The mathematics of debt sustainability is based on the idea that the government’s primary surplus must equal the stock of outstanding public debt to GDP ratio multiplied by the difference between the real GDP growth rate and the effective real interest rate paid on existing debt. This is expressed mathematically as:
(Tt – Gt PtYt) = (rt-gt)(Bt-1 Pt-1Yt-1 )
Here’s some related information about debt sustainability:
- Debt sustainability and fiscal space
If (r−g) is less than zero, debt is always sustainable, even if it increases it will eventually converge. However, if (r−g) is close to zero and the government runs a large primary deficit, debt may increase for a long time and converge to a very high level.