## Interest-Growth Differentials and Debt Limits in Advanced Economies

_IMF Working Papers, April 6, 2018_

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## Bibliographic details
- Authors: Philip Barrett
- Published: April 6, 2018
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9781484350980.001

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### Overview
- Research question: Do persistently low nominal interest rates mean that governments can safely borrow more?
- Approach: Extension of the model of Ghosh et al. [2013] to allow for persistent stochastic changes in nominal interest and growth rates.
- Key model parameter: the long-run difference between nominal interest and growth rates; if negative, maximum sustainable debts (debt limits) are unbounded.

### Methodology
- Empirical methods used:
  - VAR-based methods
  - Spectral-based methods
- Outcome of estimation methods:
  - Both VAR- and spectral-based methods produce negative point estimates of the long-run interest-growth differential, but cannot reject positive values at standard significance levels.

### Key Findings
- The long-run difference between nominal interest and growth rates is the critical determinant of whether debt limits are bounded or unbounded.
- Empirical estimates:
  - Negative point estimates for the long-run differential from both VAR- and spectral-based methods.
  - Statistical uncertainty remains: positive values cannot be rejected at standard significance levels.
- Calibration to the UK:
  - Using positive but statistically plausible average interest-growth differentials produces debt limits which increase by only around 5% GDP as interest rates fall after 2008.
  - A tiny change in the long-run average interest-growth differential — from the 95th to the 97.5th percentile of the distribution — is sufficient to move average debt limits by the same amount.

### Calibration and Quantitative Results
- Country calibrated: United Kingdom (UK)
- Quantitative illustrations:
  - Debt limits increase by only around 5% GDP as interest rates fall after 2008 under the chosen calibration.
  - Sensitivity: movement from the 95th to the 97.5th percentile of the long-run differential distribution produces an equivalent change in average debt limits.

### Policy-Relevant Implications
- Persistence and uncertainty in nominal interest and growth rates matter critically for sustainable public debt assessments.
- Point estimates suggesting negative long-run interest-growth differentials do not, by themselves, imply that higher borrowing is safe because positive values remain statistically plausible.
- Small changes in the assumed long-run average interest-growth differential can imply large changes in estimated debt limits, highlighting high sensitivity and model uncertainty for fiscal space assessments.

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- **Interest-Growth Differentials and Debt Limits in Advanced Economies, WP/18/82, April 2018**
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_Source: https://www.imf.org/en/publications/wp/issues/2018/04/11/interest-growth-differentials-and-debt-limits-in-advanced-economies-45794_