Mortality Density Forecasts: An Analysis of Six Stochastic Mortality Models

Andrew J. G. Cairns, David Blake, Kevin Dowd, Guy D. Coughlan, David Epstein, and Marwa Khalaf-Allah

We investigate the uncertainty of forecasts of future mortality generated by a number
of previously proposed stochastic mortality models. We specify fully the stochastic
structure of the models to enable them to generate forecasts. Mortality fan charts
are then used to compare and contrast the models, with the conclusion that model
risk can be significant.

The models are also assessed individually with reference to three criteria that focus
on the plausibility of their forecasts: biological reasonableness of forecast mortal-
ity term structures; biological reasonableness of individual stochastic components of
the forecasting model (for example, the cohort e®ect); and reasonableness of forecast
levels of uncertainty relative to historical levels of uncertainty. In addition, we con-
sider a fourth assessment criterion dealing with the robustness of forecasts relative
to the sample period used to ¯t the model.

To illustrate the assessment methodology, we analyse a data set consisting of national
population data for England & Wales, for Males aged between 60 and 90 years
old. We note that this particular data set may favour those models designed for
application to older ages, such as variants of Cairns-Blake-Dowd, and emphasise
that a similar analysis should be conducted for the specific data set of interest to
the reader. We draw some conclusions based on the analysis and compare to the
application of the models for the same age group and gender for the United States
population. Finally, we note the broader application of the approach to model
selection for alternate data sets and populations.

Keywords: Stochastic mortality model, cohort erect, fan charts, model risk, fore-
casting, model selection criteria.

Analyses of proposed reforms and the viability of immigration based policies in response to ageing demographics

Krishna Kotecha


This paper briefly examines the options for reform proposed by the Pensions Commission in 2004 to sustain the UK state pension system in response to an ageing population. It further explores, under various scenarios, the long-term viability of immigration as an alternative policy response by developing a population projection
model to determine the replacement migration levels that would be required to maintain contributions (taxes) at current levels, using population data and assumptions in the public domain. The economic and social implications of immigration-based policies are also considered.

The results indicate that not only does each policy option proposed by the Pensions Commission require changes that are too large for the policy to be implemented on its own, but that a combination of options too is likely to require discomforting changes at the individual level when considered under plausible scenarios. Economic and social implications aside, the results also indicate that immigration is an inefficient and ineffective way of salvaging an ageing society. The required replacement migration levels are abnormally high and too volatile for it to be considered as a viable policy alternative.

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