Inequality Adjusted HDI

Human Development Index (HDI) is an index developed by the United Nations Development Programme (UNDP) of UNO to measure the overall development of countries. However, this index ignores the socio-economic inequalities within a country. Therefore, UNDP came up with a new method to calculate HDI that is Inequality Adjusted HDI (IHDI). IHDI has been calculated based on the work of Atkinson (1970). India ranks 104th with IHDI of 0.475 in 2020.

Properties of IHDI

  • IHDI excludes the effect of outlier values in the distribution.
  • “The IHDI accounts for inequalities in HDI dimensions by “discounting” each dimension’s average value according to its level of inequality” (UNDP).
  • It means that the effect of extreme development of the top population and negligible development of the bottom population does not dilute the HDI index of the rest of the population by large margin.
  • Therefore, the IHDI values are always lower than HDI. 

Calculation of Inequality Adjusted HDI

The indicators of human development in IHDI are the same as HDI such as Health, Education and Income (Fig. 1). However, the method of calculation of IHDI is slightly different. The steps of calculating IHDI are as below.

Fig. 1: Indicators of IHDI

Step 1: Collection of Data

Firstly, we have to calculate inequality measure (A) for all the indicators (x), separately. Therefore, we will collect the data for all the indicators for all the countries.

Step 2: Calculation of Inequality Measure (Ax)

  • At the second stage, we need to calculate Inequality measure (Ax) for each indicator, separately.
  • Before proceeding with the calculations, the data needs few adjustments. To clarify, please note that the value for mean years of schooling and expected years of schooling can not be zero in a geometric mean for calculating Ax. Therefore, all the ‘0’ values in these indicators need to be replaced by 1.
  • Similarly, we need to adjust the income data. We will replace the income values of the bottom 0.5 percentile of the distribution with the minimum of the second bottom 0.5 percentile of the distribution. In addition, we will replace the income values of the top 0.5 percentile of distribution with the minimum of the second top 0.5 percentile of the distribution.
  • Subsequently, we will calculate the arithmetic mean and geometric mean from that data for each indicator separately..
  • Lastly, we will apply the formulae for calculating Ax as follows.
  • Ax = 1 – (g/u). Here, Ax is the inequality measure of the ‘x’ indicator, ‘g’ is a geometric mean and ‘u’ is an arithmetic mean.
  • As a result, we will have one separate inequality measure (A) for health, education and income i.e. Ah, Ae and Ai, respectively.

Step 3: Calculation of Inequality Adjusted Index

We can construct the Index for health, education and income. Its formulae is as shown in Fig. 2. After applying this formulae we get the Index of Health, Education and Income denoted as ‘Ih’, ‘Ie’ and ‘Ii‘, respectively. This calculation is same as the HDI (Click Here for detail).

Fig. 2: Dimension Index for Indicators

Ultimately, when we multiply the Index of Health ‘Ih’ with (1-Ah), Index of Education ‘Ie’ with (1-Ae) and Index of Income ‘Ii‘ with (1-Ai), we get an inequality adjusted index of health, education and income, respectively.

Step 4: Calculation of IHDI

At the end, multiply the three inequality indexes as shown in formulae to get IHDI.

Fig. 3: Formulae for IHDI


To summarize, one can say that IHDI presents a clearer picture of the development of a nation because it shows the distributive effect of development in a country on its population. If IHDI increases, it means the inequality in society is declining and vice versa. It also eliminates the outlier effect on the HDI of a country.