Policies towards business science links have been driven by the concept of the entrepreneurial university, i.e. encouraging universities to directly contribute to economic development through commercialization of their discoveries, e.g. through licensing of patents or start-ups, but also through collaborative R&D with firms. However, efforts to increase the entrepreneurship of universities have seldom targeted the first two missions of universities, research and teaching. Evidence shows that any entrepreneurship can only be as strong as the quality of research and teaching. Based on a conceptual model of universities’ role in innovative activity and a review of the evidence, this paper has tried to argue that a narrow focus on linking universities with firms and society without making sure that universities’ first two missions - research and teaching - work well is an ineffective approach towards increasing the contribution of universities to innovative activity, and hence to a new growth path. In particular, the role of training graduates is not stressed enough, while by far the biggest contribution of universities to innovative activities.