# Equality, before & after taxes

The Gini index, explained

Income inequality: We already talked about that topic in another Weekly Chart a few weeks back. There I explained what the mean and the median can tell us about income inequality in a country. But hey, why use two numbers when you can use one? That’s what the Gini index is for. It’s a number between 0 and 1 that tells us how equally the total income of a country is distributed to its citizens. If the Gini index in your country is zero, your household earns exactly as much money as every other household. If the Gini index is 1, one person earns all the money. (In the worst case, that’s you.) (Because you wouldn’t be alive for long.)

But wait, inequality is not set in stone! A government has tools to re-distribute income – that’s what taxes are for (among others). Here’s a chart that shows how much the OECD member countries reduce their income inequality with taxes:

That’s a pretty long chart, so I highlighted four countries to draw your attention to: Finland, Germany, France and the United States. As we can see, the income is more equally distributed in Finland (with a Gini index of 0.26) and less equally in the US (0.39). But that’s only the situation after taxes. Before taxes, the income in all four countries is equally unequally distributed (0.5). The European countries – especially Finland – make use of taxes to bring income inequality down by a lot. The US, not so much.

### A visual explanation of the Gini index

But what is the Gini index telling us exactly? How is it calculated? Since I’m a visual thinking person, here’s a visual explanation: When plotting the cumulative percentage of total national income against the cumulative percentage of the population for a country, the resulting line is called a “Lorenz curve”. The Gini index shows us how much space exists between the Lorenz curve for your country and the Lorenz curve of a perfectly equal country. Let’s look at three Lorenz curves, to understand that better:

If we hover over the area that represents Mexico, we can learn that the 20% poorest Mexicans earn 5% of the national income. The bottom 30% earn 8%. The bottom 40% earn 13%, etc. The bottom 90% earn 60%, which means that the 10% richest Mexicans earn 40% of the national income. This distribution is pretty far away from a perfectly equal world, in which the top 10% would earn exactly 10% of the national income.

And that’s what the Gini index shows us: How far away that distribution is from perfection. Better said, the Gini index tells us how big the difference is between the perfectly equal world (the grey line) and your country[1]. The more curved the Lorenz line for your country, the bigger the difference, the higher the Gini index, the more unequal the income distribution in a country. That’s why the Gini index is zero when the income distribution of your country is completely equal: The grey line and the country line would lay on top of each other, and there would be zero space between them.

There’s a lot to say about indices: Every single one of them has shortcomings, and so does the Gini index. If you want to understand when and why the Gini index isn’t the best choice, I can recommend this great Scientific American article. Also, I’d love to visualize the Lorenz curves for aaaall the countries, but I couldn’t find a good data source. Maybe you know one? Tell me!

1. Ok, here’s the actual calculation: In the chart above, take the only-grey area; meaning, subtract the red area from the complete grey area. Then divide this area by the complete grey area (the triangle). The result is your Gini index. ↩︎