A unified approach to multilevel sample selection models

Abstract

We propose a unified approach for multilevel sample selection models using a generalized result on skew distributions arising from selection. If the underlying distributional assumption is normal, then the resulting density for the outcome is the continuous component of the sample selection density and has links with the closed skew-normal distribution (CSN). The CSN distribution provides a framework which simplifies the derivation of the conditional expectation of the observed data. This generalizes the Heckman’s two-step method to a multilevel sample selection model. Finite-sample performance of the maximum likelihood estimator of this model is studied through a Monte Carlo simulation.