of “basic opportunities” that is improperly allocated, relative to equal access across all types (Barros et al. 2011). In other words, it is a measure of how much re-distribution in access to a particular service would be required to move from the observed allocation to one in which average access was the same across types. Subject to the caveat in footnote 17, this is a perfectly plausible measure of between-type inequality in a particular dimension (that of service _j_ ). IEO-R, on the other hand, measures inequality of opportunity as the between-type share of income (or consumption) inequality. How do these two measures correlate? Do they yield essentially the same country ranking, even though their information bases are quite different, as appears to be the case with the HDI and the HOI?

It is probably too early to answer this question in cross-country terms. The overlap between the country samples in Table 1 (for which we have estimates of IEO-R) and in Table 3 (for which we have estimates of the dissimilarity index) is only ten countries, six in Latin America and four in Africa. Very little can be said, even about descriptive correlations, on the basis of such a small and unrepresentative sample. Nevertheless, for what it is worth, Figure 9 plots the IEO-R index against the dissimilarity index, averaged across its five dimensions. The correlation is -0.6989 (p-value: 0.0245), suggesting that the two alternative approaches to measuring inequality of opportunity can yield very different country rankings. It is true, of course, that in this sample the negative correlation is driven primarily by a dichotomy between Africa and Latin America, where the latter has lower dissimilarity in access to services, but a higher share of income inequality driven by unequal opportunities. Given that the IEO-R data for Africa in our sample is based on coarser partitions than in most other cases, one really should not read too much into this correlation. Nevertheless, it equally cannot be taken for granted that the IEO-R and the part of the HOI which seeks to capture inequality of opportunity are measuring the same things.

# **5. Concluding remarks**

Inequality of opportunity is a complex concept that can be measured in a number of different ways. A number of measures have recently been proposed, both under the ex-ante and the ex-post approaches, or indeed seeking a compromise between them. But most of these approaches have been applied to a single country or a very small group of countries, making cross-country comparisons impossible. Two exceptions are ex-ante measures of inequality of economic opportunity (IEO), and the Human Opportunity Index (HOI). Our review of this empirical literature yielded (roughly) comparable measures of the IEO for forty-one countries, and of the HOI for thirty-nine. Most countries in the first set are in Europe and Latin America, but there are examples from North America, Asia, Africa and the Middle-East. The second set covers countries in Africa and Latin America exclusively, and the overlap between the two samples is ten countries.

The evidence reviewed suggests that an important portion of income inequality observed in the world today cannot be attributed to differences in individual efforts or responsibility. On the contrary, it can be directly ascribed to exogenous factors such as family background, gender, race, place of birth, etc. There was considerable cross-country variation in the (lower-bound) relative measure of inequality of economic opportunity: Brazil’s share (0.32) is sixteen times as large as Norway’s. Although there certainly is noise in these measures, and various comparability caveats, there appears to be some signal as well.

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