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