remained constant over time. Hence, he can use current data on agricultural endowment to construct this measure, as the data would be highly correlated with historical agricultural endowments.

In order for it to qualify as a good instrument, we need to argue that the two necessary conditions stated above hold. The first condition, namely the _exclusion restriction_ , captures the notion that any effect of the instrument on the outcome must occur via the effect of the instrument on the treatment. In other words, we argue that conditional on the controls included in the regression, the wheat–sugar ratio has no effect on GDP per capita today, other than the effect through opportunities. The second condition, namely the _nonzero average causal effect of the instrument on the treatment_ , implies that there should be a relationship (linear in this case) between the wheat–sugar ratio and educational opportunity. If the relationship is weak, we would have weak instruments. In our case, the correlations are strong (see Figures 1 and 2) between the log wheat–sugar ratio and our measures of educational opportunities, namely the HOI and D-Index for PISA scores (Level 2 proficiency).

# **Figure 1**

**Figure 2**

<!-- Start of picture text --> Relation between Agricultural Endowments and Equality of Opportunity Relation between Agricultural Endowments and Inequality of Opportunity<br>r = 0.576*** r = -0.542***<br>0 20 40 60 80 100 0 10 20 30 40<br>Human Opportunity Index - PISA D-Index - PISA<br>Fitted values Americas Fitted values Americas<br>East Asia, South Asia & Pacific Europe & Central Asia East Asia, South Asia & Pacific Europe & Central Asia<br>Middle East and Africa Middle East and Africa<br>.6 .6<br>.4 .4<br>.2 .2<br>0 0<br>-.2 -.2<br>-.4 -.4<br>Log of Wheat Sugar Suitability Ratio Log of Wheat Sugar Suitability Ratio<br><!-- End of picture text --> Finally, for our theory to be consistent, we need to show that _firstly_ , factor endowments are related with historical measures of unequal educational opportunities; and _secondly_ , there is persistence of unequal educational opportunities from those historical measures to our current measures of unequal opportunities.

For historical data on educational achievement, we use Tutu Vanhanen’s data (in press). In particular, we use the Index of Knowledge Distribution, which is computed as the arithmetic mean of the percentage of students and literates in the country. The number of students refers to students in universities and other higher education institutions, per 100,000 inhabitants of the country.<sup>13</sup> Using this data comes at the cost of possible inaccuracies and methodological problems involved in using data from many different sources. However, the data are valuable for testing whether our story about a high endowment of wheat land relative to sugarcane land predicts a high value of the index of knowledge distribution. As this index is itself a measure of unequal opportunities, we can also perceive whether there is persistence over time, which is to say, whether today's educational opportunities are correlated with those in the past.

13 Two ways are used to calculate the percentage of Students (%): before the year 1988 the value 1000 of the variable “number of students” is equivalent to 100%; and between the years 1988-1998 the value 5000 of the same variable is equivalent to 100%. For percentage of literates we use all the adult population.

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