Table Of ContentContributions to Econometric
Theory and Application
R.A.L. Carter J. Dutta A . Ullah
Editors
Contributions to Econometric
Theory and Application
Essays in Honour of A.L. Nagar
Springer-Verlag
New York Heidelberg Berlin
London Paris Tokyo Hong Kong
R.A.L. Carter, Department of Economics, The University of Western Ontario,
London, Ontario N6A 5C2, Canada
J. Dutta, Barnard College, Columbia University, New York, NY 10027, USA
A. Ullah, Department of Economics, The University of Western Ontario,
London, Ontario N6A 5C2, Canada
Library of Congress Cataloging-in-Publication Data
Contributions to econometric theory and application - Essays in
honour of A.L. Nagar / R.A.L. Carter, J. Dutta. A. UlIah,
editors.
p. cm.
Includes bibliographical references.
1. Econometric models. 2. Econometrics. 3. Nagar, A. L.
I. Carter, R. A. L. II. Dutta, Jaysari. m. Ullah, Aman.
HB141.C6595 1990
330' .01 '5191-dc20 90-9707
Printed on acid-free paper
©1990 Springer-Verlag New York Inc.
Softcover reprint of the hardcover 1st edition 1990
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9 8 7 6 5 432
ISBN-13 :978-1-4613-9018-3 e- ISBN-13 :978-1-4613-9016-9
DOl: 10.1007/978-1-4613-9016-9
Preface
The purpose of this volume is to honour a pioneer in the
field of econometrics, A.L. Nagar, on the occasion of his sixtieth
birthday. Fourteen econometricians from six countries on four
continents have contributed to this project. One of us was his
teacher, some of us were his students, many of us were his
colleagues, all of us are his friends.
Our volume opens with a paper by L.R. Klein which
discusses the meaning and role of exogenous variables in struc-
tural and vector-autoregressive econometric models. Several
examples from recent macroeconomic history are presented and
the notion of Granger-causality is discussed. This is followed
by two papers dealing with an issue of considerable relevance
to developing countries, such as India; the measurement of
the inequality in the distribution of income. The paper by
C.T.West and H.Theil deals with the problem of measuring
inequality of all components of total income vvithin a region,
rather than just labour income. It applies its results to the
regions of the United States. The second paper in this group,
by N. Kakwani, derives the large-sample distributions of
several popular inequality measures, thus providing a method
for drawing large-sample inferences about the differences in
inequality between regions. The techniques are applied to the
regions of Cote d'Ivoire.
The next group of papers is devoted to econometric theory
in the context of the dynamic, simultaneous, linear equations
model. The first, by P.J. Dhrymes, is concerned with forecast-
ing using the final form of this model. Large-sample properties
are developed for estimators of the parameters of both the
structural and the final forms and for forecasts. The paper
by R.L. Basmann and H.-S. Hwang uses Monte Carlo simula-
tions to study the exact distributions of estimators of structural
parameters when the estimation has been preceded by a test
for identification. A question of interest here is whether the
parameter estimators and the identifiability test statistic are
v
independent. Monte Carlo methods are also used in the third
paper, by R.A.1. Carter, to obtain nonparametric estimates of
the probability density functions of the t-ratios produced by
the instrumental-variables estimator. The focus of the paper
is the effect on these density functions of alternative choices of
instruments.
The third group of papers deal with issues of econometric
theory in the context of static, simultaneous, linear equations.
In the first paper J.1. Knight investigates the exact distribu-
tion of the partially restricted reduced form estimator using
a combination of Monte Carlo integration, as distinct from
simulation, and nonparametric density estimation. He is thus
able to provide results on the shape of the distribution and its
reaction to changes in the model parameters. The second
paper in this group, by V.K. Srivastava, surveys the literature
on the properties of Nagar's' double k-class, as distinct from
k-ctass, estimators of structural parameters. Finite sample
results for the k-class estimators are extended to the double
k-class. The final paper in this group, by A. Ullah, presents
a straight forward technique for obtaining the exact moments
and distributions of many estimators and test statistics. The
method is remarkable for its simplicity and for the brevity of
its derivations.
The final group of papers is more heterogeneous than the
preceding groups. Its first paper, by J. Dutta, begins by
discussing the general technique of resampling, whose special
cases like the jacknife and the bootstrap are already famil-
iar. The method is then applied to improve estimation and
inference in the context of the linear-regression and errors-in-
variables models. Next is a paper by M.D. McCarthy which
discusses exact and asymptotic procedures for inference about
the coefficients of factor demand equations in the context of
Cobb-Douglas production functions. The techniques are then
extended to multivariate regression models with certain cross-
equation restrictions. The closing paper in the volume, by
J.H. Dreze and M. Mouchart, is, in contrast to the other
papers, written from a Bayesian perspective. But its link with
the frequentist perspective of the other papers lies in its view
vi
of classical test statistics as valuable tools for Bayesian econo-
metricians.
It is with warm wishes for many more birthdays that we
dedicate this volume to our student, teacher, colleague and
friend, A.L. Nagar.
vii
Contents
Preface v
Contributors xi
Exogeniety in Economics 1
L.R. Klein
Regional Inequality by Components
of Income 23
C. T. West and H. Theil
Large Sample Distribution of Several
Inequality Measures: With Application
to Cote d'Ivoire 50
N. Kakwani
Restricted Reduced Forms, Forecasting
and the GSLEM 82
P.J. Dhrymes
A Monte Carlo Study of Structural
Estinlator Distributions After Performance
of Likelihood Ratio Pre-Tests 132
R.L. Basmann and H.-S. Hwang
Nonparametric-Monte-Carlo Estimates
of t-Ratio Distributions in Dynamic
Si111ultaneous Linear Equations Models 160
R.A.L. Carter
The Exact Distribution of the PRRF
Estimator - A Monte Carlo Integration
Approach 196
J.L. Knight
Developments in Double k-Class
Estimators of Parameters in
Structural Equations 221
V.K. Srivastava
ix
Finite Sample Econometrics:
A Unified Approach 242
A. Ullah
On Resampling Inference in
Econometric Models 293
J. Dutta
Estimation and Testing of Regression
Coefficients in Cobb-Douglas and
Other Models 321
M.D. McCarthy
Tales of Testing Bayesians 345
J .R. Dreze and M. Mouchart
x
Contributors
R.L. Basmann
Department of Economics
State University of New York
Binghampton, New York
U.S.A.
R.A.L. Carter
Department of Economics
University of Western Ontario
London, Ontario
Canada '
P.J. Dhrymes
Department of Economics
Columbia University
New York, New York
U.S.A.
J. Dreze
Centre for Operations Research and Econometrics
Universite Catholique de Louvain
Louvain-Ia-N euve
Belgium
J. Dutta
Barnard College
Columbia University
New York, New York
U.S.A.
xi
H.-S. Hwang
Department of Economics
Texas A. & M. University
College Station, Texas
U.S.A.
N. C. Kakwani
School of Economics
University of New South Wales
Sydney, New South Wales
Australia
L.R. Klein
Department of Economics
University of Pennsylvania
Philadelphia, Pennsylvania
U.S.A.
J.L. Knight
Department of Economics
University of Western Ontario
London, Ontario
Canada
M.D. McCarthy
Department of Economics
Temple University
Philadelphia, Pennsylvania
U.S.A.
M. Mouchart
Centre for Operations Research and Econometrics
Universite Catholique de Louvain
Lou vain- la-N euv e
Belgium
xii
