National Saving, Public and Private

Households and firms save by not spending all their income; that's private saving. The government saves too, in its own way: if it collects more in taxes than it spends, the leftover is public saving, a positive number. If it spends more than it collects, it runs a deficit, and that deficit is negative public saving, because the government is borrowing instead of adding to the pool of funds available to lend. Add private saving and public saving together and you get national saving, the total supply of funds in a closed economy available to finance investment.

This identity is why a government surplus counts as saving for the whole country: the surplus is unspent income sitting in the same pool that private savers contribute to, ready to be loaned out. A deficit does the opposite, pulling from that pool to cover the government's shortfall, which is why it subtracts from national saving rather than adding to it.

National saving is exactly the supply side of the loanable funds market. When public saving falls because the deficit grows, national saving shrinks, the supply of loanable funds shifts left, and the real interest rate rises as savings become scarcer relative to the demand for borrowing. Once an economy opens to foreign capital, national saving is no longer the only source of funds for domestic investment: foreign saving can flow in or out too, so the loanable funds supply becomes national saving plus net capital inflow.