This paper introduces a general equilibrium model of endogenous technical change through basic and applied research. Basic research differs from applied research in the nature and the magnitude of the generated spillovers. We propose a novel way of empirically identifying these spillovers and embed them in a framework with private firms and a public research sector. After characterizing the equilibrium, we estimate our model using micro-level data on research expenditures by French firms. Our key finding is that uniform research subsidies can accentuate the dynamic misallocation in the economy by oversubsidizing applied research. Policies geared towards public basic research and its interaction with the private sector are significantly welfare-improving.