On Bayesian structural inference in a simultaneous equation model

Econometric issues that are considered fundamental in the development of Bayesian structural inference within a Simultaneous Equation Model are surveyed. The difficulty of specifying prior information which is of interest to economists and which yields tractable posterior and predictive distributions has started this line of research. A major issue is the nonstandard shape of the likelihood due to reduced rank restrictions. It implies that existence of structural posterior moments under vague prior information is a nontrivial issue. The problem is illustrated through simple examples using artificially generated data in a so-called limited information framework where the connection with the problem of weak instruments in classical econometrics is also described. A positive development is Bayesian inference of implied characteristics, in particular, dynamic features of a Simultaneous Equation Model. The potential of Bayesian structural inference, using a predictive approach for prior specification and using Monte Carlo simulation techniques for computational purposes, is illustrated by means of a prior and posterior analysis of the US business cycle in the period of the depression. A structural prior is elicited through investigation of the implied predictive features.