Bayesian Analysis of Sample Selection and Endogenous Switching Regression Models with Random Coefficients Via MCMC Methods

This paper develops a Bayesian method for estimating and testing the parameters of the endogenous switching regression model and sample selection models. Random coefficients are incorporated in both the decision and regime regression models to reflect heterogeneity across individual units or clusters and correlation of observations within clusters. The case of tobit type regime regression equations are also considered. A combination of Markov chain Monte Carlo methods, data augmentation and Gibbs sampling is used to facilitate computation of Bayes posterior statistics. A simulation study is conducted to compare estimates from full and reduced blocking schemes and to investigate sensitivity to prior information. The Bayesian methodology is applied to data sets on currency hedging and goods trade, cross-country privatisation, and adoption of soil conservation technology. Estimation and inference results on marginal effects, average decision or selection effect as well as model comparison are presented. The expected decision effect is broken down into average effect of individual's decision on the response variable, decision effect due to random components, and differential effect due to latent correlated random components. Application of the proposed Bayesian MCMC algorithm to real data sets reveal that the normality assumption still holds for most commonly encountered economic data