Advanced econometric theory John S. Chipman

Includes bibliographical references and index

List of figures and tables xii
Preface xiii
1. Multivariate analysis and the linear regression model 1
1.1. Introduction 1
1.2. Existence of a solution to the normal equation 7
1.3. The concept of wide-sense conditional expectation 10
1.4. Conditional expectation with normal variables 14
1.5. The relation between wide-sense and strict-sense conditional expectation 15
1.6. Conditional means and minimum mean-square error 17
1.7. Bayes estimation 20
1.8. The relation between Bayes and Gauss---Markov estimation in the case of a single independent variable 23
1.9. Exercises 27
2. Least-squares and Gauss---Markov theory 30
2.1. Least-squares theory 30
2.2. Principles of estimation 31
2.3. The concept of a generalized inverse of a matrix 33
2.4. The matrix Cauchy---Schwarz inequality and an extension 35
2.5. Gauss---Markov theory 37
2.6. The relation between Gauss---Markov and least-squares estimators 41
2.7. Minimum-bias estimation 49
2.8. Multicollinearity and the imposition of dummy linear restrictions 51
2.9. Specification error 55
2.10. Exercises 60
3. Multicollinearity and reduced-rank estimation 65
3.1. Introduction 65
3.2. Singular-value decomposition of a matrix 65
3.3. The condition number of a matrix 68
3.4. The Eckart---Young theorem 70
3.5. Reduced-rank estimation 81
3.6. Exercises 86
4. The treatment of linear restrictions 88
4.1. Estimation subject to linear restrictions 88
4.2. Linear aggregation and duality 92
4.3. Testing linear restrictions 101
4.4. Reduction of mean-square error by imposition of linear restrictions 106
4.5. Uncertain linear restrictions 108
4.6. Properties of the generalized ridge estimator 109
4.7. Comparison of restricted and generalized ridge estimators 112
4A. Appendix (to Section 4.4): Guide to the computation of percentage points of the noncentral F distribution 115
4.8. Exercises 122
5. Stein estimation 126
5.1. Stein's theorem and the regression model 126
5.2. Lemmas underlying the James---Stein theorem 132
5.3. Some further developments of Stein estimation 138
5.4. Exercises 141
6. Autocorrelation of residuals - 1 143
6.1. The first-order autoregressive model 143
6.2. Efficiency of trend estimation: the ordinary least-squares estimator 147
6.3. Efficiency of trend estimation: the Cochrane---Orcutt estimator 154
6.4. Efficiency of trend estimation: the Prais---Winsten weighted-difference estimator 157
6.5. Efficiency of trend estimation: the Prais---Winsten first-difference estimator 161
6.6. Discussion of the literature 162
6.7. Exercises 165
7. Autocorrelation of residuals - 2 167
7.1. Anderson models 167
7.2. Testing for autocorrelation: Anderson's theorem and the Durbin---Watson test 177
7.3. Distribution and beta approximation of the Durbin---Watson statistic 189
7.4. Bias in estimation of sampling variances 196
7.5. Exercises 200
8. Simultaneous-equations estimation 202
8.1. The identification problem 202
8.2. Anderson and Rubin's "limited-information maximum-likelihood" (LIML) method, 1: the handling of linear restrictions 210
8.3. Anderson and Rubin's "limited-information maximum-likelihood" method, 2: constrained maximization of the likelihood function 215
8.4. The contributions of Basmann and Theil 223
8.5. Exact properties of simultaneous-equations estimators 238
8.6. Approximations to finite-sample distributions 251
8.7. Recursive models 268
8.8. Exercises 283
9. Solutions to the exercises 287
9.1. Chapter 1 287
9.2. Chapter 2 294
9.3. Chapter 3 304
9.4. Chapter 4 309
9.5. Chapter 5 318
9.6. Chapter 6 323
9.7. Chapter 7 329
9.8. Chapter 8 334
Notes 349
Bibliography 357
Index

When learning econometrics, what better way than to be taught by one of its masters. Starting with the linear regression model, least squares, Gauss-Markov theory and the first principals of econometrics, this book guides the introductory student to an advanced stage of ability.