Category Archives: Networks

“Small and Other Worlds: Global Network Structures from Local Processes,” G. Robins et al (2005)

The global structure of a network is a function of local decisions made by agents on the network. For instance, agents may have a propensity to form triads, where A and C have a greater propensity to be connected if A is already connected to B and B to C (this is called balance theory). Given local properties such as balance theory, what should we expect the global network to look like; for instance, what will be the average path length between any two agents? The standard random graph model, a Bernoulli graph, assigns a number p(ij) of a connection between any agents i and j, but clearly this does not allow any local effects beyond the dyad level. Robins and coauthors show how to use the simulate distributions of “Markovian random graphs” that allow for examination of the changes in the distribution of the global structure when, for instance, propensity for triads decreases. The Markovian graph distribution can then be compared using maximum likelihood techniques to a Bernoulli graph distribution in order to examine the size of the effects. The statistics in this paper are not terribly complicated; over the past five years, hypothesis testing on (inherently-correlated) network data has been a booming field of research.

http://www.stats.ox.ac.uk/~snijders/RobinsPattisonWoolcock2005.pdf

“Predicting with Networks: Nonparametric Multiple Regression Analysis of Dyadic Data,” D. Krockhardt (1988)

Consider inference on a matrix dyadic data, such as predicting future income based on a binary friendship relation among i and j, or a measure of distance between i and j in a hierarchy. The problem is that OLS on the dyadic data matrix will suffer from a problem that looks like autocorrelation – by definition, the dependent variable for i is a function of i’s relations with i and j, and therefore is likely to be correlated with the dependent variable for j. Standard econometric tools like GLS have trouble here, because GLS requires a model of the autocorrelation matrix, and there is often no theoretical basis for assumptions on this matrix when using network data. Using Monte Carlo analysis, Krockhardt shows that the Quadratic Assignment Procedure (developed in the 1960s) gives accurate hypothesis tests no matter the level of autocorrelation.

http://www.andrew.cmu.edu/user/krack/documents/pubs/1988/1988%20Predicting%20with%20Networks%20-%20MRQAP.pdf

“Network Analysis in the Social Sciences,” Borgatti et al, 2009

A review article in Science on the use of social networks in the social sciences. Discusses the types of ties that might exist between nodes (including interactions and firm relations, such as “mother of”), common descriptive properties (“small world”, “homophily”, “centrality”, etc.), and types of questions concerning the formation and dynamics of such a network that have been analyzed in such a graph-theoretic framework. Fairly basic if you know the field, but useful as a mint of citations.

http://www.steveborgatti.com/papers/SNA_Review_for_Science.pdf

“The Impact of Social Structure on Economic Outcomes,” Mark Granovetter, 2005

JEP, 2005. Summary of sociological research that can be useful to economics. In particular, job search models are problematic because they don’t take into account endogeneity of a person’s social network. In societies where job turnover is low, few people have ties outside their workplace (even weak ties) and thus do not jump ship. In societies where job turnover is high, people will have many ties outside their firm, endogenously increasing job turnover. Further, non-anonymous trade is common – bankers give lower rates to their friends, cartels shut down new entrants not from “their class” out of a belief that the cartel will be hard to maintain with out-of-class newcomers. Finally, new goods need to be “accepted” – examples include life insurance and derivatives. It is sometimes seen that they are promoted by people who have no way to get their investment back.

http://www.stanford.edu/dept/soc/people/mgranovetter/documents/granimpacteconoutcomes_000.pdf

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