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

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  • D. Kuang
  • B. Nielsen
  • J. P. Nielsen

Abstract

We consider the identification problem that arises in the age-period-cohort models as well as in the extended chain-ladder model. We propose a canonical parameterization based on the accelerations of the trends in the three factors. This parameterization is exactly identified and eases interpretation, estimation and forecasting. The canonical parameterization is applied to a class of index sets which have trapezoidal shapes, including various Lexis diagrams and the insurance-reserving triangles. Copyright 2008, Oxford University Press.

Suggested Citation

  • D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Identification of the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 979-986.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:4:p:979-986
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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. Francesco Billari & Rebecca Graziani, 2024. "Age-period-cohort analysis of U.S. fertility: a realistic approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(4), pages 3021-3040, August.
    7. 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.
    8. 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.
    9. D. Kuang & B. Nielsen, 2018. "Generalized Log-Normal Chain-Ladder," Economics Papers 2018-W02, Economics Group, Nuffield College, University of Oxford.
    10. Liivika Tee & Meelis Käärik & Rauno Viin, 2017. "On Comparison of Stochastic Reserving Methods with Bootstrapping," Risks, MDPI, vol. 5(1), pages 1-21, January.
    11. Bent Nielsen, 2014. "apc: A Package for Age-Period-Cohort Analysis," Economics Papers 2014-W08, Economics Group, Nuffield College, University of Oxford.
    12. 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.
    13. Jonas Harnau, 2018. "Log-Normal or Over-Dispersed Poisson?," Risks, MDPI, vol. 6(3), pages 1-37, July.
    14. 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.
    15. 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.
    16. 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.
    17. 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).
    18. 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.
    19. Bent Nielsen, 2014. "Deviance analysis of age-period-cohort models," Economics Papers 2014-W03, Economics Group, Nuffield College, University of Oxford.
    20. 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.
    21. D. Kuang & B. Nielsen, 2018. "Generalized Log-Normal Chain-Ladder," Papers 1806.05939, arXiv.org.

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