Statistical Modelling and Projection of Mortality

Statistical Modelling and Projection of Mortality
The past century has witnessed a remarkable increase in human longevity. People
alive today can expect to live much longer than their ancestors, and to enjoy better health in their old age. Although this increase in longevity can, in principle,
enable people to live longer, more active, and fulfilled lives, it has very significant social and economic implications. For example, together with a falling birth
rate, increased longevity inevitably results in an aging population, and the unsustainability of unfunded state pension systems, in which the pension benefits of the
retired are paid from the tax receipts of the working age population. Likewise, private pension providers, such as life insurance companies and occupational pension
schemes, need to take account of future improvements in mortality when pricing
and reserving for funded pension annuities.
In recent years, various authors have proposed a variety of statistically-based mortality models that attempt to capture and represent the observed decrease in mortality rates with the passage of time, and have used these models to project such
mortality improvements into the future. The review article by Booth and Tickle
(2008) presents a comprehensive overview of such models. As a review article,
it contains a large number of references and so is a useful source document for
locating literature in this field published prior to 2008. However, many models
have been developed or extended since 2008. A search of more recent literature in
this field will locate articles on these. See also the starting references below.
In this project, you are asked to undertake a comparative analysis of the applicability of a variety of different statistically-based mortality models to the mortality
data of a chosen country, comparing their ability to capture and represent the
observed improvements in mortality in that country, and to project the future
distribution of mortality in that country, by age and gender. For each model, you
should consider the validity of the model assumptions as they pertain to your data,
the goodness-of-fit of your fitted model to the data, and the forecast accuracy and
confidence intervals of the projected mortality distribution. Historical mortality
data, by age and gender, for a variety of countries, may be obtained from the Human Mortality Database (2010). Each student will be asked to select a different
country.
It is recommended that R be used for statistical analysis and graphics. R also
has some packages and functions avaiable that have been designed specifically to
implement some of these mortality models (Hyndman, 2010; Villegas et al, 2015).
Booth, H., and Tickle, L. (2008). Mortality Modelling and Forecasting: a Review
of Methods, Annals of Actuarial Science, 3, 3{43.
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Khalaf-Allah,
M. (2011). Mortality density forecasts: An analysis of six stochastic mortality
models, Insurance: Mathematics and Economics, 48, 355{367.
Haberman, S., and Renshaw, A. (2011). A Comparative Study of Parametric
Mortality Projection Models, Insurance: Mathematics and Economics, 48, 35{55.
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Human Mortality Database (2010). University of California, Berkeley (USA),
and Max Planck Institute for Demographic Research (Germany). Retrieved from
http://www.mortality.org
Hyndman, R.J. (2010). Demography: Forecasting mortality, fertility, migration
and population data. R package version 1.07. With contributions from Heather
Booth and Leonie Tickle and John Maindonald. Retrieved from
http://robjhyndman.com/software/demography
Li, H., O’Hare, C., and Zhang, X. (2015). A semiparametric panel approach to
mortality modeling, Insurance: Mathematics and Economics, 61, 264{270.
Pitacco, E., Denuit, M., Haberman, S., and Olivieri, A. (2009). Modelling Longevity
Dynamics for Pensions and Annuity Business, Oxford University Press.
Shang, H.L., Booth, H., and Hyndman, R.J. (2011). Point and interval forecasts
of mortality rates and life expectancy: A comparison of ten principal component
methods, Demographic Research, 25, 173{214.
Villegas, A.M., Kaishev, V.K, and Millossovich, P. (2015). StMoMo: an R Package for Stochastic Mortality Modelling. Retrieved from
https://cran.r-project.org/web/packages/StMoMo/vignettes/StMoMoVignette.pdf
G. Kennedy, 23/09/18