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GOVERNMENT DOMESTIC DEBT AND THE RISK OF
DEFAULT: A POLITICAL- ECONOMIC MODEL OF THE
STRATEGIC ROLE OF DEBT
Philippe Aghion
Patrick Bolton
No.
541
October 1989
Massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 021 39
GOVERNMENT DOMESTIC DEBT AND THE RISK OF
A POLITICAL- ECONOMIC MODEL OF THE
STRATEGIC ROLE OF DEBT
DEFAULT:
Philippe Aghion
Patrick Bolton
No.
541
October 1989
1
t
•
flCBSjlWIFS
DEC2 11989
GOVERNMENT DOMESTIC DEBT
AND THE RISK OF DEFAULT
:
A Political-Economic Model of the Strategic
Role of Debt.*
by
Philippe AGHION**
and
Patrick BOLTON*"*
(forthcoming in "Capital Markets and Debt Management" edited by
Rudiger Dornbush and Mario Draghi)
MIT and DELTA, Paris.
**** Harvard University and Laboratoire
.**
d'
Econometrie de l'Ecole
Poly technique, Paris.
We are particularly grateful to Alberto Alesina for introducing us into the
field of Macroeconomics and Politics and for many useful comments. We would
also
like
to
thank
Olivier
Blanchard,
Jean-Pierre
Dan thine,
Rudiger
Dornbusch, Pietro Reichlin and Philippe Weil for very helpful discussions.
"Government Domestic Debt and the Risk of Default:
A Political-Economic Model of the Strategic Role of Debt"
By Philippe Aghion and Patrick Bolton
ABSTRACT
This paper focuses on the question of how differences in income and
asset-holdings give rise to differences in preferences concerning fiscal
policy and investigates how democratic political institutions, within a
two-party system, solve the social choice problem of what fiscal policy to
It is assumed that the
implement when voters have conflicting preferences.
party
power
its
own constituency; in
political
in
pursues the interests of
particular the left-wing party identifies with the interests of low- income
voters, and the right-wing party represents the high income voters.
These
party objectives give rise to fiscal policies where the left-wing party
favours large government expenditures on public goods with concomitant high
levels of taxation, and the right-wing party favours low levels of expenditure
and low taxes.
The party winning the elections implements the fiscal policy
it favours most.
It is shown that if default on public debt is costly for the
government, then left-wing administrations may overaccumulate public debt.
But if default on public debt is a real possibility, then right-wing
administrations may overaccumulate public debt to ensure their re-election.
Large outstanding debt changes the view of moderate voters about the left-wing
party:
they become more concerned about the government preserving the real
value of their bond holdings than about maintaining expenditure on public
goods.
This is why they switch their votes from left-wing to conservative.
I.
INTRODUCTION
of the research and controversy on macro fiscal
recently, most
Until
was about when and whether debt-financed government deficits have
policies
real effects on aggregate output and employment. This problem has typically
studied
been
in
generations
interacting
agents)
overlapping
(or
with
a
(such as
policy in
of fiscal
the role
benevolent
a
limited
favouring optimal
accumulation or in minimizing the deadweight loss of distortionary
capital
taxation)
addressed within
can be
this framework
(see Blanchard-Fischer
for an extensive discussion of this approach). Thus, a particularly
important
fiscal policy
aspect of
generational)
political
suppressed in this model is the (intra
redistributive effect
of fiscal
policy and
the consequent
conflicts arising from these distributional concerns. Behind the
representative
income
agent
maximizing a Social Welfare Function. Naturally, only
of issues
(1989)
representative
a
representative
of
government
set
of
model
a
and
question
a
in preferences
heterogeneity whether in terms of
of
lot
preferences.
or
differences
how
differences
lurks
holdings
asset
of
democratic
agent
in
income
paper focusses on the
and asset-holdings give rise to
concerning fiscal
political institutions
This
policy and investigates how
solve the social choice problem of what
fiscal policy to implement, when agents have conflicting preferences.
Our model is much inspired by the experience of public debt management
and
the political
during
conflicts surrounding
the mid-war
confronting
the
debt-overhang
it in several European countries
period. This was a time when one of the major problems
various
governments
was
how
to
deal
with
the
huge
problem inherited from World War I. Very broadly, in several
countries there was a clear conflict about fiscal policy between right-wing
parties
representing the interests of the rentiers (among others) and thus
favoring conservative fiscal policies aimed at preserving the real value of
government
parties
debt and other forms of nominal domestic savings, and left-wing
representing the
interests of
the workers and unemployed and who
policies as well as increased expenditure on
reflationary fiscal
favoured
goods. In several instances when left wing parties were elected (as
public
instance the "Cartel des gauches" in 192^ and the "Front Populnirc" in
for
shortly
there
France)
in
1936
followed
a
period of more or less high
inflation (fed by sharp increases in government spending) which amounted to
a de facto
default on public debt. Conservative governments on the contrary
practiced
severe fiscal
Alesina
(1987)
endeavoured to curb inflation (see
restraint and
an illuminating survey of the mid war debt policies in
for
Europe)
construct a model where these conflits about fiscal policy clearly
We
emerge
as
analyze
be
party in
constituency
restrict
identifies
pursue the
interests of its own
rather than a general Social Welfare Function. In this paper,
attention
These
to
a
two-party
interests of
with the
left-wing
assumed to
power is
the right-wing
average.
incomes between agents. We then
in
hands of a political party elected through majority voting. The
in the
while
differences
of
policy is determined when the government is assumed to
how fiscal
political
we
result
a
system
:
left-wing
the
party
agents having incomes below the average
party represents those agents with incomes above the
party-objectives
party favours
give
rise
to fiscal policies where the
large government expenditure on public goods with
concomitant high levels of taxation and/or high levels of indebtedness, and
the
right-wing party
levels
favours low levels of expenditure, low taxes and low
of outstanding
debt. The
fiscal policy that is implemented is the
one of the party who wins the elections.
Within
if
this model we address two sets of questions
:
first, what role
any does public debt play in the dynamic political game between the two
parties
what
future
in constraining the actions of future administrations
extent does
elections?
outstanding
current fiscal
Concerning
debt constrain
policy have
the
first
future governments
?
Second,
to
an impact on the outcome of
question,
both in
large
levels
of
terms of limiting
future expenditure on public goods and in forcing higher levels of taxation
to
victory
while
redistribution
Surprisingly,
to
however,
exploit the
government
debt in order to both
and increase
public goods
imposing higher
future by
in the
of
next elections finds it worth-
provision of
intertemporally" the
"substitute
in the
levels
large
accumulate
left-wing government anticipating the
a
conservative rival
of its
to
show that
debt. We
repay the
levels of
taxation.'
1
this is the only instance where a government wishes
commitment effect of debt. Conservative governments do not
to constrain future left-wing governments by excessively accumulating
wish
Our
debt.
results
are
the commitment
extensively with
precise
with
earlier
the
work
of
(1988)] and Persson-Svensson (1989). Section IV
Alesina-Tabellini [(1987a),
deals
contrast
in
thus
effect of
debt
.
It
discusses the
connections between these papers and ours. It also points out that
the commitment value of debt disappears when future governments are allowed
to
default on
question
have
inherited outstanding debt. Section V deals with the second
the strategic role of debt
:
impact
an
administrations
inflation
outcome
the
on
contemplate
or explicit
.
We show that current fiscal policies
future
of
possibility
the
default)
.
Our
elections
of
only
if
future
default (either through
model is one of complete information
with forward looking agents, where current fiscal policy only matters if it
changes agents' preferences about future fiscal policies. It turns out that
preference-reversals
can only
basic
point is as follows
large
levels of
debt can
occur if
there is
a risk
of default. The
A current conservative government accumulating
:
swing the
outcome of
future elections
in its
favour because its left-wing rival is rationally expected to default on the
debt while the conservative party is rationally expected to repay the debt.
The
larger
maintaining
they
change
are
the
outstanding
the real
towards
value of
the
debt
the
more voters become concerned with
debt and thus the more favourably inclined
conservative
administration. Large levels of debt
the outcome of elections to the extent that they shift the conflict
about
fiscal policy away from issues of more or less expenditure on public
goods
to issues
of more
or less monetization of the debt. Interestingly,
left-wing
may
parties
described in section
THE MODEL
economy
At
closed economy
beginning
government.
agent
way as the
V.
is composed of a
the
same
the
in
.
consider a
We
debt
use
to
government above. The circumstances in which this happens are
conservative
II.
able
be
elections
period,
are held to appoint a new
but different incomes .Each
identical preferences
Agents have
is identified
foreign debt or lending. This
continuum of agents who all live for two periods.
each
of
with no
parameter a
by a
which measures
his income in each
period (agents earn the same income in both periods). The source of agents'
is not modelled. The economy's income distribution in the absence
earnings
of
intertemporal
transfers
given
is
by
f(a)
support [0,1]. The
with
individual voters' preferences are assumed to be represented by the utility
function
:
U(c t ;g L
where
is
cc
consumption
is
log(c 1 +
consumption
special
'
debt
p log(c 2
+
of
the
;
+
(2.1)
.-
).
private
good
period
in
t
and g
is
3 is the discount factor. Of course,. this
function.
utility
g2
We
adopt
mainly
it
to
make
.
,
is provided by the government'
3
'
.
In fact,
in our
the government's role is limited to determining the level of current
expenditure
period
)
2
The public good, g t
model
gj
tractable. Our results hold for a much wider class of utility
calculations
functions'
=
of the public good
rather
a
)
1
on the
public good
as well
as the
method of
financing. In
the government can choose between various combinations of tax and
financing. In
period 2
only taxes are available to finance both the
debt repayments and the expenditure on the public good.
most
Throughout
of
(i)
taxes are not distortionary
(ii)
the
equal
by t
government
the paper
Later in
and r 2
]
the
:
rate of transformation between the private and the public good is
to one.
denote
assume that income-tax rates are
we
we shall make the additional assumptions that
to begin with,
uniform and,
paper
the
rates in
the tax
the latter assumption' ''.
we relax
periods
1
and 2 respectively. The
can choose any tax rate between zero and one'
tax rate
public goods
g[
period one
in
t.
'
.
Finally, given
and given the government's expenditure on
by the government's budget constraint
1
is given
:
JjT ia f(a)da.
-
d = gl
^
the amount of public debt accumulated in period
,
We
(2.2)
The interest rate at which the government can borrow,
r,
will be determined
endogenously in the model.
an agent
Now,
the
public good,
with income a, anticipating government expenditures on
g t and
g2
,
financed with tax rates Tj and t 2 solves the
following intertemporal consumption problem'
max
C
*-
1
"
i
C2
log(c 1 +
)
+
p log(c 2 + g 2
\
)
*
Cj +
c2
s
< a(l-Tj
< a(l-r 2
)
+
(2.3)
s.p
.
We model the political process as follows
each
At
elected
power
:
period
a left-wing
it has
:
* <1
s. t.
where p = 1+r
gj
>
there
are
two
:
political
parties
party and a right-wing party'
total control over t
and g t
.
7)
.
competing to be
Once a party is in
Prior to the election, a party
To
pursuing a particular fiscal policy if it is elected'
commit to
cannot
we
ideas,
fix
time-line below
represent
sequence
the
of
and events in the
moves
:
t
=
2
incumbent administration
new elections
chooses
parties cannot
chooses g 2 and t 2
commit to future
and how much of
policies during
the campaign
the public debt
to be repaid.
gj
'
and Tj
(d
and
p are then implicitly
determined)
Figure
new government
:
1
The party which gets at least fifty percent of the votes is elected. How do
we
distinguish between a left-wing and a right-wing party
?
We assume that
the left-wing party represents primarily the interests of those individuals
whose
income is
party
represents primarily the interest of those whose income is above the
average.
Average income
below the
More specifically,
we suppose that the left-wing party maximizes
the interests of some income group a
L
maximizes
exogenously
the interests
given, and
in the economy. The right-wing
of some
<
Ea
;
and that the right-wing party
income group o^
>
Ea.
Both a
and a
are
we do not consider the question of how a party may
wish to choose a in order to maximize the probability of being elected.
We shall be interested in the subgame perfect-equilibria of this game.
As
usual, one
solves for these equilibria backwards. This is particularly
straight-forward
uncertainty
<9)
.
in this
model since
there is perfect information and no
The only potential difficulty arises from the endogeneity
The individual
the interest-rate.
of
interest rate
equilibrium
;
savings decisions depend on
future
policy
well
as
as on
the
the latter simultaneously influences and
and
on future policy. Before solving for the perfect equilibria of the
depends
described above, we shall consider various scenarios which will serve
game
helpful
as
about
expectations
(rational)
their
agents'
We
benchmarks.
begin
solving for the optimal government
by
policies when the government is respectively a social planner, a right-wing
dictator
in period
public debt
on outstanding
default
assuming that the government does not
left-wing dictator,
and a
Then
2.
we solve
for the
political equilibrium, first assuming no default and secondly, allowing the
period-2 governments to default on outstanding public debt.
OPTIMAL POLICY
III.
A SOCIAL
DECISIONS OF
PLANNER AND OF RIGHT-WING AND
LEFT-WING DICTATORS.
Throughout
paper
this
These are
political
equilibrium.
interests
of
2
(1
'
representative
call
a
dictator
time-consistent
compare with the dynamic
government
a
pursuing the
clientele and who remains in power in periods
his own
A social
.
We
optimal
benchmarks to
the relevant
policies.
consider
only
we
planner, on
1
the other hand, maximizes the utility of a
average consumer. We are particularly interested in finding
out how much debt each type of government wants to accumulate in period
To
income
and
1.
begin with, consider the optimal savings behavior of an agent with
a.
Solving
savings function
the
maximization
problem
(2.3) yields
the following
:
pp(g,+ a(l-T, ))-(g 2 + a(l-T 2
s(a;p;T ;g
)
1
'
=
——
))
.
(3-1)
(1 + P)p
The equilibrium interest rate p is then given by the following equation
:
Jjs(a,p;T t ;g t )f (a)da
The
gj
Using equation
TjEa
=
Lemma
savings and the RHS the demand for
an d
dp
-
the two government budget-constraints,
(where Ea
denotes the average income in
one easily solves for the equilibrium interest-rate
,
equilibrium
In
:
(3-2)
supply of
(3-1)
T 2 Ea
=
d.
have
we
p
=
1/(3
for
levels
all
:
of
debt
Obvious
level
outstanding
of
debt
exceed
cannot
Ea.p
,
for otherwise the
government is unable to pay back all the public debt in period 2
Consider
periods
of
:
[0;Ea.p].
Proof
The
1
and g 2
d
+
the economy)
d e
the net
LHS represents
savings.
=
1
first
and
optimal
the
policy
chosen
by
(
l
'
'
a social planner in
We suppose that the social planner maximizes the utility
2.
a representative
The main reason for selecting this
average consumer.
social welfare function is that it allows us to characterize a point on the
Pareto-frontier
abstracting from
distributional issues
between high- and
low-income agents. This is not the case, for instance, with the utilitarian
welfare
function which corresponds to maximizing the sum of the utilities.
The latter welfare function leads to perfect equality as the social optimum
in our model* X2)
.
Thus, in period 2 the social planner chooses t 2 and g 2
utility of the consumer with income Ea
s(Ea;p;T t ;g t
log g 2
where g,
=
+
T,Ea
Ea(l-T 2
)
:
)
+
(3-3;
d
-
—
p
.
(Recall p
to maximize the
=
1/p from lemma 1)
Substituting
for g 2
it is clear that the social planner is
in (3-3)
d
indifferent
rate t,
1
e
'
31
and since the rate of transformation between
,
the public
private and
equal to
good is
one,
the social planner is
indifferent between any feasible level of expenditure on public goods
similar result
A
planner chooses t
logtc^
period
holds in
d and g
;
[
max
Since
.
(3Ea
are non-distortionary
taxes
the
second-period tax
between any
to solve
the social
In the first period,
1.
.
:
{
g )+ plog(c 2
+
g2
t
)
Tj ;d
subject to
Ea(l-T
s(Ea,p,T t ,g t
-
)
1
t,
notice
Now,
Ea
d
+
c,2
=
Ea(l-T 2
g2
=
r 2 Ea
d(c.
+
g.
that
-
=
dT
)
(3-M
s(Ea;p,T t ;g t
-
)
)
dp
;
=
(i
Consequently,
1.2)
planner is indifferent between any level of taxation t.
d(Cj+ gj
=
straightforward to see that
(i = 1,2)
;
planner
is indifferent
between
any feasible
result
that
the governments'
individuals'
government
dd
between any
level of
is reminiscent
feasible level
period
1
e
,
[0,1].
It is also
so that the social
of debt and therefore
expenditure on public goods
of the Ricardian equivalence theorem
,
.
This
to the extent
financial structure is indeterminate as a result of
intertemporal arbitrage
deficit
social
the
:
increases
today,
behaviour. That
agents
ds(a,p,T t ;g t
is to say,
when the
save more to pay future
)
increases in taxes (note that
= 1 so that one extra dollar of
dd
deficit today is exactly offset by an extra dollar of savings). However our
result
is
government
not
only in
government
more
general
than
the
Ricardian
equivalence theorem, since
expenditure decisions here are endogenous. The indeterminacy is
the financial
structure, but
also in
the optimal
level of
expenditure. One might refer to this result as "Ricardian super
10
To complete our characterization of the social optimum note
indeterminacy"
social planner
that
if the
debt
in period
to default on public oustanding
were allowed
it is easy to show that he would be indifferent between
2,
and no default. This is altogether not surprising given that taxes
default
are assumed to be nondistortionary
clear
become
will
As
below,
social
the
planner's optimal policy
differs from that of a left-wing or right-wing dictator. Consider first the
fiscal policy of a dictator of type a in period 2 (in other words,
optimal
the
optimal policy
income-group a
)
:
The government then chooses t 2 and g 2 to solve
max log(c 2
T 2 ;g 2
subject to
government which represents the interests of the
of a
:
and
+
g2
:
)
c2
=
a(l-T 2 +p.s(a,p;r t ;g t
g2
=
t 2 Ea
)
dp
-
.
(3-51
)
(where s, p, d are taken as given)
Solving
government
chooses
the
chooses
and
=
g,'
obtains
dp
easily
one
(3-5)
t,d
=
result
the
—
Ea
maximizes
t2
expenditure on
=
and g 2
1
=
Ea
-
dp
log(Cj+
g,
+
)
Ea,
the
;
Vice-versa, if a < Ea,
that
is,
the government
the public good.
In period 1, a dictator of type a chooses Tj
max
>
In other words, the government
.
to minimize expenditure on the public good.
government chooses
that if a
and d to solve
(3log(c 2 + g*
Tj ;d
subject to
:
c,
=
a(l-r,)
-
s(a,p.T ;g t
(_
and
c2
=
a(l-T*)
g,
=
T,Ea
+
d
g,
=
T ? Ea
-
dp
+
)
s(a,p,T t ;g t )p
(3-6)
11
and t" are the solutions to problem (3-5)
k»here g 2
t,
s(a,p.T t ;g t
)
Ea+d+atl-Tj
-
)
where
s^\d
(-r*Ea-d/p+a( 1—rj
)
)
=
P
One
can easily
if a < Ea,
verify that
then both
+
c
g
L
defined
in
solution
are
is to
t
in
+
(as
g,
follows that the optimal
It
.
c2
(
set Tj
decreasing in t
dictator
increasing
are
(3-6))
and
Y
=1.
Vice-versa, if a
Ea,
>
then c 1
+
g
:
and c 2
=0. Thus
so that the solution then is to set Tj
+
g,
if a
maximize tax revenues (and expenditure on public goods)
wants to
he wants to do so in both periods. The same is true if he wants to minimize
assumptions on
Given our
taxes.
dictator
a L and
maximize expenditure
wants to
dictator wants to minimize expenditure
o^
,
this
means that a left-wing
on public goods
and a right-wing
,
.
It remains to determine how much debt each type of dictator is willing
incur in
to
indifferent
fact
period
1.
A left-wing dictator, who sets Tj
between any
that both
cx + g
l
level of
and c 2
+
g2
debt below
t2
=
=1, will
be
Ea.p. This follows from the
(as defined in
remain constant as
(3-6))
the level of debt is changed. The left-wing dictator is indifferent between
debt
and taxes,
reduction
since any
in expenditure
increase in debt today implies a corresponding
on the public good tomorrow so that the increase
in utility from more expenditure on public goods today is exactly offset by
a
reduction in utility tomorrow.
To
determine
accumulate
how
in period 1,
much
debt
a
right-wing
is willing to
dictator
it suffices again to see how (c
+
l
g,
)
and (c 2
+
g2
)
vary with d. The right-wing dictator minimizes public expenditures and thus
dp
sets T =
t2 =
Total consumption in periods 1 and 2, respectively,
;
t
—
.
for an individual of type a^ then becomes
:
12
°<R
d +
d
1
Ea p
P
tt
22
c2 +
g2
a-
^
=
—
.Ea
d
(
-
1
I
d
—
s
)
+
d 1
Ea p
-^
(3-8)
(1 + P)
pj
k
H
+
Differentiating (3-7) and (3-8) with respect to
d{c x
+
gj)
!
- =-l
i
3d
Since
>
o^^
dictator
Ect
6(c 2
o^n,
(
1+p
;
strictly prefers
g2
)
Ea
1+p
(3-9)
y
conclusion that
obtain the
:
o^n
(
x
dd
Ea.)
assumption we
by
+
one obtains
d,
a right-wing
issue any public debt in period
not to
1
.
This
result
is all the more striking in that taxes are not distortionary in our
model.
The intuition
with
the
with
one
behind this result is straightforward. The consumers
incomes above the average bear most of the taxation cost of servicing
period 2.
debt in
incomes below
dollar of
In fact,
it is easy to verify that those consumers
pay less than one dollar in taxes for any
the average
debt-repayment they
receive. Therefore,
indirectly
serves
right-wing
administrations strictly
does
the
not, however,
between
role
of
explain why
debt-accumulation and
a
redistributive tax. This explains why
prefer not
no debt
debt. This
accumulation. The latter result is
because
superior
instrument of income redistribution
and
to accumulate
left-wing administrations are indifferent
obtained
taxes
debt accumulation
expenditure
public goods are a (weakly)
on
;
so that the role of debt in
redistributing income becomes irrelevant.
IV.
DYNAMIC POLITICAL EQUILIBRIUM WITH NO DEFAULT
If
elected,
expenditure
on
a
right-wing
the
public
administration
good
by
setting
.
will
the
choose
period-2
to minimize
tax
rate
13
t,
=
max<0;
t2
=
1
—
This was established in the previous section. Note that the policy
.
objective in period
of
2
of each type of administration is the same regard] ess
what fiscal policy was implemented in period
Ea
<
1
.
What affects the policy
in period 2 is only the location of the political party in power
objective
(a,
opposite and set
do the
administration will
left-wing
A
f.
<
aH
).
Voters know the policy objectives of each party and rationally foresee
what
fiscal policy each party will implement. We assume that voters always
vote
and that they vote for the party implementing the fiscal policy which
is
which
in
individual best
in their
interest'
voters
with
right-wing
group
can define an income-group, denoted by a, such that all
We
:
.
the derivation of the political equilibrium
considerably simplifies
period 2
Our model has a useful feature
]
income
this
government and
is uniquely
indifferent
are
between
the
policies of the
the left-wing government. This income
those of
all voters
determined, and
with incomes a less than a
vote for the left-wing candidate, and those with incomes a above a vote for
the
right-wing candidate.
income
shown
given
that
government representing
that a
between
of voting behavior. In section III, it was
perfect predictor
is a
words, our model has the feature that
In other
minimizing or
the income
maximizing expenditure
group Ea is indifferent
public good for any
on the
first-period fiscal policy. It follows that in our model a
there is
right-wing
majority if
a left-wing
majority
a
when
>
Ea
the median
Our
income a
discussion
so
Ea,
=
< Ea
far
and
and a
not
only
characterizes the second-period political equilibrium, but also establishes
our first important result
Proposition
1
:
:
When governments
debt,
then
strategic
past
cannot default
and
effect. In
current
on outstanding domestic
budget
other words,
deficits
public debt
used to influence the outcome of future elections.
have
no
cannot be
in
Proposition
policy and
fiscal
d e
1
[O.Ea.p]
constrain
the median
with
Thus,
.
from the
follows
the policies
each candidates' period 2
fact that
voter's preferences remain the same for any
default,
no
public
debt can only be used to
administrations as in Alesina-Tabellini
of future
[1987] and Persson-Svensson [1989]- The remaining part of this section will
be
the analysis of optimal first-period fiscal policy when the
devoted to
incumbent party knows that it will be replaced in period 2. We determine to
what
extent the party in place in period
of its opponent in period
We
knows
wants to constrain the policies
2.
where a left-wing administration in period
the case
1
that it will be followed by a right-wing administration in period 2.
Such
a situation
there
was a
may arise, for instance, if after the period-1 elections
shift in the income distribution (or a change in tastes) such
in the new elections in period 2 there is a right-wing majority (that
that
is,
begin with
1
f(a)
choose
is
its fiscal
clientele,
am
such that
policy,
?,
anticipating
log(c
:
H (r 1 ;d;g 1
policy
+
g2
e t + gj
=
r l Bx
+
d
+
c 2+ g 2
=
aL
-
—
Ea
)
(l
*
;p)
=
aL (l-Tj)
+
)
s(a L ;l/p)
that
policy
it is
the left-wing
:
We have
:
)
-
(4.1)
;p)
aL
(l
-
dp
—
(1+P)/P
g,
t,
3(c 2
)
easy to verify that
government sets
s(a L
-
s(a L ;p).p
3(c,+
Again,
right-wing
the
)
a L (l- Tl
d
y
(
by
:
r Ea
where s(a
followed
(3log(c 2
gl
the utility of its
to maximize
)
+
+
1
subject to
the left-wing administration will
Then,
.
the
administration in period 2
max
T i: d 'Si
Ea)
>
>
=
1.
More
and
+
g2
)
>
0,
so
interesting is the debt
15
tt
L
1
1
5 (c,+ g,)
Ea'p
1
1
-
:'i.2:
i
ad
+
(i
i +p
p)/p
Ecu
and
3(c,+ g-J
5l
Since
a,
<
assumption)
Ea (by
utility is increasing in
Proposition
2
C».3)
Ea
1+3
3d
both period
have that
we
,
1
and period 2
We thus obtain our second noteworthy result
d.
:
A left-wing government followed by a right-wing government
:
will
run
deficits
budget
in
order
to
"constrain" the
right-wing government.
In fact the left-wing government will choose to accumulate the maximum
sustainable
expenditure
utility
goods
.
The intuition behind Proposition
2 is
the left-wing government can increase
1.
This increases the period-1
incomes below
the average income. Perhaps
period
in
consumers with
from the
that it also increases their utility in period 2. This
most of
fact that
the tax burden of servicing the debt
on the wealthy consumers with incomes above the average. For any one
dollar
of
consumer
debt
neither
repayment
with income
debt
transfer
It
public
of all
follows
Thus
on
surprising is
falls
d = Ea.(3
:
By accumulating public debt,
simple.
more
public debt
the
right-wing
the
government in period
2,
a
less than the average is taxed less than one dollar.
accumulation
from
by
with
wealthy
no
to
default
the
poor.
amounts
to an indirect income
The only income group that is
hurt nor favored by debt accumulation is the average-income group.
follows that, from the perspective of a left-wing party, being replaced
by a right-wing party debt-accumulation is favorable in both periods.' lj)
We
is
close this section with the case where a right-wing administration
followed
by
a
left-wing
administration.
We know that the left-wing
16
will choose t 2 =
administration
administration chooses
maxlog(Cj+
gj
plog(c 2
+
)
=
?,
+
1
and g 2
(Tjjdjg^
g2
Ea
=
-
to solve
Cj +
t,
g,
.
)
Ea+d+a^ 1-Tj
(
Again
will
g,
TjEa+d+a,, (1-Tj
i +
PL
straightforward to
minimize taxes in period
)
3(c x
+
g!
1+
id
3(c 2
-
(Ea
ci.'t:
d/p)'
+
p/p
(t,
1
=0).
the right-wing administration
If we differentiate (Cj+ g
)
and
t
:
1/3
(1+P)/P
g2
)
1
1
1+
+
(4.6)
3d
This
)
-
check that
with respect to d, we obtain
(4.5)
d/p]
(Ecu-
Ea-d/p+
=
it is
(c 2 + g 2
-
)
)
1+3/p
1
c? +
so that the right-wing
:
TjEa+d+a,, (1-Tj
s. t.
dp,
3
1/P
(l + 3)/3
P
implies that a right-wing administration followed by a left-wing
administration is indifferent between any level of debt d
[
0,
€
L
Proposition
3
right-wing
A
:
administration
administration
does
not
gain
followed
by
Eal
—
3
a left-wing
by constraining the future
administration's policy choices through the accumulation of
debt.
This
result is
Persson-Svensson
when
a
[1989]
right-wing
administration.
in sharp contrast to the conclusions obtained by, say
;
and also to those obtained in the present model
administration
The reason
is
followed
by
another
right-wing
why the right-wing incumbent is indifferent is
because debt plays no indirect redistributive role when all income is taxed
away
in period
increase
2.
As a result,
any increase in debt today resulting in an
in period-1 utility is exactly offset by a decrease in utility in
17
1
period
V.
since the equilibrium interest rates is p
1,
—
=
DYNAMIC POLITICAL EQUILIBRIUM WITH COSTLESS DEFAULT
have already pointed out in section III that with no distortionary
We
taxes,
a social
period
2.
planner is
indifferent between default and no default in
first important
Our
left-wing
this section
result of
that
is
both the
government and the right-wing government strictly prefer default
period 2,
in
.
even though
non-distortionary
taxes are
.
We go on to show,
that this conclusion crucially depends on the assumption that the
however,
private and
rate
of transformation
between the
than
or) equal
As soon as the rate of transformation in different
from
one, it
to one.
longer generally
is no
true that
the public good is
(less
both types of government
strictly prefer default.
Consider
(a L
<
Ea)
first
default
the
decision
of a left-wing administration
inheriting a total debt of d. We know that such an administration
maximizes
expenditure on
public goods
by setting t,
=
1.
If it defaults,
total expenditure on public goods is given by Ea, and every consumer in the
economy
utility
gets
expenditure
period-2
>
Ea
it
If
default,
not
does
total
then
on the public good is Ea-d/p and a consumer with income a gets
utility
administration
Ea
logEa. (l6)
-
d/p
d
>
of
log[Ea
prefers
+
to
-
d/p
+
s (a; 1/p)
default
.
1/p]
if
.
and
Thus
a
only
left-wing
if
s(a L 1/p) 1/p or
;
.
s(a L ;l/p).
(5.1)
We know from the credit-market equilibrium that
d = Jjs(a,l/p)f(a)da = Es(a,l/p)
=
s(Ea,l/p).
(5.2)
:
18
last equality
The
function
s(a,l/p) in
for all d
€
;
t
Since
a.
follows from the linearity of the savings
(5-2)
a.
Ea,
<
Ea.p). Thus we obtain
(0,
Proposition
in
to default
prefers
is verified
(5-1)
:
administration (such
A left-wing
:
it follows that
that a L
positive level
on any
<
Ea)
strictly
of outstanding
public debt.
refusing
By
administration
repay
to
can increase
the
outstanding
debt,
the
left-wing
even further its expenditure on public goods.
Since savings are an increasing function of income, default becomes another
form
taxation. The
of redistributive
interests
those
of
agents
who
left-wing government represents the
benefit
from
this
redistribution
and
therefore favors default. This is alltogether not very surprising. We were,
however, astonished at first to get the next result about the incentives to
default
right-wing administration.
of a
minimize
We know that the latter wants to
expenditure on the public good and therefore sets t 2
=
(
d
max<0,
In that case, an individual with income a gets a
d
* s(a,l/p)
period-2
utility
right-wing
of
log a 1
If the
pEaJ
government
defaults,
period-2
utility becomes simply logo^ Thus a
if
not default.
it does
right-wing government defaults if and only if
(where a^
In
0^
>
a,,
>
1
+
pEa
s(aR .l/p).l/p,
:
(5.3J
Ea)
words, if the costs of increased taxation required to finance debt
repayments
outweigh the
the
average, then
out
that the
benefits to
the right-wing
government prefers to default. It turns
always greater than the benefits for any positive
costs are
level of inherited debt
those individuals with incomes above
:
19
Proposition
5
administration such that aR
A right-wing
:
>
Eg:
default on
any positive level of outstanding debt.
Proof
:
Condition (5-3) is equivalent to
Or
where
>
j£
sto^il/p)
:
d +
aR
(1-Tj
)
Ea.Tj
+
-
aR
pEaJ
sCOpil/p)
(1 + P)/P
«R
1
.Ea p
+
1
(l+p)/p
but,
a_
Ea
—
Ea
> s(a R .l/p)
>
(1+p)
since
a R (l+p)
pEa
>
pointed out
We
+
<=*
0^
aR
>
Ea.
earlier that
if there is no default,
then the agents
with
incomes above the average pay more in taxes to finance debt repayment
than
the value of their bond holdings.
the government to default. The implications of Propositions
prefer
are
far-reaching.
aL
financed
=
am
=
Ea
distortionary
equilibrium
=
.
default
If
through
a^
)
.
The
is that
is
costless,
(except
debt
This
is
reason
no one
all
why
the
there
will agree
in
cannot
not
4
and 5
exist
a
government expenditures
degenerate
the
more
does
there
political-equilibrium where
rational-expectations
are
It is then obvious that they should
striking
case
where
that taxes are not
be positive public debt in
to lending
to the
government in
20
period
consequence
these
of
default
anticipate
they
if
1
propositions
in
that
is
period
2.
Another
obvious
public debt plays neither
strategic role nor a constraining role when default is costless ex-post.'
leave it
To
Propositions
4
5
if the rate of transformation between the private
good and the public good is
1
X (X
+
and 5 are n o longer generally valid.
The
main
transformation
preferring
modification
is
'
are not robust to small changes in the parameters of
model. Specifically,
the
1
however, would be misleading. It turns out that
at that,
and
a
given
by
0)
>
X
+
1,
into
the
model when the rate of
that
the subset of income groups
is
maximization
expenditure
then Propositions
H
()
introduced
1
instead of
(respectively,
expenditure
minimization) on public goods no longer coincides with the subset of income
groups
who
maximized
prefer
default
on
public
groups who
when period-2 tax rates are
As a result,
(respectively, minimized).
middle-income
debt
strictly prefer
there exists a range of
no default. We demonstrate this
last point rigorously below and investigate the implications of this result
for the dynamic political equilibrium.
When
good
the rate
is less
other
things
between the
of transformation
private and the public
than one, supplying the public good becomes less attractive,
being
equal.
As
a
result, one should expect fewer income
groups to prefer expenditure maximization on public goods than before. This
is
indeed the
group
result we obtain here
a is elected in period
2,
:
If a government representing income
it will set the tax rate t 2 to solve
:
1
21
max log(c 2
+
subject to
g2
)
c,
:
a(l-T 2
s(a;p) .p
)
(5-'D
T 2 Ea-dp
g?
1+A
that there is no default on public debt)
(assuming
.
Notice that any dollar
1
more units of
through taxes and spent on the public good yields
raised
1+A
the public good. From the first-order conditions we obtain that
T2
=
t2
While
=
if
1
max
a<
Ea
5-5)
Ea
iO
if a
>
l7\
previous sections all income groups below the average income
in the
preferred
strictly
maximum expenditure on public goods, now only those
Ea
income groups below
prefer expenditure maximization.
1+A
If the public good is more expensive to produce one should also expect
that fewer income groups prefer default in order to increase expenditure on
the public good, and consequently that fewer possible administrations would
choose to default in period 2.
The next result shows that this intuition is indeed correct
that the first-period tax rate has been set equal to zero'
1
^
1
,
an elected government located at a assesses a default decision
Suppose
only if
first that
t2
Ea-dp
~
=
:
Ea
-
1+a
—
1+A
-
+
-.
s(a.p) .p
1.
!
Assuming
consider how
:
In that case default is attractive if and
22
or
s(a.p)
>
(5-6)
1+A
d
N/here
and
s(a,p)
:
a
+
PPl
U+A —
=
Ea-dp
^
-
1+A
)
(5-7)
(1+P)p
p is the (correctly anticipated) equilibrium interest rate in period 2
when t,
=
1
and the elected government does not default
We can then establish the following lemma
Lemma
1
3
:
d,
Proof
:
€
:
a e(0,Ba) such that if t 2 is to be chosen equal to
groups a
income
a
:
prefer
(a,l)
and
First,
€
a(0)
then all
prefer default whereas all income groups
default
no
Furthermore
.
a
is decreasing in
Ea.
equilibrium
the
government
=
(0,a)
1,
interest
rate
p
,
when
the
period-2
is expected both to set t 2 = 1 and to avoid default,
defined by
is
:
Es(a.p)
s(Ea,p)
=
=
d,
where s(a,p) is defined in (5-7)
for all a
We then have,
s(a,p)
=
d +
=
d
•
:
(s(a,p)
-
s(Ea,p))
(a-Ea)p
+
1+P
Hence (5-6) can be rewritten as
(a-Ea)p
d
>
1+A
d
+
1+p
Which in turn is equivalent to
(l+p)Ad
a < a(d) = Ea (1+A)p
We immediately verify that
d.
:
:
:
a(0)
=
Ea and that a is decreasing in
a
23
words
In
is greater than one and if t 2
goods
(20)
Furthermore,
government
chooses t,
=
1
Consider
government
debt
.
>
—
Ea
or t,
=
a chooses t 2
that
a
(left-wing)
=
1
—
Ea
=
the
default
decision
when
the
minimizes expenditure on the public good
whether the government honors
depending on
Then an agent earning income a strictly prefers the government
+
"
T
s(a,p)
:
P- S
Ea]
pp
>
a
2
dp
ad
:
implies
and defaults on
Ea
government located between a and
1+A
=
assess
in period
(
or
far
so
and a
=
agents
to default if and only if
tt
a
whereas
;
how
next
in place
debts)
its
the range of middle incomes which
1,
and no default.
when t 2
(i.e.,
analysis
our
located between
outstanding
its
=
default increases with the amount of outstanding debt,
prefer no
strictly
d.
when the rate of transformation between public and private
:
(
a -P)«
d
\
a
+
U+A
-
a
1
-
{
)
—
dp^
(
EaJ
=
(5.10)
(l+(3)p
(s(a,p) is derived assuming that the government will not default).
We can then prove the following lemma which is similar to Lemma
Lemma
2
If
:
t 2 is
minimized by the period-2 government, then all
to be
groups a
income
Ea
<
above Ea prefer default
Proof
:
We
begin by
period-2
prefer no
default
all income groups
and
deriving the equilibrium interest rate, p*
government is
=
,
.
expected to
interest rate is given by the equation
Es(a,p")
s(Ea,p*)
1.
=
d.
set g 2
=
:
,
when the
the equilibrium
:
(5-H)
24
where s(a,p) is defined in (5. 10).
ad
s(a,p
Now, let g(a) =
Ea
g(Ea) = 0.
From (5-11). we have
)
:
Furthermore g is linear in a and therefore monotonic in a.
Next, we can show that the function g is increasing in a.
(Ejdc)
have
we
Indeed,
fact that when a
(1+X)d
which
g(D
=
+
<
This follows from the
.
inequality (5-10) becomes equivalent to
1,
dA
>
and g
>
:
d.Ea,
automatically
is
>
g(l)
Ea
since
true
<
1
;
this establishes
:
;
Ea
when a
=
inequality (5-10) becomes equivalent to
,
1+A
3p*(l+p)d
>
pp*(l+p)d
+
:
p.(p*p-l),
which is violated since
Ea(l+A)
PP
hence g
Ea(l+A)-dA
"
(Ea)
<
and Lemma 2 is proved.
Lemma 2 then implies that a moderate-right-wing government located
Ea
between
and Ea chooses both no default and minimum taxation in period 2
1+A
dp')
hand a government located betwen Ea and
on the other
Ea
chooses to default and sets t 2 =
i.e. t,2
The
=
;
following
distribution
function
figures
1
0.
representing
summarize
our
the
results
period 2 and the default decision when Tj
=
:
support
of
the
income
about optimal tax rates in
25
t,
1/default
=
t,
=
dp*
1/no default
t,
a(d)
-^—/no default
=
r
=
2
O/default
1+A
Ea
Figure 2A
:
a(d)
<
1+A
Ty
1/default
=
t2
Ea
=
dp
—
—/no
oc< a
default
r?
O/default
=
)
Ea
1+A
Ea
Figure 2B
As
we shall
:
a(d) >
T7\
now see, the presence of the middle-class of incomes ae[a,Ea]
can create a situation where it is in the interest of a moderate right wing-
party
in power to excessively accumulate public debt in order to raise the
likelihood
(somewhat
of being
reelected
.
arbitrarily) defined
Recall that a left or right-wing party was
to be
a party
representing primarily the
interests of the income groups respectively below the average and above the
average. Casual empiricism suggests that this is not always an unreasonable
approximation.
party
as one
favourable
In
same
the
that puts
to
large
moderate- right- wing
spirit
more weight
public
party as
we shall define a moderate-left-wing
expenditure
one that
income groups but remains
on middle
public
on
puts more
goods
and
a
weight on middle income
groups but prefers fiscal restraint. In terms of our model, a moderate-left
party
defends
the
interests
of
income
groups
a
(
e
EcO
a,
moderate-right party represents the interests of those groups a
and
fEa
€
a
^
;Ea
.
26
The next two propositions establish that under certain conditions a
moderate right-wing party in power in period
(i)
modify
successfully
the
voting
may
1
behavior
:
of
the
median
voter by
accumulating debt and thus ensure its reelection,
(ii)
be better off by following that strategy of debt accumulation.
Consider the situation where a
Then with zero outstanding
6 debt
1+A
there is a majority in favor of a left-wing candidate (a < a
in period 2,
standing
Ea
<
.
right-wing incumbent
against a
a^
(Ea
^
,
Eot
I
.
We show in the first
proposition that for a large enough outstanding debt, a new majority arises
favouring this "moderate" right-wing incumbent.
Proposition
c
6
Ea
When am
:
is close
enough
to
&
there exists a level of
,
1+A
outstanding debt d such that all a
€
[am ,l] strictly prefer
the right-wing candidate over the left-wing challenger.
Proof
Ea
:
In what follows, we suppose that am
Let d
(a)
(b)
<
be a level of debt such that
>
—
1+A
with am close to
Ea
.
1+A
:
Ea
ad)
<
1+A
d.p* < Ea (where p* is defined in Lemma 2).
(This
debt d
condition says
!
is feasible
that it
to repay the amount of
)
Condition
(b)
is equivalent to
:
—
p.Ea
d <
(5-12)
1+p.
1+A
Whereas condition (a) is equivalent to
p.Ea
d
>
:
—
l+P
Note that these two inequalities
(5-13)
(5-12) and (5-13) are consistent
they define a non-empty set of debt levels d.
;
)
27
Using
that a(d) is continuously decreasing in d, we can
the fact
p.Ea
always choose d sufficiently close to
-
—
-
in order to have
1-3
Ea
aL
<
a(d)
<
(5-1*0
1+A
[see Figure 3 below]
a,
\
a
4—
^4-
Ea
a(d)
1+7
Figure
Ea
(=a(0))
1
3
For such a level of debt the left-wing candidate a L will default in
period
elected
if
2
analysis
that
;
this
furthermore
left-wing
we
know from the foregoing
candidate
will
set
:
Ea
t 2* =
1
and g d
.
hand the right-wing candidate o^ will not default on
the other
On
——
1+A
=
this oustanding debt, d, if elected, since we have assumed o^
furthermore
T2
=
we know
a right-wing
that such
<
Ea
candidate will set
;
:
dp'
Ea
Clearly,
:
S,
0.
=
median voter am were located below a(d)
if the
automatically
vote
for
am and a L would choose t 2
the
left-wing
candidate
aL
,
he would
since both
and default in that case. However, if
Ea
am is sufficiently close to
the level of debt d can always be
1+A
chosen such that
= 1
,
:
28
a,
a(d)
<
a
<
(by continuity of a w.r.t.
d)
of
d
such
For
choice
a
default
elected
a(d))
<
(oc
t, =
:
the
1
and
the left-wing candidate will default on d if
However,
.
government.
most preferred period-2 policy becomes
median-voter's
no
incumbent
the
by
right-wing candidate will minimize
and the
;
{
taxes t 2
h>
B
>
voter must compare the losses involved in electing
the median
So,
either
of
the
is elected he gets
dp *l
p
H
+
Ea
•
.
if
:
Ea
:
;
1+A
the left-wing candidate is
if the right-wing candidate
:
(
s la
*\
Km'*p
]
,
to show
is easy
(It
candidates
two
the median voter gets
elected,
a
-
J
that the
right-wing incumbent is given by
Tj
=0. Given
left-wing party will indeed always default)
earner
(and therefore
incumbent if and only if
a
dp
f,1
-
'l
Ea
=
,
X +A
.
t.
by the
this choice of t.
,
a
Thus the median income
voter) votes for the right-wing
:
—
Ea
i
Let am
the median
,
p s(a ,p*)
+
choice of
first period
>
(5.15)
then (5-15) is equivalent to
dam
<
Ea
s(am .p*)
(5-16)
But from the proof of Lemma 2 we know that (5-l6) is satisfied when
Ea
Ea
a =
By continuity, the same inequality
will hold for am <
1+A
1+A
.
-
29
Ea
but sufficiently close to
debt
accumulating
By
moderate
the
challenger look
left-wing
.
1+A
incumbent makes the
right-wing
the eyes of moderate voters. The latter
bad in
the government
care about preserving the real value of their savings (i.e.,
not
defaulting)
problem
for
maximizing
expenditure on
hand
one
outstanding
the
this
candidate
left-wing
the
that
he cannot commit to both
and not
defaulting on the public
is
public goods
When it comes to choosing between no default but fiscal restraint on
debt.
the
like large expenditures on public goods. The
they also
;
increased
and
spending
on
public
goods, but default on
the other, a lower-middle class voter may well prefer
debt on
former alternative
.
An incumbent moderate-right-wing party can foresee
and thus use public debt to enhance its likelihood of reelection. The
question
remains, whether
in the interest of a right-wing party to
it is
follow that strategy. The next proposition establishes this.
Proposition
7
When am
:
Ea
is sufficiently
close to
J.
right-wing
incumbent's interest
amount of debt (d
Proof
:
If the incumbent sets d
0)
>
-
0,
—A
it will be in the
to accumulate
a positive
in order to ensure its reelection.
the left-wing challenger wins the next
election so that the right-wing party's total utility is given by
—Ea—
log a^+ plog
Now
let
d
1+A
>
be
minimum
the
amount of debt necessary for the
candidate to reverse the outcome of the elections. With
right-wing
5
that
1
and
Thus,
level of public debt he gets
ftp
1
-
+
-
+ a,,-
:
1+A
"
s(a,.d,p
.,
)
in period
'
p.s (a H d p* J in period 2. (p*is given by (5.11)).
,
,
the difference in first-period total consumption (measuring
30
the costs of debt accumulation)
s
a n. 5
(
is given by
:
d
-p")
"
J7 A'
Ea
closer a m
The
is to
from the
follows
in period
the loss
zero,
,
(This directly
the lower d needs to be.
1+A
proof of
Proposition
1
6)
.
Now as d converges to
total consumption from issuing debt d
becomes negligible.
(When
d
—
p*
0,
>
—
= p" (d)
1/(3
therefore
and
s^.d.p*) given
by
(5-10) converges to zero).
But the gain in period-2 consumption is bounded away from zero
as d
f
M
—
the gain in period-2 consumption given by
0,
»
dp'l
1
P
lo7j
«
/
•
+
"
:
-
s
K' d -P
.\
J
"
^
—
E"
Y7X
converges to o^
-
>
0.
This establishes the proposition.
VI. CONCLUSION
To
.
sum up,
even though
that,
strategic
we established in this section
what have
?
We have shown
forward-looking, debt can play an important
agents are
the political game between a left-wing and a right-wing
role in
party. The particular illustration of the strategic role of debt considered
here
was
about
a
right-wing
party (21)
accumulating excessively large
amounts
of debt so as to change the preferences of the median voter in its
favour
by
financially
creating
a
situation
irresponsible in
where
the eyes
the
of a
left-wing
party
appears
majority of voters holding a
substantial fraction of their savings in government bonds.
The
monetizing
in
fact
voters
become
more
concerned
about the government
the debt, when they hold a sustantial fraction of their savings
government
experience
that
bonds,
(at least
seems
rather
plausible.
In
light
of historical
in the 20th century) it seems equally plausible that
31
administrations may
left-wing
outstanding
than right-wing administrations. The next step in
public debt
logically from
following
argument,
the
be more inclined to erode the real value of
observations
these two
-
namely,
that a right-wing administration may deliberately increase the government's
to create
indebtedness
as
ensure
to
a problem of potential monetization of the debt so
reelection
its
-
somehow
seems
less plausible. Perhaps
governments are not as cynical as we make them appear in this model
else,
Or
the
outcome of
elections. For
more conservatively.
vote
mechanism is
might be
reason
bond-holdings
has often been argued that a
instance, it
administrations partly
by right-wing
pursued
superior instruments available to manipulate
voters to become home-owners on even shareholders is
inducing more
policy
the
may have
they
?
Exactly how
similar to
because home-owners tend to
this work is not clear but perhaps
highlighted in this paper
the one
?
A third
that governments may not know exactly the distribution of
in the economy. They may then not be able to predict exactly
the preferences of voters concerning default. A fourth reason,
(perhaps the
most important of all) is that a government accumulating large deficits may
itself appear financially irresponsible and thus be voted out of office for
incompetent
management (recent events, however, do not seem to corroborate
this explanation)
any event,
In
we do
model
developed here
whole
reasoning
Other
in propositions
is summarized
about
behind these
policy)
not wish to argue that the main interest of the
government
action
propositions is
6
and
7-
Rather the
(and specifically about fiscal
as instructive
as the conclusions.
interesting aspects of the model relate to how empirically plausible
predictions
about
fiscal
policy
of
one
or the other party emerge from
simple assumptions about which income group's interests each party seeks to
promote.
Moreover a
interest
may exist between the middle-income groups and the extremes (very
low
and very
general lesson from this section is that conflicts of
high income
groups). In
this respect our model has similar
32
properties
as
one
the
[1988]. These conflicts of
Cuikerman-Meltzer
arise whenever
general and
are quite
interest
in
the public
good is not
a
good. We expect that even if there is
the private
perfect
substitute for
perfect
substitution between public and private goods, such a conflict may
if the income-tax schedule is sufficiently progressive,
exist
higher
bear most
income groups
result,
a
may
conflict
of the
costs of servicing the debt. As
concerning
arise
for then the
the
a
default decision between
middle-income earners and the other income groups. Many aspects relating to
model of course need much further development. A systematic treatment
this
of
uncertainty is
system
:
equilibrium
political
how
parties
number of
choose
parties
equilibrium emerges
Alesina-Tabellini
of
necessary. More
a democratic
needs to
their
?
?
location
If there
Finally,
and Persson-Svensson
be said
and
about the political
what
determines the
are more than two parties what
this paper
along with those of
have highlighted some of the costs
two-party system. An interesting and important project is
to investigate and formalize what the benefits of such a system are.
33
REFERENCES
Alesina,
Alberto [1988]
Public
High
(ed.).
of Large Public Debts", in Spaventa,
"The End
Debt
Experience
the
:
in
Italy,
New York
L.
:
Cambridge University Press.
Alesina,
Alberto and Guido Tabellini [1987a] "A Political Theory of Fiscal
"NBER Working Paper No.
Debt in a Democracy,
and Government
Deficits
2308, July.
Alesina,
Alberto
and
Tabellini
Guido
[1987b]
"External
Debt, Capital
Flights and Political Risk", Mimeo, Harvard University.
Alesina, Alberto and Guido Tabellini [1988] "Voting on the Budget Deficit",
MIT CEPR Discussion Paper No. 269.
Cuikerman,
Debt
Alex and Allan Meltzer [I988] "A Political Theory of Government
and
Deficits
in
a
Neo-Ricardian
Framework",
Mimeo,
Carnegie-Mellon University.
Persson,
Would
Torsten
Run
and
a
Svensson
Lars
Deficit
:
[1989] "Why a Stubborn Conservative
Policy with Time-Inconsistent Preferences",
Quaterly Journal of Economics 65, 325 - 3^6.
3^
FOOTNOTES
1.
2.
In our model even a proportional income tax has redistributive effects.
Our
for any utility function satisfying the
be obtained
results can
following properties
:
-
private and public consumption are substitutes
-
the marginal rate of substitution between the private and the
public good is increasing with consumption of the private good
d
(
dU/dcA
dcj
{
d\J/d Si
0.
<
A
utility
conflict
with
function
about fiscal
average prefer
above
average
prefer
conflict
large
properties
these
fiscal restraint
expenditure
and agents
public
default on
model regarding
in our
on
gives rise to the basic
where agents with income
our model
policy in
:
with income below
goods. Similarly, the
public debt would arise
with any utility function with the properties above.
Moreover
our
social planner
that the
Section
separability one also obtains
Ricardian super indeterminacy (provided of
result about
course
(See
assumes intertemporal
if one
III
for
a
only cares about Pareto-efficiency)
derivation
of
the
result
of
Ricardian
super indeterminacy)
3.
of the utility function, we only consider such public
Given
the form
goods
as public education, health care,
social security, etc.
;
these
can be viewed quite naturally as substitutes for private consumption.
4.
Introducing
distortionary taxation
would not
alter our main results
about
the
roles
of debt. Interesting additional effects probably arise if taxes
political
equilibrium
and
the committment and strategic
35
are distoritionary
on
.
For instance,
off between equity and efficiency. We shall
known trade
the well
the political equilibrium may depend
pursue these additional aspects in future research.
5-
In our model we have normalized the set of taxable incomes to be [0,1].
Equivalently
tax schedule
income
uniform
tax
have taken
we could
,
rate
function to be
composed of
t
[0,1]
e
an
to a
and a
redefined the consumers' utility
:
that introducing
imposing
[a,l+a], with an
to be
exemption equal
a tax
and
,
u(c)
Note
this set
upper
tax-exemption.
a
savings functions
:
lower
bound
By doing
=
t
Log(c-a)
bound on
on
1
<
so, we
taxable incomes
the
avoid an
tax
amounts to
rate when there is no
unpleasant feature
of our
that agents may have positive savings even
namely,
if all their income is taxed away (See Footnote (11)).
6.
Agents can save by holding three different assets
which
provides zero
interest rate p
Holding
;
interest
;
they can
:
they can hold cash
buy government
bonds with
or they can lend to other agents who wish to borrow.
cash is always dominated by either lending to other agents or
buying government bonds.
We
that
assume that
private
assumptions,
there is
agents
default
never
the interest
competitive capital market and
a perfectly
their
on
debts.
Given
these
rate on private loans must always be equal
to the interest rate on government bonds
(when the government does not
default on its debt)
7-
An
interesting
implications
extension
for fiscal
of
our
policy of
model
would
having more
shall investigate this in future research.
be
to
analyse the
than two parties. We
36
8.
We
that parties in power break their campaign pledges if
thus assume
is in their interest and that there is no reputational loss from
this
doing
Electoral
so.
have
programs
Judging
campaigns then
commitment
no
recent
from
are pure "cheap talk". Electoral
value
campaigns,
and
this
nobody
not
does
is fooled by them.
seem
to be a very
unrealistic assumption.
9.
A full-blown analysis of the political game with uncertainty is beyond
scope of
the
introduction
with,
We shall
of uncertainty.
issues arise with the
just mention
two
to begin
:
uncertainty about future income may result in uncertainty about
outcome
the
Several interesting
this paper.
of
elections.
future
This
may bring about default in
equilibrium so that government bonds become a risky asset. Agents then
problem ex-ante
a portfolio-choice
face
decision.
governments choose their debt policy in the
Secondly, when
first-period
instead of a simple savings
have to make difficult compromises because of
they also
uncertainty of the electoral outcome. Thirdly, interesting issues
the
arise
concerning default
when the
government is uncertain about the
distribution of bond-holdings in the economy.
10.
In
other
all
respects,
democratically-elected
above
the law
the
dictator
is
identical
to
a
government. In particular, our dictator is not
and behaves
so as to respect all constitutional rules
imposed on him.
11.
An
extremely useful
linearity
solve
with respect
for
s(a,p,T t ;g t
property of s(a,p;T t ;g t
the
)
to a.
equilibrium
This allows
)
for our purposes is the
us for instance to easily
interest-rate.
While
the
shape
of
simplifies our analysis considerably, none of our results
seem to depend directly on its specific form. This is reassuring since
linearity is probably not a robus property.
37
There are several other noteworthy features about
the government runs no deficits so that d
when
below average
with income
agents
s
=
(a.p.T ,g
0,
)
.
First,
one observes that
borrow from the capital market and
those with incomes above average lend at the equilibrium interest rate
p
=
1/(3
if and only if
,
functions
and high-income
when
the government
the
supply of
Otherwise,
.
That is,
are reversed.
save
> t2
t,
if t,
the borrowing and lending
then low income agents
t2
<
These predictions
agents borrow.
are modified
runs deficits only to the extent that the higher
more all
government-bonds, the
income-groups tend to
save.
a slightly
Second,
agents
may
have
of our
awkward feature
savings
positive
even
savings function is that
=1. They
if Tj
save, even
though all their income is taxed away. This is possible since we allow
for
negative consumption.
unpleasant
feature
normalization.
litterally.
A tax
(5)
model
our
of
rate such
=1
as t,
tax income.
have argued that this
we
simply
is
result
the
of
a
should not be interpreted
upper bounds
governments have
In practice,
can effectively
they
In footnote
This upper-bound
on how much
is normalized
to
equal one in our model.
12.
Since individual utility functions are strictly concave and identical,
the
utilitarian welfare
consumption
is
implemented
by setting
equal
function is
the
to
t
}
that
the utilitarian
of debt d
e
t2
maximized when all individuals'
average
=
1.
This outcome can be
income.
For Tj
=
t2
=
1,
it can be shown
social planner is indifferent between any level
[O.Ea.p].
13.
Since t 2 is chosen in period
14
We thus rule out voting behavior driven by ideological considerations.
This
should
2,
savings must be treated as a constant.
is clearly a very strong assumption.
point out
However, in our defense, we
that it has been widely observed that income is the
38
best predictor of voting behavior.
15-
that
Recall
government
since
government
left-wing
a
does not
followed
by another left-wing
accumulate debt to redistribute income,
need to
more efficiently redistributed through high taxes in
income is
both periods. Debt is used only because the right-wing government sets
low tax rates in period 2.
16.
We assume here that the government defaults on its outstanding nominal
debt
by running
real
value of
an infinitely-high
government debt
of other
value
inflation
inflation, so
is totally
that not only the
eroded but
also the real
nominal assets. In practice, implicit default through
(monetization of
the debt) seems more common that explicit
default.
This
is why
default
we have
focussed on
this form of default. In addition,
through inflation is more costly than explicit default to the
extent
that it also wipes out the real value of other nominal assets.
If
establih
we
that
a
government
incentives
has
to default via
inflation even though this hurts its own constituency by eroding their
private
savings then
a fortiori
these incentives are present if the
government defaults explicitly and thus does not affect the real value
of its constituency's savings.
In
footnote (17)
In
particular
we
we briefly analyse the effects of explicit default.
consider
whether
a
government
prefers explicit
default over monetization if given a choice.
17-
The
difference between
the
former case
latter
their
over
choice
explicit default
only government
case government
and monetization is that in
bonds become worthless while in the
bonds as well as all other nominal assets see
value being eroded. Creditors therefore prefer explicit default
monetization and
debtors have
between monetization
the reverse preferences. Given a
or explicit
default a government is all
39
more tempted to default explicitly on the outstanding public debt
the
of monetizing
(instead
who are
agents
the debt)
borrowers. Thus,
default differ
explicit
represents the
if it
out how the incentives for
to find
from the
interest of
incentives of
monetization in our
we must determine who are the borrowers and who are the lenders
model
in the internal capital market.
The
identity of
and lenders is most easily identified
the borrowers
when there is no outstanding government debt (d
function is given by
)
=
immediately
place when
that
=
if
1/3
his
Then the savings
(1+P")/P
intertemporal
transfers then only take
The reason is that an individual agent only wishes
.
perform intertemporal
to
p
^ t2
Tj
.
T 2 )(Ea-a)
(t 1
-
1
notes
0)
:
s(a,l/p;T ;t 2
One
=
consumption
her
or
the equilibrium interest-rate
transfers at
different in both periods.
is
Consumption smoothing is the motive for intertemporal transfers
an
!
Now,
individual agent's consumption in both periods differs only if the
tax-rates in both periods differ. Given that optimal tax-rates in both
periods
in
are either equal to zero (when a right-wing administration is
one (when
place) or
the left-wing
only two cases to consider
Tj
-
t2
=
1
(ii) Tj
-
t2
=
-1
(i)
(i)
this
In
incomes a
below
Ea borrow. When t
>
average get
government's
period
2
Consumption
a
,
there are
:
agents
case,
party is in power)
higher
with
=
1
incomes a
and t 2
=
consumption in
0,
<
Ea save and those with
the agents with incomes
period
1,
because of the
policy of maximum redistribution in that period,
(where
a
policy
smoothing then
of
than in
minimum redistribution is selected)
dictates that
they save. The opposite is
40
true for agents with income above average, which is why they borrow,
is entirely symmetric to
This case
(ii)
here low-income agents
;
in anticipation of a more redistributive policy in the future
borrow,
exactly opposite
for the
and
(i)
wealthy save.
reasons the
(Note that
these rather intuitive results depend critically on our assumptions of
expectations on
rational
tax-treatment
of savings
savings is
from
hand and on our assumptions on the
the one
on the other.
to the principle of no double
We appeal
not taxed.
In our model interest revenue
taxation to justify this assumption. Of course this principle is never
systematically
applied
practice,
in
obvious
for
reasons.
An
interesting extension of our model, thus might be to allow taxation of
interest income)
consider
Next,
government
have
how
increases
level
the
savings change when the
agent's
individual
an
of
oustanding
government debt. We
:
-
(Tj
s(«.l/ P ;T i: f 2
—
T 2 )(Ea-a)+d(l+l/p.)
^^
=
;d)
ds(.)
Thus
,
=
1
dd
As
the government
compensate
of
for expected
the borrowers
level
with d
future increases in taxes. Thus the identity
of private funds is independent of the
and lenders
of government
varies
everyone saves more so as to exactly
increases d,
the volume of borrowing and lending
(Only
debt.
d
extent that
to the
now t,2 £<1,
>
.
In
fact,
the
Ea.p/
higher is d the lower is the volume of funds exchanged in the internal
\
capital markets). Since the identity of the borrowers and lenders does
not
change
with
difference
it
d
is
now
straightforward
to default
in incentives
to
determine
explicitly rather
the
than through
monetization. Basically, a left-wing government following a right wing
government
(t 2
constituency
is mainly
where
a
=
1
right-wing
;
Tj
=
0)
prefers
composed of
government
monetization
borrowers. In
follows
a
since
its
the opposite case
left-wing
government
41
d
(t = 1
=
t,
;
)
(case
(i))-
the case
In
Finally when
arise.
explicit
=
(Tj
t2
=
the issues does not
1)
(
the right follows the right
preferred to
default is
d
=
t,
;
t,
"I
=
monetization. Since, in this final
that monetization
we establish
case,
where a left-wing government is followed by
administration
left-wing
another
mainly of borrowers
then composed
constituency is
since its
again,
prefers monetization
government
right-wing
the
,
is better
than no default,
it
follows that a fortiori explicit default is better than no default.
18.
A
interpreted in
can be
technological
units of
1+A
public
to
:
ways.
It
may be
a pure
to produce one unit of public good one requires
private good. Alternatively, it may represent a cost of
funds (A then measures the efficiency-loss of allocating funds
the
strong
public
sector)
assumption
to
.
maintain this
Whatever
suppose
and independent
constant
We
cost
several different
intrepretation
that
of transformation is
rate
the
one takes it is a
of the level of production of public goods.
assumption mainly
to remain
in the
spirit of the
model where everything is linear.
Finally, note that propositions
and 5 are false, only if A
4
A < 0, all types of government a
£
[
>
0.
When
0,1 ] prefer to default in period 2
.
(See footnote (20) infra for details).
19.
It
is easy
government.
to show that Tj
We
restrict
is optimal for a right-wing incumbent
=
attention
to
case
the
where
t.
=
for
expositional reasons. In fact a more general result can be established
that holds for all Tj £[0,1].
20.
If
A
<
matter
0,
this
set of
(See footnote (20)).
income-groups is
which income-group's
empty. All
interests they
default ex-post. This can be seen as follows
Consider
first the case where
t,
=
1
.
seek to
governments, no
promote, favour
:
Then, condition (5-6) becomes
:
42
= s(Ea,p)
= d, since t
= t
= 1
> s(a,p)
2
1+A
In other words, default is attractive, if and only if A < 0. Note that
Ea
Ea
dp
(
Next, when a >
and t,2 £s0,
1
for all a <
we can
>,
2
1+A
1+A
Ea/
\
lemma and conclude that all types a
the following
apply
default
>
Ea wish to
:
—
Ea
ad
Lemma
Proof
:
:
>
s(a,p)
a e[Ea,l]
<=>
begin by deriving the equilibrium interest rate,
We
government
period-2
the
is
expected
set
to
g2
p°
=
when
,
:
the
equilibrium interest rate is given by the equation
fo
s(a,p)f(a)da
Es(a.p)
=
=
s(Ea,p)
=
d
or
d+T 1 Ea
+
PP
1+A
^-t)
Ea(l-T.l
d(l+(3)p.
Rearranging terms one obtains
(l+A)Ea
(5-10)
p[Ea(l + A(l-T ))-dA]
1
Let a be the income group indifferent between default and no
default, then
—
Ea
ad
.
=
.
s(a,p
)
or using (5-9)
The
ad
—
Ea
d+T, Ea
adp
1+A
Ea
{
lemma now follows from the mono tonicity and linearity of the
.
,1 +
P)p
=
PP
savings function w.r.t. a.
+
a(l-Tj)
a
-
o
^3
that the proof works for any value T i e[0,l] and for any A. The
ad
simply says that any income group a satisfying
> s(a,p)
condition
Ea
property prefers default when g 2 = 0. To summarize, when Tj = 1
this
Notice
—
A <
and
verify
<
£s0,
&P\
>
the incentives
suffices
a
(
and t
=
t,
a(d) = Ea
>
to default
when t
and t 2
=
}
Lemma
which
1
default
prefer
-
Ea prefer default. It remains to
all types a
apply
(l+3)Ad
to
prefer default. Moreover, when
government
of
types
all
=
states
(this
1
Here,
.
that
it
all
lemma applies for all
(1+A)(3
value of A)
Note
.
A <
for
that
who wish to set t,
governments
into wish to set t 2
21.
=
1
when
Thus,
A < 0,
all
prefer default and all governments
prefer default as well.
=
strategic use of debt-accumulation is not the exclusive attribute
The
of
a(d) > Ea.
have
we
right-wing
possibility
that
amounts
large
administration.
debt
so
as
to
ensure
its reelection against a
[implausible] situation corresponds to the
opponent. Such
right-wing
for the symmetric
allows
model
left-wing party accumulate excessively
moderate
a
of
Our
following political configuration
:
a
a,
a„
-+-
Ea
a(d)
1+A
(1)
aR
>
Ea
,
so
that
the
=
right-wing
Ea
a(0)
candidate
defaults
on the
outstanding debt if reelected.
(Ea
\
am £
.Eoc
so that without debt-accumulation the right-wing
(2)
,
candidate
is
elected,
and
with
debt-accumulation the median-voter
w
prefers no default on the outstanding debt.
Ea
Ea
<
but close to
oc,
so that by accumulating a sufficient
(3)
L
1+X
1+X
amount of debt d, the left-wing party ends up being located above the
,
cut-off
point
Qf(d)
;
this
in turn
provides the
left-wing party will not default on d if reelected.
2385
OU
guarantee that the
Date Due
SEP* 1
*
MIT LIBRARIES DUPL
3
1
1060 D057fl1b7
1
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