## _wp0679

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---

### Introduction
- International financial integration limits national fiscal, financial, and monetary policy discretion by exposing governments to world savings and market discipline.
- Sovereign immunity is central: governments may restrain exercise of immunity with regard to debtor assets abroad but retain immunity over domestic policy, legislation, and enforcement.
- Sovereign immunity is used to derive intertemporal budget constraints and endogenous limits on public debt and deficits in a tax-smoothing framework.
- Key model implications:
  - Securities markets are incomplete in equilibrium.
  - With full information, contingent securities are required in equilibrium every period.
  - With private (incomplete) information, contingent repayments are required only when outstanding government debt exceeds a threshold.
  - Conventional bonds that are renegotiated with positive probability only as the debt limit is approached support efficient outcomes with private information.

### Sovereignty and Public Debt in the Open Economy
- Sovereign immunity: foreign governments cannot enforce contracts within national borders without cooperation of the sovereign; enforcement of private contracts depends on domestic institutions chosen by the sovereign.
- The sovereign chooses whether to honor obligations; borrowing depends on willingness to repay (models starting with Eaton and Gersovitz (1981) referenced).
- Model setup:
  - Fiscal authority smooths distortionary taxes against stochastic exogenous government expenditures, g_t.
  - Representative-agent objective: U_t = u(c_t) + E_t ∑_{s=t+1}^∞ β^{s−t} u(c_s).
  - v(T)=u(Y(T)−T) with tax-related properties Y(T)>0, Y'(T)≤0, Y'(0)=0, Y''(T)≤0 for 0≤T≤T̄, T̄>0.
  - Trade balance τ_t = Y(T_t) − c_t − g_t = T_t − g_t.

### Deficit Finance and Foreign Borrowing
- Present value of financial claims: w_t = T_t − g_t + E_t ∑_{s=t+1}^∞ β^{s−t} (T_s − g_s).  (equation (2))
- Recursive form: w_t = −(g_t − T_t) + β E_t w_{t+1}.  (equation (3))
- Participation constraints for creditors and government: w_t ≥ 0 and w_{t+1} ≥ 0 for all dates and states.
- Sovereignty constraint (willingness to repay): v(T_t) + E_t ∑_{s=t+1}^∞ β^{s−t} v(T_s) ≥ v(g_t) + E_t ∑_{s=t+1}^∞ β^{s−t} v(g_s).  (equation (4))
- Equilibrium characterized by maximizing V_t = v(T_t) − v(g_t) + β E_t V_{t+1} subject to (7) and (8).
- First-order conditions:
  - v′(T_t) = v′(T_{t+1}) if w_{t+1} > 0 and V_{t+1}(w_{t+1}) > 0.  (equation (9))
  - v′(T_t) < v′(T_{t+1}) < 0 if w_{t+1} = 0.  (inequality (10))
  - v′(T_t) > v′(T_{t+1}) < 0 if V_{t+1}(w_{t+1}) = 0.  (equation (11a))
- Implementation: state-contingent equilibrium can be implemented through continual renegotiation of standard debt contracts with actual repayments equal to w_{t+1}.

### Incomplete Information and Bond Lending
- Asymmetric information assumption: g_t observed by national authorities but not by creditors; g_t interpreted as an unobserved taste shock to the government.
- Incentive-compatibility constraint: V_t(g_t,g_t) ≥ V_t(g_t,ĝ_t) for all possible ĝ_t, with V_t(g_t,ĝ_t) ≡ v(T_t(ĝ_t)) − v(g_t) + β E_t V_{t+1}(ĝ_t).  (equations (15) and (16))
- Under full commitment and no participation constraints, conventional noncontingent bond contracts are supported and the expected present value W_t = T_t − g_t + β W_{t+1} does not depend on g_t.  (equation (17))
- First-order conditions under private information:
  - v'(T_t) = E_t v'(T_{t+1}) when participation constraints not binding.  (equation (18))
  - v'(T_t) ≤ E_t v'(T_{t+1}) < 0 when government participation constraint binds.  (inequality (19))
  - v'(T_t) ≥ E_t v'(T_{t+1}) when creditors’ participation constraints bind.  (equation (20))
- Critical debt concepts:
  - Debt limit denoted W, determined when E_t V_{t+1} = 0 (government continuation surplus zero).
  - Pivotal state g satisfies v'(g) = E v'(T̂(g_t)).  (equation (22))
  - Critical debt level ˜W defined by v'(˜W − βW + g_max) = E v'(T̂(g_t)).  (equation (25))
- Dynamics:
  - If W_t < ˜W, debt next period remains below limit with certainty; repayments are noncontingent and interest equals discount rate ρ = (1 − β)/β.
  - If ˜W ≤ W_t ≤ W, debt limit may be reached with positive probability and bond returns become stochastic (risk premium emerges).
  - Single-period budget identity in risky region: W_t = E_{t−1}[(T_t − g_t) + β W_{t+1}].  (equation (26))
  - Ex post yield r_{t+1} defined by W_{t+1} = (1 + r_{t+1}) [W_t + (g_t − T_t)].  (equation (27))
  - At the debt limit with adverse shocks, rate of return can be zero for creditors.  (equation (28))

### Debt Limits and the Government’s Budget Constraint
- Sovereign-immunity-imposed constraint w_t ≥ 0 is weaker than conventional solvency constraint lim_{s→∞} E_t β^{s−t} b_{s+1} ≤ 0.  (equations (12) and (13))
- Conventional solvency constraint requires present value of primary surplus ≥ current outstanding debt at all dates: w_t = T_t − g_t + E_t ∑_{s=t+1}^∞ β^{s−t} (T_s − g_s) ≥ b_t.  (equation (14))
- Restricting to noncontingent contracts in all events reduces the debt limit below W and reduces tax smoothing; securities are endogenous under sovereign immunity.

### Nominal Debt, Renegotiation and Debt Limits
- Nominal (domestic-currency-denominated) debt can implement state-contingent real repayments through unanticipated inflation, but:
  - Under complete information models, frequent unanticipated inflation would be required.
  - Under incomplete information, unanticipated inflation is desirable only when outstanding debt exceeds the critical threshold.
- Money and nominal debt extension:
  - Real balances example (log utility): M_t / p_t = u′(c_t) κ (1 + i_{t+1}) / i_{t+1}.  (equation (31))
  - Nominal debt B_t = p_t W_t; evolution: B_{t+1} = (1 + i_{t+1}) [B_t + p_t (g_t − T_t)].  (equation (32))
  - Real debt evolution: W_{t+1} = (p_t / p_{t+1}) (1 + i_{t+1}) [W_t + (g_t − T_t)].  (equation (33))
  - Replication requires p_t / p_{t+1} (1 + i_{t+1}) = 1 + r_{t+1}.  (equation (34))
- Enforcement of implicit contracts after excessive inflation:
  - Excessive monetary expansion reduces ex post real value of debt from W_t to W'_t where W_t > W'_t = (p_{t−1} / p_t) (1 + i_t) [W_{t−1} + (g_{t−1} − T_{t−1})].  (equation (35))
  - Market response must ensure no gain from deviation; example constraint: W_{t+1} ≤ (p_t / p_{t+1}) (1 + i''_{t+1}) [W'_t − s''_t].  (equation (36))
  - Alternatively, response via foreign-currency or real-indexed new debt: W_{t+1} ≤ (1 + r''_{t+1}) [W'_t − s''_t].  (equation (37))
- Credible upper bounds on inflation or costs of inflation (inflation aversion) are necessary for nominal-debt enforcement strategies to be effective.

### Implications for Foreign Borrowing and Reserves
- Interpretation as international borrowing: primary deficit as trade balance; outstanding debt as net foreign liabilities.
- When external debt is above the critical level:
  - Nominal noncontingent bonds can be reduced via surprise inflation.
  - Foreign-currency-denominated bonds require explicit renegotiation; renegotiation tends to be protracted and costly.
- Reserve accumulation interpretation:
  - Government can smooth taxes by accumulating reserve assets a_t with β a_{t+1} = a_t + (T_t − g_t).  (equation (40))
  - Maximization: V_t(a_t) = max { v(T_t) − v(g_t) + β E_t V_{t+1}(a_{t+1}) }.  (equation (39))
  - Reserves can be stock-out prone; when reserves reach zero with positive probability, more surplus extraction (or borrowing) is required to achieve constrained optimum.
  - A government that cannot issue debt in its own currency should issue foreign-currency or real-indexed liabilities, subject to renegotiation in constrained efficient equilibrium.

### Decentralized Equilibrium and the Current Account
- Approaching the debt limit, the trade deficit must eventually decrease and turn to surplus via higher real interest rates and relative price changes.
- Representative household conditions:
  - u′(c_t) ≥ E_t u′(c_{t+1}) in adverse shocks with net external debt above the critical level.  (equation (41))
  - Real interest rate determination: u′(c_t) = β (1 + r_{t+1}) E_t u′(c_{t+1}).  (equation (42))
  - Real interest rate rises above discount rate as external debt passes critical level, inducing saving and current-account reversal.
- With tradable and nontradable goods:
  - Real exchange rate q_t = p^T_t / p^N_t determined by marginal utilities u'_1(c^T_t,c^N_t) / u'_2(c^T_t,c^N_t).  (equation (43))
  - Intertemporal condition: u'_1(c^T_t,c^N_t) = β (1 + r_{t+1}) E_t u'_1(c^T_{t+1},c^N_{t+1}).  (equation (44))
  - Equilibrium: c^N_t = y^N_t, c^N_{t+1} = y^N_{t+1}, and W_t = c^T_t − y^T_t + β W_{t+1}.  (equation (45))
- Exchange-rate and interest-rate responses depend on elasticities of substitution across goods and time.

### Conclusion
- Sovereign ability to choose whether to honor public and private debts constrains international contract enforcement and access to international markets.
- Under sovereign immunity with information asymmetries:
  - Conventional solvency constraints may not characterize equilibrium borrowing limits.
  - Repayments become state contingent as debt limits are approached; renegotiation of noncontingent real bonds is required at the debt limit.
  - Nominal domestic-currency debt allows inflationary erosion as a mechanism for state-contingent repayments, but under incomplete information such inflationary surprises should be confined to times when outstanding debt exceeds the critical threshold.
- Monetary-policy implications:
  - Complete-information models imply frequent stochastic optimal inflation, conflicting with commitment in monetary policy.
  - Incomplete-information models imply inflationary debt reduction only near the debt limit, compatible with predictable inflation and inflation targeting when debt constraints are not binding.
  - Credible punishments and reputational equilibria limit erosion of real debt value during crises; government inflation aversion increases ability to issue domestic-currency debt internationally.
- Empirical consistency: renegotiations are infrequent; debt-to-GDP is a strong predictor of default and renegotiation; emerging market public debt is largely issued as foreign-currency noncontingent bonds or loans.

*Source: _wp0679 - References..............................................................................................................*

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

### _wp0679 - References..............................................................................................................

### Introduction
- International financial integration limits national fiscal, financial, and monetary policy discretion by exposing governments to world savings and market discipline.
- Sovereign immunity is central: governments may restrain exercise of immunity with regard to debtor assets abroad but retain immunity over domestic policy, legislation, and enforcement.
- Sovereign immunity is used to derive intertemporal budget constraints and endogenous limits on public debt and deficits in a tax-smoothing framework.
- Key model implications:
  - Securities markets are incomplete in equilibrium.
  - With full information, contingent securities are required in equilibrium every period.
  - With private (incomplete) information, contingent repayments are required only when outstanding government debt exceeds a threshold.
  - Conventional bonds that are renegotiated with positive probability only as the debt limit is approached support efficient outcomes with private information.

### Sovereignty and Public Debt in the Open Economy
- Sovereign immunity: foreign governments cannot enforce contracts within national borders without cooperation of the sovereign; enforcement of private contracts depends on domestic institutions chosen by the sovereign.
- The sovereign chooses whether to honor obligations; borrowing depends on willingness to repay (models starting with Eaton and Gersovitz (1981) referenced).
- Model setup:
  - Fiscal authority smooths distortionary taxes against stochastic exogenous government expenditures,g_t.
  - Representative-agent objective: U_t = u(c_t) + E_t ∑_{s=t+1}^∞ β^{s−t} u(c_s).
  - v(T)=u(Y(T)−T) with tax-related properties Y(T)>0, Y'(T)≤0, Y'(0)=0, Y''(T)≤0 for 0≤T≤T̄, T̄>0.
  - Trade balance τ_t = Y(T_t) − c_t − g_t = T_t − g_t.

### Deficit Finance and Foreign Borrowing
- Present value of financial claims: w_t = T_t − g_t + E_t ∑_{s=t+1}^∞ β^{s−t} (T_s − g_s).  (equation (2))
- Recursive form: w_t = −(g_t − T_t) + β E_t w_{t+1}.  (equation (3))
- Participation constraints for creditors and government: w_t ≥ 0 and w_{t+1} ≥ 0 for all dates and states.
- Sovereignty constraint (willingness to repay): v(T_t) + E_t ∑_{s=t+1}^∞ β^{s−t} v(T_s) ≥ v(g_t) + E_t ∑_{s=t+1}^∞ β^{s−t} v(g_s).  (equation (4))
- Equilibrium characterized by maximizing V_t = v(T_t) − v(g_t) + β E_t V_{t+1} subject to (7) and (8).
- First-order conditions:
  - v′(T_t) = v′(T_{t+1}) if w_{t+1} > 0 and V_{t+1}(w_{t+1}) > 0.  (equation (9))
  - v′(T_t) < v′(T_{t+1}) < 0 if w_{t+1} = 0.  (inequality (10))
  - v′(T_t) > v′(T_{t+1}) < 0 if V_{t+1}(w_{t+1}) = 0.  (equation (11a))
- Implementation: state-contingent equilibrium can be implemented through continual renegotiation of standard debt contracts with actual repayments equal to w_{t+1}.

### Incomplete Information and Bond Lending
- Asymmetric information assumption: g_t observed by national authorities but not by creditors; g_t interpreted as an unobserved taste shock to the government.
- Incentive-compatibility constraint: V_t(g_t,g_t) ≥ V_t(g_t,ĝ_t) for all possible ĝ_t, with V_t(g_t,ĝ_t) ≡ v(T_t(ĝ_t)) − v(g_t) + β E_t V_{t+1}(ĝ_t).  (equations (15) and (16))
- Under full commitment and no participation constraints, conventional noncontingent bond contracts are supported and the expected present value W_t = T_t − g_t + β W_{t+1} does not depend on g_t.  (equation (17))
- First-order conditions under private information:
  - v'(T_t) = E_t v'(T_{t+1}) when participation constraints not binding.  (equation (18))
  - v'(T_t) ≤ E_t v'(T_{t+1}) < 0 when government participation constraint binds.  (inequality (19))
  - v'(T_t) ≥ E_t v'(T_{t+1}) when creditors’ participation constraints bind.  (equation (20))
- Critical debt concepts:
  - Debt limit denoted W, determined when E_t V_{t+1} = 0 (government continuation surplus zero).
  - Pivotal state g satisfies v'(g) = E v'(T̂(g_t)).  (equation (22))
  - Critical debt level ˜W defined by v'(˜W − βW + g_max) = E v'(T̂(g_t)).  (equation (25))
- Dynamics:
  - If W_t < ˜W, debt next period remains below limit with certainty; repayments are noncontingent and interest equals discount rate ρ = (1 − β)/β.
  - If ˜W ≤ W_t ≤ W, debt limit may be reached with positive probability and bond returns become stochastic (risk premium emerges).
  - Single-period budget identity in risky region: W_t = E_{t−1}[(T_t − g_t) + β W_{t+1}].  (equation (26))
  - Ex post yield r_{t+1} defined by W_{t+1} = (1 + r_{t+1}) [W_t + (g_t − T_t)].  (equation (27))
  - At the debt limit with adverse shocks, rate of return can be zero for creditors.  (equation (28))

### Debt Limits and the Government’s Budget Constraint
- Sovereign-immunity-imposed constraint w_t ≥ 0 is weaker than conventional solvency constraint lim_{s→∞} E_t β^{s−t} b_{s+1} ≤ 0.  (equations (12) and (13))
- Conventional solvency constraint requires present value of primary surplus ≥ current outstanding debt at all dates: w_t = T_t − g_t + E_t ∑_{s=t+1}^∞ β^{s−t} (T_s − g_s) ≥ b_t.  (equation (14))
- Restricting to noncontingent contracts in all events reduces the debt limit below W and reduces tax smoothing; securities are endogenous under sovereign immunity.

### Nominal Debt, Renegotiation and Debt Limits
- Nominal (domestic-currency-denominated) debt can implement state-contingent real repayments through unanticipated inflation, but:
  - Under complete information models, frequent unanticipated inflation would be required.
  - Under incomplete information, unanticipated inflation is desirable only when outstanding debt exceeds the critical threshold.
- Money and nominal debt extension:
  - Real balances example (log utility): M_t / p_t = u′(c_t) κ (1 + i_{t+1}) / i_{t+1}.  (equation (31))
  - Nominal debt B_t = p_t W_t; evolution: B_{t+1} = (1 + i_{t+1}) [B_t + p_t (g_t − T_t)].  (equation (32))
  - Real debt evolution: W_{t+1} = (p_t / p_{t+1}) (1 + i_{t+1}) [W_t + (g_t − T_t)].  (equation (33))
  - Replication requires p_t / p_{t+1} (1 + i_{t+1}) = 1 + r_{t+1}.  (equation (34))
- Enforcement of implicit contracts after excessive inflation:
  - Excessive monetary expansion reduces ex post real value of debt from W_t to W'_t where W_t > W'_t = (p_{t−1} / p_t) (1 + i_t) [W_{t−1} + (g_{t−1} − T_{t−1})].  (equation (35))
  - Market response must ensure no gain from deviation; example constraint: W_{t+1} ≤ (p_t / p_{t+1}) (1 + i''_{t+1}) [W'_t − s''_t].  (equation (36))
  - Alternatively, response via foreign-currency or real-indexed new debt: W_{t+1} ≤ (1 + r''_{t+1}) [W'_t − s''_t].  (equation (37))
- Credible upper bounds on inflation or costs of inflation (inflation aversion) are necessary for nominal-debt enforcement strategies to be effective.

### Implications for Foreign Borrowing and Reserves
- Interpretation as international borrowing: primary deficit as trade balance; outstanding debt as net foreign liabilities.
- When external debt is above the critical level:
  - Nominal noncontingent bonds can be reduced via surprise inflation.
  - Foreign-currency-denominated bonds require explicit renegotiation; renegotiation tends to be protracted and costly.
- Reserve accumulation interpretation:
  - Government can smooth taxes by accumulating reserve assets a_t with β a_{t+1} = a_t + (T_t − g_t).  (equation (40))
  - Maximization: V_t(a_t) = max { v(T_t) − v(g_t) + β E_t V_{t+1}(a_{t+1}) }.  (equation (39))
  - Reserves can be stock-out prone; when reserves reach zero with positive probability, more surplus extraction (or borrowing) is required to achieve constrained optimum.
  - A government that cannot issue debt in its own currency should issue foreign-currency or real-indexed liabilities, subject to renegotiation in constrained efficient equilibrium.

### Decentralized Equilibrium and the Current Account
- Approaching the debt limit, the trade deficit must eventually decrease and turn to surplus via higher real interest rates and relative price changes.
- Representative household conditions:
  - u′(c_t) ≥ E_t u′(c_{t+1}) in adverse shocks with net external debt above the critical level.  (equation (41))
  - Real interest rate determination: u′(c_t) = β (1 + r_{t+1}) E_t u′(c_{t+1}).  (equation (42))
  - Real interest rate rises above discount rate as external debt passes critical level, inducing saving and current-account reversal.
- With tradable and nontradable goods:
  - Real exchange rate q_t = p^T_t / p^N_t determined by marginal utilities u'_1(c^T_t,c^N_t) / u'_2(c^T_t,c^N_t).  (equation (43))
  - Intertemporal condition: u'_1(c^T_t,c^N_t) = β (1 + r_{t+1}) E_t u'_1(c^T_{t+1},c^N_{t+1}).  (equation (44))
  - Equilibrium: c^N_t = y^N_t, c^N_{t+1} = y^N_{t+1}, and W_t = c^T_t − y^T_t + β W_{t+1}.  (equation (45))
- Exchange-rate and interest-rate responses depend on elasticities of substitution across goods and time.

### Conclusion
- Sovereign ability to choose whether to honor public and private debts constrains international contract enforcement and access to international markets.
- Under sovereign immunity with information asymmetries:
  - Conventional solvency constraints may not characterize equilibrium borrowing limits.
  - Repayments become state contingent as debt limits are approached; renegotiation of noncontingent real bonds is required at the debt limit.
  - Nominal domestic-currency debt allows inflationary erosion as a mechanism for state-contingent repayments, but under incomplete information such inflationary surprises should be confined to times when outstanding debt exceeds the critical threshold.
- Monetary-policy implications:
  - Complete-information models imply frequent stochastic optimal inflation, conflicting with commitment in monetary policy.
  - Incomplete-information models imply inflationary debt reduction only near the debt limit, compatible with predictable inflation and inflation targeting when debt constraints are not binding.
  - Credible punishments and reputational equilibria limit erosion of real debt value during crises; government inflation aversion increases ability to issue domestic-currency debt internationally.
- Empirical consistency: renegotiations are infrequent; debt-to-GDP is a strong predictor of default and renegotiation; emerging market public debt is largely issued as foreign-currency noncontingent bonds or loans.

*Source: _wp0679 - References..............................................................................................................*

### References

### _wp0679 - References

### References

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*Content derived from the document _wp0679 - References.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp0679.pdf_