Rejoinder to "Instrumented difference-in-differences".

Overview

We thank all the discussants for the careful reading and insightful comments. In our rejoinder, we extend the discussion of how the assumptions of instrumented difference-in-differences (iDID) compare to the assumptions of the standard instrumental variable method. We also make additional comments on how iDID is related to the fuzzy DID. We highlight future research directions to enhance the utility of iDID, including extensions to adjust for covariate shift in two-sample iDID design, and generalization of iDID to multiple time points and a multi-valued instrumental variable for DID.