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


  • Di Kuang

    (Dept of Statistics, University of Oxford)

  • Bent Nielsen

    () (Nuffield College, Oxford University)

  • J. P. Nielsen

    (Cass Business School, City University London)


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

    1. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(03), pages 443-518, August.
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    Cited by:

    1. Jonas Crevecoeur & Katrien Antonio & Roel Verbelen, 2018. "A time change strategy to model reporting delay dynamics in claims reserving," Papers 1801.02935,
    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. Liivika Tee & Meelis Käärik & Rauno Viin, 2017. "On Comparison of Stochastic Reserving Methods with Bootstrapping," Risks, MDPI, Open Access Journal, vol. 5(1), pages 1-21, January.
    4. Bent Nielsen, 2014. "apc: A Package for Age-Period-Cohort Analysis," Economics Papers 2014-W08, Economics Group, Nuffield College, University of Oxford.
    5. repec:eee:insuma:v:75:y:2017:i:c:p:117-125 is not listed on IDEAS
    6. 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.
    7. repec:gam:jrisks:v:6:y:2018:i:2:p:25-:d:137814 is not listed on IDEAS
    8. Bent Nielsen, 2014. "Deviance analysis of age-period-cohort models," Economics Papers 2014-W03, Economics Group, Nuffield College, University of Oxford.

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