development is also robust to inclusion of the Gini coefficient, which is averaged over 1960-2010 to mitigate the noise associated with the measure.<sup>17</sup> <Tables 3 and 4 here> Following up from the discussion earlier (in Section 3), the effect of HOI on GDP per capita is a combination of the effects of coverage _and_ inequality of educational opportunity. The effect of the D- Index on GDP, on the other hand, reflects the effect of inequality of opportunity, which is however also related (in part) to coverage in the sense that inequality by this measure is likely to be higher when coverage is lower and vice-versa. Given this feature, should the IV estimates of the D-Index be interpreted as the effect of _inequality_ of opportunity on economic development?

We would argue that such an interpretation is correct _,_ because of the way opportunities are defined here – as binary variables, where coverage is bounded above (at 100 percent). This is due to the nature of these variables – the rate of school completion or attainment of proficiency cannot exceed 100 percent – and the type of data available. Given the binary nature of these variables, an intuitive measure of inequality of opportunity cannot be fully independent of coverage. Rather the measure should capture the notion that inequality of educational opportunity in a country is likely to be higher when the basic proficiency level in education is not universal, and that there would be no inequality when every child attains the basic proficiency level.<sup>18</sup> Therefore, the estimated effect of the D-Index on per capita GDP _does_ reflect the effect of inequality of opportunity, even though the measure of the D-Index itself is partly dependent on coverage.

As in Easterly (2007), Table 4 also expands on the basic results by adding two quick robustness checks. The first check excludes the Western Hemisphere, to which Engerman and Sokoloff's original case study was limited. Excluding countries from this region, the hypothesis that inequality of opportunities inhibits development with the wheat–sugar ratio as an instrument holds “out of sample” for the rest of the world. The second check involves the inclusion of three regional dummy variables – a classification that is exogenous to the level of development of countries.<sup>19</sup> The results are robust to both the changes in specifications, although the results with the regional dummies have smaller F-statistics that could imply weak instruments.<sup>20</sup> Similar results are obtained when the HOI and D-Index are constructed using timely completion of six years of education as an alternative indicator of educational opportunity (see Table 5).<sup>21</sup> In this case, we use the “share of tropical land” as an instrument, which is related to the previously used wheat-sugar ratio, but allows for a larger number of observations for this particular opportunity measure. For all

> 17 As controls, we also use Gini coefficient adjusted to gain comparability across countries and surveys following Easterly (2007) and an alternative adjustment proposed by Solt (2009). Both of these measures produce very similar results as the one using the World Development Data.

> 18 Note that this would not apply when education proficiency is not a binary variable, but rather a continuous and unbounded variable reflecting that learning achievement is, in fact, unbounded.

> 19 The dummies correspond to Americas (includes Latin America & Caribbean region, Canada and United States); Europe and Central Asia (includes Western Europe), and Middle East & Africa; the omitted region is East Asia & Pacific (includes Japan, Australia and New Zealand).

> 20 All specifications compute robust standard errors to account for potential heteroscedasticity. See also footnote 13 regarding weak instruments.

> 21 This is interesting as the sample of countries is not the same between PISA data and Montenegro et al. (2011).

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