Difference-in-Differences Estimators When No Unit Remains Untreated

Cl\'ement de Chaisemartin, Diego Ciccia (), Xavier D'Haultf{\oe}uille and 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.

Date: 2024-05, Revised 2026-07
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