Working Paper

Inference Based on Scale, Label, and Economic Restrictions

Abstract: The results of nearly 100 prominent studies in empirical macroeconomics have been called into question by Baumeister and Hamilton (2018). 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.

JEL Classification: C11; C32;

https://doi.org/10.21799/frbp.wp.2026.36

Bibliographic Information

Provider: Federal Reserve Bank of Philadelphia

Part of Series: Working Papers

Publication Date: 2026-07-22

Number: 26-36