Algorithms for Inference in SVARs Identified with Sign and Zero Restrictions

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.