Continuous difference-in-differences with double/debiased machine learning

Lucas Z. Zhang

Papers from arXiv.org

Abstract: This paper extends difference-in-differences to settings with continuous treatments. Specifically, the average treatment effect on the treated (ATT) at any level of treatment intensity is identified under a conditional parallel trends assumption. Estimating the ATT in this framework requires first estimating infinite-dimensional nuisance parameters, particularly the conditional density of the continuous treatment, which can introduce substantial bias. To address this challenge, we propose estimators for the causal parameters under the double/debiased machine learning framework and establish their asymptotic normality. Additionally, we provide consistent variance estimators and construct uniform confidence bands based on a multiplier bootstrap procedure. To demonstrate the effectiveness of our approach, we apply our estimators to the 1983 Medicare Prospective Payment System (PPS) reform studied by Acemoglu and Finkelstein (2008), reframing it as a DiD with continuous treatment and nonparametrically estimating its effects.

Date: 2024-08, Revised 2025-07
New Economics Papers: this item is included in nep-big and nep-ecm
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