Support for many R&D and technology policies relies on empirical evidence that R&D “spills over” between firms. But there are two countervailing R&D spillovers: positive effects from technology spillovers and negative effects from business stealing by product market rivals. We develop a general framework showing that technology and product market spillovers have testable implications for a range of performance indicators, and exploits these using distinct measures of a firm’s position in technology space and product market space. We show using panel data on U.S. firms between 1981 and 2001 that both technology and product market spillovers operate, but that net social returns are several times larger than private returns. The spillover effects are also revealed when we analyze three hightech sectors in detail – pharmaceuticals, computer hardware and telecommunication equipment. Using the model we evaluate three R&D subsidy policies and show that the typical focus of support for small and medium firms may be misplaced.