discussion of “google matrix of the world trade network” by l. ermann and d.l .shepelyansky
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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 - PowerPoint PPT PresentationTRANSCRIPT
Discussion of
“Google matrix of the world trade network”by L. Ermann and D.L .Shepelyansky
Kimmo Soramäkiwww.fna.fi
14th Annual DNB Research Conference2-4 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 byother important nodes are more central, probability of a random process
Common centrality measures
Trajectory geodesic paths, paths, trails or walksTransmission parallel/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
– 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?
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
PageRank CheiRank ImportRank ExportRank
Barley
PageRank CheiRank ImportRank 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 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 tradeand 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
A B
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