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Handbook of Econometrics Vols1-5 _ Chapter 9

Chapter 9 BAYESIAN SYSTEMS ANALYSIS OF SIMULTANEOUS EQUATION This chapter discusses classical estimation methods for limited dependent variable (LDV) models that employ Monte Carlo simulation techniques to overcome computational problems in such models. | Chapter 9 BAYESIAN ANALYSIS OF SIMULTANEOUS EQUATION SYSTEMS JACQUES H. DRÈZE and JEAN-FRANCOIS RICHARD Université Catholique de Louvain Contents 1. Introduction and summary 1.1. The simultaneous equation model 1.2. Bayesian inference and identification 1.3. Bayesian treatment of exact restrictions 1.4. Bayesian analysis of the reduced form 1.5. Bayesian analysis of the structural form 1.6. Summary 1.7. Bibliographical note 2. A special case 2.1. Limited information maximum likelihood estimation 2.2. A Bayesian analogue 2.3. The normalization issue 2.4. An application 3. Identification 3.1. Classical concepts 3.2. Posterior densities and identification 3.3. Prior densities and identification 3.4. Choice of models and identification 4. Reduced-form analytics 4.1. Natural-conjugate prior densities 4.2. Further results 5. Limited information analysis 5.1. Introduction 5.2. Parameterization and invariance 5.3. Posterior conditional densities and moments 5.4. Posterior marginal densities 519 519 521 522 523 524 525 526 526 526 529 531 533 535 535 536 537 538 539 539 541 544 544 544 550 552 The authors thank David F. Hendry Teun Kloek Hans Tompa Herman van Dijk and Arnold Zellner for helpful comments on a preliminary version. They are particularly grateful to Luc Bauwens for his assistance with computations and his detailed comments on the manuscript. Handbook of Econometrics Volume I Edited by Z. Griliches and M.D. Intriligator North-Holland Publishing Company 1983 518 J. H. DrezeandJ-F. Richard 5.5. An application 555 5.6. Normalization and invariance 557 5.7. Two generalizations 559 6. Full information analysis 561 6.1. Introduction 561 6.2. A special case 561 6.3. Extended natural-conjugate prior densities 563 6.4. Seemingly unrelated regression models 567 6.5. Two-equation models 568 6.6. Applications 571 7. Numerics 579 7.1. Introduction 579 7.2. Evaluation of poly-r densities 579 7.3. Numerical integration 581 Appendix A Elements of multivariate analysis 585 .