Gini Index

liberatomilo
May 5
3 min read

Gini coefficient and inequality

Although in most economic analyses averages are used (an average of how much the economy grows, an average of labor income, an average of inflation, etc.), however, as we all know, an "average" income of USD 1000 in a population of 100 people may well mean that all 100 earn 1000, that half earn 2000 and the other half nothing, or even that one person earns 100,000 and the other 99 earn nothing. For this reason, and because one or the other scenario may have different implications for the development and welfare of a society, it is important to measure inequality.

The star indicator of inequality

Although there are many ways to measure inequality in an economy's income distribution, the most frequent way to compare inequality in different countries or historical moments is through the Gini Coefficient. It is named after the economist who created it, the Italian Corrado Gini.

How to elaborate the Gini Index:

The first step to reach the number of comparable inequality is to order all disposable incomes in an economy from lowest to highest and divide them into 10 groups. We will call each of these groups "deciles": while decile 1 will represent the poorest 10% of a population, decile 10 will include the 10% with the highest income.

Lorenz Curve

Once we have all the deciles grouped together, we plot them on a graph that on its horizontal axis shows the deciles, while on the vertical axis it shows the cumulative percentage of income received by each decile. We call this function the "Lorenz curve" and by definition it is convex - it has the shape of the second part of a smile - does it sound difficult?

Let's take an example: if decile 1 takes only 3% of the income and decile 2 takes 4%, the curve we are talking about will go from 3% (when the X-axis is 1) to 7% (when the X-axis is 2). Obviously, decile 10 must coincide with a cumulative income of 100%, since all the deciles together cannot receive more or less than the national income.

Straight line of perfect equality

Once the Lorenz Curve is plotted, a line is then drawn on the same graph that simulates a perfectly equal income distribution. That is, decile 1 receives 10% of the national income, as do deciles 2, 3 and all successive deciles. This will give us as a graphic result, a 90º line that starts at the origin and reaches 100% at decile 10.

Ok, but I wanted to calculate inequality through the Gini index, and you are only teaching me how to plot curves!

We are close to! The Gini index calculates the area between the originally plotted Lorenz Curve, and the new line of perfect equality that we plot later. Thus, the intuition we should take from Gini is "how far is the income distribution of a country from being equal". The larger the area, the greater the inequality and therefore the higher the Gini coefficient.

Why is inequality important for public policy?

While all capitalist societies carry with them an intrinsic inequality among the material conditions of their citizens, an extremely segregated and unequal society can le ad to worse indicators and even have a negative impact on economic development.

The States have many tools to mitigate this inequality, such as the tax system (with more progressive taxes), direct public spending through income transfers, indirect public spending through the provision of quality basic services in health or education, or also by participating directly in some specific markets such as the provision of food, fuel, or housing.