Several recent blog posts have discussed the Gini coefficient, in relation to income inequality. While a useful way to quickly compare countries, it's also important to recognise that it is not a magic number. In fantasy literature, there are tales of the Djinn who offered a magical solution (or three wishes), albeit one with a catch -- and it's important to recognise that this Gini also has pitfalls for the unwary.

An introduction to the Gini coefficient can be found on Wikipedia (and also on a United Nations website). In mathematical terms, it's a way to look at how something is distributed across a population. Most of the time, when commentators refer to the Gini coefficient, they are talking about distribution of income. But it could also refer to distribution of wealth, or land ownership, or number of children. i.e. Do the poorest 20% take home 5% or 10% of total income? Do the smallest 30% of families have 30% of the children?

So when people mention Gini in a debate on inequality, most of the time they are really talking about the Gini coefficient for income.

The Income Gini: does it answer our wishes?
The United Nations and CIA World Factbook calculate the Gini index on the basis of income. One reason for this is the ready availability of such statistics. Household income is a relatively easy measurement to obtain, and most national governments publish this information.

But the easy calculation isn't always the most accurate calculation. Let's see why:

Income Taxes. What matters to your pocket isn't the raw salary -- it's how much you get to take home. For example, a base pay of $2000 without income tax is no different from a $2500 salary with a 25% overall income tax. It's important to check if the Gini index was calculated using raw salary or take-home salary.

Efficiency of Income Use. Regressive taxes and expenditure can cause greater inequality than a plain Gini index would suggest. For example, let's make the reasonable assumption that every household has to buy essential goods like food, water, shelter, education and basic healthcare. We can see that for a poor household, the leftover (or "disposable") income is proportionately much less than for their well-off counterparts. Unfortunately the Gini index does not factor this in.

Welfare Benefits. Depending on where and how these are given, it may affect the validity of the Gini index. For example, if the poor in a country are given food stamps, utility vouchers or other support goods, an income Gini index would not reflect this. On the other hand, a minimum wage intervention would influence the Gini index. So would a Friedman-style Negative Income Tax, if income were assessed after taxation rather than before.

Absolute vs Relative Quality of Life. Let's do an imaginary (and admittedly slightly simplistic) experiment: If we parachuted in a thousand multinational CEOs while letting them draw the same salaries, it would increase the Gini coefficient of income. In fact it would be very bad for income inequality. But it would also make no difference to your take-home pay. In short, the Gini index is a relative measure. In fact the United Nations recognises this limitation, which is why they have the Human Development Index, which incorporates absolute measures of human welfare.

Purchasing Power. This relates to the absolute versus relative Quality of Life discussion. The cost of basic goods and services is as important a consideration as a raw income statistic.

In short, what we need is a better Gini index -- one that considers the effects of income tax, regressive taxes, welfare benefits and also real-life purchasing power.