Discussion of "Google matrix of world trade" @ DNB

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 could 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

4

Trajectory geodesic paths, paths, trails or walksTransmission parallel/serial duplication or transfer

Source: Borgatti (2004)

Centrality depends on network process

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 a

– Gi,j= aSi,j + (1- )/a N

– =0 -> a complete symmetric network

– =1 -> a 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