Table of Contents

Chapter 1 Regression Models 1

• 1.1 Introduction 1
• 1.2 Distributions, Densities, and Moments 3
• 1.3 The Specification of Regression Models 15
• 1.4 Matrix Algebra 22
• 1.5 Method-of-Moments Estimation 30
• 1.6 Notes on the Exercises 37
• 1.7 Exercises 38

Chapter 2 The Geometry of Linear Regression 42

• 2.1 Introduction 42
• 2.2 The Geometry of Vector Spaces 43
• 2.3 The Geometry of OLS Estimation 54
• 2.4 The Frisch-Waugh-Lovell Theorem 62
• 2.5 Applications of the FWL Theorem 69
• 2.6 Influential Observations and Leverage 76
• 2.7 Final Remarks 81
• 2.8 Exercises 82

Chapter 3 The Statistical Properties of Ordinary Least Squares 86

• 3.1 Introduction 86
• 3.2 Are OLS Parameter Estimators Unbiased? 88
• 3.3 Are OLS Parameter Estimators Consistent? 92
• 3.4 The Covariance Matrix of the OLS Parameter Estimates 97
• 3.5 Efficiency of the OLS Estimator 104
• 3.6 Residuals and Error Terms 107
• 3.7 Misspecification of Linear Regression Models 111
• 3.8 Measures of Goodness of Fit 115
• 3.9 Final Remarks 118
• 3.10 Exercises 118

Chapter 4 Hypothesis Testing in Linear Regression Models 122

• 4.1 Introduction 122
• 4.2 Basic Ideas 122
• 4.3 Some Common Distributions 129
• 4.4 Exact Tests in the Classical Normal Linear Model 138
• 4.5 Large-Sample Tests in Linear Regression Models 146
• 4.6 Simulation-Based Tests 155
• 4.7 The Power of Hypothesis Tests 166
• 4.8 Final Remarks 172
• 4.9 Exercises 172

Chapter 5 Confidence Intervals 177

• 5.1 Introduction 177
• 5.2 Exact and Asymptotic Confidence Intervals 178
• 5.3 Bootstrap Confidence Intervals 185
• 5.4 Confidence Regions 189
• 5.5 Heteroskedasticity-Consistent Covariance Matrices 196
• 5.6 The Delta Method 202
• 5.7 Final Remarks 209
• 5.8 Exercises 209

Chapter 6 Nonlinear Regression 213

• 6.1 Introduction 213
• 6.2 Method-of-Moments Estimators for Nonlinear Models 215
• 6.3 Nonlinear Least Squares 224
• 6.4 Computing NLS Estimates 228
• 6.5 The Gauss-Newton Regression 235
• 6.6 One-Step Estimation 240
• 6.7 Hypothesis Testing 243
• 6.8 Heteroskedasticity-Robust Tests 250
• 6.9 Final Remarks 253
• 6.10 Exercises 253

Chapter 7 Generalized Least Squares and Related Topics 257

• 7.1 Introduction 257
• 7.2 The GLS Estimator 258
• 7.3 Computing GLS Estimates 260
• 7.4 Feasible Generalized Least Squares 264
• 7.5 Heteroskedasticity 266
• 7.6 Autoregressive and Moving-Average Processes 270
• 7.7 Testing for Serial Correlation 275
• 7.8 Estimating Models with Autoregressive Errors 285
• 7.9 Specification Testing and Serial Correlation 292
• 7.10 Models for Panel Data 298
• 7.11 Final Remarks 305
• 7.12 Exercises 306

Chapter 8 Instrumental Variables Estimation 311

• 8.1 Introduction 311
• 8.2 Correlation Between Error Terms and Regressors 312
• 8.3 Instrumental Variables Estimation 315
• 8.4 Finite-Sample Properties of IV Estimators 324
• 8.5 Hypothesis Testing 330
• 8.6 Testing Overidentifying Restrictions 336
• 8.7 Durbin-Wu-Hausman Tests 338
• 8.8 Bootstrap Tests 342
• 8.9 IV Estimation of Nonlinear Models 345
• 8.10 Final Remarks 347
• 8.11 Exercises 347

Chapter 9 The Generalized Method of Moments 352

• 9.1 Introduction 352
• 9.2 GMM Estimators for Linear Regression Models 353
• 9.3 HAC Covariance Matrix Estimation 362
• 9.4 Tests Based on the GMM Criterion Function 365
• 9.5 GMM Estimators for Nonlinear Models 369
• 9.6 The Method of Simulated Moments 383
• 9.7 Final Remarks 393
• 9.8 Exercises 394

Chapter 10 The Method of Maximum Likelihood 399

• 10.1 Introduction 399
• 10.2 Basic Concepts of Maximum Likelihood Estimation 399
• 10.3 Asymptotic Properties of ML Estimators 408
• 10.4 The Covariance Matrix of the ML Estimator 415
• 10.5 Hypothesis Testing 420
• 10.6 The Asymptotic Theory of the Three Classical Tests 429
• 10.7 ML Estimation of Models with Autoregressive Errors 435
• 10.8 Transformations of the Dependent Variable 437
• 10.9 Final Remarks 443
• 10.10 Exercises 444

Chapter 11 Discrete and Limited Dependent Variables 451

• 11.1 Introduction 451
• 11.2 Binary Response Models: Estimation 452
• 11.3 Binary Response Models: Inference 460
• 11.4 Models for More Than Two Discrete Responses 466
• 11.5 Models for Count Data 475
• 11.6 Models for Censored and Truncated Data 481
• 11.7 Sample Selectivity 486
• 11.8 Duration Models 489
• 11.9 Final Remarks 495
• 11.10 Exercises 495

Chapter 12 Multivariate Models 501

• 12.1 Introduction 501
• 12.2 Seemingly Unrelated Linear Regressions 501
• 12.3 Systems of Nonlinear Regressions 518
• 12.4 Linear Simultaneous Equations Models 522
• 12.5 Maximum Likelihood Estimation 532
• 12.6 Nonlinear Simultaneous Equations Models 540
• 12.7 Final Remarks 543
• 12.8 Appendix: Detailed Results on FIML and LIML 544
• 12.9 Exercises 550

Chapter 13 Methods for Stationary Time-Series Data 556

• 13.1 Introduction 556
• 13.2 Autoregressive and Moving-Average Processes 557
• 13.3 Estimating AR, MA, and ARMA Models 565
• 13.4 Single-Equation Dynamic Models 575
• 13.5 Seasonality 579
• 13.6 Autoregressive Conditional Heteroskedasticity 587
• 13.7 Vector Autoregressions 595
• 13.8 Final Remarks 599
• 13.9 Exercises 599

Chapter 14 Unit Roots and Cointegration 605

• 14.1 Introduction 605
• 14.2 Random Walks and Unit Roots 605
• 14.3 Unit Root Tests 613
• 14.4 Serial Correlation and Unit Root Tests 620
• 14.5 Cointegration 624
• 14.6 Testing for Cointegration 636
• 14.7 Final Remarks 644
• 14.8 Exercises 644

Chapter 15 Testing the Specification of Econometric Models 650

• 15.1 Introduction 650
• 15.2 Specification Tests Based on Artificial Regressions 651
• 15.3 Nonnested Hypothesis Tests 665
• 15.4 Model Selection Based on Information Criteria 675
• 15.5 Nonparametric Estimation 677
• 15.6 Final Remarks 692
• 15.7 Appendix: Test Regressors in Artificial Regressions 692
• 15.8 Exercises 695

References 702

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