Econometric Analysis Of Cross Section And Panel Data - Wooldridge

Econometric Analysis of Cross Section and Panel Data

Je¤rey M. Wooldridge

The MIT Press
Cambridge, Massachusetts
London, England

Contents

Preface
Acknowledgments

xvii
xxiii

I

INTRODUCTION AND BACKGROUND

1

1
1.1
1.2

Introduction
Causal Relationships and Ceteris Paribus Analysis
The Stochastic Setting and Asymptotic Analysis
1.2.1 Data Structures
1.2.2Asymptotic Analysis
Some Examples
Why Not Fixed Explanatory Variables?

3
3
4
4
7
7
9

1.3
1.4
2
2.1
2.2

2.3

3
3.1
3.2
3.3
3.4
3.5

Conditional Expectations and Related Concepts in Econometrics
The Role of Conditional Expectations in Econometrics
Features of Conditional Expectations
2.2.1 Definition and Examples
2.2.2 Partial E¤ects, Elasticities, and Semielasticities2.2.3 The Error Form of Models of Conditional Expectations
2.2.4 Some Properties of Conditional Expectations
2.2.5 Average Partial E¤ects
Linear Projections
Problems
Appendix 2A
2.A.1 Properties of Conditional Expectations
2.A.2 Properties of Conditional Variances
2.A.3 Properties of Linear Projections

13
13
14
14
15
18
19
22
24
27
29
29
31
32

Basic Asymptotic TheoryConvergence of Deterministic Sequences
Convergence in Probability and Bounded in Probability
Convergence in Distribution
Limit Theorems for Random Samples
Limiting Behavior of Estimators and Test Statistics
3.5.1 Asymptotic Properties of Estimators
3.5.2 Asymptotic Properties of Test Statistics
Problems

35
35
36
38
39
40
40
43
45

vi

Contents

II

LINEAR MODELS

47

44.1
4.2

The Single-Equation Linear Model and OLS Estimation
Overview of the Single-Equation Linear Model
Asymptotic Properties of OLS
4.2.1 Consistency
4.2.2 Asymptotic Inference Using OLS
4.2.3 Heteroskedasticity-Robust Inference
4.2.4 Lagrange Multiplier (Score) Tests
OLS Solutions to the Omitted Variables Problem
4.3.1 OLS Ignoring the Omitted Variables
4.3.2 The ProxyVariable–OLS Solution
4.3.3 Models with Interactions in Unobservables
Properties of OLS under Measurement Error
4.4.1 Measurement Error in the Dependent Variable
4.4.2 Measurement Error in an Explanatory Variable
Problems

49
49
51
52
54
55
58
61
61
63
67
70
71
73
76

4.3

4.4

5
5.1

5.2

5.3

6
6.1

83
83
83
90
92
92
94
96
97
100
101

Instrumental VariablesEstimation of Single-Equation Linear Models
Instrumental Variables and Two-Stage Least Squares
5.1.1 Motivation for Instrumental Variables Estimation
5.1.2 Multiple Instruments: Two-Stage Least Squares
General Treatment of 2SLS
5.2.1 Consistency
5.2.2 Asymptotic Normality of 2SLS
5.2.3 Asymptotic E‰ciency of 2SLS
5.2.4 Hypothesis Testing with 2SLS
5.2.5 Heteroskedasticity-Robust Inferencefor 2SLS
5.2.6 Potential Pitfalls with 2SLS
IV Solutions to the Omitted Variables and Measurement Error
Problems
5.3.1 Leaving the Omitted Factors in the Error Term
5.3.2 Solutions Using Indicators of the Unobservables
Problems

105
105
105
107

Additional Single-Equation Topics
Estimation with Generated Regressors and Instruments

115
115

Contents

6.2

6.3

7
7.1
7.27.3

7.4

7.5

7.6
7.7

vii

6.1.1 OLS with Generated Regressors
6.1.2 2SLS with Generated Instruments
6.1.3 Generated Instruments and Regressors
Some Specification Tests
6.2.1 Testing for Endogeneity
6.2.2 Testing Overidentifying Restrictions
6.2.3 Testing Functional Form
6.2.4 Testing for Heteroskedasticity
Single-Equation Methods under Other Sampling Schemes
6.3.1 PooledCross Sections over Time
6.3.2 Geographically Stratified Samples
6.3.3 Spatial Dependence
6.3.4 Cluster Samples
Problems
Appendix 6A

115
116
117
118
118
122
124
125
128
128
132
134
134
135
139

Estimating Systems of Equations by OLS and GLS
Introduction
Some Examples
System OLS Estimation of a Multivariate Linear System
7.3.1 Preliminaries
7.3.2 Asymptotic Properties...