Difference-in-Differences with Time-varying Continuous Treatments using Double/Debiased Machine Learning

Michel F. C. Haddad, Martin Huber and Lucas Z. Zhang

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Abstract: We propose a difference-in-differences (DiD) method for a time-varying continuous treatment and multiple time periods. Our framework assesses the average treatment effect on the treated (ATET) when comparing two non-zero treatment doses. The identification is based on a conditional parallel trend assumption imposed on the mean potential outcome under the lower dose, given observed covariates and past treatment histories. We employ kernel-based ATET estimators for repeated cross-sections and panel data adopting the double/debiased machine learning framework to control for covariates and past treatment histories in a data-adaptive manner. We also demonstrate the asymptotic normality of our estimation approach under specific regularity conditions. In a simulation study, we find a compelling finite sample performance of undersmoothed versions of our estimators in setups with several thousand observations.

Date: 2024-10
New Economics Papers: this item is included in nep-big, nep-cmp and nep-ecm
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