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Nonparametric identification and estimation of nonclassical errors-in-variables models without additional information

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  • Xiaohong Chen

    (Institute for Fiscal Studies and Yale)

  • Yingyao Hu
  • Arthur Lewbel

    (Institute for Fiscal Studies and Boston College)

Abstract

This paper considers identification and estimation of a nonparametric regression model with an unobserved discrete covariate. The sample consists of a dependent variable and a set of covariates, one of which is discrete and arbitrarily correlates with the unobserved covariate. The observed discrete covariate has the same support as the unobserved covariate, and can be interpreted as a proxy or mismeasure of the unobserved one, but with a nonclassical measurement error that has an unknown distribution. We obtain nonparametric identification of the model given monotonicity of the regression function and a rank condition that is directly testable given the data. Our identification strategy does not require additional sample information, such as instrumental variables or a secondary sample. We then estimate the model via the method of sieve maximum likelihood, and provide root-n asymptotic normality and semiparametric efficiency of smooth functionals of interest. Two small simulations are presented to illustrate the identification and the estimation results.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP18/07.

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Date of creation: Aug 2007
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Handle: RePEc:ifs:cemmap:18/07

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  1. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  3. Raymond J. Carroll & David Ruppert & Ciprian M. Crainiceanu & Tor D. Tosteson & Margaret R. Karagas, 2004. "Nonlinear and Nonparametric Regression and Instrumental Variables," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 736-750, January.
  4. Hsiao, Ch., 1989. "Identification and Estimation of Dichotomous Latent Variables Models using Panel Data," Discussion Paper 1989-44, Tilburg University, Center for Economic Research.
  5. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, 05.
  6. 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.
  7. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
  8. Arthur Lewbel, 2004. "Estimation of Average Treatment Effects With Misclassification," Econometric Society 2004 North American Winter Meetings 210, Econometric Society.
  9. Yingyao Hu & Susanne 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.
  10. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
  11. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, vol. 65(5), pages 1201-1214, September.
  12. 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.
  13. 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.
  14. Murphy, S. A. & Van Der Vaart, A. W., 1996. "Likelihood Inference in the Errors-in-Variables Model," Journal of Multivariate Analysis, Elsevier, vol. 59(1), pages 81-108, October.
  15. Hausman, Jerry A. & Newey, Whitney K. & Ichimura, Hidehiko & Powell, James L., 1991. "Identification and estimation of polynomial errors-in-variables models," Journal of Econometrics, Elsevier, vol. 50(3), pages 273-295, December.
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Cited by:
  1. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "A note on the closed-form identification of regression models with a mismeasured binary regressor," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1473-1479, September.

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