A Flexible, Heterogeneous Treatment Effects Difference-in-Differences Estimator for Repeated Cross-Sections

This paper proposes a method to estimate treatment effects in difference-in-differences designs in which the treatment start is staggered over time and treatment effects are heterogeneous by group, time, and covariates, and when the data are repeated cross-sections. We show that a linear-in-parameters regression specification with a sufficiently flexible functional form consisting of group-by-time treatment effects, two-way fixed effects, and interaction terms yields consistent estimates of heterogeneous treatment effects under general conditions. We also show that our method is identical to an imputation estimator. The estimates are efficient and aggregation of treatment effects and inference are straightforward. We call it FLEX, because it is a flexible linear model estimated by OLS with covariates (X). We illustrate the use of FLEX with an empirical example and provide comparisons to other recently derived estimators.