Messing with the Gini
By Douglas D. Rose
from: Rebottling the Gini: why this headline measure of inequality misses everything that matters
Capitalism is killing less fortunate citizens. We will never understand how if we continue to reduce discussion about the economic gap to a single—and flawed—statistic
by Angus Deaton and Anne Case / January 27, 2020 /
https://www.prospectmagazine.co.uk/magazine/rebottling-the-gini-why-this-headline-measure-of-inequality-misses-everything-that-matters
“For the Gini, the way an individual’s income affects the index depends on their rank in the distribution and not directly on their income. If we take money from the poorest and give it to the richest, the increase in the Gini is the same no matter whether the richest person is a millionaire, a billionaire, or a multibillionaire, and this insensitivity is something to which we might reasonably object.”
[Deaton and Case argue that billionaires are the problem, hence the Gini Index is a bad measure]
The statement is not true. The Gini Index is a coefficient of variation, a measure of dispersion divided by the average. The measure of dispersion is the average absolute difference between pairs. The least dispersion is when everyone is equal, all pair differences are zero, and the Gini Index is zero. “if we take money from the poorest and give it to the richest,” in this case meaning taking from anyone and giving it to anyone else, we will have produced inequality and the Gini Index will NOT be the same, it will show more inequality.
This is generally true. In a population that includes a millionaire, a billionaire, and a multibillionaire, taking from the poor and giving to the rich will increase the differences for all pairs involving the poorest and from most pairs involving the rich. But it matters how rich the recipient is, because if the millionaire receives the funds, it will reduce his difference with the billionaire and multibillionaire, hence show less overall difference, and a lower Gini Index, than if the funds had gone to someone richer. In general, the statement is false. And so is the conclusion, that the Gini Index is a bad measure of inequality, at least for the stated reason that it doesn’t care enough about how rich the richest are.
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