Macroeconomics - Barro Chapter 14 1 C h a p t e r 1 4 Public Debt.

Macroeconomics - Barro Chapter 14

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C h a p t e r 1 4Public Debt


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The History of U.S. and U.K. Public Debt

• The nominal quantity of interest-bearing debt and the ratio of this debt to nominal GDP


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Characteristics of Government Bonds

• We assume that government bonds pay interest and principal in the same way as private bonds.

• We assume that bondholders (households in our model) regard government bonds as equivalent to private bonds.


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Characteristics of Government Bonds

• total bond holdings= Bt + Bgt

• total bond holdings=

private bonds+ government bonds• The quantity of private bonds held by all

households is still zero, because the positive amount held by one household must correspond to the debt of another household. Bt = 0 still holds in the aggregate.

• total bond holdings of all households= Bgt


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Budget Constraints and Budget Deficits

• The Government’s Budget Constraint– Gt + Vt = Tt + ( Mt− Mt−1)/ Pt

– The real value of these interest payments, it−1·(Bgt−1/Pt) adds to the government’s expenditure or uses of funds on the left-hand side of the government’s budget constraint.


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• The Government’s Budget Constraint– Expanded Budget constraint.

• Gt + Vt + it−1·(Bgt−1/ Pt )

= Tt + (Bgt − Bg

t−1)/Pt + (Mt−Mt−1)/Pt

• real purchases+ real transfers+ real interest payments

= real taxes + real debt issue

+ real revenue from money creation


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• The Government’s Budget Constraint– When nominal money, Mt, and the price level,

Pt, do not change over time, the government’s budget constraint becomes.

• Gt+ Vt+ rt−1·Bgt−1/P =

Tt+ (Bgt− Bg

t−1)/P


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• The Budget Deficit

– real government saving

= − (Bgt − Bg

t−1)/P


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• The Budget Deficit– − (Bg

t− Bgt−1)/P

= Tt − Gt+ Vt+ rt−1·Bgt−1/P

– real government saving

= real taxes− real government expenditure


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• The Budget Deficit– the government’s revenue exceeds its

expenditure, and the government has a budget surplus.

– the government has a balanced budget, and the government’s real saving is zero.


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• Public Saving, Private Saving, and National Saving– real household saving( economy-wide) =

Kt− Kt−1 + (Bgt − Bg

t−1)/ P


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• Public Saving, Private Saving, and National Saving– when we combine government and household

saving, the change in real government bonds, (Bg

t − Bgt−1)/P, cancels out. An increase in real

government bonds means that the government is saving less and that households are saving correspondingly more.

– real national saving= Kt− Kt−1


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Household’s multiyear budget constraint– C1 + C2/(1+r1) + · · · = (1+r0)·( B0/P+K0)

+(w/P)1·Ls1 +(w/P)2 · Ls

2 /(1+r1) + ·· ·

+( V1 − T1) + ( V2 − T2)/( 1 + r1)

+( V3 − T3)/[(1+ r1) · ( 1 + r2) ] + ·· ·


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• multiyear household budget constraint with government bonds– C1 + C2/(1+r1) + ··· = (1+r0)·( B0/P+Bg

0/P+K0)

+(w/P)1·Ls1 +(w/P)2 · Ls

2 /(1+r1) + ·· ·

+( V1 − T1) + ( V2 − T2)/( 1 + r1)

+( V3 − T3)/[(1+ r1) · ( 1 + r2) ] + ·· ·


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• A Simple Case of Ricardian Equivalence– The real interest rate, rt, is the same each

year: r0 = r1 = r2 = · · · = r .

– , Mt, and Pt, do not change over time. With a zero inflation rate, π, the real interest rate, r , equals the nominal rate, i .

– Real transfers, Vt, are zero each year.

– the government has a given time path of purchases, Gt


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• A Simple Case of Ricardian Equivalence– Governemnt Budget Constraint

• Gt+ r· Bgt−1/P = Tt+ (Bg

t−Bgt−1

)/P

– the government starts with zero debt, we have Bg

0/P = 0. in year 1, the government’s real interest payments, r · (Bg

0/P), are zero, and the budget constraint is

– G1 = T1 + Bg1/P


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• A Simple Case of Ricardian Equivalence– Suppose, to begin, that the government

balances its budget each year. Then, in year1, real purchases, G1, equal real taxes, T1

– Continuing on, if the government balances its budget every year, the real public debt, Bg

t /P, is zero in every year t.


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• A Simple Case of Ricardian Equivalence– if, instead of balancing its budget in year 1,

the government runs a real budget deficit of one unit?

– the deficit must come from a cut in real taxes, T1, by one unit. the real deficit of one unit requires the government to issue one unit of real public debt at the end of year 1, so that Bg

1 /P = 1.


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• A Simple Case of Ricardian Equivalence– Assume that the government decides to

restore the public debt to zero from year 2 onward, so that Bg

2 /P = Bg3 /P = · · · = 0.

– G2 + r·Bg1 /P = T2 + (Bg

2−Bg1)/P

• Bg1/P = 1 and Bg

2/P = 0


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• A Simple Case of Ricardian Equivalence– Simplified Budget Constraint

• G2 + r = T2 − 1

• T2 = G2 + 1 + r

– This equation says that the government must raise real taxes in year 2, T2, above year 2’s government purchases, G2, to pay the principal and interest, 1 + r , on the one unit of debt, Bg

1 /P, issued in year 1.


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• A Simple Case of Ricardian Equivalence

– decrease in year 1 ,s real taxes+ present value of increase in year 2 ,s taxes

= −1 + ( 1 + r)/( 1 + r)

= −1 + 1

= 0


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• A Simple Case of Ricardian Equivalence– If the government replaces a unit of real taxes

with a unit of real budget deficit, households know that the present value of next year’s real taxes will rise by one unit. Thus, the real budget deficit is the same as a real tax in terms of the overall present value of real taxes. This finding is the simplest version of the Ricardian equivalence theorem on the public debt.


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• Another Case of Ricardian Equivalence– G2 + r·Bg

1 /P = T2 + (Bg2−Bg

1)/P

• Bg2/P = Bg

1/P = 1

• G2 + r = T2

• we find again that the deficit-financed tax cut in year 1 has no income effects on households.


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• Ricardian Equivalence More Generally– C1 + C2/(1+r1) + ··· = (1+r0)·( B0/P+Bg

0/P+K0)

+(w/P)1·Ls1 +(w/P)2 · Ls

2 /(1+r1) + ·· ·

+( V1 − T1) + ( V2 − T2)/( 1 + r1)

+( V3 − T3)/[(1+ r1) · ( 1 + r2) ] + ·· ·


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• Another Case of Ricardian Equivalence– If the time path of government purchases, Gt, is

given (and if real transfers, Vt ,are zero), we can show that a higher Bg

0/P requires the government to collect a correspondingly higher present value of real taxes, Tt, to finance the debt. This higher present value of real taxes exactly offsets the higher Bg

0/P Thus, we still have no income effects on households.


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Economic Effects of a Budget Deficit

• What happens in the equilibrium business-cycle model when the government cuts year 1’s real taxes, T1, and runs a budget deficit? Economists often refer to this type of change as a simulative fiscal policy.


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• Lump-Sum Taxes– the cut in year 1’s real taxes, T1, and the

increases in future real taxes, Tt , all involve lump-sum taxes.

• these taxes is that they have no substitution effects on consumption and labor supply.

– We have found in our equilibrium business-cycle model that a deficit-financed tax cut does not stimulate the economy. In particular, real GDP, Y, gross investment, I, and the real interest rate, r , do not change


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• Labor Income Taxes– Instead of lump-sum taxes, the government

levies taxes on labor income. Consider again a reduction in year 1’s real taxes, T1, financed by a budget deficit. We assume that the fall in T1 is accompanied by a decline in the marginal income tax rate, (τw)1.


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• Labor Income Taxes– The changes in marginal income tax rates,

(τw)1 and (τw)2, affect the labor market in years 1 and 2.


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• Labor Income Taxes– The increase in (τw)2 lowers labor supply in

year 2. This decrease in labor supply leads, when the labor market clears, to a lower quantity of labor, (L2). The reduced labor input leads to a decrease in year 2’s real GDP, Y2.


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• Labor Income Taxes– a budget deficit allows the government to

change the timing of labor-income tax rates and thereby alter the timing of labor input and production.

– A budget deficit that finances a cut in year 1’s tax rate on labor income motivates a rearrangement of the time pattern of work and production—toward the present (year 1) and away from the future (year 2).


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• Asset Income Taxes– changes in the timing of asset-income tax

rates cause changes in the timing of consumption, C, and investment, I. The general point is that, by running budget deficits or surpluses, the government can change the timing of various tax rates. The government can induce changes in the timing of various aspects of economic activity: L, Y, C, and I.


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• The Timing of Taxes and Tax-Rate Smoothing– We have found that budget deficits and

surpluses allow the government to change the timing of tax rates. However, it would not be a good idea for the government randomly to make tax rates high in some years and low in others.


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• The Timing of Taxes and Tax-Rate Smoothing– The public debt has typically been managed

to maintain a pattern of reasonably stable tax rates over time. This behavior is called tax-rate smoothing.


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• Strategic Budget Deficits– This view of the Reagan-Bush budget deficits

after 1983 gave rise to a new theory called strategic budget deficits.9 The word “strategic” is used because the models involve political strategies analogous to those analyzed in game theory.


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• The Standard View of a Budget Deficit– Ricardian equivalence - a deficit-finance tax

cut does not affect real GDP and other macroeconomic variables.


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• The Standard View of a Budget Deficit– a deficit-financed tax cut makes households feel

wealthier, consumption, C1, increases.

– year 1’s inputs of labor and capital services stay the same, and real GDP, Y1 does not change.

– Since C1 increases, gross investment, I1, has to decline for given government purchases, G1.


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• The Standard View of a Budget Deficit– These long-term negative effects on capital

stock and real GDP are sometimes described as a burden of the public debt


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• The Standard View of a Budget Deficit– Finite lifetimes

• Why does a budget deficit make people feel wealthier when they have finite lifetimes? The decrease in the present value of real taxes for current generations coincides with an increase in the present value of real taxes for members of future generations. Individuals will be born with a liability for a portion of taxes to pay the interest and principal on the higher stock of real public debt.

• These people will not share in the benefits from the earlier tax cut. Present taxpayers would not feel wealthier if they counted fully the present value of the prospective taxes on descendants.


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• The Standard View of a Budget Deficit– Imperfect credit markets

• When credit markets are imperfect, some households will calculate present values of future real taxes by using a real interest rate above the government’s rate.


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Social Security

• Retirement benefits paid through social security programs are substantial in the United States and most other developed countries.

• Feldstein argue that these public pension programs reduce saving and investment.


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Social Security

• Social security is not a fully funded system.– workers’ payments accumulate in a trust fund,

which later provides for retirement benefits.

• pay-as-you-go system, in which benefits to elderly persons are financed by taxes on the currently young.


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Social Security

• economic effects of social security in a pay-as-you-go system.– When a social security system starts or

expands, elderly persons experience an increase in the present value of their social security benefits net of taxes. The increase in the present value of real transfers net of real taxes implies a positive income effect on the consumption of this group.


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Social Security

• economic effects of social security in a pay-as-you-go system.– Young persons face higher taxes, offset by the

prospect of higher retirement benefits.– the fall in consumption by the currently young

tends to be smaller in size than the increase for the currently old.

– we predict an increase in current aggregate consumption. Or, to put it another way, total private saving declines.


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Social Security

• The decline in national saving leads in the short run to a decrease in investment and, in the long run, to a reduced stock of capital.


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Open-Market Operations

• Open-market operations.– An open-market purchase occurs when the

central bank, such as the Federal Reserve, buys bonds—typically government bonds—with newly created money.

– an open-market purchase has the same effects as the unrealistic helicopter drop of money


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Open-Market Operations

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Macroeconomics - Barro Chapter 14 1 C h a p t e r 1 4 Public Debt.

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