Bayesian analysis of flexible Heckman selection models using Hamiltonian Monte Carlo

The Heckman selection model is widely used in econometric analysis and other social sciences to address sample selection bias in data modeling. A common assumption in Heckman selection models is that the error terms follow an independent bivariate normal distribution. However, real-world data often deviates from this assumption, exhibiting heavy-tailed behavior, which can lead to inconsistent estimates if not properly addressed. In this paper, we propose a Bayesian analysis of Heckman selection models that replace the Gaussian assumption with well-known members of the class of scale mixture of normal distributions, such as the Student's-t and contaminated normal distributions. For these complex structures, Stan's default No-U-Turn sampler is utilized to obtain posterior simulations. Through extensive simulation studies, we compare the performance of the Heckman selection models with normal, Student's-t and contaminated normal distributions. We also demonstrate the broad applicability of this methodology by applying it to medical care and labor supply data. The proposed algorithms are implemented in the R package HeckmanStan.