Two-way fixed effects and differences-in-differences estimators with several treatments

• Published in: Journal of econometrics Vol. 236; no. 2; p. 105480
• Main Authors: de Chaisemartin, Clément, D’Haultfœuille, Xavier
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2023; Elsevier
• Subjects: Differences-in-differences; econometrics; Economics and Finance; exhibitions; Heterogeneous treatment effects; Humanities and Social Sciences; Multiple treatments; Two-way-fixed-effects regressions; weight; C21; C23; Two-way-fixed-effects regressions; Differences-in-differences; Multiple treatments; Heterogeneous treatment effects; differences-in-differences; multiple treatments; two-way-fixed-effects regressions; heterogeneous treatment effects
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2023.105480

We study two-way-fixed-effects regressions (TWFE) with several treatment variables. Under a parallel trends assumption, we show that the coefficient on each treatment identifies a weighted sum of that treatment’s effect, with possibly negative weights, plus a weighted sum of the effects of the other treatments. Thus, those estimators are not robust to heterogeneous effects and may be contaminated by other treatments’ effects. We further show that omitting a treatment from the regression can actually reduce the estimator’s bias, unlike what would happen under constant treatment effects. We propose an alternative difference-in-differences estimator, robust to heterogeneous effects and immune to the contamination problem. In the application we consider, the TWFE regression identifies a highly non-convex combination of effects, with large contamination weights, and one of its coefficients significantly differs from our heterogeneity-robust estimator.