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This paper presents an estimation of the contribution of Higher Education Institutions (HEIs) to economic growth and the Gross Domestic Product per capita of the European (EU) countries over the period 2000–2015. For this purpose, we analyse the universities’ effects on the supply side of their national economies, especially the contribution of the R&D of HEIs to technological capital of the European (EU) countries. We proposed a methodology of counterfactual scenarios, which assume a hypothetical situation in which HEIs do not exist, to estimating the effects of HEIs, applying techniques of growth accounting. The results obtained indicate that these effects are a significant source of growth in European (EU) countries, contributing to mitigating the adverse effects of the periods of crisis. The estimates show that GDP per capita would currently be more than 11% higher than that corresponding to a scenario without HEIs. The results obtained also show significate differences in GDP per capita between European (EU) countries associated with the activity of HEIs.