Identification and Inference under Narrative Restrictions

We consider structural vector autoregressions subject to narrative restrictions, which are inequalities involving structural shocks in specific time periods (e.g. shock signs in given quarters). Narrative restrictions are used widely in the empirical literature. However, under these restrictions, there are no formal results on identification or the properties of frequentist approaches to inference, and existing Bayesian methods can be sensitive to prior choice. We provide formal results on identification, propose a computationally tractable robust Bayesian method that eliminates prior sensitivity, and show that it is asymptotically valid from a frequentist perspective. Using our method, we find that inferences about the output effects of US monetary policy obtained under restrictions related to the Volker episode are sensitive to prior choice. Under a richer set of restrictions, there is robust evidence that output falls following a positive monetary policy shock.