One reason why people are wary of increasing the age of eligibility to state pensions is perceived inequality. Some groups have lower life expectancy than the average.  This post takes one perspective on what inequality in lifespan looks like in the UK.

Life expectancy takes us only so far in telling us how long anyone might live.

• It’s not a forecast of the average lifespan in a population unless it’s a cohort life expectancy.
• It’s the average age at death in a defined population, but how long I or anyone will live depends on a whole range of factors.
• It misses information about the range of possible ages at death in a population, and inequality in lifespan is about how many people die early.

This post looks at the last point. Looking behind the life expectancy averages in recent data from the UK’s Office of National Statistics gives a more informed perspective on the distribution of lifespans.

Let’s look at two populations which represent the extreme of life expectancy in the UK’s constituent countries. Using the latest (2013-15) data: Scottish men had a period life expectancy at birth of 77.1 years and English women of 83.1 years. This means that if:

• you take a group of men born in Scotland and a group of women born in England in the period 2013-15, and,
• each of them experience the probabilities of death at each age throughout their life that were the averages in the relevant Scottish male or English female population in 2013-15, then
• the Scottish male group will die on average at age 77.1 and the English women will die on average at age 83.1.

The second point is, of course, artificial as population death rates change over time, and individuals may experience things throughout their life that increase or decrease their death rates from their starting population average.  However, we’re stuck with this artifice because we must use period life expectancies.

(We should do better by using cohort life expectancies, but these aren’t available by region. If cohort life expectancies were used they would be likely to show higher expected average lifespans – as longevity is improving – but the future gap between the population averages is harder to call.)

Even using period life data, it is possible to get a more rounded picture of what inequality looks like. Take 1,000 male babies born in Scotland in the period 2013-15 and 1,000 females born in England at the same time. The population of Scottish males is in reality much smaller to start with – there were 11 times more English baby girls born in 2015 than Scottish boys. But starting with the same number of each allows us to more easily compare what happens next.

The chart below shows the distribution of age at death for these two populations: how many are expected to die at each age, which is another way of saying how many had a lifespan of that age.

The large points on the curves are at life expectancy: 77 vs 83 years. For both groups, more people die after life expectancy than before. About 60 per cent of each group are still alive at their respective life expectancy age.

The shapes of the curves are similar but the Scottish male curve starts increasing earlier.  The advantage English females have is a postponement of age at death – their curve is further to the right.

Fewer Scottish male children survive to age 65 compared to the English girls. On this data, 836 Scottish males will live to age 65 and 915 English females. That’s 79 fewer Scottish men than English women living to age 65, from 1,000 born of each.

The mortality advantage that English women have lasts through later life. Here are the numbers alive at later ages:

	Number surviving to stated age out of 1,000 born
	Scottish men	English women	Difference
To age 65	836	915	79
To age 75	653	806	153
To age 85	334	537	203
To age 95	48	126	78
Source: longlifepensions.com using 2013-15 ONS period life tables

More English girls survive to age 95 compared to the Scottish boys. On this data, 126 English females and 48 Scottish males would be expected to live to age 95. That’s 78 more English women than Scottish men living to age 95 from 1,000 born of each.

The number of ‘extra’ English women at age 95 exceeds that of Scottish men by around the same number as at age 65, but there are proportionately more English women at ages 75 to 85.  The advantage English women have lies in lower death rates at all ages but especially at ages below age 65. This advantage accumulates to be seen in the numbers living over age 65, before the effect starts to reduce at the oldest ages.

For most populations, the curve of age at death has a similar shape of a long left hand tail, then a peak to the right hand side.  A mortality advantage or disadvantage comparison should look how far the curve sits to the right or left, and the relative ‘fatness’ of the peak, then to look beneath to see what causes the shape.

If inequality is about how many people die too early, then it is important to understand at what ages death rates are particularly high, and why, so that health policy can be directed to the causes.

A later post will consider what inequality means for age of eligibility policy. In pensions, potential inequality is not just about the age a pension might start, but also how long it needs to last.