## 1. Bivariate Correlation of Interest Rates and Fiscal Variables

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### INTRODUCTION: objectives and scope
- Main objective: reassess the effect of fiscal deficits and public debt on long-term government bond yields, exploring nonlinear effects of large fiscal deterioration and initial fiscal conditions, the impact of countries’ institutional set up, and spillovers from global financial markets.
- Evidence summary: large deficits and debt can have a marked adverse impact on bond yields, but domestic and international factors determine the magnitude.
- Paper organization:
  - Section II: channels and existing findings.
  - Sections III–IV: econometric model, data, and descriptive statistics.
  - Section V: main empirical results.
  - Conclusion: policy implications.

### Channels of impact
- National savings channel:
  - Fiscal deficits (other things given) reduce national savings and increase aggregate demand, creating excess supply of government debt and raising real interest rates.
- Yield-curve and expectations:
  - Anticipation of continuing large fiscal deficits tends to steepen the yield curve; long-term rates likely to rise more in response to anticipated fiscal deterioration.
- Credit risk and contingent liabilities:
  - Large deficits and debt raise credit risk premia and government bond yields; contingent fiscal risks (for example, from the financial sector) can exacerbate sustainability concerns.
- Inflation expectations and monetization risk:
  - Higher inflation expectations increase nominal yields via higher inflation premia and macroeconomic uncertainty, raising country risk premia and fiscal solvency concerns.
- Behavioral considerations:
  - Ricardian equivalence: forward-looking private saving may rise in response to deficits, potentially reducing impact on interest rates; heterogeneous agents can cause short-run rises in interest rates but limited long-run impact.
- Openness and capital inflows:
  - In open economies, capital inflows can complement domestic savings, possibly causing real exchange rate appreciation rather than higher real interest rates; sustainability of financing by foreign savings is uncertain.
- Term-structure and monetary policy:
  - Short-term real rates reflect cyclical conditions and monetary policy; monetary responses to fiscal pressures can transmit to long-term rates via the term structure.

### Existing empirical findings and magnitudes
- Survey evidence: about one-half of ~60 studies found a “predominantly positive significant” effect of fiscal deficits on interest rates and the other half a “mixed” or “predominantly insignificant” effect.
- Typical magnitudes reported in literature:
  - An increase in deficits by 1 percent of GDP raises long-term interest rates by 30–60 basis points.
  - An increase in the debt-to-GDP ratio of 1 percentage point is associated with an increase in interest rates of between 2 and 7 basis points.
- Selected single- and cross-country findings preserved exactly:
  - Laubach (U.S. evidence): a percentage-point increase in projected deficit-to-GDP raises the 5-year-ahead 10-year-forward rate by 20–29 basis points; a percentage point increase in projected debt-to-GDP raises the forward rate by about 3–4 basis points.
  - Ardagna (OECD, 1960–2002): 10-year nominal yields increased by more than 180 basis points during years when the primary fiscal deficit widened by more than 1½ percent of GDP in one year or 1 percent of GDP per year in two consecutive years.
  - Thomas and Wu (U.S.): a 1 percent of GDP deterioration in the 5-year-ahead projected fiscal deficit raises long-term interest rates by 30–60 basis points.
  - Chinn and Frankel: estimated impact of 5 basis points for a similar fiscal shock (using current and projected public debt).
  - Ardagna, Caselli, and Lane (16 OECD countries): 1 percent of GDP deterioration in primary balance → increase in government bond yields by 10 basis points.
- Nonlinear and initial-condition effects:
  - For OECD countries, an increase in public debt affects bond yields significantly only when initial debt levels are above 60 percent of GDP.
- Financial globalization and global factors:
  - Greater access to foreign savings has helped keep long-term yields low in large advanced economies despite higher bond supply.
  - Long-term government bond yields in largest advanced economies have become increasingly dependent on global conditions, raising cross-country correlation of long-term yields over the last two decades.

### Model specification (baseline and augmentations)
- Baseline reduced-form panel model (31 advanced and emerging market economies, annual data 1980–2007):
  - r10Y_it = α_i + β1 rM_it + β2 π_it + δ1 b_it + δ2 D_it-1 + δ3 D^2_it-1 + ρ1 z_it-1 + ε_it
  - Definitions:
    - r10Y_it: nominal yields on 10-year government bonds for country i, period t (1980–2007).
    - rM: short-term nominal interest rate.
    - π: CPI inflation.
    - b: fiscal balance in percent of GDP.
    - D: level of gross general government debt in percent of GDP.
    - z: output growth.
- Estimation: fixed effects’ least squares estimates; alternative lagged dependent variable via system GMM produced similar overall effects.
- Alternative specifications:
  - Models using primary fiscal balance, change in debt in percent of GDP, and specification with average stock of debt D*_it.
- Stationarity and tests:
  - All variables stationary per Pesaran’s ADF test except public debt, which is I(1).
  - Standard Hausman test rejected random effects.
  - Results robust to residual serial correlation, heterogeneity deviations, and adding an index of global risk perception (VIX).
- Augmented specification with interaction term:
  - r10Y_it = α_i + β1 rM_it + β2 π_it + δ1 b_it + δ2 D_it-1 + δ3 D^2_it-1 + δ4 d_it * b_it + ρ1 z_it-1 + ε_it
  - Interaction allows fiscal balance effects to vary by country characteristic d (e.g., weak initial fiscal conditions, weak institutions, low domestic savings, limited access to global capital).

### Data and descriptive analysis
- Data sources:
  - Interest rates (annual): primarily IFS database; consistency checks with Bloomberg and World Bank’s Global Financial Dataset.
  - Fiscal and macroeconomic variables: IMF’s World Economic Outlook Database, supplemented by national sources.
  - Financial market indicators: annual averages of monthly Bloomberg data.
- Sample: all G20 countries plus other advanced and emerging economies with available data for 1980–2007 (data available for 2008 but excluded to eliminate the impact of the financial crisis; including 2008 does not significantly affect regression results).
- Simple bivariate correlations (selected exact entries preserved):
  - Nominal long-term interest rate on government bond (in percent) — correlation with Short-term Interest Rate (in percent): 0.87 (***)
  - Correlation of Nominal long-term interest rate with Interest rate on treasury bills (in percent): 0.97 (***)
  - Long term minus short term rate (in percent) correlation with Nominal long-term rate: -0.09 (**) and with Short-term rate: -0.29 (***)
  - Real long-term interest rate on government bonds (in percent) correlation with Nominal long-term rate: 0.38 (***)
  - Fiscal balance in percent of GDP correlation with Nominal long-term rate: -0.25 (***)
  - Public debt in percent of GDP correlation with Nominal long-term rate: -0.12 (***)
  - Primary fiscal balance in percent of GDP correlation with Nominal long-term rate: -0.04
- Trend plots (median data for 31 economies, 1980–2008):
  - Bond yields are residuals from regressions of nominal 10-year bond yields on short-term rates and inflation with country-specific fixed effects.
  - Gross public debt weakly correlated with adjusted long-term yields; correlation strengthens after the initial decade.
  - Adjusted bond yields correlate more strongly with overall fiscal balance; declines in deficits generally coincide with sharp falls in interest rates.
  - Strongest correlation observed between long-term rates and the adjusted primary fiscal balance.

### Baseline econometric model estimates (step one)
- Key quantitative findings (Table 2, dependent variable: 10-year Government Bond Yields):
  - An increase in the overall fiscal deficit of 1 percent of GDP pushes up bond yields by 17 basis points (Column 1).
  - Instrumental variable estimation yields similar significance.
  - Using an “expected fiscal balance” indicator suggests about 20 basis points increase in bond yields for each 1 percent of GDP deterioration.
  - Change in public debt: a 1 percentage point increase in the debt ratio leads to an increase in bond yields of around 5 basis points.
  - Initial public debt has a statistically significant impact with varying size over time.
- Other baseline variable effects:
  - Short-term interest rate coefficient about 0.69–0.73 (statistically significant): "higher inflation expectations increasing short-term monetary policy rates in turn raise long-term bond yields by almost 70 basis points for each 100 basis point rate increase."
  - Inflation additional effect: small positive coefficients (e.g., 0.09*, 0.13** in columns).
  - Initial GDP growth generally insignificant except when using primary balance: higher growth compresses yields.

### Real yield estimates and consistency checks
- Real 10-year Government Bond Yields (Table 3):
  - Impact of fiscal deficit on real yields: increase of 1 percent of GDP in the deficit raises real yields by about 30–34 basis points.
  - Change in public debt in real-rate regressions: example coefficient 19.55** (Column 3).
- Consistency between deficit and debt elasticities:
  - Deficit elasticity using nominal rates ~20 basis points per 1 percentage point of GDP.
  - Deficit elasticity using real rates ~30 basis points per 1 percentage point of GDP.
  - Debt elasticity empirically estimated in range 3–5 basis points.
  - Identity b = -g/(1+g) d with g = nominal GDP growth (9.6 percent median; about 14 percent average in sample) implies a 1 percent of GDP increase in deficit results in permanent debt increase about 10 percent of GDP for the median country and about 8 percent for the average country; comparable implied debt elasticities about 2–4 basis points (nominal) and 3–4 basis points (real), consistent with regression-based 3–5 bps.
- Simulations (Table 3 model used):
  - For a permanent deterioration of overall balance by 1 percentage point of GDP over 50 years, real interest rate elasticity to 1 percent of GDP increase in debt about 3–4 basis points.

### Nonlinearities and country characteristics (step two; interaction results)
- High initial deficit:
  - A deficit above 2 percent of GDP prior to fiscal worsening raises impact on bond yields by an additional 14 basis points for each percent of GDP larger current-period deficit.
- High initial public debt:
  - Initial debt levels above 60 percent of GDP add about 6 basis points to the baseline effect of an increase in fiscal deficits.
- Large fiscal expansions:
  - Expansions above 1½ percent of GDP amplify effects.
- Institutional quality and private savings:
  - Weaker institutions (higher political risk) increase impact of fiscal deterioration by about 10 basis points.
  - Low private savings: in countries with private domestic savings lower than 10 percent of GDP, bond yields rise significantly more—by as much as 50 basis points for one percentage point of GDP increase in the deficit ratio.
- Global and market conditions:
  - High FDI (annual FDI higher than 10 percent of GDP) reduces the impact of a 1 percentage point of GDP deficit increase by about 5 basis points.
  - Global Bond Supply (average gross financing needs above 20 percent of GDP) raises the impact of a 1 percent of GDP deficit increase by an additional 10 basis points.
  - Financial Market Volatility (VIX index above 25) adds about 7 basis points to the impact of a 1 percent of GDP deficit increase.
  - High Fed Rates (US Fed rate above 4 percent) add about 13 basis points to the impact.
- Population aging:
  - Fast Population Aging (growth above 1 percent in the share of the population aged 65 or more) increases bond-yield response by about 10 basis points per 1 percent of GDP deficit increase.
- Robustness using real interest rates:
  - High-deficit countries: 1 percent of GDP increase in deficits raises real interest rates by about 30 basis points (vs. 20 bps for nominal).
  - High initial debt (above 80 percent of GDP): 1 percent increase in deficit raises real interest rates by about 30 basis points (an additional ~2 bps vs. lower-debt countries).
  - Fast population aging: elasticity of real interest rates to a 1 percent increase in deficit is 15 basis points higher than in slower-aging countries.
  - High financial market volatility: a 1 percent of GDP deficit increase raises real rates by almost 8 basis points more than in normal times.

### Quantitative policy-relevant scenarios and simulations
- Baseline elasticity: 20 basis points increase in long-term interest rates for each 1 percentage point of GDP increase in the fiscal deficit.
- Illustration: a 5 percentage points of GDP increase in the fiscal deficit could raise long-term interest rates by 100 basis points under baseline.
- Compound adverse conditions (unfavorable initial fiscal conditions, weak institutions, elevated global risk aversion) could raise the impact of 1 percentage point deficit to above 50 basis points (equivalent to a calculated debt elasticity of 5–6 basis points).
- Debt-service cost simulations (Figure 7) using IMF projections for debt in 2010 vs 2007 and estimated elasticities:
  - Advanced G-20 countries: given average increase in debt of about 20 percent of GDP, debt service costs likely to increase by more than 1½ percent of GDP.
  - Emerging markets: markedly lower impact given smaller debt increases, despite higher elasticities, assuming no pronounced spillovers from advanced economies.

### Conclusions and policy implications
- Main conclusions:
  - Impact of fiscal deterioration on long-term interest rates is significant, robust, and nonlinear.
  - Magnitude reflects initial fiscal, institutional and structural conditions, and global market spillovers.
  - Findings help explain diversity in literature by incorporating interacting variables.
- Policy implications and recommended actions:
  - Appropriate policy response is essential to contain upward pressure on interest rates over the medium term, especially in advanced economies.
  - Credible fiscal consolidation strategies that reduce uncertainty about sustainability can help cut borrowing costs for governments with large debt levels.
  - Entitlement reforms that reduce spending growth (e.g., for pensions) and tackle cost-inflation in health care services can play a key role.
  - Measures to ensure continued access to global savings and underpin investor risk appetite by anchoring medium-term expectations of fiscal sustainability and supporting economic growth can restrain the rise in long-term interest rates.
  - Strengthening fiscal frameworks:
    - Fiscal rules with a medium-term orientation and political commitment can buttress fiscal consolidation strategies and credibility.
    - Improving institutional quality and establishing independent fiscal agencies to provide objective analysis can be useful while leaving fiscal policy to elected representatives.
  - Structural reforms to stimulate economic growth can support fiscal adjustment by enhancing revenue mobilization and thereby restrain increases in long-term interest rates and debt-servicing costs.

### Appendix: countries and key dummy definitions
- Countries in sample (31): Australia; Austria; Belgium; Brazil; Bulgaria; Canada; Colombia; Denmark; Finland; France; Germany; Greece; Ireland; Italy; Japan; Korea; Malaysia; Mexico; Netherlands; Norway; Philippines; Portugal; South Africa; Spain; Sweden; Switzerland; Thailand; Turkey; United Kingdom; United States; Venezuela, Bolivarian Rep.
- Appendix Table 2 — Definition of Dummy Variables (exact definitions preserved):
  - Large Initial Fiscal Deficit: Fiscal deficit above 2 percent of GDP in the previous year
  - High Initial Debt: General government debt above 60 percent of GDP in the previous year
  - Large Fiscal Expansion: Reduction in the primary fiscal balance above 1.5 percent of GDP in the previous year
  - Fast Population Aging: Growth above 1 percent in the share of the population aged 65 or more
  - Quality of Institutions: ICRG political risk index above sample average
  - Low Private Savings: Private domestic savings lower than 10 percent of GDP
  - High FDI: Annual FDI higher than 10 percent of GDP
  - Global Bond Supply: Average gross financing needs above 20 percent of GDP
  - Financial Market Volatility: VIX index above 25
  - High Fed Rates: US Fed rate above 4 percent

*Source: _wp10184 (IMF PDF content unit).*

### 1. Bivariate Correlation of Interest Rates and Fiscal Variables ...............................................11

### 1. Bivariate Correlation of Interest Rates and Fiscal Variables

### Major sections
- 1. Bivariate Correlation of Interest Rates and Fiscal Variables ...............................................11
- 2. Impact of Deficits and Debt on Long-term Interest Rates ...................................................14
- 3. Impact of Deficits and Debt on Long-term Real Interest Rates ...........................................16
- 4. Country Characteristics and Impact of Deficits and Debt on Long-term Interest Rates .....18

### Figures listed
- Figure 1. Public Debt to GDP Ratio and Adjusted Long-Term Bond Yields .....................................12
- Figure 2. Fiscal Balance as a Ratio to GDP and Long-Term Bond Yields .........................................12
- Figure 3. Primary Fiscal Balance as a Ratio to GDP and Long-Term Bond Yields ...........................13
- Figure 4. Impact of Fiscal Balance on Bond Yields: Rolling Regression Coefficients ......................15
- Figure 5. Long-Term Bond Yields and Fiscal Balance .......................................................................19
- Figure 6. Impact of Fiscal Deficits and Country Features ..................................................................22
- Figure 7. Impact of Public Debt Increase on Debt Service .................................................................23

### Appendix and supplementary listings
- Appendix 1. List of Countries used in the Regressions ............................................................................24
- Appendix Tables
  - Appendix Table 1. Descriptive Statistics ............................................................................................................25
  - Appendix Table 2. Definition of Dummy Variables ..........................................................................................25
- References ................................................................................................................................26

*Source: _wp10184 - 1. Bivariate Correlation of Interest Rates and Fiscal Variables ...............................................11*

### INTRODUCTION

### _wp10184 - INTRODUCTION

### Introduction: objectives and scope
- Main objective: reassess the effect of fiscal deficits and public debt on long-term government bond yields, exploring nonlinear effects of large fiscal deterioration and initial fiscal conditions, the impact of countries’ institutional set up, and spillovers from global financial markets.
- Evidence summary: large deficits and debt can have a marked adverse impact on bond yields, but domestic and international factors determine the magnitude.
- Paper organization:
  - Section II: channels and existing findings.
  - Sections III–IV: econometric model, data, and descriptive statistics.
  - Section V: main empirical results.
  - Conclusion: policy implications.

### Channels of impact
- National savings channel:
  - In the standard neoclassical model, fiscal deficits (other things given) reduce national savings and increase aggregate demand, creating excess supply of government debt and raising real interest rates.
- Yield-curve and expectations:
  - Anticipation of continuing large fiscal deficits tends to steepen the yield curve; long-term rates likely to rise more in response to anticipated fiscal deterioration.
- Credit risk and contingent liabilities:
  - Large deficits and debt, especially with uncertain economic pace, raise concerns about government’s ability to service debt, increasing credit risk premia and government bond yields.
  - Emergence of contingent fiscal risks (for example, from the financial sector) can exacerbate sustainability concerns.
- Inflation expectations and monetization risk:
  - Higher inflation expectations (particularly with positive output gaps or concerns about monetization of debt) can increase nominal yields via higher inflation premia and macroeconomic uncertainty, raising country risk premia and fiscal solvency concerns.
- Behavioral considerations:
  - Ricardian equivalence: forward-looking private saving may rise in response to deficits, potentially reducing impact on interest rates.
  - If taxes are nondistortionary and individuals are heterogeneous, debt accumulation can cause a short-run rise in interest rates but may not have a pronounced long-run impact on bond yields.
- Openness and capital inflows:
  - In open economies, capital inflows can complement domestic savings, possibly causing real exchange rate appreciation rather than higher real interest rates; sustainability of financing by foreign savings is uncertain.
- Term-structure and monetary policy:
  - Short-term real rates reflect cyclical conditions and monetary policy; monetary responses to fiscal pressures can transmit to long-term rates via the term structure.

### Existing empirical findings and magnitudes
- Heterogeneity of findings across studies; earlier survey (Gale and Orszag, 2002): about one-half of ~60 studies found a “predominantly positive significant” effect of fiscal deficits on interest rates and the other half a “mixed” or “predominantly insignificant” effect.
- Typical magnitudes reported in literature:
  - An increase in deficits by 1 percent of GDP raises long-term interest rates by 30–60 basis points.
  - An increase in the debt-to-GDP ratio of 1 percentage point is associated with an increase in interest rates of between 2 and 7 basis points.
- Studies emphasizing expected deficits or projected fiscal variables generally find larger effects:
  - Expected/projected deficits often yield stronger estimated impacts than contemporaneous stock variables.
  - Laubach (U.S. evidence): a percentage-point increase in projected deficit-to-GDP raises the 5-year-ahead 10-year-forward rate by 20–29 basis points; a percentage point increase in projected debt-to-GDP raises the forward rate by about 3–4 basis points.
  - Ardagna (OECD, 1960–2002): 10-year nominal yields increased by more than 180 basis points during years when the primary fiscal deficit widened by more than 1½ percent of GDP in one year or 1 percent of GDP per year in two consecutive years.
  - Thomas and Wu (U.S.): a 1 percent of GDP deterioration in the 5-year-ahead projected fiscal deficit raises long-term interest rates by 30–60 basis points.
  - Chinn and Frankel (using current and projected public debt): estimated impact of 5 basis points for a similar fiscal shock.
- Cross-country vs. single-country differences:
  - Cross-country estimates often smaller (e.g., Ardagna, Caselli, and Lane: 1 percent of GDP deterioration in primary balance → increase in government bond yields by 10 basis points for 16 OECD countries).
  - Heterogeneity may arise from institutional and structural differences not always modeled.
- Nonlinear and initial-condition effects:
  - Impact of public debt on yields depends on initial debt levels; higher public debt raises perception of reduced debt-servicing ability and inflation risk, producing nonlinear effects. For OECD countries, an increase in public debt affects bond yields significantly only when initial debt levels are above 60 percent of GDP.
- Currency-union and spread studies:
  - In monetary unions (or relative to a benchmark such as German bonds), increases in public debt have significant but small impacts on yields, and mainly in countries with high debt levels.
- Financial globalization and global factors:
  - Greater access to foreign savings has helped keep long-term yields low in large advanced economies despite higher bond supply.
  - Integration deepened price discovery and reduced home bias, potentially mitigating domestic crowding out.
  - Long-term government bond yields in largest advanced economies have become increasingly dependent on global conditions (global risk appetite, global savings, and investment), raising cross-country correlation of long-term yields over the last two decades.
  - Short-term nominal rates remain dominated by country-specific monetary policy divergence; transmission from short to long rates has been limited.

### Model specification
- Rationale: few previous studies combined nonlinear effects, initial conditions, institutional features, and spillovers simultaneously; this paper proposes a reduced-form model to account for these.
- Baseline reduced-form panel model (31 advanced and emerging market economies, annual data 1980–2007):
  - r10Y_it = α_i + β1 rM_it + β2 π_it + δ1 b_it + δ2 D_it-1 + δ3 D^2_it-1 + ρ1 z_it-1 + ε_it
  - Definitions:
    - r10Y_it: nominal yields on 10-year government bonds for country i, period t (1980–2007).
    - rM: short-term nominal interest rate (controls for monetary policy effects on term structure).
    - π: CPI inflation.
    - b: fiscal balance in percent of GDP.
    - D: level of gross general government debt in percent of GDP.
    - z: output growth (controls for cyclical position).
    - ε: error term.
  - Estimation: fixed effects’ least squares estimates.
- Alternative specifications and robustness:
  - Lagged dependent variable version estimated via system GMM to separate short- and long-run effects; overall effect similar to static model, with short-run impact of government deficits being less than one-third of the overall effect.
  - Also estimated models using primary fiscal balance and the change in debt in percent of GDP, and a specification with average stock of debt in year t (D*_it): r10Y_it = α_i + β1 rM_it + β2 π_it + δ1 D*_it + ρ1 z_it-1 + ε_it.
  - All variables stationary per Pesaran’s ADF test except public debt, which is I(1).
  - Standard Hausman test rejected random effects.
  - Results robust to residual serial correlation and heterogeneity deviations and robust to adding an index of global risk perception (VIX).
- Augmented specification with interaction term to capture differential impact by country characteristics:
  - r10Y_it = α_i + β1 rM_it + β2 π_it + δ1 b_it + δ2 D_it-1 + δ3 D^2_it-1 + δ4 d_it * b_it + ρ1 z_it-1 + ε_it
  - Interaction term d_it * b_it allows fiscal balance effects to vary by country characteristic d (e.g., weak initial fiscal conditions, weak institutions, low domestic savings, limited access to global capital).

### Factors likely to magnify fiscal impact on yields (hypotheses for interaction effects)
- Weak initial fiscal conditions.
- Weak or inadequate institutions.
- Structural factors such as low domestic savings.
- Limited access to global capital.
- Amplification during periods of global risk aversion and uncertainty.

### Data and descriptive analysis
- Data sources:
  - Interest rates (annual): primarily IFS database; consistency checks with Bloomberg and World Bank’s Global Financial Dataset.
  - Fiscal and macroeconomic variables: IMF’s World Economic Outlook Database, supplemented by national sources.
  - Financial market indicators: annual averages of monthly Bloomberg data.
- Sample: all G20 countries plus other advanced and emerging economies with available data for 1980–2007 (data available for 2008 but excluded to eliminate the impact of the financial crisis; including 2008 does not significantly affect regression results).

*Source: _wp10184 - INTRODUCTION (IMF PDF content unit).*

### 2008. Appendix 1 provides a list of the countries in the sample and the basic descriptive

### _wp10184 - 2008. Appendix 1 provides a list of the countries in the sample and the basic descriptive

### Simple correlations and descriptive findings
- Simple bivariate correlations indicate:
  - Overall fiscal balance is negatively correlated with nominal and real long-term yields, T-bill rate, and associated with a steeper term structure.
  - Results for primary fiscal balance and public debt are less robust or counterintuitive, implying other factors matter.
- Table 1 bivariate correlations (selected entries preserved exactly as in source):
  - Nominal long-term interest rate on government bond (in percent) — correlation with Short-term Interest Rate (in percent): 0.87 (***)
  - Correlation of Nominal long-term interest rate with Interest rate on treasury bills (in percent): 0.97 (***)
  - Long term minus short term rate (in percent) correlation with Nominal long-term rate: -0.09 (**) and with Short-term rate: -0.29 (***)
  - Real long-term interest rate on government bonds (in percent) correlation with Nominal long-term rate: 0.38 (***)
  - Fiscal balance in percent of GDP correlation with Nominal long-term rate: -0.25 (***)
  - Public debt in percent of GDP correlation with Nominal long-term rate: -0.12 (***)
  - Primary fiscal balance in percent of GDP correlation with Nominal long-term rate: -0.04
- Median data for 31 advanced and emerging economies over 1980–2008 used for trend plots; bond yields are residuals from regressions of nominal 10-year bond yields on short-term rates and inflation with country-specific fixed effects.

### Trends from figures and adjusted yields
- Figure 1 (Public Debt to GDP Ratio and Adjusted Long-Term Bond Yields):
  - Gross public debt tends to be weakly correlated with adjusted long-term bond yields; correlation strengthens after the initial decade when declines in public debt associate with downward trends in yields.
- Figure 2 (Fiscal Balance as a Ratio to GDP and Long-Term Bond Yields):
  - Adjusted bond yields correlate more strongly with the overall fiscal balance; large declines in deficits generally coincide with sharp falls in interest rates, with exceptions (mid-1990s).
- Figure 3 (Primary Fiscal Balance as a Ratio to GDP and Long-Term Bond Yields):
  - Strongest correlation observed between long-term rates and the adjusted primary fiscal balance, as primary balance is not affected by interest-rate-driven debt service changes.

### Baseline econometric model estimates (step one)
- Two-step approach: baseline reduced-form (equation [1]) omitting interaction terms, then equation [2] with interaction terms. Fiscal indicators: overall balance, primary balance, public debt (all percent of GDP).
- Key results (Table 2, dependent variable: 10-year Government Bond Yields):
  - An increase in the overall fiscal deficit of 1 percent of GDP pushes up bond yields by 17 basis points (Column 1).
  - Instrumental variable estimation (fiscal balance instrumented by its lagged values) yields similar significance.
  - Using an “expected fiscal balance” indicator suggests about 20 basis points increase in bond yields for each 1 percent of GDP deterioration.
  - Change in public debt: a 1 percentage point increase in the debt ratio leads to an increase in bond yields of around 5 basis points.
  - Initial public debt has a statistically significant impact with varying size over time.
- Other baseline variable effects:
  - Short-term interest rate coefficient about 0.69–0.73 (statistically significant): "higher inflation expectations increasing short-term monetary policy rates in turn raise long-term bond yields by almost 70 basis points for each 100 basis point rate increase."
  - Inflation additional effect: small positive coefficients (e.g., 0.09*, 0.13** in columns).
  - Initial GDP growth generally insignificant except when using primary balance: higher growth compresses yields.

### Real yield estimates and consistency checks
- Real 10-year Government Bond Yields (Table 3):
  - Impact of fiscal deficit on real yields: increase of 1 percent of GDP in the deficit raises real yields by about 30–34 basis points.
  - Change in public debt in real-rate regressions: change in public debt coefficient example 19.55** (Column 3).
- Consistency between deficit and debt elasticities:
  - Deficit elasticity using nominal rates ~20 basis points per 1 percentage point of GDP.
  - Deficit elasticity using real rates ~30 basis points per 1 percentage point of GDP.
  - Debt elasticity empirically estimated in range 3–5 basis points.
  - Using identity b = -g/(1+g) d with g = nominal GDP growth (9.6 percent median; about 14 percent average in sample) implies a 1 percent of GDP increase in deficit results in permanent debt increase about 10 percent of GDP for the median country and about 8 percent for the average country; comparable implied debt elasticities about 2–4 basis points (nominal) and 3–4 basis points (real), consistent with regression-based 3–5 bps.
- Simulations (Table 3 model used) for a permanent deterioration of overall balance by 1 percentage point of GDP over 50 years yield real interest rate elasticity to 1 percent of GDP increase in debt of about 3–4 basis points.

### Nonlinearities and country characteristics (step two; Table 4 and figures)
- Interaction results (selected findings preserved exactly):
  - High initial deficit: a deficit above 2 percent of GDP prior to fiscal worsening raises impact on bond yields by an additional 14 basis points for each percent of GDP larger current-period deficit.
  - High initial public debt: initial debt levels above 60 percent of GDP add about 6 basis points to the baseline effect of an increase in fiscal deficits.
  - Large fiscal adjustments (expansions) above 1½ percent of GDP amplify effects.
  - Institutional quality and private savings:
    - Weaker institutions (higher political risk) increase impact of fiscal deterioration by about 10 basis points.
    - Low private savings: in countries with low saving ratios, bond yields rise significantly more—by as much as 50 basis points for one percentage point of GDP increase in the deficit ratio.
  - Global and market conditions:
    - High foreign investment flows (above 10 percent of GDP) reduce the impact of a 1 percentage point of GDP deficit increase by about 5 basis points.
    - Higher global bond supply (measured by gross financing needs in the sample) raises the impact of a 1 percent of GDP deficit increase by an additional 10 basis points.
    - High financial market volatility (e.g., high VIX) adds about 7 basis points to the impact of a 1 percent of GDP deficit increase.
    - High Fed rates (above 4 percent) add about 13 basis points to the impact.
  - Population aging: faster population aging increases bond-yield response by about 10 basis points per 1 percent of GDP deficit increase.
- Robustness to use of real interest rates:
  - High-deficit countries: 1 percent of GDP increase in deficits raises real interest rates by about 30 basis points (vs. 20 bps for nominal).
  - High initial debt (above 80 percent of GDP): 1 percent increase in deficit raises real interest rates by about 30 basis points (an additional ~2 bps vs. lower-debt countries).
  - Fast population aging: elasticity of real interest rates to a 1 percent increase in deficit is 15 basis points higher than in slower-aging countries.
  - High financial market volatility: a 1 percent of GDP deficit increase raises real rates by almost 8 basis points more than in normal times.

### Quantitative policy-relevant scenarios and simulations
- Illustration of magnitudes:
  - Baseline elasticity: 20 basis points increase in long-term interest rates for each 1 percentage point of GDP increase in the fiscal deficit.
  - Example: a 5 percentage points of GDP increase in the fiscal deficit could raise long-term interest rates by 100 basis points under baseline.
  - Compound adverse conditions (unfavorable initial fiscal conditions, weak institutions, elevated global risk aversion) could raise the impact of 1 percentage point deficit to above 50 basis points (equivalent to a calculated debt elasticity of 5–6 basis points).
- Debt-service cost simulations (Figure 7):
  - Using IMF projections for debt in 2010 vs 2007 and estimated elasticities:
    - Advanced G-20 countries: given average increase in debt of about 20 percent of GDP, debt service costs likely to increase by more than 1½ percent of GDP.
    - Emerging markets: markedly lower impact given smaller debt increases, despite higher elasticities, assuming no pronounced spillovers from advanced economies.

### Conclusions and policy implications (preserving exact policy emphases)
- Main conclusions:
  - Impact of fiscal deterioration on long-term interest rates is significant, robust, and nonlinear.
  - Magnitude reflects initial fiscal, institutional and structural conditions, and global market spillovers.
  - Findings help explain diversity in literature by incorporating a wider set of interacting variables.
- Policy implications and recommended actions:
  - An appropriate policy response is essential to contain upward pressure on interest rates over the medium term, especially in advanced economies.
  - Credible fiscal consolidation strategies that reduce uncertainty about sustainability can help cut borrowing costs for governments with large debt levels.
  - Entitlement reforms that reduce spending growth (e.g., for pensions) and tackle cost-inflation in health care services can play a key role.
  - Measures to ensure continued access to global savings and underpin investor risk appetite by anchoring medium-term expectations of fiscal sustainability and supporting economic growth can restrain the rise in long-term interest rates.
  - Strengthening fiscal frameworks:
    - Fiscal rules with a medium-term orientation and political commitment can buttress fiscal consolidation strategies and credibility.
    - Improving institutional quality and establishing independent fiscal agencies to provide objective analysis can be useful while leaving fiscal policy to elected representatives.
  - Structural reforms to stimulate economic growth can support fiscal adjustment by enhancing revenue mobilization and thereby restrain increases in long-term interest rates and debt-servicing costs.

*Source: Authors’ calculations and analysis in _wp10184 (2008) — panel of 31 advanced and emerging market economies, 1980–2008 (figures and tables described are from the source text).*

### Appendix 1. List of Countries used in the Regressions

### Appendix 1. List of Countries used in the Regressions

### Countries
1. Australia  
2. Austria  
3. Belgium  
4. Brazil  
5. Bulgaria  
6. Canada  
7. Colombia  
8. Denmark  
9. Finland  
10. France  
11. Germany  
12. Greece  
13. Ireland  
14. Italy  
15. Japan  
16. Korea  
17. Malaysia  
18. Mexico  
19. Netherlands  
20. Norway  
21. Philippines  
22. Portugal  
23. South Africa  
24. Spain  
25. Sweden  
26. Switzerland  
27. Thailand  
28. Turkey  
29. United Kingdom  
30. United States  
31. Venezuela, Bolivarian Rep.

### Appendix Table 1. Descriptive Statistics — Key series and summary figures
- Nominal long-term interest rate on government bond (in percent): 79 89.0 96.3 46 9.7
- Short-term interest rate (in percent): 97 81 1.30 31.3 1277.1
- Interest rate on treasury bills (in percent): 69 311.38 13.54 119.0
- Long term minus short term rate (in percent): 54 81.01 1.49 147.3
- Real long-term interest rate on government bonds (in percent): 79 53.85 3.97 103.1
- Inflation (in percent): 128 19.19 13.56 147.5
- Fiscal balance in percent of GDP: 124 2 -0.03 0.05 171.8
- Public debt in percent of GDP: 94 258.48 28.70 49.1
- Primary fiscal balance in percent of GDP: 101 20.0 10.04 575.4
- Output growth rate (in percent): 132 23.33 3.69 110.8

### Appendix Table 2. Definition of Dummy Variables
- Large Initial Fiscal Deficit  
  - Fiscal deficit above 2 percent of GDP in the previous year
- High Initial Debt  
  - General government debt above 60 percent of GDP in the previous year
- Large Fiscal Expansion  
  - Reduction in the primary fiscal balance above 1.5 percent of GDP in the previous year
- Fast Population Aging  
  - Growth above 1 percent in the share of the population aged 65 or more
- Quality of Institutions  
  - ICRG political risk index above sample average
- Low Private Savings  
  - Private domestic savings lower than 10 percent of GDP
- High FDI  
  - Annual FDI higher than 10 percent of GDP
- Global Bond Supply  
  - Average gross financing needs above 20 percent of GDP
- Financial Market Volatility  
  - VIX index above 25
- High Fed Rates  
  - US Fed rate above 4 percent

*Source: Authors’ calculations.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10184.pdf_