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14th Annual DNB Research Conference 2-4 November 2011. Discussion of “Google matrix of the world trade network” by L. Ermann and D.L .Shepelyansky. Kimmo Soramäki www.fna.fi. The paper. Investigates the properties of a particular centrality measure - Pagerank
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14th Annual DNB Research Conference 2-4 November 2011 Discussion of “Google matrix of the world trade network”by L. Ermann and D.L .Shepelyansky Kimmo Soramäkiwww.fna.fi
The paper • Investigates the properties of a particular centrality measure -Pagerank • And its applicability in describing nodes in commodities trade networks • Ties in with research developed in parallel in matrix theory, physics, sociology, computer science • Question today: can the approach be used for banking networks?
Common centrality measures Degree: number of links Closeness: distance to other nodes via shortest paths Betweenness: number of shortest paths going through the node Eigenvector: nodes that are linked byother important nodes are more central, probability of a random process
Centrality depends on network process Trajectory geodesic paths, paths, trails or walksTransmission parallel/serial duplication or transfer Source: Borgatti (2004)
Problem with EV centrality It can be (meaningfully) calculated only for “Giant Strongly Connected Component” (GSCC) Random process would end at GOUT (dangling links, dead-ends)
Pagerank solves this with “damping factor” • Damping factor a • Gi,j= aSi,j+ (1-a)/N • a=0 -> complete symmetric network • a=1 -> EV centrality • Originalstory: Web surfer will go to a random page after surfing to a page without outbound links -> How good of a story for other processes, such as trade?
How about bipartite networks • Bipartite networks have links between two types of nodes (call them exporters and importers) • Are countries in mainly exporter or importers? Doesit work better for more complex products. • How much are the results driven by the damping factor? • How much more information does Pagerank or Cheirank bring?
All commodities ExportRank PageRank CheiRank ImportRank
Barley ExportRank PageRank CheiRank ImportRank
Use it for financial stability? • Mostly interested in contagion process, high policy interest for measures of systemic importance • Quite a number of empirical papers on financial systems that look at different metrics • Interbank payments: Soramäki et al (2006), Becher et al. (2008), Boss et al. (2008), Pröpper et al. (2009), Embree and Roberts (2009), Akram and Christophersen (2010) … • Overnight loans: Atalay and Bech (2008), Bech and Bonde (2009), Wetherilt et al. (2009), Iori et al. (2008) and Heijmans et al. (2010), Craig & von Peter (2010) … • Flow of funds, Credit registry, Stock trading…: Castren and Kavonius (2009), Bastos e Santos and Cont (2010), Garrett et al. 2011, Minoiu and Reyes (2011), (Adamic et al. 2009, Jiang and Zhou 2011) … • More at www.fna.fi/blog
Interpretation for financial stability • Similar process as payments (transfer), not so sure about counterparty risk (parallel duplication) • Closest to Bech-Chapman-Garratt (2008) • “Which Bank Is the “Central” Bank? An Application of Markov Theory to the Canadian Large Value Transfer System” • Page/Cheirank as systemic importance/ vulnerability? • “too interconnected to fail” • What is the theory, what is the process in the network? • Contagion models? Cascading failures models? • How to test it? • Regressions? Simulations that emulate the process? Agent-based models?
The paper ends with: “We hope that this new approach based on the Google matrix will find further useful applications to investigation of various flows in trade and economy.”
Try it with some BIS statistics • Nodes • Countries that have out and inbound links reported • Consider GSCC only • Links • National banking systems' on-balance sheet financial claims by country • Table 9D, “Foreign claims by nationality of reporting banks, ultimate risk basis” • Look at damping factor and Page/Cheirank plane Has claim from A B Owes money to
Page vs Cheirank Systemically important Systemically important and vulnerable Systemically vulnerable