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:合成控制方法对使用小组数据的单一处理单位的处理效果进行推断,合成控制方法构建了一个控制单位结果的线性组合,以模拟处理单位的预处理结果轨迹。这种线性组合随后用于估算处理单位的反事实结果,如果在后处理期间未予处理,则用于估算治疗效果。现有的合成控制方法依赖于正确模拟反事实结果生成机制的某些方面,可能需要接近完美地匹配预处理过程。在预处理结果推断的启发下,我们获得了两个新的非参数化公式,用于模拟处理单位的平均处理效果:一个基于加权,另一个基于反事实结果和加权功能的模型。我们引入了合成控制概念,以在治疗任务的条件下获得这些识别结果。我们还根据这两个公式和一般的瞬间方法开发了两种治疗效果估计器。一个新的估计器具有双重性强性:一种是一致性的、非参数化的确定公式:一种基于加权的公式,而另一种是用于反实际结果和加权功能的模型。我们通过模拟将结果和血压模型正确地展示了巴西的性压风险。</s>