Inference Based on SVARs Identified with Sign and Zero Restrictions: Theory and Applications

Jonas E. Arias, Juan F. Rubio-Ramírez, and Daniel F. Waggoner
Working Paper 2014-1a
Revised November 2016

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In this paper we characterize agnostic and conditionally agnostic priors and propose numerical algorithms for Bayesian inference when using sign and zero restrictions to identify SVARs. As Baumeister and Hamilton (2015a) have made clear, priors play a crucial role in this environment. If the prior, subject to the sign and zero restrictions, is not conditionally agnostic, then the prior affects identification. Hence, identification does not solely come from the sign and zero restrictions stated by the researcher. Our numerical algorithms show how to do inference based on SVARs using conditionally agnostic priors and posteriors subject to sign and zero restrictions. We use Beaudry, Nam and Wang's (2011) work on the relevance of optimism shocks to show the dangers of using priors that are not conditionally agnostic subject to the sign and zero restrictions.

JEL classification: C11, C32, E50

Key words: identification, sign restrictions, simulation

The authors thank Paul Beaudry, Andrew Mountford, Deokwoo Nam, and Jian Wang for sharing supplementary material with us, and for helpful comments. They also thank Grátula Bedátula for her support and help. Without her this paper would have been impossible. This paper has circulated under the title "Algorithm for Inference with Sign and Zero Restrictions." Juan F. Rubio-Ramírez also thanks the National Science Foundation, the Institute for Economic Analysis (IAE) and the "Programa de Excelencia en Educación e Investigación" of the Bank of Spain, and the Spanish Ministry of Science and Technology ref. ECO2011-30323-c03-01 for support. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Board of Governors of the Federal Reserve System. Any remaining errors are the authors' responsibility.
Please address questions regarding content to Jonas E. Arias, Research Department, Federal Reserve Bank of Philadelphia, Ten Independence Mall, Philadelphia, PA 19106-1574,; Juan F. Rubio-Ramírez (corresponding author), Economics Department, Emory University, Atlanta, GA 30322,; or Daniel F. Waggoner, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street NE, Atlanta, GA 30309-4470, 404-498-8278,
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