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A Bayesian Model of Sample Selection with a Discrete Outcome Variable

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  • Maksym, Obrizan

Abstract

Relatively few published studies apply Heckman’s (1979) sample selection model to the case of a discrete endogenous variable and those are limited to a single outcome equation. However, there are potentially many applications for this model in health, labor and financial economics. To fill in this theoretical gap, I extend the Bayesian multivariate probit setup of Chib and Greenberg (1998) into a model of non-ignorable selection that can handle multiple selection and discrete-continuous outcome equations. The first extension of the multivariate probit model in Chib and Greenberg (1998) allows some of the outcomes to be missing. In addition, I use Cholesky factorization of the variance matrix to avoid the Metropolis-Hastings algorithm in the Gibbs sampler. Finally, using artificial data I show that the model is capable of retrieving the parameters used in the data-generating process and also that the resulting Markov Chain passes all standard convergence tests.

Suggested Citation

  • Maksym, Obrizan, 2010. "A Bayesian Model of Sample Selection with a Discrete Outcome Variable," MPRA Paper 28577, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:28577
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Meng, Chun-Lo & Schmidt, Peter, 1985. "On the Cost of Partial Observability in the Bivariate Probit Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 71-85, February.
    3. John Geweke, 2004. "Getting It Right: Joint Distribution Tests of Posterior Simulators," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 799-804, January.
    4. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
    5. Manning, W. G. & Duan, N. & Rogers, W. H., 1987. "Monte Carlo evidence on the choice between sample selection and two-part models," Journal of Econometrics, Elsevier, vol. 35(1), pages 59-82, May.
    6. Patrick Waelbroeck, 2005. "Computational Issues in the Sequential Probit Model: A Monte Carlo Study," Computational Economics, Springer;Society for Computational Economics, vol. 26(2), pages 141-161, October.
    7. 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.
    8. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    9. Terza, Joseph V., 1998. "Estimating count data models with endogenous switching: Sample selection and endogenous treatment effects," Journal of Econometrics, Elsevier, vol. 84(1), pages 129-154, May.
    10. Lee J. & Berger J.O., 2001. "Semiparametric Bayesian Analysis of Selection Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1397-1409, December.
    11. Leung, Siu Fai & Yu, Shihti, 1996. "On the choice between sample selection and two-part models," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 197-229.
    12. 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.
    13. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-1143, Nov.-Dec..
    14. Vassilis A. Hajivassiliou & Daniel L. McFadden, 1998. "The Method of Simulated Scores for the Estimation of LDV Models," Econometrica, Econometric Society, vol. 66(4), pages 863-896, July.
    15. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, January.
    16. Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2007. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9780521671736, June.
    17. Ho-Chuan Huang, 2001. "Bayesian analysis of the SUR Tobit model," Applied Economics Letters, Taylor & Francis Journals, vol. 8(9), pages 617-622.
    18. Munkin, Murat K. & Trivedi, Pravin K., 2003. "Bayesian analysis of a self-selection model with multiple outcomes using simulation-based estimation: an application to the demand for healthcare," Journal of Econometrics, Elsevier, vol. 114(2), pages 197-220, June.
    19. Partha Deb & Murat K. Munkin & Pravin K. Trivedi, 2006. "Bayesian analysis of the two‐part model with endogeneity: application to health care expenditure," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(7), pages 1081-1099, November.
    20. Chakravarty, Sugato & Li, Kai, 2003. "A Bayesian analysis of dual trader informativeness in futures markets," Journal of Empirical Finance, Elsevier, vol. 10(3), pages 355-371, May.
    21. Donald S. Kenkel & Joseph V. Terza, 2001. "The effect of physician advice on alcohol consumption: count regression with an endogenous treatment effect," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(2), pages 165-184.
    22. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    23. Keane, Michael P, 1992. "A Note on Identification in the Multinomial Probit Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 193-200, April.
    24. Chan,Joshua & Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2019. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9781108437493, September.
    25. 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.
    26. William H. Greene, 1992. "A Statistical Model for Credit Scoring," Working Papers 92-29, New York University, Leonard N. Stern School of Business, Department of Economics.
    27. Boyes, William J. & Hoffman, Dennis L. & Low, Stuart A., 1989. "An econometric analysis of the bank credit scoring problem," Journal of Econometrics, Elsevier, vol. 40(1), pages 3-14, January.
    28. Madhu Mohanty, 2002. "A bivariate probit approach to the determination of employment: a study of teen employment differentials in Los Angeles County," Applied Economics, Taylor & Francis Journals, vol. 34(2), pages 143-156.
    29. Kai, Li, 1998. "Bayesian inference in a simultaneous equation model with limited dependent variables," Journal of Econometrics, Elsevier, vol. 85(2), pages 387-400, August.
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    More about this item

    Keywords

    Markov Chain Monte Carlo; sample selection; multivariate probit;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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