Difference-in-Differences Estimators When No Unit Remains Untreated

Clément de Chaisemartin; Diego Ciccia; Xavier D'Haultfœuille; Felix Knau

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arXiv · 2405.04465

Difference-in-Differences Estimators When No Unit Remains Untreated

Clément de Chaisemartin·Diego Ciccia·Xavier D'Haultfœuille·Felix Knau

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Abstract

We study treatment-effect estimation in two-period panels where all units are untreated initially and receive strictly positive treatment doses in the second period. With quasi-untreated units receiving doses local to zero, we show that, under parallel trends, a weighted average of potential-outcome slopes is identified by a difference-in-differences estimand using quasi-untreated units as controls, and we propose a nonparametric estimator based on regression-discontinuity methods. We then develop estimators for settings without quasi-untreated units and propose a test of the homogeneous-effect assumption underlying two-way fixed-effects regressions.

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Clément de Chaisemartin, Diego Ciccia, Xavier D'Haultfœuille, Felix Knau. 2024-05-07. Difference-in-Differences Estimators When No Unit Remains Untreated. https://arxiv.org/abs/2405.04465

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