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Errors-In-Variables Models: A Generalized Functions Approach

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  • Victoria Zinde-Walsh

Abstract

Identification in errors-in-variables regression models was recently extended to wide models classes by S. Schennach (Econometrica, 2007) (S) via use of generalized functions. In this paper the problems of non- and semi- parametric identification in such models are re-examined. Nonparametric identification holds under weaker assumptions than in (S); the proof here does not rely on decomposition of generalized functions into ordinary and singular parts, which may not hold. Conditions for continuity of the identification mapping are provided and a consistent nonparametric plug-in estimator for regression functions in the L₁ space constructed. Semiparametric identification via a finite set of moments is shown to hold for classes of functions that are explicitly characterized; unlike (S) existence of a moment generating function for the measurement

Suggested Citation

  • Victoria Zinde-Walsh, 2009. "Errors-In-Variables Models: A Generalized Functions Approach," Departmental Working Papers 2009-09, McGill University, Department of Economics.
    • Handle: RePEc:mcl:mclwop:2009-09
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    References listed on IDEAS

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    1. Zinde-Walsh, Victoria, 2008. "Kernel Estimation When Density May Not Exist," Econometric Theory, Cambridge University Press, vol. 24(3), pages 696-725, June.
    2. P. C. B. Phillips, 1985. "A Theorem on the Tail Behaviour of Probability Distributions with an Application to the Stable Family," Canadian Journal of Economics, Canadian Economics Association, vol. 18(1), pages 58-65, February.
    3. Victoria Zinde-Walsh & Peter C.B. Phillips, 2003. "Fractional Brownian Motion as a Differentiable Generalized Gaussian Process," Cowles Foundation Discussion Papers 1391, Cowles Foundation for Research in Economics, Yale University.
    4. 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.
    5. 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.
    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. Phillips, Peter C.B., 1995. "Robust Nonstationary Regression," Econometric Theory, Cambridge University Press, vol. 11(5), pages 912-951, October.
    9. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    10. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(4), pages 450-463, December.
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    Cited by:

    1. Raymond Carroll & Xiaohong Chen & Yingyao Hu, 2010. "Identification and estimation of nonlinear models using two samples with nonclassical measurement errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 379-399.
    2. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(3), pages 460-471, June.
    3. 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.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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