Rethinking age-period-cohort mortality trend models

Abstract

Longevity risk arising from uncertain mortality improvement is one of the major risks facing annuity providers and pension funds. In this article, we show how applying trend models from non-life claims reserving to age-period-cohort mortality trends provides new insight in estimating mortality improvement and quantifying its uncertainty. Age, period and cohort trends are modelled with distinct effects for each age, calendar year and birth year in a generalised linear models framework. The effects are distinct in the sense that they are not conjoined with age coefficients, borrowing from regression terminology, we denote them as main effects. Mortality models in this framework for age-period, age-cohort and age-period-cohort effects are assessed using national population mortality data from Norway and Australia to show the relative significance of cohort effects as compared to period effects. Results are compared with the traditional Lee–Carter model. The bilinear period effect in the Lee–Carter model is shown to resemble a main cohort effect in these trend models. However, the approach avoids the limitations of the Lee–Carter model when forecasting with the age-cohort trend model.

Keywords:

• mortality modelling
• age-period-cohort models
• generalised linear models
• Lee–Carter models

Acknowledgements

The authors would like to acknowledge the financial support of ARC Linkage Grant Project LP0883398 Managing Risk with Insurance and Superannuation as Individuals Age with industry partners PwC, APRA and the World Bank as well as the support of the Australian Research Council Centre of Excellence in Population Ageing Research (project number CE110001029). The authors are also indebted to the comments of an anonymous reviewer that led to improvements in both the clarity and structure of this article.