  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.
