Abstract

Extreme environmental events such as intense precipitation, heatwaves, or flooding are rare but high-impact, and understanding how external drivers (e.g., climate change) affect their severity is a central challenge across environmental sciences. A natural way to quantify such effects is through extreme quantile treatment effects, which capture changes in the upper tail of an outcome distribution. However, standard methods struggle due to data scarcity and instability in the tails. To address the instability, we propose the Tail-Calibrated Inverse Estimating Equation (TIEE) framework, integrating causal inference with extreme value modelling. By combining information across quantile levels and incorporating tail behaviour directly into the estimation, the approach enables stable and interpretable inference even for very extreme events. Simulation studies and asymptotic theory support the estimator’s robustness and efficiency, particularly in the most data-sparse regimes. Focusing on extreme precipitation in the Austrian Alps, we quantify the impact of anthropogenic warming on rare, high-intensity events while accounting for atmospheric circulation patterns. The approach provides a new foundation for causal inference on rare, high-impact outcomes, with relevance across environmental risk, economics, and public health.