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Errors-in-Variables Models : A Generalized Functions Approach

  • ZINDE-WALSH, Victoria

Generalized functions are a powerful tool for examining errors-in-variables models, since they extend consideration to wide modelclasses. Schennach (Econometrica, 2007) - (S) applies this approach to prove identification in a general class of models. Here the problems addressed in (S) are revisited because various features of the generalized functions approach need to be clari?ed. The nonparametric identification theorem in (S) applies less generally than claimed (e.g. disallowing functions with fractional power growth) by relying on decomposition of generalized functions into ordinary and singular parts which may not hold. This paper highlights the issues of importance in applying generalized functions and provides the general nonparametric identification result relating it to possibility of estimation.

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Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 14-2007.

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Length: 38 pages
Date of creation: 2007
Date of revision:
Handle: RePEc:mtl:montec:14-2007
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  1. Susanne M. Schennach, 2004. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometric Society 2004 North American Summer Meetings 602, Econometric Society.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Wang, Liqun, 1998. "Estimation of censored linear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 84(2), pages 383-400, June.
  7. Peter C.B. Phillips, 1993. "Robust Nonstationary Regression," Cowles Foundation Discussion Papers 1064, Cowles Foundation for Research in Economics, Yale University.
  8. 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.
  9. Zinde-Walsh, Victoria, 2008. "Kernel Estimation When Density May Not Exist," Econometric Theory, Cambridge University Press, vol. 24(03), pages 696-725, June.
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