Reassuringly, a very similar correlation is found between the same measure of inequality of opportunity (IEO-R) and a different gauge for intergenerational (im)mobility, namely the correlation between parental and child schooling attainment. As noted earlier, the intergenerational correlations of education reported in Table 1 come from Hertz et al. (2007), and use the average years of schooling completed by a person’s mother and father as the measure of parental education. Figure 6 shows the scatter-plot for the 23 countries for which data on both variables is available. The correlation coefficient is 0.5965 (p-value: 0.0021). So, inequality of economic opportunity, as measured by IEO-R, is clearly negatively associated with two independent measures of intergenerational mobility (as opposed to persistence), one based on incomes and the other on educational attainment.

# **4. Measuring development with a penalty for unequal opportunities**

The country composition of Table 1 was determined by the availability of information on ex-ante measures of inequality of opportunity, IEO-L and IEO-R, and drew on the eight papers listed in Table 2. The last column of Table 1 contains estimates of the aggregate Human Opportunity Index, defined as a weighted average of the dimension-specific HOI.<sup>16</sup> This information was only available for ten of the 41 countries in Table 1, largely because the index has not been calculated in rich countries.

In Table 3, however, we list the component (or dimension-specific) human opportunity indices for a larger set of countries, and for the following advantages (or “basic opportunities”, or “services”): school attendance (10-14 year olds); access to water; access to electricity; access to sanitation; and whether or not the child finished primary school on time (i.e. with zero grade-age delay). The indices are multiplied by 100, so the possible range is 0-100. The 39 countries included - all of them in either Africa or Latin America - is the full set available at the time of writing. As noted earlier, they come from Molinas Vega et al. (2011) for Latin America, and World Bank (2012a, b) for Africa. Following the authors, the table also reports the simple average of the school attendance and primary school completion indices, as the HOI for education, and the simple average of the other three indices as the HOI for housing conditions. The simple average of these two numbers in turn yields the overall HOI reported in the last column of the table.

The motivation behind the HOI, as initially proposed by Barros et al. (2009), was to measure the extent to which children in various developing countries have access to basic opportunities. Although the authors do not motivate it this way, one could view the index as an example of the ex-ante approach applied to a multidimensional advantage space, with each dimension corresponding to access to a particular service – such as water or schooling – and the valuation of the opportunity set of each type being given by the coverage of the service in that type. The particular inequality index applied to that smoothed distribution of probabilities is the dissimilarity index (see equation 4).

> 16 The averaging procedure is the same suggested by Barros et al. (2011) for the HOI summary index: first calculate a HOI for education obtained as the mean of the two education components and a HOI for housing conditions (the mean of the other three components). Then obtain a summary HOI as a simple average of the two.

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