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 for repeated cross-section data in which the treatment start is staggered over time and treatment effects are heterogeneous by group, time, and observation-level covariates. 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. Under homoskedasticity assumptions the estimators are efficient, and aggregation of the treatment effects and inference are straightforward. We illustrate the use of this flexible linear model estimated by OLS with covariates (X) – FLEX – with an empirical example and provide comparisons to some benchmark estimators.