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Mixture of normals probit models

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  • John F. Geweke
  • Michael P. Keane

Abstract

This paper generalizes the normal probit model of dichotomous choice by introducing mixtures of normals distributions for the disturbance term. By mixing on both the mean and variance parameters and by increasing the number of distributions in the mixture these models effectively remove the normality assumption and are much closer to semiparametric models. When a Bayesian approach is taken, there is an exact finite-sample distribution theory for the choice probability conditional on the covariates. The paper uses artificial data to show how posterior odds ratios can discriminate between normal and nonnormal distributions in probit models. The method is also applied to female labor force participation decisions in a sample with 1,555 observations from the PSID. In this application, Bayes factors strongly favor mixture of normals probit models over the conventional probit model, and the most favored models have mixtures of four normal distributions for the disturbance term.

Suggested Citation

  • John F. Geweke & Michael P. Keane, 1997. "Mixture of normals probit models," Staff Report 237, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmsr:237
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    References listed on IDEAS

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    Cited by:

    1. Belzil, Christian & Leonardi, Marco, 2007. "Can risk aversion explain schooling attainments? Evidence from Italy," Labour Economics, Elsevier, vol. 14(6), pages 957-970, December.
    2. Christian Belzil, 2008. "Testing the Specification of the Mincer Wage Equation," Annals of Economics and Statistics, GENES, issue 91-92, pages 427-451.
    3. Conway, Karen Smith & Deb, Partha, 2005. "Is prenatal care really ineffective? Or, is the 'devil' in the distribution?," Journal of Health Economics, Elsevier, vol. 24(3), pages 489-513, May.
    4. Koop, Gary & Poirier, Dale J., 2004. "Bayesian variants of some classical semiparametric regression techniques," Journal of Econometrics, Elsevier, vol. 123(2), pages 259-282, December.
    5. Gary Koop, 2004. "Modelling the evolution of distributions: an application to Major League baseball," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(4), pages 639-655.
    6. Brodaty, Thomas & Gary-Bobo, Robert J. & Prieto, Ana, 2014. "Do risk aversion and wages explain educational choices?," Journal of Public Economics, Elsevier, vol. 117(C), pages 125-148.
    7. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
    8. Gianni Amisano & Maria Letizia Giorgetti, 2005. "Entry in Pharmaceutical submarkets: A Bayesian Panel Probit Approach," Working Papers ubs0511, University of Brescia, Department of Economics.
    9. Partha Deb & Ann M. Holmes, 2000. "Estimates of use and costs of behavioural health care: a comparison of standard and finite mixture models," Health Economics, John Wiley & Sons, Ltd., vol. 9(6), pages 475-489.
    10. Vincenzo Atella & Francesco Brindisi & Partha Deb & Furio C. Rosati, 2004. "Determinants of access to physician services in Italy: a latent class seemingly unrelated probit approach," Health Economics, John Wiley & Sons, Ltd., vol. 13(7), pages 657-668.
    11. Jorge E. Arana & Carmelo J. Leon, 2004. "Baysian Flexible Mixture Distribution Modelling of Dichotomous Choice Contingent Valuation with Heterogeneity," Econometric Society 2004 North American Summer Meetings 568, Econometric Society.
    12. Jeffrey M. Wooldridge, 2005. "Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(1), pages 39-54.
    13. Deb, Partha & Trivedi, Pravin K., 2002. "The structure of demand for health care: latent class versus two-part models," Journal of Health Economics, Elsevier, vol. 21(4), pages 601-625, July.
    14. Nikola A. Tarashev & Haibin Zhu, 2006. "The pricing of portfolio credit risk," BIS Working Papers 214, Bank for International Settlements.
    15. Arana, Jorge E. & Leon, Carmelo J., 2005. "Flexible mixture distribution modeling of dichotomous choice contingent valuation with heterogenity," Journal of Environmental Economics and Management, Elsevier, vol. 50(1), pages 170-188, July.
    16. Fruhwirth-Schnatter, Sylvia & Fruhwirth, Rudolf, 2007. "Auxiliary mixture sampling with applications to logistic models," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3509-3528, April.
    17. Deb, Partha & TRIVEDI, PRAVIN K, 1998. "Moment-based Estimation of Latent Class Models of Event Counts," University of California at San Diego, Economics Working Paper Series qt6r282286, Department of Economics, UC San Diego.
    18. Caffo, Brian & An, Ming-Wen & Rohde, Charles, 2007. "Flexible random intercept models for binary outcomes using mixtures of normals," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5220-5235, July.
    19. Geweke, John, 2003. "Econometric issues in using the AHEAD panel," Journal of Econometrics, Elsevier, vol. 112(1), pages 115-120, January.
    20. Houser, Daniel & Bechara, Antoine & Keane, Michael & McCabe, Kevin & Smith, Vernon, 2005. "Identifying individual differences: An algorithm with application to Phineas Gage," Games and Economic Behavior, Elsevier, vol. 52(2), pages 373-385, August.
    21. Michael Keane & Nada Wasi, 2013. "Comparing Alternative Models Of Heterogeneity In Consumer Choice Behavior," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(6), pages 1018-1045, September.

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