# Unit 5 The rules of the game: Who gets what and why

## 5.12 Measuring economic inequality: The Gini coefficient

It is straightforward to assess the extent of inequality between two people: for example, in Section 5.10, we compare the incomes of Angela and Bruno in four different allocations directly, using a simple bar chart. But how can we assess inequalities in larger groups, or across a whole society? We use one measure in Section 1.4: the rich/poor ratio, defined as the ratio of the average income among the richest 10% of people in a society to the average income of the poorest 10%.

Economists often use another measure of inequality, called the Gini coefficient after the Italian statistician, Corrado Gini (1884–1965). The Gini coefficient is based—like our analysis of inequality in the above Bruno and Angela example—on the differences between people in incomes, wealth, or some other measure of living standards. Compared with the rich/poor ratio, the Gini coefficient has the advantage that it includes information about everyone—not just the rich and the poor, but those ‘in the middle’ too.

To understand what this means, consider the three-person population shown in Figure 5.25. The circles represent people and the numbers within the circles indicate the income received. The numbers next to the arrows reflect the differences between the two people indicated by the arrows. The Gini coefficient is calculated from two pieces of information:

• The average of the differences between the people: In this example, it is (10 + 8 + 2)/3 = 20/3 = 6.67.
• The average income of the people: In the example, this is (12 + 4 + 2)/3 = 6.

The Gini coefficient is equal to one-half times the first number (the average difference) divided by the second number (the average income). For the example, the Gini equals $$0.5 \times 6.67/6 = 0.56$$.

The total income in this population is 18. How would the Gini change if it were distributed differently between people?

• If one person had all the income (18): The average of the differences would be (18 + 18 + 0)/3 = 12. The average income, as before, would be 6, so the Gini coefficient would be 1.
• If they all had the same income (6): Then there would be no differences between any of the pairs, so the Gini coefficient would be zero.

Figure 5.25 Income differences in a three-person population.

Another common tool for assessing the distribution of income or wealth is the Lorenz curve, which is explained and applied in Unit 2 of The Economy 2.0: Macroeconomics.

Gini coefficient
A measure of inequality of a quantity such as income or wealth, varying from a value of zero (if there is no inequality) to one (if a single individual receives all of it). It is the average difference in, say, income between every pair of individuals in the population relative to the mean income, multiplied by one-half. Other than for small populations, a close approximation to the Gini coefficient can be calculated from a Lorenz curve diagram. See also: Lorenz curve.

In general, when we calculate the Gini coefficient, we obtain a number between 0 (perfect equality) and 1 (extreme inequality). The more unequally resources are distributed among the members of the population, the larger is the Gini coefficient.

If we calculate the Gini coefficient for the distribution of income that would have resulted from the prize-sharing system described in the articles of the pirate ship Royal Rover, described in Section 5.1, we find that inequality among the pirates was low: the Gini is only 0.06.

In contrast, when the British Royal Navy’s ships Favourite and Active captured the Spanish treasure ship La Hermione, the division of the spoils on the two British men-of-war ships was far less equal: ordinary crew members received about a quarter of the income, with the remainder going to a small number of officers and the captain. Figure 5.26 compares the Gini coefficients for the three ships. By the standards of the day, pirates were unusually democratic and fair-minded in their dealings with each other.

Figure 5.26 The distribution of spoils: inequality among pirates and the British navy.

Peter T. Leeson. 2009. ‘The Invisible Hook: The Law and Economics of Pirate Tolerance’. New York University Journal of Law and Liberty, 4 (2): pp. 139–171. Robert Beatson. 1804. Naval and Military Memoirs of Great Britain, from 1727 to 1783 (vol. 3). Longman, Hurst, Rees and Orme.

### Comparing income distributions and inequality across the world

To assess income inequality within a country, we can either use total market income (all earnings from employment, self-employment, savings, and investments), or disposable income, which better captures living standards. Disposable income is what a household can spend after paying tax and receiving transfers (such as unemployment benefit and pensions) from the government.

Figure 5.27 Market income and disposable income.

In Section 1.4, we used the rich/poor ratio to compare income inequality in different countries. Here we calculate the Gini coefficient for market and disposable income in each country. We find, for example, that the Gini for market income in the Netherlands in 2020 was 0.40. By this measure, it has greater inequality than the Royal Rover, but less than the British navy ships. The Gini for disposable income in the same year was lower (0.31): redistributive government policies led to a more equal distribution.

There are many other ways to measure income inequality besides the Gini and the rich/poor ratio, but these two are widely used. Figure 5.28 compares the Gini coefficients for disposable and market income across a large sample of countries, ordered from left to right, from the least to the most unequal by the disposable income measure. The main reason for the substantial differences between nations in disposable income inequality is the extent to which governments redistribute income by taxing well-off families and transferring the proceeds to the less well off.

Figure 5.28 shows that:

We describe redistribution of income by governments in more detail in the CORE Econ Insights A world of differences: An introduction to inequality and Persistent racial inequality in the United States.

• The differences between countries in disposable income inequality (the top of the lower bars) are much greater than the differences in inequality of market incomes (the top of the upper bars).
• The US and the UK are among the most unequal of the high-income economies.
• The few poor and middle-income countries for which data are included are even more unequal in disposable income than the US but …
• … (with the exception of South Africa) this is mainly the result of the limited degree of redistribution from rich to poor, rather than unusually high inequality in market income.

Figure 5.28 Income inequality in market and disposable income across the world. View a different visualization of this data at OWiD.

OECD. Income Distribution Database. Accessed January 2023.

### Question 5.9 Choose the correct answer(s)

Read the following statements and choose the correct option(s).

• The Gini coefficient is higher when the distribution is more equal.
• The Gini coefficient is one way to measure inequality. Other tools include the rich/poor ratio and the Lorenz curve.
• The major disadvantage of the Gini coefficient is that it does not capture individuals in the middle of the distribution.
• Total market income reflects what an individual can spend after paying taxes and receiving government transfers.
• The opposite is true. The Gini coefficient is a measure of inequality. It is higher when the distribution is more unequal (or less equal).
• There are various ways of measuring inequality, including the three mentioned in the question.
• The rich/poor ratio does not capture individuals in the middle of the distribution. One advantage of the Gini coefficient is that it is calculated using the income or wealth of all individuals, at every point in the distribution.
• Total market income reflects earnings from employment, self-employment, savings, and investment. Once this figure has been adjusted for taxes paid and benefits received, it is called disposable income.

### Exercise 5.7 Calculating Gini coefficients

Draw two diagrams similar to Figure 5.25 and calculate the Gini coefficients for the following situations:

1. Incomes of 2, 4, and 22
2. Incomes of 4, 6, and 8

### Exercise 5.8 Inequality in market and disposable income

Go to the World Inequality Database website. In the dropdown menu ‘By country’, select a country that you are interested in (or the country you currently live in).

1. Using the ‘Key indicators’ and ‘More indicators’ bar on the left, create a single graph that contains the following variables:
• pre-tax income share of the top 1% of income earners
• pre-tax income share of the bottom 50% of income earners
• post-tax income share of the top 1% of income earners
• post-tax income share of the bottom 50% of income earners.
2. Describe how each variable in the graph has evolved over time.
3. Explain whether the disparities in pre-tax income shown in your graph could be considered substantively and/or procedurally fair.
4. Comparing the pre-tax and post-tax income shares, comment on the extent to which government policies have addressed income inequality in your chosen country. Use a statistic based on your graph (or another statistic based on WID data) to support your answer.