This technical note explains more formally why long-run sustainability of the government’s fiscal position depends on the interest rate it has to pay on its debt, the size of the government’s deficit after excluding interest payments, and the growth of the country’s nominal GDP
In certain circumstances a government’s fiscal position can become unsustainable – it will become unable to repay its debt or even the interest on it. To see how imagine that the country’s existing stock of debt equals £100m and that its nominal GDP equals £200m. Its debt to GDP percentage is therefore 50%. If the interest paid on its debt is 3% then, even in the absence of any other commitments, the government would have to raise £3m to pay the debt holders their promised interest. If the government planned no rise in taxation then it would have to issue an extra £3m of bonds; and so the stock of debt would grow by 3%. If the same assumed conditions were to hold next period the debt would again grow at 3%. So this force alone would cause the government’s debt to grow by 3% p.a. in nominal terms.
Now imagine that in addition the government’s other spending exceeds its tax revenue by £2m each year. The time path for government debt will therefore be £100m, £105m, £110.15m (= £105mx1.03+£2m), £115.4545m, … and so on. In this situation the country’s debt to GDP percentage will rise exponentially and eventually become unsustainable – there will no-one able to buy it. But if nominal GDP itself is also growing then this not need be the case. For example if nominal GDP grows at 10% p.a. then, even though the government is running a deficit, the debt to GDP percentage will gradually decline from 50% to 47.73%, to 45.52% and so on, and will eventually become negligible.
So the long-run sustainability of the government’s fiscal position depends on the interest rate it has to pay on its debt, the size of the government’s deficit after excluding interest payments, and the growth of the country’s nominal GDP. The greater the growth rate of nominal income and the lower the interest rate it has to pay on its debt the greater the deficit the government can run whilst still maintaining fiscal sustainability.
From this perspective, given their high current Net Debt to GDP ratios in 2016, Greece, Italy, Japan and Portugal appear most prone to fiscal unsustainability.