Comment on Bosssert , D’Ambrosio & Grenier paper

1. Comment on Bosssert, D’Ambrosio & Grenier paper BrankoMilanovic, World Bank

2. IHDI general approach • The general approach • And loss is: • The question are then: • 1) what is the correct ε? • 2) should ε be the same for all dimensions? • 3) should aggregation of dimensions in a single index also use the same ε?

3. In the past the approach was inequality aversion = 0, W = μ. • Now, inequality aversion = 1, and • Which gives the loss function as • And the new HDI has moved from being W=arithmetic mean to W=geometric mean of individual outcomes • But we do not want loss to depend so much on minimum values (or 0) as to generate loss=1 for whenever 0 appears • We modify the scale by dropping zeros

4. Certainly not an ideal solution particularly when 0s are meaningful (as in education). • But what should be our ε? Is there any way to choose between 0 and 1, or to take an intermediate value? • Do we have any theoretical basis to guide our choice? • Perhaps we do…

5. Rawls • Take a Rawlsian approach. The loss function is entirely determined by the position of the lowest recipient. It becomes • The outcome is the same as with the geometrical mean when the lowest values is 0. • Otherwise, it is a “degenerate” case of geometrical mean with (probably) even stronger implicit inequality aversion that we currently have with the geometrical mean.

6. Roemer • Or take Roemer’s approach. Let ε depend on some ratio between effort and circumstance. The greater the share of effort in total inequality across a given dimension, the less inequality aversion. • Loss function becomes • Where εj is specific to each dimension

7. One may argue that the role of effort in determining income is greater than the role of effort in determining health. That would argue for a lower ε to be attached to inequality in income • Moreover, the ratio between effort and circumstance is not the same for a given dimension in all countries • That means that ε may be both dimension and country specific: 150 countries x 3 dimensions = 450 ε. • The approach would link IHDI to inequality of opportunity literature

8. Subjective approach • Retrieve ε for each dimension from worldwide surveys of individuals (similarly to the way income inequality aversion parameters have been estimated) • Bottom line: we would have grounded ε in something more solid (Rawls, inequality of opportunity, subjective views of people) than arbitrary selection between 0 and 1.

9. Several other issues considered by BDG • Use income in untransformed form. Yes, these are “natural” units and log income artificially reduces variability. • Equivalency scales. No. Scales depend on price structure and price structure varies across countries (Lanjouw, Milanovic, Paternostro). Even for EU, it is doubtful that the scales are the same for all countries (Romania vs. Luxemburg). It also makes calculations more complex, but it is a moot point because individual data are unlikely to be available any time soon.

10. Another point: methodological nationalism • Unequal treatment of individuals across the world • Currently the index is “nationally centered” • Loss function reflects deviation of an individual outcome from a national mean • If that individual is placed in another country, her contribution will change • So the same individual outcome is treated differently depending on the country where it occurs • Should we look for a global index which could be decomposable by countries? • In other words, the yardstick against which the deviation is measured, should be global not national

11. Conclusion • If we cannot move in the short run to Rawlsian (extreme), Roemerian (difficult to calculate) or subjective estimate of ε, then the current selection of ε=1 is preferable because of its relative simplicity • The problem of truncation of the variables is an annoying one but inescapable • ε=0.5 leads, in my opinion, to a much more cumbersome expression without any clear gain in terms of being more grounded or “reasonable” than ε=1.