# Wanted: a stats Gini-us

January 25, 2008 4:34 AM Subscribe

It ought to be possible (though I know it's going to be inaccurate) to estimate the number of people earning above a certain level using a given country's GDP and Gini Coefficient. Can you help me work through the details?

I know Gini tells us less than everything about the actual shape of the distribution of income, but assuming the simplest, smooth curve, shouldn't some sort of guesstimate possible?

The final datapoint that I want for each country is the proportion of people earning above $100,000 in any given country (which I'll then multiply by population).

How would you actually do it, using Excel or whatever?

For context, this is feeding into a rough analysis of the market for a certain premium good in various countries.

Gini Coefficients around the world are listed here.

Thanks in advance!

PS. This is most certainly not a homework question, but a rather pressing business matter. My head's on the block.

I know Gini tells us less than everything about the actual shape of the distribution of income, but assuming the simplest, smooth curve, shouldn't some sort of guesstimate possible?

The final datapoint that I want for each country is the proportion of people earning above $100,000 in any given country (which I'll then multiply by population).

How would you actually do it, using Excel or whatever?

For context, this is feeding into a rough analysis of the market for a certain premium good in various countries.

Gini Coefficients around the world are listed here.

Thanks in advance!

PS. This is most certainly not a homework question, but a rather pressing business matter. My head's on the block.

The Gini Coefficient tells us the difference between a perfectly equal distribution of income, and hte actual distribution of income. I thought that by making an assumption about the shape of that distribution, and relating it to the actual size of GDP, you might be able to find out how many people earn more than, e.g. $100,000.

Currently, however, I'm just floundering around in numbers, and wondering if anyone has suggestions for actually calculating that proportion.

posted by godawful at 6:01 AM on January 25, 2008

Currently, however, I'm just floundering around in numbers, and wondering if anyone has suggestions for actually calculating that proportion.

posted by godawful at 6:01 AM on January 25, 2008

This would be possible if income distributions across nations were reliably described by a one parameter family (plus one scale) of distributions. As you can see here, that's not really true. You could use a gamma or pareto distribution if you wanted, but the result would be pretty fake.

Lots of countries publish a table of income distribution; it might be better to hunt for an OECD document on this.

posted by a robot made out of meat at 6:18 AM on January 25, 2008

Lots of countries publish a table of income distribution; it might be better to hunt for an OECD document on this.

posted by a robot made out of meat at 6:18 AM on January 25, 2008

I am not an economist, just a physicist who likes playing with distributions and poking around on Wikipedia.

What you need is a functional form for the income distribution. The Gini coefficient basically integrates any information about where the peaks and valleys of the actual income distribution is; so you're going to have to guess some plausible-seeming distribution. According to Wikipedia (that august font of knowledge), a Pareto distribution is often used for this purpose; this distribution has a parameter

It should be possible, in principle, to take this distribution and back out the percentage out people above a given income level; but my coffee hasn't quite kicked in yet, and so I'm not yet capable of holding all the details in my head. I'll think about it some more later today and pop back in with some more results if I have time.

posted by Johnny Assay at 6:20 AM on January 25, 2008

What you need is a functional form for the income distribution. The Gini coefficient basically integrates any information about where the peaks and valleys of the actual income distribution is; so you're going to have to guess some plausible-seeming distribution. According to Wikipedia (that august font of knowledge), a Pareto distribution is often used for this purpose; this distribution has a parameter

*k*which is very simply related to the Gini coefficient.It should be possible, in principle, to take this distribution and back out the percentage out people above a given income level; but my coffee hasn't quite kicked in yet, and so I'm not yet capable of holding all the details in my head. I'll think about it some more later today and pop back in with some more results if I have time.

posted by Johnny Assay at 6:20 AM on January 25, 2008

This thread is closed to new comments.

posted by ilike at 5:47 AM on January 25, 2008