In many countries, there is an ongoing debate on the public funding of the higher education (HE) system. Our goal is to examine the theoretical justification for the establishment of HE institutions and analyze the self-selection of students under different policies of student subsidies. We study nonstationary equilibria of an overlapping-generation economy in a hierarchical education system. Given the capacity constraints of Universities, we explore the impact of adding new institutions, to be called Colleges, to the HE system, focusing on three issues. Given that Colleges are less productive and less selective than Universities: (a) Should the government establish Colleges? (b) Should the government divert funds from Universities to Colleges? On the basis of long-run economic growth considerations, we obtain positive answers to both questions. (c) Then, we compare several policies of student subsidies across the board. Our results suggest that much caution is needed in the implementation of student subsidies. Specifically, targeting subsidies to the highly-ranked students in each institution may distort their self-selection across institutions and downgrade the human capital accumulation in the economy. To offset this distortion in the demand for HE it may be useful to target subsidies to the low-ranked students in each institution. Our model also accounts for several stylized facts over time: (1) the increase in the number of institutions and students, (2) the decline in College admission standards, and (3) the decline in public budget per student and the corresponding increase in out-of-pocket student payments.