Errors in the Dependent Variable of Quantile Regression Models

68 Pages Posted: 15 May 2019 Last revised: 20 Jul 2022

See all articles by Jerry A. Hausman

Jerry A. Hausman

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER)

Haoyang Liu

Federal Reserve Bank of New York

Ye Luo

Faculty of Business and Economics, The University of Hong Kong

Christopher Palmer

MIT Sloan; National Bureau of Economic Research (NBER)

Date Written: May 2019

Abstract

The popular quantile regression estimator of Koenker and Bassett (1978) is biased if there is an additive error term. Approaching this problem as an errors-in-variables problem where the dependent variable suffers from classical measurement error, we present a sieve maximum-likelihood approach that is robust to left-hand side measurement error. After providing sufficient conditions for identification, we demonstrate that when the number of knots in the quantile grid is chosen to grow at an adequate speed, the sieve maximum-likelihood estimator is consistent and asymptotically normal, permitting inference via bootstrapping. We verify our theoretical results with Monte Carlo simulations and illustrate our estimator with an application to the returns to education highlighting changes over time in the returns to education that have previously been masked by measurement-error bias.

Suggested Citation

Hausman, Jerry A. and Liu, Haoyang and Luo, Ye and Palmer, Christopher, Errors in the Dependent Variable of Quantile Regression Models (May 2019). NBER Working Paper No. w25819, Available at SSRN: https://ssrn.com/abstract=3388432

Jerry A. Hausman (Contact Author)

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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Haoyang Liu

Federal Reserve Bank of New York ( email )

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Ye Luo

Faculty of Business and Economics, The University of Hong Kong ( email )

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Christopher Palmer

MIT Sloan ( email )

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National Bureau of Economic Research (NBER) ( email )

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