Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution

This paper provides a general solution to the problem of identification and estimation of nonlinear models with misclassification error in a general discrete explanatory variable using instrumental variables. The misclassification error is allowed to be correlated with all the explanatory variables...

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Vydáno v:	Journal of econometrics Ročník 144; číslo 1; s. 27 - 61
Hlavní autor:	Hu, Yingyao
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 01.05.2008 Elsevier Elsevier Sequoia S.A
Edice:	Journal of Econometrics
Témata:	Applications Distribution theory Econometric models Economic models Error Errors Estimating techniques Estimation Exact sciences and technology Identification Instrumental variable Insurance, economics, finance Mathematics Matrix Matrix diagonalization Misclassification error Monte Carlo simulation Non-linear models Nonlinear analysis Nonlinear errors-in-variables model Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Probability Probability and statistics Probability theory and stochastic processes Restrictions Sciences and techniques of general use Simulation Statistics Studies Truth Variables Nonlinear errors-in-variables model Instrumental variable Matrix diagonalization C41 Misclassification error C14 Solution uniqueness Statistical distribution Error estimation Non parametric estimation Probability distribution Stochastic method Economic data Non linear equation Consistent estimator Distribution function Approximation theory Nonlinear errors-in-variables model; Instrumental variable; Misclassification error; Matrix diagonalization Monte Carlo method Data analysis Non linear estimation Finite sample Probability Statistical estimation Bad classification Semiparametric method Non linear system Equation system Statistical method Numerical analysis Simulation Correlation analysis Non linear model Econometrics C14; C41
ISSN:	0304-4076, 1872-6895
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Shrnutí:	This paper provides a general solution to the problem of identification and estimation of nonlinear models with misclassification error in a general discrete explanatory variable using instrumental variables. The misclassification error is allowed to be correlated with all the explanatory variables in the model. It is not enough to identify the model by simply generalizing the identification in the binary case with a claim that the number of restrictions is no less than that of the unknowns. Such a claim requires solving a complicated nonlinear system of equations. This paper introduces a matrix diagonalization technique which allows one to easily find the unique solution of the system. The solution shows that the latent model can be expressed as an explicit function of directly observed distribution functions. Therefore, the latent model is nonparametrically identifiable and directly estimable using instrumental variables. The results show that certain monotonicity restrictions on the latent model may lead to its identification with virtually no restrictions on the misclassification probabilities. An alternative identification condition suggests that the nonparametric identification may rely on the belief that people always have a higher probability of telling the truth than of misreporting. The nonparametric identification in this paper directly leads to a n-consistent semiparametric estimator. The Monte Carlo simulation and empirical illustration show that the estimator performs well with a finite sample and real data.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0304-4076 1872-6895
DOI:	10.1016/j.jeconom.2007.12.001