As mentioned in Sect. 2.1, an analogy may be applied to households. With regard to households, the initial borrowing should be equal to the present discount value of the net surplus, and the difference between income and living expenses. In other words, the consumer cannot borrow money to an extent greater than the present value of available future repayments. Similarly, in order to attain fiscal sustainability, the present value of the net surplus between tax revenue and government spending should be at least equal to the initial public debt that is outstanding.
The net balance of tax revenue and government spending (T - G) is the primary balance. We may call the surplus of this balance, which is the budget surplus excluding interest payments on public debt, the primary surplus. In other words, the primary deficit is given by the difference between public debt issuance and interest payments on public debt. With regard to households, the primary surplus corresponds to the surplus between income and living expenses. Note that the standard definition of fiscal balance is the difference between spending, including interest payment G + rB and taxes T, G + rB — T. The primary deficit (G — T) is smaller than the conventional deficit (G + rB — T) by the amount of the interest payment, rB.
The primary deficit (or surplus) is a useful indicator for judging whether fiscal management is sustainable in the long run. As explained above, sustainable government budget constraint means that the present discounted value of the future primary surplus should be at least equal to the initial public debt outstanding. In other words, in order to redeem public debt, the government should earn at least the same amount of fiscal surpluses in the future. Fiscal deficits cannot accumulate forever.
If the government has issued a lot of public debt already, it is necessary to earn a lot of primary surpluses in the long run. Producing a primary deficit is not sustainable in the long run. Hence, if public debt increases with a primary deficit, this situation is not sustainable. In contrast, if public debt increases but primary deficit decreases, this situation is sustainable in the long run. This is because the primary balance would become surplus sooner or later. From this viewpoint, it is necessary to have a negative relationship between public debt and primary surplus in the long run in order to attain the sustainability of fiscal management.