## Costly Increases in Public Debt when r < g

_IMF Working Papers, January 12, 2024_

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## Bibliographic details
- Authors: Yongquan Cao, Vitor Gaspar, Adrian Peralta-Alva
- Published: January 12, 2024
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9798400263620.001

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### Overview
- Paper quantifies the costs of a permanent increase in debt to GDP.
- Authors: Yongquan Cao, Vitor Gaspar, Adrian Peralta-Alva.
- Date: January 12, 2024.
- Method: deterministic, overlapping generations model with two assets and no risk of default.

### Model and key assumptions
- Two assets: public debt and private (productive) capital.
- Assumption: the return on private capital equals the interest rate on public debt plus an exogenously given spread.
- Analytical version of the model is used to demonstrate mechanisms; a calibrated, richer model of the US economy follows McGrattan and Prescott (2017) and includes national accounts, fixed assets, distribution of household incomes, and demographics.

### Core quantitative findings
- Increase in the debt ratio from 60 to 120 percent of GDP is associated with:
  - Reduction in the capital stock of about 15 percent.
  - Reduction in steady state GDP of about 8 percent.
- The intuition and orders of magnitude from the simple analytical model carry over to the calibrated US model.

### Intuition and mechanism
- Even when r < g, a permanent rise in the public debt ratio can lead to a significant reduction in steady-state GDP.
- Crowding out of private productive capital by public debt is the central channel given the model structure and the assumed spread between returns.

### Policy-relevant implications
- Large, permanent increases in public debt ratios can have sizable negative effects on the capital stock and steady-state GDP even in environments where r < g.
- Consideration of the composition of assets (public debt versus private capital) and the spread between returns is important for assessing long-run fiscal costs.

*IMF Working Paper: "Costly Increases in Public Debt when r < g", Yongquan Cao, Vitor Gaspar, Adrian Peralta-Alva, January 12, 2024.*

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_Source: https://www.imf.org/en/publications/wp/issues/2024/01/12/costly-increases-in-public-debt-when-r-g-543718_