Sunday, December 30, 2012

Some inequalities are more unequal than others

John Rentoul and others have been talking about economic inequality. John argues that the Gini coefficient is “the only statistical measure that captures the full extent of inequality in any population. Any other measure, such as 60 per cent of median income or the ratio between the 10th and 90th decile points, would fail to do this.”
In a sense that’s true, but for me the Gini coefficient’s strength is also its weakness. It gives you a single number for inequality in a population (from 0, meaning everyone is completely equal, to 1, meaning one person has everything) – but it can’t tell you whether that inequality is because the people at the bottom are a long way behind or the people at the top are a long way ahead.
For instance, these two sets of numbers both have a Gini of 0.13:
  • 5, 21, 22, 23, 24, 25, 26, 27, 28, 29
  • 21, 22, 23, 24, 25, 26, 27, 28, 29, 52
If we want to measure economic inequality meaningfully, we mustn’t treat it as a single phenomenon. If the very rich are racing ahead, then that’s quite a different thing from the very poor falling behind. These two phenomena have different causes and different consequences – and, if we want to do anything about them, different policies will be needed.
So I propose that rather than looking at a single Gini coefficient for everyone, we break the population down into, say, fifths. We look at the Gini among each group, from the poorest to the richest, and see how they compare.

What follows is a very crude attempt to do that (this post develops an idea I had a few years ago).
I start with this chart from the Institute for Fiscal Studies [PDF], showing household income for different percentiles of the population:
Unfortunately, the numbers that went into the chart aren’t given. So by measuring the size of the bars (I told you it was crude), I’ve reconstructed it:
It looks about right. Note that I’ve added a bar for the richest 1%, not shown in the original – perhaps because those people are hard to get data on. I’ve assumed that the gap between 99 and 100 is the same size as the gap between 98 and 99 (which I’m sure is a conservative assumption).
And, treating each percentage point as an individual, the Gini coefficient for these 100 numbers is 0.33. The IFS report gives the Gini for the whole population as 0.34, so again, I feel confident that my reconstruction of the numbers is about right.
Now I can break this down into five groups, from the poorest 20% to the richest, and calculate and compare the Gini coefficients across the spectrum:
The greatest inequalities are at the top and the bottom of the scale. To see the size of these, we can look at ratios: the Gini at the bottom is 3.6 times as high as the middle one; the Gini at the top is 4.9 times the middle one.
It would be good to see how these ratios have changed over time, and how they vary between countries. But here I really do run out of even approximate data. If better people than me agree that this approach is worthwhile, then I encourage them to give it a go.
One thing I feel confident in saying, though: John reproduces an IFS chart showing the distributional impact of government policies, and guesses that “overall inequality, as measured by the Gini coefficient, would be more or less unchanged”.
Maybe. But taking my approach, the government’s policies look like they’ll reduce the Gini at the top and increase it at the bottom and in the middle. The gap between the very rich and the fairly rich may fall, but all other gaps will grow.

1 comment:

Liam Murray said...

The fundamental problem with gini - as you point out - is the lack of context and I can't see how this approach does anything (anything material anyway) to address that?

Worth reading the JRF's Minimum Income Guarantee work each year - almost comical the lengths they go to trying to label certain things as 'essential' while others are not. From recollection last year unlimited home wifi was but a mobile still isn't...