Synthetic control methods often rely on matching pre-treatment characteristics (called predictors) of the treated unit. The choice of predictors and how they are weighted plays a key role in the performance and interpretability of synthetic control estimators. This paper proposes the use of a sparse synthetic control procedure that penalizes the number of predictors used in generating the counterfactual to select the most important predictors. We derive, in a linear factor model framework, a new model selection consistency result and show that the penalized procedure has a faster mean squared error convergence rate. Through a simulation study, we then show that the sparse synthetic control achieves lower bias and has better post-treatment performance than the un-penalized synthetic control. Finally, we apply the method to revisit the study of the passage of Proposition 99 in California in an augmented setting with a large number of predictors available.
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