## wp17117

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---

### I. Background and motivation
- In an era of high debt, low and uncertain growth and compressed global interest rates, the potential benefits of issuing instruments that better buffer against macroeconomic shocks are higher than ever.
- Average public debt in advanced economies has grown from a precrisis level of around 70 percent of GDP, to nearly 110 percent in 2016.
- Insuring against GDP and exchange rate volatility can substantially reduce risks to debt sustainability; insurance requires a premium, but low interest rates increase sovereigns’ capacity to pay and investors’ willingness to share macroeconomic risks.
- Types of instruments modeled:
  - Foreign currency denominated debt.
  - Local currency denominated debt (shields from nominal exchange rate movements).
  - Debt linked to GDP (adjusts in value with output shocks, stabilizing the debt-to-GDP ratio).
- Contribution relative to literature:
  - Incorporates currency composition and GDP-linked bonds into a sovereign default model with an endogenous credit risk premium and issuance premia for local currency and GDP-linked debt.
- Extensions and limitations:
  - Adds exchange rate shocks to growth and primary balance shocks.
  - Calibrated for representative countries in four groups: all countries, advanced economies, emerging markets, low-income countries.
  - Allows exploration of marginal impact of GDP-linked bond issuance.
  - Limitation: single-period bond setup cannot model maturity structure; maturity extension is an obvious next step.

### II. Model and key equations
- Debt dynamics (equation 1):
  - ∆푑푡 = (푟푡 − 푔푡) / (1+푔푡) . 푑푡 − 푝푏푡  (1)
  - where d_t is debt/GDP; r_t is real interest rate on debt; g_t is real GDP growth rate; pb_t is primary balance/GDP. All debt has one-year maturity.
- Fiscal reaction function (equation 2):
  - 푝푏푡 = min(훼 + 훽.푑푡, 훾) + 휀푡푝푏  (2)
- Sovereign bond return (equation 3):
  - (1+푟푡) = (1+푟∗) . (1−푝푡+1 . 휃) / (1−푝푡+1)  (3)
  - where p_{t+1} is probability of default next period; r* is risk-free rate; θ is recovery value on default.
- Debt dynamics with shocks and currency composition (equation 4):
  - ∆푑푡 = ( (1+푟∗).(1−푝푡+1.휃)/(1−푝푡+1) − 1 − 푔∗ + 휀푡푔 ). 푑푡/(1+푔∗+휀푡푔) + 푑푡 . 퐹푡 . 휀푡푒푟 − ( min(훼 + 훽.푑푡, 훾) + 휀푡푝푏 )  (4)
  - components: i) automatic debt dynamics (growth-interest differential and credit spread), ii) exchange rate shock impact proportional to foreign currency share F_t, iii) fiscal reaction and shocks.
- Debt limit and default probability (equations 5–6):
  - 푝푡+1 = 푝푟(푑푡+1 > 푑̅)  (5)
  - Fixed-point condition for debt limit 푑̅ (equation 6):
    - 푝푡+1 = Pr[ ( (1+푟∗).(1−푝푡+1.휃)/(1−푝푡+1) − 1 − 푔∗ + 휀푡푔 ). 푑̅ /(1+푔∗+휀푡푔) + 푑̅ . 퐹푡 . 휀푡푒푟 − ( min(훼 + 훽.푑̅, 훾) + 휀푡푝푏 ) ≥ 0 ]
    - The model solves numerically for the highest debt level at which default probability is below 1.
- Role of contract design:
  - Local currency bonds: adjusting F_t changes exposure to exchange rate shocks; creditors demand an exchange rate volatility premium r_{er}.
  - GDP-linked bonds: principal and coupon indexed to nominal GDP (following London Term Sheet design); as share of GDP-linked bonds increases, GDP shocks’ impact on debt-to-GDP ratio declines, and with all debt GDP-linked, GDP shocks do not affect debt-to-GDP.
  - Creditors charge a GDP volatility premium r_{gdp}. Premia are added to r* and are invariant through time and unrelated to debt level.

### III. Calibration and stylized facts
- Country groups and data:
  - Four groups: All Countries (ACs), Advanced Economies (AEs), Emerging Markets (EMs), Low-Income Countries (LICs).
  - Country group counts and observations:
    - All countries — All countries in the WEO database — 194 countries — 3,965 observations.
    - Advanced economies — As defined in the WEO database — 37 countries — 962 observations.
    - Emerging markets — All countries not designated as AEs or LICs — 79 countries — 1,566 observations.
    - Low income countries — PRGT-eligible countries as of 2015 — 73 countries — 1,415 observations.
- Key calibration elements:
  - Maximum primary balance (γ): 90th percentile of cyclically adjusted primary balances from fiscal consolidation episodes (Escolano et al., 2014).
  - Shocks (휀푡푔, 휀푡푝푏, 휀푡푒푟): from IMF WEO, demeaned; bootstrap simulations preserve contemporaneous correlations.
  - Steady-state growth g*: WEO long-run growth (1960–2015).
  - Share of foreign currency debt F_t: average share by country group from WEO.
  - Default recovery rate θ: 80 percent (calibrated from Cruces and Trebesch (2013) average face value haircut).
- Stylized calibration facts (Table 2 extract preserved):
  - Country GroupSteady state real growthg*Maximum primary balanceShare of foreign currency debtStDev - real growth shockStDev - primary balance shockStDev - exchange rate shockExchange rate volatility risk premiumReal GDP volatility risk premium
  - All countries3.36.0554.13.810.32.32.0
  - Advanced economies2.97.003.02.3n/a1n/a11.5
  - Emerging markets5.05.5504.43.99.91.92.1
  - Low income countries5.04.0704.24.610.22.32.0
  - 1 AEs are assumed to have no foreign currency denominated debt, so this shock does not apply
- Risk premia computation:
  - GDP and exchange rate volatility premiums computed using a certainty-equivalent framework with CRRA utility U(c) = 1/(1−δ) c^{1−δ}, δ = 2.
  - For each historical shock outturn, investor utility compared to utility from a guaranteed return to find the premium making the investor indifferent.
- Additional calibration notes:
  - ‘Preferred haircut’ methodology yields a median haircut around 30 percent (70 percent recovery) in present value terms, but the model uses an 80 percent recovery rate for consistency with one-period setup.

### IV. Baseline debt limits and drivers (percent of GDP)
- Baseline debt limits (defined as "the maximum sustainable debt level before a default occurs"):
  - All countries: 52
  - Advanced economies: 137
  - Emerging markets: 58
  - Low income countries: 40
- Key drivers of differences:
  - AEs can sustain a relatively high maximum primary surplus, raising their debt limit.
  - LICs: low maximum primary balance and much larger shocks reduce debt limits; higher trend growth raises the debt limit.
  - LICs and EMs: foreign currency denominated debt exposes them to exchange rate shocks, lowering their debt limits relative to AEs.
- Caveats:
  - These are averages for country groups.
  - The model does not capture concessional borrowing (especially by LICs).
  - No scope in the model for policies such as external emergency liquidity assistance, financial repression or monetary financing.
  - Endogenous interest rate reaction to default risk may not fully capture LICs’ debt dynamics due to limited access to commercial borrowing.

### V. Impact of moving to 100% local currency debt (percent of GDP)
- Debt limits with 100% local currency:
  - All countries: 78
  - Advanced economies: 137
  - Emerging markets: 98
  - Low income countries: 54
- Notable changes:
  - EMs: debt limit increases by 40 percentage points of GDP (a 70 percent increase relative to the baseline).
  - LICs: debt limit increases by 14 percentage points of GDP.

### VI. Impact of introducing GDP-linked bonds (shares of total debt; all scenarios assume 100% local currency)
- Scenarios considered: 20% GDP-linked, 50% GDP-linked, 100% GDP-linked.
- Debt limits under mixed instrument designs (percent of GDP):
  - All countries:
    - 100% local currency; 20% GDP linked: 80
    - 100% local currency; 50% GDP linked: 84
    - 100% local currency; 100% GDP linked: 84
  - Advanced economies:
    - 20% GDP linked: 152
    - 50% GDP linked: 175
    - 100% GDP linked: 238
  - Emerging markets:
    - 20% GDP linked: 106
    - 50% GDP linked: 120
    - 100% GDP linked: 140
  - Low income countries:
    - 20% GDP linked: 54
    - 50% GDP linked: 52
    - 100% GDP linked: 50
- Specific findings:
  - Modest issuance (20 percent of total debt) can significantly raise debt limits:
    - AEs: around 15 percentage points increase with 20% GDP-linked debt.
    - EMs: an 8 percentage point increase with 20% GDP-linked debt.
    - LICs: no change in the debt limit relative to the 100% local currency scenario when 20% is GDP-linked; higher GDP-volatility premium offsets benefits.
  - With 50% GDP-linked:
    - AEs: increase in the debt limit of around 40 percentage points.
    - EMs: increase of around 20 percentage points compared to the 100% local currency scenario.
  - Marginal effects can be diminishing or negative:
    - LICs: modest decrease in the debt limit when moving to full GDP-linked issuance due to GDP-risk premium effects.
    - EMs: maximum debt limit may occur below 100 percent GDP-linked coverage.
    - AEs: debt level continues to increase with the share of GDP-linked bonds, peaking at 100 percent coverage.

### VII. Sensitivity analysis on risk premia
- Exchange rate volatility risk premium analysis (relative to baseline debt level):
  - All countries: Risk premium 2.3; debt limit with 100% local currency 78; risk premium range (-/+2 %) 0.1-4.1; debt limit range (percent of GDP) 100-64; 'Break-even' risk premium (percent): 5.5
  - Emerging markets: Risk premium 1.9; debt limit with 100% local currency 98; risk premium range (-/+2 %) 0.0-3.9; debt limit range (percent of GDP) 138-78; 'Break-even' risk premium (percent): 6.0
  - Low income countries: Risk premium 2.3; debt limit with 100% local currency 54; risk premium range (-/+2 %) 1.0-5.0; debt limit range (percent of GDP) 82-42; 'Break-even' risk premium (percent): 5.1
- GDP volatility risk premium analysis (relative to baseline debt level):
  - All countries: Risk premium 2.0; debt limit with 100% local currency; 100% GDP linked 84; risk premium range (-/+2 %) 0.0-4.0; debt limit range (percent of GDP) 200-54; 'Break-even' risk premium (percent): 4.0
  - Advanced economies: Risk premium 1.5; debt limit with 100% local currency; 100% GDP linked 238; risk premium range (-/+2 %) 0.2-4.2; debt limit range (percent of GDP) 280-108; 'Break-even' risk premium (percent): 3.5
  - Emerging markets: Risk premium 2.1; debt limit with 100% local currency; 100% GDP linked 140; risk premium range (-/+2 %) 0.0-4.0; debt limit range (percent of GDP) 200-62; 'Break-even' risk premium (percent): 4.2
  - Low income countries: Risk premium 2.0; debt limit with 100% local currency; 100% GDP linked 50; risk premium range (-/+2 %) 0.0-4.0; debt limit range (percent of GDP) 134-34; 'Break-even' risk premium (percent): 3.0
- Interpretation:
  - The size of the GDP and exchange rate premium is a critical determinant of marginal changes in the debt limit.
  - Example: a 4 percentage point difference in the GDP risk premium for AEs implies a 170 percentage point difference in the debt limit.
  - The 'break even' risk premium shows the premium level that yields the same debt limit as the baseline (or the full local currency scenario for GDP risk premium); all risk premiums below the break-even increase the debt limit.

### VIII. Conclusions and policy implications
- No one-size-fits-all debt structure:
  - LICs: priority may be reducing exchange rate risk via local currency debt issuance and building institutions to raise the maximum sustainable primary balance. Intermediate steps (e.g., local currency inflation-linked bonds) may be needed due to "original sin" constraints.
  - EMs: once exchange rate risk is sufficiently reduced, GDP-linked bonds provide additional benefits.
  - AEs: largest beneficiaries; debt limits rise by 15 percentage points when GDP-linked bonds constitute one-fifth of the debt stock.
- Marginal properties of GDP-linked issuance:
  - For all economies combined, a quadratic relationship is observed between the share of GDP-linked bonds and the debt level, with the debt limit maximized at 80 percent of the total stock.
  - Sovereigns may prefer lower shares due to declining marginal benefits and other considerations.
- Additional considerations and risks:
  - Sovereign risk tolerance may favor lower debt limits to reduce debt service costs.
  - Potential unintended consequences of high GDP-linked bond shares:
    - Reduction in supply of 'safe' conventional assets.
    - Transfer of excessive risk to the private sector, potentially increasing business cycle volatility.
    - Increased risk of moral hazard or incentives to manipulate data by the sovereign.
  - Major uncertainty: risk premium demanded by investors for local currency and GDP-linked bonds; further research needed in absence of large-scale market issuance.
  - Suggested model extensions: incorporate long maturity debt; better capture policy frameworks (e.g., reserve currency issuers, currency union members).

*Source: wp17117 - selected section content as provided.*

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

### wp17117 - References .............................................................................................................

### I. BACKGROUND
- Context and motivation:
  - In an era of high debt, low and uncertain growth and compressed global interest rates, the potential benefits of issuing instruments that better buffer against macroeconomic shocks are higher than ever.
  - Average public debt in advanced economies has grown from a precrisis level of around 70 percent of GDP, to nearly 110 percent in 2016.
  - Insuring against GDP and exchange rate volatility can substantially reduce risks to debt sustainability; insurance requires a premium, but low interest rates increase sovereigns’ capacity to pay and investors’ willingness to share macroeconomic risks.
- Types of instruments modeled:
  - Foreign currency denominated debt.
  - Local currency denominated debt (shields from nominal exchange rate movements).
  - Debt linked to GDP (adjusts in value with output shocks, stabilizing the debt-to-GDP ratio).
- Contribution relative to literature:
  - Incorporates currency composition and GDP-linked bonds into a sovereign default model with an endogenous credit risk premium and issuance premia for local currency and GDP-linked debt.
  - Builds on balance-sheet models of currency crises (Krugman, 1999; Aghion and others, 1999; Jeanne and Zettelmeyer, 2002), maturity-structure literature (Sachs, 1984; Cole and Kehoe, 2000; Allen and others, 2002; IMF, 2000; IMF and World Bank, 2001; Borensztein and others, 2004; Abbas and others, 2014), and GDP-linked bond proposals (Krugman, 1988; Froot and others, 1989; Shiller, 1993, 2003; Barro, 1995; Borensztein and Mauro, 2004; Chamon and Mauro, 2005; Blanchard and others, 2016; Benford and others, 2016; Brooke and others, 2013).
- Extensions and limitations:
  - Adds exchange rate shocks to growth and primary balance shocks.
  - Calibrated for representative countries in four groups: all countries, advanced economies, emerging markets, low-income countries.
  - Allows exploration of marginal impact of GDP-linked bond issuance.
  - Limitation: single-period bond setup cannot model maturity structure; maturity extension is an obvious next step.

### II. MODEL
- Debt dynamics (equation 1):
  - ∆푑푡 = (푟푡 − 푔푡) / (1+푔푡) . 푑푡 − 푝푏푡  (1)
  - where d_t is debt/GDP; r_t is real interest rate on debt; g_t is real GDP growth rate; pb_t is primary balance/GDP. All debt has one-year maturity.
- Fiscal reaction function (equation 2):
  - 푝푏푡 = min(훼 + 훽.푑푡, 훾) + 휀푡푝푏  (2)
  - primary balance equals the minimum of the linear reaction function and a maximum primary balance γ, plus shock 휀푡푝푏.
- Sovereign bond return (equation 3):
  - (1+푟푡) = (1+푟∗) . (1−푝푡+1 . 휃) / (1−푝푡+1)  (3)
  - where p_{t+1} is probability of default next period; r* is risk-free rate; θ is recovery value on default.
- Debt dynamics with shocks and currency composition (equation 4):
  - ∆푑푡 = ( (1+푟∗).(1−푝푡+1.휃)/(1−푝푡+1) − 1 − 푔∗ + 휀푡푔 ). 푑푡/(1+푔∗+휀푡푔) + 푑푡 . 퐹푡 . 휀푡푒푟 − ( min(훼 + 훽.푑푡, 훾) + 휀푡푝푏 )  (4)
  - components: i) automatic debt dynamics (growth-interest differential and credit spread), ii) exchange rate shock impact proportional to foreign currency share F_t, iii) fiscal reaction and shocks.
- Debt limit and default probability (equations 5–6):
  - 푝푡+1 = 푝푟(푑푡+1 > 푑̅)  (5)
  - Fixed-point condition for debt limit 푑̅ (equation 6) given shocks and behavior:
    - 푝푡+1 = Pr[ ( (1+푟∗).(1−푝푡+1.휃)/(1−푝푡+1) − 1 − 푔∗ + 휀푡푔 ). 푑̅ /(1+푔∗+휀푡푔) + 푑̅ . 퐹푡 . 휀푡푒푟 − ( min(훼 + 훽.푑̅, 훾) + 휀푡푝푏 ) ≥ 0 ]  (6)
  - The model solves numerically for the highest debt level at which default probability is below 1.
- Role of contract design:
  - Local currency bonds: adjusting F_t changes exposure to exchange rate shocks; creditors demand an exchange rate volatility premium r_{er}.
  - GDP-linked bonds: principal and coupon indexed to nominal GDP (following London Term Sheet design); as share of GDP-linked bonds increases, GDP shocks’ impact on debt-to-GDP ratio declines, and with all debt GDP-linked, GDP shocks do not affect debt-to-GDP.
  - Creditors charge a GDP volatility premium r_{gdp}. Premia are added to r* and are invariant through time and unrelated to debt level.

### III. CALIBRATION
- Representative country groups and data:
  - Four groups: All Countries (ACs), Advanced Economies (AEs), Emerging Markets (EMs), Low-Income Countries (LICs).
  - Key calibration elements:
    - Maximum primary balance (γ): 90th percentile of cyclically adjusted primary balances from fiscal consolidation episodes (Escolano et al., 2014).
    - Shocks (휀푡푔, 휀푡푝푏, 휀푡푒푟): from IMF WEO, demeaned; bootstrap simulations preserve contemporaneous correlations.
    - Steady-state growth g*: WEO long-run growth (1960–2015).
    - Share of foreign currency debt F_t: average share by country group from WEO.
    - Default recovery rate θ: 80 percent (calibrated from Cruces and Trebesch (2013) average face value haircut).
- Country group definition counts:
  - All countries — All countries in the WEO database — 194 countries — 3,965 observations. Note: Time span of annual data varies by country, with an average of 20 years.
  - Advanced economies — As defined in the WEO database — 37 countries — 962 observations.
  - Emerging markets — All countries not designated as AEs or LICs — 79 countries — 1,566 observations.
  - Low income countries — PRGT-eligible countries as of 2015 — 73 countries — 1,415 observations.
- Stylized calibration facts (Table 2 summary as presented):
  - Table extract (preserve formatting and numbers as in source):
    - Country GroupSteady state real growthg*Maximum primary balanceShare of foreign currency debtStDev - real growth shockStDev - primary balance shockStDev - exchange rate shockExchange rate volatility risk premiumReal GDP volatility risk premium
    - All countries3.36.0554.13.810.32.32.0
    - Advanced economies2.97.003.02.3n/a1n/a11.5
    - Emerging markets5.05.5504.43.99.91.92.1
    - Low income countries5.04.0704.24.610.22.32.0
    - 1 AEs are assumed to have no foreign currency denominated debt, so this shock does not apply
- Risk premia computation:
  - GDP and exchange rate volatility premiums are computed using a certainty-equivalent framework with CRRA utility U(c) = 1/(1−δ) c^{1−δ}, δ = 2.
  - For each historical shock outturn (Figures A1–A12), investor utility is compared to utility from a guaranteed return to find the premium that makes the investor indifferent.
  - Higher standard deviation of growth or exchange rates implies a higher premium on these instruments.
- Additional calibration notes:
  - The ‘preferred haircut’ methodology yields a median haircut around 30 percent (70 percent recovery) in present value terms, but the model uses an 80 percent recovery rate for consistency with one-period setup. Lowering recovery reduces baseline debt limit but relative impacts of debt structures remain similar.

*Source: wp17117 - References (IMF working paper content provided).*

### 26.      Table 3 shows the ‘baseline’ debt limit, derived by this model, for a representative

### wp17117 - 26.      Table 3 shows the ‘baseline’ debt limit, derived by this model, for a representative

### Baseline debt limits by country group
- The baseline debt limit is defined as "the maximum sustainable debt level before a default occurs."
- Baseline debt limits (percent of GDP):
  - All countries: 52
  - Advanced economies: 137
  - Emerging markets: 58
  - Low income countries: 40
- Key drivers of differences:
  - AEs can sustain a relatively high maximum primary surplus, raising their debt limit.
  - LICs: low maximum primary balance and much larger shocks reduce debt limits; higher trend growth raises the debt limit.
  - LICs and EMs: foreign currency denominated debt exposes them to exchange rate shocks, lowering their debt limits relative to AEs.
- Caveats noted in the source:
  - These are averages for country groups.
  - The model does not capture concessional borrowing (especially by LICs).
  - No scope in the model for policies such as external emergency liquidity assistance, financial repression or monetary financing.
  - Endogenous interest rate reaction to default risk may not fully capture LICs’ debt dynamics due to limited access to commercial borrowing.

### Impact of moving to 100% local currency denominated debt
- Moving towards full local currency debt raises debt limits for all country groups (AEs are assumed to already have full local currency debt).
- Debt limits with 100% local currency (percent of GDP):
  - All countries: 78
  - Advanced economies: 137
  - Emerging markets: 98
  - Low income countries: 54
- Notable changes and interpretation:
  - EMs: debt limit increases by 40 percentage points of GDP (a 70 percent increase relative to the baseline). This indicates exchange rate shocks are a significant solvency risk for EMs.
  - LICs: debt limit increases by 14 percentage points of GDP. The absolute and relative impact is less than for EMs because growth and primary balance shocks remain important risks.

### Impact of introducing GDP-linked bonds (shares of total debt)
- Scenarios considered: 20% GDP-linked, 50% GDP-linked, 100% GDP-linked (all with 100% local currency).
- Debt limits under mixed instrument designs (percent of GDP):
  - All countries:
    - 100% local currency; 20% GDP linked: 80
    - 100% local currency; 50% GDP linked: 84
    - 100% local currency; 100% GDP linked: 84
  - Advanced economies:
    - 20% GDP linked: 152
    - 50% GDP linked: 175
    - 100% GDP linked: 238
  - Emerging markets:
    - 20% GDP linked: 106
    - 50% GDP linked: 120
    - 100% GDP linked: 140
  - Low income countries:
    - 20% GDP linked: 54
    - 50% GDP linked: 52
    - 100% GDP linked: 50
- Specific findings:
  - Even modest issuance (20 percent of total debt) can significantly raise debt limits:
    - AEs: around 15 percentage points increase in the debt limit with 20% GDP-linked debt—enough to accommodate the median fiscal costs of a systemic banking crisis.
    - EMs: an 8 percentage point increase—substantial and enough to accommodate additional borrowing through a typical recession.
    - LICs: no change in the debt limit relative to the 100% local currency scenario when 20% is GDP-linked; higher interest costs (GDP-volatility premium) offset benefits from reduced GDP shock.
  - With 50% GDP-linked:
    - AEs: increase in the debt limit of around 40 percentage points (enough to accommodate all but the worst tail-events).
    - EMs: increase of around 20 percentage points of GDP compared to the 100% local currency scenario.
  - Marginal effects can be diminishing or negative:
    - LICs: modest decrease in the debt limit when moving to full GDP-linked issuance; the GDP-risk premium lowers the debt level more than reduced GDP volatility raises it.
    - EMs: maximum debt limit may occur below 100 percent GDP-linked coverage.
    - AEs: debt level continues to increase with the share of GDP-linked bonds, peaking at 100 percent coverage.

### Sensitivity analysis on risk premiums
- Exchange rate volatility risk premium analysis (relative to baseline debt level):
  - Risk premium, debt limit with 100% local currency, risk premium range (-/+2 %), debt limit range (percent of GDP), 'Break-even' risk premium (percent):
    - All countries: 2.3; 78; 0.1-4.1; 100-64; 5.5
    - Emerging markets: 1.9; 98; 0.0-3.9; 138-78; 6.0
    - Low income countries: 2.3; 54; 1.0-5.0; 82-42; 5.1
- GDP volatility risk premium analysis (relative to baseline debt level):
  - Risk premium, debt limit with 100% local currency; 100% GDP linked, risk premium range (-/+2 %), debt limit range (percent of GDP), 'Break-even' risk premium (percent):
    - All countries: 2.0; 84; 0.0-4.0; 200-54; 4.0
    - Advanced economies: 1.5; 238; 0.2-4.2; 280-108; 3.5
    - Emerging markets: 2.1; 140; 0.0-4.0; 200-62; 4.2
    - Low income countries: 2.0; 50; 0.0-4.0; 134-34; 3.0
- Interpretation:
  - The size of the GDP and exchange rate premium is a critical determinant of marginal changes in the debt limit.
  - Example: a 4 percentage point difference in the GDP risk premium for AEs implies a 170 percentage point difference in the debt limit.
  - The 'break even' risk premium shows the premium level that yields the same debt limit as the baseline (or the full local currency scenario for GDP risk premium); all risk premiums below the break-even increase the debt limit.

### Conclusions and policy implications
- No one-size-fits-all debt structure:
  - LICs: priority may be reducing exchange rate risk via local currency debt issuance and building institutions to raise the maximum sustainable primary balance. Intermediate steps (e.g., local currency inflation-linked bonds) may be needed due to "original sin" constraints.
  - EMs: once exchange rate risk is sufficiently reduced, GDP-linked bonds provide additional benefits.
  - AEs: largest beneficiaries; debt limits rise by 15 percentage points when GDP-linked bonds constitute one-fifth of the debt stock.
- Marginal properties of GDP-linked issuance:
  - For all economies combined, a quadratic relationship is observed between the share of GDP-linked bonds and the debt level, with the debt limit maximized at 80 percent of the total stock.
  - Sovereigns may prefer lower shares due to declining marginal benefits and other considerations.
- Additional considerations and risks:
  - Sovereign risk tolerance may favor lower debt limits to reduce debt service costs.
  - Potential unintended consequences of high GDP-linked bond shares:
    - Reduction in supply of 'safe' conventional assets.
    - Transfer of excessive risk to the private sector, potentially increasing business cycle volatility.
    - Increased risk of moral hazard or incentives to manipulate data by the sovereign.
  - Major uncertainty: risk premium demanded by investors for local currency and GDP-linked bonds; further research needed in absence of large-scale market issuance.
  - Suggested model extensions: incorporate long maturity debt; better capture policy frameworks (e.g., reserve currency issuers, currency union members) that influence nominal GDP control and debt-to-GDP dynamics.

*Source: wp17117 - selected section content as provided*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17117.pdf_