In this paper we use a large official employer-employee dataset, which includes almost the whole universe of business firms, to document and decompose the rising graduates postgraduates wage differentials in Portugal. Using a non-parametric matching exercise, we pay particular attention to differences in the assignment of these two groups of workers across occupations and tasks. This allows us to disentangle different sources of postgraduates relative earnings and look at the creation of postgraduate jobs. We further look, however, at displacement and deskilling effects due to relative demand inertia as possible sources of such evolution of the relative earnings. Our results show that both displacement and deskilling effects, particularly of graduates with only a first-degree, appear to be at least as important as direct productivity effects in explaining postgraduates premiums. We also conclude that the relative importance of the former has been steadily increasing overtime and that, on the contrary, the net creation of high-paying, postgraduate-only jobs has been relatively modest. This suggests that postgraduate degrees have largely worked as a way of holding on to a higher ground in the labour market.