How does firm entry affect innovation incentives and productivity growth in incumbent firms? Micro-data suggests that there is heterogeneity across industries - incumbents in technologically advanced industries react positively to entry, but not in laggard industries. To explain this pattern, we introduce entry into a Schumpeterian growth model with multiple sectors which differ by their distance to the technological frontier. We show that entry threat spurs innovation incentives in technologically advanced sectors - successful innovation allows incumbents to prevent entry. In laggard sectors it discourages innovation - increased entry reduces incumbents' expected rents from innovating. We find that the empirical patterns hold using rich micro-level productivity growth and patent panel data for the UK, and controlling for the endogeneity of entry by exploiting the large number of policy reforms undertaken during the Thatcher era.