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. To explain this pattern, we use a Schumpeterian growth model with entry and multiple sectors which differ by their distance to the world technology frontier. We show that technologically advanced entry threat spurs innovation incentives in sectors close to the technology frontier - successful innovation allows incumbents to survive the threat. In laggard sectors it discourages innovation - increased entry threat reduces incumbents' expected rents from innovating. We find that the empirical patterns hold using rich micro panel data for the UK, and controlling for the endogeneity of entry by exploiting major European and UK policy reforms.