Asymptotic Theory for Econometricians (eBook)

Front Cover 1
Asymptotic Theory for Econometricians 4
Copyright Page 5
Table of Contents 8
Dedication 6
Preface 10
CHAPTER I. The Linear Model and Instrumental Variables Estimators 12
Text 12
References 23
For Further Reading 23
CHAPTER II. Consistency 24
II.1 Limits 24
II.2 Almost Sure Convergence 27
II.3 Convergence in Probability 33
II.4 Convergence in rth Mean 38
References 39
CHAPTER III. Laws of Large Numbers 40
III.1 Independent Identically Distributed Observations 40
III.2 Independent Heterogeneously Distributed Observations 43
III.3 Dependent Identically Distributed Observations 47
III.4 Dependent Heterogeneously Distributed Observations 54
III.5 Martingale Difference Sequences 62
References 71
CHAPTER IV. Asymptotic Normality 72
IV.1 Convergence in Distribution 72
IV.2 Hypothesis Testing 80
IV.3 Asymptotic Efficiency 89
References 117
CHAPTER V. Central Limit Theory 118
V.1 Independent Identically Distributed Observations 119
V.2 Independent Heterogeneously Distributed Observations 122
V.3 Dependent Identically Distributed Observations 126
V.4 Dependent Heterogeneously Distributed Observations 135
V.5 Martingale Difference Sequences 138
References 141
CHAPTER VI. Estimating Asymptotic Covariance Matrices 143
VI.1 General Structure of Vn 143
VI.2 Case 1: On (Block) Diagonal 145
VI.3 Case 2: On (Block) Band Diagonal 153
VI.4 Case 3: General Case 158
References 172
CHAPTER VII. Efficient Estimation with Estimated Error Covariance Matrices 173
VII.1 General Results 174
VII.2 Case 1: Contemporaneous Covariance 175
VII.3 Case 2: Heteroskedasticity 182
VII.4 Case 3: Serial Correlation 189
References 196
CHAPTER VIII. Directions For Further Study 197
VIII.1 Extensions of the Linear Model 197
VIII.2 Nonlinear Models 198
VIII.3 Other Estimation Techniques 199
VIII.4 Model Misspecification 200
References 200
Solution Set 202
Index 236