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Biometrika Advance Access originally published online on September 15, 2008
Biometrika 2008 95(4):979-986; doi:10.1093/biomet/asn026
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© 2008 Biometrika Trust

Miscellanea

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

D. Kuang

Department of Statistics, University of Oxford, Oxford OX1 3TG, U.K., di.kuang{at}some.ox.ac.uk

B. Nielsen

Nuffield College, Oxford OX1 1NF, U.K., bent.nielsen{at}nuffield.ox.ac.uk

J. P. Nielsen

Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ, U.K., Jens.Nielsen.1{at}city.ac.uk

Received for publication 1 June 2007. Revision received 1 January 2008.
  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.

Key Words: Age-period-cohort model • Chain-ladder model • Identification


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