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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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  • Clément de Chaisemartin

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Xavier d'Haultfoeuille

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Clément de Chaisemartin & Xavier d'Haultfoeuille, 2022. "An Optimal Bandwidth For Difference-in-Difference Estimation with a Continuous Treatment and an Heterogeneous Adoption Design," Working Papers hal-03873937, HAL.
    • Handle: RePEc:hal:wpaper:hal-03873937
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03873937
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