The Inequality-adjusted HDI:Going Backwards in the Measurement of

Human Development?

Pedro ConceiçãoChief-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

Frequency distribution.Utility function.

Income is an argument ofboth functions.

Measuring InequalityDalton’s intuitive proposal:

Ratio between actual welfare and hypothetical welfare if everyone had mean income, .

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

is the level of income per person that, if equally distributed, would yield the same level of welfare.

1

2

𝑦 1

𝑦 2

1

2

𝑦 1

𝑦 2

𝜇

1

2

𝑦 1

𝑦 2

𝜇𝑦𝐸𝐷𝐸 (𝜀 )

<

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

y

U(y)

↑ income ↑ utility ↑ welfare but income ≠ welfare