Page - (000297) - in Knowledge and Networks

294 Specifically, in this chapter we use all patent applications made by U.S. organiza- tions at the European Patent Office (EPO) from 1990 to 2004 recorded in the CRIOS-PATSTAT database. Names and addresses of inventors have been thor- oughly cleaned and standardized, because the accurate identification of individual inventors is key to a correct application of social network analysis tools. Inventors’ addresses have been linked to one of the 370 U.S. Metropolitan Statistical Areas (MSAs), using the delineation files available on the U.S. Census Bureau website (specifically, the June 2003 delineations issued by U.S. Office of Management and Budget). As customary in the literature, the co-invention network is constructed on the basis of a 5-year moving window, because the effectiveness of knowledge transmis- sion through a network’s ties decay with its age. The intensity of connection of metropolitan inventors with inventors external to the city is measured through the average distance-weighted external reach (ADWR) between inventors located in a given city and all other inventors located in all other cities. In particular, for an individual inventor i, it is defined as the sum of the recip- rocal distances to all other inventors he/she can reach in the co-invention network.1 Accordingly, the average distance-weighted external reach of city c (ADWRc ) is the distance-weighted external reach averaged across all inventors located in the city. Formally, this index is defined as follows: ADWR d nc i n j n ij c c h = = =∑ ∑1 1 1 (14.1) where nc is the number of inventors located in city c and nh is the number of inven- tors located in other cities (i.e., not located in city c), and dij is the geodesic dis- tance (i.e., shortest path) in the U.S. co-invention network between inventor i (located in city c) and inventor j (not located in city c).2 The index ranges from zero (i.e., all inventors in city c do not collaborate with any external inventor) to nh (i.e., when every inventor directly collaborates with every other inventor in every other city).3 As the literature suggests, we expect that a higher ADWRc has a positive impact on the rate of expansion and renewal of a city’s knowledge base. However, this aggregate indicator encompasses different types of external rela- tions. In this paper, we make an effort to separate out different types of relationships between local and external inventors. In particular, we can classify external linkages 1 In this paper, co-invention ties between two inventors located within the same city are considered as internal to that city, whereas a co-invention tie between two inventors located in different cities is considered as external to them, regardless of the organizational affiliation of the two inventors. 2 For disconnected (i.e., unreachable) pairs of inventors dij=∞ and therefore 1/ dij is equal to 1/¥ , in other words, zero. 3 For a fuller discussion of the advantages of this index with respect to other measures used in the literature to capture the intensity of external relations, see Breschi and Lenzi (2015). S. Breschi and C. Lenzi