Estimation and Inference of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions

Abstract

Causal inference for extreme events has many potential applications in fields such as medicine, climate science and finance. 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 approximations and uses a new causal Hill estimator for the extreme value indices of potential outcome distributions. We establish asymptotic normality of the estimators even in the setting of extremal quantiles, and we propose a consistent variance estimator to achieve valid statistical inference. In simulation studies we illustrate the advantages of our methodology over competitors, and we apply it to a real data set.

Asymmetric Dependence in Hydrological Extremes

“…Different methodologies have been proposed to study causality for environmental and climate data (Di Capua et al, 2020;Ebert-Uphoff & Deng, 2012;Runge, Bathiany, et al, 2019). There is a growing literature on methods that focus on detecting causal structures between extreme observations (Gnecco et al, 2021;Mhalla et al, 2019;Tran et al, 2021) or on estimating treatment effects on extreme outcomes (Deuber et al, 2021). In this section, we discuss that our tail coefficient has a causal interpretation in certain model classes.…”