Synthetic control (SC) methods are commonly used to estimate the treatment effect on a single treated unit in panel data settings. An SC is a weighted average of control units built to match the treated unit, with weights typically estimated by regressing (summaries of) pre-treatment outcomes and measured covariates of the treated unit to those of the control units. However, it has been established that in the absence of a good fit, such regression estimator will generally perform poorly. In this paper, we introduce a proximal causal inference framework to formalize identification and inference for both the SC and ultimately the treatment effect on the treated, based on the observation that control units not contributing to the construction of an SC can be repurposed as proxies of latent confounders. We view the difference in the post-treatment outcomes between the treated unit and the SC as a time series, which opens the door to various time series methods for treatment effect estimation. The proposed framework can accommodate nonlinear models, which allows for binary and count outcomes that are understudied in the SC literature. We illustrate with simulation studies and an application to evaluation of the 1990 German Reunification.

翻译：合成控制（Synthetic Control, SC）方法常用于面板数据中估计单个处理单元的处理效应。SC是对照组单元的加权平均值，用于匹配处理单元，其权重通常通过将处理单元的处理前结果（摘要）和测量协变量对对照组单元进行回归来估计。然而，已有研究表明，在缺乏良好拟合的情况下，此类回归估计量通常表现不佳。本文提出了一种近端因果推断框架，基于不参与构建SC的对照组单元可被重新用作潜在混淆变量的代理这一观察，正式化了SC以及最终处理组处理效应的识别与推断。我们将处理单元与SC在处理后结果的差异视为一个时间序列，这为时间序列方法在估计处理效应中的应用打开了大门。所提框架能够适应非线性模型，从而允许处理二元和计数型结果变量——这在SC文献中研究较少。我们通过模拟研究以及1990年德国统一评估的应用实例进行说明。