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ABSTRACT 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 intervention, 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. 

Abstract Policy interventions can spill over to units of a population that is not directly exposed to the policy but are geographically close to the units receiving the intervention. In recent work, investigations of spillover effects on neighbouring regions have focused on estimating the average treatment effect of a particular policy in an observed setting. Our research question broadens this scope by asking what policy consequences would the treated units have experienced under counterfactual exposure settings. When we only observe treated unit(s) surrounded by controls—as is common when a policy intervention is implemented in a single city or state—this effect inquires about the policy effects under a counterfactual neighbourhood policy status that we do not, in actuality, observe. In this work, we extend difference-in-differences approaches to spillover settings and develop identification conditions required to evaluate policy effects in counterfactual treatment scenarios. These causal quantities are policy-relevant for designing effective policies for populations subject to various neighbourhood statuses. We develop several estimators that have desirable properties. We provide an illustrative data application to the Philadelphia beverage tax study. 

Abstract To comprehensively evaluate a public policy intervention, researchers must consider the effects of the policy not just on the implementing region, but also nearby, indirectly affected regions. For example, an excise tax on sweetened beverages in Philadelphia, Pennsylvania was shown to not only be associated with a decrease in volume sales of taxed beverages in Philadelphia, but also an increase in sales in nontaxed bordering counties. The latter association may be explained by cross-border shopping behaviours of Philadelphia residents and indicate a causal effect of the tax on nearby regions, which may drastically offset the total effect of the intervention. In this paper, we adapt doubly robust difference-in-differences methodology to estimate distinct causal effects on the implementing and neighbouring control regions when they are geographically separable and data exists from an unaffected control region. Our approach adjusts for potential confounding in quasi-experimental evaluations and relaxes standard assumptions on model specification while accounting for geographically separable interference, repeated observations, spatial correlation, and unknown effect heterogeneity. We apply these methods to evaluate the effect of the Philadelphia beverage tax on taxed beverage sales in 231 Philadelphia and bordering county stores. We also use our methods to explore effect heterogeneity across geographical features.