Discussion of “Google matrix of the world trade network” by L. Ermann and D.L.Shepelyansky Kimmo Soramäki 14th Annual DNB Research Conference 2-4 November 2011

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?

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 by other important nodes are more central, probability of a random process Common centrality measures

Trajectorygeodesic paths, paths, trails or walks Transmissionparallel/serial duplication or transfer Source: Borgatti (2004) Centrality depends on network process 4

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  – G i,j =  S i,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?

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?

All commodities PageRankCheiRankImportRank ExportRank

Barley PageRankCheiRankImportRank ExportRank

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

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 AB Has claim from Owes money to

Alpha 1 (left) and 0.85 (right)

Alpha 0.5 (left) and 0 (right)

Pagerank vs Cheirank

Page vs Cheirank Systemically important and vulnerableSystemically important Systemically vulnerable

Thank you