It is well known that life expectancy has steadily and markedly increased over time in the UK. Many actuaries apparently take it as a natural law that the historic longevity trend will continue into the future.
It is well known that life expectancy has steadily and markedly increased over time in the UK. Many actuaries apparently take it as a natural law that the historic longevity trend will continue into the future. Every stochastic mortality forecast model extrapolates the observed evolution of falling mortality rates. We thereby assume that the future will be similar to the past, but what does it take to continue this trend?
Suppose the policy goal is to increase life expectancy further or, equivalently, to save as many years of life as possible. If 100 deaths could be averted, which age or age group would be the best target? The answer is simple: the younger the better, since children lose most years of life expectancy.
The problem is that the potential to reduce mortality at younger ages has been almost exhausted. Our research shows how much more effort it will take to keep life expectancy increasing at the same pace as in the past.
According to the population life table of 2013 as published by the Office for National Statistics (ONS), the most common age at death for males in England and Wales is 86. Notably, the modal age at death has increased steadily over time, while the deviation around that age has reduced. An increasing number of people die at about the same age, and these findings seem to indicate that there might be a natural limit to human life span.
In 1843, life expectancy at birth was merely 40.8 years, while by 2013 it had increased to 79.2 years. In the past 40 years, life expectancy has risen linearly by about three months per calendar year. Over this period, mortality rates were markedly reduced at all ages, mainly owing to medical advances, in particular:
- Reduced infant mortality, initially achieved through simple things like improved hygiene
- Invention of antibiotics, especially penicillin
- Measures taken to reduce the number of deaths by accident, such as the introduction of safety belts
- Reduction in mortality owing to cardiovascular disease by means of bypass operations, angioplasties and blockbuster medication.
Consequently, 99.6% of all newborn babies now survive the first year of life, 99.8% continue to live for the next 14 years and 98.4% survive between ages 15-40. The survival probability between ages 40-65 is 89.0%. These figures illustrate that we have come a long way in avoiding premature death. Figure 1 illustrates conditional survival probabilities, according to the ONS period life tables of 1843 and 2013.
These days, there is not much room left for further mortality improvements at younger ages. If all deaths prior to age 40 could be averted, life expectancy at birth would increase by only 1.3 years. Likewise, if we recorded no fatality up to age 65, then life expectancy for newborns would just rise by 4.3 years.
Since the possibility of reducing mortality at a young age has been so much diminished, future life-saving efforts must focus on the elderly.
In our research, we wanted to understand by how much the mortality rate at any given age must be decreased in order to increase life expectancy at birth by, say, one week. Using the exposed to risk in England and Wales in 2013, we calculated the number of deaths at any given age that needs to be avoided to achieve this objective. It is obvious that we only need to save a few newborns, as they would otherwise lose many years of life, while it would take saving many 80-year-olds to achieve the same effect on life expectancy at birth. We found that the effort increases exponentially with age.
We assumed that those people who die would, if saved, enjoy the same life expectancy as the rest of their birth cohort. There is no evidence as to whether that is the right assumption in this context; people of the same age may differ according to their frailty or relative risk of death. Clearly our findings would be even more pronounced if death of the elderly could only be postponed by a comparatively short period.
Figure 2 illustrates the results of our calculations. The blip in the curve relates to the irregular number of the exposed to risk in 2013, which is caused by missing births during the Second World War. In essence, we see an exponential growth of the effort required. In fact, fitting an exponential trend line yields a coefficient of determination of 0.98.
A harder climb
Life expectancy at birth has increased by about three months each calendar year for the past 40 years. This stable linear trend masks the increasing effort required to maintain it in the future. That is because the number of lives that need to be saved in order to increase life expectancy at birth by a fixed amount grows exponentially with age at death.
Mortality projection models in the life and pensions industries are often based on mortality improvement factors. It should be borne in mind that any relative change in mortality for younger ages is rather ineffective, since they are at a very low point anyway. With respect to older ages, any assumed mortality improvements require averting a large number of deaths. It is therefore questionable if even small relative changes in mortality rates for the elderly are a realistic target.
It is difficult to decrease current mortality rates, especially at older ages, because the gain in terms of additional years of life is low. It is also expensive owing to the large number of deaths at old age. It therefore becomes increasingly inefficient to keep prolonging life expectancy for the population as a whole.
In the past, life-saving actions have predominantly focused on younger people who are economically active. It remains to be seen whether we will increase our efforts and apply them to the retired population instead. If not, mortality improvement rates may level off sooner rather than later.
To keep life expectancy increasing at the same pace, it would be necessary to allocate more economic resources of our society to lifesaving of the elderly instead of wellbeing for the younger. It is not likely to happen - or is it?
Michael Ortmann is professor of mathematics at Beuth University of Applied Sciences Berlin