Source: Authors’ calculations based on data from the OECD, PISA 2012, and UNESCO Institute for Statistics.

There could be several reasons why we observe these bivariate relationships. For example, countries with higher spending in primary and secondary education may be wealthier countries that have more egalitarian and well-functioning institutions which could limit inequality. We check the robustness of these relationships by regressing our inequality index on spending in education and controlling for a few other potential confounding factors, namely average years of schooling for people 25 years or older, Gini index of income, and GDP per-capita (US$, PPP) for 2002.<sup>14</sup> While one can think of many other potentially confounding factors to control for, including this parsimonious list of variables seems intuitively appealing – they are reasonable proxies for average level of development, and the quality and egalitarianism of institutions. Our results (Table 1) show that the negative relationship between public spending on school education and inequality prevails for every subject and combination of control variables.

We find a stronger correlation between public spending in primary education and our inequality index than between public spending in secondary education and the index, which is consistent with theories of early childhood development: the earlier the intervention the more effective it is (Heckman, 2011).<sup>15</sup> In contrast, we do not find evidence of a relationship between public spending in tertiary education and inequality of opportunity. We find very similar results (with opposite signs) when considering the percentage of students at or above Level 2 of proficiency as the dependent variable (Table A3 in the Appendix), which is consistent with the high correlation between this percentage and the D-index. All in all, this shows that public spending in education, particularly in primary school education, is positively related to the percentage of individuals that show the skills necessary to participate effectively and productively in life and negatively related to the disparity in such basic skills among children of different circumstances.

At least in the limited framework in which we examine these correlations, the relationship between public spending on schooling and inequality of opportunity in achieving basic proficiency in reading, mathematics and science seems to be highly robust. One cannot infer a causal relationship between spending and learning outcomes from these findings, namely that increased public spending by itself is likely to reduce inequality of opportunity in achieving basic proficiency. But the robust association suggests a strong possibility that increased public spending on schooling contributes to reducing inequality of opportunity in combination with other factors that are unobserved in our analysis.

> 14 We draw average educational attainment from Barro and Lee (2013), who provide information on average years of education for people 25 years or older, but not older than 65. Data on Gini is obtained from Milanovic’s _all ginis_ data set. Data on GDP per-capita is drawn from IMF’s World Economic Outlook.

> 15Our results are in line with other studies analyzing these relationships: Salehi-Isfahani et al. (2013) and Ferreira and Gignoux (2014).

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