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Mixture of normals probit models

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Author Info
John F. Geweke
Michael P. Keane

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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.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Staff Report with number 237.

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Date of creation: 1997
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Handle: RePEc:fip:fedmsr:237

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Keywords: Econometric models;

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Zellner, Arnold & Rossi, Peter E., 1984. "Bayesian analysis of dichotomous quantal response models," Journal of Econometrics, Elsevier, vol. 25(3), pages 365-393, July. [Downloadable!] (restricted)
  2. John Geweke, . "Posterior Simulators in Econometrics," Computing in Economics and Finance 1996 _019, Society for Computational Economics. [Downloadable!]
  3. repec:cup:etheor:v:13:y:1997:i:1:p:32-51 is not listed on IDEAS
  4. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March. [Downloadable!] (restricted)
  5. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May. [Downloadable!] (restricted)
  6. Hausman, Jerry & McFadden, Daniel, 1984. "Specification Tests for the Multinomial Logit Model," Econometrica, Econometric Society, vol. 52(5), pages 1219-40, September. [Downloadable!] (restricted)
    Other versions:
  7. John Geweke & Michael Keane & David Runkle, 1994. "Alternative computational approaches to inference in the multinomial probit model," Staff Report 170, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  8. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March. [Downloadable!] (restricted)
  9. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(01), pages 32-51, February. [Downloadable!]
  10. 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.
  11. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November. [Downloadable!] (restricted)
  12. Geweke, John F. & Keane, Michael P. & Runkle, David E., 1997. "Statistical inference in the multinomial multiperiod probit model," Journal of Econometrics, Elsevier, vol. 80(1), pages 125-165, September. [Downloadable!] (restricted)
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  13. Koop, Gary & Poirier, Dale J., 1993. "Bayesian analysis of logit models using natural conjugate priors," Journal of Econometrics, Elsevier, vol. 56(3), pages 323-340, April. [Downloadable!] (restricted)
  14. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March. [Downloadable!] (restricted)
  15. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-82, May. [Downloadable!] (restricted)
  16. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
  17. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De. [Downloadable!] (restricted)
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  1. Partha Deb & Xing Ming & Pravin K. Trivedi, 1998. "Moment-based Estimation of Latent Class Models of Event Counts," University of California at San Diego, Economics Working Paper Series 98-12, Department of Economics, UC San Diego. [Downloadable!]
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  2. Christian Belzil, 2006. "Testing the Specification of the Mincer Wage Equation," Post-Print halshs-00142542_v1, HAL. [Downloadable!]
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  3. Vincenzo Atella & Francesco Brindisi & Partha Deb & Furio C. Rosati, 2003. "Determinants of Access to Physician Services in Italy: A Latent Class Seemingly Unrelated Probit Approach," CEIS Research Paper 36, Tor Vergata University, CEIS. [Downloadable!]
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  4. Christian Belzil & Marco Leonardi, 2006. "Can Risk Aversion Explain Schooling Attainments? Evidence from Italy," IZA Discussion Papers 2123, Institute for the Study of Labor (IZA). [Downloadable!]
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  5. Partha Deb & Karen Smith Conway, 2002. "Is Prenatal Care Really Ineffective? Or, is the 'Devil' in the Distribution?," Hunter College Department of Economics Working Papers 02/2, Hunter College: Department of Economics. [Downloadable!]
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  6. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  7. Atella Vincenzo & Francesco Brindisi & Partha Deb & Furio C. Rosati, 2002. "Determinants Of Access To Physician Services In Italy: A Latent Class Probit Approach," Departmental Working Papers 158, Tor Vergata University, CEIS. [Downloadable!]
  8. 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. [Downloadable!]
  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. Martin Kahanec, 2007. "Ethnic Specialization and Earnings Inequality: Why Being a Minority Hurts but Being a Big Minority Hurts More," IZA Discussion Papers 2650, Institute for the Study of Labor (IZA). [Downloadable!]
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  11. Jeffrey M Wooldridge, 2002. "Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity," CeMMAP working papers CWP18/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  12. Jorge E. Araña & Carmelo J. León, 2006. "Modelling unobserved heterogeneity in contingent valuation of health risks," Applied Economics, Taylor and Francis Journals, vol. 38(19), pages 2315-2325, October. [Downloadable!] (restricted)
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