Estimation of Policy-Relevant Causal Effects in the Presence of Spillovers under the Difference-in-Differences Framework

Public policy interventions are commonly evaluated using the difference-in-differences (DiD) approach. However, this approach does not directly account for the effect of the policy spilling over to neighboring regions such as nearby cities. For example, the implementation of an excise tax on sweetened beverages in Philadelphia was shown to be associated with a substantial decrease in volume sales of taxed beverages in Philadelphia but also showed an increase in beverage sales in bordering counties which were not subject to the tax. The latter association could potentially be explained by cross-border shopping behaviors of Philadelphia residents. Because spillover effects can offset the total effect of such interventions, particularly for specific sub-populations, understanding the dynamics of such effects is essential to holistically evaluate public policies.

To address these concerns, we extend difference-in-differences methods to identify the causal effects of policy interventions under various spillover conditions. We propose doubly robust estimators for the average treatment effect on the treated and on the neighboring control that relax standard assumptions on interference and model specification. Throughout, we discuss practical considerations of such analyses, including possible positivity violations and time-varying effects, as they relate to the Philadelphia beverage tax study.