Accounting for spillover when using the augmented synthetic control method: estimating the effect of localized COVID-19 lockdowns in Chile

The implementation of public health policies, particularly in a single or small set of units (e.g., regions), can create complex dynamics with effects extending beyond the directly treated areas. This paper examines the direct effect of COVID-19 lockdowns in Chile on the comunas where they were enacted and the spillover effect from neighboring comunas. To draw inference about these effects, the Augmented Synthetic Control Method (ASCM) is extended to account for interference between neighboring units by introducing a stratified control framework. Specifically, Ridge ASCM with stratified controls (ASCM-SC) is proposed to partition control units based on treatment exposure. By leveraging control units that are untreated, or treated but outside the treated unit's neighborhood, this method estimates both the direct and spillover effects of intervention on treated and neighboring units. Simulations demonstrate improved bias reduction under various data-generating processes. ASCM-SC is applied to estimate the direct and total (direct + indirect) effects of COVID-19 lockdowns in Chile at the start of the COVID-19 pandemic. This method provides a more flexible approach for estimating the effects of public health interventions in settings with interference.