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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 - 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://hal-sciencespo.archives-ouvertes.fr/hal-03873926
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    as
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    5. Bassier, Ihsaan & Manning, Alan & Petrongolo, Barbara, 2023. "Vacancy Duration and Wages," IZA Discussion Papers 16371, Institute of Labor Economics (IZA).
    6. Cl'ement de Chaisemartin & Xavier D'Haultfoeuille, 2020. "Difference-in-Differences Estimators of Intertemporal Treatment Effects," Papers 2007.04267, arXiv.org, revised Nov 2023.
    7. 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).
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    9. Ihsaan Bassier & Alan Manning & Barbara Petrongolo, 2023. "Vacancy duration and wages," CEP Discussion Papers dp1943, Centre for Economic Performance, LSE.

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