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

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  • Fabre, Anaïs
Abstract
This paper provides necessary and sufficient conditions for the Two-Way Fixed Effects (TWFE) estimator to be robust to heterogeneous treatment effects. I decompose the TWFE estimator to show that it is a weighted sum of five different types of two-by-two comparisons, with positive weights. I show that parallel trends assumptions on either the untreated or treated potential outcomes must hold for each comparison to identify the Average Treatment Effect (ATE) of the group switching treatment status, when the effect of the treatment is contemporaneous. Both parallel trends assumptions are thus necessary and sufficient for the TWFE estimator to weigh each ATE positively, when allowing treatment effects to be heterogeneous across groups and periods. I further provide sufficient conditions under which the TWFE estimator remains valid even in the presence of dynamic treatment effects. Finally, I show how to exploit all available comparisons to build unbiased estimators of the ATT and ATE.

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 Jun 2023.
    • 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. Brantly Callaway & Andrew Goodman-Bacon & Pedro H. C. Sant'Anna, 2021. "Difference-in-Differences with a Continuous Treatment," Papers 2107.02637, arXiv.org, revised Jan 2024.
    4. Kirill Borusyak & Xavier Jaravel & Jann Spiess, 2021. "Revisiting Event Study Designs: Robust and Efficient Estimation," Papers 2108.12419, arXiv.org, revised Jan 2024.
    5. Kimin Kim & Myoung-jae Lee, 2019. "Difference in differences in reverse," Empirical Economics, Springer, vol. 57(3), pages 705-725, September.
    6. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    7. 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.
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    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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