Researchers commonly use difference-in-differences (DiD) designs to evaluate public policy interventions. While methods exist for estimating effects in the context of binary interventions, policies often result in varied exposures across regions implementing the policy. Yet, existing approaches for incorporating continuous exposures face substantial limitations in addressing confounding variables associated with intervention status, exposure levels, and outcome trends. These limitations significantly constrain policymakers' ability to fully comprehend policy impacts and design future interventions. In this work, we propose new estimators for causal effect curves within the DiD framework, accounting for multiple sources of confounding. Our approach accommodates misspecification of a subset of treatment, exposure, and outcome models while avoiding any parametric assumptions on the effect curve. We present the statistical properties of the proposed methods and illustrate their application through simulations and a study investigating the heterogeneous effects of a nutritional excise tax under different levels of accessibility to cross-border shopping.

翻译：研究者通常使用差分方法（DiD）设计来评估公共政策干预。尽管存在针对二元干预的效应估计方法，但政策往往导致实施区域内的暴露水平变化。然而，现有处理连续暴露的方法在应对与干预状态、暴露水平和结果趋势相关的混杂变量方面存在显著局限性。这些不足严重制约了政策制定者全面理解政策影响并设计未来干预的能力。在本研究中，我们提出在DiD框架下针对因果效应曲线的新型估计量，能够处理多种混杂来源。我们的方法允许治疗模型、暴露模型和结果模型中的子集设定错误，同时避免对效应曲线施加任何参数假设。我们阐述了所提方法的统计性质，并通过模拟实验和一项研究案例（探讨不同跨境购物可达性下营养消费税的异质性效应）展示了其应用。