IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-04187969.html
   My bibliography  Save this paper

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 - 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
    as

    Download full text from publisher

    File URL: https://sciencespo.hal.science/hal-04187969v2/document
    Download Restriction: no
    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
    ---><---

    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. Peter Hull, 2018. "Estimating Treatment Effects in Mover Designs," Papers 1804.06721, arXiv.org.
    4. 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.
    5. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 1-19.
    6. 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.
    7. 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.
    8. 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).
    9. 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.
    10. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    11. 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.
    12. 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.
    13. 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.
    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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Goussé, Marion & Leturcq, Marion, 2022. "More or less unmarried. The impact of legal settings of cohabitation on labour market outcomes," European Economic Review, Elsevier, vol. 149(C).
    2. Liu, Jhih-Yun, 2023. "The Dust Bowl and Occupational Persistence in Agriculture," 2023 Annual Meeting, July 23-25, Washington D.C. 335779, Agricultural and Applied Economics Association.
    3. Dmitry Arkhangelsky & Aleksei Samkov, 2024. "Sequential Synthetic Difference in Differences," Papers 2404.00164, arXiv.org.
    4. Guillaume Gueguen & Claudia Senik, 2023. "Adopting telework: The causal impact of working from home on subjective well‐being," British Journal of Industrial Relations, London School of Economics, vol. 61(4), pages 832-868, December.
    5. Wrede, Matthias, 2022. "The influence of state politics on solar energy auction results," Energy Policy, Elsevier, vol. 168(C).
    6. Bernard Hoekman & Marco Sanfilippo & Margherita Tambussi, 2023. "Foreign Direct Investment and Structural Transformation in Africa," RSCAS Working Papers 2023/02, European University Institute.
    7. Luyao Xu & Hui Sun, 2024. "Study on the Impact of Carbon Emission Trading Pilot on Green Land Use Efficiency in Cities," Land, MDPI, vol. 13(4), pages 1-21, April.
    8. Gregory Faletto, 2023. "Fused Extended Two-Way Fixed Effects for Difference-in-Differences with Staggered Adoptions," Papers 2312.05985, arXiv.org, revised Apr 2024.
    9. Tanaka, Ayumu, 2023. "Estimating the Effects of GATT/WTO Membership on Trade Using Staggered Difference-in-Differences Design," SocArXiv kjzyq, Center for Open Science.
    10. Federica Daniele & Alessandra Pasquini & Stefano Clò & Enza Maltese, 2022. "Unburdening regulation: the impact of regulatory simplification on photovoltaic adoption in Italy," Temi di discussione (Economic working papers) 1387, Bank of Italy, Economic Research and International Relations Area.
    11. Mo, Jiawei, 2023. "Heterogeneous effects of urban transport infrastructure on population distribution: The role of educational access," Regional Science and Urban Economics, Elsevier, vol. 101(C).
    12. Chloé Zapha & Banque de France, 2023. "Access to Credit after Emerging from Corporate Bankruptcy," Working Papers halshs-03957890, HAL.
    13. Pinkus, David & Pozzoli, Dario & Schneider, Cédric, 2024. "Pension Fund Investment and Firm Innovation," Working Papers 1-2024, Copenhagen Business School, Department of Economics.
    14. Pedro Picchetti, 2023. "Identification in Endogenous Sequential Treatment Regimes," Papers 2311.18555, arXiv.org.
    15. Valerie Bostwick & Christopher Severen, 2022. "Driving, Dropouts, and Drive-Throughs: Mobility Restrictions and Teen Human Capita," Working Papers 22-22, Federal Reserve Bank of Philadelphia.
    16. 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.
    17. Vieira, João Pedro & Dahis, Ricardo & Assunção, Juliano, 2023. "From Deforestation to Reforestation: The Role of General Deterrence in Changing Farmers' Behavior," SocArXiv vqpkm, Center for Open Science.
    18. 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.
    19. Rico-Straffon, Jimena & Wang, Zhenhua & Panlasigui, Stephanie & Loucks, Colby J. & Swenson, Jennifer & Pfaff, Alexander, 2023. "Forest concessions and eco-certifications in the Peruvian Amazon: Deforestation impacts of logging rights and logging restrictions," Journal of Environmental Economics and Management, Elsevier, vol. 118(C).

    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. Cl'ement de Chaisemartin & Xavier D'Haultf{oe}uille, 2021. "Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey," Papers 2112.04565, arXiv.org, revised Jun 2022.
    4. 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).
    5. Dalia Ghanem & Pedro H. C. Sant'Anna & Kaspar Wüthrich, 2022. "Selection and Parallel Trends," CESifo Working Paper Series 9910, CESifo.
    6. 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.
    7. 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.
    8. 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.
    9. Maclean, J. Catherine & Pichler, Stefan & Ziebarth, Nicolas R., 2020. "Mandated Sick Pay: Coverage, Utilization, and Welfare Effects," IZA Discussion Papers 13132, Institute of Labor Economics (IZA).
    10. Mayberry, Anthony A., 2023. "Demilitarization and economic growth: Empirical evidence in support of a peace dividend," Journal of Comparative Economics, Elsevier, vol. 51(3), pages 960-988.
    11. 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.
    12. Kayaoglu, Aysegul, 2022. "Do refugees cause crime?," World Development, Elsevier, vol. 154(C).
    13. 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.
    14. Florian Schoner & Lukas Mergele & Larissa Zierow, 2021. "Grading Student Behavior," CESifo Working Paper Series 9275, CESifo.
    15. Cl'ement de Chaisemartin & Xavier D'Haultfoeuille & F'elix Pasquier & Gonzalo Vazquez-Bare, 2022. "Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period," Papers 2201.06898, arXiv.org, revised Dec 2023.
    16. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Mar 2024.
    17. Mingxia Shi & Yibo Wang, 2023. "Do Green Transfer Payments Contribute to Carbon Emission Reduction?," Sustainability, MDPI, vol. 15(5), pages 1-18, February.
    18. 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).
    19. Marcel Henkel, Eunjee Kwon, Pierre Magontier, 2022. "The Unintended Consequences of Post-Disaster Policies for Spatial Sorting," Diskussionsschriften credresearchpaper37, Universitaet Bern, Departement Volkswirtschaft - CRED.
    20. Tien Manh Vu & Hiroyuki Yamada, 2021. "Firms and regional favouritism," Economics of Transition and Institutional Change, John Wiley & Sons, vol. 29(4), pages 711-734, October.

    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:hal:journl:hal-04187969. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.