Estimation and Inference of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions
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Date
2024Type
- Journal Article
ETH Bibliography
yes
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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 dataset to estimate the extremal quantile treatment effect of college education on wage. Supplementary materials for this article are available online. Show more
Publication status
publishedExternal links
Journal / series
Journal of the American Statistical AssociationVolume
Pages / Article No.
Publisher
Taylor & FrancisSubject
Asymptomatic normality; Causality; Causal Hill estimator; Extrapolation; Extreme value theory; Propensity scoreMore
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ETH Bibliography
yes
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