econometrics Article Misclassification in Binary Choice Models with Sample Selection Maria Felice Arezzo *,† and Giuseppina Guagnano † Department of Methods and Models for Economics, Territory and Finance - Sapienza University of Rome Via del Castro Laurenziano 9, 00161 Rome, Italy * Correspondence:
[email protected]; Tel.: +39-06-49766424 † These authors contributed equally to this work. Received: 7 January 2019; Accepted: 17 July 2019; Published: 24 July 2019 Abstract: 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. Keywords: misclassified dependent variable; sample selection bias; undeclared work 1. Introduction Most empirical work in the social sciences is based on observational data that are often incomplete, and therefore unrepresentative of the population of interest, and/or affected by measurement errors. There are many types of selection mechanisms that result in a non-random sample. Some of them are due to sample design, while others depend on the behavior of the units being sampled, other than non-response or attrition.