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This paper aims to assess the effect of competition on firm-level innovation. The sample comprises the world's top corporate R&D spenders over the period 2007 to 2016. We use an industry-year indicator, the inverse of the Lerner Index, to measure the competition level. R&D expenditures are used as a proxy for innovation. Results confirm the existence of an inverted-U-shaped relationship between competition and innovation. Further analysis is undertaken by splitting the overall firm sample into services and manufacturing sectors according to technology and knowledge intensities as well as the age of companies (incumbents vs entrants). We validate the inverted-U-shaped relationship between competition and innovation for the firms in medium-high-tech and high-tech manufacturing sectors. An inverted-U-shaped relationship is also found for incumbents and entrants. The R&D of incumbents (compared to entrants) is more resilient (decreases less) when there is more competition and declines less and less quickly (relative to more competition).