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Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts

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  • A. Colin Cameron
  • Tong Li
  • Pravin K. Trivedi
  • David M. Zimmer

Abstract

This paper makes three contributions. Firstly, it uses copula functions to obtain a flexible bivariate parametric model for non-negative integer-valued data (counts). Secondly, it recovers the distribution of the difference in the two counts from a specified bivariate count distribution. Thirdly, the methods are applied to counts that are measured with error. Specifically, we model the determinants of the difference between the self-reported number of doctor visits (measured with error) and true number of doctor visits (also available in the data used). Copyright Royal Economic Socciety 2004

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  • 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.
    • Handle: RePEc:ect:emjrnl:v:7:y:2004:i:2:p:566-584
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    Cited by:

    1. Wanling Huang & Artem Prokhorov, 2014. "A Goodness-of-fit Test for Copulas," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 751-771, October.
    2. Peter J. Danaher & Michael S. Smith, 2011. "Rejoinder--Estimation Issues for Copulas Applied to Marketing Data," Marketing Science, INFORMS, vol. 30(1), pages 25-28, 01-02.
    3. Yen, Steven T. & Tan, Andrew K.G., 2011. "Fruit and vegetable consumption in Malaysia: a count system approach," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 115969, European Association of Agricultural Economists.
    4. Eugenio Miravete, 2014. "Testing for complementarities among countable strategies," Empirical Economics, Springer, vol. 46(4), pages 1521-1544, June.
    5. Fantazzini, Dean, 2008. "Econometric Analysis of Financial Data in Risk Management (continuation). Section III: Managing Operational Risk," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 11(3), pages 87-122.
    6. 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.
    7. Marra, Giampiero & Wyszynski, Karol, 2016. "Semi-parametric copula sample selection models for count responses," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 110-129.
    8. 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.
    9. 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.
    10. Miravete, Eugenio J, 2007. "Competing with Menus of Tariff Options," CEPR Discussion Papers 6279, C.E.P.R. Discussion Papers.
    11. repec:eee:jmvana:v:159:y:2017:i:c:p:82-110 is not listed on IDEAS
    12. Liang Peng & Yongcheng Qi & Ingrid Van Keilegom, 2012. "Jackknife empirical likelihood method for copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 74-92, March.
    13. So, Sunha & Lee, Dong-Hee & Jung, Byoung Cheol, 2011. "An alternative bivariate zero-inflated negative binomial regression model using a copula," Economics Letters, Elsevier, vol. 113(2), pages 183-185.
    14. 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.
    15. Stanislav Anatolyev & Nikolay Gospodinov, 2007. "Modeling Financial Return Dynamics by Decomposition," Working Papers w0095, Center for Economic and Financial Research (CEFIR).
    16. Shi, Peng & Valdez, Emiliano A., 2011. "A copula approach to test asymmetric information with applications to predictive modeling," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 226-239, September.
    17. Chen, Jian & Peng, Liang & Zhao, Yichuan, 2009. "Empirical likelihood based confidence intervals for copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 137-151, January.
    18. Pravin Trivedi & David Zimmer, 2017. "A Note on Identification of Bivariate Copulas for Discrete Count Data," Econometrics, MDPI, Open Access Journal, vol. 5(1), pages 1-11, February.
    19. Tsung-Shan Tsou, 2016. "Robust likelihood inference for multivariate correlated count data," Computational Statistics, Springer, vol. 31(3), pages 845-857, September.
    20. Hasebe, Takuya & Vijverberg, Wim P., 2012. "A Flexible Sample Selection Model: A GTL-Copula Approach," IZA Discussion Papers 7003, Institute for the Study of Labor (IZA).
    21. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2006. "Estimating liquidity using information on the multivariate trading process," Working Papers 10, Department of Applied Econometrics, Warsaw School of Economics.
    22. John Mullahy, 2017. "Individual Results May Vary: Elementary Analytics of Inequality-Probability Bounds, with Applications to Health-Outcome Treatment Effects," NBER Working Papers 23603, National Bureau of Economic Research, Inc.
    23. Steven T. Yen & Biing-Hwan Lin, 2008. "Quasi-maximum likelihood estimation of a censored equation system with a copula approach: meat consumption by U.S. individuals," Agricultural Economics, International Association of Agricultural Economists, vol. 39(2), pages 207-217, September.

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