Step by Step Innovation without Mutually Exclusive Patenting: Implications for the Inverted U

Abstract The step by step model of innovation is a benchmark model in research investigating the relationship between competition and innovation. The model assumes an industry can be in one of two states; leveled or unleveled. In an unleveled state the lagging firm is the only innovator. In a leveled state firms compete in a patent race. In this patent race successful innovation probabilities are mutually exclusive. This formulation provides mathematical tractability, but it has no other justification. I relax this assumption and use numerical simulation to demonstrate that allowing for non mutually exclusive success in innovation has important consequences for the inverted U relationship. The inverted U relationship is no longer a prediction of the model. In addition, the model predicts that patent measures will under count innovation from the leveled state, allowing for an inverted U relationship between competition and patenting under a narrow set of parameter restrictions. This theoretical exercise has important implications for understanding the current state of the empirical record on this topic.