{"title":"Bias correction for quantile regression estimators","authors":"Grigory Franguridi , Bulat Gafarov , Kaspar Wüthrich","doi":"10.1016/j.jeconom.2025.106053","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"251 ","pages":"Article 106053"},"PeriodicalIF":9.9000,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Econometrics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304407625001071","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
The Journal of Econometrics serves as an outlet for important, high quality, new research in both theoretical and applied econometrics. The scope of the Journal includes papers dealing with identification, estimation, testing, decision, and prediction issues encountered in economic research. Classical Bayesian statistics, and machine learning methods, are decidedly within the range of the Journal''s interests. The Annals of Econometrics is a supplement to the Journal of Econometrics.