Correcting the concentration index: A comment

In a recent article in this journal, Erreygers [Erreygers, G., 2008. Correcting the concentration index. Journal of Health Economics] has proposed a new measure of income-related health inequality to overcome three shortcomings of the concentration index (CI). I think Erreygers is absolutely right to probe on these issues, and I welcome his generalization of my normalization which was specific to the case of a binary health indicator. However, I have misgivings about his paper. His goal of correcting the CI so as to make it usable with interval-scale variables seems misguided. The CI reflects a commitment on the part of the analyst to measuring relative inequality. Armed only with an interval-scale variable, one simply has to accept that one can meaningfully measure only differences and therefore settle for measuring absolute inequality. Erreygers, index inevitably ends up as a measure of absolute inequality. His objection to my approach to getting round the bounds problem is that my normalization of the CI does not produce a measure of absolute inequality. But that was never my intention! In this comment I also show that - somewhat paradoxically at first glance - my index is also not a pure index of relative inequality. This seems to be an inevitable consequence of tackling the bounds issue.