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A quick trick to approximate income distributions for countries using easily available data, a ranking of estimated medians, discussion, and an interactive spreadsheet available for download.

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***Cross-posted at***

Matthew Yglesias notes

— The internet should make it easier to do an international comparison of median income. I can’t find one.

There really is a paucity of data on median income for countries other then the US.

Luckily, it's pretty easy to find Gini Coefficients for a number of countries, as well as GDP per Capita(which roughly approximates average income). Fisk distributions* are commonly used by economists to model income inequality and have been shown to do a satisfactory job. Assuming that income is distributed under a fisk distribution, then the mean and gini coefficient provide enough data to estimate the median.

Examples of the Fisk Distribution for different parameters[Wikipedia]

Conveniently, this method also allows us to estimate 30th percentiles, shares of income going to the top 10%, as well as a bunch of other measures of inequality.

Testing this method against the countries where median and average income data was available, it's generally accurate to around 5%.  This isn't perfect, but it's useful for purposes of international comparison.

For example, very poor countries are often the ones with the highest income inequality, and so looking at mean income creates an unintuitively large bias. Take a look at Afghanistan:

Estimated income distribution of Afghanistan

It also serves to illustrate the point that due to America's high income inequality, median incomes are not as high as one would expect from our very GDP per capita.  Compare America's estimated income distribution with that of The Netherlands:

Estimated income distribution of The Netherlands and the US. Rescaled for visibility.

By Median, the US is 6th, just behind The Netherlands. For full rankings, I've made a spreadsheet available that shows the mean, median, and mode for 157 countries, as well as an applet that shows calculates arbitrary income percentiles and distributions. It can be downloaded here.

Screenshot from spreadsheet applet available for download.

*There are empirical reasons to believe the Singh-Maddala distribution would do a slightly better job, but the math involved in estimation becomes a lot trickier. The larger problem is the discrepancy between GDP per capita and mean income. Does anyone have a good source for average income or consumption? It's a component of GDP(Consumption+Investment+Exports-Imports), so the data has to be out there somewhere...

Update: Thanks to Regav for providing a link to OECD data for income distributions. This closes the discrepancy between GDP per capita and income that I was worried about, and has made the spreadsheet a lot more useful. Graphs and numbers updated. A spreadsheet showing median income for the OECD block of developed countries can be found here.

***Cross-posted at***

Originally posted to davidshor on Mon Jan 18, 2010 at 03:42 PM PST.

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