Inference Based on Scale, Label, and Economic Restrictions

We show that their concern about distributional asymmetry for a typical question of interest under a uniform prior with respect to the Haar measure is actually driven by an unacknowledged sign restriction. We also demonstrate that such a prior induces symmetric prior distributions over individual impulse responses conditional on the reduced-form parameters, or more generally when the prior over the reduced-form covariance matrix rules out correlation among the residuals, as in the typical implementation of the Minnesota prior. Furthermore, we provide a theory for avoiding the pitfalls of Baumeister and Hamilton's critique. Key to our theory is a proposition establishing that any restriction can be decomposed into three types: scale, label, and economic. We use this theory to develop an algorithm for inference based on the unit modulus normalization that tackles a practical problem commonly faced by users of Bayesian SVAR methods.