Stop using the Gini coefficient!

I have felt for a while that statistical measures of aggregate inequality, such as the Gini coefficient, are not very informative because they agglomerate two different issues: high-end inequality and low-end inequality.

Here, for example, is what I said about it in a recent book review:

"According to an old joke, a statistician whose head was on fire, while his feet were encased in a block of ice, reported that, on average, he was very comfortable.  Less well-known, however, is the kinship of a sort between this poor fellow and the Italian statistician Corrado Gini, who not only devised the famous Gini coefficient, but urged its use in measuring a given society’s aggregate income or wealth inequality.

"The problem Gini missed relates to interpretation, rather than to measurement.  Under the Gini coefficient, extreme inequality at both the top and the bottom of the social scale will not statistically offset each other, giving us a false reading of zero aggregate inequality, along the lines of the fire-and-ice example.  Instead, each will raise the quantum of inequality that the measure detects.  However, the coefficient still has the defect of amalgamating two normatively distinct phenomena in a single measure.

"Low-end inequality matters because it indicates that some people are worse-off than the rest of us.  Basic human beneficence indicates trying to help such individuals.  To be similarly concerned about high-end inequality, from the standpoint of beneficence – which would oppose making those at the top worse-off as an end in itself – one needs to make the case that it is bad for everyone else.  I myself am among those who believe that the extraordinary rise, in recent decades, of the top 0.1 percent has indeed had harmful effects on the remaining 99.9 percent.  Yet whether those of us who believe this are right or wrong, both the main issues raised by high-end inequality and the main fiscal policy (and other) instruments that one might use in addressing it, are very different than those associated with addressing low-end inequality."

The problems with using Gini were most recently brought to mind by recent discussion of a paper by Bill Gale, Melissa Kearney, and Peter Orszag which asked "how much of a reduction in income inequality would be achieved from increasing the top individual tax rate to as much as 50 percent. We calculate the resulting change in income inequality assuming an explicit redistribution of all new revenue to households in the bottom 20 percent of the income distribution. The resulting effects on overall income inequality are exceedingly modest."

One issue raised here is that raising the ordinary income rate can't do anything about all economic income that isn't subject to this rate, whether because it is treated as capital gains or remains unrealized. Likewise, taxing inheritance is not part of the exercise - whereas, whether doing so is a good idea or not, it's clearly more closely related than annual taxable income to all of the Piketty issues.

More on the Gini front, however, here is part of John Quiggin's response, which is very like-minded to my view of the topic:

"What does this [i.e., the Gale-Kearney-Orszag finding] mean? Two things:

"(i) As is well known, the Gini coefficient is a lousy measure of income inequality, much more sensitive to the middle of the income distribution than to the tails. [Note: as Quiggin acknowledges, Gale et al look at considerably more than just Gini - I am telescoping the discussion here.]

"(ii) The proposed redistribution would substantially improve the welfare of the poor, with most of the burden being borne by taxpayers in or near the top 0.1 per cent.

"It’s obvious, as the authors note, that the 90-50 measure won’t change, since neither group is affected (there’s no simulation of behavioral responses which might have indirect effects). But, since the 99th percentile income is very close to $400k, there’s very little impact on this group either. But the tax, as modeled, raises a lot of money from the ultra-rich incomes. As a result, distributing the proceeds at the bottom of the distribution raises incomes substantially, which explains the big changes in the 90-10 and 99-10 ratios.

"The real lesson to be learned here, one I came to pretty slowly myself is that old-style measures looking at quintiles or even percentiles of the income distribution are no longer very relevant. The real question, in the economy of Capital in the 21st Century is how much should go to the ultra-rich."

Or at least, I would say, that's the real question insofar as one's interest is high-end inequality in particular. (With no adverse implications for the relevance of low-end inequality.)