Bias correction for quantile regression estimators

Grigory Franguridi, Bulat Gafarov and Kaspar Wüthrich

Journal of Econometrics, 2025, vol. 251, issue C

Abstract: We study the bias of classical quantile regression and instrumental variable quantile regression estimators. While being asymptotically first-order unbiased, these estimators can have non-negligible second-order biases. We derive a higher-order stochastic expansion of these estimators using empirical process theory. Based on this expansion, we derive an explicit formula for the second-order bias and propose a feasible bias correction procedure that uses finite-difference estimators of the bias components. The proposed bias correction method performs well in simulations. We provide an empirical illustration using Engel’s classical data on household food expenditure.

Keywords: Instrumental variables; Higher-order stochastic expansion; Bahadur–Kiefer expansion; Finite-difference estimators; Mixed integer linear programming (MILP); Engel curve (search for similar items in EconPapers)
JEL-codes: C21 C26 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:251:y:2025:i:c:s0304407625001071

DOI: 10.1016/j.jeconom.2025.106053

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