Regularization of Synthetic Controls for Policy Evaluation
We explore an upper bound of the mean squared prediction error (MSPE) of an arbitrary synthetic control (SC) method in predicting the counterfactual of a treated unit. This potential MSPE is essential for unifying and comparing a variety of SC methods. It is established without assuming the true outcome model or imposing a combination restriction on the SC unit, and allows for the use of auxiliary models to deal with the potential imperfect matching between the treated unit and the SC unit. We further propose a generalized SC method to regularize the squared-bias and variance components of the potential MSPE. The regularized SC method encompasses several existing SC methods or their variants, and generates useful complements to existing methods. We also show the usefulness of our method by simulation and empirical illustration.