%0 Unpublished work %T An Optimal Bandwidth For Difference-in-Difference Estimation with a Continuous Treatment and an Heterogeneous Adoption Design %+ Département d'économie (Sciences Po) (ECON) %+ Centre de Recherche en Économie et Statistique (CREST) %A de Chaisemartin, Clément %A d'Haultfoeuille, Xavier %8 2022-11-23 %D 2022 %Z Humanities and Social Sciences/Economics and FinancePreprints, Working Papers, ... %X 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. %G English %2 https://sciencespo.hal.science/hal-03873937/document %2 https://sciencespo.hal.science/hal-03873937/file/2022_dechaisemartin_dhaultfoeuille_an_optimal_bandwidth_for_difference_in_difference_estimation_with_a_continuous_treatment_and_an_heterogeneous_adoption_design.pdf %L hal-03873937 %U https://sciencespo.hal.science/hal-03873937 %~ SHS %~ X %~ SCIENCESPO %~ GENES %~ CNRS %~ ENSAE %~ AO-ECONOMIE %~ X-DEP %~ PARISTECH %~ CREST %~ ENSAI %~ X-CREST %~ IP_PARIS %~ IP_PARIS_COPIE %~ ECON-SCPO %~ SCPO_OA %~ SCPO-REPEC