Foundations of Econometrics

1.1 Introduction......Page 1
1.2 Distributions, Densities, and Moments......Page 3
1.3 The Specification of Regression Models......Page 15
1.4 Matrix Algebra......Page 22
1.5 Method of Moments Estimation......Page 30
1.6 Notes on the Exercises......Page 36
1.7 Exercises......Page 37
2.1 Introduction......Page 41
2.2 The Geometry of Vector Spaces......Page 42
2.3 The Geometry of OLS Estimation......Page 53
2.4 The Frisch- Waugh- Lovell Theorem......Page 62
2.5 Applications of the FWL Theorem......Page 68
2.6 Influential Observations and Leverage......Page 75
2.7 Final Remarks......Page 80
2.8 Exercises......Page 81
3.1 Introduction......Page 85
3.2 Are OLS Parameter Estimators Unbiased?......Page 87
3.3 Are OLS Parameter Estimators Consistent?......Page 91
3.4 The Covariance Matrix of the OLS Parameter Estimates......Page 96
3.5 Efficiency of the OLS Estimator......Page 103
3.6 Residuals and Error Terms......Page 106
3.7 Misspecification of Linear Regression Models......Page 110
3.8 Measures of Goodness of Fit......Page 114
3.10 Exercises......Page 117
4.2 Basic Ideas......Page 121
4.3 Some Common Distributions......Page 128
4.4 Exact Tests in the Classical Normal Linear Model......Page 137
4.5 Large- Sample Tests in Linear Regression Models......Page 145
4.6 Simulation- Based Tests......Page 154
4.7 The Power of Hypothesis Tests......Page 165
4.9 Exercises......Page 171
5.1 Introduction......Page 175
5.2 Exact and Asymptotic Confidence Intervals......Page 176
5.3 Bootstrap Confidence Intervals......Page 183
5.4 Confidence Regions......Page 187
5.5 Heteroskedasticity- Consistent Covariance Matrices......Page 194
5.6 The Delta Method......Page 200
5.8 Exercises......Page 207
6.1 Introduction......Page 210
6.2 Method of Moments Estimators for Nonlinear Models......Page 212
6.3 Nonlinear Least Squares......Page 221
6.4 Computing NLS Estimates......Page 225
6.5 The Gauss- Newton Regression......Page 232
6.6 One- Step Estimation......Page 237
6.7 Hypothesis Testing......Page 240
6.8 Heteroskedasticity- Robust Tests......Page 247
6.9 Final Remarks......Page 249
6.10 Exercises......Page 250
7.1 Introduction......Page 254
7.2 The GLS Estimator......Page 255
7.3 Computing GLS Estimates......Page 257
7.4 Feasible Generalized Least Squares......Page 261
7.5 Heteroskedasticity......Page 263
7.6 Autoregressive and Moving Average Processes......Page 267
7.7 Testing for Serial Correlation......Page 272
7.8 Estimating Models with Autoregressive Errors......Page 281
7.9 Specification Testing and Serial Correlation......Page 289
7.10 Models for Panel Data......Page 295
7.11 Final Remarks......Page 302
7.12 Exercises......Page 303
8.1 Introduction......Page 308
8.2 Correlation Between Error Terms and Regressors......Page 309
8.3 Instrumental Variables Estimation......Page 312
8.4 Finite- Sample Properties of IV Estimators......Page 321
8.5 Hypothesis Testing......Page 327
8.6 Testing Overidentifying Restrictions......Page 333
8.7 Durbin- Wu- Hausman Tests......Page 335
8.8 Bootstrap Tests......Page 339
8.9 IV Estimation of Nonlinear Models......Page 342
8.11 Exercises......Page 344
9.1 Introduction......Page 349
9.2 GMM Estimators for Linear Regression Models......Page 350
9.3 HAC Covariance Matrix Estimation......Page 359
9.4 Tests Based on the GMM Criterion Function......Page 362
9.5 GMM Estimators for Nonlinear Models......Page 366
9.6 The Method of Simulated Moments......Page 380
9.7 Final Remarks......Page 390
9.8 Exercises......Page 391
10.2 Basic Concepts of Maximum Likelihood Estimation......Page 396
10.3 Asymptotic Properties of ML Estimators......Page 405
10.4 The Covariance Matrix of the ML Estimator......Page 412
10.5 Hypothesis Testing......Page 417
10.6 The Asymptotic Theory of the Three Classical Tests......Page 426
10.7 ML Estimation of Models with Autoregressive Errors......Page 430
10.8 Transformations of the Dependent Variable......Page 432
10.9 Final Remarks......Page 438
10.10 Exercises......Page 439
11.1 Introduction......Page 446
11.2 Binary Response Models: Estimation......Page 447
11.3 Binary Response Models: Inference......Page 455
11.4 Models for More than Two Discrete Responses......Page 461
11.5 Models for Count Data......Page 470
11.6 Models for Censored and Truncated Data......Page 476
11.7 Sample Selectivity......Page 481
11.8 Duration Models......Page 484
11.10 Exercises......Page 490
12.2 Seemingly Unrelated Linear Regressions......Page 496
12.3 Systems of Nonlinear Regressions......Page 513
12.4 Linear Simultaneous Equations Models......Page 517
12.5 Maximum Likelihood Estimation......Page 527
12.6 Nonlinear Simultaneous Equations Models......Page 535
12.7 Final Remarks......Page 538
12.8 Appendix: Detailed Results on FIML and LIML......Page 539
12.9 Exercises......Page 545
13.1 Introduction......Page 551
13.2 Autoregressive and Moving Average Processes......Page 552
13.3 Estimating AR, MA, and ARMA Models......Page 560
13.4 Single- Equation Dynamic Models......Page 569
13.5 Seasonality......Page 574
13.6 Autoregressive Conditional Heteroskedasticity......Page 581
13.7 Vector Autoregressions......Page 589
13.8 Final Remarks......Page 593
13.9 Exercises......Page 594
14.2 Random Walks and Unit Roots......Page 599
14.3 Unit Root Tests......Page 607
14.4 Serial Correlation and Unit Root Tests......Page 614
14.5 Cointegration......Page 618
14.6 Testing for Cointegration......Page 630
14.8 Exercises......Page 638
15.1 Introduction......Page 644
15.2 Speci cation Tests Based on Arti cial Regressions......Page 645
15.3 Nonnested Hypothesis Tests......Page 659
15.4 Model Selection Based on Information Criteria......Page 669
15.5 Nonparametric Estimation......Page 671
15.6 Final Remarks......Page 683
15.7 Appendix: Test Regressors in Arti cial Regressions......Page 684
15.8 Exercises......Page 686