Modeling old-age mortality risk for the populations of Australia and New Zealand: An extreme value approach

Old-age mortality for populations of developed countries has been improving rapidly since the 1950s. This phenomenon, which is often referred to as ‘rectangularization’ of mortality, implies an increased survival at advanced ages. At the time of the 2006 Census, there were 3,154 centenarians in Australia. This number is expected to increase to 17,408 by 2028, according to the Australian Bureau of Statistics. With this increase comes different challenges to actuaries, economists and policy planners. A reliable estimate of old-age mortality would definitely help them develop various demographic and financial projections. Unfortunately, data quality issues have made the modeling of old-age mortality difficult. In more detail, the number of deaths and exposures-to-risk dwindle at advanced ages, leading to large sampling errors and highly volatile crude death rates. Moreover, ages at death are often misreported. This is because today’s centenarians were born more than 100 years ago, when record-keeping was not as exhaustive as it is today. Therefore, we need a method that can extrapolate a survival distribution to extreme ages without requiring accurate mortality data for the centenarian population. In this paper, we focus on a method called the threshold life table, proposed by Li et al. (2008). The threshold life table systematic integrates extreme value theory to the parametric modeling of mortality. More specifically, it uses the asymptotic distribution of the exceedances over threshold to model the survival distribution beyond a particular age. This age, which is known as the threshold age, is chosen to ensure that the tail of the fitted distribution is consistent with the parametric graduation for earlier ages. We use the threshold life table to model the most recent period (static) mortality rates for the populations of Australia and New Zealand. We observe a good fit to the raw data for both populations. Also, the transition from a parametric graduation to an extreme value extrapolation is fairly smooth, since the estimation method focuses on both the tail and the body of the survival distribution. Further, from the fitted models we can tell in what way the life tables for the two populations should be closed. We then extend the model to predict the highest attained age, which is commonly referred to as ‘omega’ or ω in the actuarial literature, for the populations of Australia and New Zealand. On the basis of the threshold life table, the central estimates of ω for Australia and New Zealand are 112.20 and 109.43, respectively. Our estimates of ω are reasonably consistent with the validated supercentenarian in these countries.