Uniform Priors for Impulse Responses

A previous version of this working paper was originally published in September 2022.

There has been a call for caution regarding the standard procedure for Bayesian inference in set-identified structural vector autoregressions on the grounds that the common practice of using a uniform prior over the set of orthogonal matrices induces a non-uniform prior for individual impulse responses or other quantities of interest. This paper challenges this call by formally showing that when the focus is on joint inference, the uniform prior over the set of orthogonal matrices is not only sufficient but also necessary for inference based on a uniform joint prior distribution over the identified set for the vector of impulse responses. In addition, we show how to conduct inference based on a uniform joint prior distribution for the vector of impulse responses.