A Model of
Macroeconomic
Activity
A Model of
Macroeconomic
Activity
Volume II:
The Empirical
Model
Ray C. Fair
Cowles
Special
Publication
Ballingar Publishing Company
A Subsidiary of J.B. Lippincott
l
Cambridge, Massachusetts
Company
49
This book is printed on recycled paper
Copyright @ 1976 by Ballinger Publishing Company. All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system. or
transmitted in any form or by any means, electronic mechanical photocopy,
recording or otherwise, without the prior written consent of the publisher.
International
Standard Book Number
O-88410-295-5
Library of Congress Catalog Card Number
74-12199
Printed in the United States of America
Library of Congress Cataloging in Publication Data
Fair, Ray C.
A model of macroeconomic activity.
Includes bibliographies and index.
CONTENTS
v. 1. The theoretical model-v.
1. Macroeconomics-Mathematical
models.
I. Title.
HB171.F24
339
1SBN a-88410-295-5
‘
2. The empirical model.
74-12199.
To My Parents
Table
of Contents
List of Tables
xi
List of Figures
xv
Preface
Chapter One
1.1
1.2
1.3
Chapter Two
2.1
2.2
2.3
xvii
Introduction
1
A Brief Summary
Four General Remarks About the
Specification of the Empirical Model
Linking the National Income Accounts
with the Flow-of-Funds
Accounts by Sector
1
11
13
The Complete Model
31
Introduction
A Discussion
A Discussion
31
55
67
of Table 2-2
of Table 2-l
vii
viii
Table of Contents
Chapter
Three
75
76
3.5
3.6
Four
The Household
89
4.1
4.2
Introduction
The Determination of the Unconstrained
Decisions
The Treatment of the Constraints
The Estimates of the Equations for the
Household Sector
3.4
4.3
4.4
Chapter
Five
5.1
5.2
5.3
5.4
5.5
Chapter
Six
6.1
6.2
6.3
Chapter
75
Issues
Introduction
The Treatment of Serial Correlation Problems
The Computation of the Two Stage Least
Squares Estimates
The Computation of the Full Information
Maximum Likelihood Estimates
The Solution of the Model
A Possible Estimator for Future Use
3.1
3.2
3.3
Chapter
Econometric
Sector
80
84
85
89
89
93
99
107
The Firm Sector
Introduction
The Technology of the Firm Sector and the
Measurement of Excess Labor and
Excess Capital
An Outline of the Empirical Model of the
Firm Sector
The Estimates of the Equations for the
Firm Sector
A Review of the Model of the Firm Sector
The Financial
11
Sector
107
108
115
121
132
135
Introduction
13.5
Equation 45 and the Four Stochastic
Equations in the Financial Sector
The Treatment of the Loan Constraints
135
138
Seven
The Foreign
and Government
7.1
7.2
The Foreign Sector
The tiovemment sector
Sectors
141
141
142
Table of Contents
Chapter
Eight
The Predictive
8.1
8.2
Introduction
A Comparison
of the Forecasting
Model
with Other Models
A Comparison
of the Empirical Model
and the Forecasting Model
Further Results on the Predictive Accuracy
of the Empirical Model
14s
Nine
The Properties
165
9.1
9.2
9.3
Introduction
A Brief Review of the Model
The Response of the Model to Changes in
Various Exogenous Variables
The Properties of the Model that Relate to
Five Issues in Macroeconomics
8.3
8.4
Chapter
9.4
Chapter
Chapter
Appendix
Appendix
Ten
Some
10.1
10.2
10.3
Introduction
The Computation
The Results
Eleven
A
S
Optimal
Accuracy
of the
Model
ix
of the Model
Control
Results
of the Optimal
Controls
146
149
153
165
165
167
194
197
197
198
203
213
Conclusion
Some Rasults
Technology
145
for the Alternative
217
The Forecasting
Model Used for
Comparison
Purposes
221
References
229
Index
233
About
the Author
235
List of Tables
l-l
The Five Sectors of the Model
14
1-2
The Data from the National
Accounts by Sector
16
l-3
2-l
The Data from the Flow-of-Funds
Accounts by Sector
The Complete List of Variables
Model in Alphabetic Order
2-2
The List of Equations
2-3
TSLS and FIML Estimates
Stochastic Equations
4-1
4-2
Income
23
in the
in the Model
32
42
of the 26
46
Matching of Dependent
Variables in the
Theoretical and Empirical Models for the
Household Sector
90
Matching of Explanatory
Variables in the
Theoretical and Empirical Models for
the Household Sector
92
xi
xii
List of Tables
s-1
l-1
Matching of Dependent Variables in the
Theoretical and Empirical Models for
the Firm Sector
108
The Exogenous
Sector
144
Variables
in the Government
The Ranking of the Forecasting Model
Against Eight Other Quarterly Models
147
The Predictive Accuracy of the Empirical
Model versus the Forecasting
Model
151
Further Results on the Predictive
Accuracy of the Empirical Model
154
Predicted and Actual Values for Five
Variables for the 195%1962IV
Period
158
Predicted and Actual Values for Five
Variables for the 19681-197411 Period
160
Predicted and Actual Values for Five
Variables for the 1974111-19751 Period
161
9-l
Detailed
Experimental
Results
170
9-2
Detailed
Experimental
Results
174
9-3
Detailed
Experimental
Results
178
9-4
Detailed
Experimental
Results
180
9-5
Detailed
Experimental
Results
182
9-6
Summary
for 26 Experiments
184
l&l
Control Results for the Eisenhower
Administrations
204
Control Results for the Kennedy-Johnson
Admimstrations
206
8-1
8-2
8-3
x-4
8-5
8-6
1o-2
Results
List of Tables xiii
10-3
A-l
A-2
A-3
B-l
B-2
Control Results for the Nixon-Ford
Administrations
Estimates of the Investment
the Two Technologies
Estimates of the Employment
for the Two Technologies
Estimates of the Hours
Two Technologies
208
Equation
for
218
Equation
Equation
219
for the
218
The List of Variables in the Forecasting
Model in Alphabetic Order by Sector
222
The List of Equations
Model by Sector
224
in the Forecasting
List of Figures
4-1
Desired
4-2
Desired Shape of ZR, as a Function
RBILL;
of
Desired Shape of ZJ: as a Function
1 - UR,
of
5-l
5-2
Shape of ZJ, as a Function
Expected Relationship
and HPF,
Between
of J,$
95
96
118
HPFO,
131
Preface
The work described in this volume is a continuation
of my effort to try to
improve the specification
of macroeconomic
models. The model presented
in this volume is an empirical version of the theoretical model developed in
Volume I. Three important features of the theoretical model that distinguish
it from earlier models are that it is based on solid microeconomic
foundations, it accounts explicitly for disequilibrium
effects, and it accounts for all
flows of funds in the system. These three features have been carried over to
the empirical model.
The methodology
of this study is unusual enough to require
some explanation.
There is, first of all, no unique way to specify an empirical
version of the theoretical model; the model is simply too abstract for this
to be possible. Thus, although I have been guided closely by the theoretical
model in my empirical specification, it will be clear in what follows that my
particular specification is not the only one that could be said to be consistent
with the theoretical model.
If there is no unique empirical version of the theoretical model,
the question immediately
arises as to how the theoretical
model is to be
judged. My answer to this question occurs on page 16 of Volume 1:
The author looks on a theoretical model of the sort developed in this
study as not so much true or false as useful or not useful. The model
is useful if it aids in the specification of empirical relationships that
one would not already have thought of from a simpler model and
that are in turn confirmed by the data. It is not useful if it either does
xviii
Preface
not aid in the specification of empirical relationships that one would
not have thought of from a simpler model or aids in the specification
of empirical
relationships
that are in turn refuted
by the data.
I argue in Chapter Eight that the present empirical model is
confirmed by the data in the sense of its being more accurate than other
models. It is also the case that I do not think that 1 would have been led to
the present empirical specifications
had 1 not had the theoretical model as
a guide. Consequently,
my conclusion is that as of this writing the theoretical
model is useful. Whether this conclusion holds up as new models are developed, new tests performed, and new data collected is, of course, unknown.
One can never rule out the possibility that a more accurate empirical model
will be developed that is based on a different theoretical model.
One of the key assumptions
of the theoretical model is that economic agents engage in maximizing behavior. In particular, each of the main
behavioral units in the model makes its decisions on the basis of the solution
to an optimal control problem. This is what is meant by the statement that
the model is based on solid microeconomic
foundations.
It is true, of course,
that economic agents do not actually solve optimal control problems explicitly in making their decisions. The assumption
that they do so is used here
as it is used in most of microeconomics:
as a possibly useful approximation.
As just mentioned, my way of testing whether assumptions
such as this are
useful for macroeconomic
model building is to specify a theoretical model
based on them, use the theoretical model as a guide to the specification
of
an empirical model, and then test the empirical model in standard ways.
The results that I have obtained so far suggest that the maximizing assumption
is useful for the specification of macroeconomic
models. Additional tests are
needed, however,
before one can place too much confidence
on this
conclusion.
Another basic feature of the theoretical
model is that expectations play an important
role in influencing people’s decisions (i.e., in influencing the solutions to the optimal control problems).
For the simulation
work in Volume I, most of these expectations
were assumed to be formed
in simple ways on the basis of past data. This is also true for the work in
this volume, in the sense that lagged endogenous
and lagged exogenous
variables are used as explanatory
variables in the stochzistic equations
to
try to capture expectational
effects.
It would have been possible for the simulation work in Volume I
to use more sophisticated
mechanisms
of expectation
formation.
It could
have been assumed, for example, that each behavioral unit estimates its own
relevant econometric model each period, and uses this model to forecast the
future values of the variables that it needs to know in order to solve its
control problem. Assumptions
similar to this were in fact made for some of
Preface
xix
the expectations
formed by the banks, the firms, and the bond dealer. (See
in particular the discussion on pages 205, 208, and 209 in Volume I.) Banks,
firms, and the bond dealer were assumed to estimate from past data some of
the key parameters
that influence their expectations.
Although I have not
carried out such experiments,
I doubt that the properties of the theoretical
model would be changed very much if more of these types of assumptions
were made. What is a crucial characteristic
of the model, however, is the
assumption
that behavioral units do not have perfect foresight. This is one
of the four characteristics
listed on page 3 of Volume 1 that the model was
deliberately designed to have.
Even if more sophisticated
mechanisms of expectation formation
had been postulated
in Volume 1, expectations
would still have been based
on past data. Consequently,
1 would probably still have been led to use
lagged values in the empirical model to try to capture expectational
effects.
It is true, however, that if expectations of behavioral units are fairly accurate,
one might expect actual future values to be better proxies for these expectations than are current and lagged values. I did in fact do some experimentation in the initial development
of the empirical model to see if future values
of some of the key explanatory variables (e.g., prices, wage rates, and interest
rates) explained the current values of the decision variables better than did
the current and lagged values of the explanatory
variables. This empirical
work did not support the use of future values, however, and in the end no
future values were used as explanatory
variables in any of the equations of
the empirical model. The treatment of expectations
in the empirical model
is discussed in section 1.2 of Chapter One of this volume.
In a model building effort of this sort there are a number of
detailed decisions that have to be made about how certain variables are to
be treated and about what kinds of data are to be used. Realizing that not
everyone is as interested in these details as I am, I have tried to write this
volume so that the discussion ofthese details can be easily skipped or skimmed.
In particular, 1 have relegated most of this discussion to section 1.3 of Chapter
One and to Chapter Two. Most of the discussion of econometric
issues is
contained in Chapter Three, and this material can also be easily skipped or
skimme< by readers who are not particularly interested in such things.
The first section of Chapter One, section 1.1, contains a summary
of the central features and properties of the empirical model and of the
major conclusions reached in this study. For those who are primarily interested in getting a general ideal of the properties of the model and of how it
differs from other models, reading this section should be enough. Section 1.2
contains a discussion of some of the basic principles that guided the empirical
specification,
and section 1.3 contains a discussion
of the linking of the
national income accounts with the flow-of-funds accounts by sector. Although
the details in section 1.3 can be skipped without much loss of continuity,
it
xx
Preface
should be stressed that the linking of the two accounts is an important part
of the present empirical work and has an important effect on the properties
of the model.
The complete model is presented in Chapter Two, except for the
discussion of the individual
stochastic equations.
The stochastic equations
are explained in Chapters Four, Five, Six, and Seven. These latter four
chapters are important in understanding
the model, and by considering most
of the data and econometric
issues in Chapters Two and Three, I have tried
to keep Chapters Four through Seven relatively free from discussion other
than that directly related to the specification
of the stochastic equations.
The complete model is presented in tabular form in Tables 2-1, 2-2, and 2-3
in Chapter Two, and these tables are used for reference purposes throughout
the rest of the text.
The predictive accuracy of the model is examined in Chapter
Eight, and the properties of the model are examined in detail in Chapters
Nine and Ten. The properties of the model are examined in Chapter Ten via
the computation
of optimal controls. Chapter Eleven contains some brief
concluding remarks.
This volume can be read without a detailed knowledge of Volume
1. One should, however, have some understanding
of the theoretical model
before reading this volume. At a minimum, Chapters One and Eight (Introduction and Conclusion)
in Volume I should be read to get a general idea
of the theoretical model.
I would like to stress that the empirical model presented here is
not in any direct sense an expanded 01 revised version of my earlier forecasting
model [14]. My interest in developing the forecasting model was to see if an
econometric
model could be developed that produced reasonably
accurate
forecasts when used in as mechanical
a way as possible. My interest in
Volume I, on the other hand, was theoretical and was to develop a general,
dynamic macroeconomic
model that was based on solid microeconomic
foundations
and that was not based on the restrictive assumptions
of perfect
information
and the existence of t8tonnement
processes that clear markets
every period. My interest in this volume, although empirical, is more of an
extension of my interest in Volume I than of my interest in the forecasting
model. (The forecasting
model does, however, provide a good basis of
comparison for other models in terms of prediction accuracy, and it has been
used for this purpose in Chapter Eight.)
Although
my earlier work with the forecasting
model has not
had a direct effect on the specification of the present model, some of my work
with monthly three-digit industry data has. This work is described in references [23], [21], and [15]. The results in these three studies have had an
influence on my specification
of both the theoretical and empirical models.
Some of the links between my work with the monthly three-digit industry
data and my work here are discussed in Chapter Five.
Preface
xxi
I am indebted to a number of people who have commented
on
my model building effort during the past few years. I would particularly
like
to thank Gregory Chow, Robert Hall, Donald Hester, Sharon Oster, and
James Tobin for comments that led to important
additions to this volume.
I reluctantly
assume responsibility
for any errors. Most of this study was
financed by grants from the National
Science Foundation
and the Ford
Foundation
to the Cowles Foundation
for Research in Economics at Yale
University.
Ray C. Fair
October 1975
A Model of
Macroeconomic
Activity
References
[l] Amemiya, Takeshi, “A Note on a Fair and Jaffee Model,” Econometrica, XL11 (July 1974): 759-762.
[Z] Amemiya, Takeshi, “The Nonlinear Two-Stage Least-Squares
Estimator,” Journal of Econometrics, II (July 1974): 105-110.
[3] Board of Governors of the Federal Reserve System, Division of
Research and Statistics, Flow of Funds Table Codes, July 1975.
[4] Brainard, William C., and James Tobin, “Pitfalls in Financial
Model Building,” ne American Economic Rez&w, LVllI (May 1968): 99-122.
[S] Brayton, Robert K., Fred G. Gustavson, and Ralph A. Willoughby, “Some Results on Sparse Matrices,” Mathematicsof Computation, XXIV (Ckto
b-z 1970): 937-954.
161 Britain, John A., “The Incidence of Social Security Payroll
Taxes,” The American Economic Reuiew, LX1 (March 1971): 110-125.
[7] Chow, Gregory C., “A Comparison of Alternative Estimators for
Simultaneous Equations,” Econometrica, XXX11 (October 1964): 532-553.
[Sl Chow, Gregory C., “On the Computation of Full-Information
Maximum Likelihood Estimates for Nonlinear Equation Systems,” The Review o,
Economics and Statisrics, LV (February 1973): 104-109.
[9] Chow, Gregory C., and Ray C. Fair, “Maximum Likelihood
Estimation of Linear Equation Systems with Auto-Regressive Residuals,” Annals
of Lkonomic and Social Measurement, II (January 19733: 17-28.
[lo] Cocbrane, D., and G. H. Orcutt, “Application of Least Squares
Regression to Relationships Containing Auto-Correlated
Error Terms,” Journal
of the American Statistical Associafion, XLIV (March 1949): 32-61.
[Ill
Cooper, Richard N., “Implications
of the Euro-Dollar
for
Monetary Policy and the U.S. Balance-of-Payments Deficit,” in Robert Z. Aliber,
ed., National Monetary Policies and the Infernalional Financial System (Chicago:
University of Chicago Press, 1974): 139-151.
[IZ] Fair, Ray C., “‘A Comparison of Alternative Estimators of
Macroeconomic
Models,” international
Economic Rmiew, XIV (June 1973):
261-277.
229
2.30
A Model of Macroeconomic
Activity
[13] Fair, Ray C., “A”’ Evaluation of a Short-Run
Forecasting
Model,” Infernotional Economic Review, XV (June 1974): 285-303.
1141 Fair, Ray C., A Short-Run Forvcasring Model of the United
Srafes Economy (Lexington, Mass.: D. C. Heath and Co., 1971).
[15] Fair, Ray C., “A Test of Capital-Labor
Substitution Using
Capacity Data,” 1974 (mimeo).
[I61 Fair, Ray C., “Disequilibrium in Housing Models,” The Journal
of Fin’inance.XXVII (Mas 1972): 207-221,
[17] f&-Ray
t?., “Efficient Estimation of Simultaneous Equations
with Auto-Regressive Errors by Instrumental Variables,” The RPLGV of Economics
and Statistics, LIV (November 1972): 444-449.
[18] Fair, Ray C., “Labor Force Participation, Wage Rates, and
Money Illusion,” The Review of Economics and .Sfaristics, LIII (May 1971):
164-168.
[IPI Fair, Ray C., “On the Robust Estimation of Econometric
Models,” Annals of Economic and Social Measurement, III (October 1974): 667-677.
[201 Fair, Ray C., “On the Solution of Optimal Control Problems
as Maximization Problems,” Annals of Economic and Social Mrasurement, III
(January 1974): 135-154.
[Zl] Fair, Ray C., “Sales Expectations and Short-Run Production
Decisions,” The Southern Economic Journal, XXXVli (January 1971): 267-275.
[22] Fair, Ray C., “The Estimation of Simultaneous Equation Models
with Lagged Endogenous Variables and First Order Serially Correlated Errors,”
Economctrica, XXXVIII (May 1970): 507-516.
1231 Fair, Ray C., The Short-Run Demand for Workers and Hours
(Amsterdam: North-Holland Publishing Co., 1969).
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for Markets in Disequilibrium.” Economebica, XL (May 1972): 497-514,
[25] Fair, Ray C., and Harry H. Kelejian, “Methods of Estimation
for Markets in Disequilibrium:
A Further Study,” Econometrica, XL11 (January
1974): 177-190.
[26] Fromm, Gary, and Lawrence R. Klein, “A Comparison of Eleven
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1271 Howrey, E. Philip, and Harry H. Kelejian, “Simulation versus
Analytical Solutions: The Case of Econometric Models,” Chapter 12, in Thomas
H. Naylor, ed., Con~pupuler
Simuiarion Experiments wirk Models of Economic Systems
(New York: John Wiley and Sons, 1971).
[28] Huang, H. Y., “Unified Approach t” Quadratically Convergent
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Algorithms for Function Minimization,”
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Applications, V (June 1970): 405423.
1291 IBM, %-MATH, User’s Guide, First Edition (November 1971).
1301 Klein, Lawrence R., An Essay on the Theory ofEconomic Prediction (Chicago: Markham Publishing Co., 1971).
1311 Loftus, Shirley F., “Stocks of Business Inventories in the United
States, 1928-71,” Survey of Currem Eusincss, LII (December 1972): 29-32.
1321 Maddala, G. S., and Forrest D. Nelson, “Maximum Likelihood
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231
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Economefuica, XL11 (November 1974): 1013-1030.
[33] Malinvaud,
E., Stalisdcol Methods of Economerrics, second
revised edition (Amsterdam:
North-Holland
Publishing Co., 1970).
[34] McNees, Stephen K., “How Accurate Are Economic Forecasts?”
New En&znd Economic Review (November/December
1974): 2-19.
(351 McNees, Stephen K., “The Predictive Accuracy of Econometric
Forecasts,”
New EnglandEconomic Reoiew (September/October 1973): 3-27.
(361 Nordhaus,
William, and John Shown,
“Intlation
1973: The
Year of Infancy,” Chol/enge, XVII (May-June
1974): 14-22.
[37] Powell, M, J. D., “An Efficient Method for Finding the Minimum
of a Function
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Derivatives,”
Computer
Journal, VII (July 1964): K-162.
1381 Shavell, Henry, “The Stock of Durable Goods in the Hands of
Consumers,
1946-1969,” 1970 Proceedings of the Business and Economic Sfatisfics
Section ofrhe American Srotisrical Associarion, 241-246.
[391 Young, Allao H., John C. Musgrave,
and Claudia Harkins,
“Residential
Capital in the United States, 1925-70,” Surue~ of Current Business,
Ll (November
1971): 16-27.
1401 U.S. Bureau of Economic Analysis, Fixed Nonresidential Business
Capital in the (/niled States, 1925-73, reproduced
by National Technical Information Service, U.S. Department
of Commerce,
1974.
aggregamnquestion,11,12
Abbei, Robert z., 229
excesscaPital,4,5,108-114,125,126,*17..
220
~X.XSS labor, 4.5, IO&114,126.
,2,,217220
expectations,
xvi, xvii, II, 12
Amemiya, Takeshi, 79, 120,229
asymmetries
in model, 186, 187
bank borrowing equation,
137
bill mte, determination
of, 6, 66.67,
139
bond rate equation, 137
Braina**, William C., 21,229
Braytan, Robert K., 87, 229
Brittain, John A.. 129. 229
138.
Feden, Reserve, IO, 195
financial sector, 135-139
firm sector, 107-134
fiscal policy, 9, 10, 195
flow-of-funds
questions, 5,6,
98
13-29,66,67,
capital gains equation,
137, 138
capital-labarsubstitution,
114
chow, Gregory, xix, 77,80,87,
229
Cochrane, I)., 79, 229
constrained
decisions
firm sector, 1,2,115-121
household sector, I, 2, 93-99
constraints
hours, 2x3,5,94-99,101,
labor,4,
5,115-121
loan, 2,3,5,95-99,104,138,
consumption.
2. 3.99-1.3
103, 115-121
I39
data, 7, 13-28,67-14
demand deposit equations
firm sector, 131, 132
household sector, 102
Durbin-Watson
statistic, 80
employment
equation, 126-128
equations of model, 5567,99-102,121132,135-138,14,-143
233
wwrnment
budget constraint,
142,143
go”er”me”t
sector, 142-144
Gustavson,
Fred G., 87, 229
Hester, Donald, xix
hours equation,
126-128
household sector, 89-105
housing investment,
99-105
Howrey, E. Philip, 84; 230
Huang, H.Y., 82,230
IBM, 82,230
import equation,
141
5,64,66,
234
Index
predictive accuracy
empirical model, 149-163
forecasting
madei, 146-153
price controls, 122
price equation,
12 l-1 22
w,d”ction equation, 123-124
properties
of model, 165-195
132,133,166
133,189
Jaffee, Dwight
M., 104, 120,221,230
Kelejian, Harry H., 84, 120,230
Klein, Lawrence R., 86, 146, 147, 149,230
labor force, 2, 3, 8, ‘B-103
Loftus, Shirley F., 73, 230
longrun
1esults, 193-194
tation
of, 58-60
share considerations.
4
McNees, Stephen K., 145,163,
231
methodology,
XY, xvi, 1 J-1 3
monetary POLiCY,9, 10, 195
moitgage me equation, 137
Mugrave, John C., 73,231
market
Nelson, Forest D., 120, 230
Nordhaus, William, 57, 231
Okun’s iaw, 9
optimal controls
computation
of, 198.203
results, 203-211
Orcutt, G.H., 79,229
ate*, Sharon, xix
overtime hours equation,
130, 131
regimes, 2, 115-121
robus* estimation,
87
serial correlation, 76, 77
Shavell, Henry, 73, 23,
Shove”, John, 57,23,
solution of modei, 84, 85
sparse matrices,82, 86
summaries of model, I-11,
167.192-193
132-134,
,65-
till rates, ew?cis of; 8, IO”-102,
166, ,88190,192
technology,
4, 108-114,
217-220
theoretical
model, xvi-xvii, 1-6, 90-92, 107,
108,122,123,125,127-129,
131,132,
136,139,193,,95
Tobin, James, xix, 21, 229
tifatiitic,
79, PA
two stage least squares, 7, 77.80, 153
unconstrained
decisions,
firm scct01, 1, 2, 115-121
household
sector, 1, 2, 89-93
unem~lwment
rate, 7-9.65,
I IS-119,209
variables
in model,
32-41
wage equatmn,
128-130
Willoughby,
Ralph A., 87, 229
Youn& Allan H., 13, 23,
About
the Author
Ray C. Fair was born in 1942 in Fresno, California. He received
a B.A. degree in economics from Fresno State College in 1964 and a Ph.D.
degree in economics from the Massachusetts
Institute of Technology in 1968.
From 1968 to 1974 he was an Assistant Professor of Economics
at Princeton University. He is currently an Associate Professor of Economics
at Yale University.
His primary fields of interest are econometrics,
macrpeconomics, and income distribution.
Professor Fair is the author of The Short-Run Demandfor Workers
and Hours (North-Holland,
1969), A Short-Run Forecasfing Model of the
United States Economy (D. C. Heath, 1971), A Model of Macroeconomic
Acfim’ty, vol. I (Ball&x,
1974), and various journal articles.