When Is the Two-Way Fixed Effects Estimand a Convex Combination of Treatment Effects? Necessary and Sufficient Conditions

Anaïs Fabre

No 22-1362, TSE Working Papers from Toulouse School of Economics (TSE)

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 the corresponding estimand to be 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 estimand 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

Date: 2022-09-21, Revised 2026-09
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