IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v24y2008i04p1010-1043_08.html
   My bibliography  Save this article

Quantile Regression With Mismeasured Covariates

Author

Listed:
  • Schennach, Susanne M.

Abstract

This paper establishes that the availability of instrumental variables enables the identification and the consistent estimation of nonparametric quantile regression models in the presence of measurement error in the regressors. The proposed estimator takes the form of a nonlinear functional of derivatives of conditional expectations and is shown to provide estimated quantile functions that are uniformly consistent over a compact set.

Suggested Citation

  • Schennach, Susanne M., 2008. "Quantile Regression With Mismeasured Covariates," Econometric Theory, Cambridge University Press, vol. 24(4), pages 1010-1043, August.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:04:p:1010-1043_08
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466608080390/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andrew Chesher, 2001. "Parameter approximations for quantile regressions with measurement error," CeMMAP working papers CWP02/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    3. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(3), pages 560-586, June.
    4. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    5. Hausman, J. A. & Newey, W. K. & Powell, J. L., 1995. "Nonlinear errors in variables Estimation of some Engel curves," Journal of Econometrics, Elsevier, vol. 65(1), pages 205-233, January.
    6. Wang, Liqun, 1998. "Estimation of censored linear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 84(2), pages 383-400, June.
    7. Whitney K. Newey, 2001. "Flexible Simulated Moment Estimation Of Nonlinear Errors-In-Variables Models," The Review of Economics and Statistics, MIT Press, vol. 83(4), pages 616-627, November.
    8. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    9. 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.
    10. Alberto Abadie & Joshua D. Angrist & Guido W. Imbens, 1998. "Instrumental Variables Estimation of Quantile Treatment Effects," NBER Technical Working Papers 0229, National Bureau of Economic Research, Inc.
    11. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    12. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
    13. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    14. Schennach, Susanne M., 2004. "Nonparametric Regression In The Presence Of Measurement Error," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1046-1093, December.
    15. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-318, May.
    16. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    17. 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.
    18. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    19. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    20. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July.
    21. Karim Chalak & Halbert White, 2007. "An Extended Class of Instrumental Variables for the Estimation of Causal Effects," Boston College Working Papers in Economics 692, Boston College Department of Economics, revised 30 Nov 2009.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Erich Battistin & Carlos Lamarche & Enrico Rettore, 2024. "Quantiles of the gain distribution of an early childhood intervention," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(6), pages 1045-1064, September.
    2. Sasaki, Yuya, 2015. "What Do Quantile Regressions Identify For General Structural Functions?," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1102-1116, October.
    3. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Battistin, Erich & Lamarche, Carlos & Rettore, Enrico, 2020. "Quantiles of the Gain Distribution of an Early Child Intervention," CEPR Discussion Papers 14721, C.E.P.R. Discussion Papers.
    5. Taraneh Abarin & Liqun Wang, 2012. "Instrumental variable approach to covariate measurement error in generalized linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 475-493, June.
    6. De Nadai, Michele & Lewbel, Arthur, 2016. "Nonparametric errors in variables models with measurement errors on both sides of the equation," Journal of Econometrics, Elsevier, vol. 191(1), pages 19-32.
    7. Chesher, Andrew, 2017. "Understanding the effect of measurement error on quantile regressions," Journal of Econometrics, Elsevier, vol. 200(2), pages 223-237.
    8. Gabriel Montes-Rojas, 2011. "Quantile Regression with Classical Additive Measurement Errors," Economics Bulletin, AccessEcon, vol. 31(4), pages 2863-2868.
    9. Firpo, Sergio & Galvao, Antonio F. & Song, Suyong, 2017. "Measurement errors in quantile regression models," Journal of Econometrics, Elsevier, vol. 198(1), pages 146-164.
    10. Galvao Jr, A. F. & Montes-Rojas, G., 2009. "Instrumental variables quantile regression for panel data with measurement errors," Working Papers 09/06, Department of Economics, City University London.
    11. Huixia Judy Wang & Leonard A. Stefanski & Zhongyi Zhu, 2012. "Corrected-loss estimation for quantile regression with covariate measurement errors," Biometrika, Biometrika Trust, vol. 99(2), pages 405-421.
    12. Schennach, Susanne M., 2019. "Convolution without independence," Journal of Econometrics, Elsevier, vol. 211(1), pages 308-318.
    13. Schmidt, Christoph M. & Tauchmann, Harald, 2011. "Heterogeneity in the intergenerational transmission of alcohol consumption: A quantile regression approach," Journal of Health Economics, Elsevier, vol. 30(1), pages 33-42, January.
    14. Anil K. Bera & Antonio F. Galvao Jr. & Gabriel V. Montes-Rojas & Sung Y. Park, 2014. "Which Quantile is the Most Informative? Maximum Likelihood, Maximum Entropy and Quantile Regression," World Scientific Book Chapters, in: Kaddour Hadri & William Mikhail (ed.), Econometric Methods and Their Applications in Finance, Macro and Related Fields, chapter 7, pages 167-199, World Scientific Publishing Co. Pte. Ltd..
    15. 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.
    16. Giglio, Stefano & Kelly, Bryan & Pruitt, Seth, 2016. "Systemic risk and the macroeconomy: An empirical evaluation," Journal of Financial Economics, Elsevier, vol. 119(3), pages 457-471.
    17. Daniel Wilhelm, 2015. "Identification and estimation of nonparametric panel data regressions with measurement error," CeMMAP working papers CWP34/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. 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.
    19. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers CWP36/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Eren, Ozkan & Ozbeklik, Serkan, 2013. "The effect of noncognitive ability on the earnings of young men: A distributional analysis with measurement error correction," Labour Economics, Elsevier, vol. 24(C), pages 293-304.
    21. Le Wang, 2013. "How Does Education Affect the Earnings Distribution in Urban China?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(3), pages 435-454, June.
    22. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers 36/17, Institute for Fiscal Studies.
    23. Kengo Kato & Yuya Sasaki & Takuya Ura, 2021. "Robust inference in deconvolution," Quantitative Economics, Econometric Society, vol. 12(1), pages 109-142, January.
    24. Bera Anil K. & Galvao Antonio F. & Montes-Rojas Gabriel V. & Park Sung Y., 2016. "Asymmetric Laplace Regression: Maximum Likelihood, Maximum Entropy and Quantile Regression," Journal of Econometric Methods, De Gruyter, vol. 5(1), pages 79-101, January.
    25. Hu, Yingyao, 2017. "The Econometrics of Unobservables -- Latent Variable and Measurement Error Models and Their Applications in Empirical Industrial Organization and Labor Economics [The Econometrics of Unobservables]," Economics Working Paper Archive 64578, The Johns Hopkins University,Department of Economics, revised 2021.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    2. Schennach, Susanne & White, Halbert & Chalak, Karim, 2012. "Local indirect least squares and average marginal effects in nonseparable structural systems," Journal of Econometrics, Elsevier, vol. 166(2), pages 282-302.
    3. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation for Research in Economics, Yale University.
    4. Susanne Schennach & Halbert White & Karim Chalak, 2007. "Local Indirect Least Squares and Average Marginal Effects in Nonseparable Structural Systems," Boston College Working Papers in Economics 680, Boston College Department of Economics, revised 26 Dec 2009.
    5. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers 41/12, Institute for Fiscal Studies.
    6. Yingyao Hu & Geert Ridder, 2012. "Estimation of nonlinear models with mismeasured regressors using marginal information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 347-385, April.
    7. Hu, Yingyao, 2008. "Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution," Journal of Econometrics, Elsevier, vol. 144(1), pages 27-61, May.
    8. De Nadai, Michele & Lewbel, Arthur, 2016. "Nonparametric errors in variables models with measurement errors on both sides of the equation," Journal of Econometrics, Elsevier, vol. 191(1), pages 19-32.
    9. Halbert White & Karim Chalak, 2008. "Identifying Structural Effects in Nonseparable Systems Using Covariates," Boston College Working Papers in Economics 734, Boston College Department of Economics.
    10. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(3), pages 460-471, June.
    11. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    12. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    13. Karun Adusumilli & Taisuke Otsu, 2015. "Nonparametric instrumental regression with errors in variables," STICERD - Econometrics Paper Series /2015/585, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    14. Song, Suyong, 2015. "Semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 95-109.
    15. Wang, Liqun & Hsiao, Cheng, 2011. "Method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 165(1), pages 30-44.
    16. Feng, Junlong, 2024. "Matching points: Supplementing instruments with covariates in triangular models," Journal of Econometrics, Elsevier, vol. 238(1).
    17. Susanne M. Schennach, 2013. "Regressions with Berkson errors in covariates - A nonparametric approach," Papers 1308.2836, arXiv.org.
    18. Geert Ridder & Yingyao Hu, 2004. "Estimation of Nonlinear Models with Measurement Error Using Marginal Information," Econometric Society 2004 North American Summer Meetings 21, Econometric Society.
    19. Xiaohong Chen & Han Hong & Denis Nekipelov, 2011. "Nonlinear Models of Measurement Errors," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 901-937, December.
    20. Daniel Wilhelm, 2015. "Identification and estimation of nonparametric panel data regressions with measurement error," CeMMAP working papers CWP34/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:24:y:2008:i:04:p:1010-1043_08. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.