IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v236y2023i2s0304407623001963.html
   My bibliography  Save this article

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

Author

Listed:
  • de Chaisemartin, Clément
  • D’Haultfœuille, Xavier

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-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.

Suggested Citation

  • de Chaisemartin, Clément & D’Haultfœuille, Xavier, 2023. "Two-way fixed effects and differences-in-differences estimators with several treatments," Journal of Econometrics, Elsevier, vol. 236(2).
    • Handle: RePEc:eee:econom:v:236:y:2023:i:2:s0304407623001963
    DOI: 10.1016/j.jeconom.2023.105480
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407623001963
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2023.105480?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    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..
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Athey, Susan & Imbens, Guido W., 2022. "Design-based analysis in Difference-In-Differences settings with staggered adoption," Journal of Econometrics, Elsevier, vol. 226(1), pages 62-79.
    3. Clément de Chaisemartin & Xavier D’Haultfœuille, 2023. "Two-way fixed effects and differences-in-differences with heterogeneous treatment effects: a survey," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 1-30.
    4. Peter Z. Schochet, 2021. "Statistical Power for Estimating Treatment Effects Using Difference-in-Differences and Comparative Interrupted Time Series Designs with Variation in Treatment Timing," Papers 2102.06770, arXiv.org, revised Oct 2021.
    5. Dalia Ghanem & Pedro H. C. Sant'Anna & Kaspar Wuthrich, 2022. "Selection and parallel trends," Papers 2203.09001, arXiv.org, revised Mar 2024.
    6. Baker, Andrew C. & Larcker, David F. & Wang, Charles C.Y., 2022. "How much should we trust staggered difference-in-differences estimates?," Journal of Financial Economics, Elsevier, vol. 144(2), pages 370-395.
    7. Rösner, Anja & Haucap, Justus & Heimeshoff, Ulrich, 2020. "The impact of consumer protection in the digital age: Evidence from the European Union," International Journal of Industrial Organization, Elsevier, vol. 73(C).
    8. Simon Freyaldenhoven & Christian Hansen & Jorge Perez Perez & Jesse Shapiro, 2021. "Visualization, Identification, and stimation in the Linear Panel Event-Study Design," Working Papers 21-44, Federal Reserve Bank of Philadelphia.
    9. Mikhail Mamonov & Anna Pestova & Steven Ongena, 2023. "“Crime and Punishment”? How Banks Anticipate and Propagate Global Financial Sanctions," CERGE-EI Working Papers wp753, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    10. Kayaoglu, Aysegul, 2022. "Do refugees cause crime?," World Development, Elsevier, vol. 154(C).
    11. Mark Kattenberg & Bas Scheer & Jurre Thiel, 2023. "Causal forests with fixed effects for treatment effect heterogeneity in difference-in-differences," CPB Discussion Paper 452, CPB Netherlands Bureau for Economic Policy Analysis.
    12. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    13. Chabé-Ferret, Sylvain & Reynaud, Arnaud & Tène, Eva, 2021. "Water Quality, Policy Diffusion Effects and Farmers’ Behavior," TSE Working Papers 21-1229, Toulouse School of Economics (TSE).
    14. Cl'ement de Chaisemartin & Xavier D'Haultfoeuille & F'elix Pasquier & Doulo Sow & Gonzalo Vazquez-Bare, 2022. "Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period," Papers 2201.06898, arXiv.org, revised Jul 2024.
    15. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    16. Rachel Scarfe & Daniel Schäfer & Thomas Sulka, 2024. "The Incidence of Workplace Pensions: Evidence from the UK's Automatic Enrollment Mandate," Economics working papers 2024-02, Department of Economics, Johannes Kepler University Linz, Austria.
    17. Andrea Albanese & Adrián Nieto & Konstantinos Tatsiramos, 2022. "Job Location Decisions and the Effect of Children on the Employment Gender Gap," CESifo Working Paper Series 9792, CESifo.
    18. Lin, Lihua & Zhang, Zhengyu, 2022. "Interpreting the coefficients in dynamic two-way fixed effects regressions with time-varying covariates," Economics Letters, Elsevier, vol. 216(C).
    19. Kyunghoon Ban & D'esir'e K'edagni, 2022. "Robust Difference-in-differences Models," Papers 2211.06710, arXiv.org, revised Aug 2023.
    20. Kamila Cygan-Rehm, 2022. "Lifetime Consequences of Lost Instructional Time in the Classroom: Evidence from Shortened School Years," CESifo Working Paper Series 9892, CESifo.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:236:y:2023:i:2:s0304407623001963. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.