Inference Based on Scale, Label, and Economic Restrictions

Jonas E. Arias, Juan F Rubio-Ramirez and Daniel Waggoner
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Jonas E. Arias: https://www.philadelphiafed.org/our-people/jonas-arias

No 26-36, Working Papers from Federal Reserve Bank of Philadelphia

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.

Keywords: structural vector autoregressions; unit modulus normalization (search for similar items in EconPapers)
JEL-codes: C11 C32 (search for similar items in EconPapers)
Pages: 47
Date: 2026-07-22
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DOI: 10.21799/frbp.wp.2026.36

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