Priors about Observables in Vector Autoregressions

Standard practice in Bayesian VARs is to formulate priors on the autore- gressive parameters, but economists and policy makers actually have priors about the behavior of observable variables. Our proposal is to use prior infor- mation on observables systematically. We show how this kind of prior can be used under strict probability theory principles. We state the inverse problem to be solved and we propose a numerical algorithm that works well in practical situations with a large number of parameters. We prove various convergence theorems for the algorithm. Using examples from the VAR literature, we show how priors on observables can address a priori weaknesses of standard priors, serving as a cross check and an alternative formulation.