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Chapter14
Public Debt
Macroeconomics Chapter 14
1
The History of U.S. and U.K. Public Debt

The nominal quantity of interestbearing debt and the ratio of this
debt to nominal GDP
Macroeconomics Chapter 14
2
Macroeconomics Chapter 14
3
The History of U.S. and U.K. Public Debt
Macroeconomics Chapter 14
4
The History of U.S. and U.K. Public Debt
Macroeconomics Chapter 14
5
The Data of Chinese Public Debt



From 1981
(中国市场统计年鉴2001年7-27)
1990 890.34
1991 1059.99
1992 1282.72
1993 1540.74
1994 2286.40
1995 3300.30
1996 4361.43
1997 5508.93
1998 7765.70
1999 10542.00
2000 13674.00
2008年6月末中央财政国债总余额为52385.86亿元，控制
在年末55185.85亿元国债余额限额以内 (2008年上半年国
债管理报告)
财政部部长助理张通9日表示，2009年财政政策较大幅度增
加中央财政赤字，并相应增加国债发行规模，中央财政国债
余额限额为62708.35亿元。 (2009年04月09日 16:02
来源：中国新闻网 )
Macroeconomics Chapter 14
6
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.
Macroeconomics Chapter 14
7
Characteristics of Government Bonds

total bond holdings= Bt + Bgt
total bond holdings=
private bonds+ government bonds

Bt = 0 still holds in the aggregate.

total bond holdings of all households= Bgt

Macroeconomics Chapter 14
8
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.
Macroeconomics Chapter 14
9
Budget Constraints and Budget Deficits

The Government’s 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
Macroeconomics Chapter 14
10
Budget Constraints and Budget Deficits

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
Macroeconomics Chapter 14
11
Budget Constraints and Budget Deficits

The Budget Deficit

real government saving
= − (Bgt − Bgt−1)/P
Macroeconomics Chapter 14
12
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
Macroeconomics Chapter 14
13
Budget Constraints and Budget Deficits

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.
Macroeconomics Chapter 14
14
Budget Constraints and Budget Deficits
Macroeconomics Chapter 14
15
Budget Constraints and Budget Deficits

Public Saving, Private Saving, and
National Saving


real household saving(economy-wide)
= Kt− Kt−1 + (Bgt − Bgt−1)/ P
real national saving= Kt− Kt−1
Macroeconomics Chapter 14
16
Budget Constraints and Budget Deficits
Household’s multiyear 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) ]
+ ·· ·
Macroeconomics Chapter 14
17
Budget Constraints and Budget Deficits

multiyear 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) ] + ·· ·
Macroeconomics Chapter 14
18
Budget Constraints and Budget Deficits

A Simple Case of Ricardian Equivalence
 r0 = r1 = r2 = · · · = r .



Mt, and Pt, do not change over time.
Real transfers, Vt, are zero each year.
the government has a given time path
of purchases, Gt
Macroeconomics Chapter 14
19
Budget Constraints and Budget Deficits

A Simple Case of Ricardian Equivalence

Government Budget Constraint
 Gt+ r· Bgt−1/P = Tt+ (Bgt−Bgt−1)/P

the government starts with Bg0/P = 0.

In year 1：G1 = T1 + Bg1/P
Macroeconomics Chapter 14
20
Budget Constraints and Budget Deficits

A Simple Case of Ricardian Equivalence




Suppose, to begin, that the government
balances its budget each year.
Then in year1 G1 = T1
Continuing on, if the government
balances its budget every year,
Bgt /P, =0 in every year t.
Macroeconomics Chapter 14
21
Budget Constraints and Budget Deficits

A Simple Case of Ricardian Equivalence
 now 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
Bg1 /P = 1.
Macroeconomics Chapter 14
22
Budget Constraints and Budget Deficits

A Simple Case of Ricardian Equivalence
 Assume Bg2 /P = Bg3 /P = · · · = 0.

G2 + r·Bg1 /P = T2 + (Bg2−Bg1)/P
 Bg1/P
= 1 and Bg2/P = 0
 G2
+ r = T2 − 1
 T2 = G2 + 1 + r
Macroeconomics Chapter 14
23
Budget Constraints and Budget Deficits

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
Macroeconomics Chapter 14
24
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.
Macroeconomics Chapter 14
25
Budget Constraints and Budget Deficits

Another Case of Ricardian Equivalence
 G2 + r·Bg1 /P = T2 + (Bg2−Bg1)/P

Bg2/P = Bg1/P = 1

G2 + r = T 2
Macroeconomics Chapter 14
26
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) ] + ·· ·
Macroeconomics Chapter 14
27
Budget Constraints and Budget Deficits

Ricardian Equivalence More Generally
t=1: T1 decreases 1
 t=2:
T2 increases r
 t=3:
T3 increases r
 ·· ·
we find again that the deficit-financed tax
cut in year 1 has no income effects on
households.


Macroeconomics Chapter 14
28
Budget Constraints and Budget Deficits

Ricardian Equivalence More Generally


If the time path of Gt is given (and if Vt = 0),
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.
Macroeconomics Chapter 14
29
Economic Effects of a Budget Deficit


What happens in the equilibrium businesscycle 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.
Macroeconomics Chapter 14
30
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.


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
Macroeconomics Chapter 14
31
Economic Effects of a Budget Deficit

Labor Income Taxes


The fall in T1 is accompanied by a
decline in (τw)1.
The changes in marginal income tax
rates, (τw)1 and (τw)2, affect the labor
market in years 1 and 2.
Macroeconomics Chapter 14
32
Economic Effects of a Budget Deficit
Macroeconomics Chapter 14
33
Economic Effects of a Budget Deficit
Macroeconomics Chapter 14
34
Economic Effects of a Budget Deficit

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.
Macroeconomics Chapter 14
35
Economic Effects of a Budget Deficit

Labor Income Taxes


a budget deficit allows the government
to change 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).
Macroeconomics Chapter 14
36
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 induce changes in the
timing of various aspects of economic
activity: L, Y, C, and I.
Macroeconomics Chapter 14
37
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.
Macroeconomics Chapter 14
38
Economic Effects of a Budget Deficit

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.
Macroeconomics Chapter 14
39
Economic Effects of a Budget Deficit

Strategic Budget Deficits


This view of the Reagan-Bush budget
deficits 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.
Macroeconomics Chapter 14
40
Economic Effects of a Budget Deficit


Ricardian equivalence - a deficit-finance
tax cut does not affect real GDP and
other macroeconomic variables.
The Standard View of a Budget Deficit
 a deficit-financed tax cut makes
households feel wealthier,
consumption, C1, increases。
Macroeconomics Chapter 14
41
Economic Effects of a Budget Deficit

The Standard View of a Budget Deficit


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.
Macroeconomics Chapter 14
42
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
Macroeconomics Chapter 14
43
Economic Effects of a Budget Deficit

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.
Macroeconomics Chapter 14
44
Economic Effects 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.
Macroeconomics Chapter 14
45
Social Security


Retirement benefits paid through
social security programs are
substantial in the United States and
most other developed countries.
Feldstein argues that these public
pension programs reduce saving and
investment.
Macroeconomics Chapter 14
46
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.
Macroeconomics Chapter 14
47
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.
Macroeconomics Chapter 14
48
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.
Macroeconomics Chapter 14
49
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.
Macroeconomics Chapter 14
50
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
Macroeconomics Chapter 14
51
Open-Market Operations
Macroeconomics Chapter 14
52