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

by J.A. Morales

Overview

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 = {x} denotes the sample space, and e = {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.

Product Details

ISBN-13:	9783540054177
Publisher:	Springer Berlin Heidelberg
Publication date:	04/01/1971
Series:	Lecture Notes in Economics and Mathematical Systems , #43
Edition description:	Softcover reprint of the original 1st ed. 1971
Pages:	160
Product dimensions:	7.01(w) x 10.00(h) x 0.01(d)

Table of Contents

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.- 2. The extended natural conjugate density and its properties.- 3. Posterior distributions of the structural parameters (?,—-1).- 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.- 2. The Posterior Analysis.- Conclusions.- References.