Misclassification in Binary Choice Models with Sample Selection
In parametric models, there are several reasons why the estimators can be biased and inconsistent.
We will focus on two sources of bias, namely measurement error in the dependent variable and unrepresentative samples, and we will propose an estimation method that simultaneously corrects for this double source of bias. Most empirical work is based on observational data that are unrepresentative
of the population of interest. Sample selection models attempt to correct for non-randomly selected
data in a two-model hierarchy where, on the first level, a binary selection equation determines if a particular observation will be available for the second level (outcome equation). In the case of binary choice models, we will assume that also the dependent variable of the outcome equation is binary. The likelihood function takes into account the selection mechanism and allows for unbiased
parameters estimation. We will extend this framework to the situation of a measurement error in the
dependent variable of the outcome equation. We will use a parametric approach to the estimation of the
probabilities of misclassification by incorporating them in the likelihood of a binary choice model with sample selection.