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

In this paper we characterize agnostic priors and propose numerical algorithms for Bayesian inference when using them within SVARs identified by imposing sign and zero restrictions on a function of the structural parameters. As Baumeister and Hamilton (2015a) has made clear, since the data cannot tell apart models satisfying the sign and zero restrictions, priors play a crucial role in this environment. We will emphasize the importance of agnostic priors: any prior density that is equal across observationally equivalent parameters. If the prior is not agnostic, additional restrictions to the proclaimed sign and zero restrictions become part of the identification. While our numerical algorithms use agnostic priors we will show that existing ones use non-agnostic priors. We will use Beaudry, Nam and Wang (2011) work on the relevance of optimism shocks to show the dangers of using non-agnostic priors.