Interest in the relationship between competition and innovation has seen a resurgence in the last decade. Driven by the theoretical possibility of an inverted-U relationship, current research has focused on non-linear models of competition and innovation. The empirical results that proceed from this research are mixed, including predictions of an inverted-U, a monotonically increasing and a monotonically decreasing relationship.

While much attention has been given to the theoretical possibility of a non-linear relationship, relatively little has been given to the subject of measurement. Following Carl Shapiro (2012), I define ``more competitive" as the extent to which a firm stands to lose profitable sales to its rivals should it offer inferior value to consumers. My framework implements this definition in a direct way: two firms must simultaneously choose their innovation strategies under the expectation that, should only one successfully innovate, the unsuccessful firm will have a portion of its sales stolen by its rival. The greater the portion, the more contestable, and therefore competitive, the market. This framework predicts a robust, positive relationship.

I apply my model to a sample of U.S. publicly traded manufacturing firms over the period 1962-2009. Innovation is measured via total factor productivity, and competition is measured as the elasticity of firm market value with respect to sales, where sales proxy consumer value. My measure of innovation is consistent with the fact that innovation drives long-run economic growth, and my empirical measure of competition is consistent with ``more competitive" in that it estimates how much market value a firm would have lost if it hypothetically generated less value for consumers. I estimate a dynamic panel model at the firm level with a quadratic specification in competition. My results indicate a positive and monotonically increasing relationship between competition and innovation.