Econometrica: Mar 2018, Volume 86, Issue 2

Inference Based on Structural Vector Autoregressions Identified With Sign and Zero Restrictions: Theory and Applications

https://doi.org/10.3982/ECTA14468
p. 685-720

Jonas E. Arias, Juan F. Rubio‐Ramírez, Daniel F. Waggoner

In this paper, we develop algorithms to independently draw from a family of conjugate posterior distributions over the structural parameterization when sign and zero restrictions are used to identify structural vector autoregressions (SVARs). We call this family of conjugate posteriors normal‐generalized‐normal. Our algorithms draw from a conjugate uniform‐normal‐inverse‐Wishart posterior over the orthogonal reduced‐form parameterization and transform the draws into the structural parameterization; this transformation induces a normal‐generalized‐normal posterior over the structural parameterization. The uniform‐normal‐inverse‐Wishart posterior over the orthogonal reduced‐form parameterization has been prominent after the work of Uhlig (2005). We use Beaudry, Nam, and Wang's (2011) work on the relevance of optimism shocks to show the dangers of using alternative approaches to implementing sign and zero restrictions to identify SVARs like the penalty function approach. In particular, we analytically show that the penalty function approach adds restrictions to the ones described in the identification scheme.



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Supplement to "Inference Based on Structural Vector Autoregressions Identified With Sign and Zero Restrictions: Theory and Applications"

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Supplement to "Inference Based on Structural Vector Autoregressions Identified With Sign and Zero Restrictions: Theory and Applications"

This supplement is organized as follows. Section I shows that using one-sided numerical derivatives can decrease computational time without compromising numerical accuracy. Section II tests for the variance of the importance sampler weights to be finite. Section III provides a step-by-step pseudo-code for using Algorithms 1 and 3 in the paper.

 

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