Beyond g>r: Transitional Dynamics of the Debt-to-GDP Ratio

The present paper analyzes the transitional dynamics of the government-debt-to-GDP ratio in an economy with constant interest rates, economic growth, and fiscal deficit growth. By explicitly modeling the joint evolution of government debt, fiscal deficits, and GDP, the present paper derives closed-form expressions for the debt-to-GDP ratio and characterizes its dynamic behavior. The analysis shows that even when standard long-run sustainability conditions—such as an interest rate lower than the economic growth rate—are satisfied, the debt-to-GDP ratio need not evolve monotonically. Instead, it may exhibit a single-peaked trajectory, rising temporarily before converging in the long run. The present paper identifies precise conditions under which such non-monotonic dynamics arise and illustrates them with numerical examples.