Econometric foundations:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2000
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| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVIII, 756 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0521623944 |
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| 100 | 1 | |a Mittelhammer, Ron C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Econometric foundations |c Ron C. Mittelhammer ; George G. Judge ; Douglas J. Miller |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2000 | |
| 300 | |a XXVIII, 756 S. |b graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Lehrbuch - Ökonometrie | |
| 650 | 4 | |a Ökonometrie / Theorie | |
| 650 | 4 | |a Econometrics | |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Judge, George G. |d 1925- |e Verfasser |0 (DE-588)12963221X |4 aut | |
| 700 | 1 | |a Miller, Douglas J. |d 1965- |e Verfasser |0 (DE-588)131450530 |4 aut | |
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| adam_text | Contents
Preface
xxv
I Information Processing and Recovery
1
1
The Process of Econometric Information Recovery
3
1.1
Introduction
4
1.2
The Nature of Economic Data
4
1.3
The Probability Approach to Economics
5
1.4
The Process of Searching for Quantitative Economic Knowledge
6
1.4.1
Econometric Model Components
6
1.4.2
Econometric Analysis
8
1.5
The Inverse Problem
9
1.6
A Comment
10
1.7
Notation
10
1.8
Idea Checklist
-
Knowledge Guides
12
2
Probability-Econometric Models
13
2.1
Parametric, Semiparametric, and Nonparametric Models
14
2.1.1
Parametric Models
14
2.1.2
Nonparametric and Semiparametric Models
15
2.2
The Classical Linear Regression Model
17
2.2.1
Establishing a Linkage between Dependent
and Explanatory Variables
17
2.2.2
The Distribution of
Y
around the Systematic Component
20
2.23
Inverse Problems: Estimation, Inference, and Interpretation
21
2.2.4
Some Variants of the Linear Regression Model
22
2.3
A Class of Probability Models
26
2.4
Class of Inverse Problems and Solutions
28
2.5
Concluding Comments
29
vii
CONTENTS
2.6
Exercises
30
2.6.1
Idea Checklist
-
Knowledge Guides
30
2.6.2
Problems
30
2.7
References
31
II Regression Model
-
Estimation and Inference
33
3
The Multivariate Normal Linear Regression Model: ML Estimation
35
3.1
The Linear Regression Model
35
3.1.1
The Linearity Assumption and the Inverse Problem
36
3.1.2
Linearity and Beyond: Sampling Implication
of Model Assumptions
37
3.1.3
The Parametric Model
39
3.2
Maximum Likelihood Estimation of
β
and
σ2
39
3.2.1
The Normal Linear Regression Model
40
3.2.2
The Maximum Likelihood (ML) Criterion
40
3.2.3
Maximum Likelihood Estimators for
β
and
σ2
41
3.2.4
Distribution, Moments, and Bias Properties of the ML Estimator
42
3.3
Efficiency of the Bias-Adjusted ML Estimators of
β
and
σ2
43
3.4
Consistency, Asymptotic Normality, and Asymptotic Efficiency
of ML Estimators of
β
and
σ2
44
3.4.1
Consistency
44
3.4.2
Asymptotic Normality
46
3.4.3
Asymptotic Efficiency
47
3.5
Summary of the Finite Sample and Asymptotic Sampling Properties
of the ML Estimator
48
3.6
Estimating
є
and
cov^â)
49
3.6.1
An Estimator for
є
50
3.6.2
An Estimator for covGQ)
51
3.7
Concluding Remarks
51
3.8
Exercises
53
3.8.1
Idea Checklist
-
Knowledge Guides
53
3.8.2
Problems
53
3.8.3
Computer Problems
54
3.9
Appendix: Admissibility of ML Estimator
-
Introduction to Biased Estimation
54
3.9.1
Is the ML Estimator Inadmissible?
55
3.9.2
Risk Comparisons for Restricted and Unrestricted ML Estimator
57
3.10
Appendix: Proofs
58
3.11
References
60
4
The Multivariate Normal Linear Regression Model: Inference
61
4.1
Introduction
61
4.2
Some Basic Sampling Distributions of Functions of
β
and S2
62
VUl
CONTENTS
4.3
Hypothesis Testing
64
4.3.1
Test Statistics
65
4.3.2
Generalized Likelihood Ratio (GLR) Test
65
4.3.3
Properties of the GLR Test
66
4.3.4
Testing Hypotheses Relating to Linear Restrictions on
β
67
4.3.5
Testing Linear Inequality Hypotheses
72
4.3.6
Bonferroni Joint Tests of Inequality and Equality
Hypotheses about
β
73
4.3.7
Testing Hypotheses about
σ2
74
4.4
Confidence Interval and Region Estimation
76
4.4.1
Meaning of Confidence Interval or Region
76
4.4.2
Rationale for the Use of Confidence Regions
77
4.4.3
Confidence Intervals, Regions, and Bounds for
β
77
4.4.4
Confidence Bounds on
σ2
79
4.5
Pretest Estimators Based on Hypothesis Tests: Introduction
80
4.5.1
The Pretest Estimator
80
4.5.2
The Pretest Estimator Risk Function
81
4.6
Concluding Remarks
82
4.7
Exercises
84
4.7.1
Idea Checklist
-
Knowledge Guides
84
4.7.2
Problems
84
4.7.3
Computer Exercises
85
4.8
References
85
The Linear Semiparametric Regression Model:
Least-Squares Estimation
86
5.1
The Semiparametric Linear Regression Model
86
5.2
The Problem of Estimating
β
88
5.2.1
The Squared-Error Metric and the Least-Squares Principle
89
5.2.2
The Least-Squares Estimator
90
5.3
Statistical Properties of the LS Estimator
91
5.3.1
Mean, Covariance, and Unbiasedness
92
5.3.2
GAUSS Markov Theorem:
β
Is BLUE, Not Necessarily MVUE
93
5.3.3
β
Is a Minimax Estimator of
β
under Quadratic Risk
94
5.3.4
Consistency
95
5.3.5
Asymptotic Normality
96
5.4
Estimating
ε, σ2,
and
cov^â)
97
5.4.1
An Estimator for
ε
98
5.4.2
An Estimator for
σ2
and cov(^)
99
5.5
Critique
100
5.6
Exercises
101
5.6.1
Idea Checklist
-
Knowledge Guides
101
5.6.2
Problems
101
5.6.3
Computer Exercises
102
ix
CONTENTS
5.7
References
103
5.8
Appendix: Proofs
103
6
The Linear Semiparametric Regression Model: Inference
105
6.1
Asymptotics: Why, What Kind, and How Useful?
107
6.1.1
Why?
107
6.1.2
What Kind?
108
6.1.3
How Useful?
108
6.2
Hypothesis Testing: Linear Equality Restrictions on
β
109
6.2.1 Wald
(W)
Tests
ПО
6.2.2 Lagrange
Multiplier
(LM)
Tests
114
6.2.3
The
W
and
LM
Tests under Normality
118
6.2.4
W
and LM Tests: Interrelationships and Extensions
120
6.3
Confidence Region Estimation
120
6.3.1
Wald-Based Confidence Regions
121
6.3.2
LM-Based Confidence Regions
122
6.4
Testing Linear Inequality Hypotheses and Generating Confidence
Bounds on
β
123
6.4.1
Linear Inequality Hypotheses
124
6.4.2
Confidence Bounds for c/3
125
6.5
Critique
126
6.6
Comprehensive Computer Application
127
6.7
Exercises
128
6.7.1
Idea Checklist
-
Knowledge Guides
128
6.7.2
Problems
128
6.73
Computer Exercises
129
6.8
References
129
III
Extrémům
Estimators and Nonlinear and
Nonnormal
Regression Models
131
7
Extrémům
Estimation and Inference
133
7.1
Introduction
133
7.2
ML and LS Estimators Expressed in
Extrémům
Estimator Form
136
7.3
Asymptotic Properties of
Extrémům
Estimators
136
7.3.1
Consistency of
Extrémům
Estimators
136
73.2
Asymptotic Normality of
Extrémům
Estimators
138
7.4
Asymptotic Properties of Maximum Likelihood Estimators
in an
Extrémům
Estimator Context
139
7.4.1
Consistency of the ML-Extremum Estimator
140
7.4.2
Asymptotic Normality of the ML-Extremum Estimator
141
7.5
Asymptotic Properties of the Least-Squares Estimator
in an
Extrémům
Estimator Context
142
7.5.1
Consistency of the LS-Extremum Estimator
142
7.5.2
Asymptotic Normality of the LS-Extremum Estimator
143
CONTENTS
7.6
Inference Based on
Extrémům
Estimation
144
7.6.1 Lagrange
Multiplier Tests and Confidence Regions
144
7.6.2 Wald
Tests and Confidence Regions
148
7.6.3
Pseudo-Likelihood Ratio Tests and Confidence Regions
149
7.6.4
Testing Linear Inequalities and Confidence Bounds
152
7.7
Critique
153
7.8
Exercises
154
7.8.1
Idea Checklist
-
Knowledge Guides
154
7.8.2
Problems
154
7.8.3
Computer Problems
155
7.9
References
155
8
The Nonlinear Semiparametric Regression Model:
Estimation and Inference
157
8.1
The Nonlinear Regression Model
157
8.1.1
Assumed Probability Model Characteristics: Discussion
159
8.1.2
The Inverse Problem
161
8.2
The Problem of Estimating
β
162
8.2.1
The Nonlinear Least-Squares Estimator
162
8.2.2
Parameter Identification Relative to a Probability Model
163
8.2.3
Parameter Identification Relative to the Least-Squares
Criterion and Given Data
165
8.3
Sampling Properties of the NLS Estimator
167
8.4
The Problem of Estimating
ε, σ2,
and
covOâ)
169
8.4.1
An Estimator for
ε
169
8.4.2
An Estimator for
σ2
and
covC/â)
170
8.5 Wald
Statistics: Tests and Confidence Regions
171
8.5.1
Hypotheses Relating to Differentiable Functions of
β
171
8.5.2 Wald (W)
Tests
172
8.5.3 Wald
Statistic Distribution under
На
173
8.5.4
Test Application
174
8.5.5
Confidence Region Estimation
175
8.6
LM Statistics: Tests and Confidence Regions
176
8.6.1 Lagrange
Multiplier Distribution
176
8.6.2
Classical Form of LM Test
178
8.6.3
Score Form of LM Test
178
8.6.4
LM Statistic Distribution under Ha
179
8.6.5
Test Application
179
8.6.6
Confidence Region Estimation
180
8.7
Pseudo-Likelihood Ratio Statistic: Tests and Confidence
Regions
180
8.7.1
The Pseudo-Likelihood Ratio Statistic
180
8.7.2
Distribution of PLR under Ho
181
8.73
Test and Confidence Region Application and Properties
182
xi
CONTENTS
8.8
Nonlinear Inequality Hypotheses and Confidence Bounds
183
8.8.1
Testing Nonlinear Inequalities: Z-Statistics
183
8.8.2
Confidence Bounds
185
8.9
Asymptotic Properties of the NLS-Extremum Estimator
186
8.9.1
Consistency
186
8.9.2
Asymptotic Normality
187
8.9.3
Asymptotic Linearity
190
8.9.4
Best Asymptotically Linear Consistent Estimator
191
8.10
Concluding Comments
192
8.11
Exercises
192
8.11.1
Idea Checklist
-
Knowledge Guides
192
8.11.2
Problems
193
8.11.3
Computer Exercises
193
8.12
References
194
8.13
Appendixes
195
8.13.1
Appendix A: Computation of NLS Estimates
(with Ronald
Schoenberg)
195
8.13.2
Newton-Raphson Method
195
8.13.3
Gauss-Newton Method
197
8.13.4
Quasi-Newton
Methods
198
8.13.5
Computational Issues
199
8.13.6
Appendix
В
:
Proofs
202
Nonlinear and
Nonnormal
Parametric
Regression Models
204
9.1
The Normal Nonlinear Regression Model
204
9.1.1
Maximum Likelihood—
Extrémům
Estimation
205
9.1.2
Maximum Likelihood-Extremum Inference
207
9.2
Nonnormality
209
9.2.1
A
Nonnormal
Dependent Variable, Normal Noise Component
Case: The
Box
-Сох
Transformation
209
9.2.2
A
Nonnormal
Noise Component Case
212
9.3
General Considerations in Applying the ML-Extremum
Criterion
215
9.3.1
Point Estimation
216
9.3.2
Testing and Confidence-Region Estimation
217
9.4
A Final Remark
220
9.5
Exercises
220
9.5.1
Idea Checklist
-
Knowledge Guides
220
9.5.2
Problems
220
9.5.3
Computer Exercises
221
9.6
References
221
xii
CONTENTS
IV Avoiding the Parametric Likelihood
223
10
Stochastic Regressors and Moment-Based Estimation
225
10.1
Introduction
225
10.2
Linear Model Assumptions, Estimation, and Inference Revisited
227
10.3
LS and ML Estimator Properties
229
10.3.1
LS Estimator Properties: Finite Samples
229
10.3.2
LS Estimator Properties: Asymptotics
230
10.3.3
ML Estimation of
β
and
σ2
under Conditional Normality
232
10.4
Hypothesis Testing and Confidence-Region Estimation
233
10.4.1
Semiparametric Case
233
10.4.2
Parametric Case
233
10.5
Summary: Statistical Implications of Stochastic X
235
10.6
Method of Moments Concept
235
10.6.1
Asymptotic Properties
236
10.6.2
A Linear Model Formulation
238
10.6.3
Extensions to Nonlinear Models
239
10.7
Concluding Comments
241
10.8
Exercises
242
10.8.1
Idea Checklist
-
Knowledge Guides
242
10.8.2
Problems
242
10.8.3
Computer Exercises
242
10.9
References
243
10.10
Appendix: Proofs
244
11
Quasi-Maximum Likelihood and
Estimating Equations
245
11.1
Quasi-Maximum Likelihood Estimation and Inference
247
11.2
QML-E Estimation and Inference
248
11.2.1
Consistency and Asymptotic Normality
248
11.2.2
True PDF Approximation Property and Asymptotic Normality
of Inconsistent QML-E Estimators
249
11.2.3
Consistent Estimation of the Asymptotic Covariance Matrix
251
11.2.4
Necessary and Sufficient Conditions for Consistency
and Asymptotic Normality
251
11.2.5
QML Inference
254
11.2.6
QML Generalizations
255
11.2.7
QML Summary Comments
256
11.3
Estimating Equations: LS, ML, QML-E, and
Extrémům
Estimators
256
11.3.1
Linear and Nonlinear Estimating Functions
259
113.2
Optimal Unbiased Estimating Functions: Finite Sample
Optimality of ML
261
xiii
CONTENTS
11.3.3
Consistency of the
ЕЕ
Estimator
265
11.3.4
Asymptotic Normality and Efficiency of
ЕЕ
Estimators
267
11.3.5
Inference in the Context of
ЕЕ
Estimation
268
11.4
Unifying-Linking OptEF and QML: QML-EE Estimation
and Inference
270
11.4.1
The Best Linear-Unbiased QML-EE
272
11.4.2
General QML-EE Estimation and Inference
274
11.5
Final Remarks
275
11.6
Exercises
275
11.6.1
Idea Checklist
-
Knowledge Guides
275
11.6.2
Problems
276
11.6.3
Computer Problems
277
11.7
References
277
11.8
Appendix: Proofs
279
12
Empirical Likelihood Estimation and Inference
281
12.1
Empirical Likelihood: iid Case
282
12.1.1
The EL Concept
283
12.1.2
Nonparametric Maximum Likelihood Estimate
of a Population Distribution
284
12.1.3
Empirical Likelihood Function for
θ
286
12.2
Maximum Empirical Likelihood Estimation: iid Case
292
12.2.1
Maximum Empirical Likelihood Estimator
292
12.2.2
MEL Efficiency Property
293
12.2.3
MEL Estimation of a Population Mean
294
12.2.4
MEL Estimation Based on Two Moments
297
12.3
Hypothesis Tests and Confidence Regions: iid Case
298
12.3.1
Empirical Likelihood Ratio Tests and Confidence Regions
for
0(0) 299
12.3.2 Wald
Tests and Confidence Regions for c(0)
300
12.3.3 Lagrange
Multiplier Tests and Confidence Regions for c(0)
300
12.3.4
Z-Tests of Inequality Hypotheses for the Value of c(0)
301
12.3.5
Testing the Validity of Moment Equations
301
12.3.6
MEL Testing and Confidence Intervals for Population Mean
302
12.3.7
Illustrative MEL Confidence Interval Example
303
12.4
MEL in the Linear Regression Model with Stochastic X
304
12.4.1
MEL Regression Estimation for Stochastic X
304
12.4.2
EL-Based Testing and Confidence Regions When X
Is Stochastic
306
12.4.3
Extensions to the Nonlinear Regression Model
for Stochastic X
307
12.5
MEL in the Linear Regression Model with Nonstochastic X:
Extensions to the Non-iid Case
307
12.6
Concluding Comments
309
xiv
CONTENTS
12.7
Exercises
310
12.7.1
Idea Checklist
-
Knowledge Guides
310
12.7.2
Problems
311
12.7.3
Computer Exercises
311
12.8
References
312
13
Information Theoretic-Entropy Approaches to Estimation
and Inference
313
13.1
Solutions to Systems of Estimating Equations
and Kullback-Leibler Information
313
13.1.1
Kullback-Leibler Information Criterion (KLIC)
316
13.1.2
Relationship Between the MEL Objective and KL
Information
317
13.1.3
Relationship Between the Maximum Entropy (ME) Objective
and KL Information
319
13.2
The General
MEEL
Alternative Empirical Likelihood Formulation
321
13.2.1
The
MEEL
Estimator and Likelihood
321
13.2.2
MEEL Asymptotics
322
13.2.3
MEEL
Inference
323
13.2 .4
Contrasting the Use of Estimating Functions in
ЕЕ
and
MEEL
Contexts
326
13.3
A Cross-Entropy Formalism and Solution
326
13.4
α
-Entropy: Unifying the MEL,
MEEL,
and
CEEL
Estimation Objectives
328
13.5
Application of the Maximum Entropy Principle
to the Regression Model
329
13.5.1
Stochastic X in the Linear Model
329
13.5.2
Fixed
χ
in the Linear Model
331
13.5.3
Extensions to Nonlinear Regression Models
331
13.5.4
Inference in Regression Models
331
13.6
Concluding Remarks
-
Which Criterion?
332
13.7
Exercises
334
13.7.1
Idea Checklist-Knowledge Guides
334
13.7.2
Problems
334
13.7.3
Computer Problems
334
13.8
References
335
13.9
Supplemental References
335
V Generalized Regression Models
337
14
Regression Models with a Known General Noise Covariance Matrix
339
14.1
Applying LS-ML to the Linear Model and Untransformed Data:
Ignoring that
Ψ φ Ι
340
14.1.1
Point Estimation
341
14.1.2
Testing and Confidence-Region Estimation
342
xv
CONTENTS
14.2 GLS-ML-Extremum
Analysis of the Linear Model:
Incorporating a Known
Ψ
344
14.2.1
ML-Extremum Estimators for
β
and
σ2
344
14.2.2
LS-Extremum Estimators for
β
and
σ2
:
Transformed
Linear Model
345
14.2.3
Asymptotic Properties
347
14.2.4
Hypothesis Testing and Confidence Regions
349
14.3
GLS-ML-Extremum Analysis of the Nonlinear Model:
Incorporating a Known
Φ
350
14.3.1
Estimator Properties
350
14.3.2
Hypothesis Testing and Confidence Regions
351
14.3.3
Applying NLS to Untransformed Data
352
14.4
Parametric Specifications of Noise Covanance Matrices
353
14.4.1
Estimation and Inference with AR(1) Noise
354
14.4.2
Heteroscedasticity
-
Structural Specification Known,
Parameters Unknown
355
14.4.3
General Considerations
356
14.5
Sets of Regression Equations
356
14.5.1
Sets of Linear Equations
357
14.5.2
Sets of Nonlinear Equations
359
14.6
The Estimating Equations
-
Quasi-Maximum Likelihood View:
A Unified Approach
361
14.6.1
ЕЕ
Estimation of
β
and
σ2
in the Linear Model When
Φ
Is Known
361
14.6.2
ЕЕ
Estimation of
β
and
σ2
in the Nonlinear Model When
Φ
Is Known
363
14.6.3
ЕЕ
Estimation of
β
and
σ2
in the Linear or Nonlinear
Normal Parametric Regression Model When
Φ
Is Known
364
14.6.4
QML-EE Estimation of
β
and
σ2
in the Linear or Nonlinear
Regression Model
365
14.6.5
ЕЕ
Estimation of
β
and
σ2
in Systems
of Regression Equations
366
14.7
Some Comments
367
14.8
Exercises
368
14.8.1
Idea Checklist
-
Knowledge Guides
368
14.8.2
Problems
368
14.8.3
Computer Exercises
369
14.9
References
369
15
Regression Models with an Unknown General Noise
Covariance Matrix
370
15.1
Linear Regression Models with Unknown Noise Covariance
371
15.1.1
Single-Equation Semiparametric Linear Regression Model
372
15.1.2
Single-Equation Parametric Linear Regression Model
-
The ML Approach
377
xvi
CONTENTS
15.2 System
of
Linear Regression
Equations
378
15.2.1
Estimation:
Semiparametric
Case
379
15.2.2
Testing and Confidence Regions: Semiparametric Case
380
15.2.3
ML Approach: Parametric Case
381
15.3
Nonlinear Regression Models with Unknown Noise Covariance
383
15.3.1
Single-Equation Semiparametric Nonlinear Regression Model
383
15.3.2
Estimation
383
15.3.3
Testing and Confidence Regions
384
15.3.4
Single-Equation Parametric Nonlinear Regression Model
-
ML Approach
385
15.3.5
Sets of Nonlinear Regression Equations
386
15.4
Robust Solution Methods: OLS and Robust Covariance
Matrix Estimation
387
15.4.1
Heteroscedasticity
389
15.4.2
Heteroscedasticity and Autocorrelation
391
15.5
The Estimating Equations
-
Quasi-Maximum Likelihood View:
A Unified Approach
393
15.5.1
A Unified
ЕЕ
Characterization of Inverse Problem Solutions
393
15.5.2
QML-EE Estimation
395
15.5.3
ЕЕ
Extensions
396
15.5.4
MEL and
MEEL
Applications of
ЕЕ
397
15.6
Some Comments
398
15.7
Exercises
400
15.7.1
Idea Checklist
-
Knowledge Guides
400
15.7.2
Problems
400
15.7.3
Computer Exercises
400
15.8
References
401
VI Simultaneous Equation Probability Models and General
Moment-Based Estimation and Inference
403
16
Generalized Moment-Based Estimation and Inference
405
16.1
Parameter Estimation in Just-determined and Overdetermined
Models with iid Observations: Back to the Future
406
16.1.1
OptEF Approach
409
16.1.2
Empirical Likelihood Approaches
410
16.1.3
Summary and Foreword
411
16.2
GMM Solutions for Unbiased Estimating Equations
in the Overdetermined Case
412
16.2.1
GMM Concept
412
16.2.2
GMM Linear Model Estimation
413
16.23
GMM Estimators
-
General Properties
420
16.3
IV Solutions in the Just-determined Case When
Ε[Χ ε] φ
0 423
16.3.1
Traditional Instrumental Variable Estimator
in the Linear Model
424
xvii
CONTENTS
16.3.2 GLS
as an IV Estimator
426
16.3.3
Extensions: Nonlinear IV Formulations and Non-iid
Sampling
427
16.3.4
Hypothesis Testing and Confidence Regions
428
16.3.5
Summary: IV Approach to Estimation and
Inference
429
16.4
Solutions in the Overdetermined Case When
Ε[Χ ε] φ
0 429
16.4.1
Unbiased Estimating Equations Basis for Inverse Problem
Solutions When
Ε[Χ ε] φ
0 430
16.4.2
GMM Approach
431
16.43
MEL and
MEEL
Approaches
432
16.4.4
OptEF-Quasi-ML Approach: Asymptotic Unification
of Inverse Solution Methods
436
16.4.5
Asymptotic Sampling Properties and Inference
437
16.4.6
Testing Moment Equation Validity
438
16.4.7
Relationship Between Estimator Efficiency and the Number
and Type of Estimating Equations
439
16.5
Concluding Comments
441
16.6
Exercises
443
16.4.1
Idea Checklist
-
Knowledge Guides
443
16.4.2
Problems
443
16.4.3
Computer Exercises
444
16.7
References
444
17
Simultaneous Equations Econometric Models:
Estimation and Inference
446
17.1
Linear Simultaneous Equations Models
447
17.1.1
An Equivalent Vectorized System of Equations
450
17.1.2
The Reduced-Form Regression Model
451
17.1.3
Estimating the Reduced-Form Coefficients
453
17.1.4
The Identification Problem
455
17.2
Least-Squares and GMM Estimation: The Semiparametric Case
458
17.2.1
Estimators of Parameters for a Just-Identified
Structural Equation
459
17.2.2
GMM Estimator of Parameters for an Overidentified
Structural Equation
460
17.2.3
Estimation of a Complete System of Equations
462
17.3
Maximum Likelihood Estimation in the Linear Model:
The Parametric Case
465
17.3.1
Full-Information Maximum Likelihood (FIML)
465
17.3.2
Limited Information Maximum Likelihood (LIML)
467
17.4
Nonlinear Simultaneous Equations
468
17.4.1
Single-Equation Estimation: Semiparametric Case
469
17.4.2
Complete System Estimation: Semiparametric Case
472
xviü
CONTENTS
17.4.3 Nonlinear Maximum
Likelihood Estimation:
Parametric Case
473
17.4.4
Identification in Nonlinear Systems of Equations
474
17.5
Information Theoretic Procedures
475
17.5.1
Minimum KLIC Approach:
MEEL
and MEL
476
17.5.2
MEEL
Estimation and Inference
479
17.5.3
MEL Estimation
484
17.5.4
The KLIC-MEEL-MEL Procedures: Critique
485
17.6
OptEF Estimation and Inference
486
17.6.1
The OptEF Estimator in Simultaneous Equations Models
486
17.6.2
OptEF Asymptotic Unification of Inverse Problem Solutions
487
17.7
Concluding Comments
488
17.8
Exercises
489
17.8.1
Idea Checklist
-
Knowledge Guides
489
17.8.2
Problems
489
17.8.3
Computer Problems
490
17.9
References
491
17.10
Appendix: Historical Perspective
492
VII
Model Discovery
495
18
Model Discovery: The Problem of Variable Selection
and Conditioning
497
18.1
Introduction
497
18.1.1
Experiments in Nonexperimental Model Building
498
18.1.2
The Chapter Format
499
18.2
Variable Selection Problem in a Loss or
MSE
Context
500
18.2.1
Bias-Variance Trade-Off in Incorrect Variable Selection
501
18.2.2
Statistical Implications under an
MSE
Matrix Measure
503
18.2.3
Statistical Implications under a Quadratic Risk
Function Measure
505
18.2.4
Extensions to Nonlinear Models, General Covariance
Structures, and Systems of Equations
506
18.3
Fisherian Testing and Model Choice: Critique
507
18.4
Estimated Risk Criteria and Model Choice: Mallows Cp Criterion
509
18.5
An Information Theoretic Model Selection Criterion:
Akaiké
Information
511
18.5.1
Basic Rationale for the AIC and Variants
511
18.5.2
A Comment
513
18.6
Shrinkage as a Basis for Dealing with Variable Uncertainty
514
18.6.1
Stein-Like Shrinkage Estimators
514
18.6.2
Multiple Shrinkage Estimator
515
18.7
The Problem of an Ill-Conditioned Explanatory Variable Matrix
517
18.7.1
Penalized Estimation
518
18.7.2
Finite Sample Performance
520
xix
CONTENTS
18.8 Final
Comments and
Critique
521
18.9
Exercises
524
18.9.1
Idea Checklist- Knowledge Guides
524
18.9.2
Problems
524
18.9.3
Computer Problems
524
18.10
References
525
19
Model Discovery: The Problem of Noise Covariance
Matrix Specification
528
19.1
Introduction
528
19.2
Specific Parametric Specifications of the Noise Covariance Matrix:
Estimation and Inference
530
19.2.1
AR(1) Noise
530
19.2.2
Heteroscedastic Noise: af
=
(z¡
.α)2
533
19.3
Tests for Heteroscedasticity: Rationale and Application
535
19.3.1
Types of Heteroscedasticity Tests
536
19.3.2
Motivation for Tests Based on
ε2
536
19.3.3
Motivation for the Test Based on
1η(ε2)
540
19.3.4
Motivation for Test Based on
êt
|
541
19.3.5
More Tests
542
19.4
Tests for Autocorrelation: Rationale and Application
543
19.4.1
Autocorrelation Processes
543
19.4.2
Estimation
546
19.4.3
Autocorrelation Tests
547
19.5
Pretest Estimators Defined by Heteroscedasticity
or Autocorrelation Testing
551
19.5.1
Two-Equation Linear System with Potential
Heteroscedasticity
552
19.5.2
A Heteroscedasticity Pretest Estimator
553
19.5.3
An Autocorrelation Pretest Estimator
555
19.6
Concluding Comments
556
19.7
Exercises
557
19.7.1
Idea Checklist
-
Knowledge Guides
557
19.7.2
Problems
557
19.7.3
Computer Problems
557
19.8
References
558
VIII
Special Econometric Topics
561
20
Qualitative-Censored Response Models
563
20.1
Binary-Discrete Choice Response Models
565
20.1.1
A Linear Probability Model
566
20.1.2
A Reformulated Binary Response Model
567
xx
CONTENTS
20.2 Maximum
Likelihood Estimation and Inference for the Discrete
Choice Model
570
20.2.1
Logit Model
571
20.2.2
Probit
Model
573
20.2.3
Probit
or Logit?
575
20.3
Multinomial Discrete Choice
575
20.3.1
Multinomial Logit
576
20.3.2
Information Theoretic Estimation of the Multinomial
Decision Model
581
20.3.3
Ordered Multinomial Choice
584
20.4
Censored Response Data
585
20.4.1
Censoring Versus Truncation
585
20.4.2
Tobit Model
587
20.4.3
Extensions of the Tobit Formulation
591
20.5
Concluding Remarks
592
20.6
Exercises
594
20.6.1
Idea Checklist
-
Knowledge Guides
594
20.6.2
Problems
594
20.6.3
Computer Problems
595
20.7
References
595
20.8
Appendix
597
21
Introduction to Nonparametric Density and Regression Analysis
599
21.1
Density Estimation via Kernels
601
21.1.1
Kernels
602
21.1.2
IMSE, AIMSE, and Kernel Choice
604
21.1.3
Bandwidth Choice
606
21.1.4
Other Properties and Issues
608
21.1.5
Multivariate Extensions
609
21.2
Kernel Regression Estimators
611
21.2.1
Nonparametric Regression Model Specification
612
21.2.2
Nadaraya-Watson Kernel Regression: Alias Zero-Order
Local Polynomial Regression
613
21.3
Local Polynomial Regression
622
21.4
Prequel
of Fundamental Concepts: Local Weighted Averages,
Local Linear Regressions, and Histograms
624
21.4.1
Nonparametric Regression under Repeated Sampling:
Simple Sample Means
625
21.4.2
Local Sample Means: Using Data Neighborhoods
626
21.4.3
Local Weighted Averages within Data Neighborhoods:
Local Least-Squares Regressions
628
21.4.4
Local Polynomial Regressions
629
21.4.5
Histograms: Precursor to Kernel Density Estimation
630
21.5
Concluding Comments
636
xxi
CONTENTS
21.6
Exercises
637
21.6.1
Idea Checklist
-
Knowledge Guides
637
21.6.2
Problems
637
21.6.3
Computer Problems
638
21.7
References
638
21.8
Appendix: Derivation of Equation
(21.4.31) 640
IX Bayesian Estimation and Inference
643
22
Bayesian Estimation:
General
Principles with a
Regression Focus
645
22.1
Introduction
645
22.1.1
Bayes
Theorem
646
22.1.2
A Format for Bayesian Reasoning
647
22.2
Bayesian Probability Models and Posterior Distributions
649
22.2.1
Prior Distributions
650
22.2.2
Posterior Probability Distributions
651
22.3
The Bayesian Linear-Regression-Based Probability Model
652
22.3.1
Bayesian Regression Analysis under Normality
and
Uninformative
Priors
653
22.3.2
Uninformative Priors and Proper Marginal Posteriors
654
22.3.3
Posterior Distribution under an Uninformative Prior
655
22.3.4
Marginal Posteriors
656
22.4
Bayesian Regression Analysis under Normality and Conjugate
Informative Priors
658
22.4.1
The Joint Posterior Distribution under the Conjugate Prior
660
22.4.2
The Marginal Posteriors
660
22.5
Bayesian Point Estimates
661
22.5.1
Minimum Expected Risk
663
22.5.2
Admissibility
663
22.5.3
Consistency and Asymptotic Normality
663
22.5.4
Comments on
Bayes
Estimator Properties
664
22.6
On the Use of Conjugate Priors and Coincidence of Classical
and Bayesian Estimates
665
22.7
Concluding Remarks
666
22.8
Exercises
667
22.8.1
Idea Checklist-Knowledge Guides
667
22.8.2
Problems
667
22.83
Computer Problems
668
22.9
References
669
22.10
Appendix: Bayesian Asymptotics
669
22.10.1
Bayesian Asymptotics: Specific Cases
670
22.10.2
Bayesian Asymptotics: General Considerations
672
22.103
Appendix References
674
xxii
CONTENTS
23 Alternative
Bayes Formulations
for the Regression Model
675
23.1
g-Priors
676
23.1.1
A Family of
g-priors
and Associated Posteriors
676
23.1.2
Rationalizing and Specifying g-priors
678
23.2
An Empirical
Bayes
Estimator
679
23.3
General Bayesian Regression Analysis with
Nonconjugate Informative-Uninformative Prior
682
23.3.1
Normal Noise Component
682
23.3.2 Nonnormal
Noise Component
687
23.3.3
Summary Comments
688
23.4
Bayesian Method of Moments
688
23.4.1
Continuous Entropy Formulation
691
23.4.2
A Posterior Density Function
692
23.5
Concluding Remarks
693
23.6
Exercises
694
23.6.1
Idea Checklist- Knowledge Guides
694
23.6.2
Problems
694
23.6.3
Computer Problems
695
23.7
References
696
24
Bayesian Inference
698
24.1
Credible Regions
699
24.1.1
General Principles
699
24.1.2
Highest Posterior Density Credible Regions
700
24.1.3
Credible Regions in the Regression Model
701
24.2
Hypothesis Evaluation and Decision
702
24.2.1
General Principles
703
24.3
General Hypothesis Testing and Credible Sets
in the Regression Model
704
24.3.1
Evaluating Composite Hypotheses about
β
and
Bayes
Factors
704
243.2
Evaluating Simple Hypotheses about
β
706
24.4
A Comment
708
24.5
Exercises
708
24.5.1
Idea Checklist-Knowledge Guides
708
24.5.2
Problems
708
24.5.3
Computer Problems
709
24.6
References
709
X Epilogue
711
Appendix: Introduction to Computer Simulation and
Resampling Methods
713
A.1 Pseudorandom Number Generation
713
A.1.1 Generating U(0,
1)
Pseudorandom Numbers
714
xxiii
CONTENTS
АЛЈ2
Generating Continuous
Nonuniform
Pseudorandom Numbers
715
A.1.3 Generating Discrete Pseudorandom Numbers
717
A.1.4 Evaluating the Performance of Pseudorandom
Number Generators
718
A.2 Monte Carlo Simulation
719
A.2.1 Background and Conceptual Motivation
720
A.2.2 Key Assumptions
721
A.2.3 Basic Properties of Monte Carlo Simulation Estimators
722
A.3 Bootstrap Resampling
724
A.3.1 Basic Properties of the Bootstrap
725
A.3.2 Bootstrap Simulation Procedures for Regression Models
728
A.4 Numerical Tools for Evaluating Posterior Distributions
730
A.4.1 The Gibbs Sampling Algorithm
731
A.4.2 The Metropolis-Hastings Algorithm
733
A.5 Concluding Remarks
734
A.6 Exercises
735
A.6.1 Idea Checklist
735
A.6.2 Problems
735
A.6.3 Computer Problems
735
A.7 References
736
Author Index
739
Subject Index
743
CD-ROM
Foundations Review
El Probability Theory
E2 Classical Estimation and Inference Principles
E3 Ill-Posed Inverse Problems
ELECTRONIC MANUALS
Matrix Review Manual
Econometric Examples Manual
GAUSS Tutorial and Technical Archive
GAUSS Software
XXIV
|
| any_adam_object | 1 |
| author | Mittelhammer, Ron C. Judge, George G. 1925- Miller, Douglas J. 1965- |
| author_GND | (DE-588)12963221X (DE-588)131450530 |
| author_facet | Mittelhammer, Ron C. Judge, George G. 1925- Miller, Douglas J. 1965- |
| author_role | aut aut aut |
| author_sort | Mittelhammer, Ron C. |
| author_variant | r c m rc rcm g g j gg ggj d j m dj djm |
| building | Verbundindex |
| bvnumber | BV013255040 |
| callnumber-first | H - Social Science |
| callnumber-label | HB139 |
| callnumber-raw | HB139 |
| callnumber-search | HB139 |
| callnumber-sort | HB 3139 |
| callnumber-subject | HB - Economic Theory and Demography |
| classification_rvk | QH 300 QH 310 |
| classification_tum | WIR 017f |
| ctrlnum | (OCoLC)247760144 (DE-599)BVBBV013255040 |
| dewey-full | 330.015195 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 330 - Economics |
| dewey-raw | 330.015195 |
| dewey-search | 330.015195 |
| dewey-sort | 3330.015195 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV013255040 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:42:34Z |
| institution | BVB |
| isbn | 0521623944 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009035062 |
| oclc_num | 247760144 |
| open_access_boolean | |
| owner | DE-703 DE-N2 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-20 DE-945 DE-473 DE-BY-UBG DE-739 DE-M49 DE-BY-TUM DE-384 DE-634 DE-11 DE-188 |
| owner_facet | DE-703 DE-N2 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-20 DE-945 DE-473 DE-BY-UBG DE-739 DE-M49 DE-BY-TUM DE-384 DE-634 DE-11 DE-188 |
| physical | XXVIII, 756 S. graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Mittelhammer, Ron C. Verfasser aut Econometric foundations Ron C. Mittelhammer ; George G. Judge ; Douglas J. Miller 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2000 XXVIII, 756 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Lehrbuch - Ökonometrie Ökonometrie / Theorie Econometrics Ökonometrie (DE-588)4132280-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Ökonometrie (DE-588)4132280-0 s DE-604 Judge, George G. 1925- Verfasser (DE-588)12963221X aut Miller, Douglas J. 1965- Verfasser (DE-588)131450530 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009035062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mittelhammer, Ron C. Judge, George G. 1925- Miller, Douglas J. 1965- Econometric foundations Lehrbuch - Ökonometrie Ökonometrie / Theorie Econometrics Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4132280-0 (DE-588)4123623-3 |
| title | Econometric foundations |
| title_auth | Econometric foundations |
| title_exact_search | Econometric foundations |
| title_full | Econometric foundations Ron C. Mittelhammer ; George G. Judge ; Douglas J. Miller |
| title_fullStr | Econometric foundations Ron C. Mittelhammer ; George G. Judge ; Douglas J. Miller |
| title_full_unstemmed | Econometric foundations Ron C. Mittelhammer ; George G. Judge ; Douglas J. Miller |
| title_short | Econometric foundations |
| title_sort | econometric foundations |
| topic | Lehrbuch - Ökonometrie Ökonometrie / Theorie Econometrics Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Lehrbuch - Ökonometrie Ökonometrie / Theorie Econometrics Ökonometrie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009035062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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