This paper investigates two important relationships relating to firm behaviour and performance using econometric methods. First, the relationship between product market competition and innovation is examined, and then the association between innovation and productivity is separately investigated. Data from the Australian Bureau of Statistics' Business Longitudinal Database are used in the analysis. For every measure of competition considered except one, the results of the modelling are consistent with an anti-Schumpeterian relationship between competition and innovation - that is, firms appear more likely to innovate if they face stronger competition. The results examining the relationship between innovation and productivity, although weaker than those between competition and innovation, suggest that innovation is associated with better productivity outcomes.