Modelling mortality: are we heading in the right direction?

ABSTRACT

Predicting life expectancy has become of upmost importance in society. Pension providers, insurance companies, government bodies and individuals in the developed world have a vested interest in understanding how long people will live for. This desire to better understand life expectancy has resulted in an explosion of stochastic mortality models many of which identify linear trends in mortality rates by time. In making use of such models for forecasting purposes, we rely on the assumption that the direction of the linear trend (determined from the data used for fitting purposes) will not change in the future, recent literature has started to question this assumption. In this article, we carry out a comprehensive investigation of these types of models using male and female data from 30 countries and using the theory of structural breaks to identify changes in the extracted trends by time. We find that structural breaks are present in a substantial number of cases, that they are more prevalent in male data than in female data, that the introduction of additional period factors into the model reduces their presence, and that allowing for changes in the trend improves the fit and forecast substantially.

KEYWORDS:

• Mortality
• stochastic models
• structural breaks
• forecasting

JEL CLASSIFICATION:

• C51
• C52
• C53
• G22
• G23
• J11

Acknowledgements

We are grateful to Professor Rob Hyndman for useful comments received on drafts of this article. Financial support for Li from the Australian Research Council (ARC) under Discovery Grant (DP130103210) is gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The interested reader is referred to O’Hare and Li (2015).

² We note that recently there are models focused on differences or ratios in mortality rates in an effort to make the underlying time-series components more stationary, see, for example, Haberman and Renshaw (2012, 2013) and Mitchell et al. (2013).

³ This can be found at http://www.mortality.org/ and was accessed in June 2013. The database is maintained in the Department of Demography at the University of California, Berkeley, USA, and at the Max Planck Institute for Demographic Research in Rostock, Germany.

Additional information

Funding

This work was supported by Australian Research Council (ARC) under Discovery Grant (DP130103210) is gratefully acknowledged.