Measuring inequality: a story with two ends

John Hutton says:

tackling poverty is about bringing those at the bottom closer to those in the middle. It is statistically possible to have a society where no child lives in a family whose income is below the poverty line – 60 per cent of median average income – but where there are also people at the top who are very wealthy. In fact, not only is it statistically possible – it is positively a good thing.
So rather than questioning whether high salaries are morally justified, we should celebrate the fact that people can be enormously successful in this country. Rather than placing a cap on that success, we should be questioning why it is not available to more people.

Ruth Lister responds:

On the question of inequality, the only real difference between Hutton’s ‘new progressive individualism’ and Thatcher’s reactionary individualism would appear to be that he is at least concerned about poverty. But his attempt to square his enthusiasm for inequality without limit with Labour’s commitment to the eradication of child poverty rests on shaky ground.
It may be the case that it is ‘statistically possible to have a society where no child lives in a family whose income is below the poverty line…but where there are also people at the top who are very wealthy’. However, it is not very likely. Cross-national analysis shows that poverty and the persistence of poverty are closely related to inequality: contrast the Nordics with the UK and the US. … It is easier to climb a ladder where the rungs are closer to each other and where the top is not detached from the bottom, as it is here.

The concepts of ‘poverty’ and ‘inequality’ (particularly where the former is defined partly in terms of the latter) are liable to tie people in knots.

Hutton’s right, statistically speaking, but Lister’s reply on that point is also right. Although being “at least concerned about poverty” is a bigger difference than she credits: Thatcherites didn’t care how rich the rich got or how poor the poor got; one of those attitudes is far more harmful than the other.

There’s research strongly suggesting that inequality causes personal and social ills over and above the effects of absolute levels of prosperity/poverty; this happens all the way through the income distribution, with fairly rich people stressed about keeping up with the very rich people.

But I’d argue that inequality lower down the scale is worse than that at the top: very poor people have disadvantage resulting from both their absolute and their relative conditions, whereas those on middle or moderately above average incomes only have one of these problems.

On the other hand, a society in which everyone had the same amount of money would be a disaster, and nobody seriously proposes it. I’m not aware of any attempt to calculate an optimum level of inequality.

Here’s the thing, though: economic inequality is not one single phenomenon, and trying to treat it as such will result in confusion. The Gini coefficient, for instance, is commonly used to measure overall inequality: if one person in a society has all the money, the Gini is 1; if everyone has the same amount of money, it is 0.

But this doesn’t distinguish between inequality caused by those at the top racing farther ahead and that caused by those at the bottom falling farther behind. These two phenomena have different causes, different consequences and (if they are both seen as problems) different solutions. Lister talks about “a ladder where the rungs are closer to each other” – but in fact rungs at different heights of the ladder have different gaps between them.

If there are different types of income inequality at each end of the scale, then any measurement of these has to be done separately.

Here’s a suggestion: divide the population into, say, the poorest 20%, the richest 20% and the middle 60%. Then work out separate Gini values for each of those three groups. I’d expect the middle value normally to be lower than the two end ones.

For an indication of differences within income groups, look at this chart [PDF, page 6] from the IFS:


The alternating dark and light areas represent successive deciles of the income distribution (ignore the individual bars and their heights). The middle deciles are narrow, meaning that those people’s incomes are quite similar; the sections widen as you go higher up the scale (which is perhaps only to be expected given that this chart shows cash differences rather than percentage differences). But the really wide ones are at the top and bottom, so the high- and low-income Ginis would be larger than the middle-income one.

A particularly large low-income Gini will mean that those at the bottom are a long way behind; a very large high-income Gini will mean those at the top shooting ahead.

I’m assuming that some unspecifiable degree of income inequality is a good thing (consultants earn more than nurses, etc.). I’m also assuming that a very steep slope simply won’t exist across the whole of the income scale – in the middle, a lot of people are bound to be bunched not too far apart. So we can use the level of inequality in the middle as a baseline for measuring those at either end.

We could then compare countries (or the same country over time) using the ratio between the low-income and middle-income Ginis: a higher ratio means that the income distribution becomes very unequal as you get to the bottom. Similarly for the rich-to-middle ratio.

Then, rather than arguing for the reduction of ‘inequality’ per se, one could argue that inequality at the top and/or bottom shouldn’t be so much higher than that in the middle. (Indeed, some proposals to provide a minimum income could result in a much smaller Gini at the bottom.)