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.