Identification and Bayesian Inference for Synthetic Control Methods with Spillover Effects

The synthetic control method (SCM) is widely used for causal inference with panel data, particularly when the number of treated units is small. It relies on the stable unit treatment value assumption (SUTVA), ruling out spillover effects. However, interventions often affect not only treated but also untreated units. This study proposes a novel panel data method that extends standard SCM to account for spillovers and estimate both treatment and spillover effects. The approach extends the SCM framework by incorporating a spatial autoregressive (SAR) panel data model that captures spillover patterns across units. We also develop a Bayesian inference procedure using horseshoe priors for regularization. We apply the proposed method to two empirical studies: (i) evaluating the effect of the California tobacco tax on cigarette consumption, and (ii) assessing the economic impact of the 2011 Sudan division on GDP per capita.

💡 Research Summary

The paper tackles a fundamental limitation of the synthetic control method (SCM), namely its reliance on the Stable Unit Treatment Value Assumption (SUTVA), which precludes any spillover effects from a treated unit to untreated units. Recognizing that many policy interventions generate such spillovers—through geographic proximity, trade links, or other forms of interdependence—the authors propose a novel framework that simultaneously identifies and estimates both the direct treatment effect and the spillover effects on control units.

Methodologically, the authors embed a spatial autoregressive (SAR) panel model within the SCM framework. For the control group outcomes they specify
Y_ct(d_t) = ρ