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Atlanta Fed Working Papers

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 2014-1
February 2014

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Are optimism shocks an important source of business cycle fluctuations? Are deficit-financed tax cuts better than deficit-financed spending to increase output? These questions have been previously studied using structural vector autoregressions (SVAR) identified with sign and zero restrictions and the answers have been positive and definite in both cases. Although the identification of SVARs with sign and zero restrictions is theoretically attractive because it allows the researcher to remain agnostic with respect to the responses of the key variables of interest, we show that current implementation of these techniques does not respect the agnosticism of the theory. These algorithms impose additional sign restrictions on variables that are seemingly unrestricted that bias the results and produce misleading confidence intervals. We provide an alternative and efficient algorithm that does not introduce any additional sign restriction, hence preserving the agnosticism of the theory. Without the additional restrictions, it is hard to support the claim that either optimism shocks are an important source of business cycle fluctuations or deficit-financed tax cuts work best at improving output. Our algorithm is not only correct but also faster than current ones.

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 them 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 for support.The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Jonas E. Arias, International Finance, Federal Reserve Board of Governors, 20th and C Street, N.W., Washington, DC 20551, 202-973-6124,; Juan F. Rubio-Ramírez (corresponding author), Economics Department, Duke University, Durham, NC 27708; 919-660-1865,; or Daniel F. Waggoner, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8278,

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