This paper investigates the relationship between product market competition (PMC) and innovation. A growth model is developed in which competition may increase the incremental profit from innovating; on the other hand, competition may also reduce innovation incentives for laggards. There are four key predictions. First, the relationship between product market competition (PMC) and innovation is an inverted U-shape. Second, the equilibrium degree of technological neck-and-neckness’ among firms should decrease with PMC. Third, the higher the average degree of neck-and-neckness’ in an industry, the steeper the inverted-U relationship. Fourth, firms may innovate more if subject to higher debt-pressure, especially at lower levels of PMC. We confront these predictions with data on UK firms’ patenting activity at the US patenting office. They are found to accord well with observed behavior.