Since Schumpeter's (1934) seminal work, the existing literature has examined the relationship between innovation and economic growth, arguing for a strictly positive relationship. The recent literature suggests that this relationship might be non-linear. Low levels of innovation will not affect economic growth; yet, when a certain threshold is reached, innovation significantly promotes economic growth. Using panel data information for 147 countries from 2006 to 2012, we employ threshold regressions à la Hansen (1999) to test the hypothesis of a non-linear relationship between innovation and growth. We find evidence that the relationship between innovation and growth is not linear and that only high levels of innovation increase economic growth. The results tend to be stronger when investment and public expenditure are present, suggesting that the quality of institutions is important.