Comment on Bosssert, D’Ambrosio & Grenier paper Branko Milanovic, World Bank

IHDI general approach

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…

Rawls

Roemer

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

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.

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.

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

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.