Does innovation increase or decrease with more competition when innovation follows a memory process? This thesis provides a theoretical model which analyzes the innovation and competition relationship assuming that innovation follows a memory process, i.e. the current probability of innovation success depends on previous periods’ innovation successes. I find innovation increases with more product market competition, even under the Schumpeterian context where inventions are not completely appropriable. Assuming the probability to innovate increases with past innovations; a follower firm has large incentives to innovate, even in a highly competitive environment, since the memory obtained after innovating increases its probability to innovate again and become a leader. Therefore, industries will be most of the time neck-and-neck where firms innovate to escape from competition. I test this theoretical finding using the same dataset of Aghion et al. (2005). I find ambiguous results for the innovation-competition relationship. I show that the instrumental variables used by Aghion et al. (2005) are not exogenous and the empirical model is not stable over time. I, therefore, build a database of 220 U.S. industries to analyze the innovationcompetition relationship. As in my theoretical model, I find that innovation increases with more product market competition when innovation follows a memory process. However, when the innovation process is memoryless, I find that more competition decreases the level of innovation when industries already have a high level of competition