Uniform Priors for Impulse Responses

There has been a call for caution when using the conventional method for Bayesian inference in set-identified structural vector autoregressions on the grounds that the uniform prior over the set of orthogonal matrices could be nonuniform for key objects of interest. This paper challenges this call. Although the prior distributions of individual impulse responses induced by the conventional method may be nonuniform, they typically do not drive the posteriors if one does not condition on the reduced-form parameters. Importantly, 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. We also propose variants of the conventional method to conduct inference based on a uniform joint prior distribution for the vector of impulse responses. We generalize our results to vectors of objects of interest beyond impulse responses.