Large-Sample Properties of the Synthetic Control Method under Selection on Unobservables

Understand

We analyze the synthetic control (SC) method in panel data settings with many units.

• We assume the treatment assignment is based on unobserved heterogeneity and pre-treatment information, allowing for both strictly and sequentially exogenous assignment processes.
• We show that the critical property that determines the behavior of the SC method is the ability of input features to approximate the unobserved heterogeneity.
• Our results imply that the SC method delivers asymptotically normal estimators for a large class of linear panel data models as long as the number of pre-treatment periods is sufficiently large, making it a natural alternative to the Difference-in-Differences.