## wpiea2023177-print-pdf - Section 4 analyzes the incentives for defaults and bailouts and Section 5 studies how these incentives

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---

### Literature review and empirical background
- Two families of models explaining sovereign repayment:
  - Reputation-based models (access to international capital markets; Eaton and Gersovitz (1981)).
  - Direct-cost models (trade/financial disruption; Cohen and Sachs (1986); Bulow and Rogoff (1989a, 1989b); Fernandez and Rosenthal (1990)). This paper belongs to the direct-cost family.
- Channels of output loss from default emphasized:
  - Trade and financial disruptions.
  - Risk of exit from the monetary union.
- Empirical evidence cited:
  - Rose (2005): debt renegotiation results in a decline in bilateral trade of around 8 percent a year, persisting for around 15 years.
- Distinctions and extensions relative to literature (high-level):
  - Builds on Tirole (2015), Farhi and Tirole (2018) but: shows ex-post solidarity may not generate welfare gain for debtor; adds third-country analysis; explores exit versus default; links theory with estimated bailouts.
  - Relates to Horn, Reinhart and Trebesch (2020), Broner et al. (2014), Uhlig (2014), Corsetti et al. (2018), Dellas and Niepelt (2016), Azzimonti and Quadrini (2021).

### Historical overview of Euro area assistance (summary)
- Focus countries: Cyprus, Greece, Ireland, Portugal, Spain; reviewed Hungary, Latvia, Romania (non-Eurozone).
- Key institutional/legal constraints noted:
  - Article 125 TFEU: "no-bailout clause."
  - Article 123 TFEU: prohibits ECB direct purchases of member public debt.
  - Article 122 TFEU: allows assistance under exceptional circumstances.
- Lenders and instruments:
  - "Troika": IMF, European Commission (EC), European Central Bank (ECB) — paper focuses on IMF and EC.
  - EC lending instruments: EFSM, EFSF, ESM, GLF, BoP facility.
  - IMF instruments used: SBA or EFF; normal access limits 145% of quota annually or 435% over programme lifetime; "exceptional access" overrides.
- EC programme chronology:
  - March 2010: GLF (Greece).
  - June 2010: EFSF created.
  - 2011: EFSM created.
  - September 2012: ESM created (permanent facility).

### Key figures for major programmes (selected exact values)
- Greece — Programme 1 (2010-2011):
  - Size: approximately e110 bn total.
  - Composition: e80 bn from GLF; e30 bn from IMF’s SBA programme.
  - IMF actual disbursements: e20.1 bn in six tranches between May 2010 and December 2011.
  - EC actual disbursements: e52.9 bn in six tranches between May 2010 and December 2011.
  - Bilateral apportionment: Germany e15.17 bn; France e11.39 bn; Italy e10.00 bn.
- Greece — Programme 2 (2012-2015):
  - Total: almost e180 bn (undisbursed Programme 1 + additional e130 bn).
  - IMF actual disbursements: around e11.6 bn out of a planned contribution of e28 bn.
  - EFSF commitment: e144.7 bn; EFSF disbursed approximately e141.8 bn.
- Greece — Programme 3 (2015-2018):
  - ESM committed e86 bn to Greece and disbursed e61.9 bn in total.
  - Bridge EFSM loan: e7.16 bn in July 2015.
  - Programme 3 concluded in August 2018.
- Ireland (request November 2010; approval December 2010):
  - Funding: e17.7 bn from EFSF; e22.5 bn from EFSM; e22.5 bn from IMF; e4.8 bn from Bilateral Loans.
  - Bilateral contributions: Sweden e600 million; United Kingdom e3,830 million; Denmark e400 million.
- Portugal (May 2011–June 2014):
  - EC (EFSF and EFSM) and IMF each committed approximately e26 bn for a total of e78 bn.
- Cyprus (joint IMF/ESM programme April/May 2013; exited March 2016):
  - Total approved financing: e10 bn (ESM committed e9 bn; IMF approximately e1 bn).
  - ESM disbursed e6.3 bn between May 2013 and October 2015.
  - Expected repayment between 2025 and 2031.
- Spain (ESM only):
  - Total committed e100 bn in July 2012.
  - Disbursed: e41.3 bn in December 2012 and February 2013.
  - Used to recapitalize the banking sector.
  - Expected repayment between 2022 and 2027; Spain made voluntary early repayments.

### Non-eurozone programmes (selected exact values)
- Hungary (November 2008–end 2009):
  - Total available: e6.5 bn from EC; approximately e12.5 bn from IMF.
  - EC actual disbursement: e5.5 bn.
  - IMF disbursed approximately e8.7 bn (SDR7.6 bn) between November 2008 and September 2009; repaid between February 2012 and August 2013.
- Latvia (January 2009):
  - Total available: e7.5 bn (e3.1 bn from EC; approximately e1.7 bn from IMF cited).
  - EC realized assistance: four installments of e2.9 bn between February 2009 and October 2010.
- Romania (May 2009):
  - Total available: e20 bn (e5 bn from EC; approximately e12.95 bn from IMF).

---

### Transfers estimates — motivation, methodology, and interpretation
- Objective: estimate implicit transfers in official financial assistance following Joshi and Zettelmeyer (2005).
- Benchmark discount rate: the internal rate of return on the IMF’s lending for borrower i during the Eurozone crisis, ̄r_i.
- Core net-present-value formula (notation preserved):
  - Tr_i,j_t0 = sum_{t=t0}^T NT_i,j_t / (1 + ̄r_i)^t
  - NT_i,j_t = D_i,j_t − R_i,j_t − sum_{τ=1}^i D^r_{i,j,t−τ} − i^i,j_{t−τ} D^r_{i,j,t−τ}
  - irr_i,j is the internal rate of return that sets the sequence of net transfers to zero.
- Rationale and directional bias:
  - Using IMF internal rates likely biases bailout-transfer estimates downward because:
    - EU loans are riskier than IMF loans (IMF loans legally senior per Article 13 ESM Treaty).
    - EU loans have longer maturities (positive term premium).
    - IMF programmes themselves may be subsidized.
  - Consequence: estimated transfers are interpreted as lower bounds unless exceptional scenarios (EU lending senior, shorter maturity, or IMF penalty) apply.
- Assumptions highlighted:
  - Future repayments and interest rates equal current specification (no further renegotiations).
  - Variable-rate loans proxied by adding term premium to current interest rate.

### Table 1 — selected exact numeric findings for Eurozone borrowers (preserve numbers)
- Cyprus — ESM:
  - irr_i,j: 0.82
  - ̄r_i: 1.73
  - ∆irr_i,j: 0.90
  - d_i,j: 15.48
  - P D_i,j: 6.30
  - Tr_i,j: 0.74
  - Tr_i,j/GDP_i: 3.62%
- Cyprus — IMF:
  - irr_i,j: 1.73
  - ̄r_i: 1.73
  - ∆irr_i,j: 0.00
  - d_i,j: 7.26
  - P D_i,j: 0.95
- Greece — EC:
  - irr_i,j: 0.68
  - ̄r_i: 3.26
  - ∆irr_i,j: 2.58
  - d_i,j: 20.66
  - P D_i,j: 52.90
  - Tr_i,j: 18.49
  - Tr_i,j/GDP_i: 8.18%
- Greece — EFSF:
  - irr_i,j: 1.16
  - ̄r_i: 3.26
  - ∆irr_i,j: 2.11
  - d_i,j: 37.20
  - P D_i,j: 171.20
  - Tr_i,j: 66.82
  - Tr_i,j/GDP_i: 28.19%
- Greece — ESM:
  - irr_i,j: 1.83
  - ̄r_i: 3.26
  - ∆irr_i,j: 1.43
  - d_i,j: 33.81
  - P D_i,j: 61.90
  - Tr_i,j: 16.64
  - Tr_i,j/GDP_i: 7.30%
- Greece — IMF:
  - irr_i,j: 3.26
  - ̄r_i: 3.26
  - ∆irr_i,j: 0.00
  - d_i,j: 6.70
  - P D_i,j: 31.99
- Ireland — EFSF:
  - irr_i,j: 1.83
  - ̄r_i: 2.66
  - ∆irr_i,j: 0.83
  - d_i,j: 21.98
  - P D_i,j: 17.70
  - Tr_i,j: 2.22
  - Tr_i,j/GDP_i: 1.29%
- Ireland — EFSM:
  - irr_i,j: 3.23
  - ̄r_i: 2.66
  - ∆irr_i,j: -0.57
  - d_i,j: 16.04
  - P D_i,j: 22.50
  - Tr_i,j: -1.51
  - Tr_i,j/GDP_i: -0.88%
- Ireland — IMF:
  - irr_i,j: 2.66
  - ̄r_i: 2.66
  - ∆irr_i,j: 0.00
  - d_i,j: 4.59
  - P D_i,j: 4.59
- Portugal — EFSF:
  - irr_i,j: 1.78
  - ̄r_i: 3.25
  - ∆irr_i,j: 1.46
  - d_i,j: 21.92
  - P D_i,j: 26.00
  - Tr_i,j: 5.47
  - Tr_i,j/GDP_i: 2.93%
- Portugal — EFSM:
  - irr_i,j: 3.10
  - ̄r_i: 3.25
  - ∆irr_i,j: 0.14
  - d_i,j: 15.64
  - P D_i,j: 24.30
  - Tr_i,j: 0.38
  - Tr_i,j/GDP_i: 0.21%
- Portugal — IMF:
  - irr_i,j: 3.25
  - ̄r_i: 3.25
  - ∆irr_i,j: 0.00
  - d_i,j: 5.65
  - P D_i,j: 26.39
- Spain — ESM:
  - irr_i,j: 0.93
  - ̄r_i: 2.65
  - ∆irr_i,j: 1.74
  - d_i,j: 9.14
  - P D_i,j: 41.33
  - Tr_i,j: 5.55
  - Tr_i,j/GDP_i: 0.49%

### Aggregate and cross-country quantitative conclusions (exact figures preserved)
- IMF internal rates vary from 1.73% for Cyprus to 3.26% for Greece.
- Nominal disbursements P D_i,j range from 7.25 e billion for Cyprus (36% of its 2010 GDP) to 317.82 e billion for Greece (140% of its 2010 GDP).
- Estimated net present value of transfers (selected aggregates):
  - Ireland: transfer positive but very small: 0.69 e billion, representing 0.41% of 2010 GDP.
  - Greece: transfer very substantial: 98.6 e billion, representing 42.3% of 2010 GDP.
  - Portugal and Cyprus: transfers positive and sizable, between 3.14% and 3.62% of GDP.
  - Spain: transfer less than 0.5% of GDP.
- Interpretation for non-eurozone borrowers (Table 2):
  - Hungary — BoP:
    - irr_i,j: 3.56; irr_i,IMF: 2.42; ∆irr_i,j: -1.13; d_i,j: 5.24; P D_i,j: 5.50; Tr_i,j: -0.28; Tr_i,j/GDP_i: -0.31%
  - Latvia — BoP:
    - irr_i,j: 3.09; irr_i,IMF: 2.55; ∆irr_i,j: -0.53; d_i,j: 6.92; P D_i,j: 2.90; Tr_i,j: -0.09; Tr_i,j/GDP_i: -0.49%
  - Romania — BoP:
    - irr_i,j: 3.00; irr_i,IMF: 2.70; ∆irr_i,j: -0.30; d_i,j: 7.96; P D_i,j: 5.00; Tr_i,j: -0.10; Tr_i,j/GDP_i: -0.08%
- Main interpretation:
  - Implicit transfers during the euro crisis vary substantially across eurozone countries: from small (Ireland) to extremely large (Greece).
  - Sizable transfers tied to membership in the monetary union, not merely EU membership: non-eurozone EU countries show no significant positive transfers.

---

### Model — resource constraints, portfolios, and yields (exact expressions preserved)
- Period-0 consolidated resource constraint (country i):
  - c_i0 + b_s,i1/R* = y_i0 + τ_0 − (b_i0 − b_i,i0) + (b_i1 − b_i,i1)/R_i + b_s,i0. (Eq. (3))
- Period-1 consolidated resource constraint if i repays:
  - c_i1 = y_i1 + τ_1 − (b_i1 − b_i,i1) + b_s,i1.
- Period-1 consolidated resource constraint if i defaults:
  - c_i1 = y_i1(1 − Φ) − ρ y_i1 [1 − b_i,i1 / b_i1] + b_s,i1. (Eq. (4))
- Market clearing:
  - Σ_j b_s,j1 = b_s1; Σ_j b_i,j1 = b_i1. (Eq. (5))
- Optimal portfolio first-order conditions (Eq. (6)):
  - 1/R_i − β P = ω_j λ_i,j b_i,j1.
  - 1/R* − β = ω_j λ_s b_s,j1.
- Proposition 1 (portfolio shares and yields):
  - α_i,j ≡ b_i,j1 / b_i1 = ω_j λ_i,j / ̄λ_i.
  - α_s,j ≡ b_s,j1 / b_s1 = ω_j.
  - In the bond-less limit: R* = β^−1; R_i = (β P)^−1. (Eq. (7))
- Economic implication: portfolio shares reflect liquidity services; i-debt yield includes risk-premium via P.

---

### Ex-post defaults and bailouts — key thresholds and optimal bailout policy
- Government i repays at t = 1 iff:
  - y_i1 [Φ + ρ(1 − α_i,i)] + τ_1 ≥ b_i1 (1 − α_i,i). (Eq. (8))
- Minimal transfer to avoid default:
  - τ_1 ≡ b_i1(1 − α_i,i) − y_i1 [Φ + ρ(1 − α_i,i)]. (Eq. (9))
- Minimal shock realization ̄ε for repayment without transfer:
  - ̄ε ≡ (1 − α_i,i) b_i1 / ̄y_i1 [Φ + ρ(1 − α_i,i)]^−1. (Eq. (10))
  - Note: ̄ε increases with (1 − α_i,i) b_i1 / ̄y_i1 and decreases with Φ or ρ.
  - If α_i,i = 1 then ̄ε = 0 < ε_min and there is never incentive to default.
- g’s decision to offer minimal transfer τ_1 when ε_i1 < ̄ε holds as long as:
  - Φ y_i1 + κ y_g1 ≥ α_i,u [b_i1 − ρ y_i1]. (Eq. (11))
- Threshold ε defining joint-optimal bailout region:
  - ε ≡ α_i,u b_i1 / ̄y_i1 − κ y_g1 / ̄y_i1 [Φ + ρ α_i,u]^−1. (Eq. (12))
  - ε ≤ ̄ε under α_i,g ≥ 0 and/or κ ≥ 0.
- Proposition 2 — optimal ex-post bailout (given b_i1):
  - If ε_i1 ≥ ̄ε: no default, τ_1 = 0.
  - If ε ≤ ε_i1 < ̄ε: minimal bailout τ_1 = τ_1 with probability 1 − π to avoid default.
  - If ε_i1 < ε: default, τ_1 = 0.
- Additional property: optimal bailout τ_1 is non-monotone in i’s output and discontinuous at ε_i1 = ε.

---

### Debt rollover at t = 0, Laffer curve, and political uncertainty
- Political/legal uncertainty parameter:
  - 0 ≤ π ≤ 1 is exogenous probability ex-post transfers will not be implemented.
  - Polar cases: π = 1 (full commitment to no bailout); π = 0 (full discretion / bailouts always implemented).
- Ex-ante probability of default:
  - π_d = G(ε) + π (G(̄ε) − G(ε)). (Eq. (14))
- Expected repayment Pb_i1 given face value b_i1 (Eq. (15)):
  - Pb_i1 = (1 − π_d) b_i1 + ρ ̄y_i1 [∫_{ε}^{ε_min} ε dG(ε) + π ∫_{̄ε}^{ε} ε dG(ε)].
- Fiscal revenues D(b_i1) ≡ b_i1 / R_i (Eq. (16)):
  - D(b_i1) = β b_i1 (1 − π_d) + β ρ ̄y_i1 [∫_{ε}^{ε_min} ε dG(ε) + π ∫_{̄ε}^{ε} ε dG(ε)] + λ_i.
- Debt Laffer curve D(b): key regions (definitions preserved):
  - Safe region: 0 ≤ b_i1 ≤ b ≡ y_i^min (Φ/(1 − α_i,i) + ρ) → D(b) = β b + ̄λ_i.
  - Intermediate risky region: b < b_i1 ≤ ̄b ≡ ((Φ + ρ α_i,u) y_i^min + κ y_g1) / α_i,u.
  - High-debt regions subdivided by ˆb and ̃b with specified interpretations.
- Regularity results (summary):
  - D(b) convex on [0, ˆb).
  - D(b) has non-differentiable points at b and ̄b.
  - Laffer curve reaches maximum b_max with ̄b ≤ b_max < ˆb.
  - Country i chooses debt 0 ≤ b ≤ b_max (avoiding rollover crises and multiple equilibria).
- Illustrative parameter example used to draw figures (numbers preserved):
  - ρ = 0.6, Φ = 0.2, κ = 0.05, ε_min = 0.5, ε_max = 1.5, β = 0.95, ̄y_i1 = 1, y_g1 = 2, α_i,i = 0.4, α_i,g = α_i,u = 0.3, b = 0.47, ̄b = 0.97 and ˆb = 1.4.
- Economic insight:
  - For b ≤ ̄b yields may remain equal to R* if bailouts are allowed (π small), but increase rapidly when bailouts prohibited (π large), providing a mechanism for sudden yield surges when perceptions about bailout guarantees change.

---

### Optimal debt issuance and moral hazard (exact conditions preserved)
- Country i chooses b_i1 to maximize U(b_i1) subject to constraints; first-order condition for interior solution (differentiable D):
  - D′(b_i1) = β(1 − G(̄ε)). (Eq. (17))
  - Interpretation: marginal revenue equals discounted marginal probability of repayment without transfer.
- Expanded marginal condition (Eq. (18)) — trade-off interpretation:
  - Left-hand side: (G(̄ε) − G(ε)) (1 − π) = likelihood of bailout (benefit).
  - Right-hand side: incremental expected cost raising yields via increased default probability (two components tied to ε and ̄ε).
- No-bailout (π = 1):
  - Left-hand side zero → no incentive to issue risky debt; interior solution requires ̄ε ≤ ε_min.
- With π > 0:
  - Borrower may issue risky debt to increase bailout likelihood (moral hazard / “Northern view”).
  - Lower κ (collateral cost to g) reduces incentive to bail out and disciplines borrower (reduces risk-shifting).
- Characterization by funding needs x_i0 (definition preserved) and Proposition 4:
  - If x_i0 > D(b_max): insolvency in period 0.
  - If D(b_max) ≥ x_i0 > D(b_opt): issuer constrained by funding needs; no risk shifting.
  - If D(b_opt) ≥ x_i0 > β b: issuer chooses b_opt and may engage in risk shifting.
  - If x_i0 < β b: issuer can choose safe or risky issuance; risk shifting maximal possible; condition for preferring risky issuance given by Eq. (19) (preserved).
- Comparative statics and Proposition 5 (insulation and gambling for resurrection):
  - There exists critical π_c such that for π > π_c optimal debt becomes safe (discontinuous fall from ̄b to b ≤ b).
  - g may optimally choose π < π_c (allow bailouts) to avoid immediate default in period 0 — “gambles for resurrection.”
  - Conditions under which g prefers to allow bailouts versus enforcing commitment summarized (Eq. (20) preserved).
- Policy interpretation:
  - Reducing collateral cost of default (e.g., orderly restructuring) lowers risk shifting.
  - Eliminating risk shifting does not require π = 1; π > π_c suffices.
  - g may optimally tolerate a degree of bailout discretion to avoid immediate sovereign defaults and the associated costs.

---

### Exit vs default, joint transfers, and calibration to observed bailouts
- Exit decision additive and independent to default decision; exit cut-offs do not depend on debt level.
- Proposition 7 — optimal ex-post transfers (structure preserved):
  - Total transfer τ_1 = τ_d1 + τ_e1.
  - g implements minimal transfers to avoid default and/or exit according to ε_i1 and the cut-offs:
    - If ε_i1 ≥ ̄ε_d: no default, τ_d1 = 0.
    - If ε_d ≤ ε_i1 < ̄ε_d: minimal transfer τ_d1 ≡ (b_i1 − ρ y_i1)(1 − α_i,i) − Φ_d y_i1.
    - If ε_i1 < ε_d: default, τ_d1 = 0.
    - If ε_i1 > ̄ε_e: no exit, τ_e1 = 0.
    - If ε_e ≤ ε_i1 < ̄ε_e: minimal transfer τ_e1 ≡ ∆ ̄y_i1 − Φ_e y_i1.
    - If ε_i1 < ε_e: exit, τ_e1 = 0.
- Calibration and empirical matching (selected preserved inputs and outcomes):
  - Haircut h = 0.5 (Zettelmeyer et al. (2013)).
  - Chosen Φ_d/(1 − β) ≈ 0.09 with β = 0.95 implies a flow default cost of approximately 1.5% over seven years.
  - Table A.3 sample entries (exact numbers):
    - Cyprus: b_i1 / y_i0 = 0.57; α_ii1 = 0.51; y1 / y0 = 1.04; Model (τ_i / y_i0) = 0.046; Empirical (τ_i / y_i0) = 0.045.
    - Greece: b_i1 / y_i0 = 1.09; α_ii1 = 0.80; y1 / y0 = 0.46.
    - Ireland: b_i1 / y_i0 = 0.34; α_ii1 = 0.38; y1 / y0 = 1.18; Model (τ_i / y_i0) = 0.000; Empirical (τ_i / y_i0) = 0.004.
    - Portugal: b_i1 / y_i0 = 0.75; α_ii1 = 0.35; y1 / y0 = 0.98; Model (τ_i / y_i0) = 0.160; Empirical (τ_i / y_i0) = 0.035.
    - Spain: b_i1 / y_i0 = 0.43; α_ii1 = 0.56; y1 / y0 = 1.01; Model (τ_i / y_i0) = 0.003; Empirical (τ_i / y_i0) = 0.006.
- Greece-specific interpretation:
  - Greece defaulted but did not exit and received transfer τ_1 representing 44 percent of 2010 output.
  - Infinite-horizon transfer to avoid exit (Eq. (24)) and maximum predicted transfer (Eq. (25)) depend on κ_e/(1 − β) and relative sizes: with Greece y_i0 = e224 bn and Eurozone y_g = e9,553 bn a collateral cost κ_e/(1 − β) = 0.43 × 224 / 9553 ≈ 1% would justify observed bailout size.

---

### Policy implications and extensions (concise)
- Reconciliation of narratives:
  - Northern view: collateral damage of default weakens no-bailout commitment and induces excessive borrowing by fragile countries.
  - Southern view: transfers prevent deadweight default costs but creditor countries capture most efficiency gains (limited solidarity).
  - Both views complementary to explain crisis dynamics.
- Eurozone reforms:
  - Orderly restructuring that lowers collateral cost of default should reduce risk shifting and excessive borrowing — desirable for creditor countries.
  - Strengthening strict no-bailout commitment can precipitate immediate defaults by increasing rollover costs; reforms should be gradual.
  - Common fiscal capacity would provide transfers that are ex-post efficient when shocks threaten repayment and union integrity — such transfers already substantial within the union.
- Model extensions and robustness:
  - Debt re-nationalization increases α_i,i and reduces bailout size and probability.
  - Concentration limits (higher mandated holdings by g) increase bailout probability and size.
  - Reform effort, bargaining over surplus, and debt monetization (ECB inflation) analyzed: monetization can avert defaults but imposes union-wide distortion costs; when transfers restricted, ECB may be “overburdened” and forced to monetize, creating inefficiencies.

_Italic: Source — wpiea2023177-print-pdf (excerpts provided)._

### Section 4 analyzes the incentives for defaults and bailouts and Section 5 studies how these incentives

### wpiea2023177-print-pdf - Section 4 analyzes the incentives for defaults and bailouts and Section 5 studies how these incentives

### Literature Review
- Two families of models explaining why countries repay debt:
  - Reputation-based models emphasizing access to international capital markets (Eaton and Gersovitz (1981)).
  - Direct-cost models emphasizing disruption of trade and other direct costs of default (Cohen and Sachs (1986); Bulow and Rogoff (1989a, 1989b); Fernandez and Rosenthal (1990)). The paper belongs to this second family.
- Channels of output loss from default emphasized:
  - Trade and financial disruptions.
  - Risk of exit from the monetary union.
- Empirical evidence:
  - Rose (2005) finds debt renegotiation results in a decline in bilateral trade of around 8 percent a year, persisting for around 15 years.
- Related theoretical contributions and distinctions:
  - Bulow and Rogoff (1989a): protracted debt renegotiation harms third parties allowing side-payments.
  - Mengus (2021): limited information on domestic portfolios implies direct transfers cannot be perfectly targeted.
  - Tirole (2015) and Farhi and Tirole (2018): ex-ante and ex-post forms of solidarity; two-layer bailout ("deadly embrace") between sovereign and financial balance sheets. This paper builds on them but:
    - Shows ex-post solidarity may not generate welfare gain for the debtor country.
    - Includes a third country outside the monetary union to analyze debt re-nationalization and debt monetization.
    - Explores how exit (not just default) affects optimal debt issuance and bailout formation.
    - Bridges theory with empirics by connecting model to estimated bailouts.
  - Horn, Reinhart and Trebesch (2020): financial integration matters for bailout scope.
  - Broner, Erce, Martin and Ventura (2014): home bias in sovereign debt holdings modeled; this paper shares the home bias feature but not creditor discrimination.
  - Uhlig (2014): interplay among bank holdings of domestic sovereign debt, bank regulation, default risk, and central bank guarantees; current paper does not model banks explicitly but home bias plays an important role.
  - Corsetti, Erce and Uy (2018): official lending institutions in sovereign debt/default models; different focus (restore debt sustainability via official lending conditions).
  - Dellas and Niepelt (2016): higher exposure to official lenders improves incentives to repay but lowers value of default option; current model does not distinguish private vs official lenders.
  - Azzimonti and Quadrini (2021): bailouts can be Pareto improving ex-ante via public debt as public liquidity; complementary mechanism to current paper’s creditor trade-off between immediate insolvency vs future default likelihood.
- Distinction from literature on self-fulfilling crises (Calvo (1988); Cole and Kehoe (2000)):
  - This paper departs from frameworks focused on multiple equilibria or liquidity runs and instead emphasizes observed substantial transfers (from EFSF/ESM) to periphery countries.

### Section 2 — Implicit Transfers During the Euro area crisis (overview)
- Focus: financial assistance programmes for Cyprus, Greece, Ireland, Portugal, Spain; review terms for Hungary, Latvia, Romania (non-Eurozone EU members).
- References to additional material (Table A.4, Online Appendix, Corsetti, Erce and Uy (2020), Abbas et al. (2014)) noted but not reproduced here.

### 2.1 Historical Overview — Institutional and legal context
- Relevant Treaty provisions:
  - Article 125 TFEU: the "no-bailout clause" preventing Union or Member States from assuming another Member’s debt obligations; text excerpt summarized in source.
  - Article 123 TFEU: prohibits the ECB from directly purchasing member countries’ public debt; text excerpt summarized in source.
  - Article 122 TFEU: allows Union or Member States to provide assistance under exceptional circumstances; text excerpt summarized in source.
- Despite legal constraints, during the Eurozone crisis several members lost market access and received support mainly via the EFSF and ESM.
- Lenders and programme structure:
  - "Troika": IMF, European Commission (EC), European Central Bank (ECB); paper focuses on IMF and EC.
  - EC lending instruments: EFSM, EFSF, ESM, Greek Loan Facility (GLF), Balance of Payments (BoP) facility.
  - IMF loans to high-income crisis countries used non-concessional Standby Arrangements (SBA) or Extended Fund Facilities (EFF); loans medium-term with maximum maturities up to 10 years.
  - Normal IMF access limits: 145% of quota annually or 435% over programme lifetime; "exceptional access" allowed overrides.
- EC programme evolution:
  - March 2010: GLF (Greece) marks start of large-scale EC lending.
  - June 2010: creation of EFSF (support to Greece, Ireland, Portugal).
  - 2011: creation of EFSM (assistance to Ireland and Portugal).
  - September 2012: creation of ESM (permanent facility to replace EFSF; support to Greece, Spain, Cyprus).
  - Most EC programmes (except GLF) used on-lending: lender borrows from markets and on-lends to distressed country.

### Greek Financial Assistance Programmes — key figures and chronology
- Greece had three successive programmes after 2009 revelations of understated public debt/deficit.
- Programme 1 (2010-2011):
  - Size: approximately e110 bn total.
  - Composition: e80 bn from GLF; e30 bn from IMF’s SBA programme.
  - IMF actual disbursements: e20.1 bn in six tranches between May 2010 and December 2011.
  - EC actual disbursements: e52.9 bn in six tranches between May 2010 and December 2011.
  - Bilateral apportionment: Germany e15.17 bn; France e11.39 bn; Italy e10.00 bn.
- Programme 2 (2012-2015):
  - Included undisbursed amount from Programme 1 plus an additional e130 bn for a total of almost e180 bn.
  - IMF actual disbursements: around e11.6 bn out of a planned contribution of e28 bn.
  - IMF lending instrument: EFF (first tranche March 2012; last tranche June 2014).
  - EFSF commitment: e144.7 bn; EFSF disbursed approximately e141.8 bn.
  - Programme 2 interrupted end-2014 by Greek elections; allowed to expire in June 2015 during fifth review.
- Programme 3 (2015-2018):
  - Bridge loan and transition noted: one EFSM bridge loan fore e7.16 bn in July 2015 to allow transition to Programme 3.
  - ESM committed e86 bn to Greece and disbursed e61.9 bn in total.
  - Programme 3 concluded in August 2018.

### Other Eurozone Financial Assistance Programmes — key figures
- Ireland (request November 2010; approval December 2010):
  - Funding comprised of e17.7 bn from EFSF; e22.5 bn from EFSM; e22.5 bn from IMF; e4.8 bn from Bilateral Loans (United Kingdom, Sweden, Denmark).
  - Bilateral contributions footnoted: Sweden e600 million; United Kingdom e3,830 million (£3.23 million in source text); Denmark e400 million.
- Portugal (May 2011–June 2014):
  - EC (EFSF and EFSM) and IMF each committed approximately e26 bn for a total of e78 bn.
  - Portugal allowed programme to lapse without taking final IMF tranche.
- Cyprus (joint IMF/ESM programme April/May 2013; exited March 2016):
  - Total approved financing: e10 bn (ESM committed e9 bn; IMF approximately e1 bn).
  - ESM disbursed e6.3 bn between May 2013 and October 2015.
  - Expected repayment between 2025 and 2031.
- Spain:
  - Assistance from ESM only: total committed e100 bn in July 2012.
  - Disbursed: e41.3 bn in December 2012 and February 2013.
  - Used to recapitalize the banking sector.
  - Expected repayment between 2022 and 2027; Spain made voluntary early repayments.

### Other European Bailout Programmes (non-Eurozone: Hungary, Latvia, Romania) — key figures
- Hungary (assistance November 2008–end 2009):
  - Total available: e6.5 bn from EC; approximately e12.5 bn from IMF.
  - EC actual disbursement: e5.5 bn.
  - IMF disbursed approximately e8.7 bn (SDR7.6 bn) between November 2008 and September 2009; repaid between February 2012 and August 2013.
  - EC disbursements: three installments December 2008 to July 2009; maturities between three and six years.
- Latvia (assistance January 2009):
  - Total available: e7.5 bn (e3.1 bn from EC; approximately e1.7 bn from IMF cited in source).
  - EC realized assistance: four installments of e2.9 bn between February 2009 and October 2010.
  - IMF disbursed approximately SDR1 bn between 2008 and 2010; repaid in 2013.
- Romania (assistance May 2009):
  - Total available: e20 bn (e5 bn from EC; approximately e12.95 bn from IMF).

*Italic: Source — wpiea2023177-print-pdf (excerpt provided).*

### 2.2    Transfers estimates

### 2.2    Transfers estimates

### Motivation and Methodology
- Objective: estimate implicit transfers in financial assistance for the programs described, following Joshi and Zettelmeyer (2005).
- Key methodological point: use a risk-adjusted discount rate appropriate to public assistance programmes; avoid discounting public (risk-less) loans with private (risky) market rates.
- Benchmark discount rate: the internal rate of return on the IMF’s lending for borrower i during the Eurozone crisis, ̄r_i.
- Core formula (Net-Present-Value of total transfers Tr_i,j_t):
  - Tr_i,j_t0 = sum_{t=t0}^T NT_i,j_t / (1 + ̄r_i)^t
  - NT_i,j_t = D_i,j_t − R_i,j_t − sum_{τ=1}^i D^r_{i,j,t−τ} − i^i,j_{t−τ} D^r_{i,j,t−τ}
  - irr_i,j is the internal rate of return that sets the sequence of net transfers to zero.
- Rationale for using the IMF internal rate:
  - IMF loans are legally senior to EFSF and ESM (Article 13 of the ESM Treaty), implying the correct discount rate on European loans should be higher than the IMF’s internal rate; this biases bailout estimates downward.
  - IMF interest rates are time-varying and tied to the IMF’s cost of funding and quota-related penalty adjustments; thus IMF rates capture time variation in global lending conditions.
  - IMF programme maturities (3 to 9 years) are typically shorter than European loans (10 to 30 years); a positive term premium on longer European loans biases transfer estimates downward.
- Concerns and directional bias:
  - If IMF programmes include a transfer component, using IMF rates biases estimates downward; Joshi and Zettelmeyer (2005) find no significant transfer component for high and middle income countries in IMF lending 1973–2003.
  - Estimated transfers are a lower bound for three reasons: EU programmes are riskier than the IMF’s; EU loans have longer maturity; IMF programmes themselves may be subsidized.
  - Estimates would be biased upwards only if EU lending were senior to the IMF, shorter maturity, or IMF lending carried a penalty rate; these scenarios are not viewed as serious possibilities.
- Data and assumptions:
  - Compiled disbursements, repayments, and interest payments for eight borrowing countries and five official international lenders.
  - Assumption 1: the most current specification of future repayments and interest rates equals future realized outcomes (no further renegotiations). Any favorable renegotiation would increase transfers beyond estimates.
  - Assumption 2: for variable-rate loans, proxy future interest rates by adding an estimated term premium to the current interest rate (term premium constructed from difference between forward 3-month Euribor and current 3-month Euribor).

### Results
- Table 1 (Eurozone borrowers): columns reported
  - (1) irr_i,j (internal rate of return for borrower-lender pair)
  - (2) ̄r_i (IMF internal rate of return for borrower i)
  - (3) ∆irr_i,j = ̄r_i − irr_i,j
  - (4) d_i,j (duration of the lending cycle)
  - (5) P D_i,j (sum of nominal disbursements, in e billion)
  - (6) Tr_i,j (implicit transfer, in 2010 billions of Euros)
  - (7) Tr_i,j/GDP_i (implicit transfer scaled by 2010 nominal GDP)
- Selected numeric findings from Table 1 (values preserved exactly):
  - Cyprus — ESM:
    - irr_i,j: 0.82
    - ̄r_i: 1.73
    - ∆irr_i,j: 0.90
    - d_i,j: 15.48
    - P D_i,j: 6.30
    - Tr_i,j: 0.74
    - Tr_i,j/GDP_i: 3.62%
  - Cyprus — IMF:
    - irr_i,j: 1.73
    - ̄r_i: 1.73
    - ∆irr_i,j: 0.00
    - d_i,j: 7.26
    - P D_i,j: 0.95
  - Greece — EC:
    - irr_i,j: 0.68
    - ̄r_i: 3.26
    - ∆irr_i,j: 2.58
    - d_i,j: 20.66
    - P D_i,j: 52.90
    - Tr_i,j: 18.49
    - Tr_i,j/GDP_i: 8.18%
  - Greece — EFSF:
    - irr_i,j: 1.16
    - ̄r_i: 3.26
    - ∆irr_i,j: 2.11
    - d_i,j: 37.20
    - P D_i,j: 171.20
    - Tr_i,j: 66.82
    - Tr_i,j/GDP_i: 28.19%
  - Greece — ESM:
    - irr_i,j: 1.83
    - ̄r_i: 3.26
    - ∆irr_i,j: 1.43
    - d_i,j: 33.81
    - P D_i,j: 61.90
    - Tr_i,j: 16.64
    - Tr_i,j/GDP_i: 7.30%
  - Greece — IMF:
    - irr_i,j: 3.26
    - ̄r_i: 3.26
    - ∆irr_i,j: 0.00
    - d_i,j: 6.70
    - P D_i,j: 31.99
  - Ireland — EFSF:
    - irr_i,j: 1.83
    - ̄r_i: 2.66
    - ∆irr_i,j: 0.83
    - d_i,j: 21.98
    - P D_i,j: 17.70
    - Tr_i,j: 2.22
    - Tr_i,j/GDP_i: 1.29%
  - Ireland — EFSM:
    - irr_i,j: 3.23
    - ̄r_i: 2.66
    - ∆irr_i,j: -0.57
    - d_i,j: 16.04
    - P D_i,j: 22.50
    - Tr_i,j: -1.51
    - Tr_i,j/GDP_i: -0.88%
  - Ireland — IMF:
    - irr_i,j: 2.66
    - ̄r_i: 2.66
    - ∆irr_i,j: 0.00
    - d_i,j: 4.59
    - P D_i,j: 4.59
  - Portugal — EFSF:
    - irr_i,j: 1.78
    - ̄r_i: 3.25
    - ∆irr_i,j: 1.46
    - d_i,j: 21.92
    - P D_i,j: 26.00
    - Tr_i,j: 5.47
    - Tr_i,j/GDP_i: 2.93%
  - Portugal — EFSM:
    - irr_i,j: 3.10
    - ̄r_i: 3.25
    - ∆irr_i,j: 0.14
    - d_i,j: 15.64
    - P D_i,j: 24.30
    - Tr_i,j: 0.38
    - Tr_i,j/GDP_i: 0.21%
  - Portugal — IMF:
    - irr_i,j: 3.25
    - ̄r_i: 3.25
    - ∆irr_i,j: 0.00
    - d_i,j: 5.65
    - P D_i,j: 26.39
  - Spain — ESM:
    - irr_i,j: 0.93
    - ̄r_i: 2.65
    - ∆irr_i,j: 1.74
    - d_i,j: 9.14
    - P D_i,j: 41.33
    - Tr_i,j: 5.55
    - Tr_i,j/GDP_i: 0.49%
- Aggregate and cross-country findings (from Table 1 and discussion):
  - IMF internal rates vary from 1.73% for Cyprus to 3.26% for Greece.
  - Nominal disbursements P D_i,j range from 7.25 e billion for Cyprus (36% of its 2010 GDP) to 317.82 e billion for Greece (140% of its 2010 GDP).
  - Estimated net present value of transfers:
    - Ireland: transfer positive but very small: 0.69 e billion, representing 0.41% of 2010 GDP.
    - Greece: transfer very substantial: 98.6 e billion, representing 42.3% of 2010 GDP.
    - Portugal and Cyprus: transfers positive and sizable, between 3.14% and 3.62% of GDP.
    - Spain: transfer less than 0.5% of GDP (lending directed towards bank recapitalization; different nature).
- Table 2 (non-Eurozone EU borrowers — Hungary, Latvia, Romania) findings:
  - Reported columns: irr_i,j, irr_i,IMF, ∆irr_i,j, d_i,j, P D_i,j, Tr_i,j, Tr_i,j/GDP_i.
  - Hungary — BoP:
    - irr_i,j: 3.56
    - irr_i,IMF: 2.42
    - ∆irr_i,j: -1.13
    - d_i,j: 5.24
    - P D_i,j: 5.50
    - Tr_i,j: -0.28
    - Tr_i,j/GDP_i: -0.31%
  - Latvia — BoP:
    - irr_i,j: 3.09
    - irr_i,IMF: 2.55
    - ∆irr_i,j: -0.53
    - d_i,j: 6.92
    - P D_i,j: 2.90
    - Tr_i,j: -0.09
    - Tr_i,j/GDP_i: -0.49%
  - Romania — BoP:
    - irr_i,j: 3.00
    - irr_i,IMF: 2.70
    - ∆irr_i,j: -0.30
    - d_i,j: 7.96
    - P D_i,j: 5.00
    - Tr_i,j: -0.10
    - Tr_i,j/GDP_i: -0.08%
- Interpretation of non-eurozone results:
  - Internal rates of return for EC programmes (3.00% to 3.56%) are never lower than the IMF internal rate (2.42% to 2.70%).
  - IMF loans are shorter in duration even when IMF lent more than the EC.
  - Transfer estimates are negative for these three countries (between -0.08% and -0.49% of GDP), interpreted as no transfer element embedded in EC lending to non-eurozone members.
- Main conclusions:
  - Implicit transfers during the euro crisis vary substantially across eurozone countries: from small (Ireland) to extremely large (Greece).
  - Sizable transfers are tied to membership in the monetary union, not merely membership in the European Union; non-eurozone EU countries did not receive significant transfers from the EC.

*Source: wpiea2023177-print-pdf - 2.2    Transfers estimates*

### 3.2    Resource Constraints and Market Clearing

### 3.2 Resource Constraints and Market Clearing

### Resource constraints (period t = 0 and t = 1)
- Period t = 0 consolidated resource constraint for country i:
  - c_i0 + b_s,i1/R* = y_i0 + τ_0 − (b_i0 − b_i,i0) + (b_i1 − b_i,i1)/R_i + b_s,i0. (Eq. (3))
- Period t = 1 consolidated resource constraints for country i:
  - If i repays:
    - c_i1 = y_i1 + τ_1 − (b_i1 − b_i,i1) + b_s,i1.
  - If i defaults:
    - c_i1 = y_i1(1 − Φ) − ρ y_i1 [1 − b_i,i1 / b_i1] + b_s,i1. (Eq. (4))
- Market clearing for safe bonds and i-bonds:
  - Σ_j b_s,j1 = b_s1; Σ_j b_i,j1 = b_i1. (Eq. (5))

### Interpretation of terms and mechanisms
- Period-0 resources: output y_i0, transfers τ_0 ≥ 0, net repayment of initial domestic debt (b_i0 − b_i,i0), issuance of new debt (b_i1 − b_i,i1)/R_i, safe asset holdings b_s,i0; used for consumption c_i0 and safe asset investments b_s,i1/R*.
- Period-1 default costs and recoveries:
  - Direct output loss on default: Φ y_i1.
  - Recovery to foreign investors: ρ y_i1 (b_i1 − b_i,i1)/b_i1.
- Market clearing links individual holdings to aggregate supplies b_s1 and b_i1.

---

### 3.3 Optimal Portfolios

### Optimality conditions for bond demand
- Define P_j ≤ 1 as the expected payment per unit of i’s sovereign debt for j’s household; if investors cannot be discriminated on default, P_j ≡ P.
- First-order conditions for optimal portfolios (maximizing U_j):
  - 1/R_i − β P = ω_j λ_i,j b_i,j1.
  - 1/R* − β = ω_j λ_s b_s,j1. (Eq. (6))
- Weighted average liquidity service:
  - ̄λ_i ≡ Σ_k ω_k λ_i,k.

### Proposition 1 — Optimal portfolios and equilibrium yields
- Equilibrium bond portfolios are independent of yields and reflect relative liquidity services:
  - α_i,j ≡ b_i,j1 / b_i1 = ω_j λ_i,j / ̄λ_i.
  - α_s,j ≡ b_s,j1 / b_s1 = ω_j.
  - ̄λ_i ≡ Σ_k ω_k λ_i,k.
- In the bond-less limit, equilibrium yields satisfy:
  - R* = β^−1; R_i = (β P)^−1. (Eq. (7))
- Economic implications:
  - Portfolio shares of i-debt proportional to relative liquidity benefits across investor classes and size.
  - Holdings of s-debt reflect only size differences.
  - Safe debt yield incorporates a liquidity premium; i-debt yield adds a risk-premium. In the bondless limit, liquidity premium on safe debt disappears and i-spread reflects entirely default risk (P ≤ 1).

---

### 4 Ex-Post Defaults and Bailouts

### Government default decision at t = 1
- Government repays when:
  - y_i1 [Φ + ρ(1 − α_i,i)] + τ_1 ≥ b_i1 (1 − α_i,i). (Eq. (8))
- Interpretation of terms:
  - Left-hand side: cost of default = Φ y_i1 (direct disruption) + ρ y_i1 (1 − α_i,i) (recovery paid to foreign investors) + foregone unilateral transfer τ_1.
  - Right-hand side: benefit of default = b_i1(1 − α_i,i) (debt not repaid to foreigners).
- Minimum transfer τ_1 required to avoid default:
  - τ_1 ≡ b_i1(1 − α_i,i) − y_i1 [Φ + ρ(1 − α_i,i)]. (Eq. (9))
- Minimum realization of shock ̄ε such that repayment is optimal without transfer:
  - ̄ε ≡ (1 − α_i,i) b_i1 / ̄y_i1 [Φ + ρ(1 − α_i,i)]^−1. (Eq. (10))
  - ̄ε increases with (1 − α_i,i) b_i1 / ̄y_i1 and decreases with Φ or ρ.
  - If α_i,i = 1 then ̄ε = 0 < ε_min and there is never incentive to default.

### g’s optimal ex-post transfer decision and joint efficiency
- g offers minimal transfer τ_1 = τ_1 when ε_i1 < ̄ε to avoid default.
- g prefers to transfer as long as:
  - Φ y_i1 + κ y_g1 ≥ α_i,u [b_i1 − ρ y_i1]. (Eq. (11))
  - Left-hand side: output loss from default for the union = Φ y_i1 + κ y_g1.
  - Right-hand side: union’s benefit of default = α_i,u (b_i1 − ρ y_i1).
- Threshold ε that characterizes when joint default is optimal:
  - ε ≡ α_i,u b_i1 / ̄y_i1 − κ y_g1 / ̄y_i1 [Φ + ρ α_i,u]^−1. (Eq. (12))
- Observations on thresholds:
  - ε ≤ ̄ε as long as α_i,g ≥ 0 and/or κ ≥ 0.
  - If α_i,u = 0 then ε ≤ 0 < ε_min and g always willing to bail out i.
  - When ε ≤ ε_i1 < ̄ε and g provides τ_1, i’s period-1 consumption:
    - c_i1 = y_i1 (1 − (Φ + ρ(1 − α_i,i))) + b_s,i1. (Eq. (13))
    - This is the “Southern view”: i avoids deadweight losses from default but g captures the efficiency gains.

### Proposition 2 — Optimal ex-post bailout (given b_i1)
- Define thresholds:
  - ε = α_i,u b_i1 / ̄y_i1 − κ y_g1 / ̄y_i1 [Φ + ρ α_i,u]^−1 ≤ ̄ε = (1 − α_i,i) b_i1 / ̄y_i1 [Φ + ρ(1 − α_i,i)]^−1.
- Optimal policy by realization of ε_i1:
  1. If ε_i1 ≥ ̄ε: i does not default and receives no bailout, τ_1 = 0.
  2. If ε ≤ ε_i1 < ̄ε: i receives minimum bailout τ_1 = τ_1 ≡ b_i1(1 − α_i,i) − y_i1 [Φ + ρ(1 − α_i,i)] with probability 1 − π to avoid default.
  3. If ε_i1 < ε: i defaults and receives no transfer, τ_1 = 0.
- Additional properties:
  - Optimal bailout τ_1 is non-monotone in i’s output: no bailout when output very low or very high.
  - τ_1 is discontinuous at ε_i1 = ε: avoiding default at lower ε requires larger transfers; joint surplus from avoiding default falls to zero at ε.

---

### 5 Debt Rollover Problem at t = 0 and the Debt Laffer Curve

### Political uncertainty and no-bailout enforcement
- Introduce exogenous probability 0 ≤ π ≤ 1 that ex-post transfers will not be implemented even if ex-post optimal; π captures political/legal uncertainty and partial ex-ante commitment.
  - Polar cases: π = 1 (full commitment to no bailout), π = 0 (full discretion / bailouts always implemented).
- Ex-ante probability of default:
  - π_d = G(ε) + π (G(̄ε) − G(ε)). (Eq. (14))

### Expected repayment and fiscal revenues
- Expected repayment Pb_i1 given face value b_i1:
  - Pb_i1 = (1 − π_d) b_i1 + ρ ̄y_i1 [∫_{ε}^{ε_min} ε dG(ε) + π ∫_{̄ε}^{ε} ε dG(ε)]. (Eq. (15))
  - Terms: full repayment with prob. 1 − π_d; recovery ρ y_i1 when default occurs either because ex-post optimal (ε_i1 < ε) or transfer fails to materialize with prob. π when ε ≤ ε_i1 < ̄ε.
- Fiscal revenues D(b_i1) ≡ b_i1 / R_i:
  - D(b_i1) = β P b_i1 + λ_i = β b_i1 (1 − π_d) + β ρ ̄y_i1 [∫_{ε}^{ε_min} ε dG(ε) + π ∫_{̄ε}^{ε} ε dG(ε)] + λ_i. (Eq. (16))

### Laffer curve D(b) and regions (summary)
- D(b) defines a Debt Laffer Curve. Key regions and cut-offs (described for bondless limit and uniform shocks in figure example):
  - Safe region: 0 ≤ b_i1 ≤ b ≡ y_i^min (Φ/(1 − α_i,i) + ρ). Debt is safe; D(b) = b / R* = β b + ̄λ_i.
  - Intermediate (risky if no bailout): b < b_i1 ≤ ̄b ≡ ((Φ + ρ α_i,u) y_i^min + κ y_g1) / α_i,u. Debt risky only if bailouts not allowed (π > 0). Laffer curve with discretionary bailout (π = 0) lies above no-bailout (π = 1).
  - High debt (risky even with transfers): b_i1 > ̄b. Subdivisions:
    - ̄b < b_i1 ≤ ˆb ≡ y_i^max (Φ/(1 − α_i,i) + ρ): optimal for g to let i default when y_i1 low; Laffer curve convex and peaks at b = b_max < ˆb.
    - ˆb < b_i1 ≤ ̃b ≡ ((Φ + ρ α_i,u) y_i^max + κ y_g1) / α_i,u: default would occur with certainty absent transfers; with transfers default can still be avoided if output high enough; Laffer curve decreasing here.
    - b_i1 > ̃b: i always defaults; investors expect repayment ρ ̄y_i1.
- Under regularity conditions in Appendix B.3:
  - D(b) is convex over [0, ˆb).
  - D(b) has non-differentiable points at b and ̄b with left and right differentials D′_−(b) and D′_+(b).
  - The Laffer curve reaches a maximum b_max with ̄b ≤ b_max < ˆb.
  - Country i will choose a debt level on the “correct” side of the Laffer curve: 0 ≤ b ≤ b_max, avoiding rollover crises and multiple equilibria.

### Illustrative numerical example (figure assumptions)
- The figure illustrating the Debt-Laffer Curve and contractual yields is drawn under the following parameter values (bondless limit, uniform shocks):
  - ρ = 0.6, Φ = 0.2, κ = 0.05, ε_min = 0.5, ε_max = 1.5, β = 0.95, ̄y_i1 = 1, y_g1 = 2, α_i,i = 0.4, α_i,g = α_i,u = 0.3, b = 0.47, ̄b = 0.97 and ˆb = 1.4.
- Contractual yield R(b) = (β P(b))^−1 illustrated for π = 0, π = 1 and π = 0.2 under the same parameter assumptions (bondless limit, uniform shocks).
- Economic insight:
  - For b < b ≤ ̄b, yields remain equal to R* if bailouts are allowed (debt safe with bailouts) but increase rapidly when bailouts prohibited (π > 0), providing a potential channel for rapid surge in yields when perceived bailout guarantees are removed or reinstated.

*Source: IMF working paper chapter 3.2–5 (wpiea2023177-print-pdf).*

### 5.2    Optimal Debt Issuance

### 5.2    Optimal Debt Issuance

### Model setup and objective
- Consider optimal choice of debt b_i1 in the bondless limit; portfolio shares α_{j,k} are taken as given.
- Country i’s aggregate consumption as functions of b_i1:
  - c_i0(b_i1) = (y_i0 + τ_0 − (1 − α_{i,i}) b_i0 + α_{s,i} b_s0) + (1 − α_{i,i}) D(b_i1) − α_{s,i} b_s1 / R^∗.
  - c_i1(b_i1) =
    - y_i1 − b_i1 (1 − α_{i,i}) + α_{s,i} b_s1 if ε_i1 ≥ ̄ε (repays, no transfer),
    - y_i1(1 − Φ) − ρ y_i1 (1 − α_{i,i}) + α_{s,i} b_s1 if ε_i1 < ̄ε (defaults or receives a transfer).
- Optimal debt solves:
  - max_{b_i1} U(b_i1) = c_i0(b_i1) + β[∫_{̄ε}^{ε} min c_i1(b_i1) dG(ε) + ∫_{ε}^{̄ε} max c_i1(b_i1) dG(ε)]
  - s.t. c_i0(b_i1) ≥ 0, 0 ≤ b_i1 ≤ b_max, and definitions above.
- First-order conditions with multipliers ν_0 (period 0 consumption) and μ_1 (b_i1 ≥ 0) yield:
  - 0 ∈ μ_1 + (1 − α_{i,i}) ∂D(b_i1) (1 + ν_0) − β(1 − G(̄ε))(1 − α_{i,i}),
  - ν_0 c_i0(b_i1) = 0,
  - μ_1 b_i1 = 0,
  - where ∂D(b) denotes sub-differential of D(b).

### Interior solution and marginal condition
- For interior solution (c_i0 > 0 and b_i1 > 0) where revenue curve is differentiable:
  - D′(b_i1) = β(1 − G(̄ε)). (Eq. (17))
  - Interpretation: marginal gain D′(b_i1) equals marginal cost β(1 − G(̄ε)) — the probability of repayment without transfer 1 − G(̄ε) discounted at 1/R^∗ = β.
  - Country i focuses on states where it repays without default or bailout; in default repayment is proportional to output and independent of debt level; in bailout the marginal repayment is by country g.

### Expanded optimality condition and trade-offs
- Substituting general expression for D′(b_i1) yields:
  - (G(̄ε) − G(ε)) (1 − π) = (b_i1 − ρ ̄y_i1 ε)(1 − π) g(ε) dε/db + (b_i1 − ρ ̄y_i1 ̄ε) π g(̄ε) d ̄ε/db. (Eq. (18))
- Interpretation of Eq. (18):
  - Left-hand side: likelihood of a bailout — probability that an extra unit of debt borrowed today is not repaid by i while avoiding default; a direct benefit to i.
  - Right-hand side: cost via increase in contractual yield R_i, with two components:
    - First term: cost from change in ε — increased debt raises ε, making outright default more likely; lenders expect recovery ρ y_i1 ε with probability g(ε)(1 − π), increasing yields.
    - Second term: cost from change in ̄ε — increased debt raises ̄ε, making default more likely when bailouts may not occur; lenders face loss with probability g(̄ε) π.
  - Trade-off: increased debt riskiness (higher yields) versus increased likelihood of bailout (non-repayment).

### No-bailout vs bailout effects and risk shifting
- Under no-bailout clause (π = 1):
  - Left-hand side of (18) is zero.
  - Only interior solution is ̄ε ≤ ε_min so g(̄ε) = g(ε) = 0: country i has no incentive to issue risky debt.
- Once π > 0:
  - Country i may issue risky debt (̄ε > ε_min) to maximize bailout chance in period 1.
  - Ex-post bailouts partially shield borrowers, inducing moral hazard and excessive borrowing — termed the Northern view of the crisis.
- Lower collateral cost of default for g (lower κ) increases ε, reducing probability i receives a transfer (LHS of (18)) and thus disciplining i; orderly restructuring proposals can be interpreted as lowering κ and reducing risk-shifting.

### Characterization of optimal debt by funding needs — Proposition 4
- Define funding needs in period 0:
  - x_i0 ≡ (b_i0 (1 − α_{i,i}) + α_{s,i} b_s1 / R^∗ − y_i0 − τ_0 − b_s,i0) / (1 − α_{i,i}).
- Under regularity conditions (Section B.4), optimal debt as function of x_i0:
  - If x_i0 > D(b_max): country i insolvent in period 0 and must default; no debt level ensures solvency.
  - If D(b_max) ≥ x_i0 > D(b_opt): country i issues b ∈ [b_max, b_opt) such that D(b) = x_i0 and there is no consumption in period 0; no risk shifting — issuance constrained by funding needs.
  - If D(b_opt) ≥ x_i0 > β b: country i chooses b_opt. In that range possibility of bailout leads to risk shifting since D(b_opt) > x_i0; default probability higher than necessary.
  - If x_i0 < β b: country i can issue either safe amount x_i0 / β < b or risky amount b_opt. If prefers risky debt, risk shifting is maximal. This occurs iff:
    - U(b_opt) − U(x_i0 / β) = (1 − α_{i,i}) β(1 − π) (G(̄ε) − G(ε)) [b_opt − ρ ̄y_i1 E[ε | ε ≤ ε ≤ ̄ε]] − β Φ G(̄ε) ̄y_i1 E[ε | ε < ̄ε] > 0. (Eq. (19))
- Remarks:
  - First term of (19): expected net gain from bailout.
  - Second term: expected discounted cost of default for i (borne when ε < ̄ε since bailout does not affect i’s utility).
  - No risk shifting when π = 1 or when α_{i,i} ≈ 1. Risk shifting more likely when b_opt / ̄y_i1 is high and Φ is low.

### Making i’s debt safe or “Gambling for Resurrection” (Section 5.3) — comparative statics and Proposition 5
- When bailouts are very likely (π ≈ 0) and under regularity conditions, b_opt > ̄b: i chooses high risky debt and risk shifting is maximal.
- As π increases (bailouts less certain), optimal risky debt decreases until reaching ̄b.
- There exists critical π_c such that for π > π_c the optimal debt falls discontinuously from ̄b to b ≤ b, and debt becomes safe. Thus π > π_c eliminates risk shifting even without π = 1.
- If g can choose commitment π in period 0:
  - Higher π reduces risk shifting; for π > π_c risk shifting eliminated.
  - But higher π reduces resources available to i in t = 1 and can make default in t = 0 more likely by lowering the Laffer curve maximum.
  - g may prefer π < π_c — allow possibility of bailout — if this avoids certain default in period 0: g “gambles for resurrection.”
- g’s utility (bondless limit) as function of b(π) and π:
  - U_g(b(π), π) = c_g0 + β E[c_g1] = y_g0 − b_g0 + b_i,g0 + b_s,g0 + β y_g1 + Ψ(b(π); π).
  - Ψ(b, π) defined and interpretable as net utility gain to g from i’s sovereign default decision and presence/absence of bailouts; Ψ(b; π) = 0 if i’s debt is safe.
- Optimal π satisfies dΨ(b(π); π)/dπ = ∂Ψ/∂π + (∂Ψ/∂b) db/dπ = 0.
  - Appendix shows g always prefers choose π ≥ π_c (rules out risk shifting) when i remains solvent because when π ≥ π_c, db/dπ = 0 and ∂Ψ/∂π controls sign; with Ψ = 0 and debt safe, g is indifferent; for π < π_c possible defaults with transfer lower g’s utility.
- If i could be forced into insolvency by too high π, denote D_max(π) the maximum of Laffer curve under π with dD_max(π)/dπ ≤ 0.
  - If D_max(π_c) < x_i0, i cannot honor debts and would be forced to default in period 0 if g rules out risk shifting.
  - Suppose in default in period 0 i cannot borrow so b_i1 = 0.
  - g will choose either π s.t. D_max(π) = x_i0 (max commitment consistent with avoiding default in current period) or π > π_c and let i default in initial period. g prefers former if:
    - κ y_g0 + α_{i,g0} (b_i0 − ρ y_i0) + Ψ(b_max, π) ≥ 0. (Eq. (20))
  - Eq. (20) states ex-ante g may allow ex-post bailouts (π < 1) to avoid immediate default; g gambles for resurrection since a possible future bailout can be preferable to certain present default.
- Proposition 5 (Insulation and Gambling for Resurrection):
  - If x_i0 ≤ D_max(π_c): g optimally adopts π ≥ π_c, ruling out risk-shifting and making i’s debt safe if x_i0 < b/β.
  - If x_i0 > D_max(π_c) and Eq. (20) holds: g prefers to gamble for resurrection and chooses π such that D_max(π) = x_i0, providing just enough resources in expectation to cover i’s funding needs; risk shifting is eliminated ex-ante but i’s debt remains risky and may receive a bailout in t = 1.
- Policy interpretation:
  - g more likely to adopt lenient ex-ante bailout stance (low π) when i has high initial debt or low output.
  - Eliminating risk shifting does not require strict no-bailout policy; sufficient to choose π > π_c.
  - Historical interpretation: early eurozone leniency may reflect optimal gambles to avoid immediate sovereign defaults and restructurings.

### Link to extensions and default vs exit
- The analysis motivates extension where decision to default and/or exit the monetary union are separate; costs and collateral effects differ for default (Φ^d, κ^d) and exit (Φ^e, κ^e), and exit can provide benefit ∆ ̄y_i1.
- Joint decisions and transfers can alter timing and size of bailouts; these extensions are developed in subsequent sections.

*Source: wpiea2023177-print-pdf — 5.2    Optimal Debt Issuance*

### 2. countryiexits the currency union if an only if:

### 2. countryiexits the currency union if an only if:
ε
i
1
≤ ̄ε
e
≡
∆
Φ
e
(22)

### Decision thresholds and state-space partition
- Default and exit decisions are additive and mutually independent.
- Cut-offs:
  - ̄ε
d
: cutoff for default without bailout.
  - ̄ε
e
: cutoff for exit without bailout.
  - ε
d
and ε
e
: cutoffs for default and exit respectively in the presence of transfers.
- State space (illustrated in Fig. 4) is partitioned by debt-to-potential-output b
i
1
/ ̄y
i
1
 (horizontal axis) and output gap ε
i
1
 (vertical axis) into regions:
  - High output realizations and low initial debt → more likely to repay and remain in currency union.
  - For a given output realization:
    - Higher debt levels → more likely to default; do not affect exit decision.
    - Lower ε
i
1
 → more likely to default and exit.
- Exit cut-offs ε
e
and ̄ε
e
do not depend on the country’s debt level; exit decision and receipt of τ
e
1
 depend only on ε
i
1
.

### Optimal ex-post transfers (Proposition 7)
- Total transfer: τ
1
= τ
d
1
+ τ
e
1
.
- Country g implements minimal transfers to avoid default and/or exit according to ε
i
1
:
  - When ε
i
1
≥ ̄ε
d
: country i does not default and τ
d
1
= 0.
  - When ε
d
≥ ε
i
1
< ̄ε
d
, where ε
d
=
α
i,u
b
i
1
/ ̄y
i
1
− κ
d
y
g
1
/ ̄y
i
1
Φ
d
+ ρα
i,u
< ̄ε
d
: country i does not default, and g makes a minimal transfer
    τ
d
1
≡ (b
i
1
− ρ y
i
1
)(1−α
i,i
1
) − Φ
d
y
i
1
to avoid default.
  - When ε
i
1
< ε
d
: country i defaults and g does not make a transfer to avoid default: τ
d
1
= 0.
  - When ε
i
1
> ̄ε
e
: country i does not exit and g sets τ
e
1
= 0.
  - When ε
e
≤ ε
i
1
< ̄ε
e
, where ε
e
=
∆ − κ
e
y
g
1
/ ̄y
i
1
Φ
e
< ̄ε
e
: country i does not exit and g makes transfer
    τ
e
1
≡ ∆ ̄y
i
1
− Φ
e
y
i
1
to avoid exit.
  - When ε
i
1
< ε
e
: country i exits and g sets τ
e
1
= 0.
- Intuition:
  - ε
i
1
≥ max( ̄ε
d
, ̄ε
e
): repay and stay without transfers → τ
1
= 0.
  - ε
i
1
< min(ε
d
, ε
e
): efficient to let default and exit → τ
1
= 0.
  - Mixed cases: either default but not exit, or exit but not default, with τ
1
= 0 accordingly.
  - When ε
d
≤ ε
i
1
< ̄ε
d
: positive joint surplus from not defaulting → minimal transfer τ
d
1
provided.
  - When ε
e
≤ ε
i
1
< ̄ε
e
: positive joint surplus from not exiting → minimal transfer τ
e
1
provided.
- Fig. 4: nine regions determined by ̄ε
d
, ε
d
, ̄ε
e
, ε
e
; blue region denotes bailout avoiding both default and exit.

### Empirical counterparts and calibration
- Four countries (Cyprus, Ireland, Portugal, Spain) obtained transfers interpreted as τ
d
1
 (minimal to avoid default).
- Infinite-horizon adjusted expression for minimal transfer to avoid default:
  τ
d
1
/(1−β)
y
i
0
=
b
i
1
y
i
0
h(1−α
i,i
1
) −
y
i
1
y
i
0
[ Φ
d
1−β
] (23)
  - Left-hand side τ
d
1
/(1−β)
y
i
0
: net present value of transfer relative to initial output.
  - Increases with:
    - b
i
1
/y
i
0
    - (initial debt-to-GDP)
    - (1−α
i,i
1
) (share of government debt held abroad)
    - h (haircut)
  - Decreases with Φ
d
/(1−β) applied to y
i
1
/y
i
0
.
- Calibration details and values:
  - Haircut h = 0.5 (from Zettelmeyer et al. (2013)).
  - Φ
d
/(1−β) ≈ 0.09 (chosen to minimize squared differences between observed and model-implied bailouts for the four crisis countries that avoided default).
  - With β = 0.95, this implies a flow default cost of approximately 1.5% over seven years.
- Model performance:
  - Predicts small transfers for Ireland and Spain, larger (but still small) transfer for Cyprus.
  - Over-predicts Portugal’s transfer: model 16% vs realized 3.5%.
  - Possible reason: Portugal’s larger debt-to-GDP ratio (75%) relative to Cyprus, Ireland, Spain (between 24% and 57%).
- Greece case:
  - Greece defaulted but did not exit and received transfer τ
1
representing 44 percent of 2010 output.
  - Model interpretation: ε
e
< ε
i
1
< min(ε
d
, ̄ε
e
) (region “Default, No exit, τ
1
= τ
e
1
”).
  - Infinite-horizon transfer to avoid exit:
    τ
i
1
/(1−β)
y
i
0
=
y
i
1
y
i
0
[ ∆
1−β
−
Φ
e
1−β
ε
i
1
] (24)
    - This transfer depends only on ε
i
1
and not on initial debt-to-GDP.
  - Maximum predicted transfer (for ε
i
1
= ε
e
):
    τ
i
1
/(1−β)
y
i
0
=
κ
e
1−β
y
g
y
i
0
. (25)
    - Depends on collateral cost κ
e
/(1−β) and relative size y
i
0
/y
g
.
  - 2010 outputs:
    - Greece y
i
0
= e224 bn.
    - Eurozone y
g
= e9,553 bn.
  - A collateral cost κ
e
/(1−β) = 0.43 × 224 / 9553 ≈ 1% would justify the observed bailout size.

### Policy implications and conclusions
- Reconciling narratives:
  - “Northern” view: collateral damage of default reduces credibility of no-bailout commitment and induces excessive borrowing by fiscally fragile countries.
  - “Southern” view: efficiency benefits of transfers and debt monetization that prevent default are captured by creditor country; little “solidarity.”
  - Both views are complementary and necessary to understand crisis dynamics.
- Eurozone reform implications:
  - Introducing orderly restructuring that lowers collateral cost of default should reduce risk shifting and excessive borrowing; welcomed by creditor countries.
  - However, strengthening no-bailout commitment or policies increasing probability of future default may precipitate immediate default due to higher rollover costs.
  - “Kicking the can down the road” may have merit; improving market discipline should be careful and gradual, especially for high-debt countries.
- Fiscal capacity debate:
  - A common fiscal capacity would generate transfers to fiscally fragile countries during downturns.
  - Model shows such transfers are ex-post efficient when shocks threaten repayment and union integrity.
  - These transfers are already substantial in a monetary union with collateral exposure.

*Source: wpiea2023177-print-pdf - 2. countryiexits the currency union if an only if:*

### References

### References

### Key citation themes
- Sovereign distress and euro area crisis analyses, including case studies and policy proposals:
  - Abbas, S. Ali et al., “193The Other Crisis: Sovereign Distress in the Euro Area,” in “Post-crisis Fiscal Policy,” The MIT Press, 07 2014.
  - Azzimonti, Marina and Vincenzo Quadrini, “International Spillovers and Bailouts,” NBER Working Paper 25011, National Bureau of Economic Research December 2021.
  - Brunnermeier et al., “Reconciling Risk Sharing With Market Discipline: A Constructive Approach to Euro Area Reform,” CEPR Policy Insights, January 2018, (91).
  - Corsetti, Giancarlo et al., “Offical sector lending during the euro area crisis,” Review of International Organizations, 2020, (15), 667–705.
  - Gourinchas, Pierre-Olivier, Thomas Philippon, and Dimitri Vayanos, “The Analytics of the Greek Crisis,” NBER Macroeconomics Annual, 2017.
  - Zettelmeyer, Jeromin, Christoph Trebesch, and Mitu Gulati, “The Greek debt restructuring: an autopsy,” Economic Policy, 2013,28(75), 513–563.
- Theoretical foundations on sovereign debt, crises, and monetary unions:
  - Aguiar, Mark et al., “Coordination and Crisis in Monetary Unions,” Quarterly Journal of Economics, 2015,130(4), 1727–1779.
  - Bulow, Jeremy and Kenneth Rogoff, multiple contributions including “A Constant Recontracting Model of Sovereign Debt,” Journal of Political Economy, February 1989,97(1), 155–178, and “Sovereign Debt: Is to Forgive to Forget?,” American Economic Review, 1989,79(1), 43–50.
  - Calvo, Guillermo, “Servicing the Public Debt: The Role of Expectations,” American Economic Review, 1988,78(4), 647–661.
  - Eaton, Jonathan and Mark Gersovitz, “Debt with Potential Repudiation: Theoretical and Empirical Analysis,” The Review of Economic Studies, 1981,48(2), 289–309.
  - Farhi, Emmanuel and Ivan Werning, “Fiscal Unions,” American Economic Review, 2017,12(107), 3788–3834.
  - Tirole, Jean, “Country Solidarity in Sovereign Crises,” American Economic Review, 2015,105(8), 2333–63.
- Empirical and institutional studies on crisis costs, official lending, and bailout mechanisms:
  - Horn, Sebastian, Carmen M Reinhart, and Christoph Trebesch, “Coping with Disasters: Two Centuries of International Official Lending,” Working Paper 27343, National Bureau of Economic Research June 2020.
  - Schumacher, Julian and Beatrice Weder di Mauro, “Greek Debt Sustainability and Official Crisis Lending,” Brookings Papers on Economic Activity, 2015,46(2 (Fall)), 279–305.
  - EFSF/ESM/European Commission/IMF institutional documentation and annual reports referenced throughout (multiple entries).

### Other notable references (selected)
- Acharya, Viral V and Sascha Steffen, “The “greatest” carry trade ever? Understanding eurozone bank risks,” Journal of Financial Economics, 2015,115(2), 215–236.
- Giannone, Domenico et al., “The ECB and the Inter-bank Market,” Economic Journal, November 2012,122(564), 467–486.
- Krishnamurthy, Arvind and Annette Vissing-Jorgensen, “The aggregate demand for treasury debt,” Journal of Political Economy, 2012,120(2), 233–267.
- Rockafellar, Ralph Tyrell, Convex analysis, Princeton university press, 1972.
- Woodford, Michael, “Doing without money: controlling inflation in a post-monetary world,” Review of Economic Dynamics, 1998,1(1), 173–219.

### Appendix A: Construction of the Dataset

### Data sources and general methodology
- IMF data for Cyprus, Greece, Ireland, and Portugal:
  - Source: IMF website (https://www.imf.org/).
  - Reports: actual and projected disbursements, repayments of principal, and interest payments.
  - Note: Spain did not receive IMF assistance.
- EFSF and ESM disbursements and repayment schedules for Cyprus, Greece, Ireland, Portugal:
  - Source: ESM website (https://www.esm.europa.eu/).
  - For interest payments: applied the blended rate for December 2019 to the series of outstanding debt over the lifetime of the lending cycle.
  - Acknowledgement: Data initially shared by Corsetti et al. (2020) and extended via the ESM website.
- EFSM data:
  - Ireland: Irish Treasury website.
  - Portugal: European Commission website (https://ec.europa.eu/info/).
  - Interest payments: calculated by applying the three-month euribor rate at the time of disbursement.
- Bilateral loan data to Ireland:
  - Sources: United Kingdom Treasury, Sweden Ministry of Finance, Denmark Ministry of Finance.
  - URLs listed in source content for HM Treasury, Government of Sweden Ministry of Finance, and Denmark Ministry of Finance.
- Country-level data used in Section 6.2:
  - Nominal GDP (Mneomnic NY.GDP.MKTP.CN) and Real GDP (NY.GDP.MKTP.KN): World Bank.
  - Debt levels:
    - Total debt: ECB series GFS.A.N.XX.W0.S13.S1.C.L.LE.GD.T.Z.XDC.T.F.V.N.T (where XX is two-letter country code).
    - Debt held by the non-euro area: ECB series GFS.A.N.XX.W1.S13.S1.C.L.LE.GD.T.Z.XDC.T.F.V.N.T.
  - Calculation of α (share of debt held domestically): difference between the two series divided by the total debt series.
  - Sample period: 2005-2017, split into 2005-2009 and 2010-2017 as described in the text.
  - All period-specific variables (GDP, etc.) are given as the average within these periods.
  - α is taken as the average over the whole period (time-invariant in the model).
  - Note: Greece does not have data broken down by euro area and non-euro area.

### Appendix tables and key numeric inputs (as presented)
- Table A.1: Starting Date by Programme (selected rows)
  - Cyprus ESM May, 2013
  - Cyprus IMF May, 2013
  - Greece EC May, 2010
  - Greece EFSF March, 2012
  - Greece ESM August, 2015
  - Greece IMF May, 2010
  - Hungary BoP December, 2008
  - Hungary IMF November, 2008
  - Ireland EFSF February, 2011
  - Ireland EFSM January, 2011
  - Ireland IMF January, 2011
  - Latvia BoP February, 2009
  - Latvia IMF December, 2008
  - Portugal EFSF June, 2011
  - Portugal EFSF May, 2011
  - Portugal IMF May, 2011
  - Romania BoP July, 2009
  - Romania IMF May, 2009
  - Spain ESM December, 2012
  - Note: In the case of Greece, both IMF programmes are treated as one lending cycle. Programme 2 officially begins in May 2012.
- Table A.2: IMF Quotas (in thousands of SDR) and Share of Quotas (selected rows)
  - Cyprus: Quota 140, Share of Quota 567%
  - Greece: Quota 8233, Share of Quota 3,374%
  - Hungary: Quota 1,038, Share of Quota 735%
  - Ireland: Quota 838, Share of Quota 2,322%
  - Latvia, Republic of: Quota 127, Share of Quota 775%
  - Portugal: Quota 867, Share of Quota 2,645%
  - Romania: Quota 1,030, Share of Quota 1,026%
  - Note: Share of Quotas defined as Total IMF disbursements divided by total quota as of January 2010.
- Table A.3: Inputs to model calibration, and comparison of empirical estimates and model-implied transfer values (rows)
  - Cyprus:
    - Debt to GDP Ratio (b_i1 / y_i0): 0.57
    - Debt Held by Euro Area (α_ii1): 0.51
    - RGDP Growth (y1 / y0): 1.04
    - Model (τ_i / y_i0): 0.046
    - Empirical (τ_i / y_i0): 0.045
  - Greece:
    - Debt to GDP Ratio (b_i1 / y_i0): 1.09
    - Debt Held by Euro Area (α_ii1): 0.80
    - RGDP Growth (y1 / y0): 0.46
    - Model (τ_i / y_i0): (blank in source)
    - Empirical (τ_i / y_i0): (blank in source)
  - Ireland:
    - Debt to GDP Ratio (b_i1 / y_i0): 0.34
    - Debt Held by Euro Area (α_ii1): 0.38
    - RGDP Growth (y1 / y0): 1.18
    - Model (τ_i / y_i0): 0.000
    - Empirical (τ_i / y_i0): 0.004
    - Note: Model estimate of the transfer for Ireland is positive, yet very close to zero.
  - Portugal:
    - Debt to GDP Ratio (b_i1 / y_i0): 0.75
    - Debt Held by Euro Area (α_ii1): 0.35
    - RGDP Growth (y1 / y0): 0.98
    - Model (τ_i / y_i0): 0.160
    - Empirical (τ_i / y_i0): 0.035
  - Spain:
    - Debt to GDP Ratio (b_i1 / y_i0): 0.43
    - Debt Held by Euro Area (α_ii1): 0.56
    - RGDP Growth (y1 / y0): 1.01
    - Model (τ_i / y_i0): 0.003
    - Empirical (τ_i / y_i0): 0.006

### Programme lending terms (summary of entries shown)
- Greece I (2010)
  - IMF (SBA): Standard Rate of Charge + Quota Penalty (IMF,2016); Initial Maturity 3-5 Years; No Changes.
  - EC (GLF): 3-Month Euribor + 300bp Margin (100bp Additional After 3 Years) + Up-Front 50bp Service Fee; 4-Year WAM b; Current: 3-Month Euribor + 50bp Margin + One-Time 50bp Commission Fee; 30-Year WAM.
- Greece II (2012)
  - IMF (EFF): Standard Rate of Charge + Quota Penalty (IMF,2017); Initial Maturity 4-10 Years; No Changes.
  - EC (EFSF): EFSF Cost of Funding (In Kind) (ESM, 2019) +10bp Guarantee Commission Fee cd + 0.5bp Up-Front Service Fee c + 50bp Annual Service Fee + Commitment Fee (+ Step-Up Margin on Some Loans); 17.5 Year WAM.
  - EFSF Cost of Funding (Pool Funding a, ESM (2019) + Service Fees + Commitment Fees (+ Step-Up Margin on Some Loans, waived annually thus far)); 32.5-Year WAM.
- Greece III (2015)
  - EC (ESM): ESM Cost of Funding (Pool-Funded) + 10bp Margin + 50bp Up-Front Service Fee + 0.5bp Annual Service Fee + Commitment Fee; 32.5-Year WAM; No Changes.
- Cyprus (2013)
  - IMF (EFF): Standard Rate of Charge + Quota Penalty; Initial Maturity 4-10 Years; Disbursed < e 1 bn; No Changes.
  - EC (ESM): ESM Cost of Funding (Pool-Funded) + 10bp Margin + One-Time 50bp Commission Fee + Commitment Fee (Reuters, 2013); Initial Maturity 15 Years (EFSF, 2010); Disbursed e 6.3 bn; No Changes.
- Ireland (2010)
  - IMF (EFF): Standard Rate of Charge + Quota Penalty; Initial Maturity 4-10 Years; Disbursed e 22.5 bn; No Changes.
  - EC (EFSF): Fixed-Rate Back-to-Back (EFSF, 2012a); 15-Year WAM; Disbursed e 17.7 bn; Current: Diversified Funding Strategy + Service Fee (ESM, 2019); 22-Year WAM (EFSF,2013b).
  - EC (EFSM): EU Cost of Borrowing + 292.5bp Margin (Fixed-Rate Bullet) (EU, 2011e); Initial Maturity 7.5 Years; Disbursed e 22.5 bn; Current: EU Cost of Funding (Pool-Funded)(EU, 2011c); 19.5-Year WAM (EU,2013).
- Portugal (2010)
  - IMF (EFF): Standard Rate of Charge + Quota Penalty; Initial Maturity 4-10 Years; Disbursed < e 26 bn; No Changes.
  - EC (EFSF): EFSF Cost of Funding (Fixed-Rate); 15-Year WAM (EFSF, 2012b); Disbursed e 26 bn; Current: No Changes; 22-Year WAM (EFSF,2013a).
  - EC (EFSM): EU Cost of Borrowing + 215bp Margin (EU,2011b); Initial Maturity 7.5-Year WAM; Disbursed e 24.3 bn; Current: EU Cost of Borrowing (EU, 2011d); 19.5-Year WAM (EU, 2011a).
- Spain (2012)
  - EC (ESM): ESM Cost of Funding (In-Kind) + 10bp Guarantee Commission Fee cd + 0.5bp Up-Front Service Fee c + 50bp Annual Service Fee (European Commission,2012a); 12.5-Year WAM; Disbursed e (amount not listed in excerpt).

*Source: References and Appendix A of the provided PDF content.*

### 41.3 bn

### wpiea2023177-print-pdf - 41.3 bn

### EFSF / ESM funding schemes, WAM and fees
- The EFSF originally used a “back-to-back” lending scheme; in early 2012 it formally switched to a “pool funding” scheme under the Diversified Funding Strategy. The ESM always used a pooled funding scheme.
- WAM stands for “Weighted Average Maturity,” calculated by summing the product of the duration and total amount of each repayment.
- Fee structure notes:
  - One-time fees (e.g., service fee by the GLF) are assessed only when loans are disbursed.
  - From the EFSF and the ESM: annual fees such as the 10bp guarantee commission fee or the 0.5bp service fee, and up-front fees such as the 50bp service fee.
  - The commitment fee is assessed based on changes in borrowing strategies by the relevant institutions.
- The guarantee commitment fee was cancelled in November 2012.

### Budget constraints and market clearing (model setup)
- Government of country j issues one-period bonds with face value b_j1 in period t = 0 and raises lump-sum taxes T_jt.
- Representative household in country i (no default at t = 0) faces period-0 budget:
  - c_i0 + b_i,i1/R_i + b_s,i1/R* = y_i0 − T_i0 + b_i,i0 + b_s,i0 . (B.1)
- Period-1 household consumption when i repays (r) or defaults (d):
  - If repay (r): c_i1 = y_i1 − T_i1(r) + b_i,i1 + b_s,i1 .
  - If default (d): c_i1 = y_i1(1 − Φ) − T_i1(d) + ρ y_i1 b_i,i1 / b_i1 + b_s,i1 . (B.2)
  - In default: direct cost Φ y_i1 and recovery per unit ρ y_i1 / b_i1.
- Analogous constraints for g’s household:
  - Period-0: c_g0 + b_i,g1/R_i + b_s,g1/R* = y_g0 − T_g0 + b_i,g0 + b_s,g0 . (B.3)
  - Period-1 repay/default consumption specified in (B.4); in default g suffers output loss κ y_g1.
- Governments’ budget constraints:
  - i, t=0: T_i0 + b_i1/R_i + τ_0 = b_i0 . (B.5)
  - i, t=1: T_i1(r) + τ_1 = b_i1 if repay; T_i1(d) = ρ y_i1 if default. (B.6)
  - g, t=0: T_g0 + b_g1/R* = b_g0 + τ_0 . (B.7)
  - g, t=1: T_g1(r) = b_g1 + τ_1 if repay; T_g1(d) = b_g1 if default. (B.8)
- Market clearing:
  - Σ_j b_s,j1 = b_s1 ; Σ_j b_i,j1 = b_i1 . (B.9)

### Equilibrium portfolio shares and yields (Proof of Proposition 1)
- Expected payment per unit of i’s sovereign debt for j’s household: P_j ≤ 1; when no discrimination P_j ≡ P.
- Optimal demand conditions (B.10):
  - 1/R_i − β P = ω_j λ_i,j b_i,j1
  - 1/R* − β = ω_j λ_s b_s,j1
- Aggregate share definitions (B.11):
  - α_i,j ≡ b_i,j1 / b_i1 = ω_j λ_i,j / ̄λ_i
  - α_s,j ≡ b_s,j1 / b_s1 = ω_j
  - ̄λ_i ≡ Σ_k ω_k λ_i,k is weighted average liquidity of i-debt.
- Equilibrium yields (B.12):
  - R* = [β + λ_s / b_s1]^{-1}
  - R_i = [β P + ̄λ_i / b_i1]^{-1}
- Intuition:
  - Portfolio shares proportional to relative liquidity services ω_j λ_i,j / ̄λ_i.
  - Yield on safe debt can be lower than 1/β due to liquidity premium λ_s / b_s1; similarly for i’s debt with ̄λ_i / b_i1 but increasing with default risk (P falls).

### Laffer curve: full characterization (B.3)
- Laffer curve D(b) expression (preserving notation):
  - D(b) = β b (1 − π_d(b)) + β ρ ̄y_i1 [ π ∫_{ε(b)}^{ ̄ε(b)} ε dG(ε) + ∫_{ε_min}^{ε(b)} ε dG(ε) ] + ̄λ_i
- Cut-offs:
  - ̄ε(b) = (1 − α_i,i) b / ̄y_i1 / [ Φ + ρ(1 − α_i,i) ]
  - ε(b) = α_i,u b / ̄y_i1 − κ y_g1 / ̄y_i1 / [ Φ + ρ α_i,u ]
- Probability of default:
  - π_d(b) = G(ε(b)) + π ( G(̄ε(b)) − G(ε(b)) )
- Cases and properties (selected highlights):
  - If b ≤ b ≡ y_i^{min} [ Φ/(1 − α_i,i) + ρ ], then ̄ε ≤ ε_min and debt is riskless: D(b) = β b + ̄λ_i.
  - Discontinuities at b = b and b = ̄b (and at ˆb, ̃b depending on parameters) in D′(b); analytical expressions for jumps are provided (e.g., D′(b+) − D′(b−) = −β πε_min g(ε_min) Φ / [ Φ + ρ(1 − α_i,i) ] ≤ 0 at b = b).
  - Under Assumptions 1–5 (see text), the Laffer curve is upward sloping initially, discontinuous at b, has not reached its maximum at ̄b, is continuous and concave with peak at b_max with ̄b ≤ b_max < ˆb, and exhibits two downward discontinuities of D′(b) on [0, b_max].
- Assumptions (summarized):
  - Assumption 1: πε_min g(ε_min) < 1 (comment: cannot be satisfied with power law and π = 1).
  - Assumption 2: ε g′(ε) / g(ε) > −2 (sufficient for D′′(b) < 0; uniform distribution satisfies).
  - Assumption 3: 1/π > G(̄ε(̄b)) + Φ ̄ε(̄b) g(̄ε(̄b)) / [ Φ + ρ(1 − α_i,i) ] (ensures D′(̄b−) > 0).
  - Assumption 4: Parameters such that D′′(b) < 0 for b < ˆb.
  - Assumption 5: D′(ˆb+) = β(1 − π)[ 1 − G(ε) − g(ε) ε /( Φ ε + κ y_g1 / ̄y_i1 (Φ + ρ α_i,u) ) ] < 0 (ensures peak occurs before ˆb).
- Intuition:
  - Discontinuities arise when marginal increases in b make default possible or unavoidable.
  - Under plausible assumptions (e.g., uniform distribution), the Laffer curve peak b_max < ˆb and the country will not choose debt on the “wrong side” (b > b_max).

### Optimal debt issuance (B.4)
- First-order condition for i’s rollover problem (interior solution, ignoring some discontinuities):
  - D′(b_i1) = β (1 − G(̄ε)) . (B.13)
- Regions:
  - 0 ≤ b_i1 < b: debt is safe, D′(b) = β and G(̄ε) = 0; i is indifferent over debt issuance as long as c_i0 ≥ 0.
  - b < b_i1 < ̄b: outcomes depend on π:
    - π = 0: g always bails out i, debt safe, no solution in this interval (i would issue more debt).
    - π = 1: i defaults when b > b, no solution in this interval (i would issue less debt).
    - 0 < π < 1: an interior solution may exist but second-order conditions may fail; monotone g/G helps ensure uniqueness (uniform distribution satisfies).
  - ̄b ≤ b < ˆb: under assumptions, consider subinterval (̄b, b_max) where b_max maximizes period-1 revenues; solutions depend on π and may yield unique b_opt decreasing in π for π < π_c.
- Critical bailout probability π_c where interior solution disappears:
  - π_c = G(̄ε) / [ G(̄ε) + Φ g(̄ε) ̄ε / ( Φ + ρ(1 − α_i,i) ) ]
  - If no recovery (ρ = 0): π_c = 1 / [ 1 + g(̄ε) ̄ε / G(̄ε) ] .
- Graphical summary (Figure B.1 described): D′(b) (blue), β(1 − G(̄ε(b))) (black) with discontinuities at b and ̄b; optimal debt candidates illustrated.

### Exit and default thresholds; proof snippets (B.5)
- Scaled foreign-held debt ˆb = (1 − α_i,i) b_i1 / ̄y_i1; ˆρ = ρ (1 − α_i,i).
- i prefers ND/NE (no default/no exit) to D/NE whenever:
  - − Φ d ε_i1 + ˆb − ˆρ ε_i1 ≤ 0 ⇐⇒ ε_i1 ≥ ̄ε_d = ˆb / (Φ_d + ˆρ) .
- Similar cut-offs define decisions to stay in currency union: i stays when ε_i1 ≥ ̄ε_e (as defined in proposition).
- Minimal transfers to avoid default or exit:
  - τ_d1 = [ (b_i1 − ρ y_i1) (1 − α_i,i) − Φ_d y_i1 ] / y_i1
  - τ_e1 = [ ∆ b_i1 (1 − α_i,i) − Φ_e y_i1 ] / y_i1
- g’s utility with combinations (ND/NE, D/NE, ND/E, D/E) given; comparisons yield regions where transfers are optimal:
  - If ε_i1 ≥ ̄ε_d: τ_1 = 0.
  - If ̄ε_d > ε_i1 ≥ ̄ε_e: g may make τ_d1 if U_g(ND,NE,τ_d1) > U_g(D,NE,0), equivalent to:
    - Φ_d y_i1 + κ_d y_g1 ≥ (b_i1 − ρ y_i1) α_i,u → ε_i1 ≥ ε_d = [ α_i,u b_i1 / ̄y_i1 − κ_d y_g1 / ̄y_i1 ] / [ Φ_d + ρ α_i,u ] (with ε_d < ̄ε_d).
  - If ε_i1 < ̄ε_e: combinations of τ_e1 or τ_d1 + τ_e1 considered; thresholds ε_e and ε_d govern whether g avoids exit, default, or both.

### Extensions: debt re-nationalization, concentration limits, conditionality (C.1)
- Changes in collateral or liquidity rules (e.g., ECB waivers) alter λ_i,i and λ_i,g, affecting portfolio shares (Proposition 1) and bailout thresholds (Proposition 2).
- Key comparative results (Corollary 1) for a given b_i1:
  - Debt re-nationalization (higher λ_i,i):
    - (a) increases α_i,i, reduces α_i,g and α_i,u;
    - (b) lowers ex-post default threshold ε → reduces probability of default;
    - (c) lowers ex-post bailout threshold ̄ε → reduces probability of bailout;
    - (d) reduces size of bailout τ_1.
  - Concentration limit / higher λ_i,g (or mandated higher holdings by g):
    - (a) increases α_i,g, decreases α_i,u and α_i,i;
    - (b) lowers ex-post default threshold ε → reduces probability of default;
    - (c) increases ex-post bailout threshold ̄ε → increases probability of bailout;
    - (d) increases size of bailout τ_1.
- Trade-off: waivers that increase λ_i,g relative to λ_i,i may simultaneously reduce default probability but increase bailout probability/size and may reduce reform incentives unless conditionality binds.

### Extensions: reforms, debt overhang and optimal reform effort (C.1 continued, Corollary 2)
- Simplified setup: ρ = 0, i can choose reform effort e_1 raising average output ̄y_i1 = f(e_1), cost ψ(e_1) convex.
- i solves (C.1):
  - max_{e_1} f(e_1) [ 1 − Φ ∫_{ε_min}^{̄ε} ε dG(ε) + Φ ̄ε (1 − G(̄ε)) ] − ψ(e_1)
- First-order condition (C.2):
  - f′(e_1) [ J(̄ε) ] = ψ′(e_1) where J(̄ε) ≡ [ 1 − Φ ∫_{ε_min}^{̄ε} ε dG(ε) + Φ ̄ε (1 − G(̄ε)) ] .
- Results (Corollary 2):
  - The output cost of default Φ creates a debt overhang, reducing reform effort below first-best when ε_min < ̄ε: e_1 < e_1^*.
  - Optimal ex-post bailouts do not affect optimal reform effort (Southern view): bailouts leave reform effort inefficiently low because benefits get diluted.
  - Reform effort increases with debt re-nationalization (higher λ_i,i) which lowers ̄ε; concentration limits or policies that reduce home bias lower reform effort.
- Mechanism: J′(̄ε) = − Φ ̄ε g(̄ε) ≤ 0; higher ̄ε (higher likelihood of default/bailout) lowers marginal return to reform and thus e_1.

### Extensions: bargaining over surplus (C.2)
- Introduce bargaining weight γ for i (0 < γ < 1); creditor weight = 1 − γ (baseline γ = 0).
- Transfer to i becomes (C.3):
  - τ_1(γ) = b_i1 (1 − α_i,i) − y_i1 / [ Φ + ρ (1 − α_i,i) ] + γ [ Φ y_i1 + κ y_g1 − α_i,u ( b_i1 − ρ y_i1 ) ] .
- Effects:
  - Thresholds ε and ̄ε unchanged by γ (surplus zero at ε).
  - Transfer increases with γ; i captures share γ of surplus from avoiding default.
  - Laffer curve unchanged (probability of default unaffected); first-order condition for debt gains additional γ-dependent terms—net effect on b_i1 ambiguous:
    - Additional marginal gain to i from increased probability of transfers (raises risk shifting).
    - Additional marginal cost because higher debt reduces total surplus from not defaulting on rest of world, part of which i captures.
- Conclusion: bargaining redistributes bailout surplus but leaves thresholds unchanged; ambiguous effect on debt issuance.

### Extensions: debt monetization and the overburdened ECB (C.3)
- Consider inflation-based monetization (ECB chooses inflation rate z ∈ [0, ̄z]) that reduces real debt value; distortion cost δ z y_h1 for h = i, g. Assume Φ, κ > δ z in proportion to output.
- Two polar cases analyzed: transfers always possible (π = 0) and transfers excluded (π = 1).
- Case with transfers (π = 0):
  - ECB and g’s objectives aligned (if ECB maximizes EMU welfare).
  - ECB chooses z = 0 or z = ̄z based on marginal benefit vs distortion cost.
  - No-inflation cutoff for ECB when no default:
    - ε_i1 > [ b_i1 α_i,u + b_g1 α_g,u ] / [ δ y_i1 ] − y_g1 / y_i1 ≡ ε . (C.4)
  - With monetization, transfer to keep i indifferent (C.5):
    - τ_1 = b_i1 (1 − α_i,i) (1 − z) − y_i1 [ Φ − δ z ] + z b_g1 α_g,i .
  - Monetization reduces likelihood of default: ε′ (defined in C.6) decreases with z (∂ε′/∂z < 0).
  - Entire benefit of monetization (net of distortion costs) accrues to g: z [ b_i1 α_i,u + b_g1 α_g,u − δ ] (y_i1 + y_g1) .
- Case transfers excluded (π = 1): overburdened ECB
  - ECB may use inflation to avert default when transfers impossible. With b_g1 = 0 for simplicity, minimum inflation rate to avoid default:
    - ̃z = [ b_i1 (1 − α_i,i) − Φ y_i1 ] / [ b_i1 (1 − α_i,i) − δ y_i1 ] . (C.7)
  - Inflation required increases as ε_i1 deteriorates (Φ > δ).
  - There exists threshold ̃ε below which ECB prefers to let country default rather than monetize (due to distortion costs and z̄ constraint).
  - Using inflation instead of transfers is inefficient because inflation imposes distortion costs on union; ECB is “overburdened.”
- Full characterization (C.3.3): seven thresholds ε; ε′; ε′′; ˆε; ̃ε; ε′; ε′′ define regions where combinations of default/no-default, monetization/no-monetization, transfer/no-transfer arise. Rankings and plausible parameter regimes:
  - Exclude strong fiscal dominance: assume ˆε < ε_min so ECB will choose z = 0 in case of default.
  - Two regimes:
    - Monetary dominance: ε < ε_min → ECB never inflates when transfers possible (identical to main model).
    - Weak fiscal dominance: ε′ > ε > ε′ → ECB may choose positive inflation for some realizations; equilibrium path can be:
      1) no default, no transfer, no inflation (ε_i1 > ε′),
      2) no default, transfer, no inflation (ε′ > ε_i1 > ε),
      3) no default, transfer, inflation (ε > ε_i1 > ε′),
      4) default, no inflation, no transfer (ε_i1 < ε′).
- Conclusion: when transfers are restricted (π > 0 or π = 1), the ECB may be forced to monetize to avert defaults, creating inefficiencies and political/legal tensions.

_Italic: Source: wpiea2023177-print-pdf (excerpts provided)._

### appendix for details).

### wpiea2023177-print-pdf - appendix for details)

### Equilibrium outcomes without transfers (monetary dominance with zero inflation)
- Condition: ε < ε′ so that monetary dominance applies with zero inflation in presence of transfers.
- When transfers are excluded, the possible equilibria are:
  - If output realization ini is sufficiently high: ε_i1 >ε′
    - Outcome: there is no default and no inflation.
  - If output realization ini is lower: ε′ > ε_i1 > ̃ε
    - Outcome: it requires a positive inflation rate in order not to default.
  - If output realization ini is very low: ε_i1 < ̃ε
    - Outcome: the default is optimal and there is no more incentive to inflate the debt.

*Source: wpiea2023177-print-pdf - appendix for details).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023177-print-pdf.pdf_