Lecture 16: The Government's Budget Constraint

The Government's Budget Constraint

Motivating Questions

• How do tax cuts or government transfers affect consumption, the real interest rate, and investment?

• Do fiscal deficits resulting from tax cuts or increased transfers increase interest rates and crowd out investment?

Two Views About Tax Cuts

View I

• Tax cuts create fiscal deficits.

• The government borrows to cover the deficit.

• Increased government borrowing raises interest rates.

• This negatively impacts investment.

• Consumption rises as tax cuts increase disposable income.

View II

• Tax cuts lead to higher public debt, necessitating future tax increases to repay the debt and interest.

• Households anticipate future tax increases and save the tax cut to cover them.

• Consumption remains unchanged.

• Interest rates do not rise.

• Investment is unaffected.

• This is known as Ricardian equivalence.

Question

• Which view is correct?

A Two-Period Model

• The economy consists of two periods.

Basic Units of the Model

1. The Government

2. Firms

3. Households

• This lecture introduces the government into the model.

The Government

• T_1 = taxes in period 1 (in real terms)

• T_2 = taxes in period 2 (in real terms)

• The government determines T1 and T2 . Initially, taxes are lump sum, meaning they do not depend on income or spending.

• G_1 = government spending in goods in period 1 (in real terms)

• G_2 = government spending in goods in period 2 (in real terms)

• G1 and G2 are typically exogenously given.

The Fiscal Deficit

• B_t denotes real government debt (bonds) issued in period t and maturing in period t+1.

• r_t is the real interest rate on this debt.

• Primary Fiscal Deficit = Gt - Tt

• Secondary Fiscal Deficit = G_{t}-T_{t}+r_{t-1}B_{t-1}

• Government Saving = S_{t}^{g^{}}=T_{t}-G_{t}-r_{t-1}B_{t-1}

The Government Budget Constraint in Period 1 (t = 1)

• The government finances its fiscal deficit by issuing debt, represented as B_1-B_0 .

• The budget constraint in period 1 is: B_1-B_0=G_1+r_0B_0-T_1

• Assume the government starts with no debt, so B_0 = 0.

• The budget constraint simplifies to: B_1=G_1-T_1 (1)

• When B_0 = 0, the secondary fiscal deficit equals the primary fiscal deficit in period 1.

The Government Budget Constraint in Period 2 (t = 2)

• The government budget constraint in period 2 mirrors that of period 1, with time subscripts advanced by one period: B_2-B_1=G_2+r_1B_1-T_2

• The government cannot issue debt in period 2, thus B_2 = 0.

• Rearranging, the budget constraint becomes: T_2-G_2=\left(1+r_1\right)B_1 (2)

• This equation states that the primary fiscal surplus in period 2, T_T_2-G_2, must cover the public debt, B_1 , plus interest,r_1B_1 .

The Intertemporal Budget Constraint of the Government

• Combining the period-1 and period-2 government budget constraints to eliminate B_1, gives the inter-temporal budget constraint: G1+\frac{G2}{1+r1}=T1+\frac{T2}{1+r_1} (3)

• This constraint implies that the present discounted value of government expenditures must equal the present discounted value of tax revenues for fiscal solvency.

• Fiscal solvency doesn't depend on whether G_1 is larger or small than T1 or whether G_2 is smaller or larger than T_2 as long as the stream of government purchases equals the stream of taxes in present value.

Tax Cuts Today Imply Tax Increases in the Future

• Assume a tax cut in period 1: \Delta T_1 < 0

• Assume government spending remains constant: \delta G_1=\delta G_2=0

• According to the intertemporal budget constraint (3), the government must raise taxes in period 2 by: \delta T_2=-\left(1+r\right)\delta T_1>0

• This implies that a tax cut today, with constant government spending, requires borrowing, which must be repaid with interest in period 2, necessitating a tax increase then.