## 1. Game Tree: The Effects of Contagion

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---

### Introduction and key mechanisms
- Governments provided massive support to distressed financial institutions during the recent crisis, which prevented systemic meltdown but created moral hazard incentives for banks.
- Two opposing effects of expected government bailouts on bank incentives:
  - Moral hazard effect: bailouts protect shareholders/managers and increase private risk taking.
  - Systemic insurance effect: bailouts remove an exogenous source of risk (contagion), which can increase banks' incentives to monitor loans.
- Contagion is modeled as a risk beyond an individual bank's control (cannot be managed or diversified) but endogenous to the financial system because it depends on all banks' risk taking.
- Strategic complementarity: banks take more risk when other banks take more risk, amplifying systemic risk.

### Model environment and assumptions
- Two identical, risk-neutral, profit-maximizing banks.
- Each bank i:
  - Has a loan portfolio of size 1.
  - Financed by equity k_i and deposits (or debt) 1−k_i.
  - Pays gross deposit rate r_D (not risk-sensitive thanks to deposit insurance).
  - Is protected by limited liability; owners lose invested capital if the bank fails.
- Loan portfolio success sources:
  - Idiosyncratic success with probability q_i chosen by the bank (monitoring effort).
  - Contagion: when one bank fails, there is a probability β that the other bank's portfolio becomes non-performing, independently of its monitoring.
- Monitoring cost: (1/2) c q_i^2, with c > (R − (1 − k_i) r_D) > 0 to ensure interior solution.
- For initial analysis, idiosyncratic risks are uncorrelated across banks.

### Expected profits and reaction functions (formal expressions preserved)
- Bank i expected profits:
  - E(Π_i) = q_i (1 − β (1 − q_j)) (R − (1 − k_i) r_D) − (c/2) q_i^2.  (Equation (1))
- First-order condition (reaction function):
  - q_i^ = [1 − β (1 − q_j)] (R − (1 − k_i) r_D) / c.  (Equation (2))
- Symmetric Nash equilibrium (imposing q_i = q_j = q^):
  - q^ = (1 − β) (R − (1 − k) r_D) / (c − β (R − (1 − k) r_D)).  (Equation (3))

### Main theoretical findings
- Contagion reduces private incentives to monitor:
  - Lemma 1: The equilibrium monitoring effort q^ is decreasing in the probability of contagion given failure, β: dq^/dβ < 0, and increasing in banks' capital: dq^/dk > 0.
  - In boundary cases:
    - q^ = 0 for β = 1.
    - q^ = (1/c) (R − r_D (1 − k)) for β = 0.
- Two distinct inefficiencies identified:
  - Classical moral hazard from limited liability and leverage (term (1 − k) r_D).
  - Externality from contagion (parameter β) that lowers the private return to monitoring and induces excessive risk taking.
- Strategic interaction amplifies the externality: each bank's monitoring raises the private return to monitoring of the other bank; thus, in equilibrium, banks under-monitor more than if facing the externality alone.
- Capital plays a dual role:
  - Maintains "skin-in-the-game" to reduce moral hazard.
  - By reducing bank-level risk, capital also reduces contagion and lowers risk taking in other banks (new dimension due to complementarity).

### Conceptual implications and cautions
- Government bailouts have ambiguous ex ante effects:
  - Can exacerbate moral hazard via bailout rents left to incumbents.
  - Can reduce contagion externality and thereby improve monitoring incentives (systemic insurance).
- Relative importance of effects depends on parameters:
  - Low bailout rents and high contagion probability can make bailouts welfare-improving ex ante.
- Important caveats:
  - Results do not downplay moral hazard; they highlight a trade-off.
  - Ex post considerations (costs of bankruptcy vs. public funds) may differ.
  - The analysis assumes government commitment to a bailout strategy; time-inconsistency could change outcomes (e.g., correlated risk-taking if banks expect bailouts more likely when many fail).

### Modeling scope and empirical grounding
- Focus on the contagion component that banks cannot manage or diversify.
- Contagion channels discussed in literature:
  - Macro contagion (bank failure worsens macro fundamentals).
  - Counterparty risk from interbank exposures.
  - Fire sales lowering asset prices or freezing funding markets.
- Bailouts defined broadly to include direct capital/liquidity injections and macro measures (fiscal/monetary accommodations) and typically leave bailout rents to incumbent shareholders.
- Size of bailout rents depends on intervention design and resolution frameworks.

### 3.2 Effects of Bailouts — mechanism and formal results
- Government intervenes in a failing bank with probability  ( known in advance).
- Bailout has two effects:
  - Prevents contagion: allows the other bank to survive intact and realize full profits.
  - Leaves bailout rents: failing bank keeps a share  <1 of the profits it could have made if idiosyncratically successful.
- Expected profits of bank i with intervention:
  - E(i) = (qi(1 (1 qj)(1 )) + (1 qi)) (R (1 k)rD)  c 2 qi2. (Equation (4))
- Reaction function from first-order condition:
  - bqi = (1 (1 qj)(1 ) ) (R (1 k)rD) / c. (Equation (5))
- Comparative static:
  - @bqi/@ = (1 qj)  all divided by c (R (1 k)rD). (Equation (6))

### Channels through which bailouts affect monitoring
- Systemic insurance effect (positive):
  - Bailouts reduce the threat of contagion (probability of contagion falls from (1 qj) to (1 qj)(1 )), increasing monitoring incentives.
  - Stronger when contagion threat (1 qj) is larger (higher  and/or bank j perceived as riskier).
- Moral hazard effect (negative):
  - Expectation of retaining share of profits  in failure reduces incentives to monitor.
  - Stronger when bailout rents  are larger.

### Symmetric Nash equilibrium with intervention
- Symmetric equilibrium monitoring:
  - bq() = (1 (1 ) ) (R (1 k)rD) / (c (1 ) (R (1 k)rD)). (Equation (7))

### Key result: Proposition 1
- For  <1, there exists  = c / [c (1 )(R (1 k)rD)], with d/d >0, such that:
  - If  >  then dbq()/d >0 (equilibrium monitoring increases with probability of intervention).
  - If  <  then dbq()/d <0 (equilibrium monitoring decreases with probability of intervention).
- Interpretation:
  - When probability of contagion given failure is high (high ) and bailout rents  are low, the systemic insurance effect can dominate moral hazard and increase monitoring incentives.

### 3.3 The Role of Bank Capital
- Monitoring level that internalizes contagion externality (joint maximization of (1) with qi = qj):
  - q = (1 ) (R rD(1 k)) / [c 2(R rD(1 k))]. (Equation (8))
- q > bq for any k.
- Externality-driven excess risk taking increases with higher capital:
  - d(q bq)/dk >0 and d(q/bq)/dk >0. (Equation (9))
- Intuition: Better-capitalized banks are more averse to exogenous contagion risk, so contagion externality raises their relative incentives to monitor.
- Nonetheless, capital regulation still matters:
  - Capital reduces moral hazard and also reduces contagion risk for other banks: dbqi/dkj >0.

### 3.4 The Case with Distressed Banks
- Distressed ("zombie") banks that have depleted capital (lower kj) or lower Rj reduce their own qj and impose negative externalities on healthy banks.
- Presence of distressed banks lowers screening incentives at healthy banks by increasing contagion threat and reducing returns to monitoring.
- Under these circumstances, bailout promises are more likely to improve screening incentives at healthy banks because @bqi/@ is larger when (1 qj) is greater (equation (6)).

### 4 A Model with Correlated Risks — setup and insights
- Two sectors; each bank lends to only one sector; banks can coordinate on same or different sectors.
- If banks lend to different sectors: idiosyncratic risks independent, exposed to undiversifiable contagion (as in main model).
- If banks lend to same sector: idiosyncratic risks are fully correlated; banks succeed or fail simultaneously; contagion is irrelevant in this case.
- Lending to the same sector reduces return in case of success by H (competition/compressed margins).
- Banks choose sectors sequentially (avoids coordination failure); monitoring chosen simultaneously.
- Define V = (R (1 ki)rD).

### 4.1 Contagion and Correlated Risks — key formulas and thresholds
- Different sectors (uncorrelated):
  - E(i) = qi(1 (1 qj))V  c 2 qi2. (Equation (10))
  - Nash equilibrium effort (uncorrelated sector):
    - ^q = (1 )V / (c V). (Equation (11))
  - Equilibrium profits when uncorrelated:
    - E(bU) = c/2 [ (1 )V / (c V) ]^2. (Equation (12))
- Same sector (correlated) when qi  qj:
  - E(i | qi  qj) = qi(V H)  c 2 qi2. (Equation (13))
- Same sector when qi > qj:
  - E(i | qi > qj) = qi(1 (qi qj))(V H)  c 2 qi2. (Equation (14))
- Lemma 2:
  - Continuum of symmetric Nash equilibria with qi = qj = bq2  (1 )(V H)/c ; V H/c .
  - Pareto-dominant equilibrium implemented by cheap talk: ^q = (V H)/c. (Equation (15))
  - Equilibrium profits when correlated:
    - E(bC) = c/2 [ (V H)/c ]^2. (Equation (16))
- Indifference threshold H~ between correlated and uncorrelated sectors:
  - eH = V(c V) / (c V). (Equation (17))
  - Banks lend to different sectors for H  H~, and to same sector for H < H~.
  - @H~/@ >0: higher contagion externality makes correlated investment (herding) more attractive.
- Interpretation: Severe contagion risk leads banks to herd (lend to same sector) and accept lower margins H, which raises overall risk taking. Correlated investments remove contagion exposure, making herding attractive despite lower V H.

### 4.2 Effects of Bailouts with correlated risks — formulas and Proposition 2
- Different sectors with government support probability :
  - E(i) = (qi(1 (1 qj)(1 )) + (1 qi))V  c 2 qi2. (Equation (18))
  - Nash equilibrium effort (uncorrelated sector) with bailouts:
    - bq() = (1 (1 ) )V / (c (1 )V). (Equation (19))
  - Equilibrium profits uncorrelated with bailouts:
    - E(bU | ) =  [ (1 (1 ) )V / (c (1 )V) ]^2 c/2 + V. (Equation (20))
- Same sector with bailouts, qi  qj:
  - E(i | qi  qj) = (qi + (1 qi)) (V H)  c 2 q i2. (Equation (21))
- Same sector with bailouts, qi > qj:
  - E(i | qi > qj) = (qi(1 (1 )(qi qj)) + (1 qi)) (V H)  c 2 qi2. (Equation (22))
- Pareto-dominant monitoring equilibrium when correlated with bailouts:
  - q i = q j = ^q = (1 ) (V H) / c. (Equation (23))
  - No contagion risk when correlated, so bailouts unambiguously reduce monitoring here.
  - Equilibrium profits when correlated with bailouts:
    - E(bC | ) = (1 )^2 (V H)^2 / (2c) + (V H). (Equation (24))
- Indifference condition between sectors with bailouts (defines H~):
  -  [ (1 (1 ) )V / (c (1 )V) ]^2 c/2 + V = (1 )^2 (V H)^2 / (2c) + (V H). (Equation (25))
- Key result: Proposition 2
  - For  <1 and  >  = c / [c (1 )(R (1 k)rD)] (same threshold as Proposition 1), a higher probability of government support reduces banks' incentives to invest in the same sector:
    - dH~()/d <0.
  - Interpretation: When bailouts increase monitoring in the uncorrelated sector ( > ), bailouts make uncorrelated lending relatively more attractive, reducing incentives to correlate risks (herd).
  - Caveat on credibility: If bailout expectations are higher when several banks fail at once (time inconsistency), and bailout rents are sufficiently high, government intervention may instead increase incentives to correlate risks.

### 5 Conclusions and policy implications
- Bailouts have a moral hazard effect encouraging risk taking, but also a systemic insurance effect protecting prudent banks from contagion.
- Net effect: government commitment to save systemic banks when contagion threat is high can reduce risk taking by all banks even when bailouts leave modest rents.
- Policy implications:
  - Creating impediments to timely and targeted intervention may destabilize the financial system by:
    - Making the system more unstable in the run-up to and during crises (banks neglect monitoring and/or correlate risks).
    - Leaving governments with no ex-post option but broader, less targeted bailouts that leave greater rents and are more distortive.
  - Recommended focus: increase efficiency of interventions so they can be undertaken easily and effectively while leaving bank shareholders (and other stakeholders) as little rents as possible.
- Extensions and further research suggested:
  - Rewriting model in context of short-termist behavior (fee- and volume-based banking, teaser rates, unstable short-term funding).
  - Studying international contagion spillovers (joint approach across countries with debt overhang).
  - Exploring how banking system structure (concentration, competition) affects contagion probability and interaction with bailout policy.

*Source: _wp13233 - 3.2  E§ects of Bailouts (IMF Working Paper content provided).*

### 1. Game Tree: The Effects of Contagion .................................................................... 26

### 1. Game Tree: The Effects of Contagion

### Introduction and key mechanisms
- Governments provided massive support to distressed financial institutions during the recent crisis, which prevented systemic meltdown but created moral hazard incentives for banks.
- Two opposing effects of expected government bailouts on bank incentives:
  - Moral hazard effect: bailouts protect shareholders/managers and increase private risk taking.
  - Systemic insurance effect: bailouts remove an exogenous source of risk (contagion), which can increase banks' incentives to monitor loans.
- Contagion is modeled as a risk beyond an individual bank's control (cannot be managed or diversified) but endogenous to the financial system because it depends on all banks' risk taking.
- Strategic complementarity: banks take more risk when other banks take more risk, amplifying systemic risk.

### Model environment and assumptions
- Two identical, risk-neutral, profit-maximizing banks.
- Each bank i:
  - Has a loan portfolio of size 1.
  - Financed by equity k_i and deposits (or debt) 1−k_i.
  - Pays gross deposit rate r_D (not risk-sensitive thanks to deposit insurance).
  - Is protected by limited liability; owners lose invested capital if the bank fails.
- Loan portfolio success sources:
  - Idiosyncratic success with probability q_i chosen by the bank (monitoring effort).
  - Contagion: when one bank fails, there is a probability β that the other bank's portfolio becomes non-performing, independently of its monitoring.
- Monitoring cost: (1/2) c q_i^2, with c > (R − (1 − k_i) r_D) > 0 to ensure interior solution.
- For initial analysis, idiosyncratic risks are uncorrelated across banks.

### Expected profits and reaction functions (formal expressions preserved)
- Bank i expected profits:
  - E(Π_i) = q_i (1 − β (1 − q_j)) (R − (1 − k_i) r_D) − (c/2) q_i^2.  (Equation (1))
- First-order condition (reaction function):
  - q_i^ = [1 − β (1 − q_j)] (R − (1 − k_i) r_D) / c.  (Equation (2))
- Symmetric Nash equilibrium (imposing q_i = q_j = q^):
  - q^ = (1 − β) (R − (1 − k) r_D) / (c − β (R − (1 − k) r_D)).  (Equation (3))

### Main theoretical findings
- Contagion reduces private incentives to monitor:
  - Lemma 1: The equilibrium monitoring effort q^ is decreasing in the probability of contagion given failure, β: dq^/dβ < 0, and increasing in banks' capital: dq^/dk > 0.
  - In boundary cases:
    - q^ = 0 for β = 1 (maximum contagion risk).
    - q^ = (1/c) (R − r_D (1 − k)) for β = 0 (no contagion risk).
- Two distinct inefficiencies identified:
  - Classical moral hazard from limited liability and leverage (term (1 − k) r_D).
  - Externality from contagion (parameter β) that lowers the private return to monitoring and induces excessive risk taking.
- Strategic interaction amplifies the externality:
  - Each bank's monitoring raises the private return to monitoring of the other bank; thus, in equilibrium, banks under-monitor more than if facing the externality alone.
- Capital plays a dual role:
  - Maintains "skin-in-the-game" to reduce moral hazard.
  - By reducing bank-level risk, capital also reduces contagion and lowers risk taking in other banks (new dimension due to complementarity).

### Conceptual implications and cautions
- Government bailouts have ambiguous ex ante effects:
  - Can exacerbate moral hazard via bailout rents left to incumbents.
  - Can reduce contagion externality and thereby improve monitoring incentives (systemic insurance).
- Relative importance of effects depends on parameters:
  - Low bailout rents and high contagion probability can make bailouts welfare-improving ex ante.
- Important caveats:
  - Results do not downplay moral hazard; they highlight a trade-off.
  - Ex post considerations (costs of bankruptcy vs. public funds) may differ.
  - The analysis assumes government commitment to a bailout strategy; time-inconsistency could change outcomes (e.g., correlated risk-taking if banks expect bailouts more likely when many fail).

### Modeling scope and empirical grounding
- Focus on the contagion component that banks cannot manage or diversify.
- Contagion channels discussed in literature:
  - Macro contagion (bank failure worsens macro fundamentals).
  - Counterparty risk from interbank exposures.
  - Fire sales lowering asset prices or freezing funding markets.
- Bailouts defined broadly to include direct capital/liquidity injections and macro measures (fiscal/monetary accommodations) and typically leave bailout rents to incumbent shareholders.
- Size of bailout rents depends on intervention design and resolution frameworks.

*Source: 1. Game Tree: The Effects of Contagion (excerpt).*

### 3.2  E§ects of Bailouts

### 3.2  E§ects of Bailouts

### Mechanism and model setup
- Government intervenes in a failing bank with probability ( known in advance).
- Bailout has two effects:
  - Prevents contagion: allows the other bank to survive intact and realize full profits.
  - Leaves bailout rents: failing bank keeps a share <1 of the profits it could have made if idiosyncratically successful.
- Expected profits of bank i with intervention:
  - E(i) = (qi(1 (1 qj)(1 )) + (1 qi)) (R (1 k)rD)  c 2 qi2. (Equation (4))
- Reaction function from first-order condition:
  - bqi = (1 (1 qj)(1 ) ) (R (1 k)rD) / c. (Equation (5))
- Comparative static:
  - @bqi/@ = (1 qj)  all divided by c (R (1 k)rD). (Equation (6))

### Channels through which bailouts affect monitoring
- Systemic insurance effect (positive):
  - Bailouts reduce the threat of contagion (probability of contagion falls from (1 qj) to (1 qj)(1 )), increasing monitoring incentives.
  - Stronger when contagion threat (1 qj) is larger (higher  and/or bank j perceived as riskier).
- Moral hazard effect (negative):
  - Expectation of retaining share of profits  in failure reduces incentives to monitor.
  - Stronger when bailout rents  are larger.

### Symmetric Nash equilibrium with intervention
- Symmetric equilibrium monitoring:
  - bq() = (1 (1 ) ) (R (1 k)rD) / (c (1 ) (R (1 k)rD)). (Equation (7))

### Key result: Proposition 1
- For  <1, there exists  = c / [c (1 )(R (1 k)rD)], with d/d >0, such that:
  - If  >  then dbq()/d >0 (equilibrium monitoring increases with probability of intervention).
  - If  <  then dbq()/d <0 (equilibrium monitoring decreases with probability of intervention).
- Interpretation:
  - When probability of contagion given failure is high (high ) and bailout rents  are low, the systemic insurance effect can dominate moral hazard and increase monitoring incentives.

---

### 3.3  The Role of Bank Capital
- Excess risk taking due to contagion externality cannot be reduced simply through higher bank capital.
- Monitoring level that internalizes contagion externality (joint maximization of (1) with qi = qj):
  - q = (1 ) (R rD(1 k)) / [c 2(R rD(1 k))]. (Equation (8))
- q > bq for any k.
- Externality-driven excess risk taking increases with higher capital:
  - d(q bq)/dk >0 and d(q/bq)/dk >0. (Equation (9))
- Intuition: Better-capitalized banks are more averse to exogenous contagion risk, so contagion externality raises their relative incentives to monitor.
- Nonetheless, capital regulation still matters:
  - Capital reduces moral hazard and also reduces contagion risk for other banks: dbqi/dkj >0.

---

### 3.4  The Case with Distressed Banks
- Distressed ("zombie") banks that have depleted capital (lower kj) or lower Rj reduce their own qj and impose negative externalities on healthy banks.
- Presence of distressed banks lowers screening incentives at healthy banks by increasing contagion threat and reducing returns to monitoring.
- Under these circumstances, bailout promises are more likely to improve screening incentives at healthy banks because @bqi/@ is larger when (1 qj) is greater (equation (6)).

---

### 4  A Model with Correlated Risks

### Setup and intuition
- Two sectors; each bank lends to only one sector; banks can coordinate on same or different sectors.
- If banks lend to different sectors: idiosyncratic risks independent, exposed to undiversifiable contagion (as in main model).
- If banks lend to same sector: idiosyncratic risks are fully correlated; banks succeed or fail simultaneously; contagion is irrelevant in this case.
- Lending to the same sector reduces return in case of success by H (competition/compressed margins).
- Banks choose sectors sequentially (avoids coordination failure); monitoring chosen simultaneously.

### 4.1  Contagion and Correlated Risks
- Define V = (R (1 ki)rD).
- If banks choose different sectors, expected profit identical to (1):
  - E(i) = qi(1 (1 qj))V  c 2 qi2. (Equation (10))
  - Nash equilibrium effort (uncorrelated sector):
    - ^q = (1 )V / (c V). (Equation (11))
  - Equilibrium profits when uncorrelated:
    - E(bU) = c/2 [ (1 )V / (c V) ]^2. (Equation (12))
- If banks choose same sector and qi  qj (including qi = qj):
  - E(i | qi  qj) = qi(V H)  c 2 qi2. (Equation (13))
- If qi > qj when lending same sector:
  - E(i | qi > qj) = qi(1 (qi qj))(V H)  c 2 qi2. (Equation (14))
- Lemma 2:
  - Under (13) and (14) continuum of symmetric Nash equilibria with qi = qj = bq2  (1 )(V H)/c ; V H/c .
  - Pareto-dominant equilibrium implemented by cheap talk: ^q = (V H)/c. (Equation (15))
  - Equilibrium profits when correlated:
    - E(bC) = c/2 [ (V H)/c ]^2. (Equation (16))
- Indifference threshold H~ between correlated and uncorrelated sectors:
  - eH = V(c V) / (c V). (Equation (17))
  - Banks lend to different sectors for H  H~, and to same sector for H < H~.
  - @H~/@ >0: higher contagion externality makes correlated investment (herding) more attractive.

### Interpretation
- Severe contagion risk leads banks to herd (lend to same sector) and accept lower margins H, which raises overall risk taking.
- Correlated investments remove contagion exposure (since success/failure is simultaneous), making herding attractive despite lower V H.

---

### 4.2  E§ects of Bailouts (with correlated risks)
- When government supports failing bank with probability , for different sectors:
  - E(i) = (qi(1 (1 qj)(1 )) + (1 qi))V  c 2 qi2. (Equation (18))
  - Nash equilibrium effort (uncorrelated sector) with bailouts:
    - bq() = (1 (1 ) )V / (c (1 )V). (Equation (19))
  - Equilibrium profits uncorrelated with bailouts:
    - E(bU | ) =  [ (1 (1 ) )V / (c (1 )V) ]^2 c/2 + V. (Equation (20))
- When banks lend to same sector, for qi  qj:
  - E(i | qi  qj) = (qi + (1 qi)) (V H)  c 2 q i2. (Equation (21))
  - For qi > qj:
    - E(i | qi > qj) = (qi(1 (1 )(qi qj)) + (1 qi)) (V H)  c 2 qi2. (Equation (22))
  - Pareto-dominant monitoring equilibrium when correlated with bailouts:
    - q i = q j = ^q = (1 ) (V H) / c. (Equation (23))
  - Note: No contagion risk when correlated, so bailouts unambiguously reduce monitoring here.
  - Equilibrium profits when correlated with bailouts:
    - E(bC | ) = (1 )^2 (V H)^2 / (2c) + (V H). (Equation (24))
- Indifference condition between sectors with bailouts:
  - E(bU | ) = E(bC | ) leading to equation (25), which defines threshold H~:
    -  [ (1 (1 ) )V / (c (1 )V) ]^2 c/2 + V = (1 )^2 (V H)^2 / (2c) + (V H). (Equation (25))

### Key result: Proposition 2
- For  <1 and  >  = c / [c (1 )(R (1 k)rD)] (same threshold as Proposition 1), a higher probability of government support reduces banks' incentives to invest in the same sector:
  - dH~()/d <0.
- Interpretation:
  - When bailouts increase monitoring in the uncorrelated sector ( > ), bailouts make uncorrelated lending relatively more attractive, reducing incentives to correlate risks (herd).
  - Proposition 2 gives a sufficient condition; the range where bailouts reduce correlation can be wider.
- Caveat on credibility:
  - If bailout expectations are higher when several banks fail at once (time inconsistency), and bailout rents are sufficiently high, government intervention may instead increase incentives to correlate risks.

---

### 5  Conclusions and policy implications
- Bailouts have a moral hazard effect encouraging risk taking, but also a systemic insurance effect protecting prudent banks from contagion.
- Net effect: government commitment to save systemic banks when contagion threat is high can reduce risk taking by all banks even when bailouts leave modest rents.
- Policy implications:
  - Creating impediments to timely and targeted intervention may destabilize the financial system by:
    - Making the system more unstable in the run-up to and during crises (banks neglect monitoring and/or correlate risks).
    - Leaving governments with no ex-post option but broader, less targeted bailouts that leave greater rents and are more distortive.
  - Recommended focus: increase efficiency of interventions so they can be undertaken easily and effectively while leaving bank shareholders (and other stakeholders) as little rents as possible.
- Extensions and further research suggested:
  - Rewriting model in context of short-termist behavior (fee- and volume-based banking, teaser rates, unstable short-term funding).
  - Studying international contagion spillovers (joint approach across countries with debt overhang).
  - Exploring how banking system structure (concentration, competition) affects contagion probability and interaction with bailout policy.

*Source: _wp13233 - 3.2  E§ects of Bailouts (IMF Working Paper content provided).*

### References

### _wp13233 - References

### References [1]–[26]
- [1] Acemoglu, Daron, Asuman Ozdaglar and Alireza Tahbaz-Salehi, 2012, ìSystemic Risk and Stability in Financial Networks,îMimeo, MIT.
- [2] Acharya, Viral, 2009, ìA theory of systemic risk and design of prudential bank regulation,î Journal of Financial Stability, Vol. 5(3): 224ñ255.
- [3] Acharya, Viral and Tanju Yorulmazer, 2007, ìToo Many to Fail ó An Analysis of Time Inconsistency in Bank Closure Policies,î Journal of Financial Intermediation, Vol. 16(1): 1-31.
- [4] Acharya, Viral and Tanju Yorulmazer. 2008a, ìCash in the Market Pricing and Optimal Res- olution of Bank Failures,îReview of Financial Studies, Vol. 21(6): 2705-42.
- [5] Acharya, Viral and Tanju Yorulmazer. 2008b, ìInformation Contagion and Bank Herding,î Journal of Money, Credit and Banking, Vol. 40(1), 215-31.
- [6] Allen, Franklin and Douglas Gale, 2001, ìFinancial Contagion,îJournal of Political Economy, Vol. 108(1): 1-33.
- [7] Allen, Franklin, Elena Carletti and Robert Marquez, 2011, ìCredit Market Competition and Capital Regulation,îReview of Financial Studies, Vol. 24(4): 983-1018.
- [8] Bebchuk, Lucian and Itay Goldstein, 2011, ìSelf-FulÖlling Credit Market Freezes,îReview of Financial Studies, Vol. 24(11): 3519-3555.
- [9] BIS [Bank for International Settlements], 2010, ìBasel III: A global regulatory framework for more resilient banks and banking systems,îhttp://www.bis.org/publ/bcbs189.htm.
- [10] Caballero, Ricardo and Arvind Krishnamurthy, 2003, ìExcessive Dollar Debt: Financial De- velopment and Underinsurance,îJournal of Finance, Vol. 58(2): 867ñ93.
- [11] Caballero, Ricardo and Alp Simsek, 2013, ìFire Sales in a Model of Complexity,îJournal of Finance, forthcoming.
- [12] Cordella, Tito and Eduardo Levy Yeyati, 2003, ìBank Bailouts: Moral Hazard vs. Value E§ect,îJournal of Financial Intermediation, Vol. 12(4): 300-30.
- [13] Corsetti, Giancarlo, Bernardo Guimaraes and Nouriel Roubini, 2006, ìInternational Lending of Last Resort and Moral Hazard: A Model of IMFís Catalytic Finance,îJournal of Monetary Economics, Vol. 53(3): 441-471.
- [14] DellíAriccia, Giovanni, and Robert Marquez, 2006, Lending Booms and Lending Standards, Journal of Finance, Vol. 61(5): 2511-2546.
- [15] DellíAriccia, Giovanni, Luc Laeven and Robert Marquez, 2013, ìReal Interest Rates, Leverage, and Bank Risk-Taking,îJournal of Economic Theory, forthcoming.
- [16] Diamond, Douglas W. and Raghuram G. Rajan, 2005, "Liquidity Shortages and Banking Crises,"Journal of Finance, Vol. 60(2): 615-47.
- [17] Diamond, Douglas W. and Raghuram Rajan, 2009, ìIlliquidity and Interest Rate Policy.î Mimeo, University of Chicago.
- [18] Farhi, Emmanuel and Jean Tirole. 2012, ìCollective Moral Hazard, Maturity Mismatch, and Systemic Bailouts,îAmerican Economic Review, Vol. 102(1): 60-93.
- [19] Freixas, Xavier, Bruno M. Parigi and Jean-Charles Rochet, 2000, ìSystemic Risk, Interbank Relations, and Liquidity Provision by the Central Bank,îJournal of Money, Credit and Bank- ing, Vol. 32(3), 611-38.
- [20] Goldstein, Itay and Ady Pauzner, 2004, ìContagion of Self-FulÖlling Financial Crises due to DiversiÖcation of Investment Portfolios,îJournal of Economic Theory, Vol. 119: 151-183.
- [21] Korinek, Anton, 2011, ìSystemic Risk-Taking: AmpliÖcation E§ects, Externalities, and Reg- ulatory Responsesî, Mimeo, University of Maryland.
- [22] Laeven, Luc and Fabian Valencia, ìResolution of Banking Crises: The Good, the Bad, and the Ugly,"IMF Working PaperNo. 10/146.
- [23] Lorenzoni, Guido, 2008, ìIne¢ cient Credit Booms,îReview of Economics Studies, Vol. 75: 809ñ33.
- [24] Orszag, Peter, and Joseph Stiglitz, 2002, ìOptimal Fire Departments: Evaluating Public Policy in the Face of Externalities,îThe Brookings Institution, unpublished.
- [25] Perotti, Enrico C. and Javier Suarez, 2002, ìLast bank standing: What do I gain if you fail?î European Economic Review, Vol. 46(9): 1599-1622.
- [26] Rochet, Jean-Charles and Jean Tirole, 1996, ìInterbank Lending and Systemic Risk,îJournal of Money, Credit and Banking, Vol. 28 (4): 733-762.

### Figures and captions
- Figure 1. Game tree: the effects of contagion.
  - The Figure shows payoffs of bank i depending on the realizations of its own and bank j’s monitoring effort, and the intensity of contagion.
- Figure 2: Game tree: the effects of government intervention
  - The Figure shows payoffs of bank i depending on the realizations of its own and bank j’s monitoring effort, the intensity of contagion, and the presence of government intervention.

*Source: _wp13233 - References*

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