This is “The Government Budget Constraint”, section 16.22 from the book Theory and Applications of Macroeconomics (v. 1.0).
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Like households, governments are subject to budget constraints. These can be viewed in two ways, either within a single year or across many years.
In any given year, money flows into the government sector, primarily from the taxes that it imposes on individuals and corporations. We call these government revenues. Money flows out in the form of outlays: government purchases of goods and services and government transfers. The circular flow of income tells us that any difference between government purchases and transfers and government revenues represents a government deficit.
Often, we find it useful to group taxes and transfers together as “net taxes” and separate out government purchases, as in the last line of our definition.
When outflows are less than inflows, then we say a government is running a surplus. In other words, a negative government deficit is the same as a positive government surplus, and a negative government surplus is the same as a positive government deficit.government surplus = −government deficit.
When a government runs a deficit, it must borrow from the financial markets. When a government runs a surplus, these funds flow into the financial markets and are available for firms to borrow. A government surplus is sometimes called government saving.
Tax and spending decisions at different dates are linked. Although governments can borrow or lend in a given year, a government’s total spending over time must be matched with revenues. When a government runs a deficit, it typically borrows to finance it. It borrows by issuing more government debt (government bonds).
To express the intertemporal budget constraint, we introduce a measure of the deficit called the primary deficit. The primary deficit is the difference between government outlays, excluding interest payments on the debt, and government revenues. The primary surplus is minus the primary deficit and is the difference between government revenues and government outlays, excluding interest payments on the debt.
The intertemporal budget constraint says that if a government has some existing debt, it must run surpluses in the future so that it can ultimately pay off that debt. Specifically, it is the requirement thatcurrent debt outstanding = discounted present value of future primary surpluses.
This condition means that the debt outstanding today must be offset by primary budget surpluses in the future. Because we are adding together flows in the future, we have to use the tool of discounted present value. If, for example, the current stock of debt is zero, then the intertemporal budget constraint says that the discounted present value of future primary surpluses must equal zero.
The stock of debt is linked directly to the government budget deficit. As we noted earlier, when a government runs a budget deficit, it finances the deficit by issuing new debt. The deficit is a flow that is matched by a change in the stock of government debt:change in government debt (in given year) = deficit (in given year).
The stock of debt in a given year is equal to the deficit over the previous year plus the stock of debt from the start of the previous year. If there is a government surplus, then the change in the debt is a negative number, so the debt decreases. The total government debt is simply the accumulation of all the previous years’ deficits.
When a government borrows, it must pay interest on its debt. These interest payments are counted as part of the deficit (they are included in transfers). If a government wants to balance the budget, then government spending must actually be less than the amount government receives in the form of net taxes (excluding interest).
This presentation of the tool neglects one detail. There is another way in which a government can fund its deficit. As well as issuing government debt, it can print money. More precisely, then, every year,change in government debt = deficit − change in money supply.
Written this way, the equation tells us that the part of the deficit that is not financed by printing money results in an increase in the government debt.
We often denote government purchases of goods and services by G and net tax revenues (tax revenues minus transfers) by T. The equation for tax revenues is as follows:T = τ × Y,
where τ is the tax rate on income and Y is real gross domestic product (real GDP). The deficit is given as follows:government deficit = G − T = G − τ × Y.
From this equation, the deficit depends on the following: