We test whether intellectual property rights foster or hinder innovation by estimating IV structural equations for a large sample of Swiss firms. We find that better appropriability conditions at the industry level raise the number of competitors. However, conditional on the given industry structure, individual firms face fewer competitors, if they actually use intellectual property rights. The further impact of fewer competitors is to raise R&D, when initial competition is strong, but to reduce it, when initial competition is weak ("inverted U").