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Modeling knowledge networks in economic geography: a discussion of four methods

Abstract

The importance of network structures for the transmission of knowledge and the diffusion of technological change has been recently emphasized in economic geography. Since network structures drive the innovative and economic performance of actors in regional contexts, it is crucial to explain how networks form and evolve over time and how they facilitate inter-organizational learning and knowledge transfer. The analysis of relational dependent variables, however, requires specific statistical procedures. In this paper, we discuss four different models that have been used in economic geography to explain the spatial context of network structures and their dynamics. First, we review gravity models and their recent extensions and modifications to deal with the specific characteristics of networked (individual level) relations. Second, we discuss the quadratic assignment procedure that has been developed in mathematical sociology for diminishing the bias induced by network dependencies. Third, we present exponential random graph models that not only allow dependence between observations, but also model such network dependencies explicitly. Finally, we deal with dynamic networks, by introducing stochastic actor-oriented models. Strengths and weaknesses of the different approach are discussed together with domains of applicability the geography of innovation studies.

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Notes

  1. 1.

    A burgeoning literature starts to integrate the geographical dimension in sociology and network science: see for instance the special issue 34.1 in Social Networks of January 2012 on Capturing Context: Integrating Spatial and Social Network Analysis, edited by Jimi Adams, Katherine Faust and Gina Lovasi.

  2. 2.

    See the special issue 43.3 in The Annals of Regional Science of September 2009 on Embedding Network Analysis in Spatial Studies of Innovation, edited by Edward Bergman.

  3. 3.

    For an early overview of studies that applied the gravity model in economic geography, see Lukermann and Porter (1960).

  4. 4.

    However, the term “gravity model” is not often used when studies are conducted at the micro-level. Rather scholars research the effect of geographical proximity on network formation.

  5. 5.

    In practice, it would be possible to estimate the gravity model with these techniques.

  6. 6.

    Please note that we only discuss problems specifically pertaining to network data. Other problems related to, for example, the fact that the outcome is not always a continuous numeric variable and the many zeros in the network (e.g., Helpman et al. 2008; Burger et al. 2009b) and causality (e.g., Egger 2004) are discussed elsewhere in the literature. Although these are problems that all empirical researchers are facing, a discussion of these issues is beyond the scope of this paper.

  7. 7.

    Another (non-spatial) method that controls for the network structure but is not often used in the gravity model literature is the multiple regression quadratic assignment procedure (MRQAP). A more elaborate discussion of this method can be found in the next section.

  8. 8.

    Comparable alternative specifications of remoteness terms in gravity equations are provided by Helliwell (1997) and Head and Mayer (2000).

  9. 9.

    For a more elaborate critique on the use of remoteness indices, see Anderson and Wincoop (2003).

  10. 10.

    Less well known but comparable empirical strategies in this respect are provided by Bikker (2010) and Linders et al. (2010).

  11. 11.

    The mathematical appendix and Matlab codes of the approach by Behrens et al. (2012) can be found in the Web Appendix of their article, available at the Journal of Applied Econometrics website. Likewise, James LeSage offers a spatial econometrics toolbox at http://www.spatial-econometrics.com/.

  12. 12.

    Accordingly, MRQAP is rather a particular permutation method for hypothesis testing and not a model on its own. However, we will refer to it as model in the following to keep a consistent terminology.

  13. 13.

    Besag (1974, 1975) applied this idea the context of spatial data the idea is, however, also applicable in the context of network data.

  14. 14.

    See Lusher et al. (2013) for a more detailed introduction to ERGM.

  15. 15.

    More details can be found in Robins et al. (2007).

  16. 16.

    This class of models is often referred to directly as SIENA models. SIENA stands for “Simulation Investigation for Empirical Network Analysis.” The RSiena package is implemented in the R language and can be downloaded from the CRAN website: http://cran.r-project.org/web/packages/RSiena/.

  17. 17.

    For a discussion of these assumptions, see Federico (2004), while for a summary, the reader is referred to Snijders et al. (2010a).

  18. 18.

    See Liu et al. (2013) for an example of how GM can be used to model regional networks.

  19. 19.

    As pointed out by one of the referee, it is possible to avoid complete cliquishness or to go beyond assuming symmetric ties in two-mode networks if researchers have detailed data on the level of involvement/learning of actors in a given event.

  20. 20.

    In SAOM, it is assumed that all agency ruling the dynamics of the network comes from the actors of the first mode of the two-mode network (Snijders et al. 2013). As a result, the second mode is passive and cannot decide to establish a link with the first mode. Besides, no coordination is possible between the first and second mode.

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Acknowledgments

The authors would like to thank two anonymous referees and Tom Snijders for very helpful comments and suggestions. Of course, all remaining errors are ours.

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Broekel, T., Balland, PA., Burger, M. et al. Modeling knowledge networks in economic geography: a discussion of four methods. Ann Reg Sci 53, 423–452 (2014). https://doi.org/10.1007/s00168-014-0616-2

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