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Difference-in-Differences for Continuous Treatments and Instruments with Stayers

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 - INSEE - Institut national de la statistique et des études économiques (INSEE))

  • Doulo Sow

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

  • Gonzalo Vazquez-Bare

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

Abstract

We propose difference-in-differences estimators in designs where the treatment is continuously distributed at every period, as is often the case when one studies the effects of taxes, tariffs, or prices. We assume that between consecutive periods, the treatment of some units, the switchers, changes, while the treatment of other units remains constant. We show that under a placebo-testable parallel-trends assumption, averages of the slopes of switchers' potential outcomes can be nonparametrically estimated. We generalize our estimators to the instrumental-variable case. We use our estimators to estimate the price-elasticity of gasoline consumption.

Suggested Citation

  • Clément de Chaisemartin & Xavier d'Haultfoeuille & Félix Pasquier & Doulo Sow & Gonzalo Vazquez-Bare, 2025. "Difference-in-Differences for Continuous Treatments and Instruments with Stayers," 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-03873926v2
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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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

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    6. 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.
    7. 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.
    8. 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.
    9. Bassier, Ihsaan & Manning, Alan & Petrongolo, Barbara, 2023. "Vacancy Duration and Wages," IZA Discussion Papers 16371, Institute of Labor Economics (IZA).
    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_v1, Center for Open Science.
    11. 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.
    12. 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).
    13. 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).
    14. Ihsaan Bassier & Alan Manning & Barbara Petrongolo, 2023. "Vacancy duration and wages," CEP Discussion Papers dp1943, Centre for Economic Performance, LSE.
    15. Lucas Zhang, 2024. "Continuous difference-in-differences with double/debiased machine learning," Papers 2408.10509, arXiv.org, revised Mar 2025.

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