The linear link: deriving age-specific death rates from life expectancy

The prediction of human longevity levels in the future by direct forecasting of life expectancy offers numerous advantages, compared to methods based on extrapolation of age-specific death rates. However, the reconstruction of accurate life tables starting from a given level of life expectancy at birth, or any other age, is not straightforward. Model life tables have been extensively used for estimating age patterns of mortality in poor-data countries. We propose a new model inspired by indirect estimation techniques applied in demography, which can be used to estimate full life tables at any point in time, based on a given value of life expectancy at birth. Our model relies on the existing high correlations between levels of life expectancy and death rates across ages. The methods presented in this paper are implemented in a publicly available R package

Mortality Modeling

Mortality models approximate mortality patterns or dynamics over age and time. An age pattern of mortality can be any mathematical function of mortality, such as rates, probabilities, survivorship, or death distributions. Such functions may be modeled in the form of a life table or a simplified function with some parameters. Mortality models in general fall into three main categories: (i) models designed to help understand regularities in mortality patterns and dynamics, for example where population-level mortality patterns are modeled as an emergent property of dynamics at the individual level, (ii) those that aim to predict mortality patterns, for example for purposes of pension provisions, and (iii) those aimed at mortality measurement for purposes of mortality and health monitoring. In the following, mortality modeling refers to models of mortality measurement at the population level

Introduction

Globally, the twenty-first century will witness rapid population ageing. Already in 2050, one out of five persons in the world, and one out of three in Europe, is expected to be 60 or over (UN 2015). Moreover, we have entered into a new stage of population ageing in terms of its causes, which have altered its consequences. In the first stage, lasting until the middle of the twentieth century in developed countries, population ageing was entirely due to the decline in fertility, with Sweden being commonly used as an example (Coale 1957; Bengtsson and Scott 2010; Lee and Zhou 2017). During this stage, the increase in life expectancy was primarily driven by declines in infant and child mortality. It worked in the opposite direction to the fertility decline, making the population younger since it added more years before, than after retirement (Coale 1957; Lee 1994). In the second stage of population ageing, which is the current situation, population ageing is primarily driven by the increase in life expectancy, which is now due to declining old-age mortality. As a result, more years are added after retirement than in working ages (Lee 1994). Could immigration or an upswing in fertility stop population ageing? The short answer is most likely not. The effect of migration on population aging is generally regarded as minor (Murphy 2017), and since population ageing is a global phenomenon, it will be of no general help anyway. A rapid increase in fertility is improbable and, in any case, an increase would take some 25 years before adding to the labor force. Instead, attention has been focused on how to adapt our social systems to the increasing number of elderly per worker – more so since the increase in the elderly-per-worker ratio came in parallel with a rise in per capita costs for the institutional care, home care, and general health care for the elderly