  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.
