Causal inference for extreme events has many potential applications in fields such as climate science, medicine and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome. Existing methods are limited to the case where the quantile of interest is within the range of the observations. For applications in risk assessment, however, the most relevant cases relate to extremal quantiles that go beyond the data range. We introduce an estimator of the extremal quantile treatment effect that relies on asymptotic tail approximation, and use a new causal Hill estimator for the extreme value indices of potential outcome distributions. We establish asymptotic normality of the estimators and propose a consistent variance estimator to achieve valid statistical inference. We illustrate the performance of our method in simulation studies, and apply it to a real data set to estimate the extremal quantile treatment effect of college education on wage.

翻译：极端事件的因果推断在气候科学、医学和经济学等领域具有诸多潜在应用。本文研究二元处理对连续重尾结果变量的极端分位数处理效应。现有方法仅限于感兴趣分位数位于观测值范围内的情形。然而，在风险评估应用中，最相关的情形涉及超出数据范围的极端分位数。我们提出一种基于渐近尾部近似的极端分位数处理效应估计量，并利用新的因果希尔估计量估计潜在结果分布的极值指数。我们证明了估计量的渐近正态性，并提出了一个一致的方差估计量以实现有效的统计推断。我们通过模拟研究展示了该方法的性能，并将其应用于实际数据集，估计大学教育对工资的极端分位数处理效应。