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

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  • Zhang, Rong
  • Inder, Brett A.
  • Zhang, Xibin

Abstract

A Bayesian sampling algorithm for parameter estimation in a discrete-response model is presented, where the dependent variables contain two layers of binary choices and one ordered response. The 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 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. The proposed Bayesian method represents a substantial improvement: it converges in every sample, and performs with similar or better precision than maximum likelihood. The proposed sampling algorithm is applied 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.

Suggested Citation

  • Zhang, Rong & Inder, Brett A. & Zhang, Xibin, 2015. "Bayesian estimation of a discrete response model with double rules of sample selection," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 81-96.
    • Handle: RePEc:eee:csdana:v:86:y:2015:i:c:p:81-96
    DOI: 10.1016/j.csda.2014.12.012
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