# Frequently Asked Questions - Inequality-adjusted Human Development Index (IHDI)

The HDI represents a national average of human development achievements in the three basic dimensions: a long and healthy life, knowledge and a decent standard of living. Like all averages, the HDI conceals disparities in human development across the population within the same country. Two countries with different distributions of achievements can still have the same average HDI value.

The IHDI takes into account not only the average achievements of a country on health, education and income, but also how those achievements are distributed among its population by “discounting” each dimension’s average value according to its level of inequality.

The approach is based on a distribution-sensitive class of composite indices proposed by Foster, Lopez-Calva, and Szekely (2005), which draws on the Atkinson (1970) family of inequality measures. It is computed as the geometric mean of dimension indices adjusted for inequality. The inequality in each dimension is estimated by the Atkinson inequality measure, which is based on the assumption that a society has a certain level of aversion to inequality. For details see Alkire and Foster (2010) and Technical note 2.

This is the most difficult aspect of the IHDI, as life expectancy data are aggregate indicators. However, the inequality is estimated from the abridged life tables (five-year age cohorts) and reflects the current inequality in mortality patterns—some people die under the age of one and others die at 75 or later. The quality of these estimates relies on the quality of the data in the life table.

Inequality in the education dimension is approximated by inequality in years of schooling of the adult population, drawn from nationally representative household surveys.

Expected years of schooling is an aggregate measure and inequality in its distribution is reflected in current school enrolment ratios. Certainly, there are differences in levels of inequality in the two distributions – years of schooling for adult population and the expected years of education for the school age population, with the inequality in distribution of expected years of schooling across the school-age population being lower. Thus, one can speculate that overall inequality in the HDI distribution would be reduced if expected years of schooling were used.

Years of schooling of adults is mostly derived from the highest level of schooling achieved. Using UNESCO’s country information on the duration of schooling needed for each level, the highest level of schooling is converted into years. While the duration of primary, secondary and most of post-secondary education is more or less standardized, the very high levels—masters and doctoral studies—vary across countries. However, the Atkinson measure of inequality, which is used to assess inequality in HDI education components, is less sensitive to differences at the upper end of the distribution.

The IHDI relies on data on income/consumption and years of schooling from major publicly available databases, which contain micro data from national household surveys harmonized to common international standards: Eurostat’s EU Survey on Income and Living Conditions, Luxembourg Income Study, World Bank’s International Income Distribution Database, United Nations Children’s Fund’s Multiple Indicators Cluster Survey, ICF Macro’s Demographic and Health Survey, and United Nations University’s World Income Inequality Database. For inequality in the health dimension, we used the abridged life tables from the United Nations Population Division. A list of surveys used for the 2015 IHDI estimation is given at http://hdr.undp.org.

By their very nature, income and consumption yield different levels of inequalities, with income inequality being higher than inequality in consumption. Income seems to correspond more naturally to the notion of “command over resources.” Consumption data are arguably more accurate in developing countries, less skewed by high values, and directly reflect the conversion of resources. Income data also pose technical challenges because of the greater presence of zero and negative values. In an ideal world, one would be consistent in the use of either income or consumption data to estimate inequality. However, to obtain sufficient country coverage, it was necessary to use both. The final estimates are lightly influenced by whether inequality refers to income or consumption distribution.

No. Due to data limitations and the construction, the IHDI does not capture overlapping inequalities—whether the same person is at the lower end of distributions in all three dimensions. Also at this time we are not able to estimate inequality in distribution of expected years of schooling, so the inequality in education dimension is assessed only from distribution of years of education.

Generally countries in the low human development group also tend to have higher inequality and thus larger losses in human development due to inequality, while countries in the very high group experience the least inequality in human development.

Although this is the fifth year that the IHDI has been calculated, we did not recalculate IHDI for the previous years, due to the absence of comprehensive time series of inequality in education and income for a majority of countries.

The IHDI refers to 2014. It uses the HDI indicators that refer to 2014 and measures of inequality that are based on household surveys from 2005 to 2014 and life tables that refer to the 2010-2015 period. So, the logic was to use the year to which the HDI indicators refer.

While the HDI can be viewed as an index of average achievements in human development dimensions, the IHDI measures the level of human development when the distribution of achievements across people in the society is accounted for. The IHDI will be equal to the HDI when there is no inequality, but falls below the HDI as inequality rises. The difference between the HDI and IHDI, expressed as a percentage of the HDI, indicates the loss in human development due to inequality.

The IHDI captures the inequality in distribution of the HDI dimensions. However, it is not association sensitive, meaning that it does not account for overlapping inequalities—whether the same people are at the lower end of each distribution. Also, individual values of education and income can be zero or even negative (for income), so they have been adjusted to non-negative non-zero values uniformly across countries, which reshapes the distributions to a small degree while the Atkinson inequality measure provides an approximation of the magnitude of inequality.

One of the key properties of the approach is that it is “subgroup consistent.” This means that if inequality declines in one subgroup and remains unchanged in the rest of population, then the overall inequality declines. The second important property is that the IHDI can be obtained by first computing inequality for each dimension and then across dimensions, which further implies that it can be computed by combining data from different sources, thus it is not necessary that micro data come from the same survey.

The Gini coefficient is commonly used as a measure of inequality of income, consumption or wealth. There was an attempt to apply the Gini index to measure inequality in the HDI distribution (Hicks, 1998).

The choice of the Atkinson inequality measure was guided by three factors: (i) subgroup consistency, (ii) sensitivity to the inequality in the lower end of distribution, and (iii) simplicity of computation and mathematical elegance of the resulting composite Inequality-adjusted Human Development Index.

(i) Subgroup consistency means that if inequality declines in one subgroup (region, ethnic group, etc.) and remains unchanged in the rest of population, then the overall inequality declines. The Gini coefficient does not have this property.

(ii) By its construction, the Gini coefficient puts equal weights to the entire distribution, while the Atkinson inequality measure puts more weight to the lower end, thus accounts better for child mortality, illiteracy, and income poverty.

Finally, the geometric form of the HDI in combination with the Atkinson index provides a simple and elegant path-independent composite IHDI, obtained by first computing inequality for each dimension and then across dimensions, which further implies that it can be computed by combining data from different sources (life tables and different surveys for education and income).

The IHDI and its components can be useful as a guide to helping governments better understand the inequalities across populations and their contribution to the overall loss due to inequality.

The IHDI in its current form was inspired by a similar index produced by Mexico’s national HDR. The IHDI can be adapted to compare the inequalities in different subpopulations within a country, providing that the appropriate data are available. National teams can use proxy distributions for indicators, which may make more sense in their particular case.

L’inégalité dans l’éducation est estimée approximativement par l’inégalité dans le nombre d’années de scolarisation de la population adulte, tel qu’il ressort des enquêtes représentatives auprès des ménages à l’échelle nationale.