Access to higher education depends on the interaction between social origins and academic performance: background resources boost academic skills; but even when controlling for performance, privileged students are more likely to make ambitious choices and further transitions. Recent literature has shown that inequality in educational choices is heterogeneous across countries. However, it is still not well understood how different institutional designs within countries may affect the workings of those effects and how they can strengthen or weaken the inequality of educational opportunities. Using high-quality register data from the Brazilian higher education system, our work contributes to this understanding by investigating how SES and performance interact and drive students’ choice between three different tracks: not entering higher education, entering the private system, or entering the public system. We developed a strategy to encompass multinomial choices and decompose the inequalities into primary and secondary effects. Using the Shapley Value decomposition strategy, we correct an intrinsic asymmetry that biased previous results. Our findings suggest affluent students enjoy dual advantages: high exam performance amplifies access to public universities (indirect effect) and family resources offset subpar performance, ensuring private university access (direct effect). We found no signs of multiplicative advantages.

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接受高等教育的机会取决于社会出身和学业成绩之间的相互作用：背景资源提高学术技能；但即使在控制表现的情况下，特权学生也更有可能做出雄心勃勃的选择和进一步的转变。最近的文献表明，各国教育选择的不平等存在差异。然而，人们仍不清楚各国内部不同的制度设计如何影响这些效应的发挥，以及它们如何加强或削弱教育机会的不平等。我们的工作利用巴西高等教育系统的高质量注册数据，通过调查社会经济地位和表现如何相互作用，并推动学生在三种不同的轨道之间做出选择，从而有助于这种理解：不进入高等教育、进入私立系统或进入公立系统系统。我们制定了一项包含多项选择并将不平等分解为主要影响和次要影响的策略。使用 Shapley 值分解策略，我们纠正了导致先前结果出现偏差的内在不对称性。我们的研究结果表明，富裕的学生享有双重优势：高考试成绩扩大了进入公立大学的机会（间接影响），而家庭资源抵消了低于标准的表现，确保了进入私立大学的机会（直接影响）。我们没有发现乘数优势的迹象。

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