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DEWEY
HS3I
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
A THEORY OF MILITARY DICTATORSHIP
Daron Acemoglu
Davide Ticchi
Andreas Vindigni
Working Paper 08-10
March 30, 2008
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.M415
at
A
Theory of Military Dictatorships*
Daron Acemoglu
and CIFAR
Andrea Vindigni
Davide Ticchi
University of Urbino
MIT
Princeton
March 2008
Abstract
We
investigate
how nondemocratic regimes
use
tlie
military and
how
this
can lead to the
emergence of military dictatorships. Nondemocratic regimes need the use of force in order to
in power, but this creates a political moral hazard problem; a strong military may not
remain
simply work as an agent of the
more
own
elite
but
may
The
turn against them in order to create a regime
moral hazard problem increases the cost
of using repression in nondemocratic regimes and in particular, necessitates high wages and
in line with their
objectives.
policy concessions to the military.
When
political
these concessions are not sufficient, the military
can take action against a nondemocratic regime in order to create
its
own
dictatorship.
A
more important consequence of the presence of a strong military is that once transition to
democracy takes place, the military poses a coup threat against the nascent democratic regime
until it is reformed. The anticipation that the military will be reformed in the future acts as
an additional motivation for the military to undertake coups against democratic governments.
We show that greater inequality makes the use of the military in nondemocratic regimes more
likely and also makes it more difficult for democracies to prevent military coups. In addition,
greater inequality also makes it more likely that nondemocratic regimes are unable to solve
the political moral hazard problem and thus creates another channel for the emergence of
We
show that greater natural resource rents make military coups
but have ambiguous effects on the political equilibrium in
nondemocracies (because with abundant natural resources, repression becomes more valuable
to the elite, but also more expensive to maintain because of the more severe political moral
hazard problem that natural resources induce). Finally, we discuss how the national defense
military dictatorships.
against democracies
more
also
likely,
role of the military interacts
Keywords:
with
its
involvement in domestic
politics.
coups, democracy, military, nondemocracy, political economy, political tran-
sitions.
JEL
Classification: H2, NIO, N40, P16.
*We thank seminar
participants at Brown,
CIFAR, Rochester, and Toulouse. Acemoglu
Much
gratefully acknowl-
work on this paper was done when
Acemoglu and Vindigni were visiting Yale and Collegio Carlo Alberto. They thank the Economics Department and the Leitner Program in International Political Economy at Yale and Collegio Carlo Alberto for their
edges financial support from the National Science Foundation.
hospitality.
of the
"The
class that bears the lance or holds the
musket regularly forces
that handles the spade or pushes the shuttle." Gaetano
Mosca (1939
its
rule
upon the
class
p. 228).
Introduction
1
Nondemocratic regimes almost always
groups. This repression
is
rely
on some degree of repression against competing
often exercised by a specialized branch of the state, the military}
Despite the prevalence of nondemocratic regimes throughout history and the important role
played by the military in such regimes, the typical assumption
is
agent" of some social group, such as the
little
and how the military uses
setting
up a regime more
many nondemocratic
its
elite.
There has been
that the military
is
a "perfect
systematic analysis of
why
coercive powers to support a nondemocratic regime rather than
in line
with
its
own
preferences. This question
relevant since, while
is
regimes survive with the support of the military, there are also numerous
examples of military dictatorships that have emerged either as a result of a coup against a
nondemocratic regime or against the subsequent democratic government.
In this paper,
we take
a
first
step in the analysis of the role of the military in nondemocratic
regimes and develop a theory of military dictatorships. At the center of our approach
agency relationship between the
is
elite in oligarchic
that creating a powerful military
a more powerful military
is
more
is
regimes and the military.^
a double-edge sword for the
elite.
effective in preventing transitions to
On
is
The main
the
idea
the one hand,
democracy.
On
the
other hand, a more powerful military necessitates either greater concessions to the military or
raises the risk of a military takeover.
will act as the agent of the elite in
under which oligarchies
will
We
investigate the conditions under which the military
nondemocratic regimes (oHgarchies) and the conditions
turn into military dictatorships. Our approach also sheds light on
the role of the military in coups against democracy.
If
the elite create a powerful military to
prevent democratization, then the military also plays an important role in democratic politics
until
it is
reformed, and such reform
is
not instantaneous.^ In particular, we show that faced
with a powerful military, a newly-emerging democratic regime
will either
need to make costly
Throughout the paper, the military may be thought to include the secret police and other law-enforcement
We also use the terms the military and the army interchangeably.
"Since we draw a distinction between military dictatorships and nondemocratic regimes controlled by the
elite, we use the term oligarchy to refer to the latter and nondemocracy as a general term encompassing both
military dictatorships and oligarchies.
'This assumption is consistent with O'Donnell and Schmitter's (1986) emphasis that the power of the army
plays an important role at the early stages of democratic transitions. For instance, a relatively weak army may
be easier to reform than a stronger one. Our model will show that this is generally true, but also that weaker
militaries may sometimes be more difficult to control.
'
agencies.
concessions or face a high probabihty of a coup. This coup tlireat disappears once the military
is
Interestingly, however,
reformed.
it
as soon as the opportunity arises that
early phases of a democratic regime
the anticipation that the military wiU be reformed
is
makes
—because
this creates
make
impossible for democratic governments to
difficult to control
it
the military dm-ing the
a commitment problem, making
credible promises to
compensate
it
soldiers for
not taking actions against democracy.
More
specifically,
distingxiished
by
our model economy consists of two groups, the rich
incomes (endowments). Democracy leads to redistributive
their
particular, to the provision of public goods,
is
which are beneficial
policies, in
and costly
The only way they can prevent
this
state, the military, responsible for using force
and
unwilling to allow a transition to democracy.
by creating a specialized unit of the
repressing
for the citizens
citizens,
Consequently, starting from an oligarchy in which they hold power, the
for the rich elite.
elite are
and the
elite
demands
for democratization.''
A
powerful military, however,
is
not only effective in
preventing a transition to democracy but also creates a political moral hazard problem because
it
can turn against the
elite
and take
direct control of the
to create greater redistribution towards
its
government
(for
own members). Consequently,
example, in order
the
elite
have three
potential strategies in oligarcliy: (1) no repression, thus allowing a rapid [smooth) transition
to democracy; (2) repression, while also paying soldiers an efficien.cy wage so as to prevent
military takeovers; (3) repression without significant concessions to soldiers, thus opting for
non-prevention or facing the risk of a military takeover.
We
characterize the equilibria in this environment and analyze the role of the military
The presence
in politics.
politics. If
it
will also
democracy
of a strong military changes both democratic
inherits a large military from the previous
in
democracy always wishes to prevent coups but
not be possible. In particular, soldiers realize that
reform the military reducing their
the military
when
it
rents.
has the chance to do
when
so, it
In principle, the elite
may
this
may
the opportunity arises democracy will
Since democracy cannot
commit
to not reforming
can only make current concessions to soldiers
(since promises of future concessions are not credible)
is,
nondemocratic regime, then
be confronted with a choice between making concessions to the military and facing
a coup threat. The decisive voter
that
and nondemocratic
and current concessions may not be
prevent democratization by using some combination of "carrot" and of
"sticl';,"
not only by using repression but also by making concessions and promising redistribution of income to
The scope and Umitations of such promises of redistribution have been analyzed in previous
Acemoglu and Robinson, 2000 and 2006) and here we ignore them for simplicity. We also ignore the
possibility of cooptation of some subset of the citizens using various means, such as the distribution of public
(some
work
of) the poor.
(see
jobs (see, for example, Acemoglu, Ticchi and Vindigni, 2006).
compensate the
sufficient to
our
first result
shows that
may have
large militaries
societies in
why
which nondemocratic regimes
social conflict in
is
in the past
not only intuitive but also provides us with a particular
nondemocracy may create
democracy may lead to worse economic performance during democracy because
and
citizens
up a
of the military and on the extent of inequality.
is
limited, the elite prefer to allow a
large military
When
smooth
when
military repression
is
likely to
be
effective
depends on the effectiveness
the military
not very effective or
is
transition to democracy, because such
a regime will not be highly redistributive (while repression
hand,
of the conflict
soldiers that this induces.
In oligarchy, whether the elite prefer to set
inequality
More
costs for (future) democracies.
the desire of the rich to prevent democratization by bequeathing a laxge army to
specifically,
between
have chosen
democracy and may instead end up with
difficulty consolidating
military dictatorships.^ This result
reason
a mihtary dictatorship. Consequently,
soldiers for the prospect of
is
On
likely to fail).
and inequality
the other
high, the elite prefer
is
to build a strong military for repression and deal with the political agency problem by paying
the military an efficiency wage. This equilibrium configuration will therefore correspond to a
situation in which the military
is
an agent of the
(effectively)
elite,
which
is
the presumption in
the existing literature. However, we also show that under certain circumstances the
prefer to use repression but not
their
own regime
persist
due to the repression of the
coup against the
soldiers, thus allowing military
elite
elite
and acts
citizens,
in its
whenever there
interesting implication of our
is
own
interests.
an opportunity
As the
These
for
interests involve attempting a
doing
so.'^
is
When
relatively low,
level of inequality increases
inequality
is
and most of
low, the society
it
is
in the
Most military
mocratic regimes,
is likely
is
form of
and the society remains democratic, the
government (the amount of public good provision) increases. As inequality
further, the society
is
model concerns the relationship between inequality and
democratic, but the amount of spending
size of the
coups against
though the military undertaking the repression
the size and composition of government spending.
public goods.
may
to take place along the equilibrium path. In this case, nondemocratic regimes
not an agent of the
An
pay high wages to
elite
to be nondemocratic (because
it fails
rises
to transition to democracy).
dictatorships in Central and South America, which have resulted from coups against de-
may be thought
of as being of this type.
These examples are further discussed
in
Section
6.
^Examples
of military dictatorships that have resulted from coups against oligarchic/nondemocratic regimes
include the majority of the mihtary regimes that have emerged in Peru between the 1820s and the 1930s, the
army-backed regime created in Thailand after the 1932 coup that ended the rule of the Thai absolutist monarchy,
the regime created in Egypt after Major Nasser's coup against the monarch,y, and the junta in Panama in 1968
that followed the coup by the National Guard under the leadership of Omar Torrijos.
In this case, the level of taxes and the amount of government spending depend on the nature
of the nondemocratic regime.
If it is oligarcliic,
taxes and spending are low. However,
a military dictatorship, then taxes and government spending are high, but
is
on the military
We
all
if it is
of this spending
—not on public goods.
then enrich our baseline model by introducing natural resources.
Natural resources
increase the political stakes because soldiers realize that they will be able to capture the natural
resource rents
more
if
they take power. As a result, natural resource abundance makes democracies
The
likely to fall to military coups.
On
ambiguous, however.
repression and
military.
On
may be
effect of natural resources
on oligarchic regimes
is
the one hand, the oligarchic regime has a stronger preference for
able to use the income from natural resources in order to
the other, the military
is
more tempted
buy
off
the
to undertake coups against the oligarchic
regime.
Our
baseline
model abstracts from the national defense
only use of military coercion
is
role of the military, so that the
domestic pohtics. At the end of the paper, we also use our
in
model to investigate a potentially important interaction between international and domestic
In particular,
politics.
zation.
Somewhat
we
investigate the national defense role of the military on democrati-
paradoxically,
we
defense, democratic consolidation
find that
when
becomes more
the
likely.
army
is
more important
The reason
of an international role for the military, the citizens are unable to
strong military.
credible,
The presence
of international threats
that, in the absence
commit
makes the promises
because democracy also needs the military, and
The two
is
facilitates
for national
to maintaining a
of the citizens
more
democratic consolidation.
building blocks of our approach are that the military should be considered as
a potentially self-interested body
—or
in fact, a collection of self-interested individuals
— and
that there should be a distinction between nondemocratic regimes controlled by the economic
elite ("oligarchies")
and military dictatorships. Both of these receive support from the qualita-
self-interest of the
torships,
army
emphasized
by,
are
major themes
among
The
self-interest of soldiers
and the corporate
of the political science literature
on military dicta-
tive evidence in the political science literature.
others. Finer (1976), Nordilinger (1977)
and Needier (1987).^
^This contrasts with existing models of democratic transitions or coups, such as those in Acemoglu and
Robinson (2001, 2006), where the miUtary is assumed to be a perfect agent of the ehte. This same perspective
is often adopted in political science and sociology literatures with Marxian foundations (e.g., Moore, 1966,
Luebbert, 1991). For instance, Barrington Moore's (1966) classic work suggests an explanation for divergent
paths of pohtical development in terms of different types of class coalitions. The possibility that any state
apparatus, including the army, may have some independent role as a coalition partner, is ignored. Subsequent
contributions inspired by Marxian approaches, including work by Poulzantas (1978) and Skocpol (1979), pay
greater attention to the "agency" of the state, but do not focus on the role of the military in politics nor note
Nordilinger (1977 p. 78), for example, argues that
"The great majority
of coups are partly, primarily, or entirely motivated by the
defense or enactment of the military's corporate interests."
Similarly, Needier (1987 p. 59) observes:
the military typically intervenes in politics from a combination of motives
"...
which defense of the institutional
in
interests of the military itself predominates,
although those interests are frequently construed so as to be complementary to the
economic interests of the economic
The
distinction
elite."
between oligarchic regimes and the military dictatorships
in a large political science literature (see for
references there). Huntington (1968)
example the survey
and Finer
also well rooted
in Brooker, 2000,
and the
(1976), for example, emphasize the prevalence
of authoritarian elite-controlled regimes supported
oligarchic regimes,
is
by the
military,
and contrast these with military dictatorships.
which are similar to our
Examples
of the former
include the dictatorship that Getulio Vargas established in Brazil in 1937, which was a mainly
civilian authoritarian regime, relying
on the support
of the military for its political survival,
and other Central and South American regimes formed
discussion in Section 6 below).
in the Philippines
his
More
at roughly the
same time
(see also the
recent examples include Marcos's long lasting regime
and President Fujimori's regime's
in Peru,
which was established following
de facto coup to extend his rule and powers beyond their constitutional
limits.
Both
of
these regimes were backed by the army, but the military establishment did not have important
decision-making powers.
Perhaps more
common in practice
of officers are in direct control.
(2000),
Welch and Smith
are military dictatorships,
Such military dictatorships are studied
(1974), Perlmutter (1977, 1981),
examples include the regimes established
Muhammad
after the
where the mihtary or a subset
in
in detail
by Brooker
Nordhnger (1977).* Contemporary
Pakistan by General
Ayub Khan, by General
Zia-ul-Haq and by General Pervez Musharraf, the regimes established in Turkey
coups in 1960, 1971 and 1980, in Guatemala after the coup of 1954 under the leadership
Carlos Catrillo Armas, in El Salvador in 1956 with Oscar Osorio's government, in Brazil after
we emphasize here.
'a hybrid regime type, "bureaucratic
the interactions
authoritarianism," based on a coalition between the military and the
economic elites, whose primary goal is the promotion of economic modernization, has also been identified by
O'Donnell (1973). The practical applicability of this concept has appeared quite limited though, and we do not
pursuit
it
in this paper.
the overthrow of President Joao Goulart's government in 1964, and in Greece after the military
coup of 1967. The miUtary has also been the dominant
political force in
1932 coup and has repeatedly intervened in pohtics whenever
power by nascent
Our paper
is
it
Thailand since the
perceived a threat to
its
own
civilian political institutions.^
a contribution to a number of distinct literatures.
First, there
is
now a
substantial literature on political transitions, but to the best of our knowledge, no paper in
this literature
models the relationship between the
elite
Robinson, 2006, for an overview of this literature).
and the military
(see
Acemoglu and
Consequently, this literature does not
distinguish between oligarchic regimes and military dictatorships discussed above.
Second, there
is
a large literature on political agency in democracies, where citizens try
to control politicians using elections
and other methods
(e.g.,
Barro, 1973, Ferejohn, 1986,
Besley and Case, 1995, Persson, Roland and Tabellini, 1997, 2000, Acemoglu, 2005, Acemoglu,
Golosov and Tsyvinski, 2008, Alesina and Tabellini, 2007; see Persson and Tabellini, 2000 and
Besley, 2006, for surveys).
In contrast, the potential agency relationship between the
and the military has not been modeled. In
this regard, the literature
nondemocratic regimes and other aspects of agency relationships
elite
on the organization of
in dictatorships
is
closely
related to our work.
This area includes the early important work by Wintrobe (1998), as
well as recent papers
by Acemoglu, Robinson and Verdier (2004), Egorov and Sonin (2004),
Dixit (2006) and Debs (2007a,b) focusing on nondemocratic agency relationships. These works
neither address the issue of controlling the military nor provide a framework for thinking about
the emergence of military dictatorships.
which studies the
The only exceptions
effect of the organization of the military
are Ticchi and Vindigni (2003),
on the consolidation of democracy,
and recent work by Besley and Robinson (2007), which investigates the relationship between
the military and civilian governments, though focusing on a different set of questions than our
paper.
Third, the recent literature in comparative politics of public finance
and
Tabellini, 1997, 2000, Persson
types of democratic institutions on
(e.g.,
Persson, Roland
and Tabelhni, 2003) investigates the influence of
fiscal policy
different
and economic outcomes, but does not inves-
(somewhat more speculative) interpretation to the possibilitj' of
where the elite allow a powerful military
to form but do not take steps to prevent coups can be viewed as an implicit support for military dictatorships
by the ehte. An example of this is the experience of Peru in the early 1930s. The raise of the Alianza Popular
Revolucionaria Americana (a violent revolutionary movement) led the Peruvian elites to support a coup d'fetat
by Colonel Sanchez Cerro. Roquie (1987 p. 115) describes this as follows: "The ruling classes that had long
been civilian in their orientation put aside their distrust of the military and supported the colonel's coup. The
massacres in Trujilio in 1932 involving the army and the APRA were to establish a long-lasting defensive alliance
between the military and the upper bourgeoise."
^It
is
also possible to give a slightly different
non-prevention
in oligarchy.
According to
this interpretation, the case
tigate the impact of different types of nondemocratic regimes,
and
in particular, the contrast
between ohgarchic regimes and miUtary dictatorships. Our paper adds to
modehng
the impact of different types of nondemocratic institutions on
nomic outcomes. In
fiscal
policy and eco-
particular, a distinctive implication of our theory in this respect
nondemocracies should typically have more military spending than democracies.
mentioned above, there
Finally, as
dictatorships,
though
is
approach
it
is
that
^"^
a substantial political science literature on military
this literature does not provide formal
the military and the ehte, nor does
by
this hterature
it
models of the relationship between
an agency problem. Some of the important
as
contributions in this literature have been cited above.
The
rest of the
3 characterizes the
results.
paper
organized as follows. Section 2 presents our basic model. Section
is
Markov
Perfect Equilibrium in this environment and presents our
main
Section 4 shows that the equilibria characterized in Section 3 are also the subgame
perfect equilibria.
of Section
Section 5 presents a
number
of extensions of the baseline environment
including an analysis of the implications of natural resources and international
2,
some
threats on oligarchic and democratic equilibria. Section 6 illustrates
of the
main
ideas of
our analysis with a brief discussion of the emergence and consolidation of democracy and the
role of the military in Central
America. Section 7 concludes, while the Appendix contains the
proofs omitted from the text.
2
Basic
Model
In this section,
we
We
describe the economic and political environment.
horizon economy in discrete time with a unique
maximizes
final
good.
consider an infinite
Each agent
j at time
=
t
oo
Eo^/3*(c,, + x,-,A),
(1)
t=0
where Eq
terms of the
is
the expectation at time
is
final
good, Gt
>
is
the
t
=
0, Cj^t
amount
>
denotes the consumption of the agent in
of public
good provided
at
time
t,
and
Xj,t
G
{0, 1}
an indicator function denoting the occupational choice of the agent. This variable determines
whether or not the individual benefits from the public good.
The
total population of the society
and can produce A^
>
0,
.
is
normalized to
1.
Of those
1
—n >
1/2 have low
skills
while the remaining n agents are highly skilled and can produce
A^ > A^ We will often refer to the
'"This result
is
(rich) high-skill
agents as the "elite" since at the beginning
consistent with the evidence presented in Mulhgan, Gil and Sala-i-Martin (2004), which finds
that nondemocratic regimes spend
more on the military than democracies.
they will be in control of the political system, and we
"citizens."
There are two occupations: producer and
we use the
subscript j E {L,
M, H}
high-skill producers. Soldiers
A^
or
depending on their
will refer to low-skill
soldier.
With a
slight
agents as the
abuse of notation,
to also denote low-skill producers, military (soldiers)
do not produce any output, while producers generate income
To
skill level.
simplify the analysis and reduce notation,
throughout that only low-skill agents can become
Furthermore, we also assume that
Xj,t
=
soldiers.
1 for j
and
A^
we assume
^^
= L and
Xj,t
=
otherwise. This implies
that only production workers benefit from the public good, for example, because the public
good corresponds
to services that rich agents
and the military receive through other means
(such as health care or schooling) or because the public good
is
associated with roads and
other infrastructures mostly used by low-skill production workers. This assumption
to simplify the expressions
The
and has no
size of the military at
time
necessary for national defense to
politics. In particular,
size of the military
at time
thy
at
£
for
denoted by
at
at
—
I
Xt-
We
results.
normalize the size of the military
thus the only reason for xt
We
is
repression in domestic
G {0,x}, where S >
xt
is
denote the decision to have (build) an army
corresponding to xt
G {Oil}, except that, as
>
one of two values,
xt takes
necessary for repression.
with
on our qualitative
adopted
—
x.
The government
be described below,
will
it
(social
may
group)
take a while
a newly-emerging democracy to be able to reform (disband) an already-existing army by
choosing
We
is
we assume that
{0, 1},
power chooses
in
0,
t
effect
is
also
at
—
(that
is,
there will be further constraints on the choice of at in democracy).
assume throughout that
X
<
1/2
-
n,
(2)
so that low-skill producers are always the absolute majority in the population. This imphes
median voter
that, given the policy instruments specified below, in majoritarian elections the
will
always be a low-skill producer.
Aggregate (pre-tax) output at time
Yt
where
is
i/Jj
G {1
—
cp,
t
will
be
= ipt{{l-n-
xt)
A^ +
1} captures potential distortions
7iA^)
from coups with
no coup atteiupt (against oligarchy or democracy), we have
a coup attempt, a fraction
''This
is
cp
of production
natural, since military wages are
is lost
(3)
,
(pt
=
is
recruiting,
more attractive to
though we do not do
G
(0, 1).
Instead,
When
when
there
there
is
due to the disruption created by the coup,
low-skill
than to high-skill agents. We could
is greater than those of soldiers
introduce an additional constraint to ensure that the income of rich agents
whenever the military
1-
(f)
so to simplify notation.
thus
=
(fit;
—
1
<
(j)
1.
Let us also denote
Y = {l-n)A'^+7iA^,
which
as the potential output of the economy,
to
will
(4)
apply when the
size of
the military
is
equal
to raise revenue for public
good
and there are no disruptions from coups.
Aggregate output can be taxed at the rate
provision and to pay the salaries of soldiers.
C (r^) Yt)
We
G
[0, 1]
model the distortion of the
manner: when the tax rate
in a simple reduced-form
(thus a total of
Tt
will
be
lost
is
a fraction
Tt,
costs of taxation
C (rt)
of the output
due to tax distortions. These may result from distortions
resulting because taxes discourage labor supply or savings, or because of the administrative
when
costs of collecting taxes. This fiscal technology implies that
government revenues per unit of production
will
the tax rate
is
equal to
be
rt-C{Tt).
We
assume that
C
:
— M+
»
[0, 1]
is
(5)
a continuously differentiable and strictly convex function
that satisfies the following Inada conditions (which will ensure interior solutions): C(0)
(so that there are
define f £
(0, 1)
no distortions without taxation), C"
as the level of taxation at
of the Laffer curve)
,
which
is
which
fiscal
(0)
=
and C"
(1)
>
1.
revenues are maximized
=
Let us also
(i.e.,
the peak
uniquely defined by
T^{C')-\l),
where (C")~
between
is
and
1
Tt,
the inverse of the derivative of the
C
(6)
function.
This tax rate f
is
strictly
because of the Inada conditions.
Finally, without loss of
any generality, we parameterize
A^ =
A^ and A^
as
i^r
and >1^ = -y,
—n
n
(7)
1
for
some
9
G
We
inequality.
(n, 1).
This parameterization implies that a higher 9 corresponds to greater
do not make the dependence of
A^ and A^ on
9 explicit unless this
is
necessary
for emphasis.
We
will
(citizens)
represent the
and the
elite.
economy
as a
dynamic game between
soldiers, low-skill
producers
As explained further below, given the policy instruments, there
conflict within the groups, so
we can suppose without any
loss of generality that
is
no
a representative
agent from each group
(e.g.,
commander
the
of the army, a decisive voter in democracy, or a
representative agent in oligarchy) makes the relevant policy choices. ^^
In principle, there are two state variables in this game.
The second
military from the previous period, xt-\ 6 {0, x}.
which takes one of three values, democracy D, oligarchy
St,
size of the military
The
is
first
one
the size of the
is
the political regime denoted by
M. The
E, military
(elite control)
from the previous period, X(_i, only matters because immediately following
a transition to democracy (without a coup attempt)
government to choose
=
at
and reform the
may
it
not be possible for the democratic
military. Instead,
we assume that they
have
will
to wait for one period before being able to reform the military. This assumption captures the
once a large army
realistic featirre that
is
new and
in place, a
government may not be able to disband the army immediately. The
period for
to be able to do so
it
is
weak democratic
potentially
fact that
only for simplicity and in subsection
it
5.3,
takes only one
we consider the
case where the opportunity to reform the military arises stochastically.
This structure simplifies not only the analysis but also the notation. In particular, instead of
carrying xt-i as a state variable
TD, which
occurs
and only
if,
we can
if,
X(_i
democracy
define an additional regime, "transitional"
=
=
x, st-i
E, and there has been no coup attempt.
Loosely speaking, transitional democracy corresponds to a situation in which the majority (lowproducers) have de jure political power but this
skill
power of the
=
at
is
military.
The only
not possible.
followed by St+i
St
gS =
Key
>
0,
= M.
=
D, unless there
Given
policy decisions are
wage
In addition to
i>t
G
G
[0, 1]
for soldiers,
at, Tt,
{0, 1},
'"Alternatively,
all
and
st
—D
is
that with
a successful military coup,
we
= TD,
st
is
in
= TD
is
in
which case
it
St
represent the state of the dynamic
made by the government
with
in power.
on the income of the producers, the
Wt
game
>
0,
The
policy decisions are a
level of public
and the decision regarding the
good provision,
army,
size of the
at
6
{0, 1}.
Gt and Wt, the military (the military commander) decides whether or not
ipf.
=
1
whether or not to repress the
racy
is
this description,
to undertake a coup against the regime in
by
= TD
{D,E,M, TD}.
linear tax rate Tt
Gt
st
Otherwise, in both regimes, a representative low-skill producer
immediately followed by st+i
by
between
constrained by the de facto political
Since in our baseline model transitional democracy lasts for one period,
power.
is
difference
is
power
(if
the military
is
corresponding to a coup attempt, and,
citizens in oligarchy,
we could consider a
which
citizen-candidate model
(e.g.,
is
active),
if V't
denoted by
Pf
6
0, it also
{0, 1},
elite vote.
but the analysis requires additional notation.
10
is
denoted
decides
with
Pt
—
I
Beslcy and Coate, 1997) in which in democ-
agents vote, in military only the soldiers vote, and in oligarchy only the rich
this case are identical to those presented below,
—
which
The
results in
corresponding to repression.
In addition, individuals should have a decision of whether to
apply to an army position and also soldiers should have a decision to quit the military. Both of
these decisions translate into a participation constraint that the value to a low-skill agent in the
military should be higher than the value to a low-skill producer. Assumption
that this
is
1
below ensures
always the case and to simplify notation, we do not introduce these additional
decisions explicitly. ^^
=D
particular, st+i
smooth
up a
at
—
0),
1
following
transition, there
is
=
St
then there
0,
is
a smooth transition to democracy, in
E. The important point here
is
if
in oligarchy, the military
pj
=
so that there
1,
the elite choose
an
is
and
effective military
it
demands
= TD.
Therefore,
[0,1].
of the military repression, with
the case in which the repression of the democratic
st+i
is,
Finally,
if
chooses to repress the citizens,
then transition to democracy takes place with probability n e
an inverse measure of the effectiveness
set
present but chooses not to repress
is
then the regime transitions to transitional democracy, that
and
when
that
no transitional democracy since the oligarchic regime has not
In contrast,
military.
=
(/Oj
=
oligarchy the elite choose at
If in
tt
=
n represents
corresponding to
by the military
of the citizens
is
fully effective.
We
both
also
cases,
assume that when the military attempts a coup against
is
denoted by
i/'t
=
1, it
= M,
then a military dictatorship, sj+i
s
=
M
is
= D will
st+i = D
st
we immediately have
is
i
+
St
1;
= TD,
if,
To
emerges.
on the other hand,
is
=
St
E, then the
of opportunity resulting
only arises following failed repression.
If
automatically consolidated (and thus
between the army and the
suffers
a military coup
regardless of the regime at time
coiiflict
if
t\
fails,
then
the regime at time
between the military and the
from the
failure of the
military. This description therefore implies that the transitional
—
a coup ever succeeds
elite
s
there
=
is
no repression, there
D), and
if
there
is
In other words,
loss
it
never a best response
will
and
</?(
=
coup to reform the
democracy regime,
is
s
— TD,
no army, so democracy
a coup attempt, then the conflict
enables the emergence of consolidated democracy (and thus,
D). Finally, recall that when the military attempts a coup
an income
elite
no effective repression and a democratic regime emerges immediately
and can use the window
again, s
if
if
we assume that
then the transitional period will be over and the army will be reformed at
implies that there
is
the coup succeeds,
simplify the analysis,
be absorbing). However,
also
If
(0, 1).
absorbing, so the society will remain as a mihtary dictatorship
(and in equilibrium,
t
succeeds with probability 7 6
either regime, which, in
1
—
(/>
<
1 in
equation
always be a best response
11
=
1),
the society
(3).
for low-skill
for soldiers to quit the military.
{tpt
producers to apply to the military and
it is
Throughout we adopt the convention that
even
there
if
is
fiscal
poUcies enacted at time
are implemented
t
regime change and the new regime starts enacting policies from
Moreover, the military wage Wt announced by any non-military regime
repression and no coup attempt. These wages are withheld
The government budget
constraint at time
wtXt
aggregate income at time
where Yt
is
from the
linear tax Tt,
t
if
there
is
is
t
+
l
onwards.
conditional on both
a coup attempt.
can therefore be written as
t
+ Gt<iTt-C{Tt))Yu
given in
and the left-hand
side
(3), (tj
is
(8)
- C (ti))
Yt
is
total tax revenue resulting
the total outlays of the government, consisting
of public good expenditures, Gt, and spending on the military, wtXt-
We now
variable
1.
st
summarize the timing of
At time
events.
t,
the economy starts with the state
6 S, which determines the group in power.
Unless
St
= TD,
the group in power chooses at G {0,1} and announces a
vector {rtjWtjGt) that satisfies the government budget constraint
at—1
2.
and the group
In oligarchy,
if
there
in
power only chooses {Tt,wt,Gt).
is
no military
consolidated democracy and St+i
3.
When
Xt
=
x, in
democracy and
or not to attempt a coup
probability
tpt
=
If
& {0,1}.
repress, then st+i
5.
If
0),
=
repression
0,
—
=
is
then there
= TD,
then
a transition to fully-
is
is
commander
attempted,
established (and St+i
it
decides whether
is
successful with
— M).
If
a coup
fails,
D, emerges next period.
x),
then
fails
a coup
If
7 and a military dictatorship
the elite have formed a military (xt
citizens, pt
—
in oligarchy, the military
e {0,1}.
and does not attempt a coup Vt
xt
policy
D.
a consolidated democratic regime, St+i
4.
=
[at
If St
(8).
fiscal
then st+\
it
=
D.
also decides
(probability
tt)
or
If
the military remains active
whether or not to repress the
if
the military chooses not to
— TD.
Taxes are collected and wages are paid according to the announced policy vector {Tt,wt, Gt)
if
there
is
no military coup attempt.
If
there
is
such an attempt, then wt
=
0.^'*
timing of events makes it clear that when a particular vector of policies, (rt, u'l, Gt),
announced, it is not known for sure whether this will satisfy the government budget constraint, (8), because
there might be a coup attempt reducing income and tax revenues, and also removing the burden of military
expenditures. In such cases, we assume that the amount of public good provision, Gt, is the "residual claimant,"
so that if {Tt,Wi,Gi) docs not satisfy (8) as equality, Gt adjusts up or down to ensure this.
'""This description of the
is
12
.
Finally,
with
we assume that the
=
a:_i
society starts with s
=
E,
an oligarchic regime, and
i.e.,
=
so the elite are free to either form a military of size x or leave xq
0,
also
in the
initial period.
Characterization of Equilibria
3
We now
characterize the
section.
Markov
Section
4,
Markov
in the previous
Perfect Equilibria are both simple and natural in the current context.
we show that
of om- results generalize to
all
Subgame
In
Perfect Equilibria.
Definition of Equilibrium
3.1
We first
focus on pure strategy
the dynamic
be the
H^'''
Markov
game described above up
set of
state variables, here
€
fcf
to time
t
MPE
is
on the entire
MPE
is
a natural equilibrium because
present in a very similar fashion
formally, let
i^*''^.
and
let
Markovian
on the payoff-relevant
history, condition only
it
we
when we
/i**'^
G
H^'''.
will see that the
focus on
for
:5x/C-^
In the context of the
subgame
xE^
[0, 1]
game
commitment problems
directly introduces the
same commitment problems
are
perfect equilibria.
be a Markovian strategy mapping, that
cr
cr
which assigns a value
historj' in
t,
defined as a set of Markovian strategies that are best
that are central to our analysis. However,
More
denote the history of
and stage k of the stage game of time
responses to each other given every possible history
here,
h*'^
6 S, and on the prior actions within the same stage game, denoted
st
Consequently, a
/C.
(MPE). Let
Perfect Equilibria
such histories. Strategies assign actions for any
strategies, instead of conditioning
by
game described
Perfect Equilibria of the
is,
X {0,l}^
each of the actions, the tax rate tj e
[0, 1],
the military wage wt G R+,
the level of the pubhc good Gt G M+, the decision of whether to create or reform the military
at
G
for
{0, 1},
each value of the state variable
given by
j-i^t,k
and the coup and repression decisions of the
g
/C.
//*.*;.
An MPE
is
S and
is
To characterize the dynamics
induced by the
MPE
st
1p^
G
conditional on
a best response to
itself at
of political institutions,
its
(st
I
st-i)
-.SxS
and
pt
G
{0, 1},
every possible history
we
define the one-step
past value and the limiting distribution of s
strategy profile a* as
p
{0, 1}
each combination of prior moves in the stage game
a mapping a* that
transition probability of
military,
-^[0,1] and g
13
(s)
:
5
^
[0, 1]
These concepts
will
be useful
in describing
how regimes change
and what the
in equilibrium
likelihood of different regimes are in the long run.
We
next proceed to characterizing the
MPE
by
first
determining (the net present
dis-
counted) values of different individuals (groups) under different regimes.
Values in Democracy
3.2
Let us start with the values of the three groups in democracy,
are
made by
=
st
D. Decisions
in
democracy
majoritarian voting and the median voter will always be a low-skill producer.
This implies that democracy
will
be an absorbing state as long as
future periods, and clearly, aj
=
is
democracy. In view of
this,
=
a^
chosen in
is
all
always a dominant strategy for a low-skilled producer in
we obtain the
Y
following proposition (recall that
is
defined in
(4)).
Proposition
1
The unique
democracy) involves
tax rate
t^
is
[at
=
MPE
0,Tt
—
starting in
—
T^,wt
any subgame with
— G^)
-jGt
s
— D
at each date
t,
(i.e.,
a consolidated
where the democratic
given by
r^^{Cr'{l-^),
and the
level of public
good
is
(9)
given by
G^ = (r^-C(r°))F.
Moreover, consolidated democracy
Proof.
Clearly, the
an absorbing state so that
is
median voter
is
p{D D) =
\
democracy would never choose
in
would reduce the tax base and potentially create a coup
democracy
(10)
tlireat against
1
and q [D]
at
=
1,
~
1.
since this
democracy. Therefore,
an absorbing state and the optimal policy can be characterized by the solution
to the following static maximization
problem
max
u'^(D)=
(1
-
t)
A^ + G
(11)
r6iO,l],GeR+
subject to
G<
Given the Inada conditions and the convexity
first-order condition of this
of
- C (r)) Y.
C (r),
(11) has a
unique interior solution. The
problem then gives the unique equilibrium tax rate
corresponding level of public good as
The
(r
(10).
values of low- and high-skill producers are then given by
14
as (9),
and the
.
and
Here and throughout,
D
denote the identity of
"values," that
The
tlie
Af or
TD)
in parentheses denotes the regime, while superscripts
V
u denotes per period returns and
In addition,
agent.
denotes
the net present discounted values.
value of an ex soldier in this regime
now work
will
is,
(or £,
as low-skill producers.
a^
At
=
also
is
this point,
(1
V^' {D)
it is
= V^
[D), since former soldiers
also useful to define
- r^) A^ + G^
(14)
as the net per period return to a low-skill producer in democracy. This expression will feature
frequently in the subsequent analysis.
Finally, recall that according to our parameterization
evident that
is
r^ does not depend on
due to the well-known
linear taxes (e.g.,
A^ =
[1
— 9)Y/
[\
Y and is a strictly increasing function of 9.
effect of inequality
on redistribution
in
—
n)
.
This
then
It is
last result
models of majority voting on
Romer, 1975, Roberts, 1977, Meltzer and Richard,
1981).
We
note this as a
corollary for future reference (proof omitted)
Corollary
1
The democratic tax
inequality parameterized by
3.3
t^
,
given by
(9), is strictly
increasing in the extent of
0.
Values under Military Rule
A
military regime, s
xt
G
= M,
{0, S}, the military
disbanding
this
rate
itself
can only occur when xt
=
x and
it is
government has no option to change the
(and obviously
it
an absorbing
state.
size of the military
would not want to expand the military even
if it
Since
without
could, since
would imply dissipation of the rents captured by the military among a greater number of
soldiers).
Consequently, the military government wall simply maximize the utility of soldiers
Moreover, we assume that there
subject to the government budget constraint.
is
a natural
seniority system in the military, so that current soldiers are not fired in order to hire
applicants. Then, provided that the participation constraint of soldiers
current soldiers will remain in the
in state
M the military can never
army
lose
forever
is
satisfied (see below),
and receive the military wage.
power, this problem boils
down
Finally,
to that of
because
maximizing
the static utility of a representative soldier subject to the government budget constraint.
15
new
At
this point, consider the
maximization problem of the military government. This takes
the form
u^(M)=
max
w
(15)
TG[0,l],ujeM+,G6R+
towx + G
subject
where the objective function incorporates the
good
(i.e.,
=
XM,t
f defined in
{Y - xA^)
fact that soldiers
r does not feature
in (1)). Since
(15) involves taxing at rate
<{t-C (r))
(6) to
wage
of w^'^ given
do not benefit from the public
in the objective function, the solution to
maximize tax revenues (thus maximizing the
—
constraint set) and also setting to zero the public good, Gt
soldier
,
This generates a unique per
0.
by
X
where
Y
again denotes the potential output defined in
government
as possible
is
in
and
power
it
undertaking a coup
which
is
a^ (which
will
is
ensure
is
tax rate f extracting as
is
the one where tu^
an attractive option
this.
much revenue from
the producers
proceeds to the soldiers. As noted above, the interesting
will redistribute all the
case for the current paper
1,
will set the
Evidently, as long as the military
(4).
is
high that entering the military and
sufficiently
We
for low-skill producers.
next impose Assumption
Recall that the per period utility of the low-skill agents in democracy
simply a function of the underlying parameters, given by
defined uniquely in (9) and (10)).
The
(14),
following assumption ensures that
with
w^
is
r^ and G^
sufficiently
greater than a^ so that the participation constraint of soldiers (of being in the military both
during military dictatorships, democratic regimes and oligarchies)
Assumption
is
always
satisfied.
1
7 >
-3-737—3
^7.
In particular, this assumption immediately implies that the expected value of a coup for
soldiers
is
always greater than the value of a low-skill producer in permanent democracy, that
is,
V^^ (coup)
which
tion
is
1 is
7 >
stating
sufficient to
=p
[jV^^ (M)
-f (1
-
7)
V^
{D)]
guarantee the participation constraint in
> V^ {D)
all
,
regimes. Note that
Assump-
not very restrictive. For example, as the size of the military, x, becomes small, any
satisfies this
assumption.
We
maintain Assumption
it explicitly.
16
1
throughout the paper, without
,
The
following proposition describes the equilibrium under a military rule (proof omitted).
MPE in
Proposition 2 The unique
any subgame starting with
—
ship) involves the following policy vector at each date: r^^
Moreover, military dictatorship
w^'' given in (16).
and starting with
s
M
—
Given the unique continuation equilibrium
values for individuals
who
are currently
for high-skill elite agents are given
(i.e.,
f as defined in
military dictator(6),
G^ =
=
\
and
0,
M) =
1
1.
and
of the military, for low-skill non-military
by
'
^
M
in Proposition 2, the (net present discounted)
members
yM (M) = l^^lm =
1-^ ~
^
=
an absorbing state so thatp{M
is
any point, we have q (M)
at
s
ir-C
^_
1-/?
(y - x^^)
(f))
^^''
'
X
-^^ ^ l^'
(M) =
^^^^
and
Notice that the expressions for u^ (Af ) and
becoming a
of low-skill producers
would
like to
become a
V^ (M) do
This
soldier.
not include a term for the option value
because even though each low-skill producer
is
=
not be hiring any more soldiers, since xt
soldier, the military will
x
already and there are no quits from the army.
Values in Transitional Democracy
3.4
We now
regime
turn to the analysis of transitional democracy, where
will
emerge when st^i
Moreover, this regime
fails at this point,
is
=
—
E, xt-i
indeed "transient"
then Si+i
=
D, and
if
;
x, Pi_i
there
if
there
is
St
= TD.
Recall that this
—
1
is
no coup attempt or the coup attempt
and repression
fails
(probability
a successful coup attempt, then st+i
depending on the subsequent regime, either the equilibrium of Proposition
Clearly,
of Proposition
1 will
apply.
We now
investigate policy choices
tt).
— M.
2 or that
and the reaction of the military
during the transitional period.
Suppose that the democratic government during the transitional period has announced the
policy vector [t^^,w'^^,G'^^), and to start with, let us ignore the participation constraint of
soldiers,
Now
if
soldier
which ensures that they prefer not to quit the military
the military chooses Vt
=
(that
(will
return to this below).
no coup attempt), then the value of a typical
is,
is
V^'^
{TD no
I
coup)
= u;™ +
17
(3V^ {D)
(20)
.
which incorporates the
do not receive
utility
fact that the soldiers will receive the military
We
from the public good.
value to the soldiers, which, from Proposition
= V^
consolidated democracy V^' {D)
have also substituted
and equation
1
=
t/'^
the value of a soldier
1,
V^^ {TD
coup)
=
receive the
{M)
low-skill
as in (17)
is
(cf.
given as the value in a
former soldiers
all
V^
(iW)
+
-
(1
will
(D)]
at the
become
(21)
,
the military undertakes a coup, the soldiers do not
Following a successful coup,
7.
established and the continuation value of the soldiers
Proposition
1,
{D).
V^
7)
wage w'^^ and the coup succeeds with probability
a military dictatorship
V^'^
when
fact that
the continuation
is
[7^^
/3
I
which incorporates the
for
{D). In particular, in Una with Proposition
low-skill producers, accounting for the continuation value of
if
is
(12),
next date the government will choose to reform the army and
In contrast,
wage w"^^ today and
the coup
If
2).
fails
(probability
1
—
is
given by
7), soldiers
become
producers and simply receive the continuation value of the low-skill producer in a
consolidated democracy, V'^ {D) as in (12).^^ Comparing these two expressions,
we obtain the
no-coup constraint:
V^ [TD
Using (20) and
(21), the
no coup) >
I
w^'^
is
\
coup)
(22)
no-coup constraint can be written as
w^'^
where
V^ {TD
^7
>
{u^''
-
a")
(23)
,
defined in (16) and a^ in (14). Constraint (23) defines the
minimum
military
wage
that democracy must offer to soldiers in order to prevent a coup attempt. In what follows,
will use
w'^^ for the
and t"^^
wage
for the
"transitional prevention"
(
corresponding tax
for the military to induce
Clearly, this
rate.
them
)
wage that makes
This wage
level
can be thought of as an efficiency
is,
not to undertake a coup).
of the coup 7,
and the gap between the
value that soldiers will receive in a military dictatorship, V'^
value in democracy,
The question
is
V^
whether
^
There
no
(1
—
will
satisfy the
depend on two
ly^^/ (1
this
—
factors.
minimum
The
government budget constraint,
desirable for low-skill producers to
differential taxation or further
=
and
their
military
wage
/?),
/?).
coup attempt. This
pay such a wage (and
it is
is
— a^/
(M)
whether a democratic government would pay
in order to prevent a
feasible to
{D)
this constraint hold as equality
to take the right action (that
wage depends on the success probability
we
pay
this
wage.
The
(8)).
whether
it is
The second
is
feasibility condition requires
punishments that are possible on former
18
first is
soldiers.
minimum wage
this
can be raised, that
times the number of soldiers to be
than the
maximum
revenue that
is,
w'^^x
The right-hand
less
side
is
<{t-C (f))
maximum
the
(y - xA^)
(24)
.
revenue that can be raised, since
it
involves taxation at
the revenue-maximizing rate f and the tax base consists of the entire population except the x
soldiers.
<
w"^^
Using the expression
lu^^. Alternatively,
constraint, (24),
w^^
using the expression for
satisfied
is
for ly^^ in (16), the condition (24)
if
and only
from
can be seen to be equivalent to
(23),
we
find that the feasibihty
if
w^^
-/3
1
7<
.
^7-
..,A./_,L
This condition states that preventing a coup attempt
is
(25)
feasible only
if
7
is
than some
less
Otherwise, only very high wages will discourage soldiers from attempting
critical threshold 7.
a coup and such high wages cannot be paid without violating the government budget constraint.
Note
also that
Assumption
Next, suppose that
low-skill producers to
coup? To answer
satisfied
it
1
pay
this
this question,
—and compare the
pay the necessary
7.-^''
wage or
is
them
better for
it
.
beneficial for
Is it
to face the risk of a military
suppose that a wage of w'^^ can indeed be paid
low-skill producers' utilities
no coup)
=
(l
I
—
(25)
When
under the two scenarios.
- r^^) A^ + G^^ +
i.e.,
is
they
is
I3V^ [D)
(26)
,
the utility-maximizing tax rate for the low-skill producer subject to the no-coup
is
constraint, (23),
and
G^^ >
the transitional phase.
is
the utility-maximizing level of public good spending during
Alternatively,
if
there
democracy, the value of a low-skill producer
V^ {TD
<
efficiency wage, the value of low-skill producers
V^ {TD
where t^^
thus 7
democracy to pay the wage w^^
feasible for
is
< w^^ and
ensures a^
coup)
I
-
(1
- T™)
since in this case there are no
-(t>)A^
fact.
no coup prevention during the transitional
is
+
G™ +
payments to the
utility-maximizing policy choices
expression incorporates this
(1
is
/3
military,
when coup attempts
Current output
is
(1
-
7)
V^
(£>)]
(27)
,
and now t"^^ and G'^^ denote the
are not prevented. ''
a fraction
'"This also implies that the participation constraint of soldiers
+
[jV^ (M)
1
—
in this case,
The
rest of the
of potential output (4)
V^' (TD) > V^ (D),
is
always
satisfied.
''The
full
maximization program when the
proof of Proposition
low-slcill
producer chooses not to prevent coups
3.
19
is
given in the
.
because of the disruption caused by the coup attempt and there
coup
and the regime from tomorrow on
successful
is
V^ (M)
Now
to the representative low-skill producer.
we obtain
will
is
a probabihty 7 that the
be a military dictatorship, giving value
combining the previous two expressions,
that a low-skill producer will prefer to prevent coups during transitional democracy
if
V^ {TD no
coup)
>
{TD
V'^
I
The next
proposition shows that whenever (25)
is
\
coup)
(28)
satisfied, (28) is also satisfied, so that
coups against democratic governments are always prevented when prevention
Assumption
1 is
assumed
Proposition 3 Let 7
s
— TD
• If
is
to hold throughout, thus
be defined by (25).
J G
[7,7], then the transitional
military
is
MPE in
7 >
7.
any subgame starting with
At the next
date,
= D
s'
(i.e.,
p{D TD) =
1),
\
the
implemented. The long-run equilibrium in this case involves democracy
1 is
with probability
J 6
democracy chooses the policy vector (^t^^,w'^^ ,G'^^)
reformed and the policy vector in consolidated democracy characterized in
Proposition
(7, 1],
1, i.e.,
q{D) =
1.
then transitional democracy chooses the policy vector (r^^ ,w'^^ ,G'^^^ and
the military attempts a coup,
p
Then, the unique
to
fiscally feasible.
as follows.
and prevents a military coup.
• If
we Hmit attention
is
[M TD) =
7,
I
i.e., ip
=
1.
and thus starting with
s
Consequently, we
havep{D TD) =
= TD,
— 7 and
q
{D)
=
1
\
q
(M) =
1
— 7 and
7.
Proof. See the Appendix.
The
essence of Proposition 3
ducers are better off
when coups
is
that condition (28)
are prevented.
coup prevention may require excessive
when
condition (25)
is
future,
both
low-skill
in Proposition
1,
if
to
Markovian
MPE
after s
Thus the
=D
of this inefficiency
is
made
better
off.
is
Nevertheless, as
involves reform of the military
in the
shown
and thus no
effi-
inability of the
democratic regime to commit to future
We
will see in Section 4 that the restriction
the source of coup attempts.
strategies
In particular, this will be the case
The source
.
producers and soldiers could be
ciency wages for the soldiers.
is
not be possible because
the democratic regime could promise high wages to soldiers in the
the unique
rewards to soldiers
may
a clear inefficiency in equilibria involving coups
is
(because of the economic disruption that they cause)
commitment problem;
alwajj^s satisfied, so low-skill pro-
However, this
efficiency wages.
not satisfied. There
is
not important here.
20
Instead, the
commitment problem emerges
from the underlying economics of the interaction between democracy and the mihtary
fact that the military,
A
number
whose main function here
repression,
is
of other features related to this result are
then transitional democracy
may pay even
not needed in democracy.
is
worth noting.
higher wages (and thus
we
the military than an oligarchic regime would (which
will
—the
First, if (25)
make
is
satisfied,
greater concessions) to
study in the next subsection)
.
This
again reflects the commitment problem; because democracy has no use for a large military,
cannot commit to not reforming
and thus
it
needs to make greater concessions today in order
Second, the extent of income inequality influences whether there
to prevent coup attempts.
will
it
be coup attempts against democracy. In particular, the threshold 7
the inequality parameter 9 via
its effects
on a^ and
w^'^
.
It
—a higher 9— increases w^^ and reduces a^, thus reducing
is
lower,
soldiers,
more unequal
societies. Intuitively, this
and thus the prospect
who
of
more tempted
are
becoming a
is
7.
This makes coups more
producer
is
is
V^
{D)
attractive for the current
is less
coup to secure a military dictatorship. The
rents that soldiers can appropriate in the military regime are also greater in a
society because net output
depends on
because in a more unequal society,
low-skill
to undertake a
in (25)
can be verified easily that greater
inequality
likely in
it
greater (a smaller fraction of the potential output
more unequal
Y
given in (4)
foregone as a result of the fact that some of the potential producers are joining the army).
We
state this result in the next corollary (proof in the text):
Corollary 2 Higher
more
inequality (higher 6) reduces
7 and makes coups
in transitional
democracy
likely.
Finally,
elite in
it is
compute,
also useful to
a transitional democracy.
not depend on whether there
is
for future reference, the values to soldiers
First, the value to soldiers in transitional
coup prevention or not. This
is
because
in
and the
democracy does
both cases soldiers
receive the value of a coup against democracy, either as expected return for undertaking a
coup or as a
result of the efficiency
no-coup constraint. This value
is
wages paid by the democratic government to
given by
V^ {TD) =
In contrast, the value to the
elite
13
[)V^ (M) +
(1
-
7)
V^
depends on whether 7
is
determines whether transitional democracy can prevent coups.
coup attempt
in transitional
V" {TD
coup)
i
=
democracy and the
(1
-
satisfy their
<^)
(1
elite's
- T™) A" + 13
21
value
[71/^
is
{D)]
(29)
.
greater or less than 7, which
When 7 >
7, there will
be a
given by
(M) -)-(!-
7)
V"
[D)]
.
(30)
,
In contrast,
when 7 <
7,
V" {TD
where r^^ and t'^^
=
no coup)
- r^^) A" + I3V" (D)
(l
I
refer to the tax rates defined in Proposition 3.
Values in Oligcirchy
3.5
We now
turn to the analysis of subgames starting with s
that unhke democracy, an oHgarchic regime
is
(31)
may
=
E. The key economic insight here
benefit
from having a military used
repression (thus preventing democratization). Counteracting this
problem mentioned
is
the political moral hazard
whereby the military may turn against the
in the Introduction,
for
and
elite
try to establish a military dictatorship.
In oHgarchy, the
1.
choose Xt
—
choose Xt
=
3.
choose Xt
=
strategy by
The
=
X and allow coups.
We
denote this strategy by
P
if
elite is
lemma, which
next compute the values to the
cases, the elite always supply
smooth
accept the fact that
denote this
is,
=
p
1
this
is
costly for
them
if
in
1.
This
will give
them a value
the value of the
th high-skill
(elite)
(13).
22
In
all
terms of taxes
they choose the
transition, they will set the lowest possible tax rate {t^
\
at the
whenever
corresponding to these three strategies.
no public good, since
p{D E) —
is
be stated and proved at the end.
will
elite
which
1,
indeed viable. Throughout this subsection we
V^{E,S) = A" + I3V^{D),
by
We
direct (financial) costs
Lemma
and they do not obtain any benefit from public good. Consequently,
is
"non-prevention;"
shows that the military always prefers repression, that
of the result of this
^ {D)
where V'^
(£>)
denote
the military chooses not to repress,
would obtain no benefit from having the military and pay both
strategy, that of
We
for "prevention."
E, thus the third strategy for the
We
0).
X and pay high enough military wages to prevent coups.
this section,
make use
=
x_i
N for
indirect costs (in terms of the risk of a military dictatorship).
end of
s
(recall that
by S, "smooth transition;"
third strategy would not be attractive for the elite
since they
and
have three possible strategies:
and allow immediate democratization
this strategy
2.
elite
=
0)
first
and
of
(32)
individuals in consolidated democracy given
The second
strategy for the ehte, non-prevention,
mihtary coups. In
and
V"
where
(1
V^ (M),
from
their value
-
(f))
A^
is
this strategy
=
[E, iV)
(1
-
<^)
can be written as
A^ + /3
['yV''
(M) +
(1
-
7)
given by (19),
fails
V" {D)]
(33)
,
the flow payoff to the elite (net of the disruption caused by the coup),
is
the value to the elite under military dictatorship, which occurs
is
and
successful (probability 7),
finally
the value to the elite in consolidated democracy, which occurs
military
if
an army, but not to prevent
Consequently, zero taxes are again feasible and optimal for the
coup attempt by the military
is
to create
equiUbrium, soldiers attempt a coup against the ohgarchic regime and
this
therefore receive zero wages.
elite,
is
(probability 1
—
7). Recall that here
a coup attempt against the oligarchic regime
we
given by (13),
the coup attempt by the
making use
are
fails, this
if
V^ {D),
the
if
of the
assumption that
immediately leads to a consolidated
democracy.
Finally,
if
the elite set
up an army
wage to prevent military coups, then
V^ {E, P) =
where
is
V^ {TD)
is
(1
-
r^)
and
to repress the citizens
their value
A^ + p
[(1
also
pay the required
can be written recursively as
-
n)
V" [E, P) + uV" {TD)]
(34) also incorporates that to prevent military coups the elite
have to impose a tax rate of t^ on
all
incomes
the
elite
repression
the value
fails
V^ {TD).
and the
1
political state switches to transitional
Rearranging
and
(to finance the military efficiency wage),
the state of oligarchy with prevention recurs next period with probability
tt,
(34)
,
given by (30) or (31) in the previous subsection depending on whether 7
greater than or less than 7.
probability
efficiency
—
tt,
whereas with
democracy, giving
we obtain
(34),
where, for future reference, we have written this value as a function of the probability that
repression
is
fails,
tt,
i.e.
as
V^ {E, P
it).
\
The important observation here
continuous and strictly decreasing in n.
(34),
by noting that
To
easiest
way
to see that
it is
that
V^ {E, P
decreasing
is
\
tt)
from
V" {E, P\n) = V" {E, P) > V" {TD).
characterize the equilibrium starting in a
value of the tax rate
elite
The
is
t^ necessary
subgame with
to allow for prevention,
23
=
E, we need to compute the
and then compare the values to the
from the three possible strategies outlined above. Let us
military.
s
first
look at the values to the
The
They
military has three possible strategies.
oligarchy and,
if
decide whether to attempt a coup against
they do not undertake a coup, whether or not to repress the citizens.
participation constraints of soldiers and oligarchy will
chosen.
We
repression)
,
make
sure that the last option
refer to the military's strategies as "coup", "repression" (to
and "non-repression"
(to
denote no coup and non-repression)
when they attempt
the value to the soldiers
a coup
(i/'
=
1).
The
not
is
denote no coup and
Let us
.
first
consider
Their value can then be written
as:
V^ {E
= p [tF^
coup)
I
(A/)
+
(1
-
7)
V^
(D)]
(36)
.
This expression incorporates the fact that when they attempt a coup, soldiers
will not receive
a wage and that the coup will succeed with probability 7 giving them a value of F^^ (A/) and
fail
with probability
1
—
democracy with a value
The
and p
=
of
V^
value to the soldiers
{D)
repression)
=
+ /3 [W^^ [TD) +
u;^
reflects the fact that soldiers receive
successfully carried out the necessary repression.
fact that the
same
succeeds).
instead repression
If
state will recur
is
(probability
fails
(1
-
tt)
by
V^" {E
w^
the wage
tt),
V^'^
repression)
{E
is
repression)]
—
Q
.
today because they have
1
—
tt
(i.e.,
repression) and V^'^
=
they will receive the continuation value of
we obtain that
vjP + pT^V^^ {TD)
—-^—-^—^.
"
(37)
I- P[1-7T)
therefore
repression)
{E
|
for the
as long as repression
>
V'^"
{E coup)
(38)
\
I
with V'^ [E
[tjj
(29) (recall that this expression applies regardless
I
no- coup constraint in oligarchy
\
The continuation value then accounts
greater than 7 or not). Solving the recursion above
I/^^i?
The
a coup and choose repression
tomorrow with probability
transitional democracy, V^'^ [TD), given
of whether 7
a fully consolidated
^^
when they do not attempt
I
This expression
the soldiers.
for
will transition to
the recursion
1), satisfies
V^' [E
which case the regime
7, in
coup) given in (36) and (37).^^
The
I
expressions in (37)
is the same as the value from transitional
coup) = V^^ (TD), since a coup gives them the same value regardless of which regime
it is attempted against.
Furthermore, recall also that in the MPE of the subgame beginning in transitional
democracy, soldiers have the same value regardless of whether they attempt a coup (since when a coup is
'^Notice that the value to soldiers from a coup against the oligarchy
democracy,
i.e.
V'^'
{E
\
prevented, the no-coup constraint
^'We can
is
binding).
also verify at this point that the participation constraint of soldiers in oligarchy
This participation
is
given by V'^
(E
|
repression)
> V^
{E, S), since, in view of Lemma
is
always satisfied.
whenever
it
exists,
the
be smooth transition to democracy.
Using the fact that V^ {E,S) = A^ + PV^ (D) together with the no-coup constraint (38) and Assumption 1,
ensures that the above inequality and thus the participation constraint is always satisfied.
military prefers repression to no repression.
Without the
1,
24
military, there will
.
and
(36)
immediately imply that the constraint (38)
The minimum
w^ > (Sjw^ +/3
equivalent to
is
wage consistent with coup prevention
military
.
—
(1
7) a^.
is
w^ = l3^w^ + I3{l-j)a^.
To
(39)
finance this military wage, the elite will impose a tax rate of t^, which
government budget constraint
(8),
u,Px
Combining
satisfy the
thus
={tP
and using
(40) with (39)
must
-C (r^)
we
(16),
(y - xA^)
)
(40)
.
find that this tax rate
is
implicitly
and uniquely
defined by
= ^7(f-C(f)) + /3(l-7)^7^^+C(r^),
r^
and moreover t^ G
(0,f).
convex and
C (0) =
positive.
strictly
satisfies
Thus
at
The uniqueness
0,
of
most one value of t^ can
decreasing in inequality.
satisfy (41)
Therefore,
when
of inequality on the no-coup constraint.
more
is
likely
collected for any level of r
effect of inequality
greed effect and r^
Finally,
satisfied.
it
on
is
V^'^
side are strictly
unique solution
is
inequality
is
is
t^
greater, a lower tax rate
strictly
is
is
sufficient
the outcome of two counteracting effects
become
democracy becomes
low-skill producers.
A
the military attempts a coup against the oligarchic
reduces
effect of inequality
w^
and t^
.
Counteracting
when
V^^ {M), increases
xt
—
x are also increasing
>
is
at f.
fiscal
[E
repression)
> V^
C(0)
=
{E, S)
0.
in fact proportional to the
always dominates the
effect
7 and
is
always
that,
strictly increasing in 7, the
= A^ + j3V^ {D)
To estabhsh that t^ <
by the definition of f, r — C
Moreover, when 7 = 1, we have t'' — C (r''')
is
revenues
given by
follows from the fact that
strictly increasing in
since t''
and
{M). Consequently, the outside option
I
maximized
in 9
However, the
can be verified that the participation constraint of soldiers in oligarchy
This constraint
^"That T^
(recall (17)).
decreasing in 9 (in the extent of inequality)
V'^''
7
strictly
is
the "greed" effect resulting from the fact that as inequality increases, the value to
soldiers in military dictatorship,
1;
this
First, as inequality increases
when
regime and thus this "outside option"
=
and moreover,
the soldiers because in democracy they will
consolidated democracy
is
C {)
fact that
also establishes that the tax rate
prevent coup attempts. This result
less attractive for
from the
and t?^
between
for the elite to
follows
and the remaining terms on the right-hand
Differentiation of (41) with respect to
this
t^
(41)
(t)
=
is
note from (41) that t''
t for all r < f and
strictly increasing in
{t
same conclusion holds
25
f,
(42)
—
C (r)),
for all
which implies that
7 6
[0, 1].
,
r''
<
is
is
f when
The no-coup
sumption
combined with
1,
V^
(14). Since
We
end
repression
oligarchy
constraint, (38), implies tliat
=
is
always
\
repression)
coup)
\
> V^
>
V^''
{E
{D), where
coup), while As-
\
V^
[D)
is
defined in
satisfied.
by showing that the military never chooses no coup and non-
=
The remainder
0) in oligarchy.
of the analysis of equilibrium in
presented in the next subsection in the context of the complete characterization of
MPE.
the
Lemma
and
pi
=
1 In any
MPE starting
=
subgame with
in a
St
=
E, the military never chooses
ipi
—
0.
Proof. The value
tpi
{E,S), (42)
and p
V^ [E
(36), implies
this subsection
{ip
is
> V^
(D)
V'^ {E
and
receive no
p^
=
0, is V^'^
{E
\
V^ {TD)
obtain the value V'^ {E
footnote IS),
\
=
no repression)
wage and the regime
receive the value
when they choose not
to the soldiers
in the
to
attempt a coup and not repress,
/3V^^ [TD), since, without repression, soldiers
next period will be transitional democracy where they
given in (29).
When
they choose to attempt a coup,
coup) given in (36), and since this value
we have that V'^ {E
\
> F*^ {E no
coup)
\
is
ip^
=
they
1,
equal to V^'^ {TD) (see
This imphes that in
repression).
oligarchy there exists a strategy giving the soldiers a strictly higher equilibrium payoff than no
coup and non-repression.
Equilibrium Dynamics
3.6
We now
combine the
elite's decisions in oligarch)',
Two
and
from the previous four subsections, complete the analysis of the
results
and present a
full
characterization of
MPE.
observations facilitate this analysis. First, a direct comparison of
V^ {E, N)
in (33)
V^ {E, S)
shows that
is
always greater, so the
transition to
down
V"
when such a
solution, n, exists.
^'As noted above, V'^
e
political
elite prefer
transition to repression (with prevention) can be determined in a simple manner. For
this purpose, let us define the threshold
if fr
to allowing
democracy versus building a strong military and dealing with the
moral hazard problem by paying the required efficiency wage. Second, whether the
smooth
in (32)
never choose
elite will
the non-prevention strategy. Thus the choice of the ehte in oligarchy boils
smooth
V^ {E, S)
(0, 1),
then
V"
{E,P
{E, S)
\
tx)
= V"
is
n G
{E,S)
When
[0, 1]
= V" {E,P\7r =
a solution exists,
strictly decreasing in
{E,
P
\
it)
as the unique solution
whenever
tt
26
=
tt,
tt.
it is
whereas
between
and
1
(43)
TT)
uniquely defined."^
V^
to
When
{E,S) does not depend on
such a
n.
Thus,
solution to (43) does not exist, then either
or
V" {E, S) < V" [E, P
latter case,
=
^
tt)
for all
described above has a unique
MPE,
ifn G [0,^), then whenever
T
— T^
and
and suppose
be defined as in (43)
w=
u)-^ ,
n
set
an army for repression
the elite build
and prevent military
while oligarchy persists with probability
AdPE
7 £
(i.e.,
The military chooses
coups.
2.
if
TT
G
(tt,!],
p [E
= 1—7
=
and q (M)
the elite do not build
= TD,
—
racy obtains with probability q{D)
E)
\
=
and
1,
=
—
tp
(35)
on
S and P
such that we have
when
tt
V" {E, P
<
it).
tt)
\
Moreover,
V^ {E,P\tt ^1) < V" {E,S).
second condition
is
equivalent to
the subgame obtaining in state
with T^-^ given in Proposition
i.e., if
T^ >
Remark
/3r-°,
1
When
Proposition 4
interior,
i.e.,
then
is
it
it
^ V"
r^ >
s
it
\
(D)
q
elite
The
/?
first
=
not interior
relevant.
—
i.e.,
tt
=
The necessary and
or
equivalent to
is
is
any
\
tt
if
>
=
1
V"
0,
{E,S)
defined in
tt)
{E,
G (0,1), are specified in the proof of Proposition
conditions are satisfied
when A^
is
P
\
sufficiently small).
27
4.
G
there will be
> V"
r^ <
is
{E, S)
/3t^.
The
no coup
tt
^
0)
< V"
which implies that
—only
is
0)
tt
in
t^ > P [r^ — t^^)
tt
{E, S),
=
0.
one of the two parts of
guarantee that
sufficient conditions that
the set of parameters that satisfies both of these conditions
is,
(when there
equivalent to
tt
=
\tt
1.
does not depend
(that
tt
V" {E,P
if
can also be verified that
for
tt,
when
1
V^
between
V^ {E,P
^
tt
V^ (D)] /A^
this condition
V" {E, P\tt) <V" {E, S)
is
only
condition
[V^ (TD) —
= TD,
3), It
(0, 1) if
1
never choose non-
V^ {E, S)
and
tt,
{E, S) whenever
G
—
{TD E) —
Therefore, with the conventions adopted in the definition of (43), there exists
repression only
and
and p
run consolidated democ-
(i.e.,
Next, as noted above (recall also footnote 21),
tt)).
1), set
with allocations as described in Proposition
1
a continuous and strictly decreasing function of
is
n.
[0, 1]
\
—
a
Transition to consolidated
0).
in the long
prevention, so their choice depends on the comparison of
V^ {E,P
game
(7, 1];
a
(i.e.,
we have
Proof. The argument preceding the proposition establishes that the
and
MPE.
Proposition 3 characterizes the
so that
7 when 7 G
an army
democracy occurs with probability p {D
= l—n.
E)
\
of starting in any subgame s
and q {D)
[7, 7]
[0, 1]
in the
Then, the political
y^ n.
(no coup and repression). Transitional democracy arises with probability p
unique
and
==
tt
e
tt
characterization of
full
that
for all
tt)
|
where
=E
s
we
In the former case,
[0, 1].
These observations enable us to provide a
1.
Proposition 4 Let n
1.
G
tt
I
V" {E, S) > V^ {E, P
we have
It
can be
nonempty
(for
it
is
verified that
example, both
Note
also that the requirement
When
proposition simpler.
ir
—
tt
7^
tt
only introduced to
is
make
the statement of the
the elite have two best responses, thus the equilibrium
it,
is
not unique, but either part of Proposition 4 could apply in this case.
Proposition 4 shows that the
suiEciently effective,
-
probability 1
tt
i.e.,
<
tt
choose to set up an army only
elite will
When
tt.
this happens,
it
aligns itself with the elite.
the society becomes a transitional democracy.
military. In contrast,
find
profitable to set
In this case there
is
has to
It either
by the
it
When
71"
is
with
repression
(probability
fails
Proposition 3 then implies that, in this
when
make
significant concessions to the military or risk a
repression
not very effective,
is
i.e., tt
up an army and pay the high wages necessary
>
tt,
the
elite
coup
do not
to co-opt the soldiers.
a smooth transition to a consolidated democracy.
Another important observation follows from the comparison
that
will persist, recurring
is
government pays the cost of the oligarchy having established a powerful
case, the democratic
military previously.
repression
each period. Moreover, as long as oligarchy persists, the military receives
in
high (efficiency) wages so that
tt),
oHgarchy
when
increasing in
This implies that repression
9.
is
more
of (32)
likely in
and
(35),
which shows
a more unequal society
(proof omitted):
Corollary 3 Higher
inequality (higher 9) increases
tt
and makes repression
in oligarchy
more
likely.
Now
putting the results of Proposition 3 together with those of Corollaries
rize the effects of inequality
2
on equilibrium
political
dynamics and economic
1-3,
we summa-
choices. Corollary
shows that greater inequality makes coups against transitional democracy more
likely, so
that
(conditional on a democratic regime emerging) greater inequality makes military dictatorships
more
likely.
Moreover, Corollary 3 shows that greater inequality also makes democracy more
costly for the elite
and thus encourages repression. Consequently, greater inequality has three
related effects on political dynamics. First,
powerful military more
likely.
more
likely
makes repression and the formation
Second, by encouraging repression,
of oligarchic regimes (rather than a
dictatorships
it
smooth
both because
early stages of a democratic regime
and
it
it
transition to democracy)
of a large
and
leads to a longer duration
.
Third,
it
makes military
leads to the presence of a powerful military in the
also because
it
makes
it
more
difficult for
democracy
to convince the military not to undertake a coup. In addition, however, inequality also affects
fiscal policies.
As noted
in Corollary
1,
once a
fully consolidated
democracy emerges, greater
inequahty leads to higher taxes and greater public good expenditures.
28
The combination
of
the effect of inequality on redistribution in consolidated democracy and
dynamics implies a novel pattern
sition of spending.
When
for the relationship
inequality
is
its effects
on regime
between inequality, taxes and the compo-
low, a consolidated
democracy
is
likely to
emerge, and
thus a small increase in inequality starting from a low base leads to higher taxes and greater
When
public good provision.
In such an environment, taxes are lower and
likely.
there
is
no public good provision). Therefore, the
provision
all
tax revenue
all
is
spent on the military (and
effect of inequality
on taxes and public good
likely, it also
increases the likelihood of a regime that will set high taxes and spend
the proceeds on the military (again with no public good provision).
might account
for the lack of a
across countries
(e.g., Perotti,
Subgame
The
analysis so far has focused
monotonic relationship between inequality and redistribution
Perfect Equilibria
on Markov Perfect Equilibria, which make
only on the payoff-relevant states.
MPE
is
commitment problem that
Nevertheless,
useful to
is
in
subgame
know whether
is
perfect equilibria might prevent
lead to significantly different results. In this section,
some
we
between
game up
players in the
to time
t
and stage k within the stage game.
game can be represented by a mapping a
H^'^
:
the military
Pi
£
level of the
pubhc good Gt 6
G
A
strategy profile a*
{0, 1},
is
a
The next proposition shows that
in
{0, 1}.
(i.e., if it is
SPE
if it is
may
/z*"'^
is
MPE
Subgame
»
[0,1],
and
Perfect
the history of play
A strategy profile for
— [0, 1] x R^ x {0, 1}
1K+, the decision of
and the coup and repression decisions
at
manner.
social groups that
briefly discuss the
the range of the strategy profiles again refers to the tax rate Tt S
Wt £ IR+, the
captures the
of the inefficiencies of
Equilibria (SPE) of the above-described political game. Recall that
of the
it
at the heart of our theory in a simple
implicit promises
depend
strategies
a natural equilibrium concept since
political-economic
it
These implications
1996, Benabou, 2000).
4
be possible
becomes more
nonmonotonic. Furthermore, because greater inequality makes military dictator-
is
more
ships
inequality increases further, oligarchic repression
all
,
the
where
the military wage
whether to create or reform
of the mihtary, 0^ G {0, 1}
a best response to
itself for all
/i'''^
and
G H*'^
sequentially rational).
our political
game
the
MPE and the SPE coincide,
thus
there was no loss of generality in focusing on Markovian equilibria.
Proposition 5 Suppose
identical to the
MPE
that
n
^
ft.
The
political
described in Proposition 4-
29
game
described above has a unique
SPE
Proof. First consider some history
St
= M.
Since military rule
absorbing,
is
will involve the military
maximizing
a similar history where
St
=
^*'° (i.e., at
D.
their
Now democracy
t)
where
absorbing and the same argument implies
is
Next consider a similar history with
1.
at
thus Proposition 2 applies. Next consider
utility,
that the unique sequentially rational play after this history
Proposition
game
clear that the unique sequentially rational play
it is
own
the beginning of the stage
st
= TD.
is
identical to that described in
Since there are no strategies that
can be used to punish former soldiers in democracy and the continuation play after a successful
down
coup
is
after
any history involving
and
this behavior, the
Now
and
St
uniquely, this implies that the unique sequentially rational play
—
in particular, soldiers will
Given
3.
already pinned
TD
TD
will
be the same as that characterized
undertake a coup
any history
/i*'°
is
if
the no-coup constraint in this case, (38),
response for soldiers to undertake a coup.
(12), since the
regime
will
be
S(
=
If it fails,
D, and
if it
is
is
violated.
provided by Proposition
involving either of
uniquely pinned down, the behavior after histories where
In particular,
st
= E
not satisfied,
it is
is
st
— M, D
also unique.
a unique best
they receive exactly the same value as in
succeeds, they receive the unique continuation
value associated with subgames that start with
is
the no-coup constraint, (23)
unique best respoiase of low-skill agents
since sequentially rational play after
is
if
in subsection 3.4,
S(
=
A'l.
Finally, the value to the elite
from S
which implies that the results of Proposition 4 hold as the unique subgame
also unchanged,
perfect equilibrium in this case.
5
Extensions
In this section
we provide
a
number
of extensions that are useful to
map
our theory of military
dictatorships to the data. First, recall that in Proposition 4 military dictatorships only emerge
during transitions to democracy.
In practice, there are
many
cases of military dictatorships
that result from coups against oligarchic regimes, such as those discussed in footnote 6 in the
Introduction.
Our
extension shows
first
how
a slight modification of the baseline framework
leads to coups both against democratic and oligarchic regimes.
in the next subsection.
number
abundant
about the
in the
is
how
and we would
like to
role of the military in politics
economy.
This
is
studied
natural resource abundance affects regime djaiamics.
empirically relevant because
societies
is
Second, we introduce rents from natural resources and provide a
of comparative statics about
This extension
This possibility
many
military dictatorships emerge in resource-
understand whether the model has clear predictions
when
natural resources play a more important role
investigated in subsection 5.2.
30
Third,
we show how incorporating
The key
the national defense role of the military affects our results.
when
army has a national defense
the
role,
becomes
it
easier for
findings here
democracy to commit
reforming the military, making transition to democracy easier and more
briefly illustrate that stronger oligarchic regimes
make democracy more
Throughout the
on
MPE
and
all
T
r
=
<
exists
C (r) =
>
f
T and that taxation above f
restriction
choose
to not
Finally,
less repression
and
>
is
for the tax distortion function C.
In particular,
same
C [t) —
as f defined in (6)) such that
Q for
This implies that there are no costs of taxation until
t.
prohibitively costly. Furthermore,
we assume the
following
on the fundamental parameters of the model
Y>{l + x)A^.
We
we
simplify the notation and the analysis by focusing
(not the
t
1 for all
we
form
also adopting a simpler
f and
may sometimes
likely.
that
likely.
rest of this section
we assume that there
is
(44)
maintain these assumptions throughout without stating them
Faced with the new cost schedule
for taxation, the elite still prefer zero taxes (except for
paying the military wages when they have
and military regimes would
explicitly.
moreover, by condition (44), both democratic
to);
f
set taxes equal to
simpler forms.
For example, the value to the
democracy, and
in transitional
Consequently, the value functions
.
elite in
now
take
military dictatorship, in consohdated
democracy are
y^(M) = y^(D)=
^^^^y
(45)
,
and
+ P)i^-r)A"
rHr^r.^_ii^-l3)^t
'-—
[TD) = ^^
V"
\_p
'
The
military
wage and the instantaneous payoffs
(46)
to low-skill producers in consolidated
democ-
racy are also modified similarly and become
^K4
^ "^{Y-
^-4'')
^^^d
^i
X
Also throughout these extensions. Assumption
the participation constraint of soldiers
next subsection, which
5.1
(1
_
^)
^L +
1 is in effect
and
fY.
is
(47)
sufficient to ensure that
always satisfied (except with non-prevention in the
discussed separately).
Coups Against Oligarchy
We now
to a
is
is
^
modify the basic setup and continue to assume that the absence of a military leads
smooth
transition to democracy.
When
instead the oligarchic regime chooses to create a
31
}
two additional states of the world, denoted by the variable
military, there are
state T], the elite are insulated from
democracy. In contrast, in state
and the probability
77^-'^,
whose
stochastic process,
with Pr
of
and
77j
=
[77^
—
T]^^]
additional state variable
elite
particular, in
chooses
As
=
Tpt-
MPE
any
and
=
Pf-
77^
is
is,
by
V^'^
{E
and
77^-^
and the military
77j
=
77^-^
\
subgame with
This constraint
repression)
repression)
\
is
repress.
st
is
assume that the
= E
and
binding only
> V^' {E
This
=
77^
when
repression)
before they
V"'^
it is
is still
know
{E,P)
coup), where V^'^
when the
is
77''^-'^,
(48)
=
77^
77^
=
77^'-^
\
coup)
state variable
because in state
it is still
is still
77^
and the mihtary repress
77^''^
given by (29) and V^"^ [E, P)
77^.
{E
the appropriate
if
This value
= w^ + ^{{1-^) V^
V- jB
(49),
,
('
defined in
takes the value
{E, P)
is
+ p,
is
(1
-
is
^) V'"' {E, P)]
^ g'^ d -
m)) ^;-
I
defined recursively as
[ttV^^
32
+
(48)
the value of soldiers under prevention
+
{TD)
{I
-
n) V^^ {E, P)]
we obtain
repression)
given by
with probability 7 as in the baseline
^ w^ + /S [nV^ (TD) +
the realization of
and
In
the military never
therefore given by
Combining
can leave
soldiers
a consequence of the fact that coups are only possible
this event, they succeed
I
V^ {TD)
\
the value of a soldier
and conditional on
V^^ {E
and
also
before the realization
77^.
model. The value of a typical soldier when
where
We
77 j.
t
0.
satisfied.
V^ [E
(36)
when
and independently distributed over time
the elite are insulated from coups and transitions to democracy and
(38), that
is
evolves according to an exogenous
applies without any change in this modified model.
1
starting in a
—
77^
model, coups against oligarchy can be prevented only
in the baseline
no-coup constraint
rj^
Lemma
can be verified that
does not, transition to democracy
have to decide military wage at time
the military only before the realization of
It
r]^^}. In
depends on the repression decision of the military
wage cannot be conditioned on
this
if it
realizations are identically
The
IJ-
,
both types of transitions away from oligarchy can occur.
of this event
The
as in the baseline model.
{ri^
both the threat of a coup and from possible transitions to
In particular, the military can attempt a coup and,
possible
e
rj^
/»>
d-
ff
d
-
ri)
V"
(TD)
Prom
(50),
and the no-coup constraint
(36)
prevention has the same expression of
tlie
(38),^^ the
mihtary wage consistent with coup
wage
efficiency
w^
necessary to prevent coups
against ohgarchy as in the basehne model, (39), with the only difference that, because of the
change in the
fiscal
technology, the expressions for w^^ and a^ are
now
given by (47).
With
these changes, the tax rate for the oligarchy to be able to finance the military wages necessary
to prevent coups becomes:^^
r-
The
=
a'^x
/37f
+ ^(l-7)^7—IT-
(51)
net present discounted value of the elite from prevention, starting with
—
st
E,
is
recursively defined as
V" {E, P) -
(1
-
r^)
A" + p
[(1
-
V" {E, P) + iiT:V" (TD)]
/i^)
,
and can then be rewritten as
"
where
V^ {TD)
The
(^'
'')
=
(^^)
i-g(i-%
given by (46).
is
net present discounted value of the elite from non-prevention, starting with
st
=
E,
is
then given by
V" {E, N) = a" + (3
The
first
term
in this expression,
V" {E, N) + fiV^ (coup)]
[(1
-
fi)
{1
—
fxcp)
a^ =
A^
,
is
the expected flow pa3'off to the ehte,
which takes into account that with non-prevention there
The
thus income disruption.
can take place only when
~
rj^'-
In addition,
.
denotes the expected future value to the
V^ (coup) =
from
(1
political
—
f)
will
be coups when possible and
probability that a coup will take place
77^
A^ / (1 — /3).
elite in
V^
(coup)
case there
is
=
(1
a coup.
In addition, with probability
change today and the same
.
(1
political state recurs
—
—
is
7)
fi,
V^ {D) + 7^^ (A/)
Prom
/i),
because a coup
(45),
the
we have that
elite are
tomorrow,
i.e.
insulated
St+i
=
E.
Therefore,
The
following conditions on the set of parameters are useful for the characterization of the
equilibrium of the model.
V"
=
=
- 7) V^ {D) (see footnote 18 for details).
V'^ {E, P) > V^ (E, S) and it is alwaj's satisfied.
This follows by combining the no-coup constraint, (38), V'^^ (E repression) > V^'^ {E coup), which implies
w'' >(1- P) V"' {E coup), and Assumption 1, which imphes that V'^' {TD) > V^ {D).
"Recall that
{TD)
V"^ {E
|
coup)
/S^V'^
(M)
-f-/3(l
"''The participation constraint of soldiers under prevention
is
\
I
33
|
.
Condition 2
<
fi
=
JI
/3f /
Condition 2 ensures
V"
is,
where ¥^^{£,3)
(45). If this condition did not hold, the elite
be indifferent between them when
are independent of
starting in s
=
Therefore,
vr.
/j.
=
Jl).
defined in (32), with
is
would prefer S to
V" [D)
now given by
N for any value of n
This follows since both
when Condition
would be identical to that
.B
non-prevention to smooth transition, that
tliat tlie elite strictly prefer
V" {E,S),
{E,N) >
+ /3f)
{(f)
V^
2 fails to hold, the
{E,N) and
MPE
in
(or
would
V^
{E,S)
any subgame
Proposition 4 in the previous section and would
in
not feature coups against oligarchy.^"*
The
participation constraint of soldiers under non-prevention
is
V^''{E,N)>V^[E,S),
where
V
variable
N)
{E,
-q^.
the value of soldiers under non-prevention before the realization of the
is
This value
is
defined recursively as
V^ {E, N) =
where
V'^^
{E coup)
\
is still
il-
(55)
and
V^
fj.)
{E,
{E, S)
N) + /iV^ [E coup)
I
= A^ + j3V^
[D)
V''{E\coup).
in (54),
satisfied
is
equal to
it is
^_^''^^_^.^
under non-prevention
straint of soldiers
PV'^
defined in (36), and
V''{E,N)^
Using
(54)
we obtain that the
and only
if
(55)
if
participation con-
the following condition
is
satisfied.
Condition 3
H>
If this
is
this condition is
-
(1
/3)
A^ +
means that
this strategy
always satisfied when P
is
is
/3a-^
not feasible for the
high enough, and
parameters where Conditions 2 and 3 both hold
set of
Let us next define
7f
= 1-/3
condition does not hold, the participation constraint of soldiers under non-prevention
violated and this
let
H
tt
€
[0, 1]
in a similar fashion to
is
tt
it
elite.
Moreover, notice that
can be easily verified that the
not empty.
in the previous section. In particular,
be the solution to the equation
V" {E,P\Tr^7t) = V" {E,N),
"Notice that ^ <
is
1
and
also that, except the simplification in the fiscal technology, the baseline
a special case of this extended model with
^
=
1.
34
(56)
framework
when such a
By
solution exists, with the value of prevention for the elite defined as in (52).
V^
the same argument as in the previous section,
V^
and
N)
{E,
independent of
is
V^ {E, P
uniquely defined and
any solution
it
G
^ V^
n)
\
then we set
[0, 1],
{V" {E,P\tt=1)>V"
when a
n, so that
=
tt
N)
{E,
for
{E,
any
MPE
in transitional
democracy
where
y^ ]I,
JL
model presented
the extended
defined in Condition
is
2.
U Conditions 2
MPE as follows:
above, then there exists a unique
n G
If
set T
then whenever
[0,7f),
= T^ and w = w^
=
and p
p(TD
If
IT
is
[E, N)) or
=
tt
1
given by Proposition 3
is still
features
=
E, the
elite build
w^
and a^ defined
=
[7,7], arid q
E
(tt, 1],
(D)
—
q
(M) =
/7-.
where n
tt,
defined
is
=
a
(i.e.,
1),
=
ip
p {E
E)
\
TD,
=
— jm.
l
Proposition
=
so that q (D)
when
1
1].
army for repression
the elite build an
The military chooses
dictatorship arises with probability
1
7^
is
Transitional democracy arises with probability
MPE starting in any subgame s —
= 1—7 and q{M) — 7 when 7 G (7,
and do not prevent coups.
probability
tt
that
MPE
The military chooses
while oligarchy persists with probability
fin,
and suppose
an army for repression
and prevent military coups.
(no coup and repression).
1
E)
,
s
and 3 hold and
3 characterizes the unique
2.
< V^
0)
it
(56) does not have
in this subsection
I
7G
When
Condition 2' or 3 does not hold, the
If
identical to that in Proposition 4-
1.
to (56) exists,
n
Using these observations, we obtain:
Proposition 6 Consider
fi
(0, 1)
.
=
now
(again with the only difference that the threshold 7 in (25)
(47)).
tt
|
7f
strictly decreasing in
{E, N)).
Finally, notice also that the
by
n G
^
tt
is
vr)
|
solution
V" {E, P
(when
P
p{D E) —
\
/i(l
—
p (Af
E)
|
=
ip
=
r
=
and
(i.e.,
a
—
(coup) in state fi^'
1
1), set
=
0,
Military
consolidated democracy arises with
ji-y,
while oligarchy persists with probability
7),
.
u;
Consequently, the long-run likelihood of regimes are given by q [D)
—
p{E E) =
\
(1
—
7)
and
tt
7^ tt
7.
Proof. See the Appendix.
Remark
2
The requirement that n
in Proposition 4 above.
so that the equilibrium
Proposition
6.
When n
is
it
n
not unique, but
V^
emerges when
tt
an identical
plaj's
equal to
is
Also, the case where
Propositions 6 since
^
{E,
=
ff
then the
tt,
nature
its
A''
=
|
tt
0,
35
=
0)
which
is
role to the
elite will
have two best responses,
unchanged from that described
= V^
is
assumption that
{E,
P
|
tt
=
0)
is
in
not covered in
ruled out by the restriction
tt
7^
tt.
Finally, the requirement that
^ ^
rules out the case
/i
where the
elite
obtain the same value
from non-prevention and smooth transition.
The important
additional result in Proposition 6
arise along the equilibrium path.
is
that
now coups
against oligarchy also
Previously, the threat of coups against oligarchy affected
the equilibrium allocations, but such coups never took place in equilibrium (and military
dictatorships always emerged from coups against democracy).
is
The introduction
of such coups
irnportant for two reasons. First, coups against oligarchy provide a clearer demonstration of
the political moral hazard problem facing the
elite in
army
building a strong
can turn against them. Second, the model can now potentially account
dictatorships
we observe
in practice
for
— that the army
why
the military
have different origins; some resulting from coups against
democracy, while others are preceded by non-military oligarchy regimes.
Natural Resources
5.2
In this section,
we extend the
baseline
which generates income equal to
elite
i?
>
(high-productivity agents) and
Since there are
now two
model by assuming that there
in
all
is
a natural resource,
each period. The natural resources are owned by the
of the natural resource rents initially accrue to them.
sources of income,
we allow
for
two
different
fisca,l
instruments; a tax
rate on income at the rate r (with tax distortions specified as in the beginning of this section
with the function C, so that there are no distortions until r
natural resources C £
distortions. This
is
[O;!]-
We
=
f)
and a tax rate on income from
assume that the taxation of natural resources generates no
reasonable, in view of the fact that natural resources are typically supplied
inelastically.
The
N
characterization of the
since
it
will
is
similar to before (in particular, the elite never choose
gives a smaller equilibrium payoff than S),
main observation that
regime
MPE
choose ^
simplifies the analysis
=
1,
thus taxing
all
is
and we provide fewer
details.
The
that both a military regime and a democratic
income from natural resources.
Consequently, an
analysis identical to that in Section 3 implies that military wages in a military dictatorship
and instantaneous payoffs
to low-skill agents in
democracy are
X
and
a^
= {l-f)A^ + G^,
36
(58)
where
G^ = fY + R.
These expressions exploit the
fact that r
=
f and C
=
1
1
and thus they
incorporate the additional revenues coming from natural resource rents either directly in the
wage
military
or in the
amount
good provided
of public
Let us start with a subgame where s
= TD. An
in
democracy.
analysis identical to that leading to
Proposition 3 immediately implies that low-skill producers are always better-off by preventing
coups. In fact,
now
retaining political power has
tional source of revenues
military coups
more
of the addi-
coming from natural resources. However, natural resources
also
make
attractive for the soldiers. In particular, as in Section 3 a military coup
can be prevented only
if
given the
instruments and natural resource rents, democracy
fiscal
can raise enough revenues to pay soldiers a
This
become more valuable because
feasibility constraint
now
sufficient
amount
to satisfy the no- coup constraint.
takes the form
uF^x <t{Y - xA^) +
R.
(59)
In this expression, the revenues include the income raised by taxing production at rate f and
from the taxes on natural resource rents
prevent coups
is
is
at the rate C
=
1-
The
military
wage necessary
to
no longer equal to w'^^ (defined as the wage satisfying (23) as equality), but
instead
^^^ =
with w'^ and
a'"
now
^4^7 {w''
defined by (57) and (58).
making coup prevention more
that the prevention of coups
difficult.
is
now
It is
-a^),
(60)
straightforward to verify that w'^^
> w^^,
In particular, the combination of (59) and (60) shows
possible
if
1-/3
u)^^
7
satisfies the following condition,
which
is
a
simple generalization of (25),
With
this threshold replacing 7, Proposition 3 continues to apply.^^
Appendix shows that the threshold 7
7 in the
itive;
(i?) is strictly
decreasing in R.
greater natural resource rents raise the political stakes and
attractive for soldiers (and the additional revenue available to
compensate
democracy
is
less likely to
make
of Proposition
This
is
intu-
military coups
more
democracy
soldiers for the prospect of dividing natural resources
sequently, transitional
The proof
among
is
not sufficient to
themselves).
Con-
consolidate in natural resource abundant
societies.
can again be verified that the participation constraint of soldiers is satisfied in this case as well. In particdemocracy with natural resources is V'^' (TD) > V^ (D), where V'^' (TD) =
V'^ [TD coup) = /JtV"^ (M) -h /3 (1 - 7) y^ (D), V^ [D) = a^ / (1 - /3) and V*' (A/) = w"' / (1 - 0), and
holds under Assumption 1.
^'It
ular, this constraint in transitional
I
37
.
We
stakes,
next turn to subgames starting with s
though in
this case their effects will
=
E. Natural resources will again raise political
be somewhat more complex. Recalling that the
value to the elite in the subgames starting with
obtain the value to the
elite
s
is
M and
s
=D
are given by (45) above,
+ ^/»)+g(l-t)X''^
(62)
from natural
identical to (32) in Section 3 above, except that the elite enjoy the rents
resources for one period.
we
from smooth transition as
V-'(i;.5)='^-'^".4''
which
=
on the other hand, they build a strong army and choose coup
If,
prevention, their value, as a function of n, will be given by the solution to the following
program
V"iE,P\.)=
^
'
^
'
i^
max
'
^)
A" + H - OR/n + ^nV- jTD)
'
1-/3(1-^)
fe[o,f],ce[o,i]
^
^
subject to the government budget constraint, which written as an equality takes the form
- xA^) +CR = w^
f (y
Expression (63)
is
{R) X.
(64)
obtained from the solution of a recursive equation analogous to (34), but
now
uses (46) and incorporates the fact that to prevent coups the elite have to pay the
efficiency
wage
w^ (R).
This efficiency wage has the same expression as in
w'^ and a^ are now replaced by their counterparts
w
and a^
w^'^
in (57)
and
higher
except that
(39),
(58), so that
+ (l-7)5^).
(i?)=/3(7Ti'^
(65)
Let us also denote the tax levels that solve the maximization problem in (63) by f ^ and
Comparing the maximized value
it
in
Proposition
4.
The
of this
program
to (62),
we obtain a threshold
tt
.
{R) replacing
Consequently,
rest of this proposition continues to apply.^^
(^
we have
the following characterization of equilibrium in the presence of natural resource rents.
Proposition 7 The extended model with natural resources has
that in Proposition 4 (except that
•
a higher level of
• there exists
R
R* >
7
(i?)
replaces
7 and
tt
makes democratic consolidation
and x >
sion, starting in state s
—
0,
replaces
(i?)
K^ {E,S) = A^+
{E
\
repression)
PV'' {D). Assumption
V'^ [E
1
identical to
Moreover:
= TD
less likely;
such that an increase in natural resources makes repres-
E, more
=
it).
starting in state s
likely if
x >
x, for
any
"''The participation constraint of soldiers in oligarchy under prevention
V'- {E, S), where V"'
MPE,
a unique
\
coup),
V" {E
\
coup)
is
initial
now
is
R*
given by V'''
= ^7^^^ (M) +
again ensures that this constraint
38
R>
always
/3
(1
{E
-
satisfied.
\
repression)
7)
V^
>
{D), and
Proof. See the Appendix.
The new
results in this proposition are the comparative statics
As already discussed above,
of natural resource rents.
more
to gain
size
greater natural resource abundance
and makes democratic consolidation more
increases the political stakes
military has
with respect to the
from taking control and democracy
is
difficult,
because the
not always able to compensate
soldiers for forgoing these returns.
The second
part of the proposition shows that greater natural resource abundance also
affects the likelihood of repression in oligarchy.
On
biguous, because of two opposing effects.
Nevertheless, the effect
is,
in general,
the one hand, greater natural resources
am-
make
the elite more willing to use repression in order to prevent a transition to democracy again
because of the greater political stakes.
political
On
the other hand, natural resources also intensify the
moral hazard problem because the military, once formed,
to undertake a coup.
Which
With a
natural resource rents.
and thus when the
effect
size of the
in natural resource rents
dominates depends on the
will
size of the
The
size of
larger army, per soldier rents in military dictatorship are lower
army
is
larger than a threshold f
makes repression more
baseline
model analyzed
in Sections 2
and more importantly, the only
likely.
be reformed after one period.
objective
is
and
3
>
and
R>
R*, an increase
^^
was simplified by two assumptions;
role of the military
secondly, the transitional phase in
democracy
We now
was repression
politics.
We
will also
is
the army
=
0,
is
is
is
is,
xt
=
x,
the invasion would succeed and
in Section 2,
if
To capture the
possible.
Our substantive
role of the military
except that we are
(e.g.,
such an invasion
all
still
using the
and more substantively,
a threat of invasion from another country).
is
not possible.
If,
on the other hand,
agents (including low-skill producers) receive a lower
payoff than even in the military dictatorship. This implies that
an invasion
and
always good for democratic consolidation.
model
an international threat
present, that
politics;
use this extension to investigate the claim by O'Donnell
identical to our baseline
there
firstly
the military could
i.e.,
and defense
simplified fiscal technology introduced at the beginning of this section,
we assume that
domestic
relax both of these assumptions.
and Schmitter (1986) that a weaker military
The model
in
lasted for one period,
to investigate the impact of international threats
on democratic
Xt
army and the
National Defense ctnd Democratic Consolidation
5.3
If
have stronger incentives
all
agents would like to prevent
role of international threats in the simplest possible way,
^^Here the threshold R' provided in the Appendix, is such that when R
on production income and natural resource rents to finance military wages.
,
39
> R'
,
the ehte will use both taxes
'
we assume that the
and when
power posing the threat of invasion may reform
foreign
happens, the international threat disappears.
this
We
its
own
military
do not model the behavior
of the foreign power explicitly, and instead assume that such reform happens with probability
A G (0,1) in each period.
Until the foreign threat disappears (due to reform of the foreign
military), a transitional democratic
government cannot reform the
military. After this threat
disappears, the transitional democratic government will choose to disband the military (since
there
is
no longer any foreign threat). In
this light, the current
model
is
also a generalization
of the baseline setup in Section 2, since reforming the military takes potentially longer than
one period. Finally, returning to the discussion in footnote 3 and to O'Donnell and Schmitter's
(1986) conjecture, A can be interpreted as another (inverse) measure of the relative strength of
the army, since
when A
is
low, there
purposes and the military
The
whether the foreign threat
s
= TD
no foreign threat
is
is
in this case
active
is still
is
very similar to that in Section
is
now an
2,
except that
additional state variable. Let us start in a
and with the foreign threat active (the analysis of the case where there
identical to that in Section 2
from attempting a coup,
attempting a coup
greater need for the military because of national defense
stronger. ^^
MPE
analysis of the
subgame with
is
is
[TD
V^"^
\
coup),
is still
and
is
omitted).
The
value to the military
given by (21), whereas the return from not
is
y^^ [TD
^vF^
no coup)
I
where we again use iiF^
+(i
[(1
-
A)
to denote the military
V^^ [TD
wage
coup prevention. Note, however, that the expression
\
no coup)
in transitional
for this
wage
is
+ XV^
[D)]
,
democracy when there
is
no longer the same as
in
Section 3 (see below). This value function also takes into account that the same state will recur
with probability
1
— A (when
the foreign threat remains active and there
is
no opportunity to
reform the military). Rearranging this expression, we obtain
V^^
[TD no
I
where a^
is
now
defined in (47).
The
coup)
^
^
'^
^
(1-/3)(1-/3(1-A))'
expression for w'^'^ in this extended environment can be
obtained by solving the incentive compatibility equation,
V^ [TD
\
coup)
=
V^'^
(TD
|
no coup),
as
is whether xt =
or x, and we have already investigated the implications
on democratic consolidation.
'Naturally, an even starker measure
of this mesisure of military strength
40
w^
where
As
in
is
the soldiers' wage in a military dictatorship given by (47).
our analysis in Section
are satisfied:
first,
3,
transitional democracies will prevent coups
The necessary condition
<
w^'^
Let us start with the second
Using the expressions
.
^^ /3(1-^(1-A))(^M_,L)
Condition (67)
-7(A).
high. Moreover,
—
as A
>
it
can be verified that 7 (A)
is
—
>
this condition coincides
1,
V^ {TD
no coup)
=
{I
in transitional
-
t)
I
V^ {TD, P) = V^ [TD
fact that taxes will
/?
[(1
-
G^^ =
A)
with
when
difficult
(25)).
this
is
feasible.
If
is
V^ [TD, P) + XV^
f (F
- xA^) -
[D)]
(68)
,
ui^^x incorporates the
be equal to f (given the tax distortion technology adopted at the beginning
and whatever
of this section),
democracy
A^ + G^^ +
no coup) and
\
not too
a strictly decreasing function of A and that 7 (A)
next verify that low-skill producers prefer to prevent coups
they prevent coups, their value
where
is
be successful
will
This implies the interesting result that condition (67) becomes more
1.
to satisfy as A increases (in the limit as A
We
(67)
generalization of condition (25) and shows that transitional democracies
is
can prevent coups as long as the probability that coup attempts
7
two wage
for these
the condition for the prevention of coups in transitional democracy can be written as
levels,
>
be
democracy to pay high enough wages
for the transitional
to the military again takes the form ViF^
—
two conditions
low-skill producers should prefer to prevent coups; second, they should
able to pay high enough wages to the military to achieve this.
requirement.
if
is
left
over from paying soldiers the efficiency wage goes into
public good expenditures."^ Alternatively, without prevention, the value to low-skill producers
is
V^ [TD
where O"^^
w'^^
there
=
is
0).
coup)
-
(1
I
=
t
—
-
f) (1
-
<^)
(Y — xA^),
A^ + G^^ +
(3
[7^^ (M)
since in this case zero
+
(1
-
7)
V^
[D)]
wages are paid to
,
(69)
soldiers
(i.e.,
This expression also takes into account that, as before, when a coup attempt
fails,
[l
cj))
an immediate transition to
The comparison
of
V^ {TD
\
fully consolidated
no coup) and
democracy.
V^ {TD
\
coup) shows that the low-skill pro-
ducers are better-off preventing military coups by offering a wage to the army equal to w'^^
if
and only
if
A
>
A*,
where A* G
[0, 1)
and
is
defined in the proof of Proposition S in the
Appendix. The next proposition states the main result of
^^The hypothesis that coup prevention
""it
is
is
possible, that
again straightforward to verify that Assumption
satisfied.
41
is,
1
w^''
<
this subsection.
w'^''
,
^°
ensures that G^'^
>
0.
ensures that the mihtary participation constraint
is
Proposition 8 In any subgame beginning with
MPE
s
— TD,
there exists A* G
[0, 1)
such that the transitional democratic government prevents coup attempts
7 < 7(A) andX >
and a unique
if
and only
if
A*.
Proof. See the Appendix.
This proposition has two interesting imphcations, both following from the
decreasing in A (which implies that transitional democracy
when A
consolidate
is
low).
The
first
is
here corresponds to lower A, democratic consolidation
defense role,
more
into
it
less
is
credible
emphasized in
this paper:
is
more
when
the
army
likely.
is
when
that
is
is
prevent coups and
tliere is
a
which
in national defense,
This
(A)
7
intimately related
army has an important national
threatened by reform in transitional democracy and this translates
commitments by
undertaking a coup.
likely to
and more important implication
stronger foreign threat and thus a more important role of the
to the key economic force
more
fact that
In contrast,
transitional
when A
democracy to compensate
close to 1
is
army
foreign threats and no important role of the
(meaning that
soldiers for not
tl:iere
are no serious
in national defense), concessions
transitional democratic regime are not credible for the military because they foresee
reform and are more willing to attempt coups.
by the
imminent
This result therefore highlights a new and
potentially important interaction between international and domestic politics.
The second
implication of Proposition 8
is
that,
somewhat
gests that over a certain range, democratic consolidation
is
model sug-
paradoxically, the
may be more
likely
when
the military
stronger (since a lower A corresponds to a stronger military). Therefore, the logic of com-
mitment emphasized by our approacli shows that O'Donnell and Schmitter's (1986) conjecture
about stronger militaries always making the survival of transitional democracies
need not be
comparing
may
true.
xt
=
Note that a version of
to xt
=
x.
this conjecture
was true
in
less likely
when
our baseline model,
However, our extended model here shows why this conjecture
not capture the complete set of interactions between the strength of the military and
transitional democracies because
commitments
to a strong military are
more
credible.
Persistence in Oligarchy
5.4
Finally,
we can
also incorporate persistence in oligarchy into the baseline model.
stantive pm-pose of this exercise
is
to see whether better organized democratic
The
movements
conversely less strong oligarchies) are always likely to lead to more rapid democratization.
main
result in this section
Suppose that
in the
shows wliy
this
may
not be
(or
Our
tlie case.
absence of repression, oligarchy persists with probability a £
42
sub-
(0, 1).
instead, there
If,
—
(1
a)
TT
<
repression and
is
Thus, in this extension
TT.
dation of the power of the
and the military
an
elite
democratization happens only with probability
fails,
it
a
represents a direct measure of the degree of consoli-
The
elite in oligarchy.
in oligarchy are similar to our analysis in Section 3.
^^°)
'
(l-^)(l-/3a)
and the value from prevention, as a function of
tt,
is
similar analysis again shows that non-prevention
fact,
be
Briefly, the value to
agent from smooth transition can be computed using the expressions in (46) as
^ ^^'^^-
A
analysis of the interactions between the elite
is
dominated by smooth transition
(in
the persistence of oligarchy without repression makes smooth transition more desirable
Consequently, we immediately obtain the analog of
for the elite relative to non-prevention).
Proposition
the
4:
otherwise, and
elite
choose prevention
n
if
is
below some threshold
straightforward to verify that
it is
in the next proposition, concerns the
tt
e
fr
and smooth transition
The main new
(0, 1).
result,
described
comparative statics of regime transitions with respect to
the persistence parameter a.
Proposition 9 Let
subgame beginning
the
TT
be defined by
if
in state s
subgame beginning in
is strictly
increasing in
— TD,
state s
a
V^
then
= TD,
for any
(p
>
= V^
{E, S)
tt
is strictly
n
then
(j)*
,
{E,
P
(j)*
If
fr).
no coups take place
in the
decreasing in a. If coups take place in
is strictly
where
\
G
decreasing in
a
for any
(f)
<
(p*
,
and
(0, 1].
Proof. See the Appendix.
Proposition 9 implies that the
more consolidated
in transitional
elite are less likely to
(greater a) under two related conditions:
both the value to the
opposing
tt
forces.
the elite are
{(p)
they are more
first,
when
their
power
is
when coups do not happen
democracy; second, when coups take place in transitional democracy but they
do not cause too much income disruption
the threshold
choose repression
elite
a
increases,
from smooth transition and from prevention increase.
Whether
(</>
small).
This result
increases (and thus whether repression
Whether coups take place
likely to
to a lower value of a).
forces.
likely)
depends on two
democracy and what
When
choose repression when their power
When
intuitive; as
becomes more
in transitional
determine the balance of these two
is
their costs for
coups do not take place, then
is less
consolidated (corresponding
coups are possible after democratization, then the trade-off for the
43
elite
depends on how disruptive these coups
then a lower a
when coups
are.
When
they are not very disruptive
{(j)
<
cj}*),
consolidation of elite power in oligarchy) encourages repression. However,
(less
are highly disruptive
likely after repression
and the
{(p
>
then a lower
0*),
smooth
elite prefer
a makes
transitional
democracy more
transition in order to avoid the potential
costs of coups in the future.
The
substantive implication of Proposition 9
regimes are not necessarily more
likely to
organized politically and the oligarchy
is
is
emerge
that,
somewhat
paradoxically, democratic
where the
in societies
citizens are better
weaker. In particular, a lower value of
a
in this
model
corresponds to a weaker oligarchy (and thus to a stronger democratic movement). Proposition
9 shows that
smooth
democracy may be more
transition to
corresponds to societies where the democratic movement
sufficiently consohdated, so that
The Role
6
In this section
we
they
feel less
is
weak and the power
need to create an army
high,
which
of the elite
is
for additional repression.
of the MiHtary in Recent History
number
briefly discuss a
empirical context for our theory.
We
first
of salient cases of military dictatorships to provide
contrast the role played by the military in various
how economic
Central American nations. This highlights both
namics and the
is
when a
likely
role that the military plays in pohtics.
inequality affects regime dy-
At the end
of this section,
we provide
a brief discussion of the impact of natural resource rents on the behavior of the military.
Democracy
Military and
6.1
The
in Central
America
case of Central America, and of Costa Rica in particular, provides an interesting illustra-
tion of the ideas emphasized
in explaining regime
by our theory. This case both highlights the
dynamics and
also
shows how the
role of the military
initial distribution of
income
affects the
subsequent evolution of political institutions.
Among
role played
1997).
Latin American countries, Costa Rica stands virtually alone for the very limited
by the army
During the
19'^^
in politics, since the country gained
independence
in
1821
(e.g.,
century, Costa Rica did not experience predatory caudillos
typically influential in the political
and economic
Between 1891 and 1948, there was a
single
coup
in
life
in
much
Yashar,
(who were
of the rest of Latin America).
Costa Rica, followed by a brief dictatorship.
After this episode, in 1949, the Costa Rican military was demobilized and essentially disbanded.
The
relative absence of external
and internal
conflicts during the history of
a major factor in the limited role that the military has played in this country's
44
Costa Rica
politics.
is
Even
before
its
demobilization, the Costa Rican
army was small and weak, and did not possess
the professional traditions and strength typical of
many
other South American militaries.
key factor that has led to the presence of a weak military in Costa Rica
social conflicts in this country have
been relatively Hmited. This
of factors, including the structure of the
economy
consisting of
is
is
A
that historically
because of a combinations
many
small landholders; the
absence of a large indigenous population at the time of colonization, which prevented the
Spaniards from setting up major plantations in this area; the poor endowment of natural
resources such as gold; and the high agricultural wages resulting from the scarcity of labor
due to the absence of a large (indigenous) population. Moreover, the relative homogeneity of
Costa Rica's society appears to be an important reason why Costa Rican ruling
shown limited
interest in the creation of a large
and powerful
military. "^^
The
decimated during a short
civil war.'^^
have
tradition of low
militarization of Costa Rica culminated with the formal demobilization of the
in 1949, after these were
elites
armed
forces
This decision has not been
reversed ever since.
Consistent with the predictions of our model, the demobilization of the Costa Rican army
appears to have contributed significantly to the stability of
its
nascent democratic institutions.
Consequently, Costa Rica has become the most stable democratic country in Latin America.
This
is
because of the absence of the military necessary
in part
"coup threat," perhaps
in coalition
with the economic
for the
elites. ^^
formation of an effective
Roquie (1987
p.
192), for
example, relates the success of Costa Rican democracy directly to the absence of a military
and
writes:
"No doubt because
it
corresponded to deeper motivations hnked to the social
equilibrium of the Costa Rican nation, a nonmilitary state has become today one of the bases
of
its
democratic consensus."
The
-
successful democratic consolidation of Costa Rica since the mid-twentieth century
'''For instance, describing the
economic and institutional reforms promoted during the
"liberal"
era (the
period of Latin American history roughly going from 1870 to 1930, following the phase of caudillo politics),
Mahoney
(2001
p.
266) writes that, "In Costa Rica, where the reform period was launched at the time of
independence, liberals were not faced with the kinds of political threats that led reformers elsewhere to build
large standing armies. ..The pattern of reformist Uberalism that had developed by the early twentieth century
saw neither the creation of a powerful military coercive branch that commanded a prominent position in the
state nor an associated rural economy marked by polarized class structures and a high potential for lower-class
agrarian revolts."
^^The economic elite did oppose the abolition of the armed forces, but they were overruled.
'''As emphasized in Bowman (2004), the abolition of the army in Costa Rica has helped to stabilize democratic
institutions not only directly, but also indirectly, by allowing the government to spend more in welfare and
public education. Indeed, the broad programs of income redistribution and of provision of goods and services
implemented by the National Liberation Party (the preeminent party in Costa Rican politics in the second half
of the 20"* century) have further alleviated income inequality over time, and thereby reduced the scope of social
and political conflicts.
45
stands in contrast to the different political development paths pursued by other Central Amer-
For example, highly repressive military dictatorships were established in the
ican nations.
1950s both in Guatemala and in El Salvador.
Honduras and Nicaragua,
These regimes persisted
instead, traditional oligarchic regimes led
until the 1980s.
by the
civilian elite,
In
but
supported by a significant military element, emerged during this time period.
Consistent with our model, in both Guatemala and El Salvador power militaries, initially
created by the
societies, later
elite in
order to ensure the repression of the lower strata in these highly polarized
became strong enough
These mihtary regimes lasted
for
to seize
power and establish
their
own
dictatorships.^'^
extended periods of time in both countries and were highly
authoritarian and autonomous. Their policies also led to the reproduction, or even the amplification, of the high
income inequality present in these
Honduras and Nicaragua have
out the
20'''
century.
However,
also
societies at the time of the coups. ^^
been ruled by nondemocratic governments through-
in contrast to the military dictatorships in El
Guatemala, these were personalistic or oligarchic regimes,
in
which the
military,
Salvador and
though actively
involved in repression, did not have autonomous power. In fact, the survival of nondemocratic
regimes in Honduras and Nicaragua depended more on the distribution of political patronage
through the expansion of state bureaucracy rather than the harsh repression of opponents and
"state terror,"
which have been part of the experience
the same period.
The
different
in
Guatemala and
in El
Salvador over
'^^
path of
political
development that Honduras and Nicaragua followed since
1930s (relative to Guatemala and El Salvador)
may be
traced back to the economic and insti-
tutional evolution of the two countries since the previous period of liberal reforms.
'"'in
Guatemala, the
liberal era started in 1871
Whereas
with the triumph of General Justo Rufino Barrios, and was
new major wave
"Except for a brief democratic
interlude in the early 1920s, Liberal military dictators ruled with an iron hand on behalf of the coffee ohgarchy
and foreign investors for over seventy years," (Vanden and Prevost, 2002 pp. 255-256).
^^An indication of the differences in the underlying socioeconomic conditions is provided by the average
number of economically active individuals in the agricultural sector relative to the number of farms around
1950 (see Needier, 1987, Table 5, p. 98). This ratio was 10.9 in Costa Rica, 38.2 in El Salvador and 48.1 in
Guatemala. This comparison therefore suggests a much more equal distribution of income in the agricultural
sector in Costa Rica than in El Salvador and Guatemala.
It
^^ Overall, there was some variation in the military policies implemented in Honduras and Nicaragua.
is possible that this variation might have contributed to the different timing of democratization in these two
countries. In Honduras, the army was not a bastion of support of the Can'as regime, and militarization in
Honduras remained very limited until the late 1950s. In contrast, in Nicaragua the Somoza regime promoted
the development of the National Guard as an important pillar of its control over the society. Consequently,
though a typical oligarchic regime, Nicaragua was significantly more militarized than Honduras. Nonetheless,
the army in Nicaragua did not develop into an autonomous institution, but rather into "a separate military
casta, loyal only to their own leader, not to the nation as a whole," (Millet, 1977 p. 198).
characterized by a further increment of the concentration of land ownership (also through a
of expropriation of
communal
lands cultivated by the indigenous population).
46
in
Guatemala and
in El Salvador, oificers
tional capacity to attempt coups
had both the
and to setup
structural basis for military authoritarianism
saw a further entrenchment of the
was
liberal era left
largely controlled
Guard
of the
was
own
rule, in
institu-
Honduras and Nicaragua a
Indeed, while the liberal period
lacking.
in
Guatemala and
in El Salvador, in
behind a relatively weak agrarian
by the ruling
and the
coffee elites, as well as the creation of powerful militaries
capable of independent political action
and Nicaragua the
their
political incentives
elite or dictator (for
Somoza Garcia regime
in Nicaragua).
class
both Honduras
and a military that
example, as in the case of the National
"^^
Natural Resources £ind Military Dictatorships
6.2
Our model's
predictions on the role of the military in natural resource abundant societies
is
also
broadly consistent with the historical evidence. In her authoritative work on natural resource
booms, Karl (1997) argues that the two
bated
in
political instability
many
oil
price hikes in the early 1970s
and 1980s exacer-
and regime transitions toward more repressive forms of government
"petro-states," in particular, in Iran, Nigeria, Venezuela
and Algeria. Nigeria,
example, experienced growing economic and ethnic tensions after the
witnessed the reemergence of military rule in 1983.
oil
price increases
for
and
This was followed by a new transition
to a fragile democracy between 1986 and 1991, but was again interrupted by a military coup
in 1993.
Algeria experienced a severe
tion of the president,
Mohammed
the early 1990s, which lead to the assassina-
crisis in
Boudiaf, to the cancellation of elections, and to frequent
switches between military rule and weak civilian rule.
dant endowments of other natural resources
offered
by the empirical evidence presented
may
in
Further evidence that
oil
and abun-
adversely affect democratic consolidation
is
Ross (2001), and by Jensen and Wantchekon
(2004). In particular, Ross (2001) presents evidence consistent with the notion that increases
in natural resource rents lead to increased repressive efforts
by nondemocratic governments
Jensen and Wantchekon (2004) show that in
in order to prevent or delay democratization.
African countries, the abundance of natural resources tends to
and the consolidation
of,
democracy
less likely.
In fact,
many
make both the
of the
more
transition to,
successful examples
of democratic transitions in sub-Saharan Africa are by relatively natural resource poor na^''
While, during the hberal period, the Zelaya autocracy had implemented economic and institutional reforms
setting Nicaragua on a development path similar to that of
in 1909, following a
US
Guatemala and El Salvador, things changed abruptly
intervention which lead to the creation of an informal protectorate.
After the
fall
of
which took over power relying on the support of US Marines for security,
showed little interest in preserving the coercive apparatus created by the previous regime. The Nicaraguan
army was eventually disbanded, putting an end the militarization effort of Zelaya.
Zelaya's regime, the conservative
elite,
47
tions such as Benin,
Madagascar and Mali. Instead, natural resource abundant countries have
experienced greater political turmoil and have not been successful in establishing democratic
Examples include Gabon, Cameroon, Togo, Zambia,
regimes.
Algeria, Nigeria,
Congo and
Sierra Leone.
Botswana, which
Naturally, there are exceptions to this pattern.
abundant country, has been the most successful democracy
boom was
also significant for
or nondemocratic
in
is
a natural resource
movements
Botswana had one
oil
Norway, but does not seem to have led to any military action
This
in this country.
likely reflects the fact that there is
major interaction between the strength of underlying institutions and the
resources.
The
sub-Saharan Africa.
of the
most participatory indigenous
a
effect of natural
institutions in Africa
and
a very successful transition to democracy before diamonds were discovered (see Acemoglu,
Johnson and Robinson, 2003). Norway
such
societies, greater natural resource
is
clearly a very strong, consolidated democracy.
In
wealth increases the income of the citizens, relaxes the
government budget constraint, and may contribute to more productive spending. '^^
also consistent
with the prediction of our model regarding the
in consolidated
democracy, which increases the
level of public
effect of
This
is
a positive shock to
R
good provision without
affecting
political institutions.
Concluding Remarks
7
In this paper,
we presented the
analysis of the emergence of military dictatorships and
first
the conditions under which the military will act as an effective agent of the eUte (as opposed
to acting in
its
own
interests
for research in political
and against those
economy
for
of the elite).
These questions are relevant
a number of reasons. First, most nondemocratic regimes
survive with significant support from the military, so understanding the objectives of the
military
is
important
in the
study of political transitions. Second,
practice are military regimes, and
and
persist for different reasons
we need
many nondemocracies
to understand whether military dictatorships
in
emerge
than oligarchic regimes and what their economic consequences
are.
An
investigation of these questions necessitates a
a set of individuals
who
themselves with the
elite if this is
act in their
own
interests
model
in
which the military consists of
(though they can be convinced to align
consistent with their interests).
We
introduced this feature
'^See Ross (2001 pp. 343-344) for more evidence that major oil discoveries have not had discernible adverse
on democracy in such countries as Norway, Britain and the US. See also Mehlum, Moene and Torvik
effects
(2006) for evidence of a significant interaction between institutions and natural resources in growth regressions.
48
by assuming that the means
if
of violence in the society are in the
monopoly
and
the elite decide to form a strong military, then they have to live with the political moral
hazard problem that this causes. In particular, a strong military
agent of the
with their
is
of the military,
elite,
own
but
may
them
instead turn against
objectives.
One immediate
"efficiency
not simply work as an
in order to create
a regime more in hne
implication of the political moral hazard problem
that the cost of using repression in nondemocratic regimes
need to pay
may
is
now
higher, because the elite
wages" to soldiers to prevent coups (or make other social or policy
concessions to the military).
An
to
important consequence of the presence of a strong military
democracy takes
regime until
it is
place, the military poses a
is
that once transition
coup threat against the nascent democratic
reformed. Precisely, the anticipation that the military will be reformed in the
future acts as an additional motivation for the military to undertake coups against democratic
governments. Consequently, societies where the
elite
form a strong military
prevent
in order to
democratization are more likely to later lapse into military dictatorships because the military
some
retains
of
its
power during transitional democracy and can attempt a successful coup
against democracy. This leads to a specific (and to the best of our knowledge, novel) channel
for the
emergence of military dictatorships, which appears to be consistent with the
evidence.
effects
It also
on the economic and
Our
analysis also
mocratic
how
highlights
repression during a nondemocratic era can have important
political success of a later
democratic regime.
showed how, under certain circumstances, military coups against nonde-
elites are also possible,
thus creating another channel for the emergence of military
dictatorships. In light of these results, one
types of nondemocratic regimes.
The
the militar}' acts as an agent of the
might wish to distinguish between three
first is
oligarchies
where the
rich elite are in
incentives of the elite.
The second
dictatorship that emerges as a result of a coup against a democratic regime.
from Central America discussed
The
third
The examples
likely.
power and
is
om
a military
The examples
in Section 6 ensure the relevance of this type of military dicta-
a military dictatorship that results from coups against oligarchic regimes.
of this type of military dictatorship were also discussed in the Introduction.
Our model
more
is
different
This type of regime emerges endogenously in
elite.
model depending on the technology and the
torships.
historical
also provides a range of
In particular,
we show that greater inequality makes the use
nondemocratic regimes more
military coups.
Both
comparative statics about when such dictatorships are
likely
and
of these effects
also
make
makes
it
more
difficult for
of the military in
democracies to prevent
military regimes following brief democratic episodes
49
more
In addition, greater inequality also makes
likely.
it
more
nondemocratic
likely that
regimes are unable to solve the political moral hazard problem and thus creates another channel
for the
make
We
also
show that greater natural resource
military coups against (unconsohdated) democracies
effects
elite,
emergence of military dictatorships.
on the
political equilibrium in
more
likely
problem resulting from the high natural resource
making the military necessary
is
more
in our
model; when there
is
rents.
likely
for national defense.
international politics and domestic politics.
economic force
and have ambiguous
nondemocracies, which become more valuable for the
but also more expensive to maintain because of the more severe
implies that democratic consolidation
rents
The
when
This
is
political
More importantly,
there
a
is
the model also
a potential foreign threat,
new and
logic of the result
moral hazard
is
interesting link
between
very related to the main
an international threat, concessions from democratic
regimes to the military become more credible, because democracy also needs the military.
We
view our paper as a
first
step in the study of military dictatorships and the political
agency problems that are ubiquitous between branches of the state that control the means
of violence
and the economic
area deserve further study.
elite,
First,
especially in nondemocracies.
Many
topics in this broad
a systematic empirical analysis of policy and economic
performance differences between different types of nondemocratic regimes
is
necessary. Second,
the current framework can be extended so that an alliance between the military and the
can be formed during democratic periods as
Finally, the current
well.
elite
framework already
highlighted the important interactions between international and domestic politics. However,
we did not endogenize the
political
economy equilibrium
in other countries.
A
fruitful
area for
future research appears to be the international relations aspects of the interactions between
the military and democratic regimes. In particular,
it
would be interesting to investigate how
military or democratic reforms in one country affect politics in other countries.
50
Appendix
Proof of Proposition 3
7.1
By Assumption
1,
7 >
and there
will
when 7 e
[7,7], (28)
When
7. If
7,
then the feasibihty constraint, (24),
be a coup attempt in equilibrium
G^^
=
1).
Thus we only have
democracy chooses prevention, then
which can be determined
,
st+i
— D
to
show that
and thus the
Thus the only relevant
w'^'^ that satisfies (23) as equality.
choice of t"^^ and
(V'
necessarily violated
is
satisfied.
is
transitional
must be paid
7 >
soldiers
decisions concern the
as the solution to the following
maximization
program
u-^
(rD
=
no coup)
1^ + G
(1-t)A^
max
I
(72)
re[o,i],GeR+
subject to
G<
Next, using the expressions (16) and (23),
'
{t
P
w TP =3-:^7
- C (r)) (r - xA^) - w^^x.
(r
- C
by the
first-order condition of the
A^ and moreover the
utility of low-skill
(1
If,
government budget constraint
^j.p
If,
-
utility of low-skill
taxes are set at the level t'^^ defined
program, which implies
C (r))
{Y - xA^)
(74)
,
producers during the transitional period
(r^^)) {Y
- xA^) -
G^^ —
(72) involves
_ W
=..
X
0,
will
be
w^^'x.
then taxes are determined by the
^ (JTP\
^+C{r^^),
Y -xA^
^
producers in the transitional period will be
instead, coups are not prevented, the tax rate
chosen to maximize the
0,
(73)
(8) as
T'-
and the
(1
G^^ >
- r^^) A^ + (r^^ - C
on the other hand, the solution to
{Y - xA^)
{t))
a^
Provided that the solution to (72) involves
implicitly
can be written as
lu'^^
utility of
and the
(75)
(l
—
level of public
r-^^) A^.
good provision are
a representative low-skill producer in the transitional period,
with no additional constraint, but taking into account the output disruption caused by the
51
coup, which will be forthcoming in this case. In particular, the tax
good provision G'^^
in question, are the solution to the
u^ {TD
coup)
=
max
I
(1
^
The
low-skill
where
-
/3
[jV^ {M)
we can
no coup)
\
-
-f (1
7)
V^
'
-
>
/3)
[(1
= u^ {TD
{TD
A^ + G
no coup)
\
- T^^) A^ + (r^^ coup)
-
(3-)'
C
when G^^ >
and that
depend on
t-^^ does not
{TD
V'^
-
coup),
|
u^ {TD
\
(a^
-
-
(1
r)
A^)
(1
/?
when G^^ >
0,
-
/3)
w^^x
(77)
.
—
{TD
/3)
w'^^
is
linear
satisfied at
/3
—
/3, f3'
,
such that the
left-
no
P' ^
C {f))Y <
[0, 1]
condition
P e
[0, 1].
is
is
sides are equal. Second, (77)
at
is
since in this case this condition can be written as
1,
=
in this case w"^^
/3,
imply that both the right-hand-side and
and the right-hand
{t-C (f)) Y-{f-C (f)) xA^ where (f —
and
coup) does not depend on
\
the left-hand-side of (77) are strictly decreasing hnear functions of p. Therefore, there
most one value of
coup)-|-
0, as
- xA^)] -
(r^^)) {Y
This observation, and the facts that u^
/3.
>
coup)
|
the result follows from three observations. First, from (73), (1
increasing in
(76)
J
\
.
V^ {TD
no coup)+/3y^ {D) and
\
I
Now
^'
{D)] as given by (26) and (27) above. Rearranging these expressions,
{TD
(1-/3) u^
0)
^
toG<{l-(f>){T-C (r)) (F - xA^)
write the condition for prevention to be preferred,
(1
-
r) (1
producers benefit from prevention when V'^
V^ {TD
the level of public
maximization program
Telo,i],GeK+
subject
r^^ and
a^
—
(1
—
a^x < a^ -
(1
-
f)
f) A^. Third, condition (77) also holds
and thus prevention
is
A^,
when
/3
=
0,
because
These observations imply that there
for free.
exists
such that the right-hand-side and the left-hand-side of (77) are equal, thus this
always satisfied and we have
This establishes that,
if
V^ {TD
G^^ >
0,
no coup) >
\
coup prevention
V^ {TD
\
coup)
for
any value of
always better for transitional
is
democracy.
We
applies
G>
next consider the case where
when /? G
in
[/3*, 1],
problem (72)
is
where
G>
(77) in this case
is
It is
0.
defined as the
binding (this constraint
a strictly increasing function of
the constraint
/3* is
G^^ =
/3
slack for
straightforward to show that this case
minimum
value of
implicit in
is
and the tax rate defined by
P < P* and binds
for
p >
G
6
^5
such that the constraint
1K+).
Observe that
(74) does not
P*
.
The
depend on
w^^
/3,
is
hence
equivalent of condition
can be rewritten as
T
A^ < A^ - u^ {TD
coup)
I
52
+
Y3-37
(a^
-
(1
-
7^)
^
)
•
(78)
We now
show that
right-hand side
depend on
from
P
-^
if
any
Therefore, the right-hand side
is
Maximum Theorem
(3*
,
where the
a convex function
extended
at
in the range
b
real line, h*
G
(6*, 6°°).
=
/3*
in (14)
a strictly convex function of
is
-
/3/ (1
/3),
whereas
Clearly, condition (78) holds as
h.
(3
over
by
[0, 1]
program
(72) changes. Finally, observe
than a linear function at two end points of an interval
—
/ (1
=
in 6
coup) does not
\
Stokey, Lucas and Prescott, 1989 Chapter 3), condition (77)
(e.g.
less
and A^ - u^ [TD
term on the
last
a continuous function of
set of active constraints in
is
Note that the
[/?*, 1].
hnear (increasing)
is
Moreover, since the payoff to the citizens
I.
also holds at
that
/?
by the definition of a^
positive
and (73) t'^^
(75)
Berge's
/?.
is
any
(78) holds for
/3*)
=
6°°
and
oo,
then
This establishes that (78) also holds
it is
for
also less
any
j3
G
in the
than the same function
[/3*, 1]
and completes the
proof.
Proof of Proposition 6
7.2
V^ {E, S) and V^ [E, N), given in (32) and in (53) respectively,
are independent of n, either V^ {E, S) > V" [E, N) or V" {E, S) < V" {E, N) for any value
of
(the case where V^ {E,S) = V^ {E,N) is ruled out by the assumption that
y^ Jl). If
Condition 2 does not hold, then V"^ {E, S) > V^ {E, N) and non-prevention is never chosen
First, note that,
because both
IT
fj,
by the
elite.
In this case, the equilibrium
is
the same as in Proposition
4.
When
Condition 3
does not hold, the participation constraint of soldiers under non-prevention cannot be
thus this strategy
is
not feasible and again the equilibrium from Proposition 4 apphes.
Let us then focus on the case where both Conditions 2 and 3 hold. In this case,
V^ [E, N)
and non-prevention
and preferred by the
feasible
is
the argument in the text and the definition of
any n
^
7.3
Proof of Proposition 7
We
it,
satisfied,
which establishes the
tt,
we have
that
elite to
smooth
V^ {E, P
V
transition.
^ V^
<
{E, S)
By
N)
for
strictly decreasing in
R.
\
n)
{E,
result.
begin by showing that the threshold 7 (R) defined in (61)
is
Straightforward differentiation of 7 (R) gives
7'
(R)
=
'-^ ""''-"'
P
where
w'^^
and a^ are defined
in (57)
and
expressions of w'^ and a^ defined in (47),
xw^ -a^ =
xw'^'^
z(tt)™
-
a^)
in (58). Next, observe that taking into
we obtain
-a^ = -fxA^ 53
{I
-
t)
A^ <
0.
account the
<
Therefore, 7' (R)
with equahty
0,
Next consider the decision
if
and only
of the ehte.
if
A^ =
0.
R*
First, define
as the level of natural resources
such that
w^
{R*) X
=
f {Y
- xA^)
(79)
.
R =
In other words,
R*
is
wages necessary
for
coup prevention can be financed by taxing production income only
maximum
By
possible rate f.
substituting for w^'^ and
fm
w- (R)
_„„P
^ w"^ +
expression with (79),
we have
,P
Combining
tliis
when
the level of natural resources such that
fl7
13-
,
a'" in (65),
+ (l-7)S
"
^
_
R*, total military
at the
we obtain
R.
(80)
wM — wP
^*
,
R^^ir,
T.
r-T/3(7+(l-7)S)
Claim
R*
1 Suppose that
=
vention, the elite set f
is
R >
given by (81) and
f and choose Q
>
R*
^
Then
.
to balance the
which implies
C^^^(7+(l-7)^)-^
'"
M
_
in any
MPE
'
with coup pre-
government budget constraint,
P
^^
(82)
.
Proof. The expression of the government budget constraint provided by
,p_ w^{R)x-CR
~ [Y-xA^)
^
(81
(64) implies that
'^
Using
this expression, the per period utility of the elite in oligarchy
This expression
be
everywhere decreasing in ( provided that
is
<
the case, since x
will
'
set at the
—
[1
n) by assumption,
maximum
budget constraint, that
Using the fact that
in
possible level f, and
Q
is,
and
since
C,
will
can be written as
nA^ + xA^ < Y
Y = nA^ +
(1
—
n)
which
,
A^
.
is
Therefore,
We
as given in (82).
equihbrium f^
=
f,
and that (^
is
given by (82),
^^'"^'"^^^
we have that
•
(1-/?)(1-/3(1-.))
also have
,->//,
f^
be determined to satisfy the government
can be written as
"^
always
p.,
{l-P){A" + R/n)+/3{l-r)A"
54
(63)
Moreover, using
n (R)
(62), the threshold
1
n{R)^
-^
(1
- C^) R/n - (A -
A=
-
(1
{A" + R/n)+p
^)
-
(1
f)
\
n)
is
given by
A")
A-{l-(3)V"{TD)
P
where
V^ {E, S) = V" [E, P
which
at
-
(1
A". Now
f)
since
d
-
[{\
/dR =
Q^) R)
1-/3 (7
+
-
(1
we have
_
1
-^
[1
/5
(7
+
-
(1
-
7) S)
-
(1
A-
^)]
(1
-
/3)
-
/3)
V" {TD)
%'{R)
P
A-{l-(3)V"{TD)
!-/?[(!-
C^)
P
The numerator of this
R/n - (A -
A-
n
expression
is
-
(1
-
(1
f) .4^)] (1
y^ {TD)
/3)
V^ (TD)
decreasing in
V^
and
{TD) <
(1
—
f)
^^/
(1
—
P).
Therefore,
-
[1
is
sufficient for
vr'
/3
+
(7
(i?)
>
(1
-
(A -
7) x)]
Using the
0.
(1
-
f)
which
in
turn
is
the
-
[1
same
This establishes that when
more
likely.
(7
+
(1
-
7) x)]
(1
(1
-
-
/?)
f)
(1
-
A^ =
C^) i?/n
(83)
(1-/3) {r^"
+ R/n)
,
equivalent to
is
tA" >
X
{w"'^
- w^)
as the following condition:
X
repression
/3
A -
fact that
substituting for (^ and rearranging terms, (83)
n
A") >
>
f
(1
-
-
/37) (1
n)
r(l-^7) + /3(l-7)(l-nf)
R>
R* and x >
x, n'
>
{R)
and thus higher resource rents make
This completes the proof of the proposition.
Proof of Proposition 8
7.4
V^
Using the expressions of
that G*-^^
coups
=
f
V^ {TD
{I
I
—
(f))
{D)
=
{Y — xA^), the value
to low-skill producers
coup)
= i^-^i^-^0))^'-h^rY
I
Similarly, using the facts that V'^ {D)
G^^ =
in (18), of
a^
in (47),
and the
fact
when they do not prevent
coup), given by (69), can be rewritten as
V^ {TD
that
V^ {M)
a^/ (1-/3), of
f (y
- xA^) — w'^^x >
0,
=
a^/
(1
that w'^^
55
-
is
p),
.
^^
)xA^
V^ {TD, P) = V^ {TD
\
no coup),
given by (66) and that w^' and a^ are
7) x),
,
'
when they prevent coups V^ {TD no
given by (47), the value to low-skill producers
V^ [TD
coups
if
1-/3
(TD no
V'^
--^'
^ PifxA^ _
1-/3(1 -A)
1-^
^^l^ML
=
no coup)
I
Assuming that coup prevention
coup)
>
V'^
condition
A*
{TD
>
1.
0,
-
ma\
,)
1-/3
'
X^xa^
(i_/5)(i_/3(i_A))'
_
\
Combining the previous two expressions,
coup).
this
equivalent to
is
fxA^ {^A
(/37
+pxa^
-
[(1
/3
+
-
(1
(1
/3)
+ /37) A -
left-hand-side of this inequality
=
{l
a feasible strategy, low-skill producers prefer to prevent
is
I
at A
coup),
can be rewritten as
(68),
The
\
is
-
(1
4>))
-
/3)
-
(1
(1
- 7)] +
/3) [/3 (1
-
-
(1
+
7)
/3)
(1
(1
-
/3
-
A
for all
<
[0, 1)
+ /3A) 4>a^ >
it is
such that (84) holds
F^ {TD
A*,
|
no coup)
(84)
/3) </>]}
a strictly increasing function of A and
Therefore, there exists a unique A* e
then (84) does not hold
-
strictly positive
for all
< V^ {TD
0.
|
>
A
A*.
If
coup) and the
low-skill producers prefer not to prevent coups.
Proof of Proposition 9
7.5
Using (70) and
""
(defined as
fr
(1
there
-
is
V"
{E, S)
= V"
{E,
P
+ ap {f - T^)) A"
- Pf) A^] + a/3 [(1 - f ^^ -
\
n)) can be written as
{t^ - pf
l-P
~
/3
If
(71), the threshold
a)
[(1
-
no coup
P)
V"
{TD) -
in transitional
(1
)
democracy, (46) implies
(1
V^ (TD) =
-
p)
(1
—
V" {TD)]
f)
A^ / (1 —
/3)
and
._
(l-Q^)T^
(l-a)/3f'
which
If
is
strictly decreasing in a.
coups take place along the equilibrium path in transitional democracy, then (46) yields
V^ {TD) = {i-f){l-^)A'' +
Using
this expression, the threshold
Since
T^ does not depend on
(1
-
f)
A^.
n becomes
r-P
/3
^
- ^f +
- T^)
- f - (1 -
a/3 (f
-
(1
-
a,
we obtain that the
a)
[aPcl) (1
f)
(/)
f)]
derivative of this expression
dn/da
is
proportional to
B
{<P)
=
[a (1
-
P)
r^ -
(1
-
a) (a/3 (f
- r^) 56
(/3f
- r^))]
(1
-
f) p^4>-{f
+
(1
-
r)
<P)
(1
-
P) Pr""
where
(f)
—
any
that
all
Q.
4>
71"
p e
B
{(f))
is
the numerator of dn/da. This expression
Tlierefore,
<
is
(j)*
,
it
B {4>) <
has at most one root
(so that
tt is
strictly increasing in q).
[0, 1]
and we
set p*
=
1.
4>
—
(p*
is
over the interval
strictly decreasing in a)
Moreover,
if
B (c6)
This establishes
57
Knear in
all
and
(p,
[0, 1].
for
any
has no root in
and
is
negative
This imphes
(j)
[0, 1],
>
cp*
,
then
tliat for
B
>
B {(p) <
the claims in the proposition.
{(j))
when
(so
for
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