A location-invariant estimator of extremal quantile treatment effects for heavy-tailed distributions

The paper introduces a new estimator for extremal quantile treatment effects (QTEs) in heavy-tailed distributions that remains invariant under common location shifts of the potential outcome distributions. It adapts the Fraga estimator of the extreme value index (EVI) to a causal framework using inverse propensity score weighting and replaces the traditional extrapolation formula with a difference-based scheme that cancels the location parameter. The authors prove consistency, asymptotic normality, and provide a variance estimator, and demonstrate through simulations that the method is location invariant, stable across thresholds, and achieves correct coverage.

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