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.