## _wp1348 - 1. Partition of Banks by Size

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### Introduction and research question
- Research question: establish and quantify an empirical link between tax incentives that encourage banks to finance by debt rather than equity and the likelihood of financial crises; quantify welfare gains from policies addressing debt bias.
- Conceptual chain:
  - Statutory corporate tax rate → banks’ leverage (debt bias via interest deductibility versus equity returns).
  - Aggregate bank leverage → probability of systemic banking crisis.
- Policy reforms considered:
  - Cut in the corporate tax rate.
  - Adoption of an Allowance for Corporate Equity (ACE).
  - Introduction of a ‘bank levy’.
- Contextual points:
  - Debt bias does not necessarily trigger crises but may increase vulnerability.
  - Prior welfare estimates (not reflecting financial stability) suggested small costs; this paper investigates whether including financial stability implies larger welfare losses.

### Methodology and data
- Two-step empirical strategy:
  1. Estimate effect of the statutory CIT rate on banks’ leverage using bank-level (Bankscope) and country-level (OECD Banking Statistics) data.
  2. Estimate effect of aggregate bank leverage on probability of systemic banking crisis using Laeven and Valencia (2010) crisis dates and OECD aggregate balance sheet data.
- Bank-level data and estimation:
  - Source: Bankscope; coverage: 82 countries; period: 2001 to 2011.
  - Dynamic panel regressions estimated by system GMM (Arellano and Bover (1995); Blundell and Bond (1998)); between-estimator uses OLS.
  - Dynamic equation includes lev_it, statutory CIT rate x_it, controls X_it (total bank assets and its square, ROA, GDP growth, inflation, aggregate savings), bank- and time-fixed effects, and lagged dependent variable.
  - Banks split into five size groups by asset percentiles:
    - Group 1: 0–85% (asset share 13.4)
    - Group 2: 85–90% (asset share 4.6)
    - Group 3: 90–95% (asset share 8.6)
    - Group 4: 95–97.5% (asset share 8.7)
    - Group 5: 97.5–100% (asset share 64.7)
  - Aggregate tax effect on leverage approximated by asset-weighted average of marginal coefficients across size groups.
- Country-level data and estimation:
  - Aggregated financial data: OECD Banking Statistics; coverage: 29 countries over 2001–09.
  - Macro controls from IMF World Economic Outlook: GDP growth, inflation rate, aggregate savings; control also includes average ROA.
- Crisis-probability estimation:
  - Crisis data: Laeven and Valencia (2010); “systemic banking crises” and “borderline systemic banking crisis” definitions used; banking crises assumed to last two years (second-year observations removed).
  - Sample: 29 OECD countries from 2000 to 2009.
  - Logit model: dependent variable y_ct = 1 if systemic banking crisis; main regressor: aggregate leverage; controls Z include current account balance (percent of nominal GDP) and two measures of bank liquidity (asset-side liquidity and liability-side liquidity).
  - Estimation: OLS and IV (instrumenting leverage with predicted leverage from country-level leverage equation).

### Effect of taxation on leverage — bank-level findings
- Estimator interpretation:
  - Dynamic specification: “tax (short-term)” = β1; “tax (long-term)” = β1/(1−β2).
  - Between-estimator: γ1 reflects long-run tax effect.
- Key reported coefficients and statistics (selected from Table 2 and related text):
  - Lagged Leverage coefficient in dynamic specification: 0.67***; 0.74***.
  - Tax (long-term) coefficients (various columns): 0.25***, 0.21***, 0.31***, 0.17***, 0.17***, 0.18***, 0.30***, 0.14***.
  - Log of asset coefficients (various): 0.05**, 0.05*, 0.17***, 0.16***, 0.18***, 0.14***, 0.14***, 0.17***.
  - ROA coefficients (various): -0.24***, -0.26***, -0.29***, -0.12**, -0.17***, -0.20***, -0.47***, -0.31***.
  - R2 for between-estimator ranges: 0.24 to 0.39.
  - Observations by specification: 106,649; 33,933; 120,481; 39,712; 74,852; 23,956; 45,629; 15,756.
  - Arellano-Bond AR1 P-values: 0.00; AR2 P-values: 0.04 and 0.21 reported; Hansen P-values: 0.51 and 0.09 reported.
- Main qualitative conclusions:
  - Strong positive association between CIT rate and bank leverage; long-run coefficient significant at the 1 percent level in all specifications.
  - Long-run marginal impact of CIT on individual-bank leverage lies between 0.14 and 0.31 across specifications.
  - Removing U.S. banks typically reduces coefficients somewhat.
  - Pre-crisis (2001–07) vs post-onset (2008–11) differences in estimated tax effects are minor.
- Size-split results (Table 3):
  - Dynamic-GMM long-term marginal coefficients and T-values:
    - 0-85: coefficient 0.26***; T-value 4.68
    - 85-90: coefficient 0.17***; T-value 3.74
    - 90-95: coefficient 0.61; T-value 0.53
    - 95–97.5: coefficient 0.73; T-value 0.63
    - Top 2.5 pct: coefficient 0.08; T-value 0.26
  - Between-estimator coefficients and T-values:
    - 0-85: coefficient 0.36***; T-value 16.00
    - 85-90: coefficient 0.17***; T-value 5.66
    - 90-95: coefficient 0.15***; T-value 5.60
    - 95–97.5: coefficient 0.09***; T-value 2.66
    - Top 2.5 pct: coefficient -0.01; T-value -0.24
  - Interpretation: Tax effects decrease almost monotonically with bank size; smallest banks are most tax-responsive; largest banks often show insignificant or negative between-estimates.
- Aggregate implied tax-responsiveness:
  - Asset-weighted average of marginal coefficients gives implied aggregate tax-responsiveness of 0.11 for GMM estimators and 0.08 for between estimates.

### Effect of taxation on leverage — country-level findings
- Tax (long-term) coefficients across Table 4 columns:
  - Column (1): 0.04* (0.02)
  - Column (2): 0.06*** (0.02)
  - Column (3): 0.03 (0.02)
  - Column (4): 0.04** (0.02)
  - Column (5): 0.02 (0.06)
  - Column (6): 0.09* (0.05)
- Other selected coefficients:
  - ROA: ranges -1.77*** to -1.16*** (standard errors (0.19) to (0.41))
  - GDP growth: 0.09 (0.08) to 0.14 (0.12)
  - inflation: -0.15*** (0.03) to -0.15 (0.12)
  - saving rate: 0.13*** (0.02) to 0.07* (0.04)
- Model fit and sample:
  - R2 values: 0.44, 0.50, 0.51, 0.54, 0.53, 0.52 across columns.
  - Observations: 253, 244, 199, 192, 54, 52 across columns.
  - Years and U.S. inclusion vary by column (01-11, 01-07, 08-09 patterns).
- Country-level interpretation:
  - CIT exerts a positive impact on aggregate leverage; statistical significance varies.
  - No systematic difference in tax effects before and after the financial crisis.
  - Removing U.S. banks increases estimated tax effects (e.g., 0.04 in full sample to 0.06 excluding U.S.).
  - Reported range for tax effects on aggregate leverage: 0.04–0.15 (paper-wide range).

### Effect of leverage on probability of banking crisis
- Logit and IV estimation (Tables 5 and 6) — key coefficients:
  - Leverage coefficients (Table 5):
    - Column (1): 31.47** (13.66)
    - Column (2): 31.58** (13.76)
    - Column (3): 40.19*** (14.60)
    - Column (4): 42.42 (32.03)
    - Column (5) [IV]: 139.27*** (49.52) — leverage instrumented by predicted value from Table 4 column (1)
  - Tax coefficient in Table 5 column (1): -2.40 (4.22) — negative but insignificant
  - Liquidity and current account:
    - Liability-side liquidity often negative and significant (e.g., -4.82** (1.99); -5.63*** (2.41) in column (5))
    - Current account negative and often highly significant (e.g., -14.36*** (5.24); -30.18*** (9.01) in column (5))
  - Observations in Table 5: 240, 240, 231, 240, 240
  - R-squared: 0.14, 0.14, 0.18, 0.13, 0.30
- Marginal impacts (Table 6): impact of one percentage point change in leverage on probability of crisis (percent), for selected initial leverage levels
  - Using Table 5 column (1) specification:
    - Initial leverage 88: 0.3
    - 90: 0.5
    - 92: 0.9
    - 94: 1.5
    - 96: 2.6
  - Using Table 5 column (5) IV specification:
    - Initial leverage 88: 0.0
    - 90: 0.0
    - 92: 0.5
    - 94: 7.3
    - 96: 34.8
  - Comparative studies cited:
    - Barrell et al.: for initial leverage 88: 1.7; 90: 2.7; 92: 4.3; 94: 6.9
    - Kato et al.: for initial leverage 88: 0.6; 90: 1.1; 92: 1.9; 94: 3.2
- Interpretation:
  - Effect of leverage on crisis probability is positive in all specifications but significance and magnitude vary; IV estimates imply much stronger and more convex effects at high leverage levels.
  - Marginal impact of leverage on crisis probability rises rapidly and nonlinearly as leverage increases.

### Simulations linking tax changes to crisis probability and expected output
- Tax-to-leverage responsiveness assumptions used in simulations:
  - A 1 percentage point reduction in the CIT rate reduces aggregate leverage by between 0.04 and 0.15 percentage points (range informed by bank- and country-level estimates).
  - Alternative narrower inference: 0.08–0.11 percentage points; simulations consider full 0.04–0.15 range.
- Table 7 (marginal impact of tax on probability of banking crisis) — examples combining leverage-to-crisis marginal impacts with tax-to-leverage responsiveness:
  - Using Table 6 column (1) marginal impacts (leverage→crisis):
    - Initial leverage 90: tax marginal impacts 0.02, 0.04, 0.07 (for 0.04, 0.08, 0.15 reductions in leverage per 1 percentage point CIT)
    - Initial leverage 93: 0.04, 0.09, 0.17
    - Initial leverage 96: 0.10, 0.21, 0.39
  - Using Table 6 column (5) IV marginal impacts:
    - Initial leverage 90: 0.00, 0.00, 0.01
    - Initial leverage 93: 0.08, 0.16, 0.29
    - Initial leverage 96: 1.39, 2.78, 5.22
- Interpretation of marginal impacts:
  - A 1 point change in the CIT rate is modest but effects on crisis probability can be non-negligible, especially at high initial leverage ratios.
  - Example: At aggregate leverage 96 percent, increasing the corporate tax rate from 25 to 26 percent (1 percentage point) would increase the likelihood of crisis:
    - Using column (1) estimates: between 0.1 and 0.39 percentage points
    - Using column (5) estimates: between 1.39 and 5.22 percentage points
  - At lower initial leverage (e.g., 90 percent), effects are modest.
- Policy reform simulations (three reforms; modeling assumptions):
  - 10-point cut in the CIT rate:
    - Simulations account for convexity by extrapolating a series of small changes rather than linear scaling.
  - Bank levy of 10 basis points on liabilities other than insured deposits:
    - Assumed interest rate 4 percent implies tax on interest = 10/400 = 2.5 percent; modeled as equivalent reduction in CIT rate of 2.5 percent.
    - With 1 percentage point CIT reduction reducing leverage by 0.04–0.15, the bank levy of 10 bp would reduce financial leverage by between 0.1 and 0.4 percentage points (text reports truncation at source; illustrative calculations follow the same mapping).
  - Allowance for Corporate Equity (ACE):
    - Modeled as equivalent to reducing the corporate tax rate to zero; simulated as a 28-point reduction in the CIT rate (28 being the mean CIT in the panel).
- Translating changes into expected output gains:
  - Assume mean output loss in a systemic crisis = 23 percent (Laeven and Valencia (2010): cumulative GDP loss over four years relative to pre-crisis trend).
  - Multiply change in crisis probability by expected output loss of 23 percent to obtain annual expected GDP gain associated with a policy reform.

### Simulated welfare impacts (representative outcomes from Table 8)
- Using central tax-to-leverage estimate 0.08 and combining with leverage→crisis elasticities:
  - Eliminating debt bias through an ACE gives an expected GDP gain of between 0.5 and 11.9 percent (4-year cumulative expected output gains reported).
  - A 10-percentage-point CIT cut at aggregate bank leverage of 93 percent yields cumulative expected GDP gain over 4 years between 0.1 and 0.4 percent; at leverage of 96 percent effect may go up to 9.9 percent.
  - A bank levy of 10 basis points has much smaller effects except when both tax responsiveness and initial leverage are high; estimated gain in expected GDP can rise to 3 percent in some scenarios.
- Policy ranking by simulated gains:
  - ACE produces the largest gains because it eliminates debt bias entirely.
  - CIT cut or ACE targeted to financial sector could produce large welfare gains where leverage is high, but sector-specific tax differentiation risks avoidance and distortions.
  - If sectoral differentiation is ruled out, corrective case could be made for bank levies at substantially higher rates than at present.

### Interpretation, policy implications, and conclusion
- Main inference: taxation materially affects bank leverage; aggregate leverage raises crisis probability; therefore, debt bias increases chances of financial crisis and can lead to substantial welfare costs.
- Estimated ranges:
  - Individual-bank long-run tax response: between 0.14 and 0.31.
  - Aggregate tax-responsiveness: roughly 0.04–0.15 (central estimates 0.08–0.11).
  - Marginal impact of leverage on crisis probability: highly nonlinear; small at moderate leverage, steep at very high leverage (see Table 6 values).
- Policy implications:
  - Tax reforms that reduce debt bias (ACE, CIT cuts, or bank levies) can generate nontrivial expected output gains through reduced crisis probability, especially where leverage is already high.
  - Regulation (Basel III) remains primary tool to address excess leverage; tax incentives are an additional and potentially important lever for financial stability.
- Paper’s stance: does not claim definitive causal proof but presents evidence supporting the plausibility of a meaningful link between tax-induced debt bias, higher bank leverage, and higher probability of systemic banking crises.

### Data and descriptive statistics (Appendix 1 — key figures preserved)
- Bank-level sample:
  - Source: Bankscope; sample coverage: 82 countries between 2001 and 2011.
  - Total bank-year observations = 120,481.
  - Number of banks = 13,356; panel unbalanced.
  - U.S. observations: 80,769 (67 percent of total observations).
  - Leverage definition: total liabilities divided by total assets.
  - Summary statistics (Table A1):
    - leverage: N 120,481; mean 0.881; median 0.904; std. dev. 0.096; min 0.071; max 1.000
    - tax: N 120,481; mean 0.367; median 0.400; std. dev. 0.055; min 0.000; max 0.421
    - log of asset: N 120,481; mean 12.210; median 12.041; std. dev. 1.570; min 2.477; max 21.567
    - ROA: N 120,481; mean 0.010; median 0.009; std. dev. 0.040; min -3.148; max 3.154
    - GDP growth: N 120,481; mean 0.017; median 0.019; std. dev. 0.027; min -0.177; max 0.183
    - inflation: N 120,481; mean 0.027; median 0.022; std. dev. 0.025; min -0.035; max 1.087
    - saving rate: N 120,481; mean 0.174; median 0.152; std. dev. 0.058; min -0.041; max 0.535
  - Additional notes:
    - Sample average statutory CIT rate = 36.7 percent.
    - Excluding U.S. banks, mean and median tax rates are 0.322 and 0.332.
    - Average log of total assets 12.210 implies average asset value of 1.35 billion U.S. dollars.
    - Mean ROA = 1 percent; min -314.8 percent; max 315.4 percent.
    - Mean GDP growth, inflation, and saving rate are 1.7 percent, 2.7 percent, 17.4 percent respectively.
- Country-level (macro) sample:
  - Aggregated balance sheet data: OECD Banking Statistics; coverage 2001–2009.
  - Sample: 29 countries; 253 observations.
  - Summary statistics (Table A2):
    - leverage: N 253; mean 0.930; median 0.934; std. dev. 0.024; min 0.862; max 0.973
    - asset liquidity: N 253; mean 0.238; median 0.233; std. dev. 0.088; min 0.087; max 0.512
    - liability liquidity: N 253; mean 0.536; median 0.518; std. dev. 0.161; min 0.218; max 0.956
    - current account balance: N 253; mean -0.007; median -0.008; std. dev. 0.062; min -0.159; max 0.164
    - tax: N 253; mean 0.286; median 0.290; std. dev. 0.069; min 0.125; max 0.421
    - ROA: N 253; mean 0.009; median 0.009; std. dev. 0.008; min -0.048; max 0.031
    - GDP growth: N 253; mean 0.023; median 0.026; std. dev. 0.033; min -0.143; max 0.105
    - inflation: N 253; mean 0.032; median 0.025; std. dev. 0.049; min -0.026; max 0.685
    - saving rate: N 253; mean 0.219; median 0.222; std. dev. 0.056; min 0.051; max 0.404
  - Notes:
    - Mean leverage in Table A2 higher than Table A1 because large banks tend to be more highly leveraged and account for a large share of total assets.
    - Average tax rate in Table A2 lower than Table A1 because many bank-year observations in Table A1 refer to countries with high CIT rates (U.S., Japan, Germany), which carry a larger weight in Table A1.

*Source: _wp1348 (IMF working paper excerpt).*

### 1. Partition of Banks by Size...........................................................................................

### _wp1348 - 1. Partition of Banks by Size...........................................................................................

### Main sections (by title and page)
- 1. Partition of Banks by Size......................................................................................................7
- 2. Effect of Tax on Leverage: Bank-level Data .......................................................................10
- 3. Estimated Effect of Tax on Bank Leverage for Alternative Size Groups ............................12
- 4. Effect of Tax on Leverage: Country-level Data ..................................................................12
- 5. Effect of Leverage on the Odds Ratio of a Banking Crisis ..................................................14
- 6. Marginal Impact of Leverage on the Probability of Banking Crisis ....................................15
- 7. Marginal Impact of Tax on the Probability of Banking Crisis ............................................17
- 8. Simulated 4-year Cumulative Expected Output Gain of Three Tax Reforms .....................19

### Figures
- Figure 1. Relationship between Initial Leverage and the Probability of Banking Crisis ........16

### Appendix and tables
- Appendix 1. Data .....................................................................................................................21
- Table A1. Summary Statistics of Data in the Leverage Regression using Micro Data.........21
- Table A2. Summary Statistics of Data in the Regressions using Macro Data .........................22

*Source: _wp1348 - 1. Partition of Banks by Size (PDF).*

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

### _wp1348 - References .............................................................................................................

### Introduction
- Research question: establish and quantify an empirical link between tax incentives that encourage banks to finance by debt rather than equity and the likelihood of financial crises; quantify welfare gains from policies addressing debt bias.
- Conceptual chain:
  - Statutory corporate tax rate → banks’ leverage (debt bias via interest deductibility versus equity returns).
  - Aggregate bank leverage → probability of systemic banking crisis.
- Policy reforms considered:
  - Cut in the corporate tax rate.
  - Adoption of an Allowance for Corporate Equity (ACE).
  - Introduction of a ‘bank levy’ (broadly of the kind a dozen or so countries introduced since the crisis).
- Contextual points:
  - Debt bias does not necessarily trigger crises but may increase vulnerability.
  - Prior welfare estimates (not reflecting financial stability) suggested small costs; this paper investigates whether including financial stability implies larger welfare losses.

### Methodology and Data
- Two-step empirical strategy:
  1. Estimate effect of the statutory CIT rate on banks’ leverage using bank-level (Bankscope) and country-level (OECD Banking Statistics) data.
  2. Estimate effect of aggregate bank leverage on probability of systemic banking crisis using Laeven and Valencia (2010) crisis dates and OECD aggregate balance sheet data.
- Bank-level data:
  - Source: Bankscope; coverage: 82 countries; period: 2001 to 2011.
  - Dynamic panel regressions estimated by system GMM (Arellano and Bover (1995); Blundell and Bond (1998)); between-estimator uses OLS.
  - Dynamic equation (1) structure (variables preserved as described): lev_it, statutory CIT rate x_it, vector of controls X_it (total bank assets and its square, ROA, GDP growth, inflation, aggregate savings), bank- and time-fixed effects, lagged dependent variable for sluggish response.
  - Banks split into five size groups by asset percentiles: Group 1: 0–85% (asset share 13.4%); Group 2: 85–90% (asset share 4.6%); Group 3: 90–95% (asset share 8.6%); Group 4: 95–97.5% (asset share 8.7%); Group 5: 97.5–100% (asset share 64.7%).
  - Aggregate tax effect on leverage approximated by asset-weighted average of marginal coefficients across size groups.
- Country-level data:
  - Aggregated financial data: OECD Banking Statistics; coverage: 29 countries over 2001–09.
  - Macro controls from IMF World Economic Outlook: GDP growth, inflation rate, aggregate savings; control also includes average ROA.
- Crisis-probability estimation:
  - Crisis data: Laeven and Valencia (2010); “systemic banking crises” and “borderline systemic banking crisis” definitions used; assumption: banking crises last for two years (second-year observations eliminated as not independent).
  - Sample: 29 OECD countries from 2000 to 2009.
  - Logit model (3): dependent variable y_ct = 1 if systemic banking crisis; main regressor: aggregate leverage; controls Z include current account balance (percent of nominal GDP) and two measures of bank liquidity (percent of total assets): asset-side liquidity (cash, central bank balances, securities) and liability-side liquidity (customer deposits).
  - Estimation: OLS and IV (instrumenting leverage with predicted leverage from country-level version of leverage equation).

### Effect of Taxation on Leverage (Key Estimation Details)
- Estimators and interpretation:
  - In dynamic specification: “tax (short-term)” refers to β1; “tax (long-term)” refers to β1/(1−β2) in equation (1).
  - Between-estimator: γ1 in equation (2) reflects long-run tax effect.
- Heterogeneity:
  - Responses differ substantially by bank size: smaller banks more tax-responsive than larger banks; largest banks often less responsive (potential “too-big-to-fail” effect).

### Empirical Results — Bank-level (Selected Findings and Statistics)
- Table 2 highlights (bank-level regressions, various specifications):
  - Dynamic specification: lagged Leverage coefficient reported as 0.67*** (column 1) and 0.74*** (column 2).
  - Tax (long-term) coefficients across columns: 0.25***, 0.21***, 0.31***, 0.17***, 0.17***, 0.18***, 0.30***, 0.14*** (standard errors shown in table).
  - Log of asset coefficients: 0.05**, 0.05*, 0.17***, 0.16***, 0.18***, 0.14***, 0.14***, 0.17***.
  - ROA coefficients: -0.24***, -0.26***, -0.29***, -0.12**, -0.17***, -0.20***, -0.47***, -0.31***.
  - GDP growth and inflation coefficients reported with mixed signs across columns (see table for exact values).
  - R2 for between-estimator ranges reported as 0.24 to 0.39.
  - Observations by specification: 106,649; 33,933; 120,481; 39,712; 74,852; 23,956; 45,629; 15,756 (as reported in Table 2).
  - Arellano-Bond AR1 P-values reported as 0.00; AR2 P-values reported as 0.04 and 0.21 in columns shown; Hansen P-values reported as 0.51 and 0.09.
- Main qualitative conclusion:
  - Strong positive association between CIT rate and bank leverage; long-run coefficient significant at the 1 percent level in all specifications.
  - Long-run marginal impact of CIT on individual-bank leverage lies between 0.14 and 0.31 across specifications.
  - Removing U.S. banks typically reduces coefficients somewhat.
  - Comparing pre-crisis (2001–07) and post-onset (2008–11) periods shows only minor differences in estimated tax effects.
- Size-split results (Table 3 summary):
  - Tax effects decrease almost monotonically with bank size.
  - Dynamic-GMM marginal coefficients by size: smallest banks ~0.26 (highly significant); largest banks ~0.08 (insignificant).
  - Between-estimator shows coefficients: smallest banks 0.36; largest banks -0.01.
- Aggregate implied tax-responsiveness:
  - Asset-weighted average of marginal coefficients gives implied aggregate tax-responsiveness of 0.11 for the GMM estimators and 0.08 for the between estimates.

### Effect of Leverage on the Probability of Banking Crisis (Estimation Approach)
- Logit model estimated where main parameter of interest θ1 measures impact of marginal increase in aggregate leverage on odds of crisis; expected sign θ1 > 0.
- Instruments: predicted leverage from macro-level leverage equation used to address potential correlation between lev and error term.
- Crisis events used:
  - Systemic banking crises identified for eight OECD country-events (United States in 2007; Austria, Belgium, Denmark, Germany, Ireland, Luxembourg, Netherlands in 2008).
  - Borderline systemic banking crises include seven additional events (France, Greece, Hungary, Portugal, Slovenia, Spain, Sweden in 2008).
- Note: alternative reduced-form approach (substituting CIT into crisis regression) finds tax rate insignificant and is conceptually problematic due to potential other channels and identifying assumptions.

### Simulating Tax Effects on the Probability of Crisis
- Simulation strategy: combine point estimates from the two sets of regressions (tax→leverage; leverage→crisis) to calculate impact of tax reforms on probability of crisis.
- Reduced-form substitution of CIT directly into crisis model proved problematic (CIT insignificant) and potentially confounded.

### Results — Overall Interpretation (from presented sections)
- Taxation materially affects bank leverage: long-run individual-bank leverage response to CIT is consistently positive and significant (long-run coefficients between 0.14 and 0.31).
- Larger banks are less responsive to tax incentives than smaller banks; however, because the largest banks account for a large share of assets (Group 5 asset share 64.7%), even modest tax-induced leverage changes in large banks can have aggregate implications.
- Aggregate tax-responsiveness estimated around 0.11 (GMM) and 0.08 (between), using asset-weighted averages of size-group estimates.
- The paper proceeds to estimate the effect of aggregate leverage on crisis probability and to simulate the impact of the three tax reforms on crisis likelihood and expected output (details beyond these excerpts are in subsequent sections).

*Source: _wp1348 - References (content units: Introduction; Methodology and Data; Results — as provided).*

### 0.53 and 1.91 for, respectively, the dynamic and between estimators; thus only between estimate is significant,

### _wp1348 - 0.53 and 1.91 for, respectively, the dynamic and between estimators; thus only between estimate is significant,

### Estimated Tax Effect on Bank Leverage for Alternative Size Groups (Table 3)
- Asset shares by percentile group:
  - 0-85: 13.4
  - 85-90: 4.6
  - 90-95: 8.6
  - 95–97.5: 8.7
  - Top 2.5 pct: 64.7
- Dynamic GMM estimator (long-term impact) — marginal impact coefficient and T-value:
  - 0-85: coefficient 0.26***; T-value 4.68
  - 85-90: coefficient 0.17***; T-value 3.74
  - 90-95: coefficient 0.61; T-value 0.53
  - 95–97.5: coefficient 0.73; T-value 0.63
  - Top 2.5 pct: coefficient 0.08; T-value 0.26
- Between estimator — marginal impact coefficient and T-value:
  - 0-85: coefficient 0.36***; T-value 16.00
  - 85-90: coefficient 0.17***; T-value 5.66
  - 90-95: coefficient 0.15***; T-value 5.60
  - 95–97.5: coefficient 0.09***; T-value 2.66
  - Top 2.5 pct: coefficient -0.01; T-value -0.24
- Note: Estimates as in specifications (1) and (3) of Table 2 for alternative size groups as in Table 1. *** denotes significance at 1 percent.

### Country-level data (Table 4) — Effect of Tax on Leverage: Country-level Data
- Regressions reported across columns (1)–(6); summary of key coefficients (tax (long-term) is coefficient on the CIT rate):
  - Column (1): tax (long-term) 0.04* (0.02)
  - Column (2): tax (long-term) 0.06*** (0.02)
  - Column (3): tax (long-term) 0.03 (0.02)
  - Column (4): tax (long-term) 0.04** (0.02)
  - Column (5): tax (long-term) 0.02 (0.06)
  - Column (6): tax (long-term) 0.09* (0.05)
- Other reported coefficients (selected):
  - ROA: ranges -1.77*** to -1.16*** with standard errors (0.19) to (0.41)
  - GDP growth: 0.09 (0.08) to 0.14 (0.12)
  - inflation: -0.15*** (0.03) to -0.15 (0.12)
  - saving rate: 0.13*** (0.02) to 0.07* (0.04)
- Model fit and sample:
  - R2 ranges: 0.44, 0.50, 0.51, 0.54, 0.53, 0.52 (reported across columns)
  - Observations: 253, 244, 199, 192, 54, 52 (corresponding columns)
  - US included? Yes/No pattern across columns as in table
  - Years: 01-11, 01-11, 01-07, 01-07, 08-09, 08-09
- Key interpretive findings from country-level data:
  - CIT exerts a positive impact on aggregate leverage. Statistical significance varies (from 1 percent in column (2) to insignificant in columns (3) and (5)).
  - No systematic difference in tax effects before and after the financial crisis.
  - Removing U.S. banks increases estimated tax effects in the country-level regressions (marginal impact of CIT rate 0.04 in full sample (column (1)); excluding U.S. banks increases to 0.06 (column (2))).
  - Based on bank- and country-level results, reported range for tax effects on aggregate leverage: 0.04–0.15.

### The Effect of Leverage on the Probability of Banking Crisis (Tables 5 and 6)
- Table 5: Effect of Leverage on the Odds Ratio of a Banking Crisis — key coefficients and model features:
  - Leverage coefficients (with standard errors):
    - Column (1): 31.47** (13.66)
    - Column (2): 31.58** (13.76)
    - Column (3): 40.19*** (14.60)
    - Column (4): 42.42 (32.03)
    - Column (5) [IV]: 139.27*** (49.52) — leverage instrumented by predicted value from column (1) of Table 4
  - Tax coefficient reported in column (1): -2.40 (4.22) — negative but insignificant
  - Liquid liability consistently negative and significant in many columns (e.g., -4.82** (1.99); -5.63*** (2.41) in column (5))
  - Current Accounts negative and often highly significant (e.g., -14.36*** (5.24); -30.18*** (9.01) in column (5))
  - Number of observations: 240, 240, 231, 240, 240
  - Crisis/border: columns vary between using both systemic and borderline systemic crises or only systemic crises
  - Estimators: OLS for columns (1)–(4); IV for column (5)
  - R-squared: 0.14, 0.14, 0.18, 0.13, 0.30
- Interpretation and robustness notes:
  - Effect of leverage on probability of crisis is positive in all columns but significant primarily under the broader crisis definition.
  - Excluding the U.S. increases the impact and significance of leverage.
  - Using lags for independent variables reduces significance of leverage.
- Table 6: Marginal Impact of Leverage on the Probability of Banking Crisis (marginal impact = impact of one percentage point change in leverage on probability of crisis, measured in percent)
  - For initial leverage (percent), marginal impacts from columns (1) and (5) of Table 5 and comparison studies:
    - Initial leverage 88: (1) 0.3; (5) 0.0; Barrell et al. 1.7; Kato et al. 0.6
    - Initial leverage 90: (1) 0.5; (5) 0.0; Barrell et al. 2.7; Kato et al. 1.1
    - Initial leverage 92: (1) 0.9; (5) 0.5; Barrell et al. 4.3; Kato et al. 1.9
    - Initial leverage 94: (1) 1.5; (5) 7.3; Barrell et al. 6.9; Kato et al. 3.2
    - Initial leverage 96: (1) 2.6; (5) 34.8; Barrell et al. n.a.; Kato et al. n.a.
  - Key insight: Marginal impact of leverage on probability of crisis rises rapidly and nonlinearly at higher leverage levels. Example interpretations:
    - At initial leverage 88 percent (micro sample mean), a 1 percentage point increase in leverage increases likelihood of crisis by 0.3 percentage points (specification in column (1)).
    - At initial leverage 94 percent (close to macro sample median), a 1 percentage point increase raises likelihood by 1.5 percentage points.
    - At initial leverage 96 percent (pre-crisis levels in many crisis countries), a 1 percentage point increase raises likelihood by 2.6 percentage points (column (1)) and much more in column (5).
  - Nonlinearity: Specification in column (5) implies a substantially more convex (accelerating) marginal impact as leverage rises.

### Policy Simulations (Section IV) — Linking CIT Rate, Leverage, and Crisis Probability
- Tax-to-leverage responsiveness used for simulations:
  - A 1 percentage point reduction in the CIT rate reduces aggregate leverage by somewhere between 0.04 and 0.15 percentage points (range informed by bank- and country-level estimates).
  - Alternative narrower inference: 0.08–0.11 percentage points (noted earlier) but simulations consider 0.04–0.15.
- Table 7: Marginal Impact of Tax on the Probability of Banking Crisis — combining assumed marginal impact on leverage (0.04, 0.08, 0.15) with marginal impacts of leverage on crisis from Table 6:
  - Estimates using column (1) of Table 6 (marginal impacts of leverage):
    - Initial leverage 90 percent: tax marginal impacts 0.02, 0.04, 0.07 (for 0.04, 0.08, 0.15 changes in leverage)
    - Initial leverage 93 percent: 0.04, 0.09, 0.17
    - Initial leverage 96 percent: 0.10, 0.21, 0.39
  - Estimates using column (5) of Table 6:
    - Initial leverage 90 percent: 0.00, 0.00, 0.01
    - Initial leverage 93 percent: 0.08, 0.16, 0.29
    - Initial leverage 96 percent: 1.39, 2.78, 5.22
- Interpretive findings:
  - A 1 point change in the CIT rate is modest but effects on crisis probability can be non-negligible, especially at high initial leverage ratios.
  - Example: At aggregate leverage 96 percent, increasing the corporate tax rate from 25 to 26 percent (a 1 percentage point increase) would increase the likelihood of crisis:
    - Using column (1) estimates: between 0.1 and 0.39 percentage points
    - Using column (5) estimates: between 1.39 and 5.22 percentage points
  - At low initial leverage (e.g., 90 percent), effects are modest: a higher corporate tax rate raises likelihood of crisis hardly at all.
- Three policy reforms simulated to reduce debt bias (and how they are modeled):
  - A 10-point cut in the CIT rate:
    - Simulations account for convexity by extrapolating a series of small changes (effect not simply 10 times the one-point effect).
  - A ‘bank tax’ of 10 basis points (modeled as equivalent reduction in CIT rate):
    - Bank levy of 10 basis points on liabilities other than insured deposits, assuming interest rate 4 percent, corresponds to a tax on interest of 2.5 percent (=10/400); modeled as a reduction in the CIT rate of 2.5 percent.
    - Implication: with 1 percentage point CIT reduction reducing leverage by 0.04–0.15, the bank levy of 10 bp would reduce financial leverage by between 0.1 and [text truncates at source end].
  - An ‘Allowance for Corporate Equity’ (ACE) form of corporate tax:
    - Provides deduction for normal return to equity, eliminating corporate-level tax bias toward debt; modeled as equivalent to reducing the corporate tax rate to zero.
    - Simulated as a 28-point reduction in the CIT rate (28 being the mean value of the CIT rate in the panel).
- Simulation setup:
  - Use tax-to-leverage responsiveness 0.04–0.15 per 1 percentage point CIT change.
  - Combine with nonlinear marginal impacts of leverage on crisis from Table 6 (columns (1) and (5)).
  - Extrapolate small changes to capture convexity for larger reforms.

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

### 0.4 percentage points, for example from 93 percent to 92.9 or 92.6. Eliminating debt bias

### _wp1348 - 0.4 percentage points, for example from 93 percent to 92.9 or 92.6. Eliminating debt bias

### Effects of eliminating debt bias and ACE simulations
- Eliminating debt bias altogether with an ACE would reduce leverage by 2.2 percentage points under the central estimate of 0.08: for example, from 93 to 90.8.
- With the upper bound estimate of 0.15, leverage would fall by 4.2 percentage points.
- These leverage effects are translated into impacts on the likelihood of crisis and then into expected effects on output using an assumed mean output loss of 23 percent (Laeven and Valencia (2010): cumulative GDP loss over four years relative to pre-crisis trend).
- Multiplying the change in crisis probability by the expected output loss of 23 percent gives an annual expected GDP gain associated with a policy reform.

### Simulated welfare impacts (Table 8, key outcomes)
- Table 8 reports simulated 4-year cumulative expected output gains for three tax reforms under alternative assumptions on tax-responsiveness of leverage, two initial leverage levels (93 and 96 percent), and two estimates of the impact of leverage on crisis likelihood (columns (1) and (5) of Table 6).
- Representative outcomes summarized in the text:
  - Taking the central estimate for the tax impact on bank leverage of 0.08, eliminating debt bias through an ACE gives an expected GDP gain of between 0.5 and 11.9 percent.
  - A 10-percentage-point CIT cut at aggregate bank leverage of 93 percent is estimated to yield a cumulative expected GDP gain over 4 years of between 0.1 and 0.4 percent; at leverage of 96 percent, this effect may go up to 9.9 percent.
  - A bank levy of 10 basis points has much smaller effects except when both tax responsiveness and initial leverage are high; even so, the estimated gain in expected GDP can rise to 3 percent.
- Note on definitions used in Table 8:
  - ‘CIT cut’ refers to 10 percentage point reduction in the CIT rate.
  - ‘Bank Levy’ refers to 10 basis point bank levy on all liabilities (2.5 percent lower debt bias).
  - ‘ACE’ refers to allowance for corporate equity to neutralize debt bias (assuming an initial 28 percent CIT).

### Interpretation and policy implications
- The implied welfare impact of tax reforms that ease debt bias in the financial sector can be substantial and far larger than the small deadweight losses reported for nonfinancial firms.
- The most important social costs of debt bias likely originate from its impact on financial sector risks, especially in countries where leverage ratios are already high.
- Of the three reforms studied, ACE gives the largest gains because it entirely eliminates the debt bias.
- A reduced corporate tax rate or ACE targeted only to the financial sector could produce the greatest welfare gains where leverage is high, but sector-specific corporate tax differentiation risks avoidance opportunities and distortions.
- If sectoral differentiation is ruled out, a corrective case could be made for bank levies at substantially higher rates than at present.

### Conclusion (summary of the paper's argument)
- The paper does not claim to have uncovered a direct link between tax incentives favoring debt finance and the probability of financial crisis, but presents evidence suggesting the real possibility of such a connection.
- If debt bias leads to higher aggregate bank leverage, and if higher aggregate bank leverage makes financial crisis more likely, then debt bias increases the chances of financial crisis.
- This implies potential welfare gains from mitigating debt bias that can be noticeably more than 1 percent of GDP in some calculations reported.
- Regulation (including higher and tighter capital requirements of Basel III) has the dominant role in addressing excess leverage, but tax incentives that encourage debt finance in banks are a potential risk to financial stability that deserves recognition and possible corrective action.

### Data and descriptive statistics (Appendix 1, key figures preserved)
- Bank-level data:
  - Source balance sheets: Bankscope (Bureau van Dijk).
  - Worldwide CIT rate data: KPMG’s corporate and indirect tax survey 2011.
  - Country-level controls: IMF World Economic Outlook.
  - Sample coverage: 82 countries between 2001 and 2011.
  - Observations: total bank-year observations = 120,481.
  - Number of banks = 13,356; panel is unbalanced.
  - U.S. observations: 80,769 (67 percent among the total observations).
  - Leverage definition: individual banks’ total liabilities divided by total assets.
  - Summary statistics (Table A1):
    - leverage: N 120,481; mean 0.881; median 0.904; std. dev. 0.096; min 0.071; max 1.000
    - tax: N 120,481; mean 0.367; median 0.400; std. dev. 0.055; min 0.000; max 0.421
    - log of asset: N 120,481; mean 12.210; median 12.041; std. dev. 1.570; min 2.477; max 21.567
    - squared log of asset: N 120,481; mean 151.560; median 144.995; std. dev. 39.842; min 6.133; max 465.147
    - ROA: N 120,481; mean 0.010; median 0.009; std. dev. 0.040; min -3.148; max 3.154
    - GDP growth: N 120,481; mean 0.017; median 0.019; std. dev. 0.027; min -0.177; max 0.183
    - inflation: N 120,481; mean 0.027; median 0.022; std. dev. 0.025; min -0.035; max 1.087
    - saving rate: N 120,481; mean 0.174; median 0.152; std. dev. 0.058; min -0.041; max 0.535
  - Additional notes:
    - The sample average statutory CIT rate is 36.7 percent.
    - Excluding U.S. banks, the mean and median tax rates are 0.322 and 0.332, respectively.
    - The average log of total assets of 12.210 implies an average asset value of 1.35 billion U.S. dollars.
    - The average value of ROA is 1 percent, ranging from -314.8 percent and 315.4 percent.
    - The mean GDP growth rate, inflation rate, and saving rate are, respectively, 1.7 percent, 2.7 percent, 17.4 percent.
- Country-level (macro) data:
  - Aggregated balance sheet data from OECD Banking Statistics; coverage 2001–2009.
  - Sample: 29 countries with 253 observations.
  - Summary statistics (Table A2):
    - leverage: N 253; mean 0.930; median 0.934; std. dev. 0.024; min 0.862; max 0.973
    - asset liquidity: N 253; mean 0.238; median 0.233; std. dev. 0.088; min 0.087; max 0.512
    - liability liquidity: N 253; mean 0.536; median 0.518; std. dev. 0.161; min 0.218; max 0.956
    - current account balance: N 253; mean -0.007; median -0.008; std. dev. 0.062; min -0.159; max 0.164
    - tax: N 253; mean 0.286; median 0.290; std. dev. 0.069; min 0.125; max 0.421
    - ROA: N 253; mean 0.009; median 0.009; std. dev. 0.008; min -0.048; max 0.031
    - GDP growth: N 253; mean 0.023; median 0.026; std. dev. 0.033; min -0.143; max 0.105
    - inflation: N 253; mean 0.032; median 0.025; std. dev. 0.049; min -0.026; max 0.685
    - saving rate: N 253; mean 0.219; median 0.222; std. dev. 0.056; min 0.051; max 0.404
  - Variable definitions:
    - ‘Asset liquidity’ = cash and balances with the central banks plus securities divided by assets.
    - ‘Liability liquidity’ = consumer deposit divided by assets.
    - Current account balance = current account divided by nominal GDP.
  - Note: mean leverage in Table A2 is higher than in Table A1 because large banks tend to be more highly leveraged and account for a large share of total assets; average tax rate in Table A2 is lower than Table A1 because many bank-year observations in Table A1 refer to countries with high CIT rates (U.S., Japan, Germany), which carry a larger weight in Table A1.

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

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