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

Abstract: This paper extends difference-in-differences to settings involving continuous treatments. Specifically, the average treatment effect on the treated (ATT) at any level of continuous treatment intensity is identified using a conditional parallel trends assumption. In this framework, estimating the ATTs requires first estimating infinite-dimensional nuisance parameters, especially the conditional density of the continuous treatment, which can introduce significant biases. To address this challenge, estimators for the causal parameters are proposed under the double/debiased machine learning framework. We show that these estimators are asymptotically normal and provide consistent variance estimators. To illustrate the effectiveness of our methods, we re-examine the study by Acemoglu and Finkelstein (2008), which assessed the effects of the 1983 Medicare Prospective Payment System (PPS) reform. By reinterpreting their research design using a difference-in-differences approach with continuous treatment, we nonparametrically estimate the treatment effects of the 1983 PPS reform, thereby providing a more detailed understanding of its impact.