Multiply robust difference-in-differences estimation of causal effect curves for continuous exposures.

The article focuses on developing a novel methodology for estimating causal effect curves of continuous exposures within difference-in-differences (DiD) designs, addressing multiple sources of confounding common in policy evaluations. The authors propose multiply robust estimators that relax parametric assumptions on effect curves and accommodate confounding both between treated and control groups and across varying exposure levels among the treated, under a new conditional parallel trends assumption. Simulation studies demonstrate that the proposed method yields consistent and less biased estimates compared to existing approaches, especially when some nuisance models are misspecified. The methodology is applied to evaluate the heterogeneous effects of Philadelphia's beverage excise tax, revealing significant variation in tax impact related to geographic proximity to non-taxed areas, after adjusting for socioeconomic confounders. This approach offers a flexible framework for researchers to assess policy effects with continuous exposures while accounting for complex confounding structures.