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

Author

Listed:
  • Clément de Chaisemartin

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • 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)

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.

Suggested Citation

  • Clément de Chaisemartin & Xavier D’haultfœuille, 2023. "Two-way fixed effects and differences-in-differences estimators with several treatments," Post-Print hal-04187969, HAL.
    • Handle: RePEc:hal:journl:hal-04187969
    DOI: 10.1016/j.jeconom.2023.105480
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-04187969v2
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    References listed on IDEAS

    as
    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. Ashenfelter, Orley C, 1978. "Estimating the Effect of Training Programs on Earnings," The Review of Economics and Statistics, MIT Press, vol. 60(1), pages 47-57, February.
    3. V. Joseph Hotz & Mo Xiao, 2011. "The Impact of Regulations on the Supply and Quality of Care in Child Care Markets," American Economic Review, American Economic Association, vol. 101(5), pages 1775-1805, August.
    4. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    5. Peter Hull, 2018. "Estimating Treatment Effects in Mover Designs," Papers 1804.06721, arXiv.org.
    6. Stephen G. Donald & Kevin Lang, 2007. "Inference with Difference-in-Differences and Other Panel Data," The Review of Economics and Statistics, MIT Press, vol. 89(2), pages 221-233, May.
    7. Iavor Bojinov & Ashesh Rambachan & Neil Shephard, 2021. "Panel experiments and dynamic causal effects: A finite population perspective," Quantitative Economics, Econometric Society, vol. 12(4), pages 1171-1196, November.
    8. Xavier D'Haultf{oe}uille & Purevdorj Tuvaandorj, 2022. "A Robust Permutation Test for Subvector Inference in Linear Regressions," Papers 2205.06713, arXiv.org, revised Sep 2023.
    9. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(1), pages 249-275.
    10. 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.
    11. Meinhofer, Angélica & Witman, Allison E. & Hinde, Jesse M. & Simon, Kosali, 2021. "Marijuana liberalization policies and perinatal health," Journal of Health Economics, Elsevier, vol. 80(C).
    12. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 1-19.
    13. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    14. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2021. "On Estimating Multiple Treatment Effects with Regression," Working Papers 2021-41, Princeton University. Economics Department..
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    More about this item

    Keywords

    differences-in-differences; two-way-fixed-effects regressions; multiple treatments; heterogeneous treatment effects;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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