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
• 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?
Common centrality measures
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
Centrality depends on
network process
Trajectory
geodesic paths, paths, trails or walks
Transmission parallel/serial duplication or transfer
Source: Borgatti (2004)
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 a
– Gi,j= aSi,j + (1-a)/N
– a=0 -> complete symmetric network
– a=1 -> 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
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 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
Has claim from
A
B
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
Systemically important and vulnerable
Systemically vulnerable
Thank you