The Percolation of Knowledge across Space

Despite considerable improvements in communication technologies in the last couple of decades, patent citation flows still decrease with distance. We provide evidence that this spatial decay of knowledge flows can be attributed to the spatial clustering of innovators' networks, through which knowledge percolates. Our contribution is twofold. Firstly, we provide evidence of the role of networks in the diffusion of knowledge through the study of patent citations. Secondly, we use this finding as a key ingredient of a model able to explain the aggregate effect of distance, and show that its predictions are met in our data.

Our test for diffusion along the network links relies on a novel identification strategy: we use examiner-added citations as counterfactuals for the true citations (the ones added by the firm itself). Indeed, when applying for a patent, innovators are required to give a list of all the patents on which their invention builds. This list is completed by experts from the patent office, who conduct their own search and add relevant references. By comparing the characteristics of applicant-added and examiner-added citations, and especially by looking at whether patents from linked firms are found more often in the former type of citations, we can identify the effect of the network of innovators in the diffusion of knowledge. For our tests to be computationally feasible, we need a small enough set of firms: thus, all our baseline estimations focus on Belgian patent applicants.

Our estimates show that it is 1.1 times more likely that a firm cites a patent when this patent belongs to one of its contacts than when it is outside the firm's network. Moreover, percolation really operates since this effect is not limited to direct links: we also find that the citation of a patent is 1.4 times more likely when this patent was cited by at least one of the firm's contacts than when it was unknown from its contacts. Our estimates can be replicated on other countries, as well as on a random selection of firms. They are robust to the introduction of a range of control variables, as well as to the use of an alternative identification strategy.

Incorporating these findings into a network formation model à la Chaney (2018), we are able to provide a theoretical foundation for the aggregate negative relationship between knowledge flows and distance. Along the way, the model correctly predicts two aggregate features of our data: firm sizes (measured by their number of patents) are Pareto-distributed and larger firms can access to more distant knowledge (more precisely, the average squared distance of citations is a power function of firm size). The latter finding holds both in cross-section and across time.

Authors : joint with Arthur Guillouzouic Le Corff


Thomas Chaney, "The Gravity Equation in International Trade: An Explanation", Journal of Political Economy, February 2018, forthcoming