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Analysis of Panel Data (2nd Edition, 2003) by CHENG HSIAO (University of Southern California)
Chapter 1. Introduction 1
1.1 Advantages of Panel Data 1
1.2 Issues Involved in Utilizing Panel Data 8
1.2.1 Heterogeneity Bias 8
1.2.2 Selectivity Bias 9
1.3 Outline of the Monograph 11
Chapter 2. Analysis of Covariance 14
2.1 Introduction 14
2.2 Analysis of Covariance 15
2.3 An Example 21
Chapter 3. Simple Regression with Variable Intercepts 27
3.1 Introduction 27
3.2 Fixed-Effects Models: Least-Squares Dummy-Variable
Approach 30
3.3 Random-Effects Models: Estimation of
Variance-Components Models 34
3.3.1 Covariance Estimation 35
3.3.2 Generalized-Least-Squares Estimation 35
3.3.3 Maximum Likelihood Estimation 39
3.4 Fixed Effects or Random Effects 41
3.4.1 An Example 41
3.4.2 Conditional Inference or Unconditional (Marginal)
Inference 43
3.4.2.a Mundlak’s Formulation 44
3.4.2.b Conditional and Unconditional Inferences in the
Presence or Absence of Correlation between
Individual Effects and Attributes 46viii Contents
3.5 Tests for Misspecification 49
3.6 Models with Specific Variables and Both Individual- and
Time-Specific Effects 51
3.6.1 Estimation of Models with Individual-Specific
Variables 51
3.6.2 Estimation of Models with Both Individual and
Time Effects 53
3.7 Heteroscedasticity 55
3.8 Models with Serially Correlated Errors 57
3.9 Models with Arbitrary Error Structure – Chamberlain π
Approach 60
Appendix 3A: Consistency and Asymptotic Normality of the
Minimum-Distance Estimator 65
Appendix 3B: Characteristic Vectors and the Inverse of the
Variance–Covariance Matrix of a
Three-Component Model 67
Chapter 4. Dynamic Models with Variable Intercepts 69
4.1 Introduction 69
4.2 The Covariance Estimator 71
4.3 Random-Effects Models 73
4.3.1 Bias in the OLS Estimator 73
4.3.2 Model Formulation 75
4.3.3 Estimation of Random-Effects Models 78
4.3.3.a Maximum Likelihood Estimator 78
4.3.3.b Generalized-Least-Squares Estimator 84
4.3.3.c Instrumental-Variable Estimator 85
4.3.3.d Generalized Method of Moments
Estimator 86
4.3.4 Testing Some Maintained Hypotheses on Initial
Conditions 90
4.3.5 Simulation Evidence 91
4.4 An Example 92
4.5 Fixed-Effects Models 95
4.5.1 Transformed Likelihood Approach 96
4.5.2 Minimum-Distance Estimator 98
4.5.3 Relations between the Likelihood-Based
Estimator and the Generalized Method of
Moments Estimator (GMM) 99
4.5.4 Random- versus Fixed-Effects Specification 101
4.6 Estimation of Dynamic Models with Arbitary Correlations
in the Residuals 103
4.7 Fixed-Effects Vector Autoregressive Models 105
4.7.1 Model Formulation 105
4.7.2 Generalized Method of Moments (GMM) Estimation 107Contents ix
4.7.3 (Transformed) Maximum Likelihood Estimator 109
4.7.4 Minimum-Distance Estimator 109
Appendix 4A: Derivation of the Asymptotic Covariance Matrix
of the Feasible MDE 111
Chapter 5. Simultaneous-Equations Models 113
5.1 Introduction 113
5.2 Joint Generalized-Least-Squares Estimation Technique 116
5.3 Estimation of Structural Equations 119
5.3.1 Estimation of a Single Equation in the Structural Model 119
5.3.2 Estimation of the Complete Structural System 124
5.4 Triangular System 127
5.4.1 Identification 127
5.4.2 Estimation 129
5.4.2.a Instrumental-Variable Method 130
5.4.2.b Maximum-Likelihood Method 133
5.4.3 An Example 136
Appendix 5A 138
Chapter 6. Variable-Coefficient Models 141
6.1 Introduction 141
6.2 Coefficients That Vary over Cross-Sectional Units 143
6.2.1 Fixed-Coefficient Model 144
6.2.2 Random-Coefficient Model 144
6.2.2.a The Model 144
6.2.2.b Estimation 145
6.2.2.c Predicting Individual Coefficients 147
6.2.2.d Testing for Coefficient Variation 147
6.2.2.e Fixed or Random Coefficients 149
6.2.2.f An Example 150
6.3 Coefficients That Vary over Time and Cross-Sectional Units 151
6.3.1 The Model 151
6.3.2 Fixed-Coefficient Model 153
6.3.3 Random-Coefficient Model 153
6.4 Coefficients That Evolve over Time 156
6.4.1 The Model 156
6.4.2 Predicting t
by the Kalman Filter 158
6.4.3 Maximum Likelihood Estimation 161
6.4.4 Tests for Parameter Constancy 162
6.5 Coefficients That Are Functions of Other Exogenous
Variables 163
6.6 A Mixed Fixed- and Random-Coefficients Model 165
6.6.1 Model Formulation 165
6.6.2 A Bayes Solution 168
6.6.3 An Example 170x Contents
6.6.4 Random or Fixed Parameters 172
6.6.4.a An Example 172
6.6.4.b Model Selection 173
6.7 Dynamic Random-Coefficient Models 175
6.8 An Example – Liquidity Constraints and Firm Investment
Expenditure 180
Appendix 6A: Combination of Two Normal Distributions 185
Chapter 7. Discrete Data 188
7.1 Introduction 188
7.2 Some Discrete-Response Models 188
7.3 Parametric Approach to Static Models with Heterogeneity 193
7.3.1 Fixed-Effects Models 194
7.3.1.a Maximum Likelihood Estimator 194
7.3.1.b Conditions for the Existence of a Consistent
Estimator 195
7.3.1.c Some Monte Carlo Evidence 198
7.3.2 Random-Effects Models 199
7.4 Semiparametric Approach to Static Models 202
7.4.1 Maximum Score Estimator 203
7.4.2 A Root-N Consistent Semiparametric Estimator 205
7.5 Dynamic Models 206
7.5.1 The General Model 206
7.5.2 Initial Conditions 208
7.5.3 A Conditional Approach 211
7.5.4 State Dependence versus Heterogeneity 216
7.5.5 Two Examples 218
7.5.5.a Female Employment 218
7.5.5.b Household Brand Choices 221
Chapter 8. Truncated and Censored Data 225
8.1 Introduction 225
8.2 An Example – Nonrandomly Missing Data 234
8.2.1 Introduction 234
8.2.2 A Probability Model of Attrition and Selection Bias 235
8.2.3 Attrition in the Gary Income-Maintenance Experiment 238
8.3 Tobit Models with Random Individual Effects 240
8.4 Fixed-Effects Estimator 243
8.4.1 Pairwise Trimmed Least-Squares and
Least-Absolute-Deviation Estimators for
Truncated and Censored Regressions 243
8.4.1.a Truncated Regression 243
8.4.1.b Censored Regressions 249
8.4.2 A Semiparametric Two-Step Estimator for the
Endogenously Determined Sample Selection Model 253Contents xi
8.5 An Example: Housing Expenditure 255
8.6 Dynamic Tobit Models 259
8.6.1 Dynamic Censored Models 259
8.6.2 Dynamic Sample Selection Models 265
Chapter 9. Incomplete Panel Data 268
9.1 Estimating Distributed Lags in Short Panels 268
9.1.1 Introduction 268
9.1.2 Common Assumptions 270
9.1.3 Identification Using Prior Structure of the Process
of the Exogenous Variable 271
9.1.4 Identification Using Prior Structure of the Lag
Coefficients 275
9.1.5 Estimation and Testing 277
9.2 Rotating or Randomly Missing Data 279
9.3 Pseudopanels (or Repeated Cross-Sectional
Data) 283
9.4 Pooling of a Single Cross-Sectional and a Single
Time-Series Data Set 285
9.4.1 Introduction 285
9.4.2 The Likelihood Approach to Pooling Cross-Sectional
and Time-Series Data 287
9.4.3 An Example 288
Chapter 10. Miscellaneous Topics 291
10.1 Simulation Methods 291
10.2 Panels with Large N and T 295
10.3 Unit-Root Tests 298
10.4 Data with Multilevel Structures 302
10.5 Errors of Measurement 304
10.6 Modeling Cross-Sectional Dependence 309
Chapter 11. A Summary View 311
11.1 Introduction 311
11.2 Benefits and Limitations of Panel Data 311
11.2.1 Increasing Degrees of Freedom and Lessening
the Problem of Multicollinearity 311
11.2.2 Identification and Discrimination between
Competing Hypotheses 312
11.2.3 Reducing Estimation Bias 313
11.2.3.a Omitted-Variable Bias 313
11.2.3.b Bias Induced by the Dynamic Structure
of a Model 315
11.2.3.c Simultaneity Bias 316
11.2.3.d Bias Induced by Measurement Errors 316xii Contents
11.2.4 Providing Micro Foundations for Aggregate Data
Analysis 316
11.3 Efficiency of the Estimates
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