Balancing Unobservables: Large-Sample Properties of the Synthetic Control Algorithm

Organised by

• Department of Economics

We analyse the properties of the synthetic control (SC) algorithm in settings with a large number of units. We assume that the selection into treatment is based on unobserved permanent heterogeneity and pretreatment information, thus allowing for both strictly and sequentially exogenous assignment processes. Exploiting duality, we interpret the solution of the SC optimisation problem as an estimator for the underlying treatment probabilities. We use this to derive the asymptotic representation for the SC algorithm and characterize sufficient conditions for its asymptotic normality. We show that the critical property that determines the asymptotic behavior of the SC algorithm is the ability of input features to approximate the unobserved heterogeneity. Our results imply that the SC algorithm delivers asymptotically normal estimators for a large class of linear panel data models as long as the number of pretreatment periods is large enough, making it a natural alternative to conventional methods built on Difference-in-Differences. 

Co-author: David Hirshberg, Emory University