HDI and Inequality
Milorad Kovacevic
Human Development Report Office, UNDP
Workshop on Measuring Human Development,
June 14,2013
GIZ, Eschborn, Germany
United Nations Development Programme
Human Development Report Office
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Inequality and Human Development
• Equality is at the core of the human development approach
which intrinsically pursues the value of social justice
• The country-average HDI conceals wide disparities in
distribution of HD across population within a country
• False impression: Every one within the country has the
same HDI  Equal distribution of HD within the country
• Two countries with different distributions of achievements
can have the same average HDI
HDRO
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Inequality in dimensions of HDI
• A statistical measure that characterizes the dispersion in the distribution
of some attribute – the second moment of the distribution…
or
• …a summary measure of the “loss in the social objective as compared to
the potential degree of achievement, with loss being] interpreted as the
loss that can be attributed to inequalities.”
•
Inequality in concentration of income and other forms of material
wealth
•
Inequality in distribution of other characteristics (e.g., years of
education) is often recognized, but rarely measured and always
questioned.
HDRO
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Inequality in dimensions of HDI
How to interpret inequality in health?
• Would societies be willing to shorten some people’s lives or lower their
educational achievements to lower health or education inequality?
Or
• Should societies accept the fact that some people die young--some even
before their 5th birthday? The idea is not to shorten lives but to increase
for those with low levels of survival --through policies?
HDRO
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Distributions of HDI dimensions
Disposable Income, simulated
HDRO
Distribution of years of schooling
Example: India, Source: DHS 2005/06
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Distribution of (expected) length of life,
from life tables
India 2005-2010
Age-group w
0
0.01344
1
0.00357
5
0.00548
….
25
0.0229
….
50
0.02861
55
0.03875
60
0.06059
65
0.08825
….
95
0.03692
100
0.05533
HDRO
my
0.0997024
2.605042
7.50365
27.49956
52.49948
57.50064
62.49975
67.5004
96.50081
103.9714
Afghanistan
Bangladesh
Bhutan
India
Iran
Maldives
Nepal
Pakistan
Sri Lanka
Life
Atkinson
expectancy measure(
ε=1)
49.1
0.509
69.2
0.232
67.6
0.241
65.8
0.271
73.2
0.161
77.1
0.073
69.1
0.195
65.7
0.323
75.1
0.094
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Inequality-adjusted Dimensional Indices
• Distributional data at the level of household or individual
• Variables relevant to three dimension:
Household consumption or income per capita
Years of schooling
Expected length of life
• Source of data:
Nationally representative household surveys
UN life tables
HDRO
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Inequality-adjusted Dimensional Indices
• From distributional data (𝑥1 , … , 𝑥𝑛 )  Atkinson measure of
inequality 𝐴 𝜀 ; 𝜀 = 1
𝐴𝑥 1 = 1 −
𝑥𝑖 𝑤𝑖
𝑔𝑒𝑜𝑚
=1−
𝑤𝑖 𝑥𝑖
𝑎𝑟𝑖𝑡ℎ
• Accounts for inequality of distribution of achievements in the HDI
dimension across population
• From dimensional index 𝐼𝑥 and distributional data  Inequalityadjusted (dimensional) index
𝐼 ∗ 𝑥 = (1 − 𝐴𝑥 )𝐼𝑥
• Sen’s welfare function. Discounts the average value by the level of
inequality in the dimension
HDRO
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Inequality-adjusted HDI
𝐼𝐻𝐷𝐼 =
= 𝐻𝐷𝐼 ∙
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3
𝐼 ∗ 𝐿𝐸 ∙ 𝐼 ∗ 𝑒𝑑𝑢 𝐼 ∗ 𝑖𝑛𝑐
(1 − 𝐴𝐿𝐸 ) ∙ (1 − 𝐴𝐿𝐸 ) ∙ (1 − 𝐴𝐿𝐸 )
Important properties (questionable because of the use of Life tables):
• Sub-group consistency
• Path Independence
• Distribution sensitive (higher weight at the lower and of distribution)
Foster, Lopez, Szekely (2004)
HDRO
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Interpretation of the IHDI
• HDI is the average level of Human Development
• IHDI is distribution sensitive average level of HD
• IHDI is equal to HDI if there is no inequality
• The loss in the HDI due to inequality experienced by an
average person is
𝑰𝑯𝑫𝑰
𝟑
𝟏−
= 𝟏 − (𝟏 − 𝑨𝑳𝑬 ) ∙ (𝟏 − 𝑨𝑬𝑫𝑼 ) ∙ (𝟏 − 𝑨𝑰𝑵𝑪 )
𝑯𝑫𝑰
HDRO
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Interpretation of the IHDI (contd.)
Problematic?
• HDI is the potential level of HD that can be achieved if everyone is equal
• IHDI is the actual level of HD when inequality is accounted for
• Use of Atkinson’s logic for inequality in economic welfare
𝑦𝐸𝐷𝐸 𝜀
𝐼 𝜀 =1−
𝜇
𝑦𝐸𝐷𝐸 𝜀 is the level of income per person that, if equally distributed,
would yield the same level of welfare.
•
Is it right to say:
The IHDI is the average human development achievement that if
equally distributed would yield the same level of HD as estimated by the
HDI.
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Additional Concerns
• Income index (log transformed) is adjusted by inequality from
untransformed income data
• Atkinson index cannot be calculated when zero values are
present; an arbitrary solution
• Choice of ε in the Atkinson index:
- Aversion to inequality, ε, can be both - dimension and country specific:
150 countries x 3 dimensions = 450 ε.
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Recommendation
• To avoid a misinterpretation (or a lack of a good
interpretation):
- Estimate inequality in distribution of human development
across population as a stand-alone measure
- a mean of inequalities in the distributions of the three
dimensions across the population:
- 𝟏 − 𝟑 (𝟏 − 𝑨𝑳𝑬 ) ∙ (𝟏 − 𝑨𝑬𝑫𝑼 ) ∙ (𝟏 − 𝑨𝑰𝑵𝑪 ) , or
- (𝑨𝑳𝑬 +𝑨𝑬𝑫𝑼 + 𝑨𝑰𝑵𝑪 )/𝟑
• Is there advantage of using the geometric mean?
• Computational concerns remain
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Thanks
Milorad.Kovacevic@undp.org
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