The synthetic control method (SCM) has become a popular tool for estimating causal effects in policy evaluation, where a single treated unit is observed, and a heterogeneous set of untreated units with pre- and post-policy change data are also observed. However, the synthetic control method faces challenges in accurately predicting post-intervention potential outcome had, contrary to fact, the treatment been withheld, when the pre-intervention period is short or the post-intervention period is long. To address these issues, we propose a novel method that leverages post-intervention information, specifically time-varying correlates of the causal effect called "surrogates", within the synthetic control framework. We establish conditions for identifying model parameters using the proximal inference framework and apply the generalized method of moments (GMM) approach for estimation and inference about the average treatment effect on the treated (ATT). Interestingly, we uncover specific conditions under which exclusively using post-intervention data suffices for estimation within our framework. Moreover, we explore several extensions, including covariates adjustment, relaxing linearity assumptions through non-parametric identification, and incorporating so-called "contaminated" surrogates, which do not exactly satisfy conditions to be valid surrogates but nevertheless can be incorporated via a simple modification of the proposed approach. Through a simulation study, we demonstrate that our method can outperform other synthetic control methods in estimating both short-term and long-term effects, yielding more accurate inferences. In an empirical application examining the Panic of 1907, one of the worst financial crises in U.S. history, we confirm the practical relevance of our theoretical results.

翻译：合成控制法已成为政策评估中估计因果效应的常用工具，其应用场景包括观察单个处理单元以及一组具有政策实施前后数据的异质性未处理单元。然而，当干预前周期较短或干预后周期较长时，合成控制法在准确预测反事实状态下的干预后潜在结果方面面临挑战。为解决这些问题，我们提出了一种新方法，通过在合成控制框架中利用干预后信息（特别是称为"替代变量"的因果效应时变相关因子）来改进估计。我们利用邻近推断框架建立了识别模型参数的条件，并采用广义矩估计法对处理组平均处理效应进行估计与推断。有趣的是，我们发现了特定条件，在这些条件下仅使用干预后数据即可在框架内完成充分估计。此外，我们探讨了多种扩展情形，包括协变量调整、通过非参数识别放松线性假设，以及纳入所谓"受污染"的替代变量——这类变量虽不完全满足有效替代变量的条件，但可通过简单修改所提方法加以整合。通过模拟研究，我们证明该方法在估计短期和长期效应方面均优于其他合成控制法，并产生更精确的推断。在针对1907年恐慌（美国历史上最严重的金融危机之一）的实证应用中，我们证实了理论结果的实际相关性。