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

TL;DR

This paper develops a new method for estimating and inferring the effects of treatments on extreme outcomes in heavy-tailed distributions, extending beyond observed data ranges for risk assessment.

Contribution

It introduces an extremal quantile treatment effect estimator using tail approximation and a new causal Hill estimator for extreme value indices, with proven asymptotic properties.

Findings

Estimator performs well in simulations

Method provides valid inference for extremal quantiles

Application to real data estimates college education's impact on high wages

Abstract

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.