## _wp04137

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---

### Introduction: motivation and main message
- International financial crises of the 1990s (Mexico 1994; Indonesia, Korea, Malaysia, Thailand, and Russia 1997–98) exposed vulnerability from rolling over large amounts of short-term external debt and difficulties in crisis resolution because debt was held by many uncoordinated creditors.
- Aim: assess proposals for reforming the international financial architecture in a general-equilibrium model where the structure of external debt is endogenous and arises as a solution to a commitment problem.
- Core trade-off:
  - A "dangerous" external liability structure can enhance debtor incentives to implement creditor-friendly policies.
  - Dangerous liabilities increase vulnerability to costly output-reducing rollover crises.
- Main policy implication:
  - Focus on underlying contractual incompleteness (inability to make sovereign debt contracts contingent on debtor policies) rather than solely on coordination failures between creditors.
  - Some institutional reforms (for example, a debt restructuring mechanism that facilitates orderly workouts for countries with good policies) can be Pareto improving.
- Cautionary result: some well-intentioned policies (for example, taxing dangerous forms of debt) may increase equilibrium riskiness of debt because of endogeneity of debt structures.

### Model overview and primitives
- Time structure: three periods t = 0, 1, 2.
- Many countries indexed j = 1,...,n; each country populated by a continuum of mass 1 of atomistic individuals; representative resident.
- Utility (representative resident): 0, 1, 2 (()), jjj ttt t UEc eγ = =− ∑ where j t c is period-t consumption and ( ) j eγ is the cost of domestic effort.
- Public investment:
  - Indivisible public investment of size κ in period 0 can raise expected period-2 output by y∆ if successful.
  - Without investment, period-2 output = j y.
  - If investment succeeds, period-2 output = j y + ∆y; if it fails, period-2 output = j y.
- Financing:
  - Investment financed domestically or by selling sovereign debt to foreign individuals.
  - Capital-scarce countries: 0 j y κ < must borrow from capital-abundant countries with 0 j y κ >.
  - Enough world wealth: 0 j j y n κ > ∑.
  - International debt market perfectly competitive; expected return on sovereign debt must be zero in equilibrium.
- Disposable wealth defined as: 01. j j j w y y y = + + (sum of output in all periods conditional on no investment).

### Information, effort, liquidation, and success probability
- Period-1 success probability p depends on:
  - effort e ∈ {h, l},
  - exogenous signal s,
  - fraction φ ∈ [0, 1] of investment remaining in period 2 (φ = fraction remaining; 1 − φ liquidated by foreign creditors in period 1).
  - Assessment: p = p(e, s, φ).
- Assumptions on p(e, s, φ):
  - p is increasing in φ.
  - For all s and φ: ( , , )esp φ ∀=> 0 (positivity/monotonicity).
  - High effort enhances probability of success: for all s and φ, ( , , )( , , ).ph spl sφ φ ≥
- Effort costs:
  - High effort cost: () h γ γ = .
  - Low effort cost: () l γ = 0.
  - High effort interpreted as complementary domestic investment, governance, or fiscal discipline costing γ to representative resident.
- Stochastic signal s:
  - pdf conditional on no liquidation and effort e: f_e(·). h f(·) and l f(·) strictly positive on same support [ , 1 ] p.
  - High effort shifts pdf of p to the right; existence of threshold p* such that:
    - for p < p*: f_h(p) < f_l(p)
    - for p > p*: f_h(p) > f_l(p)

### Sovereign debt contracts and liquidation thresholds
- Debt contract: triplet (d1 j, d2 j, p_l), promising repayments d1 j in period 1 and d2 j in period 2.
- Contract may specify liquidation of the project in period 1 if ( , , 1 ) p e s < p_l.
- The threshold p_l is specified ex ante in the debt contract; liquidation reduces φ and thus success probability.

### Key mechanisms and equilibrium features
- Debt "riskiness" (l p) is an instrument to discipline domestic policy effort because threat of liquidation reduces payoff to shirking.
- Endogeneity: debt structure and riskiness chosen endogenously in equilibrium to solve commitment/incentive problems.
- Coordination failures among creditors are modeled as stemming from contractual incompleteness rather than the primary inefficiency source.
- Policies addressing creditor coordination only may be second-best relative to policies/institutions addressing contractual incompleteness.

### Optimal crises and incentive constraints (section 2.3 summary)
- l p interpretable as reduced-form measure of debt riskiness: if l pp≤ debt safe (liquidation zero probability); if l pp> debt risky (positive probability of inefficient liquidation).
- Timing: period 0 contract signed; effort e set between period 0 and period 1; signal s revealed; liquidation when l . j j pp< .
- Country cannot credibly commit to e in period 0; debt contract cannot be contingent on e.
- Define pepfpdp≡∫0 1()( ) e the probability of success conditional on effort.
- Assumption (2): ()( ).pl   yph  yκγ∆<<  ∆−  — investment efficient only conditional on high effort.
- Liquidation is always inefficient: ,pyλ<∆ where λ is liquidation value.
- Incentive-compatibility condition (10): l 1 ()(), p pyd  fpdpγ + ∆−  ∆≥ ∫  where ()f∆⋅ denotes ( )( ) hl ff⋅−⋅.
- Upper bound on long-term debt defined by incentive constraint; classical debt-overhang: maximum incentive-compatible debt strictly below yy+∆.
- Risky debt can relax incentive constraint because d increases with l p over some range; derivative (12) yields positive derivative where l [, ] .ppp ∗ ∈ and maximum at l pp ∗ = .
- Proposition 1: An optimal risky debt contract must induce good policy and satisfy l 11 2 , ().dyd ydp==+.

### World equilibrium, financing capacity, and country classification
- Financing capacity: period-0 output plus maximum funds levyable abroad by issuing incentive-compatible debt.
- Financing capacity expression (13): l (), j wVp+  where l l l 1 ()()   ()() , hh p VpF p  dp   pf pdpλ=+ ∫
- Two competing effects on V(p): increasing debt riskiness reduces financing capacity via reduced expected creditor payoffs; increasing riskiness relaxes the incentive constraint and can increase financing capacity if the latter effect dominates.
- Three financing cases for capital-scarce country j depending on wealth j w:
  - Can finance with safe incentive-compatible debt if (0) j wVκ+≥  i.e., j ww    Vκ≥≡−    (14)
  - Else, can finance with incentive-compatible but risky debt if l max(   ) j p wVpκ+≥  i.e., l l max   (   ). j p wwVpκ≥≡−    (15)
  - If (15) fails, investment cannot be financed.
- Proposition 2:
  - Countries fall in two groups depending on j w relative to threshold w.
  - External debt of countries with j ww≥ , if any, is safe.
  - External debt of countries with j ww< , if any, is risky.
- Qualitative implications:
  - Two-tiered world: rich core and poor periphery; credit flows inside core are safe; flows from core to periphery are fickle and may involve liquidation risk.
  - Poorer countries must issue riskier debt in equilibrium: optimal l p decreases with w in interval [, ] ww.
  - Welfare inequality aggravated: periphery welfare strictly below commitment first-best.

### Implementation with demandable debt (section 2.3 and Proposition 3)
- Risky debt is not renegotiation-proof ex post; creditors and residents would prefer sharing renegotiation surplus pyλ∆−.
- Creditor commitment to liquidate achieved via uncoordinated liquidation rights (creditors choose to accelerate repayment).
- Demandable debt contract specification:
  - Each creditor has option between sequences 12 (, )dd and 112 2 (, )ddδδ+−.
  - Early repayment option: ask higher repayment 11 dδ+ in period 1 in exchange for lower repayment 22 dδ− in period 2.
  - Contract vector 1212 (, ,, )ddδδ.
  - Uncoordinated liquidation rights: unpaid creditor can liquidate investment up to value of his claim in period 1; nonoptional repayment 1 d fully repaid with 1 y; optional 1 δ repaid, if necessary, with liquidation proceeds; if insufficient, full liquidation and λ shared.
- Proposition 3 (implementation condition):
  - If (0)pdλ≤ , then any optimal risky debt contract l 12 (, ,)d d p can be implemented by a demandable debt contract 1212 (, ,, )ddδδ.
- Intuition:
  - Creditors ask for early repayment if 1 δ > 2 p δ, i.e., if success probability falls below threshold 1 2 . p δ δ <  (16)
  - Set ratio 12 / δ δ = l p to match liquidation threshold.
  - Demandable debt can produce self-fulfilling roll-over crises (strategic complementarity similar to Diamond-Dybvig), though multiplicity not paper’s emphasis.

### Orderly debt workouts: contractual and statutory approaches (Section III)
- Two approaches to facilitate orderly workouts:
  - Contractual: renegotiation-friendly contractual features (collective action clauses, collective representation/enforcement).
  - Statutory: bankruptcy regime for sovereigns (e.g., SDRM).
- Contractual approach with collective action clause:
  - Clause: conditional on incipient roll-over crisis ( l pp< ), debtor may ask creditors to delegate representative; negotiated agreement binds all creditors. Creditors' ex ante bargaining power denoted α.
  - With liquidation value set to zero for simplicity, renegotiation surplus = py∆; government promises repayment i 2 dyα=∆ in negotiation.
  - Clause softens punishment and reduces maximum incentive-compatible debt r d (compared with no clause).
  - Financing capacity with clause: l () r wV p+  with l l l 1 0 ()()()() . p r r hh p Vp y p f p d p d p p f p d p α = ∆ + ∫∫
  - r V p increases with α from below l V p at α=0 to above l V p at α=1.
- Proposition 4 (adoption of collective action clause):
  - There exists threshold α such that:
    - if α α ≥ , all countries that issue demandable debt put a collective action clause in it;
    - if α α < , countries issuing demandable debt adopt the clause iff their wealth exceeds threshold r w , with r w w w< ≤ ; countries with wealth between w and r w do not adopt and remain vulnerable.
- Policy-tax paradox:
  - Taxing risky debt at rate τ (pay d τ + to international agency) reduces financing capacity and forces equilibrium debt to be riskier.
  - Proposition 5: Taxing risky debt is Pareto-suboptimal — it forces countries that must issue risky debt to make it even riskier or ration them out of the market.
- Statutory approach (bankruptcy regime):
  - Modeled as non-optional collective enforcement/renegotiation mechanism (equivalent to mandatory collective action clause).
- Proposition 6 (welfare implications of bankruptcy regime):
  - If α α > , bankruptcy regime strictly increases volume of credit flows to periphery and increases their welfare.
  - If α α < , bankruptcy regime strictly decreases volume of credit flows to periphery; strictly increases welfare of countries with wealth in [, ] r w w ; strictly decreases welfare of countries with wealth in [, ] r w .
- Gate-keeping enhancement:
  - Bankruptcy regime that grants protection only to sovereigns with good pre-crisis policies achieves first-best.
  - Proposition 7: Such a gate-keeping bankruptcy regime puts the world economy at the first-best.
  - Gate-keeping makes renegotiation contingent on pre-crisis effort e, removing collateral damage of liquidation after good e.
- Practical considerations:
  - Gate-keeping requires jurisprudence to judge good vs bad policies; optimality does not require perfect accuracy.
  - Risk of excessive forbearance and time-inconsistency: governance must insulate court from short-term political influence.

### Limitations, robustness, and extensions
- Enforcement of liquidation rights can be interpreted broadly (e.g., uncoordinated litigation in foreign courts).
- Liquid reserves are not held in equilibrium by capital-scarce countries: financing reserves would require issuing more foreign debt and increasing liquidation threshold l p.
- Binary (no liquidation or complete liquidation) assumption can be generalized; bang-bang property implies optimality of binary liquidation choices.
- Indivisible investment assumption: allowing y∆ to be increasing and concave in κ complicates analysis; some poor countries may scale down investment instead of issuing risky debt.
- Relaxing timing of e (setting after s realized) still yields that demandable debt increases policy effort ex ante.
- Not allowing new borrowing in period 1 is important; allowing period-1 borrowing introduces dilution issues not addressed here.
- Extensions noted:
  - Financial contagion may create negative externalities leading to too much risky debt; scope for taxes/subsidies.
  - Risky debt can create positive externalities across multiple domestic borrowers (private sector may under-provide short-term debt).
  - Political agency problems (self-interested policymakers) could change welfare conclusions; benevolent governments assumed here.

### Technical results and propositions (selected)
- Proposition 1: Optimal risky debt contract must induce good policy and satisfy l 11 2 , ().dyd ydp==+.
- Proposition 2: Countries with j ww≥ issue safe external debt (if any); countries with j ww< issue risky external debt (if any).
- Proposition 3: If (0)pdλ≤ , any optimal risky debt contract l 12 (, ,)d d p can be implemented by a demandable debt contract 1212 (, ,, )ddδδ.
- Proposition 4: Existence of threshold α governing adoption of collective action clause; adoption patterns depend on α relative to threshold.
- Proposition 5: Taxing risky debt is Pareto-suboptimal — it can force greater equilibrium debt riskiness.
- Proposition 6: Welfare effects of statutory bankruptcy regime depend on α relative to threshold α.
- Proposition 7: Gate-keeping bankruptcy regime that protects only sovereigns with good pre-crisis policies achieves first-best.

*Source: _wp04137 - section 2.3 how such contracts can be implemented with demandable debt. For now, (PDF).*

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

### _wp04137 - References..............................................................................................................

### Introduction: motivation and main message
- The international financial crises of the 1990s (Mexico 1994; Indonesia, Korea, Malaysia, Thailand, and Russia 1997–98) exposed vulnerability from rolling over large amounts of short-term external debt and difficulties in crisis resolution because debt was held by many uncoordinated creditors.
- Aim: assess proposals for reforming the international financial architecture in a general-equilibrium model where the structure of external debt is endogenous and arises as a solution to a commitment problem.
- Core trade-off: a "dangerous" external liability structure can enhance debtor incentives to implement creditor-friendly policies, but it also increases vulnerability to costly output-reducing rollover crises; thus there is tension between incentive benefits and crisis risk.
- Main policy implication emphasized:
  - Focus on underlying contractual incompleteness (inability to make sovereign debt contracts contingent on debtor policies) rather than solely on coordination failures between creditors.
  - Some institutional reforms (e.g., a debt restructuring mechanism that facilitates orderly workouts for countries with good policies) can be Pareto improving.
- Cautionary result: some well-intentioned policies (for example, taxing dangerous forms of debt) may increase equilibrium riskiness of debt because of endogeneity of debt structures.

### Literature connections and contrasts
- Relates to closed-economy government-debt literature and external sovereign debt literature (Sachs 1984; Krugman 1985; Calvo and Guidotti 1990).
- Builds on arguments that short-term debt emergence may reflect commitment problems and that making sovereign debt harder to restructure can have ex ante benefits (Sachs and Cohen 1982; Rodrik and Velasco 2000; Detragiache and Spilimbergo 2002).
- Contrasts with models that emphasize bank-deposit liquidity provision (Diamond-Dybvig) as the driver of short-maturity debt; here, short-term debt provides incentives to borrowers rather than depositor liquidity (Chang and Velasco 1999; Diamond and Rajan 2001; Tirole 2002, 2003).
- Resonates with corporate finance literature on liability structure and creditor coordination (Diamond 1991; Berglöf and von Thadden 1994; Bolton and Scharfstein 1996; Dewatripont and Tirole 1994).

### Model overview
- Time structure: three periods t = 0, 1, 2.
- Population: many countries indexed j = 1,...,n. Each country populated by a continuum of mass 1 of atomistic individuals; representative resident.
- Utility of representative resident (as presented):
  - 0, 1, 2 (()), jjj ttt t UEc eγ = =− ∑
  - where j t c is period-t consumption, and ( ) j eγ is the cost of domestic effort.
- Public investment opportunity:
  - Indivisible public investment of size κ in period 0 that can raise expected period-2 output by y∆ if successful.
  - Without investment, period-2 output is deterministic and denoted by j y.
  - If investment succeeds, period-2 output = j y + ∆y; if it fails, period-2 output = j y.
- Financing:
  - Investment can be financed with domestic resources or by selling sovereign debt to foreign individuals.
  - Capital-scarce countries: 0 j y κ < must borrow from capital-abundant countries with 0 j y κ >.
  - There is enough world wealth: 0 j j y n κ > ∑.
  - International debt market is perfectly competitive; expected return on sovereign debt must be zero in equilibrium.
- Disposable wealth defined as:
  - 01. j j j w y y y = + + (sum of output in all periods conditional on no investment).

### Information, effort, and project liquidation
- Probability of success p in period 1 depends on:
  - policy effort e (high e h or low e l),
  - exogenous signal s,
  - fraction φ ∈ [0, 1] of the investment that remains in place in period 2 (φ = fraction remaining; 1 − φ liquidated by foreign creditors in period 1).
  - The period-1 assessment function: p = p(e, s, φ).
- Assumptions on p(e, s, φ):
  - p is increasing in φ.
  - For all s and φ: ( , , )esp φ ∀=> 0 (text indicates positivity and monotonicity assumptions).
  - High effort enhances probability of success: for all s and φ, ( , , )( , , ).ph spl sφ φ ≥
- Effort costs:
  - High effort cost: () h γ γ = .
  - Low effort cost: () l γ = 0.
  - High effort interpreted as complementary domestic investment, governance, or fiscal discipline costing γ to the representative resident.
- Stochastic signal s:
  - Captures exogenous determinants observable in period 1; probability of success increases with s; signals across countries may be correlated or not.
  - pdf conditional on no liquidation and effort e: f_e(·). h f(·) and l f(·) strictly positive on same support [ , 1 ] p.
  - High effort shifts pdf of p to the right; existence of threshold p* such that:
    - for p < p*: f_h(p) < f_l(p)
    - for p > p*: f_h(p) > f_l(p)
  - (As presented in equation (1) and Figure 1 in the source.)

### Sovereign debt contract and liquidation threshold
- Debt contract promises repayments d1 j in period 1 and d2 j in period 2: summarized as the triplet (d1 j, d2 j, p_l).
- Contract may specify liquidation of the project in period 1 if the probability of success conditional on no liquidation, ( , , 1 ) p e s, falls below threshold p_l.
- The threshold p_l is specified ex ante in the debt contract; liquidation reduces φ and thus the success probability.

### Key mechanisms and equilibrium features
- Debt "riskiness" or "dangerousness" serves as an instrument to discipline domestic policy effort because threat of liquidation reduces the payoff to shirking.
- Endogeneity: the structure and riskiness of external debt are chosen endogenously in equilibrium as responses to commitment problems and incentives.
- Coordination failures among creditors are modeled as a reflection of contractual incompleteness rather than the primary source of inefficiency.
- Consequence: policies that only address creditor coordination (coordination failure symptoms) may be second-best relative to policies or institutions that address contract incompleteness (root cause).

### Policy analysis highlights (from paper structure)
- Section III analyzes welfare effects of different forms of public intervention (examples mentioned in text):
  - Taxing dangerous forms of debt can increase equilibrium debt riskiness.
  - Creating a debt restructuring mechanism that facilitates orderly workouts for countries with good policies can be Pareto improving.
- Overall recommendation: international financial architecture reforms should target the underlying incompleteness of sovereign debt contracts and focus on institutions that allow credible conditionality or orderly restructuring.

*Source: _wp04137 - References..............................................................................................................*

### section 2.3 how such contracts can be implemented with demandable debt. For now,

### _wp04137 - section 2.3 how such contracts can be implemented with demandable debt. For now,

### Model setup and key assumptions
- l p can be interpreted as a reduced-form measure of the riskiness of debt. If l pp≤ debt is safe (liquidation occurs with zero probability); if l pp> debt is risky (positive probability of inefficient liquidation).
- Timing: period 0 debt contract is signed; policy effort e is set between period 0 and period 1 (after contract, before signal s); signal s is then revealed; liquidation occurs where l . j j pp< .
- The country cannot credibly commit to e in period 0 and the debt contract cannot be made contingent on e.
- Define pepfpdp≡∫0 1()( ) e the probability of success conditional on effort.
- Assumption (2): ()( ).pl   yph  yκγ∆<<  ∆−  — investment is efficient only conditional on high effort; “good” policy refers to implementing the high level of effort.
- Liquidation is always inefficient: ,pyλ<∆ where λ is the liquidation value.
- Individuals maximize utility; governments maximize domestic welfare; consider perfect Bayesian equilibria.

### B. Optimal Crises — objective and incentive constraint
- Country problem (3): max()(  ),UcEcceγ=+  + − d
- Budget constraints (periods 0,1,2): equations (4), (5), (6) as stated in source.
- In equilibrium, price foreigners pay equals expected value of payments to foreigners (including liquidation proceeds).
- Country welfare expression (after substitution): l l 0 0 (, )()()() () . p e Upe  wpeyepyfpdpκγλ= +  ∆− −   −   ∆− ∫
- Incentive-compatibility condition (10) (benefit of good policy vs cost), restated:
  - l 1 ()(), p pyd  fpdpγ + ∆−  ∆≥ ∫  where ()f∆⋅ denotes ( )( ) hl ff⋅−⋅.
- Upper bound on long-term debt defined implicitly by the incentive constraint; classical debt-overhang described: maximum incentive-compatible level of debt is strictly below yy+∆.
- Risky debt can relax the incentive constraint because d increases with l p over some range; differentiation (12) yields positive derivative where l [, ] .ppp ∗ ∈ and maximum at l pp ∗ = .
- Key takeaway: Risky debt disciplines domestic policy by making bad policy relatively more costly, but creates risk of unfair punishment (liquidation after good policy because of bad signal).

- Proposition 1 (optimal risky debt contract property):
  - An optimal risky debt contract must induce good policy and satisfy l 11 2 , ().dyd ydp==+.

### C. World Equilibrium — financing capacity and country classification
- Define financing capacity: period 0 output plus maximum funds levyable abroad by issuing incentive-compatible debt.
- Financing capacity expression (13): l (), j wVp+  where l l l 1 ()()   ()() , hh p VpF p  dp   pf pdpλ=+ ∫
- First derivative of V with respect to p given exactly in source.
- Two competing effects:
  - Increasing debt riskiness reduces financing capacity if creditors' expected payoff is reduced by liquidation (first term).
  - Increasing riskiness relaxes the incentive constraint (second term). If second dominates, V increases with l p (see Figure 2 in source).
- Three cases for capital-scarce country j depending on wealth j w:
  - Can finance with safe incentive-compatible debt if (0) j wVκ+≥  i.e., j ww    Vκ≥≡−    (14)
  - If not, can finance with incentive-compatible but risky debt if l max(   ) j p wVpκ+≥  i.e., l l max   (   ). j p wwVpκ≥≡−    (15)
  - If (15) fails, investment cannot be financed.
- Proposition 2:
  - Countries fall in two groups depending on j w relative to threshold w.
  - External debt of countries with j ww≥ , if any, is safe.
  - External debt of countries with j ww< , if any, is risky.
- Additional qualitative results:
  - Two-tiered world: rich core and poor periphery; credit flows inside core are safe; flows from core to periphery are fickle and may involve liquidation risk.
  - Poorer countries must issue riskier debt in equilibrium (optimal l p decreases with w in interval [, ] ww).
  - Welfare inequality aggravated: periphery welfare strictly below commitment first-best.

### D. Implementation — demandable debt and Proposition 3
- Risky debt is not renegotiation-proof ex post; creditors and residents would prefer sharing the renegotiation surplus pyλ∆−.
- Creditor commitment to liquidate can be achieved via uncoordinated liquidation rights (creditors choose to accelerate repayment).
- Demandable debt contract specification:
  - Gives each creditor option between sequences 12 (, )dd and 112 2 (, )ddδδ+−.
  - Early repayment option: ask higher repayment 11 dδ+ in period 1 in exchange for lower repayment 22 dδ− in period 2.
  - Contract vector 1212 (, ,, )ddδδ.
  - Uncoordinated liquidation rights: unpaid creditor can liquidate investment up to value of his claim in period 1; nonoptional repayment 1 d fully repaid with 1 y; optional 1 δ repaid, if necessary, with liquidation proceeds; if insufficient, full liquidation and λ shared.
- Proposition 3 (implementation condition):
  - If (0)pdλ≤ , then any optimal risky debt contract l 12 (, ,)d d p can be implemented by a demandable debt contract 1212 (, ,, )ddδδ.
- Intuition (as in appendix):
  - Creditors ask for early repayment if 1 δ > 2 p δ, i.e., if success probability falls below threshold 1 2 . p δ δ <  (16)
  - Set ratio 12 / δ δ = l p to match liquidation threshold.
  - Demandable debt can produce self-fulfilling roll-over crises (strategic complementarity similar to Diamond-Dybvig), although these multiplicities are not the paper’s emphasis.

### E. Discussion — model limitations and robustness
- Enforcement of liquidation rights: liquidation can be interpreted broadly (e.g., uncoordinated litigation in foreign courts).
- Liquid reserves are not held in equilibrium by capital-scarce countries: financing reserves would require issuing more foreign debt and increasing liquidation threshold l p.
- Assumption of only no liquidation or complete liquidation can be generalized; bang-bang property implies optimality of binary liquidation choices.
- Indivisible investment assumption: allowing y∆ to be increasing and concave in κ complicates analysis; some poor countries may scale down investment instead of issuing risky debt.
- Relaxing timing of e (setting after s realized) still yields that demandable debt increases policy effort ex ante.
- Not allowing new borrowing in period 1 is important; allowing period 1 borrowing introduces dilution issues not addressed here.

### III. Orderly Debt Workouts — contractual and statutory approaches
- Two approaches to facilitate orderly workouts:
  - Contractual: renegotiation-friendly contractual features (collective action clauses, collective representation/enforcement).
  - Statutory: bankruptcy regime for sovereigns (e.g., SDRM).
- Contractual approach — endogenous renegotiability with collective action clause:
  - Clause: conditional on incipient roll-over crisis ( l pp< ), debtor may ask creditors to delegate representative; negotiated agreement binds all creditors. Creditors' ex ante bargaining power denoted α.
  - With liquidation value set to zero for simplicity, renegotiation surplus = py∆; government promises repayment i 2 dyα=∆ in negotiation.
  - Incentive condition with clause becomes (as stated): l l 1 0 (1)(   )()(   ). p p y p f p d p   y d   p f p d p α γ + − ∆ ∆ + ∆ − ∆ ∫∫
  - Clause softens punishment: reduces maximum incentive-compatible debt r d (compared with no clause).
  - Financing capacity with clause: l () r wV p+  with l l l 1 0 ()()()() . p r r hh p Vp y p f p d p d p p f p d p α = ∆ + ∫∫
  - r V p increases with α from below l V p at α=0 to above l V p at α=1.
- Proposition 4 (equilibrium adoption of collective action clause):
  - There exists threshold α such that:
    - if α α ≥ , all countries that issue demandable debt put a collective action clause in it;
    - if α α < , countries issuing demandable debt adopt the clause iff their wealth exceeds threshold r w , with r w w w< ≤ ; countries with wealth between w and r w do not adopt and remain vulnerable.
- Policy-tax paradox:
  - Taxing risky debt at rate τ (pay d τ + to international agency) reduces financing capacity and forces equilibrium debt to be riskier.
  - Proposition 5: Taxing risky debt is Pareto-suboptimal — it forces countries that must issue risky debt to make it even riskier or ration them out of the market.
- Statutory approach — bankruptcy regime for sovereigns:
  - Bankruptcy regime modeled as non-optional collective enforcement/renegotiation mechanism (equivalent to mandatory collective action clause).
- Proposition 6 (welfare effects depend on α):
  - If α α > , bankruptcy regime strictly increases volume of credit flows to periphery and increases their welfare.
  - If α α < , bankruptcy regime strictly decreases volume of credit flows to periphery; strictly increases welfare of countries with wealth in [, ] r w w ; strictly decreases welfare of countries with wealth in [, ] r w .
- Gate-keeping enhancement:
  - A bankruptcy regime that grants protection only to sovereigns with good pre-crisis policies achieves first-best.
  - Proposition 7: Such a gate-keeping bankruptcy regime puts the world economy at the first-best.
  - Gate-keeping addresses contract incompleteness by making renegotiation contingent on pre-crisis effort e, removing collateral damage of liquidation after good e.
- Practical considerations:
  - Gate-keeping requires jurisprudence to judge good vs bad policies; optimality does not require perfect accuracy.
  - Risk of excessive forbearance and time-inconsistency: governance must insulate court from short-term political influence.

### IV. Concluding comments and extensions
- Endogeneity of debt structure implies short-term debt may be optimal ex ante for incentive reasons; optimal public interventions must consider underlying cause of fragility.
- Extensions noted:
  - Financial contagion may create negative externalities leading to too much risky debt; scope for taxes/subsidies.
  - Risky debt can create positive externalities across multiple domestic borrowers (private sector may under-provide short-term debt).
  - Political agency problems (self-interested policymakers) could change welfare conclusions: benevolent governments assumed here.

### Appendix summaries (technical proofs)
- Appendix I — Proof of Proposition 3:
  - Shows conditions under which optimal risky debt contract l 121 (, ,) (,,)dd pyy dp=+ can be implemented by demandable debt 1212 (, ,, )ddδδ.
  - Individual creditor liquidates if higher expected payoff than not; net payoff L defined and depends on fraction A of creditors liquidating.
  - Two equilibrium cases in creditor coordination (complete liquidation or all roll over) described; matching liquidation threshold requires 12 / δ δ = l p and 1 δ λ = .
  - Sufficient condition for existence across optimal l p range: (0).pdλ≤ .
- Appendix II — Proof of Proposition 7:
  - Shows maximum pledgeable output r V is larger than κ for suitable α (even at α=1), implying all countries can finance project with incentive-compatible debt; good policies implemented and court protection yields first-best ex ante welfare.

*Source: _wp04137 - section 2.3 how such contracts can be implemented with demandable debt. For now,*

### REFERENCES

### _wp04137 - REFERENCES

### Reference list

- Berglöf, Erik, and Ernst-Ludwig von Thadden, 1994, “Short-term Versus Long-term Interests: Capital Structure With Multiple Investors,” Quarterly Journal of Economics, Vol. 109, pp. 1055–84.
- Bisin, Alberto, and Adriano Rampini, 2004, “Exclusive Contracts and the Institution of Bankruptcy,” (unpublished; Evanston, IL: Northwestern University).
- Bolton, Patrick, 2003, “Towards a Statutory Approach to Sovereign Debt Restructuring: Lessons from Corporate Bankruptcy Around the World,” Staff Papers, International Monetary Fund, Vol. 50, pp. 41–71.
- ———, and David S. Scharfstein, 1996, “Optimal Debt Structure,” Journal of Political Economy, Vol. 104, pp. 1–25.
- Bolton, Patrick, and Olivier Jeanne, 2004, “Structuring and Restructuring Sovereign Debt: the Role of Seniority,” (unpublished; Washington: International Monetary Fund).
- Buiter, Willem H., and Anne Siebert, 1999, “UDROP: A Contribution to the New International Financial Architecture,” International Finance, Vol. 2, pp. 227–47.
- Calvo, Guillermo, and Pablo Guidotti, 1990, “Indexation and Maturity of Government Bonds: An Exploratory Model,” in Capital Markets and Debt Management, ed. by R. Dornbusch and M. Draghi (Cambridge: Cambridge University Press), pp. 52–82.
- Chang, Roberto, and Andrés Velasco, 1999, “Liquidity Crises in Emerging Markets: Theory and Policy,” in NBER MacroAnnual, ed. by Ben Bernanke and Julio Rotemberg (Cambridge, Massachusetts MIT Press).
- Chui, Michael, Prasanna Gai, and Andrew Haldane, 2002, “Sovereign Liquidity Crises: Analytics and Implications for Public Policy,” Journal of Banking and Finance, Vol. 26, pp. 519–46.
- De Bandt, Olivier, and Philipp Hartmann, 2002, Systemic Risk: A Survey, in Financial Crisis, Contagion and the Lender of Last Resort: A Book of Readings, ed. by C. Goodhart and G.Illing (Oxford and New York: Oxford University Press), pp. 249–98.
- De Gregorio, Jose, Barry Eichengreen, Takatoshi Ito, and Charles Wyplosz, 1999, An Independent and Accountable IMF: Geneva Reports on the World Economy 1 (London: Centre for Economic Policy Research). Available via the web at http://www.cepr.org/pubs/books/P130.asp.
- Detragiache, Enrica, and Antonio Spilimbergo, 2004, “Empirical Models of Short-Term Debt and Crises: Do They Test the Creditor Run Hypothesis?” European Economic Review, Vol. 48, pp. 379–89.
- Dewatripont, Mathias, and Jean Tirole, 1994, “A Theory of Debt and Equity: Diversity of Securities and Manager-Shareholder Congruence,” Quarterly Journal of Economics, Vol. 109, No. 4, pp. 1027–54.
- Diamond, Douglas, 1991, “Debt Maturity Structure and Liquidity Risk,” Quarterly Journal of Economics, Vol. 106, No. 3, pp. 709–37.
- ———, and Raghuram G. Rajan, 2000, “A Theory of Bank Capital,” Journal of Finance, Vol. 55, No. 6, pp. 2431–65.
- ———, 2001, “Banks, Short Term Debt and Financial Crises: Theory, Policy Implications and Applications,” Carnegie-Rochester Conference Series on Public Policy, Vol. 54, pp. 37–71.
- Dooley, Michael, 2000, “Can Output Losses Following International Financial Crises Be Avoided?” NBER Working Paper No. 7531 (Cambridge, Massashusetts: National Bureau of Economic Research).
- Eichengreen, Barry, 1999, Toward a New International Financial Architecture (Washington: Institute For International Economics).
- ———, 2003, “Restructuring Sovereign Debt,” Journal of Economic Perspectives, Vol. 17, No. 4, pp. 75–98.
- ———, and R. Portes, 1995, Crisis? What Crisis? Orderly Workouts for Sovereign Debtors (London: Center for Economic Policy Research).
- Eichengreen, Barry, and Ashoka Mody, 2004, “Do Collective Action Clauses Raise Borrowing Costs?” Economic Journal, Vol. 114, pp. 247–64.
- Gertler, Mark, and Kenneth Rogoff, 1990, “North-South Lending and Endogenous Domestic Capital Market Inefficiencies,” Journal of Monetary Economics, Vol. 26, pp. 245–66.
- Group of Ten (G-10), 1996, Resolving Sovereign Liquidity Crises (Washington).
- Group of Twenty-Two (G-22), 1998, Three Reports On International Financial Architecture Reform (Washington).
- Institute of International Finance (IIF), 2002, Action Plan: Strengthening Emerging Markets Finance (Washington).
- Jeanne, Olivier, 2000, “Debt Maturity and the Global Financial Architecture,” CEPR Discussion Paper No. 2520  (London: Center for Economic Policy Research)
- Kenen, Peter, 2001, The International Financial Architecture, What's New? What's Missing? (Washington: Institute for International Economics).
- Krueger, Anne, 2002, A New Approach to Sovereign Debt Restructuring (Washington: International Monetary Fund).
- Krugman, Paul, 1985, International Debt Strategies in an Uncertain World, in International Debt and the Developing Countries, ed. by G.W. Smith and J.T. Cuddington (Washington: World Bank), pp. 79–100.
- Miller, Marcus, and Lei Zhang, 2000, “Sovereign Liquidity Crises: The Strategic Case For a Payments Standstill,” Economic Journal, Vol. 110, pp. 335–62.
- Rodrik, Dani, and Andrés Velasco, 2000, “Short-Term Capital Flows,” in Proceedings of the 1999 Annual Bank Conference on Development Economics, ed. by B. Pleskovic and J.E. Stiglitz  (Washington: World Bank).
- Rogoff, Kenneth, 1999, “International Institutions for Reducing Global Financial Instability,” Journal of Economic Perspectives, Vol. 13, pp. 21–42.
- ———, and Jeromin Zettelmeyer, 2002, “Bankruptcy Procedures for Sovereigns: A History of Ideas,” 1976–2001, Staff Papers, International Monetary Fund, Vol. 49, No. 3, pp. 470–507.
- Roubini, Nouriel, and Brad Setser, 2004, “The Reform of the Sovereign Debt Restructuring Process: Problems, Proposed Solutions, and the Argentine Episode,” Journal of Restructuring Finance, Vol. 1, No. 1, pp. 1–12.
- Rubinstein, Ariel, 1982, “Perfect Equilibrium in a Bargaining Model,” Econometrica, Vol. 50, pp. 97–109.
- Sachs, Jeffrey, 1984, Theoretical Issues in International Borrowing, Princeton Studies in International Finance No. 54 (Princeton, NJ:  International Finance Section, Princeton University).
- ———, 1995, “Do We Need an International Lender of Last Resort?” International Finance Section, Frank D. Graham Lecture at Princeton University. Available on the Web at http://www.ksg.harvard.edu/cid/ciddirector/publicat.htmlWorking.
- ———, and Daniel Cohen, 1982, “LDC Borrowing With Default Risk,” NBER Working Paper No. 925 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Schwarcz, Steven, 2000, “Sovereign Debt Restructuring: A Bankruptcy Reorganization Approach,” Cornell Law Review, Vol. 85, pp. 101–87.
- Shleifer, Andrei, 2003, “Will the Sovereign Debt Market Survive?” American Economic Review, Vol. 93, No. 2, pp. 85–90.
- Tirole, Jean, 2002, Financial Crises, Liquidity Provision and the International Monetary System (Princeton, New Jersey: Princeton University Press).
- ———, 2003, “Inefficient Foreign Borrowing: A Dual- and Common-Agency Perspective,” American Economic Review, Vol. 93, No. 5, pp. 1678–1702.

*Source: _wp04137 - REFERENCES (PDF).*

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