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

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Listed:
  • Rong Zhang
  • Brett A. Inder
  • Xibin Zhang

Abstract

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.

Suggested Citation

  • Rong Zhang & Brett A. Inder & Xibin Zhang, 2013. "Bayesian estimation of a discrete response model with double rules of sample selection," Monash Econometrics and Business Statistics Working Papers 24/13, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2013-24
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    References listed on IDEAS

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    1. Richard Blundell & John Ham & Costas Meghir, 1989. "Unemployment and Female Labour Supply," Palgrave Macmillan Books, in: Joan Muysken & Chris Neubourg (ed.), Unemployment in Europe, chapter 1, pages 9-36, Palgrave Macmillan.
    2. Li Mingliang & Tobias Justin L, 2006. "Bayesian Analysis of Structural Effects in an Ordered Equation System," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(4), pages 1-24, December.
    3. McCulloch, Robert E. & Polson, Nicholas G. & Rossi, Peter E., 2000. "A Bayesian analysis of the multinomial probit model with fully identified parameters," Journal of Econometrics, Elsevier, vol. 99(1), pages 173-193, November.
    4. Murray D. Smith, 2003. "Modelling sample selection using Archimedean copulas," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 99-123, June.
    5. Francis Vella, 1998. "Estimating Models with Sample Selection Bias: A Survey," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 127-169.
    6. Zhang, Xibin & Brooks, Robert D. & King, Maxwell L., 2009. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Journal of Econometrics, Elsevier, vol. 153(1), pages 21-32, November.
    7. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    8. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053.
    9. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
    10. van Hasselt, Martijn, 2011. "Bayesian inference in a sample selection model," Journal of Econometrics, Elsevier, vol. 165(2), pages 221-232.
    11. Madhu Mohanty, 2001. "Testing for the specification of the wage equation: double selection approach or single selection approach," Applied Economics Letters, Taylor & Francis Journals, vol. 8(8), pages 525-529.
    12. William Greene, 2006. "A General Approach to Incorporating Selectivity in a Model," Working Papers 06-10, New York University, Leonard N. Stern School of Business, Department of Economics.
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    Keywords

    Gibbs sampler; Marginal effects; Mental illness; Metropolis-Hastings algorithm; Ordered outcome.;
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