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Copula bivariate probit models: with an application to medical expenditures

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  • Rainer Winkelmann

Abstract

The bivariate probit model is frequently used for estimating the effect of an endogenous binary regressor (the "treatment") on a binary health outcome variable. This paper discusses simple modifications that maintain the probit assumption for the marginal distributions while introducing non-normal dependence using copulas. In an application of the copula bivariate probit model to the effect of insurance status on the absence of ambulatory health care expen- diture, a model based on the Frank copula outperforms the standard bivariate probit model.

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Paper provided by Department of Economics - University of Zurich in its series ECON - Working Papers with number 029.

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Date of creation: Sep 2011
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Handle: RePEc:zur:econwp:029
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Keywords: Bivariate probit; binary endogenous regressor; Frank copula; Clayton copula;

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Find related papers by JEL classification:
  • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
  • I12 - Health, Education, and Welfare - - Health - - - Health Behavior

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  1. 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.
  2. Brigitte Dormont & Pierre-Yves Geoffard & Karine Lamiraud, 2009. "The influence of supplementary health insurance on switching behaviour: evidence from Swiss data," Health Economics, John Wiley & Sons, Ltd., vol. 18(11), pages 1339-1356.
  3. Murray D. Smith, 2003. "Modelling sample selection using Archimedean copulas," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 99-123, 06.
  4. 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.
  5. Ziggy MacDonald & Michael A. Shields, 2004. "Does problem drinking affect employment? Evidence from England," Health Economics, John Wiley & Sons, Ltd., vol. 13(2), pages 139-155.
  6. Ehsan Latif, 2009. "The impact of diabetes on employment in Canada," Health Economics, John Wiley & Sons, Ltd., vol. 18(5), pages 577-589.
  7. Wilde, Joachim, 2000. "Identification of multiple equation probit models with endogenous dummy regressors," Economics Letters, Elsevier, vol. 69(3), pages 309-312, December.
  8. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
  9. Michael T. French & Johanna C. Maclean, 2006. "Underage alcohol use, delinquency, and criminal activity," Health Economics, John Wiley & Sons, Ltd., vol. 15(12), pages 1261-1281.
  10. 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.
  11. 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.
  12. Karen Smith Conway & Andrea Kutinova, 2006. "Maternal health: does prenatal care make a difference?," Health Economics, John Wiley & Sons, Ltd., vol. 15(5), pages 461-488.
  13. Prokhorov, Artem & Schmidt, Peter, 2009. "Likelihood-based estimation in a panel setting: Robustness, redundancy and validity of copulas," Journal of Econometrics, Elsevier, vol. 153(1), pages 93-104, November.
  14. Anthony Murphy, 2005. "Score Tests of Normality in Bivariate Probit Models," Econometrics 0512004, EconWPA.
  15. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-12, March.
  16. 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.
  17. Lara Gitto & Domenico Santoro & Giuseppe Sobbrio, 2006. "Choice of dialysis treatment and type of medical unit (private vs public): application of a recursive bivariate probit," Health Economics, John Wiley & Sons, Ltd., vol. 15(11), pages 1251-1256.
  18. 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.
  19. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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Cited by:

  1. Katarzyna Bień-Barkowska, 2012. "A Bivariate Copula-based Model for a Mixed Binary-Continuous Distribution: A Time Series Approach," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 4(2), pages 117-142, June.
  2. Giampiero Marra & Rosalba Radice & Silvia Missiroli, 2014. "Testing the hypothesis of absence of unobserved confounding in semiparametric bivariate probit models," Computational Statistics, Springer, vol. 29(3), pages 715-741, June.
  3. Hasebe, Takuya, 2013. "Marginal effects of a bivariate binary choice model," Economics Letters, Elsevier, vol. 121(2), pages 298-301.

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