Inference for VARs identified with sign restrictions

There is a fast growing literature that set‐identifies structural vector autoregressions (SVARs) by imposing sign restrictions on the responses of a subset of the endogenous variables to a particular structural shock (sign‐restricted SVARs). Most methods that have been used to construct pointwise coverage bands for impulse responses of sign‐restricted SVARs are justified only from a Bayesian perspective. This paper demonstrates how to formulate the inference problem for sign‐restricted SVARs within a moment‐inequality framework. In particular, it develops methods of constructing confidence bands for impulse response functions of sign‐restricted SVARs that are valid from a frequentist perspective. The paper also provides a comparison of frequentist and Bayesian coverage bands in the context of an empirical application—the former can be substantially wider than the latter.