Topics in advanced econometrics: 2 Linear and nonlinear simultaneous equations
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1994
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 401 S. |
| ISBN: | 0387941568 3540941568 |
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MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface vii
Contents of Volume I xv
1 Extension of Classical Methods I 1
1.1 Introduction 1
1.2 A Brief Historical Review 4
1.3 The Nature of the GLSEM 6
1.4 The GLSEM: Assumptions and Notation 10
1.4.1 Assumptions and Conventions 12
1.4.2 Notation 15
1.5 Inconsistency of OLS Estimators 21
1.6 Two Stage Least Squares (2SLS) 27
1.6.1 The Original Derivation 27
1.6.2 An Alternative Formulation 28
1.7 Three Stage Least Squares (3SLS) 32
1.8 Restricted 2SLS and 3SLS Estimators 39
1.9 Tests of Prior Restrictions 42
1.9.1 Generalities 42
1.9.2 A Restricted Least Squares Interpretation of 2SLS
and 3SLS 43
Questions and Problems 50
xii Contents
Appendix to Chapter 1 53
Preliminaries to Hausman s Test 53
Examples 57
2 Extension of Classical Methods II 61
2.1 Limiting Distributions 61
2.1.1 Preliminaries 61
2.1.2 Limiting Distributions for Static GLSEM 63
2.1.3 Limiting Distributions for Dynamic GLSEM .... 70
2.2 Forecasting from the GLSEM 83
2.2.1 Generalities 83
2.2.2 Forecasting from the URF 84
2.2.3 Forecasting from the RRF 93
2.3 The Vector Autoregressive Model (VAR) 102
2.4 Instrumental Variables (IV) 104
2.4.1 2SLS and 3SLS as IV Estimators 105
2.4.2 2SLS and 3SLS as Optimal IV Estimators 109
2.5 IV and Insufficient Sample Size 115
2.5.1 The Nature of the Problem 115
2.5.2 Iterated Instrumental Variables (IIV) 116
2.6 A; class and Double fc class Estimators 119
2.7 Distribution of LM Derived Estimators 120
2.8 Properties of Specification Tests 122
2.8.1 Single Equation 2SLS 122
2.8.2 Systemwide 2SLS and 3SLS 131
2.8.3 Relation to Hausman s Test 136
Questions and Problems 139
Appendix to Chapter 2 141
Convergence of Second Moment Matrices 141
Convergence for Dependent Sequences 144
Preliminaries and Miscellaneous 144
Convergence of Second Moments of
Final Form Errors 147
3 Maximum Likelihood Methods I 153
3.1 Introduction 153
3.2 The Identification Problem 154
3.2.1 Generalities 154
3.2.2 The Simple Supply Demand Model 155
3.2.3 Identification by Exclusion Restrictions 157
3.2.4 Identification by Linear Restrictions 166
3.2.5 Identification and the Reduced Form 171
3.2.6 Covariance and Cross Equation Restrictions 177
3.2.7 A More General Framework 182
Contents xiii
3.2.8 Parametric Nonlineanties and Identification 194
3.3 ML Estimation of the RF 196
3.3.1 General Discussion and ILS 196
3.3.2 Estimation of the Reduced Form 199
3.4 FIML Estimation 201
3.5 Simplified FIML Estimators 203
3.6 Properties of Simplified Estimators 208
3.6.1 Consistency 208
3.7 Limiting Distribution of FIML 212
Questions and Problems 220
4 LIML Estimation Methods 223
4.1 The Concentrated Likelihood Function 223
4.1.1 A Subset of m* Structural Equations 223
4.2 The Single Equation LIML Estimator 230
4.3 Consistency of the LIML Estimator 234
4.4 An Interesting Interpretation of LIML 238
4.5 Indirect Least Squares (ILS) 239
4.6 Relation of LIML to Other Estimators 246
4.7 Limiting Distribution of LIML Estimators 248
4.8 Classic Identifiabihty Tests 249
Questions and Problems 256
Appendix to Chapter 4 257
Limiting Distribution of (T 1) 257
5 Nonlinear ML Methods 263
5.1 Motivation 263
5.2 A Mathematical Digression 264
5.3 Aspects of Likelihood Functions 268
5.3.1 An Interesting Inequality 269
5.4 Fisher Information 269
5.4.1 Alternative Representation of the
Information Matrix 273
5.5 The Cramer Rao Bounds 274
5.6 Martingale Properties of Likelihood Functions 277
5.7 Kullback Information 279
5.8 Convergence a.c. of ML Estimators 281
5.8.1 Independent Observations 285
5.8.2 Generalizations 291
5.9 The General Nonlinear Model (GNLM) 299
5.9.1 Consistency 299
5.9.2 Identification 303
5.9.3 Asymptotic Normality 304
5.10 The GNLM with Restrictions 310
xiv Contents
5.11 Tests of Restrictions 314
5.11.1 Generalities 314
5.11.2 The Conformity Test 315
5.11.3 The Likelihood Ratio Test 316
5.11.4 The Lagrange Multiplier Test 317
5.11.5 Equivalence of the Three Tests 317
Questions and Problems 318
6 Topics in NLSE Theory 321
6.1 Nonlinear ML 321
6.1.1 Identification 323
6.1.2 Consistency of the ML Estimator 325
6.1.3 Limiting Distribution of ML Estimators 336
6.1.4 Relation of Structural and Covanance
Parameter (ML) Estimators 342
6.1.5 Estimators in Structurally Misspecified Models . . . 348
6.2 Nonlinear 2SLS 352
6.2.1 Identification and Consistency of NL2SLS 354
6.2.2 Asymptotic Normality of NL2SLS 357
6.2.3 Choice of an Optimal NL2SLS Estimator 359
6.3 Nonlinear 3SLS 361
6.3.1 Identification and Consistency of NL3SLS 363
6.3.2 Asymptotic Normality of NL3SLS 364
6.3.3 Optimum NL3SLS and Computational Aspects . . . 366
6.4 GMM 368
6.4.1 Reformulation of GMM as NL2SLS and NL3SLS . . 368
6.4.2 Identification and Consistency 371
6.4.3 Asymptotic Normality 372
6.4.4 Tests of Restrictions 376
6.5 Causality and Related Issues 378
6.5.1 Introduction 378
6.5.2 Basic Concepts 379
Questions and Problems 383
Bibliography 387
Index 395
Contents of Volume I
Preface xi
1 Mathematical Foundations 1
1.1 Introduction 1
1.2 Sets and Set Operations 2
1.3 Limits of Sequences 4
1.4 Measurable Spaces, Algebras and Sets 10
1.5 Measures and Probability Measures 18
1.5.1 Measures and Measurable Functions 18
1.6 Integration 26
1.6.1 Miscellaneous Convergence Results 43
1.7 Extensions to Abstract Spaces 52
1.8 Miscellaneous Concepts 64
2 Foundations of Probability 74
2.1 Discrete Models 74
2.2 General Probability Models 77
2.2.1 The Measurable Space (Rn. B{Rn)) 77
2.2.2 Specification of Probability Measures 82
2.2.3 Fubini s Theorem and Miscellaneous Results .... 92
2.3 Random Variables 97
2.3.1 Generalities 97
2.3.2 Random Elements 101
xv) Contents of Volume I
2.3.3 Moments of Random Variables and
Miscellaneous Inequalities 104
2.4 Conditional Probability 110
2.4.1 Conditional Probability in Discrete Models 110
2.4.2 Conditional Probability in
Continuous Models 120
2.4.3 Independence 125
3 Convergence of Sequences I 133
3.1 Convergence a.c. and in Probability 133
3.1.1 Definitions and Preliminaries 133
3.1.2 Characterization of Convergence a.c. and
Convergence in Probability 140
3.2 Laws of Large Numbers 152
3.3 Convergence in Distribution 154
3.4 Convergence in Mean of Order p 156
3.5 Relations Among Modes
of Convergence 161
3.6 Uniform Integrability and Convergence 167
3.7 Criteria for the SLLN 177
3.7.1 Sequences of Independent Random Variables .... 177
3.7.2 Sequences of Uncorrelated Random Variables .... 190
4 Convergence of Sequences II 194
4.1 Introduction 194
4.2 Properties of Random Elements 196
4.3 Base and Separability 200
4.4 Distributional Aspects of R.E 208
4.5 Independence for Random Elements 209
4.6 Distributions of Random Elements 210
4.7 Moments of Random Elements 212
4.8 Uncorrelated Random Elements 216
4.9 Laws of Large Numbers for R.E 218
4.9.1 Preliminaries 218
4.9.2 WLLN and SLLN for R.E 219
4.10 Convergence in Probability for R.E 222
4.11 Weak Convergence 223
4.11.1 Preliminaries 223
4.11.2 Properties of Measures 226
4.11.3 Determining Classes 231
4.11.4 Weak Convergence in Product Space 233
4.12 Convergence in Distribution for R.E 235
4.12.1 Convergence of Transformed Sequences of R.E. ... 238
4.13 Characteristic Functions 245
4.14 CLT for Independent Random Variables 256
Contents of Volume I xvii
4.14.1 Preliminaries 256
4.14.2 Characteristic Functions for Normal Variables .... 258
4.14.3 Convergence in Probability and Characteristic
Functions 260
4.14.4 CLT for i.i.d. Random Variables 262
4.14.5 CLT and the Lindeberg Condition 264
5 Dependent Sequences 277
5.1 Preliminaries 277
5.2 Definition of Martingale Sequences 279
5.3 Basic Properties of Martingales 282
5.4 Square Integrable Sequences 284
5.5 Stopping Times 289
5.6 Upcrossings 304
5.7 Martingale Convergence 306
5.8 Convergence Sets 310
5.9 WLLN and SLLN for Martingales 320
5.10 Martingale CLT 322
5.11 Mixing and Stationary Sequences 337
5.11.1 Preliminaries and Definitions 337
5.11.2 Measure Preserving Transformations 341
5.12 Ergodic Theory 343
5.13 Convergence and Ergodicity 348
5.14 Stationary Sequences and Ergodicity 354
5.14.1 Preliminaries 354
5.14.2 Convergence and Strict Stationarity 356
5.14.3 Convergence and Covariance Stationarity 358
5.15 Miscellaneous Results and Examples 365
Bibliography 371
Index 373
|
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| indexdate | 2024-07-09T17:41:20Z |
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| isbn | 0387941568 3540941568 |
| language | English |
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| spelling | Dhrymes, Phoebus J. 1932-2016 Verfasser (DE-588)108367622 aut Topics in advanced econometrics 2 Linear and nonlinear simultaneous equations Phoebus J. Dhrymes New York [u.a.] Springer 1994 XVII, 401 S. txt rdacontent n rdamedia nc rdacarrier Probabilités ram (DE-604)BV009810261 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006495637&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dhrymes, Phoebus J. 1932-2016 Topics in advanced econometrics Probabilités ram |
| title | Topics in advanced econometrics |
| title_auth | Topics in advanced econometrics |
| title_exact_search | Topics in advanced econometrics |
| title_full | Topics in advanced econometrics 2 Linear and nonlinear simultaneous equations Phoebus J. Dhrymes |
| title_fullStr | Topics in advanced econometrics 2 Linear and nonlinear simultaneous equations Phoebus J. Dhrymes |
| title_full_unstemmed | Topics in advanced econometrics 2 Linear and nonlinear simultaneous equations Phoebus J. Dhrymes |
| title_short | Topics in advanced econometrics |
| title_sort | topics in advanced econometrics linear and nonlinear simultaneous equations |
| topic | Probabilités ram |
| topic_facet | Probabilités |
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