Comment on Giacomini, Kitagawa, and Read’s “Narrative Restrictions and Proxies”

Click to increase image sizeClick to decrease image size

Disclosure Statement

There are no competing interests to declare.

Funding

NOTES: Horizons at which sign restrictions are imposed are shown as shaded areas. The Bayes estimate under absolute loss, constructed as in Inoue and Kilian (2022), is shown as solid lines. The corresponding estimate under the prior is shown as dotted lines.

Acknowledgments

The views expressed in the paper are those of the author and do not necessarily represent the views of the Federal Reserve Bank of Dallas or the Federal Reserve System. I thank Atsushi Inoue, Toru Kitagawa, Mikkel Plagborg-Møller. Juan Rubio-Ramirez, the editor, the associate editor and the referee for helpful discussions.

Notes

1 Not surprisingly, the robust pointwise credible sets proposed by Giacomini and Kitagawa tend to be wider than standard pointwise credible sets for impulse responses because they embody additional uncertainty about the prior for Q. They may also be interpreted as pointwise frequentist confidence sets from an asymptotic point of view, providing an alternative to the frequentist pointwise confidence set derived in Granziera, Moon, and Schorfheide (2018). A key difference from Granziera et al.’s work is that Giacomini and Kitagawa’s approach is applicable to a wider class of models, is more computationally convenient, and does not require strong assumptions about the distribution of the reduced-form impulse responses.

2 For example, in Giacomini and Kitagawa’s model I, which corresponds to the model in Granziera et al. (2018), the identified sets in their Figure 1 accommodate persistent real output increases in response to a monetary tightening as well as persistent declines. They also accommodate oscillating response functions and effectively permanent changes in real output.

3 Another way of addressing this problem may be the alternative multiple prior approach proposed in Giacomini, Kitagawa, and Uhlig (2019), which incorporates a probabilistic belief in a specific single prior for Q and a set of alternative priors in the neighborhood of this belief. Unlike the method in Giacomini and Kitagawa (2021), this alternative approach generates a point estimate of the impulse responses under additively separable absolute loss.

4 They define the historical decomposition as the cumulative contribution of a sequence of realizations of a given structural shock between selected dates to the change in some variable over the same period. This is not the textbook definition of a historical decomposition, however, which refers to the cumulative contribution to date of all shocks of a given type to the change in some variable between selected dates (see Kilian and Lütkepohl (2017). Narrative restrictions on such historical decompositions are widely used in applied work (e.g., Zhou (2020). Although the analysis in Giacomini et al. presumably carries over to the latter type of NRs, it would have been useful to provide a comprehensive analysis.

5 Giacomini, Kitagawa, and Read (2021) empirical illustration is based on Uhlig’s (2005) model of monetary policy shocks. This choice is problematic. As formally demonstrated in Wolf (2020), the monetary policy shock is not identified in this model because the sign of the impact response of real output to a monetary policy shock is left unrestricted. It would be surprising, however, if the finding that robust pointwise credible sets tend to be wider than standard pointwise credible sets were not true more generally.

Additional information

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.