Discussion of “Narrative Restrictions and Proxies” by Raffaella Giacomini, Toru Kitagawa, and Matthew Read

I am grateful for the chance to discuss this characteristically insightful paper by Giacomini, Kitagawa, and Read (hence-forth GKR). Since the seminal contribution of Antolín-Díaz and Rubio-Ramírez (2018), narrative restrictions have rapidly become one of the go-to tools for sharpening causal inference in SVAR analysis. Giacomini, Kitagawa, and Read (2021) con-tributed greatly to our understanding of the role of subjective prior beliefs and the appropriate form of the likelihood function when exploiting such narrative information. In the new paper that is the topic of this discussion, GKR compare their pre-ferred prior-robust Bayesian inference procedure with an alter-native approach that constructs categorical proxy variables from the narrative information and uses these to estimate impulse responses via instrumental variable (IV) regressions. GKR argue that the proxy approach will likely suffer from weak IV problems when we only have narrative restrictions for a few time periods, as is often the case in practice. To add insult to injury, this cannot be addressed using existing techniques for weak-IV-robust inference in SVARs (Montiel Olea, Stock, and Watson 2021).Inthe following I will make two points. First, the proxy approach to exploiting narrative information has several appeal-ing robustness properties relative to the likelihood approaches of Antolín-Díaz and Rubio-Ramírez (2018) and Giacomini, Kita-gawa, and Read (2021): The proxy approach allows the narrative signals to be imperfect and arrive non-randomly, and further-more, the economic shocks are allowed to be non-invertible (also known as non-fundamental). Second, the weak IV prob-lem that GKR discuss can be overcome by using procedures designed for small samples, such as permutation tests.