Random walk to innovation: why productivity follows a power law

In this paper we propose a mechanism generating innovations with productivity distributed according to a power law. We assume that knowledge creation occurs as new ideas are produced from combinations of existing ideas. The productivity of an innovation is determined by an unobservable intrinsic component as well as by the productivity of the parent ideas and their parents, thus generating a network of spillovers. The second important feature is that the innovator has no global information on the network of parenthood links across ideas but has acces to local knowledge, as for example the list of cited references in a patent. The optimal behaviour of the innovator is to 'walk randomly' through the network of 'citations' as this algorithm leads to selecting highly connected parent nodes. We show that the distribution of productivity resulting from this optimal behaviour follows a power law. The intuition behind the result is that the innovator focuses his efforts on strengthening local spillovers because he has no command on the other sources of productivity. When this process of innovation is imbedded in a model a la Kortum (1997) balanced growth of output is generated.