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

Author

Listed:
  • Cl'ement de Chaisemartin
  • Xavier D'Haultfoeuille
  • F'elix Pasquier
  • Doulo Sow
  • Gonzalo Vazquez-Bare

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

  • 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.
    • Handle: RePEc:arx:papers:2201.06898
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    References listed on IDEAS

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    1. Irene Botosaru & Federico H. Gutierrez, 2018. "Difference‐in‐differences when the treatment status is observed in only one period," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 73-90, January.
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    2. 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.
    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. Naimi Johansson & Mikael Svensson, 2022. "Regional variation in prescription drug spending: Evidence from regional migrants in Sweden," Health Economics, John Wiley & Sons, Ltd., vol. 31(9), pages 1862-1877, September.
    5. Bassier, Ihsaan & Manning, Alan & Petrongolo, Barbara, 2023. "Vacancy Duration and Wages," IZA Discussion Papers 16371, Institute of Labor Economics (IZA).
    6. 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).
    7. 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.
    8. 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.
    9. Ihsaan Bassier & Alan Manning & Barbara Petrongolo, 2023. "Vacancy duration and wages," CEP Discussion Papers dp1943, Centre for Economic Performance, LSE.
    10. 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.
    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. Lucas Zhang, 2024. "Continuous difference-in-differences with double/debiased machine learning," Papers 2408.10509, arXiv.org.

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