Mortality Projections using Generalized Additive Models with applications to annuity values for the Irish population

Generalized Additive Models (GAMs) with age, period and cohort as possible covariates are used to predict future mortality improvements for the Irish population. The GAMs considered are the 1-dimensional age + period and age + cohort models and the 2-dimensional age-period and age-cohort models. In each case thin plate regression splines are used as the smoothing functions. The generalized additive models are compared with the P-Spline (Currie et al., 2004) and Lee-Carter (Lee & Carter, 1992) models included in version 1.0 of the Continuous Mortality Investigation (CMI) library of mortality projections. Using the Root Mean Square Error to assess the accuracy of future predictions, the GAMs outperform the P-Spline and Lee-Carter models over intervals of 25 and 35 years in the age range 60 to 90. The GAMs allow intuitively simple models of mortality to be specified whilst also providing the flexibility to model complex relationships between the covariates. The majority of morality improvements derived from the projections of future Irish mortality yield annuity values at ages 60, 65, 70 and 80 in 2007 in the range of annuity values calculated, assuming a 2 to 4 percent annual compound improvement in mortality rates for both males and females.