Income inequality may or may not be the best definition of poverty, but it’s certainly one that is often used. In many European countries, you’re counted as poor when your income is below 50% or so of the median income. Maybe this is the wrong way to measure poverty, but if you use absolute measures for poverty (such as a basic income, minimum consumption etc.) you’ll also face some problems. So it’s worthwhile to examine some of the usual methods for measuring income inequality and see how they hold up, while at the same time bracketing the discussion about poverty as either absolute deprivation or unequal distribution.

#### Methods for measuring income inequality

The Gini coefficient is the most widely used. It’s based on the proportion of the total income of a population that is cumulatively earned by a % of the population; a value of 0 expresses perfect equality where everyone has equal shares of income and a value of 1 expresses maximal inequality where only one person has all the income. A low Gini coefficient indicates therefore a more equal distribution. (The complete formula is here).

A disadvantage of the Gini measure is that it doesn’t capture where in the distribution the inequality occurs: is a society unequal because the top 1% has astronomically high incomes, because the poor are very poor, because there is practically no middle class, or because of some other reason?

Other measures are

- the ratio of the incomes of the top 10% (best paid) to the bottom 10% (worst paid)
- the proportion of a population with income less than 50% of the median income
- a population may be split into segments, e.g. quintiles or deciles, and each segment’s income share is then compared to each other segment’s (for example, the top 10% of the population – “top” in income terms – has x % of total income)
- some other measures are here.

These different measures can give contradictory numbers: two societies with the same Gini score can have different ratios of top-bottom, top-middle or middle-bottom incomes (see an example here). Hence, no single measure will tell us the last word about inequality in a society.

#### What is income?

The focus of all these measurement systems is income, but we should first decide what to count as income. Income doesn’t have to be cash or currency. A farmer in a poor country who grows his own products has non-cash income. Perhaps public services such as healthcare or education should count as income. And how about tax reductions, tax refunds, government benefits such as unemployment insurance, food stamps and various vouchers?

All those forms of non-cash or non-labor income are important when measuring income inequality because the poor profit disproportionately from those non-cash or non-labor related forms of income. Hence, including them in total income can make a large difference in income inequality numbers. (Higher income groups may have less or different tax refunds and their education may represent a smaller portion of their total income – the *returns* of their education may of course be higher, but those returns are typically cash based in the sense that they lead to higher labor compensation).

We should also decide if we want to use income before or after taxation; depends if we want to measure the effectiveness of redistribution or simply gross inequalities. And what about capital gains, imputed house rents from home ownership, inheritance etc. In general, how should wealth be included in income? Or shouldn’t it be?

#### How do we measure income?

Once we’ve solved the difficult problem of defining income, we’re still left with the practical problem of measuring it. Most cash income is captured in tax return data, but not all, and not equally well in all countries. Sometimes, you’ll need to use consumption data as a proxy for income data, or surveys about living standards. “Informal” income typically does not show up in tax data, but does in consumption data.

Another problem with measures of inequality is that they may be contaminated by notions of **fairness**. Some deliberately design their measurement system in such as way that inequalities look bigger than they actually are. For example, they use pre-tax inequalities because those are often larger than post-tax inequalities – a lot of tax systems are redistributive towards the poor (e.g. progressive taxation systems). Or they focus on income inequality when consumption inequality may have diminished. Others may mistakenly deduce evaluations of fairness or injustice from the simply fact of income distributions and forget that measures of income inequality are silent about who is on which side of the divide. If person A in a two person economy has twice the income of person B, then the measurement of inequality would be absolutely the same when B switches places with A. Measures of income inequality say nothing about who deserves what, about how income has been acquired, about whether some occupations should yield higher compensation (for example because we want the right incentives), or about how income should ideally be distributed.

And then there is the opposite mistake: assuming that income inequality is always necessary and just because it’s the automatic result of the fact that people have different levels of human capital and productive abilities. This is a mistake because it ignores a number of facts: no one has ever been able to prove that some abilities or occupations deserve higher wages from a moral point of view, and a lot of inequality is the result not of different abilities or efforts but of differences in luck and connections. Hence, fairness remains a legitimate concern. Contrary to the “left-wing mistake”, the “right-wing mistake” will not distort the measurement of inequality: if you believe inequality is not a problem you hardly have a reason for measuring it, let alone distort the measurement.

What I want to stress is how difficult it is to measure income inequality and how many mistakes we can make. This doesn’t mean that the numbers are rubbish. We should just be careful when drawing sweeping conclusions, that’s all.

Something more about the causes of income inequality, rather than the measurement of it, is here.