Parameter estimation for a discrete–response model with double rules of sample selection: A Bayesian approach

We present a Bayesian sampling approach to parameter estimation in a discrete– response model with double rules of selectivity, where the dependent variables contain two layers of binary choices and one ordered response. Our investigation is motivated by an empirical study using such a double–selection rule for three labor–market outcomes, namely labor force participation, employment and occupational skill level. Full information maximum likelihood (FIML) estimation often encounters convergence problems in numerical optimization. The contribution of our investigation is to present a sampling algorithm through a new reparameterization strategy. We conduct Monte Carlo simulation studies and find that the numerical optimization of FIML fails for more than half of the simulated samples. Our Bayesian method performs as well as FIML for the simulated samples where FIML works. Moreover, for the simulated samples where FIML fails, Bayesian works as well as it does for the simulated samples where FIML works. We apply the proposed sampling algorithm to the double–selection model of labor–force participation, employment and occupational skill level. We derive the 95% Bayesian credible intervals for marginal effects of the explanatory variables on the three labor–force outcomes. In particular, the marginal effects of mental health factors on these three outcomes are discussed.