Random walk to innovation: Why productivity follows a power law

This paper examines a search model in which knowledge is created as rational, but poorly informed, innovators obtain new ideas from combinations of existing ideas. We assume that the productivity of an idea is stochastic and depends on the productivity of the parental ideas. Importantly, we assume that the contribution of these parents to the productivity of the final idea is enhanced by prior use of these in knowledge creation. We identify conditions on the search costs leading to two properties: 1) the tail of the distribution of the productivity of innovations is a power law, and 2) the number of citations, i.e., times an idea is used in the process of innovation, follows a displaced power law. Both these properties are consistent with the available empirical evidence on the productivity of innovations and on patent citations.