Netconomics. Viewing A Connected World. Andreas Joseph. Centre for Chaos and Complex Networks City University of Hong Kong

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1 Netconomics Viewing A Connected World Andreas Joseph Centre for Chaos and Complex Networks City University of Hong Kong Econophysics & Networks Across Scales: May 2013, Lorentz Center, Leiden May 29, 2013

2 Overview 1 Thought I: Network Indicators for Financial Crises 2 Thought II: A Unied Framework for Network Mining 3 Thought III: A Platform - netconomics.info 4 Discussion

3 Thought I: Network Indicators for Financial Crises

4 PIN Review: The Global Financial Crisis 2008 (GFC'08) Pre-conditions and progression of the GFC'08: Strongly hierarchical global nancial system with its geographical center in the US (see below). Financial innovation, and subsequent proliferation of complex nancial products, leading to strong inter-dependencies of nancial institutions (triggered by the Basel II regulatory framework) US sub-prime mortgage crisis as an internal and local shock (failure) to the most central node. Propagation of this shock via the global nancial network of inter-dependencies. Dry-up of the inter-bank lending market, putting many systematically important institutions at risk (GFC'08). Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 4 / 56

5 PIN Proxy-Network Analysis This scenario is exactly in the realm of network science. Observations: Idea Relevant data are often deemed condential on the institutional level. Financial derivatives are often traded decentralised (OTC). The modern nancial system can be classied as an inter-connected multi-layered network structure. Because of the global nature of the modern nancial system, one may consider aggregate data on the inter-economy level. Co-Evolution of cross-border Portfolio Investment Networks (PIN). Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 5 / 56

6 PIN Proxy-Network Analysis This scenario is exactly in the realm of network science. Observations: Idea Relevant data are often deemed condential on the institutional level. Financial derivatives are often traded decentralised (OTC). The modern nancial system can be classied as an inter-connected multi-layered network structure. Because of the global nature of the modern nancial system, one may consider aggregate data on the inter-economy level. Co-Evolution of cross-border Portfolio Investment Networks (PIN). Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 5 / 56

7 PIN Proxy-Network Analysis This scenario is exactly in the realm of network science. Observations: Idea Relevant data are often deemed condential on the institutional level. Financial derivatives are often traded decentralised (OTC). The modern nancial system can be classied as an inter-connected multi-layered network structure. Because of the global nature of the modern nancial system, one may consider aggregate data on the inter-economy level. Co-Evolution of cross-border Portfolio Investment Networks (PIN). Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 5 / 56

8 PIN PIN Denition, Data and Set-up Denition Investment position (edge) of an resident/institution of one country (node) into a resident/institution of another country. Data Coordinated Portfolio Investment Survey (CPIS) of the International Monetary Fund (IMF) for 78 reporting creditor-countries, containing cross-border positions for equity securities (E), long-term (LD) and short-term debt securities between the years (end of the year). Set-up Focus on the equity- and long-term debt parts (majority): E-PIN & LD-PIN. Consider threshold graphs with e p = 50 million USD (focus and th error reduction): Maximal common percolation threshold of the LD-PIN. Extract Largest strongly connected component: Core of a sea urchin. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 6 / 56

9 PIN PIN Denition, Data and Set-up Denition Investment position (edge) of an resident/institution of one country (node) into a resident/institution of another country. Data Coordinated Portfolio Investment Survey (CPIS) of the International Monetary Fund (IMF) for 78 reporting creditor-countries, containing cross-border positions for equity securities (E), long-term (LD) and short-term debt securities between the years (end of the year). Set-up Focus on the equity- and long-term debt parts (majority): E-PIN & LD-PIN. Consider threshold graphs with e p = 50 million USD (focus and th error reduction): Maximal common percolation threshold of the LD-PIN. Extract Largest strongly connected component: Core of a sea urchin. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 6 / 56

10 PIN PIN Denition, Data and Set-up Denition Investment position (edge) of an resident/institution of one country (node) into a resident/institution of another country. Data Coordinated Portfolio Investment Survey (CPIS) of the International Monetary Fund (IMF) for 78 reporting creditor-countries, containing cross-border positions for equity securities (E), long-term (LD) and short-term debt securities between the years (end of the year). Set-up Focus on the equity- and long-term debt parts (majority): E-PIN & LD-PIN. Consider threshold graphs with e p = 50 million USD (focus and th error reduction): Maximal common percolation threshold of the LD-PIN. Extract Largest strongly connected component: Core of a sea urchin. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 6 / 56

11 PIN PIN Volume PIN volume is of the order of world-gdp, and peaks at around 60% of that at the end of The GFC'08 manifests itself most strongly in the E-PIN (oating edge nature). Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 7 / 56

12 PIN PIN Co-Evolution LD- and E- fractions of total PIN are strongly anti-correlated. Before the GFC'08, there is a continuous shift from the LD-PIN to the E-PIN. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 8 / 56

13 PIN PIN Co-Evolution LD- and E- fractions of total PIN are strongly anti-correlated. Before the GFC'08, there is a continuous shift from the LD-PIN to the E-PIN. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 9 / 56

14 PIN PIN Hierarchy The E-PIN is strongly dominated by the US. It exhibits a shell-structure with the US at its center. The LD-PIN is less hierarchical, but still dominated by a small group of countries (JP, FR, US, DE,...). Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 10 / 56

15 PIN E-PIN Properties The E-PIN expanded substantially before the GFC'08 (number of edges M and volume). While the increase in the number of nodes stagnated from about 2006 on. higher complexity Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 11 / 56

16 PIN E-PIN Properties Macroeconomic quantities, such as the S&P 1200 global stock index, scale roughly with simple network measures, such as the number of nodes M. E-PIN as proxy to quantify the stability of the global economy Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 12 / 56

17 PIN Crisis Indicator I: The Algebraic Connectivity of the E-PIN The alg. conn. of the E-PIN drops sharply, already in This fact is especially intriguing since edge density is above.3 at all times (non-sparse). Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 13 / 56

18 PIN LD-PIN Properties The LD-PIN also expanded substantially before the GFC'08 (number of edges M and volume). While the increase in the number of nodes stagnated from about 2003 on. higher complexity Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 14 / 56

19 PIN Indicator II: The Edge Density of LD-PIN The total value of equity-linked derivatives and the total outstanding amount of CDS (OTC) scale with the edge density of the LD-PIN. This allows for an indicator measuring/monitoring the inter-connectedness of nancial markets. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 15 / 56

20 PIN Indicator II: The Edge Density of LD-PIN The total value of equity-linked derivatives and the total outstanding amount of CDS (OTC) scale with the edge density of the LD-PIN. This allows for an indicator measuring/monitoring the inter-connectedness of nancial markets. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 16 / 56

21 PIN Edge Threshold Dependency: LD-PIN Almost unique percolation point at an edge strength of 50 million USD. The level of connectivity at this edge threshold e p is believed to contribute th dominantly to the global properties, while still allowing for comparability. Below/above e p, the edge density ρ shows a qualitatively dierent th behaviour ( e th 15 M USD). Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 17 / 56

22 PIN Edge Threshold Dependency: E-PIN No unique percolation point, but more oating structure. Fast expansion, which started in 2004 and stopped after the GFC'08. Edge threshold independence of the algebraic connectivity. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 18 / 56

23 PIN Conclusions The current understanding of the GFC'08 has been conrmed, while the network perspective oers a new view on nancial markets, and economics as a whole. The E-PIN and LD-PIN can be used as proxy networks to measure the state of the world economy and the global nancial architecture. Two network indicators for nancial crises have been identied: the algebraic connectivity of the E-PIN as a stability measure of global equity markets (economy). the percolation edge density of the LD-PIN as an inter-dependency measure of nancial markets. Such indicators may be of great usefulness for regulators and market participants alike, enhancing macroeconomic stability of a globalising world. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 19 / 56

24 Thought II: A Unied Framework for Network Mining

25 Composite Centrality The Concept of Composite Centrality Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 21 / 56

26 Composite Centrality Composite Centrality: Basic Ideas Measure Standardisation Desired properties of all measures: Order: Preserving. Bigger is better. Independence of the sample size. Comparable numerical ranges. Zero mean. Unit variance. Invariant Measure Composition Method to combine arbitrary standardised measures, s. t. the resulting measure is again standardised. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 22 / 56

27 Composite Centrality Measure Standardisation: A Recipe Procedure for Positive Measures: 1 Skewness: Rescaling to a mean of one. Box-Cox power-transformation. Accept the transformation if skewness could be reduced. Homogeneous measure distribution. 2 Variance: Divide all values by the corresponding sample standard deviation. Unit Variance. 3 Mean: Shift to a zero mean. 4 Order: If a smaller value is higher ranking, mirror values at the origin. Bigger-is-better ordering. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 23 / 56

28 Composite Centrality Box-Cox Transformation: Denition For a positive data set x of length N and λ R, the Box-Cox Power-Transformation is dened as x { x λ 1 λ if λ 0 ln x if λ = 0 (1) While λ is chosen to maximise the log-likelihood function log L = (λ 1) i ln x i N 2 ln ( x i x ) 2 i N (2) Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 24 / 56

29 Composite Centrality Box-Cox Transformation: Visualisation Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 25 / 56

30 Composite Centrality Measure Standardisation: An Example Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 26 / 56

31 Composite Centrality General Composite Centrality Given a set of n measures M, we dene the composite centrality as C comp (M; ω) n i=1 ω i M i, (3) σ Σ ( where σ Σ σ n s i=1 ω ) i M i is the joint sample standard deviation and ω, with ω i i = 1, is a general weighting. C comp (M) is independent of how the individual standardised measures have been combined. (This leads to the possibility to dene invariant inheritance schemes, providing additional information.) Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 27 / 56

32 Composite Centrality Statistics Review The Central Limit Theorem: Given a sample of n identically distributed and independent random variables (RV) X i with nite mean µ and variance σ 2, the sampled RV converges to a standard Normal as the sample size increases, i.e. ( n lim p i=1 X ) i nµ n σ = N (0, 1). (4) n The Lyapunov Theorem: Given a set of n random variables (RV). If all RV are independent and the 2 + δ-moments exist (for some δ > 0), the central limit theorem can be extended to include non-identically distributed RV. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 28 / 56

33 Composite Centrality A Universal Scale for Centrality Assuming that the conditions of the Lyapunov theorem hold for M ( DRT, we conclude that the composite centrality C comp M DRT comp) can be approximately described by a standard normal distribution p norm (x) = 1 [ ( x ) ] 2 exp 2π 2 (5) which oers a universal scale to measure node centralities, since it is parameter-free. Let's see!!! Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 29 / 56

34 Composite Centrality Composite Centrality: Universality Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 30 / 56

35 Composite Centrality Test of the Normal Hypothesis So far, we just assumed that the conditions of the Lyapunov theorem hold, but this may not always be the case - or cannot be proven for the general case. To check the validity of the normal hypothesis, we perform a Kolmogorov-Smirnov test (KS-test): We calculate a goodness-of-t value p, up to a precision ɛ < The KS-test compares then the maximal distance between the empirical cumulative distribution function (CDF) and the hypothetical distribution's CDF to the corresponding distance for a set of synthetic samples. The p-value is the fraction of those samples where the empirical CDF is closer to hypothetical CDF. Using a decision rule, the normal hypothesis can be rejected or accepted Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 31 / 56

36 Composite Centrality Test of the Normal Hypothesis Conservative Decision Rule Hypothesis acceptance: p > 0.1. Goodness-of-Fit Inuence Factors: number of nodes N. number of measures n. composition of measures M. edge threshold e th. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 32 / 56

37 Composite Centrality KS -Test Results: p-values in the DRT-Framework year N std. measures C C (ω) The normal hypothesis can mostly be accepted, especially for all composite measures. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 33 / 56

38 Composite Centrality A Standard Framework: D - R - T Node Centrality Criteria: Direction: incoming/outgoing - D: IN/OUT. Range: long/short - R: LO/SH. Texture: quality/quantity - T: QL/QN. A node needs to score high in all criteria to achieve a high centrality. Since the above criteria are binarily divided, we need a total of 2 3 = 8 node measures for their description. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 34 / 56

39 Composite Centrality D - R - T: Node Measures Set M DRT D - R - T description symbol IN - LO - QL in - coming ASPL l in IN - LO - QN in - coming max. ow f in IN - SH - QL in - degree d in IN - SH - QN in - strength s in OUT - LO - QL out - going ASPL l out OUT - LO - QN out - going max. ow f out OUT - SH - QL out - degree d out OUT - SH - QN out - strength s out Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 35 / 56

40 Composite Centrality An Example: The World Trade Web (WTW) Our Interest The largest strongly connected component of a threshold network: e th = 50 million USD. For the years (in ve-year steps). Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 36 / 56

41 Composite Centrality Composite Centrality Application I: Globalisation Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 37 / 56

42 Composite Centrality Composite Centrality Application II: Comparison Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 38 / 56

43 Composite Centrality Exceptionality: Idea Especially in complex networks, measures often exhibit strong - but unknown - correlations between each other. This can reduce the added value of a composite centrality analysis, since some information might get processed multiple times. The scaling of one measure with another creates a certain collective expectation. On the other hand, deviations from this expectation can be used to detect especially performing nodes or even peculiar graph congurations. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 39 / 56

44 Composite Centrality Exceptionality: Denition A component's (node or edge) exceptionality is dened as its relative deviation from this scaling: ( ) ɛ = sign C C CC (ω) f (x) (ω) f (x), (6) σ d where f (x) is the model function for the scaling and σ d is the sample standard deviation of the dierence distribution. A double-t method is used not to let outlier spoil the t. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 40 / 56

45 Composite Centrality WTW Collective Expectation Models Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 41 / 56

46 Composite Centrality WTW Export Exceptionality Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 42 / 56

47 Composite Centrality Conditional Exceptionality Diagram Statistical deviations from the scaling of total export centrality (out-going composite centrality component) under its four sub-components for the 2010-WTW. The shaded area includes the pair of "twin-nodes", Angola and Iraq, which share many of their network properties, up to the point that the great majority of their respective exports goes to a joint set of countries, without having a direct trade link by themselves. The knowledge of this conguration might be of great use for Angola and Iraq, as well as their export partners. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 43 / 56

48 Composite Centrality Summary Motivation: The ubiquity of complexity/complex networks. Idea: To nd a universal framework for the investigation and description of complex systems/networks. Methodology: Result: measure standardisation. measure composition. general scaling models. exible analysis framework (not conned to networks per se). universal scale given by the standard Normal distribution. method for spotting special network parts/congurations. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 44 / 56

49 Composite Centrality Outlook Potential applications of the proposed framework: a wider range of networks, and general complex systems. multi-ow processes, e.g. trade of dierent goods. networks of networks, e.g. transportation networks on dierent scales. interaction of networks, e.g. interaction of power-grids and telecommunication networks. connection of non-network parameters and network measures. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 45 / 56

50 Thought III: A Platform netconomics.info

51 netconomics.info Mission This platform aims at pooling and sharing knowledge and resources from researchers and practitioners from network science and economics, connecting academia, industry and international institutions. Connect people across disciplines and professions. Share resources and knowledge (data, methodology, software,...). Oer a platform for macroscopic and microscopic projects (FOC, personal,...). For contributions please mail to contact@netconomics.info. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 47 / 56

52 Your Opinion: Discussion

53 Supplement

54 Supplement PIN Content The edge threshold cuts the number of edges by about one half. Extracting the largest strongly connected component reduces the number of nodes in the network by about one half (sea urchin topology). Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 50 / 56

55 Supplement General Complex Systems: M arb distribution parameters uniform x inf = 0, x max = 1 normal µ = 10 5, σ = 10 3 log-normal µ = 0, σ = 10 exponential µ = 10 3 power-law x min = 10 5, α = 3.5 Pareto x min = 10 2, α = 3.5 Poisson µ = 20 binomial n = N, p = 0.1 Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 51 / 56

56 Supplement Limitations and Extensions of Universality Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 52 / 56

57 Supplement Exceptionality: Extension Due to the normative power of the composite centrality framework, its procedures allow for the joint investigation of the relations network non-network quantities. This opens the door to a whole universe of additional applications aimed at the understanding of dierent network processes and there interaction with external factors. Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 53 / 56

58 Supplement GDP-ASPL Scaling Models Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 54 / 56

59 Supplement WTW GDP-Export Exceptionality Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 55 / 56

60 Supplement WTW: p.c.-gdp/hdi - Out-Degree Scaling Andreas Joseph (CCCN, CityU HK) Netconomics Econophysics, Leiden '13 56 / 56

Modeling Economic Contagion/Spillover

Cambridge Centre for Risk Studies Advisory Board Research Showcase 24 January 2017 Modeling Economic Contagion/Spillover Dr. Ali Rais Shaghaghi Cambridge Centre for Risk Studies Agenda Multi-layer network