The small sample properties of estimators and tests are frequently too complex to be useful or are unknown. Much econometric theory is therefore developed for very large or asymptotic samples where it is assumed that the behaviour of estimators and tests will adequately represent their properties in small samples. Refined asymptotic methods adopt an intermediate position by providing improved approximations to small sample behaviour using asymptotic expansions. Dedicated to the memory of Michael Magdalinos, whose work is a major contribution to this area, this book contains chapters directly concerned with refined asymptotic methods. In addition, there are chapters focussing on new asymptotic results; the exploration through simulation of the small sample behaviour of estimators and tests in panel data models; and improvements in methodology. With contributions from leading econometricians, this collection will be essential reading for researchers and graduate students concerned with the use of asymptotic methods in econometric analysis.
Author(s): Garry D. A. Phillips, Elias Tzavalis
Year: 2007
Language: English
Pages: 418
Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
List of figures......Page 13
List of tables......Page 15
List of contributors......Page 17
Preface......Page 19
Acknowledgements......Page 21
Michael Magdalinos 1949–2002......Page 23
Introduction......Page 27
1 Introduction......Page 31
2 GARCH with Pearson Family Disturbances......Page 32
3 Sampling Experiments......Page 38
4 Concluding Remarks......Page 63
1 Introduction......Page 64
1.1 Where Do Valid Instruments Come From?......Page 65
2 The Traditional IV Argument, a Summary......Page 66
3.1 A Statistical Model......Page 69
3.2 Embedding a Structural into a Statistical Model......Page 70
3.3 The Linking-up Model......Page 72
3.4 Reparameterization/Restriction......Page 73
3.5 Instrumental Variables and Endogeneity/Exogeneity......Page 75
4.1 The “Implicit Reduced Form”......Page 77
4.2 Weak Instruments......Page 79
4.3 Statistical Adequacy and the Reliability of Inference......Page 80
4.4 2SLS as the Quintessential IV Estimator......Page 83
5 The Reliability of IV-based Inference......Page 85
5.1 Testing Overidentifying Restrictions/Instrument Validity......Page 86
5.2 Testing “Exogeneity”......Page 88
6 Conclusions......Page 89
1 Introduction......Page 90
2 Model and Notation......Page 91
2.1 An Alternative Approach to Obtaining Approximations for the First and Second Moments......Page 95
3 Main Results......Page 97
3.1 The Bias Approximation......Page 98
3.2 The Second-moment Approximation......Page 100
4 A Simple Simultaneous Equation Model......Page 103
5 Conclusions......Page 106
Appendix 1......Page 107
Appendix 2......Page 108
1 Introduction......Page 130
2 The Model......Page 132
3 Estimators......Page 133
3.1 Empirical Probabilities......Page 135
3.2 First-order Conditions......Page 136
4 Asymptotic Theory for Local GEL......Page 137
5 HypothesisTests......Page 139
Appendix A: Proofs of Results......Page 140
Appendix B: Auxiliary Results......Page 147
1 Introduction......Page 153
2 Moderate Deviations with i.i.d. Errors......Page 155
3 Moderate Deviations from Unity with Weakly Dependent Errors......Page 156
4 Limit Theory for the Near Stationary Case......Page 160
4.1 Remarks......Page 165
4.2 Remarks......Page 167
4.3 The Stationary Case......Page 169
5 Limit Theory for the Near Explosive Case......Page 170
5.1 Remarks......Page 175
5.2 The Explosive Case......Page 176
6 Discussion......Page 179
Appendix and Proofs......Page 180
2 Likelihood-based Inference......Page 193
3 Main Results......Page 194
4 Comments......Page 196
Appendix:The Derivations......Page 197
1 Introduction......Page 203
2.1 Notation and Assumptions......Page 204
2.2 The t Test......Page 207
2.3 The F Test......Page 209
3 Cornish–Fisher Corrected t and v-statistics for a Parametric Model of Heteroscedasticity......Page 212
4 Simulation Experiments......Page 216
5 Empirical Example: Productivity Gains from in-company Training......Page 221
Notes......Page 228
Appendix......Page 229
1 Introduction......Page 235
2 The Test Statistic and Its Asymptotic Distribution......Page 236
3 Monte Carlo Results......Page 239
Appendix A......Page 241
Appendix B......Page 248
1 Introduction......Page 250
2 Derivation of the Test Statistic......Page 251
3 An Alternative Test when the δ Test Fails......Page 256
4 Diagonal R......Page 259
1 Introduction......Page 269
2 Panel Data Models with Observed and Unobserved Common Effects......Page 272
3 A Principal Components Augmentation Approach......Page 276
4.1 Monte Carlo Design......Page 278
4.2 Alternative Estimators Considered......Page 283
4.3 Monte Carlo Results......Page 285
5 An Empirical Application......Page 303
6 Conclusions......Page 311
1 Introduction......Page 312
2 Rules for Simulation Contests......Page 314
2.1 Methodologic Aspirations for an Adequate and Impartial Design of Simulation Studies that Aim to Rank Various Alternative Inference Techniques......Page 315
3 Initial Conditions......Page 318
4.1 Generic Framework......Page 321
4.2 Instruments for Panel AR(1) Models......Page 323
4.3 Weight Matrices......Page 326
5 A Limited Monte Carlo Contest......Page 330
5.1 An Orthogonal Monte Carlo Design......Page 331
5.2 Some New Monte Carlo Findings......Page 334
6 Concluding Remarks......Page 344
Notes......Page 347
1 Introduction......Page 349
2 The Transformation Theorem......Page 350
3 A Statistical Proof, Using Conditioning and Induction......Page 351
1 Introduction......Page 356
2.1 Simplifications......Page 359
2.2 The Regular Simplex......Page 360
2.3 Surface Integration......Page 362
3 Main Results......Page 364
4 Example: Censored Normal Model......Page 372
1 Introduction......Page 377
2.1 DGP......Page 379
2.3 Closed and Open Models......Page 380
2.4 Stationary VAR......Page 381
3.1 Impulse Response Analysis......Page 385
3.2 Dynamic Multiplier Analysis......Page 389
3.3 Stationary Example......Page 390
4 Response Analysis in a Non-stationary VAR......Page 392
4.1 Non-stationary Example......Page 395
5 Conclusion......Page 397
References......Page 398
Index......Page 415
