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Identification of the age-period-cohort model and the extended chain ladder model

Author

Listed:
  • Di Kuang

    (Dept of Statistics, University of Oxford)

  • Bent Nielsen

    (Nuffield College, Oxford University)

  • J. P. Nielsen

    (Cass Business School, City University London)

Abstract

In this paper, we consider the identification problem arising in the age-period-cohort models, as well as in the extended chain ladder model. We propose a canonical parametrization based on the accelerations of the trends in the three factors. This parametrization is exactly identified. It eases interpretation, estimation and forecasting. The canonical parametrization is shown to apply for a class of index sets which have trapezoid shapes, including various Lexis diagrams and the insurance reserving triangles.

Suggested Citation

  • Di Kuang & Bent Nielsen & J. P. Nielsen, 2007. "Identification of the age-period-cohort model and the extended chain ladder model," Economics Papers 2007-W05, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:0705
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    References listed on IDEAS

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    1. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
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    Cited by:

    1. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    2. D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Forecasting with the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 987-991.
    3. Crevecoeur, Jonas & Antonio, Katrien & Verbelen, Roel, 2019. "Modeling the number of hidden events subject to observation delay," European Journal of Operational Research, Elsevier, vol. 277(3), pages 930-944.
    4. Jonas Harnau, 2018. "Misspecification Tests for Log-Normal and Over-Dispersed Poisson Chain-Ladder Models," Risks, MDPI, vol. 6(2), pages 1-25, March.
    5. Zoë Fannon & B. Nielsen, 2018. "Age-period cohort models," Economics Papers 2018-W04, Economics Group, Nuffield College, University of Oxford.
    6. Li, Hong & Lu, Yang, 2017. "Coherent Forecasting Of Mortality Rates: A Sparse Vector-Autoregression Approach," ASTIN Bulletin, Cambridge University Press, vol. 47(2), pages 563-600, May.
    7. Bent Nielsen & María Dolores Martínez-Miranda & Jens Perch Nielsen, 2016. "A simple benchmark for mesothelioma projection for Great Britain," Economics Papers 2016-W03, Economics Group, Nuffield College, University of Oxford.
    8. D. Kuang & B. Nielsen, 2018. "Generalized Log-Normal Chain-Ladder," Economics Papers 2018-W02, Economics Group, Nuffield College, University of Oxford.
    9. Liivika Tee & Meelis Käärik & Rauno Viin, 2017. "On Comparison of Stochastic Reserving Methods with Bootstrapping," Risks, MDPI, vol. 5(1), pages 1-21, January.
    10. Bent Nielsen, 2014. "apc: A Package for Age-Period-Cohort Analysis," Economics Papers 2014-W08, Economics Group, Nuffield College, University of Oxford.
    11. Beutner, Eric & Reese, Simon & Urbain, Jean-Pierre, 2017. "Identifiability issues of age–period and age–period–cohort models of the Lee–Carter type," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 117-125.
    12. Jonas Harnau, 2018. "Log-Normal or Over-Dispersed Poisson?," Risks, MDPI, vol. 6(3), pages 1-37, July.
    13. Alex Isakson & Simone Krummaker & María Dolores Martínez-Miranda & Ben Rickayzen, 2021. "Calendar Effect and In-Sample Forecasting Applied to Mesothelioma Mortality Data," Mathematics, MDPI, vol. 9(18), pages 1-17, September.
    14. Eyal Bar-Haim & Louis Chauvel & Anne Hartung, 2018. "More Necessary and Less Sufficient: An Age-Period-Cohort Approach to Overeducation in Comparative Perspective," LIS Working papers 734, LIS Cross-National Data Center in Luxembourg.
    15. Mammen, Enno & Martínez Miranda, María Dolores & Nielsen, Jens Perch, 2015. "In-sample forecasting applied to reserving and mesothelioma mortality," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 76-86.
    16. Cavallari, Lilia & Romano, Simone & Naticchioni, Paolo, 2021. "The original sin: Firms’ dynamics and the life-cycle consequences of economic conditions at birth," European Economic Review, Elsevier, vol. 138(C).
    17. Mammen, Enno & Martínez-Miranda, María Dolores & Nielsen, Jens Perch & Vogt, Michael, 2021. "Calendar effect and in-sample forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 31-52.
    18. Bent Nielsen, 2014. "Deviance analysis of age-period-cohort models," Economics Papers 2014-W03, Economics Group, Nuffield College, University of Oxford.
    19. Zoë Fannon & Christiaan Monden & Bent Nielsen, 2018. "Age-period-cohort modelling and covariates, with an application to obesity in England 2001-2014," Economics Papers 2018-W05, Economics Group, Nuffield College, University of Oxford.
    20. D. Kuang & B. Nielsen, 2018. "Generalized Log-Normal Chain-Ladder," Papers 1806.05939, arXiv.org.

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