Public Debt

Macroeconomics Chapter 14 1

Public Debt

C h a p t e r 1 4


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







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 )


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.


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


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·(Bg

t−1/Pt) adds to the government’s expenditure or uses of funds on the left-hand side of the government’s budget constraint.



The Government’s 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



Assuming Mt, Pt, do not change over time:

Gt+ Vt+ rt−1·Bgt−1/P =

Tt+ (Bgt− Bg

t−1)/P



The Budget Deficit

real government saving = − (Bg

t − Bgt−1)/P



The Budget Deficit − (Bg

t− Bgt−1)/P

= Tt − 【 Gt+ Vt+ rt−1·Bgt−1/P 】

real government saving = real taxes− real government

expenditure



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.





Public Saving, Private Saving, and National Saving

real household saving (economy-wide) = Kt− Kt−1 + (Bg

t − Bgt−1)/ P

real national saving= Kt− Kt−1



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) ] + ·· ·



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 · Ls

2 /(1+r1) + ···

+( V1 − T1) + ( V2 − T2)/( 1 + r1)

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



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



A Simple Case of Ricardian Equivalence

Government Budget Constraint Gt+ r· Bg

t−1/P = Tt+ (Bgt−Bg

t−1)/P

the government starts with Bg0/P = 0.

In year 1 ： G1 = T1 + Bg1/P




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.



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.



A Simple Case of Ricardian Equivalence Assume Bg

2 /P = Bg3 /P = · · · = 0.

G2 + r·Bg1 /P = T2 + (Bg

2−Bg1)/P

Bg1/P = 1 and Bg

2/P = 0

G2 + r = T2 − 1 T2 = G2 + 1 + r




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

= −1 + (1 + r)/(1 + r) = −1 + 1 = 0



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.



Ricardian Equivalence

HH views real taxes as equivalent to a real budget deficit.

In terms of national saving HH saving offsets government’s dissaving



Another Case of Ricardian Equivalence G2 + r·Bg

1 /P = T2 + (Bg2−Bg

1)/P

Bg2/P = Bg

1/P = 1

G2 + r = T2



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) ] + ·· ·




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.




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 Bg

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


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 stimulative fiscal policy.



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



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.







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.



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).



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.



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.



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.



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.



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 。



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.



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



The Standard View of a Budget DeficitKey assumption: A deficit-financed tax cut makes

households feel wealthier.

Two arguments: Finite lifetimes Imperfect credit markets



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.



Finite lifetimes

However, most people have private intergenerational transfers

Public debt changes the optimal private transfers

– offset the effect of public debt

Uncertainty of future taxes? – precautionary saving



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.

Thus, public debt is not a burden



Empirical evidence

Budget deficit and national saving Causality? Correlation?

US and Canada.

Israel in 1983-87


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.


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.


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.


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.


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.

Same logic as the case of a deficit-financed tax cut


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


Open-Market Operations

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Public Debt

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