Random walk to innovation: Why productivity follows a power law

Abstract

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 access to local knowledge, as for example the list of cited references in a patent. The optimal behavior 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 spilovers because he has no command on the other sources of productivity. When this process of innovation is embedded in a model a la Kortum (1997) balanced growth of output is generated.

Endogenous Production Networks

“…Our main result establishes that when firms choose the cost-minimizing combination of inputs, the economy achieves sustained growth in the long run. First, the nature of growth in our model is connected to but different from the idea of recombinant growth in Weitzman (1998), as well as the related ideas in Auerswald, Kauffman, Lobo, and Shell (2000) and Ghiglino (2012). With one more product added to the mix, the number of feasible input combinations increases to 2 n for each one of the n existing products.…”

Innovation vs. imitation and the evolution of productivity distributions

“…As in Luttmer (2007), their model does not feature an endogenous choice of the R&D strategy. Ghiglino (2012) constructs a search-based growth model that generates Pareto-distributed productivity levels focusing on the recombination of existing technologies into novel ones. In Perla and Tonetti (2014) firms can choose either to produce, or to search for existing technologies to imitate.…”

The Benefits of Risky Science

“…When applied to technological innovation, our model fits with the contemporary distinction between imitative and more radical innovations (Freeman and Soete, 1997;K€ onig et al, 2012;Acemoglu and Cao, 2015) and our use of a tree structure for sequential innovations aligns with Ghiglino (2012) and Feinstein (2015). Each firm and its workforce correspond to a scientist, building a new factory is the undertaking of a project, the increase in productivity relative to factories that have been built in the past corresponds to the value of the project, the uncertainty of the productivity increase is the uncertainty of project value, an entirely new innovation parallels the initiation of a new field, and the refinement of an existing innovation is a project along a branch of an existing field.…”