Robustness of Two-Way Fixed Effects Estimators to Heterogeneous Treatment Effects

Abstract

This paper provides necessary and sufficient conditions for the Two-Way Fixed Effects (TWFE) estimator to be robust to heterogeneous treatment effects. I decompose the TWFE estimator to show that it is a weighted sum of five different types of two-by-two comparisons, with positive weights. I show that parallel trends assumptions on either the untreated or treated potential outcomes must hold for each comparison to identify the Average Treatment Effect (ATE) of the group switching treatment status, when the effect of the treatment is contemporaneous. Both parallel trends assumptions are thus necessary and sufficient for the TWFE estimator to weigh each ATE positively, when allowing treatment effects to be heterogeneous across groups and periods. I further provide sufficient conditions under which the TWFE estimator remains valid even in the presence of dynamic treatment effects. Finally, I show how to exploit all available comparisons to build unbiased estimators of the ATT and ATE.

Reference

Anaïs Fabre, “Robustness of Two-Way Fixed Effects Estimators to Heterogeneous Treatment Effects”, TSE Working Paper, n. 22-1362, September 2022, revised June 2023.