Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models
AbstractIn 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 InfoPaper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 602.
Date of creation: 11 Aug 2004
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errors-in-variables; measurement error; Fourier transforms; nonlinear models; semiparametric estimation;
Other versions of this item:
- Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, 01.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-10-30 (All new papers)
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