Jonas E. Arias, Juan F. Rubio-RamÃrez, and Daniel F. Waggoner
Working Paper 2023-13
September 2023
Abstract:
There has been a call for caution when using the conventional method for Bayesian inference in set-identified structural vector autoregressions on the grounds that the uniform prior over the set of orthogonal matrices could be nonuniform for individual impulse responses or other quantity of interest. This paper challenges this call by formally showing that, when the focus is on joint inference, the uniform prior over the set of orthogonal matrices is not only sufficient but also necessary for inference based on a uniform joint prior distribution over the identified set for the vector of impulse responses. In addition, we show how to use the conventional method to conduct inference based on a uniform joint prior distribution for the vector of impulse responses. We generalize our results to vectors of objects of interest beyond impulse responses.
JEL classification: C11, C33, E47
Key words: Bayesian, SVARs, uniform prior, sign restrictions
https://doi.org/10.29338/wp2023-13
The authors thank Jim Hamilton, Lutz Kilian, Mikkel Plagborg-Moller, Mark Watson, and Christian Wolf for helpful comments. The views expressed here are those of 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: Juan F. Rubio-Ramírez, Federal Reserve Bank of Atlanta and Economics Department, Emory University, Atlanta, GA 30322; Jonas E. Arias, Federal Reserve Bank of Philadelphia; or Daniel F. Waggoner, Economics Department, Emory University, Atlanta, GA 30322.
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