Econometric Analysis of Cross Section and Panel Data

1095 Pages·2010·7.06 MB·English

by  Jeffrey M Wooldridge

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Econometric Analysis of Cross Section and Panel Data

Econometric Analysis of Cross Section and Panel Data
Second Edition
Je¤rey M. Wooldridge
The MIT Press
Cambridge, Massachusetts
London, England
(2010,2002,MassachusettsInstituteofTechnology
Allrightsreserved.Nopartofthisbookmaybereproducedinanyformbyanyelectronicormechanical
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ThisbookwassetinTimesRomanbyAscoTypesetters,HongKong.PrintedandboundintheUnited
StatesofAmerica.
LibraryofCongressCataloging-in-PublicationData
Wooldridge,Je¤reyM.
Econometricanalysisofcrosssectionandpaneldata/Je¤reyM.Wooldridge.—2nded.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-262-23258-6(hardcover:alk.paper)
1.Econometrics—Asymptotictheory. I.Title.
HB139.W663 2010
330.0105195—dc22 2010020912
10 9 8 7 6 5 4 3 2 1
Contents
Preface xxi
Acknowledgments xxix
I INTRODUCTION AND BACKGROUND 1
1 Introduction 3
1.1 Causal Relationshipsand Ceteris Paribus Analysis 3
1.2 Stochastic Setting and Asymptotic Analysis 4
1.2.1 Data Structures 4
1.2.2 Asymptotic Analysis 7
1.3 SomeExamples 7
1.4 Why NotFixed ExplanatoryVariables? 9
2 Conditional ExpectationsandRelatedConcepts inEconometrics 13
2.1 Role ofConditional Expectationsin Econometrics 13
2.2 Featuresof Conditional Expectations 14
2.2.1 Definitionand Examples 14
2.2.2 Partial E¤ects,Elasticities, and Semielasticities 15
2.2.3 Error Form ofModels of Conditional Expectations 18
2.2.4 Some Properties of Conditional Expectations 19
2.2.5 AveragePartial E¤ects 22
2.3 Linear Projections 25
Problems 27
Appendix 2A 30
2.A.1 Properties of Conditional Expectations 30
2.A.2 Properties of Conditional Variancesand Covariances 32
2.A.3 Properties of Linear Projections 34
3 Basic AsymptoticTheory 37
3.1 Convergence of Deterministic Sequences 37
3.2 Convergence inProbability and Boundedness inProbability 38
3.3 Convergence inDistribution 40
3.4 LimitTheorems for RandomSamples 41
3.5 Limiting Behavior of Estimators and TestStatistics 42
3.5.1 Asymptotic Properties of Estimators 42
3.5.2 Asymptotic Properties of Test Statistics 45
Problems 47
vi Contents
II LINEAR MODELS 51
4 Single-Equation Linear Model and Ordinary LeastSquares
Estimation 53
4.1 Overview of the Single-EquationLinear Model 53
4.2 AsymptoticProperties of Ordinary Least Squares 55
4.2.1 Consistency 56
4.2.2 Asymptotic Inference Using Ordinary Least Squares 59
4.2.3 Heteroskedasticity-Robust Inference 60
4.2.4 Lagrange Multiplier(Score)Tests 62
4.3 OrdinaryLeastSquaresSolutions to the Omitted VariablesProblem 65
4.3.1 Ordinary LeastSquares Ignoring the Omitted Variables 65
4.3.2 Proxy Variable–Ordinary Least Squares Solution 67
4.3.3 Models with Interactionsin Unobservables: Random
Coe‰cient Models 73
4.4 Properties of Ordinary LeastSquares under Measurement Error 76
4.4.1 Measurement Error in the Dependent Variable 76
4.4.2 Measurement Error in an Explanatory Variable 78
Problems 82
5 Instrumental VariablesEstimation of Single-Equation Linear Models 89
5.1 Instrumental Variables and Two-Stage Least Squares 89
5.1.1 Motivation forInstrumental Variables Estimation 89
5.1.2 Multiple Instruments: Two-Stage LeastSquares 96
5.2 General Treatment of Two-Stage Least Squares 98
5.2.1 Consistency 98
5.2.2 Asymptotic Normality of Two-Stage Least Squares 101
5.2.3 Asymptotic E‰ciency of Two-Stage Least Squares 103
5.2.4 Hypothesis Testing with Two-Stage Least Squares 104
5.2.5 Heteroskedasticity-Robust Inference for Two-StageLeast
Squares 106
5.2.6 PotentialPitfallswithTwo-Stage Least Squares 107
5.3 IV Solutions to theOmitted Variables and Measurement Error
Problems 112
5.3.1 LeavingtheOmittedFactors in the Error Term 112
5.3.2 Solutions Using Indicators of the Unobservables 112
Problems 115
Contents vii
6 AdditionalSingle-Equation Topics 123
6.1 Estimation with GeneratedRegressorsand Instruments 123
6.1.1 Ordinary Least Squares with GeneratedRegressors 123
6.1.2 Two-Stage Least Squares with GeneratedInstruments 124
6.1.3 GeneratedInstruments and Regressors 125
6.2 ControlFunctionApproach to Endogeneity 126
6.3 SomeSpecification Tests 129
6.3.1 Testing for Endogeneity 129
6.3.2 Testing Overidentifying Restrictions 134
6.3.3 Testing Functional Form 137
6.3.4 Testing for Heteroskedasticity 138
6.4 Correlated RandomCoe‰cient Models 141
6.4.1 When Is the Usual IVEstimator Consistent? 142
6.4.2 Control FunctionApproach 145
6.5 Pooled Cross Sections and Di¤erence-in-Di¤erencesEstimation 146
6.5.1 Pooled Cross Sections over Time 146
6.5.2 Policy Analysisand Di¤erence-in-Di¤erences Estimation 147
Problems 152
Appendix 6A 157
7 Estimating Systemsof Equationsby Ordinary Least Squares and
Generalized LeastSquares 161
7.1 Introduction 161
7.2 SomeExamples 161
7.3 System Ordinary Least Squares Estimation of aMultivariate Linear
System 166
7.3.1 Preliminaries 166
7.3.2 Asymptotic Properties of System Ordinary Least Squares 167
7.3.3 Testing MultipleHypotheses 172
7.4 ConsistencyandAsymptoticNormalityofGeneralizedLeastSquares 173
7.4.1 Consistency 173
7.4.2 Asymptotic Normality 175
7.5 FeasibleGeneralized Least Squares 176
7.5.1 Asymptotic Properties 176
7.5.2 Asymptotic Variance of Feasible GeneralizedLeastSquares
under aStandard Assumption 180
viii Contents
7.5.3 Properties of Feasible Generalized Least Squares with
(PossiblyIncorrect) Restrictionson the Unconditional
Variance Matrix 182
7.6 Testing the Useof Feasible Generalized Least Squares 183
7.7 SeeminglyUnrelated Regressions,Revisited 185
7.7.1 Comparisonbetween OrdinaryLeastSquaresand Feasible
Generalized Least Squares for Seemingly Unrelated
Regressions Systems 185
7.7.2 Systems with Cross EquationRestrictions 188
7.7.3 SingularVariance Matricesin Seemingly Unrelated
Regressions Systems 189
7.8 Linear Panel Data Model, Revisited 191
7.8.1 Assumptions forPooled Ordinary Least Squares 191
7.8.2 Dynamic Completeness 194
7.8.3 Note onTime SeriesPersistence 196
7.8.4 Robust Asymptotic Variance Matrix 197
7.8.5 Testing for Serial Correlationand Heteroskedasticity after
Pooled Ordinary LeastSquares 198
7.8.6 Feasible Generalized Least Squares Estimation under Strict
Exogeneity 200
Problems 202
8 SystemEstimation by Instrumental Variables 207
8.1 Introductionand Examples 207
8.2 General LinearSystem of Equations 210
8.3 Generalized Method of Moments Estimation 213
8.3.1 General Weighting Matrix 213
8.3.2 System Two-StageLeastSquares Estimator 216
8.3.3 Optimal Weighting Matrix 217
8.3.4 The GeneralizedMethod of Moments Three-Stage Least
Squares Estimator 219
8.4 Generalized Instrumental Variables Estimator 222
8.4.1 Derivation of the Generalized Instrumental Variables
Estimator and Its Asymptotic Properties 222
8.4.2 Comparisonof Generalized Method of Moment,
Generalized Instrumental Variables, and the Traditional
Three-Stage Least Squares Estimator 224
Contents ix
8.5 Testing Using Generalized Methodof Moments 226
8.5.1 Testing ClassicalHypotheses 226
8.5.2 Testing OveridentificationRestrictions 228
8.6 MoreE‰cient Estimation and Optimal Instruments 229
8.7 SummaryComments onChoosing an Estimator 232
Problems 233
9 Simultaneous EquationsModels 239
9.1 Scope of Simultaneous Equations Models 239
9.2 Identification in aLinear System 241
9.2.1 Exclusion Restrictions and Reduced Forms 241
9.2.2 General Linear Restrictionsand Structural Equations 245
9.2.3 Unidentified, Just Identified, and Overidentified Equations 251
9.3 Estimation after Identification 252
9.3.1 Robustness-E‰ciency Trade-o¤ 252
9.3.2 When Are 2SLS and 3SLS Equivalent? 254
9.3.3 Estimating the Reduced Form Parameters 255
9.4 Additional Topics in LinearSimultaneous EquationsMethods 256
9.4.1 Using Cross EquationRestrictions to Achieve Identification 256
9.4.2 Using Covariance Restrictions to Achieve Identification 257
9.4.3 Subtleties Concerning Identificationand E‰ciency inLinear
Systems 260
9.5 Simultaneous Equations ModelsNonlinear inEndogenous
Variables 262
9.5.1 Identification 262
9.5.2 Estimation 266
9.5.3 Control FunctionEstimation for Triangular Systems 268
9.6 Di¤erentInstruments for Di¤erent Equations 271
Problems 273
10 Basic Linear UnobservedE¤ects PanelData Models 281
10.1 Motivation: Omitted VariablesProblem 281
10.2 Assumptionsaboutthe Unobserved E¤ects and Explanatory
Variables 285
10.2.1 Randomor Fixed E¤ects? 285
10.2.2 StrictExogeneityAssumptionsontheExplanatoryVariables 287
10.2.3 Some Examplesof Unobserved E¤ects Panel Data Models 289