Identification and Estimation of Regression Models with Misclassification

• Published in: Econometrica 2006-05, Vol.74 (3), p.631-665
• Main Author: Mahajan, Aprajit
• Format: Article
• Language: English
• Subjects: Applications; Consistent estimators; Econometrics; Economic models; Error; Error rates; Estimating techniques; Estimation; Estimation methods; Estimators; Exact sciences and technology; identification; Instrumental variables estimation; Insurance, economics, finance; Linear inference, regression; Mathematics; Maximum likelihood estimation; Measurement; Measurement errors; Methodology; misclassification; Nonclassical measurement error; nonlinear models; Nonparametric inference; Parameter identification; Parametric models; Probability and statistics; Random variables; Regression analysis; Sciences and techniques of general use; Statistical methods; Statistical models; Statistics; Studies
• ISSN: 0012-9682; 1468-0262
• DOI: 10.1111/j.1468-0262.2006.00677.x

This paper studies the problem of identification and estimation in nonparametric regression models with a misclassified binary regressor where the measurement error may be correlated with the regressors. We show that the regression function is nonparametrically identified in the presence of an additional random variable that is correlated with the unobserved true underlying variable but unrelated to the measurement error. Identification for semiparametric and parametric regression functions follows straightforwardly from the basic identification result. We propose a kernel estimator based on the identification strategy, derive its large sample properties, and discuss alternative estimation procedures. We also propose a test for misclassification in the model based on an exclusion restriction that is straightforward to implement.