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

Clément de Chaisemartin, Diego Ciccia (), Xavier D'Haultfoeuille and Felix Knau

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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).

Date: 2025-01-10
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Working Paper: Two-way Fixed Effects and Differences-in-Differences in Heterogeneous Adoption Designs without Stayers (2025)
Working Paper: Two-way Fixed Effects and Differences-in-Differences in Heterogeneous Adoption Designs without Stayers (2024)
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