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.

See more below the fold or at StochasticDemocracy.com

***Cross-posted at StochasticDemocracy.com***

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.

*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 StochasticDemocracy.com***

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#### Comment Preferences

• ##### Median Is Per Person? nt(0+ / 0-)

We are called to speak for the weak, for the voiceless, for victims of our nation and for those it calls enemy.... --ML King "Beyond Vietnam"

• ##### Sorry, let me clarify(1+ / 0-)
Recommended by:
p gorden lippy

Mean income: Add up everyone's income and divide by population. This measure get's skewed by the presence of billionaires.

Median income: 50% of the population makes more then the median income, and 50% makes less.

• ##### household incomes?(0+ / 0-)

Aren't those incomes depicted in the USA/Japan graph actually household incomes?

• ##### Eh(0+ / 0-)

Actually, they're personal incomes with a computational error. It's been fixed in the spreadsheet, but I'm fixing the graph right now. Check back in an hour or so.

• ##### Median is in the middle(1+ / 0-)
Recommended by:
davidshor

It's a value that has half of the sample population lying above half lying below.

Mean = arithmetic average

Median = in the middle (half above and half below) when the values are arranged in order from low to high (or high to low)

Mode = the most frequent value in a sample population

All are measures of the central tendency of a group of numbers.

I don't know if the numbers cited are per capita or per household. The magnitude of the values cited makes me think it's per household.

• ##### Mean vs. Median(1+ / 0-)
Recommended by:
eyesoars

The mean (or average) is the total amount of income divided by the number of people. The median is the number that is in the exact middle of incomes: 50% of the country is below and 50% is above. When the mean is much higher than the median, it means people with very high incomes are increasing the average (this is why you see a long "tail" on the right side of the graph).

This means that median income is the better measure of the absolute financial position of the middle class in a country, and the difference between mean and median is a good measure of economic inequality.

• ##### Excellent(0+ / 0-)

Tipped and recc'd

I will use this, and will credit you...thanks!

"I, for one, would like to welcome our new Belgian overlords..."

• ##### This is great!(0+ / 0-)

The more good numbers one can get on a subject, the closer one gets to the truth. Generally speaking.

Moderation in most things. Except Reactors. IFR forever!