BOOK-Econometric Theory and Methods.PDF

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Contents
Preface ix
Data, Solutions, and Corrections xviii
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
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
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
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
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2 Contents
4.6 Simulation-Based Tests 155
4.7 The Power of Hypothesis Tests 166
4.8 Final Remarks 172
4.9 Exercises 172
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
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
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
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
Contents 3
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
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
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
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
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
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
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
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