Marking the 20th anniversary of the Human Development Index (HDI), the United Nations Development Programme (UNDP) has published a revised measure that also accounts for inequality (IHDI). Countries subject to severe social disparities, particularly Central and South American countries, perform worse than under the classic HDI. Even if the revised measure does not yield fundamental changes in ranking, it provides new insights for policy makers and researchers alike.Inequality, Human Development Index (HDI), Multidimensional Welfare Measurement

Guo Xu

Veronika Hümmer

English

Research Papers in Economics

German Institute
for Economic Research
Weekly Report
www.diw.de
The consequences of inequality: 
A new measure of human 
development
Guo Xu 
gxu@diw.de
Veronika Hümmer 
vhuemmer@diw.de
JEL Classification: 
O57, J32
Keywords: 
Inequality, Human 
Development Index (HDI), 
Multidimensional Welfare 
Measurement
Marking the 20th anniversary of the Human Development Index (HDI), the United 
Nations Development Programme (UNDP) has published a revised measure that also 
accounts for inequality (IHDI). Countries subject to severe social disparities, particu-
larly Central and South American countries, perform worse than under the classic 
HDI. Even if the revised measure does not yield fundamental changes in ranking, it 
provides new insights for policy makers and researchers alike.
“People are the real wealth of nations”—these were the introductory words in 
UNDP’s first Human Development Report 19901. Focusing on the meaning and 
measurement of human development, the report aimed at shifting the discourse 
towards a multidimensional concept of development. While traditional develop-
ment theory was preliminary concerned with income generation and economic 
growth, work on multidimensional poverty, particularly Amartya Sen’s “capabil-
ity approach”, set the stage for a paradigm shift: Ultimately, development is not 
about monetary wealth but enlarging people’s choices.2 Introduced in the first 1990 
report, the Human Development Index (HDI), was explicitly designed to reflect a 
multidimensional concept. One fundamental flaw, often critiqued since its creation, 
however, was its inability to capture socio-economic inequality. 
An improved measure of human development
The HDI captures three basic dimensions of human development: A long and healthy 
life (health), access to knowledge (education) and an appropriate material living 
standard (income). Each component contributes in equal measure to the aggregated 
index and was previously measured by following indicators: average life expectancy 
at birth, adult literacy rate, the gross enrollment ratio and per-capita GDP at purchas-
ing power parity (PPP). Since the most recent report in 2010, the methodology has 
been slightly revised: Adult literacy and gross enrollment rate are replaced by the 
mean and expected years of schooling, and GNI per capita replaced GDP per capita. 
In addition, the three components are aggregated differently: While the arithmetic 
1 United Nations Development Program (UNDP) (1990): Human Development Report: Concept and measurement of 
human development, Oxford University Press.
2 Sen, A. (1999), Development as freedom, Oxford University Press.
No. 35/2010
Volume 6 
December 29, 2010260
Guo Xu and Veronika Hümmer
mean implied perfect substitutionality across com-
ponents, the geometric mean explicitly accounts for 
the independent significance of each component: A 
decrease in health, for example, can no longer be 
fully compensated by an increase in education or   
income. To ensure commensurability, the HDI has 
been recalculated using the new methodology for 
169 countries between 1980 and 2010. 
A life worth living, however, is not limited to the 
factors captured in the classic HDI but extends to 
dimensions of political participation, ecological sus-
tainability and equal opportunities.3 Development 
that solely rests upon an elite’s exclusive access 
to power and resources, for example, impinges on 
the well-being of the overall populace. Economic, 
social, and political inequalities may reinforce each 
other and permanently limit the potential for human 
3 Brundtland, G. H., Khalid, M. (1987): Our common future, Oxford Uni-
versity Press.
development.4 Since the HDI does not capture in-
equality, people can live in countries with the same 
HDI score, yet still have very different opportunities 
to “live a life one has reason to value”.5 
In order to address the distributional dimension, 
the HDI was extended on its 20th anniversary.6 
The inequality-adjusted HDI (IHDI) is a measure 
of human development that corrects the HDI for 
inequality in education, health and income. When 
equality prevails across all three dimensions, HDI 
and IHDI are identical. As such, the HDI can be 
interpreted as the maximum attainable or potential 
IHDI. The greater inequality is, the lower is the 
IHDI vis-à-vis the HDI. 
Strong declines for some countries...
Accounting for inequality in the new IHDI has led to 
dramatic changes in the ranking for some countries. 
Peru is the biggest loser among the 139 countries 
reviewed in 2010: After adjustments for inequal-
ity, the Andean nation falls 26 places, from 63rd 
to 89th (table).
Among the ten countries with the largest losses in 
rank, eight are located in Central and South America. 
These are mostly countries where historically strong 
agricultural concentration has produced above-av-
erage inequality.7 Neglecting the adverse effect of 
inequality in these countries, the level of human 
development would have been vastly overstated.
There were also adjustments among the OECD 
countries. South Korea, previously ranked 12, drops 
to rank 30 once adjusted for inequality. The US, 
often cited as the anecdotal example of a highly 
developed country with high inequality, falls from 
rank 4 to rank 13. Germany, meanwhile, remains 
almost unaffected by the adjustments and moves 
from rank 10 to rank 7. 
The changes in index points are also greatest among 
Central and South American countries. The IHDI 
for Bolivia, for instance, is almost 25 index points 
below the HDI, corresponding to the difference in 
development between Norway and Brazil. Namibia, 
as an extreme case, has its HDI almost halved once 
accounting for inequality. 
4 Sen ibid.
5 Sen ibid.
6 UNDP (2010): Human Development Report: The Real Wealth of the 
Nations: Pathways to Human Development, 20th Anniversary Edition, 
Oxford University Press.
7 Cristobal, K. (2002): Why East Asia overtook Latin America: Agrarian 
reform, industrialization and development, Third World Quarterly, 23 (6), 
1073-1102.
Table
The ten biggest losers when inequality is taken into 
account
All countries (N=139) OECD nations (N=33)
HDI IHDI Difference HDI IHDI Difference
Rankings
Peru 63 89 –26 South Korea 12 30 –18
Argentina 46 67 –21 Israel 15 26 –11
Panama 54 74 –20 Chile 45 55 –10
South Korea 12 30 –18 USA 4 13 –9
Colombia 79 97 –18 Mexico 56 64 –8
Bolivia 95 112 –17 Italy 23 28 –5
Belize 78 94 –16 Ireland 5 8 –3
Brazil 73 88 –15 France 14 17 –3
Namibia 105 120 –15 Canada 8 10 –2
El Salvador 90 104 –14 Greece 22 24 –2
By comparison: Germany 10 7 3
Index points
Namibia 0.61 0.34 –0.27 Turkey 0.68 0.52 –0.16
Bolivia 0.64 0.4 –0.24 Mexico 0.75 0.59 –0.16
Micronesia 0.61 0.37 –0.24 Chile 0.78 0.63 –0.15
Peru 0.72 0.5 –0.22 South Korea 0.88 0.73 –0.15
Argentina 0.78 0.56 –0.21 Israel 0.87 0.76 –0.11
Panama 0.75 0.54 –0.21 Italy 0.85 0.75 –0.1
Belize 0.69 0.49 –0.2 USA 0.9 0.8 –0.1
Colombia 0.69 0.49 –0.2 Portugal 0.79 0.7 –0.09
Brazil 0.7 0.51 –0.19 Greece 0.85 0.77 –0.09
Guatemala 0.56 0.37 –0.19 Poland 0.79 0.71 –0.09
By comparison Germany 0.88 0.81 –0.07
HDI: Human Development Index.
IHDI:  The HDI was corrected to take into account aspects of inequality within the countries.
Both indices may have values between 0 and 1.
Sources: UNDP, http://hdr.undp.org/en/statistics/data/; calculations by DIW 
Berlin. DIW Berlin 2010
In particular Latin American countries have experienced a downgrading when 
accounting for inequality in the HDI.The consequences of inequality
261 DIW Berlin Weekly Report No. 35/2010
... but overall little change to 
countries’ rankings
Despite the extreme differences between IHDI and 
HDI in some countries, the inclusion of inequality 
in the IHDI does not lead to substantial changes 
in the general order of countries. The Spearman 
coefficient, a measure of correlation between two 
rankings, is at 0.98 for all countries—an almost 
perfect correlation. 
Indeed, the IHDI can be interpreted as a linear trans-
formation of the HDI. To illustrate this, the figure 
shows the HDI in relation to the IHDI. In absence of 
inequality, the IHDI would be the same as the HDI 
and all values would lie on the 45° line. Comparing 
the 45° line with the fitted line of the IHDI, however, 
the adjustment resembles, on average, a downward 
shift of the HDI curve. On average, the level of hu-
man development across countries is considerably 
lower once inequality within countries is taken into 
account.
Conclusion
To  mark  the  20th  anniversary  of  the  Human 
Development Index (HDI), the UNDP has published 
a revised index of human development that also ac-
counts for inequality (IHDI). Countries with large 
Before changes to the calculation method in 2010 were 
made, the Human Development Index (HDI) was calcu-
lated as an arithmetic mean of three sub-indices that 
each measures various dimensions of human develop-
ment: 
HDIARITHMETIC = 1/3 * [ INC+LE+EDUC]
Income (INC) is measured as per-capita GDP; health 
(LE) as life expectancy at birth; education (EDUC) is a 
weighted average of adult literacy (2/3) and the gross 
enrollment rate (1/3). Each component is normalized 
such that the resulting HDI lies between 0 and 1, where 
a value close to 1 reflects a high standard of develop-
ment. The methodology of the HDI can be interpreted 
as an “average of averages”: As a first step, the aver-
ages of income, health, and education are calculated 
separately; in a second step, these three averages are 
aggregated to produce a single HDI value. 
With the Human Development Report 2010, however, 
the UNDP has begun to calculate the HDI in a modified 
form. Income is now calculated using per-capita GNI 
and adult literacy and the gross enrollment rate are 
replaced by the mean and expected years of schooling. 
Instead of the arithmetic average, the sub-indices are 
now aggregated using the geometric mean: 
HDIGEOMETRIC = [INC*LE*EDUC] ^ (1/3)
Although the methodological revision leads to little 
changes in the HDI, the revised aggregation explicitly 
addresses a conceptual problem of the old HDI—the 
perfect substitutability among the three dimensions. In 
contrast to the old index, the multiplicative form implies 
that a decline in one dimension can no longer be fully 
compensated by a rise in another dimension.1 
The new Inequality-adjusted Human Development Index 
(IHDI) is derived from a special case of the Atkinson 
Index2 and accounts for inequality by discounting each 
sub-index by a factor A, the adjustment factor or “cost” 
of inequality: 
IHDI = [(1-ALE)*(1-AEDUC)*(1-AINC)]^ (1/3) * HDIGEOMETRIC
The IHDI measures inequality both within and between 
dimensions. Inequality within dimension X is measured 
by the adjustment factor AX =1-g/m, where g is the 
geometric mean and m is the arithmetic mean of distri-
bution X. Since the geometric mean assigns less weight 
to large differences3, a comparison of both means is 
an implicit measure of inequality. When g=m, there is 
no inequality and A=0. Once the distribution of the 
dimension is unequal, g becomes less than m, where the 
difference reflects the extent of inequality. Inequality 
between the dimensions is reflected similarly by the 
geometric mean of AX. If there is no inequality between 
the three dimensions, ALE=AEDUC=AINC=A. The resulting 
IHDI is thus (1-A)*HDI and is higher than in cases where 
AX is unequal.
1 To illustrate this, consider a country with no education (EDUC=0) as 
an extreme example. In the old HDI, the additive form would lead to 
the lack of education being compensated by higher income or health. 
With the new method, EDUC=0 leads to a value of 0 for the entire 
HDI.
2 Atkinson, A. B. (1970): On the measurement of inequality. Journal 
of economic theory, 2 (3), 244-263.
3 This becomes clear when the logarithm of the geometric mean is 
applied.
Box  
Calculating HDI and IHDIDIW Berlin
Mohrenstraße 58 
10117 Berlin
Tel. +49-30-897 89-0
Fax +49-30-897 89-200
ISSN 1860-3343
Translated from the 
German.
All articles are protected       
by copyright.
social disparities, particularly those in Central and South America, perform worse 
than under the previous measuring concept. Overall, however, the order of the 139 
countries changes very little. Nonetheless, the new index is likely to become an 
informative source for policy makers and researchers alike. 
Whether the IHDI will fully replace the old HDI, meanwhile, is questionable: Given 
the increased demand for disaggregated data to calculate the adjustment rates, it 
will be difficult to reconstruct the IHDI for previous decades. Instead of replacing 
the HDI, the IHDI will likely serve as a complementary indicator.
Besides education, health, and income, a comprehensive index of human develop-
ment should also include other factors, such as ecological sustainability or happi-
ness. The influential report presented in autumn 2009 by the Stiglitz Commission8, 
for instance, calls for a substantial expansion of purely economic indicators. While 
such an index would ideally reflect human development in all its aspects, the imple-
mentation is almost impossible: For example, it is unclear which factors to include 
and how each factor should be weighted to produce an aggregate index.9 The HDI 
and the IHDI, for example, assign equal weights to education, health, and income. 
Policy makers should be aware that changing prioritization can lead to consider-
ably different outcomes in HDI scores. This problem would be aggrevated in an 
even more complex index. In addition, many variables are often highly correlated, 
making redundancies unavoidable. Finally, every complex index is hampered by 
the fact that there is little reliable data for many variables, in particular in develop-
ing countries. 
8 Stiglitz, J. E., Sen, A., Fitoussi, J.-P.: Report of the Commission on the Measurement of Economic Performance and 
Social Progress, Paris, 2009.
9 Alkire, S. (2002): Dimensions of Human Development, World Development, 30, 181-205. Alkire, S. and Foster, J. 
(forthcoming): Counting and Multidimensional Poverty, Journal of Public Economics. 
Figure 
Relationship between HDI and IHDI 
2010
0.0
0.2
0.4
0.6
0.8
1.0
I
H
D
I
0.0 0.2 0.4 0.6 0.8 1.0
HDI
R = 0.9594 2
45°-line
HDI: Human Development Index.
IHDI: The HDI was corrected to take into account aspects of inequality 
within the countries.
Both indices may have values between 0 and 1. The calculations are 
based on the values for 139 countries in 2010.
Sources: UNDP, http://hdr.undp.org/en/statistics/data/;  
calculations by DIW Berlin.   DIW Berlin 2010
Overall, the order changes very little.
(First published as “Die 
Folgen der Ungleichheit: 
Ein neues Maß der men-
schlichen Entwicklung”, in: 
Wochenbericht des DIW 
Berlin Nr. 47/2010.) 

The Consequences of Inequality: A New Measure of Human Development

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The Consequences of Inequality: A New Measure of Human Development

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