Russell Davidson and James G. MacKinnon

Econometric Theory and Methods

Econometric Theory and Methods was published by Oxford University Press (New York) in October, 2003 with a 2004 copyright. The ISBN is 0-19-512372-7.

Econometric Theory and Methods provides a unified treatment of modern econometric theory and practical econometric methods at the beginning graduate level. The book is suitable for both one-term and two-term courses at the Masters or Ph.D. level. It could also be used in final-year undergraduate courses at good schools if students have sufficient preparation. Mathematical and statistical concepts are introduced as they are needed, and the level of the book increases as more theoretical tools are developed.

The method of moments is used to motivate a wide variety of estimators and tests. The geometrical approach to least squares is also used extensively. Simulation methods, including the bootstrap, are introduced quite early on. Every chapter has a large number of exercises, some theoretical, some empirical, and some involving simulation. Answers to all the exercises will be available to instructors on a CD-ROM, and answers to starred exercises (which are generally quite challenging) are available on this website.

The book deals with a large number of modern topics. In addition to bootstrap and Monte Carlo tests, these include sandwich covariance matrix estimators, artificial regressions, estimating functions and the generalized method of moments, the method of simulated moments, indirect inference, the multinomial logit model, models for duration and count data, unit roots and cointegration, nonnested hypothesis tests, conditional moment tests, and kernel estimation.

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

Author Index    722

Subject Index    726