RDP 2022-04: The Unit-effect Normalisation in Set-identified Structural Vector Autoregressions 7. Conclusion

In SVARs that are set identified using sign and/or zero restrictions, the identified set for the impulse responses to a unit shock may be unbounded. These restrictions therefore have the potential to be extremely uninformative about the effects of unit shocks. However, it may still be possible to draw useful inferences about impulse responses to a unit shock when the identified set is unbounded with positive posterior probability. Ultimately, I argue that researchers should transparently communicate about the extent to which identified sets are unbounded and what this means about the informativeness of their identifying restrictions.

The empirical exercise in this paper demonstrates the importance of these issues. The identifying restrictions on the systematic component of monetary policy considered in Arias et al (2019) never rule out the possibility that the federal funds rate does not respond on impact to a standard deviation monetary policy shock. As a consequence, the identified set for the output response to a 100 basis point monetary policy shock appears to be unbounded at all horizons and for all values of the reduced-form parameters. The identifying restrictions are therefore extremely uninformative about the magnitude of these impulse responses, standard Bayesian inference is misleading about the information contained in the data given the identifying restrictions, and posterior inferences are sensitive to the choice of conditional prior for the orthonormal matrix.

After additionally imposing the sign restrictions on impulse responses from Uhlig (2005), the identified set is bounded with very high posterior probability; nevertheless, the identifying restrictions are quite uninformative about the output effects of a 100 basis point monetary policy shock and posterior inferences remain sensitive to the choice of prior. Adding the narrative restrictions from Antolín-Díaz and Rubio-Ramírez (2018) yields a bounded identified set in 100 per cent of draws from the reduced-form posterior and leads to more informative inference about the output effects of the shock; however, it remains the case that a large share of the information in the posterior is contributed by the unrevisable component of the prior. The latter two sets of restrictions effectively rule out large declines in output following a 100 basis point shock. It is therefore possible to draw useful inferences about the effects of US monetary policy under set- identifying restrictions even though these restrictions may sometimes be extremely uninformative.