Multiply Robust Estimation of Causal Effect Curves for Difference-in-Differences Designs

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.