Some 20 years ago, J. Drèze (1962) opened a new prospect for the statistical treatment of the « simultaneous equation model » in econometrics (SEM). Indeed, he advocated the use of Bayesian methods for the analysis of such models. In particular, he pointed out the flexibility of this approach as it allows to take account not only of the a priori information provided by economic theory or observation, but more fundamentally, of the imprecise nature of this kind of information.
Ever since, it has been clear that the Bayesian approach of the SEM would be rather difficult to implement. The main problems one can identify are
1. the representation of a priori information by a prior density function which should be easily interpretable and at the same time flexible enough;
2. the numerical treatment (i.e. integration) of the posterior density so as to obtain moments and marginal densities of parameters, whether they be parameters of the structural form, of the reduced form, or functions thereof.