Bayesian Shrinkage Priors for Penalized Synthetic Control Estimators in the Presence of Spillovers

Abstract: Synthetic control (SC) methods are widely used to evaluate the impact of policy interventions, particularly those targeting specific geographic areas or regions, commonly referred to as units. These methods construct an artificial (synthetic) unit from untreated (control) units, intended to mirror the characteristics of the treated region had the intervention not occurred. While neighboring areas are often chosen as controls due to their assumed similarities with the treated, their proximity can introduce spillovers, where the intervention indirectly affects these controls, biasing the estimates. To address this challenge, we propose a Bayesian SC method with distance-based shrinkage priors, designed to estimate causal effects while accounting for spillovers. Modifying traditional penalization techniques, our approach incorporates a weighted distance function that considers both covariate information and spatial proximity to the treated. Rather than simply excluding nearby controls, this framework data-adaptively selects those less likely to be impacted by spillovers, providing a balance between bias and variance reduction. Through simulation studies, we demonstrate the finite-sample properties of our method under varying levels of spillover. We then apply this approach to evaluate the impact of Philadelphia's beverage tax on the sales of sugar-sweetened and artificially sweetened beverages in mass merchandise stores.

• The paper introduces novel Bayesian shrinkage priors (DHS and DS2) that improve estimation precision amid spillover challenges.
• It employs a weighted distance function to balance covariate differences with spatial proximity among control units.
• Simulations and a case study on Philadelphia’s beverage tax reveal superior bias reduction compared to traditional models.

Bayesian Shrinkage Priors for Penalized Synthetic Control Estimators in the Presence of Spillovers

The paper authored by Esteban Fernández-Morales, Arman Oganisian, and Youjin Lee offers an intricate exploration into the field of synthetic control (SC) methods, specifically targeting the estimation of causal effects amidst spillover scenarios. The research introduces novel Bayesian shrinkage priors, notably distance horseshoe (DHS) and distance spike-and-slab (DS2) priors, designed to enhance the precision of SC estimators in contexts where spillovers may compromise the validity of causal inferences. These methods hold promise for more accurate policy evaluation, particularly when geographically close control units might be inadvertently impacted by the intervention intended for the treated units.

Central to this work is the adaptation of penalization techniques, like the horseshoe and spike-and-slab priors, with a unique twist: the incorporation of a weighted distance function. This function balances covariate dissimilarity and spatial proximity to carefully determine the degree of shrinkage applied to each control unit within the donor pool. The study emphasizes that when geographically proximate controls are likely to undergo spillover effects, these Bayesian methods facilitate a more nuanced allocation of control units, substantially reducing potential bias in causal effect estimates.

The application of these sophisticated priors is showcased through a simulation study and a real-world analysis. The simulation meticulously assesses scenarios with varying spillover intensities, showcasing that these Bayesian approaches outperform traditional models like Bayesian structural time-series (BSTS) and generalized synthetic control (GSC) methods in terms of relative bias and coverage probability. Particularly, at lower levels of covariate dissimilarity weight ($\kappa_d$), the DHS and DS2 priors maintain closer adherence to true parameter values, demonstrating their prowess in handling spillovers more effectively than models that overlook spatial information.

The study is exemplified through an evaluation of Philadelphia’s beverage tax’s impact on beverage sales in mass merchandise stores, offering crucial insights into the practical implications and robustness of these Bayesian SC methods. The findings indicate clear reductions in sales post-intervention, even accounting for variations in $\kappa_d$, thereby underscoring the adaptability and precision of the proposed methodologies.

Given the robust framework and promising results, the advancement in Bayesian SC methods presented in the paper has potential applications beyond policy interventions into diverse research fields where spillover effects are prevalent. However, it also acknowledges limitations such as over-reliance on the cutoff parameter $\rho$ in the DS2 model, which, if miscalculated, can skew results significantly. Whilst the methodology specifically tackles single-intervention scenarios, adaptation for multiple treated units is suggested as a pathway for future research.

In conclusion, the research advances the methodology for causal inference in the context of spillover, offering practitioners in fields such as economics, public health, and social sciences robust tools for unbiased policy evaluation. Future exploration might involve expanding the applicability of these methods into non-normal and non-continuous data settings or incorporating more complex spatial metrics. These innovations could further solidify the utility and versatility of Bayesian SC methods in addressing spillover challenges across various domains.