We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds in two steps. We first specify the maximal degree to which the distribution of unobserved potential outcomes may deviate from that of observed outcomes. We then derive sharp bounds on the average treatment effects under this assumption. Our framework encompasses the popular marginal sensitivity model as a special case, and we demonstrate how the proposed methodology can address a primary challenge of the marginal sensitivity model that it produces uninformative results when unobserved confounders substantially affect treatment and outcome. Specifically, we develop an alternative sensitivity model, called the distributional sensitivity model, under the assumption that heterogeneity of treatment effect due to unobserved variables is relatively small. Unlike the marginal sensitivity model, the distributional sensitivity model allows for potential lack of overlap and often produces informative bounds even when unobserved variables substantially affect both treatment and outcome. Finally, we show how to extend the distributional sensitivity model to difference-in-differences designs and settings with instrumental variables. Through simulation and empirical studies, we demonstrate the applicability of the proposed methodology.

翻译：我们考虑在观测研究中估计平均处理效应，并提出一种针对未观测混杂变量的稳健因果推断新框架。我们的方法基于分布鲁棒优化，分为两个步骤。首先，我们指定未观测潜在结果的分布相对于观测结果分布的最大偏离程度。然后，在此假设下推导平均处理效应的紧致界。该框架将流行的边际敏感模型作为特例包含在内，并展示了所提方法如何解决边际敏感模型的核心挑战——当未观测混杂变量对处理和结果产生显著影响时，该模型会产生无信息的结果。具体而言，我们提出了一种替代性敏感模型，称为分布敏感模型，其假设未观测变量导致的处理效应异质性相对较小。与边际敏感模型不同，分布敏感模型允许存在潜在重叠不足的情况，且即便未观测变量对处理和结果均有显著影响，该模型也常能得出有信息量的边界。最后，我们展示了如何将分布敏感模型拓展至双重差分设计及存在工具变量的场景。通过仿真与实证研究，我们验证了所提方法的适用性。