# Gini-Coefficient

The Gini-coefficient is a statistical measure of inequality that describes how equal or unequal income or wealth is distributed among the population of a country. It takes a value between 0 and 1, and a higher Gini-coefficient is associated with higher inequality.

Although economics often focuses on comparing allocations of resources in terms of efficiency, how income and wealth are distributed among the population is also of great importance for policy makers. Countries with an extremely unequal distribution of income or wealth may be more vulnerable to social unrest and political instability (see also Inequality) and concerns for fairness and justice influence our opinion on different political parties and redistributional policies. In order to measure inequality and to be able to compare inequality across different countries or regions economists often use the Gini-coefficient. The Gini-coefficient is a statistical measure that is used to compare different distributions (of income or wealth). It takes into account which percentage of total income (or wealth) in a country is owned by what share of the country’s population. A value of zero (or close to zero) means that income is distributed equally across the members in a society. This would be the case if everyone had exactly the same income. A Gini-coefficient close to 1 means that the nation’s income is concentrated in the hands of very few people. For example, if you imagine a country with 100 people where one person possesses everything and all others had no income, the country´s Gini-coefficient would be equal to 1.

The Gini-coefficient is represented graphically by Lorenz-curves as seen in the figure below. On the x-axis we have the share of people ordered by their income and on the y-axis, we see the cumulative share of the total income in the country. The red line corresponds to a Gini-coefficient of 0, because income is distributed equally. In other words, the poorest 10% of the population have the same income as the richest 10% which means that each citizen has the same share of the total income of the country. In the figure below this corresponds to the red line labelled “perfect equality line”. A Gini-coefficient of 1 would mean that the richest person (or say the richest 1%) in the country owns everything, while the remaining 99% have no income. For most countries the Gini-coefficient is somewhere between 0 and 1. This corresponds to a Lorenz curve as depicted by the blue line in the figure below.

Figure: Lorenz-curve for a Gini-coefficient of 0 (red line) and a Gini-coefficient between 0 and 1 (blue line)

Lorenz-curves and therefore Gini-coefficients are used to compare two (or more) income distributions in terms of their inequality. A Lorenz-curve closer to the red line implies a lower Gini-coefficient and hence, lower levels of inequality. The further away the curve is from the red line, the more unequal income is distributed within the society. We can use the Gini-coefficient to compare inequality in different countries or regions, study how the distribution of income and wealth evolved over time, or analyse the impact of certain policies (e.g. the effect of a change in the income tax) on the distribution of incomes.

To calculate the Gini-coefficient we can as well use the Lorenz diagram. The Gini coefficient corresponding to the blue Lorenz curve in our figure can be calculated as follows: $$Gini-index = \frac{A}{A+B}$$. The area A is the area between the perfect equality line and the Lorenz curve, while area B is the area between the Lorenz curve and the axes. The greater B is relative to A, the lower the Gini-coefficient and hence, the lower the income inequality in the country.

Now we know what the Gini-coefficient measures and how to calculate it, but what’s more interesting is to compare Gini-coefficients across countries and time to see which values the Gini-coefficient takes and how inequality has evolved over time. In the table below we see the Gini coefficient for five different countries in two years –in 2000 and 2016.

 2000 2016 Germany 0.29 0.32 United States 0.4 0.41 Mexico 0.53 0.46 Italy 0.35 0.35 Norway 0.27 0.29

Each of the chosen countries has a Gini coefficient somewhere between 0.27 and 0.53. A Gini coefficient of 0.53 would be considered high and imply that income is distributed rather unequally, as is the case in Mexico. The Gini coefficient of around 0.28 for Norway implies that income is distributed more equally in this country (but of course not perfectly egalitarian). Of the five countries considered, income inequality is highest in Mexico (followed by the US) and lowest in Norway.  In three of the five countries (Germany, US and Norway), the Gini-coefficient increased between 2000 and 2016, while it decreased in Mexico. The data is taken from the World Bank which also has the data of many more countries and years for those interested in having a closer look.

Among the most famous economists studying inequality are Thomas Piketty and Emmanuel Saez. In their paper “The evolution of top Incomes: A historical and international perspective” (published 2006, in the American Economic Review), they present findings concerning changing levels of income and wealth in a variety of countries during the last century. One of the main challenges in comparing income inequality across countries is the lack of homogeneity in the data and the availability, of lack thereof, of long-run databases. One of their main findings is that during the 20th century the shares of income earned by the richest people in the society decreased decisively during wartimes and the Great Depression meaning that inequality decreased during these times.

## Good to know

While the Gini-coefficient is a useful and important measure of inequality, there are certain limitations and you might want to look at other measures of inequality as well if you are interested in studying income (or wealth) inequality to get a more accurate picture. Other commonly used measures are the Theil-index, the Hoover-index, ratios of percentiles or shares of income (comparing the mean income to the median income, etc.).