The Inequality-adjusted HDI:
Going Backwards in the
Measurement of Human
Development?
Pedro Conceição
Chief-Economist, Regional Bureau for Africa, UNDP
Second Conference on Measuring Progress
What do we Talk About when we
Talk About Inequality?
• 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] this loss [being] interpreted as the
loss that can be attributed to inequalities.”
Bossert, D’Ambrosio, and Grenier. 2013. “Measuring Inequality in
Human Development: Comments and Suggestions.”
Back to Basics
“[…]a common interpretation of the [Atkinson]
approach is welfare-based.” (p. 10)
Bossert, D’Ambrosio, and Grenier. 2013. “Measuring
Inequality in Human Development: Comments and
Suggestions.”
“[…] any measurement on inequality involves
judgments about social welfare.” (p. 257)
Anthony. B. Atkinson. 1970. “On the Measurement of
Inequality.” Journal of Economic Theory. (2): 244-263.
Revisiting Atkinson
The goal is to measure inequality to rank
income distributions in accordance with their
implications for welfare, not based on arbitrary
statistics of income inequality, of which there
are many (Gini, Theil and other entropy-based
measures, CV, V, …), yielding different rankings.
Social Welfare
Utility function.
𝑊=
𝑦𝑡𝑜𝑝 𝑖𝑛𝑐𝑜𝑚𝑒
Frequency distribution.
𝑈 𝑦 𝑓 𝑦 𝑑𝑦
0
Income is an argument of
both functions.
Measuring Inequality
Dalton’s intuitive proposal:
𝑦𝑡𝑜𝑝 𝑖𝑛𝑐𝑜𝑚𝑒
0
𝑈 𝑦 𝑓 𝑦 𝑑𝑦
𝑈 𝜇
Ratio between actual welfare and hypothetical welfare if
everyone had mean income, 𝜇.
In Britain in 1919-1920, using a logarithmic utility
function, this ratio was 0.77: income inequality inflicted a
welfare loss of 23%.
However, not invariant to linear transformations of the
utility function.
Atkinson’s Proposal
𝑦𝐸𝐷𝐸
𝐼 𝜀 =1−
𝜇
𝜀
𝑦𝐸𝐷𝐸 𝜀 is the level of income per person that, if equally
distributed, would yield the same level of welfare.
2
𝑦2
𝑦1
1
2
𝑦2
𝜇
𝑦1
1
2
𝑦2
𝑦𝐸𝐷𝐸
𝜀
𝜇
𝑦1
𝑦𝐸𝐷𝐸
𝜀
1
<𝜇
Are societies willing to lower the incomes of some people to have less inequality?
Aversion to Inequality has Policy
Implications
Source: Francesca Bastagli, David Coady, and Sanjeev Gupta. 2012.
“Income Inequality and Fiscal Policy.” IMF Staff Discussion Note.
Can we Extend this to Health and
Education?
• Would societies be willing to shorten some
people’s lives or lower their educational
achievements to lower health or education
inequality?
• The HDI “discounted” income with health and
education achievement.
• In the HD approach, health and education are not
instrumental (only), but actual measures of
welfare, yet we are analyzing their distribution as
we do for income, which is instrumental.
• Is this taking us backward in the measurement of
human development?
The Utility Function
U(y)
y
↑ income
↑ utility
↑ welfare but income ≠ welfare