Estimating the causal effect of a treatment on the entire response distribution is an important yet challenging task. For instance, one might be interested in how a pension plan affects not only the average savings among all individuals but also how it affects the entire savings distribution. While sufficiently large randomized studies can be used to estimate such distributional causal effects, they are often either not feasible in practice or involve non-compliance. A well-established class of methods for estimating average causal effects from either observational studies with unmeasured confounding or randomized studies with non-compliance are instrumental variable (IV) methods. In this work, we develop an IV-based approach for identifying and estimating distributional causal effects. We introduce a distributional IV model with corresponding assumptions, which leads to a novel identification result for the interventional cumulative distribution function (CDF) under a binary treatment. We then use this identification to construct a nonparametric estimator, called DIVE, for estimating the interventional CDFs under both treatments. We empirically assess the performance of DIVE in a simulation experiment and illustrate the usefulness of distributional causal effects on two real-data applications.

翻译：估计处理对整个响应分布的因果效应是一项重要但具有挑战性的任务。例如，人们可能不仅关心养老金计划如何影响所有个体的平均储蓄，还关心它如何影响整个储蓄分布。虽然足够大规模的随机化研究可用于估计此类分布因果效应，但在实践中它们往往要么不可行，要么涉及不依从问题。工具变量（IV）方法是一类成熟的方法，可用于从存在未测量混杂的观察性研究或存在不依从的随机化研究中估计平均因果效应。在本工作中，我们开发了一种基于工具变量的方法来识别和估计分布因果效应。我们引入了具有相应假设的分布工具变量模型，该模型在二元处理下为干预累积分布函数（CDF）导出了一个新颖的识别结果。随后，我们利用该识别结果构建了一个名为DIVE的非参数估计器，用于估计两种处理下的干预CDF。我们通过模拟实验实证评估了DIVE的性能，并通过两个真实数据应用说明了分布因果效应的实用性。