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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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Bibliographic Info

Article provided by Royal Economic Society in its journal The Econometrics Journal.

Volume (Year): 7 (2004)
Issue (Month): 2 (December)
Pages: 566-584

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Handle: RePEc:ect:emjrnl:v:7:y:2004:i:2:p:566-584

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  1. Capéraà, Philippe & Fougères, Anne-Laure & Genest, Christian, 2000. "Bivariate Distributions with Given Extreme Value Attractor," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 30-49, January.
  2. Cameron,A. Colin & Trivedi,Pravin K., 1998. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9780521635677.
  3. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
  4. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-20, May.
  5. Jerry A. Hausman & Andrew W. Lo & A. Craig MacKinlay, 1991. "An Ordered Probit Analysis of Transaction Stock Prices," NBER Working Papers 3888, National Bureau of Economic Research, Inc.
  6. Chib, Siddhartha & Winkelmann, Rainer, 2001. "Markov Chain Monte Carlo Analysis of Correlated Count Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 428-35, October.
  7. 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.
  8. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-12, March.
  9. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
  10. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
  11. Murat K. Munkin & Pravin K. Trivedi, 1999. "Simulated maximum likelihood estimation of multivariate mixed-Poisson regression models, with application," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 29-48.
  12. Miller, Douglas J. & Liu, Wei-han, 2002. "On the recovery of joint distributions from limited information," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 259-274, March.
  13. 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.
  14. Deb, Partha & Trivedi, Pravin K, 1997. "Demand for Medical Care by the Elderly: A Finite Mixture Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 313-36, May-June.
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Cited by:
  1. Prokhorov, Artem, 2008. "A goodness-of-fit test for copulas," MPRA Paper 9998, University Library of Munich, Germany.
  2. 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.
  3. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2007. "An Inflated Multivariate Integer Count Hurdle Model: An Application to Bid and Ask Quote Dynamics," CoFE Discussion Paper 07-04, Center of Finance and Econometrics, University of Konstanz.
  4. 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.
  5. 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.
  6. 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.
  7. Eugenio Miravete, 2007. "“Competing with Menus of Tariff Options”," Working Papers 07-02, NET Institute, revised Jul 2007.
  8. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2006. "Estimating Liquidity Using Information on the Multivariate Trading Process," CoFE Discussion Paper 06-04, Center of Finance and Econometrics, University of Konstanz.
  9. 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, vol. 21(1), pages 74-92, March.
  10. Stanislav Anatolyev & Nikolay Gospodinov, 2007. "Modeling Financial Return Dynamics by Decomposition," Working Papers w0095, Center for Economic and Financial Research (CEFIR).
  11. 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.
  12. 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.
  13. 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).
  14. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2006. "A Multivariate Integer Count Hurdle Model: Theory and Application to Exchange Rate Dynamics," CoFE Discussion Paper 06-06, Center of Finance and Econometrics, University of Konstanz.
  15. Agnes E. Walker & Stephen Colagiuri, 2011. "Cost-Benefit Model System of Chronic Diseases in Australia to Assess and Rank Prevention and Treatment Options," International Journal of Microsimulation, Interational Microsimulation Association, vol. 4(3), pages 57-70.

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