Ricerc@Sapienza

In empirical analysis there are positive-valued phenomena which show a very high frequency at zero, and consequently require a special treatment. A particular example is considered in the motivating case-study, where the outcome variable is the earning from off-the book work: we observe only a minority of individuals declaring to perceive a positive income from undeclared work, whereas the vast majority states to receive zero. In this framework, a solution is given by the so called two-part model, which consists of two stochastic models: the first governs whether the response variable is zero or positive and the second, conditional on its being positive, models the level. We extend the two-part model to cope with misclassification and measurement error problems: the first relating to the generating process of the zeros, the second to the generating process of the positive values of the output variable. In the motivating case-study, these errors arise from the sensitivity to compliant/non compliant behaviors. In fact, there is a concrete possibility that people actually employed off-the-book are reluctant to admit it and often declare earnings from off-the-book activities that are lower than the true ones.