2014年-IMF国际货币组织全球_Optimal_Maturity_Structure_of_Sovereign_Debt_in_Situation_of_Near_Default_43页_242kb

Summary of "Optimal Maturity Structure of Sovereign Debt in Situation of Near Default"

Core Content

This working paper by Gabriel Desgranges and Céline Rochon explores the optimal maturity structure of sovereign debt in the context of near default, focusing on the interplay between uncertainty about future macroeconomic fundamentals, fiscal effort, and the risk of default. The study is framed within a three-period model where the Sovereign issues both short-term (ST) and long-term (LT) debt in the initial period, and faces a trade-off between current fiscal effort and future default costs.

Main Viewpoints

1. Trade-off Between Fiscal Effort and Default Risk

• The Sovereign must balance the cost of default in the future with the fiscal effort required to meet its obligations in the present.
• A large issuance of long-term debt can lead to financial fragility, as it increases the likelihood of default in the final period if the macroeconomic fundamentals are poor.
• Short-term debt is considered less risky, as it does not expose the Sovereign to future default risk, but requires frequent rollover.

2. Role of Prior Uncertainty

• Prior uncertainty about future macroeconomic fundamentals plays a critical role in shaping the optimal debt portfolio and the probability of default.
• This uncertainty influences interest rates, which in turn affects the Sovereign’s debt issuance decisions.
• When expected fundamentals are moderate, the Sovereign is less likely to default, but uncertainty can lead to a choice of potential default even for the same fundamentals.

3. Hedging Role of Long-Term Debt

• Long-term debt acts as a hedging instrument against future macroeconomic shocks.
• It is more costly than short-term debt due to the risk of default, but it can reduce the cost of future debt by lowering the need for high fiscal effort.
• The interest rate is determined by the expected probability of default, and this rate is correlated with macroeconomic fundamentals.

4. Conditions for Default

• Default can only occur in the last period (t=2).
• The default probability depends on the accumulated debt burden and the realization of fundamentals.
• If the sum of ST debt issued at t=1 and LT debt is greater than the maximum fiscal effort (θ₂^H), then default occurs.

5. Strategic Debt Issuance

• The Sovereign strategically chooses a maturity structure that leads to a potential default in the final period, contingent on negative macroeconomic shocks.
• The choice of potential default is influenced by the initial issuance of long-term debt and the expectation about fundamentals.

Key Information

Debt Structure and Default

• The debt mix (ST and LT) affects the fiscal effort and the likelihood of default.
• A large issuance of LT debt in the initial period increases the risk of default in the final period if the fiscal effort is insufficient.
• The cost of default is exogenous and is represented by a penalty cost K.

Interest Rates and Default

• Interest rates are determined by the expected probability of default.
• A higher expected default probability leads to higher interest rates.
• The interest rate for LT debt is higher than the risk-free rate when the Sovereign issues a large amount of LT debt.

Market and Investor Behavior

• Investors are risk-neutral, and information is symmetric.
• Financial markets are perfectly competitive, and there is no coordination failure among investors.
• Market prices are based on the discounted expected future value of debt.

Policy Implications

• The paper suggests that international financial institutions (IFIs) can help manage default risk by offering conditioned contracts.
• These contracts provide incentives for the Sovereign to exert fiscal effort and avoid default.
• Market incompleteness, such as the lack of indexed bonds, constrains the Sovereign to choose a maturity structure that may lead to default.

Structure of the Paper

1. Introduction

   • Focuses on the maturity structure of sovereign debt in a near-default situation.
   • Highlights the trade-off between fiscal effort and default risk.

2. The Model

   • A three-period model with investors and a Sovereign.
   • Uncertainty about macroeconomic fundamentals is modeled as a real variable θ_t.
   • The Sovereign’s objective is to minimize the cost of fiscal efforts, subject to budget constraints.

3. Choice of Potential Default in the Intermediate Period

   • The Sovereign’s decision at t=1 (issuing ST debt and exerting fiscal effort) determines the default probability at t=2.
   • The model shows that potential default is a strategic choice based on debt burden and fundamentals.

4. Role of Initial Uncertainty

   • Uncertainty about fundamentals affects interest rates and debt issuance.
   • The optimal debt portfolio is influenced by prior beliefs about the future.

5. Optimal Portfolio

   • The Sovereign chooses a maturity structure that minimizes the expected cost of fiscal efforts and default.
   • The optimal portfolio depends on the expected default probability and the realization of fundamentals.

6. Concluding Remarks

   • International financial institutions play a key role in managing sovereign debt crises.
   • They can offer conditioned contracts that provide incentives for the Sovereign to exert fiscal effort and avoid default.

Conclusion

• The paper provides a theoretical framework for understanding how sovereigns choose their debt maturity structure in the face of uncertainty and potential default.
• It highlights that long-term debt can serve as a hedging instrument, but it is more costly due to the risk of default.
• Prior uncertainty about macroeconomic fundamentals is a key determinant of the probability of default and the interest rate.
• The role of international institutions is emphasized, as they can offer conditioned contracts that help discipline the Sovereign and reduce default risk.

References

• The paper cites several key works in the literature on sovereign debt crises, long-term debt, and market incompleteness.
• Notable references include Arellano (2008, 2012), Jeanne (2009), Conesa and Kehoe (2012, 2014), Cole and Kehoe (1996), and Buera and Nicolini (2004).

Mathematical Formulation

• The debt issuance at t=0 is given by:
  $$
  D = \frac{1}{1 + r} ST_0 + \frac{1 - E(\pi^D)}{(1 + r)^2} LT
  $$
• The default probability at t=2 is determined by:
  $$
  \pi^D = 0 \text{ if } ST_1 + LT \leq \theta_2^L, \quad \pi^D = \pi_2^L \text{ if } \theta_2^L < ST_1 + LT \leq \theta_2^H, \quad \pi^D = 1 \text{ if } ST_1 + LT > \theta_2^H
  $$
• The interest rate at t=1 is:
  $$
  p_1 = \frac{1 - \pi^D}{1 + r}
  $$
• The Sovereign’s cost function is:
  $$
  V = \frac{e_1^2}{\theta_1} + \pi_2^L e_2(\theta_2^L)^2 + \pi_2^H e_2(\theta_2^H)^2
  $$

This model contributes to the understanding of sovereign debt maturity structure and the role of uncertainty in default decisions. It also provides policy insights on how international institutions can help mitigate debt crises.