Table Of ContentLectu re Notes
in Economics and
Mathematical Systems
Managing Editors: M. Beckmann and W. Krelle
288
Glenn D. Rudebusch
The Estimation of
Macroeconomic Disequilibrium
Models with Regime
Classification Information
Spri nger-Verlag
Berlin Heidelberg New York London Paris Tokyo
Editorial Board
H.Albach M.Beckmann (Managing Editor)
P.Dhrymes G. Fandel J. Green W. Hildenbrand W. Krene (Managing Editor)
H. P. Kunzi K. Ritter R. Sato U. Schittko P. Schonfeld R. Selten
Managing Editors
Prof. Dr. M. Beckmann
Brown University
Providence, RI 02912, USA
Prof. Dr. W. Krene
Institut fUr Gesenschafts-und Wirtschaftswissenschaften
der Universitat Bonn
Adenauerallee 24-42, 0-5300 Bonn, FRG
Author
Dr. Glenn D. Rudebusch
Division of Research and Statistics
Board of Governors of the Federal Reserve System
Washington, DC 20551, USA
ISBN-13: 978-3-540-17757-9 e-ISBN-13: 978-3-642-45625-1
001: 10.1007/978-3-642-45625-1
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© Springer-Verlag Berlin Heidelberg 1987
2142131~543210
To my mother and father
P1tEPACE
The intractability of econometric disequilibrium models has clearly slowed their
wide application. This book examines an econometric specification of the disequilib-
rium model that incorporates non-stochastic information about market excess demand and
the prevailing market regime. This exact excess demand disequilibrium specification
can be estimated by the least squares routines found in standard statistical software
packages. It also permits a wide range of desirable structural features to be
considered, including lagged endogenous variables, an endogenous (not fixed) non-
market clearing price, and multi~le markets, and the hypothesis of market equilibrium
can be tested. This specification is illustrated in the latter half of the book by the
estimation of two macroeconomic disequilibrium models.
This research, my Ph.D. thesis, was completed at the University of Pennsylvania,
and my academic debts there are many. From the very start, Peter Pauly has provided
both encouragement and intellectual guidance. I am indebted to him for advising me
with a rare blend of intelligence and enthusiasm.
The other members of my committee were especially helpful and accessible.
Lawrence Klei~, Steven O'Connell, and Roberto Mariano, all provided careful discussion
and useful suggestions. Also, I am grateful to David Cass, the Graduate Group
Chairman, who five years ago inspired and supported an uncertain physics student in
economics.
The numerous references herein to Richard Quandt's work reflect only part of my
intellectual debt to him; in particular, he has given me much practical advice on
numerical optimization.
Finally, I thank Frank Diebold, Patricia Fossum, Regina Forlano, Susan Quant, and
David Wilcox, all who contributed, in very different ways, to this final manuscript.
G.D.R.
Washington, DC
January)5, 1987
TABLE 01' COlITBRTS
PART I: INTRODUCTION
Chapter 1: Overview and Summary........................................ 2
PART II: ECONOMETRIC SPECIFICATIONS OF THE DISEQUILIBRIUM MODEL
Chapter 2: Previous Specifications..................................... 6
2.1: The Standard Disequilibrium Specification................... 6
2.2: The Stochastic Min Specification............................ 11
2.3: Explicit Aggregation........................................ 14
Chapter 3: The Exact Excess Demand Specification ••••••••••••••••••••••• 18
3.1: The Basic Model of Exact Excess Demand...................... 18
3.2: Dynamic Links ••••••••••••••••••••••••••••••••••••••••••••••• 20
3.3: An Endogenous Price......................................... 21
3.4: Testing for Equilibrium..................................... 24
3.5: Multiple Indicators......................................... 26
3.6: Extension to Multimarket Models............................. 27
Chapter 4: Evaluating the Exact Excess Demand Specification............ 31
4.1: A Likelihood Ratio Test of the Exact Indicator.............. 31
4.2: Misspecification and Tractability of Estimation............. 37
Appendix A: Linear Spillovers.......................................... 41
PART III: ESTIMATION OF A SINGLE MARKET DISEQUILIBRIUM MODEL
Chapter 5: Model Structure -- Labor Demand and Labor Supply............ 44
Chapter 6: Excess L~bor Demand Indicators.............................. 48
Chapter 7: Estimation and Results •••••••••••••••••••••••••••••••••••••• 56
7.1: Exact Indicator Results..................................... 56
7.2: Testing the Exact Indicator ••••••••••••••••••••••••••••••••• 64
Appendix B: Definition of Variables in Part III •••••••••••••••••••••••• 71
Part IV: ESTIMATION OF A MULTlMARKET DISEQUILIBRIUM MODEL
Chapter 8: Model Structure I -- Behavior of Agents..................... 74
8.1: Household Behavior.......................................... 75
8.2: Firm Behavior............................................... 80
Chapter 9: Model Structure II -- Market Interaction •••••••••••••••••••• 86
9.1: Labor Market................................................ 86
~
9.2: Capital Goods Market •••••••••••••••••••••••••••••••••••••••• 87
9.3: Consumer Goods Market ••••••••••••••••••••••••••••••••••••••• 88
Chapter 10: Excess Demand Indicators ••••••••••••••••••••••••••••••••••• 92
10.1: Labor Market............................................... 92
10.2: Capital Goods Market....................................... 94
10.3: Consumer Goods Market...................................... 97
Chapter 11: Estimation and Results ••••••••••••••••••••••••••••••••••••• 101
Appendix C: International Trade •••••••••••••••••••••••••••••••••••••••• 110
Appendix D: Definition of Variables in Part IV ••••••••••••••••••••••••• 113
PART V: CONCLUSION
Chapter 12: Whither Disequilibrium? ••••••••••••••••••••••••••••••••••• 116
REFERENCES. • • • • • • • • • • • • • • • • •• • • • • • • • • • •• • •• • • • • • • • • • • • • • • • • • • • • • • • • •• • •• •• 120
PART I: INTRODUCTION
Chapter 1: Overview aud S_ry
The possibility that markets may not completely clear has long been recognized.
Indeed, much of traditional macroeconomics is implicitly based on the assumption that
some important markets in the economy do not equilibrate. Models in which agents may
face explicit quantity constraints on their desired supplies or demands have come to be
known as disequilibrium models. This name emphasizes that a full tStonnement on prices
has not been completed, so trades may occur at prices that are not Walrasian equilibrium
ones. It is a slight misnomer, since an equilibrium concept, albeit non-Walrasian, can
be defined within this framework (for an introduction and references, see Benassy
(1982b». We shall, however, throughout this book equate equilibrium with Walrasian
market clearing and disequilibrium with quantity rationing.
Especially in the last 15 years, large strides have been made in understanding
explicit disequilibrium econometric models, advances associated with the names of Fair,
Gourieroux, Laffont, Monfort, Quandt, Kooiman, and many others. However, while the
theory of disequilibrium models has been well developed, their empirical implementation
has lagged behind, slowed by difficulties in estimation. Indeed, there has been a
widespread fear that despite their usefulness in theoretical macroeconomic discussions
disequilibrium models would remain too complex to successfully implement economet-
rically. The research reported here is an attempt to construct and estimate some
fairly detailed macroeconometric disequilibrium models.
Several different econometric specifications of the disequilibrium model have been
proposed in the literature, none of which has dominated the others. Richard Quandt
concluded his 1982 survey of econometric disequilibrium models:
In spite of some disagreements, I still believe that the choice of the
appropriate [disequilibrium] model is an unsettled question. There
clearly are advantages and disadvantages on both sides. I hope that
further work will successfully resolve the question of which model is
more appropriate in some overall sense. Thus, numerous aspects of
disequilibrium specifications, such as the min condition, dynamics, the
nature of disturbances in the models, etc., must be subjected to tests.
We attempt to shed some light on this question of the appropriate econometric
specification for disequilihrium modeling. In addition, several structural features of
disequilibrium models are examined, including dynamics and the use of outside
3
information, which we believe should be stressed in future applied research.
Part II explores a variety of econometric specifications of the disequilibrium
model. The strengths and shortcomings of three specifications that have appeared
earlier in the literature are examined in Chapter 2. Chapter 3 presents another
specification, one which incorporates exact or non-stochastic informati.on on excess
market demand. This information eliminates the estimation difficulties that have
hindered implementation of earlier disequilibrium models. Topics of a more general
nature are also discussed, including the issue of "fixed" prices, which has preoccupied
much of the literature. We argue that the assumption of fixed prices is not necessary
for disequilibrium models, since agents may be quantity rationed in the marketplace
whenever there is a deviation from the Walrasian ideal of instantaneous price adjust
ment, not just when prices are fixed. Indeed, the assumption of exogenous prices will
not be used in the later empirical models. Finally, Chapter 4 suggests various
practical criteria for evaluating the econometric disequilibrium specifications
presented. In particular, it provides the groundwork for a likelihood ratio test of
the key assumption of exact excess demand indicators.
Part III is concerned primarily with the estimation of a disequilibrium model of
the U.S. labor market specified with exact excess demand. The structural equations are
given in Chapter 5. The labor demand and supply functions, derived from utility and
profit maximization, are identical to those in labor market equilibrium models;
however, we allow for the possibility that the wage may not clear the market and that
an excess supply or excess demand for labor may result. The corresponding equilibrium
model is nested within the disequilibrium model; thus, a formal test of the hypothesis
of market clearing is available. One of the key innovations of this work over previous
disequilibrium labor market models is the incorporation of dynamic links into the
structural equations. Chapter 6 discusses the indicators of labor market excess demand
that are used in estimation, and Chapter 7 presents results. Of particular interest is
the rejection of the hypothesis of labor market equilibrium. In addition, Section 7.2
presents comparative maximum likelihood estimates of the structural model assuming a
stochastic and a non-stochastic indicator. These estimates stress the importance of
structural specification, such as dynamic links, over mere stochastic specification,
with which much of the literature has been preoccupied, and they support the exact
4
excess demand specification as a valid econometric formulation.
The estimation of disequilibrium models is particularly difficult in a multimarket
context because the intermarket effects of rationing must be taken into account. For
complete macroeconomic analysis such a model is required; nonetheless, there have been
only a handful of macroeconomic disequilibrium models estimated (prominently Artus,
Laroque, and Michel (1984) and Kooiman and Kloek (1985», and these are limited to two
markets and a simple structure. Part IV outlines and estimates a macroeconomic
disequilibrium model with markets for labor, investment, and consumption. Besides
considering three markets, the structure, as described in Chapters 8 and 9, differs
from previous models by containing dynamic links and more microeconomic detail. In
general, it is more closely related to popular theoretical disequilibrium models (e.g.,
Malinvaud (1977». Such a structure is possible because the exact excess denmnd
econometric specification is used in estimation. Chapter 10 describes the indicators
of excess demand and excess supply for each market. Chapter 11 provides the
multimarket parameter estimates.
PART II: EOONOHETRlC SPECU'ICATIONS OF THE DISEQUILIBRIUM II>DEL
The next chapter examines three econometric formulations of the disequilibrium
model. It discusses the relative advantages and disadvantages of each specification,
with a focus on the ease and tractability of estimation. Chapter 3 introduces another
econometric disequilibrium specification, which is similar in structure to previous
specifications but includes information about excess demand in the market. Several
issues in disequilibrium modeling are also examined, including price endogeneity, tests
for equiiibrium, and the estimation of multimarket models. Chapter 4 explores the
tradeoff between the tractability of model estimation and the depth and richness of
model specification for alternative econometric specifications.
