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

Yingyao Hu

Journal of Econometrics, 2008, vol. 144, issue 1, 27-61

Abstract: 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 -consistent semiparametric estimator. The Monte Carlo simulation and empirical illustration show that the estimator performs well with a finite sample and real data.

Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (167)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4076(07)00243-6
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:144:y:2008:i:1:p:27-61

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().