Gini Coefficient

Gini Coefficient (Table of Contents)

• Formula
• Examples

What is the Gini Coefficient?

Gini coefficient is a statistical measure of distribution that is used as a gauge of economic inequality. It is also known as the Gini ratio or Gini index. It is a value between 0 and 1. A higher number indicates a greater degree of income inequality. A value of 1 indicates the highest degree of income inequality where a single individual earns the entire income of the country. A value of 0 indicates that all individuals have the same income. Thus, a value of 0 indicates perfect income equality. One of the limitations of the Gini index is that its use requires that no one has negative net wealth.

Gini Coefficient Formula

Thus, the formula for the Gini coefficient is given by:

If A=0, the Lorenz curve is the line of equality. When A=0, the Gini index is 0. In case A is a very large area and B is a small area, the Gini coefficient is large. It indicates there is huge income/wealth inequality.

Steps to Calculate the Gini Coefficient

The formula for the Gini coefficient can be calculated by using the following five simple steps:

Step 1: Organize the data into a table with the category head mentioned below.

It is important to note that all the rows have to be organized from poorest to the richest. For instance, if it is stated that the bottom 10% of the population earns 3% of income, write 0.03 in the ‘Fraction of Income’ column. Next, write 0.10 in the ‘Fraction of Population’ column. Similarly, fill these 2 columns with other percentages given.

Step 2: Fill ‘% of Population that is richer’ column by adding all terms in ‘Fraction of Population’ below that row.

For instance, we get in order to fill the first row in ‘% of Population that is richer’ column, we will add 0.50 and 0.40, which are the rows in ‘Fraction of population’ below it. Hence, we get 0.90.

Step 3: Calculate the Score for each of the rows. The formula for Score is:

Score = Fraction of Income * (Fraction of Population + 2 * % of Population that is richer).

For instance, score for the 1^st row is 0.03*(0.10+2*0.90) = 0.057

Step 4: Next, add all the terms in the ‘Score’ column. Let us call it ‘Sum’

Step 5: Calculate the Gini coefficient using the formula: = 1 – Sum

Examples of Gini Coefficient Formula

Let’s see some simple to advanced examples of the Gini coefficient equation to understand it better.

Example #1

The Gini coefficient of 2 countries based on the income of citizens is as under.

• Interpret the trend of income inequality in the two countries
• Which country has higher income inequality in 2015?

Solution:

a) Gini coefficient of Country A has shown a rising trend from 0.40 in 2010 to 0.57 in 2015. Hence, income inequality in Country A has risen in these years. Gini coefficient of Country B has fallen from 0.38 in 2010 to 0.29 in 2015. Hence, income inequality in Country B has declined over these years.

b) The coefficient of Country A has (0.57) is more than that of Country B (0.29). Hence, Country A has higher income inequality in 2015.

Example #2

In a particular country, the lowest 10% of the earners make 2% of all wages. The next 40% of earners make 13% of wages. The next 40% of earners make 45% of all wages. The highest 10% of all earners make 40% of all wages. Calculate the Gini coefficient of the country.

Solution:

Use the following data for the calculation of the Gini coefficient

Let us compile the above information in Table format. The information has to be compiled by organizing the rows from poorest to the richest.

So, the calculation of the Gini coefficient will be –

Sum of Scores = 0.038+0.182+0.27+0.04 =0.53

The coefficient will be –

Coefficient = 1 – 0.53 = 0.47

Example #3

The Administration of a village is concerned about income inequality in the village. It wants to introduce some developmental schemes to reduce income inequality. For this purpose, it requires data relating to income inequality. The Administration orders a research study about income levels in his village. Here are some findings from the research study: 6 people earn Rs 10 each, 3 people earn Rs 20 each and 1 person earns Rs 80. Calculate the Gini coefficient relating to the income inequality in the village.

Solution:

Use the following data for the calculation of the Gini coefficient

We will have to tabulate the given information. For this purpose, we will have to find a fraction of population earning what proportion of income.

So, the calculation of the Gini coefficient will be –

Sum of Scores = 0.42 + 0.15 + 0.04 = 0.61

Coefficient = 1 – 0.61 =0.39

Coefficient is 0.39

Example of Gini Coefficient Formula (with Excel Template)

In a country, there are huge skyscrapers along with humungous slums. The Chief Economist of the country believes that there is huge income inequality. He finds the following data: The lowest 20% of the earners make 2% of all income. The next 40% of earners make 10% of all income. The next 30% of earners make 20% of all income. The richest 10% of earners make 68% of all income. Calculate the Gini coefficient to give the Chief Economist a statistical measure of income inequality.

Solution:

Calculation of the Gini coefficient can be done as follows –

Step 1: Write the ‘Fraction of Income’ and ‘Fraction of Population’ data in tabular format in Excel

Step 2: Fill ‘% of Population that is richer’ column by adding all terms in ‘Fraction of Population’ below that row. For instance, in the first row under ‘% of the population that is richer’, write the formula = B3+B4+B5. Then, drag the formula to subsequent rows.

Step 3: In the score column, write =A2*(B2+2*C2). Then, drag the formula to subsequent rows.

Step 4: Calculate the sum of the scores. In cell D6, write =SUM(D2:D5)

Step 5: Write =1-D6 in cell B9. Thus, 0.676 is the Gini coefficient.

Relevance and Uses

Gini coefficient is used for analyzing wealth or income distribution. Gini coefficient can be used to compare income inequality across different population sectors. For instance, the Gini index of urban areas in a country can be compared with that of rural areas. Similarly, the Gini index of one country can be compared to that of another. It can also be used to find the trend of income inequality over a period of time. For instance, the Gini coefficient in India in the year 2000 can be compared with the coefficient of 2019.

Gini coefficient can be used along with GDP numbers. If the Gini index is increasing along with GDP, then there may not be an improvement on the poverty front for the majority of the population. On the basis of this coefficient, welfare measures can be designed for the population to reduce this income inequality.

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