This paper investigates the relationship between product market competition and innovation, finding a strong evidence of an inverted-U relationship using panel data. The authors develop a model where competition discourages laggard firms from innovating but encourages neck-and-neck firms to innovate. This model generates an inverted-U shape in the relationship between competition and innovation, with the peak of the inverted U occurring at moderate levels of competition. The model also predicts that the average technological distance between leaders and followers increases with competition, and that the inverted-U is steeper in industries with more neck-and-neck competition. Empirical evidence supports these predictions, showing that industries with higher competition have a higher average technology gap and a steeper inverted-U relationship between competition and innovation. The findings suggest that competition can both hinder and promote innovation, depending on the level of competition and the type of firms in the industry.This paper investigates the relationship between product market competition and innovation, finding a strong evidence of an inverted-U relationship using panel data. The authors develop a model where competition discourages laggard firms from innovating but encourages neck-and-neck firms to innovate. This model generates an inverted-U shape in the relationship between competition and innovation, with the peak of the inverted U occurring at moderate levels of competition. The model also predicts that the average technological distance between leaders and followers increases with competition, and that the inverted-U is steeper in industries with more neck-and-neck competition. Empirical evidence supports these predictions, showing that industries with higher competition have a higher average technology gap and a steeper inverted-U relationship between competition and innovation. The findings suggest that competition can both hinder and promote innovation, depending on the level of competition and the type of firms in the industry.