We study the optimal design of student financial aid as a function of parental income. We derive optimal financial aid formulas in a general model. For a simple model version, we derive mild conditions on primitives under which poorer students receive more aid even without distributional concerns. We quantitatively extend this result to an empirical model of selection into college for the United States that comprises multidimensional heterogeneity, endogenous parental transfers, dropout, labor supply in college, and uncertain returns. Optimal financial aid is strongly declining in parental income even without distributional concerns. Equity and efficiency go hand in hand.

中文翻译：

---

基于需求的最佳经济援助

我们研究了作为父母收入函数的学生经济援助的优化设计。我们在通用模型中推导出最佳财政援助公式。对于一个简单的模型版本，我们推导出了基本条件的温和条件，在这种条件下，即使没有分配问题，贫困学生也可以获得更多援助。我们将这一结果定量扩展到美国大学选择的经验模型，该模型包括多维异质性、内生父母转移、辍学、大学劳动力供应和不确定回报。即使没有分配问题，最佳经济援助也会使父母收入大幅下降。公平和效率齐头并进。