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Working Papers, No. 2022-10, April 2022 Crossref
Narrative Restrictions and Proxies

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.

Working papers are not edited, and all opinions and errors are the responsibility of the author(s). The views expressed do not necessarily reflect the views of the Federal Reserve Bank of Chicago or the Federal Reserve System.


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