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A copula model for dependent competing risks

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  • Simon M. S. Lo
  • Ralf Wilke

Abstract

Many popular estimators for duration models require independent competing risks or independent censoring. In contrast, copula based estimators are also consistent in presence of dependent competing risks. In this paper we suggest a computationally convenient extension of the Copula Graphic Estimator (Zheng and Klein, 1995) to a model with more than two dependent competing risks. We analyse the applicability of this estimator by means of simulations and real world unemployment duration data from Germany. We obtain evidence that our estimator yields nice results if the dependence structure is known and that it is a powerful tool for the assessment of the relevance of (in-)dependence assumptions in applied duration research.

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Paper provided by University of Nottingham, School of Economics in its series Discussion Papers with number 09/01.

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Handle: RePEc:not:notecp:09/01

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Keywords: Archimedean copula; dependent censoring; unemployment duration;

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References

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  1. Wilke, Ralf A. & Lo, Simon M. S. & Arntz, Melanie, 2007. "Bounds Analysis of Competing Risks: A Nonparametric Evaluation of the Effect of Unemployment Benefits on Imigration in Germany," ZEW Discussion Papers, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research 07-049, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  2. Rivest, Louis-Paul & Wells, Martin T., 2001. "A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 79(1), pages 138-155, October.
  3. Van den Berg, Gerard J., 2001. "Duration models: specification, identification and multiple durations," Handbook of Econometrics, Elsevier, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 55, pages 3381-3460 Elsevier.
  4. 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, American Statistical Association, vol. 24, pages 63-76, January.
  5. Jaap H. Abbring & Gerard J. van den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 65(3), pages 701-710.
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Cited by:
  1. Simon M.S. Lo & Ralf A. Wilke, . "A Regression Model for the Copula Graphic Estimator," Discussion Papers, University of Nottingham, School of Economics 11/04, University of Nottingham, School of Economics.
  2. Lo, Simon M.S. & Stephan, Gesine & Wilke, Ralf, 2012. "Estimating the Latent Effect of Unemployment Benefits on Unemployment Duration," IZA Discussion Papers 6650, Institute for the Study of Labor (IZA).
  3. Simon M.S. Lo & Ralf A. Wilke, . "Identifiability and estimation of the sign of a covariate effect in the competing risks model," Discussion Papers, University of Nottingham, School of Economics 11/03, University of Nottingham, School of Economics.
  4. Dimitrova, Dimitrina S. & Haberman, Steven & Kaishev, Vladimir K., 2013. "Dependent competing risks: Cause elimination and its impact on survival," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 464-477.
  5. Melanie Arntz & Simon Lo & Ralf Wilke, 2014. "Bounds analysis of competing risks: a non-parametric evaluation of the effect of unemployment benefits on migration," Empirical Economics, Springer, Springer, vol. 46(1), pages 199-228, February.
  6. Arntz, Melanie & Lo, Simon M. S. & Wilke, Ralf A., 2008. "Bounds analysis of competing risks : a nonparametric evaluation of the effect of unemployment benefits on migration in Germany (Revised version of the FDZ Methodenbericht No. 04/2007)," FDZ Methodenreport, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany] 200806_en, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].

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