Identification and Estimation of Regression Models with Misclassification

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 non-parametrically 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 semi-parametric and parametric regression functions follows straightforwardly from the basic identification result. We propose a kernel estimator based on the identification strategy and derive its large sample properties and also discuss alternative estimation procedures