## _wp12271

## Source details

**Canonical URL:** [_wp12271](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12271.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12271.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12271.pdf.json)

---

### I. Introduction — research question, method, and headline findings
- Research question: What factors affect the interest rate that governments pay to borrow in the long run?
- Methodological approach: panel cointegration methodology (pooled mean group, PMG) applied to a sample of 22 advanced economies over the period 1980-2010.
- Methodology advantages:
  - Allows coefficients of short-run factors to differ across countries, while the impact of long-run factors remains the same.
  - Allows sovereign borrowing costs to deviate from their long-run equilibrium levels and evaluates the extent of this deviation during the global financial crisis in Euro area countries.
- Main empirical findings:
  - In the long run, government bond yields increase by about 2 basis points in response to a 1 percentage point increase in the government debt-to-GDP ratio.
  - In the long run, government bond yields increase by about 45 basis points in response to a 1 percentage point increase in the potential growth rate.
  - About half of the deviation of sovereign bond yields from their long-run equilibrium adjusts in one year (average speed of adjustment: -0.45).
- Short-run findings (from a parsimonious model):
  - Changes in government bond yields respond to changes in the debt-to-GDP ratio, money market rate (monetary policy effect), and inflation (nominal shocks).
  - The impact of changes in the growth rate and the primary balance ratio is weaker in the short run.
- Caveat: short-run results are obtained from a very parsimonious model that does not account for some hard-to-quantify factors (for instance, policy uncertainty).

### II. Theoretical considerations and channels
- Long-run determinants emphasized:
  - Potential output growth and government debt are the two main determinants of long-run real government bond yields.
  - Representative Ramsey-model steady state expression: r = σg + θ (where g denotes real consumption growth, σ is the inverse of the intertemporal elasticity of substitution, and θ is the household’s rate of time preference). In an open economy, (1) would also include a foreign risk-free rate (r*) and exchange rate change for uncovered interest parity to hold.
- Channels through which government debt may affect real bond yields:
  - Crowding-out: fiscal expansion may crowd out private investment → lower steady-state capital stock → higher marginal product of capital → higher real interest rate.
  - Default risk premium: higher debt raises sovereign bond yields through increased default risk linked to the ratio of debt to the government’s income stream.
- Short-run influences: changes in the money market rate (monetary policy rate), unexpected inflation shocks, temporary changes in fiscal balances, and fluctuations of output growth around its potential level.

### III. Empirical evidence from existing studies (selected findings)
- Single-country estimates:
  - Engen and Hubbard (2004) and Laubach (2009): a 1 percentage point increase in the expected government debt-to-GDP ratio raises real long-term government bond yield by about 2-5 basis points (U.S. evidence).
  - Chinn and Frankel (2005) (1988-2004): reported impacts for a 1 percentage point increase in debt-to-GDP on real long-term yields:
    - Germany: 5-8 basis points
    - France, Italy, the U.K., Spain: 10-16 basis points
    - U.S.: 5 basis points (when 1988-2002 sample used; impact obscured when extended to 2004)
  - VAR studies (Plosser, 1987; Evans, 1987): do not find significant impact of unexpected fiscal changes on government bond yields.
- Panel estimates:
  - Kinoshita (2006): a 1 percentage point increase in debt-to-GDP raises real long-term yield by about 2-5 basis points (19 advanced economies).
  - Ardagna et al. (2007): linear specification → 0.6 basis point increase per 1 percentage point debt; non-linear specification → effect ranges from -2.4 basis points (minimum debt) to +3.8 basis points (maximum debt).
  - Conway and Orr (2002): effect varies with starting debt level (less than 1 basis point at 0 percent debt; about 2 basis points at 100 percent debt).
  - Faini (2006): panel estimation (10 euro area countries) → 1 percentage point increase in debt-to-GDP → about 3 basis points increase in long-term yields; greater sensitivity above 100 percent of GDP.
  - Baldacci and Kumar (2010): 1 percentage point increase in debt-to-GDP raises real long-term yield by about 0.8 basis points in G-20 economies (1980-2008).

### IV. Empirical methodology and data used in this study
- Estimator: pooled mean group (PMG) estimator of Pesaran et al. (1999), a panel error-correction model.
- Empirical specification:
  - Dependent variable: change in real bond yields (Δr).
  - Long-run determinants: potential growth rate and debt-to-GDP ratio (with interaction term Debt ratio*Dummy_EA to capture euro-area post-1999 dynamics).
  - Short-run determinants (ΔSR): changes in debt-to-GDP ratio, changes in the real money market rate (monetary policy effect), changes in inflation (nominal shocks), changes in the primary balance ratio, and changes in the growth rate.
  - Euro-area dummy (D_EA) takes value one during 1999-2010 for euro area countries.
- Data:
  - Sample: annual data for the period 1980-2010 for 22 advanced economies (some tests use 1980-2011 or restricted samples).
  - Sovereign borrowing costs: 10-year benchmark government bond yields (Datastream daily secondary market yields; annual averages).
  - Fiscal and macro variables from IMF’s World Economic Outlook Database.
- Panel unit root testing:
  - Tests used: Im-Pesaran-Shin, Fischer, Levin-Lin-Chu, Breitung, Hadri.
  - All tests support unit root for the debt-to-GDP ratio.
  - Mixed results for real bond yields (two tests support unit root) and potential growth rates (three tests support unit root).
  - Breitung and Hadri tests support unit root for all three variables, supporting use of panel cointegration.

### V. Estimation results — baseline and interpretation
- Long-run coefficients (baseline):
  - Debt-to-GDP ratio: long-run coefficient positive and significant; real bond yields rise by about 2 basis points per 1 percentage point increase in debt-to-GDP.
  - Potential growth: positive and significant; 1 percentage point higher potential growth leads to a 45 basis points average increase in real bond yields.
- Euro area effect:
  - The relationship between bond yields and long-run determinants weakened substantially in euro area countries after introduction of the euro in 1999.
  - Adding the euro-area dummy reduces the average coefficients: the average coefficient falls to 0.005 for the debt-to-GDP ratio and to -0.05 for the potential growth rate when the euro-area dummy is added (text summary).
- Speed of adjustment:
  - Speed of adjustment coefficient is negative and significant.
  - Average coefficient of -0.45 suggests almost half of the deviation of real bond yields from long-run equilibrium adjusts in one year.
- Short-run determinants (average effects reported):
  - Δ Debt ratio: 0.091***, 0.081***, 0.092*** (examples across specifications).
  - Δ Inflation: -0.141**, -0.159*, -0.160** (examples).
  - Δ Short-term real rate: 0.151***, 0.135***, 0.124*** (examples).
  - Changes in real growth rate and in primary balance ratio are generally not significant.
- Model fit and estimator validity:
  - Standard errors of residuals range between 1.52 and 1.58 (smaller than sample real-rate standard deviation 2.22).
  - Hausman test does not reject PMG estimator validity (Hausman p-values: 0.893, 0.902, 0.644 in reported columns), supporting common long-run coefficients across advanced economies.

### VI. Robustness checks and sample variations
- Excluding program countries (Greece, Ireland, Portugal): main conclusions remain unchanged.
- Adding reserve-currency dummies (U.S., Japan): long-run equilibrium real bond yields in these countries not significantly affected by reserve-currency status; qualitative impacts of other variables unchanged.
- Pre-crisis sample (ending 2007): long-run coefficients on debt-to-GDP and potential growth somewhat smaller before the crisis; short-run coefficient on changes in inflation turns insignificant in the pre-crisis sample.
- Robustness table highlights (examples):
  - Debt ratio long-run coefficients across specifications: 0.021***, 0.021***, 0.016**, 0.012**.
  - Potential growth long-run coefficients across specifications: 0.527***, 0.328**, 0.591***, 0.303**.
  - Debt ratio*Dummy_EA (1999-2009): -0.016***, -0.020***, -0.016***, -0.024***.
  - Speed of adjustment examples: -0.425***, -0.426***, -0.394***, -0.406***.
  - Observations and samples: examples include Observations: 390, 441, 441, 388; Countries: 19, 22, 22, 22; Hausman p-values: 0.93, 0.94, 1.00, 0.47; St. Dev. of residuals: 1.52, 1.53, 1.51, 1.52.

### VII. Evidence on market deviations, “underreaction” pre-crisis and “overreaction” post-crisis
- Model-based comparisons (Germany vs. other euro area countries, first half of 2012):
  - Some European periphery countries’ spreads (relative to Germany) exceeded equilibrium values implied by long-run and short-run fundamentals.
  - Several core euro area countries (e.g., Finland) exhibit spreads undershooting equilibrium due to “safe haven” effects.
  - Contrast with pre-crisis period (1999-2009): periphery spreads were lower than fundamentals implied (“underreaction” pre-crisis vs. “overreaction” post-crisis).
- Caveats:
  - Results derive from a very parsimonious model and do not account for factors likely contributing to temporary deviations (for instance, policy uncertainty).
  - Temporary market overreaction should not be interpreted as evidence against the effectiveness of fiscal adjustment.

### VIII. Key quantitative findings and selected model estimates
- Long-run responses reported in text and tables:
  - Increase by about 2 basis points in response to a 1 percentage point increase in government debt-to-GDP ratio.
  - Increase by about 45 basis points in response to a 1 percentage point increase in potential growth.
- Selected baseline PMG estimator examples (Table 4 highlights):
  - Debt ratio long-run coefficient examples: 0.014**, 0.021***, 0.025***.
  - Potential growth long-run coefficient examples: 0.649***, 0.322**, 0.393***.
  - Debt ratio*Dummy_EA (1999-2009): -0.010**, -0.020***, -0.016***.
  - Potential growth*Dummy_EA (1999-2009): -0.763***, -0.395***, -0.359**.
  - Speed of adjustment: -0.390***, -0.426***, -0.526***.
  - Short-run coefficients (averages): Δ Debt ratio 0.091***, 0.081***, 0.092***; Δ Inflation -0.141**, -0.159*, -0.160**; Δ Short-term real rate 0.151***, 0.135***, 0.124***.
  - Observations: 441; Countries: 22; Hausman p-values: 0.893, 0.902, 0.644; St. Dev. of residuals: 1.52, 1.53, 1.58.
- Robustness examples (Table 5 highlights):
  - Debt ratio long-run coefficients: 0.021***, 0.021***, 0.016**, 0.012**.
  - Potential growth long-run coefficients: 0.527***, 0.328**, 0.591***, 0.303**.
  - Short-run coefficients examples: Δ Debt ratio 0.074***, 0.081***, 0.082***, 0.082***; Δ Inflation -0.218**, -0.158*, -0.174**, -0.127; Δ Short-term real rate 0.121***, 0.136***, 0.127***, 0.153***.
  - Observations: 390, 441, 441, 388; Countries: 19, 22, 22, 22; Hausman p-values: 0.93, 0.94, 1.00, 0.47; St. Dev. of residuals: 1.52, 1.53, 1.51, 1.52.

### IX. Policy implications and recommendations
- Fiscal policy:
  - A steady pace of fiscal adjustment remains imperative for anchoring lower borrowing costs in the long run.
- Complementary measures:
  - Short-run departures of borrowing costs from long-run equilibrium should be addressed through policies aimed at reducing financial stress and market uncertainty.
- Interpretation guidance for policymakers:
  - Market overreaction during financial stress can cause temporary deviations from long-run equilibrium driven by herding behavior and increased risk aversion, not necessarily by fundamentals alone.
  - Policy responses should therefore combine credible fiscal adjustment with measures to reduce financial sector stress and policy uncertainty.

*Source: _wp12271 - IMF working paper content unit.*

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

### References

### I. INTRODUCTION
- Research question: What factors affect the interest rate that governments pay to borrow in the long run?
- Key methodological approach: panel cointegration methodology applied to a sample of 22 advanced economies over the period 1980-2010.
- Advantages of the methodology emphasized:
  - Allows coefficients of short-run factors to differ across countries, while the impact of long-run factors remains the same.
  - Allows sovereign borrowing costs to deviate from their long-run equilibrium levels and evaluates the extent of this deviation during the global financial crisis in Euro area countries.
- Main empirical findings (preserve numeric precision as stated):
  - In the long run, government bond yields increase by about 2 basis points in response to a 1 percentage point increase in the government debt-to-GDP ratio.
  - In the long run, government bond yields increase by about 45 basis points in response to a 1 percentage point increase in the potential growth rate.
  - About half of the deviation of sovereign bond yields from their long-run equilibrium adjusts in one year.
- Short-run findings:
  - Changes in government bond yields respond to changes in the debt-to-GDP ratio, money market rate (monetary policy effect), and inflation (nominal shocks).
  - The impact of changes in the growth rate and the primary balance ratio is weaker in the short run.
- Caveat: Short-run results are obtained from a very parsimonious model that does not account for some hard-to-quantify factors (for instance, policy uncertainty).

### II. DETERMINANTS OF SOVEREIGN BOND YIELDS: REVIEW OF EXISTING STUDIES

Heterogeneity of literature and methodological trade-offs
- Single-country studies: emphasize country-specific controls and relevant sample periods; limited by short time-series dimension.
- Panel data studies: improve statistical inference by expanding cross-sectional dimension; often impose homogeneity of slope coefficients (fixed effects), which may be restrictive.

A. Theoretical considerations
- Long-run real government bond yields depend on two main determinants: potential output growth and government debt.
- Representative expression from a Ramsey model steady state as presented:
  - r = σg + θ  (1)
    - where g denotes real consumption growth, σ is the inverse of the intertemporal elasticity of substitution, and θ is the household’s rate of time preference.
    - In an open economy, (1) would also include a foreign risk-free rate (r*) and exchange rate change for uncovered interest parity to hold.
- Channels through which government debt may affect real bond yields:
  - Crowding-out: fiscal expansion may crowd out private investment → lower steady-state capital stock → higher marginal product of capital → higher real interest rate (Engen and Hubbard, 2004).
  - Default risk premium: higher debt boosts sovereign bond yields through increased default risk linked to the ratio of debt to the government’s income stream (Manasse et al., 2003).
- Short-run influences on real government bond yields: changes in the money market rate (monetary policy rate), unexpected inflation shocks, temporary changes in fiscal balances, and fluctuations of output growth around its potential level.

B. Empirical evidence — selected findings (preserve numeric precision and quoted ranges)
- Single-country studies
  - Engen and Hubbard (2004) and Laubach (2009): a 1 percentage point increase in the expected government debt-to-GDP ratio raises real long-term government bond yield by about 2-5 basis points (U.S. evidence using CBO predicted fiscal variables).
  - Chinn and Frankel (2005): using 1988-2004 data for five European countries and the U.S., the impact of a 1 percentage point increase in the government debt-to-GDP ratio on real long-term government bond yields varies across countries; reported impacts range:
    - Germany: 5-8 basis points
    - France, Italy, the U.K., Spain: 10-16 basis points
    - U.S.: 5 basis points (when 1988-2002 sample used; impact obscured when extended to 2004)
  - Linde (2001) (Sweden, 1982-1996): results support that higher budget deficits induce higher sovereign borrowing costs.
  - VAR studies (Plosser, 1987; Evans, 1987): do not find that unexpected changes in fiscal variables have a significant impact on government bond yields, in contrast to static specifications.
- Panel data studies
  - Kinoshita (2006): using a panel of 19 advanced economies, a 1 percentage point increase in the government debt-to-GDP ratio raises the real long-term government bond yield by about 2-5 basis points.
  - Hauner and Kumar (2009): in the aftermath of the global financial crisis, upward pressures on yields from weakening budgetary positions were more than offset by foreign inflows driven by “safe-heaven” considerations; these effects are temporary and an upward correction in bond yields is predicted in the long run.
  - Ardagna et al. (2007): panel of 16 OECD countries (1960-2002) finds stock and flow fiscal variables matter; nonlinearities documented:
    - Linear specification: a 1 percentage point increase in the debt-to-GDP ratio → 0.6 basis point increase in long-term government bond yields.
    - Non-linear specification: the effect of a 1 percentage point increase in the debt-to-GDP ratio varies from a decrease of about 2.4 basis points for the minimum debt-to-GDP ratio in the sample to an increase of about 3.8 basis points for the maximum debt-to-GDP ratio in the sample.
  - Conway and Orr (2002): using seven OECD economies, a 1 percentage point increase in the debt-to-GDP ratio leads to:
    - less than 1 basis point increase in government bond yield starting from a 0 percent debt-to-GDP ratio,
    - about 2 basis points increase starting from a 100 percent debt-to-GDP ratio.
  - Faini (2006) (10 euro area countries, 1979-2002): public debt has no significant impact in individual country regressions, but in panel estimations a 1 percentage point increase in the debt-to-GDP ratio results in an increase of about 3 basis points in long-term government bond yields; borrowing costs of sovereigns with debt above 100 percent of GDP are more sensitive to changes in the debt-to-GDP ratio.
  - Baldacci and Kumar (2010): sample of 31 advanced and emerging economies (pre-crisis period 1980-2008), introducing debt-to-GDP ratios in linear and quadratic fashion; estimations suggest that a 1 percentage point increase in the government debt-to-GDP ratio raises the real long-term government bond yield by about 0.8 basis points in G-20 economies (both advanced and emerging).

- Methodological note on fixed effects (FE) vs. cointegration approach:
  - FE specification introduces country-specific intercepts but maintains homogeneity of slope coefficients across countries.
  - The panel cointegration methodology used in the present study formally tests whether the long-run relationship is common across advanced economies, while allowing heterogeneous short-run dynamics.

*Source: _wp12271 - References*

### 1.7 basis points in advanced G-20 economies. They also argue that the precise magnitude of

### _wp12271 - 1.7 basis points in advanced G-20 economies. They also argue that the precise magnitude of

### Key takeaways
- Most studies on advanced economies find empirical support that sovereign debt and other macroeconomic fundamentals have an impact on government bond yields.
- Pooling countries into a panel is sometimes instrumental to obtaining statistically significant results.
- The relationship between government bond yields and economic fundamentals may change over time; sensitivity of yields to government debt may increase when government debt reaches an unsustainably high level.
- Policy initiatives that reduce exchange rate risks and provide implicit bailout guarantees can change yield sensitivities; the introduction of the euro in 1999 is a notable example.
- The long-run relationship between bond yields and macroeconomic and fiscal determinants weakened during the crisis due to “safe-heaven” capital flows; such deviations are temporary and should be modeled as short-run factors, not confused with long-run determinants.

### Empirical methodology and data
- Methodology
  - Applied the pooled mean group (PMG) estimator of Pesaran et al. (1999), a panel data version of the error-correction model.
  - Empirical specification (equation (2)) models the change in real bond yields (Δr) with two long-run determinants: the potential growth rate and the debt-to-GDP ratio.
  - An interaction term with the EA dummy (D_EA) is included to account for interest rate convergence within the euro area following the introduction of the common currency (it takes the value of one during the period 1999-2010 for euro area countries).
  - Up to five short-run determinants (ΔSR) are included: changes in the debt-to-GDP ratio, changes in the real money market rate (monetary policy effect), changes in inflation (nominal shocks), changes in the primary balance ratio (short-term fiscal policy), and changes in the growth rate (cyclical fluctuations).
  - PMG advantages:
    - Differentiates between long-run (β) and short-run (δ_i) determinants.
    - Pools long-run coefficients to improve statistical inference while allowing country-specific short-run coefficient variation.
    - Can be tested against the mean-group (MG) estimator using the Hausman test; if PMG poolability restrictions are not rejected, statistical support exists for long-run coefficient homogeneity.
- Data
  - Sample: annual data for the period 1980-2010 for 22 advanced economies.
  - Sovereign borrowing costs measured by 10-year benchmark government bond yields from daily secondary market bond yields in Datastream; annual averages calculated for each country.
  - Fiscal and macroeconomic variables from the IMF’s World Economic Outlook Database.
  - Panel unit root tests applied to real bond yields, debt-to-GDP ratios, and potential growth rate variables using five tests: Im-Pesaran-Shin, Fischer, Levin-Lin-Chu, Breitung, and Hadri.
    - The first four tests are based on the null of unit root; the Hadri test is based on the null of stationarity.
    - The latter three tests require a balanced panel and were applied to a shorter version of the dataset.
    - As shown in Table 3: all tests support the unit root hypothesis for the debt-to-GDP ratio.
    - Results are mixed for real bond yields (two tests support unit root) and potential growth rates (three tests support unit root).
    - The Breitung and Hadri tests support the unit root hypothesis for all three variables, justifying use of the panel cointegration model.
- Observations on euro area dynamics
  - Figures 1 and 2 show convergence of real sovereign bond yields following introduction of the euro in 1999 until the eruption of the crisis in 2009, despite persistently wide dispersion of debt-to-GDP ratios.
  - Markets did not fully account for differences in fundamentals when pricing sovereign risk in euro area countries during this period; warrants special treatment in empirical analysis.

### Estimation results — baseline specification
- Specification and models reported in Table 4:
  - Column (1): full model.
  - Column (2): restricted model excluding insignificant coefficients.
  - Column (3): restricted model augmented by inclusion of the euro area dummy among short-run determinants.
- Long-run coefficients
  - Debt-to-GDP ratio:
    - The long-run coefficient of the debt-to-GDP ratio is positive and significant.
    - Real bond yields go up by about 2 basis points in response to a 1 percentage point increase in the debt-to-GDP ratio.
    - This estimate lies in the lower range of 2-7 basis point estimates found in previous papers (Baldacci and Kumar, 2010).
  - Potential growth:
    - The positive and significant coefficient implies faster growing countries pay higher interest rates.
    - 1 percentage point higher potential growth leads to a 45 basis points average increase in real bond yields.
- Euro area effect
  - The relationship between bond yields and long-run determinants (debt-to-GDP ratio and potential growth) has substantially weakened in euro area countries following the introduction of the euro in 1999.

*Source: IMF working paper text provided.*

### introduction of the euro. The average coefficient falls to 0.005 for the debt-to-GDP ratio and

### _wp12271 - introduction of the euro. The average coefficient falls to 0.005 for the debt-to-GDP ratio and

### Long-run and short-run coefficient findings
- Euro-area dummy effects:
  - The average coefficient falls to 0.005 for the debt-to-GDP ratio and to -0.05 for the potential growth rate when the euro area dummy is added.
  - This aligns with recent euro area studies (e.g., De Grauwe and Ji, 2012) that show markets underestimated the impact of fundamentals on sovereign bond yields in the period following the introduction of the euro and up to the eruption of the crisis.
- Speed of adjustment:
  - The speed of adjustment coefficient is negative and significant.
  - The average coefficient of -0.45 suggests that almost half of the deviation of real bond yields from their long-run equilibrium level adjusts during one year.
- Short-run determinants:
  - Short-run changes in real bond yields are:
    - Positively affected by changes in the debt-to-GDP ratio.
    - Positively affected by changes in short-term interest rates (monetary policy effect).
    - Negatively affected by changes in inflation (interpreted as a surprise effect: short-run changes in inflation in excess of expectations result in a temporary decline of real bond yields).
  - Exceptions where coefficients were not significant: changes in the real growth rate and the primary balance ratio.
- Model fit and estimator validity:
  - Standard errors of residuals range between 1.52 and 1.58, smaller than the standard deviation of real rates in the total sample (2.22).
  - The Hausman test does not reject the validity of the PMG estimator, suggesting the association between real bond yields and their long-run determinants is the same across all advanced economies.

### Robustness checks and sample variations
- Excluding program countries (Greece, Ireland, Portugal):
  - Main conclusions remain unchanged when program countries are dropped.
- Adding reserve-currency dummies:
  - Adding a U.S. dummy and a Japan dummy to the long-run equilibrium equation suggests that long-run equilibrium real bond yields in these countries were not significantly affected by their reserve currency status; the impact of other variables remains qualitatively unchanged.
- Pre-crisis sample (restricting to period ending in 2007):
  - The magnitude of long-run coefficients on the debt-to-GDP ratio and potential growth was somewhat smaller before the crisis, indicating markets paid closer attention to fundamentals after the crisis.
  - The short-run coefficient on changes in inflation turns insignificant in the pre-crisis sample.
- Overall:
  - Robustness checks confirm that main results on long-run and short-run determinants remain intact across different samples and additional controls.

### Evidence on market deviations and “overreaction”
- Model-based comparisons:
  - Comparison of actual spreads (Germany vs. other euro area countries) in the first half of 2012 to spreads predicted by seven models shows:
    - In some European periphery countries, bond yield spreads (relative to Germany) exceeded their equilibrium value determined by long-run and short-run fundamentals in the first half of 2012.
    - Several core euro area countries (e.g., Finland) exhibit spreads undershooting their equilibrium value due to “safe haven” effects.
  - Contrast with pre-crisis period (1999-2009): spreads in European periphery countries were lower than the level justified by fundamentals (“underreaction” pre-crisis vs. “overreaction” post-crisis).
- Caveats:
  - Results are obtained from a very parsimonious model and do not account for some factors likely contributing to temporary deviations (for instance, policy uncertainty).
  - Temporary market overreaction should not be interpreted as evidence against the effectiveness of fiscal adjustment.

### Key quantitative findings and model estimates
- Long-run elasticities (reported in text and tables):
  - Long-run response of government bond yields:
    - Increase by about 2 basis points in response to a 1 percentage point increase in the government debt-to-GDP ratio.
    - Increase by about 45 basis points in response to a 1 percentage point increase in the potential growth rate.
  - Table 4 (selected baseline results, PMG estimator):
    - Debt ratio long-run coefficient examples: 0.014**, 0.021***, 0.025*** (robust standard errors shown in brackets).
    - Potential growth long-run coefficient examples: 0.649***, 0.322**, 0.393***.
    - Debt ratio*Dummy_EA (1999-2009): -0.010**, -0.020***, -0.016***.
    - Potential growth*Dummy_EA (1999-2009): -0.763***, -0.395***, -0.359**.
    - Speed of adjustment: -0.390***, -0.426***, -0.526***.
    - Short-run coefficients (averages): Δ Debt ratio 0.091***, 0.081***, 0.092***; Δ Inflation -0.141**, -0.159*, -0.160**; Δ Short-term real rate 0.151***, 0.135***, 0.124***.
    - Observations: 441; Countries: 22; Hausman p-values: 0.893, 0.902, 0.644; St. Dev. of residuals: 1.52, 1.53, 1.58.
  - Table 5 (robustness examples):
    - Debt ratio long-run coefficients: 0.021***, 0.021***, 0.016**, 0.012** across specifications.
    - Potential growth long-run coefficients: 0.527***, 0.328**, 0.591***, 0.303**.
    - Debt ratio*Dummy_EA (1999-2009): -0.016***, -0.020***, -0.016***, -0.024***.
    - Potential growth*Dummy_EA (1999-2009): -0.487***, -0.395***, -0.434***, -0.381**.
    - Speed of adjustment: -0.425***, -0.426***, -0.394***, -0.406***.
    - Short-run coefficients (examples): Δ Debt ratio 0.074***, 0.081***, 0.082***, 0.082***; Δ Inflation -0.218**, -0.158*, -0.174**, -0.127; Δ Short-term real rate 0.121***, 0.136***, 0.127***, 0.153***.
    - Observations: 390, 441, 441, 388; Countries: 19, 22, 22, 22; Hausman p-values: 0.93, 0.94, 1.00, 0.47; St. Dev. of residuals: 1.52, 1.53, 1.51, 1.52.
- Data and sample:
  - Panel covers 22 advanced economies over 1980-2010 (overall sample covers 1980-2011 in some tests).
  - Dependent variable: Real long-term interest rate (nominal 10 year benchmark bond yield minus inflation divided over one plus inflation, Fisher's formula; inflation via GDP deflator).
  - Long-run determinants include general government debt ratio (percent), potential growth (real GDP growth filtered of cyclical fluctuations).
  - Short-run determinants include changes in debt ratio, changes in inflation (CPI), changes in real short-term interest rate, changes in output growth, changes in primary balance ratio.

### Policy implications and recommendations
- Fiscal policy:
  - A steady pace of fiscal adjustment remains imperative for anchoring lower borrowing costs in the long run.
- Complementary policies:
  - Short-run departures of borrowing costs from long-run equilibrium should be addressed through complementary policies aimed at reducing financial stress and market uncertainty.
- Interpretation:
  - Market overreaction during financial stress can cause temporary deviations from long-run equilibrium driven by herding behavior and increased risk aversion, not necessarily by fundamentals alone.
  - Policy responses should therefore combine credible fiscal adjustment with measures to reduce financial sector stress and policy uncertainty.

*Source: IMF working paper content unit _wp12271 - introduction of the euro. The average coefficient falls to 0.005 for the debt-to-GDP ratio and (PDF).*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12271.pdf_