## Trade-offs in Bank Resolution

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---

### Executive summary and context
- During the global financial crisis, governments in the United States and Europe used extensive public bail-outs to prevent bank failures from destabilizing the financial sector and the economy.
- Pre-reform consequences of bail-outs:
  - Reinforced expectations of future public support, undermining market discipline and potentially leading to excessive risk taking and a leverage cycle (Geanakoplos 2010).
  - Imposed large fiscal costs on taxpayers and, in some cases, threatened the financial standing of the sovereign.
- Post-crisis reform objectives:
  - Reduce likelihood of crises and minimize costs should a crisis occur by shifting burden to private investors and improving the bail-in/bail-out trade-off.
  - Make bail-outs the exception rather than the rule and delimit the role of fiscal resources in crisis resolution.
- Key institutional reform: Financial Stability Board’s Key Attributes (KA) (2011) promoting stronger early resolution powers, resolvability assessments, cross-border cooperation, and capacity for institutions to be resolved “without severe systemic disruption and without exposing taxpayers to loss. . .” while enabling “shareholders and unsecured and uninsured creditors to absorb losses.”

### Core theoretical trade-off
- Two opposing externalities drive policy choices:
  - Moral hazard from bail-outs: expectations of public support reduce market discipline, lower funding costs, and increase risk taking.
  - Spillovers from bail-ins: losses imposed on private stakeholders can create expectations of contagion, force portfolio rebalancing and sales, and threaten nondistressed banks.
- The note uses a welfare-based, micro-founded model to juxtapose these effects and to assess conditions when public sector absorption of losses may be necessary.
- Theoretical implications (summary):
  - Absent spillovers: bail-ins reallocate losses to creditors; optimal outcome is to avoid bail-outs.
  - With spillovers: bail-ins impose social costs; bail-outs trade off these externalities against moral hazard and fixed fiscal costs.
  - When spillovers are severe (e.g., aggregate shock causing systemic crisis): bail-outs can be justified and may wholly replace bail-ins in exceptional cases.
  - Time-consistency problem: ex ante pledges to limit bail-outs may falter ex post; credible resolution frameworks and transparent rules for “systemic-ness” help mitigate this.

### Key takeaways and policy implications
- Reforms have improved the trade-off:
  - Effective resolution frameworks likely reduce potential spillovers from bail-ins.
  - Better-defined constraints on public funding likely reduced expectations of future bail-outs and associated moral hazard.
  - Greater loss-absorbing capacity has reduced the probability of financial distress.
- Principles for bail-outs:
  - Bail-outs should be the exception, justified only as a last resort when financial stability is gravely threatened, and structured to mitigate associated costs.
  - When used, bail-outs should occur alongside loss sharing with private stakeholders and time-bound restructuring plans to restore long-term viability.
- Allow constrained flexibility for public funds:
  - Frameworks should permit use of some public funds, with safeguards, during systemic crises if imposing extensive private losses would unleash large spillovers.
- Further priorities to reduce recourse to bail-outs:
  - Enhance resolvability and minimize risk that bail-ins cause large spillovers.
  - Clarify which financial instruments are subject to bail-in and increase loss-absorbing capacity of major financial institutions.
  - Ensure holders of loss-absorbing capacity are those most capable of understanding and absorbing losses with low risk of transmitting further shocks.
  - Improve cross-border resolution arrangements.

### Structure of the note
- Section I: theoretical model (builds on Sandri 2015 and Cordella, Dell’Ariccia, and Marquez 2016).
- Section II: empirical evidence on moral hazard and spillovers.
- Section III: review of reform progress to enhance resolution frameworks.
- Section IV: conclusions.

### Terminology used
- “Bail-in”: ability of resolution authorities to impose losses on private stakeholders (equity and unsecured and uninsured liabilities) to recapitalize a failing bank.
- “Bail-out”: government provision of public funds to restore bank solvency.

### Implementation caveat
- Empirical evidence focuses on pre-reform episodes and uses a broad definition of bail-in; estimates likely an upper bound for spillovers under current frameworks.

---

### Formal model setup and core mechanism (Appendix I)
- Banks: continuum, heterogeneous in size; raise deposits and issue debt to finance loans.
- Loan repayment shocks: idiosyncratic and aggregate; monitoring effort m (costly) controls p = m.
- Limited liability: losses beyond capital covered by bail-in, public bail-out ξ (with fixed cost F_ξ), or combination (burden sharing). A fraction δ of bail-outs is appropriated by bank owners; remaining 1 − δ repays creditors.
- Key addition: bail-ins may produce systemic spillovers modeled in reduced form and possibly proportional to total bail-ins in the sector. Spillover channels include bankruptcy costs, macro-financial uncertainty, balance-sheet transmission, sudden reassessment of bank risk, reduced credit supply and GDP.
- Spillover intensity ξ varies across time and across countries (macro-financial conditions, interconnectedness, loss-absorbing capacity).

### Budget identity and private objective (selected expressions as presented)
- Coverage condition in distress (ε < ε̄):
  - (1 − δ) ξ + i = D R_D − ε R_L L. (Equation (2) as presented)
- Banks’ expected net return U_B (as presented):
  - U_B = − c m^2 L / 2 + p L R_L − D R_D R +
    (1 − p) [ ∫_{ε̄}^{1} (ε L R_L − D R_D R) dε + ∫_{0}^{ε̄} δ ξ R dε ].
- Creditors price debt break-even:
  - R_D = R + (1 − p) ∫_{0}^{ε̄} (i / D) dε.
- Substitution implies banks appropriate in expectation all benefits from public bail-outs (including the 1 − δ share that repays creditors).

### Social cost and planner’s objective
- Aggregate social cost C when insolvent (ε < ε̄):
  - C = (1 − p) [ 1_{ξ>0} ξ + F_ξ + ∫_{0}^{ε̄} ξ i R dε ].
- Aggregate social welfare U_S = U_B − C (expression provided in text).
- Social planner chooses bail-in share χ to maximize U_S subject to banks choosing m to maximize U_B.
- Comparative implication: bail-outs should play an important role only if spillovers ξ are particularly large.

### Additional considerations outside formal model
- Sovereign debt sustainability may weaken case for bail-outs, but bail-in spillovers that reduce GDP and tax revenue can also endanger fiscal positions.
- Competitive distortions from selective bail-outs can be mitigated by capital surcharges and levies on resolution funds.
- Implementation costs and legal/political challenges of bail-ins: litigation, cross-border issues, political opposition to transfers of ownership.
- Cross-border policymaking introduces externalities; domestic optimality may shift risks to other countries—underscores importance of cross-border resolution frameworks.

---

### Empirical evidence — overview, methodology, and caveats
- Empirical analysis focuses on pre-reform episodes; statutory bail-in regimes are new and not fully tested.
- Global sample: 841 banks across 75 countries; coverage from 2008 to 2016.
- Data: daily equity prices, CDS spreads, bond prices; quarterly balance sheet data (SNL Financial).
- Event studies use abnormal changes computed over event windows (various windows from t to t+1 … t+10) after estimating a 60-trading-day pre-event relationship with regional market equivalents.
- Identification challenges: endogeneity (authorities more likely to bail out when spillovers large); comovement may reflect information about fundamentals or regime credibility updates.

### Do bail-outs entail moral hazard? (empirical findings)
- Cross-country studies using proxies for safety net (deposit insurance, government ownership, concentration) yield mixed results.
- Evidence of too-big-to-fail funding advantage:
  - Literature documents lower borrowing costs and CDS spreads for large banks; since the crisis, the funding advantage has been reduced but not eliminated.
- Event-study evidence around key episodes:
  - Events analyzed: September 15, 2008 (Lehman bankruptcy); October 30, 2008 (TARP passage); September 30, 2008 (Dexia capital injection).
  - Large banks suffered more than small banks with Lehman failure (consistent with decline in funding-cost advantage) and enjoyed better outcomes when TARP was approved and when Dexia was recapitalized.
  - Selected illustrative regression coefficients from Table 1 (as reported):
    - Size coefficient (Lehman, equity regressions): 4.147* and 2.816 (standard errors in parentheses as reported).
    - Size coefficient (TARP, equity regressions): -8.641*** and -5.723* (as reported).
- Bank-level summary statistics (Table 2 — examples reported exactly as in source):
  - Large banks (obs./mean):
    - CDS spread: 2,361 / 157.7
    - Z-score: 1,044 / 3.9
    - Tier 1 ratio: 1,426 / 11.7
    - Leverage ratio: 936 / 9.1
    - NPL ratio: 959 / 3.2
    - ROA: 1,209 / 0.5
    - ROE: 1,223 / 9.1
  - Small banks (obs./mean):
    - CDS spread: 1,240 / 183.0
    - Z-score: 10,741 / 3.6
    - Tier 1 ratio: 11,699 / 12.4
    - Leverage ratio: 10,856 / 12.8
    - NPL ratio: 11,010 / 3.5
    - ROA: 12,609 / 0.9
    - ROE: 12,540 / 9.2
- Regression evidence on size and risk-taking (Table 3) is mixed: size often negatively associated with Z-score and Tier 1 ratio in many specifications but not uniformly robust across metrics.

### Do bail-ins entail systemic spillovers? (empirical findings)
- Identification and interpretation caveats reiterated.
- European cases (16 events analyzed):
  - In 11 out of 16 cases, equity prices for banks in EU countries other than host show negative and significant changes; in 8 of these cases, CDS spreads show significant increases.
  - Many cases occurred amid heightened systemic risk (Cyprus, Greece, Portugal, Spain, Slovenia).
  - Cyprus example: bail-in of unsecured bondholders and depositors had negative effects in other EU and non-EU countries (primarily Russian banks); effects mostly transitory with CDS spreads and equity stabilizing about a week after shock. Ad hoc bail-in of depositors led to compensation claims and may have encouraged strategic defaults, worsening NPL problems.
- United States FDIC cases (top 30 by assets among >500 FDIC failures since 2000):
  - Mixed results:
    - For equity prices: roughly half the cases show negative coefficients for banks in other states; roughly 30 percent positive; remainder insignificant.
    - For CDS spreads: about a third positive coefficients; about 10 percent negative.
  - US cases typically involved relatively small, local banks; percentages of negative significant equity-price reactions smaller than EU cases.
- Cross-holdings and holder composition:
  - Considerable cross-country variation in holders of bail-in-able debt.
  - A considerable share of bail-in-able debt is held by credit institutions; public sector and nonfinancial institutions are major holders of equities.
  - Cross holdings imply shocks to some banks can spread through losses on bail-in-able debt holdings.
  - Retail investor holdings in some countries may make bail-ins politically difficult.
- Additional tests (reported on request) show some results more consistent with spillovers than belief-updating (e.g., bilateral cross-border banking flows augment negative equity reactions in some cases; effects last up to two weeks).

---

### Resolution frameworks in practice — reforms, tools, and implementation gaps
- Practical bail-in implementation:
  - Aim: recapitalize failing bank on going-concern basis, preserve systemically important functions, minimize destruction of value.
  - Tools: statutory bail-in powers and contractual contingent capital (CoCos); statutory powers do not require creditor/shareholder consent.
- Reforms and mitigating measures:
  - Enhance total loss-absorbing capacity (TLAC) of systemic banks with clarity on qualifying claims, amounts, and intra-group location.
  - Ensure unsecured/uninsured creditors understand risks and can absorb losses; TLAC issuance by G-SIBs typically excludes short-term debt to mitigate liquidity spillovers.
  - Periodic resolvability assessments and powers to remove legal/operational impediments; cross-border resolution planning and home/host agreements on loss-absorbing capacity location.
  - Emergency liquidity assistance can mitigate spillovers but may convert into solvency support; public funding may remain necessary in extreme circumstances.
- Designing flexibility and credibility:
  - Need balance between constrained regimes (avoid bail-outs but risk inflexibility/time-inconsistency) and overly flexible regimes (risk perpetuating too-big-to-fail and fiscal exposure).
  - Flexibility should be accompanied by transparency and accountability.
- Limiting taxpayer burden if public support used:
  - Conditions for public funding: (1) temporary and only in systemic cases; (2) after bail-in of shareholders and some creditors; (3) after use of ex ante resolution funds; and/or (4) subject to ex post recovery through levies on the banking sector.
- Implementation gaps and cross-border challenges:
  - Only a subset of jurisdictions have regimes with comprehensive powers in line with the KA.
  - Much bank debt is issued in foreign jurisdictions, raising uncertainty about national resolution powers; cross-border resolution planning remains largely untested in practice.

---

### Box 1 — Fiscal implications of bail-outs (summary)
- Gross fiscal outlays related to restructuring can amount to several percentage points of GDP and may jeopardize public finances.
- Sample: 87 systemic banking crises.
- Non-monotonic relationship between up-front fiscal costs and crisis severity (as observed in Figure 1.1):
  - Up-front fiscal costs < 1 percent of GDP: output losses reach 25 percent of trend GDP.
  - Up-front fiscal costs between 1 and 5 percent of GDP: typical output loss is 13 percent of trend GDP.
  - Up-front fiscal costs > 5 percent of GDP: output losses become larger and peak NPL ratios rise.
- Peak NPL ratios reach comparable levels in cases with up-front fiscal costs < 1 percent of GDP and in the 1–5 percent of GDP band, despite differences in output loss.
- Increase in public debt rises with up-front fiscal costs, but indirect fiscal costs (increase in public debt minus up-front fiscal cost) can be lower at higher up-front fiscal costs in some cases.
- Caveats: endogeneity—authorities provide larger bail-outs when crises are more severe; expected bail-outs can create moral hazard, potentially making crises more severe.
- Empirical finding in simple OLS regressions: controlling for output loss size, correlation between up-front fiscal costs and indirect fiscal costs is negative—consistent with larger up-front support sometimes reducing indirect fiscal costs.
- Policy implication: assessing fiscal implications of bail-outs based only on up-front cost is misleading; in systemic crises, up-front bail-outs may substantially contain crisis severity and ultimately reduce indirect fiscal costs.

---

### Policy recommendations and research priorities (conclusions)
- Theoretical prescriptions:
  - When spillovers are small: rely on bail-ins; constrain bail-outs to avoid moral hazard and time-inconsistency.
  - When spillovers are severe: limited public bail-outs may be justified despite moral hazard.
  - Social welfare declines with spillover severity; policymakers should prioritize measures that reduce spillovers.
- Practical policy priorities:
  - Credibility and calibrated flexibility: allow public support only in exceptional cases with strict safeguards and transparent criteria for “systemic-ness.”
  - Enhanced prudential standards and resolution planning: increase loss-absorbing capacity of major institutions and link requirements to resolvability/living wills; improve cross-border resolution planning.
  - Consumer/investor protection: clarify which instruments may be bailed in; limit retail investor exposure to complex bail-in-able instruments (market to professional/institutional/high-net-worth investors and diversified funds); restrict cross holdings among banks; upgrade reporting/databases for monitoring.
- Research and monitoring:
  - Further research needed to measure spillovers and moral hazard under new resolution regimes.
  - Continued implementation and monitoring of TLAC, resolvability, creditor hierarchy clarity, and limits on who may hold bail-in-able claims are critical to reducing potential for severe spillovers.

---

### Sample coverage and empirical specifications (Appendix II highlights)
- Global sample: 841 banks across 75 countries; coverage from 2008 to 2016.
- Country list (as provided): Argentina, Australia, Austria, Bahrain, Bangladesh, Barbados, Belgium, Bermuda, Brazil, Bulgaria, Canada, Chile, China, Colombia, Croatia, Cyprus, Czech Republic, Denmark, Egypt, Estonia, Faroe Islands, Finland, France, Germany, Greece, Hong Kong SAR, Hungary, India, Indonesia, Iran, Ireland, Israel, Italy, Japan, Kuwait, Lebanon, Liechtenstein, Luxembourg, Malaysia, Malta, Mexico, Morocco, Netherlands, New Zealand, Nigeria, Norway, Oman, Pakistan, Panama, Peru, Philippines, Poland, Portugal, Qatar, Romania, Russia, Saudi Arabia, Singapore, Slovak Republic, South Africa, South Korea, Spain, Sri Lanka, Sweden, Switzerland, Taiwan Province of China, Thailand, Togo, Trinidad and Tobago, Turkey, United Arab Emirates, United Kingdom, United States, Venezuela, and Vietnam.
- Event-analysis construction:
  - Estimate pre-event relationship over 60 trading days; abnormal change = actual − predicted; cumulative abnormal changes summed over event windows t to t+1 … t+10.
- Regression specifications summarized for Tables 1, 4, and 5 (as described in source), with clustering of standard errors at country or state level where indicated.
- Appendix Table 2 (US bail-in events) compiled from FDIC; selection: P&A approach and among top 30 failed banks by assets since 2000.

*Italic: Source — Appendix I and Appendix II of "Trade-offs in Bank Resolution" (SDN/18/02) — sdn1802-trade-offs-in-bank-resolution PDF.*

### EXECUTIVE SUMMARY ________________________________________________________________________ 4

### EXECUTIVE SUMMARY

### Introduction and context
- During the global financial crisis, governments in the United States and Europe resorted extensively to public bail-outs to prevent bank failures from destabilizing the financial sector and the economy.
- Use of bail-outs:
  - Reinforced expectations of future public support, undermining market discipline and potentially leading to excessive risk taking and a leverage cycle (Geanakoplos 2010).
  - Imposed large fiscal costs on taxpayers and, in some cases, threatened the financial standing of the sovereign.
- Post-crisis reform objectives:
  - Reduce likelihood of crises and minimize costs should a crisis occur by shifting burden to private investors and improving the bail-in/bail-out trade-off.
  - Make bail-outs the exception rather than the rule and delimit the role of fiscal resources in crisis resolution.

### Reforms and mechanisms introduced
- Financial Stability Board’s Key Attributes (KA) of Effective Resolution Regimes, issued in 2011, advocate:
  - Stronger resolution powers available at early stages of distress.
  - Better planning, resolvability assessments, and cross-border cooperation.
  - Making systemic financial institutions resolvable “without severe systemic disruption and without exposing taxpayers to loss. . .” while enabling “shareholders and unsecured and uninsured creditors to absorb losses.”
- Bail-in powers:
  - Enable resolution authorities to recapitalize firms by reducing the nominal value (“haircut”) of bank liabilities or converting liabilities into equity.
  - Complementary measures include adequate loss-absorbing capacity requirements and resolution planning for large and complex banks.

### The core trade-off analyzed
- Two opposing externalities drive policymaker choices:
  - Moral hazard from bail-outs: expectations of public support reduce market discipline, lower funding costs, and increase risk taking.
  - Spillovers from bail-ins: imposing losses on private stakeholders can create expectations of contagion, force portfolio rebalancing and sales, and threaten nondistressed banks.
- The note uses a welfare-based, micro-founded model to juxtapose these effects and assesses conditions when public sector absorption of losses may be necessary.
- Empirical assessment (pre-reform evidence) finds:
  - Evidence consistent with moral hazard effects associated with bail-outs (expectation of bail-outs lowers funding costs and in some instances generates greater risk taking).
  - Evidence consistent with financial spillovers associated with bail-ins, with recognition that alternative interpretations exist.

### Key takeaways and policy implications
- Reforms have improved the trade-off:
  - Effective resolution frameworks (as contemplated by the KA) likely reduce potential spillovers from bail-ins.
  - Better-defined constraints on public funding likely reduced expectations of future bail-outs and associated moral hazard.
  - Greater loss-absorbing capacity has reduced the probability of financial distress.
- Bail-outs should be the exception:
  - Justified only as a last resort, exclusively when financial stability is gravely threatened, and structured to mitigate associated costs.
  - When used, bail-outs should occur alongside loss sharing with private stakeholders and time-bound restructuring plans to address underlying weaknesses and restore long-term viability.
- Allow constrained flexibility for public funds:
  - Frameworks should permit use of some public funds, with appropriate safeguards, during systemic crises if imposing extensive private losses would unleash large spillovers.
  - In such exceptional cases, the moral hazard and fiscal costs of bail-outs may be preferable to the disruptive effects of spillovers from bail-ins.
- Further priorities to reduce recourse to bail-outs:
  - Enhance resolvability and minimize risk that bail-ins cause large spillovers.
  - Clarify which financial instruments are subject to bail-in and increase loss-absorbing capacity of major financial institutions.
  - Ensure holders of loss-absorbing capacity are those most capable of understanding and absorbing losses with low risk of transmitting further shocks.
  - Improve cross-border resolution arrangements.

### Structure of the note and further analysis
- The note:
  - Presents a theoretical model in Section I to provide a framework for assessing when losses should be borne by the public versus private investors.
  - Discusses empirical evidence in Section II on moral hazard and spillovers.
  - Reviews reform progress in Section III to enhance resolution frameworks.
  - Concludes in Section IV.
- Theoretical approach:
  - Builds on Sandri 2015 and Cordella, Dell’Ariccia, and Marquez 2016.
  - Uses the term “bail-in” generically as the ability of resolution authorities to impose losses on private stakeholders (equity and unsecured and uninsured liabilities) to recapitalize a failing bank.
  - Uses “bail-out” to refer to government provision of public funds to restore bank solvency.

*Source: sdn1802-trade-offs-in-bank-resolution - EXECUTIVE SUMMARY*

### Appendix I for the formal details.

### Box 1. Fiscal Implications of Bail-outs

### Box 1. Fiscal Implications of Bail-outs

### Overview and context
- Gross fiscal outlays related to the restructuring of the financial sector can amount to several percentage points of GDP (Laeven and Valencia 2010) and may, in some cases, jeopardize the sustainability of public finances.  
- In systemic financial crises, abstaining from bail-outs can trigger a cascade of bank failures and widespread financial spillovers, which can cause a sharp contraction of GDP and tax revenues and possibly lead to a larger increase in public debt than would result from up-front and sufficiently large public support to the banking system.

### Empirical observations from a sample of crises
- Sample: 87 systemic banking crises.
- Non-monotonic relationship between up-front fiscal costs and crisis severity is observed (Figure 1.1):
  - When up-front fiscal costs are limited to less than 1 percent of GDP, output losses reach 25 percent of trend GDP.
  - When fiscal costs are between 1 and 5 percent of GDP, the typical output loss is only 13 percent of trend GDP.
  - As up-front fiscal costs exceed 5 percent of GDP, output losses become larger and peak NPL ratios rise.
- Peak nonperforming loan (NPL) ratios reach levels comparable in cases where up-front fiscal costs are less than 1 percent of GDP and in the 1–5 percent of GDP band, despite differences in output loss.
- Increase in public debt rises with up-front fiscal costs, but not commensurately with the increase in up-front fiscal costs; therefore indirect fiscal costs are lower at higher up-front fiscal costs in some cases.

### Definitions and measurement (as used in the analysis)
- x: the up-front fiscal cost of a systemic banking crisis, expressed in percent of GDP and defined as the component of gross fiscal outlays related to the restructuring of the financial sector. It includes costs associated with bank recapitalizations but excludes asset purchases and direct liquidity assistance from the treasury.
- Output loss: computed as the cumulative sum of the differences between actual and trend real GDP over the period (t, t+3) with t the starting year of the crisis and expressed in percent of trend real GDP.
- Peak NPLs: percent of total loans.
- Increase in public debt: percent of GDP and measured over (t-1, t+3).
- Indirect fiscal costs: calculated as increase in public debt minus up-front fiscal cost.

### Analytical caveats and econometric insight
- Testing these implications is difficult due to endogeneity concerns:
  - Authorities provide larger bail-outs when crises are more severe.
  - Expected bail-outs can create moral hazard, potentially leading to more severe crises.
  - These factors imply a likely positive raw correlation between bail-out size, drop in GDP, and increase in public debt.
- Yet in simple ordinary least squares regressions, controlling for the size of the output loss, the correlation between up-front fiscal costs and indirect fiscal costs is negative—corroborating the observation that larger up-front support can be associated with lower indirect fiscal costs.

### Key policy-relevant implication
- Assessing the fiscal implications of bail-outs based only on their up-front cost is misleading: in systemic banking crises, up-front bail-outs may substantially contain crisis severity and may ultimately reduce indirect fiscal costs.

*Source: Box 1. Fiscal Implications of Bail-outs, TRADE-OFFS IN BANK RESOLUTION (IMF).*

### Appendix I. A Simple Model of Bail-ins and Bail-outs

### Appendix I. A Simple Model of Bail-ins and Bail-outs

### Model setup and key primitives
- Continuum of banks heterogeneous in size with capital K distributed over support [0, K̄].
- Banks leverage up to the regulatory limit by issuing debt D, which carries interest rate R_D.
- Loans: L = K + D; lending rate R_L. Capital share κ = K / L.
- Production: Y = η A L. Productivity A is subject to shock η.
- Shock specification: η = 1 with probability p; η = ε with probability 1 − p, where ε ∈ [0,1] is uniform and bank-specific (ε = ε_i + ε_a). Good state: η = 1. Distress state: η = ε.
- Monitoring effort m chosen by bank controls p via p = m and entails pecuniary cost c m^2 L / 2, with c > 0.
- Banks fully appropriate output and set R_L = A.
- Limited liability: creditors fully repaid in the good state or in distress if ε > ε̄ where
  - ε̄ = D R_D / (L R_L). (Equation (1))
- If ε < ε̄, the funding gap must be absorbed via bail-outs (public transfer ξ with fixed cost F_ξ) and/or bail-ins (write-down i reducing creditor repayment to D R_D − i). A fraction δ of bail-outs is appropriated by bank owners; remaining 1 − δ repays creditors.

### Budget identity in distress
- When ε < ε̄ the coverage condition is:
  - (1 − δ) ξ + i = D R_D − ε R_L L. (Equation (2))

### Bank expected net return (private objective)
- Bank expected net return U_B:
  - U_B = − c m^2 L / 2 + p L R_L − D R_D R +
    (1 − p) [ ∫_{ε̄}^{1} (ε L R_L − D R_D R) dε + ∫_{0}^{ε̄} δ ξ R dε ],
  - where R is the gross risk-free rate. (Text presents same expression; see Equation (3) for rearranged form.)
- Creditors are risk-neutral, competitive, and observe m. They price debt to break even:
  - R_D = R + (1 − p) ∫_{0}^{ε̄} (i / D) dε.
- Substituting R_D back yields an expression for U_B that makes explicit that banks appropriate in expectation all benefits from public bail-outs (including the 1 − δ share that repays creditors, because bail-outs lower expected bail-ins and thus reduce R_D).

### Social cost of resolution and externalities
- Two sources of social cost when a bank is insolvent (ε < ε̄):
  1. Fiscal cost ξ (size of public transfer) and fixed cost F_ξ borne by government if bail-outs are used.
  2. Bail-in spillovers: bail-ins impose losses i on private creditors and negative externalities for the rest of society equal to ξ i, with ξ ≥ 0 controlling severity.
- Aggregate social cost C from resolving an individual bank:
  - C = (1 − p) [ 1_{ξ>0} ξ + F_ξ + ∫_{0}^{ε̄} ξ i R dε ],
    where 1_{ξ>0} is indicator equal to 1 if bail-outs are positive.
- A plausible microfoundation for ξ: spillovers proportional to overall capital shortfall in the banking sector, e.g.,
  - ξ ∝ ∫_{K} 1_{ε ≤ ε̄} [ K (κ^{-1} − 1) R_D − κ ε R_L ] φ(K) dK,
    where φ(K) is density of K and 1_{ε ≤ ε̄} indicates insolvent banks.

### Social planner objective and the trade-off
- Aggregate social welfare U_S = U_B − C:
  - U_S = − D − c m^2 L / 2 + L R_L [ p + (1 − p) ∫_{ε̄}^{1} dε ] R
    − (1 − p) [ 1_{ξ>0} F_ξ + ∫_{0}^{ε̄} ξ i R dε ].
- Social planner chooses bail-in share χ (share of unfunded liabilities D R_D − ε R_L L subject to bail-in) to maximize U_S subject to banks choosing m to maximize U_B:
  - max_χ U_S subject to m = arg max_m U_B.
- Ex post (once a shortfall occurs), bail-outs are preferable to bail-ins if spillover costs associated with bail-ins exceed the fixed cost of bail-outs.
- Ex ante, bail-outs reduce banks’ monitoring incentives (m), generating moral hazard, because bail-outs provide compensation even when ε < ε̄. Thus bail-outs lower p and increase expected insolvency frequency.
- Optimal choice trades off ex post costs of bail-ins (including spillovers parameter ξ and fixed fiscal costs) against ex ante moral hazard induced by bail-outs.
- Comparative implication: bail-outs should play an important role in bank resolution only if spillovers (ξ) are particularly large.

### Appendix II. Sample Coverage and Empirical Specifications

### Sample construction and coverage
- Global sample: 841 banks across 75 countries; coverage from 2008 to 2016.
- Selection: two steps
  1. Active bond issuers identified (Bloomberg Finance L.P. and Thomson Reuters Datastream) for senior unsecured, subordinated, and contingent convertible bonds; size (total assets) considered.
  2. Banks not selected by step 1 but ranking in the top 500 banks globally added.
- Data merged: daily equity prices, CDS spreads, bond prices; quarterly balance sheet components (SNL Financial).
- Countries covered (explicit list provided in source): Argentina, Australia, Austria, Bahrain, Bangladesh, Barbados, Belgium, Bermuda, Brazil, Bulgaria, Canada, Chile, China, Colombia, Croatia, Cyprus, Czech Republic, Denmark, Egypt, Estonia, Faroe Islands, Finland, France, Germany, Greece, Hong Kong SAR, Hungary, India, Indonesia, Iran, Ireland, Israel, Italy, Japan, Kuwait, Lebanon, Liechtenstein, Luxembourg, Malaysia, Malta, Mexico, Morocco, Netherlands, New Zealand, Nigeria, Norway, Oman, Pakistan, Panama, Peru, Philippines, Poland, Portugal, Qatar, Romania, Russia, Saudi Arabia, Singapore, Slovak Republic, South Africa, South Korea, Spain, Sri Lanka, Sweden, Switzerland, Taiwan Province of China, Thailand, Togo, Trinidad and Tobago, Turkey, United Arab Emirates, United Kingdom, United States, Venezuela, and Vietnam.

### Event analysis and construction of abnormal changes
- Figure 2: daily changes in CDS spreads and equity prices around three events plotted against bank size:
  - September 15, 2008 (Lehman bankruptcy)
  - October 30, 2008 (TARP passage)
  - September 30, 2008 (Dexia capital injection)
- Cumulative abnormal changes (Tables 1, 4, 5) computed in three steps:
  1. Estimate relationship between bank-level variable and market equivalent over 60 trading days prior to event. Market equivalents: regional indices from Thomson Reuters Datastream and Bloomberg.
  2. Abnormal change = actual change − predicted change from step 1 regression.
  3. Sum abnormal changes over event window (various windows from 1 to 10 days, i.e., t to t+1, ..., t+10).

### Regression specifications (high-level)
- Table 1 specification:
  - CAR_i = α + β S_i SIZE_i + θ_c + ε_i,
    where i indexes banks and c indexes country of residence. Regressions run separately for each of the three bailout events, with and without country fixed effects θ_c. Standard errors clustered at country level.
- Table 4 specification (for each of 16 bail-in events):
  - CAR_i = α + β C_bailin_in_country_i + γ C_EU_but_not_host_i + ε_i,
    where C_bailin_in_country_i = 1 if bank’s residence is the country where bail-in happened; C_EU_but_not_host_i = 1 if bank’s residence is an EU member but not the country where bail-in happened. For Cyprus, an additional dummy for banks resident in Russia is included. Robust to clustering standard errors at country level.
- Table 5 specification (for each of 32 US bail-in events):
  - CAR_i = α + β S_instate_i + γ S_outofstate_i + ε_i,
    where S_instate_i = 1 if bank headquartered in same state as resolved bank; S_outofstate_i = 1 if headquartered in a different US state. Robust to clustering at state level.
- Interpretation: coefficients on dummy variables in Tables 4 and 5 measure marginal impact of being “closer” to a bail-in event, conditional on a bail-in event (non-bail-in events are not included in estimation samples).

### Summary statistics and cross-sectional regressions
- Table 2: summary statistics on funding costs (CDS spread, senior unsecured bond spread, subordinated bond spread, CoCo spread), risk measures (Z-score, Tier 1 ratio, leverage ratio, NPL ratio), and profitability metrics (ROA, ROE) displayed separately for large and small banks.
  - Large banks defined as those with assets in the top percentile of full sample distribution.
  - Z-score = (equity capital ratio + return on assets) / standard deviation of return on assets (rolling window of 10 quarters).
  - Tier 1 ratio = Tier 1 capital / risk-weighted assets.
  - Leverage ratio = Tier 1 capital / total tangible assets.
  - NPL ratio = nonperforming loans / total loans.
  - ROA = return on average assets; ROE = return on average equity.
- Table 3: regressions where risk measures and profitability metrics are dependent variables. Example specification components:
  - Explanatory variables include bank size dummy S_i SIZE_i, gross loans (loans as percent of total assets), deposits (percent of total assets), Z-score in profitability regressions, plus fixed effects (bank and time or country and time). Results robust to clustering at country or bank level.
- Note: number of banks in regression tables < 841 because of missing data over estimation and/or event windows.

### Event lists (reference in source)
- The source provides detailed lists of European and US bail-in/resolution events (dates, descriptions, locations). These event lists are used in the empirical event-study analysis (Appendix Table 1 for Europe; Appendix Table 2 for US events).

*Italic: Source — Appendix I and Appendix II of "Trade-offs in Bank Resolution" (SDN/18/02) — sdn1802-trade-offs-in-bank-resolution PDF.*

### Appendix Table 2. Bail-in Events in the United States

### Appendix Table 2. Bail-in Events in the United States

### Source and compilation
- Source: Federal Deposit Insurance Corporation (FDIC).
- Compiled based on FDIC-executed resolution of failed banks as reported on the agency's website.

### Selection criteria for included cases
- Selected from more than 500 bank failures the agency handled since 2000.
- Inclusion condition: the approach used was a purchase & assumption (P&A).
- Inclusion condition: the failed bank's total assets ranked among the top 30.

### Definition and scope of "bail-in" in this appendix
- The term bail-in is used in a generic sense to capture any resolution that imposed losses on private stakeholders.

*Source: Federal Deposit Insurance Corporation (FDIC).*

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_Source: https://www.imf.org/-/media/files/publications/sdn/2018/sdn1802-trade-offs-in-bank-resolution.pdf_