This study addresses the question: Are workers who hold a university degree increasingly filling job openings meant for people with lower levels of schooling? It focuses on Portugal, where the higher education system has been expanding at a fast pace and the share of university graduates in total labour force has been increasing, but where the unemployment rate for such workers has also been increasing. The analysis relies on a remarkable dataset covering the entire workforce in manufacturing and services private sectors, to implement the conceptual framework developed by Gottschalk and Hansen (2003). Results indicate that the university wage premium increased and the proportion of university graduates working in non-university jobs declined sharply over time. Therefore, no support is found for the skepticism over investment in higher education. Results are consistent with the idea that skillbiased technological progress taking place in some sectors raises the productivity of workers with higher schooling levels, thus raising their wages, which attracts new workers with high qualifications.