To infer the treatment effect for a single treated unit using panel data, synthetic control methods construct a linear combination of control units' outcomes that mimics the treated unit's pre-treatment outcome trajectory. This linear combination is subsequently used to impute the counterfactual outcomes of the treated unit had it not been treated in the post-treatment period, and used to estimate the treatment effect. Existing synthetic control methods rely on correctly modeling certain aspects of the counterfactual outcome generating mechanism and may require near-perfect matching of the pre-treatment trajectory. Inspired by proximal causal inference, we obtain two novel nonparametric identifying formulas for the average treatment effect for the treated unit: one is based on weighting, and the other combines models for the counterfactual outcome and the weighting function. We introduce the concept of covariate shift to synthetic controls to obtain these identification results conditional on the treatment assignment. We also develop two treatment effect estimators based on these two formulas and the generalized method of moments. One new estimator is doubly robust: it is consistent and asymptotically normal if at least one of the outcome and weighting models is correctly specified. We demonstrate the performance of the methods via simulations and apply them to evaluate the effectiveness of a Pneumococcal conjugate vaccine on the risk of all-cause pneumonia in Brazil.

翻译：为了利用面板数据推断单个处理单元的处理效应，合成控制方法通过构建对照组结果的线性组合来模仿处理单元在预处理期的结果轨迹。该线性组合随后用于估算处理单元在未接受处理情况下的反事实结果，并据此估计处理效应。现有合成控制方法依赖于对反事实结果生成机制某些方面的正确建模，可能需要对预处理轨迹实现近乎完美的匹配。受邻近因果推断的启发，我们获得了两个用于处理单元平均处理效应的新型非参数识别公式：其中一个基于加权方法，另一个则结合了反事实结果模型与加权函数。我们引入协变量偏移的概念用于合成控制方法，以在条件于处理分配的情况下获得这些识别结果。基于这两个公式和广义矩估计方法，我们开发了两种处理效应估计量。其中一种新型估计量具有双重稳健性：当结果模型和加权模型中至少有一个被正确设定时，该估计量具有一致性和渐近正态性。通过仿真实验验证了方法的性能，并将其应用于评估肺炎球菌结合疫苗对巴西全因肺炎风险的有效性。