Modelling and forecasting adult age-at-death distributions

Abstract

Age-at-death distributions provide an informative description of the mortality pattern of a population, but they have generally been neglected for modelling and forecasting mortality. In this article, we use the distribution of deaths to model and forecast adult mortality. In particular, we introduce a relational model that relates a fixed "standard" to a series of observed distributions by a transformation of the age axis. The proposed Segmented Transformation Age-at-death Distributions (STAD) model is parsimonious and efficient: using only three parameters, it captures and disentangles mortality developments in terms of shifting and compression dynamics of mortality. In addition, mortality forecasts can be derived from parameters' extrapolation using time series models. We illustrate and compare our methodology with the Lee-Carter model and its variants for females in four high-longevity countries. We show that the STAD fits very well the observed mortality pattern, and that its forecasts are more accurate and optimistic than the Lee-Carter variants.

A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality

“…De Beer and Janssen (2014) also introduced an additional generalization of the Heligman and Pollard model, which also includes 10 parameters. An additional work to mention corresponds to Basellini and Camarda (2016), who showed that the distribution of deaths can be employed to understand the transformations of mortality, in particular shifting and compression of adult deaths.…”

An age-at-death distribution approach to forecast cohort mortality

“…We align each density to the distribution of the first cohort (1835), and derive f (x) as the mean of the aligned distributions. This landmark registration procedure has been suggested elsewhere as it enhances the representativeness of f (x) while improving the goodness-of fit of the model (for additional details, see Basellini and Camarda, 2019). Importantly, it should be noted that for cohorts in c 2 and c 3 , we only use the part of the aligned distribution corresponding to the observed data (i.e.…”

“…Rather than modelling mortality rates (the standard approach in mortality forecasting, as in, for example, the Lee and Carter model and its variants), our model is based on the distribution of deaths. Ageat-death distributions have recently received increasing attention in mortality forecasting (Oeppen, 2008;Bergeron-Boucher et al, 2017;Basellini and Camarda, 2019;Pascariu et al, 2019), as they provide a different and rather unexplored perspective on mortality developments that can be leveraged by forecasters. For this reason, we extend a newly introduced methodology to model and forecast adult age-at-death distributions (Basellini and Camarda, 2019) with the aim of analyzing and forecasting mortality developments across cohorts.…”

Projecting delay and compression of mortality

“…Because capturing mortality delay and compression can provide insight into adult mortality trends, it is desirable for a mortality model to have this ability (de Beer and Janssen 2016; Basellini et al 2016;Bergeron-Boucher et al 2015). As the LC model cannot decompose the compression and delay effect, it cannot identify the influence of compression and delay in life expectancy improvements.…”