## _wp06176

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---

### Motivation
- International repayments are harder to enforce than domestic repayments; literature emphasizes punishments to induce repayment.
- Common wisdom: creditors should exclude a defaulting nation from international capital markets forever.
- Historical episodes show lenders' reactions to default varied: some denied fresh credit for long periods, others granted new funds soon after default.
- Lenders discriminated in granting new loans based on perceived future profitability of the borrower’s activities.
- A complete theory of international lending should include:
  - the inability to enforce contracts, requiring punishments for breaking agreements; and
  - differential treatment received by defaulting nations as an optimal response of lenders.
- Model ingredients:
  - different types of borrowers (governments);
  - each type is identified with a specific investment project (good and bad), whose return is private information;
  - lenders can observe the realized return of the project, and can obtain a signal about the type of project if they pay a small auditing cost.
- Main claim: after default, lenders do not necessarily deny fresh credit; it is easier for a government with good projects to obtain new credit than for a government with bad projects.

### Comparison with related literature
- Cole, Dow and English (1995): explain how countries denied credit at a given point will eventually be readmitted to credit markets. This paper differs by explaining why some nations are not denied fresh credit even immediately after default.
- Grossman and Van Huyck (1988): government borrows to finance investments with a state-contingent contract; partial default does not lead to punishment; only full repudiation entails permanent exclusion. Differences with current paper:
  - Grossman and Van Huyck do not model learning by lenders; all repudiations are treated alike.
  - Current paper derives the form of the optimal contract, whereas Grossman and Van Huyck take it as given.
- Atkeson (1991): both Atkeson’s model and the present paper feature uncertainty about projects and risk of default as impediments to international lending contracts. Differences in results: Atkeson focuses on allocations free of risk of repudiation and explains capital outflows under worst realizations of national output; this paper offers a rationale for observed patterns of default, subsequent verification of investment levels, and possible lending resumption.
- Diamond (1989): in Diamond’s model, good projects never default; any default reveals a bad project and leads to permanent exclusion. Current paper differs by allowing for lender learning and differential treatment of defaulters, which can explain observed patterns inconsistent with Diamond (1989).

### Historical evidence on default and lending resumption (1820–1920)
- Period examined: 1820–1920.
- Empirical regularities:
  - Default episodes typically coincided with bad states of the economy (e.g., large drops in export revenue).
  - Examples:
    - Brazil defaulted in 1898 after a decline of 64 percent in coffee prices over the preceding five years.
    - Brazil defaulted in 1914 after a fall of almost 40 percent in coffee prices in two years.
    - Argentina (bankruptcy November 1890; lending resumed March 1891).
    - Peru (defaulted in 1876; fresh credit not obtained until 1889).
    - Bulgaria (near bankruptcy in 1899 due to bad harvests; syndicated loan in 1900).
- Lender responses after default varied:
  - Lending sometimes resumed shortly after default, even under concessionary terms (examples: Argentina 1891; Brazil 1898 and 1914; Mexico 1914; Bulgaria 1900).
  - In other cases, denial of fresh credit persisted for long periods (examples: most Latin American countries in the 1820s; Turkey 1875; Egypt 1876; Peru 1876; Greece 1893).
- Lenders distinguished between borrower uses of funds:
  - New loans more likely when past borrowing financed infrastructure or projects enhancing future growth.
  - Further credit denied when borrowed funds were used to sustain current consumption or repay older debts.
- Post-default interventions by lenders often included financial control and rights over pledged tax revenues; monitoring ranged from monetary/fiscal control to inspection of accounts.

### Environment and primitives of the theoretical model
- Horizon and agents:
  - Two-period economy; government alive for two periods; two one-period lenders (one per period).
- Government types:
  - θ ∈ {G, B} (good or bad government). Type is private information of the government.
  - Good project: requires investment x units per period; returns y_t take values y_h with probability π and y_l with probability 1-π, with y_l < y_h.
  - Bad project: requires investment xγ (1 < γ) and delivers y_l with probability one.
  - Both types yield 0 if no investment.
- Information and timing (each period subdivided into three subperiods):
  - Lender born with x units and public prior about government type.
  - Government offers contract; lender loans or stores endowment.
  - Investment realization y_t occurs (private information of government).
  - Government announces m_t about y_t (message).
  - Lender can verify by paying cost μ; verification reveals y_t and a noisy signal s_t ∈ {G, B} about government type (informative, q > 1/2).
  - After verification decision d_t ∈ {0,1}, repayments occur and agents consume; beliefs updated for next period.
- Key assumptions (preserved exactly):
  - xyylh>−−+μππ)1(      (equation (2) in source).
  - l
yx>γ        (equation (3) in source).
  - Signal informativeness: 2/1)Pr()Pr(>======qBBsGGsθθ. (equation (7) in source).
  - Additional condition on q: qq−>−1)1(π. (equation (8) in source).
- Government instantaneous utility: u = E c_t^θ for t = 1,2 (equation (4)).
- Lender utility: u = E c_t^L (equation (9)); verification cost μ enters lender budget constraint (equation (10)).
- Contracts specify: amount lent b_{t} and repayment function p_t(·) conditional on history and messages; an auditing rule m d_t(·) ∈ {0,1}.

### Observable types: form of optimal contract
- When types are observable:
  - Lender does not lend to the bad government (by (3)).
  - Proposition 1: For each t ∈ {1,2}, the feasible incentive-compatible contract between the good government and a one-period lender is a standard debt contract. For the bad government the incentive-compatible contract specifies 0 = b_t.
- Form of the debt contract (for G):
  - A fixed repayment R if the announced state is high (m_t = h), and default if announced state is low (m_t = l).
  - If default occurs the lender audits and may seize realized value y_t^l.
  - Verification occurs only when the reported state is low; auditing in the low state minimizes verification costs while satisfying participation and incentive-compatibility constraints.
- Specific contract notation (equation (33) preserved):
  - b_t = x
  - p_t(y_t, m_t, 1−ρ) = { φ if m_t = l; R if m_t = h }, with m d_t(y_t, m_t, 1−ρ) = { 1 if m_t = l; 0 if m_t = h } and φ, R ∈ [l_y, φ] as described.

### Unobservable types: learning, priors, and contract form
- When types are unobservable, the lender has prior 1−t ρ about government being good; posterior updating is Bayesian based on public history.
- Posteriors (preserved exactly):
  - G ρ: posterior when m = l and upon verification a good signal is obtained (equation (35)).
  - B ρ: posterior when m = l and upon verification a bad signal is obtained (equation (36)).
  - N ρ: posterior when m = l and no verification takes place (equation (37)).
  - Ordering: G N B ρρρ << (as stated in source).
- Lender participation cutoff:
  - ρ̃ (rho-tilde) defined as the minimum prior such that lender participates when verification occurs only in the low state with maximal feasible repayments (equation (39)):
    - μπ+−−=lh l yy yx ρ~ (preserved exactly).
  - If prior falls below ρ̃, lender sets b_t = 0.
- Propositions (preserved conclusions):
  - Proposition 2: Given priors ρ ∈ [ρ̃, 1], the feasible incentive-compatible contract during the second period is a standard debt contract with verification in the low state.
  - Proposition 3: Given priors ρ_0 ∈ [ρ̃, 1] and under conditions
    - xy yy x lhl −−+>−πππρ1 0  (equation (48) preserved exactly),
    - ππρ− <− 1 1 0  (equation (49) preserved exactly),
    the t=1 contract is a standard debt contract with verification in the low state.
  - Proposition 4: If conditions (48) and (49) are not satisfied, the t=1 contract specifies no verification for all states of the economy.
  - For the remainder of the analysis the paper assumes (48) and (49) hold; thus first- and second-period contracts take the debt form with verification in low state (equation (50) preserved).
- Interest-rate expression and monotonicity (Lemma 1):
  - Interest rate r_t defined by r_t = (x/xR_{t}) − 1_{−t ρ} in source notation; result: r_t is bounded above and below and evolves inversely with the probability 1−t ρ of the government being of the good type (statement preserved).
  - Participation constraint yields R_t expression (equation (52) preserved exactly): ()()() πρ μπρ ρ 1 1 1 1 − − − − − − = t l t t yx R (preserved form).

### Main theoretical results on default and lending resumption
- Contracts delivering default and verification only in the low reported state are incentive-compatible under the model primitives and parameter conditions.
- Reputation and learning implications:
  - Default does not necessarily lead to permanent denial of credit. After default (reported low state) the lender may verify; an informative good signal increases posterior to G ρ ≥ ρ̃ and can restore access to credit.
  - Proposition 6: For all ρ_0 ∈ [ρ̃, 1], the good government obtains new credit with higher probability (q) than the bad one does (1 − q), because the informative signal s = G is more likely (probability q > 1/2) under the good government.
  - Proposition 7: For all ρ_0 ∈ (0, 1], both governments obtain new credit with probability one (because priors remain above ρ̃).
- Intuition:
  - Verification upon reported low realizations allows lenders to distinguish (with some probability) good from bad governments, enabling relending to good governments even after bankruptcy.
  - If signals were uninformative (q = 1/2), default would unambiguously damage reputation and likely lead to denial of fresh credit; with informative signals (q > 1/2) default can be less damaging for good governments.

### Analysis, implications, and concluding remarks
- The constructed environment yields debt contracts (standard debt with verification in low state) as the incentive-compatible outcome when facing private information about project returns and project type.
- Key qualitative implications:
  - Default episodes can trigger lender scrutiny rather than automatic exclusion from capital markets.
  - Financial control and monitoring after default (historically observed) fit the model mechanism: audits/verification tied to bad states and seizing of assets in bankruptcy.
  - The ability of a defaulting government to obtain new credit depends critically on the informativeness of signals gathered during verification (q) and on priors about government type (ρ).
- Limitations and suggested extension:
  - The model assumes contracts are fully enforceable; this was not true historically (19th century). The next step proposed in the paper is embedding this framework into an environment where repayment is not enforceable and reputation effects operate endogenously.

*Source: _wp06176*

### 1.     Timing of the Model .............................................................................................

### Timing of the Model

### I. Motivation
- International repayments are harder to enforce than domestic repayments; literature emphasizes punishments to induce repayment.
- Common wisdom: creditors should exclude a defaulting nation from international capital markets forever.
- Historical episodes show lenders' reactions to default varied: some denied fresh credit for long periods, others granted new funds soon after default.
- Lenders discriminated in granting new loans based on perceived future profitability of the borrower’s activities.
- A complete theory of international lending should include:
  - the inability to enforce contracts, requiring punishments for breaking agreements; and
  - differential treatment received by defaulting nations as an optimal response of lenders.
- This paper studies an environment in which, assuming lack of enforceability of contracts, it is optimal for lenders to treat defaulting nations differently based on knowledge acquired during default.
- Model ingredients:
  - different types of borrowers (governments);
  - each type is identified with a specific investment project (good and bad), whose return is private information;
  - lenders can observe the realized return of the project, and can obtain a signal about the type of project if they pay a small auditing cost.
- Main claim: after default, lenders do not necessarily deny fresh credit; it is easier for a government with good projects to obtain new credit than for a government with bad projects.

### Comparison with related literature
- Cole, Dow and English (1995):
  - explain how countries denied credit at a given point will eventually be readmitted to credit markets.
  - This paper differs by explaining why some nations are not denied fresh credit even immediately after default.
- Grossman and Van Huyck (1988):
  - government borrows to finance investments with a state-contingent contract;
  - partial default (payments below the full amount in bad states) does not lead to punishment; only full repudiation entails permanent exclusion.
  - Differences with current paper:
    - Grossman and Van Huyck do not model learning by lenders; all repudiations are treated alike.
    - Current paper derives the form of the optimal contract, whereas Grossman and Van Huyck take it as given.
- Atkeson (1991):
  - both Atkeson’s model and the present paper feature uncertainty about projects and risk of default as impediments to international lending contracts.
  - Differences in results: Atkeson focuses on allocations free of risk of repudiation and explains capital outflows under worst realizations of national output; this paper offers a rationale for observed patterns of default, subsequent verification of investment levels, and possible lending resumption.
- Diamond (1989):
  - in Diamond’s model, good projects never default; any default reveals a bad project and leads to permanent exclusion.
  - Consequences in Diamond: borrowers converge to choosing only safe projects over time, as reputation benefits increase.
  - Empirical counterpoint: the prevalence and persistence of default episodes in some countries suggest borrowers do not converge to this behavior.
  - Current paper differs by allowing for lender learning and differential treatment of defaulters, which can explain observed patterns inconsistent with Diamond (1989).

### Model setup and approach (overview)
- The paper presents a model of lending with:
  - costly state verification;
  - private information about a government’s type of investment project; and
  - private information about the project's realized return.
- Analytical strategy:
  - Section IV (next step after preliminary exposition) examines the case in which the type of government is publicly known as a preliminary step toward obtaining the main results.

*Source: _wp06176 - 1.     Timing of the Model .............................................................................................*

### section it is proved that the form of the incentive-compatible contract is a standard debt

### section it is proved that the form of the incentive-compatible contract is a standard debt contract in which default and verification only occur when the reported state of the economy is low

### Historical evidence on default and lending resumption (1820–1920)
- Period examined: 1820–1920.
- Key empirical regularities highlighted:
  - Default episodes typically coincided with bad states of the economy (e.g., large drops in export revenue).
  - Examples of price/earnings shocks associated with defaults:
    - Brazil defaulted in 1898 after a decline of 64 percent in coffee prices over the preceding five years.
    - Brazil defaulted in 1914 after a fall of almost 40 percent in coffee prices in two years.
  - Other country episodes mentioned: Argentina (bankruptcy November 1890; lending resumed March 1891), Peru (defaulted in 1876; fresh credit not obtained until 1889), Bulgaria (near bankruptcy in 1899 due to bad harvests; syndicated loan in 1900).
- Lender responses after default varied:
  - Lending sometimes resumed shortly after default, even under concessionary terms (examples: Argentina 1891; Brazil 1898 and 1914; Mexico 1914; Bulgaria 1900).
  - In other cases, denial of fresh credit persisted for long periods (examples: most Latin American countries in the 1820s; Turkey 1875; Egypt 1876; Peru 1876; Greece 1893).
- Lenders distinguished between borrower uses of funds:
  - New loans more likely when past borrowing financed infrastructure or projects enhancing future growth.
  - Further credit denied when borrowed funds were used to sustain current consumption or repay older debts.
- Post-default interventions by lenders often included financial control and rights over pledged tax revenues; monitoring ranged from monetary/fiscal control to inspection of accounts.

### Environment and primitives of the theoretical model
- Horizon and agents:
  - Two-period economy; government alive for two periods; two one-period lenders (one per period).
- Government types:
  - θ ∈ {G, B} (good or bad government). Type is private information of the government.
  - Good project: requires investment x units per period; returns yt take values yh with probability π and yl with probability 1-π, with yl < yh.
  - Bad project: requires investment xγ (1 < γ) and delivers yl with probability one.
  - Both types yield 0 if no investment.
- Information and timing (each period subdivided into three subperiods):
  - Lender born with x units and public prior about government type.
  - Government offers contract; lender loans or stores endowment.
  - Investment realization yt occurs (private information of government).
  - Government announces mt about yt (message).
  - Lender can verify by paying cost μ; verification reveals yt and a noisy signal st ∈ {G, B} about government type (informative, q > 1/2).
  - After verification decision dt ∈ {0,1}, repayments occur and agents consume; beliefs updated for next period.
- Key assumptions (preserved exactly as in source):
  - xyylh>−−+μππ)1(      (equation (2) in source).
  - l
yx>γ        (equation (3) in source).
  - Signal informativeness: 2/1)Pr()Pr(>======qBBsGGsθθ. (equation (7) in source).
  - Additional condition on q: qq−>−1)1(π. (equation (8) in source).
- Government instantaneous utility: u = E c_t^θ for t = 1,2 (equation (4)).
- Lender utility: u = E c_t^L (equation (9)); verification cost μ enters lender budget constraint (equation (10)).
- Contracts specify: amount lent b_{t} and repayment function p_t(·) conditional on history and messages; an auditing rule md_t(·) ∈ {0,1}.

### Observable types: form of optimal contract
- When types are observable:
  - Lender does not lend to the bad government (by (3)).
  - Proposition 1 (preserved conclusion): For each t ∈ {1,2}, the feasible incentive-compatible contract between the good government and a one-period lender is a standard debt contract. For the bad government the incentive-compatible contract specifies 0 = b_t.
  - Form of the debt contract (for G): a fixed repayment R if the announced state is high (m_t = h), and default if announced state is low (m_t = l). If default occurs the lender audits and may seize realized value y_t^l.
  - Verification occurs only when the reported state is low; auditing in the low state minimizes verification costs while satisfying participation and incentive-compatibility constraints.
- Specific contract notation preserved from source (equation (33)):
  - b_t = x
  - p_t(y_t, m_t, 1−ρ) = { φ if m_t = l; R if m_t = h }, with md_t(y_t, m_t, 1−ρ) = { 1 if m_t = l; 0 if m_t = h } and φ, R ∈ [l_y, φ] as described.

### Unobservable types: learning, priors, and contract form
- When types are unobservable, the lender has prior 1−t ρ about government being good; posterior updating is Bayesian based on public history.
- Posteriors definitions (preserved exactly as in source):
  - G ρ: posterior when m = l and upon verification a good signal is obtained (equation (35)).
  - B ρ: posterior when m = l and upon verification a bad signal is obtained (equation (36)).
  - N ρ: posterior when m = l and no verification takes place (equation (37)).
  - Ordering: G N B ρρρ << (as stated in source).
- Lender participation cutoff:
  - ρ̃ (rho-tilde) defined as the minimum prior such that lender participates when verification occurs only in the low state with maximal feasible repayments (equation (39)): μπ+−−=lh l yy yx ρ~ (preserved exactly as in source).
  - If prior falls below ρ̃, lender sets b_t = 0.
- Propositions (preserved conclusions):
  - Proposition 2: Given priors ρ ∈ [ρ̃, 1], the feasible incentive-compatible contract during the second period is a standard debt contract with verification in the low state.
  - Proposition 3: Given priors ρ_0 ∈ [ρ̃, 1] and under conditions
    - xy yy x lhl −−+>−πππρ1 0  (equation (48) preserved exactly),
    - ππρ− <− 1 1 0  (equation (49) preserved exactly),
    the t=1 contract is a standard debt contract with verification in the low state.
  - Proposition 4: If conditions (48) and (49) are not satisfied, the t=1 contract specifies no verification for all states of the economy.
  - For the remainder of the analysis the paper assumes (48) and (49) hold; thus first- and second-period contracts take the debt form with verification in low state (equation (50) preserved).
- Interest-rate expression and monotonicity (Lemma 1):
  - Interest rate r_t defined by r_t = (x/xR_{t}) − 1_{−t ρ} in source notation; result: r_t is bounded above and below and evolves inversely with the probability 1−t ρ of the government being of the good type (statement preserved from source).
  - Participation constraint yields R_t expression (equation (52) preserved exactly): ()()() πρ μπρ ρ 1 1 1 1 − − − − − − = t l t t yx R (preserved form).

### Main theoretical results on default and lending resumption
- Contracts delivering default and verification only in the low reported state are incentive-compatible under the model primitives and parameter conditions.
- Reputation and learning implications:
  - Default does not necessarily lead to permanent denial of credit. After default (reported low state) the lender may verify; an informative good signal increases posterior to G ρ ≥ ρ̃ and can restore access to credit.
  - Proposition 6: For all ρ_0 ∈ [ρ̃, 1], the good government obtains new credit with higher probability (q) than the bad one does (1 − q), because the informative signal s = G is more likely (probability q > 1/2) under the good government.
  - Proposition 7: For all ρ_0 ∈ (0, 1], both governments obtain new credit with probability one (because priors remain above ρ̃).
- Intuition preserved from source:
  - Verification upon reported low realizations allows lenders to distinguish (with some probability) good from bad governments, enabling relending to good governments even after bankruptcy.
  - If signals were uninformative (q = 1/2), default would unambiguously damage reputation and likely lead to denial of fresh credit; with informative signals (q > 1/2) default can be less damaging for good governments.

### Analysis, implications, and concluding remarks
- The constructed environment yields debt contracts (standard debt with verification in low state) as the incentive-compatible outcome when facing private information about project returns and project type.
- Key qualitative implications (as stated in the source):
  - Default episodes can trigger lender scrutiny rather than automatic exclusion from capital markets.
  - Financial control and monitoring after default (historically observed) fit the model mechanism: audits/verification tied to bad states and seizing of assets in bankruptcy.
  - The ability of a defaulting government to obtain new credit depends critically on the informativeness of signals gathered during verification (q) and on priors about government type (ρ).
- Limitations and suggested extension (preserved from source):
  - The model assumes contracts are fully enforceable; this was not true historically (19th century). The next step proposed in the paper is embedding this framework into an environment where repayment is not enforceable and reputation effects operate endogenously.

*Source: section it is proved that the form of the incentive-compatible contract is a standard debt contract in which default and verification only occur when the reported state of the economy is low (extracted from the supplied IMF PDF content).*

### REFERENCES

### REFERENCES

### Cited works
- Aguiar, Mark, and Gita Gopinath, 2006, “Defaultable Debt, Interest Rates and the Current Account,” Journal of International Economics (forthcoming).
- Arellano, Cristina, 2005, “Default Risk and Income Fluctuations in Emerging Economies,” Working Paper (Minneapolis, Minnesota: University of Minnesota).
- Atkeson, Andrew, 1991, “International Lending with Moral Hazard and Risk of Repudiation,” Econometrica, Vol. 59, pp. 1069–89.
- Borchard, Edwin, 1951, State Insolvency and Foreign Bondholders, Volume 1, Yale Law School Studies, (New Haven, Connecticut: Yale University Press).
- Chang, Chun, 1990, “The Dynamic Structure of Optimal Debt Contracts,” Journal of Economic Theory, Vol. 52, pp. 68–86.
- Cole, Harold L., James Dow, and William B. English, 1995, “Default, Settlement, and Signaling: Lending Resumption in a Reputational Model of Sovereign Debt,” International Economic Review, Vol. 36, No. 2, pp. 365-85.
- Diamond, Douglas W., 1989, “Reputation Acquisition in Debt Markets,” Journal of Political Economy, Vol. 97, No. 4, pp. 828–62.
- Eaton, Jonathan and Mark Gersovitz, 1981, “Debt with Potential Repudiation: Theoretical and Empirical Analysis,” Review of Economic Studies, Vol. 48, pp. 289-309.
- Fishlow, Albert, 1985, “Lessons From the Past: Capital Markets During the 19th Century and the Interwar Period,” International Organization, Vol. 39, No. 3, pp. 383–439.
- Grossman, Herschel I., and John B. Van Huyck, 1988, “Sovereign Debt as a Contingent Claim: Excusable Default, Repudiation, and Reputation,” American Economic Review, Vol. 78, No. 5, pp. 1088–97.
- Lindert, Peter H., and Peter J. Morton, 1989, “How Sovereign Debt Has Worked,” in Developing Country Debt and Economic Performance, Vol.1, ed. by Jeffrey Sachs, (Cambridge, Massachusetts: National Bureau of Economic Research).
- Marichal, Carlos, 1989, “A Century of Debt Crises in Latin America,” (Princeton, New Jersey: Princeton University Press).
- Obstfeld, Maurice, 1986, “Rational and Self-fulfilling Balance of Payments Crises,” American Economic Review, Vol. 76, pp. 72–81.
- Townsend, Robert, 1979, “Optimal Contracts and Competitive Markets with Costly State Verification,” Journal of Economic Theory, Vol. 21, pp. 1–29.
- Wynne, William H., 1951, State Insolvency and Foreign Bondholders, Vol. 2, Yale Law School Studies, (New Haven, Connecticut: Yale University Press).

*_wp06176 - REFERENCES_*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06176.pdf_