Assessing Sign Restrictions

Abstract

This paper assesses sign restrictions via a controlled experiment. A researcher estimates a VAR on an infinite amount of data generated by a DSGE model. He or she then imposes sign restrictions on impulse responses to identify a structural shock while being agnostic about the response of a key variable of interest to this shock. Can such an agnostic identification procedure pin down the correct sign of this unconstrained response?The DSGE models of Erceg, Henderson, and Levin (2000), as well as of Smets and Wouters (2003), are used as data generating processes. Two conditions must be met for the method to unambiguously deliver the correct sign of the unconstrained impulse response. First, a sufficiently large number of restrictions must be imposed -- more than what is typically imposed in applied work. Second, the variance of the shock under study must be sufficiently large -- larger than the values provided by Bayesian estimations of the DSGE models. Hence, sign restrictions can be a useful tool to recover structural shocks from VAR residuals.

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