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

Difference-in-differences (DiD) is a cornerstone method for causal inference, i.e., the evaluation of the impact of a treatment (such as vaccination) on an outcome of interest (such as mortality), in observational studies, provided that outcomes may be observed both before and after the treatment introduction. In such studies, the observed outcomes of treated individuals before and after a treatment typically do not allow researchers to directly infer the treatment effect. This is due to confounding time trends in the treated individuals' counterfactual outcomes that would have occurred without the treatment. The DiD approach tackles this issue based on a control group not receiving the treatment and the so-called parallel trends assumption, imposing that the treated group's unobserved counterfactual outcomes under non-treatment follow the same observed mean outcome trend of the control group. While the canonical DiD setup considers a binary treatment definition (treatment versus no treatment), in many empirical applications, treatments are continuously distributed - e.g., the vaccination rate in a region. Furthermore, the treatment intensity might vary over time and a strict control group with a zero treatment might not be available across all or even any treatment period, as also argued in de Chaisemartin et al. [2024], who point to taxes, tariffs, or prices as possible treatment variables with strictly non-zero doses.