Sparse Synthetic Controls

This paper introduces a new penalized synthetic control method for policy evaluation. The proposed sparse synthetic control penalizes the number of predictors used in generating the counterfactual to improve pre-treatment fit and select the most important predictors. To motivate the method theoretically I derive, in a linear factor model framework, a model selection consistency result and a mean squared error convergence rate result. Through a simulation study, I then show that the sparse synthetic control achieves lower bias and has better post-treatment fit than the unpenalized synthetic control. Finally, I apply the method to study the effects of the passage of Proposition 99 in California in a setting with a large number of predictors.