The Conventional Impulse Response Prior in VAR Models with Sign Restrictions

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 implied prior for the structural impulse responses. We discuss how this prior may be reported and make explicit what impulse response priors a number of recently published studies specified, allowing the readers to decide whether they are comfortable with this prior. 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. Our empirical examples illustrate that the Gaussian-inverse Wishart-Haar prior need not be unintentionally informative about the impulse responses. Moreover, even when it is, there are empirically verifiable conditions under which this fact becomes immaterial for the substantive conclusions.