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A Note on Identification of Bivariate Copulas for Discrete Count Data

Author

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  • Pravin Trivedi

    (Department of Economics, Indiana University Bloomington, 100 South Woodlawn Avenue, Bloomington, IN 47405-7104, USA)

  • David Zimmer

    (Department of Economics, Western Kentucky University, 1906 College Heights Blvd., Bowling Green, KY 42101, USA)

Abstract

Copulas have enjoyed increased usage in many areas of econometrics, including applications with discrete outcomes. However, Genest and Nešlehová (2007) present evidence that copulas for discrete outcomes are not identified, particularly when those discrete outcomes follow count distributions. This paper confirms the Genest and Nešlehová result using a series of simulation exercises. The paper then proceeds to show that those identification concerns diminish if the model has a regression structure such that the exogenous variable(s) generates additional variation in the outcomes and thus more completely covers the outcome domain.

Suggested Citation

  • Pravin Trivedi & David Zimmer, 2017. "A Note on Identification of Bivariate Copulas for Discrete Count Data," Econometrics, MDPI, vol. 5(1), pages 1-11, February.
    • Handle: RePEc:gam:jecnmx:v:5:y:2017:i:1:p:10-:d:90353
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    References listed on IDEAS

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    1. 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.
    2. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    3. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2011. "An inflated multivariate integer count hurdle model: an application to bid and ask quote dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(4), pages 669-707, June.
    4. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 566-584, December.
    5. 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.
    6. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
    7. Rainer Winkelmann, 2012. "Copula Bivariate Probit Models: With An Application To Medical Expenditures," Health Economics, John Wiley & Sons, Ltd., vol. 21(12), pages 1444-1455, December.
    8. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 566-584, December.
    9. Michael S. Smith & Mohamad A. Khaled, 2012. "Estimation of Copula Models With Discrete Margins via Bayesian Data Augmentation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 290-303, March.
    10. Denuit, Michel & Lambert, Philippe, 2005. "Constraints on concordance measures in bivariate discrete data," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 40-57, March.
    11. van Ophem, Hans, 1999. "A General Method To Estimate Correlated Discrete Random Variables," Econometric Theory, Cambridge University Press, vol. 15(2), pages 228-237, April.
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    7. Arvind Kumar Yadav & Susanta Nag & Pabitra Kumar Jena & Kirtti Ranjan Paltasingh, 2021. "Determinants of Antenatal Care Utilisation in India: A Count Data Modelling Approach," Journal of Development Policy and Practice, , vol. 6(2), pages 210-230, July.
    8. Veraart, Almut E.D., 2019. "Modeling, simulation and inference for multivariate time series of counts using trawl processes," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 110-129.
    9. Giampiero Marra & Rosalba Radice & David M. Zimmer, 2020. "Estimating the binary endogenous effect of insurance on doctor visits by copula‐based regression additive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 953-971, August.
    10. Dimuthu Fernando & Mohammed Alqawba & Manar Samad & Norou Diawara, 2022. "Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(6), pages 1-52, November.
    11. Gery Geenens, 2024. "(Re-)Reading Sklar (1959)—A Personal View on Sklar’s Theorem," Mathematics, MDPI, vol. 12(3), pages 1-7, January.
    12. Dimuthu Fernando & Mohammed Alqawba & Manar Samad & Norou Diawara, 2022. "Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(6), pages 1-28, November.
    13. Jianxu Liu & Mengjiao Wang & Ji Ma & Sanzidur Rahman & Songsak Sriboonchitta, 2020. "A Simultaneous Stochastic Frontier Model with Dependent Error Components and Dependent Composite Errors: An Application to Chinese Banking Industry," Mathematics, MDPI, vol. 8(2), pages 1-23, February.
    14. Fantazzini, Dean, 2020. "Discussing copulas with Sergey Aivazian: a memoir," MPRA Paper 102317, University Library of Munich, Germany.
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    16. Mathews Joseph & Bhattacharya Sumangal & Das Ishapathik & Sen Sumen, 2022. "Multiple inflated negative binomial regression for correlated multivariate count data," Dependence Modeling, De Gruyter, vol. 10(1), pages 290-307, January.

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