Economics
Letters0165-1765/94/$07.00

44 (1994) 191-195
0 1994 Elsevier

191ScienceB.V. All rights

Ricardian equivalence
government bonds
Budget constraintNobuo

Akai*

Facultyof Economics,

Received
Acceptedreservedfor local

approach

Osaka University, Machikaneyama,

Toyonaka 560, Japan

19 May 1993
23 August 1993

Abstract
It is shown that if consumers
own land, the free rider problem does not occur because a change in local government
financing is completely reflected in the price of land. This means that the Ricardian equivalence
theorem holds not only for
natronal government
bonds but also for local government
bonds.
JEL

classification: H74

1. Introduction
The Ricardianequivalence
theorem indicates that a change in local government
financing fromtaxation to debt, keeping government
expenditure
constant,
is independent
on the consumption
path.’ But, when bonds are regional, it is said that the free rider problem arising as a result of theregional mobility makes it difficult for this theorem to hold.’
Our focus is to verify whether this problem occurs. Daly (1969) suggested that if consumers
own land, the free rider problem does not arise because a change in local government
financing iscompletelyreflected in the price of land. Following Daly, Noguchi (1981) criticized the regulationon the issuance of local government
bonds. But they do not define a model. Tsuneki(1985)
discussed it by using the frameworkof the Modigliani-Miller
Theorem.
However,
this does notinclude regional mobility explicitly and the bonds are financed by a land tax not an income tax.
The purpose of this paper is to show clearly that even when regional mobility and an income
tax are considered,
the free rider problemdoes not occur. This means that a change in local
government
financingdoes not affect the consumer’s
consumption
path, that is, the Ricardianequivalence
theorem holds even when bonds are regional.
In section 2 we set up the model with land. In section 3 the land price is derived. That the free

* The author

wishesto thank seminar participants
at Osaka University
for helpful comments
see Seater (1993).
of the burden of internal and external bond was shown by Mutoh (1985).

’ For most recent survey,’ The equivalence
SSDZ

0165-1765(93)00321-E

and suggestions.192

N. Akai

I Economics

rider problem
does not occur is derived
Conclusions
are given in section 5.

Letters 44 (1994) 191-195

in section

4 by comparing

twotypesof behavior.

2. The model
We assume that consumers live infinitely and that they are identical in preferences
and wealth.
For simplicity
we ignore the intergenerational
problem.3
In addition,
we assume that many
identical local governments
exist and finance local public goods with taxation.
Now we introduce
the land market as the regional fixed asset and all available land is held by someone. We supposethat the total amount of land in one region is fixed. Consumers
have land as the production
space.
They can receive a land revenue, defined by a, at each period. Then the representative
consumer’s
budget constraint
at period t becomes(1 + r)S,_ 1 + r, + arL, - q = c, + s, ,where r is the interest rate and is constant through time, Y is income, which is equal in all regions
and is constant,
S is the gross savings at each period, L is the amount of land owned, r is an
income tax level levied when bonds are not issued, and C is the consumption
level. Also r and Y
are given exogenously.
The subscript refers to the period.
We assume that the utility of consumers
depends on only the consumption
level. Consumers
can select the consumption
path, that is, the saving path with utility maximizing.
Here we supposethat consumers take account not only of the budget constraint of consumers but also of the budget
constraintof the regional government.
This means that consumers
can anticipate
the future tax
stream.
Now we can think of a change in local government
financing, that, is, the introductionof debt
finance and the reduction of the tax level. Here we assume that one local government
issues a newbond at period 1 and that this bond reaches maturity at period 2. When the level of per capita
local government
bonds is defined by b, the tax level of the local government
becomes rr - b at
period 1 and r2 + (1 + r)b at period 2.

3. Land priceLet p, be the land price at period t. Consumers
can get land revenue at the beginningof theperiod and can sell the land at the beginningof the next period if they want to move to anotherregion. If consumers
sell the land at period 1 and invest the sales in the money market, they canget revenue of (1 + r)pl per unit of land. While if consumers hold the land at period 1 and sell it atperiod 2, they can get land revenue of (1 + r)a and sales of p2 per unit of land.4.5 The equilibrium
price of land is achieved when the revenue in both cases is equal. The equilibrium
condition of theland market becomes(1 + r)p, = (1 + r)a +pz .
’ The Ricardianequivalence
theorem with intergenerational
problems was shown by Barro (1974).
AFor example, suppose that the land is used for agriculture.
Then a represents
the agricultural
revenue.
’ Here we assume for simplicity that a is constant.
But this assumption
is not essential to the results of this paper

193

N. Akai I Economics Letters 44 (1994) 191-195

This equation
represents
Similarly,
the equilibrium(1+ r)p, = (1tan arbitrage
condition
betweentheconditionat the next period becomes

two equations,p1 = a + a/(1 + r) +p3/(1By repeating

this operation,andtheland.

we get+ r)2.

we havep1 = {a + a/(1 + I) +a/(1+ #+*. . +pt+,/(lThis equation means that the land price is considered
convertingt to infinity, we get p1 = (1 + r)(ulr).

4. The existence

assetr)a +p3.

p2 from the above

Eliminatingmonetary+ r)‘} .
as the discounted

presentvalueof land.

Byof region mobility

Most of the papers that discuss Ricardianequivalence
assume that consumers
cannot move toanotherregion. We may be persuadedof this assumption
when we are thinking
about theproblems
between countries.
But we are considering
the problem among regions. Therefore
weallow mobility of consumers
in this section. To show the equivalenceof the regional bond, we
think of two kinds of budget constraints,
though consumers
are identical.
One is the constraint
ofa consumer
who does not change region. The other is the constraintof a consumer
who doeschange region.
4.1.

Consumer

who does not change region

We assume that a consumer cannot know the behavior of the other consumer.
Then a consumer
who does not change region anticipatesthat some consumer
may change region. Under thisanticipation,
assuming the populationin this region changes from N, at period 1 to N, at period 2,the constraintsof a consumer
who does not change region becomes(1 + r)S,, + Y, + uL, - (TV- BIN,)= C, + S,(1)

and(1 + r)S, + Y2 + uL, - (TV+ (1 + r)BIN,)= C, + S, + P,(L,- L,) ,(2)where IV, is the populationof this region at period t and B is the total level of bonds issued.
Equation(1) means that, by the issuance of local government
bond B, the tax level per capita
decreases by BIN, to r1 - BIN, at period 1. Similarly Eq. (2) means that the tax level per capita
increasesby (1 + r)BIN, to r2 + (1 + r)BIN, at period 2. Some consumers
who move to otherregions sell their land and consumers
who do not change regions buy this land at the equilibrium
land price, p2, equalizing the demand and supply of the land. The last term on the RHS of Eq. (2)shows that the amount of land held by a consumer changes from L, to L, at period 2. Since thetotal land size of the region is fixed, the equilibrium
conditionof the land market becomes
NIL, = zf = N,L, ,(3)194

N. Akai

I Economics Letters 44 (1994) 191-195

where il is the total land size of this region.
Next we consider the land price at period 2. When the population
is N, at period
revenue,RR, which a consumer can get by living in this region becomes
RR = aL, - (1 + @IN,2, the real.

With Eq. (3), we get
RR = {a - (1 + r)BIL}L,.

(4)

Equation (4) means that the real revenue per unit of land decreases
Then the land price at period 2 is derived aspz = {a - (1+ r)BIL

Using+ a/(1 + r) + u/(1 + r)2 + . . * +p,+2/(1t to infinity,

we getp2 = (1+ r)(ulr- B/L)

By converting(5), (2) is formulated+ $}to a - (1 + r)BIL.

.

(5)

.

by(1+ ‘)S, + Y2 + UL, - (T2 + (1+ @IN,)
Separatingby (1 + r)BIL= c, + s, + (1+ ?)(u/r- B/L)@

2-L,)’L,, we get(1+ r)S, + Y2 + aL, + u(L, - L,) - (T2 + (1+ @IN,)= c, + s, + {(1+Eliminatingr)ulr}(L,- ((1 + r)BIL}(L,-L,)

-L,)

.

(6)

S, , Nl, and N, from (1) and (6) with (3), we get(1+ ?){(1+r)S, + Y, + UL, - T1 - C,}= -Y2 - UL, + r2 + c, + s, + {(1+r)ulr- u}(L,-L,)(7).

The last term on the RHS vanishes in the intertemporalbudget constraint.
This is because thechange in the amount of land from L, to L, derives revenue ofh(L, - L,) at each period, and thediscounted
present value equals the land price multipliedby the change in the amount of land,is(1 + r)ulr(L, - L,). Then the constraint
is independentof L,, that is, N2. Also this equation
independentof the debt level, B. Therefore
we conclude that Ricardianequivalence
obtains forconsumers
who do not change region, even if the populationof the region varies.
4.2.

Consumer

who changes region

The land price in the region where the local government
financing does not change becomes(1 + r)ulr from section 3 similarly. This shows that consumers
who move to another region canbuy land at the land price (1 + r)ulr. With this in mind we can set out the budget constraints
ofconsumers
who change regions. At period 1 these become(1 + r)S,, + Y, + aL, - (T, -BIN,)
At period

2 consumers= C, + S, .

sell the land at the land price (1 + r)(ulr(8)- B/L)

in the region

wherelocal

N. Akai I Economics

government
bonds are issued,Therefore
the budget constraint

and buy land at the landat period 2 becomes(1+ Y)S, + Y2 + UL, - r2 + (1 + r)(ulr195

Letters 44 (1994) 191-195- BIL)L,price(1 + r)alr- (1 + r)alrL,in the other= c, + s, .

region.

(9)

The fifth term on the LHS of Eq. (9) represents
the revenue created by selling land and the sixth
term represents
the cost paid to buy land in another region.
as (7). Thus theEliminatingS, and N, from (8) and (9) with (3), we have the same equationintertemporalbudget constraintof a consumer who changes region is identical to the constraint
ofa consumer
who does not change region. Therefore,
even if they change regions to avoid theburden of local debt at the next period, consumers’
utility does not increase. Consumers
cannotbecome free riders as long as they own land, even if they move regions.

5. Conclusions
In this paper we have shown that the existenceof regional
mobility
does not affect theconsumptionpath. This fact is demonstrated
by introducing
a regional fixed asset into the model.6
The change in local government
financing affects the price of the fixed asset in this region. Since
we assume that consumers
must own land as a production
space, this change in local government
financingwill surely affect consumers.
Therefore
consumerscannot become free riders. Thismeans that, even if bonds are regional, the Ricardianequivalence
theorem holds. The regulationof regional bonds must be reconsidered.

References
Barro, R.J., 1974, Are government
bonds net wealth?, Journal of Political Economy
80, 1095-1117.
Daly, G.G., 1969, The burden of the debt and future generations
in local finance, Southern Economic Journal 36, 44-51.
Mutoh, T., 1985, The equivalenceof the burden of internal and external public debt, Economics
Letters 17, 369-372.
Noguchi, Y., 1981, On the intergenerationaltransfer of income thoroughfiscal policy, Gendai Keizai 44, 107-117 (inJapanese).
Seater, J.J., 1993, Ricardianequivalence,
Journal of Economic
Literature
31, 142-190.
Tsuneki,A., 1985, On the neutralityof local public bond in a spatial economy,
The Economic
Studies Quarterly
36,
42-52.

’ In this paper

this asset is land.