Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/339383 
Year of Publication: 
2025
Series/Report no.: 
CINCH series No. 2026/02
Publisher: 
University of Duisburg-Essen, CINCH - Health Economics Research Center, Essen
Abstract: 
This paper proposes feasible inference methods for extremal expected shortfall (ES) regressions. While standard ES regressions consider a fixed probability level, in extremal ES regressions the probability level becomes more extreme as a function of the sample size. We show that in extremal ES regressions the convergence rate of the parameter estimators is no longer root-n (as in standard ES regressions), but depends intricately on the probability level and on the tails of the outcome. For the conditional distribution of the outcome given the covariates, we work under a Pareto-type tail assumption, and we allow for serially dependent observables. We also prove that the "beyond the sample" ES can be estimated consistently by exploiting the Pareto-type tail shape. Monte Carlo simulations show the adequate size of our tests, which are based on self-normalization. Finally, an empirical application to health care spending as a function of temperature deviations demonstrates the practical usefulness of our inference and estimation tools.
Subjects: 
Expected Shortfall
Extreme Value Theory
Health Insurance
Inference
Self-Normalization
JEL: 
C12
C13
C21
I13
Q54
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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