An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls

We introduce new inference procedures for counterfactual and synthetic control methods for policy evaluation. We recast the causal inference problem as a counterfactual prediction and a structural breaks testing problem. This allows us to exploit insights from conformal prediction and structural breaks testing to develop permutation inference procedures that accommodate modern high-dimensional estimators, are valid under weak and easy-to-verify conditions, and are provably robust against misspecification. Our methods work in conjunction with many different approaches for predicting counterfactual mean outcomes in the absence of the policy intervention. Examples include synthetic controls, difference-in-differences, factor and matrix completion models, and (fused) time series panel data models. Our approach demonstrates an excellent small-sample performance in simulations and is taken to a data application where we re-evaluate the consequences of decriminalizing indoor prostitution. Open-source software for implementing our conformal inference methods is available.我们提出了适用于政策评估的反事实（counterfactual）与合成控制法（synthetic control method）的全新推断流程。我们将因果推断（causal inference）问题重构为反事实预测与结构突变检验（structural breaks testing）两类问题。借此，我们可借助共形预测（conformal prediction）与结构突变检验领域的理论洞见，开发出适配现代高维估计量的置换推断（permutation inference）流程；该流程在宽松且易于验证的条件下具备有效性，且经证明对模型设定错误（misspecification）具有鲁棒性。我们的方法可与多种用于预测政策未实施场景下反事实平均结果的方法结合使用，相关示例包括合成控制法、双重差分法（difference-in-differences）、因子模型与矩阵补全（matrix completion）模型，以及（融合）时间序列面板数据模型等。我们的方法在模拟实验中展现出优异的小样本性能，且已应用于一项实证研究，重新评估了将室内卖淫非刑事化所带来的影响。用于实现我们的共形推断方法的开源软件已公开可用。