Projecting UK mortality by using Bayesian generalized additive models

Abstract

Forecasts of mortality provide vital information about future populations, with implications for pension and healthcare policy as well as for decisions made by private companies about life insurance and annuity pricing. The paper presents a Bayesian approach to the forecasting of mortality that jointly estimates a generalized 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 UK are produced by using data from the human mortality database spanning the period 1961–2013. A metric that approximates predictive accuracy is used to estimate weights for the ‘stacking’ of forecasts from models with different points of transition between the GAM and parametric elements. Mortality for males and females is 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.