Page - (000305) - in Knowledge and Networks

302 KI P P P Pc i n ci c i= − = ∑ 1 (14.7) where Pci is the number of patents of city c in technology field i; Pc is the total number of patents of city c; and Pi is the total number of patents obtained in all U.S. cities (excluding city c) in technology field i. This index has been adjusted in order to make cities with which inventors of city c have more collaborative links (and thus knowledge exchange) have more weight in the computation of the Krugman index of city c. Similarly, only cities with which inventors of city c have external linkages enter into the computation of the index. In particular, Pi has been weighted by the frequency of co-inventing links between inventors of city c and inventors of city d, and P is the total number of patents obtained in all U.S. cities (except city c), weighted by the frequency of co-inventing links between inventors of city c and inventors of city d.10 The Krugman index ranges from 0 to 2, taking value 0 for cities whose techno- logical profile is totally identical to the average technological profile of the cities with which it has external linkages, and taking value 2 for cities that are specialized in completely different fields. Dissimilarity from the average knowledge base of all other cities with which a city has linkages can make more fruitful (and necessary) communication, knowledge exchanges, and learning and, in turn, can stimulate the recombination of internal and external knowledge. The last group of variables considered includes two further controls for other structural properties of the co-invention network within a city (i.e., based only on ties among inventors located in the same city). First, the largest connected compo- nent (LARGE) is the ratio between the number of inventors that are in the largest component of the network and the total number of metropolitan inventors. It ranges from zero (all inventors are isolates) to one (all inventors are directly or indirectly connected) and aims to capture the size and degree of internal connectivity in the co-invention network (Lobo & Strumsky, 2008). Second, the clustering coefficient (CLUST) captures the extent to which the partners of an inventor, within the city, are also partners with each other. This index ranges from zero to one, with higher values indicating that the internal city network is composed of dense cliques of collabora- tion.11 Because cliquishness can cause isolation and localism; reduce exposure to alternative ideas; and limit the access, absorption, and recombination of externally 10 More formally, Pi is defined as: P w Pi d c dc di= ≠ ∑ wherePdi is the number of patents that cityd has obtained in technological field i , andwdc is the weight of city d on all external collaborative links between inventors of city c and inventors in all other cities. 11 The computation of this index excluded those triads of inventors connected through of a joint patent and only counted the number of triads that are the outcome of independent interactions between pairs of inventors as recommended by Opsahl (2013). S. Breschi and C. Lenzi