PowerPoint Slides
to accompany
Prepared by Apostolos Serletis
University of Calgary
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1
Chapter14
Public Debt
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2
The History of Canadian Public Debt
• The nominal quantity of interest-bearing debt
and the ratio of this debt to nominal GDP in
Canada.
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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 in the
United States and the United Kingdom.
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The History of U.S. and U.K. Public Debt
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The History of U.S. and U.K. Public Debt
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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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11
Budget Constraints and Budget Deficits
• The Government’s Budget Constraint
Gt + Vt = Tt + (Mt− Mt−1)/Pt
– The first new term we have to add is the real value of
the government’s interest payments, it−1·(Bgt−1/Pt), to
the government’s expenditure or uses of funds on the
left-hand side of the government’s budget constraint.
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12
Budget Constraints and Budget Deficits
• The Government’s Budget Constraint
– Expanded Budget Constraint
Gt + Vt + it−1·(Bg t−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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Budget Constraints and Budget Deficits
• The Government’s Budget Constraint
– When nominal money, Mt, and the price level, Pt, do
not change over time, μ = π = 0 and i = r, and the
government’s budget constraint becomes
Gt + Vt + rt−1·Bgt−1/P = Tt + (Bgt − Bg t−1)/P
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Budget Constraints and Budget Deficits
• The Budget Deficit
real government saving = − (Bgt − Bgt−1)/P
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Budget Constraints and Budget Deficits
• The Budget Deficit
− (Bgt − Bgt−1)/P = Tt − [Gt + Vt + rt−1·Bgt−1/P ]
(real government saving = real taxes
− real government expenditure)
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Budget Constraints and Budget Deficits
• The Budget Deficit
– When the government’s revenue exceeds its
expenditure, the government has a budget surplus.
– When the government’s revenue is less than its
expenditure, the government has a budget deficit.
– When the government has a balanced budget the
government’s real saving is zero.
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17
Budget Constraints and Budget Deficits
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Budget Constraints and Budget Deficits
• Public Saving, Private Saving, and National
Saving
real household saving (economy-wide) =
Kt − Kt−1 + (Bgt − Bgt−1)/P
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Budget Constraints and Budget Deficits
• Public Saving, Private Saving, and National
Saving
– When we combine government and household
saving, the change in real government bonds, (Bgt −
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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20
Budget Constraints and Budget Deficits
Household’s Multi-Year Budget Constraint
C1 + C2/(1+r1) + · · · = (1+r0)·(B0/P+K0)
+(w/P)1·Ls1 +(w/P)2 · Ls2 /(1+r1) + ·· ·
+( V1 − T1) + ( V2 − T2)/( 1 + r1)
+( V3 − T3)/[(1+ r1) · ( 1 + r2) ] + ·· ·
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Budget Constraints and Budget Deficits
• Multi-Year Household Budget Constraint with
Government Bonds
C1 + C2/(1+r1) + ··· = (1+r0)·( B0/P + Bg0/P + K0)
+(w/P)1·Ls1 +(w/P)2 · Ls2 /(1+r1) + ·· ·
+( V1 − T1) + ( V2 − T2)/( 1 + r1)
+( V3 − T3)/[(1+ r1) · ( 1 + r2) ] + ·· ·
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Budget Constraints and Budget Deficits
• 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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Budget Constraints and Budget Deficits
• A Simple Case of Ricardian Equivalence
– Government Budget Constraint
Gt + r· Bgt−1/P = Tt + (Bgt−Bgt−1)/P
– Since the government starts with zero debt, we have
Bg0/P = 0.
– In year 1, the government’s real interest payments, r ·
(Bg0/P), are zero, and the budget constraint is
G1 = T1 + Bg1/P
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Budget Constraints and Budget Deficits
• A Simple Case of Ricardian Equivalence
– Suppose, to begin, that the government balances its
budget each year. Then, in year 1, real purchases,
G1, equal real taxes, T1
– Continuing on, if the government balances its budget
every year, the real public debt, Bgt /P, is zero in every
year t.
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25
Budget Constraints and Budget Deficits
• A Simple Case of Ricardian Equivalence
– What happens 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 Bg1 /P = 1.
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Budget Constraints and Budget Deficits
• A Simple Case of Ricardian Equivalence
– Assume that the government decides to restore the
public debt to zero from year 2 onward, so that Bg2 /P
= Bg3 /P = · · · = 0.
G2 + r·Bg1/P = T2 + (Bg2−Bg1)/P
• Bg1/P = 1 and Bg2/P = 0
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Budget Constraints and Budget Deficits
• 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, Bg1 /P, issued in year 1.
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Budget Constraints and Budget Deficits
• A Simple Case of Ricardian Equivalence
decrease in real taxes in year 1 + present value of
increase in taxes in year 2
= −1 + ( 1 + r)/( 1 + r)
= −1 + 1
= 0.
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Budget Constraints and Budget Deficits
• 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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Budget Constraints and Budget Deficits
• Another Case of Ricardian Equivalence
We assume that the government does not pay off in year
2 the one unit of debt, Bg1/P, issued in year 1, but carries
it over to year 3. We have
G2 + r·Bg1/P = T2 + (Bg2−Bg1)/P
• Bg2/P = Bg1/P = 1
• G 2 + r = T2
We find again that the deficit-financed tax cut in year
1 has no income effects on households.
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Budget Constraints and Budget Deficits
• Ricardian Equivalence More Generally
C1 + C2/(1+r1) + ··· = (1+r0)·( B0/P+Bg0/P+K0)
+(w/P)1·Ls1 +(w/P)2 · Ls2 /(1+r1) + ·· ·
+( V1 − T1) + ( V2 − T2)/( 1 + r1)
+( V3 − T3)/[(1+ r1) · ( 1 + r2) ] + ·· ·
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Budget Constraints and Budget Deficits
• 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 Bg0/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 Bg0/P. Thus, we still
have no income effects on households.
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33
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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Economic Effects of a Budget Deficit
• 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 have no substitution effects on
consumption and labour 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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Economic Effects of a Budget Deficit
• Labour Income Taxes
– Instead of lump-sum taxes, the government levies
taxes on labour 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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Economic Effects of a Budget Deficit
• Labour Income Taxes
– The changes in marginal income tax rates, (τw)1 and
(τw)2, affect the labour market in years 1 and 2.
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Economic Effects of a Budget Deficit
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Economic Effects of a Budget Deficit
• Labour Income Taxes
– The increase in (τw)2 lowers labour supply in year 2.
This decrease in labour supply leads, when the labour
market clears, to a lower quantity of labour, L2. The
reduced labour input leads to a decrease in year 2’s
real GDP, Y2.
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Economic Effects of a Budget Deficit
• Labour Income Taxes
– A budget deficit allows the government to change the
timing of labour-income tax rates and thereby alter
the timing of labour input and production.
– A budget deficit that finances a cut in year 1’s tax rate
on labour 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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Economic Effects of a Budget Deficit
• 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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Economic Effects of a Budget Deficit
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Economic Effects of a Budget Deficit
• 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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Economic Effects of a Budget Deficit
• 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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Economic Effects of a Budget Deficit
• Strategic Budget Deficits
– The Reagan-Bush budget deficits in the U.S. after
1983 gave rise to a new theory called strategic
budget deficits.
– The word “strategic” is used because the models
involve political strategies analogous to those
analyzed in game theory.
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Economic Effects of a Budget Deficit
• 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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Economic Effects of a Budget Deficit
• The Standard View of a Budget Deficit
– A deficit-financed tax cut makes households feel
wealthier, consumption, C1, increases.
– Year 1’s inputs of labour 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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Economic Effects of a Budget Deficit
• 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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Economic Effects of a Budget Deficit
• 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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Economic Effects of a Budget Deficit
• 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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50
Social Security
• Retirement benefits paid through social security
programs are substantial in the Canada, the
United States, and most other developed
countries.
• Feldstein argues 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-asyou-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-asyou-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 Bank of Canada, 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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