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

Author

Listed:
  • Clément de Chaisemartin

    (Sciences Po Paris)

  • Diego Ciccia

    (Northwestern University, Kellogg School of Management)

  • Xavier D’Haultfoeuille

    (CREST-ENSAE)

  • Felix Knau

    (University of Munich)

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, 2024. "Two-way Fixed Effects and Differences-in-Differences in Heterogeneous Adoption Designs without Stayers," Working Papers 2025-01, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2025-01
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