The Percolation of Knowledge across Space

Abstract

We propose an explanation for the negative effect of distance on knowledge flows, based on the fact that firms use their network to acquire new knowledge, and that a firm's network expands over its life-cycle. We build contacts in the network with past patent citations. We then use subsequent citations added by office examiners to identify how existing links influence which inventions firms rely on. We start by showing that knowledge percolates: firms are more likely to rely on patents produced by their contacts, and even by contacts of their contacts, than on similar patents from outside their close network. Building on this fact, we study a dynamic network formation model: it predicts Pareto-distributed innovator sizes, as well as an increasing relationship between an innovator's size and the distance at which it cites. We find these two predictions to hold remarkably well in the data. This implies that small innovators are responsible for most of the effect of distance measured in aggregate.