Abstract
Based on patent data in the field of genomics between 1990 and 2010, we investigate how social network relationships, various proximity dimensions (geographical, organizational, technological) and their interplay affect the likelihood of forming technological collaborations and their inventive performance. We show that the network and proximity characteristics of co-inventors enable them to access different sources of knowledge, in different geographical and organizational contexts, and finally affect the quality of inventive collaboration. Based on econometric estimations, our results enable to address the proximity paradox argument that proximity acts differently on the formation of collaborations and innovative performance. Our results partly support this paradox. Although all types of proximity positively impact on the formation of new collaborations, only organizational and technological proximities directly impact performance. Moreover, the optimal level of technological proximity critically varies given the organizational and social network context.
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Notes
Berliant and Fujita (2012) propose a similar argument in a different theoretical framework. They argue that “[i]deas in common are important for communication, whereas ideas known exclusively by one of the partners are important for bringing originality into the potential partnership” (p. 649). The two arguments are fairly similar but with a different definition of what knowledge and learning are. In this case, knowledge is represented by an individual endowment of ideas and learning is a production of new ideas, which depends on the personal stock of each individual and their overlap.
The interaction term is not equivalent to the correlation. If we consider a simple model with two variables, the interaction term captures the fact that the main effect of a variable, say \(x_{1}\), depends on the value of another variable, \(x_{2}{:}\, y = {\upbeta }_{0}+{\upbeta }_{1}x_{1}+{\upbeta }_{2}x_{2}+ {\upbeta }_{3}x_{1}x_{2}+{\upvarepsilon }\). Thus although, \(x_{1}\) has a positive impact on y, if the interaction is negative (\({\upbeta }_{3}<0\)), then the marginal impact of \(x_{1}\) is lowered when \(x_{2}\) is different from zero as the following derivative illustrates: \(\frac{\partial y}{\partial x_1 }=\beta _1 +\beta _3 x_2 \).
The database was built during a recent research project carried out by ADIS-Paris Sud, LERECO-INRA and the OST—Observatoire des Sciences et des Techniques—supported by the French national research agency (ANR—Agence National pour la Recherche).
The disambiguation of inventors’ homonymies has been dealt following the methodology proposed in Carayol and Cassi (2009).
Social Network Analysis computation has been programmed, by the authors, themselves with SAS. The SPAM modules developed by Moody (2000) have been extremely helpful.
For a different approach where affiliation data are integrated with survey data, see, for instance, Rost (2011).
Even for industry–university collaborations, most of the time there is only one affiliation for a given patent; for this reason, inventors of a given patent have the same affiliation even if the applicant designated in the patent does not employ them.
Dyadic data are typically not independent since residual involving the same individual are likely to be correlated, that is, Cov(\({\upvarepsilon }_{ij},{\upvarepsilon }_{ik})\ne 0\). In consequence, standard errors must correct for cross-observation in the error terms involving the same inventors. The quadratic assignment procedure enables to handle this non-independence using a permutation procedure. Given the number of possible dyads, the procedure is difficult to apply on the whole sample. As a robustness check, we have applied the Netlogit procedure of the SNA R package on the final sample. The results provided as a supplementary material lead to similar results (Supplement 1).
If n is the number of active inventors, n*(n-1) is the number of potential ties between these inventors. We estimate this number to be approximately 14190 European inventors. The probability of an event to occur in the sample is approximately equal to \(2133/((14190^{*}14189)/2)\) given that the sample is composed of 2133 realized links.
Rare event logit has been implemented through the ReLogit Stata routine proposed by Tomz (1999).
We only observe the performance of dyads for which patents have been applied for and this induces a selection bias. A solution would be to employ a two-stage Heckman selection model, but this requires specifying independent variables that affect the probability of a dyad to patent but that do not affect the level of citations. Since we lack a theory that would suggest such variables, we are not totally confident in this two-stage procedure. However, estimates have been implemented after bootstrapping and the Mills Ratio is not significant.
We adjust the latitude and longitude coordinates for the earth curvature; thus, the distance in km between two points \(A\) and \(B\) is computed as:
$$\begin{aligned} d(A,B)&= 6371 \times \hbox {arccos}[\hbox {sin}(\hbox {latitude}(A)) \times \hbox {sin}(\hbox {latitude}(B)) + \hbox {cos}(\hbox {latitude}(A)) \times \hbox {cos}(\hbox {latitude}(B))\\&\quad \times \hbox {cos}(|\hbox {longitude}(A) - \hbox {longitude}(B) |)]. \end{aligned}$$Model 1a introduces technological proximity in a quadratic way, since it is not significant, we do not replicate this specification in the following logit models.
The turning point is equal to coefficient of technological proximity/2*coefficient of technological proximity sq.
The marginal effect of closure with interaction is tested with a Wald test; the null hypothesis that closure\(\,=\,\)0 & closure*technological proximity\(\,=\,\)0, is rejected with a \(p\) value of 0.0394 (\(\hbox {Chi}^{2}(2)=8.34\)).
Fig. 4 
Predicted number of forward citations—closure versus non-closure
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Cassi, L., Plunket, A. Proximity, network formation and inventive performance: in search of the proximity paradox. Ann Reg Sci 53, 395–422 (2014). https://doi.org/10.1007/s00168-014-0612-6
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DOI: https://doi.org/10.1007/s00168-014-0612-6