Cautions on Tail Index Regressions

Thomas T. Yang

Papers from arXiv.org

Abstract: We revisit tail-index regressions. For linear specifications, we find that the usual full-rank condition can fail because conditioning on extreme outcomes causes regressors to degenerate to constants. More generally, the conditional distribution of the covariates in the tails concentrates on the values at which the tail index is minimized. Away from those points, the conditional density tends to zero. For local nonparametric tail index regression, the convergence rate can be very slow. We conclude with practical suggestions for applied work.

Date: 2025-10
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