In recent decades, the US has experienced a widening of the college enrolment gap between rich and poor families. This is commonly interpreted as evidence for a tightening of borrowing constraints. This paper asks whether this is indeed the case. I present an incomplete-markets overlapping-generations model with college enrolment, in which altruistic parents provide transfers to their children. In the model the rise in earnings inequality observed between 1980 and 2000 acts as the driving force for generating the trends in the data. With the help of counterfactual experiments, I find that fraction of constrained households is much higher (24 instead of 8 percent) than indicated by the narrow enrolment gap in 1980. Contrary to what the development of the enrolment gap in the data suggests, the share of constrained households actually fell (to 18 percent) between 1980 and 2000. I show that altruism is important for explaining these findings.