Asymptotic Theory for Econometricians

This book is intended to provide a somewhat more comprehensive and unified treatment of large sample theory than has been available previously and to relate the fundamental tools of asymptotic theory directly to many of the estimators of interest to econometricians. In addition, because economic data are generated in a variety of different contexts (time series, cross sections, time series--cross sections), we pay particular attention to the similarities and differences in the techniques appropriate to each of these contexts.

Preface to the First Edition	p. ix
Preface to the Revised Edition	p. xi
References	p. xiii
The Linear Model and Instrumental Variables Estimators	p. 1
References	p. 12
For Further Reading	p. 12
Consistency	p. 15
Limits	p. 15
Almost Sure Convergence	p. 18
Convergence in Probability	p. 24
Convergence in rth Mean	p. 28
References	p. 30
Laws of Large Numbers	p. 31
Independent Identically Distributed Observations	p. 32
Independent Heterogeneously Distributed Observations	p. 35
Dependent Identically Distributed Observations	p. 39
Dependent Heterogeneously Distributed Observations	p. 46
Martingale Difference Sequences	p. 53
References	p. 62
Asymptotic Normality	p. 65
Convergence in Distribution	p. 65
Hypothesis Testing	p. 74
Asymptotic Efficiency	p. 83
References	p. 111
Central Limit Theory	p. 113
Independent Identically Distributed Observations	p. 114
Independent Heterogeneously Distributed Observations	p. 117
Dependent Identically Distributed Observations	p. 122
Dependent Heterogeneously Distributed Observations	p. 130
Martingale Difference Sequences	p. 133
References	p. 136
Estimating Asymptotic Covariance Matrices	p. 137
General Structure of V[subscript n]	p. 137
Case 1: {Z[subscript t varepsilon subscript t]} Uncorrelated	p. 139
Case 2: {Z[subscript t varepsilon subscript t]} Finitely Correlated	p. 147
Case 3: {Z[subscript t varepsilon subscript t]} Asymptotically Uncorrelated	p. 154
References	p. 164
Functional Central Limit Theory and Applications	p. 167
Random Walks and Wiener Processes	p. 167
Weak Convergence	p. 171
Functional Central Limit Theorems	p. 175
Regression with a Unit Root	p. 178
Spurious Regression and Multivariate FCLTs	p. 184
Cointegration and Stochastic Integrals	p. 190
References	p. 204
Directions for Further Study	p. 207
Extending the Data Generating Process	p. 207
Nonlinear Models	p. 209
Other Estimation Techniques	p. 209
Model Misspecification	p. 211
References	p. 211
Solution Set	p. 213
References	p. 259
Index	p. 261
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Asymptotic Theory for Econometricians

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