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Discussion of “Google matrix of the world trade network” by L. Ermann and D.L .Shepelyansky

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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Discussion of “Google matrix of the world trade network” by L. Ermann and D.L .Shepelyansky

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  1. 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

  2. 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?

  3. 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

  4. Centrality depends on network process Trajectory geodesic paths, paths, trails or walksTransmission parallel/serial duplication or transfer Source: Borgatti (2004)

  5. 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)

  6. 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?

  7. 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?

  8. All commodities ExportRank PageRank CheiRank ImportRank

  9. Barley ExportRank PageRank CheiRank ImportRank

  10. 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

  11. 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?

  12. 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.”

  13. 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

  14. Alpha 1 (left) and 0.85 (right)

  15. Alpha 0.5 (left) and 0 (right)

  16. Pagerank vs Cheirank

  17. Page vs Cheirank Systemically important Systemically important and vulnerable Systemically vulnerable

  18. Thank you

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