## Abstract

This paper considers a robust Bayes inference for structural vector autoregressions, where impulse responses of interest are non-identified. The non-identified impulse responses arise if the insufficient number of equality restrictions and/or a set of sign restrictions on impulse responses are the only credible assumptions available. A posterior distribution for the set-identified impulse responses obtained via the standard Bayesian procedure remains to be sensitive to a choice of prior, even asymptotically. In order to make posterior inference free from such sensitivity concern, this paper introduces a class of priors (ambiguous belief) for the non-identified aspects of the model, and proposes to report the range of the posterior mean and posterior probability for the impulse responses as a prior varies over the class. We argue that this posterior bound analysis is a useful tool to separate the information for the impulse responses provided by the likelihood from the information provided by the prior input that cannot be updated by data. The posterior bounds we construct asymptotically converge to the true identified set, which frequentist inference in set-identified models typically concerns. In terms of implementation, the posterior bound analysis is computationally simpler, and can accommodate a larger class of zero and sign restrictions than the frequentist confidence intervals proposed by Moon, Schorfheide, and Granziela (2013).