## _wp10208

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---

### Introduction
- Research question: Empirically test the precautionary motive for bank capital—whether higher uncertainty causes banks to hold higher capital-to-assets ratios.
- Model foundation: Simple dynamic lender model based on Valencia (2008); derives a theoretical measure of uncertainty from Kimball (1990) called the relative equivalent precautionary premium (REPP).
- Data and period: U.S. commercial banks, 1995-2005.
- Key high-level findings:
  - Empirical results provide "significant and robust support" that banks facing higher uncertainty maintain higher capital-to-assets ratios.
  - Counterfactual: if uncertainty declined to the minimum observed in the sample, a weighted average reduction of slightly over 1 percentage point in bank capital ratios would follow.
  - Suggestive evidence that sensitivity to uncertainty increases during recessions.

### Theoretical framework and uncertainty measure
- Model setup:
  - Bank owners are risk-neutral shareholders maximizing discounted dividends; balance-sheet constraint links lending, debt, and capital.
  - Deposit yield decomposed as r_Dt = ρ + f_t where f_t increases with bank leverage; f_t assumed at least twice continuously differentiable.
  - First-order conditions imply optimal lending and dividend decisions depend on distribution of shocks α.
  - Calibration note used in illustrative solution: ρ = 2.5%, r = 5%, and β chosen to generate realistic capital-to-asset ratios.
  - Analytical requirement: β^{-1} > ρ (ensures well-defined solution; non-negativity constraint on dividends does not bind).
- Theoretical uncertainty measure:
  - Equivalent precautionary premium (Kimball, 1990) adapted to banking; relative equivalent precautionary premium (REPP) defined by equation (12): Et[α^{-1}] − 1 = Ψ/(l* − q*), where Ψ is the equivalent precautionary premium and REPP denotes the scaleless relative form.
  - Intuition: non-linearity in α implies variance of α matters for capital choice; REPP captures the certainty-equivalent increase in capital (or reduction in dividends) equivalent to added uncertainty.

### Empirical strategy and estimation
- Data construction and groups:
  - Merger-adjusted dataset from the Consolidated Reports of Condition and Income (CALL reports).
  - Yearly observations by averaging end-of-quarter balances; only banks active for entire 1995-2005 sample included.
  - Banks grouped by one variable at a time: size (ln total assets), Federal Reserve district, exposure to real estate lending (fraction of loans secured by real estate to total gross loans), composition of liabilities (ratio of total deposits to total liabilities), and off-balance-sheet activity (ratio of off-balance-sheet items to total assets).
- Construction of empirical REPP:
  - For each group j, compute relative capital-to-assets indicator χ_t,ji = s_t,ji / S_t where S_t is industry average capital-to-assets in year t.
  - Compute α_t,ji = χ_t,ji / χ_{t−1,ji}.
  - Use TxN_j observations for each group to estimate empirical distribution of α with a 20-point kernel estimator.
  - Compute REPP from the estimated distribution using equation (12).
- Regression specification:
  - Cross-section linear model: s_i = α_0 + α_1 REPP_i + α_2 X_i + ε_i, where s_i is bank i’s capital-to-assets ratio measured in year 2000 (mid-point), REPP_i is the bank i average REPP across grouping procedures, X_i contains controls, and regressions exclude banks with capital-to-asset ratios outside the 1st and 99th percentile.
  - Controls X_i include: Federal Reserve District dummies; ln(total assets); ratio of total deposits to total liabilities; ratio of loans secured with real estate to gross total loans; ratio of off-balance-sheet items to total assets. All non-district controls are lagged once.
  - Robustness alternative: variance-based measure VARCAR computed in the same grouped manner and used instead of REPP.
- Estimation details and robustness:
  - Table 2: coefficient on REPP is highly statistically significant with expected sign in all specifications.
  - VARCAR-based regressions (Table 3) yield qualitatively similar results: uncertainty measure positive and highly significant.
  - Subsampling robustness: 1,000 random subsamples each comprising 80 percent of banks; histogram of point estimates for α_1 concentrated around baseline estimate (Figure 4).
  - Cross-sectional year robustness: regressions run using cross-sections as of 1998 through 2002; point estimates for coefficient on REPP remain in the range 0.34-0.54 and statistically significant.
  - Notable pattern: coefficient on REPP peaks in 2001 (a recession year), suggesting stronger precautionary response in bad times.
  - Additional robustness: similar results obtained using volatility of loan growth and volatility of change in capital-to-assets ratio.

### Quantitative importance (counterfactual experiment)
- Experiment setup:
  - Compute Δs_i = α̂_1 * [REPP_i − REPP_min], where REPP_min is the minimum REPP observed in the sample and α̂_1 is the point estimate from column 6 of Table 2.
  - Exercise keeps everything else equal and reduces uncertainty to the sample minimum.
- Results:
  - Weighted average reduction in capital-to-assets ratios is slightly over 1 percentage point.
  - Distribution: reductions concentrated in the 0–1 percentage point range; some banks reduce capital-to-assets ratios by more than 1.5 percentage points.
  - Caveat: banks have alternative responses to uncertainty (securitization, liability/asset composition changes, off-balance-sheet adjustments), so the computed effect is a lower bound on total adjustment.
  - Sensitivity to business cycle: higher sensitivity during recessions implies quantitative importance is larger in bad times than the baseline >1 percentage point average.

### Conclusions and policy implications
- Main empirical conclusion: higher measured uncertainty (REPP or VARCAR) is associated with higher bank capital-to-assets ratios; effect is highly statistically significant and robust.
- Countercyclical regulation implications:
  - Countercyclical capital or provisioning tools may be effective in restraining credit during good times (when banks want to increase leverage as uncertainty declines).
  - Such tools may be less effective in bad times because banks respond to increased uncertainty by wanting to decrease leverage; calibration of countercyclical regulation must account for this behavior.
- Limitations and avenues for future research:
  - Results reflect only one margin (capital) of bank response to uncertainty; overall adjustment may be larger when considering other margins.
  - Further research needed to disentangle whether observed stronger precautionary sensitivity in recessions reflects changes in perceived risk or changes in the intensity of the precautionary motive.

*Source: _wp10208 - References..........................................  13*

### References..........................................  13

### _wp10208 - References..........................................  13

### Introduction
- Research question: Empirically test the precautionary motive for bank capital—whether higher uncertainty causes banks to hold higher capital-to-assets ratios.
- Model foundation: Simple dynamic lender model based on Valencia (2008); derives a theoretical measure of uncertainty from Kimball (1990) called the relative equivalent precautionary premium (REPP).
- Data and period: U.S. commercial banks, 1995-2005.
- Key high-level findings:
  - Empirical results provide "significant and robust support" that banks facing higher uncertainty maintain higher capital-to-assets ratios.
  - Counterfactual: if uncertainty declined to the minimum observed in the sample, a weighted average reduction of slightly over 1 percentage point in bank capital ratios would follow.
  - Suggestive evidence that sensitivity to uncertainty increases during recessions.

### Theoretical framework and uncertainty measure
- Model setup:
  - Bank owners are risk-neutral shareholders maximizing discounted dividends; balance-sheet constraint links lending, debt, and capital.
  - Deposit yield decomposed as r_Dt = ρ + f_t where f_t increases with bank leverage; f_t assumed at least twice continuously differentiable.
  - First-order conditions imply optimal lending and dividend decisions depend on distribution of shocks α.
  - Calibration note used in illustrative solution: ρ = 2.5%, r = 5%, and β chosen to generate realistic capital-to-asset ratios.
  - Analytical requirement: β^{-1} > ρ (ensures well-defined solution; non-negativity constraint on dividends does not bind).
- Theoretical uncertainty measure:
  - Equivalent precautionary premium (Kimball, 1990) adapted to banking; relative equivalent precautionary premium (REPP) defined by equation (12): Et[α^{-1}] − 1 = Ψ/(l* − q*), where Ψ is the equivalent precautionary premium and REPP denotes the scaleless relative form.
  - Intuition: non-linearity in α implies variance of α matters for capital choice; REPP captures the certainty-equivalent increase in capital (or reduction in dividends) equivalent to added uncertainty.

### Empirical strategy and estimation
- Data construction and groups:
  - Merger-adjusted dataset from the Consolidated Reports of Condition and Income (CALL reports).
  - Yearly observations by averaging end-of-quarter balances; only banks active for entire 1995-2005 sample included.
  - Banks grouped by one variable at a time: size (ln total assets), Federal Reserve district, exposure to real estate lending (fraction of loans secured by real estate to total gross loans), composition of liabilities (ratio of total deposits to total liabilities), and off-balance-sheet activity (ratio of off-balance-sheet items to total assets).
- Construction of empirical REPP:
  - For each group j, compute relative capital-to-assets indicator χ_t,ji = s_t,ji / S_t where S_t is industry average capital-to-assets in year t.
  - Compute α_t,ji = χ_t,ji / χ_{t−1,ji}.
  - Use TxN_j observations for each group to estimate empirical distribution of α with a 20-point kernel estimator.
  - Compute REPP from the estimated distribution using equation (12).
- Regression specification:
  - Cross-section linear model: s_i = α_0 + α_1 REPP_i + α_2 X_i + ε_i, where s_i is bank i’s capital-to-assets ratio measured in year 2000 (mid-point), REPP_i is the bank i average REPP across grouping procedures, X_i contains controls, and regressions exclude banks with capital-to-asset ratios outside the 1st and 99th percentile.
  - Controls X_i include: Federal Reserve District dummies; ln(total assets); ratio of total deposits to total liabilities; ratio of loans secured with real estate to gross total loans; ratio of off-balance-sheet items to total assets. All non-district controls are lagged once.
  - Robustness alternative: variance-based measure VARCAR computed in the same grouped manner and used instead of REPP.
- Estimation details and robustness:
  - Table 2: coefficient on REPP is highly statistically significant with expected sign in all specifications.
  - VARCAR-based regressions (Table 3) yield qualitatively similar results: uncertainty measure positive and highly significant.
  - Subsampling robustness: 1,000 random subsamples each comprising 80 percent of banks; histogram of point estimates for α_1 concentrated around baseline estimate (Figure 4).
  - Cross-sectional year robustness: regressions run using cross-sections as of 1998 through 2002; point estimates for coefficient on REPP remain in the range 0.34-0.54 and statistically significant.
  - Notable pattern: coefficient on REPP peaks in 2001 (a recession year), suggesting stronger precautionary response in bad times.
  - Additional robustness: similar results obtained using volatility of loan growth and volatility of change in capital-to-assets ratio.

### Quantitative importance (counterfactual experiment)
- Experiment setup:
  - Compute Δs_i = α̂_1 * [REPP_i − REPP_min], where REPP_min is the minimum REPP observed in the sample and α̂_1 is the point estimate from column 6 of Table 2.
  - Exercise keeps everything else equal and reduces uncertainty to the sample minimum.
- Results:
  - Weighted average reduction in capital-to-assets ratios is slightly over 1 percentage point.
  - Distribution: reductions concentrated in the 0–1 percentage point range; some banks reduce capital-to-assets ratios by more than 1.5 percentage points.
  - Caveat: banks have alternative responses to uncertainty (securitization, liability/asset composition changes, off-balance-sheet adjustments), so the computed effect is a lower bound on total adjustment.
  - Sensitivity to business cycle: higher sensitivity during recessions implies quantitative importance is larger in bad times than the baseline >1 percentage point average.

### Conclusions and policy implications
- Main empirical conclusion: higher measured uncertainty (REPP or VARCAR) is associated with higher bank capital-to-assets ratios; effect is highly statistically significant and robust.
- Countercyclical regulation implications:
  - Countercyclical capital or provisioning tools may be effective in restraining credit during good times (when banks want to increase leverage as uncertainty declines).
  - Such tools may be less effective in bad times because banks respond to increased uncertainty by wanting to decrease leverage; calibration of countercyclical regulation must account for this behavior.
- Limitations and avenues for future research:
  - Results reflect only one margin (capital) of bank response to uncertainty; overall adjustment may be larger when considering other margins.
  - Further research needed to disentangle whether observed stronger precautionary sensitivity in recessions reflects changes in perceived risk or changes in the intensity of the precautionary motive.

*Source: _wp10208 - References..........................................  13*

### References

### _wp10208 - References

### Major referenced topics
- Financial intermediaries, financial stability, and monetary policy (Adrian and Shin, 2008).
- Risk-based capital and bank credit allocation; causes of credit crunches (Berger and Udell, 1994; Peek and Rosengren, 1995).
- Precautionary saving and its macroeconomic relevance (Carroll and Samwick, 1998; Kimball, 1990).
- Principles of financial regulation and regulatory design (Crockett et al., 2009).
- Cyclical behavior and optimal bank capital (Estrella, 2004; Keppo and Peura, 2006).
- Leverage cycles and macroeconomic anxiety (Fostel and Geanakoplos, 2008).
- Bank portfolio allocation, capital requirements, and regulatory monitoring (Furfine, 2001).
- Bank capital channels of monetary policy and Basel II cyclical implications (Kashyap and Stein, 2004; Van Den Heuvel, 2002).
- Simulation-based stress tests of regulatory capital adequacy (Jokivuolle and Peura, 2004).
- Increasing risk and its economic consequences (Rothschild and Stiglitz, 1971).
- Banks' buffer capital, bank leverage, and financial stability (Valencia, 2008; Valencia, 2010).

### Figures and charts (captions and notes)
- Figure 1: Model-implied Capital-to-Assets Ratio and REPP.
- Figure 2: Histograms. Note: 1=Boston, 2=New York, 3=Philadelphia, 4=Cleveland, 5=Richmond, 6=Atlanta, 7=Chicago, 8=St.Louis, 9=Minneapolis 10=Kansas City, 11=Dallas, 12=San Francisco. Distribution of Banks by District. Note: As of the year 2000.
  - Capital-to-assets Ratio: Total Equity/Total Assets; axis labels include 5, 10, 15, 20, 25.
  - Real Estate Lending: Real Estate Loans/Total Loans; axis labels include 0, .2, .4, .6, .8, 1.
  - Liability Composition: Total Deposits/Total Liabilities; axis labels include 0, .2, .4, .6, .8, 1.
  - Off-Balance Sheet Items: Off-Balance Sheet Items/Total Assets; axis labels include 0, .2, .4, .6, .8.
  - Size: Natural Logarithm of Assets; axis labels include 5, 10, 15, 20.
- Figure 3: Effects of a Reduction in Uncertainty. Buffer Capital weighted average; horizontal label shows Percentage Points Reduction in Capital Ratios with values 0.5 1.5 2.5 3.5 4.5 5.
- Figure 4: Distribution of Point Estimates in Random Samples.

### Key statistics — Table 1: REPP per Group and Overall
- Category Summary Statistics
  - Number of Observations: 68607
  - Size: Mean 1.50, Std. Deviation 0.87, Min 0.74, Max 3.21
  - Federal Reserve District: Mean 1.30, Std. Deviation 1.08, Min 0.60, Max 5.77
  - Off-balance sheet activity: Mean 1.55, Std. Deviation 1.20, Min 0.56, Max 4.27
  - Real Estate Lending: Mean 1.70, Std. Deviation 1.35, Min 0.75, Max 5.11
  - Composition of liabilities: Mean 1.47, Std. Deviation 1.01, Min 0.56, Max 4.20
  - Overall: Mean 1.52, Std. Deviation 0.59, Min 0.65, Max 4.47

### Estimation notes and key coefficients — Table 2: Estimation Output (Dependent Variable: Capital-to-assets Ratio; Estimation is through OLS. Robust standard errors reported in parenthesis. *** p<0.01, ** p<0.05, * p<0.1)
- Column (1)
  - Constant: 9.53*** (0.122)
  - REPP: 38.37*** (8.27)
  - Observations: 6,113
  - R-squared: 0.005
- Column (2)
  - Constant: 8.79*** (0.404)
  - REPP: 38.61*** (8.27)
  - Size, ln(assets): 0.06* (0.033)
  - Observations: 6,112
  - R-squared: 0.005
- Column (3)
  - Constant: 8.81*** (0.405)
  - REPP: 38.65*** (8.27)
  - Size, ln(assets): 0.06* (0.033)
  - Off-balance sheet activity/Total Assets: -0.002*** (0.001)
  - Observations: 6,112
  - R-squared: 0.006
- Column (4)
  - Constant: 9.21*** (0.576)
  - REPP: 38.39*** (8.28)
  - Size, ln(assets): 0.06 (0.035)
  - Off-balance sheet activity/Total Assets: -0.002*** (0.001)
  - Deposits/Total Liabilities: -0.39 (0.378)
  - Observations: 6,112
  - R-squared: 0.006
- Column (5)
  - Constant: 9.24*** (0.628)
  - REPP: 37.88*** (8.32)
  - Size, ln(assets): 0.07** (0.037)
  - Off-balance sheet activity/Total Assets: -0.015*** (0.005)
  - Deposits/Total Liabilities: -0.40 (0.433)
  - Federal reserve district dummy (Boston): -0.39* (0.228)
  - Observations: 6,082
  - R-squared: 0.006
- Column (6)
  - Constant: 8.72*** (0.682)
  - REPP: 51.86*** (9.65)
  - Size, ln(assets): 0.07* (0.037)
  - Off-balance sheet activity/Total Assets: -0.015*** (0.001)
  - Deposits/Total Liabilities: -0.42 (0.434)
  - Federal reserve district dummies coefficients and standard errors:
    - Boston: -1.20*** (0.369)
    - New York: 0.01 (0.375)
    - Philadelphia: 0.370 (0.374)
    - Cleveland: 0.031 (0.288)
    - Richmond: 0.62** (0.279)
    - Atlanta: 0.13 (0.235)
    - Chicago: 0.41* (0.232)
    - St. Louis: 0.60** (0.244)
    - Minneapolis: 0.56** (0.241)
    - Kansas City: 0.57** (0.230)
    - Dallas: 0.40* (0.240)
  - Observations: 6,082
  - R-squared: 0.012

### Estimation notes and key coefficients — Table 3: Estimation Output (Dependent Variable: Capital-to-assets Ratio using VARCAR; same estimation notes)
- Column (1)
  - Constant: 9.87*** (0.064)
  - VARCAR: 0.01*** (0.002)
  - Observations: 6,113
  - R-squared: 0.004
- Column (2)
  - Constant: 9.12*** (0.404)
  - VARCAR: 0.01*** (0.002)
  - Size, ln(assets): 0.07* (0.033)
  - Observations: 6,112
  - R-squared: 0.004
- Column (3)
  - Constant: 9.13*** (0.405)
  - VARCAR: 0.01*** (0.002)
  - Size, ln(assets): 0.06* (0.033)
  - Off-balance sheet activity/Total Assets: -0.002*** (0.001)
  - Observations: 6,112
  - R-squared: 0.005
- Column (4)
  - Constant: 9.54*** (0.576)
  - VARCAR: 0.01*** (0.002)
  - Size, ln(assets): 0.06 (0.035)
  - Off-balance sheet activity/Total Assets: -0.003*** (0.001)
  - Deposits/Total Liabilities: -0.40 (0.378)
  - Observations: 6,112
  - R-squared: 0.005
- Column (5)
  - Constant: 9.55*** (0.628)
  - VARCAR: 0.01*** (0.002)
  - Size, ln(assets): 0.07** (0.037)
  - Off-balance sheet activity/Total Assets: -0.015*** (0.005)
  - Deposits/Total Liabilities: -0.40 (0.433)
  - Federal reserve district dummy (Boston): -0.37* (0.228)
  - Observations: 6,082
  - R-squared: 0.005
- Column (6)
  - Constant: 8.98*** (0.682)
  - VARCAR: 0.01*** (0.002)
  - Size, ln(assets): 0.07* (0.037)
  - Off-balance sheet activity/Total Assets: -0.014*** (0.001)
  - Deposits/Total Liabilities: -0.41 (0.434)
  - Federal reserve district dummies coefficients and standard errors:
    - Boston: -1.90*** (0.389)
    - New York: -0.02 (0.375)
    - Philadelphia: 0.331 (0.374)
    - Cleveland: 0.418 (0.286)
    - Richmond: 0.74*** (0.282)
    - Atlanta: 0.26 (0.239)
    - Chicago: 0.43* (0.231)
    - St. Louis: 0.65** (0.245)
    - Minneapolis: 0.60** (0.243)
    - Kansas City: 0.70*** (0.234)
    - Dallas: 0.49* (0.242)
  - Observations: 6,082
  - R-squared: 0.014

### Cross-sectional results — Table 4: Estimation output for different cross-sections (Dependent Variable: Capital-to-assets Ratio; Estimation is through OLS. Robust standard errors reported in parenthesis. *** p<0.01, ** p<0.05, * p<0.1)
- Year 1998 (selected coefficients)
  - Constant: 9.10*** (0.684)
  - REPP: 34.46*** (9.375)
  - Size, ln(assets): 0.08** (0.037)
  - Off-balance sheet activity/Total Assets: -0.019* (0.010)
  - Federal reserve district dummies (selected): Boston -0.67* (0.384); Richmond -0.563** (0.224); Dallas 0.29 (0.241)
  - Observations: 6086
  - R-squared: 0.008
- Year 1999 (selected coefficients)
  - Constant: 8.84*** (0.682)
  - REPP: 39.76*** (9.430)
  - Size, ln(assets): 0.08** (0.037)
  - Off-balance sheet activity/Total Assets: -0.012 (0.012)
  - Observations: 6084
  - R-squared: 0.009
- Baseline year 2000 (selected coefficients)
  - Constant: 8.71*** (0.682)
  - REPP: 51.86*** (9.655)
  - Size, ln(assets): 0.06* (0.036)
  - Off-balance sheet activity/Total Assets: -0.014*** (0.005)
  - Deposits/Total Liabilities: -0.42 (0.434)
  - Federal reserve district dummy (Boston): -1.20*** (0.369)
  - Observations: 6082
  - R-squared: 0.012
- Year 2001 (selected coefficients)
  - Constant: 8.97*** (0.675)
  - REPP: 53.49*** (9.313)
  - Size, ln(assets): 0.06 (0.036)
  - Off-balance sheet activity/Total Assets: -0.013*** (0.002)
  - Deposits/Total Liabilities: -0.48 (0.449)
  - Federal reserve district dummy (Boston): -1.12*** (0.345)
  - Observations: 6082
  - R-squared: 0.014
- Year 2002 (selected coefficients)
  - Constant: 9.10*** (0.668)
  - REPP: 50.21*** (9.261)
  - Size, ln(assets): 0.06* (0.035)
  - Off-balance sheet activity/Total Assets: -0.008*** (0.001)
  - Deposits/Total Liabilities: -0.27 (0.452)
  - Federal reserve district dummy (Boston): -0.92** (0.369)
  - Observations: 6083
  - R-squared: 0.013

*Source: _wp10208 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10208.pdf_