A unified framework for dynamic treatment effect estimation in interactive fixed effect models

We present a unifying identification strategy of dynamic average treatment effect parameters for staggered interventions when parallel trends are valid only after controlling for interactive fixed effects. This setting nests the usual parallel trends assumption, but allows treated units to have heterogeneous exposure to unobservable macroeconomic trends. We show that any estimator that is consistent for the unobservable trends up to a non-singular rotation can be used to consistently estimate heterogeneous dynamic treatment effects. This result can apply to data sets with either many or few pre-treatment time periods. We also demonstrate the robustness of two-way fixed effects imputation to certain parallel trends violations and provide a test for its consistency. A quasi-long-differencing estimator is proposed and implemented to estimate the effect of Walmart openings on local economic conditions.