On the Role of Covariates in the Synthetic Control Method

Abadie et al. (2010) derive bounds on the bias of the Synthetic Control estimator under a perfect balance assumption on both observed covariates and pretreatment outcomes. In the absence of a perfect balance on covariates, we show that it is still possible to derive such bounds, but at the expense of relying on stronger assumptions on the effects of observed and unobserved covariates, and of generating looser bounds. We also show that a perfect balance on pre-treatment outcomes does not generally imply an approximate balance for all covariates, even when they are all relevant. Our results have important implications for the implementation of the method.