Imperfect Synthetic Controls

The synthetic control method assumes the existence of a perfect synthetic control, which cannot exist if the outcomes of the treated unit are outside of the "convex hull" or the outcomes are functions of transitory shocks. However, synthetic controls for untreated units may include the treated unit, independently identifying the treatment effect. This paper introduces an estimator which generates synthetic controls for all units and develops moment conditions which are valid given transitory shocks. I also introduce a weighting metric which asymptotically excludes units without appropriate synthetic controls. For inference, the paper proposes a permutation test which accounts for heteroscedasticity.