The Government Budget Constraint

For a household that can borrow and lend freely at a market-determined interest rate, the intertemporal budget constraint requires that the present value of its current and future consumption cannot exceed the value of its current assets plus the present value of its future labor income.

6.1.1 Government Deficits, Debt, and Solvency

Consider a government that chooses a stream of primary government expenditure C_g(t), a stream of taxes T(t), and has a stock of outstanding government debt D(t). Government expenditure can be financed by either taxes or the accumulation of government debt. Government debt accumulates according to

where r(t) is the real interest rate at time t.

The right-hand side of (6.1) denotes the government deficit, the extent to which current taxes fall short of total government expenditure. A government deficit means that the government is accumulating government debt.

The solution of the differential equation (6.1) for the accumulation of government debt gives us the government intertemporal budget constraint in the form¹

where .

The intertemporal budget constraint of the government (6.2) states that at any initial time 0, as time goes to infinity, the present value of primary government expenditure plus the present value of government debt must be equal to the present value of tax revenues minus the initial level of government debt.

Clearly, a solvent government cannot maintain a government debt with a positive present value as time goes to infinity. The present value of its debt should be tending to zero, or even become negative. Hence, the condition for a solvent government is that the first term of (6.2) on the left tends to a nonpositive number:

Expression (6.3) is the transversality condition that any solvent government must satisfy. The present value of government debt cannot be positive as time goes to infinity. Thus, (6.3) denotes the limits to the accumulation of government debt.

From (6.2) and (6.3), the intertemporal government budget constraint for a solvent government can be written as

As in the case of the representative household model in chapter 4, we can define the average real interest rate between time 0 and time t as

With this definition, (6.4) can also be written as

The government budget constraint does not stop the government from having debt continuously, or even from increasing the stock of its debt. However, the present value of future government debt as time goes to infinity cannot possibly be positive. As for households, this restriction implies that the government must satisfy the transversality condition (6.3), which can also be written as

For example, if the real interest rate is positive, a positive constant stock of real government debt—which means that the government never pays it back—satisfies the transversality condition and therefore the government budget constraint.

Apart from the overall government deficit, it is also worth defining another measure of fiscal policy, C_g(t) −T(t), which is called the primary government deficit. This measures the extent to which current taxes fall short of primary government expenditure, which excludes interest payments on outstanding debt. The primary deficit is a very informative index of the contribution of fiscal policy to the evolution of government debt. For example, we can write the intertemporal government budget constraint (6.4) as

Expressed in this form, the government budget constraint requires that the current stock of government debt must be smaller than or equal to the present value of current and future primary surpluses (negative primary deficits). A government that has a positive level of debt must be committed to a policy of future primary surpluses that, in present-value terms, are at least as high as its current stock of debt. Otherwise, it does not satisfy its intertemporal budget constraint, and its fiscal policy is not sustainable.

Whether the government budget constraint (in the sense that we have defined it) is satisfied determines whether a given budgetary policy is sustainable over time. Real government debt cannot be growing at a rate higher than the real interest rate. When it does, the government follows an unsustainable budgetary policy.

In what follows, we shall concentrate on budgetary policies that satisfy the sustainability criterion (6.3), which is the same as satisfying the intertemporal budget constraint (6.4).

6.2