8/ We implement the method in the fdid package, now on CRAN. Tutorial here:
yiqingxu.org/packages/fdi...
Thanks to many for helpful suggestions!
7/ We explore several extensions of FDID, including incorporating covariates and accommodating continuous G and repeated cross-sectional data.
FDID has many connections with continuous-treatment DID settings, as well as Bartik designs, that we plan to study in future work.
6/ We also show that canonical DID can be seen as a special case of FDID if researchers are willing to add an exclusion restriction: one group’s treatment effect of exposure to event is zero. This is essentially a type of SUTVA restriction.
5/ Each esiatmand requires different identification assumptions. In particular, with no anticipation and parallel trends, the DID estimator identifies effect modification, not G's causal effect. Identifying the latter needs much stronger assumptions.
4/ Using the analytical framework from the factorial experiment literature, we formulate FDID as a research design that can target several interpretable estimands.
The key conceptual innovation is to augment the potential outcome with two indices: baseline factor g and exposure to the event z.