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Previous research provided ambiguous results on the association between average student performance and inequality of opportunity measured by the effect of family background on student achievement. In this paper we explore this association distinguishing between inequality of opportunity at the bottom and the top of the score distribution using a two step method. In the first step, we use quantile regression models to estimate the family background effect at different points of the distribution within each country in PISA 2000-2009. In the second step, we analyse the association between these estimates and the mean achievement of countries. Both cross-section and country fixed-effect estimates indicate that while there is no clear pattern for the bottom of the distribution, lower inequality of opportunity at the top of the distribution goes strongly together with higher mean achievement. In other words, countries where family background has a weaker impact on achievement among the most able students tend to perform better. In short, there is indeed a positive association between equality of opportunity and mean student performance, at least for some groups of students.
