1. Comments on Measuring Inequality in Human Development Second Conference on Measuring Human Progress NY, March 4-5, 2013 Carmen Herrero

2. Preliminares It is agreed that inequality should be incorporated in the measurement of Human Development In the 2010 Report, the IHDI was launched as a way of so doing Problems and criticisms Proposals

3. The IDHI On the positive side Takes inequality into account Applies a common theoretical idea: ede Provides a message of Loss due to inequality Problematic facts Criticisms on the way the ede is applied Unlogged income vs logged The comparison with the HDI is misleading Normalization: lower cut-offs and zeroes Data sources

4. I IHDI The ede is taken via the Atkinson inequality measure for =1. Individual zeroes put problems Different datasets to obtain the means and the inequality Path independence Log vs no logs in income Actual HDI vs Potential HDI: Focus on the loss Alternative proposal Another Atkinson measure =1/2 Collect data at the individual or household level Path vs No path-independence No logs in income IHDI is the one, but if distributions were more equal…Focus on the gain

5. EU-SILC Well-being: Household disposable income. It generates pc income and equivalent income Knowledge: highest ISCED level attained (qualitative) Health: SAE (self-assesed health) (qualitative) They treat all variables as quantitative, and provide different versions with different parameters and treatments of the zeroes. AP: Aggregate data: gender disparities Means of achievements for men and women Substitute all men/women by the mean Take the geometric mean of the three AP: Data at the individual level, for EU

6. Some Fundamentals What is the message the UD Reports should convey?  Give a picture of the relative situation of HD  Evolution  Policy orientation to improve Facts  Governments look mostly to HDI  The IHDI was difficult to understand, and thus, neglected Main point  Is it essential to take inequality into consideration as a starting point?  Real capabilities vs potential capabilities

7. Some ideas The HD Report provides an exercise of compromising between what is desirable and what is possible Possibility mostly deals with data (availability, quality and comparability) Desirability is usually taken as a sort of benchmark. But there is no unanimity about what such a benchmark sould be. First question: Can we agree upon some fundamentals? Is the IHDI a mean of means and as that we should use the same mean across individuals and across dimensions?

8. Theory There are sound ways of characterizing the IHDI from a theoretical perspective. If a society is represented by the (normalized) achievements of its population in the relevant dimensions, then, the geometric mean of the ede in each achievement across population is the only Index that satisfies monotonocity, symmetry, scale, separability and minimum lower boundedness Thus the exact formulation of the current IHDI can be characterized this way but, in general this approach does not fulfill path-independence.

9. Inequality across and within dimensions Inequality across dimensions is given by the aggregator Inequality within dimensions is given by the ede Warning: Inequality w.d. (ede) should be taken on the normalized variables. Taking IHDI as the primitive is what is done here. The selection of the ede is what give different ways of taking into consideration inequality w.d. Keeping path-independence comes at the cost of changing the aggregator.

10. Variables It is better to take a single variable for each dimension Variables for health and knowledge. This is a question of interpretation of the capabilities aproach. Distribution of achievements vs future possibilities. Parsimony Quantitative vs qualitative variables. Some treatments available for capturing inequality for qualitative variables. Warning: Careful in the comparison: control for characteristics. It could be that some inequalities are not a bad signal (progress) Some comparisons across countries are difficult to sustain (different population structure, demographic conditions…)

11. Conclusion The current HDI is a particular case of the family of IHDI, when there is no concern for inequality within dimensions The particular form of the ede should be chosen and justified carefully, otherwise it could be complicated to understand and accept the index (mostly if it is decided to stand for it as the primary one) Inequalities in health and knowledge should be considered with caution. Variables should be carefully chosen and the meaning of inequality be clear. Otherwise it could be better to keep inequality on the income variable only (correlation) The lack of individual data may be addressed by taking groups. This also has to be carefully defined. Gender, age, ethniticity, may distort the comparability across countries