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

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 SVARs. We call this family of conjugate posterior distributions 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 distribution 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 implement 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.