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(http://arxiv.org/abs/1103.5027) by L. Ermann and D.L .Shepelyansky at

De Nederlandsche Bank conference "Complex systems: Towards a better

understanding of financial stability and crises"

(http://bit.ly/tj6G2h)

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- 1. 14th Annual DNB Research Conference2-4 November 2011Discussion of“Google matrix of the world trade network”by L. Ermann and D.L .ShepelyanskyKimmo 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 could be used for banking networks
- 3. Common centrality measuresDegree: number of linksCloseness: distance to othernodes via shortest pathsBetweenness: number of shortestpaths going through the nodeEigenvector: nodes that are linked byother important nodes are more central,probability of a random process
- 4. Centrality depends onnetwork processTrajectory geodesic paths, paths, trails or walksTransmission parallel/serial duplication or transfer Source: Borgatti (2004) 4
- 5. Problem with EV centralityIt can be (meaningfully) calculated only for “Giant StronglyConnected Component” (GSCC) Random process would end at GOUT (dangling links, dead-ends)
- 6. Pagerank solves this with“damping factor”• Damping factor – Gi,j= Si,j – complete symmetric network – EV centrality• Original story: 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? Does it 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 PageRank CheiRank ImportRank ExportRank
- 9. Barley PageRank CheiRank ImportRank ExportRank
- 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 theGoogle matrix will find further useful applicationsto investigation of various flows in tradeand 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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