When Do Sign Restrictions Work?

Abstract

This paper addresses the following question: A researcher imposes sign restrictions on impulse responses in a VAR and leaves the response of some variable of interest to some structural shock unconstrained. Under which conditions do the imposed restrictions uniquely pin down the correct sign of the unconstrained response? To answer this question, two DSGE models are used to back the VAR representation of certain observables and apply the sign restriction method: the Erceg, Henderson, and Levin (2000) model as well as the Smets and Wouters (2003) model. Two conditions must be met for the method to unambiguously deliver the correct sign of unconstrained impulse responses. First, a sufficiently large number of restrictions must be imposed - more than what is typically employed in applied work. Second, the variance of the shock under study must be sufficiently large - larger than the estimates provided from the Bayesian DSGE models. Hence, sign restrictions can be a useful tool to recover structural shocks from VAR residuals.

Keywords: Sign restrictions, structural VAR, monetary shocks, technology shocks

JEL Classification: E32, C32