Friday, March 19, 2010

Income Distributions around the World

In my last, and much lighter post Who cares about the average income! I talked about the heavy tailed nature of income distributions. Here’s a link to some actual income distributions for the USA, India, Japan and France (scroll all the way to page 3 and look at Figure 1 on that page). Of course, the data for India includes only that of taxpayers and most of India has insufficient income to pay taxes so this is grossly misrepresentative. And unfortunately, the authors also note that the Indian data, even for taxpayers, is incomplete relative to the other countries for the reason that: “In spite of the best of our efforts in collecting the equivalent data from the Income Tax Department of the Government of India or the Reserve Bank of India, we are unable to give or compare with any better data”.

But before you eagerly click on the link, note that when you take a heavy tailed distribution that looks like the graph on the left below (where the number of people that have a particular income is equal to that income raised to some negative power) and convert the axes into log units it turns into a straight line which is easy to recognize visually.

Since many income distributions tend to have such power law properties (misleadingly called a power law since there is no law here, it is just a power relationship), they are generally shown in the log-log coordinate form to easily be able to distinguish them from other kinds of heavy tailed distributions which are not power laws.

It’s a pity that power law distributions are not taught alongside the normal distribution in school since if you work with them a few times they become as easy to intuit. More importantly though is that this arrangement describes so much of nature and society that we would gain a much better understanding of our world.

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