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PERSISTENCE OF CIVIL WARS
Daron Acemoglu
Davide Ticchi
Andrea Vindigni
Working Paper 09-25
September 16, 2009
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E52-251
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This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://ssrn.com/abstract = 1474961
Persistence of Civil Wars*
Daron Acemoglu
and CIFAR
MIT
Davide Ticchi
University of Urbino
Andrea Vindigni
Princeton
September 2009.
Abstract
A
notable feature of post- World
provide a theory of the persistence of
rebellious factions only
opens the way
this
by creating a
War
II civil
civil
wars.
of ending insurrections.
by
civil
is
their very long average duration.
civilian
We
government can successfully defeat
relatively strong army. In weakly-institutionalized polities
for excessive influence or
rents are largely unaffected
wars
The
coups by the military. Civilian governments whose
wars then choose small and weak armies that are incapable
Our framework
shows that when
also
take more decisive action against rebels, they
may be
the size necessary for fighting the insurrection, as a
civilian
governments need to
forced to build over-sized armies, beyond
commitment
to not reforming the military
in the future.
Keywords:
civil
wars, commitment, coups, military, political transitions, political econ-
omy.
JEL
Classification
Numbers:
*We thank Roland Benabou,
2009
for
comments.
Acemoglu
H2, N10, N40, P16.
acknowledges the hospitality of Einaudi Institute
project.
EEA
Barcelona
NSF. Vindigni
gratefully
Pierre Yared, Fabrizio Zilibotti and conference participants in
gratefully acknowledges financial support from the
for
Economics and Finance during the completion of
this
1
Introduction
One
of the
striking facts of the post- World
most
long average duration of
that this
is
largely
civil
Weberian monopoly of
While the
violence,
major question: why has the
War
scholars
political
weak
for
why
weak
politically
civil
civil
the unusually
wars
wars
World War
states since
is
states,
compelling,
weakness of many post- World
we provide an explanation
is
Hironaka, 2008, Kalyvas, 2006) argue
politically
between
link
international politics
II
(e.g.,
and persistence of
Central to our explanation
polities.
Some
due to the proliferation of
the onset of decolonization.-
In this paper,
wars.
1
War
may persist
and
II
which lack the
it
raises another
II states
persisted? 3
in weakly-institutionalized
the political moral hazard problem generated by a strong
is
military (Acemoglu, Ticchi and Vindigni, 2010a).
In weakly-institutionalized polities, the
checks that would prevent a strong military from intervening in domestic politics are absent.
This makes the building of a strong army a double-edge sword for
even
if
such an army
is
many
civilian
governments,
necessary for defeating rebels and establishing the monopoly of violence
over their territory.
We
formalize these ideas using a simple dynamic game.
by an
trolled
elite,
opposition group
army
The
is
which derives rents from holding power.
elite
can instead choose a larger
size
army, which will end the
complicated by the fact that the
is
downsizing the military once the
necessary for defeating the rebels,
Civil
faces
government
armed
is
con-
rebellion from an
minimum
scale of the
ending this armed rebellion and establishing the monopoly of violence.
increase the role of the military in domestic politics.
action
It
civilian
a group of different ethnicity or religion). The
(e.g.,
insufficient for
The
civil
war
may
elite
is
also
The
civilian
civil
war, but this will also
government-military inter-
cannot credibly commit to not reforming and
over. Consequently, a stronger military,
attempt a coup. Thus the
elite often face
which
is
a choice
wars during the nineteenth and early twentieth century were usually relatively short; the average
length of a civil war between 1900 and 1944 was one and half years. After World
of civil wars has tripled to over four years.
The number
War
II,
the average duration
of ongoing civil wars has also increased dramatically
since 1945. For example, an average of about twenty civil wars per year were ongoing concurrently in the 1990s,
corresponding to a rate approximately ten times the historical average since the nineteenth century. The surge
in
the number of ongoing
rate of outbreak of
"Many
many new
(see, e.g.,
new
civil
wars has been mainly due to the increase
Hironaka (2008).
in
average duration rather than
in
the
conflicts. See, e.g.,
political scientists point out that decolonization increased the
states lacked the
monopoly
of coercion
and the
number
political capacity
of independent states, but
common among Western
states
Herbst, 2004, Centeno, 2002).
Acemoglu, Robinson and Santos- Villagran (2009) argue that weakness of central governments may arise
an equilibrium outcome when non-state armed actors provide support to one of the factions competing for
control of the central government.
as
between a persistent
war versus the
civil
another strategy for the
to build
elite:
the military after the end of the
civil
civil
war
(since the over-sized
analysis shows that
monopoly
army
is
both the
persis-
outcomes. 4
when the
elite's rents
are relatively unaffected by
of violence, for example, because the civil
strong army. In contrast,
war
is
in
a remote area or
when the
likely to build a strong
rebels pose a
more
its
it
lack of
does not
be unwilling to build a
costly threat to their rents, the elite
is
army, either risking the possibility of a coup after the end of the
war or accepting excessive concessions to an over-sized army.
civil
Our framework
of the state.
also generates a novel substitutability
and via
Our work
model higher
in our
strong armies (because
elite)
between
fiscal
and
political capacity
While these capacities are generally thought to be complements
and Persson, 2009),
it
this channel,
is
fiscal
it
contributes to the persistence of
likely
(2003) and Herbst (2004),
among
Besley
civil
and more costly to the
wars.
related to several different literatures in comparative politics.
is
(e.g.,
capacity raises the equilibrium cost of building
makes military dictatorships both more
ture on the causes of civil wars
civil
strong enough to resist
in weakly-institutionalized polities
interfere with their control of natural resources, then the elite will
more
to not reforming
wars and the emergence of over-sized armies with excessive influence on domestic
politics are possible equilibrium
Our
also points out to
an over-sized army as a commitment
any attempt to reform). This suggests that
tence of
Our framework
risk of a coup.
The
large litera-
surveyed in Blattman and Miguel (2009). Fearon and Laitin
others, emphasize the role of
wars, while the duration of civil wars
is
weak
states in the emergence of
studied in Collier, Hoeffler, and Soderbom (2004),
de Rouen and Sobek (2004), Hegre (2004), Fearon (2007), Powell (2004, 2009) and Yared
(2009).
polities,
Our paper
is
also related to the small
economics literature on weakly-institutionalized
the problems of weak states, and the analysis of state formation, including Acemoglu,
Robinson and Verdier (2004), Acemoglu (2005), Acemoglu, Ticchi and Vindigni (2010b), and
Besley and Persson (2009), and to the political economy literature on regime transitions
e.g.,
Acemoglu and Robinson, 2006, Acemoglu, Egorov and Sonin,
2009).
Our
(see,
analysis of
the political moral hazard problem between the civilian government and the military builds
An illustrative example of a regime unwilling to build a strong army despite ongoing civil wars, most likely
because of fear of increasing the power of the military in the future, is Zaire (Congo) under Mobutu (e.g.,
Snyder, 1992). An example of a regime building an over-sized army is Egypt under Mubarak in his fight against
Muslim Brotherhood (Owen, 2004). An example of a regime building a strong army to fight communist rebels
and then facing a coup is the Philippines under Marcos.
Digitized by the Internet Archive
in
2011 with funding from
Boston Library Consortium
Member
Libraries
http://www.archive.org/details/persistenceofcivOOacem
on Acemoglu, Ticchi and Vindigni (2010a). The
and complementary work by
closely related
Besley and Robinson (2010) also emphasizes the cost of concessions that the civilian govern-
ment must make
to the military
and analyze the choice between strong armies and "tinpot"
militaries.
The
organized as follows. Section 2 presents our basic model. Section 3
results
and Section 4 characterizes the equilibrium and present our
results. Section 5 concludes.
The Model
2
We
5R,
is
some preliminary
contains
main
paper
rest of the
consider a society consisting of four social groups, the
and the
M. Each
military,
agent j at time
t
=
elite,
E, the citizens, L, the rebels,
maximizes
oo
EoXyfe,i + rj,t),
(!)
t=o
where Eo
is
the expectation at time
consumption of the
final
t
good (equal
by each individual whose group
is
in
=
0, j3
€
(0, 1) is
the discount factor,
and
to disposable income),
power
at
time
t,
Tjj,
>
>
Cj >t
denotes the
a rent appropriated
is
representing non-monetary payoffs from
holding power or returns from natural resources or other income sources.
The
size of the elite is
which
size of the military,
assume that only the
X£
< x m < Xh <
normalized to
will
The
size of the citizens is equal to n, while the
be determined endogenously,
citizens are recruited into the army,
The minimum
n.
1.
order and national defence.
size of the
An army
army, X(,
is
of size larger than the
is
x t at time
refer to
Xh as an "over-sized army"
A<
has a productivity
There are three
civil
war
necessary for maintaining law and
minimum
The
either represent a
D
is
civilian
Each
elite
level X(
can be chosen to
become obvious
agent has productivity
a,
shortly,
and each
citizen
Citizens recruited into the military do not produce any income.
political states St
(rebellion);
dictatorship.
a.
.
For simplicity, we
and that x e {xe,x m ,Xh}, where
deal with the rebels as explained further below. For reasons that will
we
t.
€ {W, D,A1},
W corresponds to a
civilian
a civilian regime (democracy) without rebellion; and
government, with or without rebellion,
is
M
regime with
is
a military
ruled by the elite and can
democracy (including a captured democracy) or a non-democratic regime
ruled by an oligarchy. Instead, in a military dictatorship, the military
Payoff-relevant states will be given by elements of
{W,D,M}
x {xe,Xm,Xh}-
commander
(or a
group
of officers)
the
is
in
power.
Since our focus
initial political state is so
=
W —a
is
=
military dictatorship
assume that a military coup
also
is
If
Both
actions
s
the rebellion
we assume
simplify the analysis,
= M,
this will
not possible starting from s
—
civil
war and coups cause economic
apply in
all
= W. Thus
and reduces
inefficiencies. Civil
incomes by a factor 6 £
all
5)a and that of each citizen
The government
pay the
are used to
—
is (1
future dates.
costly (this
must be
salaries of soldiers.
6) A. Similarly,
possible transitions
satisfied at
the military
incomes are reduced by a factor
all
rate f
>
and
0,
Laffer curve).
after t
=
becomes
not equipped to run the
is
[0, 1],
f,
<fi
£
taxation
The government budget
assuming that
is
prohibitively
constraint, which
each period, thus takes the form
t
\s t
)x t
<
T(x
t
\s t
)(a t
+(n-
x )A
t
t
(2)
),
where w(x t \s t ) and T(x t \s t ) denote the military wage and the tax rate with an army of
in the political state s t
We
no further
s
size
xt
.
next describe transitions in greater detail. As noted above, we start in so
a transition to
[0, 1].
and these revenues
We model tax distortions in a simple way,
some
makes f the peak of the
w(x
= D when
the rebellion
(civil
The
possibility of another rebellion.
war)
is
and
defeated,
— W.
There
for simplicity, there is
probability that the rebellion will be defeated
a function of the strength of the state (the size of the army). In particular, we assume that
the
civil
war ends with probability p(x) £
p(x ( )
This implies that when x t
will persist
is
We
war disrupts economic trans-
with proportional taxation Tf £
collects revenues
there are no costs of taxation until
is
is
that the
so that the income of each elite
[0, 1],
economy, and thus under a military dictatorship,
is
that
W-*.D-*M.
are
(1
we have
absorbing: once
is
we assume
wars,
D, but the military can attempt a coup against
= M. To
s
civil
regime under a rebellion.
civilian
defeated, there will be a transition to s
democracy and cause a transition to
on the persistence of
=
=p<
xg, there is
end the
civil
in each period,
p{x m
)
=
p(x h )
=
1.
state. In contrast, a
1
—p, that the
civil
war
moderate or an over-sized army
war immediately. In addition, however, strong armies, x £ {x m x^},
,
can undertake a coup against the civilian government once the
them a double-edge sword
where
a "high likelihood," probability
because of the weakness of the
sufficient to
[0, 1]
for the
incumbent
civilian
civil
war
government,
for
is
defeated. This
makes
they defeat the rebels,
but
may attempt
The
a coup after the end of the conflict.
strong army, x m and the over-sized strong army, x^,
,
difference
between intermediate-sized
that the former can be downsized by
is
the civilian government, and the probability that civilian government can do this within any
given period
is
equal to A €
In contrast, an over-sized army, x
[0, 1].
=
x^,
strong enough to
is
withstand any attempt to reform and can thus never be reformed and downsized by a civilian
government. The
initial size of
beginning of time
t
We
If
also
so,
he
soldier has to put effort,
which costs h >
caught with probability q e
is
soldiers during times of civil war.
the
decided by the civilian government at the
represent the
The
elite.
rebels
assumptions, and there
is
no
is
0, in
fighting the rebels.
punished by losing
his
wages"
for
will lead to "efficiency
6
economy described
and the
and
(0, 1),
one period. This imperfect monitoring technology
for
We
is
0.
assume that each
he does not do
wage
=
the military, xq,
citizens
so far as a
dynamic game between the
do not play an active
conflict within groups, so that
are taken by a representative agent from each group
the
(e.g.,
role
soldiers
and
because of our simplifying
we can suppose that
commander
of the
decisions
army and a
representative elite agent in a civilian government).
More
1.
formally, the timing of events starting in s t
The
civilian
government chooses the
Wt subject to the constraint that Xt
time
x
r
size Xf of the
-i, either
if
W or D
is
as follows:
army, sets taxes
Xt-\
=
Tt
and military wages
Xjr or if the state of the
world at
such that the army cannot be reformed, and subject to the budget constraint
t is
Then
if st
The
2.
=
=
(2).
= W:
rebels are defeated with probability p(xt)
inducing a transition to st+i
=
D. Otherwise, St+i
and the
= W,
civil
war ends permanently,
and the same sequence
of events
is
repeated.
=
If s t
2.
If
civilian
If xt
D:
x -\
t
= xm
and the
state of the world
is
such that the military can be reformed, the
government decides whether or not to reform
= xm
government.
or Xt
A
=
it
(if
there
is
no reform, then x t
Xh, the military decides whether to attempt a
coup succeeds with probability
The imperfect monitoring assumption and
1,
coup against the
inducing a transition to
st
= xm
).
civilian
= M.
Without
would be binding during the civil war, and thus wages would
depend on expectations of future coups and military wages. Allowing for perfect monitoring or for more severe
punishments do not affect our general results.
the resulting efficiency wage simplify the exposition.
this feature, the participation constraint of soldiers
.
In state
St
= M,
which
is
absorbing, the military government chooses taxes and military
wages subject to the government budget constraint
In the following,
we characterize the Markov Perfect Equilibrium (MPE)
game between the
political
(2).
elite
and the
As a
military.
first
of the
dynamic
step in this characterization,
we
write the values (discounted present value) of the players as functions of payoff-relevant state
variables (st,x t ),
where
st
G
{W,D,M}
and
G {xg,x m ,Xh}.
xt
Values and Strategies of the Military
3
Let us start in the political state
cost h for each soldier
= W.
s
and shirking
detected only with probability
is
equilibrium military wage during the
We
and Vindigni, 2010b).
Since fighting against the rebels requires an effort
civil
assume that
war needs to be
this
wage
at least
q,
the incentive compatible
h/q
(see
Acemoglu, Ticchi
also satisfies the participation constraint
ensuring that citizens are weakly better off as soldiers than as producers (for example, h/q
—
(1
f()A, with f( defined in (3), would be sufficient for this).
income disruption generated by the
constraint (2)
civil
must be
-
provided that this tax rate
Next consider the
is less
than the
=
political state s
iorie{l,m,h},
maximum
D.
no longer necessary, thus military wages
x
If
=
=
(1
—
T() A,
where Tg
is
then coups are not feasible and
xg,
civilian
)
the state
elite
T( balancing the
x G {x mi Xh\^ the army
Sj
=
D, that
is,
V AI
as a soldier,
i.e.,
after the rebels
{
(2) is T(
=
(4)
+ nA).
X(A/(a
a coup against the democratic government in
have been defeated. Consequently,
and Vindigni (2010a), there
{D,x,\coup)
X( are
-^^,
government budget
may attempt
=
need to take into account the strategy of the military to
as in Acemoglu, Ticchi
and working
the equilibrium tax rate in this case. Consequently, the value of
VM {D, Xi = V L (D, Xi )=
When
effort
be determined by the participation constraint,
will
a soldier and the value of a civilian under democracy and x
where the tax rate
(3)
feasible rate, f
which makes a soldier indifferent between working as a
we
Taking into account the
war, the tax rate that satisfies the government budget
{l-6){a + (n-Xi)A)q
is
>
will
6
set fiscal policy.
In particular,
be a no coup constraint of the form:
< V M (D,x |nocoup)
1
in these cases the
for
i
G {m, h)
,
(5)
which the
elite
must
satisfy
if
they wish to prevent coups;
V M (D, Xjjcoup)
and
VM
(D,Xi\no coup)
denote the values of soldiers with an army size of Xi when they undertake a coup and when
they choose not to do
so.
military regime, and let
regime
this
is
To
R
derive the implications of the no coup constraint,
consider a
first
denote the rents that soldiers receive in such a regime. Recall that
absorbing and since there are no costs of taxation until f soldiers will set this
,
tax rate and redistribute the proceeds as wages to themselves. Therefore,
VM
(M,
Xl
R + f{1
)=
-
& <"+
<
n"
*'>
A) /X
>
forzGim,/,},
which takes into account that incomes are reduced by a fraction
—
running the economy, and only n
taxation are distributed equally
among
Consider next the case where x
the value to the military
is
ternatively, the elite could
them not
VM
—
=
citizens are
i.e.,
expression for the efficiency wage
Xh (with
in production.
s
=
D).
If
wage" to the
to satisfy the
(D,Xh\no coup)
=
wfi
elite
is
The proceeds from
do not prevent coups,
as given by (6) for
w£,
soldiers,
no coup constraint,
+ f3V M (D,Xh\coup),
where
w£
when
is
make
to
(5).
straightforward to derive, since there
reforming the military. Therefore, the value to the military
V
the
= V M (M, Xh)
"efficiency
is
working
because the military
<p,
the soldiers, thus the division by X{ in the denominator.
(D, x/j|coup)
pay an
to attempt coups
x,;
(6)
When
is
no
=
i
it
x
h.
worth
=
Alfor
Xh, the
possibility of
the elite pay such a wage
is
the level of the efficiency wage
that makes (5) hold as equality, and this expression takes into account that in the next period
the military must receive the value that
because the
wage
w^
elite will
will
efficiency wage).
This implies that the efficiency
be given by
and the tax rate that
satisfies
it
may
f{l-(j))(a
+ {n-x h )A)
+
R,
(7)
the government budget constraint in this case
rf
***
= »(l-fl+
a+ (n - Xh)..A
is
(8)
.
not be feasible for the civilian government to pay such high wages to
soldiers because in the
government budget constraint,
prevention with an army of size x^
(7),
can get with a coup (either by undertaking a coup, or
pay them the necessary
w hP =
However,
it
we obtain that coups
is
feasible only
starting with x
=
if
(2),
we need
w^x^ <
to have r
f (a
+
(n
—
<
x/,)
f.
A).
Hence, coup
Thus from
x^ can be prevented provided that
J
hR
* * t<(a+ (n- Xh)nn
A)
7
s ^-
(9)
Let us next consider the case where x
wm
by paying an efficiency wage
V M (D, x m \no
coup)
= xm
then the value to each soldier
,
= w? + (3{W L (D, x e +
military,
and the
soldiers will receive the value
then the soldiers
(1
)
which now takes into account that with probability
and downsize the
V
=
(again with s
civilian
(D,xe) as given by
will receive the value
is:
If
the
elite
prevent coups
7
- X)V M (D, xjcoup)],
there will be an opportunity to reform
A,
government
D).
will
use this opportunity, and thereafter,
(4). If
there
no opportunity
is
from a coup (either because they
will
undertake a coup
or because the no coup constraint, (5), will be satisfied with equality). Using (4)
VM (D,xm \no
can compute
from a coup
=
of size x
given by
is
Xm,
-A)
+
&h = f(a +
nA))
+
(1
The
P*
,
where
- P*)f(a +
<
/3*
R^, where
1 is
A)/x m
(n
any
1
f(a
+
specifically,
R <
to satisfy (5)
'
This
is
and
Rh ensures that
-
C
(10)
—
and
Xfl )A)/xi1
Rm =
{3A(1
—
— X(A/(a +
.
is,
when
soldiers
know
that they will
they will receive efficiency wages without
4>*
h
<
1
so that for values of
army
(x
</>
G
=
[$£,
xt)-
1]
it
will
be feasible
In contrast,
Rm < R
the value of soldiers after the realization of the state of nature that the military cannot be reformed.
/3(1
-
A))[f (1
-
(f)
w m necessary for prevention is
+ (n-x m )A)/x m + R\/(\ - /?) -
wage
\))[T{l-<t>){a
balancing the government budget
(1
only when: 8
states that military rents in military dictatorship are in-
to prevent coups with an over-sized
W* = (1-/3(1-
=
value
but are worthwhile when they do not receive efficiency wages. More
In this case, the efficiency
r£
(5)
+ (n-x m )A)
- x h )A)/x h
(n
sufficient influence in the civilian regime, that
risk of downsizing,
The
A)).
.
termediate, so that military dictatorships are not desirable
have
-
implicitly defined by the following equation (3*A(1
part of Assumption
first
)
- x m )A)/x m =
(n
/3(1
we
(5),
following assumption, which allows us to
Rm < R <
(1)
-
/?)]/(l
"
f(a
interesting cases.
+ (1 - /3)f(o + (n - xm
[4>* ,\] and Xe (A*,l].
h
>
j3
T e )x m A
+ (n-x m )A)\
we impose the
nA))
(2) 4>£
(3)
T(a
more novel and economically
1
-
-
(1
space, in the remainder,
Assumption
x e A/{a
r e )A/{l
and
Repeating the same analysis as above, we find that with an army
(6).
0(1
focus on the
+ /?A(1 -
[w^
^
>
To save
=
be feasible to satisfy the no coup constraint,
will
it
coup)
to reform,
/3A(1
-T
t
)A/(\ -
/3),
and the tax rate
is
+ x m R/(a +
(n
- x m )A)}/(\ -
/3)
- p\[x m /(a +
(n
- xm
)
A)} (1
-
r e ) A/(l
-
p).
-
ensures that preventing coups with an intermediate-sized army (x
the probability of potential reform,
In particular,
implies that
when A 6
(A*,
can never be
(10)
1],
The second part
Rm <
the assumption ensures that
=
)
where f(
is
(D,xg)
civil
war
(1
-
ft) (1
given by (3) and f
an ongoing
probability
V
to the elite
Then
1.
1).
assumption
this
G
<p
[<££, 1]
1]
so
so that
never feasible. Finally, the third part of
first
part of the assumption
is
meaningful.
dynamic
of the
when
there
is
a
game by determining what
political
civil
civil
war.
war and the
size of the military is
X( can be written as
V E {W, x t =
is
is
choose as a response to the ongoing
elite will
as A approaches to
1
indeed feasible, and A £ (A*,
is
when
MPE
MPE
characterize the
The expected value
x
R^, so that the
Characterization of the
we
not feasible
is
of the assumption then imposes that
coup prevention with an intermediate-sized military
type of army the
m =
<\>*
)
and coups cannot be prevented with
satisfied
that prevention of coups with over-sized military
In this section
(i.e., <p*
A* be defined as the value of A such that
let
intermediate-sized army.
4
m >
high
A, is sufficiently
= xm
p
=
civil
=
p
((1
(since
—
is
-
S)a
+
f
+ 15
[
PV
E (D, x
e +
)
the rent accruing to the
elite
-
(1
V E (W, x t
p)
when they
)]
,
power but there
are in
war. This expression incorporates the fact that the rebels are defeated with
(xg) in each period,
T()a
+ r)/(l — /3),
an army of
size xg
and subsequently the continuation value
where
r is the
cannot attempt a coup,
state). Therefore, the value to the elite of choosing
V E lw
{
_
~~(1 -
,
e)
£) ((1
-
1,
f *) (1
-
s
=D
with x
in
=
xe
is
an absorbing
a small army, in the midst of a
fla
+
f)
+
/3p((l
-rt)a +
when
the elite choose an
army
of size x
= xm
,
is
power without a
civil
war,
is
r)
Ulj
(l-/3)(l-/3(l-p))
'
Given Assumption
exogenous rent of being
to the elite
then coups cannot be
prevented, and thus their value can be written as
V E (W,x m = (l-f m )(l-6)a + f +
)
where fm
is
given by
(3).
A((l
f3
- u)a + r)
1-/3
(1-
A) (1 - f) (1
:i2)
1-/3
This expression takes into account that rebels are defeated in one
period and, in the following period, the army
is
reformed with probability
A,
while reforms are
not possible with the complementary probability and the military undertakes a coup.
Finally,
in the
if
the
subgame
and
feasible,
=
choose x
elite
Xh, their value
depends on whether coups
Assumption
starting after the defeat of the rebels. Given
clearly optimal. Hence, the value to the elite in this case
V E (W,x h =
)
-
(1
ffc)(l
-5)a +
+ /3
f
(1
~
such prevention
1,
is
is
^
(13)
,
9
defined in
is
be prevented
Tj + r
1
where r^
will
(8).
In light of this discussion, the potential strategies for the elite are: (1) form an over-sized
military
and prevent coups, thus remaining
defeat the rebels,
(x/i),
influential military; (2)
form an intermediate army (x m ), defeat the
army
military takeover; (3) choose a small
To compare these three
and thus allow
(xe),
on
and
(12) are
independent of
p.
but face the
rebels,
V E (W, xg) = V E (W,xe\p)
options, note that
rebels (hence the explicit conditioning
power but with a very
army
while V B (W, Xh) and
p),
risk of
for persistent civil war.
a strictly increasing function of the probability p that a small
(13)
in
defined in (11)
will defeat
[xg]
the
V E (W, x m ) defined
This implies that there exists a threshold p 6
[0, 1]
is
in
such
V E (W,Xf p V E (W, xg\p = p) whenever p ^ p, and a threshold p* e [0,1] such that
V E (W,x m ^ V E (W, xg\p = p*) whenever p ^ p*. It can be verified that both thresholds are
always smaller than 1, because the value to the elite when x = xg and p = 1 is always greater
that
l )
)
than their value when choosing Xh and x m
>
In particular, p
(1
Otherwise
_ re
)
(1
-
=
p
(1
- /?)
V E {W,Xf < V E (W, xg)
l)
always be preferred by the
set
<
S)a
0. Similarly,
p*
>
However, these thresholds need not be positive.
V E (W, x/,) > V E (W, X(\p =
when
only
.
elite to
-
fh )
for all
p €
(1
(1
that
0),
is,
-6)a + p{l- r£)
and
[0, 1],
a
when
+ /3(r-f).
in this case, a small
(14)
army
(xg) will
an over-sized one (x^), and by convention, in this case we
when
{1-Tt)(l-S)a < {l-0){l-fm ){l-S)a+p\(l-Te)a+0(l-\)(l-t){l-4>)a+/3(\r-r),
and thus when
this condition
the reader should bear in
is
not satisfied, the
mind that both
always prefer xg to x m
elite
p and p* can be
thresholds,
,
.
In
(15)
what
follows,
R
(16)
zero.
Let us finally introduce the following condition
- rm )(l -
(t/i
If
the
4>)a/(\
—
elite
ft),
5) a
<
1-/3
(1
-
A)(r
+
+ {n ~
cpa)
chose not to prevent a coup, they would receive
which can be
verified to
be
less
than
(13).
10
r(l
V
-
<f>))Xa
a
(W,
x/,)
=
(1
—
+
T'/iJfl
^
(n
-
— Xh)A
<5)a
+ r + j3(l -
f)(l
can be verified that when this condition
It
army
prefer an over-sized
We now
The
1
Then
and p £
satisfied
is
war
MPE
=
x
sized army,
=
ends, the civilian
xm
and the
,
Suppose that condition (16)
3.
army, x
=
x^, the civil
but with high wages
The
MPE with
civil
and there
government
and the
elite
is
is
the following structure.
not satisfied and p £
(the elite)
1].
an intermediate-
there
is
possibility of a
dictatorship.
and p £
[0,p),
war ends immediately, and
and concessions for the
,
remains in power.
war ends immediately, but
satisfied
\p*
persistence of civil war. After
is
[0,p*), then the elite choose
and the formation of a military
military coup
),
dynamic economy. 10
in this
xg,
Suppose that (16) does not hold and p £
2.
l )
or that (16)
[p, 1]
the elite choose a small army, x
(or if) the civil
V E (W,x/ > V E (W,x m
game above has a unique
political
Suppose that (16)
satisfied,
an intermediate one.
provide a characterization of the
Proposition
1.
to
is
then the
elite
choose an over-sized
government remains
civilian
in power,
military.
following corollary provides comparative statics of the key thresholds.
Corollary
1
The threshold p
is
nondecreasing in
r, S,
(ft,
and
it is
nonincreasing in
f, f,
x^,
R.
The threshold p*
and
in 5,
also in r
Proposition
1
is
is
if
nonincreasing in
X
is
the
f, i,
xm
<j>,
,
is
independent of R, and
or
when p >
p*
main
—
nondecreasing
high enough and nonincreasing in r otherwise.
result of the paper.
It
shows that the
army, and will not establish a monopoly of violence over
p > p
is
i.e.,
when a small army
is
elite will
choose a small
its territory, at least for
a while,
not too ineffective at fighting the rebels.
Note, however, that both thresholds p and p* can be very small or equal to zero, so
small army
as
p
—
>
when
war
1
is
r
is
0, if
is
maintained, the
both thresholds are
low relative to
ongoing
(for
The argument
zation of the
civil
MPE
f,
that
war can
when
example because the
1
shows that such an outcome
the elite receive significant rents even
civil
when a
persist for a very long time (in the limit forever
zero). Corollary
is,
when
war
is
in peripheral areas
the text gives the main idea of the proof of this proposition.
and a formal proof are provided in the Appendix.
in
1
1
is
more
when the
and does not
A more
likely
civil
interfere
detailed characteri-
with the rents that the
from corruption or natural resources). Small armies and
elite receive
persistent civil wars are also
more
likely
when
5
low relative to
is
the elite and of the citizens) relatively small under
makes
Finally, a high f also
makes a military dictatorship more
first, it
equilibrium path); second,
making
do
so).
this configuration
it
more expensive
it
civil
more
likely
(when these happen along the
makes a military dictatorship more
from controlling the government) also makes the
all
of the influence of
When
cases, the reason
why
attractive for soldiers, thus
no coup constraint (when they prefer to
elite
more
R
(high rents for the military
likely to
choose a small army and
army
the elite prefer a small
is
that they are afraid
and a potential coup by a strong army following the end of the
the elite decide to fight the rebels more vigorously to end the
do so using one of two
different strategies.
In the
loss (of
because of two distinct channels:
costly to the elite
for the elite to satisfy the
making the income
war, and high under military regimes.
For reasons related to the second channel, a high level of
a weak state. In
<f>,
first
civil
civil
war.
war, they can
one, they build an intermediate-sized
army, but because of their inability to commit to not downsizing the army after the
ends, they cannot satisfy the no coup constraint, and there
is
civil
war
a positive probability of a coup
along the equilibrium path. In the second one, they build an over-sized army as a commitment
to not reforming the military in the future. This
amounts
to
making permanent concessions
(high wages and other policy concessions) to the military as the price that the elite have to
pay
for fighting the rebels
that in this case this
hands of the
An
between
of the state
power
it
monopoly
of violence
is
sort of
monopoly of
violence. Note, however,
mostly in the hands of the military not in the
government.
interesting implication of the model, again highlighted by Corollary
tutability
(e.g.,
civilian
and establishing some
is
fiscal
high.
and
This
is
political capacity of the state.
f
is
a novel substi-
high, the fiscal capacity
generally thought to increase the political capacity of the state
Besley and Persson, 2009). However, a higher
in the
When
1, is
hands of the military
if
fiscal
capacity also puts more economic
they decide to attempt a coup. Through this channel,
discourages the civilian government from building a strong military and the monopoly of
violence necessary for political capacity.
Finally,
it is
also useful to observe that the entire analysis
is
predicated on the possibility
that the military, once sufficiently large, can take control of the government. In this sense, the
model represents the workings of
politics in a weakly-institutionalized polity,
112
which does not
place major constraints on the exercise of military power.
Concluding Remarks
5
We
presented a simple model where
the state.
The
civil
wars persist because of the endogenous weakness of
government, assumed to be under the control of an
civilian
forgo the establishment of the
monopoly of violence over
elite,
may
prefer to
allowing an ongoing
its territory,
civil
war, because, given the weak institutions, the elite are afraid of building a strong military. This
fear
the military after the
more
when
particularly relevant
is
likely.
civil
war
is
the civilian government
over,
and
this
is
civilian
war
is
military coup
government, when
to build an over-sized
to not reforming the military after the threat of the civil
army
as a
it
needs
commitment
gone.
view this paper as part of our broader research on the interaction between civihan
segments of the society and the military, and on the
force.
unable to commit to not reforming
commitment problem makes a
One, potentially paradoxical, response of the
to prevent the continuation of the civil war,
We
is
Our simple model shows how
ability of society to control the use of
this interaction is affected
the same time determines the persistence of the
civil
by an ongoing
civil
war and
at
war. Other interesting directions would
be to investigate how international relations (including possibility of international wars and
international trade) affect the balance of power between the
society
and the
military,
of the government
may
and
also
affect the
how
elite,
non-elite elements in the
the interplay between the military and civihan branches
development of the
fiscal
capacity of the state.
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Appendix
Additional Details on the Characterization of the
We
first
state a version of our
Proposition 2 Define
and p* are
Suppose that p
unique
1.
MPE with
^
p*
Then when
>
set t u
=
(a): (16) is satisfied
= W,
St
2.
= w =
u >
can
be
h/q and the
army cannot
dictatorship
is
wages given by
3.
The
civil
wu —
(1
wu =
f (1
and the
civil
war ends
periods,
i.e.,
xu
su
When p =
p*
in parts
1
=D
,
or (b) (16)
hold,
p
=
0.
hold, set p*
— T()A and
(1
andp G
—
=
=
xe, set Tt
war ends with
some date
at
not satisfied
is
xt
i.e.,
= D
su
and pay
ft,
probability
(p*, 1].
p
in each
the elite choose x u
t,
(i.e.,
= xm
xq
war ends
,
set tq
in the
and in
A,
— T()A and
Then, at time
[0,p*).
same
=
fm
=
xg,
the elite remain in
= D
for all
—
<p)(a
x/,,
for
is
i.e.,
in the
+
(n
— x m )A)/x m and
,
satisfied
=
xq
same
u >
andp £
x^, set tq
period.
the elite set t u
all
=
[0,p).
=
xm
,
=
and
=
t
=
=
xg, set r u
1
T(,
—
A
and a permanent military
sets t u
M for
=
u>
all
?h, pay military wages
be
sets military
f,
Then, at time
w u = w^
the military
1,
With probability
1.
The military cannot
= r^
the elite choose
0,
choose x u
u >
su
=
At time
this case the elite
su
t
pay military wages given by
,
period.
The military chooses x u
established.
choose an over-sized army,
and
and (15)
(14)
and (15) does not
0,
be reformed, the military undertakes a coup,
Suppose that condition (16)
(7),
=
civil
war ends
wu =
i.e.,
reformed with probability
pay military wages
the
When
t.
an intermediate- sized army,
= w =
p
(p, 1],
h/q.
if) the civil
pay military wages
all
andp €
Suppose that (16) does not hold and p £
wq
formally.
as in the text.
the elite choose a small army,
After (or
0.
T(,
power) for
more
Then, the political game described in the main text has a
.
military wages given by wt
t
1,
the following structure.
Suppose that
period
p and p*
(14) does not hold, set
p and p
7^
Proposition
result,
the thresholds
When
interior.
main
MPE
t
=
1.
0,
Wo =
reformed in
the elite
w=
all
h/q,
future
given respectively by (8) and
1.
configurations in parts
1
and 2 are MPEs, and when p
and 3 are MPEs.
16
=
p, configurations
Proof. Condition (16)
When
rearranging terms.
is
obtained from
V E {W,x h > V E (W,x m
)
this condition is satisfied, the elite prefer
an intermediate one (x m ), so that their choice
V E (W, xg) = V E (W, X(\p)
that
p that a small army
defined in (11)
is
whenever p ^
and
it is
p.
Moreover, p
strictly positive if
is
[0, 1]
V E (W, Xh)
if
an over-sized army
x^ and x
V E (W, x^)
in (13)
such that V E (W,
=
xg.
(rr/,)
to
Then, note
is
independent on
E
^ V (W,
£/,)
X(\p
p.
= p)
V E (W, Xh) < V (W, X(\p = 1),
> V E (W, xg\p = 0), which is equivalent to
always strictly lower than
and only
using (13) and (12) and
a strictly increasing function of the probability
(xg) will defeat the rebels, while
This implies that there exists a threshold p G
=
be between x
will
)
as
1
This establishes parts 1(a) and 3 of the proposition.
(14).
When condition
sized
army
(16) does not hold,
V
(W, x^)
< V E (W, x m ),
=
(x m ) to an over-sized one (x^) and, therefore, x
the elite prefer an intermediate-
x^
is
never chosen. Similarly to
V E (W, xt) increasing in p and V E (W, x m defined in (12), independent
on p follows that there exists a threshold p* €
such that V E (W, x m ^ V E (W, X{\p = p*)
whenever p ~ p*. Again, p* is always strictly lower than 1 as V E (W, x m < V E (W, x^\p = 1),
E (W,x
while
is strictly positive if and only if V
m > V E (W,X(\p = 0), which is equivalent
the previous case, from
),
[0, 1]
)
)
it
)
to (15). This establishes parts 1(b)
When p =
p,
V E (W,Xh)
figurations in parts
1
1
have two best responses and con-
xq), the elite will
and 3 are MPEs. Again, when p
configurations in parts
=
p*
V E (W,x m = V E (W, xe),
)
,
and
and 2 are MPEs.
Proof of Corollary
The
=
and 2 of the proposition.
V E (W,
1
following relation
£ = V E (W, x e \p) - V E (W, x h =
)
implicitly defines the threshold probability
p ^
p.
Suppose that
have no
effect
on
p,
this threshold
and the
is
p such that
V E {W, x^) ^ V E (W, xe\p = p) whenever
interior (otherwise, small
changes in the parameters would
results in the corollary apply directly).
Using the implicit function theorem, we have that
dp
OS
=
dC/dd
dC/dp
where
fir
dC
Pf\/Ectt7
*.\4C\
dV
?(W,xe\p)
dp
dp
17
>
0.
(17)
I
Then, using
(3)
and the
dV E (W,x e \p)/d5 = -a/ (I dC
/3(1
-p)) and
E
= dV (W,x e \p)
—
17/(1
<5)
>
—
f/j/(l
6),
we obtain
-a. Therefore, we have
l-/3(l-p)
0, i.e.,
that p
is
(17),
we
Using the same procedure and taking into account
= -{dC/dr)/{dC/dp) >
=
/3a(l-p)
)
55
9(5
This combined with (17) implies that dp/ 85
dp/dr
and drh/dS
dV E {W,x h )/d5 =
dV E (W,x h
"
86
=
dr^/dS
fact that
increasing in 6 as stated.
also obtain:
dV E {W,x
- dV E (W,x h )/dr =
as
dC/dr =
as
dC/df = dV E {W,x ( \p)/df - dV E {W,x h )/df
e
\p)/dr
-/?(l-p)/(l-/?(l-p))<0.
=
dp/dr
-{dC/df)/{dC/dp) <
=
/?(l-p)/(l-/3(l-p))>0.
dpldx h
= -{dC/dx h )/{d£/dp) <0&sdC/dx h = -dV E (W,x h )/dx h = a{l-6)
I
—
>
where
we have used
in the last expression
f}a(dT? 'dxh)
'(1
and dr p /dxh
are both strictly positive (see (3) and (8)).
dp/dr
0.
/3)
= -(dC/dt)/{dC/dp) <
In the last expression,
also
do
for the
dp/d<f>
0,
=
as
we have taken
the fact that dfhjdxh
=
/3a (1
r^
into account the expression for
-
0) / (1
in (8) (as
-
/?)
we
>
will
next two cases).
-(8jC/8(f>)/{dC/8p)
>
= -dV E {W, x h )/d(p = -par/
as dC/d<j>
dp/dR = -{dC/dR)/{dC/dp) <
{n-x h )A) >
dC/df = -dV E {W,x h )/dr
(8f h /dx h )-
-dV E {W,x h )/dR
dC/dR =
as
=
(1
- j3) <
/3ax h /(l
-
0.
/3)(a
+
0.
This completes the proof of the
first
part of the corollary.
For the second part, consider the relation
T = V E (W, x
e
\p*)
- V E (W, x m =
)
that implicitly defines the threshold probability p* such that
whenever p ^ p*
Again we consider the case where
V E (W, x m ^ V E (W, xg\p = p*)
this threshold
)
is
interior.
From
the implicit
function theorem
dp*
df/dS
d6
dT/dp*
>0,
because
dT
dV E {W,x
Since as in the previous case, df(/d5
e
\p*)
>0.
(18)
dp*
dp*
=
f^/(l
18
—
S)
and df m /dS
=
f m /(l
—
6),
we have
dV E (W, x e \p*)/dS =
-o/(l -
/3(1
aV £ (^
d£ =
"
show that
d_T_
p*
is
dy £ (W, x m )/d<5 =
aV E (W, x m
|p*)
increasing in r
1-/3(1-^*)
A
if
dr
monotonically decreasing in
is
_
)
dr
A, dJ-
observations and (18) imply that dp* /dr
high enough and vice versa, note that
_p_
1
when A =
>
/dr
-a, and thus
/3a(l-p*)
)
9(5
E
E
= dV (W,x t \p*) _ dV (W,x m
dr
is
and
p*))
55
<9<5
In order to
ar f
-
-
/?
*
f
\1 -
and
_
P
/3{l
dJ- /dr
= — (dJ-/dr)/(dJ-/dp*) >
-
p*)
<
for
\
J
when A =
1.
These
high levels of A and
vice versa.
Again, taking into account (18), we have the following results:
dp*/df
= -(dT/df)l(dT/dp*) <
dT/df = dV E (W,x e \p*)/df - dV E {W,x m )/df =
as
/3(l-p*)/(l-/?(l-p*))>0.
dp*/dx m
5){dfrn/dx m )
dp*/df
= -(df/dxm )/(dF/dp*) <
>
because df m /dx m
>
= -{dT/df)/{dT/dp*) <
as
dT/dx m = -dV E (W,x m )/dx m =
a(l -
(see (3)).
as
dT/df = -dV E (W,x m )/df =
/3o(l
-
A)(l -
<p)/(i-p)>o.
dp*/dcf>= -(dF/d(/>)/(dF/dp*)
<0asdJr /dcp= -dVE {W,x m )/d^ = 0a(l-f)/(l-0) >
0.
dp* /dR
=
as
V E (W, X(\p*)
and
V E (W, x m
)
are both independent on R.
This completes the second part of the corollary.
111