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Errors in the Dependent Variable of Quantile Regression Models

Author

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

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

  • Jerry A. Hausman & Haoyang Liu & Ye Luo & Christopher Palmer, 2019. "Errors in the Dependent Variable of Quantile Regression Models," NBER Working Papers 25819, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:25819
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    1. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Quasi Likelihood Ratio Inference on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897, Cowles Foundation for Research in Economics, Yale University.
    2. DiNardo, John & Fortin, Nicole M & Lemieux, Thomas, 1996. "Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach," Econometrica, Econometric Society, vol. 64(5), pages 1001-1044, September.
    3. Lin, Dajun & Lutter, Randall & Ruhm, Christopher J., 2018. "Cognitive performance and labour market outcomes," Labour Economics, Elsevier, vol. 51(C), pages 121-135.
    4. Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639, arXiv.org.
    5. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    6. Wei, Ying & Carroll, Raymond J., 2009. "Quantile Regression With Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1129-1143.
    7. Hausman, J. A. & Abrevaya, Jason & Scott-Morton, F. M., 1998. "Misclassification of the dependent variable in a discrete-response setting," Journal of Econometrics, Elsevier, vol. 87(2), pages 239-269, September.
    8. An, Yonghong & Hu, Yingyao, 2012. "Well-posedness of measurement error models for self-reported data," Journal of Econometrics, Elsevier, vol. 168(2), pages 259-269.
    9. Denis Chetverikov & Bradley Larsen & Christopher Palmer, 2016. "IV Quantile Regression for Group‐Level Treatments, With an Application to the Distributional Effects of Trade," Econometrica, Econometric Society, vol. 84, pages 809-833, March.
    10. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008. "A Bayesian mixed logit-probit model for multinomial choice," Journal of Econometrics, Elsevier, vol. 147(2), pages 232-246, December.
    11. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    12. Thomas Piketty & Emmanuel Saez, 2006. "The Evolution of Top Incomes: A Historical and International Perspective," American Economic Review, American Economic Association, vol. 96(2), pages 200-205, May.
    13. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
    14. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-1160, September.
    15. Jerry Hausman, 2001. "Mismeasured Variables in Econometric Analysis: Problems from the Right and Problems from the Left," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 57-67, Fall.
    16. Bruce D. Meyer & Wallace K. C. Mok & James X. Sullivan, 2015. "Household Surveys in Crisis," Journal of Economic Perspectives, American Economic Association, vol. 29(4), pages 199-226, Fall.
    17. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843, Elsevier.
    18. Stephen R. Cosslett, 2004. "Efficient Semiparametric Estimation of Censored and Truncated Regressions via a Smoothed Self-Consistency Equation," Econometrica, Econometric Society, vol. 72(4), pages 1277-1293, July.
    19. 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.
    20. Bollinger, Christopher R, 1998. "Measurement Error in the Current Population Survey: A Nonparametric Look," Journal of Labor Economics, University of Chicago Press, vol. 16(3), pages 576-594, July.
    21. David H. Autor & Lawrence F. Katz & Melissa S. Kearney, 2008. "Trends in U.S. Wage Inequality: Revising the Revisionists," The Review of Economics and Statistics, MIT Press, vol. 90(2), pages 300-323, May.
    22. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    23. David Powell, 2013. "A New Framework for Estimation of Quantile Treatment Effects Nonseparable Disturbance in the Presence of Covariates," Working Papers WR-824-1, RAND Corporation.
    24. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    25. Schennach, Susanne M., 2008. "Quantile Regression With Mismeasured Covariates," Econometric Theory, Cambridge University Press, vol. 24(4), pages 1010-1043, August.
    26. Griliches, Zvi, 1977. "Estimating the Returns to Schooling: Some Econometric Problems," Econometrica, Econometric Society, vol. 45(1), pages 1-22, January.
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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 & 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. "Distributional Effects with Two-Sided Measurement Error: An Application to Intergenerational Income Mobility," Papers 2107.09235, arXiv.org, revised Jun 2024.
    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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