## The standard Gini coefficient – a misleading measure of inequality

7 May, 2013 at 09:19 | Posted in Statistics & Econometrics | 1 CommentIt is by now generally accepted that the sharp rise in income and wealth inequality in the US and much of Western Europe over the 1990s and 2000s was one of the bulldozer forces behind the rise in financial fragility. And it has long been accepted that the Gini coefficient is the workhorse measure of inequality. But it is not generally recognized that the coefficient is normally defined in a way which biases the measure in a

downwarddirection, making inequality seem less large than another version of the coefficient would suggest. By this alternative measure inequality is much higher than is generally thought. The standard measure is misleading us into thinking that economic growth is more “inclusive’ than it is.Recall that the Gini coefficient is a number between zero and one that measures the degree of inequality in the distribution of income in a given society (named after an Italian statistician, Corrado Gini). The coefficient is zero for a society in which each member receives exactly the same income; it reaches its maximum value (bounded from above by 1.0) for a society in which one member receives all the income and the rest nothing.

As normally defined the Gini says that inequality remains constant—growth remains ‘inclusive’—if all individuals (or countries by average income) experience the same

rateof growth, and rises only when upper incomes grow faster than lower incomes. So inequality remains constant if a two person (or two country) distribution x = (10, 40) becomes y = (20, 80). Yet the income gap has grown from 10 to 40.It is at least as plausible to say that inequality remains constant—growth remains inclusive—when all individuals (countries) experience the same

absoluteaddition to their incomes; say from x = (10, 40) to y* = (20, 50). If upper income individuals (countries) experience bigger absolute additions, inequality increases, and growth is not inclusive.The normal Gini could be called the Relative Gini. The Gini based on absolute changes could be called the Absolute Gini—defined as the Relative Gini multiplied by the mean income. In the above illustration, the Relative Gini for both distributions is the same, at 0.3. But as mean income doubles from 25 to 50 in the transition from x to y, the Absolute Gini doubles, from 7.5 to 15.0.

The Absolute Gini typically rises much more frequently and by much more than than the Relative Gini, and its use would make ‘income inequality’ into a more salient political issue. For obvious reasons, the Relative Gini could be called a ‘rightist’ measure, and the Absolute Gini a ‘leftist’ measure …

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To me, (10, 20) is more unequal than (40, 50); and I’m a “leftist”! Interesting, though.

Comment by Alex Hanin— 7 May, 2013 #