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Two-way Fixed Effects and Differences-in-Differences in Heterogeneous Adoption Designs without Stayers

Author

Listed:
  • Clément de Chaisemartin

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Diego Ciccia

    (Kellogg [Northwestern] - Kellogg School of Management [Northwestern University, Evanston] - Northwestern University [Evanston])

  • 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)

  • Felix Knau

    (LMU - Ludwig Maximilian University [Munich] = Ludwig Maximilians Universität München)

Abstract

We consider treatment-effect estimation under a parallel trends assumption, in designs where no unit is treated at period one, all units receive a strictly positive dose at period two, and the dose varies across units. There are therefore no true control groups in such cases. First, we develop a test of the assumption that the treatment effect is mean independent of the treatment, under which the commonly used two-way fixed-effects estimator is consistent. When this test is rejected or lacks power, we propose alternative estimators, robust to heterogeneous effects. If there are units with a period-two treatment arbitrarily close to zero, the robust estimator is a difference-in-difference using units with a period-two treatment below a bandwidth as controls. Without such units, we propose non-parametric bounds, and an estimator relying on a parametric specification of treatment-effect heterogeneity. We use our results to revisit Pierce and Schott (2016) and Enikolopov et al. (2011).

Suggested Citation

  • Clément de Chaisemartin & Diego Ciccia & Xavier d'Haultfoeuille & Felix Knau, 2025. "Two-way Fixed Effects and Differences-in-Differences in Heterogeneous Adoption Designs without Stayers," SciencePo Working papers Main hal-03873937, HAL.
    • Handle: RePEc:hal:spmain:hal-03873937
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03873937v2
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