## 12. Capitalization in Euro Area Banks, 1997–2008

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---

### I. Introduction — channels through which tight financial conditions affect euro area activity
- Four main channels:
  - Increase in bank funding costs may be passed on via higher lending rates; retail lending rates have gone up somewhat since mid-2007 (continuation of prior trend).
  - Banks may limit credit available at given prices (stricter lending standards); bank lending surveys indicate considerable tightening since mid-2007.
  - Higher costs of corporate bond and equity financing limit substitution from bank financing; corporate bond and credit default spreads have widened and stock markets have fallen since the start of the crisis.
  - Financial accelerator effects: depressed asset prices reduce collateral values; asset prices have declined precipitously.
- Recent data:
  - Monetary aggregates have decelerated.
  - Bank credit to the private sector has decelerated (continued slowdown to households and incipient slowdown in corporate credit).
  - Equity and bond issuance by nonfinancial firms has decelerated.
- Preview of empirical conclusions:
  - Bank loan supply responds negatively to declines in banks’ soundness.
  - A cutback in bank loan supply is likely to weaken economic activity.
  - A positive shock to the corporate bond spread lowers industrial output.
  - Risk indicators improved beginning in 2002–03, then deteriorated since 2007.
  - Combining expert loss estimates with econometric links implies currently estimated banking sector losses translate into a negative 2 percentage point impact on real output in the euro area (with considerable uncertainty).

### II. Empirical evidence

H3: A. Linkages between bank characteristics and lending behavior
- Objective: assess whether bank loan supply is adversely affected by deteriorating financing conditions (bank soundness).
- Data and model:
  - Disequilibrium supply-demand model estimated with bank-by-bank panel data for the 50 largest euro area banks, 1997–2007 (BankScope data).
  - Supply-side variables include distance to default (DD) calculated for each bank (Appendix I).
- Key estimated relationships (all signs as expected and significant):
  - Loan growth explained by bank’s DD (positive), real GDP growth (positive), lending rate and net interest margin (negative), and bank size approximated by total value of loans (negative).
- Quantitative finding:
  - A one-standard-deviation drop in the DD is associated with a year-on-year real growth of credit that is 1.5 percentage points lower than otherwise.
- Robustness checks:
  - Replacing DD by probability of distress (PD) yields expected negative sign in loan supply.
  - Country-level aggregated DDs used to link to output analysis.
  - Pairwise Granger causality: DD is influenced by real GDP and real credit over two–four quarters; DD influences real credit (but not GDP) with a lag of six quarters.

H3: B. Linkages between bank loan supply and aggregate output
- Identification strategy:
  - Instrumental variables (IV) approach using country-specific shocks to money demand as instruments for loan supply (Driscoll, 2004 approach).
  - Three-step scheme: estimate output on loan growth; recover money demand shocks; reestimate output on loan growth instrumented by money demand shocks.
- Data and sample:
  - Country-level quarterly data Q1 1999–Q3 2008 for 11 euro area countries (Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Portugal, Spain).
  - Key variables: real GDP, M3, deposit rates, bank loans to nonfinancial corporations (M3 and bank loans deflated by GDP deflator).
- Main estimates:
  - OLS (reduced-form) estimate: an increase in real bank credit of 10 percentage points is associated with an increase in real GDP of about 1.5 percentage points (coefficient ~0.15).
  - IV (instrumented by money demand shocks) estimate: coefficient on bank loans falls to 0.10 (instrumented coefficient), implying an increase in bank loans of 10 percentage points leads to an increase in real GDP of about 1 percentage point.
- Instruments validity:
  - Country-specific money demand shocks positively and significantly predict bank loan growth.
  - Robustness: using the spread between three-month euro LIBOR and German bund rate as instrument for credit risk did not affect quantitative predictions.
- Interpretation:
  - A cutback in bank loan supply is likely to have a negative impact on economic activity; estimated magnitude: 10 percentage point decline in bank loan supply → about 1 percentage point decline in real GDP (IV estimate).

H3: C. Linkages between corporate financing conditions and economic activity
- Variable and approach:
  - Corporate bond spread = yield on corporate bond (risky) minus yield on government bond (riskless) of same maturity.
  - Monthly VAR for January 1999–January 2009 with corporate bond spread (BBB yield minus government), annual growth in industrial production, and annual change in real effective exchange rate. Baseline VAR includes three lags.
- Quantitative result:
  - One-standard-deviation shock to corporate bond yield (~60 basis points) reduces the growth rate of industrial output, peaking at about 0.25 percent decline in 8–20 months.
  - Effect statistically significant at 95 percent confidence bands.
- Robustness:
  - Results robust across alternative VAR specifications and ratings (AA and A tested as sensitivity).

H3: D. Risk transfers among banks, nonbank companies, and the public sector — Contingent Claims Analysis (CCA)
- Method:
  - CCA combines balance sheet data with market-price information (marked-to-market valuation, contingent liabilities) to assess default probabilities and expected losses across sectors (Appendix III).
- Findings:
  - Default indicators for banking system and nonbank corporate sector: improvement beginning in 2002–03, followed by major deterioration in second half of 2007 and 2008.
  - Expected losses for banking system declined steadily since 2002–03 but deteriorated in 2007–2008; expected losses for largest banks move closely with nonperforming loan ratio and tend to lead it by one to two quarters.
  - Public sector default probability shows gradual decline beginning 2002–03; daily-period sovereign spreads and default probabilities move in line with market-quoted government debt spreads.
  - Public sector default probabilities are substantially lower (generally below 0.2 percent) than those in prior CCA studies of emerging markets (where one-year sovereign default probabilities were often in the range 2–6 percent).
  - If public sector guarantees 100 percent of expected bank losses, public-sector default probabilities increase considerably (illustrating potential fiscal risk from banking sector guarantees).
- Recent market turbulence effects:
  - Since mid-2007, banks have been affected more severely than nonbank corporates: reduced market capitalization and increased volatility decreased implied assets, increased their volatility, lowered DD measures, and increased expected losses.

### III. Quantitative implications
- Starting point: estimated losses in euro area commercial banks (estimates evolved with crisis):
  - IMF April 2008 GFSR reported subprime-related losses in euro area banks as of March 2008 of US$45 billion.
  - Latest estimates of total exceptional losses in euro area global banks may be as large as 10 times that amount.
  - Calculations underlying October 2008 GFSR suggest total exceptional losses in large banks in continental Europe close to $500 billion.
- Capital and leverage implications:
  - Estimated losses correspond to about 14 percent of euro area banks’ capital and reserves.
  - Current ratio of capital to total (unweighted) assets at 5.6 percent (Figure 12). If losses of 14 percent of capital materialize and nothing else changes, capital-to-assets ratio would decline to 4.8 percent.
  - To keep leverage ratio at 5.6 percent after loss, assets would need to shrink by 14 percent.
  - If banks aim to deleverage (increase leverage ratio to 5.9 percent — sample maximum), assets would need to go down by 19 percent.
  - Increasing leverage ratio to 7 percent (beyond recent historical experience but plausible) would imply a decline in assets of 31 percent.
- Translating lending declines into GDP effects using Section II.B estimates:
  - 10 percentage point decline in loan supply → ~1 percentage point decline in real GDP.
  - Loan decline of 14 percent → 1.4 percentage points loss in real GDP.
  - Loan decline of 19 percent → 1.9 percentage points loss in real GDP.
  - Loan decline of 31 percent → 3.1 percentage points loss in real GDP.
- Market-based DD alternative:
  - Average DD was 0.0 in late 2008 (Figure 5), compared with higher historical levels; (further DD-based calculations discussed in paper).

### IV. Summary of core empirical magnitudes and implications
- Bank soundness and lending:
  - One-standard-deviation drop in DD → 1.5 percentage points lower year-on-year real credit growth.
- Bank credit → GDP:
  - OLS estimate: 10 percentage point increase in bank credit → ~1.5 percentage point increase in real GDP (coefficient ~0.15).
  - IV estimate (instrumented by money demand shocks): 10 percentage point increase in bank credit → ~1 percentage point increase in real GDP (coefficient 0.10).
- Corporate bond spreads → industrial output:
  - One-standard-deviation shock (~60 basis points) → peak decline in industrial output growth of about 0.25 percent in 8–20 months.
- Banking sector loss scenarios → GDP:
  - Estimated banking sector losses corresponding to about 14 percent of banks’ capital → loan decline ~14 percent → GDP loss ~1.4 percentage points.
  - If deleveraging pushes assets down 19 percent → GDP loss ~1.9 percentage points.
  - Larger deleveraging to 31 percent asset decline → GDP loss ~3.1 percentage points.
- Paper’s combined headline estimate:
  - Currently estimated banking sector losses would translate into a negative 2 percentage point impact on real output in the euro area (with considerable uncertainty around this estimate).

### IV. CONCLUSIONS

H3: Key findings on financial–real linkages
- A deterioration in the financial health of banks could translate into a lower bank loan supply; this effect is statistically significant.
- A cutback in bank loan supply is likely to have a negative impact on economic activity in the euro area; this effect is statistically significant.
- These findings are not dissimilar to the literature on the bank lending channel in the United States, which generally finds strong evidence that banks decrease their loan supply in response to tighter financing conditions, but little evidence that the cutback in bank loan supply lowers real activity.
- Higher costs of corporate bond financing tend to weaken industrial production.
- Risk indicators for the banking, corporate, and public sectors in the euro area show a steady improvement in balance sheets beginning in 2002–03, followed by a major deterioration in 2007 and especially 2008, reflecting a combination of the increased market volatility and lower capitalization. Conditions as of late 2008 were the worst in the whole sample (since the early 1990s).

H3: Quantitative estimates of the GDP impact from banking losses (preserving source figures)
- Using market-implied estimates (market’s guess) of conditions in mid-2007, this translates into a decline in real credit of 19 percentage points.
- Using the estimates from Section II.B., the 19 percentage point decline in real credit translates into a real GDP decline of some 1.9 percentage points.
- The two methods (projected capital losses and market-implied credit contraction) yield broadly similar estimates of the likely GDP impact.
- The paper’s estimates suggest that current estimates of losses in the banking sector would mean a loss of 2 percentage points in euro area GDP, but with substantial uncertainty around this estimate.
- The difference between the two approaches reflects factors such as the extent to which the banks will (or will not) be recapitalized; the extent of recapitalization is not trivial to estimate, making the market’s guess a useful alternative input.

H3: Uncertainties and caveats
- The calculations illustrate linkages between financial sector soundness and real economic developments, and also illustrate the challenges of quantifying the exact relationship.
- There is substantial uncertainty relating to the impact of recapitalization and, more generally, to the impact on market confidence.
- The estimate of about 2 percentage points impact on output is associated with "substantial uncertainty" (text emphasis preserved).

### Appendix I — Calculating the distance to default (method and calibration details)
- DD measure based on the structural valuation model of Black and Scholes (1973) and Merton (1974).
- Default probability in period t for horizon T years given by equation (AI.3); numerator referred to as “distance to default.”
- Estimation requires asset value V_t and asset volatility A_σ; solved from equations (AI.4) and (AI.5) when E_t (market value of equity), σ_E (equity price return volatility), and D (face value of liabilities) are known; d1 and d2 given by (A.6) and (A.7).
- Calibration and data choices:
  - Time horizon T usually fixed at one year.
  - E_t corresponds to market value of the firm (number of shares outstanding times closing share price).
  - σ_E corresponds either to historical equity volatility or implied volatility; derived by standard deviation of daily share price returns over a one-year period (around 260 days).
  - D assumed equal to face value of short-term liabilities plus half of face value of long-term liabilities; liability data from Bankscope; “Deposits and Short-Term Funding” represents short-term liabilities; long-term liabilities derived by deducting short-term liabilities from “Total Liabilities.” Annual balances intrapolated to obtain daily liability data.
  - Risk-free rate r is the one-year government bond yield in the same currency.
- Portfolio DD:
  - Portfolio DD defined as P_Pt = P_t LA σP μP )5.0()/ln( −+ = (notation and descriptive explanation preserved in the source), where aggregate portfolio assets and liabilities are used and portfolio mean and variance embed asset return covariances across institutions.
  - Portfolio DD tracks a lower bound to the joint probabilities of failure and is always higher than the weighted sum of individual firms’ DDs; associated portfolio probability of default is always lower than the actual probability of joint failures of sets of firms in the portfolio.

*Source: _wp0969 - 12. Capitalization in Euro Area Banks, 1997–2008 (PDF chapter).*

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

### References

### Tables
- 1. Demand and Supply in the Disequilibrium Model, 1997–2007 ..........................................22
- 2. OLS Regression of Output on Loans ...................................................................................23
- 3. First Stage IV Regression: Loans on Money Demand Shocks ............................................23
- 4. Second Stage IV Regression of Output on Loans................................................................23

### Figures
- 1. Euro Area: Money Market and Retail Lending Rates, 2003–08 .........................................16
- 2. Euro Area: Changes in Credit Standards to Enterprises and Households, 2005–08 ...........17
- 3. Euro Area: Corporate and Equity Market Prices, 2007–08 .................................................18
- 4. Euro Area: Growth in Bank Loans and Securities Issuance, 2003–08 ................................19
- 5. Euro Area: Distance to Default for Banks, 1991–2008 .......................................................20
- 6. Euro Area: Excess Demand for Loans, 1997–2008.............................................................20
- 7. Euro Area: Growth in Real Output and Bank Loans, 2000–08 ...........................................20
- 8. Euro Area: Corporate Debt Issuance, 1990–2008 ...............................................................21
- 9. Euro Area: Response of Annual Growth in Industrial Production to One Standard 
  Deviation Innovation in Corporate Spread ..............................................................................21
- 10. Euro Area: Estimated Default Probability (Banks and Non-Banks),1991–2008 ..............21
- 11. Euro Area: Estimated Default Probability (Public Sector), 1997–2008 ............................22

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0969.pdf*

### 12. Capitalization in Euro Area Banks, 1997–2008 ................................................................22

### 12. Capitalization in Euro Area Banks, 1997–2008

### I. Introduction — channels through which tight financial conditions affect euro area activity
- Four main channels:
  - Increase in bank funding costs may be passed on via higher lending rates; retail lending rates have gone up somewhat since mid-2007 (continuation of prior trend).
  - Banks may limit credit available at given prices (stricter lending standards); bank lending surveys indicate considerable tightening since mid-2007.
  - Higher costs of corporate bond and equity financing limit substitution from bank financing; corporate bond and credit default spreads have widened and stock markets have fallen since the start of the crisis.
  - Financial accelerator effects: depressed asset prices reduce collateral values; asset prices have declined precipitously.
- Recent data: monetary aggregates have decelerated; bank credit to the private sector has decelerated (continued slowdown to households and incipient slowdown in corporate credit); equity and bond issuance by nonfinancial firms has decelerated.
- Preview of empirical conclusions:
  - Bank loan supply responds negatively to declines in banks’ soundness.
  - A cutback in bank loan supply is likely to weaken economic activity.
  - A positive shock to the corporate bond spread lowers industrial output.
  - Risk indicators improved beginning in 2002–03, then deteriorated since 2007.
  - Combining expert loss estimates with econometric links implies currently estimated banking sector losses translate into a negative 2 percentage point impact on real output in the euro area (with considerable uncertainty).

### II. Empirical evidence

H3: A. Linkages between bank characteristics and lending behavior
- Objective: assess whether bank loan supply is adversely affected by deteriorating financing conditions (bank soundness).
- Data and model:
  - Disequilibrium supply-demand model estimated with bank-by-bank panel data for the 50 largest euro area banks, 1997–2007 (BankScope data).
  - Supply-side variables include distance to default (DD) calculated for each bank (Appendix I).
- Key estimated relationships (all signs as expected and significant):
  - Loan growth explained by bank’s DD (positive), real GDP growth (positive), lending rate and net interest margin (negative), and bank size approximated by total value of loans (negative).
- Quantitative finding:
  - A one-standard-deviation drop in the DD is associated with a year-on-year real growth of credit that is 1.5 percentage points lower than otherwise.
- Robustness checks:
  - Replacing DD by probability of distress (PD) yields expected negative sign in loan supply.
  - Country-level aggregated DDs used to link to output analysis.
  - Pairwise Granger causality: DD is influenced by real GDP and real credit over two–four quarters; DD influences real credit (but not GDP) with a lag of six quarters.

H3: B. Linkages between bank loan supply and aggregate output
- Identification strategy:
  - Instrumental variables (IV) approach using country-specific shocks to money demand as instruments for loan supply (Driscoll, 2004 approach).
  - Three-step scheme: estimate output on loan growth; recover money demand shocks; reestimate output on loan growth instrumented by money demand shocks.
- Data and sample:
  - Country-level quarterly data Q1 1999–Q3 2008 for 11 euro area countries (Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Portugal, Spain).
  - Key variables: real GDP, M3, deposit rates, bank loans to nonfinancial corporations (M3 and bank loans deflated by GDP deflator).
- Main estimates:
  - OLS (reduced-form) estimate: an increase in real bank credit of 10 percentage points is associated with an increase in real GDP of about 1.5 percentage points (coefficient ~0.15).
  - IV (instrumented by money demand shocks) estimate: coefficient on bank loans falls to 0.10 (instrumented coefficient), implying an increase in bank loans of 10 percentage points leads to an increase in real GDP of about 1 percentage point.
- Instruments validity:
  - Country-specific money demand shocks positively and significantly predict bank loan growth.
  - Robustness: using the spread between three-month euro LIBOR and German bund rate as instrument for credit risk did not affect quantitative predictions.
- Interpretation:
  - A cutback in bank loan supply is likely to have a negative impact on economic activity; estimated magnitude: 10 percentage point decline in bank loan supply → about 1 percentage point decline in real GDP (IV estimate).

H3: C. Linkages between corporate financing conditions and economic activity
- Variable and approach:
  - Corporate bond spread = yield on corporate bond (risky) minus yield on government bond (riskless) of same maturity.
  - Monthly VAR for January 1999–January 2009 with corporate bond spread (BBB yield minus government), annual growth in industrial production, and annual change in real effective exchange rate. Baseline VAR includes three lags.
- Quantitative result:
  - One-standard-deviation shock to corporate bond yield (~60 basis points) reduces the growth rate of industrial output, peaking at about 0.25 percent decline in 8–20 months.
  - Effect statistically significant at 95 percent confidence bands.
- Robustness:
  - Results robust across alternative VAR specifications and ratings (AA and A tested as sensitivity).

H3: D. Risk transfers among banks, nonbank companies, and the public sector — Contingent Claims Analysis (CCA)
- Method:
  - CCA combines balance sheet data with market-price information (marked-to-market valuation, contingent liabilities) to assess default probabilities and expected losses across sectors (Appendix III).
- Findings:
  - Default indicators for banking system and nonbank corporate sector: improvement beginning in 2002–03, followed by major deterioration in second half of 2007 and 2008.
  - Expected losses for banking system declined steadily since 2002–03 but deteriorated in 2007–2008; expected losses for largest banks move closely with nonperforming loan ratio and tend to lead it by one to two quarters.
  - Public sector default probability shows gradual decline beginning 2002–03; daily-period sovereign spreads and default probabilities move in line with market-quoted government debt spreads.
  - Public sector default probabilities are substantially lower (generally below 0.2 percent) than those in prior CCA studies of emerging markets (where one-year sovereign default probabilities were often in the range 2–6 percent).
  - If public sector guarantees 100 percent of expected bank losses, public-sector default probabilities increase considerably (illustrating potential fiscal risk from banking sector guarantees).
- Recent market turbulence effects:
  - Since mid-2007, banks have been affected more severely than nonbank corporates: reduced market capitalization and increased volatility decreased implied assets, increased their volatility, lowered DD measures, and increased expected losses.

### III. Quantitative implications
- Starting point: estimated losses in euro area commercial banks (estimates evolved with crisis):
  - IMF April 2008 GFSR reported subprime-related losses in euro area banks as of March 2008 of US$45 billion.
  - Latest estimates of total exceptional losses in euro area global banks may be as large as 10 times that amount.
  - Calculations underlying October 2008 GFSR suggest total exceptional losses in large banks in continental Europe close to $500 billion.
- Capital and leverage implications:
  - Estimated losses correspond to about 14 percent of euro area banks’ capital and reserves.
  - Current ratio of capital to total (unweighted) assets at 5.6 percent (Figure 12). If losses of 14 percent of capital materialize and nothing else changes, capital-to-assets ratio would decline to 4.8 percent.
  - To keep leverage ratio at 5.6 percent after loss, assets would need to shrink by 14 percent.
  - If banks aim to deleverage (increase leverage ratio to 5.9 percent — sample maximum), assets would need to go down by 19 percent.
  - Increasing leverage ratio to 7 percent (beyond recent historical experience but plausible) would imply a decline in assets of 31 percent.
- Translating lending declines into GDP effects using Section II.B estimates:
  - 10 percentage point decline in loan supply → ~1 percentage point decline in real GDP.
  - Loan decline of 14 percent → 1.4 percentage points loss in real GDP.
  - Loan decline of 19 percent → 1.9 percentage points loss in real GDP.
  - Loan decline of 31 percent → 3.1 percentage points loss in real GDP.
- Market-based DD alternative:
  - Average DD was 0.0 in late 2008 (Figure 5), compared with higher historical levels; (further DD-based calculations discussed in paper).

### IV. Summary of core empirical magnitudes and implications
- Bank soundness and lending:
  - One-standard-deviation drop in DD → 1.5 percentage points lower year-on-year real credit growth.
- Bank credit → GDP:
  - OLS estimate: 10 percentage point increase in bank credit → ~1.5 percentage point increase in real GDP (coefficient ~0.15).
  - IV estimate (instrumented by money demand shocks): 10 percentage point increase in bank credit → ~1 percentage point increase in real GDP (coefficient 0.10).
- Corporate bond spreads → industrial output:
  - One-standard-deviation shock (~60 basis points) → peak decline in industrial output growth of about 0.25 percent in 8–20 months.
- Banking sector loss scenarios → GDP:
  - Estimated banking sector losses corresponding to about 14 percent of banks’ capital → loan decline ~14 percent → GDP loss ~1.4 percentage points.
  - If deleveraging pushes assets down 19 percent → GDP loss ~1.9 percentage points.
  - Larger deleveraging to 31 percent asset decline → GDP loss ~3.1 percentage points.
- Paper’s combined headline estimate:
  - Currently estimated banking sector losses would translate into a negative 2 percentage point impact on real output in the euro area (with considerable uncertainty around this estimate).

*Source: _wp0969 - 12. Capitalization in Euro Area Banks, 1997–2008 (PDF chapter).*

### 8.0 in mid-2007. Using the estimates in Section II.A, this translates into a decline in real

### IV. CONCLUSIONS

### Key findings on financial–real linkages
- A deterioration in the financial health of banks could translate into a lower bank loan supply; this effect is statistically significant.  
- A cutback in bank loan supply is likely to have a negative impact on economic activity in the euro area; this effect is statistically significant.  
- These findings are not dissimilar to the literature on the bank lending channel in the United States, which generally finds strong evidence that banks decrease their loan supply in response to tighter financing conditions, but little evidence that the cutback in bank loan supply lowers real activity.  
- Higher costs of corporate bond financing tend to weaken industrial production.  
- Risk indicators for the banking, corporate, and public sectors in the euro area show a steady improvement in balance sheets beginning in 2002–03, followed by a major deterioration in 2007 and especially 2008, reflecting a combination of the increased market volatility and lower capitalization. Conditions as of late 2008 were the worst in the whole sample (since the early 1990s).

### Quantitative estimates of the GDP impact from banking losses (preserving source figures)
- Using market-implied estimates (market’s guess) of conditions in mid-2007, this translates into a decline in real credit of 19 percentage points.  
- Using the estimates from Section II.B., the 19 percentage point decline in real credit translates into a real GDP decline of some 1.9 percentage points.  
- The two methods (projected capital losses and market-implied credit contraction) yield broadly similar estimates of the likely GDP impact.  
- The paper’s estimates suggest that current estimates of losses in the banking sector would mean a loss of 2 percentage points in euro area GDP, but with substantial uncertainty around this estimate.  
- The difference between the two approaches reflects factors such as the extent to which the banks will (or will not) be recapitalized; the extent of recapitalization is not trivial to estimate, making the market’s guess a useful alternative input.

### Uncertainties and caveats
- The calculations illustrate linkages between financial sector soundness and real economic developments, and also illustrate the challenges of quantifying the exact relationship.  
- There is substantial uncertainty relating to the impact of recapitalization and, more generally, to the impact on market confidence.  
- The estimate of about 2 percentage points impact on output is associated with "substantial uncertainty" (text emphasis preserved).

### Empirical approaches and data used
- The paper applies a broad range of empirical approaches and estimation methods to bank-level, country-level, and aggregate data.  
- The estimates can be used to calculate the potential impact of banking sector losses on future economic growth in the euro area.

---

### Appendix I — Calculating the distance to default (method and calibration details)
- The distance-to-default (DD) measure is based on the structural valuation model of Black and Scholes (1973) and Merton (1974).  
- The default probability in period t for a horizon of T years is given by equation (AI.3) (notation as in the source), where N is the cumulative normal distribution, V_t is the value of assets in period t, r is the risk-free rate, and A_σ is the asset volatility. The numerator in equation (AI.3) is referred to as “distance to default.”  
- Estimating default probabilities requires knowing both the asset value and asset volatility. The asset value and volatility correspond to economic (market) values rather than accounting figures and are estimated by solving equations (AI.4) and (AI.5) for the asset value and volatility when E_t (market value of equity), σ_E (equity price return volatility), and D (face value of liabilities) are known; d1 and d2 are given by (A.6) and (A.7).  
- Calibration and data choices (preserved from source text):  
  - The time horizon, T, is usually fixed at one year.  
  - The value of equity, E_t, corresponds to the market value of the firm (number of shares outstanding times closing share price on a particular day).  
  - The equity volatility, σ_E, corresponds either to historical equity volatility or implied volatility from equity options; derived by calculating the standard deviation of daily share price returns over a one-year period (around 260 days).  
  - The face value of liabilities, D, is usually assumed equal to the face value of short-term liabilities plus half of the face value of long-term liabilities. The liability data are obtained from Bankscope; “Deposits and Short-Term Funding” represents short-term liabilities; long-term liabilities are derived by deducting short-term liabilities from “Total Liabilities.” To obtain daily liability data from annual balance sheets, the data are intrapolated between two year-end balances.  
  - The risk-free rate, r, is the one-year government bond yield in the same currency as those of the market and balance sheet data.  
- Once the asset value and volatility are estimated, the default probability of the firm can be derived from equation (AI.3).  
- Portfolio DD: the portfolio DD is defined (text preserved) as P_Pt = P_t LA σP μP )5.0()/ln( −+ = (notation and descriptive explanation preserved in the source), where aggregate portfolio assets and liabilities are used and portfolio mean and variance embed asset return covariances across institutions. The portfolio DD tracks a lower bound to the joint probabilities of failure and is always higher than the weighted sum of individual firms’ DDs; the associated portfolio probability of default is always lower than the actual probability of joint failures of sets of firms in the portfolio.

*Source: Excerpt from IMF Working Paper (content unit provided).*

### APPENDIX II

### APPENDIX II

### Theoretical framework and model setup
- Framework: An IS/LM model augmented with a credit channel of monetary transmission (Bernanke and Blinder, 1988).
- Objective: Identify loan supply effects (bank lending channel) separate from the interest rate channel.
- Structure: Four equations per country i in the euro area, covering three markets: loan market, money market, and goods market.

- Loan demand (from households and firms):
  - it d it l = itititt d it yrlνπχρτ++−=,  (AII.1)
  - Variables: it y = output; it ρ = loan interest rate; t r = bond interest rate (common across countries); it ν = loan demand shock.
  - Interpretation: loan rate varies across countries; bond rate is common (well-integrated bond market, segmented loan markets).

- Loan supply:
  - it s it wpmrl+−++−=)(βμρλ,  (AII.2)
  - Variables: )( it it pm− = money supply deviation; it w = loan supply shock.
  - Interpretation: supply depends on deposits (as a way to generate loans), loan rate it ρ, and bond rate t r (loans and bonds are imperfect substitutes).

- Money market equilibrium:
  - it d ittititit rrypmεδγ+−−=−)(,  (AII.3)
  - Variables: d it r = country-specific deposit rate; it ε = country-specific money demand shock.
  - Note: money supply it m is determined by the European Central Bank (ECB).

- Goods market / Aggregate output:
  - it ittit zry+−−=αρθ.  (AII.4)
  - Variables: it z = country-specific shock.

- Reduced-form solutions for output and loans (joint endogeneity):
  - ititittit zvlry παχ χ παχ α παχ α παχ θ + + + − + + + =  (AII.5)
  - ititititittit rwvyrl μχ χδβ μχ χ μχ μ μχ πμχβγ ε μχ χβ παχ θ + + + + + − + + + + + + =.  (AII.6)
  - Implication: bank loans and output are jointly determined, creating an identification problem between demand and supply effects.

### Identification strategy (demeaning / shutting down interest rate channel)
- Approach: Transform each variable it x into deviation from its cross-sectional mean: x~ it = x it − (1/N) ∑ N i=1 x it.
- Rationale (Driscoll, 2004): Demeaning across cross-sectional units effectively "shuts down" the common interest rate channel (the country-invariant bond rate t r drops out), aiding separation of loan supply effects from interest rate effects.
- Demeaned model equations:
  - it d it vyl++−= ~ ~ ~ πρχ  (AII.1’)
  - it it it it s it wpml+−+=) ~ ~ ( ~ ~ βρμ  (AII.2’)
  - it d it it it it rypmεδγ++=− ~~~~  (AII.3’)
  - it it it zy+−=ρα ~ ~ .  (AII.4’)

- Demeaned reduced-form expressions:
  - it it it it zvly παχ χ παχ α παχ α + + + − + = ~ ~  (AII.5’)
  - it it it it it it rwvyl ~~ ~ μχ χδβ μχ χ μχ μ μχ πμχβγ ε μχ χβ + + + + + − + + + + =.  (AII.6’)

- Instrument relevance:
  - Money demand shock it ε is correlated with demeaned loans l~ it but not with demeaned output y~ it except through its effect on l~ it.
  - Therefore, money demand shocks are good candidates for instruments to isolate loan supply effects.

### Estimation procedure
- Step 1 (First stage): Estimate a money demand function for each euro area country to obtain shocks it ε.
  - Use an instrumental variable estimation in a pooled panel OLS regression with demeaned values of all variables to test whether money demand shocks have a significant effect on aggregate lending.

- Step 2 (Second stage): Use estimated money demand shocks it ε as instruments in a regression of loans on output (using demeaned series) to isolate the supply effect of bank lending on real activity.

- Key identification point: By using cross-sectional demeaning and money demand shocks as instruments, the method aims to separate the bank lending channel (loan supply effects) from the general interest rate channel in a multicountry euro-area panel.

*Source: APPENDIX II, _wp0969 - APPENDIX II*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0969.pdf_