Bayesian Full Information Structrual Analysis: with an Application to the Study of the Belgian Beef Market

ISBN-13: 9783540054177 / Angielski / Miękka / 1971 / 160 str.

J. A. Morales

Opis

1 1. Statement of the problem. Bayes' theorem provides a very powerful tool for statistical inference, especially when pooling information from different sources is appropriate. Thus, prior information resulting from economic theory and/or from previous (real or hypothetical) samples can be combined with the information embodied in new observations; and this operation can be performed formally, within a rigorous mathematical framework. To introduce the Bayesian analysis of the simultaneous equations model, we shall base our presentation in the very convenient exposition given by Dreze in his presidential adress to the . S' 2 C f Second World ongress 0 the Econometr1c oC1ety. The Bayesian method in statistics is usually presented as follows Consider the joint probability density function f(x.e) defined on the product space X x9, where X = denotes the sample space, and e = denotes the parameter space, If we decompose the joint density f(x,e) in a conditional density f(x/e) and a marginal lThe beginning of this section reviews some very well known proposi- tions of Bayesian analysis. Those who are familiar with the subject can skip this part, and start with p.5. 2J.H.Dreze. "Econometrics and Decision Theory". Presidential adress delivered at the Second World Congress of the Econometric Society.

Spis treści

I. Bayesian Full Information Analysis of the Simultaneous Equations Model.- 1. A review of the problem of identification in a Bayesian approach and the specifications of the prior density functions.- 1.1. The statistical model and notation.- 1.2. The problem of identification in a Bayesian context and the choice of prior distributions.- 2. The extended natural conjugate density and its properties.- 2.1. The extended natural conjugate density of all the parameters of the model.- 2.2. The extended natural conjugate density bearing on the parameters of a model with prior exclusion restrictions.- 2.3. Interpretation of the extended natural conjugate density.- 3. Posterior distributions of the structural parameters (?, ?-1).- 3.1. The joint a posteriori density of (?, ?-1).- 3.2. The marginal density function of ?.- Appendix to Part I. Some properties of the Wishart density function and the matric variate-t-density function.- II. Empirical illustration of a Bayesian Full Information Analysis. The analysis of the Belgian beef market.- 1. The model and the a priori information.- 1.1. The model of Calicis.- 1.2. Two equations models for the Belgian beef market.- 1.3. The likelihood function and the a priori density function.- 1.4. A description of the sources of prior-information.- 1.5. The complete specification of the prior density function.- 2. The Posterior Analysis.- 2.1. The posterior distributions.- 2.2. Comments on the results of the posterior analysis.- Conclusions.- References.