Yesterday, the UK government increased its levy on the banks, and bank bosses were reportedly ‘furious’. Next week the UK banks will announce their end-of-year results and the size of the bonus pools which they shall distribute to their lucky employees. It is a good guess that many of the public will be ‘furious’ when they learn just how big those bonuses may be. It is time for banks to stop apologise

Bankers’ bonuses provide a graphic – and headline-grabbing – description of the issues and impact of inequality. In many economies income inequality has been rising, especially in the wake of the financial crisis, which bankers are widely blamed for causing and to the poverty-causing effects of which they alone seem largely immune.

So how unfair is our nation in what its members can earn? To paraphrase George Orwell, some countries are more unequal than others. In Sweden, most people are roughly as wealthy as each other. In sub-Saharan Africa, there is a huge number of very poor people, and a few wealthy ones. How do we measure inequality across time and groups? Can we fruitfully compare two countries, say, the UK and America, and conclude that one has greater inequality than the other, or they are roughly the same? And can we find a single number that sums up how the inequalities within a nation?

The Pareto index, which we described in part one, is perhaps the oldest measure of income inequality. Pareto famously pointed out that, in Italy, 80% of the wealth was owned by 20% of the population. In Britain at the time he found that 70% of the wealth was owned by 30% of the population. His Pareto Index is mathematically derived from such considerations. Large Pareto indices correspond to a smaller proportion of very high income people.

Another widely used method of measuring income inequality is mathematically easier to grasp. Suppose we add up the income and the individual in sequence from the poorest to the richest: so we add person 1, then person 2, and at the same time we add income of person 1 to income of person 2, and so on until we’ve added up the whole group. As we go along we plot the results on a graph. The result is called the Lorenz curve. It illustrates for any point what percentage of income the poorest % of the population receive. In the example below, the poorest 50% of the population own between them about 15% of the nation’s wealth. The curve shows in a single line the extent that income and/or wealth are distributed unequally in society or a group. If everyone in a nation had exactly the same income, the curve would be the diagonal straight line which forms the 45˚ line of equality on the graph below:

The blue area enclosed between the equality line and the Lorenz curve is the “area of inequality” **I**. The greater the blue area, the more inequality there is. This can give us the single number we are looking for that measures inequality. It is called the Gini index, and it is the blue area divided by the total area under the line of equality. The equation for it is **G=I/I+Q**. Since it is a proportion, it ranges between zero (perfect equality) and one (perfect inequality: the rightmost person has all the income, and the area of inequality is the whole triangle **I+Q**).

In practice, Gini numbers tend to range between 0.2 and 0.6. A list of countries and their Gini coefficients shows that Sweden has a Gini index of .23, the UK is at .34, the USA is at .45, and South Africa, at .65, is the most unequal of the lot. Countries with **G** around 0.20 tend to have low inequality, moderate inequality is around 0.25, high inequality is around 0.35, and extreme inequality around 0.50. Gini coefficients are a powerful tool, but it is problematic to use these indices to compare large countries with small countries, and its validity depends directly on the quality of the statistical data used to calculate it. However, as a rule, it can be used to find trends towards equality or inequality: Gini coefficients in most advanced and emerging economies have been increasing in the last thirty years, with some exceptions. In the UK, **G** increased most in the 1980s; you could say that the Thatcher era was when the gap between rich and poor widened most quickly.

Another measure of inequality, which I will use in next instalment, is the share of income by percentile, namely how much of the total income goes to the bottom 10%, or the top 50%, or 20% (say, the squeezed middle class) or 5% (the well-off) or 1% (the affluent) of the population. This allows a better look at how inequality changes over time and across countries and at the complex causal relationship between inequality, economic growth and financial services.

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