We study the dependence of incentives for product innovation on the presence, or absence, of parallel trade. The common assertion is that the presence of parallel trade lowers the incentive for product innovation. Our results support this assertion for some parameter values. However, there are cases in which the presence of parallel trade increases research intensity. For this to occur the innovating firm must already produce and export another good. Further, the new good and the old must be close substitutes and have different transportation costs.