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Likelihood Based Estimation in a Panel Setting: Robustness, Redundancy and Validity of Copulas

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This paper considers the estimation of likelihood-based models in a panel setting. That is, we have panel data, and for each time period separately we have a correctly specified model that could be estimated by MLE. We want to allow non-independence over time. This paper shows how to improve on the QMLE. It then considers MLE based on joint distributions constructed using copulas. It discusses the efficiency gain from using the true copula, and shows that knowledge of the true copula is redundant only if the variance matrix of the relevant set of moment conditions is singular. It also discusses the question of robustness against misspecification of the copula, and proposes a test of the validity of the copula. GMM methods are argued to be useful analytically, and also for reasons of efficiency if the copula is robust but not correct.

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Paper provided by Concordia University, Department of Economics in its series Working Papers with number 09002.

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Date of creation: 12 Jan 2009
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Handle: RePEc:crd:wpaper:09002

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  1. 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.
  2. Murray D. Smith, 2003. "Modelling sample selection using Archimedean copulas," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 99-123, 06.
  3. 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.
  4. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  5. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-12, March.
  6. Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2004. "Efficient Estimation of Semiparametric Multivariate Copula Models," Vanderbilt University Department of Economics Working Papers 0420, Vanderbilt University Department of Economics.
  7. Wooldridge, Jeffrey M., 1991. "Specification testing and quasi-maximum- likelihood estimation," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 29-55.
  8. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modeling the Differences in Counted Outcomes using Bivariate Copula Models: with Application to Mismeasured Counts," Working Papers 43, University of California, Davis, Department of Economics.
  9. W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 1-14.
  10. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
  11. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  12. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, 05.
  13. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
  14. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-87, October.
  15. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
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Cited by:
  1. Rainer Winkelmann, 2011. "Copula bivariate probit models: with an application to medical expenditures," ECON - Working Papers 029, Department of Economics - University of Zurich.
  2. Azam Dehgani & Ali Dolati & Manuel Úbeda-Flores, 2013. "Measures of radial asymmetry for bivariate random vectors," Statistical Papers, Springer, vol. 54(2), pages 271-286, May.
  3. Shulin Zhang, & Ostap Okhrin, & Qian M. Zhou & Peter X.-K. Song, 2013. "Goodness-of-fit Test for Specification of Semiparametric Copula Dependence Models," SFB 649 Discussion Papers SFB649DP2013-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Wanling Huang & Artem Prokhorov, 2010. "A Goodness-of-fit Test for Copulas," Working Papers 10002, Concordia University, Department of Economics, revised Apr 2010.
  5. Rainer Winkelmann, 2009. "Copula-based bivariate binary response models," SOI - Working Papers 0913, Socioeconomic Institute - University of Zurich.
  6. Anatolyev, Stanislav & Khabibullin, Renat & Prokhorov, Artem, 2014. "An algorithm for constructing high dimensional distributions from distributions of lower dimension," Economics Letters, Elsevier, vol. 123(3), pages 257-261.
  7. 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).
  8. Christine Amsler & Artem Prokhorov & Peter Schmidt, 2011. "Using Copulas to Model Time Dependence in Stochastic Frontier Models," Working Papers 11002, Concordia University, Department of Economics.

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