The Role of the Prior in Estimating VAR Models with Sign Restrictions

Abstract

Several recent studies have expressed concern that the Haar prior typically employed in estimating sign-identified VAR models may be unintentionally informative about the implied prior for the structural impulse responses and hence about their posterior. In this paper, we provide evidence that the quantitative importance of the Haar prior for posterior inference has been overstated. We show that the influence of the Haar prior tends to be negligible in structural VAR models that are tightly identified by sign restrictions (possibly in conjunction with narrative restrictions or exclusion restrictions), as is common in applied work. Such models imply a narrow identified set for the impulse responses, so which model is selected among the structural models in the identified set, becomes quantitatively unimportant. We also demonstrate that the alternative Bayesian approach to estimating sign-identified VAR models proposed by Baumeister and Hamilton (2015) suffers from the same conceptual shortcoming as the conventional approach in that it may imply an unintentionally informative impulse response prior. JEL code: C22, C32, C52, E31, Q43