The Conventional Impulse Response Prior in VAR Models With Sign Restrictions

Abstract

Some studies have expressed concern that the Gaussian-inverse Wishart–Haar prior typically employed in estimating sign-identified VAR models may be unintentionally informative about the prior for the structural responses. We discuss what features to look for in this prior in the absence of specific prior information about the responses, building on the notion of weakly informative priors in Gelman et al. (2013), and in the presence of such information. Empirical examples illustrate that the Gaussian-inverse Wishart–Haar prior need not be unintentionally informative. Even when it is, there are empirically verifiable conditions under which this fact becomes immaterial for the substantive conclusions.