  Heckman selection model is the most popular econometric model in analysis of
data with sample selection. However, selection models with Normal errors cannot
accommodate heavy tails in the error distribution. Recently, Marchenko and
Genton proposed a selection-t model to perform frequentist' robust analysis of
sample selection. Instead of using their maximum likelihood estimates, our
paper develops new Bayesian procedures for the selection-t models with either
continuous or binary outcomes. By exploiting the Normal mixture representation
of the t distribution, we can use data augmentation to impute the missing data,
and use parameter expansion to sample the restricted covariance matrices. The
Bayesian procedures only involve simple steps, without calculating analytical
or numerical derivatives of the complicated log likelihood functions.
Simulation studies show the vulnerability of the selection models with Normal
errors, as well as the robustness of the selection models with t errors.
Interestingly, we find evidence of heavy-tailedness in three real examples
analyzed by previous studies, and the conclusions about the existence of
selection effect are very sensitive to the distributional assumptions of the
error terms.
