IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/17-06.html
   My bibliography  Save this paper

Identification and estimation of nonclassical nonlinear errors-in-variables models with continuous distributions using instruments

Author

Listed:
  • Yingyao Hu

    (Institute for Fiscal Studies and Johns Hopkins University)

  • Susanne M. Schennach

    () (Institute for Fiscal Studies and Brown University)

Abstract

While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary dataset containing correctly measured observations, this paper establishes that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors-in-variables models with continuously distributed variables. The main identifying assumption is that, conditional on the value of the true regressors, some "measure of location" of the distribution of the measurement error (e.g. its mean, mode or median) is equal to zero. The proposed approach relies on the eigenvalue-eigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to order the eigenfunctions so that the decomposition is unique. The authors propose a convenient sieve-based estimator, derive its asymptotic properties and investigate its finite-sample behavior through Monte Carlo simulations. An example of application to the relationship between earnings and divorce rates is also provided.

Suggested Citation

  • Yingyao Hu & Susanne M. Schennach, 2006. "Identification and estimation of nonclassical nonlinear errors-in-variables models with continuous distributions using instruments," CeMMAP working papers CWP17/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:17/06
    as

    Download full text from publisher

    File URL: http://cemmap.ifs.org.uk/wps/cwp1706.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
    2. 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.
    3. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    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. Hoderlein, Stefan & Winter, Joachim, 2010. "Structural measurement errors in nonseparable models," Journal of Econometrics, Elsevier, vol. 157(2), pages 432-440, August.
    2. Flavio Cunha & James J. Heckman & Susanne M. Schennach, 2010. "Estimating the Technology of Cognitive and Noncognitive Skill Formation," Econometrica, Econometric Society, vol. 78(3), pages 883-931, May.
    3. D’Haultfœuille, Xavier & Février, Philippe, 2015. "Identification of mixture models using support variations," Journal of Econometrics, Elsevier, vol. 189(1), pages 70-82.
    4. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "Nonparametric identification of regression models containing a misclassified dichotomous regressor without instruments," Economics Letters, Elsevier, vol. 100(3), pages 381-384, September.
    5. 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.
    6. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    7. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric identification and estimation of nonclassical errors-in-variables models without additional information," CeMMAP working papers CWP18/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Sriya Iyer & Chander Velu & Melvyn Weeks, 2014. "Divine Competition: Religious Organisations and Service Provision in India," Cambridge Working Papers in Economics 1409, Faculty of Economics, University of Cambridge.
    9. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(03), pages 460-471, June.
    10. Yingyao Hu & Arthur Lewbel & Susanne M. Schennach, 2007. "Nonparametric identification of the classical errors-in-variables model without side information," CeMMAP working papers CWP14/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Christoph Breunig & Enno Mammen & Anna Simoni, "undated". "Nonparametric Estimation in case of Endogenous Selection," SFB 649 Discussion Papers SFB649DP2015-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. El-Attar, Mayssun, 2009. "Could Education Promote the Israeli-Palestinian Peace Process?," IZA Discussion Papers 4447, Institute for the Study of Labor (IZA).
    13. 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.
    14. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ifs:cemmap:17/06. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Emma Hyman). General contact details of provider: http://edirc.repec.org/data/cmifsuk.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.