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### I. INTRODUCTION
- Financial turmoil originating with the collapse of the subprime mortgage market in the US has claimed more than US$ 600 bn. in losses to financial firms and produced a significant contraction in bank lending standards.
- Purpose: develop a model to study credit crunches and explore policy options; situates model in literature linking financial factors and the real economy and emphasizes breakdown of Modigliani and Miller (1958) in presence of information costs.
- Model advantages over existing bank models:
  - Infinite-horizon feature.
  - Non-linear solution preserving banks’ precautionary motives.
- Model overview:
  - Two players: borrowers and a monopolistic bank.
  - Borrowers’ creditworthiness is constant over time (the Bernanke, Gertler, and Gilchrist (1999) financial accelerator is shut down).
  - Bank faces constraints in raising funds; funding costs increase when solvency declines.
  - Negative shocks → dividend cuts first, then lending reductions if necessary → persistent credit crunches even after transitory shocks.
  - Bank exhibits precautionary motive: higher optimal capital when credit risk increases.
- Policy implication: government bailouts (recapitalization policies) may be reasonable during systemic financial pressures.

### II. BANKS AND THE REAL ECONOMY
- Stylized fact: periods of significant financial distress are often followed by sizable and long-lasting contractions in bank credit.
- Two channels for credit contractions:
  - Credit channel via borrowers’ external finance wedge (countercyclical with net worth).
  - Supply-side channel via lenders’ financial condition (focus of this paper).
- Empirical consensus: lending responds significantly to the financial structure of the lender.
- Identification challenge acknowledged: disentangling loan demand from loan supply; paper models bank-side propagation consistent with empirical findings.

### III. THE MODEL
- Environment and agents:
  - Monopolistic bank and continuum of ex-ante identical borrowers.
  - Borrower-bank relationship: risky debt contract with costly monitoring; bank justified by cost efficiency in screening and monitoring.
  - Entrepreneurs live for two periods, endowment normalized to 1, invest in capital k at unit price, production over two periods with full depreciation at end.
- A. The Loan Contract (key equations and definitions)
  - Production at t+2: y_{t+2} = α_{t+2} Φ_{t+2} k_{t+2} with k_{t+2} = l_{t+1}.
  - α and Φ are i.i.d., lognormal shocks; E[Φ] = 1 and E[α] > 0; supports α ∈ (0, ∞) and Φ ∈ [Φ, Φ̄].
  - Monitoring/bankruptcy costs: 1 ≥ u > 0, fraction of project value.
  - Entrepreneur return: π(R_t, l_t, α_{t+2}, Φ_{t+2}) = (l_{t+1}) α_{t+2} Φ_{t+2} − R_t l_t.
  - Default cutoff ᾱ defined by (l_{t+1}) α_{t+2} Φ_{t+2} − R_t l_t = 0.
  - Bank revenues (ex-post) aggregate across borrowers: G = M[α, l, R, Φ]; expected revenues time-invariant (financial accelerator shut down).
  - Participation constraint: E_t[(1+ρ_{t+1})(1+ρ_{t+2})] = (1+ρ)^2 and (7) holds with equality under take-it-or-leave-it offers.
- B. The Bank’s Optimization Problem
  - Objective: risk-neutral stockholders choose lending l_t, dividends d_t, and deposits c_t to maximize market value Max E_t Σ_{s=t}^∞ β^{s-t} d_s.
  - State variables: book value of bank capital n_t and outstanding loans o_t (two-period maturity).
  - Key transitions:
    - n_{t+1} = G(o_t, Φ_{t+1}) + l_t + (1+ρ_{t+1}) c_t − f_t − c_t − l_t? (represented as equation (11) in text).
    - o_{t+1} = l_t.
  - Credit market frictions: cost f_t linked to bank leverage, f increasing and at least twice continuously differentiable in deposits; equity issuance infinitely costly.
  - Constraints: deposit feasibility c_t ≥ o_t + l_t + (n_t − d_t) with equality holding given f and no cash return; dividend non-negativity d_t ≥ 0.
  - Impatience assumption: 1/β > 1+ρ ensures not fully self-funded.
  - Bellman formulation summarized in equations (15)–(19).
- C. Solution and policy functions
  - Numerical solution via endogenous gridpoints method (Carroll (2006)); reformulation uses middle-of-period and end-of-period state variables.
  - End-of-period capital θ_t = n_t − d_t and value-to-go 𝒱_t(θ_t, λ_t, λ_{t−1}) = E_t β V_{t+1}(n_{t+1}, λ_t).
  - First-order conditions:
    - ∂𝒱/∂θ = 1 (equation (24)): marginal value of retained capital equals marginal cost of dividends.
    - ∂𝒱/∂λ = 0 (equation (25)): marginal value of outstanding loans set to marginal cost of raising funds.
  - Marginal cost of lending includes [ρ_{t+1} + f_t + (λ_t + λ_{t−1} − θ_t) ∂f/∂λ] times ∂V_{t+1}/∂n, equated to ∂V_{t+1}/∂λ.
  - Policy functions d(n_t, l_{t−1}) and l(n_t, l_{t−1}) are non-linear with kinks where dividend constraint binds; non-decreasing in bank capital and non-increasing in outstanding loans.
  - Asymmetry: negative shocks can trigger sharp contractions in lending while positive shocks may not produce symmetric expansions.
- D. Risk and the Target Level of Solvency
  - Target solvency arises from trade-off between impatience and decreasing marginal value of bank capital induced by f.
  - For low capital, marginal value of capital high → retain earnings; for high capital, marginal value low → distribute dividends; target where balanced.
  - Effects of assumptions:
    - If f linear, marginal value could be uniformly higher/lower and bank might hold no deposits.
    - Decreasing impatience increases target solvency (1/β − 1 approaches ρ).
  - Precautionary motive: increasing variance of productivity shocks shifts marginal value of capital upward → higher target solvency.
  - Empirical note: Valencia (2006) finds median reduction in bank capital of 8 percent if risk decreased to lowest sample level.

### IV. QUANTITATIVE EXPERIMENTS
- Negative productivity shock experiments (Figure 4):
  - 1 standard deviation shock: solvency returns to target rapidly, adjustment mainly via dividends.
  - Stronger shock: dividend cuts insufficient; bank cuts lending and restores capital gradually via retained earnings; lending returns to target only after several periods despite borrower creditworthiness unchanged.
- Interest rate shock (Figure 5):
  - One-period increase in deposit rate ρ raises funding costs and deteriorates bank capital due to maturity mismatch; credit crunch emerges until solvency restored.
- Sensitivity results (Table 3):
  - For a 2-standard-deviation negative productivity shock, contraction in lending on impact more than doubles when impatience increases from 1 percent to 3 percent.
  - Upward shift in f halves the contraction at low impatience relative to baseline.
- Empirical alignment: Hancock, Laing, and Wilcox (1995) find loan categories take two to three years to adjust after bank capital shocks.

### V. BANK RECAPITALIZATION
- Key insight: transitory shocks can generate persistent credit crunches; restoring solvency is necessary to escape crunch.
- Public recapitalization modeled as a one-time unexpected event from bank perspective.
- Numerical experiment (Figure 6):
  - Without capital injection, lending returns to normal in 9 periods (interpretable as 9 years under calibration).
  - With recapitalization sized to restore lending to long-run target (via solving FOC equation (25)), recovery is much faster.
- Relationship between recapitalization size and credit crunch severity (Figure 7):
  - Credit crunch severity computed as cumulative difference between long-run and actual levels of lending.
  - Cumulative difference becomes exactly zero when recapitalization reaches 63 percent of target capital.
- Solvency regions (Table 4):
  - Thresholds:
    - Minimum capital θ_l below which bank collapses without recapitalization (absorbing state).
    - θ_h above which bank restores solvency by cutting dividends without persistent crunch.
  - Numerical thresholds in example: θ_l = 7.7% of long-run target θ* and θ_h = 72.5% of long-run target θ*.
- Policy implication: banking bailouts/recapitalizations during severe financial distress can be justified to avoid costly persistent credit crunches.

### VI. CONCLUSIONS
- Contribution: tractable framework modeling a bank as a firm with imperfect capital markets and an optimal financial structure that varies with perceived lending risk.
- Mechanism: bank capital acts as cushion; small shocks are absorbed via precautionary buffer, larger shocks produce persistent credit crunches—even for one-time i.i.d. shocks—generating serial correlation in lending responses.
- Asymmetric propagation: negative shocks have stronger persistence than positive ones.
- Policy takeaway: recapitalization can materially shorten and reduce the severity of credit crunches; targeted public recapitalizations may be welfare-improving during systemic distress.

### APPENDIX — Calibration and Solution Details (key numerics)
- Calibration parameters used in numerical solutions:
  - 1/β = 0.965
  - 1+E[ρ] = 1.025
  - Deposit interest rate discretely distributed: {1.015, 1.025, 1.035} with probabilities {0.25, 0.50, 0.25}
  - E[α] = 1.07
  - σ_α = σ_Φ = 0.04
  - Bankruptcy costs u = 0.20
  - f = 0.8 (c/(l+o))^{100}
- Target implications at calibration:
  - Spread between contractual lending and deposit rates of 3%
  - Solvency ratio 13.5%
  - Borrower leverage ratio 61%
- Solution algorithm:
  - Terminal condition: V_T(n_T,l_{T−1}) = n_T with d_T = n_T and no new loans.
  - Backward induction with endogenous gridpoints; augment state grid with θ_t* where dividend constraint binds.
  - Convergence criterion: ||d_t(n,l) − d_{t−1}(n,l)|| ≤ 0.0001 and ||l_t(n,l) − l_{t−1}(n,l)|| ≤ 0.0001.
  - Expectations approximated using Gaussian quadrature with 3 points.
- Agency-costs variant:
  - Alternative: Φ realization private to bank; depositors face monitoring cost λ in bankruptcy.
  - Bank closure condition: 0 ≥ (1+ρ_{t+1}) c_{t} + G(l_{t−1}, l_t, Φ_{t+1}) − l_t − c_t (equation (35)).
  - Depositor expected return condition: E_t[j(l_{t−1}, l_t, ρ_t, c_t, Φ_{t+1})] ≥ γ_t c_t with equality under price-taking depositors.
  - Example plotted in Figure 8 assumes l_{t−1} = l_t = l*, λ = 0.40, γ_t = 1.025 with other parameters at baseline.

*Source: _wp08248 - References.................................................................................................................................*

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

### References................................................................................................................................31

### I. INTRODUCTION
- The financial turmoil originating with the collapse of the subprime mortgage market in the US has claimed more than US$ 600 bn. in losses to financial firms and produced a significant contraction in bank lending standards.
- The US Congress passed a bailout package to alleviate capital-constrained financial institutions; this paper develops a model to study credit crunches and explore policy options.
- The paper situates itself in the literature linking financial factors and the real economy, emphasizing the breakdown of Modigliani and Miller (1958) in the presence of information costs.
- Key empirical and theoretical references motivating the model include Bernanke, Gertler, and Gilchrist (1996, 1999), Bernanke and Gertler (1989, 1990), Kiyotaki and Moore (1997), Gertler (1992), Greenwald and Stiglitz (1993), Fuerst (1995), Carlstrom and Fuerst (1997, 2001), Levin, Natalucci, and Zakrajsek (2004), Adrian and Shin (2008a and 2008b).
- Two stated advantages of the model over existing bank models: infinite-horizon feature and non-linear solution, which preserve banks’ precautionary motives.
- Model overview:
  - Two players: borrowers and a monopolistic bank.
  - Borrowers’ creditworthiness is constant over time (the Bernanke, Gertler, and Gilchrist (1999) financial accelerator is shut down).
  - Bank faces constraints in raising funds; funding costs increase when solvency declines.
  - Optimal financial structure arises; negative shocks lead first to dividend cuts, then to lending reductions if necessary, producing persistent credit crunches even after transitory shocks.
  - Bank exhibits a precautionary motive: higher optimal capital when credit risk increases.
- Policy implication highlighted: government bailouts (recapitalization policies) may be reasonable during systemic financial pressures.

### II. BANKS AND THE REAL ECONOMY
- Stylized fact: periods of significant financial distress are often followed by sizable and long-lasting contractions in bank credit.
- Two channels for credit contractions:
  - Credit channel via borrowers’ external finance wedge (countercyclical with net worth).
  - Supply-side channel via lenders’ financial condition (focus of this paper).
- Empirical consensus: lending responds significantly to the financial structure of the lender (examples: Bernanke and Lown (1991), Peek and Rosengren (1994, 1995), Hancock and Wilcox (1994), Kashyap and Stein (1995, 2000), Cetorelli and Goldberg (2008)).
- Evidence that deterioration in banks’ financial health has real effects: Bernanke (1983), Dell’Ariccia, Detragiache, and Rajan (2005), Gibson (1995, 1997), Klein, Peek, and Rosengren (2002), Peek, Rosengren, and Tootell (2003), Caballero, Hoshi, and Kashyap (2008), Adrian and Shin (2008a and 2008b).
- Identification challenge: disentangling demand from supply in loan contractions; paper proceeds to model bank-side propagation consistent with empirical findings.

### III. THE MODEL
- Environment:
  - Monopolistic bank and continuum of ex-ante identical borrowers.
  - Borrower-bank relationship: risky debt contract with costly monitoring; bank justified by cost efficiency in screening and monitoring.
  - Entrepreneurs live for two periods, endowment normalized to 1, invest in capital k at unit price, production over two periods with full depreciation at end.
- A. The Loan Contract
  - Production at t+2: y_{t+2} = α_{t+2} Φ_{t+2} k_{t+2} with k_{t+2} = l_{t+1}.
  - α and Φ are i.i.d., lognormal shocks; E[Φ] = 1 and E[α] > 0; supports α ∈ (0, ∞) and Φ ∈ [Φ, Φ̄].
  - Monitoring/bankruptcy costs: 1 ≥ u > 0, fraction of project value.
  - Entrepreneur return: π(R_t, l_t, α_{t+2}, Φ_{t+2}) = (l_{t+1}) α_{t+2} Φ_{t+2} − R_t l_t.
  - Existence of cutoff ᾱ solving (l_{t+1}) α_{t+2} Φ_{t+2} − R_t l_t = 0; default when α < ᾱ.
  - Bank revenues (ex-post) aggregate across borrowers: G = M[α, l, R, Φ] as in equation (9), shutting down financial accelerator since expected revenues time-invariant.
  - Entrepreneurs compare project return to depositing endowment: E_t[(1+ρ_{t+1})(1+ρ_{t+2})] = (1+ρ)^2; participation constraint (7) holds with equality under take-it-or-leave-it offers.
- B. The Bank’s Optimization Problem
  - Risk-neutral stockholders choose lending l_t, dividends d_t, and deposits c_t to maximize market value: Max E_t Σ_{s=t}^∞ β^{s-t} d_s.
  - State variables: book value of bank capital n_t and outstanding loans o_t (loans are two-period maturity).
  - Transition equations:
    - n_{t+1} = G(o_t, Φ_{t+1}) + l_t + (1+ρ_{t+1}) c_t − f_t − c_t − l_t? (represented as equation (11) in text).
    - o_{t+1} = l_t.
  - Credit market frictions modeled via cost f_t linked to bank leverage, with f increasing and at least twice continuously differentiable in deposits; equity issuance is infinitely costly.
  - Constraint: c_t ≥ o_t + l_t + (n_t − d_t) and holds with equality given f and no cash return.
  - Dividend non-negativity: d_t ≥ 0.
  - Impatience assumption: 1/β > 1+ρ ensures not fully self-funded.
  - Bellman formulation summarized in equations (15)–(19).
- C. Solution
  - Numerical solution via endogenous gridpoints method (Carroll (2006)); appendix contains parameter values and algorithm.
  - Reformulated with middle-of-period and end-of-period state variables: end-of-period capital θ_t = n_t − d_t and value-to-go 𝒱_t(θ_t, λ_t, λ_{t−1}) = E_t β V_{t+1}(n_{t+1}, λ_t).
  - First-order conditions:
    - ∂𝒱/∂θ = 1 (equation (24)): marginal value of retained capital equals marginal cost of dividends.
    - ∂𝒱/∂λ = 0 (equation (25)): marginal value of outstanding loans set to marginal cost of raising funds.
  - Marginal cost of lending includes [ρ_{t+1} + f_t + (λ_t + λ_{t−1} − θ_t) ∂f/∂λ] times ∂V_{t+1}/∂n, equated to ∂V_{t+1}/∂λ.
  - Policy functions d(n_t, l_{t−1}) and l(n_t, l_{t−1}) are non-linear with kinks where dividend constraint binds; non-decreasing in bank capital and non-increasing in outstanding loans.
  - Asymmetry: negative shocks can trigger sharp contractions in lending while positive shocks may not produce symmetric expansions.
- D. Risk and the Target Level of Solvency
  - Target solvency arises from trade-off between impatience and decreasing marginal value of bank capital induced by f.
  - For low capital, marginal value of capital high → retain earnings; for high capital, marginal value low → distribute dividends; target where balanced.
  - Effects of assumptions:
    - If f linear, marginal value could be uniformly higher/lower and bank might hold no deposits.
    - Decreasing impatience increases the target level of solvency (1/β − 1 approaches ρ).
  - Precautionary motive: increasing variance of productivity shocks shifts marginal value of capital upward → higher target solvency.
  - Empirical note: Valencia (2006) finds median reduction in bank capital of 8 percent if risk decreased to lowest sample level.

### IV. QUANTITATIVE EXPERIMENTS
- Experiment 1: one-period negative productivity shocks (Figure 4).
  - Shock scenarios distinguished by size:
    - 1 standard deviation shock: solvency returns to target rapidly, adjustment mainly via dividends.
    - Stronger shock: dividend cuts insufficient; bank cuts lending and restores capital gradually via retained earnings; lending returns to target only after several periods despite borrower creditworthiness unchanged (financial accelerator shut down).
- Interest rate shock (Figure 5):
  - One-period increase in deposit rate ρ raises funding costs and deteriorates bank capital due to maturity mismatch; credit crunch emerges until solvency restored.
- Sensitivity to impatience and financial friction intensity (Table 3):
  - For a 2-standard-deviation negative productivity shock, contraction in lending on impact more than doubles when impatience increases from 1 percent to 3 percent.
  - Upward shift in f halves the contraction at low impatience relative to baseline.
- Empirical alignment: Hancock, Laing, and Wilcox (1995) find loan categories take two to three years to adjust after bank capital shocks.

### V. BANK RECAPITALIZATION
- Transitory shocks can generate persistent credit crunches; restoring solvency is necessary to escape crunch.
- Public recapitalization treated as a one-time unexpected event from bank perspective.
- Numerical experiment (Figure 6):
  - Without capital injection, lending returns to normal in 9 periods (interpretable as 9 years under calibration).
  - With recapitalization sized to restore lending to long-run target (via solving FOC equation (25)), recovery is much faster.
- Relationship between recapitalization size and credit crunch severity (Figure 7):
  - Credit crunch severity computed as cumulative difference between long-run and actual levels of lending.
  - Cumulative difference becomes exactly zero when recapitalization reaches 63 percent of target capital.
- Solvency regions (Table 4):
  - There exists minimum capital θ_l below which bank collapses without recapitalization (absorbing state).
  - There exists θ_h above which bank restores solvency by cutting dividends without persistent crunch.
  - For θ_t such that θ_l < θ_t < θ_h bank may recover without recapitalization, but gradually.
  - Numerical thresholds in example: θ_l = 7.7% of long-run target θ* and θ_h = 72.5% of long-run target θ*.

### VI. CONCLUSIONS
- Model contribution: tractable framework modeling bank as firm with imperfect capital markets and an optimal financial structure that varies with perceived lending risk.
- Mechanism: bank capital acts as cushion; small shocks are absorbed via precautionary buffer, larger shocks produce persistent credit crunches—even for one-time i.i.d. shocks—generating serial correlation in lending responses.
- Asymmetric propagation: negative shocks have stronger persistence than positive ones.
- Policy implication: banking bailouts/recapitalizations during severe financial distress can be justified to avoid costly persistent credit crunches.

### Figures and Tables (as described in the text)
- Figures referenced: Figure 1 (Bank Credit as Percentage of GDP), Figure 2 (Optimal Policy Functions), Figure 3 (Target Level of Solvency), Figure 4 (Responses to a Negative Transitory Productivity Shock), Figure 5 (Responses to an Interest Rate Increase), Figure 6 (Responses to a Large Negative Shock, With and Without Recapitalization), Figure 7 (Credit Crunch Severity and Bank Recapitalization), Figure 8 (Deposit Interest Rate).
- Tables referenced: Table 1 (Bank’s Sequence of Events), Table 2 (Public Recapitalization Costs for Selected Crises Episodes), Table 3 (Sensitivity Analysis to a 2-σ Productivity Shock), Table 4 (Bank’s Solvency Regions).

### APPENDIX
- E. Calibration
  - Parameters used in numerical solutions:
    - 1/β = 0.965
    - 1+E[ρ] = 1.025
    - Deposit interest rate discretely distributed: {1.015, 1.025, 1.035} with probabilities {0.25, 0.50, 0.25}
    - E[α] = 1.07
    - σ_α = σ_Φ = 0.04
    - Bankruptcy costs u = 0.20
    - f = 0.8 (c/(l+o))^{100}
  - These values generate at the target: spread between contractual lending and deposit rates of 3%, solvency ratio 13.5%, and borrower leverage ratio 61%.
- F. Solution Algorithm
  - Terminal condition: assume bank liquidated at some T with d_T = n_T and no new loans; V_T(n_T,l_{T−1}) = n_T.
  - Backward induction approach with endogenous gridpoints: solve first-order conditions (24) and (25) for θ_t* and λ_t* given λ_{t−1}; augment state grid with θ_t* for accuracy where dividend constraint binds.
  - Policy function construction via piecewise linear interpolation; convergence criterion: ||d_t(n,l) − d_{t−1}(n,l)|| ≤ 0.0001 and ||l_t(n,l) − l_{t−1}(n,l)|| ≤ 0.0001.
  - Expectations approximated using Gaussian quadrature with 3 points (no material difference with more points).
- G. Agency Costs in the Depositor-Bank Relationship
  - Alternative modeling: Φ realization private to bank; depositors face monitoring cost λ in bankruptcy.
  - Bank closed if book equity ≤ 0: condition 0 ≥ (1+ρ_{t+1}) c_{t} + G(l_{t−1}, l_t, Φ_{t+1}) − l_t − c_t (equation (35)).
  - Depositor expected return condition E_t[j(l_{t−1}, l_t, ρ_t, c_t, Φ_{t+1})] ≥ γ_t c_t holds with equality under price-taking depositors.
  - Example: Figure 8 plots resulting interest rate making depositor participation constraint bind assuming l_{t−1} = l_t = l*, λ = 0.40, γ_t = 1.025 with other parameters at baseline.

*Italicized source: Content extracted from _wp08248 - References.................................................................................................................................*

### References

### References

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- Diamond, D., and R. Rajan (1999): “A Theory of Bank Capital,” working paper 7431, National Bureau of Economic Research.
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- Kashyap, A., and J. Stein (1995): “The Impact of Monetary Policy on Bank Balance Sheets,” Carnegie-Rochester Conference Series on Public Policy, 42, 151–195.
- Meh, C., and K. Moran (2004): “Bank Capital, Agency Costs, and Monetary Policy,” working paper 2004-6, Bank of Canada.
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- Valencia, F. (2006): “Banks’ buffer capital: how important is banks’ precautionary motive?,” unpublished manuscript, Johns Hopkins University, available upon request.
- Hancock, D., A. Laing, and J. Wilcox (1995): “Bank capital shocks: Dynamic effects on securities, loans, and capital,” Journal of Banking and Finance, 19, 661–677.
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### Financial Accelerator, Credit Channel, and Business Cycles
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- __________ (1995): “The Capital Crunch: Neither a Borrower nor a Lender Be,” Journal of Money, Credit and Banking, 27(3), 625–38.
- __________ (1997): “The International Transmission of Financial Shocks: The Case of Japan,” American Economic Review, 87(4), 495–505.
- __________ (1999): “Japanese Banking Problems: Implications for Lending in the United States,” New England Economic Review, (Jan), 25–36.
- __________ (2000): “Collateral Damage: Effects of the Japanese Bank Crisis on Real Activity in the United States,” American Economic Review, 90(1), 30–45.
- Klein, M., J. Peek, and E. Rosengren (2002): “Troubled Banks, Impaired Foreign Direct Investment: The Role of Relative Access to Credit,” American Economic Review, 92(3), 664–682.
- Cetorelli, N. and L. Goldberg (2008): “Banking Globalization, Monetary Transmission, and the Lending Channel,” working paper 14101, National Bureau of Economic Research.

### Empirical Evidence on Lending, Investment, and Real Effects
- Driscoll, J. C. (2004): “Does bank lending affect output? Evidence from the U.S. states,” Journal of Monetary Economics, 51(3), 451–71.
- Gibson, M. (1995): “Can Bank Health Affect Investment? Evidence from Japan,” Journal of Business, 68(3), 281–308.
- __________ (1997): “More Evidence on the Link between Bank Health and Investment in Japan,” Journal of the Japanese and International Economies, 11(3), 296–310.
- Peek, J., E. Rosengren, and G. Tootell (2003): “Identifying the Macroeconomic Effect of Loan Supply Shocks,” Journal of Money, Credit and Banking, 35(6), 931–46.
- Hancock, D., A. Laing, and J. Wilcox (1995): “Bank capital shocks: Dynamic effects on securities, loans, and capital,” Journal of Banking and Finance, 19, 661–677.

### Theoretical and Methodological Contributions
- Modigliani, F., and M. Miller (1958): “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economic Review, 48(3), 261–97.
- Gale, D., and M. Hellwig (1985): “Incentive-Compatible Debt Contracts: The One-Period Problem,” Review of Economic Studies, 52(4), 647–63.
- Townsend, R. (1979): “Optimal Contracts and Competitive Markets with Costly State Verification,” Journal of Economic Theory, 21(2), 265–935.
- Holmstrom, B., and J. Tirole (1997): “Financial Intermediation, Loanable Funds, and the Real Sector,” The Quarterly Journal of Economics, 112(3), 663–91.
- Greenwald, B., and J. Stiglitz (1993): “Financial Market Imperfections and Business Cycles,” The Quarterly Journal of Economics, 108(1), 77–114.
- Blinder, A., and J. Stiglitz (1983): “Money, Credit Constraints, and Economic Activity,” American Economic Review, 73(2), 297–302.
- Bernanke, B., and C. Lown (1991): “The Credit Crunch,” Brookings Papers on Economic Activity, 1991(2), 205–39.
- Stein, J. (1998): “An Adverse-Selection Model of Bank Asset and Liability Management with Implications for the Transmission of Monetary Policy,” RAND Journal of Economics, 29(3), 466–486.
- Judd, K. (1998): Numerical Methods in Economics, chap. 7, pp. 261–62. The Massachusetts Institute of Technology Press, Cambridge.
- Mas-Colell, A., M. W., and J. Green (1995): Microeconomic Theory, chap. 14, pp. 480–81. Oxford University Press, New York.
- Carroll, C. (2004): “Theoretical Foundations of Buffer Stock Saving,” working paper 10867, National Bureau of Economic Research.
- __________ (2006): “The Method of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems,” Economics Letters, 91(3), 312–20.
- Geiregat, C. (2001): “Financial Structure and Aggregate Fluctuations,” Ph.D. thesis, The Johns Hopkins University, Baltimore, Maryland.

### Crisis Narratives and Historical Studies
- Bernanke, B., M. Gertler, and S. Gilchrist (1996): “The Financial Accelerator and the Flight to Quality,” The Review of Economics and Statistics, 78(1), 1–15.
- Christiano, L., R. Motto, and M. Rostagno (2004): “The Great Depression and the Friedman-Schwartz hypothesis,” working paper 10255, National Bureau of Economic Research.
- Christiano, L. J., and J. M. Davis (2006): “Two Flaws In Business Cycle Accounting,” Working Paper 12647, National Bureau of Economic Research.
- Bernanke, B. (1983): “Nonmonetary Effects of the Financial Crisis in Propagation of the Great Depression,” American Economic Review, 73(3), 257–76.
- Gorton, G. (2008): “The Panic of 2007”, working paper 14358, National Bureau of Economic Research.
- Burnside, C., M. Eichenbaum, and S. Rebelo (2000): “On the Fundamentals of Self-fulfilling Speculative Attacks,” Discussion Paper 2565, Center for Economic Policy Research.
- Caballero, R., T. Hoshi, and A. Kashyap (2008): “Zombie Lending and Depressed Restructuring in Japan,” American Economic Review, forthcoming.

*Source: _wp08248 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08248.pdf_