Second, the studies differ in the number of types used for the decomposition and, naturally, in the exact set of circumstances used in each case. On one extreme, the Cogneau and Mesple-Somps study has a mere three types for Uganda, based on father’s occupation and education levels, while on the other Pistolesi has 7,680 types, constructed on the basis of information on age (20 levels), parental education (4 levels for the mother and 4 for the father), occupational group of the father (6 categories), individual ethnic group (2 categories), individual region of birth (2 categories). There is, fortunately, a middle range of studies which account for most countries in the sample, with 72 to 108 types each. Nevertheless, results for Africa and the US should certainly be interpreted with caution, in light of the number of types used in each case. Finally, a third comparability caveat, on which we have already dwelled, is the fact that some studies use non-parametric estimates while others use parametric ones.

Bearing these caveats in mind, Table 1 nevertheless illustrates the substantial variation in inequality levels across countries – both in advantages and in opportunities. The mean log deviation for incomes (or the corresponding advantage indicator) ranges from 0.083 in Denmark to 0.675 in South Africa. Norway, Slovenia and Sweden also have comparatively low levels of overall inequality, while Brazil and Guatemala stand out at the upper end. Inequality of opportunity levels (IEO-L) range from 0.003 in Norway and 0.005 in Slovenia to 0.199 in Guatemala and 0.223 in Brazil. In other words, the level of inequality in the distribution of _values of opportunity sets across types_ (the smoothed distribution described in Section 2) in Brazil is almost three times as large as the inequality (measured by the same index) in the distribution of _actual incomes_ in Denmark. One can also observe substantial differences in IEO-L among countries at closer levels of development, and more methodologically comparable: Madagascar’s level of inequality of opportunity is twice that of Ghana; those of the US and the UK are ten times those of Norway and almost four times higher than Denmark’s.

The ratio of these two inequality measures, i.e. the (lower bound) share of the overall inequality due to inequality of opportunity (IEO-R), also varies substantially, from 0.02 in Norway to 0.34 in Guatemala. Slovenia also has a remarkably low inequality of opportunity ratio, at 0.05, while Brazil closely follows Guatemala in the upper tail, at around 0.32. Figure 2 shows the range of relative measures of inequality of opportunity graphically, for the entire sample, highlighting those countries where consumption (actual or predicted) was used instead of earnings or incomes.

It may be of interest to look at how these measures of inequality of opportunity correlate with some other important variables. Output per capita, overall income inequality, and measures of intergenerational mobility – a concept closely related to I.Op. – are natural candidates. Figures 3, 4, 5 and 6 depict the associations between the relative measure of inequality of opportunity (IEO-R) and four other variables – log per capita GNI, total inequality, the intergenerational elasticity of income, and the intergenerational correlation of education. Figure 3 reveals a non-linear relationship between inequality of opportunity and the level of development, as measured by log per capita income levels. In fact, the association appears to have an inverted-U shape, much as the “Kuznets curve” that used to be hypothesized for the relation between income inequality and the “level of development”. The regression of IOR on a quadratic of log GNI is shown in the figure; the coefficient on the linear term is 0.32 (p-value: 0.05), and that on the quadratic term is -0.017 (p-value: 0.05).

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