The paper studies the patterns of volatility in firm growth rates and stock prices during the early phase of the life-cycle of an old economy industry, the US automobile industry from 1900-1930, and a new economy industry, the US PC industry from 1974-2000. In both industries, firm growth rates are more volatile in the period in which innovation is the most "radical". This is also the period in which stock prices are more volatile. The comparison sheds light on the co-evolution of industrial and financial volatility and the relationship between this co-evolution and mechanisms of Schumpetarian creative destruction. Results provide insight into the debate on whether the statistical behavior of firm growth rates is well represented by Gibrat's Law.