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

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  • Fabre, Anaïs

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.

Suggested Citation

  • Fabre, Anaïs, 2022. "Robustness of Two-Way Fixed Effects Estimators to Heterogeneous Treatment Effects," TSE Working Papers 22-1362, Toulouse School of Economics (TSE), revised Jul 2025.
    • Handle: RePEc:tse:wpaper:127362
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    References listed on IDEAS

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    1. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    2. Rossi, Pauline & Villar, Paola, 2020. "Private health investments under competing risks: Evidence from malaria control in Senegal," Journal of Health Economics, Elsevier, vol. 73(C).
    3. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    4. Chabé-Ferret, Sylvain & Voia, Anca, 2019. "Are Grassland Conservation Programs a Cost-Effective Way to Fight Climate Change? Evidence from France," SocArXiv cx8j6, Center for Open Science.
    5. Brantly Callaway & Andrew Goodman-Bacon & Pedro H. C. Sant'Anna, 2021. "Difference-in-Differences with a Continuous Treatment," Papers 2107.02637, arXiv.org, revised Dec 2025.
    6. Kirill Borusyak & Xavier Jaravel & Jann Spiess, 2024. "Revisiting Event-Study Designs: Robust and Efficient Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(6), pages 3253-3285.
    7. Kimin Kim & Myoung-jae Lee, 2019. "Difference in differences in reverse," Empirical Economics, Springer, vol. 57(3), pages 705-725, September.
    8. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
    9. Jonathan Roth, 2022. "Pretest with Caution: Event-Study Estimates after Testing for Parallel Trends," American Economic Review: Insights, American Economic Association, vol. 4(3), pages 305-322, September.
    10. Roth, Jonathan & Sant’Anna, Pedro H.C. & Bilinski, Alyssa & Poe, John, 2023. "What’s trending in difference-in-differences? A synthesis of the recent econometrics literature," Journal of Econometrics, Elsevier, vol. 235(2), pages 2218-2244.
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