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.
- Debt sustainability analysis
The Debt Sustainability Framework (DSF) is a tool that helps low-income countries make borrowing decisions that match their financing needs with their ability to repay. The DSF requires countries to regularly analyze their projected debt burden and vulnerability to economic and policy shocks.
- Stochastic DSA
This probabilistic tool uses the historical volatility and co-movement of macroeconomic variables to produce a fan chart around the deterministic debt path. Fan charts can be used to calculate probabilities attached to certain sustainability indicators.
