## _wp1268

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---

### Introduction
- Crisis features: large collapse in asset values, severe deterioration of financial intermediaries’ balance sheets, freezing of credit markets, dramatic contraction in output; motivating forceful interventions by governments and central banks.
- Purpose: develop a dynamic stochastic general equilibrium model to assess the impact of rare but large shocks to the net worth of financial intermediaries and explore welfare implications of recapitalization policies.

### Model structure and financial frictions
- Sectors and agents:
  - Three sectors: households (continuum of risk-averse workers who deposit savings), financial intermediaries (continuum subject to idiosyncratic shocks, raise deposits and lend to real firms), and firms in the non-financial corporate (real) sector (borrow from financial intermediaries, hire workers, earn returns subject to idiosyncratic shocks).
  - All three sectors face exogenous net worth losses; financial and real firms pay dividends at an exogenous rate.
- Contracting friction:
  - Costly state verification à la Townsend (1979) with monitoring cost fractions μ_f and μ_r, generating spreads between lending and borrowing rates and limited enforcement via bankruptcy thresholds.
  - Financial frictions present in both financial intermediaries and real firms (double layer), allowing comparison of shocks across sectors and assessment of wealth transfers.
- Key equations and decision variables (select):
  - Real-sector insolvency threshold: ω_r = l_{r,t} (1 + r_{r,t}) / (k_t A_t).
  - Financial-sector insolvency threshold: ω_f = d_{f,t} (1 + i_{f,t}) / ( l_{f,t} (1 + r_t) ).
  - Leverage choices: λ_{r,t} = k_{r,t} / e_{r,t}; λ_{f,t} = l_{f,t} / e_{f,t}.
  - Aggregate relationships:
    - L_{r,t} = E_{r,t} (λ_{r,t} − 1)
    - K_t = E_{r,t} λ_{r,t}
    - E_{r,t+1} = (1−D_r) E_{r,t} Π_{r,t} − Υ_{r,t+1}
    - D_{f,t} = E_{f,t} (λ_{f,t} − 1)
    - L_{f,t} = E_{f,t} λ_{f,t}
    - E_{f,t+1} = (1−D_f) E_{f,t} Π_{f,t} − Υ_{f,t+1}
  - State space reduction: triplet (E_{r,t}, E_{f,t}, i_t).
- Solution method:
  - Global solution methods with endogenous gridpoints (building on Carroll (2006)), due to large departures from steady state in systemic crises.

### Calibration and key quantitative targets
- Frequency: quarterly.
- Production and preferences:
  - Depreciation δ = 2.5%
  - Capital share α = 36%
  - Discount factor β = 0.994 → steady state risk-free deposit rate i_t roughly 2 percent annual.
- Monitoring costs and idiosyncratic risk:
  - Monitoring costs: μ_f = 0.12 (financial), μ_r = 0.36 (real).
  - Idiosyncratic risk distributions: lognormal mean-one.
    - Standard deviation real sector = 0.22
    - Standard deviation financial sector = 0.06
  - Exogenous dividend rate D_r = D_f = 4.7%
- Aggregate net worth shock calibration:
  - Absolute loss equal to proportion Φ of total net worth E_h + E_f + E_r.
  - Φ = 4% chosen so that when loss affects financial sector, GDP falls by about 4% (as experienced by the US in 2008Q4).
  - Shock probability: each shock is realized with probability 1 over 75 (expected once every 75 years).
- Steady state targets (Table 1; model vs data):
  - Leverage Financial Sector: Model 7.5, Data 10.3
  - Leverage Real Sector: Model 2.4, Data 2.0
  - Risk Spread Financial Sector: Model 40 bps, Data 44 bps
  - Risk Spread Real Sector: Model 127 bps, Data 110 bps
  - Bankruptcy Rate Financial Sector: Model 3.0 %, Data 2.1 %
  - Bankruptcy Rate Real Sector: Model 3.1 %, Data 3.0 %

### Responses to net worth shocks — main experiments and findings
- Experiment design:
  - Baseline shock: exogenous reduction in total net worth equal to 4% of total net worth; compared when loss is allocated to household, financial, or real sector.
  - Impulse responses reported as percent deviations from deterministic steady state; one period = one quarter.
- A. Financial sector as amplifier (real-sector-origin shocks)
  - Introducing frictions in financial sector raises borrowing wedge for real firms and reduces leverage and capital in steady state.
  - For baseline calibration, responses to shocks originating in the real sector are virtually unchanged with and without frictions in the financial sector because the intermediation margin charged by financial sector remains fairly stable.
  - Model omission: does not include endogenous asset prices (a channel important in other literature).
- B. Financial sector as shock generator (sector-concentrated shocks)
  - Equal absolute net worth loss Φ = 4% concentrated on financial sector:
    - Financial-sector capitalization suffers a much larger percentage loss (financial net worth smallest, leverage highest).
    - Outcomes: higher financial-sector leverage and borrowing spreads; severe impairment of intermediation; large contraction in deposits and loans; deposit risk-free rate falls while lending rate rises; large decline in GDP similar in magnitude to the 2008 US recession.
  - Loss concentrated on real sector:
    - Lower capitalization → reduced capital and output, higher marginal return on investment → real-sector leverage increases → higher borrowing spreads; households reduce consumption to smooth; slow recovery and gradual de-leveraging of real sector.
  - Loss concentrated on household sector:
    - Lower household wealth → lower deposits and lending → lower output; output reduction moderate relative to financial- and real-sector shocks.
    - Deposit rate increases (contrast: deposit rate falls when financial sector is hit), inducing household consumption cut and supporting new investment.
  - Main conclusion: output losses are much larger when net worth loss is concentrated on the high-leverage financial sector, motivating targeted recapitalization.

### Recapitalization policies — welfare assessment and financing sources
- Conceptualization:
  - Recapitalization modeled as wealth transfers across sectors (government equity injections, debt-to-equity conversion, asset swaps above market rates, lax monetary policy) implemented abstractly as redistributions of net worth.
  - Recapitalization implemented upon occurrence of net worth shock; financing sources considered: households, real sector, or both.
  - Model assumption: no moral hazard in modeled recapitalizations.
- Welfare metric:
  - Welfare gains ν defined as permanent percentage increase in consumption that makes household indifferent between world without recapitalization and with recapitalization:
    - (1 + ν)^{1−γ} v_h(E_h, E_f, E_r) = ṽ_h(Ē_h, Ē_f, Ē_r) (equation (26)).
  - Gains evaluated both at deterministic steady state of non-recapitalization economy and at each model’s own steady state (with recapitalization).
- Quantitative findings:
  - Full recapitalization of financial sector financed entirely by households:
    - Welfare gains equal permanent increase in consumption of 0.12%.
  - Gains decrease if a lower share of recapitalization is financed by households (i.e., more financed by real sector), but remain positive even if financing entirely from real sector.
    - Rationale: financial sector’s higher leverage implies moving funds from real to financial sector supports larger lending and investment; recapitalization reduces bankruptcies aiding capital re-accumulation.
  - Comparing steady-state welfare (with recapitalization) yields somewhat larger gains than introducing recapitalization at non-recapitalization steady state because recapitalizations raise expected return on savings by avoiding negative real interest rates during financial crises, stimulating capital accumulation and higher net worth steady states.
  - Welfare gains are exponentially increasing in shock size (Figure 6): larger shocks yield rapidly larger welfare gains.
    - Policy implication: if implementation costs of recapitalizations have a fixed component, policies should be reserved for large shocks.

### Uncertainty shocks — idiosyncratic risk and interaction with recapitalization
- Role of idiosyncratic risk:
  - Idiosyncratic risk and costly monitoring generate agency costs via limited liability and bankruptcy risk.
- Experiment:
  - Permanent increase/decrease in financial-sector idiosyncratic uncertainty equal to 20 percent of baseline σ_f (baseline σ_f = 0.06; experiment ±20% of that).
  - Decrease in idiosyncratic risk:
    - Spreads on financial intermediaries’ borrowing rates decrease → financial intermediaries increase leverage and lending → deposit demand increases → consumption discouraged, savings rise, risk-free rate up → borrowing costs for real firms fall → real-sector leverage, capital, and output rise.
    - Financial-sector net worth gradually decreases as lower idiosyncratic risk reduces upside returns under limited liability; real-sector net worth increases due to lower borrowing costs.
  - Effects reverse symmetrically for an increase in idiosyncratic risk.
- Key implication:
  - Reduction in idiosyncratic uncertainty (e.g., through financial innovation, securitization, CDS) can increase financial-sector leverage and thereby increase vulnerability to aggregate shocks.
- Recapitalization and idiosyncratic risk:
  - Welfare gains from recapitalizing financial sector (funds from households) vary non-monotonically with idiosyncratic risk:
    - As idiosyncratic risk decreases from baseline, welfare gains initially increase (due to increased leverage raising potential amplification).
    - For further reductions, gains decrease because financial frictions become less relevant.
    - Overall: non-monotonic relationship between welfare gains from recapitalization and financial-sector idiosyncratic risk.

### Conclusion — quantitative lessons and policy messages
- Model contributions:
  - Dynamic-stochastic general equilibrium with financial frictions in both financial intermediaries and real firms; global solution methods enable analysis of rare but large shocks.
- Main quantitative findings:
  - Shocks impairing financial sector balance sheets generate largest output contractions due to high leverage.
  - Recapitalizing financial sector after large net worth shocks can yield substantial welfare gains; baseline experiment: up to 0.12% permanent consumption increase when financed by households (comparable to gains from eliminating business cycle fluctuations).
  - Welfare-maximizing funding source: households (but financing from real sector can still yield positive gains).
  - Gains increase with shock size and can be amplified following reductions in financial-sector idiosyncratic risk (through higher leverage), but the relationship is non-monotonic.
- Policy-relevant messages:
  - Targeted recapitalization of financial sector following large balance-sheet shocks can be welfare-improving.
  - Recapitalization policies are most valuable for large, rare shocks when implementation costs have fixed components.
  - Further research directions: detailed comparisons of implementation mechanisms, moral hazard implications, and macroprudential policies to contain leverage across sectors.

*Source — Excerpt from IMF working paper (_wp1268) including introduction, model description, calibration overview, literature comparison, and policy discussion.*

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

### References

### Introduction
- The recent crisis featured a large collapse in asset values, severe deterioration of financial intermediaries’ balance sheets, freezing of credit markets, and a dramatic contraction in output, prompting forceful interventions by governments and central banks.
- The paper develops a dynamic stochastic general equilibrium model to assess the impact of rare but large shocks to the net worth of financial intermediaries and to explore the welfare implications of recapitalization policies.

### Model structure and financial frictions
- Three sectors: households (continuum of risk-averse workers who deposit savings), financial intermediaries (continuum subject to idiosyncratic shocks, raise deposits and lend to real firms), and firms in the non-financial corporate (real) sector (borrow from financial intermediaries, hire workers, earn returns subject to idiosyncratic shocks).
- All three sectors face the risk of exogenous net worth losses; financial and real firms pay dividends to households at an exogenous rate.
- Financial frictions are modeled with a costly state verification problem à la Townsend (1979), generating spreads between lending and borrowing rates and preventing efficient market reallocation of capital.
- Key model feature: financial frictions on both the financial intermediaries and the real sector (double layer), allowing comparison of shocks across sectors and assessment of wealth transfers between sectors.
- Global solution methods are used because systemic banking crisis shocks move the system significantly away from steady state.

### Calibration and key quantitative findings
- The model is calibrated to U.S. data.
- A given net worth loss produces a much larger GDP contraction when it hits financial intermediaries rather than households or real firms, primarily due to the high leverage of financial intermediaries.
- Welfare gains from recapitalizing the financial sector with funds from the household sector are equivalent to a permanent increase in consumption by 0.15%.
  - The paper notes this 0.15% consumption-equivalent gain is comparable to the gains a standard RBC model without financial friction would predict from eliminating business cycle fluctuations.
- Financing recapitalization with resources from the real sector can still be welfare enhancing because financial intermediaries are more leveraged than real firms.

### Role of idiosyncratic risk and leverage dynamics
- The level of idiosyncratic volatility controls the importance of financial frictions under costly state verification; with idiosyncratic volatility at zero, the model collapses to a standard frictionless world.
- Reductions in idiosyncratic volatility reduce financial frictions (beneficial) but lead to a gradual increase in the leverage of financial intermediaries (making the economy less resilient to financial sector shocks), potentially increasing welfare gains from recapitalization.

### Relation to prior literature
- Builds on costly state verification frameworks used by Carlstrom and Fuerst (1997) and Bernanke, Gertler and Gilchrist (1999), and extends previous models by incorporating a financial sector with frictions.
- Differs from Chen (2001) and Meh and Moran (2010) by using costly state verification (allowing time-varying borrowing spreads and recapitalization financed from the real sector) rather than limited enforcement.
- Differs from Hirakata, Sudo and Ueda (2011) in modeling a competitive banking sector (not monopolistic) and in using global solution methods rather than log-linear approximation.
- Shares purpose with Gertler and Karadi (2010) and Del Negro et al. (2011) in analyzing unconventional policies, but focuses on recapitalizations rather than credit policies and liquidity support.
- Kollmann, Roeger and in’t Veld (2012) study bank aid policies’ impact on GDP; this paper examines implications for welfare.

### Policy implications and recapitalization
- Output losses depend on which sector suffers the net worth shock, motivating recapitalization policies aimed at shifting losses to sectors better able to absorb them.
- Recapitalization transfers can be implemented through various channels (monetary easing, fiscal policy adjustments, asset purchases, equity injections financed by taxpayers); the paper evaluates welfare gains from exogenously redistributing wealth without focusing on a specific implementation.
- Given the substantial welfare gains identified for rare but large financial sector shocks, designing and implementing recapitalization policies is potentially as important as countercyclical policies aimed at smoothing business cycle fluctuations.

*Source: Excerpt from IMF working paper (_wp1268) including introduction, model description, calibration overview, literature comparison, and policy discussion.*

### Section III. Section IV presents quantitative experiments showing the model responses to net

### _wp1268 - Section III. Section IV presents quantitative experiments showing the model responses to net

### II. THE MODEL — structure and key equations
- Economy: closed, three sectors — household, financial, real.
- Real sector firms:
  - Entrepreneurs invest in productive capital k_t using net worth e_r_t and loans l_r_t.
  - Production revenues net of depreciation δ: ( (1−δ) k_t + k_t^α n_t^{1−α} − n_t W_t ) ω^r_{t+1}.
  - Optimal labor demand: n^*_t = k_t ( (1−α) / W_t )^{1/α}.
  - Expected net revenues summary: k_t A_t ω^r_{t+1}, with A_t defined as (k^{−α}( (1−α)/W_t )^{(1−α)/α}) (exact expression in text).
  - Agency problem via costly state verification: monitoring cost fraction μ_r; risky debt optimal contract.
  - Insolvency condition: l_r_t (1 + r_r_t) ≥ k_t A_t ω^r_{t+1}. Threshold ω_r = l_r_t (1 + r_r_t) / (k_t A_t).
  - Market return condition: (1 + r_t) = (1−μ_r) ∫_{0}^{ω_r} (k_t / l_r_t) A_t ω_r dΩ_r(ω_r) + (1−Ω_r(ω_r))(1 + r_r_t).
  - Entrepreneur expected profit Π_r_t as integral over ω_r (equation (7)); optimization reduces to choosing leverage λ_r_t = k_r_t / e_r_t.
  - Aggregate relationships:
    - L_r_t = E_r_t (λ_r_t − 1)
    - K_t = E_r_t λ_r_t
    - χ_r_t = D_r E_r_t Π_r_t
    - E_{r,t+1} = (1−D_r) E_r_t Π_r_t − Υ_{r,t+1}
  - Net worth shocks Υ_{r,t+1} hit at end of period (reduced-form for asset value shocks).

- Financial sector:
  - Financial entrepreneurs: net worth e_f_t, deposits d_f_t; lend l_f_t = e_f_t + d_f_t to real sector.
  - Lending revenues: l_f_t (1 + r_t) ω^f_{t+1}, with ω^f mean-one idiosyncratic shock.
  - Insolvency threshold ω_f = d_f_t (1 + i_f_t) / ( l_f_t (1 + r_t) ).
  - Participation constraint: (1 + i_t) = (1−μ_f) ∫_{0}^{ω_f} (l_f_t / d_f_t) (1 + r_t) ω_f dΩ_f(ω_f) + (1−Ω_f(ω_f))(1 + i_f_t).
  - Financial entrepreneur objective reduces to choosing leverage λ_f_t = l_f_t / e_f_t as function of (1 + r_t) / (1 + i_t).
  - Aggregate relationships:
    - D_f_t = E_f_t (λ_f_t − 1)
    - L_f_t = E_f_t λ_f_t
    - χ_f_t = D_f E_f_t Π_f_t
    - E_{f,t+1} = (1−D_f) E_f_t Π_f_t − Υ_{f,t+1}

- Equilibrium in credit markets:
  - Aggregate marginal product of capital A_t determined by aggregate capital K_t: A_t = (k^{−α} K_t^{α−1}) (expression in text).
  - For given i_t and capitalization E_f_t, E_r_t, equilibrium r_t solves L_r(E_r_t, r_t) = L_f(E_f_t, r_t, i_t).
  - State space reduces to triplet (E_r_t, E_f_t, i_t).

- Household sector:
  - Representative household maximizes CRRA utility with risk aversion γ; supplies fixed labor N.
  - Net worth evolution:
    - E_{h,t+1} = (E_{h,t} − C_{h,t})(1 + i_t) + χ_r_t + χ_f_t + W_t − Υ_{h,t+1}
  - Deposits supply: D_{h,t} = E_f_t (λ_f − 1).
  - Value function:
    - V_h(E_{h,t}, E_{r,t}, E_{f,t}) = max_{C_t} { u(C_{h,t}) + β E_t[ V_h(E_{h,t+1}, E_{r,t+1}, E_{f,t+1}) ] }
  - Transition equations included for E_h, E_f, E_r (equations (22)-(25)).
  - Solution method: global solution methods building on Carroll (2006)’s method of endogenous gridpoints.

### III. CALIBRATION — parameters and steady state targets
- Frequency: quarterly.
- Production parameters:
  - Depreciation δ = 2.5%
  - Capital share α = 36%
- Discount factor β = 0.994 → steady state risk-free deposit rate i_t roughly 2 percent annual.
- Identification: match leverages, spreads, and bankruptcy rates in real and financial sectors in steady state.
- Chosen parameter values:
  - Monitoring costs: μ_f = 0.12 (financial), μ_r = 0.36 (real).
  - Idiosyncratic risk distributions: lognormal mean-one.
    - Standard deviation real sector = 0.22
    - Standard deviation financial sector = 0.06
  - Exogenous dividend rate D_r = D_f = 4.7%
- Aggregate net worth shock calibration:
  - Absolute loss equal to proportion Φ of total net worth E_h + E_f + E_r.
  - Φ = 4% chosen so that when loss affects financial sector, GDP falls by about 4% (as experienced by the US in 2008Q4).
  - Shock probability: each shock is realized with probability 1 over 75 (expected once every 75 years).
- Table 1 steady state values and targets (model vs data):
  - Leverage Financial Sector: Model 7.5, Data 10.3
  - Leverage Real Sector: Model 2.4, Data 2.0
  - Risk Spread Financial Sector: Model 40 bps, Data 44 bps
  - Risk Spread Real Sector: Model 127 bps, Data 110 bps
  - Bankruptcy Rate Financial Sector: Model 3.0 %, Data 2.1 %
  - Bankruptcy Rate Real Sector: Model 3.1 %, Data 3.0 %

### IV. RESPONSES TO NET WORTH SHOCKS — main experiments and findings
- Experiment setup:
  - Analyze shocks that reduce net worth in household, financial, or real sector.
  - Baseline shock: exogenous reduction in total net worth equal to 4% of total net worth; compare when loss allocated to household, financial, or real sector.
  - Each period is one quarter; impulse responses shown as % deviations from deterministic steady state.
- A. Financial sector as amplifier (real-sector-origin shocks)
  - Compare economy with and without financial frictions in financial sector (shut down by setting μ_f or ω_f variance to zero).
  - Introducing frictions in financial sector raises borrowing wedge for real firms, reduces leverage and capital in steady state.
  - Key result: responses to shocks originating in the real sector are virtually unchanged with and without frictions in the financial sector (for baseline calibration).
    - Reason: intermediation margin charged by financial sector remains fairly stable in response to real-sector disruptions.
  - Note: model does not include endogenous asset prices — a channel often important for amplification in other literature.

- B. Financial sector as shock generator (shocks concentrated by sector)
  - When equal absolute net worth loss (Φ = 4%) is concentrated on the financial sector:
    - Financial sector capitalization suffers a much larger percentage loss (financial net worth smallest, leverage highest).
    - Results: much higher financial-sector leverage and borrowing spreads; severe impairment of intermediation; large contraction in deposits and loans; strong reduction in deposit risk-free rate and increase in lending rate; large decline in GDP similar in magnitude to the 2008 US recession.
  - When loss concentrated on real sector:
    - Lower capitalization → reduced capital and output, higher marginal return on investment → real-sector leverage increases → higher borrowing spreads. Household reduces consumption to smooth; slow recovery and gradual de-leveraging of real sector.
  - When loss concentrated on household sector:
    - Lower household wealth → lower deposits and lending → lower output, but reduction in output is moderate relative to financial- and real-sector shocks.
    - Deposit rate increases (in contrast to financial-sector shock where deposit rate falls), inducing household to cut consumption and support new investment.
  - Main conclusion: output losses are much more pronounced if net worth loss is concentrated on high-leverage financial sector. This motivates targeted recapitalization policies.

### V. RECAPITALIZATION POLICIES — welfare assessment and financing sources
- Recapitalization conceptualization:
  - Wealth transfers across sectors (government equity injections, debt-to-equity conversion, asset swaps above market rates, lax monetary policy) modeled abstractly as redistributions of net worth.
  - Recapitalization implemented upon occurrence of net worth shock; can be financed by households, real sector, or both.
  - No moral hazard in modelized recapitalizations (per model structure and assumptions).
- Welfare metric:
  - Welfare gains ν defined as permanent percentage increase in consumption that would make household indifferent between world without recapitalization and with recapitalization:
    - (1 + ν)^{1−γ} v_h(E_h, E_f, E_r) = ṽ_h(Ē_h, Ē_f, Ē_r) (equation (26)), where tilde denotes values with recapitalization.
  - Two comparison cases:
    - Gains evaluated at deterministic steady state of non-recapitalization economy (introducing recapitalization).
    - Gains evaluated at each model’s own steady state (having recapitalization).
- Quantitative findings:
  - If financial sector fully recapitalized and funds come entirely from household sector:
    - Welfare gains equal permanent increase in consumption of 0.12%.
  - Gains decrease if a lower share of recapitalization is financed by households (i.e., more taken from real sector), but remain positive even if financing is entirely from real sector.
    - Explanation: financial sector’s higher leverage implies moving funds from real to financial sector supports larger lending and investment; recapitalization also reduces bankruptcies aiding capital re-accumulation.
  - Comparing steady-state welfare (having recapitalization) yields somewhat larger gains than introducing recapitalization at non-recapitalization steady state:
    - Channel: recapitalizations raise expected return on savings by avoiding negative real interest rates during financial crises, stimulating capital accumulation and higher net worth steady states.
  - Welfare gains are exponentially increasing in size of shock:
    - Figure 6 traces gains from full recapitalization financed by households as function of shock size; larger shocks yield rapidly larger welfare gains.
    - Policy implication: if implementation costs of recapitalizations have a fixed component, policies should be reserved for large shocks.

### VI. UNCERTAINTY SHOCKS — idiosyncratic risk in financial sector and interaction with recapitalization
- Idiosyncratic risk role:
  - Idiosyncratic risk and costly monitoring generate agency costs through limited liability and bankruptcy risk.
- Experiment:
  - Permanent increase/decrease in idiosyncratic uncertainty in financial sector equivalent to 20 percent of baseline standard deviation (baseline σ_f = 0.06; experiment ±20% of that).
  - Impulse responses show:
    - Decrease in idiosyncratic risk → spreads on financial intermediaries’ borrowing rates decrease → financial intermediaries increase leverage and lending → deposit demand increases → consumption discouraged, savings rise, risk-free rate up → borrowing costs for real firms fall → real-sector leverage, capital, and output rise.
    - Net worth in financial sector gradually decreases as lower idiosyncratic risk reduces upside returns under limited liability; net worth in real sector increases due to lower borrowing costs.
    - Effects reverse symmetrically for increase in idiosyncratic risk.
- Key implication and parallel to pre-2007:
  - Reduction in idiosyncratic uncertainty (e.g., via financial innovation, securitization, CDS) can increase leverage in financial sector and thereby increase vulnerability to aggregate shocks.
- A. Recapitalization policies and idiosyncratic risk:
  - Welfare gains from recapitalizing financial sector (funds from households) vary non-monotonically with idiosyncratic risk:
    - As idiosyncratic risk decreases from baseline, welfare gains initially increase (due to increased leverage raising potential amplification of shocks).
    - For further reductions in idiosyncratic risk, gains decrease because financial frictions become less relevant.
    - Result: non-monotonic relationship between welfare gains from recapitalization and financial-sector idiosyncratic risk.

### VII. CONCLUSION — summary of quantitative lessons
- Model contributions:
  - Dynamic-stochastic general equilibrium with financial frictions in both financial intermediaries and real firms; global solution methods enable analysis of large shocks.
- Main quantitative findings:
  - Shocks impairing financial sector balance sheets generate largest output contractions due to high leverage.
  - Recapitalizing financial sector after large net worth shocks can yield substantial welfare gains (e.g., up to 0.12% permanent consumption increase in baseline experiment when financed by households), comparable to gains from eliminating business cycle fluctuations.
  - Welfare-maximizing funding source: households (but financing from real sector can still yield positive gains).
  - Gains increase with shock size and can be amplified following reductions in financial-sector idiosyncratic risk (through higher leverage), but relationship is non-monotonic.
- Policy-relevant messages:
  - Targeted recapitalization of financial sector following large balance-sheet shocks can be welfare-improving.
  - Recapitalization policies are most valuable for large, rare shocks when implementation costs have fixed components.
  - Further research directions: detailed comparisons of implementation mechanisms, moral hazard implications, and macroprudential policies to contain leverage across sectors.

*Italic: Source — _wp1268 - Section III. Section IV presents quantitative experiments showing the model responses to net (PDF chapter/section).*

### REFERENCES

### _wp1268 - REFERENCES

### Key citations on financial frictions and business cycles
- Arellano, Christina, Yan Bai, and Patrick Kehoe, 2011, “Financial Markets and Fluctuations in Uncertainty,”Unpublished Paper.
- Bernanke, Ben, Mark Gertler, and Simon Gilchrist, 1999, “The Financial Accelerator in a Quantitative Business Cycle Framework,”Handbook of Macroeconomics, Vol. 1, pp. 1341-1393.
- Bloom, Nicholas, Max Floetotto, and Nir Jaimovich, 2011, “Really Uncertain Business Cycles,” Unpublished Paper.
- Carlstrom, Charles T., and Timothy S. Fuerst, 1997, “Agency Costs, Net Worth, and Business Fluctuations: A Computable General Equilibrium Analysis,”The American Economic Review, Vol. 87, No. 5, pp. 893-910.
- Chen, Nan-Kuang, 2001, “Bank Net Worth, Asset Prices and Economic Activity,”Journal of Monetary Economics, Vol. 48, pp. 415-436.
- Christiano, Lawrence, Roberto Motto, and Massimo Rostagno, 2009, “Financial Factors in Economic Fluctuations,”Working Paper.
- Gertler, Mark, and Nobuhiro Kiyotaki, 2009, “Financial Intermediation and Credit Policy in Business Cycle Analysis,”Handbook of Monetary Economics, Vol. 3.
- , and Peter Karadi, 2010, “A Model of Unconventional Monetary Policy,”Journal of Monetary Economics, Vol. 58, No. 1, pp. 17-34.
- Gilchrist, Simon, Jae W. Sim, and Egon Zakraj
ˇ
sek, 2010, “Uncertainty, Financial Frictions, and Investment Dynamics,”Working Paper.
- Kollmann, Robert, Werner Roeger, and Jan in’t Veld, 2012, “Fiscal Policy in a Financial Crisis: Standard Policy vs. Bank Rescue Measures,”American Economic Review Papers and Proceedings (forthcoming).
- Meh, C
 ́
esaire A., and Kevin Moran, 2010, “The Role of Bank Capital in the Propagation of Shocks,”Journal of Economic Dynamics & Control, Vol. 34, pp. 555-576.
- Quadrini, Vincenzo, and Urban Jermann, 2011, “Macroeconomic Effects of Financial Shocks,” American Economic Review.Forthcoming.

### Monetary policy, unconventional measures, and crisis response
- Del Negro, Marco, Gauti Eggertsson, Nubuhiro Kiyotaki, and Andrea Ferrero, 2011, “The Great Escape? A Quantitative Evaluation of the Fed’s Non-Standard Policies,”Working Paper.
- C
 ́
urdia, Vasco, and Michael Woodford, 2009, “Credit frictions and optimal monetary policy,” BIS Working Papers 278, Bank for International Settlements, ).
- Hirakata, Naohisa, Nao Sudo, and Kozo Ueda, 2011, “Capital Injection, Monetary Policy, and Financial Accelerators,”IMES Discussion Paper No. 2011-E-10.
- Gertler, Mark, and Nobuhiro Kiyotaki, 2009, “Financial Intermediation and Credit Policy in Business Cycle Analysis,”Handbook of Monetary Economics, Vol. 3.
- , and Peter Karadi, 2010, “A Model of Unconventional Monetary Policy,”Journal of Monetary Economics, Vol. 58, No. 1, pp. 17-34.

### Theoretical foundations on contracts, monitoring, and credit cycles
- Gale, Douglas, and Martin Hellwig, 1985, “Incentive-Compatible Debt Contracts: The One-Period Problem,”The Review of Economic Studies, Vol. 52, No. 4, pp. 647-663.
- Holmstrom, Bengt, and Jean Tirole, 1997, “Financial Intermediation, Loanable Funds, and the Real Sector,”Quarterly Journal of Economics, Vol. 112, No. 3, pp. 663-691.
- Kiyotaki, Nobuhiro, and John Moore, 1997, “Credit Cycles,”Journal of Political Economy, Vol. 105, No. 2, pp. 211-248.
- Lucas, Robert E., Jr., 1987,Models of Business Cycles(Basil Blackwell, New York).
- Townsend, Robert M., 1979, “Optimal Contracts and Competitive Markets with Costly State Verification,”Journal of Economic Theory, Vol. 21, No. 2, pp. 265-935.
- Williamson, Stephen, 1987, “Costly Monitoring, Loan Contracts, and Equilibrium Credit Rationing,”The Quarterly Journal of Economics, Vol. 102, No. 1, pp. 135-145.
- Gale, Douglas, and Martin Hellwig, 1985, “Incentive-Compatible Debt Contracts: The One-Period Problem,”The Review of Economic Studies, Vol. 52, No. 4, pp. 647-663.

### Computational methods and applied modeling techniques
- Carroll, Christopher D., 2006, “The Method of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems,”Economics Letters, Vol. 91, No. 3, pp. 312-20.
- Carlstrom, Charles T., and Timothy S. Fuerst, 1997, “Agency Costs, Net Worth, and Business Fluctuations: A Computable General Equilibrium Analysis,”The American Economic Review, Vol. 87, No. 5, pp. 893-910.
- Christiano, Lawrence, Roberto Motto, and Massimo Rostagno, 2009, “Financial Factors in Economic Fluctuations,”Working Paper.
- Gilchrist, Simon, Jae W. Sim, and Egon Zakraj
ˇ
sek, 2010, “Uncertainty, Financial Frictions, and Investment Dynamics,”Working Paper.

*IMF Working Paper references list from _wp1268 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp1268.pdf_