How does firm entry affect innovation incentives in incumbent firms? Micro data suggest that there is heterogeneity across industries. Specifically, incumbent productivity growth and patenting is positively correlated with lagged greenfield foreign firm entry in technologically advanced industries, but not in laggard industries. In this paper we provide evidence that these correlations arise from a causal effect predicted by Schumpeterian growth theory - the threat of technologically advanced entry spurs innovation incentives in sectors close to the technology frontier, where successful innovation allows incumbents to survive the threat, but discourages innovation in laggard sectors, where the threat reduces incumbents' expected rents from innovating. We find that the empirical patterns hold using rich micro panel data for the United Kingdom (UK). We control for the endogeneity of entry by exploiting major European and UK policy reforms, and allow for endogeneity of additional factors. We complement the analysis for foreign entry with evidence for domestic entry and entry through imports.