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:

Gini Coefficient Equation

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?

Income Disparity Since WWII

[1] From Ferris Bueller’s Day Off:

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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About Frank Moraes

Frank Moraes is a freelance writer and editor online and in print. He is educated as a scientist with a PhD in Atmospheric Physics. He has worked in climate science, remote sensing, throughout the computer industry, and as a college physics instructor. Find out more at About Frank Moraes.

0 thoughts on “Gini Coefficient

  1. …There can be no doubt that the wealth gap in the United States has isanecred dramatically over recent years. It is my opinion that the gap is already unsustainable. Unfortunately, the gap is increasing and shows little sign of narrowing.As many know, I believe the isanecred wealth gap is the result of fundamental shifts in America’s economic landscape. These shifts include, but are not limited to, technological advances that obviate the need for labor and the ease of shipping American jobs to low cost overseas labor markets.While taxing the rich would succeed in taking away money from the top of the economic ladder it will not provide meaningful work for those lower on the ladder. Rather, it will further empower a corrupt and incompetent government by providing yet more money to be squandered by lifelong politicos and bureaucrats. In other words, the wealth gap will be lessened by making everybody poorer.Arguably, money could be taken from the top and simply redistributed to those lower on the ladder. Almost 50% of American households pay no income tax already so this is already a work in progress. My Dad used to say that idle hands are the devil’s playthings. I think he was right. What kind of society will exist if a relatively small percent works and generates the wealth while a relatively large percent lives on government hand outs? Not a very good society, I’d say.So, what options do we have between wholesale wealth redistribution and a society of a few "haves" with many "have nots"? I believe there are a number of options:1. Aggressively enforce our immigration laws. Illegal immigration of uneducated people increases the supply of those with limited work skills thereby depressing the wages of those at the bottom of the economic ladder. Illegal immigration keeps the poor poor.2. Encourage collective bargaining. It is imperative that people willing to put in an honest day’s work receive an honest day’s wage. Creating a societal rung of working poor makes the wealth gap worse and discourages people from seeking employment. Discouraged people make for poor citizens and poor parents.3. Tax businesses who export jobs to low cost countries. Many of the countries where our jobs are being shipped use various techniques to create uneven playing fields. The Chinese use currency manipulation for example. America’s corrupt political elite is one of the only entities in the world willing to sell out its own people in order to curry favor with well heeled special interests. This must end.4. Reinvent education. I list this last because it is the least important. Our educational system is broken, there is no doubt. However, even even if the system could be fixed tomorrow the impact of that fix would not be felt for years. Additionally, excessive focus on the education system provides a relatively painless alternative to taking the short term actions required to address the wealth gap. Too many use education as a crutch to avoid other, more difficult decisions.As I’ve written before – I am open to alternate, practical and timely alternatives to addressing the wealth gap in the United States. So far, I have heard none.4/21/11 12:25 PM

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