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.

翻译：本文为政策评价引入了新的惩罚性合成控制方法。拟议的稀有合成控制方法惩罚了用于产生反事实的预测器的数量,以改善预处理的适合性和选择最重要的预测器。在理论上,为了激励这种方法,I在线性要素模型框架内得出一个选择一致性示范结果和平均平方差错趋同率结果。通过模拟研究,我随后表明稀有的合成控制取得了比未受约束的合成控制更好的偏差和后处理能力。最后,我运用这一方法在有大量预测器的情况下研究加利福尼亚州第99号提案通过的影响。