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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Xavier D’Haultfoeuille: CREST-ENSAE

No 2025-01, Working Papers from Center for Research in Economics and Statistics

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).

Pages: 44 pages
Date: 2024-07-26
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http://crest.science/RePEc/wpstorage/2025-01.pdf CREST working paper version (application/pdf)

Related works:
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 (2025)
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