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Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models

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  • Susanne M Schennach

Abstract

This paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of Fourier transforms of conditional expectations of observable variables. For parametrically specified regression functions, we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged-in nonparametric kernel density estimate. Both the identification and the estimation methodologies rely on Fourier analysis and on the theory of generalized functions. The finite-sample properties of the estimator are investigated through Monte Carlo simulations. Copyright The Econometric Society 2007.

Suggested Citation

  • Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    • Handle: RePEc:ecm:emetrp:v:75:y:2007:i:1:p:201-239
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2007.00736.x
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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