It is crucial to successfully quantify causal effects of a policy intervention to determine whether the policy achieved the desired outcomes. We present a deterministic approach to a classical method of policy evaluation, synthetic control (Abadie and Gardeazabal, 2003), to estimate the unobservable outcome of a treatment unit using ellipsoidal optimal recovery (EOpR). EOpR provides policy evaluators with "worst-case" outcomes and "typical" outcomes to help in decision making. It is an approximation-theoretic technique that also relates to the theory of principal components, which recovers unknown observations given a learned signal class and a set of known observations. We show that EOpR can improve pre-treatment fit and bias of the post-treatment estimation relative to other econometrics methods. Beyond recovery of the unit of interest, an advantage of EOpR is that it produces worst-case estimates over the estimations produced by the recovery. We assess our approach on artificially-generated data, on datasets commonly used in the econometrics literature, and also derive results in the context of the COVID-19 pandemic. Such an approach is novel in the econometrics literature for causality and policy evaluation.

翻译：成功量化政策干预的因果关系至关重要,以确定政策是否取得了预期结果。我们对传统的政策评价、合成控制方法(Abadie和Gardeazabal,2003年)提出一种决定性的方法,用以评估使用半脱线最佳恢复(EOPR)的治疗单位的不可观察结果。EOpR向政策评价者提供“最坏情况”的结果和“典型”结果,以帮助决策。这是一种近似理论技术,它也与主要组成部分理论有关,该理论根据一个学习的信号类和一套已知观测结果,恢复了未知的观测结果。我们表明,EOpR可以改进治疗后估计相对于其他计量生态方法的预处理适合性和偏差。除了回收利息单位之外,EOpR的优点是,它对复苏产生的估计得出最坏情况的估计。我们评估了我们关于人为生成的数据的方法,即生态计量文献中常用的数据集,还从COVID-19大流行性研究中得出结果。这种方法在生态计量和因果关系的文献中是新颖的。