In this paper, we investigate the responsiveness of the demand for college to changes in student aid arising from a Danish reform. We separately identify the effect of aid from that of other observed and unobserved variables such as parental income. We exploit the combination of a kinked aid scheme and a reform of the student aid scheme to identify the effect of direct costs on college enrollment. To allow for heterogeneous responses due to borrowing constraints, we use detailed information on parents' assets. We find that enrollment is less responsive than found in other studies and that the presence of borrowing constraints only deters college enrollment to a minor extent.