Abstract
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.
Highlights
The average human lifespan has been increasing consistently throughout the developed nations in the last hundred years or so
In Australia, period life expectancy at age 60 has grown from 16.5 years in 1950 to 25.0 years in 2017; in New Zealand, it has increased from 16.9 years in 1950 to 24.0 years in 2013
We have conducted a thorough examination on several old and new link functions for their applications in modelling how old-age survival probabilities evolve across time in Australasia
Summary
The average human lifespan has been increasing consistently throughout the developed nations in the last hundred years or so. The increasing area under the survival curve over time refers to the extent of rectangularisation This concept is one of the major analytical frameworks in demographic research and can be further adapted to describe past changes in survival levels and predict future survival rates. Hatzopoulos and Haberman (2015) used the complementary log-log link function and age-cohort effects within the duce this knowledge gap by examining extensively a number of link functions on survival probabilities and modelling the evolution of the parameters and so the survival rates over time. We attempt to reduce this knowledge gap by examining extensively a number of link functions on survival probabilities and modelling the evolution of the parameters and so the survival rates over time. To the best of our knowledge, our paper provides the first attempt to incorporate macroeconomic factors into the survival rate projection models.
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