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Difference-in-Difference Estimators with Continuous Treatments and No 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'Haultfœuille

    (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 - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Gonzalo Vazquez-Bare

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

Abstract

Many treatments, such as prices, taxes, or temperatures, are continuous in nature. Empirical researchers usually rely on two-way fixed effect regressions to estimate treatment effects in such cases. However, such estimators are not robust to heterogeneous treatment effects in general and rely on the linearity of treatment effects. We develop a difference-in-difference strategy for continuous treatments without imposing such restrictions when there are no stayers: treatment of all units changes between consecutive periods. We extend the nonparametric results of de Chaisemartin et al. (2023) to this setup and present a parametric approach that overcomes some limitations of the nonparametric approach.

Suggested Citation

  • Clément de Chaisemartin & Xavier d'Haultfœuille & Gonzalo Vazquez-Bare, 2024. "Difference-in-Difference Estimators with Continuous Treatments and No Stayers," SciencePo Working papers Main hal-04888940, HAL.
    • Handle: RePEc:hal:spmain:hal-04888940
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-04888940v1
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