Extreme quantile treatment effects (eQTEs) measure the causal impact of a treatment on the tails of an outcome distribution and are central for studying rare, high-impact events. Standard QTE methods often fail in extreme regimes due to data sparsity, while existing eQTE methods rely on restrictive tail assumptions or on interior-quantile theory. We propose the Tail-Calibrated Inverse Estimating Equation (TIEE) framework, which combines information across quantile levels and anchors the tail using extreme value models within a unified estimating equation approach. We establish asymptotic properties of the resulting estimator and evaluate its performance through simulation under different tail behaviours and model misspecifications. An application to extreme precipitation in the Austrian Alps illustrates how TIEE enables observational causal attribution for very rare events under anthropogenic warming. More broadly, the proposed framework establishes a new foundation for causal inference on rare, high-impact outcomes, with relevance across environmental risk, economics, and public health.

翻译：极端分位处理效应（eQTEs）衡量干预对结果分布尾部的因果影响，是研究罕见高影响事件的核心议题。标准分位处理效应（QTE）方法因数据稀疏性在极端区间常失效，而现有eQTE方法依赖于严格的尾部假设或内部分位理论。我们提出尾校准逆估计方程（TIEE）框架，该框架结合不同分位水平的信息，并在统一估计方程方法中使用极值模型锚定尾部。我们建立了该估计量的渐近性质，并通过模拟不同尾部行为及模型误设情况评估其性能。针对奥地利阿尔卑斯山极端降水的应用案例表明，TIEE能够在人为变暖背景下对极稀有事件实现观测因果归因。更广泛而言，该框架为罕见高影响结果的因果推断奠定了新基础，对环境风险、经济学及公共卫生领域具有重要应用价值。