Can Public Debt Be Sustainable? - A Contribution to the Theory of the Sustainability of Public Debt

Abstract

The sustainability of government’s financial situation has two aspects: solvency and liquidity. The government is solvent if it satisfies its intertemporal budget constraint. In the steady state of a growing economy, the government is solvent if the public-debt-to-GDP ratio is constant and the real interest rate on government debt exceeds the growth rate of real GDP. The government is liquid if its instantaneous budget constraint is satisfied. According to Gärtner 2009, for a constant primary-deficit-to-GDP ratio, this steady state debt-to-GDP ratio is unstable if the real interest rate on government debt exceeds the growth rate of real GDP. Hence, there seems to be a tension between sustainability concerning government’s solvency and sustainability concerning government’s liquidity if the latter is defined as stability of the steady state debt-to-GDP ratio. This leads to the main research question of this paper: Is it true that in a growing economy a constant debt-to-GDP ratio can only be stable if the government’s solvency constraint is violated? Or put differently: Is it true that public debt cannot be sustainable? Obviously, one counterexample is enough to show that a proposition does not hold in general. Such a counterexample based on the Solow growth model is presented in the paper. Hence, in general, sustainability of public debt is possible in the sense, that both the solvency constraint and the liquidity constraint with a stable steady state debt-to-GDP ratio are satisfied for a set of parameter constellations.

Keywords: Public debt, sustainability, stability, public capital, economic growth

JEL Classification: E62, H60, O40