Bayesian Sampling Algorithms for the Sample Selection and

1I am very grateful to Tony Lancaster for sparking my interest in the topic and providing helpful com-ments, suggestions and guidance along the way. Frank Kleibergen and participants at the Micro Lunch and the Econometrics Seminar at Brown provided valuable feedback. All remaining errors are my own. Comments are most welcome. Please do not circulate without permission. Contact: Martijn_van_Hasselt@Brown.edu This paper considers two models, namely a sample selection model and a two-part model, for an outcome variable that contains a large fraction of zeros, such as individual expenditures on health care. The sample selection model assumes two phases that determine the outcome: a decision process and an outcome process. Both of these processes may be correlated and, conditional on a favorable decision, the outcome is observed. The two-part model assumes that the decision and outcome processes are uncorrelated. The paper addresses the problem of selecting between these two models. Under a Gaussian specification of the likelihood the models are nested and inference can focus on the correlation coefficient. Using a fully parametric Bayesian approach, I present sampling algorithms for the model parameters that are based on data augmentation. In addition to the sampler output of the correlation coefficient, a Bayes factor can be computed to distinguish between models. The paper illustrates all methods and their potential pitfalls using simulated datasets.