimulates current investment in both job creation and physical capital which augment employment and productive capacity in the next period. In the short run, these investments must be financed with an output increase induced by a lower than normal reservation productivity choice and by a reduction in consumption. However, because of the consumption smoothing motive, the limited ability to increase output by increasing utilization through reductions in job destruction, and the complementarity of physical capital and labor, more investment of both types is made in subsequent periods as well, i.e., the shock is propagated. 20 Followingthe literature, home production b cannot be used to create capital by assumption. It is simply consumed.

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A negative shock has an immediate and sharp negative effect on output along the job destruction margin. Although the effect is cushioned by the reallocation of existing capital to those jobs that continue, rental rates fall on impact in response to the decrease in demand for capital induced by job destruction and will be expected to fall further in the future as a consequence of the persistence in the shock. The result is a reduction in capital formation and job creation which has the effect of reducing output further in the future. Again the consumption smoothing motive interacting with the job creation and destruction process propagates the shock into the future. As a consequence of the adjustment mechanisms described above, the simulated model implies strong first- and second-order autocorrelation in output growth rates, substantial persistence in the response of physical capital to negative productivity shocks, and a substantial magnification of the effects of productivity shocks on aggregate output. Neither the RBC model nor the augmented model featuring job matching but exogenous job destruction, like those of Merz (1995) and Andolfatto (1996), explain these features of the aggregate time-series data. As in Cole and Rogerson's (1996) reduced form analysis of the Mortensen and Pissarides job creation and destruction model, the calibrated version of the extended model studied by den Haan et al. (1997) also reproduces all the job flow time series stylized facts.

5. Technological progress and job reallocation Search and matching models have been used to address the old "luddite" question of the influence of technological progress on job flows and unemployment levels. The common view is that new technology destroys jobs. Of course, innovations also generate new job creation. But, the resulting reallocation of workers from the old to new jobs may require an intervening unemployment spell. In this section, we explore the relation between the exogenous rate of technological progress and steady-state employment. The analysis that follows suggests that the extent to which technical progress is "embodied" is critical. The distinction between embodied and disembodied technology is Solow's. In his original growth model [Solow (1956)], any improvement in technology instantaneously affected the productivity of all factors of production currently employed. But later he introduced the vintage model of embodied technical change in which productive improvements is a property of new capital investment only [Solow (1959)]. In the latter case, to capture the productivity benefits of technical change, older capital vintages must be replaced with the most recent equipment. Our analysis begins by making the original assumption of disembodied technology. We show that if the rate of interest is independent of the rate of technological progress, faster technological progress leads to more job creation in the steady state. The dominant effect in this case is one of"capitalization". Because the costs of job creation are paid initially, faster technological progress implies a lower effective discount rate on future profits, leading to a higher present discounted value for profits [see Pissarides

D.T. Mortensen and C.A. Pissarides

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(1990), Chapter 2]. The effect o f faster growth on j o b destruction is, however, o f indeterminate sign. We then consider the vintage model in the sense that "new capital" is assumed to be embodied only in newly created jobs. We show that under the assumption that the same worker cannot be m o v e d from an old j o b to a new one without intervening unemployment, steady-state unemployment is higher at faster rates o f technological progress [as in A g h i o n and Howitt (1994)] 21.

5.1. Disembodied technology

L e t p ( t ) represent the aggregate productivity parameter but now expressed as a function o f time t. We assume that the rate o f technological progress g is constant, exogenous, and less than the rate o f time discount, i.e.,

P

-g


(5.1)

P We treat r as a constant independent o f g 22. The other restrictions made are the same as in the basic model o f Section 2.1, with the additional assumption that unemployment income is also a function o f time. We assume for simplicity that b(t) = bp(t). This assumption is needed to ensure the existence o f a steady-state growth equilibrium and is plausible in a long-run equilibrium when p(t) is an aggregate productivity parameter 23. The j o b creation and j o b destruction conditions o f Section 2.1 change in an obvious way. Because all parameters in the value expressions (2.4), (2.5), (2.7) and (2.8) are multiplied by p(t), and the wage equation still satisfies either (2.20) or (2.23), there is an equilibrium where all value expressions grow at constant rate g. Intuitively, the firm that has a j o b with value J(x, t) at time t, expects to make a capital gain o f dJ(x, t)/dt ==-J(x) = gJ(x) on it. The same holds true for the value o f a j o b to the worker, W(x, t), and the value o f unemployment, U(x, t), where the capital gain is, respectively, gW(x) and gU(x). But the value o f a vacant job, V(t), because it is zero

21 Mortensen and Pissarides (1998) consider a more general case of adoption of the new technology at a cost and show that the two cases that we consider here are two limiting cases, the first case approached when the adoption cost tends to zero and the second when the adoption cost tends to infinity. The main result of the paper is that there is a critical level of the adoption cost below which the dominant influences on job creation and job destruction are those described here under disembodied technology and above which the dominant influences are those described under embodied technology. See also Aghion and Howitt (1998, chapter 4) for more analysis of this issue. 22 Eriksson (1997) embeds the model in an optimizing (Ramsey) growth model and shows that the restriction that the effective discount rate decline with the rate of growth can be violated by feasible parameter values. He also considers the effects of growth on unemployment in an endogenous growth framework. 23 Making b(t) a proportional function of the equilibrium wage rate would not change the results.

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1209

by the free entry condition, does not change. It is this asymmetry between V(t) on the one hand and the other asset values on the other that creates the capitalization effect of faster growth. We do not reproduce all the value expressions with growth but show instead the value of a continuing job to the firm, (2.4):

rJ(x, t) = p(t) x - w(x, t) + 3.

fR [J(z, t) - J(x, t)] dF(z)

(5.2)

+ Z F ( R ) [ V ( t ) - p ( t ) T - J(x, t)] + J(x, t).

The capital gain to the firm is shown as an addition to revenues from continuing the job. Replacing the capital gain by its steady-state value, we get 1

(r - g) J(x, t) = p(t) x - w(x, t) + )~ fR [J(z, t) - J(x, t)] dF(z)

(5.3)

+ ~ F ( R ) [ V ( t ) - p ( t ) T - J ( x , t)].

The main result of the introduction of growth can be seen from Equation (5.3). Because all value expressions grow at the constant rate g, wages will also grow at the constant rate g, and so all time-dependent variables in Equation (5.3) can be written as proportional functions of p(t). Letting then J ( x , t) = p(t) J ( x ) and using similar notation for the other time-dependent variables, we can re-write Equation (5.3) in the same form as Equation (2.4), except that the discount rate r is replaced by r - g . It is straightforward to work through the model of Section 2 with the assumption that all time-dependent variables are proportional functions of aggregate productivity and show that there is a solution for the job creation and job destruction flows that replicate the solution shown in Figure 6 but with r replaced by r - g . Hence, under the assumption that r - g falls monotonically in g, we find that faster disembodied technological progress increases market tightness 0 but has ambiguous effects on the reservation productivity R. Therefore, faster growth increases job creation, decreases the duration of unemployment but has ambiguous effects on job destruction and the incidence of unemployment in general. However, much of the literature on the effects of growth on unemployment concentrates on the obsolescence effects of new technology on job destruction (see the next section) and ignores the idiosyncratic reasons for job destruction. This assumption, also adopted in Pissarides (1990, Chapter 2), is justified in the long-rma context by the fact that most variations in the job destruction rate in the data are high-frequency, with, at least in the European context where there have been substantial changes in the unemployment rate, virtually a constant job destruction flow across business cycles. This fact justifies a 0, 1 restriction on the support of the distribution of idiosyncratic shocks. In this case, variations in R do not influence the job destruction rate, which is equal to 2~, and so the effect of faster growth is to increase job creation and reduce unemployment.

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D.T. Mortensen and C.A. Pissarides

5.2. Adoption through "'creative destruction '"

New technology cannot always be adopted by existing jobs. Much of public discussion and a large body of literature deals with the situation where the adoption of new technology requires the creation of new jobs with new capital equipment. This process of implementation is referred to in the literature as "creative destruction", because old jobs have to be destroyed to release the resources for the creation of new jobs [see Aghion and Howitt (1992, 1994), Grossman and Helpman (1991), and Caballero and Hammour (1994)]. In this section we assume that the process of creative destruction induces a transition of the worker to unemployment and search for a new job. We demonstrate that more rapid technological progress under these assumptions induces more labor reallocation and so higher unemployment because of both lower job creation rate and higher job destruction rate. In order to emphasize the new element of the model we abstract from idiosyncratic productivity shocks. Instead, heterogeneity in productivity arises because older jobs embody less productive technology and a job is destroyed when the technology embodied becomes obsolete. Given that current technological improvements affect only productivity in newly created jobs, we need to distinguish between the date at which a job is created, its vintage v, and the current date, denoted as t. The expected present value of both future profit J and wage income W for a given job-worker match depends on the job's vintage and the current date. These value functions solve the following asset pricing equations: rY(v, t) = p ( v ) x - w(v, t) - 6Y (v, t) + J (v, t),

(5.4)

r W ( v , t) = w(v, t) - 6[W(v, t) - U(t)] + W(o, t),

where x represents job match productivity, w(v, t) is the wage paid on a job of vintage v at date t, 6 > 0 represents an exogenous job separation rate, and U(t) is the value of unemployed search at t. The fixed cost of investment in a new job, denoted as p(t)C, is incurred when the match forms. The investment is specific to a job, i.e., it is "irreversible" with no outside option value once the match forms. The recruiting costs, p(t) c, are modelled as a cost per vacancy posted. New vacancies enter at every date until market tightness is such that the value of creating a vacancy, V(t), is zero, i.e. r V ( t ) = q(O)[J(t, t) - p ( t ) C ] - cp(t) = 0,

(5.5)

where q(O) is the rate at which vacancies are filled. Similarly, the value of unemployment solves the asset pricing equation r U ( t ) = p(t) b + Oq(O)[W(t, t) - U(t)] + U(t),

(5.6)

where p ( t ) b represents the opportunity cost of employment and where Oq(O) is the rate at which workers find vacancies. As before, recruiting costs, the investment required to

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

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create a match, and the opportunity cost of employment grow at rate g by assumption to assure the existence o f a balanced growth path equilibrium solution to the model. We assume that the wage bargain divides the surplus value o f a continuing match in fixed proportion, i.e.,

/3J(v, t) = (1 -/3)[W(v, t) - U(t)],

(5.7)

where/3 represents the worker's share 24. Because Equations (5.4) and (5.6) imply

(r + 6)J(v, t) =p(v)x - w(v, t) + J(v, t), (r + ~)[W(v, v) - U(t)] = w(v, t) - rU(t) + W(v, t), the wage contract that supports the assumed bargaining outcome (5.7) is

w(v, t) =/3p(v)x +p(t) ((1 -/3) b +/3 (cO + Oq(O) C)) by virtue of the free entry condition (5.5). The first term on the worker's productivity while the second captures the worker's option firm. Because the latter grows at the rate of technological progress stationary, every job becomes obsolete eventually. By substituting from the wage equation into the first of Equations

(5.8) right reflects the value outside the but the former is (5.4), we obtain

(r+6)J(v,t) = (1-/3)p(v)x-p(t)((1 -/3)b+/3(c0+ Oq(O)C))+J(v,t).

(5.9)

Indeed, Equation (5.9) holds only for t - v ~< r where r is the optimal economic lifespan of a job. The employer's choice of a job's economic life maximizes its value, i.e.,

J(v't)=max~r ~JtF+~[(1-/3)P(V)x-p(s)[(1-/3)b+/3(cO+Oq(O)C)]]

(5.10)

× e-(r+6)(s-t) ds}. The maximal value o f a new job at time t is the special solution to this equation satisfying the balance growth equation J(t,t) = J°(O)p(t) where, given the normalization p(0) = 1,

J°(O) =- J(O, O) = m a x { f 0 T [ ( 1 - / 3 ) x - e gs [(1 -/3) b + / 3 ( c 0 + Oq(O)C)]]e -(r+~)s ds}. (5.11) 24 Here workers do not share the cost of initial investment by accepting a lower starting wage for an initial period of employment as assumed in Section 2. Instead, the initial wage is equal to the continuing wage at initial productivity. Although equilibrium market tightness will be too low relative to a social optimum initially, the qualitative behavior of a model under a jointly efficient wage bargain would be much the same. See Caballero and Hammour (1994, 1996) for more discussion of this issue.

D.T. Mortensen and C.A. Pissarides

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The first-order condition for a positive optimal choice of the economic life of a job equates stationary match product with the rising opportunity cost of continuing an existing match, i.e. (1 -/3) x - [(1 -/3) b +/3(c0 + Oq(O) C)] egr = 0.

(5.12)

Since J(t, t) = J°(O)p(t), the free entry condition (5.5) can be written as

c = q(O)[J°(O)- C]. (5.13) A search equilibrium is characterized by any market tightness and age at job destruction pair (0", r*) that solves Equations (5.12) and (5.13). Because the right-hand side of Equation (5.13) is strictly decreasing in 0, equilibrium market tightness is unique. Of course, given 0", the associated equilibrium value of the optimal job age at destruction, r*, is the unique solution to Equation (5.12). Since Equations (5.12), (5.13) and (5.11) imply c + C = J°(O*) = (1 -/3)x for* [1 - eg(s_r.)] e_(r+~)xds ' q(O*)

(5.14)

a necessary but hardly sufficient condition for the existence of a positive equilibrium pair (0", •*) is that match productivity x exceed the opportunity cost of employment b. Indeed, given this condition, an economically meaningful equilibrium exists only if both recruiting and creation costs, c and C, are sufficiently small. Because the surplus value of a match decreases with the rate of technological progress, g, for every value of market tightness by virtue of Equation (5.1 l) and the envelope theorem, namely

OJ o

Og

~r* [segS (( 1 -/3)b+/3(c0" + O*q(O*)C))] e (r+~)"ds < 0,

and because both the value of a job and the rate at which vacancies are filled decrease with market tightness, the free entry condition (5.13) implies that market tightness falls with the growth rate, i.e.,

)

00" _ ( q(0*) 2 OJ ° Og ~,cq'(O*)+q(~O*)2°oJ--~ ~ g

<0.

Because the left-hand side of (5.14) is decreasing in g and the right-hand side is increasing in both g and z*, it follows that the economic life of a new job also falls with the rate of growth, i.e., Or* _

Og

_ cq'(0*/ o0* _ ( 1 -/3) xeg r* for* (r * - s)e -(r+d-g) s ds q(o*) ~g

<0.

(1 -/3)xge gr* for* e (r+~-g)s ds

To derive the implications of these facts for unemployment and job flows, first note that job creation at time t is

I~(t) = O*q(O*) u(t). (5.15) Job destruction is equal to the flow of jobs that attain the age of optimal obsolescence plus the flow of all jobs that experience exogenous destruction. As the fraction of jobs

Ch. 18: Job Reallocation, EmploymentFluctuations and Unemployment

1213

of each cohort that survive to age ~ is e -~r given the exogenous destruction hazard is 6, the job destruction flow at time t is

D(t) = e-ar*K(t - z'*) + 611 - u(t)].

(5.16)

Hence, the steady-state unemployment rate that equates job creation and job destruction flows through time is u* =

6 di + (1 - e-~*)O*q(O*)"

(5.17)

It increases with the rate o f embodied technical progress because both market tightness and the economic life of an existing job decline with g and because the unemployment duration hazard Oq(O) is increasing in 0. Technological progress in this model adversely effects worker flows into and out of employment for two reasons. The first is a restriction that we have imposed on the model, namely, that when a machine is replaced because of obsolescence the worker that was employed on that machine is also replaced. This assumption also underlies the work of Aghion and Howitt (1994) and Caballero and Hammour (1996) and is derived from Schumpeter's notion of "creative destruction". The idea is that when a job is destroyed it is replaced by a technologically more advanced one, with positive effects on factor productivity. The second is a particular assumption about the timing of job creation costs. The implication of the first restriction for the job destruction flow is straightforward enough: faster technological progress necessitates more job destruction. Job creation also fails in our model when there is faster technological progress because as the life of a job becomes shorter, the expected present value o f future profit attributable to a job falls. It may turn out to be surprising that even when the interest rate is independent of growth faster growth does not have a countervailing effect on the present discounted value of profits. Since in the expressions that we have derived for the surplus from a job the effective discount rate is r - g, profits are discounted at lower rate. So faster growth has a "capitalization" effect on the profits stream. Our results, however, show that this capitalization effect is dominated by the negative influence on the present value calculation implied by the shorter life of a job. Aghion and Howitt's (1994) model of the adoption of new technology is essentially the same as the one in this section, yet it has a bigger capitalization effect that is not always dominated by the shorter life of the job. This effect is implied by the assumption that there are job set-up costs that have to be paid before the firm begins the recruiting process. In this case the profit stream is discounted more heavily, since the zero profit restriction requires that the present discounted value of profits at the date the vacant job is created must equal to the set-up costs.

6. OECD unemployment differences We saw in Section 1 that the unemployment experiences of OECD countries over the last thirty years have been different from each other. This is all the more surprising

1214

1). T. Mortensen and C.A. Pissarides

because with increasing openness and trade, and with the global oil and material shocks of the 1970s, the shocks affecting OECD countries cannot have been very different in different countries. The different experience of OECD countries is most likely due to a different response of each country to common shocks, due to different market structures, or to differences in policy. The most frequently discussed contrast in OECD experience is that between the USA and "Europe". Although the contrast is often exaggerated, especially in the more popular discussions, there is some truth in the basic argument, that whereas wages at the lower end of the wage distribution fell in the USA with unemployment remaining the same on average, in most of Europe wages increased but unemployment increased too. We saw in Section 1 that there appears to be a trade off between the increase in wage inequality and the increase in unemployment experienced by OECD countries. Figure 4 shows that over the 1980s the USA experienced a bigger increase in inequality and a smaller increase in unemployment (in fact, a decrease) than the major European countries. The experience documented in Figure 4 is most likely a response to a heterogeneous aggregate productivity shock that can be decomposed into two parts, one that shifted the productivity distribution to the right and one that widened the range of the distribution for given mean. There has been a long debate in the literature as to whether the second component of the shock, the one that worsened prospects for unskilled workers but improved them for skilled ones, was due to a technology shock, associated for example with computerization, or to a trade shock, associated with the expansion of trade with newly industrialized nations in South East Asia and Latin America. Our analysis, and more generally the search and matching framework, is one that can be used to analyze the consequences of the shocks, whatever their source. In this section we survey the key influences that have been identified in the literature as the causes of the experience of OECD countries summarized in Section 1. In a discussion of this kind, it is difficult to avoid a discussion of labor market policy, especially if one were to discuss the unemployment experiences of countries like Spain and Sweden and why they have been different from the median European experience 25. The detailed modelling and discussion of labor market policies, however, will take us beyond the scope of our chapter. We mention instead policy influences in passing, using parameters that we already have in our analysis to represent the effects of policy. Two parameters in particular are relevant to our discussion, unemployment income b, which we take also to represent the generosity of the unemployment insurance system, and the firing cost T , which we take to stand for employment protection legislation. The active labor market policies pursued by Sweden, and to a lesser degree by some other

2s There has been a large literature on the unemployment experience of each of these cotmtries. For Spain, see for example, Blanchard et al. (1995), Dolado and Jimeno (1997) and Marimon and Zilibotti (1998). For Sweden, see Calmfors (1995) and Ljungqvist and Sargent (1995). See also Scarpetta (1996) for a cross-countryOECD study.

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

1215

countries, can be shown in the model by reductions in the job creation cost C, though this does not do justice to the complexity and sophistication of some of the targeted policies in operation. 6.1. 'Skill-biased' technology shocks

As noted above, changes in technology that raise the productivity of skilled workers relative to that of unskilled is one of the explanations given for the recent increase in US wage dispersion. It has been argued that these same shocks may have generated the observed increases in European unemployment [see the OECD Jobs Study (1994), Krugman (1994) and others] 26. The reason for the different response is a different labor market policy regime. In Europe, where higher level of unemployment compensation, minimum wages, and employment protection restrict accommodation through downward wage adjustment, the response is likely to be higher unemployment, particularly among the unskilled. The purpose of this section is to explore this hypothesis within the equilibrium search and matching framework. In the Mortensen-Pissarides model, a producing unit is a job-worker match. To capture skill differences across workers, one can simply reinterpret the parameter p as an efficiency unit measure of the worker's skill. Given two workers in an identical match, the relative product per time period of the second worker is equal to the ratio P2/P~ where pi, i = 1,2, represents the "skill" of each. Let P, a set of real numbers, represent the set of skill types and G : P --+ [0, 1] denote the distribution of the labor force population over these types. Given this formalization, a pure skill-biased shock to technology can be interpreted as a meanpreserving increase in the spread of G. In this section we argue that such a shock will increase unemployment in the Mortensen-Pissarides framework and that the extent of the increase is likely to be larger for economies with high level of unemployment compensation and stringent employment protection laws. Given the assumption that skill differences are observable, as say they would be if associated with different levels of education, we can consistently assume that the labor market is segmented along skill lines. Across markets the reservation levels of the idiosyncratic shock and market tightness can differ. In the sequel, let R(p) and 0(p) characterize equilibrium relationships between these two endogenous variables and worker skill. Obviously, these functions, which satisfy the job creation and job destruction conditions Equations (2.22) and (2.26), and the steady-state Beveridge condition (2.3), determine the equilibrium relationship between unemployment and skill of interest in this section. The qualitative differences in both market tightness 0 and the reservation value of the idiosyncratic component of match product R at two different skill levels are readily

26 Acemoglu (1996, 1998) explains changes in unemployment and wage inequality in terms of endogenoustechnologychanges and changes in labor supply.

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D.T. Mortensen and C.A. Pissarides

Table 3 Baseline parameter values Parameter

Symbol(s)

Value

Discount rate Matching elasticity Recruiting cost Creation cost Productivity shock frequency Minimum match product Value of leisure Worker's share Firing Cost

r tl m~o) C A y b /3 T

0.02 per quarter 0.5 0.3 ,per worker 0.3 per worker O.1 0.68 per quarter 0.62 per quarter 0.5 0 per worker

predicted by the model. For a more skilled worker, one characterized by a higher value of general productivity parameter p, the relative opportunity cost of employment, the ratio b/p, is lower. Given the assumption that hiring and firing costs increase proportionately with p, the job destruction relation, D D in Figure 6, is lower given a higher value o f p and the job creation relation C C is unaffected by variation in p. As a consequence, markets for the more skilled are tighter, unemployment durations are shorter. Furthermore, the reservation value of idiosyncratic productivity is lower in markets for the more skilled and, consequently, the incidence of unemployment is lower. These inferences are consistent with empirical findings to the extent that the level of education is a good indicator of skill. As the unemployment rate is a positive number by definition, the fact that it declines with the skill parameter p implies that the unemployment-skill profile is convex, at least on average. To the extent that the relationship has this shape, any increase in the mean-preserving spread of the distribution of relative productivity, defined above as a 'skill-biased' technology shock, will increase unemployment. This effect can explain the run up in European unemployment rates relative to those in the USA if European labor policies increase the convexity of the unemployment-skill profile. In short, if unemployment compensation and employment protection has a larger relative impact on the unemployment of unskilled workers, then the same 'skill-biased' technology shock increases unemployment more in countries with these policies. To ascertain whether this explanation has force, we calibrate a simple version of the model and then use it to compute the implied unemployment-skill profile for different policy regimes. A matching function of the Cobb-Douglas form is assumed with elasticity with respect to unemployment equal to t/, i.e., ln(q(0)) = -t/ln(0). The distribution of idiosyncratic shocks is assumed to be uniform on the support [7, 1], i.e., F ( x ) = (x - y)/(1 - 7)Vx c [7, 1]. The baseline parameters used in the computations are reported in Table 3. Except for value of income while unemployed b and the minimum

1217

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

.25 0.2 u(0.77, 1.1,p) u(0.77, 0,p) u(0.62, 0,p) 0.1

0 0

0.8

I

I

I

I

0.9

1

1.1

1.2

1.3

Fig. 8. Unemployment-skillprofiles.

match product },, which are chosen so that the steady-state unemployment rate of a worker of average skill (p = 1) is 6.5% and the average duration of an unemployment spell for such a worker is 3 months, values which reflect experience in the USA over the past twenty years, the parameter values are similar to those assumed and justified in Mortensen (1994b) and Millard and Mortensen (1997). To obtain parameters that reflect the European experience, we maintain the same values of all parameters except for unemployment income b and firing cost T which are chosen to yield the same average unemployment rate but an average spell duration of 9 months. The results, b = 0.77 and T = 1.1, are consistent with the fact that unemployment compensation and the implicit cost of employment protection are both substantially higher is Europe than in the USA and the fact that unemployment spells are much longer in Europe. The computed unemployment-skill profiles for three different policy parameter combinations are illustrated in Figure 8. Specifically, each curve is a plot of the equilibrium unemployment function u(b, T , p ) for value of the skill parameter p. The flattest profile corresponds to low unemployment compensation and no employment protection policy, the base line case of (b, T) = (0.62, 0). Given a more generous unemployment compensation but still no employment protection, (b, T) = (0.77, 0), the profile lies everywhere above the original but is substantially more convex, i.e., the steady-state unemployment rate of the less skilled is more responsive to the level of unemployment compensation. Adding employment protection, as illustrated by the solid curve representing the case (b, T) = (0.77, 1.1), actually lowers the unemployment rate of the more skilled but raises that of the unskilled. In short, employment protection policy induces even more convexity into the unemployment-skill profile.

D.T. Mortensen and C.A. Pissarides

1218

In sum, a given 'skill-biased' technology shock increases unemployment by more when unemployment compensation and the implicit firing cost associated with employment protection policy are higher in the Mortensen-Pissarides model. The magnitudes of the computed differences in unemployment rates across skills suggest that indeed shocks of this form could well explain the secular rise in European unemployment rates relative to the USA in the 1980s. Returning now briefly to the question of participation, recall that alongside the relative (and absolute) rise in European unemployment there has also been a decline in participation rates. We saw in this section that once the model is reinterpreted as one where there are many submarkets, one for each skill, the policy changes that we have described can be shown to have a bigger impact on the market returns of the lower skills than those of the higher skills. I f we now require that participation of skill group p takes place only when the total net r e m m from that group exceeds some fixed cost, any policy or other change that increases unemployment because of the relative decline in the returns from a job match will also increase the threshold participation skill, the one below which no participation takes place. The reasons given here for the rise in European unemployment are ones that reduce the net returns from the participation of low skilled workers and so they are ones that can also explain a fall in the overall participation rate of these groups.

6.2. Mean-preserving shocks to idiosyncratic productivity A substantial fraction of the increased US wage inequality has also occurred within identifiable skill and education groups. In the Mortensen and Pissarides model earnings dispersion of this form could result as a consequence of greater variation in match specific idiosyncratic productivity. Following Arrow (1965), suppose that the idiosyncratic component of productivity is written as a function of a multiplicative parameter h, so

x(h) = x + h(x - 2 ) ,

(6.1)

where h ~> 0 is a parameter and 2 is the mean of the distribution. We shall consider the effect of a shift in h on the steady-state equilibrium, evaluated in the neighborhood of the old equilibrium, h = 0. In order to make the analysis more meaningful for the question in hand, we assume that p2 >~ rU, i.e. that the reservation wage of the unemployed job seekers is below mean productivity. This ensures that the multiplicative shock reduces the productivity of at least some active low-productivity jobs. Reworking the job creation and job destruction conditions with x(h) replacing x is straightforward. The job creation condition (2.22) becomes

c -(1-[3)((l+h)(1-R) q(O) r + )~

C- T

)

,

(6.2)

Ch. 18: Job Reallocation, EmploymentFluctuationsand Unemployment

1219

whereas the job destruction condition (2.26) becomes

P(I +h)R-hp2q P(Ir+;~ +h)J" fR1 (z-R)dF(z) = b - r p T +

cO.

(6.3)

Equilibrium is still shown by the two lines of Figure 6. Higher h shifts the DD line up, implying higher reservation productivity at all levels of market tightness, because the productivity of the marginal job is now worse. But higher h also shifts the CC line to the right, because, for given reservation productivity greater than zero, the benefits from the higher productivity of jobs above the mean outweigh the costs from the lower productivity of jobs below the mean, the tail of which is truncated. Thus, job creation unambiguously goes up at given unemployment stock but the effect of the higher h on job destruction is ambiguous from the diagram alone. Differentiation of Equations (6.2) and (6.3) with respect to h, however, shows that at h = 0, the reservation productivity rises unambiguously (see Appendix A). So both job creation and job destruction rise at given unemployment when there is a multiplicative productivity shift. The effect of this shift on unemployment is ambiguous. On impact, unemployment rises, because job destruction leads job creation, but whether unemployment rises or falls in steady state depends on whether the direct impact on job destruction or job creation dominates. The effect on wage inequality is also ambiguous, because, although the range of productivities falls, the productivity of the marginal job may rise or fall. The impact on the productivity of the marginal job, when evaluated at h = 0, is given by

OR(h) Oh

_

OR Oh (2- R).

(6.4)

We note, however, the following. If the impact of the multiplicative shock on reservation productivity is large, it is more likely that job destruction will dominate job creation and unemployment will rise in equilibrium, and also that the productivity of the marginal job will rise (or fall less) than otherwise. If, on the other hand, the impact of the multiplicative shock is large on market tightness and small on the reservation productivity, it is more likely that unemployment will eventually fall and the productivity of the marginal job will also fall. Thus, in countries where there are conditions that amplify the impact of multiplicative shocks on job destruction, their consequence is an increase in unemployment associated with a decrease (or small increase) in inequality. In countries where the reverse happens, the consequence of multiplicative shocks is to increase inequality but either reduce or increase unemployment by a smaller amount. We can identify one factor in our analysis that might play a role in explaining the difference between the experience of Europe and the USA, though the explanation cannot be a complete one. This is the parameter representing labor's bargaining strength,/3. The Appendix shows that higher/3 implies lower impact of h on 0, though the impact ofh on R is not likely to depend on/3 at plausible values of/3 [more precisely

1220

D.T. Mortensen and C.A. Pissarides

when/3 is in the neighborhood of the elasticity of the matching function with respect to unemployment, or the elasticity of q(0)]. Therefore, countries with more powerful labor organization when hit by a shock that increases inequality are likely to experience more unemployment, through less job creation, than countries with less powerful labor. It is often asserted that labor is more powerful in Europe than in the USA, either because of more powerful trade unions or because of legislation that favors labor. So this could be one factor behind the different unemployment experience of the two continents. With regard to inequality, however, the model does not have strong predictions 27. 6.3. Other influences

Several other influences on the equilibrium unemployment rate have been investigated in the empirical literature, in search of the elusive explanation for the rise in European unemployment. Virtually all the determinants of the equilibrium rate discussed in Section 3 have been, at one time or another, listed as possible causes of higher unemployment in Europe. This includes, in addition to unemployment income and trade union power discussed above, the real rate of interest, taxes on wages, which reduce the net surplus from a job match, "mismatch", by which is usually meant more heterogeneity in the labor market and which is represented by a shift of the aggregate matching function, employment protection legislation, which increases the costs of job destruction, and on the positive side "active labor market policies", which reduce the job creation costs and costs of labor to the firm. As we saw in Section 2.3, higher real rate of interest reduces market tightness but has ambiguous effects on the reservation productivity. At given unemployment rates job creation falls. In terms of the Beveridge diagram, real interest rates have ambiguous impact on the Beveridge curve but rotate the job creation line down. It has been argued, however, that empirically higher real interest rates have depressed employment in the OECD, i.e. that the job creation effect dominates over the job destruction effect [Phelps (1994)]. Taxes on employment reduce the net surplus from the job, so whether they reduce job creation or not depends on their influence on non-employment income. If nonemployment income is not taxed, their effects on the equilibrium of the model is similar to a rise of non-employment income, i.e. they reduce job creation and increase job destruction at given unemployment rate. Taxes, however, may also have distortionary effects if they are not proportional to incomes, a topic that would take us beyond the scope of our chapter 28. 27 One prediction is that the lowest wage is almost certain to rise when the multiplicativeshock arrives, because of the increase in the reservationproductivityand in market tightness. Then, it becomes likely that the cross effect of h and/3 on the lowest wage is also positive, so countries with less powerful labor experience more increase in inequality. (These results are not proved here.) 28 Pissarides (1998), Mortensen (1994a), and Millard and Mortensen (1997) all study tax effects using search equilibrium models. See also Daveri and Tabellini (1997), who explain the slowdown in growth and rise in unemploymentin Europe by tax increases on labor.

Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

1221

Mismatch can arise in our framework in the following sense. The aggregate matching function conceals a lot of heterogeneity in the labor market. It is a convenient modelling device when our interest is in aggregate changes rather than individual employment histories. Out of all the interactions between the many heterogeneous groups in the population, a stable relationship emerges between the job matching rate and the stocks of aggregate unemployment and vacancies. But if conditions are such that the type of workers and jobs available change, either in skill requirement or in location, the aggregate outcome from the interaction between those groups is also likely to change. An increase in mismatch shifts the aggregate matching function down at all levels of vacancies and unemployment. Mismatch bears some relationship to the more commonly discussed, in the US literature, "sectoral shifts hypothesis", though it is more general [Lilien (1982)]. It also bears some relationship to the older view of "structural" unemployment, which was thought to be unemployment arising from fast structural change in the economy as a whole. In Europe, mismatch has been proposed by Jackman et al. (1989), Layard et al. (1991) and others as a cause of the rise in European unemployment. The oil, technology and other real shocks of the 1970s and 1980s increased the speed with which unemployed workers needed to adapt to the changing requirements of employers. This led to increased mismatch, which increased unemployment at given vacancies. Although neither the sectoral shifts hypothesis in the USA, nor the mismatch hypothesis in Europe, has had much success in accounting for a large fraction of employment fluctuations, we look here at the implications of the mismatch hypothesis within the search and matching framework. The argument is that because labor in Europe is less mobile than in the USA, a problem aggravated by the longer durations of unemployment in Europe, the changing requirements of jobs lead to bigger and more prolonged shifts of the aggregate matching function. Mismatch in the formal model is shown as a fall in the productivity of the aggregate matching process, i.e. a downward shift of the transition rate q(O) at all values of 0. This shifts the job creation line in Figure 6 down, reducing both market tightness and the reservation productivity. But in addition, mismatch has the implication that for given market tightness, the rate of job matching is lower. This implies, in our model, a shift of the Beveridge curve out, over and above any effects that there might be through job creation and job destruction. It is this additional shift in the Beveridge curve that has attracted most attention in the discussions of mismatch in the search literature 29. It is clear that the overall effect of increased mismatch on equilibrium unemployment is uncertain, because of the three interacting effects: less job entry at given

29 See Jackman et al. (1989) for the United Kingdom, Abraham and Katz (1986) and Blanchard and Diamond (1989) for the USA and Jackman et al. (1990) for an international comparison of Beveridge ctuve shifts. Andolfatto (1996) incorporates a stochastic shift parameter in the matching fucntion in his calibrations of the search and matching model.

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D.T. Mortensen and C.A. Pissarides

unemployment, less job destruction and less job creation at given vacancies and unemployment. The empirical literature, however, invariably takes the latter effect, shown in the diagrams by the outward shift of the Beveridge curve, as the one that dominates on unemployment. Of course, a sufficient condition for this is that for given O, the fall in q(O) due to the direct effect of increased mismatch dominate the fall in )~F(R) due to the indirect effect from the fall in the reservation productivity. But since the job creation line in the Beveridge curve diagram (Figure 7) rotates down when mismatch increases, the effect of increased mismatch on equilibrium job vacancies is thought in the empirical literature to be unimportant. It is this latter property (higher unemployment at given vacancies), which has been a feature of the 1980s rise in European unemployment, that has attracted research in this area. Countries with more restrictions in job separations are ones that have higher values for the firing cost T. We saw that those countries should experience less job creation and job destruction at given unemployment rate, through lower R and 0. The effect on equilibrium unemployment is ambiguous but the effect on job reallocation is negative. This result might explain why job reallocation rates differ across countries. In an analysis of the data on job reallocations given in Section 1 and the employment protection provisions in different countries as constructed by the OECD, Garibaldi et al. (1997) found a clear relationship between employment protection legislation and job reallocation. Given, however, the Beveridge curve equation that defines equilibrium unemployment, there is no reason to expect a correlation between job reallocation and equilibrium unemployment 30. Firing costs might also explain, to some extent, the differences between the job reallocation rates between small and large firms. Usually large firms in Europe are subject to many more restrictions on firing workers, imposed either by legislation or by trade unions. In Italy, where there are severe restrictions on job separations in large firms, many more small firms come into operation and job reallocation rates in those small firms are comparable to those in the USA [see Contini et al. (1995)]. Finally, lower job creation costs lead to more job creation at given unemployment and more job destruction. Once again, the effects on equilibrium unemployment are ambiguous. Many European governments, however, have tried to encourage job creation by giving incentives which reduce job creation costs. One of the criticisms levelled against such policies is that they encourage the creation of "unstable" jobs that do not stay in operation for long periods. This argument is valid in our analysis but still hiring subsidies may be justified, particularly if the worker's effective share of match-specific investments in training and information are less than their share of continuing match surplus [Mortensen (1996)].

30 Bertola and Rogerson(1997) claim that job reallocationrates do not differ as much across countries as they should be expectedto do, given differencesin firing costs. They explain this by the differences in wage inequalitythat characterizescountries, and which tends to reducejob reallocationrates.

Ch. 18: Job Reallocation, EmploymentFluctuationsand Unemployment 7. C o n c l u d i n g

1223

remarks

We have demonstrated that the search and matching approach provides a rich framework for the analysis of aggregate employment fluctuations and of the observed differences in average unemployment rates across countries. Calibrations o f the models track the cyclical fluctuations in the job creation and job destruction flows reasonably well. The framework provides a convenient medium for the analysis of policy influences on unemployment, which lie at the heart of the explanations of average unemployment differences across countries. Although there is still no consensus on the causes of the higher unemployment rates in Europe than in the USA, we have shown how policy influences, in particular the unemployment insurance system and employment protection legislation, can contribute to the differences in both unemployment rates and wage inequality. Wages in the models that we have examined are determined by a fixed rule that shares the economic rents that each employer-worker match creates. Other methods of wage determination are also consistent with our framework and some promising work is being done in this area of research. We discuss some of this work in our companion chapter for the Handbook of Labor Economics. Another promising area of current research is the interaction between technology, capital and labor in markets with frictions. This area of research provides a natural framework for the analysis of hold-up problems and problems of obsolescence and growth. We discussed some work in this area in this chapter but much remains to be done.

Appendix

A. Mathematical

appendix

A. 1. Mean-preserving shifts in productivity Differentiation of Equation (6.3) with respect to the parameter h and evaluation of the result at h = 0 gives

I-~[I-F(R)] N=(~-R)-~

(z-R)dF(z)-~cN. (A.1)

Differentiation also of (6.2) with respect to h gives

c~l 0 0 _ 1-[3 [ I _ R _ O R 1 Oq(O) Oh r + )~ ~ "

(1.2)

Substitution of OR~Oh from Equation (A.1) into (A.2) reveals that the sign of O0/Oh is the same as the sign of 1- R -

2 - R - v ~ z f / ( z - R) dF(z) 1- ~

2, [1 - F ( R ) ]

(A.3)

D.T. Mortensen and C.A. Pissarides

1224

Multiplying out the denominator o f Equation (A.3) and collecting terms, we find that the sign of the terms in (A.3) is the same as the sign of 1 - 2 - -r +- ~ ,

(1 - z) dF(z),

(1.4)

which is unambiguously positive since 1- 2 =

J01

(1 - z) dF(z).

(1.5)

Hence, the effect of higher h is positive on both R and 0.

A.2. Labor's bargaining strength Differentiation of Equation (6.3) with respect to/3 gives

[

l

3~

1-~--~[1-F(R)]

OR_

0/3

1

1-~

[

~

o0]

cO + /3c-~

(A.6)

Differentiation of Equation (6.2) gives

ctl O0 Oq(O)O/3

c q(0)(1-/3)

1 OR (1 - / 3 ) r +)~ 0/3'

(A.7)

Substitution of 00/0/3 from Equation (A.7) into (A.6) reveals that the sign of 0R/0/3 is the same as t/-/3. So R reaches a unique maximum at/3 = ~/, which is also the efficient point, when the search externalities are internalized [see Hosios (1990)]. Although there is no reason why the two parameters should be equal, the usual restriction on/3 in symmetric bargaining situations is fi = ½ and the empirical evidence on t/suggests that it is close to 0.5 so the restriction/3 = t/is a convenient simplification that may be adopted. We shall do so in the derivations in this Appendix. Under the restriction then that

OR

o/3

- 0,

(A.S)

the effects of labor's bargaining strength on market tightness become 00 0/3-

0 t/(1 -/3)'

(A.9)

Turning now to the question of the cross partials of h and/3 on R and 0, i.e. on the response of reservation productivity and market tightness to a multiplicative

Ch. 18: Job Reallocation, Employment Fluctuationsand Unemployment

1225

productivity shift in countries with different labor bargaining strength, we immediately find from Equation (A.9) that 020

1

OhO/3

00

7/(1 -/3) Oh

< 0.

(A.10)

So in countries with m o r e powerful labor, the positive response o f market tightness to the productivity shock is smaller. The cross partial o f R is calculated by differentiating Equation (A. 1) with respect to/3. This shows that the sign o f the cross partial 02R/OhO/3 is the same as the sign o f 1

00

1 - fi oh

020 /3-OhO/3"

(A.11)

Making use o f Equations (A.2) and (A.10), we easily find that the sign o f Equation (A.11) is the same as

1

/3(1 - r/) (1 - / 3 ) r/'

(A.12)

i.e., at fl = t/, it is zero.

References Abraham, K.J., and L.E Katz (1986), "Cyclical unemployment: sectoral shifts or aggregate disturbances?", Journal of Political Economy 94:507-522. Acemoglu, D. (1996), "Changes in unemployment and wage inequality: an alternative theory and some evidence", Discussion Paper No. 1459 (CEPR, July). Acemoglu, D. (1998), "Why do new technologies complement skills? Directed technical change and wage inequality", Quarterly Journal of Economics 113:1055-1089. Aghion, P., and P. Howitt (1992), "A model of growth through creative destruction", Econometrica 60:323-350. Aghion, P., and P. Howitt (1994), "Growth and unemployment", Review of Economic Studies 61(July): 477-494. Aghion, P., and P. Howitt (1998), Endogenous Growth Theory (MIT Press, Cambridge, MA). Akedof, G.A., A. Rose and J.L. Yellen (1998), "Job switching and job satisfaction in the U.S. labor market", Brookings Papers on Economic Activity 1998(2):495-582. Andolfatto, D. (1996), "Business cycles and labor market search", American Economic Review 86: 112-132. Andolfatto, D., and P. Gomme (1996), "Unemployment insurance, labor market dynamics, and social welfare", Carnegie-Rochester Conference Series on Public Policy. Arrow, KJ. (1965), "The theory of risk aversion", lecture 3 of K.J. Arrow, Aspects of the Theory of Risk-Bearing (Yrjo Jahnssoninsaatio, Helsinki). Bertola, G., and R.J. Caballero (1994), "Cross-sectional efficiency and labour hoarding in a matching model of unemployment", Review of Economic Studies 61 (July):435-456. Bertola, G., and R. Rogerson (1997), "Institutions and labor reallocation", European Economic Review 41(June): 1147-1171.

1226

D.Z Mortensen and C.A. Pissarides

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Ch. 18: Job Reallocation, Employment Fluctuations and Unemployment

1227

Friedman, M. (1968), "The role of monetary policy", American Economic Review 58:1-17. Galbraith, J.K. (1996), "Inequality and unemployment: an analysis across time and countries", mimeograph (University of Texas at Austin). Garibaldi, R, J. Konings and C.A. Pissarides (1997), "Gross job reallocation and labour market policy", in: D.J. Snower and G. de la Dehesa, eds., Unemployment Policy: Government Options for the Labour Market (Cambridge University Press, Cambridge) 467-489. Grossman, G.M., and E. Helpman (1991), "Quality ladders and product cycles", Quarterly Journal of Economics 106:557-586. Hall, R.E. (1995), "Lost jobs", Brookings Papers on Economic Activity 1995(1):221 256. Hansen, B. (1970), "Excess demand, unemployment, vacancies, and wages", Quarterly Journal of Economics 84(February): 1~3. Hansen, G.D. (1985), "Indivisible labor and the business cycle", Journal of Monetary Economics 16(November) :309-327. Hosios, A.J. (1990), "On the efficiency of matching and related models of search and unemployment", Review of Economic Studies 57:279-298. Howitt, R (1988), "Business cycles with costly search and recruiting", Quarterly Journal of Economics 103 (February): 147-166. Jackman, R., R. Layard and C.A. Pissarides (1989), "On vacancies", Oxford Bulletin of Economics and Statistics 51 (November):377-394. Jackman, R., C.A. Pissarides and S. Savouri (1990), "Labour market policies and unemployment in the OECD", Economic Policy 11:449-490. Jovanovie, B. (1979), "Job matching and the theory of turnover", Journal of Political Economy 87: 972-990. Krugman, R (1994), "Past and prospective causes of high unemployment", in: Reducing Unemployment: Current Issues and Policy Options (Federal Reserve Bank of Kansas City, August 1994). Kydland, EE., and E.C. Prescott (1982), "Time to build and aggregate fluctuations", Econometrica 50:1345 1370. Layard, R., S. Nickell and R. Jaekman (1991), Unemployment: Macroeconomic Performance and the Labour Market (Oxford University Press, Oxford). Lilien, D.M. (1982), "Sectoral shifts and cyclical unemployment", Journal of Political Economy 90: 777 793. Ljungqvist, L., and T. Sargent (1995), "The Swedish unemployment experience", European Economic Review 39:1043-1070. Lucas Jr, R.E. (1987), Models of Business Cycles (Basil Blackwell, New York). MacLeod, W.B., and J.M. Malcomson (1993), "Investments, holdup, and the form of market contracts", American Economic Review 83:811-837. Marimon, R., and E Zilibotti (1998), "'Actual' versus 'virtual' employment in Europe. Is Spain different?", European Economic Review 42:123-153. Martin, J.R (1994), "The extent of high unemployment in OECD countries", in: Reducing Unemployment: Current Issues and Policy Options (Federal Reserve Bank of Kansas City, August 1994). Merz, M. (1995), "Search in the labor market and the real business cycle", Journal of Monetary Economics 36:269-300. Millard, S.P., and D.T. Mortensen (1997), "The unemployment and welfare effects of labour market policy: a comparison of the U.S. and U.K.", in: D. Snower and G. de la Dehesa, eds., Unemployment Policy: Government Options for the Labour Market (Cambridge University Press, Cambridge). Mortensen, D.T. (1978), "Specific capital and labor turnover", The Bell Journal of Economics 9(2): 572-586. Mortensen, D.T. (1982a), "The matching process as a noncooperative/bargaining game", in: J.J. McCall, ed., The Economics of Information and Uncertainty (University of Chicago Press, Chicago, IL) 233-254.

1228

D.T. Mortensen and C.A. Pissarides

Mortensen, D.T. (1982b), "Property rights and efficiency in mating, racing, and related games", American Economic Review 72:968-979. Mortensen, D.T. (1994a), "Reducing supply side disincentives to job creation" in: Reducing Unemployment: Current Issues and Policy Options (Federal Research Bank of Kansas City). Mortensen, D.T. (1994b), "The cyclical behavior of job and worker flows", Journal of Econorrfic Dynamics and Control 18:1121-1142. Mortensen, D.T. (1996), "The unemployment and income effects of active labor market policy: the case of the U.K.", in: H. von Christian Drager, E Pissulla, and A.W. yon Czege, eds., More Competition, More Jobs Is Full Employment an Illusion? (Nomos Verlagsgesellschaft, BadenrBaden). Mortensen, D.T., and C.A. Pissarides (1994), "Job creation and job destruction in the theory of unemployment", Review of Economic Studies 61(July):397-415. Mortensen, D.T., and C.A. Pissarides (1998), "Technological progress, job creation and job destruction", Review of Economic Dynamics 1:733-753. Mortensen, D.T., and C.A. Pissarides (1999), "Unemployment responses to 'skill-biased' technology shocks: the role of labor market policy", Economic Journal 109(April):242-265. OECD (1994), Jobs Study (OECD, Paris). Phelps, E.S. (1967), "Phillips Curves, expectations of inflation and optimal unemployment over time", Economica 34:254-281. Phelps, E.S. (1968), "Money-wage dynamics and labor-market equilibrium", Journal of Political Economy 76:679-711. Phelps, E.S. (1994), Structural Slumps (Harvard University Press, Cambridge, MA). Phelps, E.S., et al. (1970), Microeconomic Foundations of Employment and Inflation Theory (Norton, New York). Pissarides, C.A. (1984a), "Search intensity, job advertising and efficiency", Journal of Labor Economics 2(January):128-143. Pissarides, C.A. (1984b), "Efficient job rejection", Economic Journal Conference Papers 94:97-108. Pissarides, C.A. (1985), "Short-rnn equilibrium dynamics of unemployment, vacancies and real wages", American Economic Review 75(September):676-690. Pissarides, C.A. (1986), "Trade unions and the efficiency of the natural rate of unemployment", Journal of Labor Economics 4(October):582-595. Pissarides, C.A. (1990), Equilibrium Unemployment Theory (Basil Blackwell, Oxford). Pissarides, C.A. (1994), "Search unemployment with on-the job search", The Review of Economic Studies 61 (July):457-477. Pissarides, C.A. (1998), "The impact of employment tax cuts on unemployment and wages; the role of unemployment benefits and tax structure", European Economic Review 42(January): 155-183. Rubinstein, A., and A. Wolinsky (1985), "Equilibrium in a market with sequential bargaining", Econometrica 53:1133-1150. Scarpetta, S. (1996), "Assessing the role of labour market policies and institutional settings on unemployment: a cross-country study", OECD Economic Studies No. 26 (OECD, Paris). Solow, R.M. (1956), "A contribution to the theory of economic growth", Quarterly Journal of Economics 70(1):65-94. Solow, R.M. (1959), "Investment and technical progress", in: Mathematical Methods in the Social Sciences (Stanford University Press, Stanford, CA). Stigler, G.J. (1962), "Information in the labor market", Journal of Political Economy 70:94-105. Wolinsky, A. (1987), "Matching, search, and bargaining", Journal of Economic Theory 42(August): 311-333. Yashiv, E. (1997), "The determinants of equilibrium unemployment", Working Paper CR 600/1997 (HEC).

AUTHOR INDEX

Amman, H.M. 368, 535 Anderson, E. 564 Anderson, E.W. 368, 369 Ando, A., s e e Modigliani, E 762 Andolfatto, D. 994, 1158, 1173, 1203, 1207, 1221 Andres, J., s e e Blanchard, O.J. 1214 Araujo, A. 323 Arellano, M. 787 Arifovic, J. 455, 465, 472, 521-523, 525-527, 531 Arrow, K. 664, 1033, 1042 Arrow, K.J. 1218 Arthur, W.B. 454, 476, 534 Ascari, G. 1041 Aschauer, D.A. 1656, 1657 Asea, P., s e e Mendoza, E. 1439 Ashenfelter, O. 618, 1038, 1039 Askildsen, J.E. 1074 Atkeson, A. 575, 610, 786, 847, 1298, 1675, 1718, 1720 Atldnson, A.B. 1673, 1676, 1680, 1682, 1718 Attanasio, O.P. 564, 607, 608, 610-613, 752, 753, 756, 759, 769, 777, 779, 781,783, 784, 787, 789-794, 796, 797, 802, 1264, 1655 Auerbach, A.J. 380, 549, 576, 588, 590, 591, 593, 616, 821, 1624, 1634, 1635, 1639, 1652, 1718 Auerbach, A.J., s e e Feldstein, M.S. 904, 906 Auernheimer, L. 1449 Auster, R. 474 Autor, D. 577 Axilrod, S.H. 1493 Azariadis, C. 262, 264, 271, 289, 389, 395, 516, 527, 658, 660, 661, 1035

Abel;A.B: 818,831, 834, 835, 994, 1069, 1237, 1251, 1253, 1265, 1266, 1268, 1271, 1272, 1284, 1285, 1651 Abowd, J. 567, 568, 570, 571,616, 759 Abraham, J. 1039 Abraham, K.G. 1058 Abraham, K.J. 1183, 1221 Abramovitz, M. 208 Abramowitz, M. 865, 887 Acemoglu, D. 852, 1215 Adam, M. 500 Adams, C. 1538 Adelman, EL., s e e Adelman, I. 9 Adelman, I. 9 Ag6nor, RR. 1543, 1572 Aghion, R 264, 665, 672, 715,719, 1157, 1208, 1210, 1213, 1377, 1450, 1454, 1465 Aiyagari, S.R. 442, 547, 552, 566, 567, 983, 1140, 1293, 1631 Aizenman, J. 1497, 1538, 1540 Akaike, H. 217 Akerlof, G. 1344 Akeflof, G.A. 198, 397, 1034, 1035, 1039, 1157, 1200 al Nowaihi, A. 1415, 1422, 1437 Alesina, A. 162, 277-279, 692, 1404, 1416, ..... 1422-1426,...1.430~1432, 1438, 1439, 1446, 1449, 1450, 1454, 1460, 1461, 1464-1466, 1469, 1471, 1518, 1522, 1540 Alesina, A., s e e Tabellini, G. 1456, 1465 Alessie, R. 774, 775 Allais, M. 661, 1309 Alien, D.S. 871 Allen, E 576 Almeida, A. 1432, 1495 Alogoskoufis, G.S. 166, 214, 215 Altonji, J. 615 Altonji, J., s e e Hayashi, E 796 Altonji, J.G. 789 Altug, S. 584, 595, 611,612, 785, 786, 792 Alvarez, E 575, 996 Ambler, S. 944, 1062, 1067 American Psychiatric Association 1325

Bacchetta, P. 1344 Bacchetta, E, s e e Feldstein, M. 1637 Bachelier, L. 1316 Backus, C.K. 549 Backus, D. 1017, 1031, 1270, 1405, 1414, 1415 Backus, D.K. 9, 42, 45, 938, 1316, 1708 I-1

I-2 Bade, R. 1432, 1438 Bagehot, W. 155, 1485, 1515 Bagwell, K. 1125 Bagwell, K., s e e Bernheim, B.D. 1647 Bailey, M.J. 1643 Bairoch, P. 719, 724 Baker, J.B. 1125 Balasko, Y. 427, 506 Balassa, B.A. 705 Balke, N.S. 6, 61, 114, 204, 205, 221 Ball, L. 42, 72, 199, 1023, 1037, 1039, 1041, 1127, 1415, 1499, 1504, 1542, 1632, 1650, 1651 Ball, R. 1321 Ballard, C. 1639 Banerjee, A., s e e Aghion, R 1377 Bange, M.M., s e e De Bondt, W.E 1321 Banks, J. 751, 758, 759, 770, 783, 788, 790-792 Banks, J., s e e Attanasio, O.P. 756, 759, 793, 794 Bannerjee, A.V 1332 Bansal, R. 1255 Barberis, N. 1294, 1322 Barclays de Zoete Wedd Securities 1238 Barkai, H. 1572 Barnett, S. 831 Barnett, W. 538, 540 Barone, E. 702 Burro, R.J. 101, 157, 158, 173, 237, 245, 246, 252, 269, 271,272, 277-281,284, 643, 651, 657, 659, 671, 675, 681, 683-685, 688, 689, 691-694, 696, 943, 974, 1023, 1055, 1155, 1404, 1405, 1411, 1412, 1414, 1415, 1425, 1438, 1439, 1466, 1485-1489, 1637, 1641, 1642, 1645, 1662, 1675, 1702, 1705, 1707 Barsky, R. 43, 558, 564, 565 Barsky, R., s e e Solon, G. 579, 1058, 1102, 1106 Barsky, R., s e e Warner, E.J. 1019 Barsk-y, R.B. 182, 215, 216, 1149, 1237, 1277, 1294-1296, 1653 Barth, J.R. 1657 Bartle, R.G. 76 Barueci, E. 525 Basar, T. 1449 Basu, S. 399, 402, 433, 983, 992, 994, 1069, 1080-1082, 1096, 1097, 1117, 1142 Bates, D.S. 1310, 1324 Baumol, W.J. 252, 269

Author

Index

Baxter, M. 9, 11, 12, 45, 203, 380, 430, 934, 938, 974, 980, 992, 1296, 1404 Bayoumi, T. 161,211,216, 2t7, 219 Bayoumi, T., s e e Mussa, M. 208 Bazaraa, M.S. 331 Bean, C., s e e Blanchard, O.J. 1214 Bean, C.R. 785, 1497 Beaudry, E 99, 395, 413, 592, 1264 Beaulieu, J.J. 801,802, 876 ' Becket, G. 592, 653 Becker, G.S. 317, 1645 Becket, G.S., s e e Ghez, G. 615, 752, 759 Becket, R. 369 Beetsma, R. 1411, 1436, 1438 Bekaert, G. 1281 Bell, D.E. 1313 Bellman, R. 336, 340 Belsley, D. 882, 887, 888, 892 Beltratti, A. 524, 525 Ben-David, D. 265, 278 Ben Porath, Y. 577, 582 Benabou, R. 1017, 1018, 1031, 1128, 1129, 1469, 1472, 1473 B~nabou, R. 268 Benartzi, S. 1290, 1312, 1313 B6nassy, J. 507 Benassy, J.-E 1506 Benhabib, J. 283, 395, 399-405, 408, 412-414, 417, 419, 421,423-427, 431,433-435, 437, 442, 505, 550, 847, 1145, 1449, 1465, 1467, 1472 Benigno, E, s e e Missale, A. i450 Benjamin, D. 161 Bennett, R. 395 Bensaid, B. 1446, 1449 Benveniste, A. 476, 531 Benveniste, L.M. 321 Bergen, M., s e e Dutta, S. 1019, 1020 Bergen, M., s e e Levy, D. 1014, 1015, 1019 Bergen, P.R. 1041 Berger, L.A. 1330 Bergsla'Sm, V. 538 Bernanke, B.S. 68, 72, 76, 83, 89, 91 93, 114, 144, 178, 182-184, 800, 856, 857, 1036, 1343, 1345, 1346, 1352, 1357, 1361, 1363, 1365, 1369, 1371, 1373, 1376-1378, 1495, 1578 Bernard, A.B. 254, 271,287, 288 Bernard, V.L. 1321 Bernheim, B.D. 1646, 1647, 1649, 1654, 1659, 1660

Author

Index

Berry, M., s e e Dreman, D. 1320 Berry, T.S. 1618 Bertocchi, G. 474 Bertola, G. 643, 708, 801, 821,834, 835, 840, 843, 1187, 1222, 1472, 1580 Bertsekas, D.E 326 Besley, T. 856 Betts, C.M. 217 Beveridge, S. 1062, 1143 Bewley, T. 566, 1155 Bhaskar, V. 1037 Bianchi, M. 290, 292 Bikhchandani, S. 1332 Bils, M. 694, 910, 912, 983, 1053, 1059, 1069, 1070, 1072, 1075, 1076, 1078-1081, 1085, 1087, 1102, 1104, 1119, 1120, 1130 Bils, M.J. 579 Binder, M. 271, 1092 Binmore, K. 462 Binmore, K.G. 1188 Bisin, A. 427 Bismut, C., s e e Benabou, R. 1017, 1018, 1031 Bizet, D. 380 Bjorck, A., s e e Dahlquist, G. 337 Black, E 417, 1280, 1310, 1331, 1507 Blackwell, D. 320 Blad, M., s e e B6nassy, J. 507 Blanchard, O.J. 40-42, 211, 216, 217, 391, 416, 471,504, 643,660, 818, 852, 877, 887, 888, 890, 892, 906, 912, 1013, 1030, 1033, 1034, 1036, 1041, 1112, 1130, 1162, 1173, 1176, 1183, 1184, 1194, 1202, 1214, 1221, 1266, 1491, 1634, 1635, 1645, 1650 Blanchard, O.J., s e e Missale, A. 1450 Blank, R. 579 Blinder, A. 587, 750, 1018-1020, 1038 Blinder, A.S. 41,876, 881,887, 893, 903, 904, 907, 908, 910, 1018, 1085, 1118, 1344, 1485, 1499, 1660 Blinder, A.S., s e e Bernanke, B.S. 83, 91, 93 Bliss, C. 1461, 1465 Bliss, R., s e e Fama, E.E 1280 Blomstrom, M. 277, 279, 280 Bloomfield, A. 156 Blume, L.E. 321,322, 474 Blume, L.E., s e e Bray, M. 474 Blundell, R. 572, 602, 611,612, 620, 764, 770, 779, 781,783, 788, 790-792, 797 Bltmdell, R., s e e Banks, J. 758, 759, 770, 783, 788, 790-792

I-3 Boadway, R. 1463 Bodnar, G. 1318 B6hrn, V. 475, 646 Bohn, H. 1465, 1622, 1650, 1691 Boldrin, M. 362, 399, 400, 506, 962, 1062, 1284, 1297, 1465 Bolen, D.W. 1325 Bollerslev, T. 1236, 1280 BoRon, E, s e e Aghion, E 1377, 1450, 1454, 1465 Bona, J.L. 313 Boothe, P.M. 1658 Bordo, M.D. 152, 155-160, 162, 164-167, 182, 184, 185, 194, 202-204, 207-209, 211,215, 217~21, 1404, 1438, 1590 Bordo, M.D., s e e Bayoumi, T. 161 Bordo, M.D., s e e Belts, C.M. 217 Borenstein, S. 1124 Boschan, C., s e e Bry, G. 8 Boschen, J.E 139 Boskin, M.J. 618 Bossaerts, E 454 Bosworth, B., s e e Collins, S. 653 Bourguignon, E, s e e Levy-Leboyer, M. 222 Bovenberg, A.L., s e e Gordon, R.H. 1637 Bovenberg, L., s e e Beetsma, R. 1411 Bowen, W. 619 Bowman, D. 1313 Boyd, W.H., s e e Boleu, D.W. 1325 Boyle, M., s e e Paulin, G. 751 Boyle, E 380 Boyle, P.P., s e e Tan, K.S. 334 Brainard, W.C. 817 Brauch, R., s e e Paulin, G. 751 Braun, R.A. 974 Braun, S.N., s e e K r a n e , S.D. 876, 877 Bray, A. 1290 Bray, M. 454, 463, 465, 466, 473-475, 527 Brayton, E 1043, 1344, 1485 Brayton, E, s e e Hess, G.D. 1485, 1509 Breeden, D. 1246 Breiman, L. 289 Bresnahan, T.E 911,912 Bretton Woods Commission 208 Broadbent, B. 1412 Broadbent, B., s e e Barro, R.J. 1412 Broadie, M., s e e Boyle, P. 380 Brock, W.A. 319, 407, 455, 528, 532, 547, 552, 556, 942, 951, 1507 Brown, C. 585 Brown, E, s e e Ball, R. 1321

1-4 Brown, S. 1242 Browning, E. 1463 Browning, M. 598, 606, 607, 610-612, 750, 752, 771,778, 787, 792, 798, 803 Browning, M., s e e Attanasio, O.P. 607, 608, 610, 611,613, 779, 789, 791, 1655 Browning, M., s e e Blundell, R. 611,612, 779, 781,783, 790, 791 Broze, L. 487, 488 Brugiavini, A. 775 Brugiavini, A., s e e Banks, J. 770, 788 Brumberg, R., s e e Modigliani, E 761 Brumelle, S.L., s e e Puterman, M.L. 336, 338 Brunner, A.D. 104 Brunnel, K. 179, 183, 191, 1025, 1491 Bruno, M. 471, 1090, 1496, 1538, 1539, 1543, 1553 Bry, G. 8 Bryant, R.C. 1043, 1491, 1497, 1516-1518 Bryant, R.R. 1313 Buchanan, J.M. 1631, 1642 Buchholz, T.G. 1643 Buckle, R.A. 1019 Bufinan, G. 1543 Buiter, W. 1030, 1521 Bulirsch, R., s e e Stoer, J. 334 Bull, N. 1675, 1711 Bullard, J. 466, 507, 509, 515, 526 Bullard, J., s e e Arifovie, J. 527 Bulow, J. 1448, 1449 Burdett, K. 1173, 1196 Bureau of the Census 1618, 1619 Burns, A.E 5, 8, 931,934 Burns, A.E, s e e Mitchell, W.C. 8, 44 Burnside, C. 399, 930, 980-985, 994, 1078, 1142, 1162 Burfless, G. 618, 620 Butkiewiez, J.L. 1621

Caballe, J. 578 Caballero, R.J. 399, 749, 771, 794, 801, 802, 821-823, 828, 830, 832, 834-838, 840-842, 844, 846, 847, 852, 855, 856, 994, 1032, 1157, 1158, 1160, 1187, 1210, 1211, 1213, 1472 Caballero, R.J., s e e Bertola, G. 801,821, 834, 840, 843, 1187 Cagan, E 157, 161,203, 1534 Cage, R., s e e Paulin, G. 751 Calmfors, L. 1214

Author

Index

Calomiris, C.W. 169, 181, 183, 187, 191, 1376 Calvo, G.A. 389, 397, 408, 419, 422, 1030, 1032, 1034, 1114, 1346, 1360, 1363, 1389, 1400, 1415, 1428, 1445-1447, 1449, 1450, 1535, 1538, 1539, 1546, 1552, 1554, 1557, 1563, 1564, 1568, 1569, 1571-1573, 1582, 1583, 1587-1589, 1591, 1592, 1596, 1597, 1599-1603, 1605 Cameron, S. 589 Campbell, J. 92 Campbell, J.R. 846, 847, 994 Campbell, J.Y. 763, 764, 769, 784, 930, 961, 1120, 1140, 1141, 1145, 1150, 1235-1238, 1251, 1255, 1257, 1258, 1261, 1264-1266, 1268, 1270, 1272, 1274, 1275, 1280, 1284, 1286, 1290, 1320, 1655 Canavese, AJ. 1543 Canetti, E.D., s e e Blinder, A.S. 1018, 1118 Canjels, E. 55 Canova, F. 283,376, 377, 379 Cantor, R. 1344 Canzoneri, M.B. 159, 160, 1405, 1414, 1415, 1507, 1508 Capie, E 154, 163, 222, 1438 Caplin, A. 849, 850 Caplin, A.S. 801,910, 1031, 1032 Card, D. 580, 1016, 1148 Card, D., s e e Abowd, J. 567, 568, 570, 571, 616, 759 Card, D., s e e Ashenfelter, O. 1038, 1039 Cardia, E. 1655 Cardia, E., s e e Ambler, S. 1062, 1067 Cardoso, E. 1543 Carey, K., s e e Bernanke, B.S. 178, 182 Carlson, J. 473 Carlson, J.A. 904 Carlson, J.A., s e e Buckle, R.A. 1019 Carlson, J.B. 104 Carlstrom, C. 1348, 1357, 1368, 1378, 1379 Carlton, D. 1129 Carlton, D.W. 1018-1020 Carmichael, H.L. 1155 Carpenter, R.E. 876, 881,912, 1344 Carroll, C.D. 567, 572, 573, 593, 759, 762, 769, 771,785, 788;793;'1264, :1344,1653, 1655 Case, K.E. 1323 Casella, A. 1463, 1465 Caselli, E 277-279, 283, 284, 286

Author

Index

Cass, D. 244, 246, 247, 295, 389, 516, 643, 649, 662, 942, 948, 1673 Cass, D., s e e Balasko, Y. 427 Castafieda, A. 380 Cazzavilan, G. 426 Cecchetti, S.G. 182, 217, 876, 1015, 1016, 1018, 1019, 1251, 1265, 1270, 1272, 1294, 1296 Cecchetti, S.G., s e e Ball, L. 1037 Chadha, B. 1031, 1542 Chah, E.Y. 775 Chamberlain, G. 283, 286, 785 Chamberlain, T.W. 1334 Chamley, C. 400, 851, 1439, 1673, 1675, 1693, 1697, 1699 Champsaur, , P. 538, 463 Chan, L. 1321 Chan, L.K.C. 1653 Chandler, L.V. 176 Chang, C.C.Y., s e e Chamberlain, T.W. 1334 Chaff, V.V. 72, 124, 397, 422, 672, 697, 698, 700, 701, 709, 715, 720, 722, 723, 974, 1036, 1037, 1040-1042, 1371, 1448, 1449, 1459, 1488, 1489, 1578, 1673-1676, 1691, 1699, 1708-1710, 1720, 1723 Chari, V.V.,s e e Atkeson, A. 1675, 1718, 1720 Chatterjee, S. 996, 1126 Chatterji, S. 475, 507 Chattopadhyay, S.K., s e e Chatterji, S. 475, 507 Chen, N. 1281 Chen, X. 476, 532 Cheung, C.S., s e e Chamberlain, T.W. 1334 Chevalier, J.A. 1122, 1123 Chiappori, P.A. 391,395, 516 Childs, G.D. 882 Chinn, M., s e e Frankel, J. 1497 Chiffnko, R.S. 815, 817, 1058, 1066, 1086, 1344, 1367 Chiswick, B., s e e Becker, G. 592 Cho, D. 278 Cho, I.-K. 455, 465, 524, 525 Cho, J.O. 974, 976, 1025, 1036 Cho, J.O., s e e Bils, M. 983, 1075, 1079, 1104 Chou, R.Y. 1236, 1280 Chou, R.Y., s e e Bollerslev, T. 1236, 1280 Choudhfi, E.U., s e e Bordo, M.D. 184, 194 Chow, C.-S. 326, 334 Chow, G.C. 1294 Christensen, L.R. 673, 688

1-5 Christiano, L.J. 43, 67-70, 83, 84, 89, 91-94, 99, 108, 109, 114, 115, 124, 137, 143, 144, 314, 329, 330, 339, 347, 349, 350, 355, 362, 364, 367, 369, 370, 376, 377, 379, 426, 504, 547, 764, 881, 888, 909, 952, 962, 974, 1011, 1017, 1018, 1021, 1030, 1038, 1089, 1100, 1296, 1365, 1369, 1708, 1736 Chffstiano, L.J., s e e Aiyagafi, S.R. 1140 Chffstiano, L.J., s e e Boldrin, M. 962, 1284, 1297 Christiano, L.J., s e e Charl, VV 72, 1449, 1673, 1675, 1676, 1691, 1699, 1708 1710, 1720, 1723 Chung, K.L. 299 Clarida, R. 95, 96, 136, 422, 1364, 1368, 1486 Clark, D., s e e Kushner, H. 476 Clark, J.M. 816 Clark, K.B. 602, 1173 Clark, RB., s e e Mussa, M. 208 Clark, T.A. 173 Clark, T.E. 1091, 1485 Cochrane, J. 1120 Cochrane, J.H. 101, 211, 796, 1234, 1246, 1249, 1296 Cochrane, J.H., s e e Campbell, J.Y. 1237, 1251, 1284, 1286 Coe, D.T. 265 Cogley, T. 211,395, 547, 967, 1142, 1503 Cohen, D. 271 Cohen, D., s e e Greenspan, A. 798, 844, 847 Cob_n, R., s e e Modigliani, E 1321 Cole, H.L. 576, 1163, 1194, 1201-1203, 1207, 1446, 1449, 1603 Cole, H.L., s e e Chaff, V.V. 1459 Coleman, T. 601 Coleman, W.J. 367, 380 Coleman II, W.J. 114 Coleman II, W.J., s e e Bansal, R. 1255 Collins, S. 653 Conference Board 43 Congressional Budget Office 1618, 1619, 1621, 1624-1627, 1639, 1640, 1660 Conley, J.M., s e e O'Barr, W.M. 1332 Conlon, J.R. 1032 Constantinides, G.M. 559, 567, 781,803, 1237, 1284, 1291, 1293 Constantinides, G.M., s e e Ferson, W.E. 1284 Contini, B. 1177, 1178, 1180, 1200, 1222 Cook, T. 194, 195, 1493

I-6 Cooley, T.E 42, 69, 97, 101, 115, 124, 137, 376, 380, 408, 411, 549, 847, 954, 962, 974, 1376, 1463, 1736 Cooley, T.E, s e e Cho, J.O. 974, 976, 1025, 1036 Cooper, R. 204, 398, 824 Cooper, R., s e e Azariadis, C. 395 Cooper, R., s e e Chatterjee, S. 996, 1126 Cootner, EH. 1316 Corbo, V. 1543, 1554 Correia, I. 974, 1537, 1675, 1720, 1733 Cossa, R. 584 Council of Economic Advisers 1639 Cox, D. 705 Cox, W.M. 1621 Cox Edwards, A., s e e Edwards, S. 1543, 1554, 1555, 1575 Crawford, V.E 475 Crossley, T., s e e Browning, M. 610, 798 Croushore, D. 1485, 1653 Crucini, M.J. 178, 705 Crucini, M.J., s e e Baxtel, M. 1296 Cukierman, A. 1404, 1414, 1415, 1432, 1437, 1438, 1450, 1456, 1463, 1465 Cukierman, A., s e e Alesina, A. 1424, 1426 Cukierman, A., s e e Brunner, K. 1025 Cummings, D., s e e Christensen, L.R. 673, 688 Cummins, J.G. 822, 856, 1344 Cunliffe Report 161 Currie, D. 454, 504 Cushman, D.O. 95, 96 Cutler, D.M. 797, 1290, 1320, 1321, 1624 Cyrus, T., s e e Frarlkel, J.A. 280 Dahlquist, G. 337 Daniel, B.C. 1647 Daniel, K. 1322 Danthine, J.-P. 329, 370, 952, 962, 1002, 1157 Darby, M.R. 166 Dasgupta, P. 655, 656 d'Autttme, A. 487 DaVanzo, J. 618 Daveri, E 1220 Davidson, J. 750 Davies, J.B. 766 Davis, D. 1033 Davis, P.J. 333 Davis, S.J. 1151, 1152, 1160, 1161, 1176, 1178, 1180, 1194, 1199

Author

Index

Davis, S.J., s e e Attanasio, O.P. 796, 797 Davutyan, N. 156 Dawid, H. 523, 527 De Bondt, W.E 1307, 1320, 1321, 1323 de Fontnouvelle, E, s e e Brock, W.A. 528 De Fraja, G. 1037 De Gregorio, J. 1546, 1551, 1573, 1575, 1577 de Haan, J., s e e Eijffinger, S. 1404, 1438 de la Torre, M. 41 De Melo, J., s e e Corbo, V. 1543 de Melo, J., s e e Hanson, J. 1543 De Melo, M. 1535, 1551 De Pablo, J.C. 1543 de Soto, H. 695 Deaton, A. 752, 756, 764, 771,775, 776, 783, 785, 787, 794, 798, 1344 Deaton, A., s e e Blinder, A. 750 Deaton, A., s e e Browning, M. 611, 612, 752, 787, 792 Deaton, A.S. 1264 Deaton, A.S., s e e Campbell, J.Y. 764 Debelle, G. 1489, 1518, 1522 DeCanio, S. 454, 463 DeCecco, M. 155 Degeorge, E 1321 DeKock, G. 158 DeLong, J.B. 252, 279, 695, 1042, 1290, 1324 DeLong, J.B., s e e Barsky, R.B. 1237, 1277, 1294~1296 den Haau, W.J. 271,347, 354, 369, 994, 1166, 1194, 1203, 1204, 1206, 1207 Denardo, E.V. 320 Denison, E.E 237, 653 Denizer, C., s e e De Melo, M. 1535, 1551 Denson, E.M. 40 Desdoigts, A. 290 DeTray, D.N., s e e DaVanzo, J. 618 Devereux, M. 952, 1466, 1471 Devereux, M., s e e Alessie, R. 775 Devereux, M., s e e Beaudry, P. 395,413 Devereux, M.B. 1126 Devereux, M.B., s e e Beaudry, E 99 Devine, T.J. 1166 Dewatripont, M., s e e Aghion, P. 1157 Dezhbakhsh, H. 1039 Di Tella, G., s e e Canavese, A.J. 1543 Diamond, P. 796 Diamond, P., s e e Shafir, E. 1316 Diamond, EA. 661, 1157, 1161, 1162, 1173, 1188, 1634, 1645, 1684, 1718

Author

Index

Diamond, EA., s e e Blanchard, O.J. 41, 42, 1162, 1173, 1183, 1184, 1194, 1202, 1221 Diaz-Alejandro, C.E 1543 Diaz-Gimenez, J., s e e Castafieda, A. 380 Dickens, W.T., s e e Akerlof, G.A. 198 Dickey, D.A. 53, 54, 212 Dickinson, J. 618 Dicks-Mireaux, L., s e e Feldstein, M. 1633 Diebold, EX. 6, 11 Dielman, T., s e e KaUick, M. 1325 Dixit, A. 824, 829, 844, 1115, 1121, 1126 Dixit, A.K., s e e Abel, A.B. 835 Dixon, H. 537 Dodd, D.L., s e e Graham, B. 1323 Dolado, J. 1437 Dolado, J.J. 1214 Dolde, W. 1318 Dolde, W..C., s e e Tobin, J. 773 Domar, E. 640 Domberger, S. 1019 Dominguez, K. 164, 182 Domowitz, I. 1020, 1083, 1093 Doms, M. 823, 838 Donaldson, J.B., s e e Constantinides, G.M. 1293 Donaldson, J.B., s e e Danthine, J.-P. 329, 370, 952, 962, 1002, 1157 Doob, J.L. 299 Dornbusch, R. 198, 1043, 1543, 1562, 1563, 1565, 1568, 1582, 1590, 1637 Dotsey, M. 370, 952, 974, 1032, 1043, 1522, 1652 Drazen, A. 1463, 1465, 1541, 1580 Drazen, A., s e e Alesina, A. 162, 1450, 1461, 1465, 1540 Drazen, A., s e e Azariadis, C. 262, 264, 271, 289, 527, 658, 660 Drazen, A., s e e Bertola, G. 1580 Drazen, A., s e e Calvo, G.A. 1571 Dreman, D. 1320, 1323 Dreze, J. 770 Drifflll, J., s e e Backus, D. 1405, 1414, 1415 Driskill, R.A. 1042 Drudi, F. 1450 Drugeon, J.E 426 Dueker, M.J. 1485 Duffle, D. 380 Duffle, D., s e e Constantinides, G.M. 567, 781, 1237, 1291 Duffy, J. 257, 439, 473, 500 Duffy, J., s e e Arifovic, J. 527

I-7 Duffy, J., s e e Bullard, J. 526 Duguay, E 215 Dumas, B. 561, 564 Dunlop, J.T. 939, 1059 Dunn, K.B. 800, 1284 Dunne, T., s e e Doms, M. 823, 838 Dupor, B. 994 Durkheim, 1~. 1331 Durlauf, S.N. 254, 262-264, 268, 270, 271, 287, 289, 303, 550, 905 907 Dm-lauf, S.N., s e e Bernard, A.B. 254, 271,287, 288 Dutta, EK. 380 Dutta, S. 1019, 1020 Dutta, S., s e e Levy, D. 1014, 1015, 1019 Dutton, J. 156 Dyl, E.A. 1334 Dynan, K.E. 770

Easley, D., s e e Blume, L.E. 321,322, 474 Easley, D., s e e Bray, M. 474 Easterly, W. 277-279, 281, 675, 703, 1538, 1547, 1553, 1560, 1561 Easterly, W., s e e Bruno, M. 1553 Eaton, J. 719 Eberly, J.C. 801,802, 1344 Eberly, J.C., s e e Abel, A.B. 831, 834, 835, 994 Echenique, E 1551, 1561 Eckstein, O. 1344 Eden, B. 1019, 1023 Edin, D.A. 1457 Edwards, S. 1538, 1543, 1554, 1555, 1575, 1578-1580 Edwards, S., s e e Cukierman, A. 1456, 1465 Edwards, W. 1322 Eichenbaum, M. 83, 94, 96, 99, 100, 137, 184, 549, 550, 785, 799, 800, 803, 885, 888, 905407, 912, 957, 1084 Eichenbaum, M., s e e Aiyagari, S.R. 1140 Eichenbaum, M., s e e Burnside, C. 399, 930, 980-985, 994, 1078, 1142, 1162 Eichenbaum, M., s e e Chaff, VV 72, 1449 Eichenbaum, M., s e e Christiano, L.J. 43, 6770, 83, 84, 89, 91-94, 99, 108, 115, 124, 137, 143, 144, 376, 377, 379, 764, 974, 1011, 1021, 1038, 1089, 1100, 1365, 1369, 1708, 1736 Eichenbaum, M.S., s e e Christiano, L.J. 881, 888

I-8 Eichengreen, B. 152, 154-157, 160, 162 164, 168, 178, 185, 187, 189, 204, 208, 209, 211,219, 1449, 1465, 1590 Eichengreen, B., s e e Bayolmai, T. 211, 216, 217, 219 Eichengreen, B., s e e Bordo, M.D. 162 Eichengreen, B., s e e CaseUa, A. 1463, 1465 Eijffinger, S. 1404, 1432, 1438 Eisner, R. 817, 1310, 1621, 1622 Ekeland, I. 1689 E1 Karoui, N. 835 Elias, V.J. 673 Ellison, G. 475, 1124 Ellson, R.E., s e e Bordo, M.D. 157 Elmendorf, D.W. 1439 Elmendorf, D.W., s e e Ball, L. 1650, 1651 Elmendorf, D.W., s e e Feldstein, M. 1656 Emery, K.M. 215 Emery, K.M., s e e Balke, N.S. 114 Engel, E., s e e Caballero, R.J. 801, 802, 821, 835-838, 840-842, 994, 1032, 1158 Engelhardt, G. 1344 Engle, R., s e e Bollerslev, T. 1280 Engle, R.E 50 Engle, R.E, s e e Chou, R.Y. 1236, 1280 Englund, E 9 Epstein, L.G. 556, 558, 564, 565, 744, 769, 1250, 1256 Erceg, C. 1041 Erceg, C.J., s e e Bordo, M.D. 182 Eriksson, C. 1208 Erlieh, D. 1314 Ermoliev, Y.M., s e e Arthur, W.B. 476 Escolano, J. 1718 Esquivel, G., s e e Caselli, E 277-279, 283,284, 286 Esteban, J.-M. 264 Estrella, A. 43, 1281, 1485 Evans, C. 982 Evans, C.L. 105 Evans, C.L., s e e Bordo, M.D. 182 Evans, C.L., s e e Christiano, L.J. 67, 68, 70, 83, 84, 89, 91-94, 99, 108, 137, 143, 144, 1011, 1021, 1038, 1089, 1100, 1365, 1369 Evans, C.L., s e e Eiehenbaum, M. 83, 94, 96, 137 Evans, G.W. 425, 426, 453-455, 461-465, 468, 470, 472-478, 480, 481, 483, 484, 487, 489-492, 495-497, 500, 502, 504-507, 509-513, 516, 518-521,526-528, 530-532, 1025, 1125

Author

Index

Evans, M. 182 Evans, P. 283, 1635, 1647, 1656-1659 Faig, M. 1675, 1720 Fair, R. 1416, 1425 Fair, R.C. 876, 1077, 1491 Fair, R.C., s e e Dominguez, K. 182 Falcone, M. 326 Fallick, B.C. 855 Fama, E.E 1235, 1280, 1281, 1307, 1316, 1320-1323 Farber, H. 1200 Farmer, R. 662, 1002 Farmer, R.E. 391,395, 396, 411-414, 427-430, 434, 437, 500, 505 Farmer, R.E., s e e Benhabib, J. 395, 399-402, 408, 412-414, 417, 425,427, 431,433-435, 442, 505 Farrell, J. 1121 Faust, J. 69, 217, 1416, 1425, 1437 Fanvel, Y. 1573 Favaro, E. 1554, 1555 Fay, J.A. 1077, 1103 Fazzari, S.M. 818, 1344 Fazzari, S.M., s e e Carpenter, R.E. 881,912, 1344 Fazzari, S.M., s e e Chirinko, R.S. 1066, 1086 Featherstone, M. 1332 Federal Reserve Board 176 Feenberg, D. 60 Feenstra, R. 1569 Feenstra, R.C., s e e Bergen, ER. 1041 Feiwel, G.R. 535 Feldman, M. 474 Feldstein, M. 44, 197, 1485, 1497, 1498, 1622, 1631, 1633, 1636, 1637, 1639, 1656, 1660 Feldstein, M.S. 904, 906 Felli, E. 1083, 1122 Fellner, W. 641,657 Ferejohn, J. 1425 Fernald, J.G., s e e Basu, S. 399, 402, 433, 994, 1117, 1142 Fernandez, R. 1543, 1562 Ferris, S.P. 1314 Ferson, W.E. 1284 Festinger, L. 1314 Fethke, G. 1037 Fiebig, D.G., s e e Domberger, S. 1019 Filippi, M., s e e Contini, B. 1177, 1178, 1180, 1222 Fillion, J.E 1498

Author

Index

Finch, M.H.J. 1543 Finegan, T.A, s e e Bowen, W. 619 Finn, M. 981, 1091 Fiorina, M. 1425 Fischer, A.M., s e e Dueker, M.J. 1485 Fischer, S. 182, 197, 202, 215, 216, 1025, 1026, 1155, 1404, 1405, 1438, 1449, 1489, 1496, 1498, 1538, 1542, 1547, 1561, 1582 Fischer, S., s e e Blanchard, O.J. 471,643, 660, 1013, 1033, 1034, 1036, 1491, 1635 Fischer, S., s e e Bruno, M. 1538 Fischer, S., s e e Debelle, G. 1489, 1518, 1522 Fischhoff, B, 1319, 1326 Fischhoff, B., s e e Lichtenstein, S. 1318 Fishe, R.P.H. 173 Fisher, I, 154, 157, 203, 1316, 1321, 1343, 1372, 1377, 1485 Fisher, J. 92 Fisher, J., s e e Boldrin, M. 962, 1284, 1297 Fisher, J., s e e Christiano, LA. 314, 347, 349, 350, 355, 362, 364, 962, 1296 Fisher, J.D.M. 910, 1368, 1375, 1376, 1378 Fisher, J.D.M., s e e Campbell, J.R. 846 Fishlow, A. 155 Flandreau, M. 154 Flannery, B.P., s e e Press, W.H. 329-334, 343, 348, 356, 365 Flavin, M. 572, 749, 763, 784 Flemming, J.S. 773 Flood, R.R 152, 158, 202, 408, 1428, 1429, 1438, 1507, 1595, 1596 Flood, R.P., s e e Garber, P.M. 165 Florovsky, G. 1326 Forbes, K. 277, 278 Ford, A.G. 155 Fore, D., s e e Roseveare, D. 1626 Foresi, S., s e e Backus, D.K. 1316 Forteza, A., s e e Echenique, E 1551, 1561 Fortune, P. 1310 Foufoula-Georgiou, E., s e e Kitanidis, EK. 326 Fourgeaud, C. 454, 465, 473, 475 Fox, B.L. 326 Foxley, A. 1543 Frankel, J. 1497 Frankel, J.A. 280, 281, 1590, 1637 Franses, RH. 289 Fratianni, M. 1431 Freeman, R, 577 Fregert, K. 1016 French, K. 1280

I-9 French, K.R., s e e Fama, E.E 1235, 1281, 1320, 1323 Frenkel, J.A. 203, 1630 Frenkel, J.A., s e e Aizenman, J. 1497 Frennberg, P. 1238 Friedman, B.M. 43, 44, 1632, 1642 Friedman, D. 475 Friedman, J.H, s e e Breiman, L. 289 Friedman, M. 46, 48, 61, 137, 154, 160, 162, 168, 172, 176, 179, 180, 185, 189, 195, 203, 222, 275, 376, 572, 761, 762, 943, 1011, 1173, 1325, 1485, 1488, 1496, 1537, 1674, 1720 Froot, K. 1266, 1316 Frydman, R. 453, 454, 474, 528, 536, 539 Fuchs, G. 464, 474 Fudenberg, D. 455, 475, 1155 Fudenberg, D., s e e Ellison, G. 475 Fuerst, T. 99, 974, 1378 Fuerst, T.~ s e e Carlstrom, C, 1348, 1357, 1368~ 1378, 1379 Fuhrer, J.C. 454, 905, 908, I039, 1040, 149I, 1518 Fuhrer, J.C., s e e Carroll, C.D. 769, 785 Fukuda, S.-i, 875 Fuller, W.A., s e e Dickey~ D.A. 53, 54, 212 Fullerton, D. 576, 588, 616 Funldaouser, R. 699 Futia, C. 299 Galbraith, J.K. 1182 Gale, D. 389, 475, 849, 851, 1376 Gale, D., s e e Chamley, C. 851 Gale, W.G. 1646 Galeotti, M. 909, 1086, 1124 Gali, J. 395, 405~407, 426, 429, 434, 993, 994, 1117, 1119, 1120, 1129 Gali, J. 67, 69, 217 Gali, J., s e e Benhabib, J. 424 Gali, J., s e e Clarida, R. 96, 136, 422, 1364, 1368, 1486 Gallarotti, G.M. 154 Gallego, A.M. 321,322 Galor, O. 262, 263, 272, 660 Gandolfi, A.E., s e e Darby, M.R. 166 Garber, P.M. 165, 1323, 1543 Garber, EM., s e e Eichengreen, B. 187, 189 Garber, P.M., s e e Flood, R.P. 408, 1595, 1596 Garcia, R. 790 Garibaldi, P. 1180¢ 1222 Garratt, A. 504

1-10 Garratt, A., s e e Carrie, D. 454, 504 Garriga, C. 1675, 1718 Gaspar, J. 324, 369 Gastil, R.D. 689 Gatti, R., s e e Alesina, A. 1432 Gavin, W. 1485 Geanakoplos, J.D. 395, 458, 1322 Gear, C.W. 346 Geczy, C.C., s e e Brav, A. 1290 Gelb, A., s e e De Melo, M. 1535, 1551 Genberg, H. 165, 1428 Geoffard, RY., s e e Chiappori, RA. 391 Gerlach, S., s e e Baechetta, E 1344 Gersbach, H. 1376 Gertler, M. 83, 92-94, 1040, 1343, 1348, 1366, 1373, 1374, 1376-1378 Gertler, M., s e e Aiyagari, S.R. 1293, 1631 Gertler, M., s e e Bernanke, B.S. 92, 144, 183, 856, 857, 1036, 1345, 1346, 1352, 1357, 1365, 1369, 1371, 1373, 1376-1378, 1578 Gertler, M., s e e Clarida, R. 95, 96, 136, 422, 1364, 1368, 1486 Geweke, J. 34, 334 Geweke, J., s e e Barnett, W. 540 Geweke, J.E 89 Ghali, M., s e e Surekha, K. 908 Ghez, G. 615, 752, 759 Ghezzi, E 1572 Ghosh, A.R. 202, 207, 208 Giavazzi, E 167,203, 1438, 1446, 1449, 1580 Giavazzi, E, s e e Missale, A. 1450 Gibson, G.R. 1307 Gigerenzer, G. 1308, 1318 Gilbert, R.A. 195 Gilchrist, S. 847, 1344 Gilchrist, S., s e e Bernanke, B.S. 856, 1036, 1345, 1373, 1376 Gilchrist, S., s e e Gertler, M. 83, 92-94, 1366, 1373, 1374, 1376 Gill, EE. 329 Gilles, C., s e e Coleman II, W.J. 114 Gilson, R.J. 1154 Giovannini, A. 156, 158, 160, 166, 169, 380 Giovannini, A., s e e Giavazzi, F. 167 Gizycki, M.C., s e e Gruen, D.K. 1316 Glasserman, E, s e e Boyle, E 380 Glazer, A. 1456, 1465 Glomm, G. 712, 1472 Glosten, L. 1280 Goetzmann, W., s e e Brown, S. 1242

Author

Index

Goetzmann, W.N. 1242, 1252, 1314, 1320, 1333 Goff, B.L. 159 Gokhale, J. 750 Gokhale, J., s e e Auerbach, A.J. 1624 Goldberg, RK., s e e Attanasio, O.P. 777 Goldfajn, I., s e e Dornbusch, R. 1590 Goldstein, M., s e e Mussa, M. 208, 1637 Gomes, J. 994, 1159 Gomme, R 962, 1062 Gomme, R, s e e Andolfatto, D. 1173 Gomme, R, s e e MacLeod, W.B. 1157 Goodfriend, M. 88, 120, 121, 156, 173, 191, 194-196, 764, 1013, 1117, 1346, 1509, 1514, 1515 Goodhart, C., s e e Capie, E 154 Goodhart, C.A.E. 193 Goodhart, C.A.E., s e e Almeida, A. 1432, 1495 Goodhart, C.E.A. 1438, 1495, 1507, 1508, 1514 Goodman, A. 797 Goolsbee, A. 839, 843, 848 Gordon, D.B. 128, 134 Gordon, D.B., s e e Barro, R.J. 158, 1155, 1405, 1411, 1415, 1438, 1485-1489 Gordon, D.B., s e e Leeper, E.M. 69 Gordon, R. 1030 Gordon, R.H. 1637 Gordon, R.J. 40, 46, 48, 49, 181, 1542 Gordon, R.J., s e e Balke, N.S. 6, 61,204, 205, 221 Gorman, W.M. 553, 556, 782, 803 Gorton, G., s e e Calomiris, C.W. 181 Gottfries, N. 463, 1121, 1122 Gould, D.M. 1551, 1559, 1561 Gourieroux, C. 487 Gourieroux, C., s e e Broze, L. 487, 488 Gourieroux, C., s e e Fourgeaud, C. 454, 465, 473, 475 Gourinchas, E-O. 609, 1344 Graham, B. 1323 Graham, EC. 1656, 1657 Grandmont, J.-M. 439, 454, 460, 464, 474, 475, 481,507, 514, 526, 661 Granger, C. 34 Granger, C.W.J. 881,903 Granger, C.W.J., s e e Engle, R.E 50 Gray, J.A. 1025, 1026, 1038 Green, D., s e e MaCurdy, T.E. 619, 620 Green, E. 575

Author

Index

Green, I-I., s e e Beaudry, P. 592 Greenberg, D., s e e Burtless, G. 618 Greenberg, D.H., s e e DaVanzo, J. 618 Greenspan, A. 199, 798, 844, 847, 1630 Greenwald, B. 857, 1122, 1377 Greenwood, J. 380, 550, 576, 664, 692, 962, 980, 995 Greenwood, J., s e e Cooley, T.E 847 Greenwood, J., s e e Gomes, J. 994, 1159 Greenwood, J., s e e Gomme, P. 962, 1062 Gregory, A.W. 376, 377 Gregory, A.W., s e e Devereux, M. 952 Grier, K.B. 253 Griffiths, M., s e e Dolado, J. 1437 Griliches, Z. 541 Grilli, V. 95, 1404, 1432, 1438, 1439, 1465 Grilli, V., s e e Alesina, A. 1430 Gfilli, V., s e e DeKock, G. 158 Grilli, V., s e e Drazen, A. 1463, 1465, 1541 Grilli, V.U. 169 Gros, D., s e e Adams, C. 1538 Gross, D. 857, 1344 Gross, D.B., s e e Goolsbee, A. 839 Grossman, G.M. 264, 639, 672, 715, 1210, 1464 Grossman, H.J. 158, 1415, 1449 Grossman, S.J. 801, 1237, 1242, 1246, 1268, 1291, 1293 Grout, EA. 852 Gruen, D.K. 1316 Guerra, A. 1546, 1606, 1607 Guesnerie, R. 439, 454, 460, 464, 465, 474, 475, 506, 511,516, 526 Guesnerie, R., s e e Chiappori, P.A. 391, 395, 516 Guesnerie, R., s e e Evans, G.W. 464 Guidotti, EE. 1537, 1588, 1603, 1675, 1720 Guidotti, EE., s e e Calvo, G.A. 1447, 1450 Guidotti, EE., s e e De Gregorio, J. 1546, 1551, 1573, 1575, 1577 Guiso, L. 772 Guiso, L., s e e Galeotti, M. 909 Gulde, A.M., s e e Ghosh, A.R. 202, 207, 208 Gultekin, M. 1317 Gultekin, N.B., s e e Gultekin, M. 1317 Guo, J.-T., s e e Farmer, R.E. 395, 427-430, 434, 505 Guo, J.-T. 416, 427 Gurley, J.G. 1507 Gust, C. 1041 Guttman, E, s e e Erlich, D. 1314

1-11 Haberler, G. 185 Hahn, E 661 Hahn, T., s e e Cook, T. 194, 1493 Hahn, W. 479 Hairault, J.-O. 1036 Haldane, A.G. 1432, 1438, 1485, 1495, 1497 Haley, W.J. 585 Hall, G. 911 Hall, R.E. 399, 556, 573, 595, 607, 608, 673, 679, 680, 683-686, 702, 765, 767-769, 784, 789, 791, 794, 817, 856, 930, 982, 1068, 1070, 1079, 1089, 1092, 1095, 1096, 1141-1143, 1145, 1151-1153, 1157, 11601164, 1200, 1261, 1485, 1493, 1498, 1655, 1656 Hall, S., s e e Currie, D. 454, 504 Hall, S., s e e Garratt, A. 504 Hailerberg, M. 1460, 1465 Haltiwanger, J., s e e Caballero, R.J. 821, 837, 838, 840-842, 1158 Haltiwanger, J., s e e Cooper, R. 824 Haltiwanger, J.C. 881 Haitiwanger, J.C., s e e Abraham, K.G. 1058 Haltiwanger, J.C., s e e Davis, S.J. 1151, 1152, 1160, 1161, 1176, 1178, 1180, 1194, 1199 Hamermesh, D. 577 Hamilton, A. 1659 Hamilton, J. 963 Hamilton, J.D. 12, 72, 80, 182, 1118, 1265 Harnmerlin, G. 344 Hammour, M.L., s e e Caballero, R.J. 846, 847, 852, 855, 856, 1157, 1158, 1160, 1187, 1210, 1211, 1213, 1472 Hannerz, U. 1332 Hansen, B. 1194 Hansen, B.E. 38, 39 Hansen, G.D. 547, 55l, 602, 976, 977, 1200 Hansen, G.D., s e e Cooley, T.E 69, 97, 101, 115, 124, 137, 380, 408, 411,974, 1736 Hansen, L.P. 547, 555, 556, 558, 572-574, 768, 769, 784, 882, 915, 1234, 1246, 1249, 1250, 126l, 1294, 1295 Hansen, L.P., s e e Anderson, E.W. 368, 369 Hansen, L.P., s e e Cochrane, J.H. 1234, 1246, 1249 Hansen, L.P., s e e Eichenbaum, M. 549, 550, 785, 799, 800, 803 Hanson, J. 1543 Hansson, B., s e e Frennberg, P. 1238 Harberger, A.C. 1554, 1590

1-12 Harden, I., s e e von Hagen, J. 1439, 1460, 1465 Hardouvelis, G.A. 1281 Hardouvelis, G.A., s e e Estrella, A. 43, 1281 Harris, R., s e e Cox, D. 705 Harrison, A. 277, 279, 280 Harrison, S.G., s e e Christiano, L.J. 426 Harrison, S.H. 402 Harrod, R. 640 Hart, O. 852, 1154 Hartwick, J. 656 Harvey, A.C. 9 Harvey, C.R. 1236, 1280 Hashimoto, M. l 152 Hassett, K.A. 815, 818, 843, 1344 Hassett, K.A., s e e Auerbach, A.J. 821 Hassett, K.A., s e e Cummins, J.G. 822, 856, 1344 Hassett, K.A., s e e Fallick, B.C. 855 Hassler, J. 9, 1238 Haug, A.A., s e e Dezhbakhsh, H. 1039 Haugen, R.A., s e e Ferris, S.P. 1314 Hause, J.C. 569 Hausman, J. 620 Hausman, J., s e e Burtless, G. 620 Hawley, C.B., s e e O'Brien, A.M. 776 Hayashi, E 773, 775, 776, 785, 788, 790, 796, 800, 818, 1649 Head, A., s e e Devereux, M.B. 1126 Heal, G., s e e Dasgupta, E 655, 656 Heal, G.M., s e e Ryder Jl, H.E. 1284 Heaton, J. 380, 547, 569, 803, 1242, 1255, 1284, 1293 Heckman, J.J. 576, 578, 579, 582, 584-587, 590, 592, 593, 595, 601-603, 605, 615-617, 620-624, 752, 759, 1166 Heckman, J.J., s e e Ashenfelter, O. 618 Heckman, J.J., s e e Cameron, S. 589 Heckman, J.J., s e e Cossa, R. 584 Heckman, J.J., s e e Killingsworth, M.R. 550, 601, 1148 Heijdra, B.J. 1119, 1120, 1126 Heinemann, M. 495, 525 Hellwig, M., s e e Gale, D. 1376 Helpman, E. 203, 1580 Helpman, E., s e e Coe, D.T. 265 Helpman, E., s e e Drazen, A. 1580 Helpman, E., s e e Grossman, G.M. 264, 639, 672, 715, 1210, 1464 Hendershott, RH. 1333 Henderson, D.W. 1497

Author

Index

Henderson,D.W., s e e Bryant, R.C. 1491, 1497, 1516 Henderson, D.W., s e e Canzoneri, M.B. 160, 1507, 1508 Hendry, D., s e e Davidson, J. 750 Hercowitz, Z. 664 Hercowitz, Z . , s e e Barro, R.J. 1023 Hercowitz, Z., s e e Greenwood, J. 550, 664, 962, 980 Herrendorf, B. 1415, 1436, 1438 Hess, G.D. 9, 1485, 1509 Hester, D.A. 871 Heston, A., s e e Summers, R. 238, 301, 640, 673-675, 677, 680, 681,689, 720 Hetzel, R.L. 180 Heymann, D. 506, 1539, 1540, 1543 Hibbs, D. 1400, 1425 Hildenbrand, W. 535, 537 Himarios, D., s e e Graham, EC. 1656, 1657 Himmelberg, C.R, s e e Gilchrist, S. 1344 Hiriart-Urruti, J.B. 331 Hirschhorn, E., s e e Cox, W.M. 1621 Hirschman, A. 1540 Hirshleifer, D., s e e Bikhchandard, S. 1332 Hirshleifer, D., s e e Daniel, K. 1322 Hobijn, B., s e e Franses, EH. 289 Hodrick, R. 9, 12, 34, 428, 931,932 Hodrick, R.J., s e e Bekaert, G. 128l Hodrick, R.J., s e e Flood, R.P. 1507 Hoelscher, G. 1658 Hoffmaister, A. 1561, 1589 Hoffman, D.L. 51,412 Hoffmann, K.-H., s e e Hammerlin, G. 344 Holbrook, R. 569 Holmstrom, B. 1376, 1417, 1418, 1425 Holt, C.A., s e e Davis, D. 1033 Holt, C.C. 882, 885, 888, 909, 910, 912 Holtham, G., s e e Bryant, R.C. 1491, 1497, 1516 Holtz-Eakin, D., s e e Blinder, A.S. 41 Hommes, C.H. 529, 532 Hommes, C.H., s e e Brock, W.A. 455, 528, 532 Honkapohja, S. 464, 481,507, 535 Honkapohja, S., s e e Evans, G.W. 425, 426, 454, 455, 46I, 464, 465, 468, 470, 472-478, 480, 481,483,484, 487, 489-492, 495-497, 502, 504-507, 509-513, 516, 518-521, 526-528, 530-532, 1025 Hooker, M.A., s e e Fuhrer, J.C. 454

Author

Index

Hooper, P., s e e Bryant, R.C. 1043, 1491, 1497, 1516-1518 Hopenhayn, H. 672, 708, 994 Hopenhayn, H.A. 844 Horioka, C., s e e Feldstein, M. 1636 Horn, H. 1415 Hornstein, A. 549, 996 Hornstein, A., s e e Fisher, J.D.M. 910 Horvath, M. 994 Horvath, M., s e e Boldrin, M. 962, 1062 Hoshi, T. 1344 Hosios, A.J. 1193, 1224 Hotz, V.J. 792, 803 Houthakker, H.S. 803 Howard, R. 336 Howitt, E 389, 399, 455, 506, 507, 514, 515, 517, 521,527, 1174, 1508 Howitt, E, s e e Aghion, P. 264, 665, 672, 715, 719, 1208, 1210, 1213 Howrey, E.P., s e e Fair, R.C. 1491 Hoynes, H.W., s e e Attanasio, O.P. 753 Hsieh, C.-T. 673,687 Hubbard, R.G. 567, 569, 572, 573, 593, 771, 776, 794, 797, 856, 1344, 1376, 1660 Hubbard, R.G., s e e Cummins, J.G. 822, 1344 Hubbard, R.G., s e e Domowitz, I. 1020, 1083, 1093 Hubbard, R.G., s e e Fazzari, S.M. 818, 1344 Hubbard, R.G., s e e Gertler, M. 1376 Hubbard, R.G., s e e Hassett, K.A. 815, 818, 843, 1344 Huberman, G., s e e Kahn, C. 1154 Huffrnan, G.W. 437 Huffrnan, G.W., s e e Greenwood, J. 380, 962, 980 Huggett, M. 380, 576, 593 Hulten, C. 664 Hultgren, T. 1100 Humphrey, T.M. 1485 Humphreys, B.R. 909 Hurd, M.D. 780 Hybels, J., s e e Kallick, M. 1325 Hyslop, D., s e e Card, D. 1016 Ibbotson, R. 1321 Iden, G., s e e Barth, J.R. 1657 Ikenberry, G.J. 163 Im, K. 283 Imrohoroglu, A. 797 Ingberg, M., s e e Honkapohja, S. 535 Ingram, B. 984

1-13 Inman, R., s e e Bohn, H. 1465 Intriligator, M., s e e Griliches, Z. 541 Ireland, P.N. 129, 194, 1036, 1492, 1494, 1497 Irish, M., s e e Browning, M. 611, 612, 752, 787, 792 Irons, J., s e e Faust, J. 1416, 1425 Irwin, D.A. 178 Isard, E, s e e Flood, R.P. 158, 1429, 1438 Islam, N. 283-285, 287, 653 Ito, T. 1425 Iwata, S., s e e Hess, G.D. 9 Jackman, R. 1221 Jackxnan, R., s e e Layard, R. 1098, 1176, 1177, 1221 Jackwerth, J.C. 1310 Jaeger, A., s e e Harvey, A.C. 9 Jaffee, D.M. 1376 Jagannathan, R., s e e Glosten, L. 1280 Jagannathan, R., s e e Hansen, L.E 547, 1234, 1246, 1249 James, H., s e e Bernanke, B.S. 183, 184 James, W. 1330 Janis, I. 1332 Jappelli, T. 776, 780, 790, 1344 Jappelli, T., s e e Guiso, L. 772 Jeanne, O. 156, 1041 Jeanne, O., s e e Bensaid, B. 1446, 1449 Jefferson, P.N. 1485, 1509 Jegadeesh, N. 1321 Jegadeesh, N., s e e Chan, L. 1321 Jensen, H. 1415, 1427 Jensen, H., s e e Beetsma, R. 1436, 1438 Jensen, M. 1344 Jeon, B.N., s e e von Fttrstenberg, G.M. 1333 Jermann, U.J. 1296 Jermalm, U.J., s e e Alvarez, E 575 Jermann, U.J., s e e Baxter, M. 980, 992 Jewitt, I., s e e Buiter, W. 1030 Jimeno, J.E, s e e Blanchard, O.J. 1214 Jimeno, J.E, s e e Dolado, J.J. 1214 John, A., s e e Cooper, R. 398 Johnson, H.G. 702, 704, 705 Johnson, E, s e e Goodman, A. 797 Johnson, P.A., s e e Durlauf, S.N. 254, 263, 264, 270, 271,289, 303 Johnson, EG., s e e Banks, J. 751 Johnson, S.A. 345, 381 Jones, C.I. 237, 264, 290, 292, 672, 696, 714-716, 718, 719

1-14 Jones, C.I., s e e Hall, R.E. 673, 679, 680, 683-686, 702, 856 Jones, L.E. 245, 257, 261, 380, 672, 709, 711-713, 720, 1675, 1711 Jones, L.E., s e e Chaff, V.V. 715, 1578 Jones, M. 1540 Jonsson, G. 1404, 1411, 1415, 1426, 1438 Jonung, L. 159, 1485 Jonung, L., s e e Bordo, M.D. 152, 215, 217, 220, 221 Jonung, L., s e e Fregert, K. 1016 Jorda, O. 881 Jorgenson, D. 664 Jorgenson, D.W. 817 Jorgenson, D.W., s e e Christensen, L.R. 673, 688 Jorgenson, D.W., s e e Hall, R.E. 817 Jorion, P., s e e Goetzmann, W.N. 1242, 1252, 1320 Jovanovic, B. 702, 848, 1200 Jovanovic, B., s e e Greenwood, J. 664, 692 Judd, J.P. 1485, 1487, 1512, 1516 Judd, K. 590, 1652 Judd, K., s e e Bizer, D. 380 Judd, K.J., s e e Gaspar, J. 324, 369 Judd, K.L. 314, 324, 340, 343, 347, 348, 350, 354, 1673, 1675, 1694 Judson, R. 663 Judson, R., s e e Porter, R. 1509 Juhn, C. 569, 619 Jun, B. 474 Juster, ET. 777 Juster, T., s e e Barsky, R. 558, 564, 565 Kaas, L., s e e B6hm, V 646 Kafka, A. 1543 Kahaner, D. 329, 333 Kahn, C. 1154 Kahn, C.M., s e e Blanchard, O.J. 391,504 Kahn, J., s e e Crucini, M.J. 178, 705 Kahn, J.A. 897, 910 Kahn, J.A., s e e Bils, M. 910, 912, 1053, 1078, 1079, 1085 Kahneman, D. 1308, 1309, 1311 Kahneman, D., s e e Thaler, R.H. 1313 Kahneman, D., s e e Tversky, A. 1308, 1315, 1319, 1330 Kalaba, R., s e e Bellman, R. 340 Kaldor, N. 237, 238, 240, 640, 941 Kalecki, M. 1054 Kallick, M. 1325

Author

Index

Kamihigashi, T. 428 Kaminsky, G.L. 1550, 1553, 1590 Kandel, S. 1235, 1252, 1253, 1265, 1270, 1272 Kandoff, M. 475 K a n e , A . , s e e Chou, R.Y. 1236, 1280 Kaniovski, Y.M., s e e Arthur, W.B. 476 Kaplan, S.N. 856, 1344 Karatzas, I., s e e E1 Karoui, N. ' 835 Karras, G., s e e Cecchetti, S.G. 217 Kashyap, A.K. 137, 877, 88l, 886, 903, 906, 912, 1018, 1344, 1374, 1376 Kashyap, A.K., s e e Cecchetti, S.G. 876 Kashyap, A.K., s e e Hoshi, T. 1344 Kashyap, A.K., s e e Hubbard, R.G. 1344 Katz, L. 577, 578 Katz, L., s e e Autor, D. 577 Katz, L.E, s e e Abraham, K.J. 1183, 1221 Katz, L.E, s e e Cutler, D.M. 797 Katz, L.W., s e e Blmlchard, O.J. 1176 Kaufman, H. 1344 Keane, M.P. 608, 609, 786, 790 Keefer, P., s e e Knack, S. 1466, 1471 Kehoe, EJ., s e e Atkeson, A. 847, 1675, 1718, 1720 Kehoe, P.J., s e e Backus, C.K. 549 Kehoe, P.J., s e e Baekus, D.K. 9, 42, 45, 938, 1708 Kehoe, P.J., s e e Chaff, V.V. 124, 397, 422, 672, 697, 698, 700, 701, 709, 720, 722, 723, 974, 1036, 1037, 1040-1042, 1371, 1448, 1449, 1488, 1489, 1673-1676, 1691, 1699, 1708-1710, 1720, 1723 Kehoe, P.J., s e e Cole, H.L. 1449 Kehoe, T.J. 314, 380, 389, 391,574, 575 Kehoe, T.J., s e e Cole, H.L. 1446, 1449, 1603 Kehrer, K.C., s e e Moffitt, R.A. 618 Kelly, M. 271 Kemmerer, E.W. 173 Kendrick, D.A., s e e Amman, H.M. 535 Kenen, EB. 165, 1496 Kennan, J. 803 Kessler, D. 1646 Keynes, J.M. 158, 161, 1055, 1059, 1537 Kiefer, J. 476 Kiefer, N.M., s e e Burdett, K. 1173 Kiefer, N.M., s e e Devine, T.J. 1166 Kiguel, M. 1535, 1543, 1546, 1554, 1555 Kihlstrom, R.E. 563 Kiley, M.T. 422, 423, 1041, 1117, 1129 Killian, L. 87

Author

Index

Killingsworth, M.R. 550, 601, 1148 Kim, J. 129, 1036 Kim, K. 377, 379 K J m , M . , s e e Nelson, C.R. 1320 Kim, S. 95 Kim, S.-J. 672, 711-714 Kimball, M., s e e Barsky, R. 558, 564, 565 Kimball, M., s e e Carroll, C.D. 762, 771 Kimball, M.S. 556, 770, 1036, 1041, 1056, 1114, 1117, 1127, 1653 Kimball, M.S., s e e Basu, S. 983, 992, 994, 1069, 1080, 1081, 1117 Kimbrough, K.P. 1537, 1675, 1676, 1720, 1732 Kindahl, J., s e e Stigler, G. 1018 Kindleberger, C.R 162 King, M. 199, 1333, 1485, 1489 King, R.G. 9, 46, 54, 69, 101,278, 369, 391, 429, 435, 545, 549, 649, 672, 689, 692, 711-713, 929, 931,932, 939, 941,945, 953, 954, 971, 995, 1036, 1041, 1043, 1062, 1140, 1364, 1367, 1491 King, R.G., s e e Barro, R.J. 974 King, R.G., s e e Baxter, M. 9, 11, 12, 430, 934, 974 King, R.G., s e e Dotsey, M. 974, 1032, 1043 King, R.G., s e e Goodfriend, M. 1013, 1117, 1346, 1515 King, S. 101 Kirby, C. 1320 Kirman, A.P. 475, 528, 536, 539-541 Kitanidis, EK. 326 Kiyotaki, N. 524, 852, 857, 1353, 1356, 1376, 1378, 1379 Kiyotaki, N., s e e Blanchard, O.J. 1033, 1034 Kiyotaki, N., s e e Boldrin, M. 399 Kleidon, A.W. 1320 Klein, B. 202, 215, 216 Klein, L. 941 Klemperer, P.D. 1121 Klenow, EJ. 663, 673, 679, 680, 683-686, 694, 702, 705, 707 Klenow, EJ., s e e Bils, M. 694 Klenow, EJ., s e e Heckman, J.J. 578 Klock, M., s e e Silberman, J. 1316 Knack, S. 1466, 1471 Kneese, A. 656 Knowles, S. 277, 278 Kocherlakota, N. 574, 954, 985, 1234, 1251, 1253 Kocherlakota, N., s e e Cole, H.L. 576

1-15 Kocherlakota, N., s e e Ingram, B. 984 Kocherlakota, N.R. 271,673, 694 Kochin, L., s e e Benjamin, D. 161 Kollintzas, T. 904-907 Kollman, R. 1085 Kon-Ya, E, s e e Shiller, R.J. 1316 Konings, J., s e e Garibaldi, P. 1180, 1222 Koopmans, T. 931,942, 948 Koopmans, T.C. 244, 246, 247, 295, 643, 649, 1673 Koopmans, T.J. 9 Kormendi, R.C. 278-281,671, 1656, 1657 Komai, J. 703 Kortum, S., s e e Eaton, J. 719 Kosobud, R., s e e Klein, L. 941 Kosters, M.H. 618 Kotkin, B., s e e Bellman, R. 340 Kotlikoff, L. 1448, 1449, 1465 Kotlikoff, L., s e e Hayashi, E 796 Kotlikoff, L.J. 780, 1624, 1646 Kotlikoff, L.J., s e e Auerbach, A.J. 380, 549, 576, 588, 590, 591, 593, 616, 1624, 1634, 1635, 1639, 1652, 1718 Kotlikoff, L.J., s e e Gokhale, J. 750 Koyck, L.M. 816 Kramer, C., s e e Flood, R.R 1596 Krane, S.D. 876, 877 Kxemer, M., s e e Blanchard, O.J. 852 Kremer, M., s e e Easterly, W. 277, 278, 281, 675 Kreps, D.M. 540, 557, 1256 Kreps, D.M., s e e Bray, M. 474 Kreps, D.M., s e e Fudenberg, D. 475 Krieger, S. 380, 843, 847 Krishnamurthy, A. 1376, 1378 Kroner, K.E, s e e Bollerslev, T. 1236, 1280 Krueger, A., s e e Autor, D. 577 Krueger, A.O. 673, 679, 699 Krueger, J.T. 104, 105 Krugman, P. 1215, 1536, 1590, 1592, 1594, 1596, 1601, 1605, 1606, 1632 Krusell, E 380, 547, 566, 567, 994, 1293, 1445, 1473 Krusell, P., s e e Greenwood, J. 664 Kuan, C.-M. 476 Kugler, P. 1281 K u h , E . , s e e Meyer, J.R. 817 Kumhof, M. 1596 Kurz, M. 474 Kushner, H. 476 Kushner, H.J. 476

1-16 Kusko, A.L. 1327 Kuttner, K., s e e Evans, C.L. 105 Kuttner, K.N., s e e Friedman, B.M. 43, 44 Kuttner, K.N., s e e Krueger, J.T. 104, 105 Kuznets, S. 941 Kuznets, S., s e e Friedman, M. 572 Kwiatkowski, D. 212 Kydland, EE. 9, 42, 158, 428, 547, 549, 578, 929, 953, 956, 957, 962, 980, 981, 1058, 1059, 1140, 1141, 1145, 1167, 1195, 1400, 1405, 1415, 1449, 1485, 1486, 1488, 1557, 1561, 1673, 1708 Kydland, EE., s e e Backus, C.K, 549 Kydland, EE., s e e Backus, D,K, 1708 Kydland, EE., s e e Bordo, M.D, 158, 160, 185, 215, 1438 Kydland, EE., s e e Hotz, V.J. 792, 803 Kyle, A,S., s e e Campbell, J.Y. 1290 La Porta, R. 1240, 1320 Labadie, P., s e e Giovannini, A. 380 Labadie, P.A., s e e Coleman II, W.J. 114 Lach, S. 1019 Ladron de Guevara, A. 317 Laffont, J., s e e Gourieroux, C. 487 Laffont, J.J., s e e Kihlstrom, R.E. 563 Laffont, J.-J, 538 Lahiri, A. 1539, 1571, 1578, 1579, 1597 Lai, K.S. 876 Laibson, D. 1653 Laidler, D. 1485 Lakonishok, J. 1323 Lakonishok, J., s e e Chan, L. 1321 Lam, P.-S., s e e Cecehetti, S.G. 1251, 1265, 1270, 1272, 1294, 1296 Lam, P.S. 802 Lambert, J.D. 346 Lambertini, L. 1457, 1465 Lamo, A.R. 290 Lamont, O.A., s e e Kashyap, A.K. 881, 912, 1344, 1374 Landi, L., s e e Barucci, E. 525 Lane, P. 1472 Langer, E.J. 1329 Lansing, K . , s e e Guo, J.-T. 416 Lapham, B.J., s e e Devereux, M.B. 1126 Laroque, G., s e e Fuchs, G. 464, 474 Laroque, G., s e e Grandmont, J.-M. 464, 474, 475, 481,507 Laroque, G., s e e Grossman, S.J. 801 Lau, L. 664

Author

Index

Lau, S.H.P. 1037 Lawrance, E. 607 609 Layard, R. 1098, 1176, 1177, 1221 Layard, R., s e e Jackman, R. 1221 Layne-Farrar, A., s e e Heckman, J.J. 578 Lazaretou, S. 159 Lazear, E.P. 1660 Lazear, E.E, s e e Hall, R.E. 1152 League of Nations 162 Leahy, J. 844, 1332 Leahy, J., s e e Caballero, RA. 823, 828, 830 Leahy, J., s e e Caplin, A. 849, 850 Leamer, E.E. 282 Lebow, D.E. 215, 1016 Lebow, D.E., s e e Blinder, A.S. 1018, 1118 Lee, C. 1324 Lee, J.-W., s e e Barro, R.J. 277~81, 671, 681, 683-685, 688, 689, 691-694 Lee, J.-W. 703 Lee, J.Y. 395 Lee, K. 284 Lee, T.H., s e e Granger, C.W.J. 881,903 Leeper, E.M. 69, 74, 83, 93, 101, 128, 132, 134, 137, 418, 420, 1036, 1089, 1369, 1518, 1520, 1631 Leeper, E.M., s e e Faust, J. 69, 217 Leeper, E.M., s e e Gordon, D,B. 128, 134 Lefort, E, s e e Caselli, E 277-279, 283, 284, 286 Lehmann, B.N. 1321 Leibfritz, W., s e e Roseveare, D. 1626 Leiderman, L. 1432, 1438, 1495, 1543 Leiderman, L., s e e Bufman, G. 1543 Leiderman, L., s e e Calvo, G.A. 1552, 1600 Leiderrnan, L., s e e Kaminsky, G.L. 1550 Leijonhufvud, A. 152, 202, 215 Leijonhufvud, A., s e e Heymarm, D. 1539, 1540 Lemareehal, C., s e e Hiriart-Urruti, J.B. 331 LeRoy, S.E 1235, 1319 Lettau, M. 470, 472, 524, 527, 1293, 1297 Leung, C. 271 Levhari, D. 1450, 1465 Levin, A. 283, 1017, 1031, 1035, 1036, 1038 Levin, A., s e e Brayton, E 1043, 1344, 1485 Levine, D.K., s e e Fudenberg, D. 455, 475 Levine, D.K., s e e Kehoe, T.J. 380, 389, 391, 574, 575 Levine, J. 1332 Levine, P,, s e e al Nowaihi, A. 1415, 1422, 1437

Author

Index

Levine, R. 269, 277-282, 390, 423, 671, 694, 1376 Levine, R., s e e King, R.G. 278, 689, 692 Levy, D. 1014, 1015, 1019 Levy, D., s e e Carpenter, R.E. 876 Levy, D., s e e Dutta, S. 1019, 1020 Levy-Leboyer, M. 222 L6vy-Strauss, C. 1331 Lewis-Beck, M. 1425 Li, J.X. 326 Li, Y., s e e Johnson, S.A. 345, 381 Lichtenstein, S. 1318 Lichtenstein, S., s e e Fischhoff, B. 1319 Lilien, D.M. 1160, 1183, 1221 Lilien, D.M., s e e Hall, R.E. 1153 Lillard, L. 569, 572 Limongi, E, s e e Przeworski, A. 1466 Lin, C., s e e Levin, A. 283 Lindbeck, A. 1098, 1425, 1465 Lindert, E 156 Lioni, G., s e e Contini, B. 1177, 1178, 1180, 1222 Lippi, E 1432 Lippi, E, s e e Cukierman, A. 1438 Lippi, M. 217 Lipsey, R.E., s e e Blomstrom, M. 277, 279, 280 Liu, C.Y., s e e Conlon, J.R. 1032 Liviatan, N., s e e Cukierrnan, A. 1437 Liviatan, N., s e e Kiguel, M. 1535, 1543, 1546, 1554, 1555 Lizondo, J.S. 1538 Lizzeri, A. 1459 Ljung, L. 474, 476, 481,482 Ljungqvist, L. 1214 Lo, A.W. 1321 Lo, A.W., s e e Campbell, J.Y. 1255, 1257, 1258, 1261, 1266, 1270, 1320 Loayza, N.V. 708 Lochner, L., s e e Cossa, R. 584 Lochner, L., s e e Heckman, J.J. 576, 578, 582, 584, 586, 587, 590, 592, 593 Lockwood, B. 1411, 1415 Lockwood, B., s e e Herrendorf, B. 1436, 1438 Lohman, S. 1416-1418, 1425, 1431, 1438 Londregan, J., s e e Alesina, A. 1425 Long, J. 929, 952, 953, 994 Loomes, G. 1313 Lopez-de-Silanes, E, s e e La Porta, R. 1240 Lorentz, A.L. 344 Lothian, J.R., s e e Darby, M.R. 166

1-17 Loury, G.C. 299 Lovell, M.C. 881,893,908, 910 Lown, C., s e e Bernanke, B.S. 1343 Lucas, DA. 1035, 1036, 1042 Lucas, D.J., s e e Heaton, J. 380, 547, 569, 1255, 1293 Lucas, R. 398, 424, 425, 641, 651,929, 932, 953 Lucas, R.E. 46, 50, 380, 1158, 1446, 1449 Lucas, R.E., s e e Stokey, N.L. 314, 318-321, 346, 951,998, 999 Lucas J1, R.E. 67, 88, 158, 238, 245, 264, 265, 293, 454, 457, 463, 474, 545, 547, 554, 559, 561, 575, 578, 582, 583, 615, 616, 672, 710-715, 720, 797, 102~1024, 1043, 1195, 1268, 1489, 1490, 1495, 1500, 1592, 1673, 1675, 1699, 1711, 1723, 1728 Lucas Jr, R.E., s e e Atkeson, A. 575 Lucas Jr, R.E., s e e Stokey, N.L. 271,299 Ludvigson, S. 785, 788, 1344, 1652 Lundvik, E, s e e Hassler, J. 9, 1238 Lusardi, A. 608, 790, 791 Lusardi, A., s e e Browning, M. 606, 771 Lusardi, A., s e e Garcia, R. 790 Luttmer, E.G.J. 575 Lyons, R.K., s e e Caballero, R.J. 399

Maberly, E.D., s e e Dyl, E.A. 1334 Macaulay, ER. 173 MacAvoy, P.W., s e e Funkhouser, R. 699 Maccini, L.J. 881,893, 894, 903,907 Maccini, L.J., s e e Blinder, A.S. 887, 904, 910, 1344 Maccini, L.J., s e e Durlauf, S.N. 905-907 Maccini, L.J., s e e Haltiwanger, J.C. 881 Maccini, L.J., s e e Humphreys, B.R. 909 MacDonald, R., s e e Bordo, M.D. 156 Mace, B.J. 796 Mackay, D. 1307 MacKinlay, A.C., s e e Campbell, J.Y. 1255, 1257, 1258, 1261, 1266, 1270, 1320 MacKinlay, A.C., s e e Lo, A.W. 1321 MacLeod, W.B. 1157, 1186 MaCurdy, T.E. 551, 567-569, 572, 592, 595, 615, 616, 619-621,752, 759, 767, 792, 975, 1148, 1149 MaCurdy, T.E., s e e Attanasio, O.E 792 MaCurdy, T.E., s e e Blundell, R. 602, 620 MaCurdy, T.E., s e e Heckman, J.J. 615 Maddala, G.S. 275

1-18 Maddison, A. 288, 673-675, 677, 678, 720, 721 Madison, J. 1659 Mailath, G.J., s e e Kandori, M. 475 Makhija, A.K., s e e Ferffs, S.E 1314 Malcomson, J.M., s e e MacLeod, W.B. 1157, 1186 Malinvaud, E., s e e Blanchard, O.J. 1214 Malkiel, B. 1316 Mankiw, N.G. 135, 158, 159, 173, 216, 244246, 252-255, 269-271,277-279, 289, 397, 567, 653, 655, 660, 673, 679-686, 694, 749, 785, 790, 800, 961, 1281, 1290, 1292, 1638, 1702, 1742 Mankiw, N.G., s e e Abel, A.B. 1266, 1651 Mankiw, N.G., s e e Ball, L. 42, 1023, 1632, 1650, 1651 Mankiw, N.G., s e e Barro, R.J. 1637 Mankiw, N.G., s e e Barsky, R.B. 1653 Mankiw, N.G., s e e Campbell, J.Y. 769, 784, 1261, 1264, 1290, 1655 Mankiw, N.G., s e e Elmendorf, D.W. 1439 Mankiw, N.G., s e e Hall, R.E. 1485, 1493, 1498 Mankiw, N.G., s e e Kimball, M.S. 1653 Mann, C.L., s e e Bryant, R.C. 1043, 1491, 1497, 1516-1518 Manuelli, R.E., s e e Chari, VV. 715, 1578 Manuelli, R.E., s e e Jones, L.E. 245, 257, 261, 380, 672, 709, 711-713, 720, 1675, 1711 Man, C.S., s e e Dotsey, M. 370, 952 Marcet, A. 314, 326, 348, 351,454, 455, 464, 465, 468, 473-476, 480, 494, 499, 525, 528-530, 532, 1675, 1705, 1707 Marcet, A., s e e Canova, E 283 Marcet, A., s e e den Haan, W.J. 347, 354, 369 Margarita, S., s e e Beltratti, A. 524, 525 Margaritis, D. 474 Mariano, R.S., s e e Seater, J.J. 1656, 1657 Mariger, R.R 1344 Marimon, R. 455, 464, 472, 475, 523, 531, 1214 Marimon, R., s e e Evans, G.W. 483, 509, 527, 528, 531 Marion, N., s e e Flood, R.P. 1429, 1438 Mark, N.C., s e e Cecchetti, S.G. 1251, 1265, 1270, 1272, 1294, 1296 Marris, S. 1632 Marschak, J. 582, 1043 Marshall, A. 203 Marshall, D.A., s e e Bekaert, G. 1281

Author

Index

Marshall, D.A., s e e Marcet, A. 326, 348, 351, 455 Marston, R., s e e Bodnar, G. 1318 Marston, R.C. 164 Martin, J.P. 1181 Mas-Colell, A., s e e Kehoe, T.J. 380 Masciandaro, D., s e e Grilli, V 1404, 1432, 1438, 1439, 1465 Masson, A., s e e Kessler, D. I646 Masson, E, s e e Chadha, B. 1542 Masson, P.R. 1554, 1588 Matheny, K.J. 395, 441 Matsukawa, S. 1037 Matsuyama, K. 395, 399 Matthieson, D., s e e Mussa, M. 208 Mauro, P. 277 Mauro, P., s e e Easterly, W. 1538 Maussner, A. 528 Mayhew, S. 1310 McAfee, R.P., s e e Howitt, E 389, 399, 506, 517, 521 McCallum, B.T. 83, 173, 184, 198, 203, 408, 487, 488, 496, 503, 1022, 1026, 1043, 141l, 1426, 1432, 1437, 1438, 1485, 1487, 1488, 1490, 1491, 1493, 1495, 1500, 1502, 1506-1510, 1512, 1515-1519, 1631 McCulloch, J.H., s e e Dezhbakhsh, H. 1039 McElroy, M. 619 McFadden, D. 1314, 1316, 1328 McGrattan, E.R. 348, 974 McGrattan, E.R., s e e Anderson, E.W. 368, 369 McGrattan, E.R., s e e Chaff, V.V. 124, 397, 422, 672, 697, 698, 700, 701, 709, 720, 722, 723, 974, 1036, 1037, 1040-1042, 1371 McGrattan, E.R., s e e Marimon, R. 455, 475, 523 McGuire, W.J. 1332 McIntire, J.M., s e e Carlson, J.B. 104 McKelvey, R.D. 380 McKibbin, W.J., s e e Henderson, D.W. 1497 McKinnon, R. 1496 McKinnon, R.I. 166, 207 McLaughlin, K.J. 1016, 1152 McLean, I., s e e Eichengreen, B. 157 McLennan, A. 474 McLennan, A., s e e McKelvey, R.D. 380 McManus, D.A. 908 Means, G.C. 1082 Meckling, W., s e e Jensen, M. 1344 Medeiros, C. 1554, 1555

Author

Index

Medoff, J.L., s e e Fay, J.A. 1077, 1103 Meehl, P. 1319 Meghir, C. 611,613, 775, 804 Meghir, C., s e e Arellano, M. 787 Meghir, C., s e e Attanasio, O.P. 793, 794 Meghir, C., s e e Blundell, R. 611, 612, 779, 781, 783, 790-792 Meghir, C., s e e Browning, M. 607, 611,778 Meguire, E, s e e Kormendi, R.C. 278-281,671, 1656, 1657 Mehra, R. 547, 961, 1234, 1236, 1249, 1251, 1264, 1268, 1270, 1272, 1289, 1312 Mehra, R., s e e Constantinides, G.M. 1293 Mehra, R., s e e Danthine, J.-E 329, 370, 952 Meigs, A.J. 191 Melenberg, B., s e e Alessie, R. 774 Melino, A., s e e Blanchard, O.J. 912 Melino, A., s e e Epstein, L.G. 558, 565 Melino, A., s e e Grossman, S.J. 1242 Melnick, R., s e e Bruno, M. 1539 Meltzer, A.H. 162, 169, 17~176, 178, 179, 185, 204, 215-217, 222, 1466, 1485, 1543 Meltzer, A.H., s e e Brunner, K. 179, 183, 191, 1025 Meltzer, A.H., s e e Cukierman, A. 1414, 1450, 1463 Mendoza, E. 1439, 1571, 1579 Mendoza, E., s e e Calvo, G.A. 1591, 1600, 1601 Meredith, G., s e e Chadha, B. 1542 Merton, R. 1275 Merton, R.K. 389, 1333 Merz, M. 994, 1158, 1173, 1203, 1207 Metivier, M., s e e Benveniste, A. 476, 531 Metzler, L.A. 867 Meyer, J.R. 817 Mihov, I., s e e Bernanke, B.S. 72, 76, 83, 89, 114, 1365, 1369 Milesi-Ferretti, G.-M., s e e Mendoza, E. 1439 Milesi-Ferretti, G.-M. 1425, 1426, 1597 Milgrom, P. 475, 1322 Millard, S.P. 1217, 1220 Miller, B.L. 566 Miller, M., s e e Lockwood, B. 1411, 1415 Miller, M., s e e Modigliani, E 1343 Miller, R.A., s e e Altug, S. 584, 595, 611,612, 785, 786, 792 Mills, E 1082 Mills, J., s e e Erlich, D. 1314 Mills, L.O., s e e Boschen, J.E 139 Mills, T.C. 204

1-19 Mills, T.C., s e e Capie, E 163, 1438 Mincer, J. 581,592, 684 Minehart, D., s e e Bowman, D. 1313 Mirman, L., s e e Levhari, D. 1450, 1465 Mirman, L.J., s e e Brock, W.A. 319, 547, 552, 556, 942, 951 Miron, J.A. 173, 216, 876, 907, 1242 Miron, J.A., s e e Barsky, R.B. 1149 Miron, J.A., s e e Beaulieu, J.J. 876 Miron, J.A., s e e Feenberg, D. 60 Miron, J.A., s e e Mankiw, N.G. 173, 216, 1281 Mirrlees, J.A. 1154 Mirrlees, J.A., s e e Diamond, P.A. 1684 Mishkin, ES. 101, 183,216, 1023, 1380, 1432, 1438 Mishkin, ES., s e e Bernanke, B.S. 1495 Mishkin, ES., s e e Estrella, A. 1485 Mishkin, ES., s e e Hall, R.E. 607, 608, 789, 1655 Mishra, D. 1416, 1425 Missale, A. 1450 Mitchell, B.R. 222 Mitchell, W.C. 8, 44, 1053 Mitchell, W.C., s e e Burns, A.E 5, 8, 931,934 Mitra, K. 530, 532 Mnookin, R.H., s e e Gilson, R.J. 1154 Modiano, E.M. 1543 Modigliani, E 761,762, 780, 1321, 1343, 1646, 1656, 1657 Modigliani, E, s e e Dreze, J. 770 Modigliani, E, s e e Holt, C.C. 882, 885, 888, 909, 910, 912 Modigliani, E, s e e Jappelli, T. 780 Modigliani, E, s e e Samuelson, P.A. 643 Moffitt, R. 752, 787 Moffitt, R.A. 618 Moler, C., s e e Kahanel, D. 329, 333 Mondino, G. 1540 Monfort, A., s e e Gourieroux, C. 487 Monro, S., s e e Robbins, H. 476, 478 Montgomery, E. 1017, 1018 Montiel, P. 1539 Montiel, P., s e e Ag6nor, ER. 1543 Montrucchio, L. 330 Montrucchio, L., s e e Boldrin, M. 362 Moore, B.J. 455, 475, 496 Moore, G.H. 1059 Moore, G.H., s e e Zarnowitz, V. 40 Moore, G.R., s e e Fuhrer, J.C. 905, 908, 1039, 1040, 1518

1-20 Moore, J., s e e Kiyotaki, N. 852, 857, 1353, 1356, 1376, 1378, 1379 Moreno, D. 481 Morgan, D. 1374 Morrison, C.J. 1086 Mortensen, D.T. 1157, 1158, 1162, 1163, 1173, 1182, 1183, 1187, 1188, 1194, 1198, 1203, 1208, 1217, 1220, 1222 Mortensen, D.T., s e e Burdett, K. 1173, 1196 Mortensen, D.T., s e e Millard, S.P. 1217, 1220 Morton, T.E. 338 Mosser, RC. 910 Motley, B., s e e Judd, J.P. 1485, 1487, 1512, 1516 Mroz, T.A. 618 Mroz, T.A., s e e MaCurdy, T.E. 592, 752 Muellbauer, J., s e e Deaton, A. 783 Mueller, D. 1464 Mulligan, C.B. 346, 1150 Mundell, R.A. 1496 Murphy, K. 581 Murphy, K., s e e Juhn, C. 569, 619 Murphy, K., s e e Katz, L. 577, 578 Murphy, K.M. 262, 278, 1082 Murray, C.J., s e e Nelson, C.R. 11 Murray, W., s e e Gill, EE. 329 Musgrave, R.A. 1631, 1661 Mussa, M. 208, 1404, 1637 Mussa, M., s e e Flood, R.R 152, 202, 1428 Mussa, M.L., s e e Frenkel, J.A. 203 Muth, J.E 457, 473, 484 Muth, J.E, s e e Holt, C.C. 882, 885, 888, 909, 910, 912 Myerson, R. 1459 Nakamura, A. 618 Nakamura, M., s e e Nakamura, A. 618 Nalebuff, B., s e e Bliss, C. 1461, 1465 Nance, D.R. 1318 Nankervis, J.C., s e e McManus, D.A. 908 Nash, S., s e e Kahaner, D. 329, 333 Nason, J.M., s e e Cogley, T. 395, 547, 967, 1142, 1503 Natanson, I.P. 342 NBER 8 Neale, M.A., s e e Northcraft, G.B. 1315 Negishi, T. 559 Nelson, C.R. 11, 211, 213, 264, 969, 1264, 1320 Nelson, C.R., s e e Beveridge, S. 1062, 1143 Nelson, D.B. 182

Author

Index

Nelson, E. 1035 Nerlove, M. 283, 284 Neumann, G.R., s e e Burdett, K. 1173 Neusser, K. 941 Neves, J., s e e Correia, I. 974 Neves, P., s e e BlundeU, R. 792 Ng, S., s e e Garcia, R. 790 Nickell, S., s e e Layard, R. 1098, 1176, 1177, 1221 Niekell, S.J. 823 Nicolini, J.P., s e e Marcet, A. 455, 530, 532 Niederreiter, H. 334 Nilsen, O.A., s e e Askildsen, J.E. 1074 Nishimura, K., s e e Benhabib, J. 403-405, 425, 435 Nordhaus, W. 1400, 1425 North, D. 1449 Northcraft, G.B. 1315 Novales, A. 803 Nurkse, R. 163, 203 Nyarko, Y. 465, 474 O'Barr, W.M. 1332 O'Brien, A.M. 776 O'Brien, A.E 181 Obstfeld, M. 159, 164, 165, 407, 1411, 1415, 1429, 1438, 1449, 1507, 1571, 1588, 1590, 1592, 1630 Obstfeld, M., s e e Froot, K. 1266 O'Connell, S.A. 1650 Odean, T. 1314, 1323 O'Driseoll, G.P. 1643 OECD 1181, 1182, 1215, 1620 Office of Management and Budget 1622 Officer, L. 155 Ogaki, M., s e e Atkeson, A. 610, 786 Ohanian, L.E. 1036 Ohanian, L.E., s e e Cooley, T.E 42, 962, 974 O'Hara, M., s e e Blume, L.E. 321,322 Ohlsson, H., s e e Edin, D.A. 1457 Okina, K. 1508 Okun, A.M. 1014, 1541 Oliner, S.D. 137, 820, 1374, 1376 Oliner, S.D., s e e Cummins, J.G. 856 Olsder, G., s e e Basar, T. 1449 Olshen, R.A., s e e Breiman, L. 289 Oppers, S. 154 Orphanides, A. 198, 1485 Ortega, E., s e e Canova, E 376, 377, 379 Ortigueira, S., s e e Ladron de Guevara, A. 317 Ostry, J. 1568

Author

Index

Ostry, J., s e e Montiel, P. 1539 Ostry, J.D., s e e Ghosh, A.R. 202, 207, 208 Owen, ED., s e e Knowles, S. 277, 278 Ozler, S. 1457, 1465 Ozler, S., s e e Alesina, A. 277-279, 1460, 1466, 1471 Paarsch, H., s e e MaCurdy, T.E. 619, 620 Paeelli, L., s e e Contini, B. 1177, 1178, 1180, 1222 Packal~n, M. 525 Padilla, J., s e e Dolado, J. 1437 Pagan, A., s e e Kim, K. 377, 379 Pagan, A.R. 9, 69, 108 Pagano, M., s e e Giavazzi, E 203, 1438, 1446, 1449, 1580 Pagano, M., s e e Jappelli, T. 776 Papageorgiou, A. 334 Papageorgiou, C., s e e Duffy, J. 257 Paquet, A., s e e Ambler, S. 944 Parekh, G. 87, 109 Parente, S.L. 672, 674, 702, 708 Parke, W.R., s e e Davutyan, N. 156 Parker, Jr., s e e Barsky, R. 43 Parker, J., s e e Gourinchas, P.-O. 609, 1344 Parker, J.A. 1120 Parker, J.A., s e e Solon, G. 579, 1058, 1102, 1106

Parkin, M. 1037, 1412, 1415, 1506 Parkin, M., s e e Bade, R. 1432, 1438 Pashardes, E, s e e Blundell, R. 781 Paskov, S.H. 334 Patel, J., s e e Degeorge, E 1321 Patinkin, D. 407, 1506, 1507, 1630, 1643 Paulin, G. 751 Paxson, C., s e e Deaton, A. 798 Paxson, C., s e e Ludvigson, S. 788 Pazos, E 1534 Peles, N., s e e Goetzmann, W.N. 1314 Pencavel, J. 550, 601,605, 975, 1148 Peralta-Alva, A. 374 Perli, R. 402, 431,435 Perli, R., s e e Benhabib, J. 425, 426, 437 Perotti, R. 1466, 1469, 1472 Perotti, R., s e e Alesina, A. 1439, 1464, 1465 Perron, R 264 Perry, G.L., s e e Akerlof, G.A. 198 Persson, M. 1447, 1449 Persson, T. 278, 692, I400, 1403, 1413, 1415-1418, 1420, 1421, 1425, 1433, 1435, 1437-I440, 1442, 1445, 1448-1450, 1454,

1-21 1456, 1459, 1460, 1465, 1466, 1469, 1470, 1490 Persson, T., s e e Englund, E 9 Persson, T., s e e Hassler, J. 9, 1238 Persson, T., s e e Horn, H. 1415 Persson, T., s e e Kottikoff, L. 1448, 1449, 1465 Persson, T., s e e Persson, M. 1447, 1449 Pesaran, H. 487 Pesaran, M.H., s e e Binder, M. 271 Pesaran, M.H, s e e Im, K. 283 Pesaran, M.H., s e e Lee, K. 284 Pestieau, EM. 1718 Petersen, B.C., s e e Carpenter, R.E. 881,912, 1344 Petersen, B.C., s e e Domowitz, I. 1020, 1083, 1093 Petersen, B.C., s e e Fazzari, S.M. 818, 1344 Petterson, E 1457 Pflug, G., s e e Ljung, L. 476 Phaneuf, L. 1028, 1039, 1041 Phelan, C. 380, 575, 796 Phelan, C., s e e Atkeson, A. 1298 Phelps, E. 944, 1025, 1026, 1039 Phelps, E.E., s e e Frydman, R. 453, 454, 474, 528, 536, 539 Phelps, E.S. 46, 168, 1059, 1098, 1121, 1122, 1157, 1173, 1176, 1192, 1220, 1537, 1538, 1720, 1724 Philippopoulus, A., s e e Lockwood, B. 1415 Phillips, A.W. 1510 Phillips, A.W.H. 46 Phillips, L.D., s e e Lichtenstein, S. 1318 Phillips, EC.B., s e e Kwiatkowski, D. 212 Pieard, P. 1157 Pieper, EJ., s e e Eisner, R. 1621 Pierce, J.L. 195 Piketty, T., s e e Aghion, E 1377 Pindyck, R. 1072 Pindyek, R.S. 835, 910, 912 Pindyck, R.S., s e e Abel, A.B. 835 Pindyck, R.S., s e e Caballero, R.J. 844 Pippenger, J. 156 Pischke, J.-S., s e e Jappelli, T. 790 Pischke, J.-S. 764 Pissarides, C.A. 774, 1163, 1173, 1183, 1184, 1188, 1193, 1194, 1200, 1203, 1207, 1209, 1220 Pissarides, C.A., s e e Garibaldi, P. 1180, t222 Pissarides, C.A., s e e Jacl~anan,R. 1221

1-22 Pissarides, C.A., s e e Mortensen, D.T. 1158, 1182, 1183, 1194, 1198, 1203, 1208 Plosser, C.I. 952, 954, 958, 961, 963, 1094, 1658 Plosser, C.I., s e e King, R.G. 9, 54, 369, 391, 429, 435, 549, 929, 931, 941, 945, 954, 995 Plosser, C.I., s e e Long, J. 929, 952, 953, 994 Plosser, C.I., s e e Nelson, C.R. 11,211, 213, 264, 969 Plutarchos, S., s e e Benhabib, J. 437 Polemarchakis, H.M., s e e Geanakoplos, J.D. 395, 458 Policano, A., s e e Fethke, G. 1037 Pollak, R.A. 803 Pollard, S. 161 Poole, W. 192, 1514, 1515 Poonia, G.S., s e e Dezhbakhsh, H. 1039 Popper, K. 376 Porter, R. 1509 Porter, R.D., s e e LeRoy, S.F. 1235, 1319 Porteus, E.L., s e e Kreps, D.M. 557, 1256 Portier, E 1068, 1126 Portier, E, s e e Hairault, J.-O. 1036 Posen, A. 1404, 1426, 1432, 1438 Posen, A., s e e Mishkin, ES. 1432, 1438 Poterba, J.M. 159, 1235, 1320, 1465, 1648, 1655 Poterba, J.M., s e e Cutler, D.M. 1290, 1320, 1321 Poterba, J.M., s e e Feldstein, M. 1633 Poterba, J.M., s e e Kusko, A.L. 1327 Power, L., s e e Cooper, R. 824 Pradel, J., s e e Fotu'geaud, C. 454, 465, 473, 475 Praschnik, J., s e e Hornstein, A. 549 Prati, A. 162 Prati, A., s e e Alesina, A. 1446, 1449 Prati, A., s e e Drudi, E 1450 Prescott, E.C. 178, 365, 545, 675, 700, 702, 930, 934, 952, 954, 956, 957, 961, 963, 982, 1033, 1296, 1488, 1489, 1710 Prescott, E.C., s e e Chari, V.V 1488, 1489, 1674 Prescott, E.C., s e e Cooley, T.F. 376, 549, 954 Prescott, E.C., s e e Hansen, G.D. 602 Prescott, E.C., s e e Hodrick, R. 9, 12, 34, 428, 931,932 Prescott, E.C., s e e Kydland, EE. 9, 42, 158, 428, 547, 549, 929, 953, 956, 957, 962, 980, 981, 1058, 1059, 1140, 1141, 1145,

Author

Index

1167, 1195, 1400, 1405, 1415, 1449, 1485, 1486, 1488, 1673, 1708 Prescott, E.C., s e e Lueas Jr, R.E. 547, 554 Prescott, E.C., s e e Mehra, R. 547, 961, 1234, 1236, 1249, 1251, 1264, 1268, 1270, 1272, 1289, 1312 Prescott, E.C., s e e Parente, S.L. 672, 674, 708 Prescott, E.C., s e e Stokey, N.L. 951,998, 999 Prescott, E.S. 380 Press, W.H. 329-334, 343, 348, 356, 365 Preston, I., s e e Banks, J. 759, 783, 790, 791 Preston, I., s e e Blundell, R. 572, 764, 797 Priouret, E, s e e Benveniste, A. 476, 531 Pritchett, L. 237 Pritchett, L., s e e Easterly, W. 277, 278, 281, 675 Przeworski, A. 1466 Psacharopoulos, G. 685 Puterman, M.L. 336, 338, 339 Quadrini, V., s e e Cooley, T.E 1376 Quadrini, V., s e e Krusell, P. 1445, 1473 Quah, D. 254, 263, 268, 272, 275, 283, 287, 288, 290292, 294, 299 Quah, D., s e e Leung, C. 271 Quail, D.T., s e e Blanehard, O.J. 211, 216, 217 Quah, D.T., s e e Durlauf, S.N. 550 Quandt, R.E. 34 Quattrone, G.A. 1329 Rabin, M. 1319 Rabin, M., s e e Bowman, D. 1313 Rabinowitz, P., s e e Davis, PJ. 333 Radner, R. 952 Radner, R., s e e Benhabib, J. 1465 Ramey, G. 281,852, 1157, 1159 Ramey, G., s e e den Haan, W.J. 994, 1166, 1194, 1203, 1204, 1206, 1207 Ramey, G., s e e Evans, G.W. 455, 461,462 Ramey, V.A. 67, 876, 885, 897, 902, 905-907, 909, 911,914, 1084, 1089 Ramey, V.A., s e e Bresnahan, T.E 911,912 Ramey, VA., s e e Chah, E.Y. 775 Ramey, V.A., s e e Ramey, G. 281 Ramos, J. 1543 Ramsey, E 643, 649 Ramsey, EP. 1673 Rankin, N. 1025 Rankin, N., s e e Dixon, H. 537 Rapping, L., s e e Lucas Jr, R.E. 615, 616

Author

1-23

Index

Rasche, R.H., s e e Hoffman, D.L. 51,412 Ratti, R.A. 1497 Ravikumar, B., s e e Chatterjee, S. 1126 Ravikumar, B., s e e Glomm, G. 712, 1472 Rawls, J. 1662 Ray, D., s e e Esteban, J.-M. 264 Rayack, W. 579 Razin, A. 1715 Razin, A., s e e Frenkel, J.A. 1630 Razin, A., s e e Helpman, E. 203, 1580 Razin, A., s e e Mendoza, E. 1439 Razin, A., s e e Milesi-Ferretti, G.-M. 1597 Rebelo, S.T. 245, 260, 261, 709, 952, 1546, 1568, 1578-1581, 1606 Rebelo, S.T., s e e Burnside, C. 399, 930, 980, 982-985, 994, 1078, 1142 Rebelo, S.T., s e e Correia, I. 974 Rebelo, S.T., s e e Easterly, W. 703 Rebelo, S.T., s e e Gomes, J. 994, 1159 Rebelo, S.T., s e e King, R.G. 9, 54, 369, 391, 429, 435, 545, 549, 649, 672, 711-713, 929, 932, 945, 954, 995, 1062, 1140 Rebelo, S.T., s e e Stokey, N.L. 578, 583, 672, 709, 711,714, 954 Redish, A. 154, 155, 166 Redish, A., s e e Betts, C.M. 217 Redmond, J. 161 Reichenstein, W. 101 Reichlin, L., s e e Evans, G.W. 1125 Reichlin, L., s e e Lippi, M. 217 Reid, B.G., s e e Boothe, EM. 1658 Reinhart, C.M. 1545, 1546, 1551, 1553, 1561, 1572, 1573 Reinhart, C.M., s e e Calvo, G.A. 1538, 1539, 1552, 1588, 1600 Reinhart, C.M., s e e Kaminsk-y, G.L. 1553, 1590 Reinhart, C.M., s e e Ostry, J. 1568 Renelt, D., s e e Levine, R. 269, 277-282, 390, 423, 671,694 Reserve Bank of New Zealand 1500 Resnick, L.B., s e e Levine, J. 1332 Restoy, E 1272 Revelli, R., s e e Contini, B. 1177, 1178, 1180, 1200, 1222 Revenga, A., s e e Blanchard, O.J. 1214 Rey, E, s e e Aghion, E 1157 Ricardo, D. 1642 Rich, G. 1514 Richard, S.E, s e e Hansen, L.P. 556 Richards, S., s e e Meltzer, A.H. 1466

Rietz, T. 1252, 1272, 1296 Riley, J. 1461, 1465 Rios-Rull, J. 943 Rios-Rull, J.-V., s e e Castafieda, A. 380 Rios-Rull, J.-V. 380 Rios-Rull, V., s e e Krusell, P. 1445, 1473 Ritter, J.R. 1321 Ritter, J.R., s e e Ibbotson, R. 1321 Rivers, D. 840 Rivlin, T.J. 343 Rob, R., s e e Jovanovic, B. 702 Rob, R., s e e Kandori, M. 475 Robb, R., s e e Heckman, J.J. 752 Robbins, H. 476, 478 Roberds, W., s e e Hansen, L.E 573, 574 Roberts, H.V. 1307 Roberts, J., s e e Milgrom, E 475 Roberts, J.M. 1013, 1033, 1040, 1116, 1118, 1505

Roberts, J.O., s e e Lebow, D.E. 215 Roberts, K. 1466 Robertson, J.C., s e e Pagan, A.R. 69, 108 Robinson, D. 217 Robinson, J. 1054, 1120 Robinson, S., s e e Meltzer, A.H. 204, 216, 217, 222 Rockafellar, R.T. 325 Rockoff, H. 155, 157 Rockoff, H., s e e Bordo, M.D. 160 Rodriguez, C.A. 1562, 1563, 1565, 1568 Rodriguez-Clare, A., s e e Klenow, EJ. 663, 673, 679, 680, 683 686, 694, 702, 705, 707 Rodrik, D., s e e Alesina, A. 278, 692, 1466, 1469 Rogers, C. 1449, 1450 Rogers, D., s e e Fullerton, D. 576, 588, 616 Rogerson, R. 551,602, 976-978, 1145 Rogerson, R., s e e Benhabib, J. 402, 550, 1145 Rogerson, R., s e e Bertola, G. 1222 Rogerson, R., s e e Cho, J.O. 976 Rogerson, R., s e e Cole, H.L. 1163, 1194, 1201-1203, 1207 Rogerson, R., s e e Greenwood, J. 550, 995 Rogerson, R., s e e Hopenhayn, H. 672, 708, 994 Rogerson, R., s e e Parente, S.L. 702 Rogoff, K. 961, 1415-1418, 1420, 1422, 1425, 1429, 1432, 1434, 1438 Rogoff, K., s e e Bulow, J. 1448, 1449 Rogoff, K., s e e Canzoneri, M.B. 1507, 1508

1-24 Rogoff, K., s e e Obstfeld, M. 407, 1507, 1590, 1630 Rojas-Suarez, L. 1575 Roland, G., s e e Persson, T. 1460 Roldos, J. 1578 Roll, R. i328 Romer, C.D. 6, 69, 92, 137, 183, 187, 204, 205, 1618 Romer, D. 237, 643, 649, 651,661,930, 1013, 1034, 1140, 1157, 1163, 1635, 1661 Romer, D., s e e Ball, L. 1023, 1037, 1041, 1127 Romer, D., s e e Frankel, J.A. 280, 281 Romer, D., s e e Mankiw, N.G. 244-246, 252255, 269-271,277-279, 289, 653, 655, 660, 673, 679-683, 685, 686, 1638 Romer, D.H., s e e Romer, C.D. 69, 92, 137 Romer, EM. 238, 245, 260, 261,264, 265, 271, 278, 280, 398, 424, 425, 641, 651, 665, 672, 705-707, 715-717, 719, t638 Romer, EM., s e e Evans, G.W. 425, 426, 506, 521 Rose, A., s e e Akerlof, G.A. 1200 Rose, A.K., s e e Eichengreen, B. 1590 Rose, A.K., s e e Frankel, J.A. 1590 Rosen, A., s e e Meehl, E 1319 Rosen, S. 584, 5 8 5 , 976 Rosensweig, J.A. 1659 Rosenthal, H., s e e Alesina, A. 1425, 1426 Roseveare, D. 1626 Ross, L. 1319 Ross, S., s e e Brown, S. 1242 Ross, S.A. 1331 Rossmla, R.J. 879, 881,886, 907 Rossana, R.J., s e e Maccini, L.J. 881, 893, 894, 903, 907 Rossi, EE., s e e Jones, L.E. 380, 672, 711-713, 1675, 1711 Rotemberg, J.J. 67, 68, 395, 397, 406, 407, 423, 429, 434, 838, 910, 974, 996, 1020, 1033, 1034, 1036, 1040, 1041, 1043, 1044, 1055, 1056, 1058, 1062, 1063, 1067-1069, 1074, 1081, 1082, 1088-1090, 1092, 1093, 1106, 1t07, 1114, 1116, 1118, 1123-1125, 1129, 1143, 1144, 1365, 1464, 1492, 1494, 1497 Rotemberg, J,J., s e e Mankiw, N.G. 785 Rotemberg, J.J., s e e Pindyck, R. 1072 Rotemberg, J.J., s e e Poterba, J.M. 159 Rothschild, M. 823 Rotwein, E. 1011

Author

Index

Roubini, N. 1439, 1465 Roubini, N., s e e A|esina, A. 277-279, 1404, 1423, 1425, 1460, 1466, 1471 Roubini, N., s e e Grilli, V 95 Roubini, N., s e e Kim, S. 95 Rouwenhorst, K.G. 1296 Royer, D., s e e Balasko, Y. 506 Rubinstein, A. 1188 Rubinstein, A., s e e Binmore, K.G. 1188 Rubinstein, M. 554-556 Rubinstein, M., s e e Jackwerth, J.C. 1310 Rudd, J.B., s e e Blinder, A.S. 1018, 1118 Rudebusch, G.D. 69, 104, 196, 1493 Rudebusch, G.D., s e e Diebold, EX. 6 Rudebusch, G,D., s e e 0liner, S.D. 137, 820, 1374, 1376 Rudebusch, R.G. 11 Rudin, J. 1040 Ruhm, C. 1152 Runkle, D., s e e Glosten, L. 1280 Rtmkle, D., s e e Keane, M.E 608, 609, 786, 790 Runkle, D.E, 789, 790, 1655 Runkle, D.E, s e e Geweke, J.E 89 Rtmkle, D.E., s e e Mankiw, N.G. 135 Russek, ES., s e e Barth, J.R. 1657 Rust, J. 314, 317, 336 Rust, J., s e e Amman, H.M. 535 Rustichini, A., s e e Benhabib, J. 400, 847, 1449, 1467, 1472 Rustichini, A., s e e Boldrin, M. 400, 1465 Ryder, H. 587 Ryder Jr, H.E. 1284

Sabelhaus, J., s e e Gokhale, J. 750 Sachs, J. 1590, 1591 Sachs, J., s e e Bruno, M. 1090 Sachs, J., s e e Roubini, N. 1439, 1465 Sachs, J.D. 252, 703 Sack, B., s e e Galeotti, M. 909 Sadka, E., s e e Razin, A. 1715 Sahay, R. 1535 Sahay, R., s e e Fischer, S, 1538, 1547, 1561 Saint Marc, M. 222, 223 Saint-Paul, G. 1162, 1472 Saint-Paul, G., s e e Blanchard, O.J. 1214 Sakellaris, E, s e e Barnett, S. 831 Sala-i-Martin, X. 269, 277, 279 282, 659, 694

Author

1-25

Index

Sala-i-Martin, X., s e e Barro, R.J. 237, 245, 246, 252, 269, 271, 272, 278, 284, 643, 651,657, 659, 671,675, 1637 Salge, M . 499 Salmon, C.K., s e e Haldane, A.G. 1485, 1497 Salmon, M. 525 Salmon, P., s e e Kirman, A.P. 536, 539-541 Saloner, G., s e e Rotemberg, J.J. 910, 1058, 1093 Salter, W.E.G. 848 Sampson, L., s e e Fanvel, Y. 1573 Samuelson, P.A. 46, 643, 661, 1311, 1634 Samwick, A. 609 Samwick, A.A., s e e Carroll, C.D. 567 Sandmo, A., s e e Atkinson, A.B, 1718 Sandroni, A. 1293 Sanguinetti, E 1540 Sanguinetti, P., s e e Heymann, D. 506 Sanguinetti, R, s e e Jones, M. 1540 Santaella, J. 1543 Santos, M., s e e Caballe, J. 578 Santos, M.S. 321-323, 326, 327, 335, 353, 354, 382, 590, 1266 Santos, M.S., s e e Bona, J.L. 313 Santos, M.S., s e e Ladron de Guevara, A. 317 Santos, M.S., s e e Peralta-Alva, A. 374 Sargent, T. 162, 198, 929 Sargent, T., s e e Ljungqvist, L. 1214 Sargent, T., s e e Lucas Jr, R.E. 582 Sargent, T., s e e Marimon, R. 455, 523 Sargent, T.J. 73, 121, 135, 417, 418, 453, 455, 457, 458, 464, 465, 489, 504, 523, 524, 529-531,763, 888, 1023, 1024, 1145, 1506, 1507, 1519, t542, 1543,-t630;.t631 Sargent, T.J., s e e Anderson, E.W. 368, 369 Sargent, T.J., s e e Cho, I.-K. 455, 465, 524, 525 Sargent, T.J., s e e Evans, G.W. 530 Sargent, T.J., s e e Hansen, L.R 558, 573, 574, 882, 915, 1294, 1295 Sargent, T.J., s e e Marcet, A. 454, 464, 465, 468, 473~476, 480, 494, 499, 525, 528, 529, 532, 1675, 1705, 1707 Sattinger, M. 577, 578 Satmders, A. 181 Sauvy, A. 222 Savage, L.J. 1308, 1324 Savage, L.J., s e e Friedman, M. 1325 Savastano, M.A. 1589 Savastano, M.A., s e e Masson, RR. 1554, 1588

Savin, N., s e e Bray, M. 454, 465, 466, 473, 475, 527 Savin, N., s e e Ingram, B. 984 Savin, N.E., s e e McManus~ D.A. 908 Savouri, S., s e e Jackman, R. 1221 Sayers, R.S. 156 Sbordone, A. 983 Sbordone, A., s e e Cochrane, J. 1120 Sbordone, A.M. 1078, 1099, 1108, 1118, 1128 Scammell, W.M. 156 Scarpetta, S. 1214 Schaling, E. 1437 Schaling, E., s e e Eijffinger, S. 1432, 1438 Schaller, H., s e e Moore, B.J. 455 Scharfstein, D., s e e Chevalier, J.A. 1122, 1123

Scharfstein, D., s e e Hoshi, T. 1344 Scheinkman, J., s e e Ekeland, I. 1689 Scheinkman, J., s e e Heckman, J.J. 579 Scheinkman, J.A. 566 Scheinkman, J.A., s e e Benveniste, L.M. 321 Schiantarelli, E, s e e Galeotti, M. 909, 1086, 1124

Schrnidt, R, s e e Kwiatkowski, D. 212 Schmidt-Hebbel, K., s e e Easterly, W. 1538 Schmitt-Groh6, S. 406, 407, 416, 418, 429, 431,435 Schmitt-Groh6, S., s e e Benhabib, J. 419, 421, 423 Schmitz Jr, J.A. 672, 695-697, 699 Schnadt, N., s e e Capie, F. 154 Scholes, M., s e e Black, E 1310, 1331 Scholz, J.K., s e e Gale, W.G. 1646 • Sch6nhofer, M. 515 Schopenback, P., s e e Erlich, D. 1314 Schotter, A. 1415 Schuh, S. 877, 881,912 Schuh, S., s e e Davis, S.J. 1151, 1152, 1160, 1161, 1178, 1194, 1199 Schuh, S., s e e Fuhrer, J.C. 905, 908 Schuh, S., s e e Humphreys, B.R. 909 Schultz, T.W. 653 Schumaker, L.L. 344, 345 Schwartz, A., s e e Thaler, R.H. 1313 Schwartz, AJ. 156, 161, 173, 180, 204, 1515 Schwartz, A.J., s e e Bordo, M.D. 159, 165, 184, 194, 203, 204, 208, 217, 1404, 1590 Schwartz, A.J., s e e Darby, M.R. 166 Schwartz, A.J., s e e Friedman, M. 61, 137, 154, 162, 172, 176, 179, 180, 185, 189, 222

1-26 Schwert, G.W. 1236, 1280 Schwert, G.W., s e e French, K. 1280 Seater, I I 1621, 1654, 1656, 1657 Sedlacek, G., s e e Heckman, I I 578, 579 Sedlacek, G.J., s e e Hotz, VJ. 792, 803 Segal, I.B. 1157 Senhadji, A.S., s e e Diebold, EX. 11 Sentana, E., s e e King, M. 1333 Seppala, J., s e e Marcet, A. 1675, 1705, 1707 Seslnick, D. 746, 751 Shafir, E. 1316, 1324, 1329 Shafir, E., s e e Tversky, A. 1324 Shapiro, C. 1157 Shapiro, C., s e e Farrell, J. 1121 Shapiro, M. 938, 980 Shapiro, M., s e e Barsky, R. 558, 564, 565 Shapiro, M.D. 138, 818, 1069, 1075, 1655 Shapiro, M.D., s e e Dominguez, K. 182 Shapiro, M.D., s e e Mankiw, N.G. 135 Shapiro, M.D., s e e Ramey, VA. 67, 1089 Sharma, S., s e e Masson, P.R. 1554, 1588 Sharpe, S. 1344 Shaw, E.S., s e e Gurley, J.G. 1507 Shaw, K. 584 Shay, R.P., s e e Juster, ET. 777 Shea, J. 402, 608, 790, 983, 1117 Sheffrin, S.M., s e e Driskill, R.A. 1042 Shefrin, H. 1313, 1317, 1321, 1330 Shell, K. 389, 391,516 Shell, K., s e e Balasko, Y. 427 Shell, K., s e e Barnett, W. 540 Shell, K., s e e Cass, D. 389, 516, 662 Shepard, A., s e e Borenstein, S. 1124 Sherali, D.H., s e e Bazaraa, M.S. 331 Sheshinski, E. 1031, 1037 Sherry, C.M., s e e Bazaraa, M.S. 331 Shiller, R.J. 173, 1234, 1235, 1238, 1249, 1290, 1316, 1317, 1319, 1320, 1323, 1324, 1327, 1330-1332 Shiller, R.J., s e e Campbell, J.Y. 1235, 1265, 1280, 1320 Shiller, R.J., s e e Case, K.E. 1323 Shiller, R.J., s e e Grossman, S.J. 1242, 1246, 1268, 1291 Shin, M.C., s e e Puterman, M.L. 339 Shin, Y., s e e Im, K. 283 S l f m , Y . , s e e Kwiatkowski, D. 212 Shleifer, A. 1317, 1324 Shleifer, A., s e e Barberis, N. 1294, 1322 Shleifer, A., s e e Bernheim, B.D. 1646 Shleifer, A., s e e DeLong, J.B. 1290, 1324

Author

Index

Shleifer, A., s e e La Porta, R. 1240 Shleifer, A., s e e Lakonishok, J. 1323 Shleifer, A., s e e Lee, C. 1324 Shleifer, A., s e e Murphy, K.M. 262, 278, 1082 Shoemaker, C.A., s e e Johnson, S.A. 345, 381 Shor, N.Z. 331 Shoven, J.B. 705, 708 Shoven, J.B., s e e Ballard, C. , 1639 Sibert, A., s e e Rogoff, K. 1416, 1417, 1420, 1425 Sichel, D., s e e Oliner, S.D. 820 Siegel, i i 1312, 1313 Silberman, J. 1316 Simldns, S. 931 Simmons, B. 163 Simon, H.A., s e e Holt, C.C. 882, 885, 888, 909, 910, 912 Simons, H.C. 852, 1485 Simonsen, M.H., s e e Dornbusch, R. 1543, 1565 Sims, C.A. 34, 44, 69, 83, 93, 95, 99, 105, 121, 128, 129, 131, 132, 134, 144, 397, 418, 539, 673, 694, 1509, 1518, 1520, 1631 Sims, C.A., s e e Hayashi, E 788 Sims, C.A., s e e Leeper, E.M. 69, 74, 83, 93, 101, 128, 132, 134, 1036, 1089, 1369 Sinai, A., s e e Eckstein, O. 1344 Singer, B. 292 Singer, B., s e e Heckman, I I 1166 Singleton, K. 1270 Singleton, K.J., s e e D u n n , K.B. 800, 1284 Singleton, K.J., s e e Hansen, L.P. 547, 555, 556, 768, 769, 784, 882, 1234, 1246, 1250, 1261 Siow, A., s e e Altonji, J.G. 789 Skinner, B.E 1328 Skinner, J.S. 771,772 Skinner, J.S., s e e Hubbard, R.G. 567, 569, 572, 573, 593, 771,776, 794, 797, 1660 Slade, M.E. 1015 Slemrod, J., s e e Shapiro, M.D. 1655 Slovic, P., s e e Fischhoff, B. 1319 Small, D.H., s e e Hess, G.D. 1485, 1509 Small, D.H., s e e Orphanides, A. 1485 Smetters, K.A. 1647 Smith, A.A., s e e Krusell, P. 380, 547, 566, 567, 994 Smith Jr, A.A., s e e Krusell, P. 1293 Smith, C.W., s e e Nance, D.R. 1318 Smith, E.L. 1312

Author

Index

Smith, G.W., s e e Devereux, M. 952 Smith, G.W., s e e Gregory, A.W. 376, 377 Smith, R., s e e Alogoskoufis, G.S. 166, 214 Smith, R.P., s e e Lee, K. 284 Smithson, C.W., s e e Nance, D.R. 1318 Snower, D., s e e Blanchard, O.J. 1214 Soares, J., s e e Cooley, T.E 1463 S6derlind, R, s e e Hassler, J. 9, 1238 S6derstr6m, T., s e e Ljung, L. 476 Soerensen, J.E 528 Solnick, A., s e e Judd, K.L. 340 Solon, G. 579, 1058, 1102, 1106 Solon, G., s e e Barsky, R. 43 Solow, R.M. 237, 244, 246, 257, 643, 656, 664, 681, 929, 930, 942, 950-952, 1140, 1207, 1638 Solow, R.M., s e e Blanchard, O.J. 1214 Solow, R.M., s e e Blinder, A.S. 1660 Solow, R.M., s e e Hahn, E 661 Solow, R.M., s e e Samuelson, P.A. 46 Sommariva, A. 222 Sonnenschein, H., s e e Hildenbrand, W. 535, 537 Sorger, G., s e e Hommes, C.H. 529, 532 Souleles, N., s e e Jappelli, T. 790 Spear, S.E. 465 Spear, S.E., s e e Marimon, R. 455, 531 Spiegel, M.M., s e e Benhabib, J. 283 Spilerman, S., s e e Singer, B. 292 Spulber, D.,see Caplin, A.S. 801, 1031, 1032 Spynnewin, E 803 Srba, E, s e e Davidson, J. 750 Srinivasan, T.N. 705 Stacchetti, E., s e e Jones, L.E. 720 Stafford, E, s e e Holbrook, R. 569 Stafford, E, s e e Ryder, H. 587 Staiger, D. 49, 50 Staiger, R. 1415 Staiger, R.W., s e e Bagwell, K. 1125 Stambaugh, R.E, s e e French, K. 1280 Stambaugh, R.E, s e e Kandel, S. 1235, 1252, 1253, 1265, 1270, 1272 Stark, T., s e e Croushore, D. 1485 Starr, R.M., s e e Chah, E.Y. 775 Startz, R., s e e Nelson, C.R. 1264 Statman, M., s e e Shefrin, H. 1313, 1317, 1330 Stedinger, J.R., s e e Johnson, S.A. 345, 381 Stein, J.C., s e e Kashyap, A.K. 137, 881,912, 1344, 1374, 1376 Stengel, R.E 904

1-27 Stephen, P., s e e Ryder, H. 587 Sterling, A., s e e Modigliani, E 1656, 1657 Stigler, G. 1018 Stigler, G.J. 1173 Stigler, S.M. 275 Stiglitz, J., s e e Dixit, A. 1115, 1121, 1126 Sfiglitz, J., s e e Greenwald, B. 857, 1122, 1377 Stiglitz, J., s e e Jaffee, D.M. 1376 Stiglitz, J.E. 1675, 1696, 1718 Stiglitz, J.E., s e e Atkinson, A.B. 1673, 1676, 1680, 1682, 1718 Stiglitz, J.E., s e e Shapiro, C. 1157 Stock, J.H. 9, 11, 39, 43, 45, 50-54, 821, 878, 919, 934, 938, 939, 1011, 1021, 1404, 1674 Stock, J.H., s e e Feldstein, M. 44, 1485, 1497, 1498 Stock, J.H., s e e King, R.G. 54, 941 Stock, J.H., s e e Staiger, D. 49, 50 Stockman, A. 1578 Stockman, A.C. 549 Stockman, A.C., s e e Baxter, M. 203, 938, 1404 Stockman, A.C., s e e Darby, M.R. 166 Stockman, A.C., s e e Gavin, W. 1485 Stockman, A.C., s e e Ohanian, L.E. 1036 Stocks, Bonds, Bills and Inflation 1639 Stockton, D.J., s e e Lebow, D.E. 215, 1016 Stoer, J. 334 Stoker, T., s e e Blundell, R. 770, 788 Stokey, N., s e e Alvarez, E 996 Stokey, N., s e e Lucas Jr, R.E. 559, 561 Stokey, N., s e e Milgrom, R 1322 Stokey, N.L. 271,299, 314, 318-321,346, 578, 583, 672, 705, 709, 711, 714, 951, 954, 998, 999, 1674 Stokey, N.L., s e e Lucas, R.E. 380, 1446, 1449 Stokey, N.L., s e e Lucas Jr, R.E. 158, 1673, 1675, 1699, 1723, 1728 Stone, C.J., s e e Breiman, L. 289 Strang, G. 82 Strongin, S. 83-85, 87, 114 Strotz, R.H. 1653 Strotz, R.H., s e e Eisner, R. 1310 Stroud, A.H. 334 Stuart, A. 1485 Stulz, R.M. 1317 Sturzenegger, F., s e e Dornbusch, R. 1543 Sturzenegger, E, s e e Guo, J.-T. 427 Sturzenegger, E, s e e Mondino, G. 1540

1-28 Suarez, J. 1378 Subrahmanyam, A., s e e Daniel, K. 1322 Sugden, R., s e e Loomes, G. 1313 Suits, D., s e e Kallick, M. 1325 Summers, L.H. 961 Summers, L-.H., s e e Abel, A.B. 1266, 1651 Summers, L.H., s e e Alesina, A. 1432 Summers, L.H., s e e Bernheim, B.D. 1646 Summers, L.H., s e e Blanchard, O.J. 416, 1635 Summers, L.H., s e e Carroll, C.D. 759, 793, 1655 Summers, L.H., s e e Clark, K.B. 602, 1173 Summers, L.H., s e e Cutler, D.M. 1290, 1320, 1321 Summers, L.H., s e e DeLong, J.B. 279, 695, 1042, 1290, 1324 Summers, L.H., s e e Easterly, W. 277, 278, 281, 675 Summers, L.H., s e e Kotlikoff, L.J. 780, 1646 Summers, L.H., s e e Mankiw, N.G. 785 Summers, L.H., s e e Poterba, J.M. 1235, 1320, 1648 Summers, R. 238, 301, 640, 673-675, 677, 680, 681,689, 720 Sun, T. 1270 Sundaram, R.K., s e e Dutta, RK. 380 Sundaresan, S.M. 1284 Sunder, S., s e e Marimon, R. 455, 472, 531 Surekha, K. 908 Sussman, O., s e e Suarez, J. 1378 Svensson, J. 1466, 1471, 1472 Svensson, L.E.O. 156, 197, 417, 1033, 1034, 1273, 1411, 1432, 1434, 1489, 1493, 1494, 1498, 1504 Svensson, L.E.O., s e e Englund, E 9 Svensson, L.E.O., s e e Kotlikoff, L. 1448, 1449, 1465 Svensson, L.E.O., s e e Leiderman, L. 1432, 1438, 1495 Svensson, L.E.O., s e e Persson, M. 1447, 1449 Svensson, L.E.O., s e e Persson, T. 1449, 1450, 1454, 1456, 1465 Swagel, P., s e e Alesina, A. 277-279, 1460, 1466, 1471 Swan, T.W. 244, 246, 247, 643 Sweeney, J., s e e Kneese, A. 656 Swoboda, A., s e e Genberg, H. 165 Symansky, S.A., s e e Bryant, R.C. 1491, 1497, 1516 Szafarz, A., s e e Adam, M. 500

Author

Szafarz, A.,

see

Index

Broze, L. 487, 488

Tabellini, G. 1414, 1415, 1450, 1456, 1464, 1465 Tabellini, G., s e e Alesina, A. 1446, 1449, 1450, 1454, 1465, 1518, 1522 Tabellini, G., s e e Cukierman, A. 1456, 1465 Tabellini, G., s e e Daveri, E 1220 Tabellini, G., s e e Edwards, S. 1538 Tabellini, G., s e e Grilli, V. 1404, 1432, 1438, 1439, 1465 Tabellini, G., s e e Ozler, S. 1457, 1465 Tabellini, G., s e e Persson, T. 278, 692, 1400, 1403, 1413, 1415 1418, 1420, 1421, 1425, 1433, 1435, 1437-1440, 1442, 1445, 1448, 1449, 1459, 1460, 1466, 1469, 1470, 1490 Taber, C., s e e Heckman, J.J. 576, 578, 582, 584, 586, 587, 590, 592, 593 Taguas, D., s e e Blanchard, O.J. 1214 Tallarini Jr, T.D., s e e Hansen, L.R 558, 1294, 1295 Tallman, E.W., s e e Rosensweig, J.A. 1659 Talvi, E. 1543, 1571, 1604 Tan, K.S. 334 Tanner, S., s e e Banks, J. 758, 792 Tanzi, V 1741 Tarshis, L. 939, 1059 Tauchen, G. 367 Taylor, A., s e e Obstfeld, M. 164, 165 Taylor, C. 1330 Taylor, J.B. 46, 182, 314, 397, 408, 417, 422, 454, 474, 487, 489, 495, 545, 1011, 1013, 1015, 1017, 1025, 1027-1031, 1037-1039, 1042, 1043, 1113, 1364, 1411, 1485, 1487, 1488, 1490, 1497, 1505, 1507, 1512, 1513, 1516, 1518, 1542, 1582 Taylor, J.B., s e e Phelps, E. 1025, 1026 Taylor, L.D., s e e Houthakker, H.S. 803 Taylor, S.E. 1330 Tejada-Guibert, J.A., s e e Johnson, S.A. 345, 381 Teles, R, s e e Correia, I. 1537, 1675, 1720, 1733 Telmer, C.I., s e e Backus, D.K. 1316 Temin, E 162, 179, 180, 183, 184 Temple, J. 276 Terlizzese, D., s e e Guiso, L. 772 Terna, R, s e e Beltratti, A. 524, 525 Terrones, M. 1425 Teruyama, H., s e e Fukuda, S.-i. 875 Tesar, L., s e e Mendoza, E. 1439

Author

Index

Tesar, L., s e e Stockman, A.C. 549 Tetlow, R., s e e Fillion, J.E 1498 Teukolsky, S.A., s e e Press, W.H. 329-334, 343, 348, 356, 365 Thaler, R., s e e Froot, K. 1316 Thaler, R., s e e Lee, C. 1324 Thaler, R.H. 1313, 1317 Thaler, R.H., s e e Benartzi, S. 1290, 1312, 1313 Thaler, R.H., s e e De Bondt, W.E 1307, 1320, 1323 Thaler, R.H., s e e Shefrin, H. 1317 Thaler, R.H., s e e Siegel, J.J. 1312 The Economist 1238, 1632 Theunissen, A.J., s e e Whittaker, J. 1508 Thomas, J. 994 Thomas, J.K., s e e Bernard, VL. 1321 Thomas, T.J. 161 Thompson, S.C., s e e Taylor, S.E. 1330 Thomson, J.B., s e e Carlson, J.B. 104 Thornton, H. 1485 Thurow, L. 759 Tieslau, M.A., s e e Hoffman, D.L. 412 Tillmann, G. 474 Timberlake, R.H. 169, 174 Timmermann, A.G. 454, 455, 500, 530 Tinbergen, J. 817 Tirole, J. 1266, 1650 Tirole, J., s e e Fudenberg, D. 1155 Tirole, J., s e e Holmstrom, B. 1376 Titman, S., s e e Jegadeesh, N. 1321 Tobin, J. 773, 817, 818, 1643 Tobin, J., s e e Brainard, W.C. 817 Tobin, J., s e e Eichengreen, B. 168 Todd, R, s e e Heckman, J.J. 578, 582 Todd, R., s e e Cl~istiano, L.J. 1365 Toharia, D., s e e Blanchard, O.J. 1214 Toma, M. 174, 177, 187, 190 Toma, M., s e e Goff, B.L. 159 Tommasi, M. 1540 Tommasi, M., s e e Jones, M. 1540 Tommasi, M., s e e Mondino, G. 1540 Topel, R. 578 Topel, R., s e e Juhn, C. 619 Topel, R., s e e Murphy, K. 581 Tornell, A. 1466, 1472, 1590 Tornell, A., s e e Lane, E 1472 Tornell, A., s e e Sachs, J. 1590, 1591 Townsend, R.M. 453, 461,474, 529, 795, 796, 1350, 1376

1-29 Townsend, R.M., s e e Phelan, C. 380, 575, 796 Traub, J.E 338 Traub, J.E, s e e Papageorgiou, A. 334 Trehan, B. 159 Tria, G., s e e Felli, E. 1083, 1122 Triffin, R. 157, 165 Trostel, RA. 1652 Tryon, R., s e e Brayton, E 1043, 1344, 1485 Tsiddon, D. 1031 Tsiddon, D., s e e Lach, S. 1019 Tsitsiklis, J.N., s e e Chow, C.-S. 326, 334 Tsutsui, Y., s e e Shiller, R.J. 1316 Tullio, G. 156 Tullio, G., s e e Sommariva, A. 222 Tullock, G., s e e Grier, K.B. 253 Tuncer, B., s e e Krueger, A.O. 699 Yurnovsky, S. 474 Tversky, A. 1308, 1315, 1319, 1324, 1330 Tversky, A., s e e Kahneman, D. 1308, 1309, 1311 Tversky, A., s e e Quattrone, G.A. 1329 Tversky, A., s e e Shafir, E. 1316, 1324, 1329 Tversky, A., s e e Thaler, R.H. 1313 Tybout, J., s e e Corbo, V. 1543 Tylor, E.B. 1331 Uhlig, H. 70 Uhlig, H., s e e Lettau, M. 524, 1297 Uhlig, H., s e e Taylor, J.B. 314 United Nations 681 Uppal, R., s e e Dumas, B. 564 Uribe, M. 1539, 1578, 1589 Uribe, M., s e e Benhabib, J. 419, 421,423 Uribe, M., s e e Mendoza, E. 1571, 1579 Uribe, M., s e e Schmitt-Groh~, S. 416, 418, 431 US Bureau of the Census 585 Uzawa, H. 578, 651,710 Valdes, R., s e e Dornbusch, R. 1590 Valdivia, V, s e e Christiano, L.J. 504 Van Huyck, J.B., s e e Grossman, H.J. 158, 1415, 1449 van Wineoop, E., s e e Beaudry, E 1264 Van Zandt, T., s e e Lettau, M. 470, 472 Vasicek, O. 1270 V6gh, C., s e e Guidotti, EE. 1675, 1720 V6gh, C.A. 1535, 1538, 1542, 1543, 1546, 1550, 1554, 1588 V6gh, C.A., s e e Bordo, M.D. 158

1-30 V6gh, C.A., s e e Calvo, G.A. 1428, 1535, 1538, 1539, 1546, 1554, 1557, 1563, 1564, 1568, 1571, 1572, 1582, 1587-1589, 1597, 1605 Vdgh, C.A., s e e De Gregorio, J. 1546, 1551, 1573, 1575, 1577 V6gh, C.A., s e e Edwards, S. 1578-1580 V6gh, C.A., s e e Fischer, S. 1538, 1547, 1561 V6gh, C.A., s e e Guidotti, EE. 1537, 1588, 1603 V6gh, C.A., s e e Hoffiaaaister, A. 1561, 1589 V6gh, C.A., s e e Lahiri, A. 1597 V~gh, C.A., s e e Rebelo, S.T. 1546, 1568, 1578, 1579, 1581, 1606 V~gh, C.A., s e e Reinhart, C.M. 1545, 1546, 1551, 1553, 1561, 1572, 1573 V6gh, C.A., s e e Sahay, R. 1535 Vela, A., s e e Santaella, J. 1543 Velasco, A. 416, 1446, 1449, 1450, 1459, 1465, 1540 Velasco, A., s e e Sachs, J. 1590, 1591 Velasco, A., s e e Tommasi, M. 1540 Velasco, A., s e e Tomell, A. 1466, 1472, 1590 Venable, R., s e e Levy, D. 1014, 1015, 1019 Venegas-Martinez, E 1571 Ventura, G., s e e HuggeR, M. 380 Veracierto, M. 994 Verdier, T., s e e Saint-Paul, G. 1472 Vetterling, WT., s e e Press, WH. 329-334, 343, 348, 356, 365 Viana, L. 1543 Vickers, J. 1414, 1415 Vigo, J., s e e Santos, M.S. 321,322, 326, 327, 335 Vinals, J., s e e Goodhart, C.E.A. 1438, 1495 Vishny, R.W., s e e Barberis, N. 1294, 1322 Vishny, R.W., s e e La Porta, R. 1240 Vishny, R.W, s e e Lakonishok, J. 1323 Vishny, R.W, s e e Murphy, K.M. 262, 278, 1082 Vishny, R.W, s e e Shleifer, A. 1324 Visscher, M., s e e Prescott, E.C. 700 Vives, X. 474, 532 Vives, X., s e e Jun, B. 474 Volcker, P.A. 1630 von Furstenberg, G.M. 1333 von Hagen, J. 1439, 1460, 1465 von Hagen, J., s e e Eiehengreen, B. 1465 von Hagen, J., s e e Fratianni, M. 1431 yon Hagen, J., s e e Hallerberg, M. 1460, 1465 von Weizs/icker, C. 641,650, 657 Vredin, A.E., s e e Bergstr6m, V. 538

Author

Index

Vuong, Q.H., s e e Rivers, D. 840 Wachtel, E 1658 Wachtel, E, s e e Evans, M. 182 Waehter, S.M., s e e Goetzmann, WN. 1333 Wadhwani, S., s e e King, M. 1333 Wagner, R.E., s e e Buchanan, J.M. 1631 Waldmann, R.J., s e e DeLong, J.B. 1290, 1324 Walk, H., s e e Ljung, L. 476 Walker, M., s e e Moreno, D. 481 Wallace, N., s e e Sargent, T.J. 417, 418, 489, 1024, 1506, 1507, 1519, 1630 Waller, C. 1431 Waller, C., s e e Fratianni, M. 1431 Wallis, K., s e e Kreps, D.M. 540 Walsh, C.E. 1433, 1434, 1437, 1438, 1490 Walsh, C.E., s e e Trehan, B. 159 Walsh, C.E., s e e Waller, C. 1431 Wang, EA. 1322 Wang, J. 1237, 1293 Wang, L.-T., s e e Dezhbakhsh, H. 1039 Wang, T., s e e Dumas, B. 564 Warner, A.M., s e e Sachs, J.D. 252, 703 Warner, E.J. 1019 Wascher, W., s e e Lebow, D.E. 1016 Watson, J., s e e den Haan, W.J. 994, 1166, 1194, 1203, 1204, 1206, 1207 Watson, J., s e e Ramey, G. 852, 1157, 1159 Watson, M.W 6, 50, 547, 931 Watson, M.W, s e e Bernanke, B.S. 144 Watson, M.W., s e e Blanchard, O.J. 1266 Watson, M.W., s e e Canjels, E. 55 Watson, M.W, s e e King, R.G. 46, 54, 939, 941 Watson, M.W, s e e Staiger, D. 49, 50 Watson, M.W, s e e Stock, J.H. 9, 43, 45, 50-52, 821, 878, 919, 934, 938, 939, 1011, 1021, 1404, 1674 Webb, S., s e e Goodman, A. 797 Webber, A., s e e Capie, E 222 Weber, G. 774 Weber, G., s e e Alessie, R. 774, 775 Weber, G., s e e Attanasio, O.P. 611-613, 756, 769, 781, 783, 784, 787, 790, 791, 793, 794, 1264, 1655 Weber, G., s e e Blundell, R. 781 Weber, G., s e e Brugiavini, A. 775 Weber, G., s e e Meghir, C. 611,613, 775, 804 Weber, M. 1331 Weder, M. 403, 437 Wehrs, W, s e e Carlson, J.A. 904

Author

Index

Weibull, J., s e e Lindbeck, A. 1465 Weil, D.N., s e e Mankiw, N.G. 173, 216, 244~ 246, 252-255, 269-271,277-279, 289, 653, 655, 660, 673, 679-683, 685, 686, 1638 Weil, E 547, 1235, 1250, 1253, 1256, 1647 Weil, R, s e e Blanchard, O.J. 1650 Weil, E, s e e Restoy, E 1272 Weingast, B., s e e North, D. 1449 Weinstein, M.M. 182 Weisbrod, S.R., s e e Rojas-Suarez, L. 1575 Weiss, A., s e e Greenwald, B. 1122 Weiss, L., s e e Scheinkman, J.A. 566 Weiss, Y. 583 Weiss, Y., s e e Blinder, A. 587 Weiss, Y., s e e Lillard, L. 569, 572 Weiss, Y., s e e Sheshinski, E. 1031, 1037 Weitzman, M.L. 1689 Welch, E 579 Welch, I., s e e Bikhchandani, S. 1332 Wen, J.E, s e e Devereux, M. 1466, 1471 Wen, L. 427, 431 Wenzelburger, J., s e e Brhm, V 475 Wemer, A., s e e Dombusch, R. 1543, 1563, 1568 West, K.D. 871, 876, 880, 882, 885, 887, 888, 894, 896, 897, 900, 902, 905-908, 913, 919, 1028, 1041, 1320, 1497 Whalley, J. 705 Whalley, J., s e e Ballard, C. 1639 Whalley, J., s e e Shoven, J.B. 705, 708 Whalley, J., s e e Srinivasan, T.N. 705 Wheatley, S. 1242, 1261 Wheelock, D.C. 177, 179 Wheelock, D.C., s e e Calomiris, C.W 187, 191 Whinston, M.D., s e e Segal, I.B. 1157 White, E., s e e Bordo, M.D. 159 White, E.N. 180 White, H. 524 White, H., s e e Chen, X. 476, 532 White, H., s e e Kuan, C.-M. 476 Whited, T. 1344 Whited, T., s e e Hubbard, R.G. 1344 Whiteman, C. 487 WhiR, W. 326 Whittaker, J. 1508 Wickens, M.R., s e e Robinson, D. 217 Wicker, E. 162, 176, 177, 179-181, 1543 Wicksell, K. 203, 1485, 1631 Wieland, V., s e e Orphanides, A. 1485 Wigmore, B.A. 163, 183

1-31 Wilcox, D. 1242 Wilcox, D., s e e Kusko, A.L. 1327 Wilcox, D.W 1655 Wilcox, D.W., s e e Carroll, C.D. 769, 785 Wilcox, D.W., s e e Cecchetti, S.G. 876 Wilcox, D.W, s e e Kashyap, A.K. 137, 877, 886, 903, 906, 912 Wilcox, D.W, s e e Orphanides, A. 198, 1485 Wilcox, D.W., s e e West, K.D. 908 Wildasin, D., s e e Boadway, R. 1463 Wilkinson, M. 881 Williams, J.C., s e e Brayton, E 1043, 1344, 1485 Williams, J.C., s e e Gilchrist, S. 847 Williams, J.C., s e e Wright, B.D. 347, 348 Williamson, J. 1597 Williamson, O.E. 852 Williamson, S. 1376 Willis, R., s e e Heckrnan, J.J. 602, 623 Wilson, B., s e e Saunders, A. 181 Wilson, C.A. 408 Wilson, R. 554, 796 Winter, S.G., s e e Phelps, E.S. 1121 Woglom, G. 1127 Wohar, M.E., s e e Fishe, R.P.H. 173 Wojnilower, A. 1344 Wolf, H., s e e Dornbusch, R. 1543 Wolf, H., s e e Ghosh, A.R. 202, 207, 208 Wolff, E. 664 Wolfowitz, J., s e e Kiefer, J. 476 Wolinsky, A. 1188 Wolinsky, A., s e e Binmore, K.G. 1188 Wolinsky, A., s e e Rubinstein, A. 1188 Wolman, A.L., s e e Dotsey, M. 974, 1032, 1043 Wolman, A.L., s e e King, R.G. 1036, 1041, 1043, 1364, 1367 Wolters, J., s e e Tullio, G. 156 Wong, K.-E 108 Wood, G.E., s e e Capie, E 163, 1438 Wood, G.E., s e e Mills, T.C. 204 Woodford, M. 389, 395, 406, 407, 409, 418, 421-423, 439, 454, 473-476, 481,483, 507, 516, 518, 521,662, 1036, 1157, 1507, 1509, 1518-1520, 1537, 1630, 1675, 1676, 1720, 1731 Woodford, M., s e e Bernanke, B.S. 1361, 1363 Woodford, M., s e e Boldrin, M. 506 Woodford, M., s e e Farmer, R.E. 395, 396 Woodford, M., s e e Guesnerie, R. 439, 454, 460, 465, 474, 475, 506, 511,516, 526

1-32 Woodford, M., s e e Kehoe, T.J. 380 Woodford, M., s e e Lucas Jr, R.E. 1023 Woodford, M., s e e Rotemberg, J.J. 67, 68, 395, 406, 407, 429, 434, 974, 996, 1020, 1041, 1043, 1044, 1055, 1056, 1062, 1063, 1067-1069, 1074, 1081, 1082, 1088-1090, 1092, 1093, 1106, 1107, 1118, 1123-1125, 1129, 1143, 1144, 1365, 1492, 1494, 1497 Woodford, M., s e e Santos, M.S. 1266 Woodward, P.A., s e e Baker, J.B. 1125 Wooldridge, J., s e e Bollerslev, T. 1280 Wozniakowski, H., s e e Traub, J.E 338 Wright, B.D. 347, 348 Wright, M.H., s e e Gill, RE. 329 Wright, R. 1158 Wright, R., s e e Benhabib, J. 402, 550, 1145 Wright, R., s e e Boldrin, M. 399 Wright, R., s e e Burdett, K. 1196 Wright, R., s e e Greenwood, J. 550, 995 Wright, R., s e e Hansen, G.D. 976 Wright, R., s e e Kiyotaki, N. 524 Wright, R., s e e Parente, S.L. 702 Wright, R., s e e Rogerson, R. 978 Wurzel, E., s e e Roseveare, D. 1626 Wynne, M. 974 Wyrme, M.A., s e e Huffman, G.W 437 Wyplosz, C., s e e Eichengreen, B. 168, 1590 Xie, D. 425 Xie, D., s e e Benhabib, J. 425 X i e , D . , s e e Rebelo, S.T. 952 Xu, Y. 344 Yashiv, E. 1200 Yellen, J.L., s e e Akerlof, G.A. 397, 1034, 1035, 1039, 1157, 1200 Yeo, S., s e e Davidson, J. 750 Yi, K.-M., s e e Kocherlakota, N.R. 271 Yin, G.G., s e e Kushner, H.J. 476 Yong, W., s e e Bertocchi, G. 474 Yorukoglu, M., s e e Cooley, T.E 847

Author

Index

Yorukoglu, M., s e e Greenwood, J. 576 Yotsuzuka, T. 1649 Young, A. 664, 672, 673, 687, 716 Young, J., s e e Wachtel, R 1658 Yu, B., s e e Hashimoto, M. 1152 Yun, T. 1026, 1036

Zarazaga, C.E. 1540 Zarazaga, C.E., s e e Kydland, EE. 1557, 1561 Zarnowitz, V 9, 40 Zeckhauser, R., s e e Degeorge, E 1321 Zeckhauser, R.J., s e e Abel, A.B. 1266, 1651 Zeira, J., s e e Galor, O. 262, 263 Zejan, M., s e e Blomstrom, M. 277, 279, 280 Zeldes, S.P. 566, 607 609, 771,789, 790, 802, 1344, 1655 Zeldes, S.P., s e e Barsky, R.B. 1653 Zeldes, S.R, s e e Hubbard, R.G. 567, 569, 572, 573, 593, 771,776, 794, 797 Zeldes, S.P., s e e Mankiw, N.G. 790, 1290 Zeldes, S.P., s e e Miron, J.A. 876, 907 Zetdes, S.R, s e e O'Connell, S.A. 1650 Zellner, A. 34 Zenner, M. 497 Zha, T., s e e Cushman, D.O. 95, 96 Zha, T., s e e Leeper, E.M. 69, 74, 83, 93, 101, 128, 132, 134, 1089, 1369 Zha, T., s e e Sims, C.A. 69, 83, 93, 99, 128, 129, 131, 132, 134, 144 Zhang, L., s e e Lockwood, B. 1411, 1415 Zhou, Z., s e e Grossman, S.J. 1237, 1293 Zhu, X. 1708 Zilcha, I., s e e Becker, R. 369 Zilibotti, E, s e e Gali, J. 405, 426 Zilibotti, E, s e e Marimon, R. 1214 Zin, S.E., s e e Epstein, L.G. 556, 558, 564, 744, 769, 1250, 1256 Zingales, L., s e e Kaplan, S.N. 856, 1344

SUBJECT INDEX

accelerator 884, 890, 896, 909 accelerator model 816, 817 accelerator motive 867, 902 activist vs. non-activist policies 1485 actual law of motion (ALM) 466, 472, 490, 511 adaptive expectations 453, 465 adaptive learning 464, 472, 493, 510 stability under 471 adaptively rational expectations equilibrium 532 adjustment costs 800, 1072 employment 1075 hours 1075 in investment 1296 non-convex 821,839 production 867, 892, 893, 900 hazard 835, 836, 840 speed of 881,889, 908 age distribution 753, 848 aggregate convexity 843 aggregate demand 1617, 1628, 1630 aggregate human capital 583, 590-593 aggregate productivity 1195 aggregate productivity shock 1204 heterogeneous 1214 aggregate shocks 578, 582, 865 aggregation 548-594, 604, 605, 614, 615, 745, 781, 804, 836, 849, 910 across commodities 782 AK model 672, 673, 709-715, 720, 733 allocation rules 1688, 1723 alternative dating 499 amplification 841, 1145, 1158, 1159, 1161 anchoring 1314-1317, 1322 animal spirits 395, 517, 521,941 anomalies 1307, 1308, 1316, 1317, 1321, 1322, 1333, 1334 approximation error 326-345, 351-382 arbitrage 1246 ARMA models 489, 496, 501 Arrow-Debreu equilibrium 795

asset-price channel 1378 asset prices, variable 1356 asset pricing models with feedback 500 asset pricing with risk neutrality 498 associated differential equation 519 asymmetric fixed costs 825 asymmetry in adjustment of employment 1158 asymptotic stability 479, 639 autarky 853 automatic stabilizers 1660 average cohort techniques 787

backlog costs 884 backstop technology 656 balance-of-payments (BOP) crises 1534, 1535, 1553 balanced-budget rule 1631 balanced growth path 50, 392, 393, 424, 425, 427 band-pass filter, s e e BP filter bank lending channel 1376 Barro, R. 1640, 164~1646 Bayesian learning 474 Bayesian updating 461,465 Belgium 1619 Bellman's Principle of Optimality 998 bequest motive 745, 780, 1624, 1646, 1647 strategic 1646 best practice 848 /3-convergence 659 Beveridge curve 1194, 1196, 1221, 1222 bilateral bargaining problem 1157 black market premium 671,688, 689, 691-694, 703 Blanchard-Kahn technique 505 Bolivia 1631 boom-recession cycle 1550, 1552, 1581 bootstrap methodology 79 BOP crises, s e e balance-of-payments crises borrowers' net worth 1345 1-33

1-34 borrowing constraint 566, 575, 593, 595, 597, 598, 772, 775, 1293 see also capital market imperfections; credit market imperfections; liquidity constraints Boschen-Mills index 139-142 bottlenecks 842, 843 bounded rationality 454, 464 BP (band-pass) filter 12, 933, 934 Bretton Woods 152, 153, 163-168, 188, 190, 192, 199, 202-204, 206~09, 211,213, 215, 218-220 Brownian motion 825, 845 regulated 845 bubble-free solution 1524 bubble solutions 1522 bubbles 499 explosive 499 budget deficit 1619 budget surplus 1619 buffer-stock saving 771, 1653, 1654 building permits 45 Burns-Mitchell business cycle measurement 932 business cycles 865, 927-1002, 1620, 1621, 1659 s e e also cycles; fluctuations in aggregate activity facts about 934, 938, 939, 956 general equilibrium models 67 in RBC model 968 measuring 932 persistence of 939 table of summary statistics 956, 957 US facts 934 USA 935-938, 956 Cagan model of inflation 497 calculation equilibrium 462 calibration 545, 550, 567, 601,614, 616 Canada 45 capacity utilization 41,427, 431,930 modeling of 980 rate of 981 steady-state rate of 984 capital 1617, 1687 broad measure 701 desired 816, 842 frictionless 832, 838 human 673, 678, 679, 681-687, 701, 710, 713, 714, 716-718, 720, 732, 734

Subject I n d e x see also human capital organizational 700, 701 physical 678-683, 701,710, 713, 714, 721, 732 specific 1154 stock of 1629, 1630, 1632, 1633, 1636-1638, 1648, 1652, 1656 target 820 unmeasured 701,702 vintage 702 capital accumulation 942, 1203 general equilibrium nature of 946 optimal 946 perpetual inventory method 944 capital budgeting 1623 capital controls 1588 capital imbalances, establishments' 837 capital intensities 641,644, 679, 680, 682, 685, 686 capital investment decision 1349 capital/labor substitution 856 capital market imperfections 1648, 1649 s e e also borrowing constraint; credit market imperfections capital taxation 1661, 1708 optimality of zero 1693 capital utilization 848 CARA utility 794 cash-in-advance constraint 397, 1722 cash-credit model 1720, 1721 "catching up with the Joneses" 1284 certainty equivalence 762 Chamley result 1698 characteristics model 578, 579, 582, 602 characterization of equilibria 487, 489 Cholesky factor 80 classification 262, 289, 303 classifier systems 465, 523 closed economy 1714 closed-form solution 769 club-convergence 660 Cobb-Douglas production function in RBC model 944, 950 "cobweb" model 456 coefficient of relative risk aversion 1249 cohort data 78t cohort effects 576, 577, 590-592, 617, 753, 754 cointegration 50, 750, 820, 838, 877-881, 885-887, 903, 1266 collateral 857

1-35

Subject lndex

commitment 574, 575, 1488, 1523 technology 1688, 1723 vs. flexibility 1489 commodity space 1686 comparative advantage 547, 548, 577-579, 584, 587 comparative dynamics measured by impulse response 967, 968, 970 competitive equilibrium 844, 845, 1677, 1688, 1722 competitive trajectory 650 complementarity 1161 complements 599, 601,611-613, 855 complete markets 553, 558, 563, 595, 602, 786, 1688 computation of (approximate) solutions 525 computational general equilibrium (CGE) 705, 708 computational intelligence 465 computational tool 455 conditionally linear dynamics 475, 481 conditioning 556, 594, 597-599, 601,605, 612, 613 consistent expectations equilibria 529 constant returns to scale 639, 831, 1687 in RBC model production fimction 995 consumer expectations 45 consumer theory 603 consumer's budget constraint 1264, 1712, 1728 consumption 40, 545, 546, 548-558, 560-564, 566, 567, 572-576, 587, 590, 594-603, 605-614, 616, 621, 1276 behavior in US business cycles 938 empirical 1344 estimates 605-614 'excess' sensitivity 524 growth 1233, 1242, 1276 inequality in 797 permanent-income hypothesis 943 private 1687 procyclical 433~435 smoothing 805 in RBC model 967 time-averaged data 1242 consumption-based asset pricing 1249 consumption expenditure 745 Consumption Expenditure Survey (CEX) 750 consumption per capita 643 consumption taxes 1692 contract multiplier 1028

contractual problems 849 control rights 852 control variables 688, 689 convergence 240, 245-276, 284-288, 290, 295, 296, 659 global 486 local 519 probability of 480 speed of 531,659 convergence analysis 454, 477-479 convertibility 153, 160 convertibility rules 209, 213 convex adjustment costs 818, 823 coordination failures 461 coordination of beliefs 391 comer solutions 804 cost &capital 817, 1344 cost shifters 906, 912 cost shock 867, 884, 899, 907, 908, 912 Costa Rican tariff reform 707 costly state verification 1349 creative destruction 848, 1210, 1213 credibility 1536, 1603 credit chains 1378 credit constraints 856 credit market 847 imperfections 1343 see also borrowing constraint; capital market imperfections segmentation 1575, 1577 cross-country regression 276, 281 cross-section least-squares regression 269 cross-sectional density 840 of establishments' capital imbalances 837 cross-sectional growth regression 252, 269273, 275, 276, 284-289, 671, 675, 694 literature 688 crossover 522 crowding out 1632, 1633, 1636, 1638, 1648, 1652, 1654 currency crises 1534 current account deficit 1598 Current Population Survey 796 curse of dimensionality 843, 847 customer markets 1120 cycles 460, 507, 509, 526, 865 deadweight loss 1631, 1632, 1639, 1640, 1662 debt contract 1350 debt-deflation 1372

1-36 debt neutrality 1644 debt-income ratio 1630 debt--output ratio 1619 decentralized economy 547, 575, 576, 602 decision rule 888-890 deficits 1617 nominal 1621 real 1621 demand shocks 865, 884, 889 892, 895, 898, 1055 demographic transition 658 demographic variables 793 demographics 547, 551-615, 744 and retirement behavior 758 depreciation 642, 1633 detrending and business cycle measurement 932 difference models of habit 1284 difference-stationary models 764 difference-stationary process 211,215, 1497 differential equation 472 diminishing returns 639 separately to capital and augmented labor 653 dirty floating 1587 discount factor 548, 555-557, 561,567, 588, 595, 606, 607, 609, 610, 616 disinflation, output costs of 1542 disjunction effect 1324 disparity in GDP 675 disparity in incomes 674 distribution dynamics 263, 290-295, 299 distribution of country incomes 674 distribution of relative GDP 674 dividend growth 1233, 1242, 1276 dollarization 1589 domestic debt 1595, 1601 domestic policy regime 153, 202 Dornbusch-type model 502 DSGE, s e e dynamic stochastic general equilibrium models durability 798, 1242 durable goods 549, 746, 799, 1550, 1552, 1573, 1575 dynamic economic models 312, 313 Dynamic New Keynesian (DNK) framework 1346 dynamic programming 834 dynamic stochastic general equilibrium (DSGE) models 930, 1139, 1145, 1150, 1157, 1166

Subject Index

models with job search

1158

earnings 546, 567-573, 577-588, 592, 593, 598, 605, 615, 623 s e e also wages structural equation 582 variance 569 572, 578, 586 econometric approaches 237 economic growth 1617, 1641; 1651 economic relationship 852 education 577, 578, 580, 584, 602, 607, 609, 613, 615, 622, 623, 653 eductive approaches 462, 464 effective labor 650 efficiency of terminations 1152 efficiency units 566, 658 s e e also labor in efficiency units efficiency wages 577, 578, 1098, 1157, 1159, 1160 efficient equilibrium 854 efficient markets 1307, 1308, 1316, 1319-1322, 1333 elastic labor supply 1145 elasticity 545, 546, 550-552, 563, 579, 580, 592-594, 596-601,605, 607, 610, 614-617, 620 of capital supply 1714 long run 838 of demand, varying 1119 of intertemporal substitution 552, 557, 561, 564, 597, 600, 601,614, 615, 769, 791, 1148, 1250 of investment 857 of labor supply schedule 1147 of substitution 645 election 522 embodied technology 1207 embodiment-effect 664 employment 39 employment contract 1153 employment fluctuations 1173, 1194 employment protection 1215, 1217 employment relationship 1157 endogenous fluctuations 506, 531 endogenous growth models 238, 241,243, 245, 257, 259, 261, 264, 265, 269, 271, 297, 506, 651,653, 1711 entry 1067 variable 1125 entry and exit 551,602, 615, 616, 824, 844 envelope theorem in RBC model 998

1-37

Subject Index

"episodic" approach 1560 e-SSE 520 Epstein-Zin-Weil model 1259 equipment 840 equity premium puzzle 1234, 1245, 1249, 1250 error correction model 750 E-stability 463, 466, 468, 471-473,488, 490, 491,504, 511 iterative 463 strong 473, 483, 491,512 weak 473, 483, 512 Euler equation 314, 345-347, 349-352, 354, 355, 364, 368, 371, 373, 374, 381, 382, 555-558, 566, 567, 575, 597, 598, 606, 607, 609, 611,621,650, 765, 767, 794, 805 undistorted 1713 Euler equations 745, 791 excess bond re~rns 1276, 1277, 1280 excess sensitivity 772, 784, 785, 790 excess smoothness puzzle 747 excess stock returns 1249, 1276, 1277 excess volatility 1319, 1320 excessive destruction 856 exchange rate 527, 531, 1658 anchor 1588 and markups 1122 arrangements 167, 203 exchange-rate-based stabilization 1535, 1543, 1553, 1559 empirical regularities 1546 existence of competitive equilibrium in RBC model 1002 exit, delayed 850 see also entry and exit exogenous growth models 261 exogenous technological progress 650 expectation functions 453, 461,464 expectational stability, s e e E-stability expectations, average 528 expectations hypothesis of term structure 1281 experience 582, 584, 590, 602 experimental evidence 530 exports 41 extensive margins 843 external effects 390, 399-401, 403-405, 424-427, 431,433-435, 437 external finance premium 1345 external habit models 1284 externalities in RBC model 1002

factor-saving bias 641 factors of production 909 Family Expenditure Survey (FES) 746, 750 family income 564, 569, 589 Federal Reserve 153, 168, 169, 172-182, 184~202, 219 feedback derivative 1510 proportional 1510 feedback rule 68, 71 feedforward networks 524 financial accelerator 1345 financial development 671,688, 692 financial markets, role in economic growth 1376 firing cost 1186, 1214, 1222 fiscal authorities 1524 fiscal deficits 1538, 1594, 1604 fiscal increasing returns 416 fiscal policy 672, 692, 694, 712, 715, 1580, 1617, 1624 countercyclical 1617, 1660 fiscal theory of price-level determination 1520, 1524 fixed costs 390, 426, 435, 828, 848, 911 flow-fixed costs 831 fixed effect 787 flexible accelerator 816, 865, 893, 903 flexible cyclical elasticity 842 flexible neoclassical model 817 floating exchange rate 1582 fluctuations in aggregate activity 547, 549, 552, 556, 569, 1053 s e e also business cycles induced by markup variation 1055, 1104 France 45 free entry condition 844, 845 frictionless neoclassical model 817 Friedman rule 1720 Frisch demands 595-597, 603 Frisch labor supply 1146 full-order equilibrium 530 functional forms 550, 583, 584, 588, 598, 601, 607, 611,623 fundamental solution 498 fimdamental transformation 852 gain sequence 469, 475 decreasing 469 fixed 469 small 470

1-38 general equilibrium 543-625, 888 generational accounting 1624 genetic algorithms 465, 521,525 Germany 45, 1631 global culture 1332, 1333 GLS 788 gold standard 153-190, 199-220 Golden Rule 1650 Gorman-Lancaster technology 800 government budget constraint 1687, 1719 consumption 671,691,694, 1687, 1736 rate to GDP 688, 689 debt 1617, 1687 production 672, 695, 701 production of investment 699 purchases 41 purchases and markups 1120 share 692 in GDP 671,689 in investment 695, 696 in manufacturing output 696 in output 693 gradual adjustments 823 gradualism 849 Granger causality 34 Great Depression 153, 163, 175, 178, 180-184, 199, 200, 213, 1343 Great Inflation of the 1970s 153 great ratios of macroeconomics 939, 940 gross domestic product (GDP) per capita 674 per worker 671 gross substitutes 1731 growth cycles 9 growth accounting 678, 687, 688 growth miracles in East Asia 709 growth-rate targets 1524 maximum growth rate 677, 726, 728, 732 habit formation 798, 802, 1237, 1284 habits 564, 802 Harrod-Domar models 640 hazard rate constant 839 effective 836 increasing 840 hedging demand 1275 Herfindahl index 824 heterogeneity 546, 547, 552, 553

Subject lndex

in firms 1366 in learning 527 in values of job matches 1152 of preferences 545, 558, 563 unobserved 779, 831 heterogeneous agents 843, 1237, 1290 heterogeneous consumers 1686 Hicks composite commodity 766 Hicksian demand decomposition in RBC model 971 hiring rate 1161 histogram 840 historical counterfactual simulations 1523 history-dependent aggregate elasticity 841 Hodrick-Prescott filter, see HP filter hold-up problems 852 home production 402, 417, 431,702 home sector 435 homotheticity 1725, 1728, 1733 Hotelling's rule 657 HP (Hodrick-Prescott) filter 12, 932, 933 human capital 527, 546, 547, 576, 577, 583-592, 594, 639, 653, 1638, 1712 hump-shaped impulse responses 405, 436, 1374 hump-shaped profiles 755 hyperinflation (seignorage) 509, 520, 531, 1631 hysteresis and threshold effects 455, 530 i.i.d, model 1739 identification problem 75-78 global identification 76, 77 local identification 76 underidentification 76, 77 idiosyncratic risk 795, 1290 idiosyncratic shocks 840 in productivity 1183 imbalances 826 imperfect competition 665 implementability constraint 1677, 1689, 1719, 1729 implicit collusion 1123 imports 41 impulse 1140 impulse response measure of comparative dynamics 967 to productivity in RBC model 967 impulse response functions 74, 81, 85, 86, 90, 98, 100, 102, 107, 110, 112, 133, 140, 397, 411,430, 431,880, 894

Subject Index inaction range 832 Inada conditions 645 income distribution, cross-country 671 income elasticity 1681 income inequality 797 income processes 569, 574, 610 income tax 672 income uncertainty 1652 incomplete contracts 853, 854, 856 incomplete markets 566-576, 1742 indeterminacy 491, 494, 506, 1161, 1506, 1691 nominal 418, 1506, 1524 of price level 215, 216, 415, 417, 419, 423 real 413, 415, 416, 418, 419, 423 indicator, cyclical 1062 indivisible labor model, role in RBC model 977 industry equilibrium 888, 889 inequality 745, 795 infinite-horizon consumption program 647 inflation 42, 1534, 1536, 1630 and business cycles 939 and markups 1128 inertia 1562 level 198 persistence 166, 211,213-215 rate 1738 autocorrelation 1738, 1739 variability 207 inflation correction 1621 inflation forecast targeting 1504 inflation-indexed bonds 1271 inflation-indexed consol 1269 inflation targeting 1499, 1505 vs. price-level targeting 1497 inflation tax 1538, 1720 inflationary expectations 1281 information externality 849 information pooling 849 information set 455 informational problems 849-851,858 infrequent actions 825 instability 481,519 of interest rate pegging 514 of REE 507 institutional factors 852 instrument feasibility 1507 instrument instability 1517 instrument variable 1492, 1524 instrumental variables (IV) estimator 787

1-39 instrumental variables (IV) regression 1261 insurance 745, 795 integrated world capital market 1297 interest rate 43, 1620, 1621, 1629, 1630, 1634, 1635, 1637, 1639, 1648, 1652, 1653, 1657-1659 nominal 1524 interest rate instrument 1514 interest rate policy 1596 interest rate smoothing 1509 intermediate-goods result 1684, 1720, 1733 intermediate-goods taxation 1676 intermediate input use 1081 internal habit models 1284 international capital flows 1636-1638 International Financial Statistics (IFS) 1238 international reserves 1594 intertemporal allocation 761 intertemporal budget 555, 561,647, 661 intertemporal budget constraint 1259, 1268 intertemporal CAPM 1275 intertemporal channel 1142 intertemporal elasticity of labor supply 1149 of substitution in leisure 1147 intertemporal marginal rate of substitution 1245 intertemporal non-separabilities 775 intertemporal optimization 745 intertemporal substitution 1055, 1150 "intervention" policy 1587 intradistribution dynamics 274, 292 intratemporal first-order conditions 775 inventories, target 894 inventories of finished goods 887 inventory fluctuations 1084 procyclical 872-882, 898, 900, 909 inventory investment 865 inventory sales ratio 871 inventory-sales relationship 867 investment 40, 641 collapse 851 competitive equilibrium 844 delays 1365 distortions 672, 695 698 empirical 1344 expected 839 frictionless 832 lumpy 822, 823 share in output 693, 699 spike 823, 824, 857

1-40 investment (cont'd) tax incentives 843 US manufacturing 840 investment episode 823 investment-output ratio 714 irrational expectations 1237, 1293 irregular models 490, 493, 505 irreversibility cons~aint 832 irreversible investment 822, 828, 832 iso-elastic utility function 606, 607, 610 Italy 1619 Ito's lemma 825 Japan 45 Jensen's inequality 1247 job-finding rate, cyclical behavior of 1162 job loss 1151 job search 1143, 1150, 1158, 1162 job-specific capital 1152 job to job flows 1198, 1200 job-worker separations 1184 jobs creation 846, 1150, 1158, 1161, 1173, 1176, 1178, 1185, 1201, 1219 cost 1187, 1193, 1215, 1222 creation and destruction, international comparison 1178 destruction 846, 1150, 1158, 1160, 1166, 1173, 1176, 1178, 1185, 1197, 1201, 1219 rate 1151, 1152 flow 1197 international comparison 1180 reallocation 1222 termination 1152 cost 1193 joint production 853 joint surplus 1157 just-in-time 871 Kaldor facts about economic growth 941 Keynes, J.M. 1660 Keynesian analysis 1628 Keynesian consumption function 761 Kreps-Porteus axiomatization 744 Krugman model 1592 Kulm-Tucker multiplier 774 labor 1687 bargaining strength 1219 labor-augmentation 651

Subject Index

labor contract 1154 labor force 1174 labor force status 602, 603, 607, 611, 614, 623 labor hoarding 1076, 1078, 1097 labor in efficiency units 650 see also efficiency units labor income 1237, 1275, 1290 labor market 855 policy 1214 restrictions 672, 695 labor power 1220 labor productivity 42 labor regulations 852 labor share 1059 labor supply 546-553, 562, 577, 585, 587, 592, 594, 596, 598, 599, 601,602, 605, 606, 608, 610-621,623, 744, 777, 792, 1150, 1296 elasticity 975, 1371 in RBC model 975 empirical 1148 endogenous in RBC model 945 extensive margin 976 female 611 fixed costs of working 976 indivisible labor model 976 male 611 substitution effect 975 unobserved effort of 930 labor tax rate, autocorrelation 1739 lack of credibility 1569, 1572, 1581 Latin America 1543 laws of large numbers 837 leading example 488, 493 learning 453, 488 by doing 664 in games 475 in misspecified models 528 least squares learning 465, 467, 526 social 849 stability under 496 statistical 493 learning dynamics, persistent 455 learning equilibria 515 learning rules 439, 454 econometric 472 finite-memory 474 fixed-gain 511 statistical 465 learning sunspot solutions 494 learning transition 531

Subject Index

Legendre Clebsch condition 904 levels accounting 678-687 leverage 1280 life cycle 583, 586~588, 593, 595, 601, 603, 604, 609, 615, 620, 621, 744, 749, 752, 754, 760, 792, 793 life cycle-permanent income model 760 life expectancy 691-693 lifetime budget constraint 647 see also intertemporal budget likelihood function 840 linear allocation rules 554, 563, 564 linear commodity taxes 1677 linear filter 11 linear model 467, 487, 842 with two forward leads 501 linear-quadratic model 457, 865, 876, 882, 903, 904 liquidity 1255, 1591 liquidity constraints 745, 772, 773, 789, 1654 see also borrowing constraint liquidity variables 817 log-linearization 788 long-term bonds 1255, 1280 low-equilibrium trap 646 Lucas aggregate supply model 457 Lucas critique 1491 Lucas program 67 lumpy project 823 Lyapunov theorems 479 M2 44 M1 velocity 50 machinery, price of 696 macroeconomics 639 magical thinking 1328, 1329 maintenance 823 maintenance investment 839 major and infrequent adjustments 823 managed float 152, 153, 167, 202, 204, 207 manufacturers 870 marginal cost schedule 1054 declining 1066 marginal production costs 867, 890, 892, 896, 899, 902, 905, 907 marginal profitability of capital 830 marginal rate of substitution 549, 551,554-557, 559, 560, 598, 622, 765 heterogeneity 620-623 marginal utility 767 market capitalization 1239

1-41 market clearing 1021-1024, 1026, 1035 expected 1021, 1024-1027 market imperfection 390, 405, 424, 426, 433 market structure 546, 553, 558, 575, 598 market tightness 1185 market work 550, 594, 601 Markov chain 1708, 1736 Markov process 1264 markup 399, 400, 406, 407, 426, 429, 431, 1053 average 1068 countercyclical 406, 1113 for France 1068 cyclical 1092 desired 1056 measurement 1058 models of variation 1055, 1112 procyclical 1113, 1128 variable 406, 407 variation in desired 1129 Marshallian demands 597 martingale 767 martingale difference sequence 487 match capital 1152 matching function 1183 matching model 1163 Maximum Principle 650 measure of financial development 691 measurement error 518, 546, 561, 572-574, 609, 616, 1242 "mechanieal" approach 1560 mechanism design 1154 Medicare 1622, 1626 men 550, 552, 607, 615, 620 mental compartments 1317 menu costs 397 microeconomic data 543-625, 745 microeconomic lumpiness 824 microfomadations 761 military purchases 1088 Mincer model 568, 569, 581,582, 584, 592 minimal state variable solutions, see MSV solutions mismatch 1221 mismeasurement of average inflation 1254 Modigliani-Miller theorem 1343 monetary accommodation 1539 monetary base 44, 1507, 1524 monetary economies 1720 monetary model with mixed datings 500

1-42 monetary policy 692, 695, 715, 1012, 102Zl~ 1037, 1281, 1630, 1660, 1720 optimal, cyclical properties of 1736 monetary policy rule 1364 monetary policy shocks 65-145 effect 69 on exchange rates 94-96 on US domestic aggregates 91 94 on volatility 123-127 identification schemes 68-70, 1369 Bernanke-Mihov critique 115-123 Bernanke-Mihov test 119-121 empirical results 121 123 Coleman, Gilles and Labadie 114, 115 narrative approach 136 141 s e e also Romer and Romer shock pitfalls 134-136 plausibility 100-104 assessment strategies 114-123 problems 143-145 interpretations 71 73 non-recursive approaches 127-134 output effects 1129 recursiveness assumption 78-127 s e e also recursiveness assumption responses to 1368 monetary regimes 153, 168, 178, 202, 204, 211,216, 220 money 44, 1011-1013, 1020-1029, 1031-1033, 1035, 1036, 1040, 1041 money anchor 1588 money-based stabilization 1535, 1543, 1554, 1558, 1582 money demand 50, 598, 1603, 1736 consumption elasticity of 1725 interest elasticity of 1736 money growth rate 1738 money-in-the-ufility-ftmction model 1720, 1728 money supply 1536 money velocity 1588 s e e also M1 velocity monopolies 695 monopolistic competition 1033-1036, 1041, 1042 monotonicity 830 Morgan Stanley Capital International (MSCI) 1238 MSV (minimal state variable) solutions 488, 493, 502 and learning 503

Subject Index

locally (in)determinate 490 non-MSV solutions 493 multiple competitive equilibria 1679 multiple equilibria 1539, 1603 multiple REE, see u n d e r R E E multiple solutions 487, 1506, 1524 multiple steady states 460 multiple strongly E-stable solutions 501 multiplicity of steady states 658, 662 multivariate models 502 with time t dating 505 mutation 522 Muth model 465, 484, 525 myopia 1653, 1654 Nash bargain, generalized 1189 National Account 751,752 national accounting identities 1628 National Bureau of Economic Research (NBER) 6, 8 national income 1617 national saving 1628, 1629, 1637, 1639, 1641, 1652, 1659-1662 natural experiments 822 natural rate 1176 natural resources 639 negative income tax experiments 1148 neoclassical exogenous growth model 243,261, 673 neoclassical growth model 245, 246, 252, 259, 269, 272, 276, 639, 695, 697, 701, 1140 basis for RBC model 942 neoclassical theory of investment 817 net convergence effect 692, 693 net present value rule 835 net worth and the demand for capital 1352 neural networks 465, 524 neurons 524 noise case of small 513 intrinsic 507 noise traders 1290 noisy k-cycle 513 noisy steady states 483, 509 nominal anchor 207, 211, 215, 216, 1535, 1542, 1557 nominal income targeting 1505 non-durables 746 non-nested models 840 non-random attrition 787 non-Ricardian policy 418

1-43

Subject Index

non-Ricardian regime 418 non-separability of consumption and leisure 759 non-state-contingentnominal claims 1722 Non-Accelerating Inflation Rate of Unemployment (NAIRU) 46 nonlinear models 468 nonlinearity 828, 839 nonparametric techniques 532 numerical algorithms 320, 324, 326, 328, 348, 358, 378 numerical solutions 318, 326, 352, 805 obsolescence 848 OECD 685, 718, 719, 1174 OECD adult equivalence scale 757 oil prices, effects of 1089 one-sector model 639 one-step-ahead forward-looking reduced form 506 open economy 1714 open market operations 1722 openness 703 operationality 1486, 1523 opportunism 851, 858 opportunity costs 854 optimal control 1490 optimal debt policy 1639, 1659, 1660, 1662 optimal fiscal policy 1686 optimal investment path 834 optimal national saving 1617 optimal tax theory 1692 optimal trajectory 650 optimal wedges 1692 optimum quantity of money rule 1537 option to wait 832, 834 ordinary differential equation (ODE) approximation 468, 478 orthogonality conditions 785 out-of-sample forecasting 840 out-of-steady-state behavior 649 output 1687 output levels 206 output variability 208, 211 overconfidence 1319-1323, 1325, 1326, 1328 overhead labor 1065 overidentifying restrictions 768 overlapping contracts models 495, 1582 overlapping generations model 390, 395, 397, 398, 427, 458, 546, 549, 576~94, 660, 1634, 1635, 1645-1647

overparametrization 473 overreaction 1319-1322 overtaking 650 overvaluation 1563 panel data 275, 283-287, 295, 781 Pareto weights 559-564, 796 partial adjustment model 821,838 participation 574, 601, 1218 path dependence of adaptive learning dynamics 455 peacetime 1699 Penn World Table 674, 680 pent-up demand 841 perceived law of motion (PLM) 466, 472, 490, 511 perceptron 524 perfect competition 831 perfect foresight 650 perfect insulation 846 perfect-insurance hypothesis 796 periodic or chaotic dynamics 646 see also cycles permanent-income hypothesis 749, 1641, 1662 permanent shocks 216-219 perpetual inventory method 680 persistence 870-882, 891, 893, 900, 902, 904, 1142, 1162, 1166, 1739 of business cycles, see persistence under business cycles of fluctuations 527 of inflation 1537 peso problem 1252 pessimism 1295 Phillips curve 46, 1056, 1363, 1542 planner's problem in RBC model 997, 1002 policy 455 affecting labor markets 672 distorting investment 695 impeding efficient production 672 policy accommodation 1538 policy function 320-381 political rights 671, 689 political stability 671,688, 692 Ponzi scheme 1650 population aging 1625, 1640 population growth 941 endogenous 639 power utility 1249

1-44 precautionary saving 744, 770, 1253, 1288, 1653 preference parameters 550, 555, 556, 558, 567, 601, 605 preferences 546-550, 552, 553, 556-558, 564, 565, 567, 572, 582, 593, 601, 604, 605, 607, 608, 610, 614, 616, 617, 623 additive 594 conditional 778 functional forms 550 Gorman polar 766, 783 heterogeneity 545, 552, 558-565, 567, 593, 594, 609, 621,623 homogeneity 553-556, 577 of representative agent in RBC model 942 quadratic 762, 770 present-value model of stock prices 1264 log-linear approximation 1265 present-value neutrality 573 price elasticity 1681 price functions 1723 price puzzle 97-100 price rules 1688 price-cost margin 1053 s e e also markup price-dividend ratio 1265, 1266, 1276 prices 42 of machinery 696 of raw materials 1082 pricing, equilibrium 555, 602, 845 primal approach 1676 primary budget 1619 principal-agent problems 1345 principles of optimal taxation 1676 private and public saving 1629 private information 574-576, 849 production costs, non-convex 897, 911 production economy 1686 production efficiency 1684, 1735 production function 548-550, 578, 579, 581, 583-586, 588, 590, 591,594 non-Cobb-Douglas 1064 production possibilities surface 401 production smoothing 876, 877, 884, 895, 1085 production to order 887 production to stock 887 productivity 552, 553, 566, 583, 602, 1057 cyclical 938, 1094 deterministic growth of 943 general 1192, 1193

Subject lndex

growth of 942 shocks 930, 943, 965, 972 amplification of 963 modeled as first-order autoregressive process 963 persistence of (serial correlation) 952, 963 RBC model's response to 964 remeasurement of 982, slowdown 664 profit function 830 profits 1057 cyclical 1100 projection facility (PF) 480 propagation of business cycles 865 propensity to consume 762 property rights 852, 856 proportional costs 825 proportional taxes 1687 prospect theory 1308-1313 protection of specific investments 1154 "provinces" effect 1540 proxies for capital utilization 1080 prudence 771 PSID 783 public consumption 1581 public debt 1601, 1603 public finance 1676 public saving 1629, 1641 putty-clay models 847, 848 q-theory 817 s e e also Tobin's q average q 817, 818 "flexible q" 818 marginal q 818 fragility of 828 quadratic adjustment cost model 823, 838 Quandt Likelihood Ratio (QLR) 34 quantitative performance 1578, 1581 quantitative theory 671-673, 695-719 see also dynamic stochastic general equilibrium models quasi-magical thinking 1329, 1330 Ramsey allocation problem 649, 1679, 1691, 1692, 1713, 1719, 1723, 1729 Ramsey equilibrium 1678, 1688, 1723, 1729, 1732 Ramsey growth model 1651, 1652 Ramsey prices 1679

1-45

Subject Index

random walk 767, 1316, 1319, 1702, 1706, 1738, 1742 geometric 825 range of inaction 826 rate of arrival of shocks 1193 rate of discount 1193 rate of return 566, 577, 582, 595, 606, 610 ratio models of habit 1284 rational bubbles 499, 1266 rational expectations 453 transition to 454 rational learning 461 rationalizability 464 rationing 857 RBC models, see real business cycle Reagan, R. 1641 real balance model 489, 496 real business cycle (RBC) 394, 402, 413, 427, 428, 437, 442, 505, 843, 928, 1296 amplification of productivity shocks in 958, 967 as basic neoclassical model 942 baseline model 1143, 1709, 1736 failures 1144 calibration 953-955, 959 competitive equilibrium 999 concave planning problem 1002 contingent rules 1000 criticisms 961 depreciation rate of capital 944 discount factor 942 modified 945 endowments in 943 extensions 994 firm's problem 1001 government spending and taxes in 974 high risk aversion model 1709 high-substitution version calibration 985, 987 decision rules for 985 ingredients of 984 probability of technical regress 989, 990 role of capacity utilization in 985 role of indivisible labor in 985 sensitivity to measurement of output 992 sensitivity to parameters 990, 991 simulation of 986 household's problem 1000 importance of consumption smoothing in 967

Inada conditions on production function 996 interest rate effects 973 internal propagation in 967 labor demand for 956 supply of 956 Lagrangian for 946 lifetime utility 996 market clearing 1001 production function in 943 RBC model as basic neoclassical model 942 simulations of 957 solution certainty equivalence 952 dynamic programming 951 linear approximations 949 loglinear approximations 952 rational expectations 951 steady state of 947 transformation to eliminate growth 944 transitional dynamics of 948 transversality condition for 946 wage effect in 973 wealth effects in 971 with nominal rigidities 974 real exchange rate 1547 real interest rate 1220, 1233, 1276, 1286 measurement of 939 real marginal cost 1053 real shocks 1174 real wage 1296 reallocation of workers 1160, 1183, 1199 recession now versus recession later 1535, 1557 recursive algorithm 468, 475, 479, 486 recursive least squares 467 recursive least squares learning 494 recursive utility 557 recursiveness assumption 68, 73, 78-127 benchmark identification schemes 83 85 F F policy shock 87, 88 influence of federal funds futures data 104-108 NBR policy shock 88 NBR/TR policy shock 89 problems 97 results 85 robustness 96, 97 sample period sensitivity 108-114

1-46 recursiveness assumption (cont'd) relation with VARs 78-83 REE (rational expectations equilibria) 452 cycles 458 multiple 454, 467 reduced order limited information 529 unique 484 reflecting barriers 828 regime switching 426 regression tree 289 regular models 490 regulation barrier 832 relative price of investment to consumption 696-698, 700, 701 reluctance to invest 828, 832 renegotiation 1153, 1155 renewable/nonrenewable resources 655, 656 rental prices 588, 590, 592 of capital 1000 reorganization 1160, 1161 representative agent 556, 557, 560, 561,563, 587, 601, 838, 1249, 1259, 1268 in RBC model altered preferences in indivisivle labor 977 altruistic links 943 preferences of 942 representative household 643 representativeness heuristic 1319, 1322, 1327 reproduction 522 research and development (R&D) 664, 672, 692, 695, 708, 709, 715-719 residence-based taxation 1715 restricted perceptions equilibrium 529 restrictions in job separation 1222 restrictions on government policy 1707 retailers 869 retirements 839 returns to scale 639 decreasing 656 increasing 652, 653, 664, 828, 830, 1066 social 460, 509, 521 Ricardian equivalence 418, 1617, 164~1659, 1661 Ricardian regime 418 Ricardo, D. 1640 risk 546, 547, 552, 554-558, 563-567, 569, 572, 575, 593, 606 risk adjustment 555, 557, 558 risk aversion 547, 552, 556-558, 564-566, 606, 771

Subject Index risk premium 1246, 1247, 1250 risk price 1236, 1280 risk-sharing in indivisible labor version of RBC model 977 riskfree rate puzzle 1235, 1252 robustness approach 1491, 1523 Romer and Romer shock 137-142 rule-like behavior 1487, 1522 rule-of-thumb decision procedure 524 rules 152-154, 156, 158, 160, 166, 168, 184, 200, 208, 219, 220 rules vs. discretion 1485 Rybczinski theorem 404

(S,s) model 801,802, 831,910, 911 sacrifice ratio 1541 saddle point 405, 649 saddle point stability 490 Sargent and Wallace model 489 saving 641 private 1628, 1629, 1632-1634, 1637, 1641, 1648 'saving for a rainy day' equation 764 scale effects 672, 715, 716, 718, 719 school attainment 691 school enrollment 681,684 post-secondary 683 primary 683 secondary 681-683 schooling 576-578, 581-592 sclerosis 856 scrapping 844, 847, 855, 856 endogenous 844 search and matching approach 1173, 1183 search efficiency 1162 search equilibrium 1186 search externalities 506 seasonal adjustment 1242 seasonal variations in work volume 1149 second-best solutions 849 secondary job loss 1163 sector-specific external effects 402 sectoral shifts hypothesis 1221 securities market 1722 seignorage model 460, 471, 509, 525, 530, 1741 selection criterion 468 selection device 454 self-fulfilling fluctuations 506 separability 556, 602, 603,607, 608, 612, 613, 617, 1725, 1728, 1733

S u b j e c t Index

tests 611 separation rate 1151 Sharpe ratio 1249 shock absorber 1699, 1710, 1739 shock propagation 1203 shocks and accommodation 1539 shopping-time model 1720, 1732 shopping-time monetary economy 1732 short-term bonds 1280 short-term maturity debt 1603 ~r-convergence 659 Sims-Zha model 128-134 empirical results 131 134 skill-biased technology shock 1215, 1216, 1218 skills 546, 547, 569, 576-579, 581,582, 584, 586-588, 590-594, 623 slow adaption 480 slow speed of adjustment 877, 894 small durables 798 small open economy 1715 small sample 820 small versus large firms 1373 smooth pasting conditions 827 Social Security 1619, 1622, 1624, 1626, 1635 Solow residual 930, 1140, 1141 as productivity measure 962 in growth accounting 962 mismeasurement 962 solvency conditions 575 specificity 851,852, 856 spectral analysis 11 SSE, s e e stationary sunspot equilibria stability conditions 454 stabilization 1534, 1562 stabilization goals 153 stabilization time profiles 1547 stable equilibrium point 481 stable roots 393 staggered contracts model 1012, 1013, 1024, 1027, 1030, 1032, 1039 staggered price and wage setting 1012, 1013, 1027, 1030, 1031, 1033, 1035-1037, 1040 staggered price setting 397, 422, 423, 1129, 1363 staggered-prices formulation 1582 standardized employment deficit 1621 state-contingent claims 555, 602 state-contingent returns on debt 1687, 1699 state-dependent pricing 1031, 1032 state dynamics 477

1-47 state prices 1294 stationary distribution of RBC model 999 stationary sunspot equilibria (SSE) 408, 517 c-SSE 517 near deterministic solutions 520 steady states 468, 507, 525, 549-551,576, 592, 598, 639 of RBC model 944 sterilization 1595 sticky price models 503, 1113 stochastic approximation 468, 475, 476 stochastic discount factor 1234, 1245 log-normal 1246 stochastic growth model 546-577, 592 stochastic simulations 1516, 1523 stock market 1310, 1312, 1313, 1315, 1316, 1320-1328, 1331, 1333 stock market volatility puzzle 1235, 1236, 1268, 1276, 1280 stock prices 43 stock return 1233, 1240 stockout costs 884, 885 Stolper-Samuelson theorem 404 Stone price index 783 storage technologies 574, 575 strategic complementarity 1129 strategic delays 858 strong rationality 464 structural model 462 structural shifts 530 structures 840 subgame perfection 1679 subjective discount factor 548, 552, 561,593, 595, 609, 616 subsistence wage 657 substitutes 577, 590, 591,613, 616 sunk costs 858 sunspot equilibria 454, 515 sunspot paths 662 sunspot solutions 495 s e e also learning sunspot solutions sunspots 489, 515 supply of capital 846 supply price of labor 1192, 1193 supply shocks 1129 supply-side responses 1577 surplus 853 surplus consumption ratio 1286 survivorship bias 1242 sustainability 1597

1-48 T-mapping 467, 471,512 Tanzi effect 1741 target points 826 target variables 1492, 1523 tariff 672, 695, 703-707 taste shift 778 tax see also labor tax rate; capital taxation distortionary 1651, 1652, 1654 on capital income 1686 on employment 1220 on international trade 703 policy 672, 708 rate 1441 on private assets 1709 reforms 822 smoothing 1655, 1659, 1662, 1705 intertemporal 1617 source-based 1715 system 1679 Taylor expansion 1265 Taylor rule 1364 technological change 1708 technological embodiment 848 technological progress 641, 1207, 1213 disembodied 1207, 1208 endogenous 639 Harrod-neutral, Hicks-neutral 944 labor-augmenting 944 purely labor-augmenting 650 technological regress, probability of in RBC models 930 technology adoption 672, 708 technology shocks 1141, 1142, 1736 temporariness hypothesis 1569, 1572 temporary shocks 216 temporary work 1165 term premium 1255 term structure of interest rates 1270 termination costs 708 thick-market externality 1161 threshold externalities 527 thresholds 258-262, 276, 289 time-additive utility function 661 time aggregation 881 time-consistent behavior 1488 time dependency 799 time-dependent pricing 1031, 1032 time-inconsistent behavior 1653 time preference 547, 588 time preference rate 1253

Subject Index

time series 264, 272, 287, 288 time series volatility 756 time to build 832, 850 time-varying aggregate elasticity 841 timing assumption 469 Tobin's q 817, 1296 see also q-theory total factor productivity (TFP) 42, 673, 678, 687, 688, 702 trade deficit 1630, 1658, 1659 trade policy 672, 692, 694, 702 training 577, 582-584, 586-592, 653 transition rates 1166 transversality conditions 392, 393, 400, 650 Treasury bills 1233 trend-stationary models 764 trend-stationary process 10, 211, 1497 trigger points 830 tuition costs 583, 588, 590 twin deficits 1630 two-stage least squares estimation 1261 uncertainty 545-547, 556, 558, 564, 566, 567, 569, 572, 574, 575, 593, 605, 606, 620, 621,623, 744, 1627, 1653 underinvestment 852, 854 underreaetion 1319-1322 unemployment 546, 569-571, 578, 579, 1143, 1150, 1158, 1161, 1162, 1173, 1174, 1194, 1214 experiences of OECD countries 1213 natural level 1157 rise in 1182 serial correlation 1163 unemployment compensation 1217 unemployment income 1214 unemployment inflow and outflow rates 1181 unemployment rates 1176 unemployment spell duration hazard 1184 unemployment-skill profile 1216 unified budget 1619 uniform commodity taxation 1676, 1726 union bargaining 1098 uniqueness of equilibrium in RBC model 1002 unit root 11 United Kingdom 45 univariate models 488, 497 unstable equilibrium point 481 utility function 548 550, 556 558, 560, 594, 596, 597, 599-601,606, 607, 610

1-49

Subject lndex

momentary in RBC model 944 offsetting income and substitution effects 944 utility recursion 557 utilization of capital 1079 vacancies 41, 1194 vacancy chain 1200 vacancy duration hazard 1184 value function 319-327, 329, 335, 336, 340, 345, 351 355, 357 359, 365, 368, 378 value matching 827 variable costs 828 variety, taste for 705 vector autoregression (VAR) 73, 438 definition 73 vintage capital models 847, 848 volatility employment 1157 inventories 869, 870 monetary aggregates 1599 vote share 1455 wage bargaining 1130 wage contract 1173, 1186 wage inequality 1182, 1214, 1218, 1219

wages 42, 547, 550-553, 556, 566-569, 572, 577-579, 581,587, 593,595-601,603-607, 611,612, 616, 617, 619, 621,623, 1181, 1629, 1637 see also earnings cyclical 939 equilibrium 556 fixed 1157 marginal 1069 rigidity 1055 war of attrition 1540 wars 1619, 1642, 1656, 1661 1663, 1699 wealth distribution 556, 561,567, 572, 593 wealth-output ratios 1240 wealth shock 1372 welfare costs of macroeconomic fluctuations 1297 welfare theorems, role in RBC analysis 1001 wholesalers 869 within-period responses 599 women 550, 552, 607, 615, 620, 623 worker flows 1180 into unemployment 1164 worker turnover 1176 works in progress inventories 887 yield spread

1256, 1280