This paper presents a dynamic general equilibrium model with two structurally identical open economies. Trade liberalization promotes innovation and growth when intellectual property rights (IPR) protection is sufficiently weak. Trade on the other hand does not affect innovation and growth when IPR protection is strong. We show that this result holds for both horizontal and vertical endogenous growth models, which have so far had contradictory predictions on how trade affects innovation. The reason for this supposed contradiction are implicit IPR protection assumptions in the two different types of growth models, strong protection in the horizontal model and weak protection in the vertical model. The IPR protection assumption makes a big difference for the size of the gains from trade. In a simple numerical example we show that assuming weak IPR protection can imply more than five times higher overall gains from trade. We also build a North–South model and add another aspect of IPR protection influencing the duration of Northern patents, namely imitation in the South. In the asymmetric model with a competitive fringe in the South, IPR protection no longer plays a crucial role for the dynamic gains from trade.