A study on link functions for modelling and forecasting old-age survival probabilities of Australia and New Zealand

Forecasting survival probabilities and life expectancies is an important exercise for actuaries, demographers, and social planners. In this paper, we examine extensively a number of link functions on survival probabilities and model the evolution of period survival curves of lives aged 60 over time for the elderly populations in Australasia. The link functions under examination include the newly proposed gevit and gevmin, which are compared against the traditional ones like probit, complementary log-log, and logit. We project the model parameters and so the survival probabilities into the future, from which life expectancies at old ages can be forecasted. We find that some of these models on survival probabilities, particularly those based on the new links, can provide superior fitting results and forecasting performances when compared to the more conventional approach of modelling mortality rates. Furthermore, we demonstrate how these survival probability models can be extended to incorporate extra explanatory variables such as macroeconomic factors in order to further improve the forecasting performance.