The impact of government debt on the long-run natural real interest rate – a quantitative evaluation

ABSTRACT

Persistently low natural real interest rates are a problem for monetary policy and financial stability. I analyse to what extent a permanent increase in government debt that is financed by higher taxes could raise the long-run natural real interest rate. As a measurement tool, I use an incomplete markets model with capital and government bonds. Increasing the public debt/GDP ratio by one percentage point raises the real interest rate by between 0.4 and 1.5 basis points, depending on the degree of inequality generated by the model and the tax instrument used to balance the government’s budget constraint. I also show that the interest rate effect of a change in public debt/GDP predicted by the model is significantly smaller than its empirical counterpart for the US, due to the fact that the model understates the empirical fraction of households that are constrained in their consumption decision.

KEYWORDS:

• Natural interest rate
• government debt
• borrowing limits
• incomplete markets
• crowding out

JEL CLASSIFICATION:

• E43
• E6
• H6

Acknowledgments

I would like to thank Sigrid Röhrs for her long-term collaboration on related projects. I am also grateful to Laura Zwyssig for many useful comments. All errors are my own.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ In a balanced growth path equilibrium, public debt, GDP as well as all other aggregate variables (with the exception of the interest rate and aggregate labor supply) grow at the rate of technological progress.

² Recall from note 1 that on the balanced growth path, both public debt and GDP grow at the rate of technological progress. Dividing by GDP therefore ensures stationarity of public debt.

³ See Röhrs and Winter (2015), Figure 1 (third panel), for the long-run relationship between the interest rate and debt/GDP if the labour income tax is adjusted. Röhrs and Winter (2016), Figure 3, displays this relationship if the tax on total income is adjusted.

⁴ See Röhrs and Winter (2015), Figure 1 in their Online appendix.

⁵ I implicitly assume that the financial crisis did not affect the model’s parameters. It is beyond the scope of this article to explain why interest rates have fallen. Tighter borrowing constraints might have played an important role, see, e.g., Guerrieri and Lorenzoni (2011), in which case the interest rate response reported here should be seen as a lower bound.

⁶ I evaluate the fraction of constrained households at the long-run average public debt/GDP ratio of 0.67.

⁷ Gomes, Michaelides, and Polkovnichenko (2013) show that a higher interest rate response can be generated in an incomplete markets model with aggregate risk and in which households have a finite lifetime. However, in the absence of an operational intergenerational transfer motive, assuming a finite lifetime implies that households perceive government bonds as net worth (see Barro 1974)), even in the absence of borrowing constraints.