Economic Networks - Coping with Crises in Complex Socio

Introduction Ownership Trade and lending Queries DebtRank DebtRank Application Conclusion

Economic NetworksCoping with Crises in Complex Socio-Economic Systems

G. Caldarelli1

1IMT Alti Studi Lucca, ItalyInst. of Complex Systems CNR, Dep. Physics Univ. "Sapienza" Rome, Italy

MOCAP ConferencePostdam October 5th 2012

Guido Caldarelli FOC project and Economic Networks


Economic Network and Stability

Do Networksincrease/decreasestability?Consequently, can wecreate/remove them?How networks affecttraditional financialagents activity?



Financial Networks and Systemic Risk

European Central Bank’s view1 on monitoring systemic stability:

1 develop new concepts and models2 take into account networks3 build integrated information systems4 look at new systemic risk indicators

1ECB Issing Report 2009Guido Caldarelli FOC project and Economic Networks


Scientific activity

http://www.focproject.net

Forecasting

What is feasible:Estimating systemic riskSimulating plausible future scenarios



Financial Networks and Systemic Risk

Systemic risk is the probability that a large fraction of financialinstitutions go in distress at the same time.

Systemic crisis1 have large costs for the real economy and the society,2 can emerge endogenously, without an external shock.

Financial institutionsform a global networkof financial ties (e.g.lending, or equity)Derivatives createadditional andundisclosed ties



Economic Networks

Networks appear at all the levels of Economic SystemsOwnershipTradeLendings

Finally the social network of investors can help in identifyingtrends



Web of Property

If property is diffused, bankruptcy is limited to a single companyand few subcompanies.



World Property Net

An analysis of 43,000 companies worldwide showed that arelatively small group of banks own a disproportionally large setof them

1 Barclays plc2 Capital Group Companies Inc3 FMR Corporation4 AXA5 State Street Corporation6 JP Morgan Chase & Co.7 Legal and General Group plc8 ....



Control

From public data we can checkwho owns whom (and thenumber of shares)Out of 30 Millions of companieswe can find 43,000Trans-national Companies (TNC)

Take home message

147 topholders in the core of the TNC network, control nearly40% of the TNC value.

S. Vitali, J. B. Glattefelder, S. Battiston, PLOS One, 6(10): e25995 (2011)


Introduction Ownership Trade and lending Queries DebtRank DebtRank Application ConclusionWorld Trade Web Banks

WTW Data

Analysis is done on various years2

M.-A. Serrano, M. Boguñà and A. Vespignani, J. Ec. Int. & Contr. 2, 111-124 (2007)

2http://www.intracen.org/menus/countries.htm and http://www.tswoam.co.uk/world



WTW Modelling

GDPThe GDP determines the property of the network

A fitness model based on GDP reproduces the dataxi =

wi∑Nj=1 wj

f (xi , xj) =δxixj

1 + δxixj

where wi is the GDP of country i and δ > 0 is the only freeparameter of the model

G. Caldarelli, A. Capocci, P. De Los Rios and M.-A, Muñoz, PRL 89, 258702 (2002)



The product taxonomy



The country product matrix

The information is a rectangular matrix Mcp(Mij = 0,1)In year 2000 we have 129 countries and 779 products.

M =

AlbaniaArgentina

...Zimbabwe

M11 M12 . . . M1Np

M21 M22 . . . M2Np...

.... . .

...MNc1 MNc2 . . . MNcNp

0111 0112 . . . 9710

0111 = Growing of Cereals, but rice0112 = Growing of Rice. . .

9710 =Service-Producing Activities of Private Households



The two “projected matrices”

TransposeIf M is Nc × Np then

C := MMT is Nc × Nc

P := MT M is Np × Np

Cij = [MMT ]ij = # products produced by both countries i , jPij = [MT M]ij = # countries producing both products i , j



A simple topological analysis

One simple analysis is to define a dissimilarity xij

Define the sets Si and Sjof i,j neighborsCompute the number ofelements N(S) in thesesets

Dissimilarity

One used formula is xij = 1− 2 N[S(i)∩S(j)]N[S(i)]+N[S(j)]

or equivalently

xij = 1− 2Cij

Cii + Cjj



Network of competition

We can cluster Countries according to their products



Network of sectors



Network of sectors

PARTS AND ACCESSORIES OF MOTOR VEHICLES



Trade Networks

Trade aggregated or not, is anetworkWe can learn from the structureof trade webWe can use networks to visualizehidden information

Take home message

Networks quantify, importance & centrality of countries andtheir competition

A. Tacchella et al., http://arxiv.org/abs/1108.2590 (2011)



Networks out of regulations

European Central Bank must avoid liquidity crises



ECB policy

ECB

Bank 1

Bank 2

Bank 3

The requirement to depositcash the 2% of all depositand debts into the nationalbanks generates tradingbetween banks.



Dataset

e-MIDThe data set analysed is the electronic broker market forinterbank deposit e-MID reference dataset. This data iscomposed by 586007 overnight transactions (i.e. payments ofloans done in 24 hours) concluded from January 1st ,1999 toDecember 31st ,2002. The network is composed by a set of Nbanks. The average number of active banks is 〈N〉 = 140connected by an average number of links L = 200. In case ofmultiple transactions among banks i and j we count just onelink.



The structure of the market



Intraday Bank Networks

Large banks borrow franticallySmall banks mostly lendThe system is intrinsically fragile

Take home messageIn a complex systems reasonable requests produceunexpected results

G. De Masi, G. Iori, G. Caldarelli PRE 74 066112 (2007)



Querylogs

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20091102 20100113 20100326 20100609 20100819 20101029

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AMZN Volumes

Date

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Vol

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Trading VolumesQuery Volumes

Take home message

Queries are correlated with market trends

I. Bordino et al. http://arxiv.org/abs/1110.4784



Dataset

In the period May 1st2010 - April 30th2011:we took market volumes of the 100 stocks in NASDAQ100;we looked in the querylog for:

the tickers (apple –> aapl)the name of the company (and in case cleaned the results);

we aggregate the data at the level of day (Googletrendsaggregates at the time width of week).

CorrelationWe measured a correlation between the two time series

For both datasets we focus on n = 250 working days during theabove period.



Pearson Correlation Coefficient

The time-lagged Pearson cross correlation r(δ) coefficientbetween two time series Xt and Yt is:

r(δ) =∑n

t=1(Xt − X )(Yt+δ − Y )√∑nt=1(Xt − X )2

√∑nt=1(Yt+δ − Y )2

(1)

X , Y are the sample average of the two time seriesδ is a time lag.To reduce short-term fluctuations, for each time series, we alsoaverage the signal at a given time t with the w − 1 previouspoints. We use windows of width w = 1,2,3,5.



Pearson Correlation Coefficient

Time evolution of query-logs normalised volumes for the ticker"NVDA" compared with the trading-volume of the "NVIDIACorporation". plain lines (positive time lag) are always larger thandashed lines (negative timelag). Therefore suggesting that searchvolumes anticipate trading



Results

W CCF-5 -4 -3 -2 -1 0 1 2 3 4 5

1 0.03431 0.08416 0.09454 0.11437 0.19947 0.35302 0.28022 0.13923 0.08929 0.07361 0.057832 0.06015 0.09980 0.13057 0.17726 0.29583 0.40793 0.36126 0.22151 0.13363 0.10112 0.087733 0.07526 0.11693 0.16489 0.25045 0.35252 0.42378 0.39275 0.29334 0.19062 0.13354 0.108475 0.11506 0.17759 0.25169 0.32711 0.39177 0.43181 0.41197 0.35715 0.29148 0.22416 0.16403

Table : Average Cross-correlation time series for nasdaq-100companies (query: Ticker)



Granger Causality test

DefinitionWe want to determine whether a time series X (t) is useful inforecasting another time series Y (t).

X (t) Granger-causes Y (t) if Y (t) can be better predicted usingboth the histories of X (t) and Y (t) rather than using only thehistory of Y (t).The test can be assessed by regressing Y (t) on its owntime-lagged values and on those of X (t).An F-test is then used to examine if the null hypothesis thatY (t) is not Granger-caused by X (t) can be rejected.



Results

Dataset lag (days) Direction %p < 5% %p < 1% Avg reduction in RSSQ (100 tickers) 1 Q → T 48% 32% 5.2%Q (100 tickers) 1 T → Q 15% 5% 1.5%U (100 tickers) 1 U → T 48% 36% 5.4%U (100 tickers) 1 T → U 16% 4% 1.74%Q (100 tickers) 2 Q → T 52% 40% 6.9%Q (100 tickers) 2 T → Q 22% 8% 2.31%U (100 tickers) 2 U → T 53% 41% 7.6%U (100 tickers) 2 T → U 25% 8% 2.8%Q (82 tickers) 1 Q → T 53.66% 36.59% 5.71%Q (82 tickers) 1 T → Q 14.6% 6.1% 1.48%U (82 tickers) 1 U → T 53.66% 41.46% 6.04%U (82 tickers) 1 T → U 17.07% 4.88% 1.84%Q (82 tickers) 2 Q → T 57.32% 45.12% 7.66%Q (82 tickers) 2 T → Q 23.17% 7.32% 2.39%U (82 tickers) 2 U → T 57.32% 46.34% 8.35%U (82 tickers) 2 T → U 22.99% 8.54% 2.97%

Table : Granger Causality Test



Financial and Economic Networks and Systemic Risk

RobustnessAs in infrastructural networks, economic and financial systemsform an interconnected web with unexpected fragilities

If you consider a financial network you would like to knowwhich ties connect the various financial institutions;what is the global effect of bankruptcy;how network theory can help in controlling and possiblyrecovering.



Importance for policy makers

Network theory allows to sort out relevant information. Inparticular we can use a centrality measure to assess locallythe global impact that a default might have.

Centrality measure:more central moresystemicallyimportantit’s not just a rankingmeasures total losscaused to the system



Take-Home Message

DebRank is a novel indicator to identifySIFI (Systemically Important Financial Institutions)groups of SIFI

DebtRank overcomes some limitations instandard stress-test techniques incl. default-cascade algostandard network mesures (e.g. betweenness, centralityetc.)



Take-Home Message

DebRank is a novel indicator to identifySIFI (Systemically Important Financial Institutions)groups of SIFI

DebtRank overcomes some limitations instandard stress-test techniques incl. default-cascade algostandard network mesures (e.g. betweenness, centralityetc.)


Introduction Ownership Trade and lending Queries DebtRank DebtRank Application ConclusionCentrality Dynamics

Which is the best choice?

Vertex Status (too big to fail)

Degree (too connected to fail)



Terminology

Aij= amount invested by i in the funding of jAi= total amount invested by i defined as Ai =

∑l Ail

Ei = capital of i . When Ei < γ the institution defaultsγ= positive thresholdWij= impact of i on j defined as Wij = min{1,Aij/Ej}vi= relative economic value of i defined as vi = Ai/

∑l Al

di= debt of iφi=fragility of i defined as φ(i) = di/Ei



DebtRank Centrality

We starting from feedback centrality adapted to financialdistressA node is more important if it impacts on many valuableand important nodes

ci =∑

j

Wijvj +∑

j

Wijcj → c = (I −W )−1Wv

Centrality measures total outgoing flow, includingreverberationStrategy: keep real impact and tame the reverberation inthe cycles by excluding walks already visited



Debt Rank Dynamics

continuous variable hi ∈ [0, 1].3 possible states, undistressed, distressed, inactive:si ∈ {U, D, I}.Sf : set of nodes in distress at time 1. hi(1) = ψ ∀i ∈ Sf ;hi(1) = 0∀i /∈ Sf , and si(1) = D ,∀i ∈ Sf ; si(1) = U ∀i /∈ Sf .

hi(t) =min{

1,hi(t − 1) +∑

j

Wjihj(t − 1)}, where j | sj(t − 1) = D

si(t) ={

D if hi(t) > 0 & si(t − 1) 6= IU otherwise,



DebtRank value

DefinitionThe DebtRank of a set S is defined as

R =∑j∈S

hj(T )vj −∑j∈S

hj(1)vj

If S is the network and the initial condition is ’only one node indistress’ we can assess the effect of a single default on thewhole system.



How to compute

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h=0.5

h=0.5

h=0.5

h=0 h=0

h=0 h=0

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h=1

h=0.5

h=0.5

h=0.5

h=0.25 h=0.25

h=0 h=0

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7 8

h=1

h=0.5+

0.125

h=0.5

h=0.5

h=0.25+

0.125

h=0.25

h=0.125 h=0.125


Introduction Ownership Trade and lending Queries DebtRank DebtRank Application ConclusionData Figures

A Specific Case of Study: the FED

The Federal Reserve System (FED) is the central banksystem USA.FED serves as lender of last resort not excludingemergency lending facilities as, for example, the discountwindow.FED during the credit crisis of 2007, put in place severalemergency programs to assist individual institutions forinstance the support to the AIG, and the help extended toJP Morgan in acquiring Bear Sterns.The supreme court of the United States asked to releaseexposure data to the public in batches on Dec. 1, 2010,March 31 and July 6 of 2011.



FED Data

The data is especially relevant to systemic risk because1 it covers specifically the emergency loans, i.e., those loans

for which FED is the lender of last resort.2 it allows to obtain insights into the financial fragility of many

key players in the US, as well as in the global financialsystem.



The network of exposure

The original FED dataset consists of 30 thousands pdf pages.Each entry reports the name of the borrowing institution, thecredit channel used for financing, the origination date and thematurity date of each loan.

Bloomberg data

Bloomberg analysed the FED dataset releasing a set of excelfiles on Dec 23, 2011. Data consists of a set of 407 dailytimeseries’ of outstanding debt and market capitalizations.



The time evolution

17/03/08 Bearn Sterns acquired by JP Morgan Chase (240 M US $)

18/09/08 Lehman Brothers default after payback of 38.5 M US$ to FED

16/09/08 Citigroup announced losses for 2.8 G US$

07/03/09 All institutions collectively got at the minimum of market capitalization



The star-like network

As always happens in this kind of data only partialinformation is availableWe got only the ties between FED and Institutions

Reconstructing informationWe took banks’ investment in each others equity share as aproxy of all exposures

(Orbis 2007 Database of 43060 TransNational Companies)Vitali S, Glattfelder JB, Battiston S, The Network of Global Corporate Control. PLoS ONE 6 e25995 (2011)



The plots

We take about 20 amongst the largest financial institutionswith debt larger than 5 Millions USDThe nodes are positioned within a circle of radius R=1,centred in 0.The distance of each node from the center is proportionalto DebtRankAlso the angle (∈ [0,10π]) grows in the spiral withDebtRank

Scatter plot of DebtRank versus asset size,fraction (in percentage) of the total of the asset size in thenetwork.The size of each bubble is proportional to the outstandingdebt of the institutionwhile the color reflects its fragility



periods 1-2



periods 3-4



periods 5-6


Introduction Ownership Trade and lending Queries DebtRank DebtRank Application ConclusionImportance FOC project

Systemic Risk - Global Perspectives

Perfect storm, unforeseen.Big banks are to big-to-fail. We have to rescue the financialsystem.Liquidity drainage: call the plumber and squeezelow-income tax payers

Surely, an issue isNetwork architecture, resilience, liquidity flowI.e. a “plumbing” issue




























Indicators of Systemic Importance

Standard stress-test approach based on default cascades.Issues:

only default mattersalmost never systemic defaults

Standard network approachmeasures of centrality do not have an economic meaning

eigenvector centralitybetweenness, degree, closeness, etc.



Conclusion

The economy is composed by a series of networks

Individuals determining markettrendsCompanies trading andinteractingBanks providing liquidityCountries organizing trade andproduction

Take home message

All the above features can be explained by network of networks



The FOC Consortium

CNR-IMT (RM-LU, I) A. Gabrielli, F. Pammolli, L. PietroneroU. Marche (Ancona, I) L. Bargigli, D. Delli Gatti, M. Gallegati

ETH (Zürich, CH) S. Battiston, M. Puliga, F. SchweitzerCITY (London UK) G. Iori, S. JafareySaïd BS (Oxford UK), F. Reed-Tsochas, A. GerigYahoo! (Barcelona) A. Gionis, I. Bordino, A. Ukkonen, I. WeberECB (Frankfurt, EU) M. Grande, O. Castrén

From September 2011JSI (Ljubljana, SLO) I. Mozetic, M. GrcarRBI (Zagreb, CRO) T. Smuc, V. ZlaticELTE (Budapest, H) I. Kondor

From March 2012BU (Boston, USA) I. Vodenska, H. Gene Stanley

KY (Kyoto, J) Y. Fujiwara, H. Aoyama,


Documents

Economic Networks - Coping with Crises in Complex Socio