Nonparametric Identification and Estimation of Nonclassical Errors-in-Variables Models Without Additional Information

Xiaohong Chen, Yingyao Hu and Arthur Lewbel ()
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Xiaohong Chen: Yale University

No 676, Boston College Working Papers in Economics from Boston College Department of Economics

Abstract: This paper considers identification and estimation of a nonparametric regression model with an unobserved discrete covariate. The sample consists of a dependent variable and a set of covariates, one of which is discrete and arbitrarily correlates with the unobserved covariate. The observed discrete covariate has the same support as the unobserved covariate, and can be interpreted as a proxy or mismeasure of the unobserved one, but with a nonclassical measurement error that has an unknown distribution. We obtain nonparametric identification of the model given monotonicity of the regression function and a rank condition that is directly testable given the data. Our identification strategy does not require additional sample information, such as instrumental variables or a secondary sample. We then estimate the model via the method of sieve maximum likelihood, and provide root-n asymptotic normality and semiparametric efficiency of smooth functionals of interest. Two small simulations are presented to illustrate the identification and the estimation results.

Keywords: Errors-In-Variables (EIV), Identification; Nonclassical measurement error; Nonparametric regression; Sieve maximum likelihood. (search for similar items in EconPapers)
JEL-codes: C20 C14 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2007-08-08
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Working Paper: Nonparametric identification and estimation of nonclassical errors-in-variables models without additional information (2007)
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Persistent link: http://EconPapers.repec.org/RePEc:boc:bocoec:676

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