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

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  • Wang, Liqun
  • Hsiao, Cheng

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Fourier deconvolution; Identifiability; Instrumental variables; Measurement error; Method of moments; Root-n consistency; Semiparametric estimator; Simulation-based estimator;

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References

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  1. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
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  3. Susanne M. Schennach, 2004. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometric Society 2004 North American Summer Meetings 602, Econometric Society.
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  16. 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.
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Cited by:
  1. Michele De Nadai & Arthur Lewbel, 2012. "Nonparametric Errors in Variables Models with Measurement Errors on both sides of the Equation," Boston College Working Papers in Economics 790, Boston College Department of Economics, revised 01 Jul 2013.
  2. Susanne Schennach, 2012. "Measurement error in nonlinear models- a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Taraneh Abarin & Liqun Wang, 2012. "Instrumental variable approach to covariate measurement error in generalized linear models," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(3), pages 475-493, June.
  4. Zhang, Jun & Feng, Zhenghui & Zhou, Bu, 2014. "A revisit to correlation analysis for distortion measurement error data," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 116-129.
  5. Kunitomo, N. & McAleer, M.J. & Nishiyama, Y., 2010. "Moment Restriction-based Econometric Methods: An Overview," Econometric Institute Research Papers EI 2010-61, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  6. Victoria Zinde-Walsh, 2009. "Errors-In-Variables Models: A Generalized Functions Approach," Departmental Working Papers 2009-09, McGill University, Department of Economics.
  7. Susanne Schennach, 2013. "Convolution without independence," CeMMAP working papers CWP46/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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