Are GovernmentBonds Net Wealth?

RobertJ. Barro
University
ofChicago

The assumptionthatgovernment bonds are perceivedas net wealthby

the privatesectoris crucialin demonstrating real effects
ofshiftsin the
stockofpublicdebt.In particular,thestandardeffects of"expansionary"
fiscalpolicyon aggregatedemandhingeon thisassumption.Government
bondswillbe perceivedas netwealthonlyiftheirvalue exceedsthecap-
italized value of the impliedstreamof futuretax liabilities.This paper
considersthe effectson bond values and tax capitalization of finite
lives,imperfect privatecapital markets,a government monopolyin the
productionof bond "liquidityservices,"and uncertaintyabout future
tax obligations.It is shown within the context of an overlapping-
generationsmodel thatfiniteliveswill not be relevantto the capitaliza-
tion of future tax liabilities so long as current generationsare
connectedtofuturegenerations by a chain ofoperativeintergenerational
transfers (eitherin the directionfromold to youngor in the direction
fromyoung to old). Applicationsof this resultto social securityand
to other typesof imposed intergenerational transferschemesare also
noted.In thepresenceofimperfect privatecapital markets,government
debt issue will increasenet wealth if the governmentis more efficient,
at themargin,than theprivatemarketin carryingout the loan process.
Similarly,if the governmenthas monopolypower in the production
ofbond "liquidityservices,"thenpublic debt issuewill raisenetwealth.
Finally,the existenceof uncertaintywith respectto individualfuture
tax liabilitiesimplies that public debt issue may increase the overall
riskcontainedin householdbalance sheetsand therebyeffectively re-
duce householdwealth.

The assumption that government bonds are perceived as net wealth by

the private sector plays an important role in theoretical analyses of
monetary and fiscal effects.This assumption appears, explicitly or im-
plicitly,in demonstratingreal effectsof a shiftin the stock of public debt
I have benefitedfromcomments on earlierdraftsby GaryBecker,BenjaminEden,
MiltonFriedman, MertonMiller,JoseScheinkman,Jeremy Siegel,and CharlesUpton.
The NationalScienceFoundationhas supportedthisresearch.
[Journalof Political Economy,1974, vol. 82, no. 6]
(? 1974 by The University of Chicago. All rights reserved.

I 095

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 Io96 JOURNAL OF POLITICAL ECONOMY

(see, e.g., Modigliani 1961, sec. IV; Mundell 1971; and Tobin 1971,
chap. 5), and in establishing nonneutrality of changes in the stock of
money (Metzler 1951, sec. VI). More generally, the assumption that
governmentdebt issue leads, at least in part, to an increase in the typical
household's conception of its net wealth is crucial for demonstrating a
positive effecton aggregate demand of "expansionary" fiscal policy, which
is defined here as a substitutionof debt for tax finance for a given level of
governmentexpenditure (see, e.g., Patinkin 1964, sec. XII.4; and Blinder
and Solow 1973, pp. 324-25). The basic type of argument in a full-
employment model is, following Modigliani (1961), that an increase in
government debt implies an increase in perceived household wealth;
hence, an increase in desired consumption (a component of aggregate
demand) relative to saving; hence, an increase in interest rates; and,
finally,a decline in the fractionof output which goes to capital accumula-
tion. However, this line of reasoning hinges on the assumption that the
increase in government debt leads to an increase in perceived household
wealth. In a non-fullemploymentcontext it remains true that the effectof
public debt issue on aggregate demand (and, hence, on output and
employment) hingeson the assumed increase in perceived household wealth.
It has been recognized for some time that the future taxes needed to
finance governmentinterestpayments would imply an offsetto the direct
positive wealth effect. For example, in a paper originally published in
1952, Tobin (1971, p. 91) notes: "How is it possible that society merely
by the device of incurring a debt to itselfcan deceive itselfinto believing
that it is wealthier? Do not the additional taxes which are necessary to
carry the interestcharges reduce the value of other components of private
wealth?" Bailey (1962, pp. 75-77) has gone somewhat furtherby arguing:
"It is possible that households regard deficit financing as equivalent to
taxation. The issue of a bond by the government to finance expenditures
involves a liability for future interest payments and possible ultimate
repayment of principal, and thus implies future taxes that would not be
necessary if the expenditures were financed by current taxation. . . . If
future tax liabilities implicit in deficit financing are accurately foreseen,
the level at which total tax receipts are set is immaterial; the behavior of
the communitywill be exactly the same as ifthe budget were continuously
balanced."
There seem to be two major lines of argument that have been offered
to defend the position that the offsetof the future tax liabilities will be
only partial.' One type of argument, based on finitelives, supposes that

' Of course, most analyses of governmentdebt effectsdo not offera specificdefense

forthisposition.For example,Blinderand Solow (1973, p. 325, n. 8) say: "This [analysis]
includes governmentbonds as a net asset to the public. We are well aware offbut not
persuaded by, the argumentswhich hold that such bonds are not seen as net worthby
individualsbecause of the implied futuretax liability."

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 GOVERNMENT BONDS I097

the relevanthorizonforthe futuretaxes (whichmightcorrespondto the

remainingaveragelifetimes ofthecurrenttaxpayers)will be shorterthan
thatfortheinterestpayments.2 Accordingly, a streamofequal values for
interestpaymentsand taxes will have a net positivepresentvalue. This
argumenthas been used explicitlyby Thompson (1967, p. 1200). The
second type of argument,usually based on imperfectprivate capital
markets,supposesthat the relevantdiscountrate fortax liabilitieswill
be higherthanthatfortheinterestpayments.Hence, evenwithan infinite
horizonfortax liabilities,a streamof equal values forinterestpayments
and taxeswill have a net positivepresentvalue. This argumenthas been
used by Mundell (1971).3
The firstpart of thispaper deals with the effectof governmentbond
issue on the calculus of individualwealth in an overlapping-generations
economywith physicalcapital where individualshave finitelives. No
elementsof"capital marketimperfections" are introducedintothismodel.
The keyresulthereis that,so longas thereis an operativeintergenerational
transfer(in thesenseof an interiorsolutionforthe amountofbequest or
giftacrossgenerations),therewill be no net-wealtheffectand, hence,no
effecton aggregatedemand or on interestratesof a marginalchange in
governmentdebt. This result does not hinge on currentgenerations'
weighingthe consumptionor utilityoffuturegenerationsin any senseon
an equal basis with own consumption,nor does it depend on current
generations'placingany directweightat all on theconsumptionor utility
of any futuregenerationotherthan the immediatedescendant.Current
generationsact effectively as thoughtheywere infinite-lived when they
are connected to futuregenerationsby a chain of operative inter-
generationaltransfers.
The analysisthenshowsthatsocial securitypaymentsare analogous to
changes in governmentdebt. Marginal changes in this type (or other
types) of imposed intergenerational transfershave no real effectswhen
currentand futuregenerationsare alreadyconnectedby a chain ofopera-
tive discretionarytransfers.The effectsof inheritancetaxes and of
"transactioncosts"forgovernment bond issueand tax collectionsare also
considered.It is shown that inheritancetaxes do not affectthe basic
results,but thatthepresenceofgovernment transactioncostsimpliesthat
the net-wealtheffectofgovernment bonds would actuallybe negative.
The second part of the paper deals with the existenceof imperfect
privatecapital markets.It is shownthat,to the extentthat public debt

2 This typeof argumentapplies to head taxes or to taxes based on wage income, but
not to taxeswhich are based on the value of nonhumanassets.This distinctionhas been
made by Mundell (1971, pp. 9, 10).
3 A different
line ofargumentthatleads to a similarconclusionis thatthe government
acts like a monopolistin the provisionof the liquidity servicesyielded by its liabilities.
I discussthisargumentin part III, below.

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 Io98 JOURNAL OF POLITICAL ECONOMY

issue entailsa loan fromlow-discount-rate to high-discount-rate individ-

uals, a positivenet-wealtheffectresultsifthegovernment is moreefficient
thantheprivatemarketin carryingout thissortofloan. If thegovernment
is moreefficient onlyovera certainrange,and ifthepublicchoiceprocess
determines theamountofgovernment debtissuein accordwithefficiency
criteria,it is again true at the margin that the net-wealtheffectof
government bond issueis nil.
The thirdpart of the paper discussesgovernmentdebt as a bearerof
nonpecuniary"liquidityservices."It is shownthatifthegovernment acts
like a competitiveproducerof theseservices,as would be dictatedby a
public choice process which reflectsefficiencycriteria,then the net-
wealtheffect ofgovernment bond issuewould be zero on thiscount.More
generally,the net-wealtheffectwould be positiveif the governmentacts
like a monopolistand would be negative if the governmentis an
overproducerof liquidityservices.
The last partof the paper deals withthe riskcharacteristics ofgovern-
mentdebt and of the tax liabilitiesassociatedwiththe interestpayments
on thisdebt. It is arguedthatifrelativetax liabilitiesare known,a change
in government debt will not altertheoverallriskcontainedin household
balance sheets.When relativetax liabilitiesare uncertain,the effectof
governmentdebt issue on the overall riskmay be positiveor negative,
dependingon the natureof the tax systemand on the transactioncosts
associatedwithprivateinsurancearrangements.

I. The Effect of Finite Lives-a Model with Overlapping Gener-

ation
A. SetupoftheModel
I use here a versionof the Samuelson (1958)-Diamond (1965) over-
lapping-generations model with physicalcapital. Each individual lives
two periods,which will be distinguishedby the superscripts y (young)
and o (old). Generationsare numberedconsecutively beginningwith the
generationwhichis currently old (subscript1); followedbyitsdescendant,
whichis currently young (subscript2); followedby its descendant;and
so on. I assumeherethatthereare thesame numberofpeople, N, in each
generation,and that all individualsare identicalin termsoftastesand
productivity. I also abstractfromany technologicalchange over time.
The membersof each generationwork(a fixedamountof timeset equal
to one unit) onlywhileyoungand receivean amountofwage incomew.
Expectationson w for futureperiods (i.e., for futuregenerations)are
assumedto be staticat thecurrentvalue. Assetholdings(A) taketheform
ofequitycapital (K). Subsequently,government bonds are introducedas
an additionalformin whichassetscan be held.The rateofreturnon assets

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 GOVERNMENT BONDS IO99

is denotedbyrand is assumedto be paid out once perperiod.Expectations

on r forfutureperiodsare assumed to be staticat the currentvalue. A
memberof the ith generationholds the amountof assetsA. while young
and the amountA' whileold. The asset holdingwhileold constitutes the
provisionof a bequest,whichis assumed to go to the immediatedescen-
dant, a member of generationi + 1. Since the focus of the analysis
concernsshiftsin tax liabilitiesand governmentdebt fora givenlevel of
governmentexpenditure,it is assumed forconveniencethat the govern-
mentneitherdemands commoditiesnor providespublic services.In this
section,it is also assumedthatthe amountsofgovernment debt and taxes
are zero. Using the letterc to denote consumption,and assumingthat
consumptionand receiptofinterestincomebothoccur at the startof the
period,thebudgetequationfora memberofgeneration1,whois currently
old, is
Ay + A' = c' + (I - r)A'.(1
The totalresourcesavailable are theassetsheld whileyoung,AY, plus the
bequestfromthe previousgeneration,A'. The total expenditureis con-
sumptionwhile old, c7, plus the bequest provision,A', which goes to a
memberof generation2, less interestearningsat rate r on this asset
holding.
The budgetequationformembersofgeneration2 (and, moregenerally,
formembersof any generationi > 2) is, assumingthatwage payments
occur at the startof theyoungperiod,
w=c + ( -r)AY, (2)
and, forthe old period,
Ay + AO -cO + (I - r)AO. (3)
A portionofthelifetime resourcesofa memberofgenerationi goes to a
bequest provision,A ', which I assume is motivatedby a concernfora
memberof generationi + 1. This concerncould be modeled by intro-
ducing eitherthe (anticipated) consumptionlevels or attainable utility
ofa memberofgenerationi + 1 intotheutilityfunctionfora memberof
the ith generation.For the purpose of the presentanalysis,the crucial
conditionis that thisutilitydepend on the endowmentof a memberof
generationi + 1 ratherthan, per se, on the gross bequest, A . (The
distinctionbetweenthe grossbequest and the net bequest,whichdeter-
minesthe endowmentof i + 1, will be discussedbelow.) So long as a
memberofgenerationi can transfer resourcesto a memberofgeneration
i + 1 onlythroughthe transfer of unrestricted
purchasingpower (which
rulesout the "meritgood" case discussedin n. 8 below), thetwo typesof
modelsof interdependent preferences-concernwith consumptionlevels
and concernwith attainableutility-will be equivalentin the sense of

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 I IOO JOURNAL OF POLITICAL ECONOMY

indirectly implying a concern for the endowment of a member of

generation i + 1.
For present purposes, it is convenient to assume that the utility of a
member of generation i depends solely on own two-period consumption,
cyand c?, and on the attainable utilityof his immediate descendant, Us*1.
The asterisk denotes the maximum value of utility,conditional on given
values of endowment and prices. Hence, the utilityfunctionfora member
of the ith generation has the form,4

Ui = Ui(c', C7,U1+1) (4)

Subsequently, I consider the implications of entering the attainable
utility of a member of the previous generation, Us* 1, as an additional
argument of the Ui function.
Each member of generation 1 determines his allocation of resources
to maximize U1, subject to equations (1)-(4) and to the inequality
conditions, (cl, c', A?) ? 0 for all i. The key restrictionhere is that the
bequest to the member of the next generation cannot be negative.5 The
choice of bequest, subject to this restriction,takes into account the effect
of A' on generation 2's resources, the impact of U2 on U1, and the chain
dependence of U2 on U*, of U3 on U4, etc. The solution to this problem
will take the general form

= cO(Ay + AO, w, r),

1 (5)
A= (Ay + AO - c ) = AO(A + AO, w, r).
1-r

Similarly, formembers of generation 2 (and, more generally,formembers

of any generation i > 2), the solution would take the form,

cY = c Y(A , w, r),
2 2 1
A4Y= (w - cY) = A Y(A 0, w, r),
1 - r (6)
= c?(Ay + AO, w, r),

A2?
= (A2 + A1 -c ?) = A0(AY + A , w, r).
1- r

4A memberof generationi is assumed to be concernedwith own consumptionand

with the attainable indifferencesurfaceof his descendant.Further,it is supposed that a
memberof generationi can attach a metricto generationi + l's indifference surface
which makes it comparable to cyand c, in termsof generatingU1 in the formof eq. (4).
The nature of this sort of utilityfunctionis discussed in the general contextof inter-
dependentpreferences in Becker (1974, sec. 3.A).
I have not imposed the condition,A- > 0, so that young individuals are allowed
to issueinterest-bearing
debton themselves.If issued,thesedebtsare assumedto be perfect
substitutesforequity capital. These debts correspondto the consumptionloans which
have been discussedby Samuelson (1958).

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 GOVERNMENT BONDS I 0I

The model can be closed, as in Diamond (1965, pp. 1130-35), by

specifyinga constant-returns-to-scaleproduction function that depends
on the amounts of capital and labor input, and by equating the marginal
products of capital and labor to r and w, respectively.The value of r for
the current period would then be determined in order to equate the
supply of assets to the demand-that is,

K(r, w) =A' + Ay, (7)

where K (r, w) is such as to equate the marginal product of capital to r.

The current demand for assets, Al + Ay, depends, from equations (5)
and (6), on r, w, and the previous period's value of K, which is equal to
A + A'. Since the number of people in each generation is assumed to
equal a fixed number N, it is not necessary to enter this number explicitly
into the aggregate asset demand in equation (7). Similarly, N is omitted
fromthe aggregate formulationsbelow. Since N is constant and technical
change is not considered, the current and previous periods' values of K
would be equal in a steady state.
With the marginal product of labor equated to w and with constant
returnsto scale, output is given by

y=rK + w. (8)

Equations (2), (3), (7), and (8) imply a commodity market clearing
condition,
CO + Cy + AK =y, (9)
where AK denotes the change in capital stock from the previous to the
currentperiod. The value of AK would be zero in a steady state, but the
present analysis is not restrictedto steady-statesituations.

B. Government
Debt

Suppose now that the governmentissues an amount of debt, B, which can

be thought of as taking the form of one-period, real-valued bonds. These
bonds pay the specified amount of real interest, rB, in the current
period and the specified real principal, B, in the next period.6 It is
supposed that asset holders regard equity and government bonds as
perfectsubstitutes.It can be assumed, forsimplicity,that the government
bond issue takes the formof a helicopter drop to currentlyold (generation
1) households. Equivalently, it could be assumed that the bonds were
sold on a competitive capital market, with the proceeds from this sale
used to effecta lump-sum transferpayment to generation 1 households.

6 The amount of bond issue would be limited by the government'scollateral, in the

sense of its taxing capacity to financethe interestand principal payments (see n. 12
below).

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 I I02 JOURNAL OF POLITICAL ECONOMY

Allowingsome portionof the proceedsto go to generation2 households

would not alterany ofthe basic conclusions.
The futureinterestpaymentson thegovernment debt mustbe financed
in some manner. Further,the principalmay eventuallybe paid off-
thatis, the government may not reissuethe bonds when theycome due
in the next period. I assume, provisionally,that the currentperiod's
interestpaymentsare financedby a lump-sumtax levy on generation2
households(whileyoung),and thatthe principalis paid offat the begin-
ningofthenextperiodby an additionallump-sumtax levyon generation
2 households(while old). In this setup thereis no directeffectof the
government debtissueand itsfinancingon generation3 and latergenera-
tions.I examine,subsequently, the implicationsofimposingsome part of
thetaxeson generationsofthe moredistantfuture.
The generation1 budget constraintis now

Ay + A' + B = cl + (1 -r)A7, (10)

whereB represents the lump-sumtransferpayment,whichis assumedto
occur at the beginningof the period. For generation2, the current
budgetconstraintis now
w = cy + (1 - r)A? + rB, (11)
whererB representsthe tax levyforthe governmentinterestpayments.
The nextperiod'sbudgetconstraintforgeneration2 is now
Ay + AO = co + (1 - r)AO + B,
where B representsthe tax levy for repaymentof principal.The two
constraintson generation2 can be combined into a single two-period
budgetequation,
w + (1 -r)AO -B = cy + (1 -r)co + (1 -r)2A . (12)
The formofequation (12) impliesthattheutilityattainableby a member
ofgeneration2 can be writtenin theindirectform,

U2 = r)AO - B, w, r],
f2*[(1 - (13)
thatis, the"net bequest," (1 - r)AO - B, determinesthe "endowment"
formembersofgeneration2.
From equation (10), it is also clear that co varies inverselywith
(1 - r)AO - B for a given value of Ay + AO. Hence, given the pre-
determinedvalue of cy,and usingequations (4), (10), and (13), U1 can
be writtenin theform,

U1 = U1(cy,co, U2*) = fl[(1 - r)Aj -B; cl, Ay + AO,w, r].

For givenvaluesofcY, AY + A , w,and r,thechoiceproblemformembers
of generation1 amounts to the optimal selectionof the net bequest,

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 GOVERNMENT BONDS I I03

(1 - r)A' - B, subject to the constraint that the gross bequest, A', be

nonnegative. In particular, if the solution to this problem is associated
with a value of A' in the interior-that is, if the constraint, A' > 0, is
not binding-any marginal change in B would be met solely by a change
in A' that maintains the value of the net bequest, (1 - r)A' -B. This
response in AO will keep unchanged the values of c', cY, ci, and A'.
Hence, the utility levels attained by members of generations 1, 2, etc.,
will be unaffectedby the shiftin B.
In terms of the effecton r, the current asset market clearing condition
of equation (7) would now be modified to

K(r, w) + B = AO + Ay (14)

The increase in B implies a one-to-one increase in the asset supply on the

left-handside of equation (14). However, AO rises by 1/(1 - r) times the
change in B in order to maintain the size of the net bequest, (1 - r)A - B.
Further, with cy fixed, the increase in rB (taxes) in equation (11) implies
that Ay falls by r/(l - r) times the change in B. On net, total asset
demand on the right-hand side of equation (14) rises one-to-one with B,
so that no change in r is required to clear the asset market. Equivalently,
the commodity market clearing condition, as expressed in equation (9),
continues to hold at the initial value of r because the bond issue has no
impact on aggregate demand.
Essentially, a positive value of B, financed by a tax levy on the next
generation, enables a member of the old generation to "go out" insolvent
by leaving a debt forhis descendant. However, if,prior to the government
bond issue, a member of the old generation had already selected a positive
bequest, it is clear that this individual already had the option of shifting
resources fromhis descendant to himself,but he had determined that such
shifting,at the margin, was nonoptimal. Since the change in B does not
alter the relevant opportunity set in this sense, it follows that-through
the appropriate adjustment of the bequest-the values of current and
futureconsumption and attained utilitywill be unaffected. On the other
hand, if a member of generation 1 were initially at a corner where
A = 0-in particular, if A < 0 would have been chosen had it been
permissible-then an increase in B creates a relevant new opportunity.
In this situation a generation 1 household would react by increasing c0
along with B, as long as the corner solution for AO still applied. The
upward shiftin B would then correspond to an excess of earning-asset
supply over demand (even after taking account of a shiftin AY), which
would tend to raise the value of r. This increase in r would induce a drop
in capital formation,which constitutesthe real effectof governmentdebt
issue which has been described by Modigliani (1961). However, the main
point is that the existence of this governmentdebt effecthinges on a non-

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 I I04 JOURNAL OF POLITICAL ECONOMY

operative bequest motive-that is, on households being at the corner

where the amount of bequest is zero. 7
It should be stressed that the crucial consideration for the above result
is an operative intergenerational transfer, rather than an operative
bequest motive per se. For example, the transfercould take the form of
parental expenditure on children's education, etc., during the overlapping
tenure of parent and child.8 Further, the transfercould be occurring in
the direction opposite to that specified above. In particular, U* could be
entered as an argument of the U2 function,and the possibilityofgiftsfrom
the young to the old generation could be introduced. In that case the
same conclusions on the effectof a change in the government debt would
be reached if a "gift motive" were operative.9 The mechanism through
which changes in B were offsetwould then be an alteration in the amount
of giftsfrom young to old, rather than an alteration of the amount of
bequests fromold to young.
The results will now be extended to a situation where the taxes which
finance the government debt affect some generations which are not
currentlyalive. The extension will be made explicitlyonly to generation 3,
since the extension to generations further advanced in the future is
straightforward.
Suppose now that the current period's interestpayments are financed
by a lump-sum tax levy on (young) generation 2, the next period's interest
payments (on the reissued bonds) are financed by a lump-sum tax levy on
(young) generation 3, and the principal is paid off by a lump-sum tax
levy on (old) generation 3.1O The generalization of the earlier results to
this situation can be demonstrated by working backward fromgeneration
3. By analogy to equation (13), the attainable utilityof generation 3 can

7 When householdsare not identical, the aggregate effectof governmentdebt issue

will depend on the fractionof householdsat a corner.As long as some householdsare in
thissituation,a shiftin B will have some upward effecton r in thismodel. However, this
effectwould be "small" ifthe fractionofhouseholdsat a cornerweresmall. The role of a
bequest motivein eliminatingthe perceived net-wealtheffectof governmentdebt has
also been discussedby Miller and Upton (1974, pp. 176-79).
8 The previousresultson the effectofB mightriothold ifparentswere concernedwith
specificconsumptioncomponentsof their children ("merit goods"), ratherthan with
theirchildren'sattainable utility.Formally,Uj in eq. (4) could depend on (components
of) c'+1 or c+i, ratherthan on U:+1 . If generationi can tie its aid to generationi + 1
to a specifictypeof expenditure(as could be the case foreducation), the previousresults
would not hold if this tied aid were an effectiveconstraint-in the sense of forcingthe
next generationto "purchase" more of the item than it otherwisewould-and if the
parentswere not making any other transferswhich were equivalent to the transferof
general purchasingpower. Becker (1974, sec. 3.C) presentsa detailed discussion of the
meritgoods case in an analogous context.
9 A model which allows fora reciprocaldependencebetween Uj and U +{ is formally
similar to the model discussed by Becker (1974, sec. 3.A) in the context of transfer
paymentsamong membersof a family.
'o I do not deal here with the possibilityof net governmentdebt issue during the
old-age tenureof generation2. No new considerationswould arise here (see however,
n. 12 below).

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 GOVERNMENT BONDS I 105

be writtenin the indirectform,

U3* =f3*[(1 - r)A?
B, w, r], -

where (1 - r)AO - B now determinesthe endowmentformembersof

generation3. Since generation2 no longerpays offthe governmentdebt
principal,itsbudgetequationis modifiedfromtheformofequation (12) to
w + (1 - r)AO - B = cy + (1 - r)cO+ (1 - r)[(l - r)AO- B].
For given values of w, r, and the net bequest from generation 1,
(1 - r)A7 - B, generation2 would select an optimalvalue of the net
bequest to generation3, (1 - r)A? - B. This net bequest would be
invariantwithB as long as the solutionforAO were interior.Assuming
thatthissolutionis interior,the attainableutilityof generation2 can be
writtenin theindirectform,
U2* =f2*[(l - r)AO - B tv, r],
whichcoincidesin formwithequation (13). The situationhas therefore
been reduced to the previouscase in which marginalchangesin B led
solely to changes in AO which kept (1 - r)A0 - B constantwithout
affectingany values ofconsumptionor attainedutility.
The three-generation resultsgeneralizeto the case in which taxes are
leviedon mgenerations, withthemthgenerationpayingofftheprincipal.
By startingwithgenerationmand progressing backward,it can be shown
forall 2 < i < m - 1 that,if Ai is interior,Uj* can be writtenin an
indirectformas a function of(1 - r)A'. - B. As longas all inheritance
choicesare interior" (as anticipatedby currentgenerations),shiftsin B
implyfullycompensatingshiftsin bequests,so as to leave unchangedall
values of consumption and attained utility.12
" Intuitively,if this condition is violated forsome generations,the impact of these
violations on currentbehavior should be less importantthe furtherin the futurethe
violatinggenerations.I make no claim to having proved thisconjecture.
12 This line of proofdoes not apply as m -+ 0o. The main issue seems to be whether
the assumptionthat the principalis eventuallypaid offis crucial. If the amount of out-
standinggovernmentdebt were constant,theimpact oftheprincipalon currentdecisions
would become negligibleforlarge m as long as r > 0. However, a difficulty arises here
when B is allowed to grow over time. Suppose that the growthof B were limited to the
growthof the government'scollateral in the sense of its taxing capacity, which depends
in turn on the growthof real income. Suppose that the growthrate of real income is
equal to n, which can be viewed as the combined effectsof population growthand
technicalprogress,which are now allowed to be positive. In that case the presentvalue
of the principalwould have to become negligible as m -* o if n < r. The situationin
which n > r applies is inefficientin that it is associated with a capital stockin excess of
the golden rule level (see, e.g., Diamond 1965, p. 1129). It is possible in Diamond's
model (p. 1135) that the competitiveequilibrium can be in this inefficientregion.
However, thissituationis not possible in growthmodels where individuals are infinite
lived and utilityis discounted(see, e.g., Koopmans 1965). As long as intergenerational
transfersare operative,the overlapping-generations model would seem to be equivalent
to theinfinite-life
modelin thisrespect- thatis, thepossibilityofinefficiency in Diamond's
model seemsto hinge on finitelives with inoperativeintergenerationaltransfers. Hence,
when these transfers are operative,n < r would be guaranteed,and the possibilityof
perpetualgovernmentfinanceby new debt issue could thenbe ruled out.

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 I io6 JOURNAL OF POLITICAL ECONOMY

The results in this section have demonstrated that changes in govern-

ment debt would not induce any alteration in consumption plans even in a
model where (1) the present generations have finitelives, (2) the present
generations may, in some sense, give lesser weight to the consumption or
utility of future generations than they give to own consumption, and
(3) the present generation may give no direct weight at all to the con-
sumption or utility of generations beyond their immediate descendants
(who are also finite-lived).
A sufficientcondition forchanges in governmentdebt to have no impact
on consumption plans and, hence, no effecton aggregate demand and
interestrates is that the solution for the current generations' inheritances
be interior,and that the solutions for futuregenerations' inheritances (as
perceived by current generations) also be interior. More generally, the
result will hold as long as current generations are connected to all future
generations by a chain of operative intergenerational transfers,either in
the direction fromold to young or in the direction fromyoung to old.
The derivation of conditions under which the solution for inter-
generational transferwould be interior appears to be a difficultproblem
and would seem to require some specialization of the form of the utility
functions in order to make any headway. However, it seems clear that
bequests are more likely to be positive the smaller the growth rate of w
(assuming that w is now viewed as variable across generations), the
higher the interestrate, the higher the relative weight of Ui* 1 in the Uj
function,and the larger the value of B." The reverse conditions favor a
giftfromyoung to old.'4

C. Social Security
Paymentsand OtherImposedIntergenerational
Transfers
The above results on government debt also apply to social securitypay-
ments."5 Suppose that a scheme is instituted which immediately begins
payments to the current old generation (generation 1) of amount S,
financed by a lump-sum tax levy of amount S on the current young
13 In a more general contextB should be viewed as outstandingpublic debt less the

value ofphysicalcapital held by the government.

14 There is an alternativeargument,which Gary Beckerrefers to as the "enforcement
theoryof giving," which suggeststhat bequest motiveswould typicallybe operative.
Suppose that,insteadof receivingutilityfromthe perceivedutilityof his child, a parent
is concernedwithown consumptionand withthe amountof attention,etc., shownby his
child during their overlapping tenure. Suppose, further,that the child has some in-
formationon thesize ofhis parents'estateand that-acting as a good optimalcontroller-
he regulatesthe amount of attentionas a functionof the estatesize. In thissituationthe
estatewould surelybe positiveif parentsplace a high value on gettingat least a small
amount of attention,and if the child provides no attentionwhen the estate is zero.
However,althougha positiveestatecould be guaranteedin thisfashion,it seemsthatthe
previousconclusionsabout the marginal effectof B on consumptionplans would not
hold in this model. The nature of the interactionsbetweenparentsand childrenwould
have to be analyzed morefullyforthiscase.
15 The view ofsocial securityas analogous to governmentdebt has also been taken by
Miller and Upton (1974, pp. 182-84).

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 GOVERNMENT BONDS I I07

generation(generation2). Generation2 expectsto receivea transferof

amountS whileold, financedby a lump-sumtax levyon (young)genera-
tion3, etc. It is assumedherethatan individual'spaymentreceivedwhile
old is independentofhisown contribution to theschemewhileyoung,and
that neitherthe old receipt nor the young paymentdepends on the
amountofwork,income,etc.Assuminginteriorbequests(whichwouldbe
guaranteedby a sufficiently highvalue ofS), a changein S would induce
thecurrentold generation(generation1) to maintainitschoiceofcl and,
correspondingly, to raise A' by 1/(1 - r) timesthe change in S. This
increasedinheritancewouldjust offsettheincreasedtax liabilityimposed
on (young)generation2. With its consumptionunchanged,generation2
would use its own highersocial securityreceiptto raise its bequest to
generation3, A', by 1/(1 - r) timesthe change in S. As in the case of
changesin government debt, ifthe solutionsforbequest are interior,the
impactof a marginalchange in S would be solelyon the size ofbequests
and not at all on the patternof consumption.'6 The same resultswould
followin the case of operativeintergenerational transfers
fromyoungto
old, witha marginalincreasein S implyinga corresponding reductionin
the size of giftsfromyoungto old.
The resultsfor social securitypaymentswould apply also to other
programswhich amount to imposedintergenerational transferschemes.
In particular,public supportof education involvesa forcedtransferof
resourcesfromold to young. In the main, thissortof imposed transfer
would be offsetby adjustmentsin the oppositedirectionof discretionary
transfers.17

D. Inheritance
Taxes
Suppose now thatinheritances(or gifts)are taxed at a proportionate
rate
T. In particular,the bequestfroma memberofgenerationi, Ai, yieldsa

16
As in the case ofgovernment debt issue,theformalproofdependson the assumption
that the scheme is eventuallyliquidated (see n. 12 above). The consumptionpatterns
would also not be affectedby a social securityschemethatinvolvedthe accumulationofa
government"trustfund."Assumingthatthe fundwereheld in theformofearningassets,
an increasein the fundwould be equivalent to a negativegovernmentdebt issue. Real
effectsofa social securitysystemwould arise ifthe paymentswere contingenton the work
behavior of the old generation.In that case therewould be allocative effectsproduced
by the disincentiveto workin later years.
17 On a theoreticallevel, government education programswill involve real effectsto
theextentthat(1) thereis an efficiency difference
betweenpublic and privateproduction
ofeducation,(2) public expenditureon education is pressedsufficiently far so that a re-
duction of discretionarytransfers cannot occur on a one-for-onebasis, and (3) thereare
distributionaleffectsinvolving relative educational expendituresand tax liabilities
acrossfamilies.As an empiricalmatter,Peltzman (1973) has shownthatpublic subsidies
forhighereducation are offsetto an extentof about 75 percentby reductionsin private
expendituresfor higher education. However, Peltzman's 75 percent figuredoes not
coincide with the desired estimateof the effecton discretionarytransfers, since other
componentsof discretionarytransfers may also be affectedand (on the otherside) since
not all privateexpendituresforeducation constituteintergenerational transfers.

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 I io8 JOURNAL OF POLITICAL ECONOMY

net receipt to his descendant, a member of generation i + 1, of size

(1 - z)A'. Of course, the tax receipts must also go somewhere. Suppose
that these receipts are transferredto members of generation i + 1 (while
old) in accordance with a rule that is independent of the size of each
individual's inheritance.
Since an individual's contribution to general tax revenue will typically
be valued by him at less than an equal amount of own income, it is clear
that an increase in - will tend to lower the amount of intergenerational
transfers.In particular, the higher the value of T, the less likely that a
bequest or giftmotive will be operative. Suppose, however, that the value
of - is sufficientlylow that all intergenerational transfersare operative,
even if at reduced levels. In this case the previous resultson the effectof a
change in government debt remain valid.
Consider the situation in which the principal on the governmentdebt is
paid offby generation 2. Equation (10) continues to apply in the presence
of inheritance taxes, but equation (12) must be modified to

w + (1 -r)(l - T)A' + (1 -r)TA' -B

= Cy + (1 -r)c' + (1 -r)2A'

where TA' represents the transferto a member of (old) generation 2

corresponding to his share of the receipts fromthe total taxes paid on the
average generation 1 bequest, A'. In deciding on a plan for consumption
and intergenerational transfers,an individual is assumed to treat zA'
as exogenous. Consider the conjecture that, when B rises, each member
of generation 1 continues to respond by maintaining the value of cj and,
hence, by maintaining the value of the net pretax bequest, (1 - r)A - B.
This response requires an increase in AO by 1/(1 - r) times the increase
in B. Each individual's net posttax bequest would fall in this case, but this
fall would be offset,at least on average, by an increase in the transfersto
generation 2 which are financed from the inheritance tax receipts, zA1.
In this circumstance, the individual values of cy,co, and AO-and, hence,
the attained value of U2 would remain fixed.Hence, by maintaining the
net pretax bequest, each member of generation 1 achieves the same
combination of co and U2 as before the shiftin B. On the other hand, if
an individual member of generation 1 decided to increase his net pretax
bequest, while all other members held their net pretax bequests fixed,
it would turn out for this individual that U2 would increase, while co,
would decrease. The termson which an individual can exchange co for U2
depend on T and r, and these terms have not been altered by the change
in B. Further, when the transferto generation 2 of size TAO is included,
there is also no change in an individual's overall wealth position. There-
fore, the pattern which maintains the net pretax bequest-and thereby

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 GOVERNMENT BONDS I109

involves no shift in co or Ut-must be the optimal pattern for an

individual. It followsthat constancyof the net pretax bequest for all
membersof generation1 is the equilibriumsolution.'" In this case, a
marginalshiftin B again has no effecton consumptionpatterns.
The basic conclusionhereis thatthe existenceof taxeson intergenera-
tional transfersmakes less likelyan interiorsolutionforthese transfers,
but ifthesetransfersare operative,even ifat reducedlevels,themarginal
effectofB on consumptionplans-and, hence,on r-remains nil.

Costs
E. BondIssueand Tax-Collection
Suppose now thattheissueofgovernment debt and thecollectionoftaxes
to financethisdebt involvetransactioncosts. In particular,in the case
wheretheprincipalis paid offby generation2, supposethata netissueof
B to generation1 is now associated with a tax levy of (1 + y)rB on
(young) generation2 and a levy of (1 + y)B on (old) generation2.
That is, y amountsto a proportionaltransactioncost associated with
government supposenow
debt issue and tax collection.'9For simplicity,
thatthe inheritancetax rate is zero. Equation (10) again remainsvalid,
but equation (12) is now modifiedto

w + (1 -r)A' -(1 + y)B =Cy+ (1 -r)c' + (1 -r)2AO. (15)

Consider, again, the conjecturethat, when B rises, co and, hence,
(1 - r)A'1 - B remain fixed. From equation (15), y > 0 implies a
negative-wealtheffecton generation2, so that U2 would fall. Since this
effectwould be anticipatedby generation1, it can be supposed in the
normal case that AO would actually rise by somewhat more than
1/(1 - r) timesB, so thatco wouldfall.In general,y > 0 impliesthatan
increasein B amountsto an overallnegative-wealth effect,whichwould
18 The equilibrium satisfiestwo properties:(1) each individual chooses his bequest
optimally,subject to a given choice of bequests by all other individuals; and (2) all
individualschoosethesame value fortheirbequests.It can also be shownthatthesolution
that maintains the net pretax bequest for all individuals is the unique equilibrium.
Finally, it can be noted that the solution involvesthe assumptionthat each individual
perceives the shiftin the transferterm, TA , associated with the average responseof
bequeststo the changein B. Alternatively, ifindividualstreatedrAOas fixed,theywould
view an increasein B as, effectively, a negativechange in wealth. The typicalresponse
would be a reductionin co, which would be associated with an increasein AO by more
than 1/(1 - r) timesthe change in B. In the aggregate,therewould be an increase in
desired saving, AO + A', which would lead to a reductionin r and to an increase in
capital formation.In particular,if the shiftin transfers associated with inheritancetax
revenues,TP1, is not perceived,the effectswould be opposite to the standard case in
whichperceivednet wealth riseswith B.
19 If the initial debt issue is associated with a decrease in othertaxes, ratherthan an
increase in transfers, there could be an offsetting reductionin transactioncosts. The
parametery,whichis assumed to be positive,mustbe interpretedin this net sense.

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 I 110 JOURNAL OF POLITICAL ECONOMY

typicallyinvolvereductionsin bothco and U2*.This effectcan be seen by

combiningequations(10) and (15) intothesingletwo-generation budget
equation,

Ay + AO-YB + w = co +e? (1 -r)co + (1 -r)2AO. (16)

The decline in total resourceson the left-handside of equation (16)
producedby an increasein B would typicallybe reflectedin declinesin all
termson theright-hand side-cl, cy,co, and AO.
In thiscircumstancethe effecton r of a shiftin B would be unclear.
The commoditymarketclearingconditionofequation (9) would now be
modifiedto include the resourcesdevotedto bond and tax transactions.
The revisedmarketclearingconditionwould be

co + cy + AK + yrB =y.
The effectofB on currentr will depend on whether,fora givenvalue of
r, the sum, cO + cy,fallsby more or less than the increasein yrB.This
relationshipseemsto be ambiguous.20

II. Imperfect Capital Markets

This part of the paper analyzes the implicationsof divergencesamong
individualdiscountrates.This sourceofa net-wealth effectforgovernment
bonds has been stressedby Mundell (1971), who arguesthat,because of
high discountrates for some individuals,the taxes which financethe
government debt will not be fullycapitalized-hence, an issueofgovern-
mentbonds will involvea net-wealtheffect.To analyze thiseffect,it is
necessaryto construct a somewhatdifferent model.Suppose thatthereare
now twotypesofindividuals-thosewho have a low discountrate,rl,and
thosewho have a highdiscountrate,rh.It can be supposedthatthehigh-
discount-rate individualshave relatively"bad collateral,"so that loans
to theseindividualsinvolvehightransactioncosts,whichare reflectedin
high (net-of-default-risk)borrowingrates.21In particular,suppose that
the two discountratesare relatedaccordingto
rh = (1 + )r1,
where)i > 0 represents
theproportionaltransactioncostsinvolvedin the
loan process.22I suppose in this part of the paper that both typesof
20
From eq. (16), the negativewealth effectis yB, which is the presentvalue of the
flow,yrB.The sum, cl + c', will fall by as much as yrBif the total "propensityto con-
sume" associatedwiththe negative"income" flow,yrB,is equal to one.
21
In thisrespectsee Barro (1974).
22 I am assumingthat the rhindividuals are actually borrowing,so that rhrepresents

both theirborrowingrate and theirmarginal discount rate. Alternatively,r,,could be

viewed as a marginaldiscountrate which could be somewherebetween the borrowing
and lendingrates,as in Hirshleifer(1958).

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 GOVERNMENT BONDS IIII

since the effectof finitelives has already

individualsare infinite-lived,
been examinedabove.
It is convenientto suppose thatgovernment debt now takesthe form
ofa perpetuitythatcarriesa real interestpaymentofi per year. Suppose
that the governmentissues an additionalbond of this type. This bond
would be purchased by a low-discount-rate individual and would be
evaluated as B = i/rl.23Suppose then that the governmentuses the
lump-sum proceeds from this sale, B, to effecta lump-sum transfer(or
lump-sum tax reduction) to individuals, and suppose that a fractiona of
this transfergoes to r, discount rate individuals and a fraction (1 - a) to
rhdiscount rate individuals. Finally, the taxes forfinancingthe government
interestpayments are (1 + y)i, where y represents,as in section IE, the
proportional transaction costs associated with government bond sale and
tax collection. Suppose that these taxes are distributed across discount
rates in the same manner as the lump-sum proceeds24-that is, a fraction
o to r1 individuals and a fraction (1 - a) to rhindividuals.
Consider, in turn, the wealth effectsfor the r, and rhgroups. The bond
sale itselfinvolves no wealth effectforthe r1group. The lump-sum transfer
to r1 individuals is cB = ci/rl, while the present value of the ri share of
Clearly, if y > 0, the
tax liabilities, discounted at rate ri, is (1 + y)oci/rl.
net-wealth effect for r, individuals is negative, as it was in the case
discussed in section IE, where all discount rates were equal.
For the rh group, the lump-sum proceeds are (1 - oc)B = (1 - )1/rj,
while the present value of the tax liability, discounted at rate rh, is
(1 + y)(l - ca)i/rh. Using rh = (1 + ))rl, the net-wealth effecthere can
be expressed as

(1- )i( 1( -1 + v' (

r I_ + x)- ((1 /(2 - 4)
Ti I + 2/ ri(l + X)

which is positive if > y. That is, the net-wealth effectfor the rh group
is positive if y, which measures the governmenttransaction costs forbond
issue and tax collection, is smaller than 2, which measures the private
transaction costs implicit in the existing pattern of (net-of-default-risk)
discount rates. To the extent, 1 - a, that the transferpayment and tax
liability involve the rh group, the government bond issue amounts to
effectinga loan from the low-discount-rate to the high-discount-rate
individuals. On the other hand, this sort of transfercould already have

23 This analysisabstractsfromany "liquidity yield" of bonds (see part III, below).

24 If the fractionsfortransferand tax liability vary, then the wealth effectson the
two discount-rategroupsare likelyto be in oppositedirections.The net effecton current
consumptiondemand would depend, in part, on relativepropensitiesto consume,which
are not obvious. In any event,thiscase would amountto the effectofincome distribution
on consumptiondemand, ratherthan the effectof governmentbond issue per se on
net wealth and consumptiondemand.

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 1112 JOURNAL OF POLITICAL ECONOMY

been accomplished privately,except that the transactioncosts, as

measuredby i, made this transfer marginallyunprofitable.Hence, the
government-induced transferimplied by its bond issue can raise net
wealthonlyif the governmentis more efficient than the privatecapital
marketin carryingout thissortoflendingand borrowingoperation.
Some additionalobservations can be made concerningthisresult.First,
if the government is reallymore efficient than the privatemarketin the
lendingprocess (presumablybecause the benefitsof economiesof scale
[in information?]and the ability to coerce outweighthe problemsof
government incentiveand control),it maybe able to exploitthisefficiency
betterby a direct-loanprogram,ratherthan by the sortof bond issue
describedabove. In my simplemodel, a fractionoaof transfers and tax
liabilitiesinvolvedthe r1group,and thisprocessentaileda dead-weight
lossto theextentthaty > 0. A programwhichlimitedtheloan recipients
to high-discount-rate individualswould be more efficient in thisrespect.
However,the information requirements forthissortof programmay be
much greaterthan thosefora programwhich does not attemptto dis-
criminate--in thetransfer and tax liabilityaspects-among discountrates.
The crucialpointwhichcan make thebond issueworkas a loan program
is that the purchasersof the bonds automaticallydiscriminateamong
themselvesas to theirdiscountrates.
Second, thegovernment maybe moreefficient thanthe privatemarket
only over a certain range of B. In particular,there may be a sufficiently
largevalue ofB such that,at themargin,the net-wealtheffectofgovern-
ment debt is zero. If the public choice processleads to thisvalue of B
(as it shouldon efficiency grounds),then,at the margin,the net-wealth
effect ofgovernment bondswould be zero,despitethecontinuedexistence
of "imperfect privatecapital markets."25

III. A Government Monopoly in Liquidity Services

Suppose now thatgovernment debt providesa formof"liquidityservice"
to the holder,in additionto the directinterestpayments.Suppose that,
at the margin,theseservicesare valued at the amountL per bond per
year. Hence, in the contextwhereall individualshave the same discount
rate,r, an additionalperpetualgovernment bond would be evaluated as
B = (i + L)/r.
The taxes forfinancingthe governmentdebt can be thoughtof as the
interestcosts, i, plus any costs involved with the process of creating

25 Of course,government debt issue would be "productive" in a total sense even in

the case wherethe marginalnet wealth effectwas nil. However,it is thismarginaleffect
which entersinto analysesof (marginal) fiscaland monetarypolicies.

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 GOVERNMENT BONDS 1113
liquidityservices(whichcould involvethe y-typecostsdiscussedabove).
Suppose that c denotesthe marginalcostsper bond per year associated
withtheproductionofliquidityservices.Hence, at themargin,thewealth
effectofa changein government debt will be

-(i + L) --(i + c) =-(L -c).

r r r
If the public choice processis such as to motivatethe government to act
likea competitive producerofliquidityservices(as it shouldon efficiency
grounds),thenL = c and themarginal-wealth effectofgovernment debt
would be nil. On the other hand, if the governmentoperates mono-
so thatL > c, thenthemarginal-wealth
polistically, effectofgovernment
debtwould be positive. 26 However,it is also possiblethatthegovernment
overextendsits productionof liquidityservices,so that L < c and the
marginal-wealth effectof governmentdebt would be negative.This last
case correspondsimplicitlyto the one discussed above in section IE,
whereL = 0 and c > 0 were assumed.
Of course,liquidityservicescan also be providedby privateproducers.
If the typesof servicesrenderedby privateand public debt instruments
are close substitutes,and if the private marketis competitive,then
governmental monopolypowercan arise here onlyto the extentthat,at
themargin,thegovernment is moreefficientthantheprivatemarketas a
producerof liquidityservices.Even ifthe government is a moreefficient
producer over a certain range, a sufficient expansion of government
"output" would eliminatethisefficiency differentialat the marginif the
productionofliquidityservicesis, at leasteventually,subjectto increasing
marginalcosts.As in the case of an imperfect privatecapital market,as
discussedabove, thenet-wealtheffectofgovernment debt dependson the
relativeefficiencyat themarginofgovernment versusprivateproduction.

IV. Risk and Asset Substitutability

The previoussectionshave dealt withthenet-wealtheffectofgovernment
debt.I have notdiscussedexplicitly in thesesectionstheriskcharacteristics
ofgovernment bonds,tax liabilities,and theothertypesofavailable assets
and liabilities.Tobin (1971, p. 2) has argued: "The calculus of total
wealth is less importantthan the change in the compositionof private
balance sheets that the governmentengineersby borrowingfromthe
public-forcingon taxpayersa long-term debt ofsome uncertainty while
providingbond-holdershighlyliquid and safe assets. Since no one else
26 Of course,thisobservationwould also apply to government
money,which yields a
zero rate ofexplicitinterest.The usual real balance effectforoutsidemoneyassumesthat
the marginalcost to the governmentof maintainingreal balances is zero, and that the
governmentacts like a monopolistin determiningits supplyof real balances.

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 I I14 JOURNAL OF POLITICAL ECONOMY

can performthe same intermediation,the government'sdebt issues

probably do, withinlimits,augment private wealth. Anotherway to
make the point is to observethat futuretax liabilitiesare likelyto be
capitalizedat a higherdiscountratethanclaimsagainstthegovernment."
I have already considered,above, argumentsforeffectively discounting
tax liabilitiesat a higherrate because of finitelives, imperfectprivate
capital markets,and a governmentmonopoly in the productionof
liquidityservices,and theseargumentsneed notbe repeatedhere.In this
part of the paper, I will considerbrieflysome implicationsof the risk
characteristicsof governmentbonds and of the futuretax liabilities
associatedwiththefinanceof thesebonds.
Suppose,first, thattherewereno uncertainty about therelativeburden
of the (lump-sum)tax liabilitiesthat financethe governmentdebt. In
thissituationtheuncertainty in an individual'sreal tax burdenassociated
with governmentinterestpaymentswould reflectsolely the variability
over timein the real-interest paymentsthemselves.In termsof present
in
values,thevariability the tax liabilitieswould reflectthevariabilityin
pricesand interestrates-that is, the samefactorswhichlead to variability
in real bond values. In particular,holdingsofgovernment debt-amount-
ingto a claimto a certainfractionoftotalgovernment interestpayments-
would be the perfecthedge againstvariationsin tax liabilities.27In this
contexta simultaneousincreasein governmentinterestpayments(i.e.,
government bonds) and in thetax liabilitiesforfinancingthesepayments
would notinvolveany netshiftin theriskcompositionofprivatebalance
sheets.28
Suppose now that the tax liabilitiesare subjectto an additionalvari-
abilityconcerningthe relativeburdenacross individuals.Suppose, first,
thatthevariationin relativetaxesis purelyrandom,in the senseofbeing
unrelatedto variationsin relativeincome,etc. In thatcase, it is clear that
an individual'stax liabilityassociatedwithgovernment interestpayments
would be subjectto a sourceofvariabilityabove thatofthe totalinterest
payments.In particular,the fractionalholdingsof governmentbonds
which correspondsto the expectedfractionof tax liabilitieswould no
longerprovide a perfecthedge against variationsin the tax liabilities.
Of course,it would be possibleforindividualsto utilizeprivateinsurance
marketsto reduce the risksassociated with variationsin relative tax
liability.However, to the extent that insurance arrangementsentail
transactioncosts, the risk associated with relativeliabilitywould not
generallybe fullyeliminated.In thiscase an increasein government bonds
would producea net increasein the riskcontainedin householdbalance

27 I am ignoring
hereeffects ofthegovernment
structure
whichrelateto thematurity
debt. In order to provide a perfecthedge, an individual's holding of debt by maturity
would have to correspondto the overall maturitydistribution.
28 There could be an effecton individuals who do not hold any government bonds
(or assetssubjectto similarrisks).

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 GOVERNMENT BONDS III5

sheets-that is, therewould be a decline in effective householdwealth.

The typicalhouseholdreactionwould be twofold:first,an increasein
desiredtotal saving,and, second, a shiftin portfoliocompositionaway
frommoreriskyassets,such as equitycapital,and towardlessriskyassets.
The impacton theequityrateofreturn,and, hence,on capital formation
would dependon whichofthesetworesponseswas thedominantforce.
The above discussionwould be altered to the extentthat variations
in tax liabilityreflectvariationsin income.In thiscontextthevariationin
relativetax liabilitiescan serveto reduce the netvariabilityin disposable
income-that is, the incometax works,in part,like a public programof
income insurance. If the income-offsetting featureof taxes were the
dominantelementin relativetax variability,thena shiftin government
bondscould lead to a reductionin theoverallriskcontainedin household
balance sheets.In that case the effectson desired total saving and on
portfoliocompositionwould be opposite to those described above.
However,it should also be noted that the public programof income
insurancewhich is implied by an income tax systemwill also involve
transactioncosts.There are costsassociatedwithadministration and with
individualreportingeffort,as well as "moral hazard" costs associated
withincentivesforearningincome.A fullanalysisof thewealtheffect of
governmentbonds under tax
different systems would have to involve a
of
comparisonofthesetypes public transactioncostsagainst thetransaction
costsassociatedwiththe poolingofincomerisksunderprivateinsurance
arrangements.
One finalobservationcan be made here. The argumentin the early
literaturefora net-wealtheffectofgovernment bonds-for example,that
given by Modigliani (1961)-involved a neglect of the tax liabilities
associatedwiththefinancingofthedebt. Similarly,Tobin's argumentfor
effects based on theriskcompositionofhouseholdbalance sheetsseemsto
neglectthe tax liabilitiesas an elementof thesebalance sheets.It seems
clear that,eitherin thesenseofeffects on perceivedtotalwealth,or in the
sense of the risk compositionof household portfolios,the impact of
changes in governmentdebt cannot be satisfactorily analyzed without
an explicittreatment ofthe associatedtax liabilities.Once thevariability
in relativetax liabilityis considered,thereseem to be no clear results
concerningtheeffect ofgovernment debtissueon theoverallriskcontained
in householdbalance sheets.The net effecthingeson the extentto which
variationsin relativetax liabilityreflectvariationsin relativeincome,
and on the transactioncosts for public programsof income insurance
relativeto thoseofprivateprograms.

V. Summary and Conclusions

This paper has focusedon the questionofwhetheran increasein govern-
ment debt constitutesan increase in perceivedhouseholdwealth. The

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 I I I6 JOURNAL OF POLITICAL ECONOMY

effectof finitelives was examined within the context of an overlapping-

generations model of the economy. It was shown that households would
act as though they were infinitelylived, and, hence, that there would be
no marginal net-wealth effect of government bonds, so long as there
existed an operative chain of intergenerational transfers which con-
nected current to future generations. Net-wealth effectsassociated with
imperfectprivate capital marketsand with a governmentmonopoly in the
production of liquidity services were shown to depend on the assumption
that the government was more efficient,at the margin, than the private
market either in the loan process or in the production of liquidity services.
Further, the introduction of government transaction costs for bond
issue and tax collection implied that the net-wealth effectof government
bonds could be negative. Finally, a consideration of the riskcharacteristics
of governmentdebt and of the tax liabilities associated with the financing
of this debt suggested that an increase in government bonds could raise
the overall risk contained in household balance sheets. However, this
effectdepends on the nature of the tax system and on the transaction
costs associated with private insurance arrangements.
The basic conclusion is that there is no persuasive theoretical case for
treatinggovernmentdebt, at the margin, as a net component of perceived
household wealth. The argument for a negative wealth effect seems,
a priori, to be as convincing as the argument for a positive effect.Hence,
the common assertion (as in Patinkin 1962, chap. 12, p. 289) that the
marginal net-wealth effectof government bonds is somewhere between
zero and one and is most likely to lie at some positive intermediate value
has no a priori foundation. If, in fact, the marginal net-wealth effectwere
negligible, the implications for monetary and fiscal analysis would be far-
reaching. In particular, in the case where the marginal net-wealth effect
of government bonds is close to zero, (1) the Metzler-type argument for
nonneutralityof changes in the stock of outside money would not be valid,
(2) a change in the stock of government debt would have no effecton
capital formation,and, more generally, (3) fiscal effectsinvolving changes
in the relative amounts of tax and debt finance for a given amount of
public expenditure would have no effecton aggregate demand, interest
rates, and capital formation.2 9

References
Bailey, M. J. National Incomeand thePrice Level. New York: McGraw-Hill, 1962.
Barro, R. J. "The Loan Market, Collateral, and Rates of Interest." Center for
Math. Studies in Bus. and Econ., Univ. Chicago, Report 7401, January 1974.

29 The usual fiscalanalysisinvolvesa shiftin the flowof government

debt ratherthan
a one-timeshiftin the stock.The zero net-wealtheffectapplies also to the flowcase if
individualsperceivethe implicationsof the currentflowforthe futuretime path of the
stockof governmentdebt.

This content downloaded from 129.049.005.035 on December 10, 2016 02:39:50 AM

All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
 GOVERNMENT BONDS I I I 7
Becker, G. S. "A Theory of Social Interactions." J.P.E. 82, no. 6 (November/
December 1974): 1063-93.
Blinder, A. S., and Solow, R. M. "Does Fiscal Policy Matter?" J. PublicEcon.
2 (November 1973): 319-37.
Diamond, P. A. "National Debt in a Neoclassical Growth Model." A.E.R. 60
(December 1965): 1126-50.
Hirshleifer,J. "On the Theory of Optimal Investment Decisions." J.P.E. 66,
no. 4 (August 1958): 329-52.
Koopmans, T. C. "On the Concept of Optimal Economic Growth." In The
EconometricApproachto Development Planning.Amsterdam: North-Holland, 1965.
Metzler, L. "Wealth, Saving, and the Rate of Interest." J.P.E. 59, no. 2 (April
1951): 93-116.
Miller, M. H., and Upton, C. W. Macroeconomics:A Neoclassical Introduction.
Homewood, Ill.: Irwin, 1974.
Modigliani, F. "Long-Run Implications of Alternative Fiscal Policies and the
Burden of the National Debt." Econ. J. 71 (December 1961): 730-55.
Mundell, R. "Money, Debt, and the Rate of Interest." In Monetary Theory,
edited by R. Mundell. Pacific Palisades, Calif.: Goodyear, 1971.
Patinkin, D. Money,Interest,and Prices. 2d ed. New York: Harper & Row, 1964.
Peltzman, S. "The Effect of Public Subsidies-in-Kind on Private Expenditures:
The Case of Higher Education." J.P.E. 81, no. 1 (January/February 1973):
1-27.
Samuelson, P. A. "An Exact Consumption-Loan Model of Interest with or
without the Social Contrivance of Money." J.P.E. 66, no. 6 (December 1958):
467-82.
Thompson, E. A. "Debt Instruments in Macroeconomic and Capital Theory."
A.E.R. 67 (December 1967): 1196-1210.
Tobin, J. Essays in Economics.Vol. 1. Macroeconomics.
Amsterdam: North-Holland,
1971.

This content downloaded from 129.049.005.035 on December 10, 2016 02:39:50 AM

All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).