  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.
