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Copula-based bivariate binary response models

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  • Rainer Winkelmann

    ()
    (Socioeconomic Institute, University of Zurich)

Abstract

The bivariate probit model is frequently used for estimating the effect of an endogenous binary regressor on a binary outcome variable. This paper discusses simple modifications that maintain the probit assumption for the marginal distributions while introducing non-normal dependence among the two variables using copulas. Simulation results and evidence from two applications, one on the effect of insurance status on ambulatory expenditure and one on the effect of completing high school on subsequent unemployment, show that these modified bivariate probit models work well in practice, and that they provide a viable and simple alternative to the standard bivariate probit approach.

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File URL: http://www.soi.uzh.ch/research/wp/2009/wp0913.pdf
File Function: first version, 2009
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Bibliographic Info

Paper provided by Socioeconomic Institute - University of Zurich in its series SOI - Working Papers with number 0913.

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Length: 26 pages
Date of creation: Aug 2009
Date of revision:
Handle: RePEc:soz:wpaper:0913

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Keywords: Bivariate probit; binary endogenous regressor; Frank copula; Clayton copula;

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  1. Murphy, Anthony, 2007. "Score tests of normality in bivariate probit models," Economics Letters, Elsevier, vol. 95(3), pages 374-379, June.
  2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  3. Koenker, Roger & Yoon, Jungmo, 2009. "Parametric links for binary choice models: A Fisherian-Bayesian colloquy," Journal of Econometrics, Elsevier, vol. 152(2), pages 120-130, October.
  4. Wendy A. Stock & T. Aldrich Finegan & John J. Siegfried, 2009. "Completing an Economics PhD in Five Years," American Economic Review, American Economic Association, vol. 99(2), pages 624-29, May.
  5. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-12, March.
  6. Mingliang Li, 2006. "High school completion and future youth unemployment: new evidence from High School and Beyond," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 23-53.
  7. Murray D. Smith, 2005. "Using Copulas to Model Switching Regimes with an Application to Child Labour," The Economic Record, The Economic Society of Australia, vol. 81(s1), pages S47-S57, 08.
  8. Trivedi, Pravin K. & Zimmer, David M., 2007. "Copula Modeling: An Introduction for Practitioners," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(1), pages 1-111, April.
  9. Wilde, Joachim, 2000. "Identification of multiple equation probit models with endogenous dummy regressors," Economics Letters, Elsevier, vol. 69(3), pages 309-312, December.
  10. van Ophem, Hans, 1999. "A General Method To Estimate Correlated Discrete Random Variables," Econometric Theory, Cambridge University Press, vol. 15(02), pages 228-237, April.
  11. D. Fabbri & C. Monfardini, 2006. "Style of practice and assortative mating: a recursive probit analysis of cesarean section scheduling in Italy," Working Papers 557, Dipartimento Scienze Economiche, Universita' di Bologna.
  12. Zimmer, David M. & Trivedi, Pravin K., 2006. "Using Trivariate Copulas to Model Sample Selection and Treatment Effects: Application to Family Health Care Demand," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 63-76, January.
  13. Ribar, David C, 1994. "Teenage Fertility and High School Completion," The Review of Economics and Statistics, MIT Press, vol. 76(3), pages 413-24, August.
  14. van Ophem, Hans, 2000. "Modeling Selectivity in Count-Data Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 503-11, October.
  15. Murat K. Munkin & Partha Deb & 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.
  16. Evans, William N & Schwab, Robert M, 1995. "Finishing High School and Starting College: Do Catholic Schools Make a Difference?," The Quarterly Journal of Economics, MIT Press, vol. 110(4), pages 941-74, November.
  17. Francis Vella, 1999. "Do Catholic Schools Make a Difference? Evidence from Australia," Journal of Human Resources, University of Wisconsin Press, vol. 34(1), pages 208-224.
  18. Artem Prokhorov & Peter Schmidt, 2009. "Likelihood Based Estimation in a Panel Setting: Robustness, Redundancy and Validity of Copulas," Working Papers 09002, Concordia University, Department of Economics.
  19. Murray D. Smith, 2003. "Modelling sample selection using Archimedean copulas," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 99-123, 06.
  20. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
  21. Munkin, Murat K. & Trivedi, Pravin K., 2008. "Bayesian analysis of the ordered probit model with endogenous selection," Journal of Econometrics, Elsevier, vol. 143(2), pages 334-348, April.
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