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：量化政策干预的因果效应对于判断政策是否实现预期目标至关重要。我们提出一种确定性方法，用于经典的政策评估方法——合成控制法（Abadie和Gardeazabal, 2003），通过椭球最优恢复（Ellipsoidal Optimal Recovery, EOpR）来估计处理单元的不可观测结果。EOpR为政策评估者提供"最坏情况"结果和"典型"结果以辅助决策。这是一种近似理论技术，与主成分分析理论相关，能够在给定学习到的信号类别和一组已知观测值的情况下恢复未知观测值。我们证明，相比其他计量经济学方法，EOpR可以改进预处理拟合度以及后处理估计的偏差。除了恢复目标单元外，EOpR的一个优势是能对恢复产生的估计结果提供最坏情况估计。我们在人工生成数据、计量经济学文献常用数据集上进行评估，并在COVID-19大流行背景下推导相关结果。这种方法在计量经济学文献中针对因果性和政策评估具有创新性。