Reconciling Models of Diffusion and Innovation: A Theory of the Productivity Distribution and Technology Frontier

We study how endogenous innovation and technology diffusion interact to determine the shape of the productivity distribution and generate aggregate growth. We model firms that choose to innovate, adopt technology, or produce with their existing technology. Costly adoption creates a spread between the best and worst technologies concurrently used to produce similar goods. The balance of adoption and innovation determines the shape of the distribution; innovation stretches the distribution, while adoption compresses it. On the balanced growth path, the aggregate growth rate equals the maximum growth rate of innovators. While innovation drives long-run growth, changes in the adoption environment can influence growth by affecting innovation incentives, either directly, through licensing of excludable technologies, or indirectly, via the option value of adoption.