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Errors in the Dependent Variable of Quantile Regression Models

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  • Jerry Hausman
  • Haoyang Liu
  • Ye Luo
  • Christopher Palmer

Abstract

We study the consequences of measurement error in the dependent variable of random‐coefficients models, focusing on the particular case of quantile regression. 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. Monte Carlo evidence verifies our method outperforms quantile regression in mean bias and MSE. Finally, we 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

  • Jerry Hausman & Haoyang Liu & Ye Luo & Christopher Palmer, 2021. "Errors in the Dependent Variable of Quantile Regression Models," Econometrica, Econometric Society, vol. 89(2), pages 849-873, March.
    • Handle: RePEc:wly:emetrp:v:89:y:2021:i:2:p:849-873
    DOI: 10.3982/ECTA14667
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    Citations

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    Cited by:

    1. Demetrescu, Matei & Hosseinkouchack, Mehdi & Rodrigues, Paulo M. M., 2023. "Tests of no cross-sectional error dependence in panel quantile regressions," Ruhr Economic Papers 1041, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    2. Martina Pons, 2022. "The impact of air pollution on birthweight: evidence from grouped quantile regression," Empirical Economics, Springer, vol. 62(1), pages 279-296, January.
    3. Chen, Liang & Dolado, Juan José & Gonzalo, Jesús & Pan, Haozi, 2023. "Estimation of characteristics-based quantile factor models," UC3M Working papers. Economics 37095, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Jerry Hausman & Haoyang Liu & Ye Luo & Christopher Palmer, 2021. "Errors in the Dependent Variable of Quantile Regression Models," Econometrica, Econometric Society, vol. 89(2), pages 849-873, March.
    5. Paulo M.M. Rodrigues & Matei Demetrescu, 2022. "Cross-Sectional Error Dependence in Panel Quantile Regressions," Working Papers w202213, Banco de Portugal, Economics and Research Department.
    6. Brantly Callaway & Tong Li & Irina Murtazashvili, 2021. "Nonlinear Approaches to Intergenerational Income Mobility allowing for Measurement Error," Papers 2107.09235, arXiv.org, revised Dec 2021.
    7. Zongwu Cai & Meng Shi & Yue Zhao & Wuqing Wu, 2020. "Testing Financial Hierarchy Based on A PDQ-CRE Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202011, University of Kansas, Department of Economics, revised Jul 2020.
    8. Uribe, Jorge M. & Mosquera-López, Stephania & Arenas, Oscar J., 2022. "Assessing the relationship between electricity and natural gas prices in European markets in times of distress," Energy Policy, Elsevier, vol. 166(C).

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    More about this item

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • I24 - Health, Education, and Welfare - - Education - - - Education and Inequality
    • I26 - Health, Education, and Welfare - - Education - - - Returns to Education
    • J30 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - General

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