We discuss a simple model in which parents and children make investments in the children’s education, investments for other purposes, and parents can transfer cash to their children. We show that for an identifiable set of parent-child pairs, parents will rationally under-invest in their child’s education. For these parent-child pairs, additional financial aid will increase educational attainment. The model highlights an important feature of higher education finance, the "expected family contribution" (EFC) that is based on income, assets, and other factors. The EFC is neither legally guaranteed nor universally offered: Our model identifies the set of families that are disproportionately likely to not provide their full EFC. Using a common proxy for financial aid, we show, in data from the Health and Retirement Study, that financial aid increases the educational attainment of children whose families are disproportionately likely to under-invest in education. Financial aid has no effect on the educational attainment of children in other families. The theory and empirical evidence identifies a set of children who face quantitatively important borrowing constraints for higher education.