Algorithms for Inference in SVARs Identified with Sign and Zero Restrictions

TL;DR

This paper introduces algorithms for Bayesian inference in SVARs with sign and zero restrictions, extending existing methods to handle zero restrictions efficiently.

Contribution

It develops new algorithms that extend sign restriction methods to zero restrictions, enabling non-rejection sampling and nonempty set checks in SVARs.

Findings

Algorithms perform well with rich sign restrictions

Extensions allow for efficient sampling without rejection

Applied to US monetary policy model with positive results

Abstract

I develop algorithms to facilitate Bayesian inference in structural vector autoregressions that are set-identified with sign and zero restrictions by showing that the system of restrictions is equivalent to a system of sign restrictions in a lower-dimensional space. Consequently, algorithms applicable under sign restrictions can be extended to allow for zero restrictions. Specifically, I extend algorithms proposed in Amir-Ahmadi and Drautzburg (2021) to check whether the identified set is nonempty and to sample from the identified set without rejection sampling. I compare the new algorithms to alternatives by applying them to variations of the model considered by Arias et al. (2019), who estimate the effects of US monetary policy using sign and zero restrictions on the monetary policy reaction function. The new algorithms are particularly useful when a rich set of sign restrictions substantially truncates the identified set given the zero restrictions.