Optimal Debt to GDP: A Quantitative Theory

44 Pages Posted: 24 Jul 2023

See all articles by Johannes Brumm

Johannes Brumm

Karlsruhe Institute of Technology

Jakob Hußmann

Karlsruhe Institute of Technology - Department of Economics and Management

Date Written: July 11, 2023

Abstract

We analyze public debt policies within a calibrated stochastic OLG model with distortionary taxation. The risk-free interest rate is realistically sensitive to public debt and lower than the growth rate. The risky rate is substantially higher due to convenience benefits of public debt, idiosyncratic return risk, and aggregate risk. To discern welfare assessment from fiscal analysis, we define and compare welfare-maximizing debt (WMD) and deficit-maximizing debt (DMD). Although free-lunch deficits can reduce tax distortions, DMD tends to exceed WMD. Both rise if the risk-free rate falls due to increases in risk, convenience benefits, or longevity, but not necessarily if it falls due to lower growth or government spending. Taking market power into account barely changes DMD yet substantially reduces WMD. When wealth inequality is included, the middle class favors debt lower than the WMD in the representative agent case, whereas the rich favor much higher debt-to-GDP ratios.

Keywords: public debt, debt-to-GDP ratio, free-lunch deficits, real interest rate, risk premium, risk-sharing, convenience yield, distortionary taxation, market power, wealth inequality

JEL Classification: E43, E62, H62, H63

Suggested Citation

Brumm, Johannes and Hußmann, Jakob, Optimal Debt to GDP: A Quantitative Theory (July 11, 2023). Available at SSRN: https://ssrn.com/abstract=4510125 or http://dx.doi.org/10.2139/ssrn.4510125

Johannes Brumm (Contact Author)

Karlsruhe Institute of Technology ( email )

Kaiserstraße 12
Karlsruhe, Baden Württemberg 76131
Germany

Jakob Hußmann

Karlsruhe Institute of Technology - Department of Economics and Management ( email )

Kaiserstraße 12
Karlsruhe, Baden Württemberg 76131
Germany

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