The diffusion of knowledge in the world generates positive externalities if knowledge flows increase the productivity of R&D. Our work analyzes knowledge diffusion and knowledge externalities in generating innovation and in determining productivity. We first estimate the determinants of knowledge flows across 141 sub-national regions in 19 countries of Europe and North America as revealed by patent citation between US-granted patents. Then we estimate the impact of these flows on productivity of R&D resources in generating innovation (patenting) and productivity (TFP). While we find that knowledge diffusion depends on geographical and technological distance and is well described by a pseudo-gravity model, we do not find evidence of significant positive externalities from existing knowledge.