Fabre, Anaïs (2025) Robustness of two-way fixed effects estimators to heterogeneous treatment effects. TSE Working Paper, n. 22-1362, Toulouse

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Abstract

This paper studies the Two-Way Fixed Effects (TWFE) estimator in a general setting where multiple groups can enter and exit a binary treatment over time. It establishes necessary and sufficient conditions for this estimator to correspond to a convex combination of Average Treatment Effects (ATEs). I show that the TWFE estimator is a weighted sum of five different types of two-by-two comparisons, with positive weights. Parallel trends assumptions on either the untreated or treated potential outcomes must hold for each comparison to identify the ATE of the group switching treatment status. When treatment effects are contemporaneous but can be heterogeneous across groups and over time, both parallel trends assumptions are thus necessary and sufficient for the TWFE estimator to be a weighted sum of ATEs, with positive weights. Under parallel trends on the untreated potential outcomes and on the first exposure to treatment, the presence of dynamic treatment effects is necessary — but not sufficient — for this result to break.