Pressure on public finances has increased scrutiny of public support for innovation. We examine two particular issues. First, there have been many recent calls for the (relatively new) UK R&D subsidy to be extended to other "research" activities, such as software. Second, argument still rages about the efficacy of direct public spending on R&D via spending on academic research councils, universities, and government undertaken work on civil and military R&D. To evaluate these questions we use data on market sector productivity, R&D and non-R&D intangible assets, and public sector R&D spending. We look for evidence of market sector spillovers from intangible investment and from public R&D. We find (a) no evidence of spillover effects from intangible investment at the market sector level, including from R&D, (b) strong evidence of market sector spillovers from public R&D spend on research councils, and (c) no evidence of market sector spillovers from public spending on civil or defence R&D. Our findings tentatively suggest that for maximum market sector productivity impact government innovation policy should focus on direct spending on research councils.