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Department of Economics
Working Paper Series
EMERGENCE AND PERSISTENCE OF
INEFFICIENT STATES
Daron Acemoglu
Davide Ticchi
Andrea Vindigni
Working Paper 06-32
November 27, 2006
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Emergence and Persistence of
Daron Acemoglu
MIT
Inefficient States*
Andrea Vindigni
Davide Ticchi
University of Urbino
Princeton
November 2006
Abstract
Inefficiencies in the bureaucratic organization of the state are often
factors in retarding economic development.
inefficient organizations
has received very
Why
little
certain societies choose or end
attention, however. In this paper,
simple theory of the emergence and persistence of inefficient states.
and poor
which
We
individuals.
will
show
The
rich are initially in power,
choose redistributive policies.
that,
may be
viewed as important
The
up with such
we present a
society consists of rich
but expect to transition to democracy,
Taxation requires the employment of bureaucrats.
under certain circumstances, by choosing an
inefficient state structure, the
and capture democratic politics. This enables them to
reduce the amount of redistribution and public good provision in democracy. Moreover, the
inefficient state creates its own constituency and tends to persist over time. Intuitively, an
inefficient state structure creates more rents for bureaucrats than would an efficient state
structure. When the poor come to power in democracy, they will reform the structure of the
state to make it more efficient so that higher taxes can be collected at lower cost and with
rich
able to use patronage
lower rents for bureaucrats. Anticipating this,
when
the society starts out with an inefficient
organization of the state, bureaucrats support the rich,
We
show that
who
set lower taxes
but also provide
enough political support, the coalition
of the rich and the bureaucrats may not only choose an inefficient organization of the state,
but they may further expand the size of bureaucracy so as to gain additional votes. The model
shows that an equilibrium with an inefficient state is more likely to arise when there is greater
inequality between the rich and the poor, when bureaucratic rents take intermediate values
and when individuals are sufficiently forward-looking.
rents to bureaucrats.
Keywords:
in order to generate
bureaucracy, corruption, democracy, patronage politics, political economy,
public goods, redistributive politics.
JEL
Classification: P16, Hll, H26, H41.
*We thank Miriam Golden, Guide- Tabellini and seminar participants at IGIER-Bocconi, the Latin American
Meetings of the Econometric Society, and Yale for useful comments and suggestions. Acemoglu gratefully
acknowledges financial support from the National Science Foundation and the hospitality of the Yale Economics
Department. Vindigni gratefully acknowledges the hospitality of Collegio Carlo Alberto and of the Yale Leitner
Program
in International Political
Economy.
Introduction
1
There are large cross-country differences
efficiency of the state organization (e.g.,
back at
least to Tilly (1990),
in the extent of bureaucratic corruption
World Bank,
2004).
An
influential
argument, dating
maintains that differences in "state capacity" are an important
determinant of economic development. 1 The evidence that
many
less-developed economies in
sub-Saharan Africa, Asia and Latin America only have a small fraction of their
in tax revenue
and the
and invested by the government
(e.g.,
GDP
raised
Acemoglu, 2005) and the correlation
between measures of state capacity and economic growth
(e.g.,
Rauch and Evans, 2000)
are
also consistent with this view. Societies with limited state capacity are also those that invest
goods and do not adopt
relatively little in public
poor.
2
Brazil provides a typical example of a society, where the state sector has been relatively
inefficient
poor
policies that redistribute resources to the
(e.g.,
and democratic
politics has
generated only limited public goods and benefits for the
Gay, 1990, Evans, 1992, Weyland 1996, Roett, 1999).
we construct a
In this paper,
political
economy model, which
links the
emergence and
persistence of inefficient states to the strategic use of patronage politics by the elite as a
of capturing democratic politics.
of public goods
Democratic capture enables the
and redistribution, but
therefore provides a unified answer both to the question of
some
why
societies
and why many democracies pursue
certain democracies
inefficient policies.
may
why
the provision
elite to limit
at the cost of aggregate inefficiencies.
means
Our approach
inefficient states
emerge
in
relatively pro-elite policies. It also suggests
exhibit relatively poor economic performance
and adopt various
3
Our model economy
consists of two groups, the rich elite
and poor
citizens. Linear taxes
can
be imposed on both groups, with the proceeds used to finance public good investments. The
rich are generally
opposed to high
levels of taxes
and public good investments. Tax
collection
requires that the state employs bureaucrats to prevent individuals from evading taxes, but
bureaucrats themselves also need to be given incentives so that they exert effort (or do not
accept bribes).
The
efficiency with
measure of the organization of the
which a central authority can monitor the bureaucrats
state. Political
competition
is
modeled
either
is
our
by assuming
the existence of two parties, respectively aligned with the rich and the poor, or by allowing free
'See, for example,
Evans (1989, 1995), Levi (1989), Migdal (1988), Epstein (2000), Herbst (2000), Centeno
(2002) and Kohli (2004).
See, for example, Etzioni-Halevy (1983) on the importance of state capacity and bureaucratization for the
development of the welfare state in the West, and Rothstein and Uslaner (2005) on the importance of state
capacity for income redistribution.
On the comparative post-war growth performance of democracies, see, for example, Barro (1999).
entry into the political arena by citizen candidates (Osborne and Slivinski, 1996, Besley and
Coate, 1997). In both cases, there
no commitment to
is
policies before elections
and the party
that comes to power chooses the policy vector, including taxes, public good provision, and
bureaucratic wages, and whether to reform the efficiency of the state institutions. Democratic
competition
political
rich or
interesting
by the
fact that bureaucrats
poor parties (candidates) and their support
We
in
made
is
may be
pivotal in the
consider two possible organizations of the state: the
which bureaucrats
"inefficient"
inefficient,
one
in
will
be detected
easily
they
if
which monitoring bureaucrats
fail
may
first is
an
support either the
outcome
of elections.
"efficient" organization,
to exert effort, while the second
is difficult.
In equilibrium,
when the
is
an
state
is
bureaucrats need to be paid rents in order to induce them to perform their roles of
tax collection and inspection. The presence of rents creates the possibility of patronage politics,
whereby bureaucrats may support the party that
In a society that
is
will
always dominated by the rich
maintain the
elite
or that
is
inefficient structure.
permanently
in
4
democracy
(with a poor citizen as the median voter), the political process produces an efficient organization
and no benefits
of bureaucracy, since an inefficient state creates additional costs
holding power.
Our main
the control of the rich
beneficial to choose
an
result
elite)
and
that
is
is
when the
power
in democracy, there will
Therefore,
if
the rich
elite,
the current bureaucrats
when
for the rich elite to capture the
find
it
poor median voter comes
be bureaucratic reform, reducing their rents from then on.
in
power, choose an inefficient organization of the state,
—who are receiving rents—prefer to support the
with the poor. Consequently, an
may
the state so as to exploit patronage politics to
limit redistribution. In particular, bureaucrats realize that once the
to
those
society starts out as nondemocratic (under
expected to transition to democracy, the rich
inefficient organization of
for
inefficient state organization
rich rather
emerges as a
political
than vote
instrument
democratic decision-making process by fostering a coalition
between themselves and the bureaucrats.
It is also
only emerges in equilibrium, but also persists;
noteworthy that the
when the
state
is
inefficient state
inefficient,
not
the bureaucrats
vote for the party of the rich, which chooses not to reform the bureaucracy and continues to
maintain the support of the existing bureaucrats and thus
Our
its political
power.
analysis shows that patronage politics typically leads not only to the emergence
and
persistence of an inefficient state apparatus, but also to the overemployment of bureaucrats.
4
In our basic model, the assumption that the main role of bureaucrats is tax inspection is not essential. The
important feature is that an inefficient state organization must pay bureaucrats rents in order to provide them
with the right incentives. Bureaucrats' role as tax inspectors becomes important in the extension in subsection
5.3,
where they can be bribed by producers evading
bureaucrats' main role
is
tax inspection throughout.
taxes.
We
simplify the presentation by assuming that
This
is
because the rich
may
prefer to hire additional (unnecessary) bureaucrats so as to boost
Consequently, a captured democracy will typically feature an inefficient
their party's votes.
state (bureaucracy), provide relatively few public goods
This pattern of bureaucratic inefficiency
bureaucrats.
corrupt and low-capacity bureaucracies in
and Rauch and Evans, 2000).
We
also
many
racy and makes
is
democratic outcomes.
An
developed countries
Geddes, 1991,
(e.g.,
more
inefficient state is
likely
when
because greater inequality raises the equilibrium tax rate
more appealing
it
consistent with the stylized view of
5
show that the equilibrium with an
greater inequality. This
less
is
and employ an excessive number of
for the rich to create
an
inefficient state also requires
inefficient state
in
there
is
democ-
apparatus to prevent
intermediate levels of rents/ "efficiency
wages" for bureaucrats; when rents are limited, bureaucrats would not support the
rich,
while
too high rents would make the inefficient state equilibrium prohibitively costly for the rich
elite.
Finally,
an
inefficient state is
because bureaucrats support the
The
number
rest of the
paper
is
more
likely to arise
inefficient state in
organized as follows.
of case studies that illustrate
when agents
are
order to obtain future rents.
Section 2 provides a brief discussion of a
how patronage
politics
has been used to limit redis-
tribution towards the poor and also discusses the related literature.
basic economic
and
political
more forward-looking,
Section 3 outlines the
environment. Section 4 characterizes the equilibria of the baseline
model both under permanent nondemocratic and democratic regimes
as benchmarks,
and more
importantly, under a regime that starts out as nondemocratic and becomes democratic thereafter.
We
show that
state organization
and a
sufficiently large
Section 5 generalizes this framework in a
may
choose an inefficient
in order to create
a majority coalition.
environment the rich
in this last political
bureaucracy
number
elite
of directions; in particular,
it
allows for
more
general contracts with bureaucrats, considers a citizen-candidate setup for political competition,
and allows producers to bribe bureaucrats to evade
distinctive implication of our approach
sector employees
taxes. Section 6 briefly investigates a
about the relationship between relative wages of public
and the amount of public good provision
in democracies.
We
report cross-
country correlations consistent with this implication. Section 7 concludes, while the Appendix
contains
5
some
of the proofs omitted
Even with the overemployment
majority in the electorate.
methods such as lobbying
from the
text.
of bureaucrats, bureaucrats
In practice, the elites
may be
and the rich
elite
may
not have an absolute
able to control the political system using other
in addition to the support of the bureaucrats. Here, we isolate our main mechanism
by focusing on a baseline model where the rich are able to capture democracy without any lobbying or other
non-electoral activities.
Motivation and Related Literature
2
In this section,
relate our
we
paper to the existing literature
2.1
Patronage
The
experiences of
patronage
number
briefly discuss a
in political
Politics, Inefficient States
many
societies in Latin
and
politics, inefficient states
Several authors
distribution of large
(e.g.
economy.
and
Elite Control
elite control.
Here we
inefficient
briefly
mention three cases.
and oversized bureaucracy comes from
Gay, 1990, Weyland 1996, Roett, 1999) have argued that the
numbers of public
jobs,
both
in the public administration
tatal organizations, has created a pattern of patronage politics in Brazil.
6
and
The
in paras-
control over
these jobs has enabled traditional elites to preserve their political power and limit the
of public
good provision and
Brazil, elites
amount
redistribution.
have been able to control
of repression
of redistribution
and democratic
Patronage
and
also
America, Asia and Africa illustrate the link between
Perhaps the most transparent example of
Brazil.
and
of case studies that motivate our analysis
amount
In fact, despite the high level of inequality in
politics for
much
of the 20
t/l
relatively short periods of military rule.
and public good provision does not show marked
century with only limited
Interestingly, the
differences
amount
between military
periods.
politics has often
ensured that even those in poorest neighborhoods of Rio have
supported the traditional parties rather than
socialist or social
democratic parties running
on platforms of greater public good provision and redistribution (Gay, 1990).
Students of
Brazilian politics have noted the role of public sector employees in this process. For example,
Roett (1999
p.
91) writes "state
company employees emerged
supporter of the patrimonial order"
pressures from the
IMF and
as being
among
the strongest
In return, successive governments have withstood external
.
have not reformed the public sector, despite the "public perception
that public-sector workers were overpaid and underworked" (Roett, p.
97).
The
process of
reforming the public sector has started only recently and progressed slowly.
Another example of
cialiste
effective
patronage politics
is
provided by the policies of Parti So-
(PS) of President Leopold Sedar Senghor in Senegal.
After independence,
PS
faced
increasing challenges from various different opposition groups, including urban workers and
farmers.
Nevertheless,
it
managed
to preserve
its
power, with relatively limited amount of
some branch of the Brazilian public sector. Evans
commonly recognized as a huge cabide de emprego (source of jobs) and
In the early 1980s, about 4 million people had a job in
(1992) observes that the Brazilian state
is
remarks that in contrast to the Weberian conception, recruitment of public employees
to merit but to political connections.
in Brazil
is
not related
repression, largely owing to
amount
PS
of political liberalization
also exploited its
In fact, Senghor
use of patronage politics.
its
promoted some
and allowed the creation of a multi-party system. However,
incumbency advantage
to manipulate the democratic process
an extensive patronage network centered on the state apparatus and parastatal
estingly,
it
was precisely during
of
sector. Inter-
this period of democratization that the size of the public sector
grew substantially (Boone 1990, Beck, 1997). Boone (1990
"The strategic allocation
by creating
government jobs coopted
347) describes this process
p.
restive intellectuals
as:
and professionals and
incorporated them into political factions anchored in the state bureaucracy." Thanks to this
successful implementation of patronage politics,
PS
much
retained
of
its
power following the
transition to democracy.
A
from
final
Italy.
that the
A
tries.
example of the
The
rise of
patronage politics
in the face of political
competition comes
evolution of the Italian bureaucracy in the post- WWII decades demonstrates
mechanism that our model
identifies
significant extension in the Italian
Democratic Party (DC)
may
operate even in relatively developed coun-
bureaucracy was initiated by the Italian Christian
in the 1950s after the electoral challenge
from the Communist Party
increased sharply, especially following the 1953 political elections. Until the defeat in
War
II,
as the
Italian politics
dominant
World
DC emerged
DC created a
was dominated by Mussolini's dictatorship. After the war,
party. In the 1950s, faced
by
electoral challenge
from the
left,
highly disorganized and oversized bureaucracy, which subsequently became a natural source of
political
support and patronage
for the party.
the expansion of the bureaucracy
"The massive system
after 1953
was
Golden (2003
p.
199) describes the motive for
as:
of political patronage that the leaders of the
their aggregate
answer
...
DC
constructed
to enlarging the party's aggregate vote
share while protecting the incumbency advantage of individual legislators."
In part with the support of the bureaucracy that
it
created,
DCs dominance
of Italian politics
continued until the 1980s and prevented the formation of a left-wing government.
2.2
Related Literature
Our paper
is
related to a
number
of different literatures.
The
first is
the political science and
sociology literature on the organization of the state and the bureaucracy mentioned above.
In contrast, there
is
relatively little
reaucracy in economics.
Some
work on the
internal organization of the state
and bu-
exceptions include Acemoglu and Verdier (1998), Dixit (2002),
Egorov and Sonin (2005) and Debs
(2006).
None
of these papers investigate the relationship
between patronage
politics
and the emergence of the
inefficient state as
a method of limiting
redistribution.
Our paper
why
First, the reason
to control political
models of
elites
number
also related to a
is
the
power
elite
in a
both
As
on choose
inefficient institutions is
such, our paper
Baron
Grossman and Helpman
(1994), Dixit,
in
which traditional
(1997),
elites are able to
small literature on the inefficiency of the form of redistribution
is
Becker and Mulligan (2003) and Wilson (1990) argue that
to our work.
of redistribution are chosen as a
way
is
and Grossman
capture democratic
of future redistribution.
is
Nevertheless, there
basic Becker-Mulligan- Wilson story,
it is
bureaucracy
is
inefficient
methods
of redistribution (see also
Coate
not clear
chosen by the rich in order to limit the
is
why
also
an important distinction; in the
the society can commit to the form of
and not to the amount of redistribution. In contrast,
redistribution
also closely related
a close connection between this idea and the main
our paper, whereby an inefficient state
in
inefficient
amount
of limiting the
and Morris, 1995, Rodrik, 1995). There
mechanism
related to other
is
Acemoglu and Robinson (2006b).
politics, e.g.,
an
later
democratic regime.
and Helpman (1996), and models
amount
and
initially
manipulating policies in democratic settings, including lobbying models, such
as Austen-Smith (1987),
The
of other strands of the literature in political economy.
in
our model the choice of
a way of affecting the future political equilibrium so as to bring
the party aligned with the interests of the rich to political power, and via this channel, to
limit the provision of public
goods and taxation. As such, our mechanism
is
also related to
the rationale for inefficient redistribution suggested in Saint-Paul (1996) and Acemoglu and
Robinson (2001), where a
politically powerful
group may push
for inefficient
forms of transfers
in order to maintain its future political power.
There
is
also a small literature
on how politicians may distort
sons. Papers in this literature include
employment) are chosen
Shleifer
models where
policies for strategic rea-
inefficient policies (such as excessive state
in order to gain votes (e.g., Fiorina
and
Noll, 1978, Geddes, 1991,
and Vishny, 1994, Lizzeri and Persico, 2001, Robinson and Torvik, 2005).
papers suggest that
inefficient choices (including wasteful investments, large
and
systems) are
inefficient fiscal
made
Still
budget
other
deficits,
in order to constrain future politicians (e.g., Glazer,
and Svensson, 1989, Tabellini and Alesina, 1990, Aghion and Bolton, 1990,
1989, Persson
Cukierman, Edwards, and Tabellini, 1992). None of these papers feature the mechanism of an
elite creating
an
inefficient state structure to
maintain their political power
in the face of
an
emerging democracy.
Our model
is
also related to the literature
on comparative
politics
and public finance
(e.g.,
Persson and Tabellini, 2003, Ticchi and Vindigni, 2005), which investigates sources of
differences in fiscal policies
among
democracies.
Our approach suggests an
alternative, but
complementary, source of variation, related to the desire and the ability of the economic
elite
to dominate democratic politics, which can generate both differences in the level of public
goods provision and
Finally, our
in the efficiency of the state.
approach
is
related to sociological analyses of "cooptation" in
and
existing elites in the Marxist sociology
political science literatures. In particular,
(1980 pp. 228-234) argues that the control of the state apparatus
economic
elites in
hegemony
a mechanism through which the
in
a crucial objective of the
Gramsci, 1971). However, this literature neither articulates
elite
may accomplish
such a strategy relative to other options.
Basic
is
Therborn
democracy, which they achieve using strategies including cooptation (see
also the discussion of
3
democracy by
these objectives nor models the costs of
7
Model
Description of the Economic Environment
3.1
Consider the following discrete time infinite-horizon economy populated by a continuum
1
of
agents, each of which has the following risk-neutral preferences
oo
BqJ2 P* (4 + Gt-hef),
t=o
at time
Cj
>
t
=
0,
where Eo
is
the expectations at time
=
0,
all
agents, e?t
€
necessary in some occupations), and h
There are two types of agents: n
>
denote poor agents by the symbol
by H, and
also use
C and
{0, 1} is
(0, 1) is
>
is
the cost of
Ti to denote the set of
his skill;
AL
for
is
the level of
1
—n
are rich (high-skill).
(corresponding to low-productivity), and rich agents
K
of investment in infrastructure,
income depending on
>
effort.
1/2 are poor (low-skill), while
L
Gt
j),
the discount factor,
the effort decision of the agent (which will be
poor and rich agents.
There are two occupations: producer and bureaucrat.
amount
@ 6
denotes the consumption of the agent in question (agent
public good enjoyed by
We
t
>
0,
is
In each period, as long as some
undertaken, each producer generates an
poor agents and
AH > AL
for rich agents.
If
the
Another major difference between the Marxist approaches and ours is that in our model bureaucrats can
most Marxist approaches, the state apparatus is, ultimately,
controlled by the economic elite (e.g., Miliband, 1969, Poulantzas, 1978, Therborn, 1980). In this respect, the
notion of bureaucracy and state apparatus in our model is also different from that of Max Weber, which views
bureaucracy as an "apolitical" organization, with no goals or interests. See also Alford and Friedland (1985) for
a critical discussions of Marxist and non-Marxist theories of the state.
side either with rich or poor agents, whereas in
investment in infrastructure
K
is
not undertaken at time
that period. Producers receive and
A
set of agents
The
linear tax rate r t
K,
is
their
income net of taxes.
denoted by Xt are bureaucrats at time
but receive a net wage of wt
wage income).
consume
then no agent can produce within
t,
>
from the government
role of bureaucrats
6
[0, 1]
is
they do not pay taxes on their
(i.e.,
tax collection.
on earned incomes
These agents do not produce,
t.
we
In particular,
same
irrespective of whether the individual
is
rich or poor.
To
it
will
This tax rate
simplify the discussion,
we assume that only poor agents can become bureaucrats. This assumption
for the results, since
investment
in order to finance the infrastructure
additional spending on the public good Gt and the wages of bureaucrats.
the
a
will allow for
is
not necessary
be evident below that low-productivity poor agents always prefer
bureaucracy more than the high-productivity rich agents (see Remark 2 below).
Both
and poor agents can try to evade
rich
taxes.
We
assume that
to evade taxes, he gets caught with probability p(xt), where
p
:
[0, 1]
twice continuously differentiable, and strictly concave function with
number
the
Xt
= Lfx
of bureaucrats exerting positive effort at time
e tdj-
More
t.
—
p
if
an individual
[0, 1] is
(0)
an increasing,
=0, and x denotes
t
formally, this
This expression incorporates the fact that bureaucrats
tries
defined as
is
who do not
exert effort
are not useful. 8
If
an individual
simplicity,
this
is
caught evading taxes,
is
we assume that
all
of his
income during that period
not an important assumption).
We
also
assume that there
is
full
not observed.
is
anonymity in the
This implies that
future punishments on tax evaders are not possible. Moreover, because of limited
>
more
0,
liability, i.e.,
serious punishments are not possible.
Since effort
is
costly,
their effort decision.
probability
For
income does not accrue to the government either (though
this
market, so that the past history of individual producers
Cj
is lost.
qt
We
at time
t.
bureaucrats will exert effort only
assume that
If
if
they do not exert
if
their
effort,
compensation depends on
bureaucrats are caught with
they are not caught, they receive the wage wt, and
if
they are
caught shirking, they lose their wage, but are not fired from the bureaucracy. This assumption
simplifies the algebra
The
and the exposition considerably and
probability of detection
qt
=
1)
=
1,
so that with
an
relaxed in subsection 5.1 below.
depends on the quality of the organization of the state
("efficiency of the state"). In particular,
q{I
is
efficient
we allow two
levels of efficiency, It
€
{0, 1},
such that
organization of the state any shirking bureaucrat
is
Alternatively, instead of inducing bureaucrats to exert effort, it may be important to ensure that they do
not accept bribes from the individuals supposed to pay taxes (e.g., Acemoglu and Verdier, 1998, 2000). We
investigate a variant of our model with corruption in subsection 5.3.
immediately caught, while q (I
=
0)
=
qo
<
I,
so that with an inefficient organization shirking
1=1
bureaucrats are not necessarily detected. To simplify the analysis we assume that
no cost relative to /
At each
=
0.
has
9
date, the political system chooses the following policies:
•
A
•
The wage
•
A
•
The number
•
A
tax rate on
all
earned income r t 6
€ R+.
rate for bureaucrats wt
level of public
[0, 1].
good Gt 6 K+.
of bureaucrats hired,
Xt €
[0, 1].
decision on the organization of the state for the next date, It G {0, 1}
of the state at the current date, It-i,
is
—the efficiency
part of the state variable, determined by choices
in the previous period.
The
additional restrictions on these policies are as follows:
1.
The government budget
2.
If
Xt > Xt-i, then
decide to quit
if
constraint (specified below) has to be satisfied at every date.
existing bureaucrats cannot be fired (although each bureaucrat can
he finds this beneficial). Moreover,
are hired and a fraction
(Xt —
X -\) /X
randomly chosen irrespective of
We
t
Xt < Xt-i, then no new bureaucrats
of the bureaucrats
is
fired (those fired
=
(rt,wt, Gt,
being
their past history).
denote a vector of policies satisfying these restrictions by p t
X
t
,
It)
6
71.
Description of the Political System
3.2
We
t
if
will consider three different political
1.
Permanent nondemocracy: the
the rich can vote, and since
all
environments:
rich elite are in
rich agents have the
available set of policies, the policy vector
will
power
at all dates,
same policy preferences over the
most preferred by a representative
when an
We
rich elite
be implemented.
In general, one can imagine that setting up a more efficient state apparatus
ditures.
meaning that only
may
involve additional expen-
ignore those both to simplify the algebra and also to highlight that inefficient states can arise even
efficient
organization
is
costlessly available.
Permanent Democracy: the
2.
starting at
=
t
regime
The
paper.
way
a simple
To
start with,
for
at
The
comparison.
t
=
0,
and
third one
some
of capturing the idea that
democracy
anticipating that
elites,
power
rich elite are in
two environments are
It is
the majority, are in power at
dates
all
in all future dates, the
be democratic with majoritarian elections.
will
first
who form
(or at all dates there are elections as described below).
Emerging Democracy: the
3.
citizens,
some point
will arrive at
we model the democratic system
is
our main focus in this
decisions are originally taken by
—in
this case right at date
=
t
l.
10
a very simple way, by assuming that there
in
are two parties, one run by an elite agent and one run by a poor agent, and that bureaucrats
cannot run
We
for office.
denotes that party
P
is
P
use the symbols
elected to office at date
to the policies they will implement once they
R
and
to denote these parties
Parties are unable to
t.
come
to power.
and dt
= P
make commitments
Thus whichever party
receives
the majority of the votes comes to power and the agent in control of the party chooses the
own
policy vector that maximizes his
Downsian models
utility.
of political competition
the election. Instead,
it is
This
last
assumption departs from the standard
where parties commit to
closer to the literature
on citizen-candidate models, which
discussed further in subsection 5.2 (see also Alesina, 1988).
we
will consider
candidate, and
it is
be
Specifically, in subsection 5.2,
we
will
show that the same
results apply
with
this richer setup. Nevertheless,
two parties to highlight the main
forces.
Timing of Events
3.3
To
will
a richer model of democratic politics, where each agent can run as a citizen-
useful to start with the simpler environment with only
economic
their policy platform before
recap, the timing of events within each date
•
The
{N,
society starts with
D}
,
a set Xt-i
some
C C
the set of bureaucrats
political regime,
of agents
X -\
t
efficiency of the state, It-\
€
is:
who
are already bureaucrats (since,
must be a subset
{0, 1}.
nondemocracy or democracy,
i.e.,
st
£
by assumption,
of the set of poor agents),
and a
level of
Then:
10
In this case, the society is nondemocratic at date t = 0, and we assume that it will become democratic for
exogenous reasons at date t = 1. It is possible to model democratization as equilibrium institutional change along
the lines of the models of endogenous democratization in the literature (see Acemoglu and Robinson, 2006a, for
a discussion and references), but doing so would complicate the analysis without generating additional economic
insights in the current context.
10
1.
2.
individuals j G
In democracy,
all
j decides vj G
{P,R}.
In democracy, the elected party or in
the policy vector p t
3.
Observing
=
,
agent decides
G K.
is
denoted by the same symbol without any risk of confusion).
~
f° r
an
* ne
" cn
agents.
The number
of bureaucrats at
J Xtdj \ i-e., the minimum of the number of bureaucrats chosen
power and the number of people applying to or remaining in bureaucracy.
then min
in
elite
individual
and each individual j G Xt-\ decides whether to quit bureau-
Naturally, by assumption, \l
by the polity
i.e.,
each individual j £ Xt~\ decides whether to apply to become a
this vector,
cracy, Xf G {0, 1} (which
t is
or party R,
nondemocracy the representative
(T t ,w t ,Gt,X t ,It )
bureaucrat, Xt G {0, 1}
time
P
vote for either party
[0, 1]
<
Xt,
,
This also determines the current set of bureaucrats, Xt.
4.
Each bureaucrat decides whether
f-p X e{dj,
5.
to exert effort, e{
and thus the probability
€ {0,1}, which determines x
t
=
of detection of individuals evading taxes.
Production takes place and each producer decides whether to evade taxes or not, denoted
by
4
G {0,1}.
6.
A
fraction
7.
A
fraction q t
8.
Taxes are collected, remaining bureaucrats are paid their wage, wt, and the public good
G
t
is
p
(x ( ) of producers evading taxes are caught.
=
q {It-lj of shirking bureaucrats are caught
supplied.
Naturally, the society starts with
bureaucrats.
We
also
X-\
suppose that I-\
except the actions at time
4
and punished.
t
=
0,
=
=
0,
i.e.,
in the initial date there are
no incumbent
(though this has no bearing on any of our results
since the choice of It
G
{0, 1}
is
without any
costs).
Characterization of Equilibria
We now
characterize the equilibrium of the environments described above.
Definition of Equilibrium
4.1
Throughout, we focus on pure strategy Markov Perfect Equilibria (MPE). 11
We
focus on
MPE
both because
bureaucrats more
MPE is unique and is relatively straightforward
MPE makes the emergence of a coalition between the rich and the
in the current context the
to characterize and also because the focus on
difficult (since there
cannot be "commitment" to future rents
11
for bureaucrats).
Recall that Markovian strategies condition only on the payoff-relevant state variables (and
An MPE
on the prior actions within the same stage game).
defined as a set of Markovian
is
strategies that are best responses to each other given every history. In the current
S =
aggregate state vector can be represented as
time
political regime at
t,
I -\ G {0, 1}
t
previous period, and Xj_i
is
(s t
t
,
game, the
It-\,Xt-\) G S, where s t G {N,
D}
is
the
the efficiency of the bureaucracy inherited from the
is
the size of the bureaucracy inherited from the previous period. 12
Individual actions will be a function of the aggregate state vector St and the individual's
identity, in particular,
representing whether the individual
Thus
rich producer or a bureaucrat.
which party to vote
B}
a t G {L, H,
G {P,R}, whether to apply
for, i.e., v\
Xt G {0, 1}, whether to evade taxes, z\ G {0, 1},
6
to exert effort, e\
the choice of
It
G
{0, 1}, Tt
a
An MPE
We
is
:
G
Xt G
[0, 1],
strategies can
S x
{L, H,
a mapping a* that
B)
is
a slight abuse of notation,
we
each individual will decide
remain) in bureaucracy,
is
a producer, and whether
Finally, strategies also include
M+ when
the individual
the party
is
R} x
{0, l}
3
x
x
[0, 1]
x R+.
[0, n]
best response to itself at every possible history.
will
use v (I
H, B}
when
risk of confusion,
no
and Gt G
a poor producer,
be represented by the following mapping
-» {P,
of group a G {L,
is
the individual
if
subcomponents of a rather than the
will often refer to
there
n],
[0,
at,
(or to
{0, 1}, if the individual is a bureaucrat.
Thus Markovian
leader.
and
as a function of St
is
\
a) to
entire strategy profile,
denote the voting strategy of an individual
as a function of the efficiency of the state institutions.
we
will
and with
Moreover,
use the index j to denote individuals or groups
interchangeably.
4.2
Preliminary Results
We now
state a
Lemma
number
1 If p(xt)
<r
of results that will be useful
t
,
then z{
~
for
all j
£
X
t
,
throughout the analysis.
all
i-e.,
Proof. Write the payoff of an individual producer j ^
and the
size of (effort-exerting)
V}
bureaucracy
= max { (1 -
Tt ) A*,
is
xt
X
t
producers evade taxes at time
at time
t
when
the tax rate
is
t.
rt
as
(1-p (x t ))
A*
}
+ G + /3V->+1
t
(a*)
,
In addition, for each individual we could specify whether the individual is currently a bureaucrat, i.e.,
whether j 6 Xt -i and whether he is a party leader as part of the individual-specific state vector. Nevertheless,
Markovian strategies can be defined without doing this, which simplifies the notation.
12
A3
where
is
is
the productivity of this individual, and a*
is
the optimal policy, so that
The
his
income
first,
(1
—
Tt)
The
in taxes.
A3
,
is
what the individual
second, (1
— p(x
A3
t ))
is
,
his
probability (1 —p(xt)), but
Limited
liability implies c\
PVt+i ( a *)
max term
§i ven
is
caught and
>
home
loses all his current
and the current behavior has no
if
he pays a fraction r t of
his full productivity
A3
with
income with probability p(xj).
effect
on the continuation value
the anonymity assumption. This expression immediately establishes that the
will pick tax evasion,
Since with tax evasion there
we need
(a*)
expected consumption when evading
In particular, in this case, the individual takes
taxes.
consume
will
t
The max incorporates two
the discounted optimal continuation value for the individual.
terms.
0V 3+1
i.e.,
is
z\
—
<
iip(xt)
0,
Tt, as
claimed in the lemma.
Lemma
no government revenue,
implies that in equilibrium
1
to have the following incentive compatibility constraint for producers
p{x
>
t )
n
to be satisfied. Alternatively, defining
TTtosp-'V),
(1)
producers' incentive compatibility constraint can be expressed
xt >
It
and
is
(2)
sufficient to ensure that all individuals
can be easily
verified that since p(-)
strictly concave,
tt
() defined in (1)
is
is
13
(tj)
tt
This condition requires the number of bureaucrats exerting
This constraint
as:
effort to
be greater than
7r(rt).
choose not to evade taxes.
strictly increasing, continuously differentiable
strictly increasing, continuously differentiable
and
strictly convex.
Lemma
2 //
w < -,
(3)
t
It
then e\
=
for
all
j
G Xt,
i.e.,
Proof. Write the payoff
detection probability
is
bureaucrats will shirk at time
of a bureaucrat j
G
X
qt )
w
at time
t
t
t.
when the wage
rate
is
wt and the
q t as
V}
13
all
- max {w -h,(lt
t
}
+ G + PV j+1
t
t
(a*)
,
This condition can also be interpreted as a "state capacity constraint" since, given the effective
it determines the maximum tax rate.
bureaucracy,
13
size of
the
where a*
is
the optimal policy, so that
for the individual.
effort
The max operator
and receiving the wage
PVf+1
(a*)
is
incorporates two terms representing the payoff to exerting
wt
for sure,
— h, and
the payoff to shirking. Since, by assumption,
bureaucrats cannot be fired for shirking and limited
to shirking
that
we have
Remark
—
is (1
qt)
=
e\
Whenever wt <
Wt-
t
caught shirking. Given
it is
this,
h/qt, the
as claimed in the
1 In subsection 5.1 below,
bureaucracy. In this case,
is
X
£
for all j
the discounted optimal continuation value
we
will allow
liability
max
for
>
0,
the payoff
lemma.
bureaucrats caught shirking to be fired from
clear that the optimal contract involves firing a bureaucrat
the condition in
Lemma 2 will have to be forward-looking,
imagine a stationary equilibrium, where today and in
wage rate
c?t
operator will pick the second term, so
into account the future rents that the bureaucrat will lose
to f, the
makes sure that
bureaucrats
is
if
he
taking
caught shirking. In particular,
future periods the tax rate
all
if
w, and the probability of getting caught
is
equal
then the
is q,
necessary condition (3) would become
w-h
(l-f)A L
^
1-/3
since the left-hand side
1-/3
.
„,
v
y/
V
what the individual would
is
whereas the right-hand side
is
^w-h
-1-PJ
/
'
by exerting
receive
effort at
every date,
the payoff to deviating for one period, and then switching
to exerting effort from then on (implicitly using the one-step ahead deviation principle, see
Fudenberg and
Chapter
Tirole, 1991,
getting caught with probability
q,
4).
In particular, the right-hand side has the individual
receiving nothing today
from then on, and not getting caught with probability
1
— q,
and then receives the discounted version of the left-hand
effort).
A
bureaucrat
who
and the wage of a
in
which case he receives
side (as he switches
loses his job always receives the
producer
low-skill
wage of a
w
today
back to exerting
low-skill
producer from
then on, since along the equilibrium path, there will be no further hiring into bureaucracy.
Rearranging terms, the above inequality can be expressed
,< fl(1
.^ + kM.
In a stationary equilibrium where bureaucrats are fired
replace (3), and
when
it is
compatibility constraint,
satisfied, all
(5),
below
as:
when caught
(4)
shirking, condition (4) will
bureaucrats will shirk. Correspondingly, the incentive
will
change to the converse of
this condition.
We
return
to a further analysis of this case in subsection 5.1.
If
bureaucrats are expected to shirk,
all
individuals will evade taxes and there will be no
tax revenues. Consequently, the infrastructure investment
14
K could not be financed and there
would be no production. Thus, the society
also needs to satisfy the incentive compatibility
constraint of the bureaucrats given by
w > -,
(5)
t
Qt
where
qt
—
q(It-i). This constraint
choose to exert
is,
effort.
is
necessary and sufficient to ensure that
In addition, (poor) individuals must prefer to
bureaucrats
all
become bureaucrats. That
the participation constraint
w >(l-T )A L +
t
t
h,
(6)
needs to be satisfied so that bureaucrats receive at least as
much
as they
would obtain
in
private production.
Remark
2
If rich
corresponding to
agents could become bureaucrats, the equivalent participation constraint,
agents would be
(6), for rich
w > (l-T )A H +
t
Comparison
more
of this inequality with condition (6)
this inequality
The above
lemma
t,
poor agents are always
clear that
Our assumption that
rich agents
cannot
therefore enables us to avoid imposing explicit conditions to ensure that
not satisfied and (6)
is
it
discussion, in particular
is.
Lemmas
1
and
2,
immediately establishes the following
(proof omitted)
Lemma
all
makes
willing to enter bureaucracy than rich agents.
become bureaucrats
h.
t
and
3 In any
MPE,
=
all
z\
l
for
j
=
conditions (2), (5) and (6) must hold and e\
£
X
t
and
1
for
all
j
6 Xt and
all t.
In other words, in any equilibrium the incentive compatibility constraints of producers
and bureaucrats and the participation constraint
evades taxes and
Prom Lemma
all
bureaucrats exert
of bureaucrats are satisfied,
and no producer
effort.
3 (and the fact that only poor agents
follows that, as long as the constraints (2)
and
become bureaucrats),
(5) are satisfied,
it
immediately
the government budget con-
straint can be written as:
K+G
where the left-hand
ture,
side
is
t
+w
t
X
t
<
(1
-
n) r t A
H+
(n
-
X
t)
rt A
L
government expenditures, consisting of the investment
spending on public goods and bureaucrats' wages, while the right-hand side
15
(7)
,
in infrastrucis
government
tax receipts collected from rich and poor agents. This expression takes into account that
bureaucrats exert effort and no producer evades taxes.
Moreover,
(7) highlights
all
that in our
model, taxation reduces output through a particular general equilibrium mechanism; the gov-
ernment can
by hiring bureaucrats and bureaucrats themselves do not produce
raise taxes only
any output.
lemma
Finally, the following
Lemma
4 Rich agents always
always vote for party P,
i.e.,
vote for party R,
for
all
Equilibria under permanent democracy
parison to our
main
political
and then transitioning
Proposition
at each
t
>
=P
dt
G = GD =
t
and t
is
(1
The
there exists a unique
h,
=
vh
1,
d Ah
+
=
(1
- t d ) AL +
[n
-
7T
the unique solution to the
max(l
r,G
-
following results are straightforward:
is
n) t
=^
R, and poor producers
>
Xt—i, v\
and the following policy vector
-
—
7i, v\
environment, which involves the society starting as nondemocratic
to democracy.
It
G
all j
and permanent nondemocracy are of interest as a com-
Under permanent democracy,
1
for
i.e.,
C and j ^
&
j
stated without proof:
is
Permanent Democracy and Nondemocracy
Equilibria under
4.3
immediate and
is
(t
d
))
r
MPE.
implemented
X =
ir
t
D AL -
[(l
(t
In this equilibrium,
at each
t
>
0:
d
)
,
- rD ) A L +
h]ir (r
D - K,
)
(8)
maximization problem:
-t)A l + G
(9)'
v
subject to
G =
Proof. By
(1-ti)tA h
Lemma
4, for all
+
{n-ir(T)]TA L -
j
G C,
v\
vote and form the majority starting at t
decisive voter j'
G C can be written
=
=
[(1
-
t)
AL +
h]ir {t)
- K.
P. Under permanent democracy, the poor can
0,
thus
dt
— P
for all
t.
Then the
payoff to the
as
Vf ^(l-^At + Gt+pV^io*),'
where again a*
is
the optimal policy and (3Vt\i
value for this individual.
The continuation
(a-*)
3
is
the discounted optimal continuation
value /3Vt +1 (a*)
16
is
unaffected by current policies,
thus the optimal policy can be determined as a solution to the following program:
(1-t)A l + G
max
(10)
t,w,X,I,G
subject to
7r(T)
<
X
maxi ——— ,(1 -r)A L + h\
<
w
G <
(1
<
It is
evident that
chosen in
first
all
It
=
1
t
>
is
slack (since this
periods
three constraints
objective function), so
0.
we have
X=
rium, the following policy vector
and t
is
=
1,
w =
t
-wX-K
- X] tA l
=
0j
so will always be
it
would allow an increase
in
w = max {/i, (1 —
r)
periods where
=
(t)
and
r°
is
all
(1
is
It
G, raising the value of the
A L + h\ =
(1
— r) A L +
1, i.e., for all t
>
0.
h.
Strict
uniquely defined.
implemented
- rN A L +
)
there exists a unique
at each
t
>
X = n (t n
h,
t
MPE.
In this equilib-
0:
)
,
G - GN =
t
0,
the unique solution to the equation
[(1
-
r)
AL +
h]
n
(r)
-
(1
- re) tA h
-'[re
-tt
Proof. Under permanent nondemocracy, the rich retain
payoff to the representative rich individual
Vl =
where
[re
G.
Proposition 2 Under permanent nondemocracy,
It
tA h +
Moreover, there cannot be a solution in which any one of the
then ensures that
ir (•)
re)
relaxes the second constraint relative to it
Substituting these equalities yields (9) for
convexity of
-
cr* is
(1
j'
rA L +
political
K=
power
0.
forever.
(11)
Then
the
£ 7i can be written as
- r) AH + Gt +.0V&1 (O,
the optimal policy and /3V/+1 (u*)
this individual.
(r)]
is
the discounted optimal continuation value for
Because the continuation value /3V^+1 (a*)
17
is
unaffected by current policies,
the optimal policy can be determined as a solution to the following program:
(1- t)A h +
max
G
(12)
t,w,X,I,G
subject to
<
7t(t)
max
-— Al-T)A
UW
h
+ h) < w
J
G < (1— n) tA h +
<
It is
again evident that
be chosen.
X=
in
it
(t)
It
—
Moreover, the
and
program
1
it
- X] tA l -
[n
first
wX - K
G.
relaxes the second constraint relative to
w = max {/i, (1 —
(12),
X
=
It
so will always
0,
three constraints must again hold as equalities, so
L
r) yl
+
/i}
=
—
r)
G =
0,
(1
follows immediately that
L
A +
we have
Substituting for these equalities
/i.
and the
strict
n
convexity of
() again
ensures the uniqueness of the solution to (11).
The main conclusion from both
benchmark
of these
political
politically decisive agents choose a policy vector consistent
always involves an efficient organization of the state,
to
make the
i.e., It
environments
with their own
=
1 for all t
>
0.
state inefficient. Consequently, both consolidated democratic
regimes involve 1
=
1.
Moreover,
in
interests,
There
is
and
this
no reason
and nondemocratic
both regimes the capacity of the state
in the sense that constraint (2) holds as equality
that the
is
is
fully utilized
and the minimum number of bureaucrats
necessary to prevent tax evasion are employed.
It
is
straightforward to see that the unique solution (r D ,G°) in (9) involves t d
since infrastructure spending,
>
0,
has to be financed (and for the same reason,
However, because raising further revenues involves the employment of
in Proposition 2).
bureaucrats which
K
> 0,
N
r
>
is
costly, it
is
possible that the solution to (9) involves
GD —
0. If this
were
the case, there would be no difference between the political bliss points of poor and rich agents
given in Propositions
we
are
more
Condition
It
1
and
2
and thus no
interesting political conflict. Therefore, throughout
interested in the case where the following condition
1
The solution
can be verified that
to (9) involves
if
GD >
the gap between
A
is
satisfied:
0.
and
AL
is
small and n' (t)
condition will be violated. Therefore, this condition imposes that there
inequality in society and raising taxes
is
is
is
large, this
a certain degree of
not excessively costly, so that the poor would
a higher level of public good provision than the
18
rich.
When
Condition
1 is satisfied, it
like
also
follows that r
D > t n and
the bureaucracy
4.4
more
Lemma 5 In
N
Gt — G = 0,
Proposition
MPE,
an
and t
n(r N ),G = G N =
t
=
R
6
vector at
all
dates
=
1,
change
be
will
elections.
efficient state institutions,
= R
=
and It
—
We
i.e.,
where
at date
=
0, the
lemmas.
the rich will choose their political
w = (l- t n ) A l +
then
1,
state,"
X =
h,
t
=
t
— tw ) A l +
(l
meaning that once the party of the poor
P, then dt
t'
>
>
=P
for
all
t'
>
t,
and we have
it
(t
n
),
X =
h,
t
P
is
being elected
;
elected, the results
the following equilibrium policy
t:
t
X = ir(T D ),
h,
(13)
t
h]7T(T
D )-K,
given by (9).
is
1).
Now
in (13)
is
the optimal policy of the citizens in permanent democ-
suppose that party
P
chooses the policy vector specified in the lemma.
we
start with It
that v (I
=
1
that v (I
=
1
|
|
=
1
is
in
power at time
Since this includes
as part of the payoff-relevant state vector.
B)
=
P. Then party
B)
^
P, but
X
P
wins the majority at time
< n — 1/2. Then,
party
P
t
and suppose that
t,
It
=
+ 1.
it
the following
1,
Suppose that a*
such
is
Alternatively suppose
again wins the majority at time
In both cases, repeating this argument for the next period shows that party
P
t
+ 1.
keeps power at
dates and establishes the lemma.
To complete the proof we only need
X
=
t
start with a series of
involves choosing the policy vector wt
w = (l-T D )A L +
racy (Proposition
all
the size of
the solution to the equivalent of program (12) in the proof of
1,
Proof. The policy vector
period,
n and
)
permanent nondemocracy.
= G D = (l-n)T D A H +[n-n{T D )]T D A L -[{l-T D )A L +
t
and r D
(t
it
apply subsequently:
Lemma
G
>
)
establishes that the party representing the poor, party
an "absorbing
If dt
d
m
0.
The next lemma
1
(t
given by (11).
is
Proposition 2 for party
of Proposition
in
n
2:
dt
if
Proof. Given that It
It
strictly increasing,
interesting case with regime
shows that with
bliss point as in
is
is
power and from then on there
first result
to office
(•)
Equilibrium with Regime Change
look at the
rich are in
Our
n
permanent democracy than
larger in
is
Political
We now
since
,
> n—
to rule out the case
where v
(I
=
1
|
B)
= R
and
1/2 (the proof to eliminate the case where bureaucrats randomize between the two
19
way
parties in a
to bring party
is
costly for the rich (recall
It
=
Then from Lemma
1.
R
to
program
power
t
bureaucrat
utility of the
VB
(R)
is
the same as a poor producer.
=
1
The
|
B)
=R
V B (d),
- t n ) A L + PVJ
<
(1-t d )A l + G d +
will
=
choose
fact that the last
also the utility that
Then denoting
(a*)
I3V3{cj*)
(P),
a bureaucrat
term
the maximal utility of a poor
is
will receive
when party
P
is
in power,
cannot be a best response, completing the proof of the lemma.
intuition for this result
as follows.
is
Once the party
choose their preferred policy vector, which includes
will
R
and 1
we have
(1
where the inequality follows from the
v (I
=R
B)
t
=
= VB
is
|
X = r(T N ), G = G N = 0.
the utility of a bureaucrat supporting party d by
Since this
1
5,
t
agent.
=
(12) in the proof of Proposition 2), party
w =(l-r N )A L + h,
This implies that the
Since v (I
identical).
is
It
of the poor wins
=
1,
an
and given an
election, they
efficient state,
bureaucrats will have no reason to support the rich party and the poor will continue to win
future periods and the organization of the state will continue to be efficient.
elections in
all
An
organization of the state ensures that bureaucrats receive no rents and receive the
efficient
same payoff
as
poor producers. Thus they
point of the poor will be implemented in
it-i
is
=
1
—
i-e.,
when
the state
all
is efficient
will also
support party P, and the political
future periods. This
—the
rich will not
lemma
also implies that
bliss
when
be able to win a majority. This
related to the basic idea of our approach: the rich can only convince bureaucrats to vote
for their party
by committing to giving them rents and
organization of the state
We
is inefficient, i.e.,
—
next investigate whether or not the rich
vote for their party starting with It -\
of the rich,
The
It -\
next
Lemma
when
lemma
in
power,
will
—
0.
this
can only be achieved when the
0.
may be
Since there
is
able to convince the bureaucrats to
no commitment to
choose policies in line with
its
characterizes these policies starting with It-\
7 Suppose that It-\
=
0,
then wt
=
h/qo.
20
Moreover,
policies, the
party
(the rich agents') preferences.
=
0.
if dt
—
R, then Gt
=G =
0,
and
dt
if
=
P, then Gt
= GD
given by the solution to the following maximization program:
max (1 K
t,G
AL + G
r)'
(14)'
v
subject to
G = (l-n)TAH + [n-ir(T)]TAL -.—ir(T)-K.
Qo
Proof. That any party, when
follows immediately
Lemma
from
power and inheriting
in
The
follows immediately
choose
will
GD
from the program
as in (14),
additional restriction that
Remark
involve
rich
=
u>t
imposing
u>t
and the poor
is
The next lemma provides necessary
—
Lemma
MPE, d = R,
8 In an
when
as there,
sufficiently high, the solution to the
starting with It -\
K
h/qo.
To
h/qo
cannot be
= GE =
see that party
P
with the
(10),
m
h/qo.
With the same reasoning
0.
=
=
io t
choose Gt
will
go back to the maximization problem
3 As with the solution to the maximization problem
GD =
R
fact that party
in (12) after
suffices to
it
choose
0, will
investment in infrastructure
3 (otherwise, the
financed and there will be zero production).
—
It~\
the solution to (14)
(9),
may
the level of inequality between the
program
(14) will involve
GD >
0.
conditions for the party of the rich to win an election
0:
i.e.,
t
(1
-
q
)
the rich will
->
win the election
- rD ) A L + GD +
(1
at
^G
time
t,
if It-i
=
0,
D
(15)
,
P
<?0
and
X >n-\,
(16)
t
where
GD
Proof.
is
given by
Lemma
(8),
GD
is
given by (14), and t d
6 establishes that It-i
consider the scenario in which party
bureaucrat will be
v\
= R
fired).
in
given by
necessary.
—
and
(9).
Now
suppose that It-i
X
X -\
€ X
t
>
which individual j
Then, his net per-period payoff
will
t
t
is
be Wt
(so that
=
and
no current
pivotal and chooses
—
h
=
(1
—
qo) h/qo,
lifetime utility of
Vi
In contrast,
is
chooses It
Consider the case
in all future periods.
and give him a
R
=
is
if
j
& Xt were
-
-i-il^^.
1-p
to choose v\
Vi
= P when
pivotal, his value
= ±-h+G D +pvi+1
21
(17)
go
.
would be
(18)
when party
P
last expression incorporates the fact that
if
V +l
3
where
This
t
the continuation value
is
bureaucracy, setting It
The comparison
=
1,
of (17)
and that /
and
it
R
power from then on, given by
in
the poor are in power, they reform the
an absorbing
state.
—as a weak inequality—as a necessary condition
when they
Condition (16)
are pivotal.
were violated, bureaucrats would not be pivotal and party
half of the votes even with
both (15) and
all
=
=
of bureaucrats voting v\
(16) are necessary.
sufficient to ensure dt
Moreover, (15)
—
also necessary
is
R would receive less
than
R. This argument establishes that
as a strict inequality
R, since when both of these conditions hold,
strategy for bureaucrats to vote for party
and the
1 is
(18) gives (15)
for bureaucrats to support party
since, if
—
is
R whenever It-i =
—and
(16) are also
a weakly dominant
it is
and the coalition of bureaucrats
rich have a majority.
Lemma
which the bureaucrats
8 determines the conditions under
and
(a rich agent running for office)
will
will
support party
R
be numerous enough to give them the majority.
Condition (16) requires the size of the bureaucracy to be sufficient to give the majority to
party
R
when
all
bureaucrats. vote with the rich. Nevertheless,
X—
size of bureaucracy. In particular, at
To ensure that
Let us
first
it
n—
w—
we need to consider two cases separately.
r E as the tax rate that party R would choose
does,
define
E
h/qo- Clearly, r
it
K, given
(r
E
)
is
- - (1 - n) r E A H -
necessary to avoid tax evasion,
first
X=
it
[n
(t
e
)
,
and the
The second
that bureaucratic wages are equal
-
R
is
vr
(r
E
when
)}
r
the
E AL
+K=
0.
(19)
minimum number
of bureaucrats
are employed.
case corresponds to the one where
optimal size of bureaucracy for party
satisfied
as its unconstrained optimal
given by the unique solution to the equation
In other words, t e balances the government budget
The
actual
government budget may not balance.
1/2, the
policy to finance the investment in infrastructure,
to
n — 1/2 may not be the
it
{t
e > n—
)
also sufficient to
1/2, so that the unconstrained
make
sure that condition (16)
is
rich have a majority.
case applies
when
this inequality
does not hold,
i.e.,
when
-it
{t
e
)
< n—
1/2.
In this case, the unconstrained optimal policy for the rich would not satisfy (16), and party
R
cannot win the election with the
win an
election only
if
X
>n—
1/2,
minimum number
and with
of bureaucrats.
Instead, party
this larger size of bureaucracy,
22
R
can
budget balance
S.E
given by the solution to
requires the greater tax rate f
l\h
2/
It
a A"
AH - =-t*
!-B A h +
{l-n)f-E
rich to
7r
(t-
5
t
),
E < te
go
The
either t
The
the
maximum
max
is
<r E
is
given by
(l
tt
f
,
(t
e
)
and n
—
1/2,
,
and whenever
and correspondingly,
}.
be able to generate
for the rich to
remains to check whether the rich
inefficient state in order to
(t
and
,
td
is
_
0)
given by
maintain political
this question:
te
(9),
—
(I
d - te
)
^
^_
Under the
is inefficient).
- r D ) AH +
Ah
to set It
>G d
=
for
all t if the
given by (19), and f
is
B)
|
—R
rule of party
(that
E
is
given by (20).
they will vote for party
is,
P, the per period return of the
,
,
R
^
^
.
For the second part, note that party
,
(l-f E )A H >
_ T D^ A H + G D^
AH + p
G D When t e > f E party R can remain
period return (l — r E ) A H which establishes
and obtain the per
r£
>
also have f
in power. It
and
,
(8),
whenever the state
is
we
),
lemma answers
following
Proof. Suppose that bureaucrats play v
rich
E
of
{'r
and commit to an
{1
GD
(20)
is satisfied:
e > fE
orr E
R
(r
9 Suppose that condition (15) holds. Then the rich prefer
following condition
where
> n
1/2
from the bureaucrats to remain
in democracy.
Lemma
is
needs to set
prefer to pursue this strategy
power
—
have provided the necessary conditions
results so far
sufficient votes
R
0.
This implies that the size of the bureaucracy necessary for the
.
form a winning coalition
the tax rate that party
K=
2
can be verified that whenever n
n — 1/2 <
:.
*
can always choose
in
power by choosing
the
its
first
7"
=
part (21).
myopic optimum when
in
power. This will give a representative rich agent utility
VR =
Here
(l
- t e ) Ah
is
(1
- rE ) A H +
-L-
current consumption, and
(3
[(1
- td ) AH + G D
]
[(l
- td ) Ah + GD
]
.
/ (1
— /?)
uation value, which follows from the observation that since, by assumption, r E
n — 1/2 >
7r
E
(r
implies that party
X=
and thus party
)
P
will
win
n — 1/2 and guarantee
the higher rate f
.
This
all
R
will lose the election at the
elections in
to be in
will give
all
power
next date.
forever,
(1
-
if)
1-/3
23
the contin-
< t E we have
,
Then Lemma
future dates. Alternatively, party
6
R can choose
but at the expense of taxing the rich at
a representative rich agent utility
yn
is
A"
'
Comparison of
VR
Remark 4
Condition
If
were not
1
the conditions in
satisfied,
1
does not hold,
that neither part of condition (21) could hold. This
system of patronage
inefficient
Now
putting
these
all
(15)
It
and (21)
=
for
>
R
the rich party
0,
be
9 could never
and t d = r E
sat-
so
,
a direct consequence of the fact that a
is
necessary for the rich to set up
obtain:
environment with emerging democracy.
the political
hold, then there exists a
all t
(21).
politics.
lemmas together we
Proposition 3 Consider
is
Lemma
we have G D —
between the rich and the poor
significant conflict in policies
an
second part of
in the previous expression gives the
when Condition
In particular,
isfied.
VR
with
unique
MPE.
In
If conditions
this equilibrium, the rich elite
choose
always remains in power and the following policies are
implemented:
w
t
— X
=
,
t
= max{7r(r £ ) ,n-
1/2}
,
go
G
where t e
is
given by (19) and f
the unique
MPE
unique policy vector
is
0,
andr = max {t E ,t e }
t
,
given by (20).
involves
It
=
1
in the initial period,
and for
all t
>
1
dt
,
and
{l-r D )A L +
X = n(T D ),
=
G
t
= G D = {l-n)r D A H +[n-n(T D )}T D A L -[(l-T D )A L + h}n(T D )-K,
given by
is
Lemma
9,
h,
t
(9).
first
part of the proposition follows immediately from combining
which provide the conditions, summarized by
(15)
and
(21),
the rich relative to living under the rule of party P.
P
is
in
is
8
desirable for
(15) or (21) does not hold, then
power and the second part of the proposition follows immediately from
and Proposition
Remark
When
Lemma
under which the
party of the rich, R, can convince the bureaucrats to vote for them, and this
party
the
is
t
Proof. The
6
=P
w
and t d
and
= GE =
on the other hand, one or both of conditions (15) and (21) hold with the reverse inequal-
If,
ity,
t
Lemma
1.
5 Proposition 3 does not cover the case in which one of conditions (15) and (21)
holds as equality; in this case the
MPE
is
no longer unique.
24
It is
straightforward to see that
poor party could receive the majority of the votes, or the
in such a case, either the rich or the
rich could
be indifferent between maintaining an
inefficient
and an
efficient state.
We do
not
describe the equilibrium in these cases to avoid repetition and to save space.
Remark
6
It
can also be verified that the set of parameter values where It
equilibrium in Proposition 3
high values of
j3
is
our
major
first
result.
are in power temporarily at time
and a
straightforward
way
emerges as an
of doing this
is
to consider
as in the proof of Proposition 5 in the Appendix.
Proposition 3
who
A
nonempty.
is
—
t
large (inefficient) bureaucracy as a
establishes the possibility that the rich elite,
It
=
0,
way
may
choose an inefficient state organization
of credibly committing to providing rents to
This enables them to create a majority coalition consisting of themselves and
bureaucrats.
This coalition implements policies
the bureaucrats, and thus capture democratic politics.
that support low redistribution and low provision of public goods, but creates high rents for
more
bureaucrats. Perhaps
interestingly, after
inefficient state institutions persist
fact that at
efficient.
any date these
The reasoning
bureaucrats in the
by keeping an
is
and the
t
=
1,
even when the society
This
rule of the rich continue.
inefficient institutions
is
democratic, the
is
in spite of the
can be reformed at no cost and made more
related to the formation of the coalition between the rich
first place.
The
rich realize that they will
inefficient state structure
and creating
and the
be able to maintain power only
sufficient rents for bureaucrats. If these
rents disappear, bureaucrats will ally themselves with the poor, since their net income will be
the same as the net income of poor producers (recall
Lemmas
5
and
6).
It is precisely
the
presence of inefficient state institutions creating rents for the bureaucrats that induces them to
support the policies of the
Recognizing
rich.
this,
when
in
power the
rich choose to maintain
the inefficient state structure. At the next date, the party representing the rich receives the
support of the bureaucrats and the
continues.
The model
and the persistence
state than they
therefore generates a political
of inefficient state institutions.
economy theory
for
both the emergence
14
would have been under permanent democracy
(recall
Proposition
1
inefficient
and
Lemma
the size of the bureaucracy can be greater than under permanent democracy. This could be
the case
14
consequently, the rich remain in power and the cycle
noteworthy that even though taxes are lower in the equilibrium with
It is also
9),
rich;
when
The nature
the rich
elite hire
more bureaucrats than necessary
for
preventing tax evasion
from the persistence of policies arising in Coate and Morris (1999),
is not on persistence of a certain set of
collective decisions within a given institutional framework, but on the persistence of the inefficiency of state
Hassler et
al.
of persistence here
(2003), or
is
different
Gomes and
Jehiel (2005), because the focus
institutions.
25
—
in order to create a majority in favor of the persistence of the inefficient state
X
where
>
tt
(t £ )
In particular, note that bureaucracy will be
.
control of the elite than in
i.e.,
in the case
more numerous under the
democracy whenever
tt
(t
d
)
<n-
Since in this case equation (21) implies that t e
1/2.
< t d we must
also have
,
n (r E )
<
tt
(t
d <
)
n — 1/2 and thus
X
> n
(t
e
.
)
Consequently, the rich not only choose an inefficient state organization, but they also choose
overemployment of bureaucrats,
number
the
of bureaucrats
in the sense that
strictly greater
is
capture of democratic politics by the rich
bureaucracy
is
now
than that necessary
elite therefore creates
unnecessarily large and
for tax inspection.
an
inefficient state,
The
with
poorly monitored and overpaid bureaucrats, and also leads to a situation in which the capacity
of the state
is
not fully utilized. These inefficiencies imply that the allocation of resources in
a captured democracy
is
worse than in a nondemocracy (or than in a perfectly functioning
democracy). Naturally, these
number
inefficiencies
have a political rationale, which
is
to increase the
of bureaucrats that will vote for the party aligned with the rich, so that the rich can
maintain political power in the future.
Interestingly, because creating
efficient
one (which
is
an
inefficient
bureaucracy
is
more
costly than creating an
smaller and gives bureaucrats no rents), the citizens are worse off in
a nonconsolidated (emerging) democracy, where they are taxed at rate
max {t e ,t
\,
than
they would be under a consolidated nondemocracy, where they are only taxed at rate t n
max
{r
,t
}.
Moreover, the rich are also worse
off in this
<
equilibrium than they would be in
a permanent nondemocracy, since they are paying higher wages to bureaucrats and possibly
employing an excessive number of them.
4.5
We
Comparative Statics
next investigate the conditions under which the equilibrium involves the emergence and
persistence of inefficient state institutions.
The
following proposition establishes that a certain
degree of inequality between the poor and the rich
high discount factor,
/?,
(i.e.,
and intermediate bureaucratic
a high
level of
rents, (1
—
A
/A L ), a
sufficiently
qo) h/qo, are necessary for
the emergence of inefficient state institutions.
Proposition 4 Consider an economy characterized
and
the function
p
(•)
.
Holding
all
L
H
by the parameters (f3,n,A ,A ,K,h,qo)
other parameters constant, we have:
26
1.
there exists a
>
1
2.
there exist a'
>
1
3.
there exists
such that
and
9>0
Proof. For the
E
(21)
A H /A L <
that if (1
AL — A H
>
A H jA L >
O
,
is
necessary for It
G D / (1 —
GD >
necessary for
a', is
O ).
=
sum
4;
=
1;
ft
<
implies It
=
1;
It
=
l.
be violated and the conditions
1 will
and Proposition
9
Suppose
this is the case.
some minimal
there exists
such that
O
,
a'
It
efficient, i.e.,
inspection of the maximization problem
Lemma
of the other terms
<
this implies that there exists
always
h/qo £ (H,6), then
3 that
0,
is
A H /A L >
Remark
Since G D >
0.
Since the
0.
go)
Condition
cannot hold. Then the result follows from
For the second part, recall from
(15)
—
Remark
part simply recall
first
then the state
a,
such that as long as
(0, 1)
and 9 such
immediately shows that as
(9)
if
£
O
on the
level of inequality, say
such that
hand
right
<
for all
3.
From Proposition
(0, 1)
in
(1
3,
—
side of (15)
(15) will
condition
go)
is
h/qo
=
positive,
be violated and thus
= l-
It
—
For the third part, note that bureaucratic rents are equal to h/qo — h
(1
—
go) h/qo,
which
needs to be greater than or equal to the right hand side of (15). Let this right hand side be
denoted by 9 (and note that
This implies that we need
value of
(1
—
(21) cannot
(1
—
0). If (1
satisfied,
thus
It
=
1.
—
>
h/qo
go)
say #0i such that
go) h/qo,
be
>
9
h/qo
go)
<
then (15)
9,
will
9
>
0.
Next observe from
te
=
1-
It is
evident that
This implies that for
/(
=
0,
be violated and It
=
1.
(19) that there exists a
when te —
1,
we need h/qo <
9q
condition
and thus
(l-qo)h/qo<9. U
The
first
part of the proposition implies that a certain level of inequality
the emergence of an inefficient state.
not be redistributive and
will
it
This
is
is
necessary for
with limited inequality, democracy
intuitive;
not be worthwhile for the rich to set up an inefficient
will
bureaucracy in order to keep the poor away from power. The second part implies that the
high discount factor
is
also necessary for the
because bureaucrats vote
the future. Instead,
if
GD >
0.
If their
R
as an "investment"
,
that
inefficient state.
is,
This follows
to obtain higher returns in
they deviate and vote for party P, in the current period they receive
both the same high wages
P,
for party
emergence of the
(since It
=
0)
and the positive
discount factor were very small,
to convince bureaucrats to support their party.
15
level of public
it
good provided by party
would be impossible
for rich agents
Finally, the third part of the proposition
implies that bureaucratic rents need to take intermediate values. If bureaucratic rents are very
10
Robinson (2001) and Acemoglu and Robinson (2006b) also obtain the result that higher discount factors
lead to greater inefficiencies. However, in these models the source of inefficiency is very different. In
particular, inefficient political equilibria arise when pivotal agents
elites or rulers
are sufficiently patient and
may
—
thus take inefficient actions in order to secure their future political survival.
27
—
small, bureaucrats
would not support the party of the
they are very large,
rich. If
it
becomes
prohibitively costly for the rich to control democratic politics.
While Proposition 4 shows that a certain degree of inequality
is
necessary for It
=
0, it
does
not establish that inequality has a monotonic effect on the likelihood of an inefficient state.
The next
distribution in the economy,
Y=
income,
— n)
(1
Proposition 5 Suppose
1
—
7T
(t
<
)
Then
1.
a simultaneous increase in
i.e.,
A H + nA L
that
(r)
ix
there exists
the inefficient state equilibrium,
AH
and decrease
of the
in
AL
income
such that
remains constant.
log-concave in r and t
is
/3
restrictive assumptions.
we mean a mean-preserving spread
In this proposition, by greater inequality
mean
somewhat more
proposition establishes this result under
G
such that for
(0, 1)
i.e., It
=
more
0,
d
all j3
given by (9) satisfies r D
>
greater inequality
/3,
<
makes
likely.
Proof. See the Appendix.
Remark
7 The condition that n
p (x) that
takes the power function form,
this condition.
violated,
The condition
that
we would have that the
non-increasing in
A
L
(see the
(r) is log-concave
td <
i.e.,
1
—
p
tt
utility of the
(x)
is
=
Pqx 01
D
(r ) <
poor
in
not very restrictive. For example, any
Po
for
1 is also
>
and a G
natural;
democracy
(l
if
(0, 1), satisfies
this condition
were
— t d ) A l + G d would
be
Appendix).
In addition to generalizing the
part of Proposition
first
4, this result
implies that taxes (and
public spending) can be higher in more equal societies, because unequal societies are more likely
to create inefficient bureaucracies to limit taxation and public spending. This result therefore
presents an alternative explanation to the often-discussed negative cross-sectional correlation
between inequality and redistribution
5
Perotti, 1996,
Benabou, 2000).
Extensions
In this section,
we
discuss a
bureaucrats to be fired
straint of bureaucrats
will lose
when he
ment where each
number
when they
is
Third,
of extensions of our
benchmark model.
First,
we allow
are caught shirking, so that the incentive compatibility con-
forward-looking and takes into account the rents that a bureaucrat
gets caught not exerting effort. Second,
we
allow a richer political environ-
individual can run for office (form a party) as a citizen-candidate, so that
bureaucrats can also form their
rich.
(e.g.
we consider the
own party and compete
against the party of the poor and the
case where the moral hazard problem of bureaucrats arises from
their temptation to accept bribes that
might be offered by taxpayers.
28
Equilibrium
5.1
The main
When
Bureaucrats Can Be Fired
result of the previous section, Proposition 3,
when they
bureaucrats cannot be fired
was derived under the assumption that
are caught shirking.
This simplified the analysis by
enabling us to write the incentive compatibility constraint of bureaucrats in the simple form
As discussed
of condition (5).
Remark
in
when they
allow bureaucrats to be fired
optimal.
is
The
this
was mainly
discussion in
Remark
firing
is
clear that
the incentive compatibility constraint of bureaucrats, the equivalent of
be:
Given
this condition, all of the results
ifications. In particular
Lemma
any
Gt
10 Consider
MPE,
=
GE
if a\
=
0,
=R
are caught
- p{1
(1
(5), in this case,
would
-^ h
(22)
.
from the previous section apply with appropriate mod-
we have (proof omitted):
environment where bureaucrats can
the
and It -i
where f
=
we have
0,
w =
t
fi
(l
- fE)
Then
be fired for shirking.
L
A +
-
(1
(3
(1
-
q
))
h/q
in
and
the solution to
is
(±-e(i-«o))h -
Hl _ f E )AL+
A,
from the viewpoint
when they
bureaucrats
now
establishes that, in a stationary equilibrium,
1
w>P(l-r)A L +
We
for expositional reasons.
are caught shirking. It
which commits to
of discouraging shirking, a contract
shirking
1
(1
- n) t e A h -
[n
- Xm
f
]
EAL
+K=
(23)
9o
= max {n
where X m
(f
E
)
,
n — 1/2}
.
Moreover, we have the following generalization of
Lemma
Lemma
9 (proof omitted):
11 Consider the environment where bureaucrats can
any
MPE,
It-i
=
the rich will
win the election
at time
t
only
if
there
0; if bureaucrats prefer to support the party of the rich,
P
(1
_ rE) AL +
^LlM-M h >
(J
be fired for shirking.
an
is
i.e.,
rich-bureaucrat coalition has the majority,
if the
_ TD) A L + G D +
i.e.,
inefficient state,
D
-^G
P
l
(24)
,
if
* >n-i
(25)
t
where f
is
given by (23),
GD
is
given by
(8),
td
i.e.,
if
<70
and
Then in
is
given by
(9),
and
GD
is
given by the
solution to
max(l-r)^l L +
G
T,G
subject to
{l-n)rA H +[n-n(T)]TA1
/3 ( 1
.r E )AL + (l-l3(l-qo))<7o
29
n
(r)
- K.
this equilibrium
Furthermore, the rich prefer
(t
and choose
d - rE AH >
)
GD
It
=
at time
3:
the political environment with emerging
bureaucrats can be fired
caught shirking.
MPE
one in which the rich
is
elite
=
Tt
—
f
where f
,
involves
is
h/qQ
))
,
conditions (24) and (26) hold, the unique
in the initial period
X =
max {n
t
E ,n)
(f
and for
all t thereafter,
implemented
the following policies are
at all dates:
G = GE =
1/2},
t
0,
It
—
1 in the initial period,
(1
and for
all t
>
1
a\
,
= P
and
t
t
Combining
Proof.
Lemma
under which the party of the
10 and
rich,
Lemma
immediately from
Lemma
6
-n
(t
d
)}
t d Al
-K-
and
(26),
R, can convince the bureaucrats to vote for them, and this
P
do not hold, then party
[n
MPE
the unique policy vector
11 provides the conditions, (24)
When
desirable for the rich relative to living under the rule of party P.
or both,
and
given by (23).
- t d ) A L + h, X = vr (t d ), G = G D = (1 - n)r D A H +
- t d ) A L + h] n (t d ), and t d as given by (9).
=
[(1
is
q
)
=
democracy and suppose that
one or both of conditions (24) and (26) hold with the reverse inequality, the unique
If
wt
- f E A L + (1-[3{1-
(1
[3
It
power and
the rich party always remains in
Wt
choose
if
if
(26)
Proposition 6 Consider
Then,
only
.
These two lemmas give the following analogue to Proposition
if
t
is
in
instead (24) or (26),
power and the second part of the proposition follows
and Proposition
1.
Proposition 6 demonstrates that the main results from Proposition 3 generalize to the
environment where bureaucrats can be
worth noting, however.
factor,
is
makes the emergence
/?,
can be
but
main
One important
caught shirking.
analysis, Proposition 4
of an inefficient state
more
difference
is
showed that a higher discount
likely.
Instead,
when bureaucrats
the relationship between the discount factor and the emergence of inefficient states
fired,
more complex. Higher
rents,
In our
fired if
(5
again increases the importance that bureaucrats attach to future
also reduces the level of rents, because being fired
it
from bureaucracy becomes more
costly.
5.2
Political Equilibrium Citizen- Candidates
The previous
between
P
analysis limited the political system under
and R, the two parties representing the
justified this
democracy
interests of the
by assuming that bureaucrats are not allowed
are not allowed to run for office,
it is
to a two-party competition
to
run
poor and the
for office.
Even
if
rich.
We
bureaucrats
possible that a party representing their interest might
30
form.
If
such a party forms, bureaucrats
may
vote for that party, and the coalition between
the rich and the bureaucrats, choosing low public good provision and low taxes,
We now
materialize.
investigate whether in general
we expect
this to
may
not
be the case or not when
multiple parties can enter the political system.
We
follow
Osborne and
Slivinski's (1996)
and Besley and Coate's (1997) citizen-candidate
model, where each individual agent can run as a candidate and upon election chooses his mostpreferred policy vector. This setup
make
not
The problem with the
office.
we used above,
and the policy vector was chosen
credible policy promises
was elected
quite similar to the one
is
since parties could
after a politician (party)
citizen-candidate models in general
is
that
when more
than two parties compete, coordination among the citizens regarding which party has a chance
to win the election
voting stage.
is
important
for the
outcomes and typically lead to multiple equilibria in the
To avoid these problems, we consider the
following modification of the standard
citizen-candidate model:
Each individual can decide
1.
is
taken to be small
utility
and run
to form a party
(in particular,
we
for office,
and
where e
\ 0).
will consider the case
from coming to power, but simply benefit from being
in
this has cost e,
which
Individuals derive no
power by implementing
policies
that are in line with their interests.
2.
Given
ferable votes,
all
parties that are running for office, individuals vote using ballots with trans-
meaning that each individual ranks
all
parties in strict order of preference.
particular, the vote of individual j can be represented as \\
distinct elements of {R, P,
according to the
rule,
first
B},
e.g.,
vJ — RBP.
In the
t
Then
preferences of the voters.
the party that gets the lowest fraction of votes
to the second-ranked choice of the voters
who had
is
= i^h,
first stage,
as
is
where
i\,i2
and
In
£3 -are
parties are allocated votes
standard with this type of voting
eliminated, and
its
votes are allocated
originally voted for this party. This process
continues until one of the parties has a majority.
To simplify the
discussion, in this section
we assume that bureaucrats cannot be
caught shirking, so the incentive compatibility constraint for bureaucrats
though
this has
Given
no
effect
this setup, the notion of
analysis in this case
Lemma
on any of the
is still
given by (5)
results in the section.
Markov
Perfect Equilibrium
is
is
modified accordingly.
The
a weakly dominant strategy for each individual.
Proof. The transferable votes imply that
is
if
tractable thanks to the following series of lemmas:
12 Truthful ranking
individual
is
fired
pivotal, has a choice
at
any stage of the elimination process, either an
between two options, and thus
31
is
better off ranking his
more
preferred
outcome above a
any choice
Lemma
of the
is
13 In any MPE, there
same
two
outcome. Alternatively, the individual
a best response. This establishes that truthful ranking
group.
Proof. The
(or
less preferred
Thus the
will
never
be
maximum number
two bureaucrats)
of parties
be
will
not pivotal,
weakly dominant.
more than one party operated by an individual
result follows since the policies chosen
rich agent or
is
is
is three.
by two parties run by two poor agents
Moreover, from
identical.
agent ranks parties truthfully, thus the addition of a
new party
will
Lemma
12,
each
not change the equilibrium
probability that a party run by a poor individual, a rich individual or a bureaucrat wins the
election.
Thus conditional on a party run by a poor agent
other poor agent to incur the cost e
Lemma
>
and form a
existing, there
is
no point
for
any
party.
13 then enables us to simply look at the (truthful) preference ranking of each
individual over at three parties {P, R, B}, corresponding to parties run by a poor individual,
a rich individual and a bureaucrat (there
is
no source
of confusion in this notation, since
there can at most be one party run by a poor agent, one run by a rich agent, and one run
by a bureaucrat). To do
types of parties.
parties
P
and
R
of bureaucrats).
bureaucrat.
Lemma
The
Our previous
We
Gt
0,
know
the policies that will be chosen by the three
R
trying to
is
come
to office by attracting the votes
therefore only need to look at the policy choice of a party run by a
following
—
to
analysis already establishes the policies that will be chosen by
(provided that party
14 Taking future
policy vector:
we need
this,
lemma
characterizes this choice:
election results as given, the party d t
X = min [X -i,n (t b )},
wjb
—
arg
would choose the following
and (t b ,w b ) such
t
t
=B
that
max w
subject to
mm{X ^,ir(T)}w + K
t
Proof.
<
(1
-
tA h +
n)
[n
- min {X
t
_i,7r (r)}]
tA l
.
This immediately follows by writing the program to maximize the return to a
bureaucrat (without allowing
firing of existing bureaucrats):
w+G
max
T,w,X ,I,G
t
32
subject to
min{X _i,7r(r.)}
<
X
-r) A L +
<
to
G <
(1
t
in;is
-ttt,(1
!
/i I
•iVtT
<
constraint. Notice that
Lemma
n)
rA H + n -X] tA l [
wX - K
G.
would maximize
Intuitively, bureaucrats
-
their
wages subject to the government budget
14 applies taking the results of future elections as given.
If
the
current bureaucratic government could influence the outcome of future elections, this could
be beneficial
for
it
only by increasing Xt above min {Xt_i,7r (t
government budget constraint) make
this policy vector
even
)},
which would (from the
less attractive to
poor and rich
agents.
The key
government
to the results in this section
is
the following observation: because a bureaucratic
maximize wages paid to bureaucrats (and provide no public goods),
will
a lower utility to poor agents than a rich government would do. As a result,
To show
bureaucratic government will never get elected.
vote of individual j at time
means that the
party
t
by Vj which
,
is
this
more
we
it
will see that a
formally, let us denote the
= PRB
a ranking over {P, R, B}. For example, vj
individual ranks the poor party
first,
the rich party second in the bureaucratic
last.
We now
Lemma
15
have the following rankings
IfjEH,
If.j
€ £ and
If j
6 X, thenv{
Proof.
We
j
<£
Proposition
then v£
for individuals:
= RPB.
X, then w\
= PRB.
= BRP.
have already established that voters rank parties truthfully, so that
rank their own party
first.
(3) to attract
Assuming that party
the bureaucrats,
the poor as second choice; hence,
if
to the bureaucrats since neither of
j
offers
wB
party
B
get
the rich are in power. Hence,
chooses a wage
for
voters
implements the policy characterized
we have that bureaucrats indeed
€ X, then Vj
them
R
all
= BRP.
in
prefer the rich to
Moreover, the poor prefer the rich
any public good, but the rich tax
less
than the
bureaucrats. This follows since both the rich and the bureaucrats choose to finance
if
yields
K, and
bureaucrats higher than the wage h/qo that the bureaucrats
if
j
G C and
33
j
£ X, then v^
= PRB.
Finally, the second
choice of the rich
is
for the poor,
both because the poor would provide a positive amount of
the public good rather than zero as the bureaucrats would, and because the poor would tax
then the bureaucrats given that the marginal cost of taxation for the poor
less
zero for the bureaucrats (who are not taxed by assumption).
vf
It follows
positive,
is
that
and
j £ 7i, then
if
= RPB. n
Lemma
15 implies that the poor,
when they cannot have a majority by
themselves,' will
support the rich party, thus as long as the bureaucrats are not in majority by themselves,
X
t
<
1/2 and the rich pursue the policy in Proposition
3,
we
have dt
will
=
i.e.,
R. This implies
that the rich can continue to use same political strategies as in the previous section to control
democracy.
political decision-making in
Now
combining the previous lemmas, we have the following proposition, which mirrors
Proposition
3.
Proposition 7 Consider
environment with emerging democracy and free
the political
entry by citizen candidates. Suppose e [
1/2, where t
e
game, only a party run by a rich agent
—
by It
for
0,
all t,
If
w —
where f
is
X —
t
,
max {71-
,n-
(r^)
MPE
The unique equilibrium policy vector
1/2},
is
is active,
G = GE =
t
MPE
=
1
t
case
(21) hold.
Then, from
Lemma
15,
when
The assumption that X-\ =
assumption that tt (t e ) < 1/2 ensure
X
never win an election.
X-i <
1/2,
when
and the
the rich party
crat incurs the cost e j
argument as
is
in power. Therefore,
to form a party,
the policy in Proposition 3
(if
[
to
when
<
for
it
(t
d <
)
[n
First,
-
and for
all t,
it
(t
d
)]
t d Al
all
-
suppose that con-
1/2, the bureaucratic party
implies that in the initial period
that
X
<
the rich party
1/2 continues to be the
is
in power,
and thus bureaucrats support party
in the proof of Proposition 3. Next,
no poor agent incurs the cost s
election,
given
is
involves only a party run by a poor
Proof. This proposition can be proved by backward induction.
and
<
= max {t e ,t e },
and r t
0,
the unique equilibrium policy vector involves It
t
ditions (15)
)
given by (20).
defined by (9), then the unique
and
5
(t-
of the citizen- candidate political
t>l,VH= {l-r D )A L + h, X = n(T D ), G = G D = {l-n)T D A H +
[(l-T D )A L + h]n{T D )-K.
will
it
one or both of conditions (15) and (21) holds with the reverse inequality and
d
1/2, where t
agent
h/q
t
is active.
and (21) and
that conditions (15)
Then, in any
defined by (19) above.
is
and
that
political
R
no bureau-
by the same
knowing that bureaucrats support party R,
compete against party
R
as long as party
R is
choosing
they did deviate from this policy, then a poor party can win an
and thus a poor agent
will find
it
beneficial to enter
34
and form a party since
e
I 0;
thus despite the fact that party
P
R has
would not be running, party
vector as in Proposition 3). Finally, since e
cannot be an equilibrium
J 0, it
same policy
to adopt the
for
no
rich agents
to form a party, since such a party would create strictly positive gains for each rich agent,
the cost of creating a party
The proof
inequality
is
of the cases
e J 0.
is
where one or both of conditions
and
(15)
(21) hold with the reverse
similar.
This proposition therefore shows that our main results regarding the use of an
way by the
state as a
The
is
enriched to allow free entry by citizen-candidates of any
additional insights that
interesting in this case
is
producers prefer to support the party of the
B, since the
inefficient
rich elite to control the democratic political process continue to apply
even when the political structure
occupation.
and
is
that
when the poor
R, rather than the party of the bureaucrats,
rich,
would impose high taxes and provide no public goods (spending
latter
all
the
proceeds on bureaucratic wages).
Bureaucratic Corruption
5.3
We now briefly
discuss an extension of our basic
the side of bureaucrats
is
not related to their
model
effort,
in
which the moral hazard problem on
but to whether or not they accept bribes
from producers evading taxes. This source of moral hazard problem
we
as the effort choice of bureaucrats. Moreover,
will see
below that
is
arguably as important
it
leads to an interesting
pattern of de facto regressive taxation as a result of successful patronage politics by the rich
elite.
The economic and
a two-party system.
political
The only
environment
difference
is
similar to the baseline version of the
is
that the bureaucrats no longer have an effort choice.
>
Instead, producers that have evaded taxes can pay a bribe b
them
in order to avoid
corruption
inefficient
is
if
6
{0, 1}.
we allow
When
/
=
and corruption
is
two
for
1,
detected with probability q(I
there
=
1)
levels of
is
=
an
1.
First,
When
=
loses the bribe
after
=
described by
organization of the state and
=
qo
0,
<
the state organization
1.
is
We make a number of
is
limited to only one period; the
but receives no other punishment. Second,
payments and other income confiscated are
we assume that
0)
1
efficiency,
we assume that a bureaucrat caught accepting
bribes loses his wage and the bribe, but the punishment
producer paying the bribes
monitoring
efficient
detected with probability q (I
assumptions to simplify the exposition.
constraint. Third,
to the bureaucrat inspecting
paying taxes.
Similar to the baseline model,
the state variable
model with
lost
all
and thus do not enter the government budget
matching with a bureaucrat, the producer has
35
bribe
all
the
bargaining power and makes a take-it-or-leave-it bribe offer to the bureaucrat.
assumptions can be relaxed without changing our main
there
the
concave while x/
is
is
a range for x G
minimum
(1
[0,
— x)
is
convex and both are equal to zero
x m such that p{x)
]
> x/
that the region where p(x)
—
(1
x)
is
from
The
policies of the rich.
(6), since
> x/ (1 —
We
x
—
assume that x m
there
is
inefficient so that q
is
0.
is
—
Therefore,
lower than
and characterize the
go
participation constraint of the bureaucrat
no cost of
t
is
slightly
that
effort. It requires
w >(l-T )A L
The
x).
for
irrelevant for the equilibrium.
Let us start with the case where the state
different
Note that the function
x).
bureaucracy necessary to finance the infrastructure K, which ensures
size of the
most preferred
< x/ (1 —
parameter values, p(x)
that, for the relevant part of the
p{x)
results.
that each bureaucrat can be matched with at most one producer and
we assume
Finally,
All of these
(27)
.
t
incentive compatibility constraint for bureaucrats (5)
is
now
replaced by the following
"no bribe constraint"
w >
t
where
b t is
(1
-
go)
[wt
+
bt )
(28)
,
the bribe offered to the bureaucrat by a producer.
Intuitively, the right
hand
side of (28) represents the expected return of a bureaucrat that accepts a bribe b u given by
the
sum
of the
wage and the
condition (28) does not hold,
by the probability of not being detected.
bribe, weighted
it
is
not possible to prevent the corruption of bureaucrats by
producers. 16 Condition (28) implies that, given the public sector wage
than a threshold
b
(w t )
will
what
maximize
follows,
we drop time
when they do not pay
(z
=
0)
taxes
(ii)
bribing
is
When
X, G, and the
in power, the rich
decision variable z 6
whether to pay taxes. The expected
^— w,
= p (x) max j A H
Expression (30) incorporates the following
(x);
only bribes higher
utility
is
[
with probability p
,
(29)
subscripts to simplify notation.
their per-period utility with respect to r, w,
uH
t
= -^—w.
{0, 1}, which, as before, designates their decision of
of the rich
w
be accepted, where
b(w)
In
If
1
-
<?o
facts:
1
+
[1
(i)
G.
(30)
producers are inspected by a bureaucrat
detected with probability
:6
- p (s)] A H +
J
qo; (iii)
the bribe offered by the
Van Rijckeghem and Weder (2001) provide evidence that higher public sector wages relative to manufacturing wages reduce the scope for the corruption of the public administration.
36
rich to bureaucrats
(29);
and
(iv)
when
Expression (30)
is
p
equal to the lowest acceptable bribe b(w)
is
inspected, the income of a rich producer
maximized subject
Or)
is
=
qow/
max {A
(1
—
qo) defined in
— qow/
(1
—
go)
,
0}.
to the following constraints
max / A L - -S°— w ,o\ +
1-90
I
J
xw + G +
and subject to the participation constraint
[1
- p (x)] A L <
K <{u-x)tA l
(1
-
r)
AL
(31)
,
(32)
,
Constraint (31) requires
(27) of the bureaucrats.
that the poor prefer to pay taxes to tax evasion. This constraint has to be satisfied since at
least
one class must pay taxes, otherwise
investment,
K
(this
is
because,
it
would not be possible to finance the infrastructure
the poor prefer to evade taxes, the rich will do so a fortiori).
if
Constraint (32) implies that the government budget constraint
the fact that public revenues
Lemma
16 Suppose
come from the taxation
that the rich prefer not to
pay
GE =
and
for
some r G
=
taking account of
of the poor only.
taxes.
W E =(l-qQ )A L /qQ
'p(x)
is satisfied,
Then
their optimal policies involve
(33)
,
T,
(34)
[0, 1].
Proof. See the Appendix.
We
rich.
will
next show that given
(33)'
Substituting for these expressions,
and
(34), the equilibrium involves tax evasion
we obtain the
utility of the rich
by the
when they evade taxes
as
uH
In contrast,
when a
(z
= 0) = (1-t)A h + t (A h - A L
(35)
.
)
rich agent pays the tax rate (while all others evade taxes) his utility
would be
uH
{z
=
l)
= (1-t)A h
<
(1-t)A h + t(A h
= uH (z =
Next
let
f
(36)
,
-A L ),
0).
denote the unique value of t satisfying the government budget constraint
(32),
at the candidate equilibrium with the rich agents evading taxes
„(^Y*—to AL + K=[n-ir(f E )]TJS A L
Qo
37
,
(37)
where
As
is
7r
()
is
again defined in
main
in the
(1).
two cases to consider depending on whether n — n (t e )
analysis, there are
greater than or less than 1/2. Here
many
there are sufficiently
majority,
i.e.,
n—
tt
(t
simplify the analysis by focusing on the case where
bureaucrats so that, together with the rich, they are the absolute
<
)
we
The converse
1/2.
case with
n —
(r
tt
>
)
1/2 necessitates that
the rich create an inefficiently large bureaucracy in order to win the election. Since the results
we do not
in this case are again similar,
Lemmas
5
and 6 continue apply
ever vote for the poor, there
is
them
discuss
in this extension.
in this modified environment. In particular,
if
bureaucrats
a permanent transition to an equilibrium with an efficient state
lemma
with the poor in power within one period from the election. The following
characterizes
the policy vector that the poor would implement in the period they win the election
existing organization of the state
when the
Lemma
state
is
-
(1
inefficient
and
the
also the policy vector that they will choose
efficient.
17 Suppose
max
is
when
r)
=P
that d±
and consider
the following
maximization program:
AL + G
T,G,W
subject to
G = z{l-n)rA H +
and
(1
Then
is
[n-Tr(T)]TA L -
(r))
max ^A L -
(tt
(t))
max j A H -
t)
Al <
p
(tt
p
—
JZ^m^ o| +
y
w, where z 6
'
w,
{0, 1}
the policy vector that the poor
+
1
[1
[1
- p (tt (r))] A L <
- p (tt
term in the
last
=
1, is
would choose when It-i
given by Tt
two inequalities
The penultimate
is
=
t
,
Gt
constraint
When
It -\
is
—
1
=
=
q$.
=
rt
0,
r)
AH
—
f
,
Gt
,
,
q (I)
program
in this
lemma
two inequalities becomes
=
and z
1,
or z
= GD w = w D
,
t
,
=
1
and
the first
last constraint allows the
rich.
represents the "no
program
Notice that
the penultimate one will also be satisfied automatically
and the state
,
The policy vector that the poor would
no tax evasion constraint of the
satisfy the
-
(1
AL
r)
G D w — w D when
inequality in the maximization
satisfied,
AH <
-
equal to zero.
tax evasion" constraint for the poor, while the
whether or not to
(r))]
(1
denotes the decision of the rich whether to pay taxes.
given by the solution to this program when q (I)
choose when It-\
K
vm (t) -
is efficient,
bribery
zero.
38
is
not possible and the
to choose
if
this last
H > A L ).
(since A
max term
in the last
=
0,
The next two lemmas
Lemmas
are the analogues of
under which the bureaucrats are willing to vote
in
which they are
Lemmas
similar to those of
Lemma
Itr-l
=
power to the one
in
8
and
for the rich,
which the poor are
and the
in
rich prefer the allocation
power. Since their proofs are
they are omitted.
9,
18 In an MPE, the rich
in
and 9 and determine the conditions
8
win the election
will
at time
t
(i.e.,
dt
= R)
if
only
if
0.
1
-<7o
AL >
(1
-
(wD +
P)
GD) +
[(1
- t d ) A L + GD
(38)
~\
,
<?0
where
w D GD
,
and
f
,
GD
are defined in
Lemma
17.
Condition (38) implies that the bureaucrats prefer to be in an inefficient state under the
rule of the rich, given the
poor. In fact,
whereas
if
"wage policy" that
they vote for the
is
optimal for the
for one period (while the state
than voting
the bureaucrats obtain a wage equal to (1
rich,
they vote for the poor, they obtain a wage of
if
rich, rather
is inefficient),
wD
—
go)
for the
A L /qo,
and public with provision of
GD
and subsequently a payoff equal to the payoff of
the poor under an efficient state.
Lemma
19 Suppose
the following condition
_
[I
where f
Proof.
with an
It is
p
(jr
and G D
A H + £D] <
are defined in
immediate that
(f
)
as in
)
Lemma
(39)
is
(^))]
fr
17,
and f
,
AH + p ^
is
sufficient to
the tax rate f
to living under
Lemma
_p
[j
(-*))
is
all t if
The
(
A H _ AL)
(39)
ensure that the rich prefer to be in power
evade taxes and pay bribes equal to
AL
with
democracy with taxes and public good provision given
17.
lower than the expected payoff that they get
they are in power).
for
given by (37).
Condition (39) states that the payoff to the rich when the state
are in power)
=
is satisfied
inefficient state, set
probability
by t
$J>)
GD
and
Then, the rich prefer to set It
that condition (38) holds.
is efficient
when the
state
latter payoff reflects the following facts: only the
payers are inspected with probability p
(ir
Or
))
=
f
,
and the
is
(and the poor
inefficient
(and
poor pay taxes, tax
rich offer a bribe equal to
AL
to the bureaucrat inspecting them.
The
its
following proposition characterizes the equilibrium with bureaucratic corruption. Since
proof follows that of Proposition 3
closely, it is
39
omitted.
ditions (38)
and (39)
MPE
hold, the unique
and for
the initial period
Then, if con-
the political environment with emerging democracy.
Proposition 8 Consider
the rich party
all t thereafter,
following policies are implemented at
=
Wt
one in which the rich
is
R
elite
choose It
=
in
always remains in power and the
all dates:
tf*
lzM A\
=
Xt
= *(**),
<7o
G
where t e
pay a
is
0,
= te
and r t
= A L when
inspected.
on the other hand, one or both of conditions (38) and (39) hold with the reverse inequal-
MPE
the unique
vector
involves
It
=
for
1
and for
all t,
all t
>
1, dt
— P
and
the unique policy
is
where t
D =(l-¥>)A L
X
= n{TD ),
w
t
=
G
t
= G D = (l-n)f D A H +[n-7T(f D )}f D A L -{l-T D )A L 7r{f D )-K,
and
ti
G
Proof. The
are defined in
first
remains to be proved
inequality, the
poor
t
,
Lemma
17.
part of the proposition follows from
is
when one
that
will
be in power. To see
evading taxes. Moreover, as before,
if
rich
would have
rich
under It ~i
p
is
(tt
(t))
max ( A H
this constraint
is
democracy to setting up an
the state
(1
[l
— p (tt (v
is efficient
with the reverse
elite
(i.e.,
It
=
1),
inefficient state
and
the poor will be in
would not prefer an
inefficient state
since the "no tax evasion constraint" for the
,
^—w, ol +
1-90
some tax
to rich agents, which
))]
than f
violated (since
straint will be satisfied at
— t') A h
(39) hold
part that
is
I
,
and
The only
straightforward since to prevent tax evasion by themselves, the
to set a higher tax rate
=
16-19.
note that these conditions (with the reverse
this,
power. Therefore, we only have to show that the rich
and no tax evasion. This
Lemmas
or both of conditions (38)
inequality) are sufficient for the rich to prefer
At f
,
given by (37). Moreover, only the poor pay taxes, while the rich evade taxes and
bribe equal to b
If,
ity,
= GE =
t
AH
.
is
- p (tt (t)')1 A h <
[1
(1
-
r)
AH
.
J
it
rate r'
satisfied as equality for
is
).
Thus,
E which would give a per-period
E max [A H — qow/ (1 —
than (n (r
>
strictly less
AL
f
,
p
))
Therefore, the rich are always better off evading taxes
when
This establishes that conditions (38) and (39) holding with reverse inequality are
the equilibrium with the poor in power to emerge.
40
this conutility of
qo)
,
0}
+
in power.
sufficient for
The most
mocratic
interesting result in Proposition 8
is
do not pay any taxes at
politics, the rich
L
equal to the tax burden on poor agents, A
that,
all.
when they
Instead, they (sometimes) pay bribes
This implies that patronage politics turns de jure
.
proportional taxation into a de facto regressive one. In other words,
able to set
up an
inefficient state
and receive the support
to limit redistribution and public
are able to capture de-
when
the rich elite are
of bureaucrats, they are not only able
good provision, but they are
also able to shift
most of the
burden of taxation to the poor. Consequently, the tax rate faced by the poor may be higher
when corruption
An
6
A
is
possible than in the baseline
model where both
Empirical Implication and
distinctive empirical implication of our
model
and public good
provision.
wages when the
elite
and poor pay taxes.
Some Evidence
is
that democracies where relative wages of
bureaucrats are high should provide fewer public goods. This
crats are paid higher relative
rich
because,
is
all else
equal, bureau-
use patronage politics to limit redistribution
In contrast, a naive intuition
may
suggest that relative wages of
bureaucrats and public good provision should be correlated positively, either because
there
is
greater provision of public goods,
more
when
activities are entrusted to bureaucrats
and
they need to be paid more, or because countries with a greater willingness to tax will spend
more both on public employment and on public good
We
provision. 17
next look at the cross-country correlation between the relative wages of bureaucrats
and public good provision among democracies. Our measure
crats
is
average wage of public-sector employees relative to
for 1991-2000.
Our main measure
of public
GDP
good provision
GDP for 1991-1998, and we also
of GDP as an alternative dependent
is
wage
of the relative
of bureau-
per capita from World
total (central)
Bank
government ex-
penditure as a fraction of
look at social services and welfare
spending as a fraction
variable.
18
Both
of these variables
are from the IMF's International Financial Statistics (see the details in the Appendix).
focus on democracies,
than or equal to
we
limit the
To
sample to countries with an average Polity score greater
5 over the period 1991-1998,
which corresponds to "stable democracies"
Persson and Tabellini, 2003). Our baseline sample contains 51 observations. Figure
1
(see
shows
the correlation between the relative wages of bureaucrats and government expenditure share of
17
An
may be that, with a fixed government budget, higher public sector wages would
government to reduce the rest of public good expenditures. In practice, there is considerable variation
in the level of government budgets, and we will see below that same results apply with a measure of spending
on social services and welfare.
We choose the total government expenditure as our main measure, both because wc have more observations
on this variable and also because the alternative, social services and welfare spending share of GDP, is heavily
influenced by the age structure of the population. See below.
alternative intuition
force the
41
GDP. A
strong negative relationship
is
with most European countries hav-
visible in the figure,
ing lower relative wages for bureaucrats and government expenditures than in Latin
and Asian countries (there are few African countries
The
regression corresponding to Figure
The
bust standard errors in parentheses.
government expenditure share of
approximately
5.
Column
GDP
1
is
in our sample).
shown
column
in
1
of Table
with the ro-
1,
wages and
correlation between relative bureaucratic
is
statistically highly significant,
2 of the table controls for
more on public goods and income per capita
GDP
with a
t-statistic of
per capita. Richer countries spend
also correlated with relative bureaucratic wages.
is
This regression shows that log income per capita
is
indeed significant, but the relationship be-
tween relative bureaucratic wages and government expenditures remains strong (the
ficient of
democracy
score,
which
and has
insignificant
is
coefficient
Column
declines from -4.96 to -3.63, which continues to be significant at less than 1%).
controls for the Polity
American
little effect
3 also
on the coef-
the relative wage of bureaucrats. Figure 2 shows the conditional correlation between
relative bureaucratic
3 of Table
The same negative
1.
Column
wage and government expenditure share
relationship as in Figure
GDP corresponding to column
of
1 is
again visible.
4 controls for the age structure of the population, in particular the fraction of
We
the population between the ages of 15-64 and the fraction over the age of 65.
expect
the age structure of the population to have a direct effect on Social Security spending and
thus also on total government expenditures.
The
results in
column 4 show that controlling
for
the age structure variables significantly reduces both the coefficient estimate of the relative
The
bureaucratic wage and the standard errors.
standard error of 0.85, which
Columns
percentage of
5-8 repeat the
GDP
as the
is still
same
significant at
coefficient estimate
now
is
-1.82,
with a
5%.
regressions using social services
and welfare spending
dependent variable. The results are similar to those
for
as a
government
expenditure and typically stronger, except when we control for the age structure variables. In
particular, in
columns
5-8, relative bureaucratic
wage
is
significant at less
than 1%. Once we
include the controls for the age structure of the population, however, the relationship between
the relative bureaucratic wage and social services and welfare spending
is
no longer
significant;
the coefficient estimate declines significantly and the standard error doubles. This result might
reflect the fact that social services
of the population
and there
and welfare spending are
is little
closely related to the age structure
cross-sectional variation left once
we
control for the age
structure variablesas.
In addition to the results
shown
in
Table
1,
we have
also
"semi-stable" democracies (those with Polity scores between
42
experimented with including
and
5).
The
results are similar
but slightly weaker. The results are also similar when we construct the sample using Freedom
House measures of
political
various other controls.
The
and
We
civil rights.
also checked the robustness of the results to
results are broadly similar
when we
control for the legal origin of
the country, for parliamentary versus presidential systems, for majoritarian versus proportional
democracies, and for the age of democracy. Nevertheless, the results are significantly weakened
or disappear
when we
since, as Figures 1
it
of continent
full set
and 2 show, the
American and Asian
Overall,
control for a
dummies. This
results reflect the contrast of
is
not entirely surprising,
European countries
countries.
appears that there
is
a significant negative relationship between government
expenditure and the relative wages of bureaucrats, which becomes weaker
for the age structure of the
correlation
is
to Latin
when we
control
population and for continent dummies. While this cross-country
not as robust as we would
like it to be, it is
nonetheless encouraging for our
approach, since the negative relationship between relative wages of bureaucrats and government
expenditure
is
a counter-intuitive implication of our model and a naive intuition would have
suggested the opposite relationship between these two variables.
7
Concluding Remarks
Inefficiencies in the bureaucratic organization of the state are often
factor in retarding economic development.
opment emphasize the
Many
viewed as an important
sociological accounts of comparative devel-
role of state capacity (or lack thereof) in explaining
are able to industrialize
and modernize
ficient state organizations
(e.g.,
why some
Evans, 1995, Migdal, 1988).
societies
In addition, inef-
appear to coincide with limited amounts of public good provision
and redistribution towards the poor. Existing approaches do not address the question
certain societies choose or end
up with such
inefficient organizations
and do not
of
why
clarify the
relationship between inefficient state organizations and limited redistribution.
We presented
a simple theory of the emergence and persistence of inefficient states, in which
the organization of the public bureaucracy
redistributive politics. In particular,
is
manipulated by the rich
by instituting an
them
little
We
public good provision and there
also
to limit the extent of
and public good provision. Captured democracies not only
but also create a number of major distortions: the structure of the state
too
showed that an
may be overemployment
inefficient state creates its
43
order to influence
inefficient state structure, the elite are
able to use patronage and capture democratic politics. This enables
redistribution
elite in
limit redistribution,
is
inefficient, there is
of bureaucrats.
own constituency and tends
to persist
over time.
would an
he
will
an
Intuitively,
inefficient state structure creates
When the median
efficient state structure.
reform the structure of the state to make
it
more
(poor) agent comes to power in democracy,
more
efficient so
be collected at lower cost (especially in terms of lower rents
this,
when the
organization of the state
rents for bureaucrats than
is inefficient,
that the higher taxes can
for bureaucrats).
bureaucrats support the
Anticipating
rich,
who
set
lower taxes but pay high wages to bureaucrats. In order to generate enough political support,
the coalition of the rich and the bureaucrats
the state, but they
may
The model shows
further
expand the
correlated because higher inequality
an
of elite control in
inefficient state organization
tures in a
number
size of
bureaucracy so as to gain additional votes.
when democratic
interesting implication of this result
The pattern
not only choose an inefficient organization of
that an equilibrium with an inefficient state
greater income inequality and
is
may
is
is
more
likely
when
there
An
taxes are anticipated to be higher.
may be
that inequality and redistribution
makes the capture
of democratic politics
democracy based on patronage
politics
more
negatively
likely.
and the emergence
of
bears some resemblance to the inefficient bureaucratic strucIn addition to these case studies,
of countries.
we provided cross-country
correlations consistent with a distinctive implication of our model, that
among democracies
there should be a negative relationship between the relative wages of state employees and the
amount
The
of public
good provision.
general message from our analysis
some democracies
may become
will
is
that "not
all
democracies are created equal" while
;
adopt policies that redistribute to poorer segments of the
captured by traditional
elites.
These captured democracies not only choose low
levels of redistribution, but, as part of their political rationale for survival,
create a range of inefficiencies.
Our model suggests that
to the relatively poor performance of a
Analyses of the
effect of
methods via which the
rich
number
they also typically
these inefficiencies might be related
of democracies in Latin
America and Asia. 19
such policies on economic growth and investigations of other
may
limit the
are interesting areas for future work.
amount
of redistribution in democratic politics
Another interesting area
careful empirical analysis of the relationship
between the variation
expenditure, relative wages of state employees and potential
1
society, others
elite
for further
study
in the extent of
is
a
more
government
capture of democratic
politics.
poor economic performances of Latin American democracies is
beyond the scope of the current paper. Nevertheless,
it may be conjectured that the political environment may be more conducive to populism when the majority of
the population fare relatively badly under democracy (see Acemoglu, 2007) and the type of democratic capture
studied in this paper is likely to limit the benefits of democracy for the majority of the population.
Another potential
"populism".
political factor in the
Why some countries pursue populist policies is
44
Appendix A: Omitted Proofs
Proof of Proposition 5
7.1
Consider changes in inequality that keep mean pre-tax income,
Y=
—
(1
n)
A H + nA L
,
constant. This
implies the following simple relationship between the pre-tax incomes of rich and poor agents:
Y-nA
—
—n
„„
AH =
L
,
,
40)
.
1
To prove the desired
when
to hold
there
is
we need
result,
to
greater inequality,
show that
and
(15)
when A L
i.e.,
(21) in
lower (and
is
Lemmas
AH
is
8
and 9 are more
likely
given by (40)).
Let us rewrite condition (15) as
—h
>
<7o-i-goL
that more generally
X=
~
~j^G D
l
'
Lemma
Next, consider condition (21) in
_ r D )/_A L + G D +
"
(1
v
9.
max {n (t e ) n —
,
Suppose
first
that
(41)
P
te > r
i.e.,
,
when
X=
-n
(r
E
)
(recall
1/2}). Then, combining the government budget constraint
with (40) gives
(19)
7T
„s
"
(t
e
K
h
)
Y-n{T E )A L
+ v
Y
q
wL
_,, e
g )A l
-tt(t
'
(
42 )
e
Substituting for t from this expression, condition (21) can be rewritten as
h
Instead,
and
when r E < f
,
G E \ Y-n(r E )A L
f
the size of the bureaucracy
K
X=n—
is
_
1/2
=
A.
Solving for f
from
(20)
(40) as
+K
Y-\A L
Xh/qp
E
the relevant part of condition (21), (l
- fE\ AH >
(1
-
(3)
[
'
'
(l
- te ) Ah +
- t d ) A h + GD
[(l
,
]
can
be expressed as
-
< \
-
{ [(1
13)
t
e
+
(t
These three expressions define 9, 6 and 8
be created under two different scenarios:
1.
if
X=
7r
(t
e
)
and
if
.
Now
if
X=n—
1/2
=
will
A and
if
increase with income inequality.
1
to 2 or vice versa in a
first
inefficient state will
6;
h/q
<T.
prove that higher inequality makes the inefficient state equilibrium more likely by showing
decreasing in the level of inequality
We
(45)
conditions (41) and (45) are satisfied, which requires
that the upper thresholds (9 in case
from
-K}=T.
summarizing our analysis, an
< h/q <
9<
We
(Y - \A L )
conditions (41) and (43) are satisfied, which requires
6
2.
G D /A H )}
d -
We
way
1
and 9
in case 2) are increasing
and the lower threshold,
—these naturally imply that the intervals A = 8 — 9 and A* = 8
will also
to
make
show that an increase
the inefficient state less
establish an intermediate result:
45
in inequality
likely.
9, is
—9
does not cause a switch
Claim
We
1
have
8r D
1
_
dAL ~ ~ tt"
and
8A L
(r D )
program
first-order condition of
first-order condition (48) therefore
YThe
solution for t d
that t d
<
<0,
(46)
AiLL
interior
td
-
1
tt
(t
t
dY -
(48)
.
1
(t
tt
d (A l +
)
h)
is
(49)
.
becomes
tt'
(t
d (A l +
h)
)
always positive since
is
d <
)
K-
(47)
is
the equilibrium level of the public good (8) provided by the poor
,
GD =
The
)
+ h)
an
(9) for
8t
(40)
p
(A L
dG D
Using
(t
tt'
T E TT (r E )
>0.
E
E
Y-ir'{T ){T A L + h/q )-Tr{T B )A L
dr 1
Proof. The
+
ensures that r D
- AL =
0.
(50)
K
>
1.
Differentiating (50) gives (46).
<
needs to be financed. Moreover, the assumption
Next, differentiating the government budget constraint (19) and using (40) gives (47), where the
e is always to the left of the peak of the Laffer curve.
is positive since t
denominator
Next, given the definition of 8 in (41) we obtain that
89
1
SUA*"
where the expression
i-
_ rD _ ^
[1
(
T
D)]
>Q
(51)
90
for the limit uses the fact that
dG D
(A L ) jdA L
exists,
is
finite
and
is
independent
and the inequality again follows from the assumption that t d < 1 — tt (t d ) < 1. This inequality
implies that for sufficiently high /?, the inefficient state becomes more attractive to bureaucrats as the
on
/3,
level of inequality increases.
We now
show that higher
by a decrease
inequality, represented
in
AL
with
the inefficient state also more attractive to the rich by increasing 9 and 6
AH
given by (40), makes
.
Consider two cases:
Case
From
1:
X = tt(t e
(49),
).
we have
T
DY =
Gd + K +
tt
(t
d (A l +
)
h)
(52)
Substituting (52) into (43) and some algebra gives
Ah
tx{t b )
Ah
tt(t e )
v
(53)
'
Next, note that
d [{A H -
A L /A H
)
8 [A L /A H
]
dA L
8
[1/tt (r
g
)]
_
dA L
8
[tt
(t
p
)
]
AH
dA L
/tt
8A L
(t
e
)}
_
w' (t
[tt
(
(t
46
3t 1
)
r B)]
d 8t d
)
tt{t e ) 8A l
tt'
e
l-n(A H y
2
tt
8A L
(t
d
)
<0
<0
n' (r
[k(t e )Y
g dr 1
)
8A L
<0
and from
(49), using (50),
8G L
di
8A L
8A L
AL -
n (r
D
<
)
0.
(54)
Differentiating (53), in turn, gives
8B
nir'
dA L
(r
E 8t e A h - A L
)
u nD
G
+TT
n
A H - Al
[T z
A"
dAL
A L -n
A H dA L
tt(t e )
Al
-tt t
d
(t
,'
A^_
'
r
AH
tt{t e )
A"
EtfdAL
fr( T
l
+
)
(„-D
d
{t
)
tt(t e )
l-n(A H
AH
dr D
GD +
2
)
l-n(A H
n
(t
8A l
d
) tt'
(r
\tt{t e ))
2
GD +
)
g 8t e
)
dA L
2
{A L
+
h)
8A l
which can be rewritten as
x'
89
8A L
e dr E A H
+ dA L A 1
[tt{t e
)
tt
D
- (r )
E
TT (T
L
TT
(T E )
n(r°)
AH
J
d 8t d
tt' (t
)
e
tt{t
~8A^~
(t
d
) tt'
(t
\tt{t e )}
)
+
G
A"
[7r{T Ef d A^
+
-A L ^ D
1-rE
(t
)
e 8t e
)
2
+
n
AH - AL
AL
-r D +
+
A"
A"
1
tt(t e )
(A L
dA^
GD +
AH
+
- n (A H
(55)
)
h)
'
)
Since
tt
d
(t
/tt
)
8t e /8A l >
e
(t
),
0,
8t d /8A l <
are negative. Furthermore,
tt(t e )
8A^
A +h +
where the right and side of
concavity of
tt
and n >
>
(56)
(t) implies that
(t
e
all
),
the terms in (55) except the last
tt(t e )
tt(t e )
(r
-tt'
1
D
)
+
tt'
tt"
{t
d
)
{t d )
+
tt
It
1-
(t)]
>
tt" (t)
(t)
tt
and
is
(56)
sufficient to ensure that (56) is negative.
the terms in (55) including tt {t d ) /tt (t e ) are negative, and therefore
as desired. Note that this conclusion holds irrespective of the value of /3.
This implies that
line,
we have
obtained using the expression for 8r D /8A L in (46). Now, the log-
is
[tt'
tt
all
Case 2: X = n - 1/2 = A.
The proof parallels that of case
(1/2)A L we obtain
1.
From
(45), using (52)
and the
fact that
Y — XA L =
89/8A L <
(1
— n) A H +
,
= j\(1-P)t e {Y-\A l )+P
tt
(r
D {A L +
)
L
h)+K- Xt d A l + G d - (l-"M* + (l/2M Gg
(57)
Note that
8[{{\-n)A H + {\/2)A L )/A H
8A L
47
Y
]
2(1
HY
-n){A H
)
(58)
Differentiating (57)
and using
(54), (58)
and the
8r E /8A L
fact that
and
exists
is
independent of
/?,
we have
/3-i
8A L
A
;
v
v
'
1
Y
8A L
v
dA L
'
(l- n )A H +
AH
nD
2(1 -n){A H f
/o\
(l
i
(1/2)
AaL
dA L
v
'
^V-w.'
dA L
'
which can be rewritten as
3-i
'!.")
K
<M'")
8A L
'
v
A
'
\
,--(-1'
dA L
"
'"'
v
'
—
\A H -A L 8t d ..L ( «--1 A L \
-A 2
i" 3A 1
2 AH
V
Since 8t
d /8A L <
0,
d >
)
(t
tt'
n > 1/2 and ^ L <
0,
AH
,
negative. Therefore, a sufficient condition to ensure that (59)
*' (r D
)
L
§g (A
where the right hand side of
(60)
+ h) + *
is
negative for sufficiently high
The proof
ft
=
-«> (r°)
7r(r
all
is
D
.
n){A nf
w
G +
'
terms
than n (t d ) are
in (59) other
negative
is
1
±^ff
+n
(r°)
<
(60)
0,
obtained using the expression for dr D /8A L in (46). This condition
equivalent to (56) and the log-concavity of
is
(t°)
.
.
2(1
7r
(t)
is
ensure
sufficient to
it.
This establishes that 88
as desired.
so far has established that the lower threshold 8 declines as inequality increases
the upper thresholds 8 and 8
is
/8A L
increase as inequality increases.
To complete the proof of the
and that
proposition,
we need to ensure that there would be no switch from the wider to the smaller interval, which could
happen if we have a switch from t e > f to t e < f
or vice versa. However, as /3 — 1, we have that
>
,
(21)
is
equivalent to
if
if
rE
>f E
& X = max{^(T B ),n-l/2}= W (r B
te
<t e
& X = max
so that for
(5
{tt
{t
e ),ti-
1/2}
)
=n- 1/2 =
A
sufficiently large, at the point of a possible switch,
d - te Ah >
)
and
(t
and
(r D
te
=
f
,
GD
- f£) AH > GD
we have
8
= 8.
This
completes the proof.
Proof of
7.2
Lemma
16
Suppose that the bureaucratic wage
is
given by
wE
in (33).
(28) of the bureaucrats inspecting low-skill producers
as large as their
bribes,
income
AL
.
Holding r
is
fixed, a decrease in
and thus reduce government revenues to
Then the
incentive compatibility constraint
even when the producers offer a bribe
from w E will allow bureaucrats to accept
satisfied
w
zero. Therefore,
it
cannot be optimal. Increasing
w
is
also not beneficial for the rich.
Condition
wE
,
(31),
on the other hand, ensures that the poor choose to pay taxes. Holding
increasing taxes would induce the poor not to pay taxes and
taxes
is
the rich
also not beneficial.
is
Given
(33)
and
(34),
decreasing in G, so that this variable
is
it is
is
w
fixed at
therefore not beneficial. Reducing
also straightforward to verify that the utility of
set equal to zero.
This argument shows that (33) and (34) gives a stationary point of the optimization problem of the
the rich will not find it beneficial to change either one of x or w by itself. To complete the
rich, since
48
we need to show that it is also not beneficial to change x and w simultaneously. We will do this
by showing that the payoff function of the rich is strictly quasi-concave. Consider the problem of the
rich if they do not pay taxes. Clearly, constraints (31) and (32) in equilibrium hold as equalities. We
can thus solve out for the tax rate from the government budget constraint as
proof,
T
= xw +
-
(n
K+G
x)
AL
we obtain
Substituting this expression into (31),
K+G
w=
[Qo/{l-<lo)](n-x)p(x)-x'
> (1 — qo) A L /qo (which will be true in equilibrium). Now, substituting (61) in the
provided that
= 0, we can represent the
objective function of the rich (30), and observing that this is maximized at
w
G
problem of the
rich as the following single dimensional
maxt/
If this
unique
problem
is
= AH -
strictly quasi-concave,
(n-z) - (l-q )x/q p(x)
it
must have a unique
,,,/
(X) =
U
,,
U (x) to be strictly
= 0. For this, it is
For
1
+
(1
-
go)
-
/q p (x)
[(n-x) quasi concave,
sufficient for
-
it is
(1
concave
pay
in x.
-
2
go)
\p'
jx) x] /q
- qo)x/q
\p jx)}
\p (re)]
+
(1
-
-"•
p(x)}
sufficient that its
2
I
(1
2
second derivative
q )p(x) /q
—
(1
-
go)
\p'
is
negative
(x) x] /go
[
when
to
be
can be easily verified that this is always the case since p (x) is increasing and
This completes the proof that (33) and (34) is optimal for the rich when they prefer not
strictly decreasing in x. It
to
Corresponding to this
solution.
be unique levels of r and w, since these variables are defined uniquely by the
To check that this function is indeed strictly quasi-concave, note that
x, there will
previous equalities.
U' (x)
(x)
maximization problem
taxes.
49
Appendix B: Data Sources and Definitions
Our dataset
builds
on the cross-country dataset compiled by Persson and Tabellini (2003) (henceforth
PT). Our sample of "stable democracies" consists of countries with an average Polity score greater than
or equal to 5 over the period 1991-1998. We also report results with a sample containing all democracies
over the period 1991-1998). With the
(defined as countries with average Polity score greater than
exception of the average government wage to per capita GDP (which comes from the World Bank), all
our variables are from PT's dataset. These variables are the following:
Central government expenditures as a percentage of GDP: constructed using the item
Government Finance-Expenditures in the IFS, divided by GDP at current prices and multiplied by 100.
IMF-IFS CD-Rom and IMF-IFS Yearbook.
Consolidated central government expenditures on social services and welfare as percentage of GDP: from the GFS Yearbook, divided by GDP and multiplied by 100. Source: IMF-GFS
Yearbook 2000 and IMF-IFS CD-Rom.
Log GDP per capita: per capita real GDP defined as real GDP per capita in constant dollars
(chain index) expressed in international prices, base year 1985. Data through 1992 are taken from the
Penn World Table 5.6, while data on the period 1993-98 are computed from data taken from the World
Development Indicators, the World Bank. These later observations are computed on the basis of the
latest observation available from the Penn Word Tables and the growth rates of GDP per capita in the
subsequent years computed from the series of GDP at market prices (in constant 1995 U.S. dollars) and
population, from the World Development Indicators.
Sources: Penn World Tables - mark 5.6 (PWT), available on
Source:
http://datacentre2.chass.utoronto.ca/pwt/docs/topic.html.
The World Bank's World Development
Indicators, available
on
http://www.worldbank.org.
Polity: score for democracy, computed by subtracting the AUTOC score from the DEMOC score,
and ranging from +10 (strongly democratic) to -10 (strongly autocratic).
(DEMOC) is
the index of autocracy (democracy), derived from codings of the competitiveness of political participa-
AUTOC
tion, the regulation of participation, the
openness and competitiveness of executive recruitment, and
constraints on the chief executive.
Source: Polity IV Project (http://www.cidcm.umd.edu/inscr/polity/index.htm).
Age structure variables: percentage of population between the ages of 15 and 64 in the total
population and percentage of population over the age of 65 in the total population.
Source:
World Development Indicators
CD-Rom
1999.
GDP: mean value of the average government
between 1991 and 2000. It is computed as the average of the two data points
available for the periods 1991-95 and 1996-2000. When data for one of the two periods are not available,
only the available time period is used. The variable is calculated by dividing the average government
wage by the GDP per capita figure. The average government wage is calculated as the total central
government wage bill divided by the number of employees in total central government. The total central
government wage bill is the sum of wages and salaries paid to central government employees, including
armed forces personnel. The number of employees in total central government is the sum of total civilian
central government and the Armed Forces.
Source: Schiavo-Campo, de Tommaso and Mukherjee (1997), Table A-3,
Average government wage
wage
to per capita
relative to per capita
GDP
http://www-wds.worldbank.org/external/default.
50
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60(H
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