Title: Projecting UK Mortality using Bayesian Generalised Additive Models,
Abstract: Forecasts of mortality provide vital information about future populations,
with implications for pension and health-care policy as well as for decisions
made by private companies about life insurance and annuity pricing. Stochastic
mortality forecasts allow the uncertainty in mortality predictions to be taken
into consideration when making policy decisions and setting product prices.
Longer lifespans imply that forecasts of mortality at ages 90 and above will
become more important in such calculations.
This paper presents a Bayesian approach to the forecasting of mortality that
jointly estimates a Generalised Additive Model (GAM) for mortality for the
majority of the age-range and a parametric model for older ages where the data
are sparser. The GAM allows smooth components to be estimated for age, cohort
and age-specific improvement rates, together with a non-smoothed period effect.
Forecasts for the United Kingdom are produced using data from the Human
Mortality Database spanning the period 1961-2013. A metric that approximates
predictive accuracy under Leave-One-Out cross-validation is used to estimate
weights for the `stacking' of forecasts with different points of transition
between the GAM and parametric elements.
Mortality for males and females are estimated separately at first, but a
joint model allows the asymptotic limit of mortality at old ages to be shared
between sexes, and furthermore provides for forecasts accounting for
correlations in period innovations. The joint and single sex model forecasts
estimated using data from 1961-2003 are compared against observed data from
2004-2013 to facilitate model assessment.