On the Role of Covariates in the Synthetic Control Method

We derive conditions under which the original result of Abadie et al (2010) regarding the bias of the Synthetic Control (SC) estimator remains valid when we relax the assumption of a perfect match on observed covariates. We then show that, even when the conditions for the first result are valid, a perfect match on pre-treatment outcomes does not generally imply an approximate match for all covariates. Taken together, our results show that a perfect match on covariates should not be required for the SC method, as long as there is a perfect match on a long set of pre-treatment outcomes.