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An Optimal Bandwidth For Difference-in-Difference Estimation with a Continuous Treatment and an Heterogeneous Adoption Design

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Abstract

We propose a difference-in-difference estimator with a continuous treatment. We consider an heterogeneous adoption design where no unit is treated at period one, all units receive a strictly positive treatment dose at period two, and there are units with a treatment dose close to zero at period two. Our estimator uses "quasi-stayers", namely units with a period-two treatment below a bandwidth, as a control group to infer the counterfactual outcome evolution without treatment. We propose an optimal bandwidth that minimizes an asymptotic approximation of the estimator's mean-squared-error.
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Dates and versions

hal-03873937 , version 1 (27-11-2022)

Licence

Attribution - NonCommercial - CC BY 4.0

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  • HAL Id : hal-03873937 , version 1

Cite

Clément de Chaisemartin, Xavier d'Haultfoeuille. An Optimal Bandwidth For Difference-in-Difference Estimation with a Continuous Treatment and an Heterogeneous Adoption Design. 2022. ⟨hal-03873937⟩
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