  We consider structural vector autoregressions subject to 'narrative
restrictions', which are inequality restrictions on functions of the structural
shocks in specific periods. These restrictions raise novel problems related to
identification and inference, and there is currently no frequentist procedure
for conducting inference in these models. We propose a solution that is valid
from both Bayesian and frequentist perspectives by: 1) formalizing the
identification problem under narrative restrictions; 2) correcting a feature of
the existing (single-prior) Bayesian approach that can distort inference; 3)
proposing a robust (multiple-prior) Bayesian approach that is useful for
assessing and eliminating the posterior sensitivity that arises in these models
due to the likelihood having flat regions; and 4) showing that the robust
Bayesian approach has asymptotic frequentist validity. We illustrate our
methods by estimating the effects of US monetary policy under a variety of
narrative restrictions.
