Observations on the world today.

Sunday, April 25, 2004

Gini Coefficient in a Bottleneck 

The Gini coefficient is defined as
a number between 0 and 1, where 0 means perfect equality (everyone has the same income) and 1 means perfect inequality (one person has all the income, everyone else earns nothing).
Of course, this is an exagerated simplification, but I will explain more on that soon. The Gini Coeficient is determined by first plotting a curve called the Lorenze curve which is defined as:
a graph that shows, for the bottom x% of households, the percentage y% of the total income which they have. The percentage of households is plotted on the x axis, the percentage of income on the y axis.

A perfectly equal income distribution in a society would be one in which every person has the same income. In this case, the bottom N% of society would always have N% of the income. Thus a perfectly equal distribution can be depicted by the straight line y=x; we call this line the line of perfect equality.

A perfectly inequal distribution, by contrast, would be one in which one person has all the income and everyone else has none. In that case, the curve would be at y=0 for all x<100, and y=100 when x=100. We call this curve the line of perfect inequality.
An example of a Lorenze curve is given on the linked page and looks like this:

If everyone had the same income, the red line would travel along the green line and the Gini would equal zero. If all of the money was in the hands of a single individual, the red line would travel along the base line and up the blue line on the right, and the Gini would equal one.

To determine the Gini, the total area of the triangle formed by the green, blue and base lines is divided by the total area inside the curve or the area defined by the green and red lines. Then that number is converted into a decimal. I estimate that in this example, the curve has an area of roughly 3.915% of the triagle, so it has a Gini of roughly .3915.

However, according to the US census bureau, this country has not had a Gini that good since well before 1985. (See page 32 of this pdf) The most recent Gini is .462 and that is based on the disparity in incomes in this country, which has been growing at an alarming rate. The current disparity levels are as follows:
Lowest quintile = 3.5% of overall income
Second quintile = 8.8% of overall income
Third quintile = 14.8% of overall income
Fourth quintile = 23.3% of overall income
Highest quintile = 49.7% of overall income
The groups who have been hit the hardest by this widening gap in the last few years have been the second and third quintiles. Since Bush took office, these two groups have seen their actual income levels drop 5.8% and 3% respectively. And that is not even adjusted for inflation, which would probably make it worse.

Incidentally, if you want to se that Gini plotted on a Lorenz curve:

Okay, that's probably not accurate. Hey, gimme a break. I'm not a mathematician.

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