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

See all articles by Clément de Chaisemartin

Clément de Chaisemartin

SciencesPo - Sciences Po - Department of Economics

Xavier D'Haultfœuille

Center for Research in Economics and Statistics (CREST)

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

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

Clément De Chaisemartin (Contact Author)

SciencesPo - Sciences Po - Department of Economics ( email )

28, rue des Saints-Pères
Paris, Paris 75007
France

Xavier D'Haultfoeuille

Center for Research in Economics and Statistics (CREST) ( email )

5 avenue Henry le Chatelier
Palaiseau, 91120
France

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