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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. 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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