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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," Working Papers hal-03873926, HAL.
    • Handle: RePEc:hal:wpaper:hal-03873926
    DOI: 10.2139/ssrn.4011782
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03873926
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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. 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.
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    Cited by:

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    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. 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).
    8. 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.
    9. 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.
    10. Ihsaan Bassier & Alan Manning & Barbara Petrongolo, 2023. "Vacancy duration and wages," CEP Discussion Papers dp1943, Centre for Economic Performance, LSE.
    11. 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.
    12. Lucas Zhang, 2024. "Continuous difference-in-differences with double/debiased machine learning," Papers 2408.10509, arXiv.org.

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