Public Debt Dynamics When r < g: Stability Is not Guaranteed

This paper reexamines the stability of public debt dynamics in economies where real interest rate is lower than real economic growth rate (r g). While this condition is often interpreted as ensuring debt sustainability, we develop a simple dynamic model in which the real interest rate depends endogenously on public-debt-to-GDP ratio. Using difference equations, we show that a low-debt steady state can become unstable if the debt ratio temporarily exceeds a critical threshold. Once this threshold is crossed, the endogenous rise in interest rates destabilizes debt dynamics and leads to divergence, even without expectation-driven crises or default risk. The results suggest that the r g condition should be viewed as a local, state-dependent criterion rather than a guarantee of long-run fiscal safety.