The conditional average treatment effect (CATE) is the best measure of individual causal effects given baseline covariates. However, the CATE only captures the (conditional) average, and can overlook risks and tail events, which are important to treatment choice. In aggregate analyses, this is usually addressed by measuring the distributional treatment effect (DTE), such as differences in quantiles or tail expectations between treatment groups. Hypothetically, one can similarly fit conditional quantile regressions in each treatment group and take their difference, but this would not be robust to misspecification or provide agnostic best-in-class predictions. We provide a new robust and model-agnostic methodology for learning the conditional DTE (CDTE) for a class of problems that includes conditional quantile treatment effects, conditional super-quantile treatment effects, and conditional treatment effects on coherent risk measures given by $f$-divergences. Our method is based on constructing a special pseudo-outcome and regressing it on covariates using any regression learner. Our method is model-agnostic in that it can provide the best projection of CDTE onto the regression model class. Our method is robust in that even if we learn these nuisances nonparametrically at very slow rates, we can still learn CDTEs at rates that depend on the class complexity and even conduct inferences on linear projections of CDTEs. We investigate the behavior of our proposal in simulations, as well as in a case study of 401(k) eligibility effects on wealth.

翻译：条件平均处理效应（CATE）是基于基线协变量衡量个体因果效应的最佳指标。然而，CATE仅捕捉（条件）平均值，可能忽略对治疗选择至关重要的风险与尾事件。在聚合分析中，通常通过测量分布处理效应（DTE）来解决此问题，例如处理组之间分位数或尾部期望的差异。理论上，可对每个处理组分别拟合条件分位数回归并取其差值，但该方法对设定错误缺乏鲁棒性，且无法提供模型无关的最优类内预测。我们提出了一种新的鲁棒且模型无关的方法，用于学习一类问题的条件分布处理效应（CDTE），包括条件分位数处理效应、条件超分位数处理效应，以及基于$f$-散度的一致风险测度下的条件处理效应。该方法通过构建特殊的伪结果量，并利用任意回归学习器将其对协变量进行回归实现。其模型无关性体现在可提供CDTE在回归模型类上的最优投影；鲁棒性表现为，即使以极慢的非参数速率学习这些干扰项，我们仍能通过类复杂度依赖的速率学习CDTE，甚至对CDTE的线性投影进行推断。我们通过仿真研究以及401(k)资格对财富影响的案例分析验证了该方法的性能。