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Difference-in-Differences Estimators of Intertemporal Treatment Effects

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)

Abstract

We study treatment-effect estimation, with a panel where groups may experience multiple changes of their treatment dose. We make parallel trends assumptions, but do not restrict treatment effect heterogeneity, unlike the linear regressions that have been used in such designs. We extend the event-study approach for binary-and-staggered treatments, by redefining the event as the first time a group's treatment changes. This yields an eventstudy graph, with reduced-form estimates of the effect of having been exposed to a weakly higher amount of treatment for ℓ periods. We show that the reduced-form estimates can be combined into an economically interpretable cost-benefit ratio.

Suggested Citation

  • Clément de Chaisemartin & Xavier d'Haultfoeuille, 2022. "Difference-in-Differences Estimators of Intertemporal Treatment Effects," SciencePo Working papers Main hal-03873903, HAL.
    • Handle: RePEc:hal:spmain:hal-03873903
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03873903
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    More about this item

    Keywords

    Differences-in-differences; Dynamic treatment effects; Heterogeneous treatment effects; Event-study graph; Parallel trends; Panel data; Policy evaluation; Cost-benefit analysis;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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