Identification and Inference Under Narrative Restrictions

Abstract

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 (multipleprior) 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.

Estimating the Effects of Monetary Policy in Australia Using Sign‐restricted Structural Vector Autoregressions*

“…For example, restrictions on the sign of the monetary policy shock or its relative contribution to changes in the cash rate in specific historical episodes ('narrative restrictions') could potentially sharpen identification (e.g. Antolín-Díaz & Rubio-Ramírez, 2018;Giacomini et al, 2021a). Another potentially useful avenue would be to identify other structural shocks, which should in principle help to identify the monetary policy shock.…”

Narrative Restrictions and Proxies

“…Arias et al 2018). However, Giacomini et al (2021a) -henceforth, GKR -point out some undesirable features of this approach. Under shock-sign restrictions, the likelihood function possesses flat regions, which implies that a component of the prior is never updated by the data.…”