## _wp0744

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### I. Introduction and research objective
- Purpose: Explore whether increasing international openness increased financial risk for Bank of Ireland (BoI), Allied Irish Banks PLC (AIB), and Anglo Irish Bank Corp. PLC (Anglo IB) over 1994–2005, and whether international linkages produced contagion risk.
- Key measures and methods:
  - Distance to default (DD) as comprehensive bank default-risk measure (combines stock returns, leverage, asset volatility).
  - Rolling correlations of changes in DD between Irish banks and major European and U.S. banks.
  - Multinomial ordered logit model of coexceedances: probability that a number of Irish banks experience a large negative shock the same day as banks in other countries, controlling for Ireland-specific and global factors.
- Definition of large shocks: bottom 15th percentile of the weekly difference in the daily DD of all banks (cut-off point = -0.070).

### II. Distance to Default measure, dataset, and key statistics
- DD definition and estimation:
  - Based on Black-Scholes/Merton structural model; equity viewed as a call option on bank assets with strike equal to book value of liabilities.
  - Asset value and asset volatility estimated from one year of daily equity return data; accounting value of liabilities for the relevant year used.
  - IMF MFD FP Distance to Default Database methodology (assets approximated as equity market value plus book value of liabilities).
- Sample coverage and frequency:
  - Daily DD data for 40 banks in 8 countries: France (2), Germany (4), Ireland (3), Italy (6), the Netherlands (2), Spain (4), the United Kingdom (5), United States (14).
  - Sample period: January 1994 to November 2005.
  - Observations per bank: typically 3105 daily observations, except one U.K. bank with 2522 and one Netherlands bank with 2803.
- Sample summary statistics (selected):
  - Total observations for dd: n = 123,304; Mean dd = 5.19; Median dd = 5.00; Std Dev = 2.33; Min = -2.16; Max = 27.17.
  - Observations for ∆dd/|dd|: n = 123,104; Mean = 0.02; Median = 0.00; Std Dev = 3.15; Min = -236.53; Max = 895.32.
  - Coexceedances IRL: n = 3,105; Mean = 0.36; Median = 0.00; Std Dev = 0.71; Min = 0.00; Max = 3.00.
  - Cut-off point (negative 15th percentile of ∆dd/|dd|): -0.070.
  - Pooled average DD: 5.2; pooled median DD: 5.0.
  - Mean DD by country example range: 3.3 (Italy) to 7.7 (Spain).
  - Three Irish banks’ mean DD: about 6; median about 5.7.
  - Largest negative percentage change observed: -237 percent.
  - Largest positive percentage change observed: 895.32 (as reported in ∆dd/|dd| max).

### III. Evidence of external linkages and sector structure
- Irish banking sector concentration:
  - BoI, AIB, and Anglo IB represent about 45 percent of total banking assets but nearly 80 percent of the domestic retail market.
- Identified external linkage types:
  - Direct equity exposures through overseas expansion and ownership stakes; loan-book exposures abroad; deposit and funding sources from other countries; presence of foreign banks operating in Ireland; participation in securities and asset management; holdings of CRT instruments (covered bonds, CDS, ABS); direct and indirect exposures to foreign property markets.
- Specific exposures and ratios:
  - Overseas loan-book exposures to the United Kingdom: AIB nearly 28 percent, BoI 44 percent, Anglo IB 41 percent of loan books.
  - AIB U.S. operations: 2 percent of its loan book; U.S. and Polish investments contributed a combined 16 percent to AIB’s pretax profit in the first half of 2005.
  - Anglo IB: about 5 percent of its loan book exposed to the U.S.
  - Average loan-to-deposit ratio for Ireland: exceeds 150 percent.
  - Market funding dependence: AIB and BoI fund about 40 percent of lending in the market; Anglo IB market funding requirement about 35 percent.
  - Nonresident interbank borrowing and debt securities issued and held by nonresidents in 2004: 83 percent vis-à-vis non-Euro area residents.
  - Covered bonds holdings: almost 60 percent held by other Euro Area members; 25 percent held in USD by other countries.
  - Supervisory liquidity requirement: 25 percent of deposits and short-term liabilities must be covered by liquid assets.
- Inferred directional exposures (BIS-based interpretation):
  - Net nonbank asset position countries exposing Ireland to credit risk: Austria, France, Germany, Italy, the Netherlands, Spain, United States.
  - Ireland’s positive net bank exposure in Italy and Spain (and previously the U.S., Austria, France) may expose Ireland to credit risk potentially leading to liquidity risk.
  - If Ireland has a negative net bank-asset position vis-à-vis a country, Ireland faces liquidity risk if that lender country encounters problems: Germany, U.K., Belgium, Netherlands, and currently the U.S., Austria, France.

### IV. Correlation patterns, shocks, and co-movement trends
- DD level patterns:
  - General increase in DD starting in 2003 for all countries; upward trend for France, Italy, and Eastern Europe.
  - Irish banks: DD declined around 1997 until end-1999; negative shock during 2002; recovery starting in 2003.
- Correlation and rolling-correlation findings:
  - Correlations of DD between Ireland and other countries are on average positive and quite high for the Netherlands, the U.K., the U.S., and Spain.
  - Three subperiods:
    - pre-Euro: 1/3/1994–12/31/1998.
    - post-Euro: 1/1/1999–9/11/2001.
    - post-September 11th: 9/12/2001–11/25/2005.
  - Subperiod patterns:
    - Correlations generally become much smaller or negative in the post-Euro period compared with pre-Euro.
    - Correlations increase to very high levels in the post-September 11th period.
  - Rolling one-year average pair-wise correlations increased over time, stronger in 2003–04; decreased in 1999 with Euro introduction; increased after 2001.
  - Ireland–U.K. rolling correlations: high during whole period except 1999.
  - Ireland correlations with France, Italy, Spain: seem to have increased over time.
  - Ireland correlations with continental Europe: generally negative during 1999–2001.
- Percentage-change shocks (∆dd/|dd|):
  - Mean of percentage change = 0.00 (reported as zero mean).
  - Most volatile period for Ireland: 1999–2000.
  - Fewer shocks in 2003–05 than earlier decade; external reporting example: FitchRatings reported credit events fell to 37 in 2005 from 94 in 2003.

### V. Econometric evidence on contagion (coexceedances and multinomial logit)
- Dependent variable:
  - Coexceedance count: number of banks in a country whose weekly percentage change in DD was in the negative 15th percentile on a given day; outcomes limited to 0, 1, and 2 or more coexceedances for countries with more than two banks.
- Model specification and controls:
  - Multinomial ordered logit for j = 0, 1, 2 (2 denotes 2 or more).
  - Regressors include lagged Irish coexceedances (Cct-1), number of coexceedances in other countries (Cdt), and vector Fc of Ireland-specific and global shocks.
  - Fc variables include: systemic risk indicator (sum of indicators for Euro Area index, NASDAQ, ISEQ), weekly change in NASDAQ volatility (GARCH(1,1)), weekly change in ISEQ volatility (GARCH(1,1)), and weekly change in yield of Irish 10-year government bond (interest rate IRL).
  - GARCH(1,1) NASDAQ estimates: Const = 7.52E-05 (std error = 6.54E-06; z = 11.5; p = 0.00); εt-12 coeff = 0.65 (std error = 0.03; z = 16.97; p = 0.00); σt-12 coeff = 0.38 (std error = 0.01; z = 24.02; p = 0.00).
  - GARCH(1,1) ISEQ estimates: Const = 7.79E-05 (std error = 4.46E-06; z = 17.46; p = 0.00); εt-12 coeff = 0.67 (std error = 0.04; z = 15.34; p = 0.00); σt-12 coeff = 0.22 (std error = 0.02; z = 12.52; p = 0.00).
- Main ordered multinomial logit findings (basic and extended models):
  - Persistence: Coexceedances own lagged coefficient = 2.16** (std error = 0.07) — positive and significant.
  - Systemic risk: coefficient = 0.81** (std error = 0.06) — positive and significant.
  - Interest rate IRL: coefficient = 2.18** (std error = 0.41) — positive and significant.
  - Volatility ISEQ: not significant in basic specification.
  - Contagion from other countries (extended model):
    - U.K.: Contagion UK coefficient = 0.13** (std error = 0.069) and in some specifications 0.17* (std error = 0.09).
    - U.S.: Contagion US coefficient = 0.27** (std error = 0.06) and other columns show 0.20**, 0.23**, 0.38** (std errors = 0.08 or 0.06 in various columns).
    - Netherlands: Contagion NL coefficient = -0.21** (std error = 0.09) in some specifications (negative and significant).
    - Contagion coefficients for FR, GER, IT, SP generally insignificant or mixed.
  - Relative magnitude example:
    - U.S. coefficient = 0.27; U.K. coefficient = |0.13| → relative U.S. influence = (0.27/|0.13|) = 2.1 (Ireland).
    - Figure 9 relative U.S. influence reported examples: ESP 0.6; FRA 1.3; IRL 2.1; GER 17.0 (benchmarking U.S. influence against U.K.).
- Bank-specific findings (extended models for AIB, Anglo IB, BoI):
  - AIB: evidence of contagion from the U.K. (10 percent significance), the U.S.; Spain and Netherlands show effects (Netherlands negative).
  - Anglo IB: contagion from Italy (10 percent significance) and the U.S.
  - BoI: contagion from the U.S.
  - Two-way contagion detected between AIB and BoI; Anglo IB and BoI.
  - Pseudo-R2 values across specifications: examples include 0.31; 0.32; 0.393; 0.408; 0.351; 0.362; 0.327; 0.347.
- Period-specific multinomial results (Table 10):
  - Pre-Euro (Jan. 1994–Dec. 1998):
    - Contagion UK = 0.29** (std error = 0.12); Contagion GER = 0.22* (std error = 0.12).
    - Systemic risk = 1.17** (std error = 0.17).
    - Pseudo-R2 = 0.339.
  - Post-Euro (Jan. 1999–9/11/2001):
    - Contagion US = 0.28** (std error = 0.11); Contagion UK = 0.20* (std error = 0.12).
    - Volatility US = -20.65* (std error = 12.81).
    - Systemic risk = 0.46** (std error = 0.12).
    - Pseudo-R2 = 0.322.
  - Post-September 11 (12/9/2001–Nov. 2005):
    - Contagion US = 0.18* (std error = 0.11).
    - Systemic risk = 0.76** (std error = 0.10).
    - Pseudo-R2 = 0.286.
- Robustness checks:
  - Reducing U.S. banks from 14 to top 5 leaves U.S. influence unchanged.
  - Using monthly changes in DD does not change U.S. and U.K. influence; contagion from Netherlands disappears.
  - Changing tail threshold does not qualitatively change U.S. and U.K. results.
  - Pattern over subperiods: stronger Europe linkages earlier, stronger U.S. linkages later.

### VI. Interpretation of mechanisms
- Systemic shocks (large stock market moves) increase probability of multiple Irish banks being simultaneously in DD tail.
- Interest-rate channel: changes in long-term Irish government bond yields positively related to Irish coexceedances (example: interest rate IRL coeff = 2.18**; std error = 0.41) — link via long-term lending/mortgage rates and large bank exposure to real estate and variable-rate lending.
- Contagion channels consistent with empirical findings:
  - Balance-sheet linkages through subsidiaries and net-asset exposures (aggregate positive net-asset exposures in the U.S.; large negative net-asset exposure to the U.K. in aggregate).
  - Off-balance-sheet exposures: derivatives and CRT instruments can transmit U.S./U.K. market risks without direct loan exposures.
  - Interbank and derivative counterparties producing bank-specific two-way linkages (AIB–BoI; Anglo IB–BoI).

### VII. Policy implications and recommendations
- Use DD-based contagion analysis to inform financial stability monitoring without specifying a single contagion channel.
- Supervisory and regulatory suggestions for Irish authorities (CBFSAI and supervisors):
  - Stress test specific categories of exposures of Irish banks to both the U.S. and the U.K.
  - Collect more information on types and counterparties of derivative positions and risk transfers through structured products of Irish banks, given potential off-balance-sheet exposures to U.S. or U.K. property markets.
  - Monitor rapidly growing use of CRT products and derivatives that could transmit foreign property-market risks to Irish banks.
  - Maintain attention to supervisory liquidity requirement (25 percent coverage) and large loan-to-deposit ratio (exceeds 150 percent) to mitigate liquidity-driven contagion risk.
- Rationale emphasized:
  - Even where consolidated balance-sheet exposures to the U.S. are not large, derivatives and off-balance-sheet positions may imply significant contagion channels.

### VIII. Caveats, limitations, and data issues
- Equity-price-based DD measures may not capture non-equity banking links (securities, insurance) and rely on listed banks only.
- Small sample of listed banks per country; may not represent entire banking systems.
- Irish sample banks cover less than 50 percent of system assets though nearly 80 percent of domestic retail market.
- Low frequency of large shocks; results could be driven by episodic events (e.g., tech-bubble burst in 2000, 2002 events).
- BIS consolidated data may overstate interdependencies if many banks resident in Ireland operate primarily in the Financial Services Center with nonresident counterparties.
- Multinomial logit coefficient estimates should not be read as marginal effects; relative impacts can be compared via coefficient ratios (example provided: U.S. relative effect benchmarked against U.K. = 2.1 for Ireland).

*Source: _wp0744 (excerpts from the referenced IMF working paper).*

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

### _wp0744 - References

### I. Introduction and research objective
- Purpose: Explore whether increasing international openness increased financial risk for the three major Irish banks (Bank of Ireland (BoI), Allied Irish Banks PLC (AIB), Anglo Irish Bank Corp. PLC (Anglo IB)) over 1994–2005, and whether international linkages produced contagion risk.
- Methodological approach:
  - Use distance to default (DD) as a comprehensive measure of bank default risk (combines stock returns, leverage, asset volatility).
  - Analyze rolling correlations of changes in DD between Irish banks and major European and U.S. banks.
  - Estimate contagion risk using a multinomial logit model for coexceedances: probability that a number of Irish banks experience a large negative shock on the same day as banks in other countries, after controlling for Ireland-specific and global factors.
- Definition of "large shocks": bottom 15th percentile of the weekly difference in the daily DD of all banks (15th percentile threshold chosen to include higher-probability incidences, not only crisis scenarios).

### II. Sources and channels of contagion (Box 1 — literature survey)
- Enumerated channels of cross-country contagion risk:
  - Bank deposit runs (Freixas, Parigi and Rochet 2000).
  - Wholesale funding channels (intermediation, investment banking, securities trading, asset management, business banking).
  - Liquidity and credit risk in interbank markets (Allen and Gale 2000; Freixas, Parigi and Rochet 2000).
  - Unidentified channels: contagion in financial markets absent explicit links due to asymmetric information (Morgan 2002).

### III. Evidence of external linkages of the Irish banking sector
- Banking system structure:
  - BoI, AIB, and Anglo IB represent about 45 percent of total banking assets but nearly 80 percent of the domestic retail market.
- Identified external linkage types:
  - Direct equity exposures through overseas expansion and ownership stakes.
  - Loan-book exposures abroad.
  - Deposit and funding sources from other countries and presence of foreign banks operating in Ireland.
  - Stock market participation via securities and asset management.
  - Holding of credit risk transfer (CRT) instruments (covered bonds, CDS, ABS).
  - Direct and indirect exposures to foreign property markets.
  - BIS measures of net asset positions and consolidated claims (Figures referenced in source).
- Specific factual exposures and ratios:
  - AIB, BoI, and Anglo IB overseas loan-book exposures to the United Kingdom: AIB nearly 28 percent, BoI 44 percent, Anglo IB 41 percent of loan books.
  - AIB U.S. operations: 2 percent of its loan book; AIB had a large stake in a U.S. regional bank and majority ownership in a Polish bank; U.S. and Polish investments contributed a combined 16 percent to AIB’s pretax profit in the first half of 2005 (Standard&Poor’s 2006).
  - Anglo IB: about 5 percent of its loan book exposed to the U.S.
  - Average loan-to-deposit ratio for Ireland: exceeds 150 percent.
  - Market funding dependence: AIB and BoI fund about 40 percent of lending in the market; Anglo IB market funding requirement about 35 percent.
  - Nonresident interbank borrowing and debt securities issued and held by nonresidents in 2004: 83 percent vis-à-vis non-Euro area residents.
  - Covered bonds holdings: almost 60 percent held by other Euro Area members; 25 percent held in USD by other countries.
  - Irish banks’ sample (pooled) average DD: 5.2; median DD: 5.0.
  - Mean DD by bank ranges from 3.3 (Italy) to 7.7 (Spain).
  - The three Irish banks have mean DD about 6; median about 5.7.
  - Supervisory liquidity requirement: 25 percent of deposits and short-term liabilities must be covered by liquid assets.

- Inferred likely contagion channels and directions (based on BIS and other evidence):
  - Countries with which Ireland has a net nonbank asset position likely expose Ireland to credit risk in loans and other asset markets: Austria, France, Germany, Italy, the Netherlands, Spain, and the United States.
  - Ireland’s positive net bank exposure in Italy and Spain, and previously the U.S., Austria and France, possibly exposes Ireland to credit risk that could lead to liquidity risk.
  - If Ireland has a negative net bank-asset position vis-à-vis a country, it faces liquidity risk if that lender country experiences problems: Germany, U.K., Belgium, Netherlands, and currently the U.S., Austria, and France.

- Caveats and data limitations:
  - Analysis uses equity prices of banking groups and may not capture non-equity banking links (securities, insurance).
  - Small sample of listed banks in each country; may not be representative of whole systems.
  - Irish sample banks comprise less than 50 percent of the banking system by assets (but a much larger share of the retail market).
  - Number of large-shock observations is low; results may be driven by large events such as the 2000 tech-bubble burst.

### IV. Trends in interdependencies using Distance to Default (DD)
- DD definition and estimation:
  - Based on Black-Scholes option-pricing model; equity viewed as a call option on bank assets with strike equal to book value of total liabilities.
  - DD = number of asset value standard deviations away from the default point (book value of liabilities equals market value of assets).
  - Market value of assets is unobservable and estimated from equity values and accounting measures of liabilities.
- Observed DD trends and country patterns:
  - General increase in DD starting in 2003 for all countries, indicating global improvement in bank health in the last two years of the sample.
  - Upward trend over the past decade for France, Italy, and Eastern Europe (Poland and Hungary average).
  - Irish banks: trend decline in DD around 1997 continued until end-1999; negative shock during 2002 (after-effects of September 11, 2001 and possibly AIB’s U.S. subsidiary scandal in 2002); recovery starting in 2003 to levels comparable to late 1990s.
- Empirical findings on interdependencies and contagion:
  - Rolling correlations in percentage changes in DD indicate increasing simultaneous occurrence of shocks across countries over the last decade.
  - Evidence of significant cross-border interdependencies from the U.K., U.S., and the Netherlands to Ireland (following Gropp, Lo Duca and Vesala (2005) approach).
  - Contagion risk appears to have shifted from Europe in the pre-Euro period to the U.S. in the post-Euro period.
- Modeling specifics referenced:
  - Use of rolling correlations of ∆DD/|DD| and HP (Hodrick-Prescott) trends of DD.
  - Multinomial logit model used to analyze daily coexceedances of weekly percentage change in DD (January 1994–November 2005) and by period.

### V. Key statistics and datasets mentioned
- Sample period: January 1994–November 2005.
- Large-shock threshold used: bottom 15th percentile of weekly difference in daily DD.
- Pooled average DD: 5.2; pooled median DD: 5.0.
- Mean DD by country example range: 3.3 (Italy) to 7.7 (Spain).
- Three Irish banks’ mean DD: about 6; median about 5.7.
- Loan-to-deposit ratio for Ireland: exceeds 150 percent.
- Market funding shares: AIB and BoI about 40 percent each; Anglo IB about 35 percent.
- Nonresident interbank borrowing and nonresident-held debt securities in 2004: 83 percent vis-à-vis non-Euro area residents.
- Covered bonds holdings: almost 60 percent held by other Euro Area members; 25 percent held in USD by other countries.
- AIB & Polish/U.S. contribution: U.S. and Polish investments combined contributed 16 percent to AIB’s pretax profit in the first half of 2005.

### VI. Principal conclusions and implications for monitoring financial stability
- Increasing international openness of Irish banks has coincided with greater international interdependencies in bank risk as measured by DD.
- Significant cross-border interdependencies to Ireland originate from the U.K., U.S., and the Netherlands; the dominant source of contagion appears to have shifted from Europe pre-Euro to the U.S. post-Euro.
- Co-movements in DD reflect interdependencies that encompass many channels of contagion (equity exposure, loan exposure, interbank and securities markets, CRT instruments, property markets), including contagion in the absence of explicit bilateral links.
- Monitoring implications:
  - Contagion analysis based on DD can inform financial stability monitoring without requiring specification of a single contagion channel.
  - Authorities should account for exposures via wholesale funding, CRT instruments, and foreign loan-book and equity exposures when assessing systemic risk.
  - Supervisory liquidity requirements (25 percent coverage) and attention to high loan-to-deposit ratios (exceeding 150 percent) are important in mitigating liquidity-driven contagion risk.
- Limitations to consider in interpretation:
  - Results sensitive to small sample of listed banks and to episodic large shocks (e.g., tech-bubble burst, 2002 events).
  - BIS data may overstate interdependencies if many banks resident in Ireland operate primarily in the Financial Services Center with nonresident counterparties.

*Source: _wp0744 - References (excerpts from the referenced IMF working paper).*

### Box 2. The Distance to Default Measure and Data Issues

### Box 2. The Distance to Default Measure and Data Issues

### Definition and interpretation of Distance to Default (DD)
- DD is based on the structural valuation model of Black and Scholes (1973) and Merton (1974).
- The DD "tells us by how many standard deviations the log of [the assets-to-debt] ratio needs to deviate from its mean in order for default to occur."
- Key variables as described:
  - Vt is the firm’s assets value with mean r and volatility σA.
  - Xt is the book value of the debt at time t, with maturity equal to T.
- The market value of equity is viewed as a call option on the firm’s assets VA, with strike price Xt. Default occurs when VA/Xt < 1.
- Declines in the (VA,t / Xt) ratio are equivalent to declines in capitalization. DD combines equity-return information with leverage and asset volatility information.

### Estimation methodology and data inputs
- Asset value and asset volatility correspond to forward-looking economic values and are estimated using equity data (not balance-sheet accounting figures).
- The DD measures used here are estimated by the IMF MFD FP Distance to Default Database with the methodology described in Vassalou and Xing (2004), except:
  - The value of assets is taken to be equal to the value of equity plus the book value of liabilities.
- At each date:
  - The value of assets, the return on assets and its volatility are derived using the Black-Scholes option-pricing formula.
  - Estimation uses one year of daily equity return data preceding the estimation date.
  - The accounting value of liabilities for the relevant year is used.

### Sample coverage and frequency
- Dataset: daily DD data for 40 banks in 8 countries:
  - France (2 banks), Germany (4 banks), Ireland (3 banks), Italy (6 banks), the Netherlands (2 banks), Spain (4 banks), the United Kingdom (5 banks), and the United States (14 banks).
- Sample period: January 1994 to November 2005.
- Inclusion criteria: all banks listed on a stock exchange with DD available from the IMF FP Distance to Default Database.
- Exclusions: four banks dropped because DD not available for the entire period (one bank for France, one for the United Kingdom, and two banks for Italy).
- Relative size: banks in the sample are generally quite large relative to the EU population of banks and represent a high fraction of total assets of commercial banks in each country.
- Observations per bank:
  - For each bank, the sample contains 3105 daily observations,
  - except one U.K. bank with 2522 observations and one bank from the Netherlands with 2803 observations.

### Correlation patterns in DD across countries and subperiods
- Table-level finding: correlations of DD between Ireland and other countries are on average positive, and quite high for the Netherlands, the U.K., the U.S., and Spain.
- Three subperiods analyzed (past decade split):
  - pre-Euro period: 1/3/1994 to 12/31/1998
  - post-Euro period: 1/1/1999 – 9/11/2001
  - post-September 11th period: 9/12/2001-11/25/2005
- Subperiod findings:
  - Correlations generally become much smaller or negative in the post-Euro period compared with the pre-Euro period.
  - Correlations increase to very high levels in the post-September 11th period.
- Rolling correlations (one-year):
  - Average pair-wise correlation (across all country pairs) appears to increase over time, stronger in the 2003–04 period.
  - Average pair-wise correlation decreased in 1999 with the introduction of the Euro, and increased after 2001.
  - Over the last couple of years of improving bank health (near the end of the sample) correlations seem to have diminished.
  - Ireland–U.K. rolling correlations: high during whole period except 1999.
  - Ireland correlations with France, Italy, and Spain: seem to have increased over time.
  - Ireland correlations with continental Europe: generally negative during 1999–2001.

### Shocks in DD and percentage-change analysis
- Definition of shocks: weekly percentage change in DD for each bank, (∆ddit / |ddit|).
- Sample statistics and extremes:
  - The mean of the percentage change in DD is zero.
  - The largest negative change is 237 percent (a sizable shock).
- Time patterns in percentage-change series:
  - Most volatile period for Ireland: 1999–2000 (also volatile for the U.K. and France).
  - Italy, the Netherlands, Spain, and Germany experienced large shocks in 2001–03.
  - Fewer shocks in 2003–05 than in the decade before, possibly reflecting benign macroeconomic conditions and a benign credit cycle.
  - Example statistic from external reporting cited: FitchRatings (2005) reported a sharp drop in credit events to 37 in 2005 from 94 in 2003.

### Measuring simultaneous large shocks (coexceedances) and econometric approach
- Motivation: capture simultaneous occurrence of shocks across countries.
- Two empirical tools used:
  - Simple correlations (Table 5) in percentage change in DD between Ireland and other countries.
  - One-year rolling correlations (Figure 7) in percentage change in DD between Ireland and other countries.
- Findings on co-movement of shocks (∆dd / |dd|):
  - On average, correlations between Ireland and other countries are positive.
  - Correlations stronger for the U.K. and the U.S. than for other European countries.
  - Unlike correlations in DD levels, correlations in (∆dd / |dd|) are strongest in the pre-Euro period and weakest in the post-Euro period (but still positive).
  - Rolling correlations over the whole decade:
    - Decreasing over time for Germany, the U.K., and the U.S.
    - No clear trend for other countries.
    - The average of rolling correlations across all country pairs has a positive trend over the last decade, suggesting increasing global interdependencies.

### Econometric framework for contagion using coexceedances
- Extreme-value approach: focus on negative tail of distribution of weekly changes in DD because distributions exhibit fat tails and correlation is higher for larger shocks.
- Large shocks defined as the negative 15th percentile of the common distribution of the percentage change in DD across all banks.
- Coexceedance measure: number of banks in a given country that are simultaneously in that tail on the same day.
- Estimation method: multinomial ordered logit model to estimate the probability of j = 0, 1, 2 (number of Irish banks in the tail simultaneously) as a function of:
  - lagged number of coexceedances in Ireland (Cct-1),
  - number of coexceedances in other countries (Cdt),
  - a vector Fc of Ireland-specific and global shocks.
- Model specifics:
  - j = 0, 1, 2 corresponds to 0 banks in the tail, 1 bank in the tail, and 2 or more banks in the tail.
  - Fc comprises Ireland-specific and global shocks affecting Ireland.
  - Estimations performed in three sets: base model, extended model, and extended model for each of the three large Irish banks.
- Base model controls and persistence:
  - The base model includes Fc and persistence in Irish coexceedances Cct-1.
  - Four variables used to represent Fc; one described in the source:
    1) Systemic risk indicator:
      - Measures the number of stock markets experiencing a large shock at time t.
      - Indicator equals one if a stock market of a given country experienced a shock in the bottom 15th percentile of weekly return changes, zero otherwise.
      - Calculated for:
        - Euro Area stock market index (N100 or Euronext Top 100 Index),
        - U.S. (NASDAQ),
        - Irish stock market (ISEQ or Irish Overall Index),
        - Data source: Bloomberg.
      - The systemic risk control is the sum of the three indicator variables and ranges from 0 to [value truncated in source].

*Source: Box 2. The Distance to Default Measure and Data Issues (excerpt).*

### 3. This control should be positively related to the number of coexceedances in Ireland.

### _wp0744 - 3. This control should be positively related to the number of coexceedances in Ireland.

### Controls, variables, and data construction
- Controls included in regressions:
  - Systemic risk—large stock market movements in Ireland and elsewhere.
  - U.S. stock market volatility—weekly change in NASDAQ volatility estimated with a GARCH(1,1): σt2 = α + βσt-12 + γεt-12, using maximum likelihood. GARCH estimation results reported in Table 8.
  - Irish stock market volatility—weekly change in ISEQ volatility (GARCH(1,1) reported in Table 8).
  - Interest rate shock—weekly change in the yield of the Irish 10-year government bond; expected to be positively related to the number of coexceedances.
- Definition of the dependent variable:
  - Coexceedances: number of banks whose weekly percentage change in the distance to default (∆ddit / |ddit-1|) was in the 15th percentile negative tail on a given day.
  - Outcomes limited to 0, 1, and 2 or more coexceedances for countries with more than two banks.
- Sample and descriptive statistics (Table 6 and Table 7):
  - Total observations for dd: n = 123,304; Mean dd = 5.19; Median dd = 5.00; Std Dev = 2.33; Min = -2.16; Max = 27.17.
  - Observations for ∆dd/|dd|: n = 123,104; Mean = 0.02; Median = 0.00; Std Dev = 3.15; Min = -236.53; Max = 895.32.
  - Coexceedances IRL: n = 3,105; Mean = 0.36; Median = 0.00; Std Dev = 0.71; Min = 0.00; Max = 3.00.
  - Coexceedances US: n = 3,105; Mean = 1.76; Median = 0.00; Std Dev = 2.88; Min = 0.00; Max = 14.00.
  - Cut-off point (negative 15th percentile of ∆dd/|dd|): -0.070.
  - Sample composition by country (Table 7): Total banks = 40. Ireland: 3 banks; USA: 14 banks; UK: 5; Germany: 4; France: 2; Spain: 4; Netherlands: 2; Italy: 6.
- Time pattern:
  - Time pattern of coexceedances in Ireland shown in Figure 8: most turbulent period 1999–2000; calmest mid-1990s and the last couple of years.

### GARCH(1,1) volatility estimates (Table 8)
- US stock market volatility—NASDAQ:
  - Const = 7.52E-05; std error = 6.54E-06; z-stat = 11.5; p-value = 0.00.
  - εt-12 coefficient = 0.65; std error = 0.03; z-stat = 16.97; p-value = 0.00.
  - σt-12 coefficient = 0.38; std error = 0.01; z-stat = 24.02; p-value = 0.00.
- Ireland stock market volatility—ISEQ:
  - Const = 7.79E-05; std error = 4.46E-06; z-stat = 17.46; p-value = 0.00.
  - εt-12 coefficient = 0.67; std error = 0.04; z-stat = 15.34; p-value = 0.00.
  - σt-12 coefficient = 0.22; std error = 0.02; z-stat = 12.52; p-value = 0.00.

### Main econometric findings (ordered multinomial logit results; Tables 9 and 10)
- Basic model findings (Ireland, Table 9):
  - Coexceedances own lagged: coefficient = 2.16**; std error = 0.07. (Positive and significant — persistence/stickiness.)
  - Systemic risk: coefficient = 0.81**; std error = 0.06. (Positive and significant.)
  - Interest rate IRL: coefficient = 2.18**; std error = 0.41. (Positive and significant.)
  - Volatility ISEQ: not significant in basic specification.
  - Volatility US: sometimes significant with negative sign in extended specifications (see Table 9 entries).
- Extended model findings—contagion from other countries (Table 9):
  - Evidence of contagion to Ireland from:
    - U.K.: Contagion UK coefficient = 0.13**; std error = 0.069 (basic) and 0.17*; std error = 0.09 (extended in some columns).
    - U.S.: Contagion US coefficient = 0.27**; std error = 0.06 (basic); other extended columns show significant positive US coefficients (e.g., 0.20**, std error = 0.08; 0.23**, std error = 0.08; 0.38**, std error = 0.08).
    - Netherlands: Contagion NL coefficient = -0.21**; std error = 0.09 (negative and significant in some specifications).
  - Contagion coefficients for FR, GER, IT, SP generally insignificant or mixed signs across specifications.
- Relative magnitude of U.S. contagion to Irish banks (from main text and Figure 9):
  - U.S. coefficient = 0.27; U.K. coefficient = |0.13| → relative U.S. influence = (0.27/|0.13|) = 2.1.
  - Figure 9 reports relative U.S. influence for selected Euro-area countries: ESP 0.6; FRA 1.3; IRL 2.1; GER 17.0 (noting interpretation: black patches show U.S. influence benchmarked against U.K. influence).
- Bank-specific extended model (three Irish banks, Table 9):
  - AIB: evidence of contagion from the U.K. (10 percent significance), the U.S., Spain, and Netherlands (negative coefficient).
  - Anglo IB: contagion from Italy (10 percent significance) and the U.S.
  - BoI: contagion from the U.S.
  - Two-way contagion detected between:
    - AIB and BoI.
    - Anglo IB and BoI.
  - Pseudo-R2 values reported across specifications (examples from Table 9): 0.31; 0.32; 0.393; 0.408; 0.351; 0.362; 0.327; 0.347 (varied by model and bank).
- Period-specific results (Table 10):
  - Pre-Euro period (Jan. 1994 - Dec. 1998):
    - Contagion GER: coefficient = 0.22*; std error = 0.12 (evidence of U.K. and Germany contagion at 10%).
    - Contagion UK: coefficient = 0.29**; std error = 0.12.
    - Systemic risk: coefficient = 1.17**; std error = 0.17.
  - Post-Euro period (Jan. 1999 - 11 Sept. 2001):
    - Contagion US: coefficient = 0.28**; std error = 0.11; Contagion UK = 0.20*; std error = 0.12 (evidence of U.S. and U.K. contagion at 10%).
    - Volatility US: coefficient = -20.65*; std error = 12.81 (negative and significant at 10%).
    - Systemic risk: coefficient = 0.46**; std error = 0.12.
  - Post-September 11 period (12 Sept. 2001 - Nov. 2005):
    - Contagion US: coefficient = 0.18*; std error = 0.11 (evidence only from the U.S. at 10%).
    - Systemic risk: coefficient = 0.76**; std error = 0.10.
  - Pseudo-R2 across periods: 0.339 (pre-Euro), 0.322 (post-Euro), 0.286 (post-September 11).
- Robustness checks and sensitivity:
  - Reducing the number of U.S. banks from 14 to 5 (top 5) leaves U.S. influence on Irish banks unchanged.
  - Using monthly changes in DD rather than weekly does not change U.S. and U.K. influence; contagion from Netherlands disappears.
  - Changing the tail threshold does not qualitatively change results for U.S. and U.K.
  - Pattern of contagion changes over subperiods: stronger Europe linkages earlier, stronger U.S. linkages later, consistent with results above.

### Interpretation and mechanisms
- Systemic shocks (large stock market movements) increase the probability of multiple Irish banks being simultaneously in the tail.
- Interest rate channel:
  - Changes in long-term Irish government bond yields (interest rate IRL) are positively related to Irish coexceedances; examples: interest rate IRL coefficient = 2.18** (std error = 0.41) in basic model—link interpreted via long-term lending/mortgage rates and large Irish bank exposure to real estate and variable loan-rates.
- Contagion channels:
  - Balance sheet linkages: subsidiaries and net-asset exposures (aggregate data show positive net-asset exposures in the U.S. for Irish-resident banks and large negative net-asset exposure to the U.K. in aggregate).
  - Off-balance-sheet exposures: derivatives and credit risk transfers (CRT) can expose Irish banks to U.S. and U.K. market risks even without direct loan exposures.
  - Interbank and derivative counterparties and two-way bank-specific linkages (AIB–BoI; Anglo IB–BoI) may reflect interbank funding and offsetting derivative positions.

### Policy implications and recommendations
- Suggested actions for Irish authorities (CBFSAI and supervisors):
  - Stress test specific categories of exposures of Irish banks to both the U.S. and the U.K.
  - Collect more information on types and counterparties of derivative positions and risk transfers through structured products of Irish banks, given potential off-balance-sheet exposures to U.S. or U.K. property markets.
  - Monitor rapidly growing use of CRT products and derivatives that could transmit foreign property-market risks to Irish banks.
- Rationale:
  - Even where aggregate consolidated balance sheet exposures to the U.S. are not large, derivatives and off-balance-sheet exposures may imply significant contagion channels.

### Caveats, limitations, and data issues
- Equity-price-based measures:
  - Analysis uses equity prices of banking groups (DD measures) but discusses international links often associated with banking balance-sheet exposures without always explicitly tracing securities and insurance linkages.
- Coverage and representativeness:
  - Small group of listed banks used per country; may not represent entire banking system.
  - Irish listed banks in the empirical study comprise less than 50 percent of the system in total assets, though nearly 80 percent of the domestic retail market is covered by the three major listed banks (BOI, AIB, Anglo IB).
- Low frequency of large shocks:
  - Number of observations experiencing large shocks is low; results could be driven by large shocks associated with the tech-bubble burst of 2000.
- Interpretation notes:
  - Coefficient estimates in multinomial logit should not be read as marginal effects; relative sizes can be compared by ratio of coefficients (example: U.S. relative effect benchmarked against U.K. = 2.1 for Ireland).

*Source: IMF working paper content unit _wp0744 - 3. This control should be positively related to the number of coexceedances in Ireland.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp0744.pdf_