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Method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models

  • Wang, Liqun
  • Hsiao, Cheng

This paper deals with a nonlinear errors-in-variables model where the distributions of the unobserved predictor variables and of the measurement errors are nonparametric. Using the instrumental variable approach, we propose method of moments estimators for the unknown parameters and simulation-based estimators to overcome the possible computational difficulty of minimizing an objective function which involves multiple integrals. Both estimators are consistent and asymptotically normally distributed under fairly general regularity conditions. Moreover, root-n consistent semiparametric estimators and a rank condition for model identifiability are derived using the combined methods of the nonparametric technique and Fourier deconvolution.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 165 (2011)
Issue (Month): 1 ()
Pages: 30-44

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Handle: RePEc:eee:econom:v:165:y:2011:i:1:p:30-44
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Weiss, Andrew A., 1993. "Some aspects of measurement error in a censored regression model," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 169-188, March.
  2. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
  3. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
  4. 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.
  5. Liqun Wang & Cheng Hsiao, 2007. "Two-stage estimation of limited dependent variable models with errors-in-variables," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 426-438, 07.
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  7. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  8. Whitney Newey, 1999. "Flexible Simulated Moment Estimation of Nonlinear Errors-in-Variables Models," Working papers 99-02, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. 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.
  10. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
  11. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
  12. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, 01.
  13. 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.
  14. Hsiao, C., 1992. "Nonlinear Latent Variable Models," Papers 9211, Southern California - Department of Economics.
  15. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
  16. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  17. Aigner, Dennis J. & Hsiao, Cheng & Kapteyn, Arie & Wansbeek, Tom, 1984. "Latent variable models in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 23, pages 1321-1393 Elsevier.
  18. Liqun Wang & Alexandre Leblanc, 2008. "Second-order nonlinear least squares estimation," Annals of the Institute of Statistical Mathematics, Springer, vol. 60(4), pages 883-900, December.
  19. Amemiya, Yasuo, 1990. "Two-stage instrumental variables estimators for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 44(3), pages 311-332, June.
  20. Wang, Liqun, 1998. "Estimation of censored linear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 84(2), pages 383-400, June.
  21. Wang, Liqun, 2002. "A simple adjustment for measurement errors in some limited dependent variable models," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 427-433, July.
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