On the Rank Condition of Tail Index Regressions and a Comparative Study with Extremal Quantile Regression
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. Taking this into account, we provide additional regularity conditions and establish the corresponding asymptotic theory. For more general specifications, the conditional distribution of the covariates in the tails concentrates on the values that minimize the tail index. This…