## 1. Global Network Centrality Measures (Average, 2018) ## Source details **Canonical URL:** [1. Global Network Centrality Measures (Average, 2018)](https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022171-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2022/english/wpiea2022171-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2022/english/wpiea2022171-print-pdf.pdf.json) --- ### Overview and motivation - Rapid expansion of cross-border trade and financial operations increased global interconnectedness (global trade about tenfold and international financial flows about 45 times over the past 40 years). - Interconnectedness delivers benefits (efficiency, GVCs, diversification) but increases vulnerability to contagion (examples: Lehman Brothers collapse 2008, taper tantrum 2013, COVID-19). - Rising global debt and the number of countries in high risk of debt distress or in debt distress raise the likelihood of debt defaults and underscore the need to understand systemic implications. ### Model structure and contagion mechanism - Framework: a multilayered network model incorporating trade, interbank lending, portfolio positions (CPIS), and FDI positions (CDIS) for 63 economies (2018 coverage ≈ 80 percent of global GDP). - Key modeling features: - Economies (nodes) start with foreign exchange reserves R_i0. - Balance of payments dynamics determine reserve changes ∆R_i,t via trade and net foreign asset/liability positions (assets a_ij, interest rates r_j,t, nominal effective exchange rates e_j,t). - A liquidity crisis and potential solvency crisis arise when an economy cannot fulfill interest payments on its external liabilities and defaults. - Contagion occurs through direct exposure: creditor economies experience reserve losses equal to their exposure to the defaulted amount; if reserves are depleted, they default and contagion cascades. - The baseline model considers interest payments only (repayments of principal excluded). - For simplicity: once an economy defaults it cannot re-enter the network; initial trade balances are assumed in equilibrium; six reserve-currency issuers are assumed not to incur default (France, Germany, Japan, United Kingdom, United States, and People’s Republic of China). ### Data and network layers - Data sources (2018, 63 economies): DOTS (imports/exports), BIS Locational International Banking Statistics (interbank), IMF CPIS (portfolio investment), IMF CDIS (FDI). - Network visualization includes four layers: Exports, Imports, Portfolio Investment (CPIS), Direct Investment (CDIS), Interbank Transactions (BIS), and net asset positions (A+B+C). ### Centrality measures (definitions and interpretation) - Four centrality measures computed for each network layer: degree, strength, alpha (geometric average of degree and strength with alpha set to 0.5), and eigenvector centrality. - Degree: number of links (connections) per node. - Strength: sum of dollar-weighted link values (w_ij) for a node. - Alpha: geometric mean of degree and strength (captures importance of both links and weights). - Eigenvector centrality: influence of a node accounting for the centrality of its neighbors. - Interpretation: economies with higher centrality are more efficient channels for shock transmission; multilayer view captures channels that a single-layer analysis would miss. ### Key statistics (Table 1: Global Network Centrality Measures, Average, 2018) - Degree, Strength, Alpha, Eigenvector (averages by layer): - Exports — Degree: 59.0; Strength: 235,500.2; Alpha: 2,978.1; Eigenvector: 0.117 - Imports — Degree: 60.1; Strength: 236,393.5; Alpha: 3,034.5; Eigenvector: 0.100 - Portfolio Investment (CPIS) — Degree: 46.8; Strength: 663,002.4; Alpha: 4,160.2; Eigenvector: 0.095 - Direct Investment (CDIS) — Degree: 40.9; Strength: 507,928.7; Alpha: 3,656.8; Eigenvector: 0.126 - Interbank Positions (BIS) — Degree: 34.4; Strength: 400,328.6; Alpha: 2,892.1; Eigenvector: 0.080 - Additional reported network facts: - Average node in the imports layer: ~60 links (out of 62 available nodes). - Average node in the interbank layer: ~34 links. - Minimum import linkages: Mongolia (52 linkages); Mongolia also least connected through exports (35 linkages). - 29 economies are fully connected (62 linkages) through imports. - Minimum interbank linkages: Bolivia (13 linkages); 12 economies are fully connected in interbank layer. ### Stress-testing exercise and metrics - Simulation setup: - Scenarios: each of the 63 economies is shocked individually (one-at-a-time initial default), simulations run on a 5-year horizon. - The initial shock: economy defaults on interest payments due to all counterparts; contagion proceeds via reserve losses in creditor economies. - Reserve depletion is the criterion for subsequent defaults (baseline assumes full reserve depletion for default). - Vulnerability indices: - Country vulnerability index V_i(C) ∈ [0,1]: V_i(C) = min{1, (R_i(0) − R_i(t)) / R_i(0)}; V_i(C) = 0 means no reserve losses; V_i(C) = 1 means reserves fully depleted. - Global vulnerability index GV(C) ∈ [0,1]: weighted average of individual vulnerabilities with weights R_i(0) / Σ_j R_j(0). ### Stress-testing results (high-level findings and quantitative summaries) - Contagion breadth: - Maximum number of subsequent economies falling into debt default observed in simulations: 25 (following the initial default of economy number 10 in the ordering used). - Average number of defaults across scenarios: 12.1. - Global vulnerability index distribution: - Average GV across scenarios: 0.09. - Median GV: 0.11. - 75th percentile GV: 0.168. - Interpretation: a non-negligible set of initial-default scenarios generate significant global vulnerability; economies that induce larger global vulnerability tend to be more interconnected across layers. - Channel importance: - Portfolio investment channel shows the largest average strength and highest alpha centrality, suggesting portfolio investment appears very important for shock transmission even though trade (imports degree) shows higher average connectivity by degree. - Eigenvector centrality is largest on average for direct investment (CDIS), consistent with the role of global value chains. ### Conclusions and policy implications - Main conclusions: - Debt defaults can induce large and highly non-linear systemic effects as measured by reserve losses at the economy and global level. - Topological structure of cross-economy interconnectedness plays an instrumental role in aggregate outcomes: many economies can be systemically important beyond conventional size or openness metrics. - Policy applications: - At country level: model can identify systemic importance of individual economies and inform national surveillance and contingency planning. - At multilateral level: model can quantify global systemic impact and inform the design and optimal size of the global financial safety net. - Extensions and robustness considerations: - Model can be extended to: - Set a more realistic foreign exchange reserve threshold for default (rather than full depletion). - Include amplification channels such as asset price co-movement and country risk premia. - Incorporate endogenous policy responses (exchange rate, monetary, fiscal adjustment). - Including additional amplification channels and alternative default thresholds would likely increase subsequent affected economies, aggregate reserve losses, and global vulnerability — potentially strengthening the case for stronger domestic policy responses or a larger global safety net. ### Appendix Table I. List of Economies - Australia - Austria - Bahrain, Kingdom of - Barbados - Belgium - Bolivia - Brazil - Bulgaria - Canada - Chile - China - Costa Rica - Cyprus - Czech Republic - Denmark - Estonia - Finland - France - Germany - Greece - Hong Kong SAR* - Hungary - Iceland - India - Indonesia - Ireland - Israel - Italy - Japan - Kazakhstan - Korea, Republic of - Kuwait - Latvia - Lithuania - Luxembourg - Macao SAR* - Malaysia - Malta - Mauritius - Mexico - Mongolia - Netherlands - New Zealand - Norway - Pakistan - Panama - Philippines - Poland - Portugal - Romania - Russian Federation - Singapore - Slovak Republic - Slovenia - South Africa - Spain - Sweden - Switzerland - Thailand - Turkey - United Kingdom - United States - Uruguay - Note: *Special Administrative Region, People’s Republic of China. *Source: wpiea2022171-print-pdf — “The Systemic Impact of Debt Default in a Multilayered Global Network Model”, Section: 1. Global Network Centrality Measures (Average, 2018).* ### References ............................................................................................................. ### References ### Section header and location - References ......................................................................................................................................................... 20 ### Figures listed - 1. Selected Debt Indicators ................................................................................................................................... 4 - 2. The Multilayered Network Model ..................................................................................................................... 10 - 3. Number of Subsequent Economies Falling into Debt Default ......................................................................... 12 - 4. Interconnectedness and Default— Selected Centrality Measures and Economies ........................................ 13 - 5. Global Vulnerability Index ............................................................................................................................... 14 - 6. Interconnectedness and Global Vulnerability—Selected Centrality Measures and Global Vulnerability Index ............................................................................................................................................................................ 15 ### Tables - TABLES *Source: wpiea2022171-print-pdf - References (https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022171-print-pdf.pdf)* ### 1. Global Network Centrality Measures (Average, 2018) ................................................................. ### 1. Global Network Centrality Measures (Average, 2018) ### Overview and motivation - Rapid expansion of cross-border trade and financial operations increased global interconnectedness (global trade about tenfold and international financial flows about 45 times over the past 40 years). - Interconnectedness delivers benefits (efficiency, GVCs, diversification) but increases vulnerability to contagion (examples: Lehman Brothers collapse 2008, taper tantrum 2013, COVID-19). - Rising global debt and the number of countries in high risk of debt distress or in debt distress raise the likelihood of debt defaults and underscore the need to understand systemic implications. ### Model structure and contagion mechanism - Framework: a multilayered network model incorporating trade, interbank lending, portfolio positions (CPIS), and FDI positions (CDIS) for 63 economies (2018 coverage ≈ 80 percent of global GDP). - Key modeling features: - Economies (nodes) start with foreign exchange reserves R_i0. - Balance of payments dynamics determine reserve changes ∆R_i,t via trade and net foreign asset/liability positions (assets a_ij, interest rates r_j,t, nominal effective exchange rates e_j,t). - A liquidity crisis and potential solvency crisis arise when an economy cannot fulfill interest payments on its external liabilities and defaults. - Contagion occurs through direct exposure: creditor economies experience reserve losses equal to their exposure to the defaulted amount; if reserves are depleted, they default and contagion cascades. - The baseline model considers interest payments only (repayments of principal excluded). - For simplicity: once an economy defaults it cannot re-enter the network; initial trade balances are assumed in equilibrium; six reserve-currency issuers are assumed not to incur default (France, Germany, Japan, United Kingdom, United States, and People’s Republic of China). ### Data and network layers - Data sources (2018, 63 economies): DOTS (imports/exports), BIS Locational International Banking Statistics (interbank), IMF CPIS (portfolio investment), IMF CDIS (FDI). - Network visualization includes four layers: Exports, Imports, Portfolio Investment (CPIS), Direct Investment (CDIS), Interbank Transactions (BIS), and net asset positions (A+B+C). ### Centrality measures (definitions and interpretation) - Four centrality measures computed for each network layer: degree, strength, alpha (geometric average of degree and strength with alpha set to 0.5), and eigenvector centrality. - Degree: number of links (connections) per node. - Strength: sum of dollar-weighted link values (w_ij) for a node. - Alpha: geometric mean of degree and strength (captures importance of both links and weights). - Eigenvector centrality: influence of a node accounting for the centrality of its neighbors. - Interpretation: economies with higher centrality are more efficient channels for shock transmission; multilayer view captures channels that a single-layer analysis would miss. ### Key statistics (Table 1: Global Network Centrality Measures, Average, 2018) - Degree, Strength, Alpha, Eigenvector (averages by layer): - Exports — Degree: 59.0; Strength: 235,500.2; Alpha: 2,978.1; Eigenvector: 0.117 - Imports — Degree: 60.1; Strength: 236,393.5; Alpha: 3,034.5; Eigenvector: 0.100 - Portfolio Investment (CPIS) — Degree: 46.8; Strength: 663,002.4; Alpha: 4,160.2; Eigenvector: 0.095 - Direct Investment (CDIS) — Degree: 40.9; Strength: 507,928.7; Alpha: 3,656.8; Eigenvector: 0.126 - Interbank Positions (BIS) — Degree: 34.4; Strength: 400,328.6; Alpha: 2,892.1; Eigenvector: 0.080 - Additional reported network facts: - Average node in the imports layer: ~60 links (out of 62 available nodes). - Average node in the interbank layer: ~34 links. - Minimum import linkages: Mongolia (52 linkages); Mongolia also least connected through exports (35 linkages). - 29 economies are fully connected (62 linkages) through imports. - Minimum interbank linkages: Bolivia (13 linkages); 12 economies are fully connected in interbank layer. ### Stress-testing exercise and metrics - Simulation setup: - Scenarios: each of the 63 economies is shocked individually (one-at-a-time initial default), simulations run on a 5-year horizon. - The initial shock: economy defaults on interest payments due to all counterparts; contagion proceeds via reserve losses in creditor economies. - Reserve depletion is the criterion for subsequent defaults (baseline assumes full reserve depletion for default). - Vulnerability indices: - Country vulnerability index V_i(C) ∈ [0,1]: V_i(C) = min{1, (R_i(0) − R_i(t)) / R_i(0)}; V_i(C) = 0 means no reserve losses; V_i(C) = 1 means reserves fully depleted. - Global vulnerability index GV(C) ∈ [0,1]: weighted average of individual vulnerabilities with weights R_i(0) / Σ_j R_j(0). ### Stress-testing results (high-level findings and quantitative summaries) - Contagion breadth: - Maximum number of subsequent economies falling into debt default observed in simulations: 25 (following the initial default of economy number 10 in the ordering used). - Average number of defaults across scenarios: 12.1. - Global vulnerability index distribution: - Average GV across scenarios: 0.09. - Median GV: 0.11. - 75th percentile GV: 0.168. - Interpretation: a non-negligible set of initial-default scenarios generate significant global vulnerability; economies that induce larger global vulnerability tend to be more interconnected across layers. - Channel importance: - Portfolio investment channel shows the largest average strength and highest alpha centrality, suggesting portfolio investment appears very important for shock transmission even though trade (imports degree) shows higher average connectivity by degree. - Eigenvector centrality is largest on average for direct investment (CDIS), consistent with the role of global value chains. ### Conclusions and policy implications - Main conclusions: - Debt defaults can induce large and highly non-linear systemic effects as measured by reserve losses at the economy and global level. - Topological structure of cross-economy interconnectedness plays an instrumental role in aggregate outcomes: many economies can be systemically important beyond conventional size or openness metrics. - Policy applications: - At country level: model can identify systemic importance of individual economies and inform national surveillance and contingency planning. - At multilateral level: model can quantify global systemic impact and inform the design and optimal size of the global financial safety net. - Extensions and robustness considerations: - Model can be extended to: - Set a more realistic foreign exchange reserve threshold for default (rather than full depletion). - Include amplification channels such as asset price co-movement and country risk premia. - Incorporate endogenous policy responses (exchange rate, monetary, fiscal adjustment). - Including additional amplification channels and alternative default thresholds would likely increase subsequent affected economies, aggregate reserve losses, and global vulnerability — potentially strengthening the case for stronger domestic policy responses or a larger global safety net. *Source: IMF Working Paper excerpt — “The Systemic Impact of Debt Default in a Multilayered Global Network Model” (section: 1. Global Network Centrality Measures (Average, 2018)).* ### Appendix Table I. List of Economies ### Appendix Table I. List of Economies ### Economies included in the sample - Australia - Austria - Bahrain, Kingdom of - Barbados - Belgium - Bolivia - Brazil - Bulgaria - Canada - Chile - China - Costa Rica - Cyprus - Czech Republic - Denmark - Estonia - Finland - France - Germany - Greece - Hong Kong SAR* - Hungary - Iceland - India - Indonesia - Ireland - Israel - Italy - Japan - Kazakhstan - Korea, Republic of - Kuwait - Latvia - Lithuania - Luxembourg - Macao SAR* - Malaysia - Malta - Mauritius - Mexico - Mongolia - Netherlands - New Zealand - Norway - Pakistan - Panama - Philippines - Poland - Portugal - Romania - Russian Federation - Singapore - Slovak Republic - Slovenia - South Africa - Spain - Sweden - Switzerland - Thailand - Turkey - United Kingdom - United States - Uruguay ### Notes - *Special Administrative Region, People’s Republic of China. *Appendix Table I. List of Economies — IMF Working Paper The Systemic Impact of Debt Default in a Multilayered Global Network Model, Working Paper No. WP/2022/171* --- _Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022171-print-pdf.pdf_