Bayesian estimation of a discrete response model with double rules of sample selection

We present a Bayesian sampling algorithm for parameter estimation in a discrete-response model, 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 labour-market outcomes, namely labour-force participation, employment and occupational skill level. It is of particular interest to measure the marginal effects of some mental health factors on these labour-market outcomes. The contribution of our investigation is to present a sampling algorithm, which is a hybrid of Gibbs and Metropolis-Hastings algorithms. In Monte Carlo simulations, numerical maximization of likelihood fails to converge for more than half of the simulated samples. Our Bayesian method represents a substantial improvement: it converges in every sample, and performs with similar or better precision than maximum likelihood. We apply our sampling algorithm to the double-selection model of labour-force participation, employment and occupational skill level, where marginal effects of explanatory variables, in particular the mental health factors, on the three labour-force outcomes are assessed through 95% Bayesian credible intervals. The proposed sampling algorithm can easily be modified for other multivariate nonlinear models that involve selectivity and are difficult to estimate by other means.