Abstract

The subgroup average treatment effect, which evaluates effects for

predefined subpopulations, is often more interpretable than the pointwise conditional average treatment effect. In this paper, we focus on the extreme subpop-

ulations and propose the conditional tail expectation treatment effect (CTE2).

By combining inverse probability weighting technique with extreme value theory, we propose an estimator for the CTE2 at extreme levels. We establish the

asymptotic normality of the estimator through a novel multivariate causal tail

empirical process framework. The finite-sample performance of the estimator is

demonstrated through simulation studies. We further illustrate the utility of the

estimator by applying it to estimate the CTE2 of college education on wages.

Key words and phrases: extreme value statistics; heavy tails; tail dependence; causal inference *Corresponding author. E-mail: deyuanli@fudan.edu.cn 1

Information

Preprint No.SS-2025-0421
Manuscript IDSS-2025-0421
Complete AuthorsZi Miao, Liujun Chen, Deyuan Li
Corresponding AuthorsDeyuan Li
Emailsdeyuanli@fudan.edu.cn

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Acknowledgments

The authors are sincerely grateful to the Editor, the Associate Editor and

two anonymous referees for their thoughtful reading, insightful comments

and helpful suggestions, which have substantially improved the clarity and

quality of this paper. Liujun Chen’s research was partially supported by

the National Natural Science Foundation of China grants 12301387 and

12471279, and the Fundamental Research Funds for the Central Universities

grant WK2040250122. Deyuan Li’s research was partially supported by the

National Natural Science Foundation of China grant 12471279.

Supplementary Materials

The supplementary material includes detailed proofs of Theorems 1–5 from

the main paper, along with auxiliary explanations, lemmas, and propositions.

Additionally, we present supplementary simulation results that

complement the findings in the main paper.

Supplementary materials are available for download.