Two-step Parametric Estimation of Binary Treatment Effects in the Presence of Misclassification and Endogeneity for Cross-Sectional and Panel Data

I propose a parametric two-step estimator that corrects for the bias arising from measurement error in a binary endogenous regressor, in cross-sectional and panel data settings. The model incorporates asymmetric (unequal) misclassification rates for false negatives and false positives and is directly generalised to the symmetric misclassification case. It is demonstrated that consistent estimation of the binary treatment effect and the remaining structural form parameters is achieved via modified MLE (MMLE) estimation of the reduced form binary discrete choice model and, via modified least squares (MSL) estimation of the structural form augmented by a misclassification-corrected control function. The model is identified by the nonlinearity of the endogeneity correction terms.