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From atheoretical to informed mortality modelling

Published online by Cambridge University Press:  17 April 2015

D. French  and
C. O’Hare
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Abstract

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Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 21 , Issue 1 , March 2016 , pp. 95 - 96
Copyright
© Institute and Faculty of Actuaries 2015 

Summary

A recent period of low inflation and low interest rates has highlighted the importance of mortality risk to actuarial practice. In order to better understand changing patterns of mortality, the profession has recognised the need to gain insights from other disciplines and established the Mortality Research Steering Group. Our recent research funded by an Institute and Faculty of Actuaries (IFoA) Pump-priming grant follows this research agenda by incorporating insights from demography, health economics, epidemiology and financial econometrics to mortality modelling.

Stochastic mortality models exploit patterns of common variation in deaths data across ages over time. The Lee and Carter (Reference Lee and Carter1992) model provided the seminal approach to mortality modelling using a principal components analysis of mortality data with one common factor. Subsequent innovations include modelling the cohort effect (Currie, Reference Currie2006; Renshaw and Haberman, Reference Renshaw and Haberman2006), adding a second period effect (Cairns et al., Reference Cairns, Blake and Dowd2006) and adding additional factors for varying mortality improvement rates across ages (Plat, Reference Plat2009). These models are able to describe the dynamics of mortality but fail to explain and identify what has influenced historical trends and whether or not these trends will continue into the future.

Our first paper (French and O’Hare, Reference French and O’Hare2014) addresses three research questions: Can the factors found in conventional stochastic mortality-forecasting models be associated with real-world trends in health-related variables? Does inclusion of health-related factors in models improve forecasts? Do resulting models give better forecasts than existing stochastic mortality models? Using a methodology developed to put an economic interpretation on latent factors extracted in modelling business cycles (Bai and Ng, Reference Bai and Ng2002; Reference Bai and Ng2006), we identify the statistical factors used in conventional mortality forecasting models with exogenous factors deemed plausible by a separate health economics and epidemiological literature. The incorporation of the identified exogenous factors into a recently developed mortality forecasting method (King and Soneji, Reference King and Soneji2011) generally improves forecasts and gives results comparable or better than a selection of conventional models.

The second paper (French, Reference French2014) adds to a recent literature developed on modelling mortality in multiple populations together. In longevity risk contracts, a fixed amount is paid based on expected mortality rates in return for a payment based on actual realised mortality rates (a ‘q-forward’). The reference population for the purpose of pricing these products is based on the mortality experience of a given national population. However, the mortality experience of the population used in pricing the hedging instrument may differ from the population of the pension plan (Li and Hardy, Reference Li and Hardy2011; Dowd et al., Reference Dowd, Cairns, Blake, Coughlan and Khalaf-Allah2011). The purpose of this paper is to suggest a reason why mortality in different populations may be related based on an economic literature on technology and knowledge diffusion. Health technology diffusion from the US to the UK is first demonstrated. Then based on the assumptions that mortality improves in different populations as health knowledge and technology improve and that these improvements diffuse from a leader country to follower countries (Skinner and Staiger, 2009), a theoretical model is developed which identifies how health production inputs have been neglected in existing models. An empirical analysis based on US and UK mortality data validates this approach.

These studies contribute to mortality research forthcoming from interdisciplinary initiatives organised by the IFoA such as the 2009 Joining Forces conference and 2011 Emerging trends in mortality and longevity symposium. The findings will be of interest to actuaries working in the pensions and life areas where longevity risk is a significant factor which as yet has not been fully understood.

References

Bai, J. & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191–221.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2006). Evaluating latent and observed factors in macroeconomics and finance. Journal of Econometrics, 131(1–2), 507–537.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D. & Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73(4), 687–718.CrossRefGoogle Scholar
Currie, I.D. (2006). Smoothing and forecasting mortality rates with P-splines. Talk given at the Institute of Actuaries, June 2006.Google Scholar
Dowd, K., Cairns, A.J., Blake, D., Coughlan, G.D. & Khalaf-Allah, M. (2011). A gravity model of mortality rates for two related populations. North American Actuarial Journal, 15(2), 334–356.CrossRefGoogle Scholar
French, D. (2014). International mortality modelling - an economic perspective. Economics Letters, 122(2), pp 182–186.CrossRefGoogle Scholar
French, D. & O’Hare, C. (2014). Forecasting Death Rates Using Exogenous Determinants. Journal of Forecasting, 33(8), pp 640–650.Google Scholar
King, G. & Soneji, S. (2011). The future of death in America. Demographic Research, 25, 1–38.Google ScholarPubMed
Lee, R.D. & Carter, L.R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
Li, J.S. & Hardy, M.R. (2011). Measuring basis risk in longevity hedges. North American Actuarial Journal, 15(2), 177–200.CrossRefGoogle Scholar
Plat, R. (2009). On stochastic mortality modeling. Insurance: Mathematics and Economics, 45(3), 393–404.Google Scholar
Renshaw, A.E. & Haberman, S. (2006). A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38(3), 556–570.Google Scholar
Skinner, J. & Staiger, D. (2009). Technology diffusion and productivity growth in health care, National Bureau of Economic Research. Working Paper 14865.Google Scholar