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