When Is the Use of Gaussian-Inverse Wishart-Haar Priors Appropriate?

Abstract

We provide evidence that the quantitative importance of the Haar prior for posterior impulse response inference has been overstated. How sensitive posterior inference is to the Haar prior depends on the width of the identified set. This width depends not only on how much the identified set is narrowed by the identifying restrictions but also on the data through the reduced-form model parameters. Hence, the role of the Haar prior can be assessed only on a case-by-case basis. We show by example that when the identification is sufficiently tight, posterior inference based on a Gaussian-inverse Wishart-Haar prior is justified.