IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i2d10.1007_s00362-017-0956-y.html
   My bibliography  Save this article

The distribution of unobserved heterogeneity in competing risks models

Author

Listed:
  • Yang Lu

    (University of Paris-13, Sorbonne Paris Cité, CEPN, UMR-CNRS 7234)

Abstract

We show that in a large class of proportional hazard competing risks models, the distribution of the bivariate frailty among survivors converges to a limiting distribution. This generalizes the result of Abbring and van den Berg (Biometrika 94(1):87–99, 2007), who show that in a single spell duration model, the frailty distribution converges to the gamma distribution. The resulting limiting distribution has an interpretation in terms of partition of a gamma distribution, and allows for both positive and negative correlation between the survival variables. This result provides a natural and flexible specification for the frailty in competing risks models.

Suggested Citation

  • Yang Lu, 2020. "The distribution of unobserved heterogeneity in competing risks models," Statistical Papers, Springer, vol. 61(2), pages 681-696, April.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:2:d:10.1007_s00362-017-0956-y
    DOI: 10.1007/s00362-017-0956-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-017-0956-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-017-0956-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. David Hanagal, 2009. "Weibull extension of bivariate exponential regression model with different frailty distributions," Statistical Papers, Springer, vol. 50(1), pages 29-49, January.
    2. Jaap H. Abbring & Gerard J. Van Den Berg, 2007. "The unobserved heterogeneity distribution in duration analysis," Biometrika, Biometrika Trust, vol. 94(1), pages 87-99.
    3. 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, vol. 65(3), pages 701-710, August.
    4. Guillaume Horny, 2009. "Inference in mixed proportional hazard models with K random effects," Statistical Papers, Springer, vol. 50(3), pages 481-499, June.
    5. Yongheng Deng & John M. Quigley & Robert Van Order, 2000. "Mortgage Terminations, Heterogeneity and the Exercise of Mortgage Options," Econometrica, Econometric Society, vol. 68(2), pages 275-308, March.
    6. Omey, E. & Willekens, E., 1989. "Abelian and Tauberian theorems for the Laplace transform of functions in several variables," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 292-306, August.
    7. Baker, Michael & Melino, Angelo, 2000. "Duration dependence and nonparametric heterogeneity: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 96(2), pages 357-393, June.
    8. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-956, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hess, Wolfgang & Persson, Maria, 2010. "The Duration of Trade Revisited. Continuous-Time vs. Discrete-Time Hazards," Working Papers 2010:1, Lund University, Department of Economics.
    2. Hess, Wolfgang & Persson, Maria, 2009. "Survival and Death in International Trade - Discrete-Time Durations of EU Imports," Working Papers 2009:12, Lund University, Department of Economics.
    3. Bart Cockx & Muriel Dejemeppe, 2005. "Duration dependence in the exit rate out of unemployment in Belgium. Is it true or spurious?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(1), pages 1-23, January.
    4. Wolfgang Hess & Maria Persson, 2012. "The duration of trade revisited," Empirical Economics, Springer, vol. 43(3), pages 1083-1107, December.
    5. Adriaan Kalwij, 2014. "An empirical analysis of the importance of controlling for unobserved heterogeneity when estimating the income-mortality gradient," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(30), pages 913-940.
    6. Nicoletti, Cheti & Rondinelli, Concetta, 2010. "The (mis)specification of discrete duration models with unobserved heterogeneity: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 159(1), pages 1-13, November.
    7. Zhang, Tao, 2003. "A Monte Carlo study on non-parametric estimation of duration models with unobserved heterogeneity," Memorandum 25/2003, Oslo University, Department of Economics.
    8. Lee, Myoung-jae & Johansson, Per, 2013. "A Simple Approach to Treatment Effects on Durations When the Treatment Timing is Chosen," IZA Discussion Papers 7249, Institute of Labor Economics (IZA).
    9. Nicoletti, Cheti & Rondinelli, Concetta, 2006. "The (mis)specification of discrete time duration models with unobserved heterogenity: a Monte Carlo study," ISER Working Paper Series 2006-53, Institute for Social and Economic Research.
    10. Sciulli, Dario, 2006. "Making the italian labor market more flexible: an evaluation of the treu reform," UC3M Working papers. Economics we063408, Universidad Carlos III de Madrid. Departamento de Economía.
    11. Albanese, Andrea & Picchio, Matteo & Ghirelli, Corinna, 2020. "Timed to Say Goodbye: Does Unemployment Benefit Eligibility Affect Worker Layoffs?," Labour Economics, Elsevier, vol. 65(C).
    12. Damien Échevin & Bernard Fortin, 2011. "Physician Payment Mechanisms, Hospital Length of Stay and Risk of Readmission: a Natural Experiment," CIRANO Working Papers 2011s-44, CIRANO.
    13. Gianna Giannelli & Ursula Jaenichen & Claudia Villosio, 2012. "Have Labor Market Reforms at the Turn of the Millennium Changed the Job and Employment Durations of new Entrants?," Journal of Labor Research, Springer, vol. 33(2), pages 143-172, June.
    14. Dario Sciulli & Antonio Menezes & José Vieira, 2012. "Unemployment Duration and Disability: Evidence from Portugal," Journal of Labor Research, Springer, vol. 33(1), pages 21-48, March.
    15. Ohinata, A., 2011. "Did the US Infertility Health Insurance Mandates Affect the Timing of First Birth?," Discussion Paper 2011-102, Tilburg University, Center for Economic Research.
    16. Gómez-Déniz, E. & Pérez-Rodríguez, J.V., 2019. "Modelling bimodality of length of tourist stay," Annals of Tourism Research, Elsevier, vol. 75(C), pages 131-151.
    17. Jaap H. Abbring & Gerard J. Van Den Berg, 2007. "The unobserved heterogeneity distribution in duration analysis," Biometrika, Biometrika Trust, vol. 94(1), pages 87-99.
    18. Yolanda F. Rebollo-Sanz & Nuria Rodriguez Planas, 2016. "When the Going Gets Tough... Financial Incentives, Duration of Unemployment and Job-Match Quality," Working Papers 16.11, Universidad Pablo de Olavide, Department of Economics.
    19. Bijwaard, Govert, 2011. "Unobserved Heterogeneity in Multiple-Spell Multiple-States Duration Models," IZA Discussion Papers 5748, Institute of Labor Economics (IZA).
    20. Échevin, Damien & Fortin, Bernard, 2014. "Physician payment mechanisms, hospital length of stay and risk of readmission: Evidence from a natural experiment," Journal of Health Economics, Elsevier, vol. 36(C), pages 112-124.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:61:y:2020:i:2:d:10.1007_s00362-017-0956-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.