Two-way Fixed Effects and Differences-in-Differences in Heterogeneous Adoption Designs without Stayers
60 Pages Posted: 13 Dec 2022 Last revised: 21 Nov 2024
Date Written: November 23, 2022
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: Suggested Citation
de Chaisemartin, Clément and d'Haultfoeuille, Xavier,
Two-way Fixed Effects and Differences-in-Differences in Heterogeneous Adoption Designs without Stayers
(November 23, 2022). Available at SSRN: https://ssrn.com/abstract=4284811 or http://dx.doi.org/10.2139/ssrn.4284811
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