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

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

By Jess Benhabib, Jesse Perla, Christopher Tonetti
January 2017Working Paper No. 3496

We study how innovation and technology diffusion interact to endogenously determine 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. Whether and how innovation and diffusion contribute to aggregate growth depends on the support of the productivity distribution. With finite support, the aggregate growth rate cannot exceed the maximum growth rate of innovators. Infinite support allows for “latent growth”: extra growth from initial conditions or auxiliary stochastic processes. While innovation drives long-run growth, changes in the adoption process can influence growth by affecting innovation incentives, either directly, through licensing excludable technologies, or indirectly, via the option value of adoption.