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

• URL: http://arxiv.org/abs/2410.21105v1
• Date: Mon, 28 Oct 2024 15:10:43 GMT
• Title: Difference-in-Differences with Time-varying Continuous Treatments using Double/Debiased Machine Learning
• Authors: Michel F. C. Haddad, Martin Huber, Lucas Z. Zhang,
• Abstract summary: We propose a difference-in-differences (DiD) method for continuous treatment and multiple time periods. Our framework assesses the average treatment effect on the treated (ATET) when comparing two non-zero treatment doses.
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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.

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