## _wp09143 - 7. International Sample: Proxy Measures of (near) Failure

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---

### Introduction and research objective
- Examines how bank competition affects risk of bank failure when banks choose portfolios of risky loans and risk-free assets simultaneously.
- Revisits conventional wisdom that more competition increases instability by incorporating loan-market competition a la Stiglitz-Weiss and banks’ holdings of risk-free assets.
- Central mechanism: the “BDN effect” — higher loan rates reduce entrepreneurs’ effort (z), increasing borrowers’ default risk and thereby affecting bank failure probabilities.

### Theoretical model — structure and key mechanisms
- Two-date economy; three agent classes: entrepreneurs, depositors, banks; all agents risk-neutral.
- Entrepreneurs operate a project of normalized size 1 with output yz + z (y random on [0, A], z deterministic from effort); effort cost c(z) strictly increasing, convex.
- Entrepreneur optimal effort z solves (1) with FOC (2); best-response z = z_L(R) with dz/dR < 0 (equation (3)): higher loan rate ⇒ lower entrepreneur effort (BDN effect).
- Banks collect deposits d and split into risky loans l and riskless asset x: l + x = d.
- Bank failure threshold Y* defined so profits = 0 at Y*; probability of failure = F(Y*).
- Cournot competition among N banks; symmetric interior equilibrium characterized by lending-rate condition (13), deposit-rate condition (14), and failure threshold (15).
- Comparative statics with respect to N:
  - Total deposits increase with N (equation (16)).
  - Total loans increase with N (equations (17)–(19)); hence dL/dN > 0.
  - dY*/dN decomposes into deposit and loan channels (equation (20)): dY*/dN = (∂Y*/∂D) dD/dN + (∂Y*/∂L) dL/dN.
  - If BDN effect weak (∂Y*/∂L > 0), increased competition (higher N) unambiguously increases risk (dF(Y*)/dN > 0).
  - If BDN effect strong (∂Y*/∂L < 0 and sufficiently large), increased competition can decrease risk (dF(Y*)/dN < 0).
  - As N → ∞, BDN effect can dominate: L Y* z → − and competition can reduce failure risk.

### Numerical examples (linear demand/supply, uniform return)
- Two calibrated panels:
  - Panel A: No BDN effect — probability of bank failure increases with N.
  - Panel B: Strong BDN effect — probability of bank failure declines with N.
- Panel A: No BDN effect (columns: Number of banks | profits per bank | total loans | total deposits | loans/deposits | Probability of bank failure [F(Y*)])
  - 2 | 3.953 | 5.367 | 7.000 | .766 | 0.059
  - 3 | 2.255 | 5.977 | 7.880 | .758 | 0.070
  - 5 | 1.023 | 6.598 | 8.750 | .753 | 0.082
  - 10 | 0.315 | 7.169 | 9.550 | .750 | 0.092
  - 20 | 0.090 | 7.491 | 10.000 | .749 | 0.098
  - 30 | 0.043 | 7.611 | 10.160 | .749 | 0.100
  - 50 | 0.016 | 7.721 | 10.290 | .750 | 0.102
  - 100 | 0.003 | 7.841 | 10.400 | .754 | 0.104
- Panel B: Strong BDN effect
  - 2 | 4.181 | 5.667 | 7.000 | .808 | 0.077
  - 3 | 2.503 | 5.957 | 7.880 | .755 | 0.067
  - 5 | 1.515 | 5.508 | 8.750 | .629 | 0.062
  - 10 | 0.672 | 5.669 | 9.550 | .593 | 0.050
  - 20 | 0.293 | 5.941 | 10.000 | .594 | 0.041
  - 30 | 0.142 | 6.661 | 10.160 | .655 | 0.034
  - 50 | 0.011 | 7.811 | 10.290 | .759 | 0.027
  - 100 | 0.003 | 7.861 | 10.400 | .756 | 0.025

### Empirical strategy — measures and samples
- Competition measure:
  - Hirschman-Herfindahl Index (HHI) of deposit concentration baseline proxy; under symmetric Cournot HHI = N^−2.
  - HHI conditioned on banks’ size and costs, market size, and demand for banking services.
- Risk measures:
  - Z-score: Z = (ROA + EA) / σ(ROA) (EA = equity/asset ratio); Z monotonically related to probability of failure.
  - Loan-loss proxies used to gauge BDN effect; deteriorating loan loss ratios predicted with stronger BDN effect as competition increases.
  - “Failed or near-failed banks” indicator in international panel: extreme low outliers of accounting capital plus current profits standardized by assets (FAIL5, FAIL10).
- Samples:
  - U.S. cross-section: 2,500 U.S. unit banks, cross-section June, 2003; mean (median) asset size $80.8 million ($50.2 million); county-level FRB deposit HHIs; 32 monopoly markets; top decile median HHI = 5733, bottom decile median HHI = 1244.
  - International panel: about 3,000+ banks in 134 non-industrialized countries, 1993–2004, Bankscope; bank-year observations ≈ 13,000–18,000 depending on variable availability; excludes U.S., EU, Switzerland, Nordic countries, Japan.

### Main empirical findings (U.S. and international samples)
- Three principal empirical results:
  1. Bank probability of failure (Z-score and international near-failure indicator) is positively and significantly related to concentration (HHI), ceteris paribus.
  2. Loan-to-asset (or loan-to-deposit) ratio is negatively and significantly associated with concentration (HHI).
  3. Loan-loss ratios deteriorate as competition increases; competition increases are associated with worse loan-loss measures — evidence of BDN effect.
- U.S. sample summary statistics:
  - Mean Z-score ≈ 36.
  - Average deposit HHI = 2856 (excluding savings and loans), = 2655 (including savings and loans).
  - Sample coverage: 46 of 50 states, 1280 counties used in clustering.
- Interpretation:
  - Increased competition (lower HHI) associated with lower bank failure probabilities and lower loan-to-asset ratios; loan-loss proxies worsen with competition, consistent with BDN effect.

### U.S. sample — key regression results and coefficients
- Regression 2.3: transformed loans-to-deposits ratio negatively and significantly related to both HHI measures at about the one percent confidence level.
- U.S. regressions (Table 2) — selected coefficients (robust OLS and clustered):
  - HHI0:
    - Z-score: -0.000425** [0.047]; -0.000425** [0.044]
    - LA_cox: -0.0000220** [0.014]; -0.0000220** [0.017]
  - LASSET:
    - Z-score: -4.272*** [0]; -4.272*** [5.77e-11]
    - LA_cox: 0.125*** [9.65e-09]; 0.125*** [0.000000017]
  - LABGRO:
    - Z-score: -11.75** [0.025]; -11.75** [0.021]
    - LA_cox: 0.395* [0.054]; 0.395* [0.052]
  - CTI:
    - Z-score: -1.853*** [0.00060]; -1.853*** [0.00070]
    - LA_cox: -0.0686*** [0.0033]; -0.0686*** [0.0031]
  - Observations: 2498; R-squared: Z-score 0.099; LA_cox 0.182.

### U.S. sample — loan loss measures (Table 5)
- Dependent variables:
  - LLM1 = Provision for loan and lease losses / Net loans and leases (June 2003).
  - LLM2 = Loan loss allowance / Net loans and leases (June 2003).
- HHI0 coefficients:
  - LLM1: 0.000000198** [0.021]
  - LLM2: 0.000000805*** [0.0094]
- Observations: 2498; R-squared: LLM1 0.032; LLM2 0.025.
- Interpretation: more concentration associated with greater loan losses as percentage of total loans — consistent with BDN effect.

### International sample — data, key statistics, and regressions
- Sample variation:
  - GDP per capita at PPP ranges from US$ 440 to US$ 21,460.
  - Median Z-score ≈ 19; wide range including negative values.
  - Median HHI ≈ 1900; range 391 to 10,000.
  - Correlation HHI and GDP per capita: -0.30.
  - Correlation HHI and asset size: -0.26.
- Summary statistics (Panel B):
  - Z-score (time series): Mean 44.21, Median 19.16, Std. Dev. 68.73, Min -40.5, Max 497.6.
  - LA: Mean 0.47, Median 0.48.
  - HHIA: Mean 2651, Median 1918, Std. Dev. 2354, Min 391, Max 10,000.
  - GDPPC: Mean 6021, Median 5930, Std. Dev. 3727, Min 440, Max 21,460.
- International regressions (Table 4) — selected coefficients:
  - L.HHIA:
    - Zscore (FFE): -12.245*** [0.00329]; (AB): -24.868** [0.0233]
    - LAcox (FFE): -0.294*** [0.00557]; (AB): -0.189** [0.0376]
  - L.LASSET: LAcox 0.177*** [0.0000882]
  - L.CTI and macro controls show mixed significance across specs.
  - Observations vary across specs: e.g. 15574, 12182, 8428; number of banks e.g. 3098, 2966, 2417.
- Interpretation: more concentrated markets (higher HHIA) associated with higher failure risk (lower Z-score) and lower lending ratios; dynamic specifications strengthen HHI effect on Z-score in some estimates.

### International loan-loss and proximate failure measures
- Loan-losses (Table 6):
  - Dependent variable NPL (impaired loans / gross loans); firm fixed effects clustered by country.
  - L.HHIA: 0.042** [0.0431]; 0.057* [0.0995]
  - L.LPOP: 0.291*** [0.000996]; L.GROWTH: -0.004*** [0.00289]
  - Observations: reported 73,966 and 171; number of firms: 1,847 and 1,731.
  - Interpretation: greater concentration associated with greater non-performing loans.
- Proximate failure indicators (Table 7):
  - Dependent variables FAIL5 and FAIL10 (5th and 10th percentiles of (profits + equity)/assets).
  - L.HHIA coefficients:
    - FAIL5 pooled: 1.366*** [0.00000259]; FAIL5 random effects: 1.500*** [0.000439]
    - FAIL10 pooled: 1.072*** [0.00000385]; FAIL10 random effects: 1.829*** [0.00000125]
  - L.LASSET positive and highly significant across specs (e.g. 0.454*** [0]).
  - Observations: 14703; number of firms: 3230.
  - Interpretation: higher concentration associated with greater incidence of proximate failures.

### Synthesis of theoretical and empirical results
- Theoretical:
  - Competition can increase or decrease bank failure risk depending on BDN effect strength.
  - If no BDN effect, competition increases failure risk; if strong BDN effect, competition can reduce failure risk.
  - Loan/deposit ratio response to competition is theoretically ambiguous.
- Empirical (U.S. and international):
  - More competition (lower HHI) ceteris paribus associated with lower probability of bank failure (higher Z-score) and lower loan-to-asset ratios.
  - Loan-loss measures rise with competition (loan portfolio quality worsens), consistent with BDN effect.
  - Competition is positively and significantly associated with loan/deposit (or loans-to-assets) ratios in tests reported.
- Two main takeaways:
  - No compelling theoretical or robust empirical evidence that banking stability decreases with competition; empirical work here suggests more competition is associated with lower risk of failure.
  - Competition is positively and significantly associated with banks’ willingness to lend (loan/deposit ratio), an important policy consideration.

*Source: _wp09143 - 7. International Sample: Proxy Measures of (near) Failure (chapter/section text).*

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

### _wp09143 - References................................................................................................................................25

### Tables listed in the References section
- 1. U.S. Sample .........................................................................................................................30
- 2. U.S. Sample Regressions .....................................................................................................31
- 3. International Sample ............................................................................................................32
- 4. International Sample Regressions........................................................................................33
- 5. U.S. Sample Loan Loss Measures .......................................................................................34
- 6. International Sample Loan Loss Measures ..........................................................................35

*Source: _wp09143 - References..............................................................................................................*

### 7. International Sample: Proxy Measures of (near) Failure .....................................................36

### 7. International Sample: Proxy Measures of (near) Failure

### Introduction and research objective
- Examines how bank competition affects risk of bank failure when banks choose portfolios of risky loans and risk-free assets simultaneously.
- Revisits conventional wisdom that more competition increases instability by incorporating loan-market competition a la Stiglitz-Weiss and banks’ holdings of risk-free assets.
- Central mechanism: the “BDN effect” — higher loan rates reduce entrepreneurs’ effort (z), increasing borrowers’ default risk and thereby affecting bank failure probabilities.

### Theoretical model — structure and key mechanisms
- Two-date economy (date 0 investment, date 1 consumption); three agent classes: entrepreneurs, depositors, banks; all agents risk-neutral.
- Entrepreneurs operate a project of normalized size 1 with output yz + z (y random on [0, A], z deterministic from effort); effort cost c(z) strictly increasing, convex.
- Entrepreneurs borrow only from banks; banks offer simple debt contracts: bank receives L R if entrepreneur does not default (default when L(yz) + ? < R — model defines default as L yz + R condition).
- Entrepreneur optimal effort z solves (equation labels preserved in text):
  - Expected profit written as expression (1) and first-order condition (2).
  - Best-response function z = z_L(R) with dz/dR < 0 (equation (3)): higher loan rate ⇒ lower entrepreneur effort (the BDN effect).
- Banks collect deposits d and invest in riskless asset (yield r per unit invested) and risky loans l; balance sheet: l + x = d (with x invested in risk-free asset).
- Bank failure threshold Y* defined so that profits = 0 at Y*; probability of failure = F(Y*).
- Cournot competition among N banks; symmetric interior equilibrium characterized by system including:
  - Lending-rate condition (13): lending rate equals r + risk premium + market-power rents on loan side.
  - Deposit-rate condition (14): deposit rate equals r + market-power rents on deposit side.
  - Bank failure threshold (15): Y* = function of r, R_D, L, z, etc.
- Comparative statics with respect to number of banks N:
  - Total deposits increase with N (equation (16)).
  - Total loans increase with N (equations (17)–(19)); hence dL/dN > 0.
  - Change in bank failure threshold Y* with N decomposes into deposit and loan channels (equation (20)): dY*/dN = (∂Y*/∂D) dD/dN + (∂Y*/∂L) dL/dN.
  - If BDN effect weak (∂Y*/∂L > 0), increased competition (higher N) unambiguously increases risk (dF(Y*)/dN > 0).
  - If BDN effect strong (∂Y*/∂L < 0 and sufficiently large in magnitude), increased competition can decrease risk (dF(Y*)/dN < 0).
  - There exists a threshold N beyond which the BDN effect becomes strong: as N → ∞, L Y* z → − and BDN effect dominates.

### Numerical examples (linear demand/supply, uniform return)
- Two calibrated panels illustrate possible outcomes:
  - Panel A: No BDN effect — as N increases, probability of bank failure increases; loans/deposits ratio first declines then increases.
  - Panel B: Strong BDN effect — as N increases, probability of bank failure declines monotonically; loans/deposits ratio exhibits U-shaped relationship with N.
- Table values (columns: Number of banks | profits per bank | total loans | total deposits | loans/deposits | Probability of bank failure [F(Y*)])
  - Panel A: No BDN effect
    - 2 | 3.953 | 5.367 | 7.000 | .766 | 0.059
    - 3 | 2.255 | 5.977 | 7.880 | .758 | 0.070
    - 5 | 1.023 | 6.598 | 8.750 | .753 | 0.082
    - 10 | 0.315 | 7.169 | 9.550 | .750 | 0.092
    - 20 | 0.090 | 7.491 | 10.000 | .749 | 0.098
    - 30 | 0.043 | 7.611 | 10.160 | .749 | 0.100
    - 50 | 0.016 | 7.721 | 10.290 | .750 | 0.102
    - 100 | 0.003 | 7.841 | 10.400 | .754 | 0.104
  - Panel B: Strong BDN effect
    - 2 | 4.181 | 5.667 | 7.000 | .808 | 0.077
    - 3 | 2.503 | 5.957 | 7.880 | .755 | 0.067
    - 5 | 1.515 | 5.508 | 8.750 | .629 | 0.062
    - 10 | 0.672 | 5.669 | 9.550 | .593 | 0.050
    - 20 | 0.293 | 5.941 | 10.000 | .594 | 0.041
    - 30 | 0.142 | 6.661 | 10.160 | .655 | 0.034
    - 50 | 0.011 | 7.811 | 10.290 | .759 | 0.027
    - 100 | 0.003 | 7.861 | 10.400 | .756 | 0.025

### Empirical strategy — measures and samples
- Key empirical contributions:
  - Uses theory-guided measures of competition and risk.
  - Jointly assesses competition’s effects on bank risk and asset allocation.
  - Employs two distinct samples to test robustness: a U.S. cross-section and an international panel.
- Measurement of competition:
  - Uses Hirschman-Herfindahl Index (HHI) of deposit concentration as the baseline proxy for market power under symmetric Cournot assumptions (HHI = Σ market shares^2, in symmetric case given by N^−2).
  - Conditions HHI on measures of banks’ size and costs, market size, and demand for banking services to capture heterogeneity that can affect HHI independently of market power rents.
- Measurement of risk:
  - Z-score: Z = (ROA + EA) / σ(ROA), where EA = equity/asset ratio, ROA = return on assets, σ(ROA) = standard deviation of ROA; Z monotonically related to probability of failure.
  - Loan-loss proxies (loan loss variables) used to gauge the BDN effect empirically: as competition increases, loan loss ratios are predicted to deteriorate if BDN effect present.
  - “Failed or near-failed banks” indicator in international panel: identifies extreme low outliers of accounting capital plus current profits standardized by assets, used because direct failure observations are obscured by interventions and reorganizations.
- Samples:
  - U.S. cross-section: 2,500 U.S. banks (unit banks operating in a single rural county), cross-section June, 2003; mean (median) asset size $80.8 million ($50.2 million); FRB deposit HHIs available at county level; sample includes 32 monopoly markets; when sorted by HHI, top decile median HHI = 5733, bottom decile median HHI = 1244.
  - International panel: about 3,000+ banks in 134 non-industrialized countries, 1993–2004, from Bankscope (Fitch-IBCA); bank-year observations range from about 13,000 to 18,000 depending on variable availability; excludes the U.S., EU, Switzerland, Nordic countries, and Japan to mitigate market-definition error.
- Empirical identification and controls:
  - For U.S. sample, regression specification: X_ij = α + β HHI_j + γ Y_j + δ Z_ij + ε_ij, where X_ij is bank i’s Z-score or loan-to-asset ratio in county j, HHI_j is county deposit HHI, Y_j county controls, Z_ij bank controls.
  - Controls include LASSET (ln total bank assets), CTI (non-interest operating costs / total income), TOTALY (median per-capita county income × population), LABGRO (labor force growth), UNEM (unemployment), FARM (rural farm population ratio), and state fixed effects; county-level clustering used in standard errors (1280 counties).
  - Loan-to-deposit ratio transformed via Cox transform to map unit interval to real line: x_cox = ln(x/(1−x)).

### Main empirical findings (U.S. and international samples)
- Three principal empirical results reported:
  1. Bank probability of failure (measured two ways: Z-score and the international near-failure indicator) is positively and significantly related to concentration (HHI), ceteris paribus.
  2. Loan-to-asset (or loan-to-deposit) ratio is negatively and significantly associated with concentration (HHI).
  3. Loan-loss ratios (proxy for borrowers’ default risk / BDN channel) deteriorate as competition increases; across both U.S. and international samples, competition increases are associated with worse loan-loss measures — implying the BDN effect is present in the data.
- U.S. sample summary statistics cited:
  - Mean Z-score ≈ 36.
  - Average deposit HHI = 2856 (excluding savings and loans), = 2655 (including savings and loans).
  - Sample coverage: 46 of 50 states, 1280 counties used in clustering.
- Interpretation:
  - Empirical evidence indicates that increased competition (lower HHI) is associated with lower bank failure probabilities (higher stability) together with lower loan-to-asset ratios and deteriorating loan-loss measures as competition increases.
  - Theory implies that the observed decrease in bank failure risk with more competition requires the presence of a sufficiently strong BDN effect; empirical deterioration in loan-loss proxies with competition supports the presence of the BDN effect in the data.

### Implications and synthesis
- Theoretical implication: Competition’s effect on bank stability is ambiguous a priori — it increases risk when the BDN effect is weak, but can reduce risk when the BDN effect is strong; competition also alters banks’ asset allocation between loans and risk-free assets, with welfare consequences.
- Empirical implication: Across both U.S. and international evidence presented, higher concentration (higher HHI) is associated with higher bank failure probability and higher loan-to-asset ratios; conversely, more competition is associated with lower bank failure risk and lower loan-to-asset ratios, but loan portfolio quality worsens with competition, consistent with a BDN effect acting in the data.
- Quantitative sample details relevant for interpretation:
  - U.S. cross-section: 2,500 banks (June, 2003); mean asset size $80.8 million; median $50.2 million; wide HHI dispersion (top decile median 5733, bottom decile median 1244); 32 monopoly markets present in sample.
  - International panel: 3,000+ banks in 134 countries; bank-year observations ≈ 13,000–18,000 for 1993–2004.

*Source: _wp09143 - 7. International Sample: Proxy Measures of (near) Failure (chapter/section text).*

### 2.3 shows that the (transformed) ratio of loans to deposits is negatively and significantly

### _wp09143 - 2.3 shows that the (transformed) ratio of loans to deposits is negatively and significantly

### U.S. sample: loan-to-deposit ratio and local market competition
- Regression 2.3 shows that the (transformed) ratio of loans to deposits is negatively and significantly related to both HHI measures at about the one percent confidence level.
- The (transformed) loan-to-deposit ratio is:
  - positively and significant related to:
    - growth rate in county labor force LABGRO
    - the size of the market TOTALLY
    - bank size LASSET
  - negatively and significantly related to:
    - bank operating costs CTI
- Regression 2.4 adds the county clustering procedure; this has little effect on confidence intervals.
- Summary interpretation for the U.S. sample:
  - More competitive bank markets are associated with greater risk of failure and a higher ratio of loans to assets.
  - Both findings are robust and consistent with the theoretical model when the BDN effect is present and sufficiently strong.

### International sample: data, measures, and key statistics
- Sample variation:
  - GDP per capita at PPP ranges from US$ 440 to US$ 21,460.
  - Median Z-score is about 19; the Z-score exhibits a wide range including negative values and values close to 0.
  - Median HHI is about 1900 and ranges from 391 to the monopoly value of 10,000.
- Correlations noted:
  - Correlation between HHI and GDP per capita: -0.30 (negative and significant).
  - Correlation between HHI and asset size: -0.26 (negative and significant).
  - Implication: relatively richer countries have less concentrated banking systems; size of banking market (GDP per capita) related to concentration.
- Z-score definition used:
  - Zt = (ROAt + EAt) / σ(ROAt), where ROA is return on average assets, EA is equity-to-assets ratio, and σ(ROA) is the standard deviation computed as in the source.
  - Time-averaged Z-score series correlates about 0.89 with the previously computed Z-score.
- Regression framework:
  - Panel regressions estimated with firm fixed effects and lagged independent variables.
  - Country-specific controls Yt: real GDP growth, inflation, GDP per capita, log population, exchange rate to the US dollar.
  - Firm controls Zij: LASSET (log total bank assets) and CTI (non-interest operating costs/total income).
  - Two regression types:
    - Static fixed effect panel (ρ = 0), standard errors clustered by country; specifications with and without firm controls.
    - Dynamic panel (one lag of dependent variable) using Arellano and Bond (1991) GMM; instruments are lags t-2, t-3, etc.; one-step estimator reported; Sargan tests based on two-step estimator.
- Key empirical findings (Table 4 summarized):
  - For both the Z-score and the (Cox-transformed) loans-to-assets ratio, the sign associated with the HHI is negative and significant in both fixed effects and dynamic panel regressions.
  - In dynamic panel regressions with Z-score as dependent variable (4.3), the absolute size of the HHI coefficient doubles relative to static estimates.
  - In dynamic regressions with loans-to-assets as dependent variable (4.6), the size of the HHI coefficient declines.
  - Larger banks exhibit higher insolvency risk: coefficient on bank size is negative and highly significant.
- Interpretation for international sample:
  - Similar to the U.S. sample, more concentrated bank markets are ceteris paribus associated with higher risk of bank failure and lower loan-to-asset ratios, consistent with the model when the BDN effect is sufficiently strong.

### Alternative risk measures: loan loss measures and actual failures
- General caveats:
  - Loan loss measures capture default risk in the loan portfolio but not necessarily overall bank failure risk (asset allocation to risk-free assets matters).
  - Loan loss indicators are of independent interest to the extent they correlate with borrower failure probability.
- U.S. sample loan-loss measures:
  - Two measures used: loan loss provisions (income-statement expense reflecting expected future write-offs) and loan loss allowance (historical experience); both scaled by net loans and leases.
  - Table 5 (four regressions: robust OLS and robust OLS with county clustering) includes full set of controls.
  - In all four regressions, the coefficient on the HHI index is positive and significant at usual confidence levels.
  - Interpretation: more concentration in US unit banking markets is ceteris paribus associated with greater loan losses as a percentage of total loans — consistent with a BDN effect (as concentration increases and banks raise loan rates, borrower default risk increases).
- International loan-loss measures:
  - Fixed effects regressions using impaired loans to gross loans (Bankscope definitions) reported in Table 6.
  - The sign associated with HHI is positive and significant both without and with firm controls.
  - Interpretation: for the international sample, more concentration is ceteris paribus associated with greater loan losses, consistent with U.S. findings.
- Actual failures (or near failures) as dependent variable:
  - Direct (0,1) failure indicators are preferred but rare and hard to interpret (failures uncommon; rescues obscure official failure lists).
  - U.S. sample: tests infeasible due to uniformly good health in 2003 (out of 2500 banks only five had (equity + current profits)/assets < five percent; no sample bank had negative equity).
  - International sample: two proxy failure measures constructed, FAIL5 and FAIL10, corresponding to the 5th and 10th percentiles of the distribution of (profits + equity)/assets across time and countries.
  - Table 7: two Logit regressions (pooled and random effects) using the same explanatory variables as prior regressions.
    - In all regressions, the coefficient on HHI is positive and significant, as are coefficients on bank size and costs.
    - Conclusion: more concentration is ceteris paribus associated with a greater incidence of bank failures.

### Main conclusions and policy-relevant implications
- Theoretical summary:
  - Increased competition can either increase or decrease bank failure risk; the direction depends on model specification and the presence and strength of the BDN effect.
  - If no BDN effect is present, increased competition will always increase risk of bank failure.
  - If a BDN effect is present and sufficiently strong, increased competition can decrease risk of bank failure.
  - The loan/deposit ratio may increase or decrease with competition in theory; the direction is ambiguous.
- Empirical summary (two samples, multiple specifications):
  - Relationship between competition and bank risk of failure:
    - Negative relationship found: more competition (lower HHI) is ceteris paribus associated with a lower probability of bank failure (higher Z-score).
    - International sample yields similar results using (0,1) near-failure indicators.
  - Loan loss measures:
    - Loan losses are positively and significantly related to HHI in both samples (more concentration → greater loan losses).
    - Two interpretations:
      - If loan losses proxy overall bank risk, findings align with increased competition associated with lower bank failure risk.
      - If loan losses proxy borrower default probability, findings are consistent with a BDN effect (more concentration → higher loan rates → higher borrower default).
  - Asset composition:
    - Tests with both samples find a positive and highly significant relationship between competition and the loans-to-assets (or loan/deposit) ratio: increased competition increases banks’ willingness to lend.
- Two main takeaways:
  - There are neither compelling theoretical arguments nor robust empirical evidence that banking stability decreases with the degree of competition. Theoretical predictions depend on model specification and may be reversed; empirical work here suggests more competition is associated with lower risk of failure.
  - Empirically, competition is positively and significantly associated with the loan/deposit ratio in all tests performed. This relation adds a dimension for policy makers to consider when evaluating costs and benefits of banking competition; if these results hold, the policy implication would appear to favor more competition in banking.

*Source: _wp09143 - 2.3 shows that the (transformed) ratio of loans to deposits is negatively and significantly*

### Chapter 17 in

### Chapter 17 in Handbook of Industrial Organization, Vol. II

### Literature cited
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### U.S. sample — variable definitions (Panel A)
- Z-score: (rate of return on assets + ratio of equity to assets) ÷ standard deviation of the rate of return on assets, quarterly data
- LA: Total loans ÷ total assets, quarterly average over 3 years
- LASSET: Natural logarithm of bank assets
- ROA: (defined in context above)
- CTI: Ratio of non-interest expense to interest income + non-interest income of banks, quarterly average over 3 years
- Market structure:
  - HHI0: Hirschmann-Herfindahl Index computed with banks only
  - HHI100: Hirschmann-Herfindahl Index computed with banks and savings and loan associations
- County controls:
  - LABGRO: Percentage growth in labor force 1999 – 2003
  - UNEM: Unemployment rate, 2003
  - FARM: Ratio of agricultural population ÷ total population in 2003
  - TOTALY: Median income in 1999 * number of households. $million.

### U.S. sample — summary statistics (Panel B)
- LABGR: Mean 0.0062, Std. Dev. 0.0671, Min -0.2420, Max 0.2718
- UNEM: Mean 5.8261, Std. Dev. 2.4747, Min 1.4000, Max 21.8000
- FARM: Mean 0.0706, Std. Dev. 0.0563, Min 0.0000, Max 0.4086
- LASSET: Mean 10.8132, Std. Dev. 0.8095, Min 7.6917, Max 16.7759
- CTI: Mean 0.4630, Std. Dev. 0.9072, Min 0.0247, Max 29.1276
- TOTALY: Mean 3740.0, Std. Dev. 4100.0, Min 611.7, Max 6780.0
- HHI0: Mean 2855.67, Std. Dev. 1577.69, Min 881.67, Max 10000.00
- HHI100: Mean 2655.90, Std. Dev. 1540.73, Min 719.65, Max 10000.00
- Z-score: Mean 35.5870, Std. Dev. 16.7554, Min 3.0910, Max 261.8150
- LA: Mean 0.5715, Std. Dev. 0.1465, Min 0.0000, Max 0.9556

### U.S. sample regressions — key coefficient estimates (Table 2)
- Dependent variables: Z-score and LA_cox (Cox transform of LA). Columns 2.1 and 2.3: robust OLS. Columns 2.2 and 2.4: robust OLS with clustering on counties.
- HHI0:
  - Z-score columns: -0.000425** [0.047]; -0.000425** [0.044]
  - LA_cox columns: -0.0000220** [0.014]; -0.0000220** [0.017]
- LASSET:
  - Z-score: -4.272*** [0]; -4.272*** [5.77e-11]
  - LA_cox: 0.125*** [9.65e-09]; 0.125*** [0.000000017]
- LABGRO:
  - Z-score: -11.75** [0.025]; -11.75** [0.021]
  - LA_cox: 0.395* [0.054]; 0.395* [0.052]
- UNEM:
  - Z-score: -0.397*** [0.0094]; -0.397** [0.011]
  - LA_cox: -0.00303 [0.63]; -0.00303 [0.63]
- FARM:
  - Z-score: 5.495 [0.51]; 5.495 [0.54]
  - LA_cox: 0.444 [0.17]; 0.444 [0.18]
- CTI:
  - Z-score: -1.853*** [0.00060]; -1.853*** [0.00070]
  - LA_cox: -0.0686*** [0.0033]; -0.0686*** [0.0031]
- TOTALLY:
  - Z-score: -9.63E-10 [0.40]; -9.63E-10 [0.41]
  - LA_cox: 1.06e-10*** [0.0016]; 1.06e-10*** [0.0022]
- Constant:
  - Z-score: 86.20*** [0]; 86.20*** [0]
  - LA_cox: -1.007*** [0.000052]; -1.007*** [0.000053]
- Observations: 2498 (for all columns)
- R-squared: Z-score regressions 0.099; LA_cox regressions 0.182
- Alternative regressions reported with HHI100 show:
  - HHI100: -0.000418* [0.059]; -0.000418* [0.053] for Z-score
  - HHI100: -0.0000234** [0.012]; -0.0000234** [0.017] for LA_cox

### International sample — data description (Table 3)
- Panel data: about 3,000+ banks in 134 countries excluding major developed countries, period 1993 to 2004.
- Bank variables:
  - Z-score(t) = (ROA(t) + EA(t)) / σ(ROA)t (definitions shown)
  - LA(t) / LA.cox(t): Gross loan-to-asset ratio / Cox transform
  - LASSET(t): Log of total assets (in US $)
  - CTI(t): Operating cost to income ratio
- Market structure:
  - HHIA(t): Hirschmann-Herfindahl Indexes based on accounting assets
- Macroeconomic variables:
  - GDPPC(t): Per-capita GDP at PPP
  - LPOP(t): Log Population
  - GROWTH(t): Real GDP Growth
  - INFL(t): Average CPI Inflation Rate
  - ER(t): Domestic currency/US$ exchange rate

### International sample — summary statistics (Panel B)
- Z-score (time series): Mean 44.21, Median 19.16, Standard Deviation 68.73, Minimum -40.5, Maximum 497.6
- LA: Mean 0.47, Median 0.48, Std. Dev. 0.22, Min 0.05, Max 0.92
- LASSET: Mean 12.91, Median 12.5, Std. Dev. 2.03, Min 3.8, Max 20.4
- CTI: Mean 69.96, Median 1.76, Std. Dev. 0.68, Min 6.7, Max 96.3
- HHIA: Mean 2651, Median 1918, Std. Dev. 2354, Min 391, Max 10,000
- GDPPC: Mean 6021, Median 5930, Std. Dev. 3727, Min 440, Max 21,460
- GROWTH: Mean 3.85, Median 2.97, Std. Dev. 5.79, Min -12.6, Max 12.8
- INFL: Mean 33.1, Median 8.4, Std. Dev. 13.7, Min -11.5, Max 527.2

### International sample regressions — key coefficient estimates (Table 4)
- Dependent variables: Zscore and LAcox. Estimation methods: FFE (firm fixed effects), AB (Arellano and Bond one-step GMM). Robust p-values in brackets; * 10%, ** 5%, *** 1%.
- L.HHIA:
  - Zscore: -12.245*** [0.00329] (FFE), -14.078* [0.0583] (FFE), -24.868** [0.0233] (AB)
  - LAcox: -0.294*** [0.00557] (FFE), -0.311* [0.0635] (FFE), -0.189** [0.0376] (AB)
- L.GDPPC:
  - Zscore: -0.001 [0.296], -0.002 [0.140], -0.006*** [0.00243]
  - LAcox: 0.00 [0.353], -0.000*** [0.663], 0.000*** [0.000170]
- L.LPOP:
  - Zscore: 12.561 [0.500], -12.638 [0.542], -15.946 [0.665]
  - LAcox: -1.147*** [0.00553], -1.774*** [0.0000802], -1.259*** [6.50e-08]
- L.GROWTH:
  - Zscore: -0.099 [0.420], 0.007 [0.962], 0.143 [0.506]
  - LAcox: 0.022*** [0.0000108], 0.020*** [0.00000410], 0.005*** [0.00534]
- L.INFL: generally not significant (p-values reported)
- L.ER: significant negative effects on Zscore and LAcox; p-values e.g. [0.000198], [3.89e-09], [0.000125], [0]
- L.LASSET:
  - Zscore: -3.558** [0.0119], -0.988 [0.669], 0.161*** [0.000132] (varies by specification)
  - LAcox: 0.177*** [0.0000882]
- L.CTI: mixed signs and significance across specifications; examples include 0.028** [0.0180] and -0.001*** [0.000169]
- L.Zscore and L.LAcox included in AB specifications:
  - L.Zscore: 0.061*** [0.00152]
  - L.LAcox: 0.573*** [0]
- Constant varies by specification (examples: 9.921 [0.871], 43.353** [0.0372], 143.574 [0.238])
- Observations: ranges reported across specifications, e.g. 15574, 12182, 8428, 6476, 11312, 9259, 615
- Number of banks: multiple counts reported, e.g. 3098, 2966, 2417, 3326, 3037, 2593
- Diagnostic statistics:
  - M1 (p-value) 0.00 for reported AB specs
  - M2 (p-value) reported as 0.27 and 0.73 for some AB specs
  - Sargan Test (p-value) 0.39 and 0.43 for two-step versions

### U.S. sample — loan loss measures (Table 5)
- Dependent variables:
  - LLM1 = Provision for loan and lease losses / Net loans and leases in June 2003
  - LLM2 = Loan loss allowance / Net loans and leases in June 2003
- Key coefficients (Columns .1 and .3: robust OLS; .2 and .4: robust OLS clustered on counties):
- HHI0:
  - LLM1: 0.000000198** [0.021]
  - LLM2: 0.000000805*** [0.0094]
- LASSET:
  - LLM1: 0.000659** [0.016]
  - LLM2: -0.00131* [0.064]
- CTI:
  - LLM1: 0.000744*** [0.000017]
  - LLM2: -0.0002490 [0.10]
- TOTALLY: reported as 0-0*** with p-values [0.37] and [0.00069] across columns
- Constant:
  - LLM1: -0.00645** [0.038]
  - LLM2: 0.0305*** [0.00021]
- Observations: 2498
- R-squared: LLM1 0.032; LLM2 0.025
- Regressions with HHI100 show similar positive small coefficients:
  - HHI100 LLM1: 0.000000225** [0.012]
  - HHI100 LLM2: 0.000000902*** [0.0069]

### International sample — loan loss measures (Table 6)
- Dependent variable: NPL = ratio of impaired (non-performing) loans to gross loans
- Estimation: firm fixed effects, standard errors clustered by country. Robust p-values in brackets.
- L.HHIA: 0.042** [0.0431]; 0.057* [0.0995]
- L.GDPPC: 0.00 [0.987]; 0.00 [0.861]
- L.LPOP: 0.291*** [0.000996]; 0.233*** [0.00532]
- L.GROWTH: -0.004*** [0.00289]; -0.004*** [0.00256]
- L.ER: -0.000*** [0]; 0.000*** [0.0000114]
- L.LA: 0.027 [0.554] (not significant)
- L.CTI: 0.000*** [0.00818]
- Constant: -0.837*** [0.00262]; -0.694*** [0.00762]
- Observations: 73,966 and 171 (two reported counts)
- Number of firms: 1,847 and 1,731 (two reported counts)

### International sample — proximate failure measures (Table 7)
- Dependent variables: FAIL5 and FAIL10 are the 5th and 10th percentile of the distribution (sum of profits and equity capital) across time and countries.
- Estimation: pooled Logit and random effects Logit. Robust p-values in brackets.
- L.HHIA:
  - FAIL5 pooled: 1.366*** [0.00000259]
  - FAIL5 random effects: 1.500*** [0.000439]
  - FAIL10 pooled: 1.072*** [0.00000385]
  - FAIL10 random effects: 1.829*** [0.00000125]
- L.GDPPC:
  - Negative and significant at varying levels, e.g. -0.000*** [0.00160] (FAIL5 pooled)
- L.LPOP:
  - FAIL5 pooled: -0.087*** [0.00969]
  - FAIL5 random effects: -0.083 [0.108]
- L.GROWTH:
  - FAIL5 pooled: -0.030*** [0.01000]
  - FAIL5 random effects: -0.041*** [0.000651]
  - FAIL10 random effects: -0.020* [0.0535]
- L.ER: small negative significant coefficients in some specifications, e.g. -0.000* [0.0998], -0.000** [0.0212]
- L.LASSET:
  - Positive and highly significant across specifications, e.g. 0.454*** [0], 0.546*** [0], 0.464*** [0], 0.668*** [0]
- L.CTI: positive and significant, e.g. 0.004*** [0], 0.003*** [0.000000308]
- Constant terms: large negative highly significant, e.g. -9.068*** [0], -11.787*** [0]
- Observations: 14703 across reported panels
- Number of firms: 3230 repeated across panels

*Source: _wp09143 - Chapter 17 in (PDF).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09143.pdf_