## 1. Banking Crises in Advanced Economies Identified Using the Von Hagen and Ho (2007)

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### I. Introduction and purpose
- Aim: estimate to what extent the higher capital requirements under the Basel III framework will lead to higher loan rates and slower credit growth.
- Context and Basel III parameters (as presented in the source):
  - Minimum common equity tier 1 (CET1) ratio of 4.5 percent.
  - Conservation buffer of 2.5 percent.
  - Additional countercyclical capital buffer of up to 2.5 percent, implying an equity to risk-weighted asset ratio between 7 and 9.5 percent over the credit cycle for bank holding companies, with more stringent rules for LCFIs.
  - Most new regulations phased in over the 2013-2015 period, with the capital conservation buffer phased in by end 2018.

### II. Empirical approach and model
- Structural foundation:
  - Builds on Chami and Cosimano (2010) capital channel model; bank’s decision to hold capital modeled as a call option on optimal future loans.
  - Loan rate determined as a weighted average of marginal cost of deposits and equity; loan rate rises when marginal cost of equity > marginal cost of deposits.
- Crisis identification (Von Hagen and Ho (2007) IMP index):
  - IMP formula: IMP_t = (Δγ_t / σ_Δγ) + (Δr_t / σ_Δr) + (Δy_t / σ_Δy).
  - Criteria for crisis identification: (i) IMP exceeds the 98.5 percentile, 97 percentile, and 95 percentile of the sample distribution for each advanced economy; and (ii) the increase in IMP from the previous period is at least five percent.
- Estimation methodology:
  - Bank-by-bank data for advanced economies for 2001-2009 from Bankscope.
  - Three bank groupings: (i) the 100 largest banks worldwide by total assets in 2006; (ii) commercial banks/BHCs in advanced economies that experienced a banking crisis between 2007 and 2009; (iii) commercial banks/BHCs in advanced economies that did not experience a banking crisis between 2007 and 2009.
  - Empirical estimation relies on a generalized method of moments (GMM) procedure with:
    - First-stage: bank capital holdings specified in terms of previous-period changes in capital, interest expenses, and non-interest expenses (negative and convex relationship hypothesized).
    - Second-stage: loan rate regressed on predicted optimal bank capital, interest and non-interest expenses, and the level of economic activity.
    - Final stage: total loans regressed on predicted loan rate to obtain interest elasticity of loan demand.

### III. Key quantitative findings — impact of capital on loan rates and volumes
- Impact of capital on loan rates:
  - A one percent increase in the equity-to-asset ratio is associated with:
    - 0.12 percent increase in the loan rate for the 100 largest banks.
    - 0.09 percent average increase for banks in countries that experienced a banking crisis during 2007-09.
    - 0.13 percent average increase for banks in countries that did not experience a banking crisis during 2007-09.
  - For a projected 1.3 percentage point increase in the equity-to-asset ratio required by Basel III:
    - Estimated increase in the loan rate is 16 basis points for the 100 largest banks.
    - Corresponds to an upper bound of 0.12 percent higher return on equity relative to the marginal cost of deposits.
  - If the “excessive credit growth” regulation is invoked (requiring up to an additional 2.5 percentage points in equity-to-asset ratio):
    - Loan rates would be raised further by up to 31 basis points.
    - Additional capital requirement for LCFIs predicted to raise the loan rate by 0.12 percent times the additional equity-to-asset ratio.
- Impact of capital on loan volumes:
  - Combined loan rate and loan demand estimates imply:
    - A 1.3 percentage point increase in the equity-to-asset ratio is predicted to reduce loans for the 100 largest banks by 1.3 percent in the long run.
    - A declaration of “excessive credit growth” (up to 2.5 percentage points additional equity) predicted to reduce loans by about 2.5 percent in the long run.
  - Country-by-country estimations (assuming a 1.3 percentage point increase):
    - Average reduction in loan volume in crisis countries: 4.6 percent in the long run.
    - Average reduction in loan volume in non-crisis countries: 14.8 percent in the long run.
- Interest elasticity of loan demand (estimated):
  - About -0.33 for the 100 largest banks.
  - Country-level estimates range from -0.92 percent for the United States to -6.61 percent for Denmark.
- Upper bound on the net cost of raising equity (return on equity relative to marginal cost of deposits):
  - Ranges from 0 basis points in Canada to 26 basis points in Japan.

### IV. Descriptive statistics and crisis identification details
- Data: annual commercial banks and BHCs for advanced countries from Bankscope, 2001-2009.
- IMP crisis identification data: IMF International Financial Statistics for 1992:Q1-2010:Q2.
- Using the 98.5 percentile cutoff of IMP, crisis countries between 2007 and 2009 identified: Austria, Belgium, Germany, Greece, Netherlands, Sweden, Spain, Italy, the United Kingdom and the United States.
- Cross-checks and exceptions:
  - Laeven and Valencia (2010) largely concordant; Japan and New Zealand crises in 2008 captured only by IMP (not included in crisis grouping here due to data limitations).
  - Switzerland’s 2008 crisis captured only by Laeven and Valencia (IMP data unavailable for Switzerland); Switzerland is included in the crisis grouping per Laeven and Valencia.
- Profitability and capital adequacy (100 largest banks):
  - Return on equity (ROE): 17 percent in 2006; -3 percent in 2008; 1.4 percent in 2009.
  - Decline in ROA attributed to a one percent increase in noninterest expense ratio and a near tripling of the loan loss provision ratio between 2006 and 2008, amplified by an equity multiplier (A/E) of over 19.5.
  - A 0.6 percent decline in (NII + SG –TAX)/A from 2007 to 2008.
  - Net interest margin remained fairly stable between 2006 and 2008 and increased by 0.07 percent in 2009.
  - Interest expense to total assets ratio increased by 0.4 percent between 2006 and 2008, reversed by 1.15 percent in 2009.
  - Largest BHCs maintained:
    - Tier 1 equity to risk weighted assets significantly above the 4 percent Basel II requirement.
    - Total capital to risk weighted assets significantly above the 8 percent requirement.
    - Equity to asset ratio always above 5 percent.
  - Implication: Basel II did not prevent large BHCs from suffering substantial losses; evidence of off-balance sheet activity to circumvent capital requirements.

### V. Empirical tests and estimation diagnostics (first- and second-stage GMM summaries)
- First-stage (capital choice) highlights for the 100 largest banks:
  - Interest expense ratio coefficient: -0.63*** (standard error 0.15).
  - Interest expense ratio * initial equity-to-asset ratio coefficient: 0.113*** (0.04).
  - Noninterest expense ratio coefficient: -0.78*** (0.16). Interaction with initial equity-to-asset ratio: 0.107*** (0.02).
  - Ratio of nonperforming loans to assets coefficient: -0.000679 (0.00095); interaction with initial equity-to-asset ratio: 0.0009*** (0.0002).
  - Logarithm of assets coefficient: -0.227** (0.00095).
  - Constant: 7.05*** (1.87).
  - Observations: 388.
  - R-squared: 0.851. Adjusted R-squared: 0.8363.
  - Bandwidths: set to 2 for regressions for the largest banks and 4 for bank regressions at the country level.
  - Interpretation: adjusted R-square of 0.84 supports the optimal equity equation (3) for the largest banks; convexity of option value of capital is confirmed.
- Second-stage (loan rate) highlights for the 100 largest banks:
  - Equity-asset ratio coefficient on interest income ratio: 0.122*** (0.0249).
  - Interest expense ratio coefficient: 0.947*** (0.0240).
  - Noninterest expense ratio coefficient: 0.184*** (0.0325).
  - Ratio of nonperforming loans to assets coefficient: 0.000173 (0.000304).
  - Logarithm of assets: -0.0434 (0.0410).
  - Constant: 1.417** (0.644).
  - Observations: 388.
  - R-squared: 0.933. Adjusted R-squared: 0.9274.
  - Implication: long-run relation; estimated effect not attributable to temporary asymmetric information effects.
- Loan demand (third stage) for largest banks:
  - Loan demand coefficient on predicted loan rate: -0.2447607** (0.1005815).
  - Estimated elasticity of loan demand: -0.33 (calculation: -0.24*(4.02/2.52) as reported).
  - Interpretation: a one percent increase in the predicted loan rate leads to a reduction in loans by the largest banks by about 1.3 percent.

### VI. Country-level estimation results (summaries)
- First-stage capital-choice results:
  - Change in equity-to-asset ratio had predicted sign for U.S., U.K., Greece, Switzerland, Canada, Denmark, Ireland; statistically significant for U.K., Switzerland, Denmark, Canada.
  - Interest expense ratio and its interaction generally had predicted signs and were significant for crisis countries except Greece; among non-crisis countries, Canada, Denmark, Czech Republic, Ireland had correct and significant coefficients.
  - Logarithm of assets negative for most countries; significant at 1 percent for U.K. and Canada.
- Second-stage loan-rate results:
  - Equity and interest expense ratios have predicted signs and are significant at 5 percent for most countries except equity ratio in Canada and Korea.
  - Noninterest expense ratio positive on loan income for all countries; statistically significant except Switzerland, Denmark, Ireland, Japan.
  - Nonperforming loans insignificant for most countries.
  - Variables explain between 96 percent and 67 percent of changes in interest income ratio for crisis-country group and between 45 percent and 85 percent for non-crisis group.
- Loan demand elasticities across countries:
  - Elasticity of loan demand ranges from -0.92 for the United States to -6.61 for Denmark (country-specific elasticity estimates reported in Tables 9 and 10a).
  - Consequently, banks across most countries operate at loan levels associated with positive marginal revenue (|elasticity| > 1) except largest banks where |elasticity| < 1.

### VII. Estimated impact of Basel III (detailed)
- Proxy and baseline ratios reported:
  - Sample largest banks Tier 1 ratio (2009) in studies: 10.5 percent (BIS Group 1) and 10.3 percent (CEBS Group 1); sample largest banks Tier 1 ratio: 10.3 percent.
  - Total capital ratio: 14 percent (BIS/CEBS) vs 13.7 percent for the sample.
  - Equity-to-actual asset ratio in sample: 5.7 percent.
- Largest banks (1.3 percentage point increase from 5.7 percent to 7.0 percent):
  - Increase in loan rate: 0.159 percent (calculation: 0.122 * 1.3 percent).
  - This implies a 3.9 percent increase in the loan rate when using ratio 0.159/4.02.
  - Given long-run elasticity of loan demand -0.33, implies overall reduction of loans by 1.3 percent for the largest banks.
  - Table 10a summary for a 1.3 percentage point increase:
    - Largest banks: Impact on loan rate 0.16; Net cost of raising equity 0.12; Elasticity of loan demand -0.33; Percentage change in loans -1.28.
- Cross-country impacts (Table 10a highlights for a 1.3 percentage point increase):
  - Crisis countries average: Impact on loan rate 0.11; Net cost 0.08; Elasticity -2.80; Percentage change in loans -4.55.
  - Other countries average: Impact on loan rate 0.22; Net cost 0.17; Elasticity -2.60; Percentage change in loans -14.76.
  - Country examples:
    - Germany: Impact on loan rate 0.15; Net cost 0.12; Elasticity -1.83; Percentage change in loans -7.16.
    - U.K.: 0.08; 0.06; -2.57; -4.35.
    - U.S.: 0.17; 0.13; -0.92; -2.97.
    - Canada: 0.00; 0.00; -1.67; -0.16.
    - Denmark: 0.25; 0.19; -6.61; -32.61.
    - Ireland: 0.28; 0.22; -1.00; -6.46.
    - Japan: 0.34; 0.26; -1.11; -19.81.
- Crisis-period sensitivity (2001–07 regressions):
  - Excluding crisis period, estimated impact on loan demand of 1.55 percent for largest banks — higher than entire sample (1.3 percent) because interest elasticity of loan demand is larger in the earlier period.
  - Table 10b summary (2001–07):
    - Largest banks: Impact on loan rate 0.15; Net cost 0.11; Elasticity -0.42; Percentage change in loans -1.55.

### VIII. Policy implications and interpretation
- Main quantitative conclusions:
  - The largest banks would raise lending rates by on average 16 basis points to increase equity-to-asset ratio by 1.3 percentage points required under Basel III.
  - With estimated long-run elasticity of loan demand -0.33 for the largest banks, lending rates increase implies loan growth decline by 1.3 percent in the long run.
  - Country heterogeneity: net cost of raising equity by 1.3 percentage points ranges from 0 basis points in Canada to 26 basis points in Japan; elasticities of loan demand range from -0.92 (U.S.) to -6.61 (Denmark). Average impact on loan growth for crisis countries: -4.9 percent (text summary).
- Countercyclical capital buffer implications:
  - An additional 2.5 percent countercyclical capital requirement would be predicted to reduce the largest banks loans by 2.5 percent.
  - Recommendation: declaration of "excessive credit growth" (triggering the countercyclical buffer) should be closely coordinated with monetary policy decision-making to avoid simultaneous excessive policy-tightening; conversely, the countercyclical capital requirement should be considered part of the monetary authority’s tool kit.
- Broader implications and regulatory responses:
  - Small predicted increases in lending rates can incentivize regulatory arbitrage and shift activity toward the shadow-banking sector; example cited: a corporation could save $1.6 million on each $1 billion borrowed from a financial institution that has circumvented the additional capital requirement.
  - Need for complementary regulation: increased regulation of the shadow banking sector may be needed to complement banking and LCFI reforms.
  - Effects on LCFIs and market structure: additional capital requirements on LCFIs act as a tax, leading to higher loan rates or smaller return on equity; LCFIs could lose business to smaller institutions not subject to extra capital requirements, potentially incentivizing break-up of LCFIs.
  - Policymakers should identify drivers of high loan-demand elasticities or high net cost of equity in countries where Basel III has large predicted impacts (e.g., Denmark, Japan).

*Source — _wp11119 (extracted content provided).*

### 1. Banking Crises in Advanced Economies Identified Using the Von Hagen and Ho (2007)

### 1. Banking Crises in Advanced Economies Identified Using the Von Hagen and Ho (2007)

### I. Introduction and purpose
- Aim: estimate to what extent the higher capital requirements under the Basel III framework will lead to higher loan rates and slower credit growth.
- Context:
  - Basel III tightens the definition of bank capital, requires banks to hold a larger amount of capital for a given amount of assets, and expands coverage of bank assets.
  - Key Basel III elements cited: minimum common equity tier 1 (CET1) ratio of 4.5 percent; conservation buffer of 2.5 percent; additional countercyclical capital buffer of up to 2.5 percent, implying an equity to risk-weighted asset ratio between 7 and 9.5 percent over the credit cycle for bank holding companies, with more stringent rules for LCFIs.
  - Most new regulations phased in over the 2013-2015 period, with the capital conservation buffer phased in by end 2018.

### II. Empirical approach and model
- Structural foundation:
  - Builds on Chami and Cosimano (2010) capital channel model; bank’s decision to hold capital modeled as a call option on optimal future loans.
  - Loan rate determined as a weighted average of marginal cost of deposits and equity; loan rate rises when marginal cost of equity > marginal cost of deposits.
- Estimation methodology:
  - Uses bank-by-bank data for advanced economies for 2001-2009 from Bankscope.
  - Three bank groupings: (i) the 100 largest banks worldwide by total assets in 2006; (ii) commercial banks/BHCs in advanced economies that experienced a banking crisis between 2007 and 2009; (iii) commercial banks/BHCs in advanced economies that did not experience a banking crisis between 2007 and 2009.
  - Banking crises identified using the index of money market pressure (IMP) from Von Hagen and Ho (2007):
    - IMP formula: IMP_t = (Δγ_t / σ_Δγ) + (Δr_t / σ_Δr) + (Δy_t / σ_Δy)  (as presented in the source).
    - Criteria for crisis identification: (i) IMP exceeds the 98.5 percentile, 97 percentile, and 95 percentile of the sample distribution for each advanced economy; and (ii) the increase in IMP from the previous period is at least five percent.
  - Empirical estimation relies on a generalized method of moments (GMM) procedure:
    - First-stage: bank capital holdings specified in terms of previous-period changes in capital, interest expenses, and non-interest expenses (negative and convex relationship hypothesized).
    - Second-stage: loan rate regressed on predicted optimal bank capital, interest and non-interest expenses, and the level of economic activity.
    - Final stage: total loans regressed on predicted loan rate to obtain interest elasticity of loan demand.

### III. Key quantitative findings
- Impact of capital on loan rates:
  - A one percent increase in the equity-to-asset ratio is associated with:
    - 0.12 percent increase in the loan rate for the 100 largest banks.
    - 0.09 percent average increase for banks in countries that experienced a banking crisis during 2007-09.
    - 0.13 percent average increase for banks in countries that did not experience a banking crisis during 2007-09.
  - For the projected 1.3 percentage point increase in the equity-to-asset ratio required by Basel III:
    - Estimated increase in the loan rate is 16 basis points for the 100 largest banks.
    - This corresponds to an upper bound of 0.12 percent higher return on equity relative to the marginal cost of deposits (evidence against the Modigliani-Miller Theorem).
  - If the “excessive credit growth” regulation is invoked (requiring up to an additional 2.5 percentage points in equity-to-asset ratio):
    - Loan rates would be raised further by up to 31 basis points.
    - An additional capital requirement for LCFIs predicted to raise the loan rate by 0.12 percent times the additional equity-to-asset ratio.
- Impact of capital on loan volumes:
  - Combined loan rate and loan demand estimates imply:
    - A 1.3 percentage point increase in the equity-to-asset ratio is predicted to reduce loans for the 100 largest banks by 1.3 percent in the long run.
    - A declaration of “excessive credit growth” (up to 2.5 percentage points additional equity) predicted to reduce loans by about 2.5 percent in the long run.
  - Country-by-country estimations (assuming a 1.3 percentage point increase):
    - Average reduction in loan volume in crisis countries: 4.6 percent in the long run.
    - Average reduction in loan volume in non-crisis countries: 14.8 percent in the long run.
- Interest elasticity of loan demand (estimated):
  - About -0.33 for the 100 largest banks.
  - Country-level estimates range:
    - -0.92 percent for the United States.
    - -6.61 percent for Denmark.
- Upper bound on the net cost of raising equity (return on equity relative to marginal cost of deposits):
  - Ranges from 0 basis points in Canada to 26 basis points in Japan.

### IV. Descriptive statistics and crisis identification details
- Data: annual commercial banks and BHCs for advanced countries from Bankscope, 2001-2009.
- Banking crisis identification:
  - Based on IMP using IMF International Financial Statistics data for 1992:Q1-2010:Q2.
  - Using the 98.5 percentile cutoff of IMP, identified crisis countries between 2007 and 2009 include: Austria, Belgium, Germany, Greece, Netherlands, Sweden, Spain, Italy, the United Kingdom and the United States.
  - Cross-checked with Laeven and Valencia (2010); the two methods largely concordant except:
    - Japan and New Zealand crises in 2008 captured only by IMP (data limitations meant they are not included in the crisis grouping used here).
    - Switzerland’s 2008 crisis captured only by Laeven and Valencia (IMP data unavailable for Switzerland), so Switzerland is included in the crisis grouping per Laeven and Valencia.
- Profitability and capital adequacy (100 largest banks):
  - Return on equity (ROE) for the 100 largest banks: 17 percent in 2006; -3 percent in 2008; 1.4 percent in 2009 (drop of twenty percentage points between 2006 and 2008).
  - Decomposition of ROE via ROA and equity multiplier:
    - Decline in ROA attributed to a one percent increase in noninterest expense ratio and a near tripling of the loan loss provision ratio between 2006 and 2008, amplified by an equity multiplier (A/E) of over 19.5.
    - A 0.6 percent decline in (NII + SG –TAX)/A from 2007 to 2008.
    - Net interest margin remained fairly stable between 2006 and 2008 and increased by 0.07 percent in 2009.
    - Interest expense to total assets ratio increased by 0.4 percent between 2006 and 2008, reversed by 1.15 percent in 2009.
  - Despite large ROE declines, the largest BHCs kept:
    - Tier 1 equity to risk weighted assets significantly above the 4 percent Basel II requirement.
    - Total capital to risk weighted assets significantly above the 8 percent requirement.
    - Equity to asset ratio always above 5 percent.
  - Implication: Basel II did not prevent large BHCs from suffering substantial losses, consistent with evidence they used off-balance sheet activity to circumvent capital requirements.

### V. Policy implications and interpretation
- Small predicted increases in lending rates can nonetheless incentivize regulatory arbitrage and shift activity toward the shadow-banking sector:
  - Example cited: a corporation could save $1.6 million on each $1 billion borrowed from a financial institution that has circumvented the additional capital requirement.
- Need for complementary regulation:
  - Increased regulation of the shadow banking sector may be needed to complement banking and LCFI reforms.
- Effects on LCFIs and market structure:
  - Additional capital requirements on LCFIs act as a tax, leading to higher loan rates or smaller return on equity.
  - LCFIs could lose business to smaller institutions not subject to extra capital requirements, potentially incentivizing break-up of LCFIs.
- Considerations for countercyclical monetary policy:
  - The negative effect of invoking the “excess credit growth” regulation (e.g., a 2.5 percent reduction in loans) should be accounted for when designing monetary policy; central banks’ policy rate adjustments aimed at slowing expansions may need modification to avoid excessive slowdown.

*Source: _wp11119 - 1. Banking Crises in Advanced Economies Identified Using the Von Hagen and Ho (2007)*

### 0.5 percentage point increase in the loan loss provision ratio that are amplified by the sharp

### _wp11119 - 0.5 percentage point increase in the loan loss provision ratio that are amplified by the sharp

### Key empirical findings on profitability and capital during the financial crisis
- A 0.5 percentage point increase in the loan loss provision ratio is amplified by the sharp increase in the equity multiplier between 2006 and 2009.
- The equity multiplier for this group of banks is less than half of the equity multiplier of the 100 largest BHCs in the 2006-2008 period but increases substantially in 2009.
- Contrary to the finding for the largest 100 BHCs, the noninterest expense ratio declined by one percentage point between 2006 and 2009 for the other group.
- Similar results are reported in Table 4 for the banks in countries that did not experience a financial crisis except that the decline in ROE is larger for this group of banks because of their larger equity multiplier.
- The financial crisis had a significant negative impact on bank profitability including banks in countries that did not experience a crisis, though the impact is recorded under different headings for each group of banks.
  - For the 100 largest banks, the declines in ROE were mostly associated with increases in noninterest expenses and increases in nonperforming loans.
  - For the other two groups of banks, the declines were mostly directly associated with capital losses on marketable securities.
- As a consequence, banks experienced a significant deterioration in their equity to asset ratios except in the case of the largest 100 banks for which equity to asset ratios tend to be considerably lower.
- A small percentage of the decline can also be attributed to NII because of the decline in off-balance sheet assets. It is presumed that taxes did not change appreciably over this period.
- Acharya, Schnabl, and Suarez (2009) explain how off-balance sheet items of large bank holding companies in the U.S. led to significant capital losses during the financial crisis.

### Specification of the empirical tests (model structure and expectations)
- Choice of capital
  - Following Chami and Cosimano (2001, 2010), capital is modeled as a call option where the strike price is the difference between expected optimal loans and loans supported by capital.
  - If the optimal loans next period exceed the capital-supported limit, the bank faces a lost opportunity measured by the shadow price on the capital constraint; total capital then has positive option value and banks hold more capital than required.
  - If future loan demand shocks are below the critical level, total capital has zero payoff.
  - Banks with more capital have a higher strike price and thus an increase in capital leads to a decrease in demand for future capital, K’.
  - An increase in the marginal cost of loans leads banks to forecast higher future marginal cost and to reduce capital today.
  - An increase in marginal revenue (stronger economic activity) increases optimal loans and optimal capital.
- Formal relation for bank choice of capital (equation (3) as presented in the source):
  - The relation is specified with log terms, interactions with A/K, and includes Δ× terms; the source presents equation (3) and associated notation exactly as given.
- Convexity and sign expectations (preserving notation and signs as in the source):
  - Call options are generally decreasing and convex in the strike price.
  - Expectation: 0 21  A K aa such that 0 2 a , 0 1 a.
  - Similarly expected: 0 3 a , 0 4 a , 0 5 a and 0 6 a.
  - Interpretation: a decrease in past capital lowering the strike price should lead to a significant increase in current total capital; effect smaller when bank has more initial capital, consistent with convexity.
  - A decrease in interest and non-interest expenses should lead to an increase in bank capital at a decreasing rate.
- Loan rate determination
  - Banks have monopoly power and choose loan rate rL so marginal revenue of loans equals marginal cost.
  - Marginal cost includes deposit interest rate rD, noninterest marginal factor costs C L and C D, and depends on RAROC; total marginal cost MC is given in equation (4) (preserved as presented).
  - rK is the return on equity; A is total assets; D is deposits; capital K’ = A - D.
  - Marginal cost increases with an increase in bank capital only if ݎ ௄ ൐ ݎ ஽ ܥ൅ ஽ (preserving source notation). Such an effect would violate the Modigliani-Miller (1958) Theorem.
  - The marginal revenue of loans depends on economic activity (M). The optimal loan rate equation is given as equation (5) in the source.
  - Comparative statics implied by equation (5): an increase in deposit rate, noninterest cost of deposits, or provision for loan losses increases the loan rate; an increase in RAROC (measured by optimal capital asset ratio K’/A) increases marginal cost and loan rate; an increase in economic activity M raises marginal revenue and loan rate.
- Bank loans (demand)
  - With monopoly power, loan demand L depends on the optimal loan rate and economic activity M; modeled as equation (6) in the source:
    - L = c0 + c1 * rL + c2 * M (preserving the functional form as presented).
  - Expected signs: increase in loan rate reduces demand for loans; increase in economic activity increases demand.
  - c1 and c2 capture long-run responses of loans to changes in loan rates and economic activity.
  - Variables are non-stationary (I(1)); the null hypothesis of no cointegration was rejected (cointegration found).
  - Group mean panel ADF cointegration tests require at least 7 years of consecutive observations; cointegration test could not be conducted for Sweden and Ireland because of insufficient consecutive observations.

### Empirical strategy and estimation approach
- Simultaneity and estimation
  - Banks simultaneously choose capital, loan rate, and quantity of loans; estimation uses a generalized method of moments (GMM) procedure.
  - First stage: estimate capital regression (3) to obtain projected or optimal capital.
    - Instruments: change in capital-to-asset ratio, interest expense ratio, noninterest expense ratio, nonperforming loans to total assets ratio, and interaction of each with previous period capital-to-asset ratio.
  - Second stage: use predicted demand for capital in the loan rate regression (5); GMM estimations use the Bartlett kernel to yield heteroskedasticity- and autocorrelation-consistent (HAC) standard errors.
  - Third stage: estimate demand for loans (6) using loan rates predicted by GMM.
- Data, sample, and panel structure
  - Estimations for three groupings of banks use data for the 2001 to 2009 period.
  - For the group of the 100 largest banks worldwide, country and year dummies are included.
  - For the other two groupings—banks in advanced economies that experienced a banking crisis between 2007 and 2009, and banks in advanced economies that did not experience a banking crisis between 2007 and 2009—estimations are conducted on a country-by-country basis and include year dummies.
  - Number of banks in each estimation depends on degree of concentration of banking system and data availability in the Bankscope database.
- Estimation diagnostics and reporting
  - GMM estimations report heteroskedasticity- and autocorrelation-consistent standard errors in parentheses.
  - For the largest banks, Tables 5 and 6 provide estimates of the capital choice equation (3) and the loan rate equation (5); Tables 7 and 8 report results for each advanced economy.
  - For the 100 largest banks, the dependent variable in the first stage capital equation (3) is the equity to asset ratio.
  - Table 5 (summary from source): for the 100 largest banks, choice of bank capital in a given period was negatively related to the prior change in the equity to asset ratio, 0 1 a, and, contrary to expectations, negatively related to the interaction between this change and the initial level, 0 2 a, but these effects are not significant.
  - The interest expense to asset ratio has the expected negative sign (0 3 a) and is statistically significant at the one percent level: a one percent increase in the interest expense ratio reduces banks’ holding of equity by (value reported in the source tables).

*Source: IMF working paper content as provided in the supplied PDF content unit.*

### 0.63 percent. The interaction term with the initial equity-to-asset ratio,

### _wp11119 - 0.63 percent. The interaction term with the initial equity-to-asset ratio,

### Empirical findings on capital choice (first-stage GMM)
- Interest expense ratio coefficient: -0.63*** (standard error 0.15).
- Interest expense ratio * initial equity-to-asset ratio coefficient: 0.113*** (0.04).
- Interpretation: banks with a one percent higher equity-to-asset ratio would reduce their optimal holding of equity by only 0.52 percent for a one percent increase in the interest expense ratio (textual implication from interaction term sign and magnitude).
- Noninterest expense ratio coefficient: -0.78*** (0.16). A one percent increase in noninterest expense ratio leads to a 0.78 percent reduction in capital, reduced to 0.67 percent for a bank with one percent higher equity-to-asset ratio.
- Noninterest expense ratio * initial equity-to-asset ratio: 0.107*** (0.02).
- Ratio of nonperforming loans to assets coefficient: -0.000679 (0.00095) — negative but not statistically significant; its interaction with initial equity-to-asset ratio: 0.0009*** (0.0002).
- Logarithm of assets coefficient: -0.227** (0.00095). Evidence suggests banks with one percent more assets hold 0.23 percent less equity relative to assets.
- Constant: 7.05*** (1.87).
- Observations: 388.
- R-squared: 0.851.
- Adjusted R-squared: 0.8363.
- Bandwidths: set to 2 for regressions for the largest banks and 4 for bank regressions at the country level.
- Adjusted R-square of 84 percent (0.84) supports the optimal equity equation (3) for the largest banks; convexity of option value of capital is confirmed.

### Loan rate determinants (second-stage GMM)
- Equity-asset ratio coefficient on interest income ratio: 0.122*** (0.0249). A one percent increase in the equity-to-asset ratio yields a statistically significant 12 basis points increase in the interest income ratio (loan rate) for the 100 largest banks.
- Interest expense ratio coefficient: 0.947*** (0.0240). A one percent increase in the interest expense ratio leads to an increase in the interest income to asset ratio of 0.95 percent.
- Noninterest expense ratio coefficient: 0.184*** (0.0325). A one percent increase in the noninterest expense ratio changes the interest income ratio by 0.18 percent.
- Ratio of nonperforming loans to assets coefficient: 0.000173 (0.000304) — positive but insignificant.
- Logarithm of assets: -0.0434 (0.0410).
- Constant: 1.417** (0.644).
- Observations: 388.
- R-squared: 0.933.
- Adjusted R-squared: 0.9274.
- Implication: long-run relation — estimated effect not attributable to temporary asymmetric information effects.

### Loan demand elasticities and implications for largest banks
- Loan demand coefficient on predicted loan rate (largest banks): -0.2447607** (0.1005815).
- Estimated elasticity of loan demand for largest banks: -0.33 (calculation: -0.24*(4.02/2.52) as reported).
- Interpretation: a one percent increase in the predicted loan rate leads to a reduction in loans by the largest banks by about 1.3 percent.
- Conclusion: largest banks operate at loan levels associated with negative marginal revenue since |elasticity| < 1, and customers have few substitutes for bank loans.

### Country-by-country estimations (first- and second-stage summaries)
- Countries with crisis (selected): U.S., Germany, U.K., Greece, Sweden, Switzerland. Non-crisis sample includes Canada, Czech Republic, Denmark, Ireland, Japan, Korea.
- Change in equity-to-asset ratio had predicted sign (0_1 < a) for U.S., U.K., Greece, Switzerland, Canada, Denmark, Ireland; statistically significant for U.K., Switzerland, Denmark, Canada.
- Interest expense ratio results: countries that experienced a crisis have correct signs (0_3 < a and 0_4 > a) and are statistically significant except Greece. Among non-crisis countries, Canada, Denmark, Czech Republic, Ireland had correctly signed and significant coefficients.
- Noninterest expense ratio and its interaction show statistically significant and correct signs for U.S., U.K., Greece, Sweden, Switzerland, Denmark, Korea.
- Logarithm of assets negative for most countries — larger banks have smaller equity-to-asset ratios; significant at 1 percent for U.K. and Canada.
- Second-stage (loan rate) country results:
  - Equity and interest expense ratios have predicted signs and are significant at 5 percent for most countries, except equity ratio in Canada and Korea.
  - Noninterest expense ratio positive on loan income for all countries; statistically significant except Switzerland, Denmark, Ireland, Japan.
  - Nonperforming loans insignificant for most countries.
  - Variables explain between 96 percent and 67 percent of changes in interest income ratio for crisis-country group, and between 45 percent and 85 percent for non-crisis group.
- Loan demand elasticities across countries (Table 9 / Table 10a):
  - Elasticity of loan demand ranges from 0.92 percent in the United States to 6.61 percent in Denmark (country-specific elasticity estimates reported in Table 9 and summarized in Table 10a).
  - Consequently, banks across most countries operate at loan levels associated with positive marginal revenue.

### Estimated impact of Basel III (1.3 percentage point increase in equity-to-asset ratio from 5.7 percent to 7 percent)
- Proxy assumptions:
  - Sample largest banks Tier 1 ratio (2009) in studies: 10.5 percent (BIS Group 1) and 10.3 percent (CEBS Group 1); sample largest banks Tier 1 ratio: 10.3 percent.
  - Total capital ratio: 14 percent (BIS/CEBS) vs 13.7 percent for the sample.
  - Equity-to-actual asset ratio in sample: 5.7 percent (identical to net CET1 for Group 1 banks in BIS study).
- Estimated effects for largest banks:
  - A 1.3 percentage point increase in equity-to-asset ratio would increase the loan rate by 0.159 percent (calculation: 0.122 * 1.3 percent).
  - This implies a 3.9 percent increase in the loan rate when using ratio 0.159/4.02 (text: "This increase in capital would lead to a 3.9 percent (0.159/4.02) increase in the loan rate when the equity-to-asset ratio is used to proxy for the new regulation.")
  - Given long-run elasticity of loan demand -0.33, this implies an overall reduction of loans by 1.3 percent for the largest banks.
  - Table 10a summary for a 1.3 percentage point increase:
    - Largest banks: Impact on loan rate 0.16; Net cost of raising equity 0.12; Elasticity of loan demand -0.33; Percentage change in loans -1.28.
- Cross-country impacts (Table 10a highlights):
  - Crisis countries average: Impact on loan rate 0.11; Net cost 0.08; Elasticity -2.80; Percentage change in loans -4.55.
  - Other countries average: Impact on loan rate 0.22; Net cost 0.17; Elasticity -2.60; Percentage change in loans -14.76.
  - Country examples:
    - Germany: Impact on loan rate 0.15; Net cost 0.12; Elasticity -1.83; Percentage change in loans -7.16.
    - U.K.: 0.08; 0.06; -2.57; -4.35.
    - U.S.: 0.17; 0.13; -0.92; -2.97.
    - Canada: 0.00; 0.00; -1.67; -0.16.
    - Denmark: 0.25; 0.19; -6.61; -32.61.
    - Ireland: 0.28; 0.22; -1.00; -6.46.
    - Japan: 0.34; 0.26; -1.11; -19.81.
- Crisis-period sensitivity:
  - Using only data through 2007 (excluding crisis period), estimated impact on loan demand of 1.55 percent for largest banks — higher than entire sample (1.3 percent) because interest elasticity of loan demand is larger in the earlier period.
  - Table 10b (2001–07 regressions) summary:
    - Largest banks: Impact on loan rate 0.15; Net cost 0.11; Elasticity -0.42; Percentage change in loans -1.55.
    - Crisis-country averages and non-crisis averages differ; impact generally larger when crisis period excluded for largest banks.
- Comparison with other studies:
  - BIS (2010d) and CEBS (2010): mean GDP-weighted lending rate increase across 53 models 16.7 basis points over eight years and 15 basis points respectively — broadly consistent with column 1 in Table 10a.
  - Kashyap, Stein, and Hanson (2010) calibrated upper bound: 6 basis points — significantly lower than estimates here.
  - Impact on loan volume for largest banks here is 30 percent lower than BIS estimate of -1.89 percent (GDP weighted mean over 48 quarters), while predicted impact is significantly higher for individual countries.

### Policy-relevant conclusions and recommendations
- Main quantitative conclusions:
  - The largest banks would raise lending rates by on average 16 basis points to increase equity-to-asset ratio by 1.3 percentage points required under Basel III.
  - With an estimated long-run elasticity of loan demand of -0.33 for the largest banks, lending rates increase implies loan growth decline by 1.3 percent in the long run.
  - Country heterogeneity: net cost of raising equity by 1.3 percentage points ranges from 0 basis points in Canada to 26 basis points in Japan; elasticities of loan demand range from 0.92 percent (U.S.) to 6.6 percent (Denmark). Average impact on loan growth for crisis countries: -4.9 percent (text summary).
- Countercyclical capital buffer implications:
  - An additional 2.5 percent countercyclical capital requirement would be predicted to reduce the largest banks loans by 2.5 percent.
  - Policy coordination recommendation: a declaration of "excessive credit growth" (triggering the countercyclical buffer) should be closely coordinated with monetary policy decision-making to avoid simultaneous excessive policy-tightening; conversely, the countercyclical capital requirement should be considered part of the monetary authority’s tool kit.
- Broader implications:
  - Deviations from Modigliani-Miller assumptions are confirmed for the 100 largest banks and across many countries.
  - Banks treat capital as a call option consistent with Chami and Cosimano (2001, 2010) — holding more capital allows greater flexibility to issue more loans in the future.
  - Policymakers should identify drivers of high loan-demand elasticities or high net cost of equity in countries where Basel III has large predicted impacts (e.g., Denmark, Japan).

*Italic: Source — _wp11119 (extracted content provided).*

### REFERENCES

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*Source: _wp11119 - REFERENCES*

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