1 Introduction 1
1.1 Panel Data: Some Examples 1
1.2 Why Should We Use Panel Data? Their Bene?ts and Limitations 4
Note 9
2 The One-way Error Component Regression Model 11
2.1 Introduction 11
2.2 The Fixed Effects Model 12
2.3 The Random Effects Model 14
2.3.1 Fixed vs Random 18
2.4 Maximum Likelihood Estimation 19
2.5 Prediction 20
2.6 Examples 21
2.6.1 Example 1: Grunfeld Investment Equation 21
2.6.2 Example 2: Gasoline Demand 23
2.6.3 Example 3: Public Capital Productivity 25
2.7 Selected Applications 28
2.8 Computational Note 28
Notes 28
Problems 29
3 The Two-way Error Component Regression Model 33
3.1 Introduction 33
3.2 The Fixed Effects Model 33
3.2.1 Testing for Fixed Effects 34
3.3 The Random Effects Model 35
3.3.1 Monte Carlo Experiment 39
3.4 Maximum Likelihood Estimation 40
3.5 Prediction 42
3.6 Examples 43
3.6.1 Example 1: Grunfeld Investment Equation 43
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3.6.2 Example 2: Gasoline Demand 45
3.6.3 Example 3: Public Capital Productivity 45
3.7 Selected Applications 47
Notes 47
Problems 48
4 Test of Hypotheses with Panel Data 53
4.1 Tests for Poolability of the Data 53
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4.1.3 Examples 57
4.1.4 Other Tests for Poolability 58
4.2 Tests for Individual and Time Effects 59
4.2.1 The Breusch–Pagan Test 59
4.2.2 King and Wu, Honda and the Standardized Lagrange
Multiplier Tests 61
4.2.3 Gourieroux, Holly and Monfort Test 62
4.2.4 Conditional LM Tests 62
4.2.5 ANOVA F and the Likelihood Ratio Tests 63
4.2.6 Monte Carlo Results 64
4.2.7 An Illustrative Example 65
4.3 Hausman’s Speci?cation Test 66
4.3.1 Example 1: Grunfeld Investment Equation 70
4.3.2 Example 2: Gasoline Demand 71
4.3.3 Example 3: Strike Activity 72
4.3.4 Example 4: Production Behavior of Sawmills 72
4.3.5 Example 5: The Marriage Wage Premium 73
4.3.6 Example 6: Currency Union and Trade 73
4.3.7 Hausman’s Test for the Two-way Model 73
4.4 Further Reading 74
Notes 74
Problems 75
5 Heteroskedasticity and Serial Correlation in the Error Component Model 79
5.1 Heteroskedasticity 79
5.1.1 Testing for Homoskedasticity in an Error Component Model 82
5.2 Serial Correlation 84
5.2.1 The AR(1) Process 84
5.2.2 The AR(2) Process 86
5.2.3 The AR(4) Process for Quarterly Data 87
5.2.4 The MA(1) Process 88
5.2.5 Unequally Spaced Panels with AR(1) Disturbances 89
5.2.6 Prediction 91
5.2.7 Testing for Serial Correlation and Individual Effects 93
5.2.8 Extensions 103
Notes 104
Problems 104
4.1.1 Test for Poolability under u ～ N(0, σ I
4.1.2 Test for Poolability under the General Assumption u ～ N(0,)55
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6 Seemingly Unrelated Regressions with Error Components 107
6.1 The One-way Model 107
6.2 The Two-way Model 108
6.3 Applications and Extensions 109
Problems 111
7 Simultaneous Equations with Error Components 113
7.1 Single Equation Estimation 113
7.2 Empirical Example: Crime in North Carolina 116
7.3 System Estimation 121
7.4 The Hausman and Taylor Estimator 124
7.5 Empirical Example: Earnings Equation Using PSID Data 128
7.6 Extensions 130
Notes 133
Problems 133
8 Dynamic Panel Data Models 135
8.1 Introduction 135
8.2 The Arellano and Bond Estimator 136
8.2.1 Testing for Individual Effects in Autoregressive Models 138
8.2.2 Models with Exogenous Variables 139
8.3 The Arellano and Bover Estimator 142
8.4 The Ahn and Schmidt Moment Conditions 145
8.5 The Blundell and Bond System GMM Estimator 147
8.6 The Keane and Runkle Estimator 148
8.7 Further Developments 150
8.8 Empirical Example: Dynamic Demand for Cigarettes 156
8.9 Further Reading 158
Notes 161
Problems 162
9 Unbalanced Panel Data Models 165
9.1 Introduction 165
9.2 The Unbalanced One-way Error Component Model 165
9.2.1 ANOVA Methods 167
9.2.2 Maximum Likelihood Estimators 169
9.2.3 Minimum Norm and Minimum Variance Quadratic Unbiased
Estimators (MINQUE and MIVQUE) 170
9.2.4 Monte Carlo Results 171
9.3 Empirical Example: Hedonic Housing 171
9.4 The Unbalanced Two-way Error Component Model 175
9.4.1 The Fixed Effects Model 175
9.4.2 The Random Effects Model 176
9.5 Testing for Individual and Time Effects Using Unbalanced Panel Data 177
9.6 The Unbalanced Nested Error Component Model 180
9.6.1 Empirical Example 181
Notes 183
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10 Special Topics 187
10.1 Measurement Error and Panel Data 187
10.2 Rotating Panels 191
10.3 Pseudo-panels 192
10.4 Alternative Methods of Pooling Time Series of Cross-section Data 195
10.5 Spatial Panels 197
10.6 Short-run vs Long-run Estimates in Pooled Models 200
10.7 Heterogeneous Panels 201
Notes 206
Problems 206
11 Limited Dependent Variables and Panel Data 209
11.1 Fixed and Random Logit and Probit Models 209
11.2 Simulation Estimation of Limited Dependent Variable Models with
Panel Data 215
11.3 Dynamic Panel Data Limited Dependent Variable Models 216
11.4 Selection Bias in Panel Data 219
11.5 Censored and Truncated Panel Data Models 224
11.6 Empirical Applications 228
11.7 Empirical Example: Nurses’ Labor Supply 229
11.8 Further Reading 231
Notes 234
Problems 235
12 Nonstationary Panels 237
12.1 Introduction 237
12.2 Panel Unit Roots Tests Assuming Cross-sectional Independence 239
12.2.1 Levin, Lin and Chu Test 240
12.2.2 Im, Pesaran and Shin Test 242
12.2.3 Breitung’s Test 243
12.2.4 Combining p-Value Tests 244
12.2.5 Residual-Based LM Test 246
12.3 Panel Unit Roots Tests Allowing for Cross-sectional Dependence 247
12.4 Spurious Regression in Panel Data 250
12.5 Panel Cointegration Tests 252
12.5.1 Residual-Based DF and ADF Tests (Kao Tests) 252
12.5.2 Residual-Based LM Test 253
12.5.3 Pedroni Tests 254
12.5.4 Likelihood-Based Cointegration Test 255
12.5.5 Finite Sample Properties 256
12.6 Estimation and Inference in Panel Cointegration Models 257
12.7 Empirical Example: Purchasing Power Parity 259
12.8 Further Reading 261
Notes 263
Problem