Narrative Restrictions and Proxies

Abstract

We compare two approaches to using information about the signs of structural shocks at specific dates within a structural vector autoregression (SVAR): imposing ‘narrative restrictions’ (NR) on the shock signs in an otherwise set-identified SVAR; and casting the information about the shock signs as a discrete-valued ‘narrative proxy’ (NP) to point-identify the impulse responses. The NP is likely to be ‘weak’ given that the sign of the shock is typically known in a small number of periods, in which case the weak-proxy robust confidence intervals in Montiel-Olea et al. (2021) are the natural approach to conducting inference. However, we show both theoretically and via Monte Carlo simulations that these confidence intervals have distorted coverage — which may be higher or lower than the nominal level — unless the sign of the shock is known in a large number of periods. Regarding the NR approach, we show that the prior-robust Bayesian credible intervals from Giacomini et al. (2021a) deliver coverage exceeding the nominal level, but which converges towards the nominal level as the number of NR increases.

Keywords: weak instruments, sign restrictions, impulse-response analysis, prior sensitivity

JEL Classification: C11, C32, C36