## wpiea2019265-print-pdf

## Source details

**Canonical URL:** [wpiea2019265-print-pdf](https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019265-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2019/wpiea2019265-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2019/wpiea2019265-print-pdf.pdf.json)

---

### Introduction and context
- The global financial crisis (GFC) demonstrated that capital is a bank’s strongest defense against losses from adverse asset-value movements.
- Policymakers strengthened capital requirements culminating in the adoption of the Basel III regulatory framework in 2010.
- Key Basel III numeric requirements described:
  - Common Equity Tier 1 ratio (CET1): 4.5 percent.
  - Minimum Tier 1 capital: 6 percent of RWA.
  - Total capital (Tier 1 plus Tier 2): at least 8 percent of RWA.
  - Capital Conservation Buffer (CET1 during good times): 2.5 percent of RWA.
  - Additional countercyclical buffers: up to 2.5 percent of RWA.
  - Minimum leverage ratio (Tier 1 capital to total assets): 3 percent.

### Empirical question and strategy
- Central research question:
  - Does higher bank capital reduce the cost of equity, consistent with the theoretical prediction that equity becomes cheaper as leverage decreases?
- Approach:
  - Use an ex-ante measure of cost of equity implied by stock prices and analysts’ earnings forecasts (COE).
  - Direct empirical specification regressing cost of equity on capital ratios and bank- and country-level controls.
  - Cross-country, bank-level sample covering 62 countries over 1991–2017 (more than 16,000 bank-year observations).

### Key empirical findings and statistics
- Baseline estimates:
  - A one percentage point increase in the equity-to-assets ratio reduces the cost of equity by about 18 basis points.
  - At very low bank capital levels (first quartile of the sample), a one percentage point increase in the equity-to-assets ratio reduces cost of equity by 79 basis points.
- Additional findings:
  - Investors value sheer equity capital most; other components of Tier 1 capital have very slight effects and Tier 2 capital effects are insignificant.
  - The magnitude of capital’s impact on cost of equity is larger for banks with lower capital ratios.
  - Capital has a stronger effect on banks’ cost of equity in developing countries than in advanced countries.
- Comparative empirical references:
  - Kashyap et al. (2010) estimate that each 1 percentage point increase in capital raises a bank’s weighted average cost of capital by about 2.5 basis points.
  - Admati and Hellwig (2013) argue for minimum equity-to-assets ratios between 20 and 30 percent.

### Policy implications and recommendations
- Empirical evidence indicates that increasing bank equity reduces banks’ cost of equity, supporting the use of the Modigliani-Miller framework to quantify funding-cost effects of higher capital requirements.
- If cost of debt also declines with higher capital, the effect of higher capital requirements on weighted average cost of capital—and thus on lending rates—could be far lower than suggested by critics.
- Higher capital requirements can therefore come at little or no cost to borrowers while delivering financial-stability benefits.
- Policy caution: actions taken by some countries to loosen bank capital regulations may be ill advised and should be reconsidered in light of these findings.

### Data and sample
- Sample size and coverage:
  - More than 16,000 bank-year observations for 62 countries spanning 1991–2017.
- Data sources include:
  - DataStream (bank equities), I/B/E/S (analyst forecasts), Thomson Reuters and Bloomberg (bank financial statements), International Financial Statistics, World Development Indicators, Financial Structure database.
- Observations vary by country, year, and variable due to data availability.

### Implied cost of equity (dependent variable)
- COE constructed as the average estimate from four models: Claus and Thomas (2001) (rCT), Gebhardt et al. (2001) (rGLS), Easton (2004) (rES), and Ohlson and Juettner-Nauroth (2005) (rOJN).
- Estimation notes:
  - rOJN estimated in closed form.
  - rCT, rGLS, rES require numerical techniques with solutions bounded between 0 and 100 percent.
- Forecast inputs:
  - Positive one-, two-, and three-year-ahead mean forecasted earnings per share (FCFFFt+j) and long-term growth rate forecasts from I/B/E/S.
  - Missing or negative FCFFFt+j substituted with historical earnings per share estimated from beginning-of-year book value per share and three-year median return on equity by year, country, and industry.
  - Observations discarded when none of the implied COE estimates converge or are undefined.

### Bank capital measures (main explanatory variables)
- EQUITY: ratio of total equity to total assets (financial leverage).
- TIER1: Tier 1 capital divided by risk-weighted assets (regulatory Tier 1 ratio).
- TOTCAP: (Tier 1 + Tier 2) divided by risk-weighted assets (total capital ratio).
- Tier composition:
  - Tier 1 composition: common stock, retained earnings, perpetual noncumulative preferred stock.
  - Tier 2 composition: hybrid capital, subordinated debt, revaluation reserves, loan loss reserves.
- Authors note limitations of risk-weighted ratios and justify using EQUITY as a primary investor-relevant measure.

### Control variables
- Bank-level controls:
  - PROV: loan loss provisions to total loans.
  - INEFF: salaries and benefits to total assets.
  - ROA: return on assets.
  - DEP: deposits to total assets.
  - SIZE: natural logarithm of total assets.
  - RSTD: lagged standard deviation of daily returns over one year.
  - BETA: lagged beta.
  - MTOV: lagged one-year turnover volume.
  - NPL: lagged non-performing loans to total loans.
  - BTM: book-to-market ratio.
- Country-level controls:
  - LNGDPC: natural logarithm of GDP per capita.
  - INFL: expected inflation rate proxied by annual realized inflation.
  - MCAP: stock market capitalization to GDP.

### Summary statistics and descriptive patterns
- Panel C (full sample) means, medians, standard deviations, and N:
  - COE mean 0.121; P50 0.108; STD 0.058; N 16,776.
  - EQUITY mean 0.087; P50 0.083; STD 0.039; N 16,776.
  - TIER1 mean 0.130; P50 0.118; STD 0.078; N 8,998.
  - TOTCAP mean 0.153; P50 0.139; STD 0.077; N 8,754.
  - SIZE mean 2.246; P50 1.979; STD 2.051; N 16,776.
  - PROV mean 0.764; P50 0.440; STD 1.028; N 16,776.
  - INEFF mean 0.013; P50 0.013; STD 0.006; N 16,776.
  - ROA mean 0.010; P50 0.011; STD 0.029; N 16,776.
  - DEP mean 0.668; P50 0.713; STD 0.173; N 16,776.
  - LNGDPC mean 10.054; P50 10.403; STD 1.046; N 16,776.
  - INFL mean 0.032; P50 0.027; STD 0.034; N 16,776.
  - MCAP mean 0.955; P50 1.070; STD 0.493; N 16,776.
- Cross-country medians (Panel A highlights):
  - Minimum COE: Australia 9.8 percent (0.098).
  - Maximum COE: Lebanon 25.1 percent (0.251).
  - EQUITY range: Belgium minimum 3.1 percent (0.031) to Serbia maximum 15.7 percent (0.157).
  - TIER1 range: Italy minimum 7.4 percent (0.074) to Serbia maximum 18 percent (0.180).
  - TOTCAP range: Italy minimum 11.3 percent (0.113) to Nigeria maximum 20.4 percent (0.204).
- Time series medians (Panel B):
  - COE fell cumulatively about 3 percentage points between 1991 and 2017 (from 12.9 percent to 10 percent).
  - EQUITY rose cumulatively 4 percentage points between 1991 and 2017 (from 6 percent to 10 percent).
  - EQUITY increased from 8.3 percent in 2007–2008 to 10 percent in 2017.
  - TIER1 and TOTCAP increased substantially over the 27-year sample, gains split roughly evenly pre- and post-GFC.
- Correlations (Panel D):
  - COE negatively correlated with capital measures:
    - EQUITY (-0.090).
    - TIER1 (-0.081).
    - TOTCAP (-0.062).
  - Correlations significant at the 1% level.

### Graphical evidence
- Scatterplots (Figure 2) show clear negative associations between COE and each capital measure (EQUITY, TIER1, TOTCAP) in the full sample.
- Selected-country scatterplots (Germany, U.K., U.S., India, Malaysia, Thailand) display similar negative associations.

### Main multivariate results
- Baseline regression specification:
  - COE_t = α0 + β1 CAPITAL_{t-1} + β2 CONTROLS_{t-1} + FE (country and year) + ε_t.
- Primary result: bank capital negatively associated with cost of equity across specifications.
- EQUITY (columns (1)–(3) Table 2):
  - EQUITY negative and significant at 1% across specifications.
  - Economic magnitudes:
    - One standard deviation increase in EQUITY (0.039) ⇒ 72-basis-point drop in COE (reported: -0.186*0.039 = -0.0072).
    - A 10-percentage-point increase in EQUITY reduces COE by 1.86 percentage points (reported: -0.186*0.10 = -0.0186).
- TIER1 and TOTCAP (columns (4)–(9) Table 2):
  - TIER1 coefficient consistently negative and significant at 1%.
  - Economic magnitude smaller than EQUITY:
    - One standard deviation increase in TIER1 (0.078) ⇒ 26-basis-point drop in COE (reported: -0.034*0.078 = -0.0026).
  - TOTCAP results qualitatively similar to TIER1; Tier 2 capital not priced by stockholders (Tier 2 coefficient insignificant).
- Control variable signs and significance:
  - PROV positive and significant.
  - ROA negative and significant.
  - DEP negative and significant.
  - SIZE negative and significant.
  - LNGDPC negative and significant.
  - INFL positive and significant.
  - MCAP negative and significant.

### Robustness checks
- Market-risk controls (Table 3):
  - RSTD positive and significant in some specifications.
  - BETA positive and highly significant when included.
  - MTOV negative and significant in EQUITY specifications.
  - Main capital coefficients remain negative and significant.
- Asset quality and valuation controls:
  - NPL positive and significant when included; capital coefficients unchanged.
  - BTM positive and significant; capital coefficients robust.
- Alternative COE measures (Table 4):
  - Replacing COE with individual implied measures (rCT, rES, rGLS, rOJN), the principal component (rPCA), or averages (rES_GLS) yields consistent negative and significant capital coefficients.
  - Panel B: RPM (COE − 10-year U.S. Treasury yield) negatively and significantly associated with each capital measure.
- Endogeneity and alternative estimators (Table 5, Panel A):
  - Bank-level averages: capital averages negatively associated with COE averages.
  - Fama-MacBeth: capital retains negative predictive power.
  - Two-stage least squares (2SLS): instruments = country-year averages of capital excluding focal bank; under-identification and weak-identification tests reject problems; second-stage maintains negative and significant capital coefficients.
- Sample composition (Table 5, Panel B):
  - Excluding U.S. banks: negative capital–COE relationship persists.
  - U.S.-only sample: negative and significant capital coefficients remain.

### Additional analyses (Section 4) — Heterogeneity
- Motivation: explore heterogeneity by capitalization level, country development, and bank size.

A. Low vs. High Bank Capitalization
- Methods:
  - Split sample by country-year median of the capital measure (below vs above median).
  - Quartile regressions across capital distribution.
- Findings:
  - Capital effect stronger for below-median (low-capitalized) banks.
  - Quartile regressions show nonlinear relationship:
    - EQUITY coefficient in first quartile much larger in absolute value than in higher quartiles.
    - Example: one percentage point increase in equity ratio for banks in first quartile lowers COE by 79 basis points (reported: -0.789 coefficient in Panel B first quartile).
  - Interpretation: marginal value of additional equity greater where regulatory minima likely binding; marginal effect declines at higher capital levels.

B. Advanced vs. Developing countries
- Findings:
  - Capital lowers COE in both groups.
  - Magnitude larger for developing countries; difference-in-coefficients t-test confirms stronger effect in developing countries.
  - Interpretation: investors place greater value on additional capital in developing-country banks.

C. Small vs. Large banks
- Findings:
  - Negative capital–COE relationship holds for both small and large banks.
  - Some coefficient magnitudes differ across size groups; overall result not driven by bank size.

### Conclusion (Section 5)
- Main empirical contribution:
  - Consistent with theory, banks operating with higher equity ratios enjoy lower costs of equity.
  - Baseline: a one percentage point increase in equity-to-assets ratio reduces COE by 18 basis points.
  - Effect larger for low-capitalized banks; at the lowest quartile, a one percentage point increase in EQUITY lowers COE by 79 basis points.
- Policy implication:
  - Within a Modigliani-Miller framework, higher equity capital requirements should not necessarily raise banks' overall funding costs because the cost of equity declines with higher equity capital; accounting for likely declines in borrowing costs, overall funding costs may not increase and could decrease.
- Caveat and future research:
  - Further research needed to analyze cost of debt and overall cost of funding effects of higher bank capital before definitive conclusions on implications for lending and real activity.

*Source: wpiea2019265-print-pdf - REFERENCES (excerpt).*

### REFERENCES

### wpiea2019265-print-pdf - REFERENCES

### Introduction and context
- The global financial crisis (GFC) demonstrated that capital is a bank’s strongest defense against losses from adverse asset-value movements, with low-capital banks facing insolvency, acquisitions, or government bailouts.
- Policymakers strengthened capital requirements culminating in the adoption of the Basel III regulatory framework in 2010.
- Key Basel III numeric requirements described:
  - Common Equity Tier 1 ratio (CET1): 4.5 percent (up from Basel II’s 2 percent).
  - Minimum Tier 1 capital: 6 percent of RWA (includes 4.5 percent CET1 and 1.5 percent additional Tier 1).
  - Total capital (Tier 1 plus Tier 2): at least 8 percent of RWA.
  - Capital Conservation Buffer (CET1 during good times): 2.5 percent of RWA.
  - Additional countercyclical buffers: up to 2.5 percent of RWA.
  - Minimum leverage ratio (Tier 1 capital to total assets): 3 percent.

### Empirical question and strategy
- Central research question: Does higher bank capital reduce the cost of equity, consistent with the theoretical prediction that equity becomes cheaper as leverage decreases?
- Approach:
  - Use an ex-ante measure of cost of equity implied by stock prices and analysts’ earnings forecasts (COE), rather than ex-post realized returns.
  - Direct empirical specification regressing cost of equity on capital ratios and bank- and country-level controls.
  - Cross-country, bank-level sample covering 62 countries over 1991–2017 (more than 16,000 bank-year observations).

### Key empirical findings and statistics
- Baseline regression results:
  - A one percentage point increase in the equity-to-assets ratio reduces the cost of equity by about 18 basis points.
  - At very low bank capital levels (first quartile of the sample), a one percentage point increase in the equity-to-assets ratio reduces cost of equity by 79 basis points.
- Additional findings:
  - Investors value sheer equity capital most; other components of Tier 1 capital have very slight effects and Tier 2 capital effects are insignificant.
  - The magnitude of capital’s impact on cost of equity is larger for banks with lower capital ratios.
  - Capital has a stronger effect on banks’ cost of equity in developing countries than in advanced countries.
- Comparative empirical results referenced:
  - Kashyap et al. (2010) estimate that each 1 percentage point increase in capital raises a bank’s weighted average cost of capital by about 2.5 basis points.
  - Admati and Hellwig (2013) argue for minimum equity-to-assets ratios between 20 and 30 percent (as a policy stance).

### Relation to literature and theory
- The paper validates the Modigliani-Miller (M-M) prediction that required return on equity falls as leverage decreases, providing empirical evidence that markets price the change in bank risk due to additional equity.
- Contrasts with prior work:
  - Baker and Wurgler (2013) used a two-stage approach with U.S. banks and found ambiguous links between beta and realized returns; this paper uses COE and a global sample to test the relationship directly.
  - Admati et al. (2013) and others questioned the empirical validity of the leverage–cost-of-equity relationship; this study documents a robust negative relationship.

### Policy implications and recommendations
- Empirical evidence indicates that increasing bank equity reduces banks’ cost of equity, supporting the use of the M-M framework to quantify funding-cost effects of higher capital requirements.
- If cost of debt also declines with higher capital (as suggested by theory and some evidence), the effect of higher capital requirements on weighted average cost of capital—and thus on lending rates—could be far lower than suggested by critics.
- Higher capital requirements can therefore come at little or no cost to borrowers while delivering financial-stability benefits.
- Policy caution: actions taken by some countries to loosen bank capital regulations may be ill advised and should be reconsidered in light of these findings.

*Source: wpiea2019265-print-pdf - REFERENCES (excerpt).*

### Section 4 provides additional analyses, and Section 5 concludes the paper.

### wpiea2019265-print-pdf - Section 4 provides additional analyses, and Section 5 concludes the paper.

### Data and sample
- Sample: more than 16,000 bank-year observations for 62 countries spanning 1991–2017.
- Data sources: DataStream (bank equities), I/B/E/S (analyst forecasts), Thomson Reuters and Bloomberg (bank financial statements), International Financial Statistics, World Development Indicators, Financial Structure database, etc.
- Observations vary by country, year, and variable due to data availability.

### Implied cost of equity (dependent variable)
- COE constructed as the average estimate from four models: Claus and Thomas (2001) (rCT), Gebhardt et al. (2001) (rGLS), Easton (2004) (rES), and Ohlson and Juettner-Nauroth (2005) (rOJN).
- Note on estimation:
  - rOJN estimated in closed form.
  - rCT, rGLS, rES require numerical techniques with solutions bounded between 0 and 100 percent.
- Forecast inputs: positive one-, two-, and three-year-ahead mean forecasted earnings per share (FCFFFt+j) and long-term growth rate forecasts from I/B/E/S.
- Missing or negative FCFFFt+j substituted with historical earnings per share estimated from beginning-of-year book value per share and three-year median return on equity by year, country, and industry.
- Observations discarded when none of the implied COE estimates converge or are undefined.

### Bank capital measures (main explanatory variables)
- EQUITY: ratio of total equity to total assets (financial leverage).
- TIER1: Tier 1 capital divided by risk-weighted assets (regulatory Tier 1 ratio).
- TOTCAP: (Tier 1 + Tier 2) divided by risk-weighted assets (total capital ratio).
- Tier 1 composition: common stock, retained earnings, perpetual noncumulative preferred stock.
- Tier 2 composition: hybrid capital, subordinated debt, revaluation reserves, loan loss reserves.
- Authors note limitations of risk-weighted ratios and justify using EQUITY as a primary investor-relevant measure.

### Control variables
- Bank-level controls:
  - PROV: loan loss provisions to total loans (asset quality).
  - INEFF: salaries and benefits to total assets (inefficiency).
  - ROA: return on assets (profitability).
  - DEP: deposits to total assets (funding stability/liquidity).
  - SIZE: natural logarithm of total assets.
- Country-level controls:
  - LNGDPC: natural logarithm of GDP per capita.
  - INFL: expected inflation rate proxied by annual realized inflation.
  - MCAP: stock market capitalization to GDP (stock market development).

### Summary statistics and descriptive patterns
- Panel C (full sample) means and medians:
  - COE mean 0.121; P50 0.108; STD 0.058; N 16,776.
  - EQUITY mean 0.087; P50 0.083; STD 0.039; N 16,776.
  - TIER1 mean 0.130; P50 0.118; STD 0.078; N 8,998.
  - TOTCAP mean 0.153; P50 0.139; STD 0.077; N 8,754.
  - SIZE mean 2.246; P50 1.979; STD 2.051; N 16,776.
  - PROV mean 0.764; P50 0.440; STD 1.028; N 16,776.
  - INEFF mean 0.013; P50 0.013; STD 0.006; N 16,776.
  - ROA mean 0.010; P50 0.011; STD 0.029; N 16,776.
  - DEP mean 0.668; P50 0.713; STD 0.173; N 16,776.
  - LNGDPC mean 10.054; P50 10.403; STD 1.046; N 16,776.
  - INFL mean 0.032; P50 0.027; STD 0.034; N 16,776.
  - MCAP mean 0.955; P50 1.070; STD 0.493; N 16,776.
- Cross-country medians (Panel A highlights):
  - Minimum COE: Australia 9.8 percent (0.098).
  - Maximum COE: Lebanon 25.1 percent (0.251).
  - EQUITY range: Belgium minimum 3.1 percent (0.031) to Serbia maximum 15.7 percent (0.157).
  - TIER1 range: Italy minimum 7.4 percent (0.074) to Serbia maximum 18 percent (0.180).
  - TOTCAP range: Italy minimum 11.3 percent (0.113) to Nigeria maximum 20.4 percent (0.204).
- Time series medians (Panel B):
  - COE fell cumulatively about 3 percentage points between 1991 and 2017 (from 12.9 percent to 10 percent).
  - EQUITY rose cumulatively 4 percentage points between 1991 and 2017 (from 6 percent to 10 percent).
  - EQUITY increased from 8.3 percent in 2007–2008 to 10 percent in 2017.
  - TIER1 and TOTCAP increased substantially over the 27-year sample, gains split roughly evenly pre- and post-GFC.
- Correlations (Panel D):
  - COE negatively correlated with capital measures: EQUITY (-0.090), TIER1 (-0.081), TOTCAP (-0.062); correlations significant at the 1% level.
  - Other controls generally correlated with COE in theoretically consistent directions.
  - Authors report low multicollinearity among controls.

### Graphical evidence
- Scatterplots (Figure 2) show clear negative associations between COE and each capital measure (EQUITY, TIER1, TOTCAP) in the full sample.
- Selected-country scatterplots (Germany, U.K., U.S., India, Malaysia, Thailand) display similar negative associations.

### Main multivariate results
- Baseline regression specification: COE_t = α0 + β1 CAPITAL_{t-1} + β2 CONTROLS_{t-1} + FE (country and year) + ε_t.
- Primary result: bank capital negatively associated with cost of equity across specifications.
- EQUITY (columns (1)–(3) Table 2):
  - EQUITY negative and significant at 1% across specifications including bank and country controls.
  - Economic magnitudes:
    - One standard deviation increase in EQUITY (0.039) ⇒ 72-basis-point drop in COE (calculation reported: -0.186*0.039 = -0.0072).
    - A 10-percentage-point increase in EQUITY reduces COE by 1.86 percentage points (reported: -0.186*0.10 = -0.0186).
- TIER1 and TOTCAP (columns (4)–(9) Table 2):
  - TIER1 coefficient consistently negative and significant at 1%.
  - Economic magnitude smaller than EQUITY:
    - One standard deviation increase in TIER1 (0.078) ⇒ 26-basis-point drop in COE (reported: -0.034*0.078 = -0.0026).
  - TOTCAP results qualitatively similar to TIER1; Tier 2 capital not priced by stockholders (unreported regressions show Tier 2 coefficient insignificant).
- Control variable signs:
  - PROV positive and significant (higher provisions ⇒ higher COE).
  - ROA negative and significant (more profitable banks ⇒ lower COE).
  - DEP negative and significant (higher deposit funding ⇒ lower COE).
  - SIZE negative and significant (larger banks ⇒ lower COE).
  - LNGDPC negative and significant (richer countries ⇒ lower COE).
  - INFL positive and significant (higher expected inflation ⇒ higher COE).
  - MCAP negative and significant (more developed stock market ⇒ lower COE).

### Robustness checks
- Additional market-risk controls (Table 3):
  - RSTD (stock return standard deviation) positive and significant in some specifications.
  - BETA positive and highly significant when included.
  - MTOV (market turnover) negative and significant when included for EQUITY specifications.
  - Main capital coefficients (EQUITY, TIER1, TOTCAP) remain negative and significant with these additions.
- Asset quality and valuation controls:
  - NPL (nonperforming loans / loans) positive and significant when included; capital coefficients unchanged in sign and significance.
  - BTM (book-to-market) positive and significant; capital coefficients robust.
- Alternative COE measures (Table 4):
  - Replacing COE with individual implied measures (rCT, rES, rGLS, rOJN), the principal component (rPCA), or averages (rES_GLS) yields consistent negative and significant capital coefficients.
  - Panel B: risk premium (RPM = COE − 10-year U.S. Treasury yield) is negatively and significantly associated with each capital measure, alleviating concerns about the low interest-rate environment driving results.
- Endogeneity and alternative estimation methods (Table 5, Panel A):
  - Bank-level averages (time averages by bank) regressions: capital averages negatively associated with COE averages.
  - Fama-MacBeth (yearly cross-sectional regressions averaged over time, Newey-West t-stats): capital retains negative predictive power for cross-section of COE.
  - Two-stage least squares (2SLS): instruments = country-year averages of capital excluding focal bank; under-identification and weak-identification tests reject problems; second-stage results maintain negative and significant capital coefficients.
- Sample composition (Table 5, Panel B):
  - Excluding U.S. banks: negative capital–COE relationship persists.
  - U.S.-only sample: negative and significant capital coefficients remain.
- Conclusion from robustness: main inference (higher equity capital ⇒ lower cost of equity) survives multiple checks, alternative measures, estimators, and sample splits.

### Additional analyses (Section 4)
- Motivation: explore heterogeneity in capital–COE effect by capitalization level, country development, and bank size.

A. Low vs. High Bank Capitalization
- Two approaches:
  - Split sample by country-year median of the capital measure (below vs above median).
  - Quartile regressions across capital distribution.
- Findings (Table 6, Panel A & B):
  - Capital effect stronger for below-median (low-capitalized) banks than for above-median banks.
    - Example: EQUITY coefficient below-median (column (1)) more than twice magnitude of above-median (column (2)); difference-in-coefficients t-test indicates statistically higher COE decrease for low-capitalized banks.
  - Quartile regressions show nonlinear relationship:
    - EQUITY coefficient in first quartile much larger in absolute value than in higher quartiles.
    - Example: one percentage point increase in equity ratio for banks in first quartile lowers COE by 79 basis points (reported: -0.789 coefficient in Panel B first quartile ⇒ -0.00789 for a 1-percentage-point change? authors state "low-quartile effect ... lowers its cost of equity by a significant 79 basis points").
  - Interpretation: additional equity is valued more at low capitalization levels where regulatory minima are more likely binding; marginal effect declines at higher capital levels.

B. Advanced vs. Developing countries
- Sample split into developed and developing country banks (Table 6, Panel C).
- Findings:
  - Capital lowers COE in both groups (coefficients negative and significant).
  - Magnitude larger for developing countries (columns for developing countries show much higher coefficients).
  - Difference-in-coefficients t-test confirms stronger effect in developing countries.
  - Interpretation: investors place greater value on additional capital in developing-country banks, likely due to higher perceived baseline risk and weaker institutional frameworks.

C. Small vs. Large banks
- Sample split by SIZE median into small and large banks (Table 6, Panel D).
- Findings:
  - Negative capital–COE relationship holds for both small and large banks.
  - Some coefficient magnitudes differ across size groups, but overall result not driven by bank size.

### Conclusion (Section 5)
- Main empirical contribution:
  - Consistent with theory, banks operating with higher equity ratios enjoy lower costs of equity.
  - Baseline: a one percentage point increase in equity-to-assets ratio reduces COE by 18 basis points (reported baseline estimate).
  - Effect is larger for low-capitalized banks; at the lowest quartile, a one percentage point increase in EQUITY lowers COE by 79 basis points.
- Policy implication:
  - Within a Modigliani-Miller framework, higher equity capital requirements should not necessarily raise banks' overall funding costs because the cost of equity declines with higher equity capital; accounting also for likely declines in borrowing costs, overall funding costs may not increase and could decrease.
- Caveat and future research:
  - Further research needed to analyze cost of debt and overall cost of funding effects of higher bank capital before definitive conclusions on implications for lending and real activity.

*Source: wpiea2019265-print-pdf (IMF Working Paper content provided).*

### References

### wpiea2019265-print-pdf - References

### References
- Admati, A.R., DeMarzo, P.M., Hellwig, M.F., Pfleiderer, P., 2013. Fallacies, Irrelevant Facts, and Myths in the Discussion of Capital Regulation: Why Bank Equity is Not Socially Expensive. Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2013_23, Max Planck Institute for Research on Collective Goods.
- Admati, A.R., Hellwig, M.F., 2013. The bankers’ new clothes: What’s wrong with banking and what to do about it. Princeton University Press. (Excerpts and links available at http://bankersnewclothes.com/).
- Anderson, T. W., 1951. Estimating linear restrictions on regression coefficients for multivariate normal distributions. Annals of Mathematical Statistics 22, 327–351.
- Baker, M.P. Wurgler, J., 2013. Do strict capital requirements raise the cost of capital? Banking regulation and the low risk anomaly. NBER Working paper.
- Bekaert, G., Harvey, C., 2000. Foreign speculations and emerging equity markets. Journal of Finance 55, 565–613.
- Belkhir, M., 2013. Do subordinated debtholders discipline bank risk-taking: Evidence from risk management decisions. Journal of Financial Stability 9, 705-719.
- Belkhir, M., Saad, M., Samet, A. 2019. Stock extreme illiquidity and the cost of capital. Journal of Banking and Finance, forthcoming.
- Beltratti, A., Stulz, R.M., 2012. The credit crisis around the globe: Why did some banks perform better? Journal of Financial Economics 105, 1-17.
- Berger, A.B., El Ghoul, S., Guedhami, O., Roman .R.A., 2018. Competition and Banks’ Cost of Equity Capital: Evidence from Relatively Exogenous Differences in Regulation. Working paper.
- Berger, A.N., Bowman, C.H.S., 2013. How does capital affect bank performance during financial crises? Journal of Financial Economics 109, 146-176.
- Botosan, C.A., Plumlee, M.A., Wen, H., 2011. The Relation between Expected Returns, Realized Returns, and Firm Risk Characteristics. Contemporary Accounting Research 28, 1085-1122.
- Chen, K.C.W., Chen, Z., Wei, K.C.J., 2011. Agency costs of free cash flow and the effect of shareholder rights on the implied cost of equity capital. Journal of Financial and Quantitative Analysis 46, 171–207.
- Chen, K.C.W., Chen, Z.-H., Wei, K.C.J., 2009. Legal protection of investors, corporate governance, and the cost of equity capital. Journal of Corporate Finance 15, 279–289.
- Chen, Z., Li, O.Z., Zou, H. 2016. Directors’ and Officers’ Liability Insurance and the Cost of Equity. Journal of Accounting and Economics 61, 100-120.
- Claus, J., Thomas, J., 2001. Equity premia as low as three percent? Evidence from analysts' earnings forecasts for domestic and international stock markets. Journal of Finance 56, 1629-1666.
- Cragg, J.G., Donald, S.G., 1993. Testing identifiability and specification in instrumental variable models. Econometric Theory 9, 222 – 240.
- Del Negro, M., Giannone, D., Giannoni, M.P., Tambalotti, A., 2018. Global trends in interest rates. NBER Working Paper No. 25039.
- Demirguc-Kunt, A., Detragiache, E., Meerouche, O., 2013. Bank Capital: Lessons from the Financial Crisis. Journal of Money, Credit and Banking 45, 1147-1164.
- Demsetz, R.S., and Strahan, P.E., 1997. Diversification, Size, and Risk at Bank Holding Companies. Journal of Money, Credit and Banking 29, 300-313.
- Deng, S., Elyasiani, E., Mao, C.X., 2007. Diversification and the cost of debt of bank holding companies. Journal of Banking and Finance 31, 2453-2473.
- Dhaliwal, D., Heitzman, S., Li, O., 2006. Taxes, leverage, and the cost of equity capital. Journal of Accounting Research 44, 691-723.
- Easton, P., 2004. PE ratios, PEG ratios, and estimating the implied expected rate of return on equity capital. Accounting Review 79, 73-95.
- Elliott, D.J., 2013. Higher bank capital requirements would come at a price. Working paper.
- Fama, E.F., MacBeth, J.D., 1973. Risk, return and equilibrium: Empirical tests. Journal of Political Economy 81, 607-636.
- Frankel, R., Lee, C. 1998. Accounting valuation, market expectation, and cross-sectional stock returns. Journal of Accounting and Economics 25, 283–319.
- Gebhardt, W., Lee, C., Swaminathan, B., 2001. Towards an implied cost of capital. Journal of Accounting Research 39, 135-176.
- Hail, L., Leuz, C., 2006. International differences in cost of equity capital: do legal institutions and securities regulation matter? Journal of Accounting Research 44, 485-531.
- Hail, L., Leuz, C., 2009 Cost of capital effects and changes in growth expectations around U.S. cross-listings. Journal of Financial Economics 93, 428-454.
- Jayaraman, S., Milbourn, T.T., 2012. The role of stock liquidity in executive compensation. The Accounting Review 87, 537-563.
- Kashyap, A.K., Stein, J.C., Hanson, S., 2010. An analysis of the impact of 'substantially heightened' capital requirements on large financial institutions. Working paper.
- Li, Y., Ng, D., Swaminathan, B., 2013. Predicting market returns using aggregate implied cost of capital. Journal of Financial Economics 110, 419-436.
- Modigliani, F., Miller, M.H., 1958. The cost of capital, corporation finance and the theory of investment. American Economic Review, 261–297.
- Newey, W.K., West, K.D., 1987. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–08.
- Ohlson, J., Juettner-Nauroth, B., 2005. Expected EPS and EPS growth as determinants of value. Review of Accounting Studies 10, 349-365.
- Pastor, L., Sinha, M., Swaminathan, B., 2008. Estimating the inter-temporal risk-return tradeoff using the implied cost of capital. Journal of Finance 63, 2859– 2897.
- Saad, M., Samet, A., 2017. Liquidity and the implied cost of equity capital. Journal of International Financial Markets, Institutions, and Money 51, 15-38.
- Sanderson, E., Windmeijer, F., 2016. A weak instrument F-test in linear IV models with multiple endogenous variables. Journal of Econometrics 190, 212–221.

### Appendix A: Variables, definitions, and sources
- Panel A. Implied Cost of Equity
  - R_CT — Implied cost of equity estimated using the Claus and Thomas (2001) model. Authors’ calculation based on I/B/E/S and DataStream.
  - R_GLS — Implied cost of equity estimated using the Gebhardt et al. (2001) model. As above
  - R_OJ — Implied cost of equity estimated using the Ohlson and Juettner-Nauroth (2005) model. As above
  - R_ES — Implied cost of equity estimated using the Easton (2004) model. As above
  - COE — Equally weighted average of R_ES, R_OJ, R_CT, and R_GLS. As above
  - R_ES_GLS — Equally weighted average of R_ES and R_GLS. As above
  - R_PCA — Principal component of R_ES, R_OJ, R_CT, and R_GLS. As above
  - RPM — Risk premium, which is equal to cost of equity measured by COE minus the 10 year U.S. Treasury bond yield. As above

- Panel B. Capital ratio variables
  - EQUITY — The lagged equity-to-assets ratio. Authors’ calculation based on Bloomberg, DataStream, and Reuters.
  - TIER1 — The lagged (Tier 1 /Risk weighted assets) ratio. As above
  - TOTCAP — The lagged ((Tier 1+Tier 2)/Risk weighted assets) ratio. As above

- Panel C. Bank-level control variables
  - PROV — The lagged loan loss provision to total loans ratio. Authors’ calculation based on Bloomberg, DataStream, and Reuters.
  - INEFF — The lagged (Salaries and benefits/total assets) ratio. As above
  - ROA — The lagged return on assets ratio. As above
  - DEP — The lagged (Total deposits/Total assets) ratio. As above
  - SIZE — The lagged natural logarithm of the bank’s total assets in US dollar. As above
  - RSTD — The lagged standard deviation of daily returns over one year period. As above
  - BETA — The lagged beta estimated as the covariance between the firm returns and the market return relative to the variance of the market returns. As above
  - MTOV — The lagged one-year turnover volume. As above
  - NPL — The lagged non-performing loans to total loans ratio. As above
  - BTM — The book-to-market ratio. As above

- Panel D. Country-level control variables
  - LNGDP — The lagged logarithm of GDP per capita. International Financial Statistics and World Development Indicators
  - INFL — The lagged inflation measured as the annualized yearly median of a country-specific one-year-ahead realized monthly inflation rate. As above
  - MCAP — The lagged (Total stock market capitalization/GDP) ratio at the country level. As above

### Appendix B: Cost of equity models
- 1. Claus and Thomas (2001) model
  - Description: Assumes clean surplus accounting; current share price expressed in terms of the cost of equity, current book value, forecasted abnormal earnings, and perpetual abnormal earnings growth. Explicit forecast horizon is set at five years, beyond which forecasted residual earnings grow at the expected inflation rate.
  - Forecasted abnormal earnings: ae is given by forecasted earnings minus a charge for the cost of equity.
  - Valuation equation (solved numerically for r_CT):
    - FF_t = B_t + sum_{τ=1}^{5} ae_{t+τ} / (1 + r_CT)^{τ} + ae_{t+5} / (1 + i_t) / (r_CT − i_t) (1 + r_CT)^{5}, (B.1)
    - where P_t represents stock price at time t, i_t is defined as the long-term abnormal earnings growth rate calculated using the annualized yearly median of a country-specific one-year-ahead realized monthly inflation rate. B_t is the current book value per share (at the beginning of year t), ae_{t+τ} = FEPS_{t+τ} − r_CT * B_{t+τ−1}, B_{t+τ} is the forecasted book value per share for year t+τ—measured using the clean surplus relationship—and r_CT is the cost of equity capital. Eq. (B.1) is solved numerically for r_CT.

- 2. Gebhardt et al. (2001) model
  - Description: Assumes clean surplus accounting; share price expressed in terms of the cost of equity, current book value, and forecasted ROE and book value. Explicit forecast horizon set at three years, beyond which forecasted ROE decays to a target ROE by the twelfth year and remains constant afterward.
  - Valuation equation (solved numerically for r_GLS):
    - FF_t = B_t + sum_{τ=1}^{11} (FROE_{t+τ} − r_GLS) / (1 + r_GLS)^{τ} * B_{t+τ−1} + (FROE_{t+12} − r_GLS) / r_GLS * B_{t+11} / (1 + r_GLS)^{11}, (B.2)
    - where P_t and B_t are refined as in previous models; FROE_{t+τ} is the forecasted ROE for year t+τ; and r_GLS is the cost of equity capital. Eq. (B.2) is solved numerically for r_GLS.

- 3. Ohlson and Juettner-Nauroth (2005) model
  - Description: Extension of the Gordon constant growth model. Allows share price to be expressed in terms of the cost of equity, the one-year-ahead earnings forecast, and the near-term and perpetual growth forecasts. Explicit forecast horizon is set at one year, after which forecast earnings grow at near-term rates, which decay into a perpetual rate.
  - Near-term earnings growth: average of i) the growth rates of FEPS from year t+1 to year t+2, and ii) the I/B/E/S long-term growth forecast (LTG). Perpetual growth rate is the expected inflation rate.
  - Valuation equation (solved analytically for r_OJN):
    - FF_t = FEPS_{t+1} (g_t − i_t + r_OJN * d_{t+1}) / r_OJN (r_OJN − i_t), (B.3)
    - where P_t is the stock price recorded 10 months after the fiscal year-end; FEPS_{t+τ} represents the forecasted earnings for year t+τ, g_t = 0.5 * (FEPS_{t+2} / FEPS_{t+1} − 1 + CCL_t); d_t is the expected dividend payout at time t, estimated using the average dividend payout over the last three years; i_t is the forecasted earnings growth at time 3, measured as the realized inflation in year t+1; and r_OJN is the cost of equity capital. Eq. (B.3) is solved analytically for r_CT. The model requires that FEPS_{t + 2} > 0 and FEPS_{t + 1} > 0 to yield a positive root.

- 4. Easton (2004) model
  - Description: Generalization of the Price-Earnings-Growth (PEG) model. Expresses current share price in terms of the cost of equity, the expected dividend payout, and one- and two-year-ahead earnings forecasts. Explicit forecast horizon is set at two years, after which forecasted abnormal earnings grow in perpetuity at a constant rate.
  - Valuation equation (solved numerically for r_Easton):
    - FF_t = (FEPS_{t+2} − FEPS_{t+1} (1 − r_Easton_t * d_{t+1})) / r_Easton_t^{2}, (B.4)
    - where P_t, FEPS_{t+τ} and d_t are defined as in the previous model. Knowing all the parameters, Eq. (B.4) is solved numerically for r_Easton. The model requires that FEPS_{t + 2} > 0 and FEPS_{t + 1} > 0 to yield a positive root.

*wpiea2019265-print-pdf - References*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019265-print-pdf.pdf_