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Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models

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  • Susanne M. Schennach

Abstract

In linear specifications, the bias due to the presence of measurement error in a regressor can be entirely avoided when either repeated measurements or instruments are available for the mismeasured regressor. The situation is more complex in nonlinear settings. While identification and root n consistent estimation of general nonlinear specifications have recently been proven in the presence of repeated measurements, similar results relying on instruments have so far only been available for polynomial specifications and absolutely integrable regression functions. This paper addresses two unresolved issues. First, it is shown that instruments indeed allow for the fully nonparametric identification of general nonlinear regression models in the presence of measurement error. Second, when the regression function is parametrically specified, a root n consistent and asymptotically normal estimator is provided. The starting point of the proposed approach is a system of two functional equations that relate conditional expectations of observed variables to the regression function of interest, as first proposed by Hausman, Ichimura, Newey and Powell (1991) for polynomial specifications. It is shown that these two equations have a unique solution, thus establishing identification. The proposed estimation procedure relies on the same functional equations, and the proof of asymptotic normality and root n consistency is based on standard results regarding the asymptotics of semiparametric estimators

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 602.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:602

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Keywords: errors-in-variables; measurement error; Fourier transforms; nonlinear models; semiparametric estimation;

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  1. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
  2. J. A. Hausman & W. K. Newey & J. L. Powel, 1988. "Nonlinear Errors in Variables: Estimation of Some Engel Curves," Working papers 504, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
  4. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  5. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  6. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, 01.
  7. repec:cup:etheor:v:11:y:1995:i:3:p:560-96 is not listed on IDEAS
  8. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
  9. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November.
  10. 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.
  11. Joel L. Horowitz & Marianthi Markatou, 1993. "Semiparametric Estimation Of Regression Models For Panel Data," Econometrics 9309001, EconWPA.
  12. Horowitz, Joel L & Markatou, Marianthi, 1996. "Semiparametric Estimation of Regression Models for Panel Data," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 145-68, January.
  13. Hsiao, Cheng, 1983. "Identification," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 4, pages 223-283 Elsevier.
  14. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
  15. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
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