# Gini Coefficient

The Gini Coefficient is a number between zero and one that measures income inequality, or more generally, how non-randomly distributed a sample is. If everyone in the nation made exactly the same amount, the Gini Coefficient would be zero. If one person had all the money, it would be one. It is defined as follows:

In this equation, y is the income and i is the income bin or “slot.” One interesting thing about this is that although this equation converges to zero as all the bin values approach each other, it does not when all the bins approach zero (except one). As the number of bins increase, the equation does converge to one. Or maybe I’m wrong. I’ve checked it a couple of times and ways. I’ll look at it tomorrow with fresh eyes.

Let’s look at a five bin system: US household incomes (the lower bound) in the five quintiles:

1. \$0
2. \$18,500
3. \$34,738
4. \$55,331
5. \$88,030

Putting these numbers in the equation, we get a Gini Coefficient of 0.43.

How unequal is this? In The Great Divergence, Timothy Noah presents some data from 2005. In that year, the United States had a value of 0.37. (It is almost certainly higher now, but the main issue is that I’ve only done a rough calculation here.) There are only three countries out of the 30 in the OECD that are more unequal: Portugal (0.42), Turkey (0.43), and Mexico (0.47).

We’re number one! We’re number one!

### Update 30 June 2012 9:18 pm

This has been bugging me all day, but in fact, the equation really does seem to behave the way I said above. (I can post a proof if anyone is interested. Anyone? Anyone?[1]) I got the equation from Wikipedia. In general, Wikipedia is very good when it comes to mathematics. Anyway, if anyone can figure out the error (which is most likely mine), please let me know.

Also from the same Wikipedia page, this amazing graph of income disparity since World War II. My, what is that country with the long positive trend?

Interestingly, as far as I know, Ben Stein believes in supply side economics, otherwise known as, anyone? Anyone? Something D-O-O Economics? Voodoo economics.

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