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, Stock, and Watson 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, Kitagawa, and Read deliver coverage exceeding the nominal level, but which converges toward the nominal level as the number of NR increases.

The Transmission of Supply Shocks in Different Inflation Regimes

“…The instrumental variable we use consists of few non-zero data points and can thus be characterized as a sparse instrument. Giacomini et al (2022) argue that sparse instruments, often constructed from narrative restrictions, are likely to be weak instruments.…”

Identification and Inference under Narrative Restrictions

“…Giacomini, Kitagawa and Read (2022a) explore the performance of the weak-instrument robust frequentist inferential procedures from Montiel Olea, Stock and Watson (2021) when using narrative proxies; these procedures may suffer from size distortions when the sign of the shock is known in a small number of periods.…”