As before, the same exercise is repeated defining the opportunity as timely completion of sixth grade (results available upon request). The coefficients on the HOI and D-Index are always statistically and economically significant with only modest reductions seen when ethnic fractionalization is controlled for.

Tables 9A and 9B show the estimates for the effects of the HOI and D-Index PISA test scores on institutional quality using the same controls as before. As in Tables 8A and 8B, the coefficients on the HOI and D-Index are always statistically and economically significant, with modest reductions in the coefficients seen when ethnic fractionalization is controlled for.<sup>26</sup> < Tables 9A and 9B here>

# **Overidentification test**

To check the robustness of our results, we also need to test the validity of our instruments in more detail. For an IV approach to work, the instrument must be: (i) uncorrelated with the unobserved error term and (ii) correlated with the endogenous explanatory variable. As shown in Section 3, our instrument, the wheat-sugar suitability ratio in arable land, appears to satisfy the second condition quite well.

The first requirement, however, cannot be tested definitively as it arises from a correlation between the instrument and an unobserved component of the error. One of the most problematic parts of any IV exercise is establishing that the selected instrument meets this so-called exclusion restriction. In our case it would imply that conditional on the pre-treatment controls, the wheat–sugar ratio affects the outcome, i.e. GDP per capita today, infant mortality or institutional quality, only through its effect on educational opportunities and not through any other variable. And it would imply that the share of tropical land does not directly affect the level of development, infant mortality and institutional quality, other than through its effect on the HOI and D-Index of completing sixth grade on time.

If we have more than one instrumental variable, we can effectively test whether these are uncorrelated with the structural error, with the null hypothesis being that all instruments are uncorrelated with the error term. The usual econometric approach is to run a test of overidentification. These tests are far from definitive, as “passing the test” merely implies a failure to reject the exclusion restriction. To run the test, we need an alternative instrument for equality of opportunity. The variable “share of tropical land” described earlier is a good candidate, as it is used as an instrument for the variable completing sixth grade on time. There is considerable consensus in the literature that the tropics variable affects income through social and political institutions rather than directly. For the tropics variable to be of use here as an instrument, its effects on institutions also must go through equality of opportunity rather than through any other mechanism.

The results on the over-identification tests fail to reject the exclusion restriction, by a considerable margin in all of the specifications, when the outcome variable is GDP per capita, institutional quality or malnutrition (see Table 10). When the outcome variable is infant mortality, the over-identification tests fail to reject the exclusion restriction in all cases but one.<sup>27</sup> Thus in almost all cases the over-identification

> 26 Results are qualitatively similar using other development measures as well as the different measures of equality of opportunity used in this paper. These regression outputs are available upon request.

> 27 The one where the hypothesis of exclusion restriction is rejected is for the case for infant mortality using the HOI and D-Index for PISA test scores data. However, the overidentification test fails to reject the hypothesis when the opportunity is defined as completing sixth grade on time, using data from household surveys.

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