### Gini Index or Gini Coefficient

GDP, the metrics defined in the previous article, is the measure to calculate the size of a country's economy, but it fails to capture the inequality present in society. It is commonly used to measure the income or wealth distribution among a population. An Italian statistician Corrado Gini has defined this measure.

The value of the coefficient ranges from 0 to 1. The value '0' represents perfect equality, and it indicates that all the citizens of a country earn the same income. The value '1' represents total inequality, indicating that a single citizen of a country earns all the income.

The formula as defined by Word Bank to calculate the Gini index is

where

1. x_i and x_j are the individual incomes,

2. \$N\$ is the population size, and

3. overline{X} is the average or mean income.

A low income and high-income population may have the same Gini index. For example, Turkey and the U.S. both had income Gini coefficients around 0.39-0.40 in 2016, according to the OECD, though Turkey's GDP per person was less than half the U.S.'s (in 2010 dollar terms)

### Human Development Index (HDI)

The human development index is a composite measure used as an indicator of 'potential' human development.

It measures the development across three dimensions, healthy life (H), Knowledge (K) and Standard of Living (SoL).

#### HDI = f(H, K, SoL)

The Life Expectancy Index (LEI) is used to measure a healthy life which is defined as:

#### H= LEI = Life Expectancy (LE)- 20/(85-20)

The Knowledge or Education Index is measured as:

where

(i) MYSI is the Mean Year of Schooling Index, which is equal to:

(ii) EYSI is Expected Years of Schooling Index, which is equal to:

The Standard of Living (SOL) is measured in terms of Income Index (II), which is defined as:

Then HDI is equal to:

Mahbub ul Huq and Amartya Sen, two scientists from Pakistan and India, have defined these metrics. The value of HDI lies between 0 and 1. A higher value of HDI is desired, and it indicates a higher life span, higher schooling year and high-income level per capita.

A developed country is a country with an HDI value greater than 0.7.