Measuring income inequality: The Lorenz curve and Gini coefficient
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Explanation of the Lorenz curve and Gini coefficient.
In previous videos you have already seen that the prosperity in a country can be very unevenly distributed. This video explains the ways to calculate inequality: The Lorenz curve and the Gini coefficient.
Let’s start with the Lorenz curve. Suppose there are 10 people living in a country, who together earn 100 euros. Let’s assume that everyone earns 10 euros. Because everyone earns the same amount, there is no inequality. We put the poorest person on the left in the graph. This person, like the rest, earns 10 euros. The 2nd person also earns 10 euros. Together they earn 20 euros. So this is their accumulated income, which we call cumulative income, which is 20% of total income. The 3rd person also earns 10 euros and the income added up with the other persons is 30% of the total income. We can also do this for the other 7 people, creating a diagonal line. There is no inequality with this diagonal line; everyone earns the same amount of money.
Let’s adjust the example. We have 10 people who together earn 100 euros.
The first person earns 1 euro. That is 1% of the total income of 100 euros. The second person earns 2 euros, which is 2% of the total income. The first and second person therefore together earn 3% of the total income. The third person earns 3 euros, which is 3% of the total income. The first 3 people together earn 6% of the total income. The 4th earns 5 euros, the 5th 7 euros and the 6th 9 euros. The first 6 people together earn 27 euros, which is 27% of the total income.
The 7th person earns 11 euros, the 8th person 14 euros and the 9th person 18 euros. The first 9 people together earn 70 euros, which is 70% of the total income.
The last person must therefore earn 30 euros, which is 30% of the total income.
As you can see the line has become very skewed. The more there is a curve in the line, the more skewed the income distribution. The poorest people earn very little, while a few rich people earn a lot of money. We can make such a curve for each country.
From this Lorenz Curve we can calculate the gini coefficient. We call the area from the diagonal to the real income distribution “A”. We call the area from the curve to the axes “B”. The formula for the gini coefficient is A divided by the total area. If the curve runs diagonally, there is complete equality. Because A is 0, the gini coefficient is also 0. The lower the gini coefficient, the more evenly the income is distributed in a country.
If the curve is very skewed, then A’s surface is very large. A divided by the total area is almost 1. The closer to 1, the more unevenly the income is distributed. The lowest score on the gini coefficient is 0.24; countries like this have a low degree of inequality, while the highest score worldwide is 0.63. These are countries with very unequal income distribution.
So you learned that income inequality can be represented in a lorenz curve and that we can measure inequality using the gini coefficient.
Calculating the Gini Coefficient
Understanding the Gini Coefficient
This video explains the concept of Gini Coefficient using simple illustrations. For more information on the Gini Coefficient and the Key Household Income Trends in Singapore, visit www.singstat.gov.sg.
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