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

Clément de Chaisemartin and Xavier D’haultfœuille
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Xavier D’haultfœuille: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique

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Abstract: 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-indifferences 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.

Keywords: differences-in-differences; two-way-fixed-effects regressions; multiple treatments; heterogeneous treatment effects (search for similar items in EconPapers)
Date: 2023-10
Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-04187969v2
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Citations: View citations in EconPapers (17)

Published in Journal of Econometrics, 2023, 236 (2), pp.105480. ⟨10.1016/j.jeconom.2023.105480⟩

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Related works:
Journal Article: Two-way fixed effects and differences-in-differences estimators with several treatments (2023)
Working Paper: Two-way Fixed Effects and Differences-in-Differences Estimators with Several Treatments (2023)
Working Paper: Two-way fixed effects and differences-in-differences estimators with several treatments (2023)
Working Paper: Two-way Fixed Effects and Differences-in-Differences Estimators with Several Treatments (2022)
Working Paper: Two-way Fixed Effects and Differences-in-Differences Estimators with Several Treatments (2022)
Working Paper: Two-way Fixed Effects and Differences-in-Differences Estimators with Several Treatments (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04187969

DOI: 10.1016/j.jeconom.2023.105480

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