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.

翻译：合成控制方法往往依赖于对被处理单位的预处理特性(所谓的预测器)进行匹配。预测器的选择及其加权方式在合成控制估计器的性能和可解释性方面起着关键作用。本文件提议使用一种稀疏的合成控制程序来惩罚用于产生反事实的预测器的数量,以选择最重要的预测器。我们在一个线性系数模型框架内得出一种新的模型选择一致性结果,并表明受处罚的程序具有更快的平均正方形误差趋同率。通过模拟研究,我们然后表明稀疏的合成控制在合成控制器的性能和可解释性方面作用较低,其后处理性能优于非强制性合成控制。最后,我们采用这种方法,在有大量预测器的辅助环境下,重新审查对加利福尼亚州第99号提案通过情况的研究。