My attempt to answer this question.
Universities undertake two major tasks: teaching and research (the third being the
administration required to manage these processes). There are then at least two
possible mechanisms whereby these tasks affect economic growth.
a. Teaching. More skilled students raises the human capital of the workforce
and so growth.
b. Research. New knowledge spills over to other sectors, raises their
knowledge capital and so leads to new products, services, methods of
production etc.
This note attempts to quantify these effects.