Handbook of applied econometrics and statistical inference

718 Pages·2002·3.82 MB·English

by  Aman Ullah

HANDBOOK OF
APPLIED ECONOMETRICS
AND STATISTICAL INFERENCE
EDITED BY
AMAN ULLAH
University of California,Riverside
Riverside,California
ALAN T. K.WAN
City University of Hong Kong
Kowloon,Hong Kong
ANOOP CHATURVEDI
University of Allahabad
Allahabad,India
Marcel Dekker, Inc. New York Basel
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Copyright 2002 by Marcel Dekker. All Rights Reserved.
ISBN: 0-8247-0652-8
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To the memory of Viren K. Srivastava
Prolific researcher,
Stimulating teacher,
Dear friend
Copyright 2002 by Marcel Dekker. All Rights Reserved.
Preface
This Handbook contains thirty-one chapters by distinguished econometri-
ciansandstatisticiansfrommanycountries.Itisdedicatedtothememoryof
ProfessorVirenKSrivastava,aprofoundandinnovativecontributorinthe
fields of econometrics and statistical inference. Viren Srivastava was most
recently a Professor and Chairman in the Department of Statistics at
Lucknow University, India. He had taught at Banaras Hindu University
andhadbeenavisitingprofessororscholaratvariousuniversities,including
Western Ontario, Concordia, Monash, Australian National, New South
Wales, Canterbury, and Munich. During his distinguished career, he pub-
lished more than 150 research papers in various areas of statistics and
econometrics (a selected list isprovided).His most influentialcontributions
are in finite sample theory of structural models and improved methods of
estimationinlinearmodels.Thesecontributionshaveprovidedanewdirec-
tionnotonlyineconometricsandstatisticsbutalsoinotherareasofapplied
sciences. Moreover, his work on seemingly unrelated regression models,
particularly his book Seemingly Unrelated Regression Equations Models:
Estimation and Inference, coauthored with David Giles (Marcel Dekker,
Copyright 2002 by Marcel Dekker. All Rights Reserved.
Inc., 1987), has laid the foundation of much subsequent work in this area.
Severaltopicsincludedinthisvolumearedirectlyorindirectlyinfluencedby
his work.
In recent years there have been many major developments associated
with the interface between applied econometrics and statistical inference.
This is true especially for censored models, panel data models, time series
econometrics, Bayesian inference, and distribution theory. The common
ground at the interface between statistics and econometrics is of consider-
ableimportanceforresearchers,practitioners,andstudentsofbothsubjects,
and it is also of direct interest to those working in other areas of applied
sciences. The crucial importance of this interface has been reflected in sev-
eral ways. For example, this was part of the motivation for the establish-
ment of the journal Econometric Theory (Cambridge University Press); the
HandbookofStatisticsseries(North-Holland),especiallyVol.11;theNorth-
Holland publication Handbook of Econometrics, Vol. I–IV, where the
emphasis is on econometric methodology; and the recent Handbook of
AppliedEconomicStatistics(MarcelDekker,Inc.),whichcontainscontribu-
tions from applied economists and econometricians. However, there
remains a considerable range of material and recent research results that
are of direct interest to both of the groups under discussion here, but are
scattered throughout the separate literatures.
This Handbook aims to disseminate significant research results in econo-
metrics and statistics. It is a consolidated and comprehensive reference
source for researchers and students whose work takes them to the interface
betweenthesetwodisciplines.Thismayleadtomorecollaborativeresearch
between members of the two disciplines. The major recent developments in
boththeappliedeconometricsandstatisticalinferencetechniquesthathave
been covered are of direct interest to researchers, practitioneres, and grad-
uate students, not only in econometrics and statistics but in other applied
fields such as medicine, engineering, sociology, and psychology. The book
incorporates reasonably comprehensive and up-to-date reviews of recent
developments in various key areas of applied econometrics and statistical
inference,anditalsocontainschaptersthatsetthesceneforfutureresearch
intheseareas.Theemphasishasbeenonresearchcontributionswithacces-
sibility to practitioners and graduate students.
The thirty-one chapters contained in this Handbook have been divided
into seven major parts, viz., Statistical Inference and Sample Design,
Nonparametric Estimation and Testing, Hypothesis Testing, Pretest and
Biased Estimation, Time Series Analysis, Estimation and Inference in
Econometric Models, and Applied Econometrics. Part I consists of five
chapters dealing with issues related to parametric inference procedures
and sample design. In Chapter 1, Barry Arnold, Enrique Castillo, and
Copyright 2002 by Marcel Dekker. All Rights Reserved.
Jose´ Maria Sarabia give a thorough overview of the available results on
Bayesian inference using conditionally specified priors. Some guidelines
are given for choosing the appropriate values for the priors’ hyperpara-
meters, and the results are elaborated with the aid of a numerical example.
Helge Toutenburg, Andreas Fieger, and Burkhard Schaffrin, in Chapter 2,
considerminimaxestimationofregressioncoefficientsinalinearregression
model and obtain a confidence ellipsoid based on the minimax estimator.
Chapter 3, by Pawel Pordzik and Go¨tz Trenkler, derives necessary and
sufficient conditions for the best linear unbiased estimator of the linear
parametric function of a general linear model, and characterizes the sub-
space of linear parametric functions which can be estimated with full effi-
ciency.InChapter4,AhmadParsianandSyedKirmaniextendtheconcepts
ofunbiasedestimation,invariantestimation,Bayesandminimaxestimation
for the estimation problem under the asymmetric LINEX loss function.
These concepts are applied in the estimation of some specific probability
models. Subir Ghosh, in Chapter 5, gives an overview of a wide array of
issues relating to the design and implementation of sample surveys over
time, and utilizes a particular survey application as an illustration of the
ideas.
The four chapters of Part II are concerned with nonparametric estima-
tion and testing methodologies. Ibrahim Ahmad in Chapter 6 looks at the
problem of estimating the density, distribution, and regression functions
nonparametrically when one gets only randomized responses. Several
asymptotic properties, including weak, strong, uniform, mean square, inte-
grated mean square, and absolute error consistencies as well as asymptotic
normality,areconsideredineachestimationcase.Multinomialchoicemod-
els are the theme of Chapter 7, in which Jeff Racine proposes a new
approach to the estimation of these models that avoids the specification
of a known index function, which can be problematic in certain cases.
Radhey Singh and Xuewen Lu in Chapter 8 consider a censored nonpara-
metric additive regression model, which admits continuous and categorical
variables in an additive manner. The concepts of marginal integration and
local linear fits are extended to nonparametric regression analysis with cen-
soringtoestimatethelowdimensionalcomponentsinanadditivemodel.In
Chapter9,MezbahurRahmanandAmanUllahconsideracombinedpara-
metricandnonparametricregressionmodel,whichimprovesboththe(pure)
parametric and nonparametric approaches in the sense that the combined
procedureisless biased thantheparametricapproachwhilesimultaneously
reducingthemagnitudeofthevariancethatresultsfromthenon-parametric
approach. Small sample performance of the estimators is examined via a
Monte Carlo experiment.
Copyright 2002 by Marcel Dekker. All Rights Reserved.
In Part III, the problems related to hypothesis testing are addressed in
three chapters. Anil Bera and Aurobindo Ghosh in Chapter 10 give a com-
prehensive survey of the developments in the theory of Neyman’s smooth
testwithanemphasisonitsmerits,andputthecasefortheinclusionofthis
test in mainstream econometrics. Chapter 11 by Bill Farebrother outlines
severalmethodsforevaluatingprobabilitiesassociatedwiththedistribution
of a quadratic form in normal variables and illustrates the proposed tech-
nique in obtaining the critical values of the lower and upper bounds of the
Durbin–Watson statistics. It is well known that the Wald test for autocor-
relationdoesnotalwayshavethemostdesirablepropertiesinfinitesamples
owingtosuchproblemsasthelackofinvariancetoequivalentformulations
of the null hypothesis, local biasedness, and power nonmonotonicity. In
Chapter 12, to overcome these problems, Max King and Kim-Leng Goh
consider the use of bootstrap methods to find more appropriate critical
values and modifications to the asymptotic covariance matrix of the esti-
mates used in the test statistic. In Chapter 13, Jan Magnus studies the
sensitivity properties of a ‘‘t-type’’ statistic based on a normal random
variablewith zero meanand nonscalar covariancematrix. Asimpleexpres-
sionfortheevenmomentsofthist-typerandomvariableisgiven,asarethe
conditions for the moments to exist.
Part IV presents a collection of papers relevant to pretest and biased
estimation. In Chapter 14, David Giles considers pretest and Bayes estima-
tion of the normal location parameter with the loss structure given by a
‘‘reflectednormal’’penaltyfunction,whichhastheparticularmeritofbeing
bounded. In Chapter 15, Akio Namba and Kazuhiro Ohtani consider a
linear regression model with multivariate t errors and derive the finite sam-
ple moments and predictive mean squared error of a pretest double k-class
estimator of the regression coefficients. Shalabh, in Chapter 16, considers a
linear regression model with trended explanatory variable using three dif-
ferent formulations for the trend, viz., linear, quadratic, and exponential,
and studies large sample properties of the least squares and Stein-rule esti-
mators. Emphasizing a model involving orthogonality of explanatory vari-
ables and the noise component, Ron Mittelhammer and George Judge in
Chapter 17 demonstrate a semiparametric empirical likelihood data based
informationtheoretic(ELDBIT) estimatorthathasfinite sampleproperties
superior to those of the traditional competing estimators. The ELDBIT
estimator exhibits robustness with respect to ill-conditioning implied by
highly correlated covariates and sample outcomes from nonnormal,
thicker-tailed sampling processes. Some possible extensions of the
ELDBIT formulations have also been outlined.
Time series analysis forms the subject matter of Part V. Judith Giles in
Chapter 18 proposes tests for two-step noncausality tests in a trivariate
Copyright 2002 by Marcel Dekker. All Rights Reserved.
VAR model when the information set contains variables that are not
directlyinvolvedinthetest.Anissuethatoftenarisesintheapproximation
of an ARMA process by a pure AR process is the lack of appraisal of the
quality of the approximation. John Galbraith and Victoria Zinde-Walsh
address this issue in Chapter 19, emphasizing the Hilbert distance as a
measure of the approximation’s accuracy. Chapter 20 by Anoop
Chaturvedi, Alan Wan, and Guohua Zou adds to the sparse literature on
Bayesian inference on dynamic regression models, with allowance for the
possibleexistenceofnonnormalerrorsthroughtheGram–Charlierdistribu-
tion. Robust in-sample volatility analysis is the substance of the contribu-
tion of Chapter 21, in which Xavier Yew, Michael McAleer, and Shiqing
Ling examine the sensitivity of the estimated parameters of the GARCH
andasymmetricGARCHmodelsthroughrecursiveestimationtodetermine
the optimal window size. In Chapter 22, Koichi Maekawa and Hiroyuki
HisamatsuconsideranonstationarySURsystemandinvestigatetheasymp-
totic distributions of OLS and the restricted and unrestricted SUR estima-
tors. A cointegration test based on the SUR residuals is also proposed.
Part VI comprises five chapters focusing on estimation and inference of
econometric models. In Chapter 23, Gordon Fisher and Marcel-Christian
Voia consider the estimation of stochastic coefficients regression (SCR)
modelswithmissingobservations.Amongotherthings,theauthorspresent
a new geometric proof of an extended Gauss–Markov theorem. In estimat-
ing hazard functions, the negative exponential regression model is com-
monly used, but previous results on estimators for this model have been
mostly asymptotic. Along the lines of their other ongoing research in this
area, John Knight and Stephen Satchell, in Chapter 24, derive some exact
properties for the log-linear least squares and maximum likelihood estima-
tors for a negative exponential model with a constant and a dummy vari-
able.Minimumvarianceunbiasedestimatorsarealsodeveloped.InChapter
25,MurraySmithexaminesvariousaspectsofdouble-hurdlemodels,which
areusedfrequentlyindemandanalysis.Smithpresentsathoroughreviewof
the current state of the art on this subject, and advocates the use of the
copula method as the preferred technique for constructing these models.
Rick VinodinChapter26discusses howthepopular techniquesofgeneral-
izedlinearmodelsandgeneralizedestimatingequationsinbiometricscanbe
utilized in econometrics in the estimation of panel data models. Indeed,
Vinod’s paper spells out the crucial importance of the interface between
econometrics and other areas of statistics. This section concludes with
Chapter 27 in which William Griffiths, Chris Skeels, and Duangkamon
Chotikapanich take up the important issue of sample size requirement in
the estimation of SUR models. One broad conclusion that can be drawn
Copyright 2002 by Marcel Dekker. All Rights Reserved.
from this paper is that the usually stated sample size requirements often
understate the actual requirement.
The last part includes four chapters focusing on applied econometrics.
ThepaneldatamodelisthesubstanceofChapter28,inwhichAmanUllah
and Kusum Mundra study the so-called immigrants home-link effect on
U.S.producertradeflowsviaasemiparametricestimatorwhichtheauthors
introduce. Human development is an important issue faced by many devel-
oping countries. Having been at the forefront of this line of research,
Aunurudh Nagar, in Chapter 29, along with Sudip Basu, considers estima-
tionofhumandevelopmentindicesandinvestigatesthefactorsindetermin-
ing human development. A comprehensive survey of the recent
developments of structural auction models is presented in Chapter 30, in
which Samita Sareen emphasizes the usefulness of Bayesian methods in the
estimation and testing of these models. Market switching models are often
used in business cycle research. In Chapter 31, Baldev Raj provides a thor-
ough review of the theoretical knowledge on this subject. Raj’s extensive
survey includes analysis of the Markov-switching approach and generaliza-
tions to a multivariate setup with some empirical results being presented.
Needless to say, in preparing this Handbook, we owe a great debt to the
authors of the chapters for their marvelous cooperation. Thanks are also
due to the authors, who were not only devoted to their task of writing
exceedingly high quality papers but had also been willing to sacrifice
much time and energy to review other chapters of the volume. In this
respect, we would like to thank John Galbraith, David Giles, George
Judge, Max King, John Knight, Shiqing Ling, Koichi Maekawa, Jan
Magnus, Ron Mittelhammer, Kazuhiro Ohtani, Jeff Racine, Radhey
Singh, Chris Skeels, Murray Smith, Rick Vinod, Victoria Zinde-Walsh,
and Guohua Zou. Also, Chris Carter (Hong Kong University of Science
andTechnology),HikaruHasegawa(HokkaidoUniversity),Wai-KeongLi
(City University of Hong Kong), and Nilanjana Roy (University of
Victoria) have refereed several papers in the volume. Acknowledged also
is the financial support for visiting appointments for Aman Ullah and
AnoopChaturvediattheCityUniversityofHongKongduringthesummer
of1999 when the ideaofbringing together thetopics ofthis Handbook was
firstconceived.WealsowishtothankRussellDekkerandJenniferPaizziof
MarcelDekker,Inc.,fortheirassistanceandpatiencewithusintheprocess
of preparing this Handbook, and Carolina Juarez and Alec Chan for secre-
tarial and clerical support.
Aman Ullah
Alan T. K. Wan
Anoop Chaturvedi
Copyright 2002 by Marcel Dekker. All Rights Reserved.
Contents
Preface
Contributors
Selected Publications of V.K. Srivastava
Part 1 Statistical Inference and Sample Design
1. Bayesian Inference Using Conditionally Specified Priors
Barry C. Arnold, Enrique Castillo, and Jose´ Marı´a Sarabia
2. Approximate Confidence Regions for Minimax–Linear
Estimators
Helge Toutenburg, A. Fieger, and Burkhard Schaffrin
3. On Efficiently Estimable Parametric Functionals in the General
Linear Model with Nuisance Parameters
Pawel R. Pordzik and Go¨tz Trenkler
4. Estimation under LINEX Loss Function
Ahmad Parsian and S.N.U.A. Kirmani
Copyright 2002 by Marcel Dekker. All Rights Reserved.