Measuring inequality

Tim says that inequality falls in recessions, because top incomes are determined by market forces and so fall whilst bottom incomes are welfare benefits which, barring reforms, are fixed in real terms. The data seem to support his view; the Gini coefficient for post-tax and benefit incomes did fall slightly between 2006-07 and 2009-10.

But how meaningful are Gini coefficients? Consider the three societies in my table. All are equally rich, with an average income of 7. Which is the most unequal?

If we look at the incomes of the poor, C is unequal. There, three people have an income of half or less of median income. In B, no-one has so low an income. In A only two do.

But if we look at the gap between the rich and the median, we get the opposite ranking. Society B is highly unequal, whilst C is egalitarian.

If we take the ratio of top incomes to bottom incomes, C is most unequal and B is most equal. However, if we take the absolute gap in incomes, the opposite is true.

So, which society is the equal one? Gini coefficients cannot adjudicate here. They are all the same, by construction. In society C there are small inequalities at the top, but big ones between average and bottom. In B, there are big inequalities in the top half and small ones near the bottom. These inequalities cancel out.

I don’t think my example is contrived. You can think of society B as one with a “squeezed middle” -  individuals ranked 2 to 6 are worse off than in society A - and with “winner take all” features that generate a very wealthy minority, but with a relatively generous welfare state. If you like, it’s a New Labour society. Or if you like, it's a society in which the richest manage to get government bail-outs whilst the middle class suffers.

Society C, however, is the opposite. It‘s a bourgeois society, with a big middle class but a weak welfare state.

Which is preferable? Utilitarians can’t adjudicate, as average incomes are the same. Nor can the egalitarian who looks only at Gini coefficients, as these too are all the same. Rawlsians would prefer society B, as this maximizes the position of the worst-off member. Others, though, might prefer C, as it gives us a six in nine chance of getting an average income or better, whilst society B gives us only a four in nine chance and A gives a five in nine chance. Still others might find B least attractive, if they fear adverse social or political consequences of having a very wealthy elite, or if they have (non-consequential) libertarian objections to the large transfers that fund the welfare state.

My only point here is perhaps a trivial one - that simple measures such as Gini coefficients (or I suppose any other single measure) tell us very little about complex phenomena such as inequality. 

Comments

[Matthew]

You're right, although I think drawing a Lorenz curve helps explain the different societies (and doing so makes me prefer b)

[Jon]

Also, don't forget that the Gini co-efficient only measures monetary income. So two countries could have identical Ginis, but one might have free medical care for all citizens, free housing for all citizens, free education for all citizens, and the other might have none of these, and the two would appear to have identical levels of equality.

[Jim]

Does all this mean if (or when) the Gini rises again you won't be berating the Tories for creating rising inequality?

[Paolo]

I would argue that the answer depends on: 1) which society is more easily tractable (i.e. in reducing inequality); and 2) the multiplier effect of reduced inequality (i.e., in which society GDP will grow most when inequality is reduced).

On the first one, loss aversion suggest that Society B is less tractable, as the super-rich would resist (through lobbying or political capture)redistributive interventions. Tractability also depends on what type of social mobility do you have: either the bad type where people swaps rankings but inequality stays the same overall (zero sum game); or the good type where only low income rankings move towards the median.

This last point is strongly related to the multiplier effect of a reduction in inequality. This would suggests that in society C, libertarian objections to large transfers to lift up low-incomes could be overcome by arguing that everyone will be better of thanks to the multiplier effect. This is less likely to be the case in society B, where the super rich will likely be the residual claimant of any multiplier effects, thus undermining support from the squeezed middle-classes for this type of intervention in the first place. What I am saying is that I have the impression that Society C could be more tractable and resilient to economic shocks.

[jungle]

"Tim says that inequality falls in recessions, because top incomes are determined by market forces and so fall whilst bottom incomes are welfare benefits which, barring reforms, are fixed in real terms."

The key phrase surely is "barring reforms". As the current political debate about freezing/cutting benefits shows, such "reforms" do seem to occur in recessions. Those least able to fund campaigns against themselves bearing the cost of the recession will tend to bear most of the cost of the recession, one way or another.