Identification and Bayesian Inference for Synthetic Control Methods with Spillover Effects

TL;DR

This paper extends the synthetic control method to account for spillover effects in panel data by integrating a spatial autoregressive model and Bayesian inference, enabling more accurate causal estimates in interconnected units.

Contribution

It introduces a novel Bayesian SCM framework that models spillover effects using SAR and horseshoe priors, addressing a key limitation of traditional SCM.

Findings

Effectiveness demonstrated in tobacco tax case study

Accurate spillover effect estimation in Sudan GDP analysis

Enhanced causal inference with spillover considerations

Abstract

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.