The debt-dynamics equation, simulated.
Move growth, the real interest rate, and the primary balance to see how debt-to-GDP evolves. Stress tests show what happens under adverse shocks. The math is simple; the policy implications rarely are.
Built and reviewed by Stephen Omukoko Okoth
Mathematical Economist · ex-Morgan Stanley FI · Equilar
Inputs
Starting point
Inputs
The dynamics
Verdict
Debt-to-GDP in year 15: 96.9%
Debt path is rising — adjustment needed.
The interest-growth differential (r − g = 1.0%) is the structural force on debt dynamics. To stabilize debt at the current level, you'd need a primary balance of ~0.7% of GDP.
Key numbers
The fiscal math
r − g
1.0%
Interest minus growth
Stabilizing PB
0.7%
Primary balance to hold debt flat
Adjustment needed
1.7%
Primary balance gap
Year 15 debt
96.9%
Trajectory
Baseline + 3 stress tests
Three independent shocks: growth slows by 2pp, real rates rise by 200bp, primary balance worsens by 2pp. Compare each to baseline.
Common questions
What is debt sustainability?
Whether a country can keep paying its debts under realistic future conditions, without resorting to default, monetization, or wealth-destroying adjustment. The math comes down to whether the debt-to-GDP ratio is on a stable, falling, or exploding trajectory.
What is the 'r minus g' that everyone quotes?
The interest-growth differential — real interest rate on debt minus real GDP growth. When r > g, debt-to-GDP rises automatically (compounding effect dominates). When r < g, debt-to-GDP can stabilize or fall even with modest deficits — most developed economies post-2008 lived in r < g.
What is the primary balance?
Government revenue minus non-interest spending. It strips out debt service to focus on the policy choice you can actually control today. A country running a primary surplus is paying down debt before interest; a primary deficit means borrowing to cover even basic operations.
What's a sustainable debt level?
It depends. Japan operates at 250% of GDP, but it borrows in its own currency from domestic savers. Emerging markets typically face stress around 60-70%, especially if debt is foreign-currency denominated. The IMF DSA framework is the canonical analysis.