## _wp15111

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---

### Major findings and results
- The 2007–2009 financial crisis revealed large gaps in bilateral sectoral exposure data; in response the IMF and FSB launched the Data Gaps Initiative in 2009 with 20 recommendations.
- Recommendation 15: the Inter-Agency Group (IAG) shall develop a strategy to promote compilation and dissemination of the balance sheet approach (BSA), flow of funds, and sectoral data more generally, starting with the G-20 economies; Data on nonbank financial institutions should be a particular priority.
- This paper estimates missing "from-whom-to-whom" information from aggregate balance sheets for G-4 economies (Euro Area, Japan, U.K., and U.S.) and combines sectoral accounts with CPIS, IIP, and BIS data to compute cross-border exposures between country-sector pairs.
- At the country level in all G-4 economies, exposures in debt securities increased considerably after the financial crisis; cross-border exposures in debt securities remained stable overall.
- Exposures increased notably vis-à-vis governments at both the country and cross-border level.
- Exposure shifts: cross-border exposures vis-à-vis the U.S. government increased, while cross-border exposures vis-à-vis U.S. other financial intermediaries decreased.
- Exposures in loans and equities contracted sharply during the period of rising exposures to government debt securities after the financial crisis:
  - The decline in loan exposures was much larger at the cross-border level than at the country level.
  - The decline in equity exposures was more accentuated at the country level than at the cross-border level.
- Sectoral and country-specific behaviour after the crisis:
  - Monetary financial institutions resident in the U.K. were the sector that reduced its national and cross-border loan exposures most.
  - U.S. monetary financial institutions substantially decreased their national loan exposures.
  - In the Euro Area, MFIs reduced loan exposures while OFI and NFC increased theirs, suggesting emergence of alternative funding sources after the drying-up of bank credit.
  - Unlike most countries, monetary financial institutions in Japan increased their cross-border exposures in loans after the crisis.
- Shock simulations indicate the exposure of the domestic financial sector to the government sector increased considerably after the financial crisis.

### Data sources, scope, and methodological features
- Primary data sources:
  - Principal Global Indicators (PGI) website for financial balance sheets broken down by instrument and institutional sector.
  - Coordinated Portfolio Investment Survey (CPIS) for cross-border portfolio investments by counterparty country and instrument type (debt securities and equities).
  - Bank for International Settlements (BIS) locational statistics for banks' total foreign claims by counterparty country (and recently by counterparty sector).
  - International Investment Position (IIP) dataset for countries' cross-border investments by instrument and partly by sector.
- SNA-based sectoring: seven main institutional sectors defined by the SNA are used:
  - nonfinancial corporations (NFC)
  - the central bank and other monetary financial institutions (MFI)
  - other financial intermediaries and financial auxiliaries (OFI)
  - insurance corporations and pension funds (INS)
  - general government (GOV)
  - households and non-profit institutions serving households (HH)
  - the rest of the world (ROW)
- Key data limitations and methodological assumptions:
  - The vast majority of countries do not provide full "from-whom-to-whom" counterparty sector detail; even G-4 economies provide only limited such data.
  - Cross-border exposures in sectoral accounts are aggregated under ROW and lack a counterparty-country breakdown; the paper combines sectoral accounts with CPIS, BIS, and IIP to derive cross-border exposures.
  - For geographical breakdown of loan exposures, BIS banking statistics are used as a proxy and it is assumed the whole-economy loan foreign claims follow the same geographical breakdown as banks' total foreign claims.
  - The paper does not distinguish between portfolio and direct investments; it implicitly assumes that the sectoral and geographical breakdown of direct investments follows the same distribution as portfolio investments because:
    - CDIS outward investments are netted and can include negative values.
    - CDIS is only available after 2009.
    - The IIP dataset does not provide sectoral breakdown of direct investments.
  - BIS locational statistics are used (unconsolidated/residence basis) to match the residence-based nature of sectoral accounts.
- Specific data availability features for G-4 economies:
  - Euro Area:
    - Sectoral breakdown for loans and deposits within countries and within the Euro Area.
    - MFI deposit liabilities with counterparty HH and NFC within countries and across euro area countries.
    - MFI holdings of securities with counterparty MFI and GOV within countries and across euro area countries.
    - MFI holdings of shares and other equity with counterparty MFI within countries and across euro area countries.
  - Japan:
    - Sectoral breakdown of holdings of government debt securities.
    - Almost complete sectoral breakdown for loans (financial sector as borrower not broken down by MFI, OFI, and INS, but it is as a lender sector).
  - U.K.:
    - Sectoral breakdown of holdings of government debt securities.
    - Sectoral breakdown of borrowings in loans from the ROW sector.
    - Sectoral breakdown of holdings of deposits and equities from the ROW sector.
  - U.S.:
    - Sectoral breakdown of holdings of government debt securities.
    - Sectoral breakdown of holdings of agency and GSE debt securities (but not of the whole OFI sector debt securities).

### Comparative balance sheet structure observations (2012:Q2)
- MFI liabilities:
  - The deposit funding base share of euro area and Japanese MFI is much larger than that of U.S. and U.K. MFI.
  - In the Euro Area a relatively large share of MFI funding comes via bond issuances; U.S. MFI have a large share of equity funding.
  - The forty percent of U.K. MFI’s liabilities shown as “other” consists mainly of financial derivatives that for the other three countries are given as “debt securities other than shares.”
- MFI assets:
  - Euro area MFIs keep a larger share of assets in currency and deposits.
  - U.S. and Japanese MFIs invest a large part of assets in debt securities, reflecting high issuance of sovereign bonds in both countries.
- OFI and INS asset allocations:
  - Japanese OFI invest a larger share of assets in loans and a smaller share in debt securities and equities compared with OFI in other G-4 economies.
  - Japanese INS have the largest share invested in debt securities, reflecting high issuance of bonds by the Japanese GOV held domestically.
  - U.S. and U.K. INS have a relatively large share of assets invested in equities; euro area INS invest less in equities but more in mutual fund shares.
  - U.S. INS invest the smallest share in loans.
- Household (HH) and NFC portfolios:
  - Japanese HH keep the largest share of assets in currency and deposits.
  - U.S. HH diversify more across instruments, invest relatively small share in currency and deposits and relatively high share in equities.
  - In most G-4 economies, HH keep a very high share of assets in insurance and pension reserves.
- Additional data notes and precision points:
  - The share of currency in “Currency and Deposits” is very small (0 percent in the U.K. and Euro Area, and around 5 percent in the U.S. and Japan).
  - Central bank assets are relatively small compared to unconsolidated assets of other MFIs (approx. 26 percent in the U.S., 17 percent in Japan, 7 percent in the Euro Area, and 4 percent in the U.K. by the end of 2014).

### Methodology: estimating bilateral exposures and connecting networks
- Estimating bilateral exposures within countries:
  - Sectoral accounts are a closed system but do not provide counterparty information; bilateral exposures estimated instrument-by-instrument using maximum entropy techniques followed by the RAS algorithm.
  - Maximum entropy distributes assets and liabilities evenly across counterparties, yielding dense exposure networks and providing risk lower bounds.
  - Minimum density approach provides a risk upper bound by minimizing linkages.
  - For N sectors and instrument k: bilateral exposures a_ij^k form an NxN matrix; aggregate assets A_i^k (row sums) and liabilities L_j^k (column sums) are observed; N^2 unknowns versus 2N knowns require maximum entropy assumptions.
  - Example heuristic: initial guess a_ij^k = 0.3 x 0.2 = 0.06 of outstanding assets/liabilities in k when sector i holds 30 percent of assets in k and sector j issued 20 percent of liabilities in k.
  - Diagonal elements not restricted to zero except for the ROW sector diagonal (intra-ROW claims are zero by dataset construction).
  - RAS algorithm adjusts the estimated matrix to satisfy adding-up and zero constraints.
  - Accuracy assessed in Appendix II using actual “from-whom-to-whom” Euro Area data; estimated links are treated consistently across countries to preserve comparability.
- Combining sectoral accounts with CPIS, BIS, and IIP to connect country networks:
  - Claims of sector i in country A vis-à-vis sector j in country B computed as: country A's foreign claims (ROW liabilities in country A) × share of country B in country A’s foreign claims (CPIS) × sector i's share in holdings of foreign assets in country A (IIP) × sector j's share in country B’s liabilities held by nonresidents (IIP).
  - Sectoral accounts, CPIS, and IIP data are consistent: compiled foreign claims by country and instrument are virtually equal.

### Networks visualization and construction (2007:Q2 vs 2012:Q2)
- Networks constructed instrument-by-instrument for 2007:Q2 and 2012:Q2 using stock data for debt securities, loans, and equities.
- Nodes represent sectors; node size proportional to a sector's holdings of liabilities in a given instrument.
- Links from sector i to sector j represent sector i's claims vis-à-vis sector j; link width proportional to the ratio of a bilateral claim to the creditor sector’s total consolidated assets.
- Cross-border exposures use a separate reference base for link widths.
- Only linkages above the median exposure are drawn (one median for intra-country exposures and another for inter-country exposures).

### Debt securities — networks and changes (2007:Q2 → 2012:Q2)
- 2007:Q2 — Top 3 bilateral national exposures:
  - INS_JP -> GOV_JP 30.7%
  - MFI_JP -> GOV_JP 25.1%
  - GOV_US -> OFI_US 21.7%
- 2007:Q2 — Top 3 bilateral cross-border exposures:
  - MFI_UK -> NFC_US 2.11%
  - MFI_UK -> MFI_EA 1.82%
  - MFI_UK -> GOV_EA 1.76%
- 2012:Q2 — Top 3 bilateral national exposures:
  - INS_JP -> GOV_JP 42.6%
  - MFI_JP -> GOV_JP 35.1%
  - INS_UK -> ROW_UK 19.0%
- 2012:Q2 — Top 3 bilateral cross-border exposures:
  - HH_JP -> GOV_US 1.84%
  - MFI_JP -> GOV_US 1.23%
  - HH_JP -> GOV_EA 1.12%
- Changes and aggregates:
  - Size of all GOV nodes increased; Japanese and U.K. GOV more than doubled debt securities outstanding between 2007:Q2 and 2012:Q2.
  - U.S. OFI debt securities outstanding decreased.
  - National exposures in debt securities on average increased by +0.3pp.
  - Increase mainly vis-à-vis governments: +2.4pp overall; particularly Japan: +4.0pp and U.S.: +3.1pp.
  - In Japan, INS and MFI exposures to GOV increased to 43 percent and 35 percent of these sectors' total assets, respectively.
  - Largest decreases in national exposures included vis-à-vis OFI in the U.S.: -3.5pp.
  - Cross-border exposure shifts:
    - Foreign sectors sold OFI-issued debt securities and moved to government debt.
    - Exposure increased mainly vis-à-vis U.S. GOV: +0.3pp.
      - Japanese MFI increased exposures to U.S. GOV by +0.7pp.
      - Japanese other sectors increased exposures to U.S. GOV by +1pp.
    - Cross-border exposures to U.S. other sectors decreased by -0.5pp.
    - Exposures to euro area MFI decreased by -0.3pp.
    - U.K. MFI sector reduced its cross-border exposures most: -0.5pp.
    - U.K. and euro area MFI decreased exposures to foreign GOV: -0.2pp.
    - U.K. and euro area other sectors increased exposures to foreign GOV: +0.3pp.
- Valuation note:
  - Debt values are expressed in USD; between 2007 and 2012 the USD appreciated vis-à-vis the EUR, JPY, and GBP, implying the paper likely underestimates the increase in GOV debt in the Euro Area, Japan, and U.K.

### Loans — network structure, exposures, and changes (2007:Q2 vs 2012:Q2)
- 2007:Q2 — Top 3 bilateral national exposures:
  - MFI_US -> HH_US 32.1%
  - OFI_US -> HH_US 28.2%
  - OFI_JP -> NFC_JP 21.4%
- 2007:Q2 — Top 3 bilateral cross-border exposures:
  - MFI_UK -> MFI_EA 5.7%
  - MFI_EA -> NFC_UK 4.0%
  - MFI_UK -> NFC_US 2.8%
- 2012:Q2 — Top 3 bilateral national exposures:
  - MFI_US -> HH_US 26.7%
  - OFI_US -> HH_US 24.9%
  - OFI_JP -> NFC_JP 22.8%
- 2012:Q2 — Top 3 bilateral cross-border exposures:
  - MFI_EA -> NFC_UK 3.5%
  - MFI_UK -> MFI_EA 2.7%
  - MFI_UK -> NFC_US 1.6%
- Key findings on loans:
  - Biggest debtors in loans: NFC and HH sectors in the U.S. and Euro Area; HH_U.S. is the biggest.
  - U.S. MFI and OFI national exposures vis-à-vis HH amount to 32.1 percent and 28.2 percent of their assets, respectively.
  - Cross-border exposures in loans decreased considerably between 2007:Q2 and 2012:Q2.
  - National and cross-border exposures in loans decreased on average by -0.1pp between 2007:Q2 and 2012:Q2; relative decrease larger for cross-border exposures.
- Sectoral changes (national exposures):
  - GOV in the U.S. increased exposures by +1.9pp (particularly vis-à-vis NFC +3.0pp and HH +6.1pp).
  - GOV in the Euro Area increased exposures by +0.2pp (particularly vis-à-vis NFC +1.4pp and HH +1.0pp).
  - OFI and NFC in the Euro Area increased loan exposures by +0.8pp and +0.7pp, respectively.
  - MFIs in the U.K., U.S., and Euro Area reduced loan exposures substantially; OFI in the U.S. and U.K. also reduced exposures.
  - Largest decreases in national loan exposures toward: U.K. HH (-1.2pp), ROW (-0.9pp), OFI (-0.8pp), NFC (-0.6pp), and U.S. HH (-0.7pp).
- Sectoral changes (cross-border exposures):
  - Japanese MFI sector increased its cross-border exposures by +0.1pp and received increased cross-border exposures by +0.01pp.
  - U.S. MFI cross-border exposures remained broadly unchanged.
  - U.K. MFI sector reduced its cross-border exposures by -0.9pp.
  - Cross-border exposures in loans were mainly reduced towards euro area MFI (-0.6pp) and U.S. other sectors (-0.1pp).

### Equities — network, valuation effects, and changes (2007:Q2 vs 2012:Q2)
- 2007:Q2 — Top 3 bilateral national exposures:
  - INS_US -> NFC_US 27.3%
  - HH_US -> NFC_US 26.2%
  - INS_UK -> ROW_UK 23.9%
- 2007:Q2 — Top 3 bilateral cross-border exposures:
  - HH_EA -> NFC_US 3.62%
  - HH_UK -> NFC_EA 2.75%
  - HH_UK -> NFC_US 2.44%
- 2012:Q2 — Top 3 bilateral national exposures:
  - NFC_UK -> ROW_UK 24.9%
  - INS_US -> NFC_US 20.3%
  - INS_UK -> ROW_UK 20.0%
- 2012:Q2 — Top 3 bilateral cross-border exposures:
  - HH_EA -> NFC_US 4.65%
  - HH_EA -> NFC_UK 2.41%
  - HH_UK -> NFC_US 2.18%
- Valuation and index context:
  - Equity liabilities are market valued.
  - In 2012:Q2 the Eurostoxx 50 and the Nikkei 225 were still 50 percent below their value in 2007:Q2; S&P 500 and FTSE 100 were only 10–15 percent below their value in 2007:Q2.
- Key findings on equities:
  - Cross-border exposures were less reduced from 2007 to 2012 than national exposures: national exposures decreased on average by -0.9pp, cross-border exposures decreased on average by -0.1pp.
  - Share of direct investments in equity foreign investments increased by 10pp between 2007 and 2012 for G-4 economies (IIP data).
- Sectoral changes:
  - INS decreased equity exposures most in U.K. (-3.6pp), Japan (-2.9pp), U.S. (-2.4pp).
  - Equity exposures most reduced vis-à-vis NFC in: Euro Area (-3.8pp), Japan (-3.6pp), U.K. (-3.0pp), U.S. (-2.3pp).
  - Euro Area and U.S. increased equity exposure vis-à-vis ROW by +1.0pp and +0.6pp, respectively.
- Cross-border equity changes:
  - Euro area other sectors increased exposures by +0.1pp; exposure to U.S. other sectors increased to 4.7 percent of their assets and to U.K. other sectors to 2.5 percent.
  - U.K. other sectors and MFI reduced exposures by approx. -0.35pp each.
  - Cross-border exposures were mainly reduced vis-à-vis other sectors in the Euro Area (-0.3pp) and in Japan (-0.2pp).

### Shock simulations — scenarios, results, and amplification
- Simulation setup:
  - Financial networks estimated for quarters 2002:Q2 to 2012:Q2.
  - Three shock scenarios analyzed:
    1. GOV debt securities in each country lose 20 percent of their value; analyze first-round impact on equity of domestic financial sectors.
    2. Same 20 percent GOV debt shock, allowed to propagate through domestic sectors via cross-sector equity holdings until convergence.
    3. Debt securities of U.S. other sectors and GOV lose 20 percent of their value; calculate impact on other G-4 economies.
- Network and methodology notes:
  - Number of links fixed over time; only link strengths vary.
  - National networks nearly complete; cross-border exposures allowed between MFIs and foreign MFI, other sectors, and GOV.
  - Focus on weighted node degrees (centrality measure) over time.
  - Shock propagation channel modeled via mark-to-market valuation of equity holdings; HH and GOV do not transmit shocks because they do not issue equity.
- Weighted node degree findings:
  - Average node degree standardized at one in 2002.
  - Node degree increased most for debt securities between 2002 and 2012; between 2 to 3 times larger in 2012 than in 2002.
  - Most node degrees increased considerably from 2002 until mid-2008, decreased shortly thereafter, then remained relatively stable (loans) or increased (debt securities and equities).
  - Japan exception: loan node degrees relatively stable 2002–2012; debt securities node degrees rose after the crisis.
  - Euro Area and U.K. node degrees seem to have increased more than U.S. and Japan for considered instruments.
- Impact of a 20 percent GOV debt devaluation — first-round and final (domestic):
  - First-round: in 2002 a 20 percent devaluation in GOV debt securities in the U.S., Euro Area, and U.K. would cause a mark-to-market drop of approx. 15 percent in domestic financial sectors’ equity.
  - By mid 2012 the same shock would cause equity devaluation of:
    - 30 percent in the U.S.
    - 30 percent in the U.K.
    - 20 percent in the Euro Area
  - Japanese financial sectors could not buffer a 20 percent devaluation before 2004 and after 2008 (losses > 1, i.e., higher than equity value).
  - Final total loss after propagation via equity holdings (ratio over equity and amplification factor):
    - Before crisis: 20 percent GOV devaluation caused losses ~3 percent of equity; final total loss after propagation was 1.8 times the initial shock.
    - After crisis: same devaluation caused claim losses amounting to 6 percent of equity; amplification factor increased to approximately 2.
    - Japan: small amplification factor of 2; U.S.: smallest loss as share of equity and smallest amplification factor.
    - U.K.: highest amplification factor; final total loss eight times the initial loss by mid 2012.
    - Euro Area: amplification factor increased from 3 to 5 between 2002 and 2012.
    - By mid 2012 financial sectors’ losses due to a 20 percent GOV devaluation amounted to approximately one third of equity in Japan and the U.K., and 18 percent in the Euro Area.
- International spillovers from U.S. shocks:
  - U.S. other sectors (HH, INS, OFI, NFC) and U.S. GOV are systemically important in G-4 networks.
  - After the crisis, cross-border exposures to U.S. other sectors decreased but exposures to U.S. GOV increased.
  - After 2009 all sectors in the other G-4 economies were more exposed to the U.S. government than to U.S. other sectors.
  - Exposures vis-à-vis U.S. other sectors decreased in the Euro Area and U.K., remained stable in Japan.

### Conclusions, implications, and suggested extensions
- Method and contributions:
  - Uses sectoral accounts merged with CPIS, BIS, and IIP to estimate bilateral financial exposures between sectors in G-4 economies.
  - First paper to compare national financial exposures across G-4 economies and to consider cross-border interconnections beyond the banking sector.
- Summary of empirical findings:
  - National exposures in debt securities vis-à-vis governments increased, particularly in the U.S. and Japan.
  - Cross-border exposures in debt securities vis-à-vis governments generally increased, notably Japanese sectors’ exposures to the U.S. government.
  - Cross-border exposures in loans decreased much more than national exposures; for equities the opposite holds.
  - Exposures in the U.K., particularly in the MFI sector, and to a lesser extent in the Euro Area, decreased more than exposures in the U.S. and Japan.
  - Differences may reflect differing policy responses to the financial crisis (fiscal stimulus vs. austerity).
- Suggested extensions for future work:
  - Estimate financial networks for a wider range of countries once data are available.
  - Decompose changes in exposures between 2007 and 2012 into volume and valuation changes.
  - Use bilateral claims to calculate debt service flows between sectors.
- Policy-relevant message:
  - Sectoral accounts data are a powerful tool for assessing financial stability; broader "from-whom-to-whom" sectoral accounts would improve assessment of interconnectedness and vulnerabilities.

### Appendix highlights — estimation accuracy and largest exposure changes (2007:Q2 to 2012:Q2)
- Estimation accuracy:
  - The ECB provides complete from-whom-to-whom information for loans in the Euro Area, enabling assessment of the accuracy of estimated bilateral exposures.
  - Maximum entropy techniques tend to spread financial exposures evenly across all sectors, which:
    - has the potential of underestimating extreme exposures and overestimating small exposures;
    - implies the approach is likely to underestimate risk, so estimated links represent risk lower bounds.
  - Empirical comparison for loans in 2007:Q2:
    - Observed MFI exposure to NFC relative to their assets is 20 percent; observed MFI exposure to HH is 23 percent.
    - Estimated measures are 18 percent (MFI→NFC) and 13 percent (MFI→HH).
  - Overall accuracy metric:
    - The mean absolute error in the estimation of exposures relative to total assets is 1.5 pp.
- Appendix III selected largest changes (2007:Q2 → 2012:Q2):
  - Debt securities — Average differences in creditor’s exposure:
    - National exposures 0.34
    - Cross-border -0.03
  - Loans — Average differences in creditor’s exposure:
    - National exposures -0.12
    - Cross-border -0.12
  - Equity — Average differences in creditor’s exposure:
    - National exposures -0.87
    - Cross-border -0.09
  - Examples of largest creditor increases (pp) — National exposures:
    - INS_JP 2.63 (debt securities)
    - MFI_JP 2.31 (debt securities)
    - GOV_US 1.89 (loans)
    - NFC_US 0.94 (equity)
  - Examples of largest creditor decreases (pp) — National exposures:
    - MFI_UK -2.06 (loans)
    - MFI_US -1.76 (loans)
    - INS_UK -3.57 (equity)
    - INS_US -2.40 (equity)

*Source: _wp15111 - References (IMF working paper content provided).*

### References .............................................................................................................

### _wp15111 - References

### Major findings and results
- The 2007–2009 financial crisis revealed large gaps in bilateral sectoral exposure data; in response the IMF and FSB launched the Data Gaps Initiative in 2009 with 20 recommendations.
- Recommendation 15: the Inter-Agency Group (IAG) shall develop a strategy to promote compilation and dissemination of the balance sheet approach (BSA), flow of funds, and sectoral data more generally, starting with the G-20 economies; Data on nonbank financial institutions should be a particular priority.
- This paper estimates missing "from-whom-to-whom" information from aggregate balance sheets for G-4 economies (Euro Area, Japan, U.K., and U.S.) and combines sectoral accounts with CPIS, IIP, and BIS data to compute cross-border exposures between country-sector pairs.
- At the country level in all G-4 economies, exposures in debt securities increased considerably after the financial crisis; cross-border exposures in debt securities remained stable overall.
- Exposures increased notably vis-à-vis governments at both the country and cross-border level.
- Exposure shifts: cross-border exposures vis-à-vis the U.S. government increased, while cross-border exposures vis-à-vis U.S. other financial intermediaries decreased.
- Exposures in loans and equities contracted sharply during the period of rising exposures to government debt securities after the financial crisis:
  - The decline in loan exposures was much larger at the cross-border level than at the country level.
  - The decline in equity exposures was more accentuated at the country level than at the cross-border level.
- Sectoral and country-specific behaviour after the crisis:
  - Monetary financial institutions resident in the U.K. were the sector that reduced its national and cross-border loan exposures most.
  - U.S. monetary financial institutions substantially decreased their national loan exposures.
  - In the Euro Area, MFIs reduced loan exposures while OFI and NFC increased theirs, suggesting emergence of alternative funding sources after the drying-up of bank credit.
  - Unlike most countries, monetary financial institutions in Japan increased their cross-border exposures in loans after the crisis.
- Shock simulations indicate the exposure of the domestic financial sector to the government sector increased considerably after the financial crisis.

### Data sources, scope, and methodological features
- Primary data sources:
  - Principal Global Indicators (PGI) website for financial balance sheets broken down by instrument and institutional sector.
  - Coordinated Portfolio Investment Survey (CPIS) for cross-border portfolio investments by counterparty country and instrument type (debt securities and equities).
  - Bank for International Settlements (BIS) locational statistics for banks' total foreign claims by counterparty country (and recently by counterparty sector).
  - International Investment Position (IIP) dataset for countries' cross-border investments by instrument and partly by sector.
- SNA-based sectoring: seven main institutional sectors defined by the SNA are used:
  - nonfinancial corporations (NFC)
  - the central bank and other monetary financial institutions (MFI)
  - other financial intermediaries and financial auxiliaries (OFI)
  - insurance corporations and pension funds (INS)
  - general government (GOV)
  - households and non-profit institutions serving households (HH)
  - the rest of the world (ROW)
- Key data limitations and methodological assumptions:
  - The vast majority of countries do not provide full "from-whom-to-whom" counterparty sector detail; even G-4 economies provide only limited such data.
  - Cross-border exposures in sectoral accounts are aggregated under ROW and lack a counterparty-country breakdown; the paper combines sectoral accounts with CPIS, BIS, and IIP to derive cross-border exposures.
  - For geographical breakdown of loan exposures, BIS banking statistics are used as a proxy and it is assumed the whole-economy loan foreign claims follow the same geographical breakdown as banks' total foreign claims.
  - The paper does not distinguish between portfolio and direct investments; it implicitly assumes that the sectoral and geographical breakdown of direct investments follows the same distribution as portfolio investments because:
    - CDIS outward investments are netted and can include negative values.
    - CDIS is only available after 2009.
    - The IIP dataset does not provide sectoral breakdown of direct investments.
  - BIS locational statistics are used (unconsolidated/residence basis) to match the residence-based nature of sectoral accounts.
- Specific data availability features for G-4 economies (Box 1 summary; see Appendix I for detail):
  - Euro Area (ECB, Euro area accounts, MFI balance sheets):
    - Sectoral breakdown for loans and deposits within countries and within the Euro Area.
    - MFI deposit liabilities with counterparty HH and NFC within countries and across euro area countries.
    - MFI holdings of securities with counterparty MFI and GOV within countries and across euro area countries.
    - MFI holdings of shares and other equity with counterparty MFI within countries and across euro area countries.
  - Japan (BOJ, Flow of Funds):
    - Sectoral breakdown of holdings of government debt securities.
    - Almost complete sectoral breakdown for loans (financial sector as borrower not broken down by MFI, OFI, and INS, but it is as a lender sector).
  - U.K. (ONS, U.K. Economic Accounts, the Blue Book):
    - Sectoral breakdown of holdings of government debt securities.
    - Sectoral breakdown of borrowings in loans from the ROW sector.
    - Sectoral breakdown of holdings of deposits and equities from the ROW sector.
  - U.S. (FRB, Flow of Funds):
    - Sectoral breakdown of holdings of government debt securities.
    - Sectoral breakdown of holdings of agency and GSE debt securities (but not of the whole OFI sector debt securities).

### Comparative balance sheet structure observations (2012:Q2 and related notes)
- MFI liabilities:
  - The deposit funding base share of euro area and Japanese MFI is much larger than that of U.S. and U.K. MFI.
  - In the Euro Area a relatively large share of MFI funding comes via bond issuances; U.S. MFI have a large share of equity funding.
  - The forty percent of U.K. MFI’s liabilities shown as “other” consists mainly of financial derivatives that for the other three countries are given as “debt securities other than shares.”
- MFI assets:
  - Euro area MFIs keep a larger share of assets in currency and deposits.
  - U.S. and Japanese MFIs invest a large part of assets in debt securities, reflecting high issuance of sovereign bonds in both countries.
- OFI and INS asset allocations:
  - Japanese OFI invest a larger share of assets in loans and a smaller share in debt securities and equities compared with OFI in other G-4 economies.
  - Japanese INS have the largest share invested in debt securities, reflecting high issuance of bonds by the Japanese GOV held domestically.
  - U.S. and U.K. INS have a relatively large share of assets invested in equities; euro area INS invest less in equities but more in mutual fund shares.
  - U.S. INS invest the smallest share in loans.
- Household (HH) and NFC portfolios:
  - Japanese HH keep the largest share of assets in currency and deposits.
  - U.S. HH diversify more across instruments, invest relatively small share in currency and deposits and relatively high share in equities.
  - In most G-4 economies, HH keep a very high share of assets in insurance and pension reserves.
- Additional data notes and precision points:
  - To state the funding base precisely would require splitting currency and deposits, separating central bank from other MFIs, and using consolidated data to exclude inter-MFI deposits; these modifications would probably not change the main message.
  - The share of currency in “Currency and Deposits” is very small (0 percent in the U.K. and Euro Area, and around 5 percent in the U.S. and Japan).
  - Central bank assets are relatively small compared to unconsolidated assets of other MFIs (approx. 26 percent in the U.S., 17 percent in Japan, 7 percent in the Euro Area, and 4 percent in the U.K. by the end of 2014).

### Analytical contributions relative to prior literature
- Advances beyond earlier work:
  - Extends sectoral accounts network analysis to compare interlinkages across G-4 economies.
  - Allows cross-border exposures beyond the banking sector and breaks down cross-border exposures by instrument and sector.
  - Demonstrates that developments in cross-border exposures vary across instruments and sectors; aggregate bank-claims data (BIS) alone may obscure such differences.
- Relation to prior findings:
  - Confirms that after the crisis cross-border exposures in loans decreased while cross-border exposures in debt securities remained stable and increased vis-à-vis governments.
  - Builds on Castrén and Kavonius (2009) and Castrén and Rancan (2014) by extending scope to G-4 economies and nonbank sectors.

*Source: _wp15111 - References (IMF working paper content provided).*

### Box 3 shows how the net worth (financial assets minus financial liabilities) of different

### Box 3. Evolution of Financial Balance Sheets

### Net worth evolution by sector (2002:Q2–2013:Q2)
- HH are the biggest creditors in the economy; NFC and GOV are the biggest debtors.
- Net worth of financial intermediaries is practically zero, reflecting their role as intermediaries.
- After the outbreak of the financial crisis GOV indebtedness increased considerably in G-4 economies.
- The increase in GOV borrowing coincided with an increase in savings of HH and NFC, likely from precautionary savings and the drying-up of bank lending; GOV had to compensate the decrease in private sector demand.
- The rise of the so-called shadow banking sector (often defined as nonbank financial intermediaries) gained importance over time.

### OFI-to-MFI asset ratios and cross-country patterns
- The ratio of OFI's assets to MFI's assets changed over time in G-4 economies:
  - U.S.: OFI sector at times amounted to almost double the size of the traditional banking sector.
  - Japan: OFI sector prior to the crisis had assets amounting to 50 percent of the traditional banking system sector.
  - Euro Area and U.K.: OFI sector corresponded to approximately 30–40 percent of the size of the traditional banking system.
- After the outbreak of the financial crisis:
  - OFI sector in the U.S. and in Japan shrank relative to the traditional banking system.
  - OFI sector increased relative to the traditional banking system in the Euro Area and in the U.K.

### Cross-sector correlations and net lending (1999:Q1–2012:Q4)
- Sectoral accounts available for seven institutional sectors in the G-4 economies over time permit correlation analysis.
- Table 1 (matrix dimension 20x20) covers 5 sectors (GOV, HH, MFI, NFC, and ROW) from 4 countries; variables ordered by sectors; diagonal filled with 1.
- Key inferences for net lending:
  - Main nonfinancial sectors (NFC, HH, GOV) tend to increase or decrease net lending at the same time within a sector across G-4 countries (cross-border correlations within these sectors are fairly positive).
  - Government acts countercyclically, compensating increases in net lending elsewhere by increasing its budget deficit (correlation of government's net lending with HH and NFC’s net lending is negative).
  - ROW sector's net acquisition of assets and net incurrence of liabilities is highly positively correlated across countries, implying common pull and push factors for capital flows in G-4 economies.

### Methodology: building and connecting networks
- Estimating bilateral exposures within countries:
  - Sectoral accounts are a closed system but do not provide counterparty information; bilateral exposures estimated instrument-by-instrument using maximum entropy techniques followed by the RAS algorithm.
  - Maximum entropy distributes assets and liabilities evenly across counterparties, yielding dense exposure networks and providing risk lower bounds.
  - Minimum density approach provides a risk upper bound by minimizing linkages; matching algorithms exist between these extremes.
  - For N sectors and instrument k: bilateral exposures a_ij^k form an NxN matrix; aggregate assets A_i^k (row sums) and liabilities L_j^k (column sums) are observed; N^2 unknowns versus 2N knowns require maximum entropy assumptions.
  - Example heuristic: if sector i holds 30 percent of assets in instrument k and sector j issued 20 percent of liabilities in k, initial guess a_ij^k = 0.3 x 0.2 = 0.06 of outstanding assets/liabilities in k.
  - Diagonal elements not restricted to zero except for the ROW sector diagonal (intra-ROW claims are zero by dataset construction).
  - RAS algorithm adjusts the estimated matrix to satisfy adding-up and zero constraints.
  - Accuracy assessed in Appendix II using actual “from-whom-to-whom” Euro Area data; preference stated not to mix observed bilateral exposures with estimated ones to preserve PGI comparability and avoid inconsistent treatment across countries.

- Combining sectoral accounts with CPIS, BIS, and IIP data to connect country networks:
  - Claims of sector i in country A vis-à-vis sector j in country B computed by multiplying: country A's foreign claims (ROW liabilities in country A) × share of country B in country A’s foreign claims (from CPIS) × sector i's share in holdings of foreign assets in country A (from IIP) × sector j's share in country B’s liabilities held by nonresidents (from IIP).
  - Example: foreign claims of Japanese MFI vis-à-vis U.S. GOV in debt securities = Japanese ROW sector's liabilities in debt securities × share of U.S. in Japanese foreign debt security claims (CPIS) × MFI’s share in holdings of foreign debt securities in Japan (IIP) × GOV’s share in U.S. liabilities in debt securities held by nonresidents (IIP).
  - Sectoral accounts, CPIS, and IIP data are consistent: compiled foreign claims by country and instrument are virtually equal.

### Networks visualization and construction (2007:Q2 vs 2012:Q2)
- Networks constructed instrument-by-instrument for 2007:Q2 and 2012:Q2 using stock data for debt securities, loans, and equities.
- Nodes represent sectors; node size proportional to a sector's holdings of liabilities in a given instrument.
- Links from sector i to sector j represent sector i's claims vis-à-vis sector j; link width proportional to the ratio of a bilateral claim to the creditor sector’s total consolidated assets (i.e., claim relative to creditor’s capacity to absorb loss).
- Cross-border exposures use a separate reference base for link widths (cross-border links not comparable in thickness with national exposure links).
- Only linkages above the median exposure are drawn (one median for intra-country exposures and another for inter-country exposures).
- For IIP cross-border data, “other sectors” are not split into HH, NFC, OFI, INS; HH node represents other sectors as a foreign creditor and NFC node represents other sectors as a foreign debtor. Other sectors’ cross-border claims from HH node are relativized by the sum of total financial assets of HH, OFI, and INS sectors.

### Debt securities: network observations and changes (2007:Q2 → 2012:Q2)
- 2007:Q2 snapshots:
  - Largest issuers (largest nodes): GOV in U.S., Euro Area, Japan, and U.S. OFI.
  - U.S. NFC sector had much larger debt securities outstanding than other G-4 NFC sectors (market-based corporate financing).
  - Euro area banks finance themselves relatively more via debt securities compared to other G-4 MFI sectors.
  - Largest country-level exposures: Japanese INS and MFI vis-à-vis Japanese GOV:
    - INS lending to Japanese GOV comprises 31 percent of INS total assets.
    - MFI lending to Japanese GOV comprises 25 percent of MFI total assets.
  - U.S. MFI, INS, and particularly GOV were highly exposed to the OFI sector (reflecting GSE activities).
  - Euro Area: strongest lending in debt securities from MFI and INS to GOV, and from INS to MFI.
  - U.K.: strongest lending exposure from INS to ROW, reflecting U.K.'s role as a financial hub.
- Cross-border exposures in 2007:Q2:
  - U.K. MFI largest vulnerabilities vis-à-vis:
    - U.S. other sectors: 2.1 percent of U.K. MFI's total assets.
    - Euro area MFI: 1.8 percent of U.K. MFI's total assets.
    - Euro area GOV: 1.8 percent of U.K. MFI's total assets.
  - Japanese other sectors (represented by HH node) highly exposed to U.S. other sectors.

- Changes by 2012:Q2:
  - Size of all GOV nodes increased; governments considerably increased debt outstanding.
  - Japanese and U.K. GOV more than doubled their amount of debt securities outstanding between 2007:Q2 and 2012:Q2.
  - U.S. OFI debt securities outstanding decreased.
  - National exposures in debt securities on average increased by +0.3pp.
    - Increase mainly vis-à-vis governments: +2.4pp overall; particularly Japan: +4.0pp and U.S.: +3.1pp.
    - In Japan, INS and MFI exposures to GOV increased to 43 percent and 35 percent of these sectors' total assets, respectively.
  - Largest decreases in national exposures:
    - Vis-à-vis OFI in the U.S.: -3.5pp.
    - Vis-à-vis OFI in Japan: -0.6pp.
    - Vis-à-vis MFI in the U.K.: -0.2pp.
    - Vis-à-vis MFI in the Euro Area: -0.2pp.
  - Cross-border exposure shifts:
    - Foreign sectors sold OFI-issued debt securities and moved to government debt.
    - Exposure increased mainly vis-à-vis U.S. GOV: +0.3pp.
      - Japanese MFI increased exposures to U.S. GOV by +0.7pp.
      - Japanese other sectors increased exposures to U.S. GOV by +1pp.
    - Cross-border exposures to U.S. other sectors decreased by -0.5pp (largest reduction).
    - Exposures to euro area MFI decreased by -0.3pp.
    - U.K. MFI sector reduced its cross-border exposures most: -0.5pp.
    - U.K. and euro area MFI decreased exposures to foreign GOV: -0.2pp.
    - U.K. and euro area other sectors increased exposures to foreign GOV: +0.3pp.

*Source: IMF.*

### 2012. Regarding cross-border exposures, the most noticeable difference is the increase of

### _wp15111 - 2012. Regarding cross-border exposures, the most noticeable difference is the increase of

### Debt Securities — network and changes (2007:Q2 vs 2012:Q2)
- Debt Securities 2007:Q2 — Top 3 bilateral national exposures:
  - INS_JP -> GOV_JP 30.7%
  - MFI_JP -> GOV_JP 25.1%
  - GOV_US -> OFI_US 21.7%
- Debt Securities 2007:Q2 — Top 3 bilateral cross-border exposures:
  - MFI_UK -> NFC_US 2.11%
  - MFI_UK -> MFI_EA 1.82%
  - MFI_UK -> GOV_EA 1.76%
- Debt Securities 2012:Q2 — Top 3 bilateral national exposures:
  - INS_JP -> GOV_JP 42.6%
  - MFI_JP -> GOV_JP 35.1%
  - INS_UK -> ROW_UK 19.0%
- Debt Securities 2012:Q2 — Top 3 bilateral cross-border exposures:
  - HH_JP -> GOV_US 1.84%
  - MFI_JP -> GOV_US 1.23%
  - HH_JP -> GOV_EA 1.12%
- Cross-border observation:
  - Cross-border exposures in debt securities vis-à-vis governments increased, particularly exposures of Japanese sectors vis-à-vis the U.S. government.
- Valuation note:
  - Debt values are expressed in USD; between 2007 and 2012 the USD appreciated vis-à-vis the EUR, JPY, and GBP, implying the paper likely underestimates the increase in GOV debt in the Euro Area, Japan, and U.K.

### Loans — network structure, exposures, and changes (2007:Q2 vs 2012:Q2)
- Loans 2007:Q2 — Top 3 bilateral national exposures:
  - MFI_US -> HH_US 32.1%
  - OFI_US -> HH_US 28.2%
  - OFI_JP -> NFC_JP 21.4%
- Loans 2007:Q2 — Top 3 bilateral cross-border exposures:
  - MFI_UK -> MFI_EA 5.7%
  - MFI_EA -> NFC_UK 4.0%
  - MFI_UK -> NFC_US 2.8%
- Loans 2012:Q2 — Top 3 bilateral national exposures:
  - MFI_US -> HH_US 26.7%
  - OFI_US -> HH_US 24.9%
  - OFI_JP -> NFC_JP 22.8%
- Loans 2012:Q2 — Top 3 bilateral cross-border exposures:
  - MFI_EA -> NFC_UK 3.5%
  - MFI_UK -> MFI_EA 2.7%
  - MFI_UK -> NFC_US 1.6%
- Key findings on loans:
  - Biggest debtors in loans: NFC and HH sectors in the U.S. and Euro Area; HH_U.S. is the biggest.
  - U.S. MFI and OFI national exposures vis-à-vis HH amount to 32.1 percent and 28.2 percent of their assets, respectively.
  - Cross-border exposures in loans decreased considerably between 2007:Q2 and 2012:Q2.
  - National and cross-border exposures in loans decreased on average by -0.1pp between 2007:Q2 and 2012:Q2; relative decrease larger for cross-border exposures.
- Sectoral changes (national exposures):
  - GOV in the U.S. increased exposures by +1.9pp (particularly vis-à-vis NFC +3.0pp and HH +6.1pp).
  - GOV in the Euro Area increased exposures by +0.2pp (particularly vis-à-vis NFC +1.4pp and HH +1.0pp).
  - OFI and NFC in the Euro Area increased loan exposures by +0.8pp and +0.7pp, respectively.
  - MFIs in the U.K., U.S., and Euro Area reduced loan exposures substantially; OFI in the U.S. and U.K. also reduced exposures.
  - Largest decreases in national loan exposures toward: U.K. HH (-1.2pp), ROW (-0.9pp), OFI (-0.8pp), NFC (-0.6pp), and U.S. HH (-0.7pp).
- Sectoral changes (cross-border exposures):
  - Japanese MFI sector increased its cross-border exposures by +0.1pp and received increased cross-border exposures by +0.01pp.
  - U.S. MFI cross-border exposures remained broadly unchanged.
  - U.K. MFI sector reduced its cross-border exposures by -0.9pp.
  - Cross-border exposures in loans were mainly reduced towards euro area MFI (-0.6pp) and U.S. other sectors (-0.1pp).

### Equities — network, valuation effects, and changes (2007:Q2 vs 2012:Q2)
- Equities 2007:Q2 — Top 3 bilateral national exposures:
  - INS_US -> NFC_US 27.3%
  - HH_US -> NFC_US 26.2%
  - INS_UK -> ROW_UK 23.9%
- Equities 2007:Q2 — Top 3 bilateral cross-border exposures:
  - HH_EA -> NFC_US 3.62%
  - HH_UK -> NFC_EA 2.75%
  - HH_UK -> NFC_US 2.44%
- Equities 2012:Q2 — Top 3 bilateral national exposures:
  - NFC_UK -> ROW_UK 24.9%
  - INS_US -> NFC_US 20.3%
  - INS_UK -> ROW_UK 20.0%
- Equities 2012:Q2 — Top 3 bilateral cross-border exposures:
  - HH_EA -> NFC_US 4.65%
  - HH_EA -> NFC_UK 2.41%
  - HH_UK -> NFC_US 2.18%
- Valuation and index context:
  - Equity liabilities are market valued.
  - In 2012:Q2 the Eurostoxx 50 and the Nikkei 225 were still 50 percent below their value in 2007:Q2; S&P 500 and FTSE 100 were only 10–15 percent below their value in 2007:Q2.
- Key findings on equities:
  - Cross-border exposures were less reduced from 2007 to 2012 than national exposures: national exposures decreased on average by -0.9pp, cross-border exposures decreased on average by -0.1pp.
  - Share of direct investments in equity foreign investments increased by 10pp between 2007 and 2012 for G-4 economies (IIP data).
- Sectoral changes:
  - INS decreased equity exposures most in U.K. (-3.6pp), Japan (-2.9pp), U.S. (-2.4pp).
  - Equity exposures most reduced vis-à-vis NFC in: Euro Area (-3.8pp), Japan (-3.6pp), U.K. (-3.0pp), U.S. (-2.3pp).
  - Euro Area and U.S. increased equity exposure vis-à-vis ROW by +1.0pp and +0.6pp, respectively.
- Cross-border equity changes:
  - Euro area other sectors increased exposures by +0.1pp; exposure to U.S. other sectors increased to 4.7 percent of their assets and to U.K. other sectors to 2.5 percent.
  - U.K. other sectors and MFI reduced exposures by approx. -0.35pp each.
  - Cross-border exposures were mainly reduced vis-à-vis other sectors in the Euro Area (-0.3pp) and in Japan (-0.2pp).

### Shock simulations — scenarios, results, and amplification
- Simulation setup:
  - Financial networks estimated for quarters 2002:Q2 to 2012:Q2.
  - Three shock scenarios analyzed:
    1. GOV debt securities in each country lose 20 percent of their value; analyze first-round impact on equity of domestic financial sectors.
    2. Same 20 percent GOV debt shock, allowed to propagate through domestic sectors via cross-sector equity holdings until convergence.
    3. Debt securities of U.S. other sectors and GOV lose 20 percent of their value; calculate impact on other G-4 economies.
- Network and methodology notes:
  - Number of links fixed over time; only link strengths vary.
  - National networks nearly complete; cross-border exposures allowed between MFIs and foreign MFI, other sectors, and GOV.
  - Focus on weighted node degrees (centrality measure) over time.
  - Shock propagation channel modeled via mark-to-market valuation of equity holdings; HH and GOV do not transmit shocks because they do not issue equity.
- Weighted node degree findings:
  - Average node degree standardized at one in 2002.
  - Node degree increased most for debt securities between 2002 and 2012; between 2 to 3 times larger in 2012 than in 2002.
  - Most node degrees increased considerably from 2002 until mid-2008, decreased shortly thereafter, then remained relatively stable (loans) or increased (debt securities and equities).
  - Japan exception: loan node degrees relatively stable 2002–2012; debt securities node degrees rose after the crisis.
  - Euro Area and U.K. node degrees seem to have increased more than U.S. and Japan for considered instruments.
- Impact of a 20 percent GOV debt devaluation — first-round and final (domestic):
  - First-round: in 2002 a 20 percent devaluation in GOV debt securities in the U.S., Euro Area, and U.K. would cause a mark-to-market drop of approx. 15 percent in domestic financial sectors’ equity.
  - By mid 2012 the same shock would cause equity devaluation of:
    - 30 percent in the U.S.
    - 30 percent in the U.K.
    - 20 percent in the Euro Area
  - Japanese financial sectors could not buffer a 20 percent devaluation before 2004 and after 2008 (losses > 1, i.e., higher than equity value).
  - Final total loss after propagation via equity holdings (ratio over equity and amplification factor):
    - Before crisis: 20 percent GOV devaluation caused losses ~3 percent of equity; final total loss after propagation was 1.8 times the initial shock.
    - After crisis: same devaluation caused claim losses amounting to 6 percent of equity; amplification factor increased to approximately 2.
    - Japan: small amplification factor of 2; U.S.: smallest loss as share of equity and smallest amplification factor.
    - U.K.: highest amplification factor; final total loss eight times the initial loss by mid 2012.
    - Euro Area: amplification factor increased from 3 to 5 between 2002 and 2012.
    - By mid 2012 financial sectors’ losses due to a 20 percent GOV devaluation amounted to approximately one third of equity in Japan and the U.K., and 18 percent in the Euro Area.
- International spillovers from U.S. shocks:
  - U.S. other sectors (HH, INS, OFI, NFC) and U.S. GOV are systemically important in G-4 networks.
  - After the crisis, cross-border exposures to U.S. other sectors decreased but exposures to U.S. GOV increased.
  - After 2009 all sectors in the other G-4 economies were more exposed to the U.S. government than to U.S. other sectors.
  - Exposures vis-à-vis U.S. other sectors decreased in the Euro Area and U.K., remained stable in Japan.
- Data integration advantage:
  - Combining sectoral accounts, IIP, and CPIS allows sector-by-country breakdowns of claims not possible using each dataset separately.

### Conclusions and implications
- Method and contributions:
  - Uses sectoral accounts merged with CPIS, BIS, and IIP to estimate bilateral financial exposures between sectors in G-4 economies.
  - First paper to compare national financial exposures across G-4 economies and to consider cross-border interconnections beyond the banking sector.
- Summary of empirical findings:
  - National exposures in debt securities vis-à-vis governments increased, particularly in the U.S. and Japan.
  - Cross-border exposures in debt securities vis-à-vis governments generally increased, notably Japanese sectors’ exposures to the U.S. government.
  - Cross-border exposures in loans decreased much more than national exposures; for equities the opposite holds.
  - Exposures in the U.K., particularly in the MFI sector, and to a lesser extent in the Euro Area, decreased more than exposures in the U.S. and Japan.
  - Differences may reflect differing policy responses to the financial crisis (fiscal stimulus vs. austerity).
- Suggested extensions for future work:
  - Estimate financial networks for a wider range of countries once data are available.
  - Decompose changes in exposures between 2007 and 2012 into volume and valuation changes.
  - Use bilateral claims to calculate debt service flows between sectors.
- Policy-relevant message:
  - Sectoral accounts data are a powerful tool for assessing financial stability; broader "from-whom-to-whom" sectoral accounts would improve assessment of interconnectedness and vulnerabilities.

*Source: _wp15111 - 2012. Regarding cross-border exposures, the most noticeable difference is the increase of (PDF content unit).*

### REFERENCES

### _wp15111 - REFERENCES

### References (selected)
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### Appendix I. Available actual from-whom-to-whom data (overview)
- U.S. (FRB, Flow of Funds): Securities, Loans, Equities — sectoral matrix presented for NFC, MFI, OFI, INS, GOV, HH, ROW with marked available links (x) and zeros (0) as in source.
- EA (ECB, Euro area accounts, MFI balance sheets): Securities, Loans, Equities — sectoral matrix presented for NFC, MFI, OFI, INS, GOV, HH, ROW with marked available links (x) and zeros (0) as in source.
- JP (BOJ, Flow of Funds): Securities, Loans, Equities — sectoral matrix presented for NFC, MFI, OFI, INS, GOV, HH, ROW with marked available links (x) and zeros (0) as in source.
- U.K (ONS, U.K. Economic Accounts, the Blue Book): Securities, Loans, Equities — sectoral matrix presented for NFC, MFI, OFI, INS, GOV, HH, ROW with marked available links (x) and zeros (0) as in source.

### Appendix II. Estimated vs. actual financial linkages — key findings
- The ECB provides complete from-whom-to-whom information for loans in the Euro Area, enabling assessment of the accuracy of estimated bilateral exposures.
- Maximum entropy techniques tend to spread financial exposures evenly across all sectors, which:
  - has the potential of underestimating extreme exposures and overestimating small exposures;
  - implies the approach is likely to underestimate risk, so estimated links represent risk lower bounds.
- Empirical comparison for loans in 2007:Q2 (Box 4):
  - Both estimated and actual networks look similar, with notable differences.
  - Observed MFI exposure to NFC relative to their assets is 20 percent; observed MFI exposure to HH is 23 percent.
  - Estimated measures are 18 percent (MFI→NFC) and 13 percent (MFI→HH).
  - Algorithm underestimates ROW exposure to OFI; algorithm sometimes identifies inexistent links but assigns them low weight.
  - Inexistent bilateral exposures are often correctly estimated as zero when aggregate assets/liabilities are zero in an asset class.
- Overall accuracy metric:
  - The mean absolute error in the estimation of exposures relative to total assets is 1.5 pp.

### Appendix III. Largest increases and decreases in exposures (2007:Q2 to 2012:Q2)

- Debt securities other than shares
  - Largest increases in creditor’s exposure (pp) — National exposures (By creditor / By debtor)
    - INS_JP 2.63 / GOV_JP 4.00
    - MFI_JP 2.31 / GOV_US 3.10
    - INS_UK 1.84 / GOV_UK 1.65
    - OFI_US 1.49 / GOV_EA 0.84
    - MFI_US 1.26 / ROW_UK 0.75
  - Largest increases — Cross-border exposures (By creditor / By debtor)
    - HH_UK 0.14 / GOV_US 0.39
    - MFI_JP 0.12 / GOV_UK 0.06
    - HH_JP 0.10 / MFI_US 0.03
    - HH_EA 0.09 / NFC_EA 0.03
    - MFI_US 0.02 / GOV_EA 0.03
  - Largest decreases in creditor’s exposure (pp) — National exposures (By creditor / By debtor)
    - GOV_US -2.76 / OFI_US -3.53
    - GOV_JP -0.43 / OFI_JP -0.55
    - HH_JP -0.18 / MFI_UK -0.23
    - NFC_US -0.18 / MFI_EA -0.22
    - GOV_UK -0.15 / MFI_JP -0.14
  - Largest decreases — Cross-border exposures (By creditor / By debtor)
    - MFI_UK -0.54 / NFC_US -0.57
    - MFI_EA -0.19 / MFI_EA -0.27
    - HH_US -0.02 / MFI_UK -0.08
    - MFI_US 0.02 / NFC_UK -0.03
    - HH_EA 0.09 / NFC_JP -0.01
  - Average differences in creditor’s exposure between 2007:Q2 and 2012:Q2 (pp)
    - National exposures 0.34
    - Cross-border -0.03

- Loans
  - Largest increases in creditor’s exposure (pp) — National exposures (By creditor / By debtor)
    - GOV_US 1.89 / ROW_EA 0.66
    - GOV_EA 0.92 / NFC_JP 0.58
    - OFI_EA 0.81 / GOV_EA 0.54
    - NFC_EA 0.70 / OFI_EA 0.43
    - GOV_JP 0.34 / ROW_US 0.12
  - Largest increases — Cross-border exposures (By creditor / By debtor)
    - MFI_JP 0.06 / MFI_JP 0.01
    - MFI_US 0.01 / MFI_US 0.00
    - HH_US 0.01 / NFC_JP -0.01
    - HH_UK 0.00 / NFC_UK -0.06
    - HH_JP -0.01 / NFC_EA -0.10
  - Largest decreases in creditor’s exposure (pp) — National exposures (By creditor / By debtor)
    - MFI_UK -2.06 / HH_UK -1.16
    - MFI_US -1.76 / ROW_UK -0.86
    - OFI_UK -1.08 / OFI_UK -0.84
    - OFI_US -0.97 / HH_US -0.65
    - MFI_EA -0.65 / NFC_UK -0.62
  - Largest decreases — Cross-border exposures (By creditor / By debtor)
    - MFI_UK -0.88 / MFI_EA -0.55
    - MFI_EA -0.02 / NFC_US -0.13
    - HH_EA -0.01 / NFC_EA -0.10
    - HH_JP -0.01 / NFC_UK -0.06
    - HH_UK 0.00 / NFC_JP -0.01
  - Average differences in creditor’s exposure between 2007:Q2 and 2012:Q2 (pp)
    - National exposures -0.12
    - Cross-border -0.12

- Equity
  - Largest increases in creditor’s exposure (pp) — National exposures (By creditor / By debtor)
    - NFC_US 0.94 / ROW_EA 1.03
    - NFC_UK 0.89 / ROW_US 0.60
    - GOV_JP 0.39 / OFI_US 0.35
    - ROW_US 0.23 / MFI_UK 0.12
    - OFI_US 0.14 / INS_JP -0.06
  - Largest increases — Cross-border exposures (By creditor / By debtor)
    - HH_EA 0.12 / NFC_US 0.06
    - MFI_US 0.05 / NFC_UK 0.03
    - HH_JP 0.01 / MFI_UK 0
    - MFI_JP 0 / MFI_JP -0.01
    - MFI_EA -0.08 / MFI_EA -0.09
  - Largest decreases in creditor’s exposure (pp) — National exposures (By creditor / By debtor)
    - INS_UK -3.57 / NFC_EA -3.80
    - INS_JP -2.92 / NFC_JP -3.59
    - INS_US -2.40 / NFC_UK -2.99
    - HH_EA -1.98 / NFC_US -2.30
    - HH_JP -1.90 / MFI_EA -2.07
  - Largest decreases — Cross-border exposures (By creditor / By debtor)
    - HH_UK -0.36 / NFC_EA -0.33
    - MFI_UK -0.35 / NFC_JP -0.22
    - MFI_EA -0.08 / MFI_US -0.12
    - HH_US -0.08 / MFI_EA -0.09
    - MFI_JP 0 / MFI_JP -0.01
  - Average differences in creditor’s exposure between 2007:Q2 and 2012:Q2 (pp)
    - National exposures -0.87
    - Cross-border -0.09

*Source: _wp15111 - REFERENCES (appendices and reference list as provided in the source PDF).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15111.pdf_