Researchers commonly use difference-in-differences (DiD) designs to evaluate public policy interventions. While established methodologies 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 study, we propose innovative 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 diverse effects of a nutritional excise tax.

翻译：研究者常用差异中的差异（DID）设计来评估公共政策干预。尽管在二元干预情境下估算效应的方法已经成熟，但政策往往导致实施政策的区域出现不同程度的暴露。然而，现有处理连续暴露的方法在应对与干预状态、暴露水平及结果趋势相关的混杂变量时存在显著局限。这些局限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。本研究提出针对DID框架内因果效应曲线的创新估计方法，能够应对多重混杂来源。本方法允许对处理模型、暴露模型及结果模型中的部分子集存在误设定，同时避免对效应曲线施加任何参数化假设。我们阐明了所提方法的统计性质，并通过模拟研究及一项关于营养消费税异质性效应的实证研究展示了其应用。