Misclassification in binary choice models with sample selection

Most empirical work in the social sciences is based on observational data that are often both incomplete, and therefore unrepresentative of the population of interest, and affected by measurement errors. These problems are very well known in the literature and ad hoc procedures for parametric modeling have been proposed and developed for some time, in order to correct estimate's bias and obtain consistent estimators. However, to our best knowledge, the aforementioned problems have not yet been jointly considered. We try to overcome this by proposing a parametric approach for the estimation of the probabilities of misclassification of a binary response variable by incorporating them in the likelihood of a binary choice model with sample selection.