Front Matter Page

Fiscal Affairs Department

Contents

• 1. Introduction

• 2. Motivation

  • 2.1. A motivating model

  • 2.2. Data on interest-growth differentials

• 3. Model

  • 3.1. Environment

  • 3.2. Recursive equilibrium

  • 3.3. Properties of equilibrium

• 4. Empirical properties of interest and growth rates

  • 4.1. Data on interest and growth rates

  • 4.2. Describing the dynamic behavior of interest and growth rates

  • 4.3. VAR-based inference on the long run interest-growth differential

  • 4.4. Spectral inference on the long run interest-growth differential

• 5. Estimated debt limits

  • 5.1. Estimating the surplus function

  • 5.2. The dynamic behavior of debt limits

  • 5.3. Implied historical debt limits

  • 5.4. Debt maturity and shock volatility

• 6. Conclusion

• References

• Appendixs

• A. Proofs

• B. Further empirical work

• C. Estimating the surplus function

• D. Discretizing the growth-interest rate process

• Figures

• 1. General government gross debt to GDP ratio, percent, in G7 economies 1980-2016

• 2. Central Bank interest rates in G7 economies 1980-2016

• 3. US interest-growth differentials 1880-2016

• 4. Five-year average annualized interest-growth differentials for a sample of advanced economies: 1960-2016

• 5. Test statistics and critical values for an unrestricted four-lag VAR for the USA. Vertical lines show the 5% critical values of the unconditional LR test.

• 6. Test statistics for hypothesis test of long run means. Annual data 1880-2015.

• 7. Test statistics for hypothesis test of long run means. Annualized quarterly data 1956Q1-2016Q4 (from 1960Q1 for Canada).

• 8. Comparison of point estimates and upper boundaries for interest-growth differentials in five advanced economies. Data annual 1880-2015, except where otherwise noted.

• 9. Stylized surplus function

• 10. Model impulse responses to one-standard-deviation shocks

• 11. Estimated debt limits for the UK, 1880-2015 (rolling five-year average)

• 12. Dependence of average debt limits on variance of interest-growth differentials

• 13. Dependence of average debt limits on period length

• 14. Elasticity of debt limit to interest-growth differential

• 15. Long-run interest-growth differential using alternative interest rates. Annual data, 1880-2015

• 16. Surplus function.

• 17. Discretized values for nominal interest and growth rates with D = 20, R = 3. Points shown in proportion to their ergodic frequency.

• 18. Time series of nominal interest and growth rates: data in black, discretized process in blue.

• Tables

• 1. Sample periods for interest and growth rates: Annual data

• 2. 1-lag VAR for sample of countries. Annual data 1880-2015. Robust likelihood-based standard errors in parentheses.

• 3. Multi-lag VAR for sample of countries. Annual data 1880-2015. Robust likelihood-based standard errors in parentheses.

• 4. 4-lag VAR for sample of countries. Annualized quarterly data 1956Q1-2016Q4 (from 1960Q1 for Canada). Robust likelihood-based standard errors in parentheses.

• 5. Midpoint and 95% upper critical value of Mueller-Watson prediction ranges for average interest-growth differential of next 100 years. Annual data 1880-2015.

• 6. Estimated surplus parameters for the UK, annual data 1880-2015

• 7. Multi-lag restricted VAR for sample of countries. Lon-run means are restricted to be at the 5% critical value under the unconditional LR test. Annual data 1880-2015. Robust likelihood-based standard errors in parentheses

• 8. Average spread over risk-free rate

• 9. Midpoint and 95% upper critical value of Mueller-Watson prediction ranges for average interest-growth differential of next 100 years. Annualized quarterly data 1956Q1-2016Q4 (from 1961Q1 for Canada).

• 10. Estimated restricted VAR based on data, and VAR estimated from discretized approximation simulated 100,000 periods