Empirical evidence suggests that positive externalities from R&D exceed negative ones. According to conventional wisdom, this calls for R&D subsidies. This paper develops a quality-ladder growth model with overlapping generations which evaluates the positive and normative implications of R&D subsidies and compares them with the effects of public education policy to promote R&D. Unlike standard growth models, the proposed framework accounts for the specificity of science and engineering (S&E) skills, where individuals endogenously choose the type of education, and allows for heterogeneity in individual ability. Although intertemporal knowledge spillovers are hypothesized and negative R&D externalities are absent, the analysis shows somewhat surprisingly that R&D subsidies may be detrimental to both productivity growth and welfare, in contrast to publicly provided education targeted to S&E skills. Finally, the optimal structure of public education spending on different skills is examined.