## An Introduction to Bayesian inference in econometrics

Author: Zellner, Arnold Series: Wiley series in probability and mathematical statistics Publisher: Wiley, 1971.Language: EnglishDescription: 431 p ; 24 cm.ISBN: 0471981656Type of document: BookNote: Doriot and Tanoto: for 2016-2017 coursesBibliography/Index: Includes bibliographical references List(s) this item appears in: Textbooks for Bayesian Analysis / Anil Gaba / PhD 2016-2017Item type | Current location | Collection | Call number | Status | Date due |
---|---|---|---|---|---|

Doriot Library Main Collection |
HB74 .M3 Z44
(Browse shelf) 000075758 |
Available | |||

Tanoto Library Textbook Collection (PhD) |
HB74 .M3 Z44 1971
(Browse shelf) 900209411 |
Available |

Doriot and Tanoto: for 2016-2017 courses

Includes bibliographical references

Digitized

An Introduction to Bayesian

Inference in Econometrics

Contents

I Remarks on Inference in Economics 1

1.1 The Unity of Science 1

1.2 Deductive Inference 2

1.3 Inductive Inference 4

1.4 Reductive Inference 5

1.5 Jeffreys' Rules for a Theory of Inductive Inference 7

1.6 Implications of the Rules 8

Questions and Problems 12

II Principles of Bayesian Analysis with Selected

Applications 13

2.1 Bayes' Theorem 13

2.2 Bayes' Theorem and Several Sets of Data 17

2.3 Prior Probability Density Functions 18

2.4 Marginal and Conditional Posterior Distributions

for Parameters 21

2.5 Point Estimates for Parameters 24

2.6 Bayesian Intervals and Regions for Parameters 27

2.7 Marginal Distribution of the Observations 28

2.8 Predictive Probability Density Functions 29

2.9 Point Prediction 30

2.10 Prediction Regions and Intervals 31

2.11 Some Large Sample Properties of Bayesian

Posterior Pdf's 31

2.12 Application of Principles to Analysis of the Pareto

Distribution 34

2.13 Application of Principles to Analysis of the

Binomial Distribution 38

2.14 Reporting the Results of Bayesian Analyses 40

Appendix 41

Questions and Problems 54

III The Univariate Normal Linear Regression

Model 58

3.1 The Simple Univariate Normal Linear Regression

Model 58

3.1.1 Model and Likelihood Function 58

3.1.2 Posterior Pdf's for Parameters with a Diffuse

Prior Pdf 60

3.1.3 Application to Analysis of the Investment

Multiplier 63

3.2 The Normal Multiple Regression Model 65

3.2.1 Model and Likelihood Function 65

3.2.2 Posterior Pdf's for Parameters with a Diffuse

Prior Pdf 66

3.2.3 Posterior Pdf Based on an Informative

Prior Pdf 70

3.2.4 Predictive Pdf 72

3.2.5 Analysis of Model when X'X is Singular 75

Questions and Problems 82

IV Special Problems in Regression Analysis 86

4.1 The Regression Model with Autocorrelated Errors 86

4.2 Regressions with Unequal Variances 98

4.3 Two Regressions with Some Common Coefficients 108

Appendix 1 110

Appendix 2 110

Questions and Problems 112

V On Errors in the Variables 114

5.1 The Classical EVM: Preliminary Problems 114

5.2 Classical EVM: ML Analysis of the Functional Form 123

5.3 ML Analysis of Structural Form of the EVM 127

5.4 Bayesian Analysis of the Functional Form of the EVM 132

5.5 Bayesian Analysis of the Structural Form of the EVM 145

5.6 Alternative Assumption about the Incidental

Parameters 145

Appendix 154

Questions and Problems 157

VI Analysis of Single Equation Nonlinear

Models 162

6.1 The Box-Cox Analysis of Transformations 162

6.2 Constant Elasticity of Substitution (CES)

Production Function 169

6.3 Generalized Production Functions 176

Questions and Problems 183

VII Time Series Models : Some Selected

Examples 186

7.1 First Order Normal Autoregressive Process 186

7.2 First Order Autoregressive Model with Incomplete

Data 191

7.3 Analysis of a Second Order Autoregressive Process 194

7.4 " Distributed Lag" Models 200

7.5 Applications to Consumption Function Estimation 207

7.6 Some Generalizations of the Distributed Lag Model 213

Appendix 216

Questions and Problems 220

VIII Multivariate Regression Models 224

8.1 The Traditional Multivariate Regression Model 224

8.2 Predictive Pdf for the Traditional

Multivariate Regression Model 233

8.3 The Traditional Multivariate Model with Exact

Restrictions 236

8.4 Traditional Model with an Informative Prior Pdf 238

8.5 The "Seemingly Unrelated" Regression Model 240

Questions and Problems 246

IX Simultaneous Equation Econometric

Models 248

9.1 Fully Recursive Models 250

9.2 General Triangular Systems 252

9.3 The Concept of Identification in Bayesian Analysis 253

9.4 Analysis of Particular Simultaneous Equation Models 258

9.5 "Limited Information" Bayesian Analysis 265

9.6 Full System Analysis 270

9.7 Results of Some Monte Carlo Experiments 276

9.7.1 The Model and Its Specifications 277

9.7.2 Sampling-Theory Analysis of the Model 278

9.7.3 Bayesian Analysis of the Model 278

9.7.4 Experimental Results: Point Estimates 280

9.7.5 Experimental Results: Confidence Intervals 286

9.7.6 Concluding Remarks on the Monte Carlo

Experiments 286

Questions and Problems 287

X On Comparing and Testing Hypotheses 291

10.1 Posterior Probabilities Associated with Hypotheses 292

10.2 Analyzing Hypotheses with Diffuse Prior Pdf's for

Parameters 298

10.3 Comparing and Testing Hypotheses with Nondiffuse

Prior Information 302

10.4 Comparing Regression Models 306

10.5 Comparing Distributed Lag Models 312

Questions and Problems 317

XI Analysis of Some Control Problems 319

11.1 Some Simple One Period Control Problems 320

11.2 Single-Period Control of Multiple Regression Processes 327

11.3 Control of Multivariate Normal Regression Processes 331

11.4 Sensitivity of Control to Form of Loss Function 333

11.5 Two-Period Control of the Multiple Regression Model 336

11.6 Some Multiperiod Control Problems 344

Appendix 1 354

Appendix 2 356

Questions and Problems 358

XII Conclusion 360

Appendix A 363

Appendix B 379

Appendix C 400

Bibliography 415

Author Index 423

Subject Index 427

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