## wpiea2025142-source-pdf - Appendix Figure A.1). This recent pattern has contributed to a more benign perspective

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### Major conclusion
- For the entire 50-year sample period (1976-2025) the estimated effects of debt and deficits on long-term interest rates are statistically and economically significant.
- The relationship between long-term rates and fiscal variables weakened markedly around the turn of the century, but has been becoming stronger since then as fiscal positions have started to deteriorate.
- After properly isolating confounding time trends, the impact of debt and deficits on long-term interest rates reemerges and their magnitudes appear to be on the rise.

### Identification and empirical strategy
- Builds on Laubach (2009) by focusing on long-horizon expectations of interest rates and fiscal variables to reduce confounding from short-term business-cycle factors.
- Extended controls beyond Laubach: population growth forecasts; risk aversion (Excessive Bond Premium, EBP); medium-term real GDP growth forecasts; international purchases of US debt (share of foreign-held Treasuries).
- Addresses potential positive bias from interest-rate forecasts being inputs into fiscal forecasts by examining primary deficits and using bond term premia (Adrian, Crump and Moench (2013)) as alternative dependent variable.
- Dependent variables (five alternatives): (i) 10-year Treasury yield; (ii) 5-10 year forward rate (average of yearly forward rates at 5,6,7,8 and 9 years); (iii) 10-15 year forward rate (average of yearly forward rates from 10 to 14); (iv-v) 5-year and 10-year bond term premia.
- Fiscal variables: 5-year-ahead projections of debt, fiscal balance, and primary balance from CBO sources; total of 82 observations for debt forecasts and 106 observations for deficits forecasts spanning 1976 to January 2025.
- Interest rate measures: 10-year Treasury yield; 5-10 year forward; 10-15 year forward; forward rates sourced from Gurkaynak, Sack, and Wright (2007); term premia from Adrian, Crump and Moench (2013).
- Controls: Tbill3m (preferred over survey inflation expectations); recession dummies (NBER); predicted long-term growth (CBO 5-year nominal GDP less Michigan Consumer Surveys long-term inflation expectations); 5-year ahead population growth (UN WPP); share of foreign-held Treasuries (Haver Analytics); EBP from Gilchrist and Zakrajšek (2012), updated by the Federal Reserve Board.
- Estimation equation: yt = c + α Ft + β STt + γ Xt + εt, where yt = long-term interest rates; ST = Tbill 3 months; F = fiscal variable; X = controls. Estimated by OLS with Newey-West standard errors.

### Baseline results (parsimonious model)
- Parsimonious model controls only for short-term interest rates and a linear and quadratic trend.
- Key magnitudes (parsimonious sample):
  - A 10 percent of GDP increase in expected debt is associated with an increase in long-term rates of between 20 and 30 basis points.
  - A 1 percent of GDP increase in the fiscal and primary balances is associated with a decrease in long-term rates of approximately 20 to 30 basis points.
- Out of 15 combinations in the parsimonious specifications, only 2 do not reach statistical significance (but point estimates are similar).

### Baseline results with extended controls — selected coefficient estimates (exact values preserved)
- Table 1: Main Results: Full sample (linear-quadratic trend controls; Newey-West standard errors)
  - Debt coefficients (five dependent variables, columns): 0.027 ∗∗ (0.009); 0.028 (0.018); 0.023 ∗∗ (0.013); 0.017 ∗ (0.009); 0.020 ∗ (0.012).
  - Fiscal Balances coefficients: −0.222 ∗∗∗ (0.056); −0.260 (1.550); −0.262 ∗∗∗ (0.119); −0.155 ∗∗∗ (0.049); −0.192 ∗∗∗ (0.067).
  - Primary Balances coefficients: −0.269 ∗∗∗ (0.078); −0.299 ∗∗∗ (0.103); −0.313 ∗∗∗ (0.097); −0.186 ∗∗ (0.083); −0.226 (0.483).
  - Note: 106 observations for predicted fiscal balances and 81 for debt. Fwrd = forward rates; T10 = 10-year Treasury; TPrem = term premia.
- Table 2: Extra Controls: Debt (sample size 103; Newey-West standard errors)
  - Debt: 0.017 ∗ (0.009); 0.019 ∗∗ (0.009); 0.014 ∗∗ (0.007); 0.023 ∗∗∗ (0.007); 0.025 ∗∗∗ (0.008).
  - Tbill3m: 0.216 ∗∗∗ (0.068); 0.195 ∗∗∗ (0.069); 0.458 ∗∗∗ (0.056).
  - GDP growth (next 5y): 0.287 ∗ (0.146); 0.525 ∗∗∗ (0.147); 0.084 (0.119); 0.296 ∗∗∗ (0.114); 0.364 ∗∗∗ (0.135).
  - Foreign Holdings share: −0.110 ∗∗∗ (0.030); −0.112 ∗∗∗ (0.031); −0.060 ∗∗ (0.025); −0.067 ∗∗ (0.029); −0.076 ∗ (0.042).
  - Risk (EBP): −0.033 (0.196); −0.188 (0.198); −0.111 (0.160); 0.220 (0.161); 0.228 (0.180).
  - Recession Dummy: 0.746 ∗ (0.389); 0.962 ∗∗ (0.393); 0.472 (0.318); 0.455 ∗∗ (0.202); 0.592 ∗∗ (0.238).
  - Pop growth: 2.196 ∗∗∗ (0.761); 1.930 ∗∗ (0.769); 1.542 ∗∗ (0.621); 0.778 (0.568); 0.943 (0.636).
  - Linear trend: −11.923 ∗∗∗ (2.926); −10.980 ∗∗∗ (2.955); −11.581 ∗∗∗ (2.387); −5.494 ∗∗∗ (1.970); −5.932 ∗∗∗ (2.202).
  - Quadratic trend: 1.377 (1.999); 0.349 (2.018); 1.827 (1.630); −3.380 ∗∗ (1.673); −3.420 ∗ (2.024).
  - Constant: 3.825 ∗∗∗ (1.061); 4.017 ∗∗∗ (1.071); 2.414 ∗∗∗ (0.866); 0.553 (0.587); 0.648 (0.640).
- Table 3: Extra Controls: Fiscal Balances (sample size 103)
  - Total Balances: −0.230 ∗∗∗ (0.058); −0.231 ∗∗∗ (0.058); −0.206 ∗∗∗ (0.046); −0.214 ∗∗∗ (0.047); −0.228 ∗∗∗ (0.051).
  - Tbill3m: 0.225 ∗∗∗ (0.061); 0.205 ∗∗∗ (0.062); 0.467 ∗∗∗ (0.049).
  - GDP growth (5 years ahead): 0.268 ∗ (0.136); 0.497 ∗∗∗ (0.137); 0.072 (0.108); 0.296 ∗∗∗ (0.114); 0.364 ∗∗∗ (0.135).
  - Foreign Holdings: −0.104 ∗∗∗ (0.029); −0.107 ∗∗∗ (0.029); −0.054 ∗∗ (0.023); −0.055 ∗∗ (0.021); −0.063 ∗∗∗ (0.023).
  - Risk (EBP): 0.081 (0.192); −0.064 (0.194); −0.001 (0.153); 0.220 (0.161); 0.228 (0.180).
  - Recession Dummy: 0.745 ∗ (0.401); 0.935 ∗∗ (0.405); 0.457 (0.319); 0.455 ∗∗ (0.202); 0.592 ∗∗ (0.238).
  - Pop. Growth: 1.568 ∗∗ (0.776); 1.309 ∗ (0.784); 0.914 (0.618); 0.778 (0.568); 0.943 (0.636).
  - Linear Trend: −12.195 ∗∗∗ (2.768); −11.104 ∗∗∗ (2.797); −12.115 ∗∗∗ (2.204); −5.494 ∗∗∗ (1.970); −5.932 ∗∗∗ (2.202).
  - Quadratic Trend: −0.098 (1.898); −0.996 (1.918); 0.393 (1.511); −3.380 ∗∗ (1.673); −3.420 ∗ (2.024).
  - Constant: 4.752 ∗∗∗ (0.759); 5.078 ∗∗∗ (0.767); 3.195 ∗∗∗ (0.604); 0.553 (0.587); 0.648 (0.640).
- Table 4: Extra Controls: Primary Balance (sample size 103)
  - Primary Balance: −0.245 ∗∗∗ (0.080); −0.247 ∗∗∗ (0.080); −0.237 ∗∗∗ (0.063); −0.246 ∗∗∗ (0.067); −0.257 ∗∗∗ (0.078).
  - Tbill3m: 0.226 ∗∗∗ (0.066); 0.206 ∗∗∗ (0.066); 0.473 ∗∗∗ (0.052).
  - GDP growth (5 years ahead): 0.267 ∗ (0.142); 0.496 ∗∗∗ (0.143); 0.071 (0.112); 0.293 ∗∗ (0.132); 0.361 ∗∗ (0.174).
  - Foreign Holdings: −0.118 ∗∗∗ (0.029); −0.121 ∗∗∗ (0.030); −0.065 ∗∗∗ (0.023); −0.067 ∗∗ (0.029); −0.076 ∗ (0.042).
  - Risk (EBP): 0.063 (0.201); −0.081 (0.203); −0.006 (0.159); 0.211 (0.156); 0.216 (0.171).
  - Recession Dummy: 0.673 (0.417); 0.863 ∗∗ (0.421); 0.393 (0.330); 0.399 ∗∗ (0.196); 0.530 ∗∗ (0.227).
  - Pop. growth: 2.113 ∗∗∗ (0.779); 1.856 ∗∗ (0.787); 1.367 ∗∗ (0.617); 1.261 ∗ (0.740); 1.463 (1.047).
  - Linear Trend: −11.284 ∗∗∗ (2.859); −10.191 ∗∗∗ (2.887); −11.394 ∗∗∗ (2.263); −4.821 (2.979); −5.174 (4.474).
  - Quadratic Trend: 0.685 (2.013); −0.220 (2.033); 0.792 (1.594); −2.868 (2.385); −2.820 (3.475).
  - Constant: 5.082 ∗∗∗ (0.784); 5.411 ∗∗∗ (0.792); 3.485 ∗∗∗ (0.621); 0.891 (0.561); 1.000 (0.667).

### Interpretation of control variables (empirical findings)
- Expected real GDP growth (5 years ahead) is associated with higher long-term interest rates.
- A greater share of foreign holdings of Treasuries is associated with lower interest rates.
- Recession dummy coefficient is positive (controlling for short-term rates), possibly reflecting short-term Tbill declines and expansionary fiscal policy during recessions leading to higher expected future long-term rates.
- Population growth is associated with higher long-term interest rates in these estimates.
- EBP (risk aversion) does not show consistently significant effects across specifications.

### Robustness and additional checks
- Using bond term premia (Adrian, Crump and Moench (2013)) as dependent variable yields positive and statistically significant associations of debt and deficits with higher term premia, with magnitudes comparable to those for long-term interest rates.
- Primary balance specifications help address bias from interest rate forecasts being inputs to fiscal forecasts; primary balances show significant negative associations with long-term rates and term premia.
- The post-GFC period (after 2008) presents empirical challenges due to rising debt levels and historic low interest rates; isolating time trends is critical to uncover the underlying positive impact of debt and deficits.

### Estimates over time
- Subsamples and rolling-window approach:
  - Subsamples: (i) pre-GFC years; (ii) pre-COVID years.
  - Rolling-window regressions with 40 observations each (roughly 20 years for debt windows; 15–25 years per window for balances) using full set of controls.
- Time variation:
  - Relationship between projected fiscal outcomes and long-term interest rates weakened around the turn of the century and has been increasing since the COVID-19 pandemic.

### 4.1 Pre-GFC and Pre-COVID periods — key findings
- Pre-GFC subsample (results close to Laubach (2009))
  - Debt coefficients (Table 5): 0.028 (0.012) ∗∗; 0.034 (0.016) ∗∗; 0.029 (0.014) ∗∗∗; 0.022 (0.009) ∗∗; 0.026 (0.011) ∗∗.
  - Fiscal Balances (Table 5): −0.210 (0.067) ∗∗∗; −0.245 (0.062) ∗∗∗; −0.207 (0.058) ∗∗∗; −0.137 (0.048) ∗∗∗; −0.160 (0.059) ∗∗∗.
  - Primary Balances (Table 5): −0.272 (0.066) ∗∗∗; −0.363 (0.061) ∗∗∗; −0.268 (0.076) ∗∗∗; −0.180 (0.061) ∗∗∗; −0.210 (0.068) ∗∗∗.
  - Text interpretation: A deterioration in the primary balance of 2 percentage points of GDP is associated with increase in forward rates of more than 60 basis points (pre-GFC subsample).
- Pre-COVID subsample (excluding post-2020 years)
  - Debt (Table 6): 0.020 (0.009) ∗∗; 0.022 (0.010) ∗∗; 0.019 (0.008) ∗∗; 0.021 (0.006) ∗∗∗; 0.025 (0.008) ∗∗∗.
  - Primary Balances (Table 6): −0.323 (0.119) ∗∗; −0.361 (0.111) ∗∗∗; −0.297 (0.098) ∗∗∗; −0.243 (0.067) ∗∗∗; −0.295 (0.086) ∗∗∗.
  - Fiscal Balances (Table 6): −0.250 (0.090) ∗∗∗; −0.271 (0.081) ∗∗∗; −0.229 (0.076) ∗∗∗; −0.189 (0.052) ∗∗∗; −0.231 (0.066) ∗∗∗.
  - Text emphasis: Excluding post-COVID years reduces standard errors and increases magnitudes linking fiscal balances to term premia.

### 4.2 Rolling-windows regressions — methodology and time evolution
- Methodology:
  - Rolling-window regressions use 40 observations per regression (approximately 20 years of data ending at the date displayed).
  - Window advances by dropping and adding 1 observation at each step.
  - Both debt and balances used as regressors; dependent variables include forward rates and term premia.
- Time evolution summary:
  - Coefficients linking fiscal forecasts to long-term interest rates and term premia were close to zero in the twenty or so years ending between 2005 and 2010, coinciding with low projected debt and deficits.
  - Estimated effects increase after this period as fiscal positions deteriorated, even though short-term interest rates remained low.
  - Results using primary balance and 5-year bond term premia are reported in the Appendix and are very close to 10-year results.

### 5 Conclusions
- Main empirical finding: Higher debt and deficits translate into higher long-term interest rates.
- Quantitative magnitudes for the 1976-2025 sample:
  - Long-term rates rise by 20 to 30 basis points in response to a 1 percentage point increase in the projected deficit-to-GDP ratio.
  - Long-term rates rise by 20 to 30 basis points in response to a 10 percentage points increase in the projected debt-to-GDP ratio.
- Time variation: Relationship weakened briefly around the turn of the century when the US ran primary surpluses and debt-to-GDP was low; estimated effects have increased as fiscal position deteriorated.
- Policy implication: Projected higher deficit and debt in the United States is likely to further increase long-term interest rates and debt financing costs.

*Source: IMF staff estimates, wpiea2025142-source-pdf (section 4.1–5 and Appendix excerpts).*

### Appendix Figure A.1). This recent pattern has contributed to a more benign perspective

### wpiea2025142-source-pdf - Appendix Figure A.1). This recent pattern has contributed to a more benign perspective

### Major conclusion
- For the entire 50-year sample period (1976-2025) the estimated effects of debt and deficits on long-term interest rates are statistically and economically significant.
- The relationship between long-term rates and fiscal variables weakened markedly around the turn of the century, but has been becoming stronger since then as fiscal positions have started to deteriorate.
- After properly isolating confounding time trends, the impact of debt and deficits on long-term interest rates reemerges and their magnitudes appear to be on the rise.

### Identification and empirical strategy
- The paper builds on Laubach (2009) by focusing on long-horizon expectations of interest rates and fiscal variables to reduce confounding from short-term business-cycle factors.
- Extended controls beyond Laubach include: population growth forecasts, risk aversion (Excessive Bond Premium, EBP), medium-term real GDP growth forecasts, and international purchases of US debt (share of foreign-held Treasuries).
- Concern addressed: long-term interest rate forecasts might be used as inputs into long-term debt and deficit forecasts, creating positive bias. The paper examines primary deficits and uses bond term premia (Adrian, Crump and Moench (2013) methodology) as an alternative dependent variable.
- Dependent variables used (five alternatives): (i) 10-year Treasury yield; (ii) 5-10 year forward rate (average of yearly forward rates at 5,6,7,8 and 9 years); (iii) 10-15 year forward rate (average of yearly forward rates from 10 to 14); (iv-v) 5-year and 10-year bond term premia.
- Fiscal variables: 5-year-ahead projections of debt, fiscal balance, and primary balance from CBO sources (GitHub repository and PDF reports), with a total of 82 observations for debt forecasts and 106 observations for deficits forecasts spanning 1976 to January 2025.
- Interest rate measures: 10-year Treasury yield, 5-10 year forward, 10-15 year forward; forward rates sourced from Gurkaynak, Sack, and Wright (2007). Term premia used as robustness (Adrian, Crump and Moench (2013)).
- Control choices: 3 months Treasury Bill rate (Tbill3m) preferred over survey inflation expectations; recession dummies (NBER); predicted long-term growth (CBO 5-year nominal GDP less Michigan Consumer Surveys long-term inflation expectations); 5-year ahead population growth (UN World Population Prospects); share of foreign-held Treasuries (Haver Analytics); EBP from Gilchrist and Zakrajšek (2012), updated by the Federal Reserve Board.
- Estimation equation:
  - yt = c + α Ft + β STt + γ Xt + εt
  - where yt = long-term interest rates; c = constant; ST = short-term interest rates (Tbill 3 months); F = fiscal variable of interest; X = vector of controls; ε = error term.
  - Equation (1) is estimated using OLS with Newey-West standard errors.

### Baseline results (parsimonious model)
- Parsimonious model controls only for short-term interest rates and a linear and quadratic trend.
- Key magnitude findings (parsimonious sample):
  - A 10 percent of GDP increase in expected debt is associated with an increase in long-term rates of between 20 and 30 basis points.
  - A 1 percent of GDP increase in the fiscal and primary balances is associated with a decrease in long-term rates of approximately 20 to 30 basis points.
- Out of 15 combinations in the parsimonious specifications, only 2 do not reach statistical significance (but point estimates are similar).

### Baseline results with extended controls — selected coefficient estimates (exact values preserved)
- Table 1: Main Results: Full sample (linear-quadratic trend controls; Newey-West standard errors)
  - Debt coefficients (five dependent variables, columns): 0.027 ∗∗ (0.009); 0.028 (0.018); 0.023 ∗∗ (0.013); 0.017 ∗ (0.009); 0.020 ∗ (0.012).
  - Fiscal Balances coefficients: −0.222 ∗∗∗ (0.056); −0.260 (1.550); −0.262 ∗∗∗ (0.119); −0.155 ∗∗∗ (0.049); −0.192 ∗∗∗ (0.067).
  - Primary Balances coefficients: −0.269 ∗∗∗ (0.078); −0.299 ∗∗∗ (0.103); −0.313 ∗∗∗ (0.097); −0.186 ∗∗ (0.083); −0.226 (0.483).
  - Note: 106 observations for predicted fiscal balances and 81 for debt. Fwrd = forward rates; T10 = 10-year Treasury; TPrem = term premia.

- Table 2: Extra Controls: Debt (sample size 103; Newey-West standard errors)
  - Debt: 0.017 ∗ (0.009); 0.019 ∗∗ (0.009); 0.014 ∗∗ (0.007); 0.023 ∗∗∗ (0.007); 0.025 ∗∗∗ (0.008).
  - Tbill3m: 0.216 ∗∗∗ (0.068); 0.195 ∗∗∗ (0.069); 0.458 ∗∗∗ (0.056).
  - GDP growth (next 5y): 0.287 ∗ (0.146); 0.525 ∗∗∗ (0.147); 0.084 (0.119); 0.296 ∗∗∗ (0.114); 0.364 ∗∗∗ (0.135).
  - Foreign Holdings share: −0.110 ∗∗∗ (0.030); −0.112 ∗∗∗ (0.031); −0.060 ∗∗ (0.025); −0.067 ∗∗ (0.029); −0.076 ∗ (0.042).
  - Risk (EBP): −0.033 (0.196); −0.188 (0.198); −0.111 (0.160); 0.220 (0.161); 0.228 (0.180).
  - Recession Dummy: 0.746 ∗ (0.389); 0.962 ∗∗ (0.393); 0.472 (0.318); 0.455 ∗∗ (0.202); 0.592 ∗∗ (0.238).
  - Pop growth: 2.196 ∗∗∗ (0.761); 1.930 ∗∗ (0.769); 1.542 ∗∗ (0.621); 0.778 (0.568); 0.943 (0.636).
  - Linear trend: −11.923 ∗∗∗ (2.926); −10.980 ∗∗∗ (2.955); −11.581 ∗∗∗ (2.387); −5.494 ∗∗∗ (1.970); −5.932 ∗∗∗ (2.202).
  - Quadratic trend: 1.377 (1.999); 0.349 (2.018); 1.827 (1.630); −3.380 ∗∗ (1.673); −3.420 ∗ (2.024).
  - Constant: 3.825 ∗∗∗ (1.061); 4.017 ∗∗∗ (1.071); 2.414 ∗∗∗ (0.866); 0.553 (0.587); 0.648 (0.640).

- Table 3: Extra Controls: Fiscal Balances (sample size 103)
  - Total Balances: −0.230 ∗∗∗ (0.058); −0.231 ∗∗∗ (0.058); −0.206 ∗∗∗ (0.046); −0.214 ∗∗∗ (0.047); −0.228 ∗∗∗ (0.051).
  - Tbill3m: 0.225 ∗∗∗ (0.061); 0.205 ∗∗∗ (0.062); 0.467 ∗∗∗ (0.049).
  - GDP growth (5 years ahead): 0.268 ∗ (0.136); 0.497 ∗∗∗ (0.137); 0.072 (0.108); 0.296 ∗∗∗ (0.114); 0.364 ∗∗∗ (0.135).
  - Foreign Holdings: −0.104 ∗∗∗ (0.029); −0.107 ∗∗∗ (0.029); −0.054 ∗∗ (0.023); −0.055 ∗∗ (0.021); −0.063 ∗∗∗ (0.023).
  - Risk (EBP): 0.081 (0.192); −0.064 (0.194); −0.001 (0.153); 0.220 (0.161); 0.228 (0.180).
  - Recession Dummy: 0.745 ∗ (0.401); 0.935 ∗∗ (0.405); 0.457 (0.319); 0.455 ∗∗ (0.202); 0.592 ∗∗ (0.238).
  - Pop. Growth: 1.568 ∗∗ (0.776); 1.309 ∗ (0.784); 0.914 (0.618); 0.778 (0.568); 0.943 (0.636).
  - Linear Trend: −12.195 ∗∗∗ (2.768); −11.104 ∗∗∗ (2.797); −12.115 ∗∗∗ (2.204); −5.494 ∗∗∗ (1.970); −5.932 ∗∗∗ (2.202).
  - Quadratic Trend: −0.098 (1.898); −0.996 (1.918); 0.393 (1.511); −3.380 ∗∗ (1.673); −3.420 ∗ (2.024).
  - Constant: 4.752 ∗∗∗ (0.759); 5.078 ∗∗∗ (0.767); 3.195 ∗∗∗ (0.604); 0.553 (0.587); 0.648 (0.640).

- Table 4: Extra Controls: Primary Balance (sample size 103)
  - Primary Balance: −0.245 ∗∗∗ (0.080); −0.247 ∗∗∗ (0.080); −0.237 ∗∗∗ (0.063); −0.246 ∗∗∗ (0.067); −0.257 ∗∗∗ (0.078).
  - Tbill3m: 0.226 ∗∗∗ (0.066); 0.206 ∗∗∗ (0.066); 0.473 ∗∗∗ (0.052).
  - GDP growth (5 years ahead): 0.267 ∗ (0.142); 0.496 ∗∗∗ (0.143); 0.071 (0.112); 0.293 ∗∗ (0.132); 0.361 ∗∗ (0.174).
  - Foreign Holdings: −0.118 ∗∗∗ (0.029); −0.121 ∗∗∗ (0.030); −0.065 ∗∗∗ (0.023); −0.067 ∗∗ (0.029); −0.076 ∗ (0.042).
  - Risk (EBP): 0.063 (0.201); −0.081 (0.203); −0.006 (0.159); 0.211 (0.156); 0.216 (0.171).
  - Recession Dummy: 0.673 (0.417); 0.863 ∗∗ (0.421); 0.393 (0.330); 0.399 ∗∗ (0.196); 0.530 ∗∗ (0.227).
  - Pop. growth: 2.113 ∗∗∗ (0.779); 1.856 ∗∗ (0.787); 1.367 ∗∗ (0.617); 1.261 ∗ (0.740); 1.463 (1.047).
  - Linear Trend: −11.284 ∗∗∗ (2.859); −10.191 ∗∗∗ (2.887); −11.394 ∗∗∗ (2.263); −4.821 (2.979); −5.174 (4.474).
  - Quadratic Trend: 0.685 (2.013); −0.220 (2.033); 0.792 (1.594); −2.868 (2.385); −2.820 (3.475).
  - Constant: 5.082 ∗∗∗ (0.784); 5.411 ∗∗∗ (0.792); 3.485 ∗∗∗ (0.621); 0.891 (0.561); 1.000 (0.667).

### Interpretation of control variables (empirical findings)
- Expected real GDP growth (5 years ahead) is associated with higher long-term interest rates.
- A greater share of foreign holdings of Treasuries is associated with lower interest rates.
- Recession dummy coefficient is positive (controlling for short-term rates), possibly reflecting short-term Tbill declines and expansionary fiscal policy during recessions leading to higher expected future long-term rates.
- Population growth is associated with higher long-term interest rates in these estimates.
- EBP (risk aversion) does not show consistently significant effects across specifications.

### Robustness and additional checks
- Using bond term premia (Adrian, Crump and Moench (2013)) as dependent variable yields positive and statistically significant associations of debt and deficits with higher term premia, with magnitudes comparable to those for long-term interest rates.
- Primary balance specifications help address bias from interest rate forecasts being inputs to fiscal forecasts; primary balances show significant negative associations with long-term rates and term premia.
- The post-GFC period (after 2008) presents empirical challenges due to rising debt levels and historic low interest rates; isolating time trends is critical to uncover the underlying positive impact of debt and deficits.

### Estimates over time
- The paper examines subsamples (i) pre-GFC years and (ii) pre-COVID years, and implements rolling-window regressions with 40 observations each (roughly 20 years for debt windows; 15–25 years per window for balances) using the full set of controls.
- The relationship between projected fiscal outcomes and long-term interest rates weakened around the turn of the century (a period of fiscal prudence and small deficits) and has been increasing since the COVID-19 pandemic.

*Source: IMF staff estimates, wpiea2025142-source-pdf.*

### 4.1  Pre-GFC and Pre-COVID periods

### 4.1 Pre-GFC and Pre-COVID periods

### Pre-GFC subsample results
- Purpose: Robustness check against the period used in Laubach (2009) where interest rates were consistently above zero and debt did not increase uninterruptedly.
- Main comparison: Estimates for the pre-GFC period are reported in Table 5 and are very close to those reported by Laubach (2009).
- Key coefficient estimates from Table 5 (each column is a separate regression; Newey-West standard errors in parentheses):
  - Debt:
    - 0.028 (0.012) ∗∗
    - 0.034 (0.016) ∗∗
    - 0.029 (0.014) ∗∗∗
    - 0.022 (0.009) ∗∗
    - 0.026 (0.011) ∗∗
  - Fiscal Balances:
    - −0.210 (0.067) ∗∗∗
    - −0.245 (0.062) ∗∗∗
    - −0.207 (0.058) ∗∗∗
    - −0.137 (0.048) ∗∗∗
    - −0.160 (0.059) ∗∗∗
  - Primary Balances:
    - −0.272 (0.066) ∗∗∗
    - −0.363 (0.061) ∗∗∗
    - −0.268 (0.076) ∗∗∗
    - −0.180 (0.061) ∗∗∗
    - −0.210 (0.068) ∗∗∗
- Interpretation highlighted in the text:
  - For this subsample, the point estimate suggests that a deterioration in the primary balance of 2 percentage points of GDP is associated with increase in forward rates of more than 60 basis points.
- Note: The paper uses fiscal balances (not fiscal deficits), explaining why the coefficients on balances are negative.

### Pre-COVID subsample results
- Excluding post-2020 years (pre-COVID sample) produces results similar in magnitude and with generally smaller standard errors compared to the full sample.
- Key coefficient estimates from Table 6 (each column is a separate regression; Newey-West standard errors in parentheses):
  - Debt:
    - 0.020 (0.009) ∗∗
    - 0.022 (0.010) ∗∗
    - 0.019 (0.008) ∗∗
    - 0.021 (0.006) ∗∗∗
    - 0.025 (0.008) ∗∗∗
  - Primary Balances:
    - −0.323 (0.119) ∗∗
    - −0.361 (0.111) ∗∗∗
    - −0.297 (0.098) ∗∗∗
    - −0.243 (0.067) ∗∗∗
    - −0.295 (0.086) ∗∗∗
  - Fiscal Balances:
    - −0.250 (0.090) ∗∗∗
    - −0.271 (0.081) ∗∗∗
    - −0.229 (0.076) ∗∗∗
    - −0.189 (0.052) ∗∗∗
    - −0.231 (0.066) ∗∗∗
- Text emphasis: When excluding post-COVID years, standard errors decrease and coefficients linking fiscal balances to term premia increase in magnitude.

### Statistical notes
- Statistical significance indicators: ∗ (p<0.1), ∗∗ (p<0.05), ∗∗∗ (p<0.01).
- Fwrd denotes forward rates; T10 is the 10 years maturity Treasury; TPremia are the term premia.
- Only fiscal controls are reported in Tables 5 and 6, but all controls are included in the regressions.

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### 4.2 Rolling-windows regressions

### Methodology
- Rolling-window regressions use 40 observations per regression (approximately 20 years of data ending at the date displayed).
- The rolling-window drops and adds 1 observation at each step.
- Both debt and balances are used as regressors; dependent variables include forward rates and term premia.

### Time evolution of coefficients (summary of Figure 2 and related text)
- Coefficients linking fiscal forecasts to long-term interest rates and term premia were close to zero in the twenty or so years ending between 2005 and 2010.
  - This coincides with a period of low projected debt and deficits (referenced to Appendix Figure A.3).
- The estimated effects increase after this period as fiscal positions deteriorated, even though short-term interest rates remained low.
- Additional note: Results using primary balance are reported in the Appendix (Appendix Figure A.4); 5-year bond term premia results are very close to those for the 10-year and are available upon request.

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### 5 Conclusions

- Main empirical finding:
  - Higher debt and deficits translate into higher long-term interest rates.
- Quantitative magnitudes for the entire 50-year sample period (1976-2025):
  - Long-term rates rise by 20 to 30 basis points in response to a 1 percentage point increase in the projected deficit-to-GDP ratio.
  - Long-term rates rise by 20 to 30 basis points in response to a 10 percentage points increase in the projected debt-to-GDP ratio.
- Time variation:
  - The relationship between long-term rates and fiscal variables has evolved over time and weakened markedly for a brief period around the turn of the century when the US ran primary surpluses and debt-to-GDP was low.
  - As fiscal position deteriorates, estimated effects increase even when low short-term interest rates are included in the sample.
- Policy implication:
  - Projected higher deficit and debt in the United States is likely to further increase long-term interest rates and debt financing costs.

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*Source: IMF staff estimates, wpiea2025142-source-pdf (section 4.1–5 and Appendix excerpts).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025142-source-pdf.pdf_