We provide robust and compelling evidence of the marked impact of tertiary education on the economic growth of less developed countries and of its the relatively smaller impact on the growth of developed ones. Our results argue in favor of the accumulation of high skill levels especially in technologically under-developed countries and, contrary to common wisdom, independently of the fact that these economies might initially produce lower-technology goods or perform technology imitation. Our results are robust to the different measures used in proxying human capital and to the adjustments made for cross-country differences in the quality of education. Country-specific institutional quality, as well as other indicators including legal origin, religious fractionalization and openness to trade have been used to control for the robustness of the results. These factors are also shown to speed up technology convergence thereby confirming previous empirical studies. Our estimates tackle problems of endogeneity by adopting a variety of techniques, including instrumental variables -for both panel and cross-section analyses- and the two-step efficient dynamics system GMM.