Using our alternative opportunity variable of completing sixth grade on time, we find that increasing the Human Opportunity Index by one point increases GDP per capita by 3.8 percentage points, reduces infant mortality rate by 0.6 percentage points, and reduces malnutrition by 0.8 percentage points. A one point increase in inequality of opportunity or the D-Index (4 percentage points) reduces per capita income by 6.7 percentage points, and increases infant mortality by 1.12 percentage points and malnutrition by 1.46 percentage points.

<Table 7 here>

# **5. Robustness of the results**

## **Testing different model specifications**

To test the robustness of our results in more detail, we first explore how sensitive the findings are to the choice of different model specifications. As we suggested when introducing the instrumental variable approach, there are some plausible competing alternatives to our theory of equality of opportunity being a key variable in explaining development outcomes. In particular, the literature has highlighted the role of inequality of outcomes, ethnic fractionalization, legal origins, latitude and longitude as well as tropical location (see Section 3). To test the alternative variables against our hypothesis, we adopt the approach of controlling for each variable in turn (taking them as exogenous), while continuing to run an IV regression of development outcomes on the inequality measures with the wheat–sugar endowment ratio as an instrument for the PISA test scores data.

Tables 8A and 8B show the estimated effects of the HOI and D-Index (based on PISA test scores) on log of GDP per capita, after controlling for the effects of ethnic fractionalization, legal origin, share of tropical land, latitude and longitude, in succession. When the effects of ethnic fractionalization are controlled for, the coefficients on the HOI and D-Index drop modestly but still have high statistical and economic significance. Introducing dummies for British, French and German or Scandinavian legal origin (Socialist legal origin is the omitted category) also leaves the significance of the HOI and D-Index unchanged, and actually increases the magnitude of the coefficients. The tropical location measure – the share of a country's cultivated land area in tropical climate zones<sup>25</sup> – was introduced by Sachs and coauthors. The tropics variable is not significant and its inclusion does not affect the significance of the HOI and D-Index. The inclusion of latitude and longitude variables reduces the coefficients on the HOI modestly and increases the coefficients on the D-Index.

Therefore, the effects of equality of opportunity – measured by the HOI and D-Index of PISA test scores – are robust to the exclusion of different variables that provide competing explanations for economic development. Interestingly, three of these variables – ethnic fractionalization, share of tropical land and latitude – have strong and significant effects on GDP per capita when the opportunity variables are not included in the specification, which disappear upon the inclusion of the HOI or D-Index.

<Tables 8A and 8B here>

> 25 Tropical climate zone is characterized as “hot and humid with no winter”, which is the most precise measure of tropical conditions.

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