IDEAS home Printed from https://ideas.repec.org/p/hal/spmain/hal-03873926.html
   My bibliography  Save this paper

Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period

Author

Listed:
  • Clément de Chaisemartin

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

  • Xavier d'Haultfoeuille

    (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)

  • Félix Pasquier

    (CREST-INSEE - Centre de Recherche en Economie et en Statistique - Institut national de la statistique et des études économiques (INSEE))

  • Gonzalo Vazquez-Bare

    (UC Santa Barbara - University of California [Santa Barbara] - UC - University of California)

Abstract

We propose new difference-indifference (DID) estimators for treatments continuously distributed at every time period, as is often the case of trade tariffs, or temperatures. We start by assuming that the data only has two time periods. We also assume that from period one to two, the treatment of some units, the movers, changes, while the treatment of other units, the stayers, does not change. Then, our estimators compare the outcome evolution of movers and stayers with the same value of the treatment at period one. Our estimators only rely on parallel trends assumptions, unlike commonly used twoway fixed effects regressions that also rely on homogeneous treatment effect assumptions. With a continuous treatment, comparisons of movers and stayers with the same periodone treatment can either be achieved by non-parametric regression, or by propensity-score reweighting. We extend our results to applications with more than two time periods, no stayers, and where the treatment may have dynamic effects.

Suggested Citation

  • Clément de Chaisemartin & Xavier d'Haultfoeuille & Félix Pasquier & Gonzalo Vazquez-Bare, 2022. "Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period," SciencePo Working papers Main hal-03873926, HAL.
    • Handle: RePEc:hal:spmain:hal-03873926
    DOI: 10.2139/ssrn.4011782
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03873926
    as

    Download full text from publisher

    File URL: https://sciencespo.hal.science/hal-03873926/document
    Download Restriction: no
    File URL: https://libkey.io/10.2139/ssrn.4011782?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. Hoderlein, Stefan & White, Halbert, 2012. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," Journal of Econometrics, Elsevier, vol. 168(2), pages 300-314.
    3. 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.
    4. Malani, Anup & Reif, Julian, 2015. "Interpreting pre-trends as anticipation: Impact on estimated treatment effects from tort reform," Journal of Public Economics, Elsevier, vol. 124(C), pages 1-17.
    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. Bassier, Ihsaan & Manning, Alan & Petrongolo, Barbara, 2023. "Vacancy duration and wages," LSE Research Online Documents on Economics 121287, London School of Economics and Political Science, LSE Library.
    2. Bassier, Ihsaan & Manning, Alan & Petrongolo, Barbara, 2023. "Vacancy Duration and Wages," IZA Discussion Papers 16371, Institute of Labor Economics (IZA).
    3. Cl'ement de Chaisemartin & Xavier D'Haultf{oe}uille, 2020. "Difference-in-Differences Estimators of Intertemporal Treatment Effects," Papers 2007.04267, arXiv.org, revised Dec 2024.
    4. Gerard J. van den Berg & Stephanie von Hinke & Nicolai Vitt, 2023. "Early life exposure to measles and later-life outcomes: Evidence from the introduction of a vaccine," Papers 2301.10558, arXiv.org.
    5. 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).
    6. Jacob E. Bastian, 2024. "The EITC in rural and economically distressed areas: More bang per buck?," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 31(1), pages 136-159, February.
    7. Bhukta, Rikhia & Pakrashi, Debayan & Saha, Sarani & Sedai, Ashish, 2024. "Community electrification and women’s autonomy," Energy Economics, Elsevier, vol. 137(C).
    8. Lebow, Jeremy & Moreno-Medina, Jonathan & Mousa, Salma & Coral, Horacio, 2024. "Migrant exposure and anti-migrant sentiment: The case of the Venezuelan exodus," Journal of Public Economics, Elsevier, vol. 236(C).
    9. Heeyun Kim, 2024. "A Fad or the New Norm for Student Access Today? Evaluating Enrollment Outcomes of Holistic Admissions in South Korea," Research in Higher Education, Springer;Association for Institutional Research, vol. 65(5), pages 1040-1064, August.
    10. Rogne, Adrian F. & Knutsen, Tora Kjærnes & Modalsli, Jørgen, 2023. "A college on every cape: Gender equality, gender segregation and higher educational expansion," SocArXiv xej64, Center for Open Science.
    11. Ihsaan Bassier & Alan Manning & Barbara Petrongolo, 2023. "Vacancy duration and wages," CEP Discussion Papers dp1943, Centre for Economic Performance, LSE.
    12. Ali Enami & Sucharita Ghosh, 2024. "Subsidized wages, small businesses, and exports: Evidence from the paycheck protection program," Review of International Economics, Wiley Blackwell, vol. 32(4), pages 1671-1697, September.
    13. Lucas Zhang, 2024. "Continuous difference-in-differences with double/debiased machine learning," Papers 2408.10509, arXiv.org.

    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. Luo, Lianfa & Cheng, Zhiming & Ye, Qingqing & Cheng, Yanjun & Smyth, Russell & Yang, Zhiqing & Zhang, Le, 2024. "Nonmonetary awards and innovation: Evidence from winning China's Top Brand Contest," China Economic Review, Elsevier, vol. 86(C).
    2. Aibo Gong, 2021. "Bounds for Treatment Effects in the Presence of Anticipatory Behavior," Papers 2111.06573, arXiv.org, revised Dec 2022.
    3. Kurt Schmidheiny & Sebastian Siegloch, 2023. "On event studies and distributed‐lags in two‐way fixed effects models: Identification, equivalence, and generalization," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(5), pages 695-713, August.
    4. 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.
    5. 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.
    6. Dalia Ghanem & Pedro H. C. Sant'Anna & Kaspar Wüthrich, 2022. "Selection and Parallel Trends," CESifo Working Paper Series 9910, CESifo.
    7. 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.
    8. Jonathan Roth & Pedro H. C. Sant’Anna, 2023. "Efficient Estimation for Staggered Rollout Designs," Journal of Political Economy Microeconomics, University of Chicago Press, vol. 1(4), pages 669-709.
    9. Cesare Righi & Timothy Simcoe, 2022. "Patenting inventions or inventing patents? Continuation practice at the USPTO," Economics Working Papers 1820, Department of Economics and Business, Universitat Pompeu Fabra.
    10. Timothy Simcoe & Cesare Righi, 2022. "Patenting Inventions or Inventing Patents? Continuation Practice at the USPTO," Working Papers 1320, Barcelona School of Economics.
    11. Philip Marx & Elie Tamer & Xun Tang, 2022. "Parallel Trends and Dynamic Choices," Papers 2207.06564, arXiv.org, revised Aug 2023.
    12. Bas Scheer & Wiljan van den Berge & Maarten Goos & Alan Manning & Anna Salomons, 2022. "Alternative Work Arrangements and Worker Outcomes: Evidence from Payrolling," CPB Discussion Paper 435, CPB Netherlands Bureau for Economic Policy Analysis.
    13. Mac Clay, Pablo & Börner, Jan & Sellare, Jorge, 2023. "Institutional and macroeconomic stability mediate the effect of auctions on renewable energy capacity," Energy Policy, Elsevier, vol. 180(C).
    14. Katrin Huber & Geske Rolvering, 2023. "Public child care and mothers’ career trajectories," Working Papers 228, Bavarian Graduate Program in Economics (BGPE).
    15. Alex Hollingsworth & Krzysztof Karbownik & Melissa A. Thomasson & Anthony Wray, 2024. "The Gift of a Lifetime: The Hospital, Modern Medicine, and Mortality," American Economic Review, American Economic Association, vol. 114(7), pages 2201-2238, July.
    16. Coury, Michael & Falconer, Liam & La Nauze, Andrea, 2024. "Wildfire smoke and private provision of public air-quality monitoring," Journal of Environmental Economics and Management, Elsevier, vol. 127(C).
    17. Binelli, Chiara & Comi, Simona & Meschi, Elena & Pagani, Laura, 2024. "Every cloud has a silver lining: The role of study time and class recordings on university students’ performance during COVID-19," Journal of Economic Behavior & Organization, Elsevier, vol. 225(C), pages 305-328.
    18. Stefan Bauernschuster & Michael Grimm & Cathy M. Hajo, 2023. "The Impact of Margaret Sanger’s Birth Control Clinics on Early 20th Century U.S. Fertility and Mortality," CESifo Working Paper Series 10421, CESifo.
    19. Bhalotra, Sonia & Clarke, Damian & Mühlrad, Hanna & Palme, Mårten, 2021. "Health and Labor Market Impacts of Twin Birth : Evidence from a Swedish IVF Policy Mandate," The Warwick Economics Research Paper Series (TWERPS) 1391, University of Warwick, Department of Economics.
    20. Jack (Peiyao) Ma & Andrea Mantovani & Carlo Reggiani & Annette Broocks & Néstor Duch-Brown, 2024. "The Price Effects of Prohibiting Price Parity Clauses: Evidence from International Hotel Groups," Economics Series Working Papers 1043, University of Oxford, Department of Economics.

    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:spmain:hal-03873926. 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: Contact - Sciences Po Departement of Economics (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.