## Maximum Sustainable Debt Across Countries: An Assessment using P-Theory

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---

### Methodological framework (Section 2)
- Framework: adopts the theoretical framework in Jiang, Sargent, Wang, and Yang (2024) to assess the maximum sustainable level of debt.
- Integrates asset-pricing blocks: the risk-free rate, a convenience yield (lowers required returns on safe debt), and a jump-risk premium tied to disaster intensity and tail thickness.
- Nests and synthesizes prior approaches: Arrow one-period-ahead securities and GDP-indexed insurance (Shiller (1994), Barro (1979)); sovereign credit constraints (Eaton and Gersovitz (1981)); convenience yields on risk-free government debt (Krishnamurthy and Vissing-Jorgensen (2012)); uninsurable jump shocks to output.
- Model government features:
  - Output evolves via a geometric jump-diffusion process; some risks hedgeable via GDP-indexed insurance, others (sudden jumps) are not.
  - Collects distortionary taxes to fund exogenous expenditures.
  - Has a default option and benefits from convenience yields.
  - Balances marginal costs and benefits of public debt.
- Debt-to-GDP evolution (as given):
  - ḃt = γ − τ(bt) − g·bt + (r − δ + π(b/ b̄))·bt + λ·bt
  - Definitions in text: r: risk free rate; δ: convenience yield; π(b/ b̄) = ζ̃(b/ b̄)^ω where ζ̃ denotes Poisson arrival rate of jump shocks and ω governs fat-tailedness.
- Default threshold and taxation:
  - Default threshold: derived by comparing value of continued servicing (raising distortionary taxes) versus default; tax distortion parameter φ captures deadweight loss from taxation; default costs include output loss α (output cost of default = 1−α) and default-related tax cost κ; maximum tax capacity may bind at τ̄.
  - Equations (preserved as in source):
    - Optimal taxes: τN = min{ τ̄, 1/φ ( v/u u t 1 + 2φ 1−α+γ+ φκγ 2 2α ! −1 ) }  (2)
    - Max sustainable debt: b̄ = (τN − γ) / ( r + ζ̃ + λ − δ − g ); (3)
    - Note: at default threshold the term r + ζ̃ + λ − δ − g is distinct from the standard r − g.

### Fiscal factors (Section 2.1)
- Role of taxation:
  - Tax distortion parameter φ captures deadweight loss; higher φ reduces capacity to service debt.
  - Tax capacity τ̄ directly affects revenue collection and sustainable debt.
- Government spending γ:
  - Higher spending increases fiscal burden; may raise the debt limit if supported by sustainably higher future tax revenue.
  - If optimal taxes approach τ̄, debt limit constrained.
- Calibration note: φ is set at 3.7 (from Jiang, Sargent, Wang, and Yang, 2024) and assumed constant across countries.

### Macroeconomic factors (Section 2.2)
- Risk-free rate r: increases in r raise borrowing costs and reduce sustainable debt.
- Debt surge probability ζ̃: higher ζ̃ (exogenous probability of sudden debt surge) worsens fiscal challenges and reduces sustainable debt.
- Economic growth g: higher g raises sustainable debt by expanding the tax base.
- Hedging cost λ: reflects additional return investors demand for volatility; higher λ reduces sustainable debt.
- Convenience yield δ: higher δ lowers borrowing costs and increases sustainable debt.

### Limited commitment factors (Section 2.3)
- Default output cost (1−α): larger output loss from default makes default less attractive and increases sustainable debt.
- Default tax cost κ: higher κ increases losses post-default, discouraging default and increasing sustainable debt.

### Data and calibration (Section 3)
- Data sources: IMF WEO database for macro-fiscal variables and IMF Sovereign Debt Monitor database for sovereign yields.
- Fiscal calibration:
  - φ = 3.7 (from Jiang, Sargent, Wang, and Yang (2024)).
  - Tax capacity τ̄:
    - For AEs: set to generate a primary surplus of 5 percent of GDP (corresponds to the 95th percentile of primary balances among advanced economies during 2000-2024).
    - For EMs: τ̄ set to 5 percent.
    - For LICs: τ̄ set to 6.7 percent.
    - Alternative uniform nonbinding τ̄ typically 0.8 (reflects an 80% tax-to-GDP ratio) for highly constrained countries.
  - Government spending γ: calibrated using historical average general government expenditures during 2000-2024.
- Macroeconomic calibration:
  - Risk-free rate r: effective real interest rate of the U.S. government averaged over 2000–2029 → 0.9 percent.
  - Convenience yield δ:
    - δ = 0.5 percent for the United States, Japan, and Germany.
    - δ = 0.1 percent for all other countries.
  - Economic growth g (historical averages since 2000, Japan uses medium-term forecasts):
    - LICs: 4.3 percent
    - EMs: 3.5 percent
    - AEs: 2.1 percent
  - Standard deviations of growth (distributional volatility):
    - EMs: 1.82 percent
    - LICs: 1.84 percent
    - AEs: 1.11 percent
  - Output volatility used for hedging cost λ (country group averages):
    - AEs average: 1.6 percent
    - EMs average: 3.1 percent
    - LICs average: 3.3 percent
  - Debt surge probability ζ̃ calibrated via Pareto for episodes with change in debt-to-GDP > 10 percent:
    - LICs: 8.2 percent
    - EMs: 5.9 percent
    - AEs: 4.3 percent
- Limited commitment calibration:
  - Default tax cost κ = 1.3 (from Jiang, Sargent, Wang, and Yang (2024)).
  - Default output cost α:
    - For AEs with sovereign spread data, α estimated by matching model-implied debt and spreads to empirical moments.
    - Where spreads unavailable for AEs, α set at conservative benchmark of 5 percent.
  - Effective spreads for EMs and LICs calibrated as effective interest rate differential relative to U.S. effective interest rate.

### Representative parameter values cited
- α = 0.95
- φ = 3.7
- κ = 1.3
- r = 0.9%
- ζ̃ = 8.2%
- λ = 3.0%
- δ = 0.1%
- g = 4.3%

### Analytical intuition and mechanism
- Government trade-off: frontloading borrowing versus backloading taxation when convenience yield positive; continuation value may fall below default value, triggering default.
- Maximum sustainable debt b̄ depends on net fiscal space (τN − γ) and an effective discounting term r + ζ̃ + λ − δ − g at the default threshold rather than the standard r − g.
- Tax capacity binding and tax distortion φ materially influence τN and hence b̄.

### Cross-Country Analysis (Section 4.1) — Key findings
- Sample: covers over 170 economies.
- Average maximum sustainable debt across countries in 2024:
  - AEs: about 124 percent of GDP
  - EMs: 76 percent of GDP
  - LICs: 57 percent of GDP
- In 2024, 54 out of 172 countries had debt levels already exceeding their estimated sustainable level; by 2029 this is projected to decline to 49 countries, holding the benchmark at the 2024 maximum sustainable debt estimates.
- Of the 54 countries with debt exceeding their sustainable level in 2024, 37 are projected to have a decline in debt by 2030.

### Drivers of cross-country differences
- Higher sustainable debt in AEs reflects:
  - Relatively stable financing conditions
  - Access to capital markets
  - High convenience yields for systemically important countries
  - Lower output volatility
  - Low probability of debt surge events
- EMs and LICs face:
  - Higher financing costs
  - Greater economic volatility
  - Higher likelihood of sudden debt surges from contingent liabilities
  - Despite higher average growth rates, these constraints limit maximum sustainable debt levels
- Many EMs and LICs have current debt levels close to estimated sustainable levels, implying limited fiscal space for additional borrowing.

### Summary statistics of selected parameters by country group (Table 1)
- Tax capacity, ̄τ (percent)
  - AEs: Mean48.99, Std. Dev14.82, 25th pct41.76, Median46.70, 75th pct54.38
  - EMs: Mean41.71, Std. Dev16.71, 25th pct30.94, Median36.89, 75th pct48.92
  - LICs: Mean39.87, Std. Dev25.24, 25th pct26.90, Median31.62, 75th pct45.25
- (1−Default cost) α (percent)
  - AEs: Mean95.42, Std. Dev1.03, 25th pct95.00, Median96.00, 75th pct96.00
  - EMs: Mean96.22, Std. Dev2.05, 25th pct94.00, Median96.17, 75th pct98.45
  - LICs: Mean95.69, Std. Dev1.06, 25th pct95.00, Median95.00, 75th pct96.79
- Spending/GDP γ (percent)
  - AEs: Mean39.34, Std. Dev8.50, 25th pct35.75, Median40.57, 75th pct45.16
  - EMs: Mean29.13, Std. Dev12.28, 25th pct21.77, Median26.50, 75th pct33.17
  - LICs: Mean22.91, Std. Dev15.32, 25th pct15.19, Median17.88, 75th pct24.81
- Hedging cost λ (percent)
  - AEs: Mean1.62, Std. Dev1.25, 25th pct0.75, Median1.21, 75th pct1.92
  - EMs: Mean3.09, Std. Dev3.01, 25th pct1.27, Median2.15, 75th pct3.43
  - LICs: Mean3.28, Std. Dev1.94, 25th pct1.82, Median2.73, 75th pct3.88
- GDP growth g (percent)
  - AEs: Mean2.12, Std. Dev1.11, 25th pct1.35, Median2.05, 75th pct2.83
  - EMs: Mean3.53, Std. Dev1.82, 25th pct2.27, Median3.39, 75th pct3.96
  - LICs: Mean4.29, Std. Dev1.84, 25th pct3.11, Median4.14, 75th pct5.67
- Parameter assumptions (selected)
  - r (Real risk-free rate, percent) Effective US rate: 0.9 for AEs, 0.9 for EMs, 0.9 for LICs
  - δ (Convenience yield, percent): 0.5 for USA, JPN, DEU; 0.1 others
  - φ (Tax distortion): Jiang, Sargent, Wang, and Yang (2024) value 3.7 for all groups
  - κ (Default tax cost): Jiang, Sargent, Wang, and Yang (2024) value 1.3 for all groups
  - ̃ζ (Debt surge probability, percent) Mean: AEs4.3, EMs5.9, LICs8.2

### Gaps to maximum sustainable debt by rating category (Table 2, LIC DSF)
- Rating # Countries Gap (percent)
  - Low 7 28.8
  - Medium 24 12.6
  - High 21 3.4
  - Distress 9 −44.0
- Note: The Gap is the difference between maximum sustainable debt and debt level. Source: IMF and World Bank.

### Gaps to maximum sustainable debt by MAC SRDSF indicators (Table 3)
- Long-term Assessment, Final Assessment: Low43.95, Moderate28.90, High16.66
- Medium-term Index/Risk Assessment, Mechanical Signal: Low46.04, Moderate20.67, High1.96
- Medium-term Index/Risk Assessment, Debt Fanchart, Mechanical Signal: Low73.62, Moderate33.09, High3.28
- Medium-term Index/Risk Assessment, Final Assessment: Low50.23, Moderate17.28, High2.38
- GFN, Mechanical Signal: Low44.50, Moderate16.91, High5.26
- Near-term Risk Assessment, Mechanical Signal: Low40.20, Moderate7.89, High-10.81
- Near-term Risk Assessment, Final Assessment: Low39.17, Moderate8.08, High-14.99
- Overall Risk of Sovereign Stress, Final Assessment: Low48.01, Moderate17.35, High-17.15
- Debt Stabilization in the Baseline (last 2 years), Mechanical Signal (0=No, 1=Yes): Low36.50, Moderate23.50
- Sustainability Assessment, Mechanical Signal (0=Sustainable with high probability, 1=Sustainable but not with high probability, 2=Unsustainable): 0:14.57, 1:-26.64, 2:-37.38
- Sustainability Assessment, Final Assessment (0=Sustainable with high probability, 1=Sustainable but not with high probability, 2=Unsustainable, 3=Sustainable): 0:36.29, 1:-24.22, 2:-24.19, 3:35.18
- Note: Values are simple averages of the gap between maximum sustainable debt and debt level, by rating group. Ratings are based on the latest MAC SRDSF assessments as of June 10, 2025.

### Model alignment with SRDSF and policy implications
- Alignment with SRDSF components:
  - Countries classified as “low risk” under the long-term assessment show an average positive debt gap of 44.0 percent of GDP, compared to 16.7 percent for those in the “high risk” category.
  - Near-term (Final Assessment): low risk gap 39.2 percent, high risk gap −15.0 percent.
  - Overall risk of sovereign stress: gap ranges from 48.0 percent (low risk) to −17.2 percent (high risk).
- Sustainability assessments coherence:
  - “Sustainable with high probability” (mechanical signal) average debt gap 14.6 percent
  - “Unsustainable” average debt gap −37.4 percent
- Policy implication:
  - Countries with debt levels close to or exceeding sustainable levels need fiscal adjustments to mitigate debt distress risk and preserve macroeconomic stability.

*Source: wpiea2025223-source-pdf (Sections 2–4).*

### Section 2 introduces the methodological framework. Section 3 details the calibration ap-

### wpiea2025223-source-pdf - Section 2 introduces the methodological framework. Section 3 details the calibration ap-

### Methodological framework (Section 2)
- Framework: adopts the theoretical framework in Jiang, Sargent, Wang, and Yang (2024) to assess the maximum sustainable level of debt.
- Integrates asset-pricing blocks: the risk-free rate, a convenience yield (lowers required returns on safe debt), and a jump-risk premium tied to disaster intensity and tail thickness.
- Nests and synthesizes prior approaches: Arrow one-period-ahead securities and GDP-indexed insurance (Shiller (1994), Barro (1979)); sovereign credit constraints (Eaton and Gersovitz (1981)); convenience yields on risk-free government debt (Krishnamurthy and Vissing-Jorgensen (2012)); uninsurable jump shocks to output.
- Model government features:
  - Output evolves via a geometric jump-diffusion process; some risks hedgeable via GDP-indexed insurance, others (sudden jumps) are not.
  - Collects distortionary taxes to fund exogenous expenditures.
  - Has a default option and benefits from convenience yields.
  - Balances marginal costs and benefits of public debt.
- Debt-to-GDP evolution (as given):
  - ḃt = γ − τ(bt) − g·bt + (r − δ + π(b/ b̄))·bt + λ·bt
  - Definitions in text: r: risk free rate; δ: convenience yield; π(b/ b̄) = ζ̃(b/ b̄)^ω where ζ̃ denotes Poisson arrival rate of jump shocks and ω governs fat-tailedness.
- Default threshold: derived by comparing value of continued servicing (raising distortionary taxes) versus default; tax distortion parameter φ captures deadweight loss from taxation; default costs include output loss α (output cost of default = 1−α) and default-related tax cost κ; maximum tax capacity may bind at τ̄.
- Equations (preserved as in source):
  - Optimal taxes: τN = min{ τ̄, 1/φ ( v/u u t 1 + 2φ 1−α+γ+ φκγ 2 2α ! −1 ) }  (2)
  - Max sustainable debt: b̄ = (τN − γ) / ( r + ζ̃ + λ − δ − g ); (3)
  - Note: at default threshold the term r + ζ̃ + λ − δ − g is distinct from the standard r − g.

### Fiscal factors (Section 2.1)
- Role of taxation:
  - Tax distortion parameter φ captures deadweight loss; higher φ reduces capacity to service debt.
  - Tax capacity τ̄ directly affects revenue collection and sustainable debt.
- Government spending γ:
  - Higher spending increases fiscal burden; may raise the debt limit if supported by sustainably higher future tax revenue.
  - If optimal taxes approach τ̄, debt limit constrained.
- Calibration note: φ is set at 3.7 (from Jiang, Sargent, Wang, and Yang, 2024) and assumed constant across countries.

### Macroeconomic factors (Section 2.2)
- Risk-free rate r: increases in r raise borrowing costs and reduce sustainable debt.
- Debt surge probability ζ̃: higher ζ̃ (exogenous probability of sudden debt surge) worsens fiscal challenges and reduces sustainable debt.
- Economic growth g: higher g raises sustainable debt by expanding the tax base.
- Hedging cost λ: reflects additional return investors demand for volatility; higher λ reduces sustainable debt.
- Convenience yield δ: higher δ lowers borrowing costs and increases sustainable debt.

### Limited commitment factors (Section 2.3)
- Default output cost (1−α): larger output loss from default makes default less attractive and increases sustainable debt.
- Default tax cost κ: higher κ increases losses post-default, discouraging default and increasing sustainable debt.

### Data and calibration (Section 3)
- Data sources: IMF WEO database for macro-fiscal variables and IMF Sovereign Debt Monitor database for sovereign yields.
- Fiscal calibration:
  - φ = 3.7 (from Jiang, Sargent, Wang, and Yang (2024)).
  - Tax capacity τ̄:
    - For AEs: set to generate a primary surplus of 5 percent of GDP (corresponds to the 95th percentile of primary balances among advanced economies during 2000-2024).
    - For EMs: τ̄ set to 5 percent.
    - For LICs: τ̄ set to 6.7 percent.
    - Alternative uniform nonbinding τ̄ typically 0.8 (reflects an 80% tax-to-GDP ratio) for highly constrained countries.
  - Government spending γ: calibrated using historical average general government expenditures during 2000-2024.
- Macroeconomic calibration:
  - Risk-free rate r: effective real interest rate of the U.S. government averaged over 2000–2029 → 0.9 percent.
  - Convenience yield δ:
    - δ = 0.5 percent for the United States, Japan, and Germany.
    - δ = 0.1 percent for all other countries.
  - Economic growth g (historical averages since 2000, Japan uses medium-term forecasts):
    - LICs: 4.3 percent
    - EMs: 3.5 percent
    - AEs: 2.1 percent
  - Standard deviations of growth (distributional volatility):
    - EMs: 1.82 percent
    - LICs: 1.84 percent
    - AEs: 1.11 percent
  - Output volatility used for hedging cost λ (country group averages):
    - AEs average: 1.6 percent
    - EMs average: 3.1 percent
    - LICs average: 3.3 percent
  - Debt surge probability ζ̃ calibrated via Pareto for episodes with change in debt-to-GDP > 10 percent:
    - LICs: 8.2 percent
    - EMs: 5.9 percent
    - AEs: 4.3 percent
- Limited commitment calibration:
  - Default tax cost κ = 1.3 (from Jiang, Sargent, Wang, and Yang (2024)).
  - Default output cost α:
    - For AEs with sovereign spread data, α estimated by matching model-implied debt and spreads to empirical moments.
    - Where spreads unavailable for AEs, α set at conservative benchmark of 5 percent.
  - Effective spreads for EMs and LICs calibrated as effective interest rate differential relative to U.S. effective interest rate.

### Representative parameter values cited (from Figure 1 note and calibration text)
- α = 0.95
- φ = 3.7
- κ = 1.3
- r = 0.9%
- ζ̃ = 8.2%
- λ = 3.0%
- δ = 0.1%
- g = 4.3%

### Analytical intuition and mechanism
- Government chooses between frontloading borrowing and backloading taxation when convenience yield positive; this can lead to default if continuation value falls below default value.
- Maximum sustainable debt b̄ depends on net fiscal space (τN − γ) and an effective discounting term r + ζ̃ + λ − δ − g at the default threshold rather than the standard r − g.
- Tax capacity binding and tax distortion φ materially influence τN and hence b̄.

### What follows (preview)
- Section 4 presents core empirical findings.
- Section 5 offers concluding remarks.
- Section 6 of Jiang, Sargent, Wang, and Yang (2024) provides detailed derivations referenced.

*Source: wpiea2025223-source-pdf (Sections 2–3).*

### 4.1  Cross-Country Analysis

### 4.1  Cross-Country Analysis

### Key Cross-Country Findings
- The analysis covers over 170 economies.
- Maximum sustainable debt varies significantly across countries and country groups.
- Across country groups, Advanced Economies (AEs) exhibit the highest sustainable debt levels, followed by Emerging Markets (EMs), and Low-Income Countries (LICs).
- The average maximum sustainable debt across countries in 2024:
  - AEs: about 124 percent of GDP
  - EMs: 76 percent of GDP
  - LICs: 57 percent of GDP
- In 2024, 54 out of 172 countries had debt levels already exceeding their estimated sustainable level; by 2029 this is projected to decline to 49 countries, holding the benchmark at the 2024 maximum sustainable debt estimates.
- Of the 54 countries with debt exceeding their sustainable level in 2024, 37 are projected to have a decline in debt by 2030.

### Drivers of Cross-Country Differences
- Higher sustainable debt in AEs reflects:
  - Relatively stable financing conditions
  - Access to capital markets
  - High convenience yields for systemically important countries
  - Lower output volatility
  - Low probability of debt surge events (e.g., recognition of contingent liabilities or government arrears)
- EMs and LICs face:
  - Higher financing costs
  - Greater economic volatility
  - Higher likelihood of sudden debt surges from contingent liabilities
  - Despite higher average growth rates, these constraints limit maximum sustainable debt levels
- Many EMs and LICs have current debt levels close to estimated sustainable levels, implying limited fiscal space for additional borrowing.

### Summary Statistics of Selected Parameters by Country Group (Table 1)
- Tax capacity, ̄τ (percent)
  - AEs: Mean48.99, Std. Dev14.82, 25th pct41.76, Median46.70, 75th pct54.38
  - EMs: Mean41.71, Std. Dev16.71, 25th pct30.94, Median36.89, 75th pct48.92
  - LICs: Mean39.87, Std. Dev25.24, 25th pct26.90, Median31.62, 75th pct45.25
- (1−Default cost) α (percent)
  - AEs: Mean95.42, Std. Dev1.03, 25th pct95.00, Median96.00, 75th pct96.00
  - EMs: Mean96.22, Std. Dev2.05, 25th pct94.00, Median96.17, 75th pct98.45
  - LICs: Mean95.69, Std. Dev1.06, 25th pct95.00, Median95.00, 75th pct96.79
- Spending/GDP γ (percent)
  - AEs: Mean39.34, Std. Dev8.50, 25th pct35.75, Median40.57, 75th pct45.16
  - EMs: Mean29.13, Std. Dev12.28, 25th pct21.77, Median26.50, 75th pct33.17
  - LICs: Mean22.91, Std. Dev15.32, 25th pct15.19, Median17.88, 75th pct24.81
- Hedging cost λ (percent)
  - AEs: Mean1.62, Std. Dev1.25, 25th pct0.75, Median1.21, 75th pct1.92
  - EMs: Mean3.09, Std. Dev3.01, 25th pct1.27, Median2.15, 75th pct3.43
  - LICs: Mean3.28, Std. Dev1.94, 25th pct1.82, Median2.73, 75th pct3.88
- GDP growth g (percent)
  - AEs: Mean2.12, Std. Dev1.11, 25th pct1.35, Median2.05, 75th pct2.83
  - EMs: Mean3.53, Std. Dev1.82, 25th pct2.27, Median3.39, 75th pct3.96
  - LICs: Mean4.29, Std. Dev1.84, 25th pct3.11, Median4.14, 75th pct5.67
- Parameter assumptions (selected)
  - r (Real risk-free rate, percent) Effective US rate: 0.9 for AEs, 0.9 for EMs, 0.9 for LICs
  - δ (Convenience yield, percent): 0.5 for USA, JPN, DEU; 0.1 others (table shows 0.5 / 0.1 and 0.1 0.1)
  - φ (Tax distortion): Jiang, Sargent, Wang, and Yang (2024) value 3.7 for all groups
  - κ (Default tax cost): Jiang, Sargent, Wang, and Yang (2024) value 1.3 for all groups
  - ̃ζ (Debt surge probability, percent) Mean: AEs4.3, EMs5.9, LICs8.2

### Gaps to Maximum Sustainable Debt by Rating Category (Table 2, LIC DSF)
- Rating # Countries Gap (percent)
  - Low 7 28.8
  - Medium 24 12.6
  - High 21 3.4
  - Distress 9 −44.0
- Note: The Gap is the difference between maximum sustainable debt and debt level. Source: IMF and World Bank.

### Gaps to Maximum Sustainable Debt by MAC SRDSF Indicators (Table 3)
- Long-term Assessment, Final Assessment: Low43.95, Moderate28.90, High16.66
- Medium-term Index/Risk Assessment, Mechanical Signal: Low46.04, Moderate20.67, High1.96
- Medium-term Index/Risk Assessment, Debt Fanchart, Mechanical Signal: Low73.62, Moderate33.09, High3.28
- Medium-term Index/Risk Assessment, Final Assessment: Low50.23, Moderate17.28, High2.38
- GFN, Mechanical Signal: Low44.50, Moderate16.91, High5.26
- Near-term Risk Assessment, Mechanical Signal: Low40.20, Moderate7.89, High-10.81
- Near-term Risk Assessment, Final Assessment: Low39.17, Moderate8.08, High-14.99
- Overall Risk of Sovereign Stress, Final Assessment: Low48.01, Moderate17.35, High-17.15
- Debt Stabilization in the Baseline (last 2 years), Mechanical Signal (0=No, 1=Yes): Low36.50, Moderate23.50
- Sustainability Assessment, Mechanical Signal (0=Sustainable with high probability, 1=Sustainable but not with high probability, 2=Unsustainable): 0:14.57, 1:-26.64, 2:-37.38
- Sustainability Assessment, Final Assessment (0=Sustainable with high probability, 1=Sustainable but not with high probability, 2=Unsustainable, 3=Sustainable): 0:36.29, 1:-24.22, 2:-24.19, 3:35.18
- Note: Values are simple averages of the gap between maximum sustainable debt and debt level, by rating group. Ratings are based on the latest MAC SRDSF assessments as of June 10, 2025.

### Model Alignment with SRDSF and Policy Implications
- The model-based maximum sustainable debt aligns closely with SRDSF components:
  - Countries classified as “low risk” under the long-term assessment show an average positive debt gap of 44.0 percent of GDP, compared to 16.7 percent for those in the “high risk” category.
  - Near-term (Final Assessment): low risk gap 39.2 percent, high risk gap −15.0 percent.
  - Overall risk of sovereign stress: gap ranges from 48.0 percent (low risk) to −17.2 percent (high risk).
- Sustainability assessments (Final Assessment) coherence:
  - “Sustainable with high probability” (mechanical signal) average debt gap 14.6 percent
  - “Unsustainable” average debt gap −37.4 percent
- Implication: The model captures systemic risks reflected in formal IMF debt sustainability diagnostics and can flag solvency concerns in vulnerable cases.
- Policy recommendation implied by results:
  - Countries with debt levels close to or exceeding sustainable levels need fiscal adjustments to mitigate debt distress risk and preserve macroeconomic stability.

*Source: Maximum Sustainable Debt Across Countries: An Assessment using P-Theory, Working Paper No. WP/2025/223.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025223-source-pdf.pdf_