IDEAS home Printed from https://ideas.repec.org/p/zur/econwp/029.html
   My bibliography  Save this paper

Copula bivariate probit models: with an application to medical expenditures

Author

Listed:
  • 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.

Suggested Citation

  • Rainer Winkelmann, 2011. "Copula bivariate probit models: with an application to medical expenditures," ECON - Working Papers 029, Department of Economics - University of Zurich.
    • Handle: RePEc:zur:econwp:029
    as

    Download full text from publisher

    File URL: https://www.zora.uzh.ch/id/eprint/51533/1/econwp029.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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, December.
    2. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    3. Jones, A., 2007. "Applied Econometrics for Health Economists: A Practical Guide," Monographs, Office of Health Economics, number 000262.
    4. 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.
    5. 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, November.
    6. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    7. 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.
    8. Brigitte Dormont & Pierre-Yves Geoffard & Karine Lamiraud, 2007. "The influence of supplementary health insurance on switching behaviour: evidence on Swiss data," Working Papers halshs-00587785, HAL.
    9. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-512, March.
    10. 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.
    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. Ehsan Latif, 2009. "The impact of diabetes on employment in Canada," Health Economics, John Wiley & Sons, Ltd., vol. 18(5), pages 577-589, May.
    13. Murray D. Smith, 2003. "Modelling sample selection using Archimedean copulas," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 99-123, June.
    14. 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.
    15. 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, November.
    16. repec:dau:papers:123456789/1623 is not listed on IDEAS
    17. 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.
    18. 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, February.
    19. Murphy, Anthony, 2007. "Score tests of normality in bivariate probit models," Economics Letters, Elsevier, vol. 95(3), pages 374-379, June.
    20. 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, May.
    21. Wilde, Joachim, 2000. "Identification of multiple equation probit models with endogenous dummy regressors," Economics Letters, Elsevier, vol. 69(3), pages 309-312, December.
    22. 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 47-57, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rainer Winkelmann, 2009. "Copula-based bivariate binary response models," SOI - Working Papers 0913, Socioeconomic Institute - University of Zurich.
    2. Hasebe, Takuya & Vijverberg, Wim P., 2012. "A Flexible Sample Selection Model: A GTL-Copula Approach," IZA Discussion Papers 7003, Institute of Labor Economics (IZA).
    3. Jörg Schwiebert, 2016. "Multinomial choice models based on Archimedean copulas," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 333-354, July.
    4. Chen, Heng & Fan, Yanqin & Wu, Jisong, 2014. "A flexible parametric approach for estimating switching regime models and treatment effect parameters," Journal of Econometrics, Elsevier, vol. 181(2), pages 77-91.
    5. Bhat, Chandra R. & Eluru, Naveen, 2009. "A copula-based approach to accommodate residential self-selection effects in travel behavior modeling," Transportation Research Part B: Methodological, Elsevier, vol. 43(7), pages 749-765, August.
    6. Jones A.M & Rice N, 2009. "Econometric Evaluation of Health Policies," Health, Econometrics and Data Group (HEDG) Working Papers 09/09, HEDG, c/o Department of Economics, University of York.
    7. 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.
    8. 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.
    9. Wanling Huang & Artem Prokhorov, 2014. "A Goodness-of-fit Test for Copulas," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 751-771, October.
    10. Chandra Bhat & Ipek Sener, 2009. "A copula-based closed-form binary logit choice model for accommodating spatial correlation across observational units," Journal of Geographical Systems, Springer, vol. 11(3), pages 243-272, September.
    11. Azam, Kazim & Pitt, Michael, 2014. "Bayesian Inference for a Semi-Parametric Copula-based Markov Chain," The Warwick Economics Research Paper Series (TWERPS) 1051, University of Warwick, Department of Economics.
    12. José Murteira & Óscar Lourenço, 2011. "Health care utilization and self-assessed health: specification of bivariate models using copulas," Empirical Economics, Springer, vol. 41(2), pages 447-472, October.
    13. Han, Sukjin & Vytlacil, Edward J., 2017. "Identification in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Econometrics, Elsevier, vol. 199(1), pages 63-73.
    14. Simon Luechinger & Alois Stutzer & Rainer Winkelmann, 2008. "Self-Selection and Subjective Well-Being: Copula Models with an Application to Public and Private Sector Work," SOEPpapers on Multidisciplinary Panel Data Research 135, DIW Berlin, The German Socio-Economic Panel (SOEP).
    15. Dalla Valle Luciana, 2016. "The Use of Official Statistics in Self-Selection Bias Modeling," Journal of Official Statistics, Sciendo, vol. 32(4), pages 887-905, December.
    16. Hidayatina, Achsanah & Garces-Ozanne, Arlene, 2019. "Can cash transfers mitigate child labour? Evidence from Indonesia’s cash transfer programme for poor students in Java," World Development Perspectives, Elsevier, vol. 15(C), pages 1-1.
    17. Manuel Arellano & Stéphane Bonhomme, 2017. "Sample Selection in Quantile Regression: A Survey," Working Papers wp2018_1702, CEMFI.
    18. Manuel Arellano & Stéphane Bonhomme, 2017. "Sample Selection in Quantile Regression: A Survey," Working Papers wp2017_1702, CEMFI.
    19. Blasch, Julia & Filippini, Massimo & Kumar, Nilkanth, 2019. "Boundedly rational consumers, energy and investment literacy, and the display of information on household appliances," Resource and Energy Economics, Elsevier, vol. 56(C), pages 39-58.
    20. Chaohsin Lin & Shuofen Hsu, 2025. "The effects of selection and moral hazard in additional health insurance in a universal healthcare system: evidence from Taiwan," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 50(2), pages 444-466, April.

    More about this item

    Keywords

    Bivariate probit; binary endogenous regressor; Frank copula; Clayton copula;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zur:econwp:029. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Severin Oswald (email available below). General contact details of provider: https://edirc.repec.org/data/seizhch.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.