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-^pr)
.
("b
B31
^415
3^1
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
The Form of Property Rights: Oligarchic
Democratic Societies
vs.
Daron Acemoglu
Working Paper 03-34
September 28, 2003
Room
E52-251
50 Memorial Drive
Cambridge, MA 02142
This
paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://ssrn.com/abstract=457724
BBWi
fv/IASSACHUSETTS INSTITUTE
OF TECHNOLOGY
The Form
of Property Rights: Ohgarchic vs.
Democratic Societies*
Daron Acemoglu
Department of Economics
Massachusetts Institute of Technology
MA 02142
Cambridge,
September
28,
2003
Abstract
This paper develops a model where there
property rights of different groups.
An
a trade-off between the enforcement of the
is
"oligarchic" society,
hands of major producers, protects their property
rights,
where
political
power
is
in the
but also tends to erect significant
entry barriers, violating the property rights of future producers. Democracy, where poUtical
power
is
more widely
to avoid entry barriers.
diffused,
When
imposes redistributive taxes on the producers, but tends
taxes in democracy are high and the distortions caused
by entry barriers are low, an ohgarchic society achieves greater efficiency. Nevertheless,
because comparative advantage in entreprenemship shifts away from the inciunbents, the
inefficiency created by entry barriers in oligarchy deteriorates over time. The typical
pattern is therefore one of the rise and decline of oligarchic societies: of two otherwise
identical societies, the one with an oligarchic organization wiU ffist become richer, but
later fall behind the democratic society. I also discuss how democratic societies may be
better able to take advantage of new technologies, and how the unequal distribution of
income in an oligarchic society supports the oligarchic institutions and may keep them in
place even when they become significantly costly to society.
Keywords: democracy, economic growth,
entry barriers, oligarchy, pohtical economy,
redistribution, sclerosis.
JEL
Classification: P16, OlO.
thank Robert Barro, Olivier Blanchard, Simon Johnson, James Robinson, and participants at
NBER Summer Institute and Harvard
University macro seminar for useful comments, and Miriam Bruhn and Alexander Debs for excellent
*I
the Canadian Institute for Advanced Research conference, the
research assistance.
Introduction
1
There
is
now
a growing consensus that institutions protecting the property rights of pro-
ducers are essential for successful long-run economic performance.^ There
is
no agreement,
however, on what constitutes "protecting the property rights of producers" or on the costs
and benefits of various
where
society
different "forms of property rights".
political
power
is
in the
One possibility
hands of the economic
elite, for
is
an
oligarchic
example, the ma-
jor producers/investors in the economy. This type of organization not only ensures that
major producers do not
enables
them
fear expropriation or high rates of taxation,
to create a non-level playing field
and a monopoly position
in essence violating the property rights of futiue potential producers
from taking advantage of
more
profit opportunities).
but also typically
The
alternative
uted, thus effectively in the hands of poorer agents
who can
excluding
democracy
is
appropriately, popuhst democracy), where political power
(i.e.,
for themselves,
is
them
(or
perhaps
more equally
distrib-
use their power to tax the
producers' profits.^ But in return, incmnbent producers will be unable to create
signifi-
cant entry barriers against entrants, ensuring better property rights for future potential
producers.'^
This paper constructs a simple model to analyze the trade-off between oligarchic and
democratic
riers.
The model
societies.
features
two pohcy
distortions: taxation
and entry bar-
Taxes, which redistribute income from entrepreneurs to workers, are distortionary
because they discourage entrepreneurial investment. Entry barriers, which redistribute
income towards the entrepreneurs by reducing labor demand and depressing wages,
tort the allocation of resources because
dis-
they prevent the entry of more productive agents
into entrepreneurship.^
^See,
among
others, the general discussions in Jones (1981),
empirical evidence in
De Long and
Shleifer (1993),
North (1981), and Olson (1982), and the
(1995), Barro (1999), Hall and
Knack and Keefer
Jones (1999), and Acemoglu, Johnson and Robinson (2001, 2002).
^Although there is a close connection between dictatorship and oligarchy, some electoral democracies
may be
"oligarchic" according to the definition here, because the economic elite controls the parties or
the electoral agenda.
Mobutu, a highly predatory state, controlled either by an
incumbent and future producers.
The focus here is not these cases, but the trade-offs between distortionary redistributive taxation and
entry barriers. A full taxonomy of regimes would distinguish predatory regimes from oligarchic and
•^In
certain societies such as in Zaire under
individual or the political
elite,
may
violate the property rights of both
democratic regimes.
*
Entry barriers
may
take the form of direct regulation, or of policies that reduce the costs of inputs,
especially of capital, for the incumbents, while raising
them
for potential rivals.
to the chaebol appear to have been a major entry barrier for
new
Cheap loans and subsidies
Korea (see, for example,
firms in South
Kang, 2002). See also La Porta, Lopez-de-Silanes and Shleifer (2003) on the implications of government
ownership of banks, which often enables incumbents to receive subsidized credit, thus creating entry
The
trade-off between these
two
different types of distortions determines
more
and generates greater aggregate output.
ohgarchic or a democratic society
is
OUgarchy avoids the disincentive
effects of taxation,
duced by entry
barriers.
create a
more
are high
and the
efficient
Democracy imposes higher
When
level playing field. ^
distortions caused
but
suffers
from the distortions
intro-
redistributive taxes, but also tends to
the taxes that a democratic society will impose
by entry
barriers are low, oligarchy achieves greater
and generates higher output; when democratic taxes are
efficiency
whether an
relatively
low and en-
try barriers create significant misallocation of resources, a democratic society achieves
greater aggregate output.
In addition, a democratic society typically generates a
equal distribution of income than an ohgarchic society, because
from entrepreneurs to workers, while an
it
redistributes
more
income
oligarchic society adopts policies that reduce
labor demand, depress wages and increase the profits of incumbents.
More
interesting are the
dynamic
trade-offs
between these poHtical regimes.
Initially,
entrepreneurs wiU tend to be those with greater productivity, so an oligarchic society
generates only hmited distortions. However, as long as comparative advantage in entre-
preneurship changes over time,
will eventually shift
it
away from the incumbents, and the
entry barriers erected in ohgarchy will become increasingly costly to efficiency.
therefore one where, of two otherwise identical societies, the oligarchy will
pattern
is
become
richer,
but later
fall
distortions,
also
democracy
is
behind the democratic
some parameter
gests that, at least under
I
A typical
The model
therefore sug-
configurations, despite its potential economic
better for long-run economic performance than the alternatives.
show that democracies may be
than oligarchic
society.
first
societies.
This
is
able to take better advantage of
new technologies
because democracy allows agents with comparative
advantage in new technology to enter entrepreneurship, while oligarchy typically blocks
new
entry.
The above
in particular
discussion takes the pohtical regime
whether the society
research in political
economy
barriers for potential entrants.
An
is
is
and the distribution of political power,
ohgarchic or democratic, as given.
A
major area of
the determination of equihbrium political institutions.
interesting case in this context
is
Mexico at the end of the nineteenth
century, where the rich ehte controlled a highly concentrated banking system, protected by entry barriers,
and the resulting lack of loans for new entrants enabled the elite to maintain a monopoly position in other
Haber (1991, 2002).
^This argument does not deny the presence of entry barriers in democratic societies, for example in
much of Western Europe, but suggests that the role of entry barriers in these instances may be to create
rents to a specific group of workers rather than protecting incumbent firms (on cross-country patterns of
labor regulation, see Djankov, La Porta, Lopez-de-Silanes and Shleifer, 2003).
sectors. See
When
should we expect a society to become oligarchic and remain so even
becomes increasingly costly?
I
when
this
analyze this question by embedding the basic setup in a
simple (and reduced-form) model of regime change where groups with greater economic
power are
also
more
likely to prevail politically. Social
groups that become substantially
richer in a given political regime
may be
protect their privileged position.
In oligarchy, incumbents have the poUtical power to
erect entry barriers to raise their profits.
able to successfully sustain that regime
These greater
and
profits, in turn, increase their
pohtical power, making a switch from oligarchy to democracy
more
difficult,
even
when
entry barriers become significantly costly.
Although the model economy analyzed in
this
paper
is
highly abstract,
sheds light on a nimiber of interesting questions.
The
economic performance of democratic and ohgarchic
societies.
ples of
both democratic and ohgarchic
societies that
growth. For example, the United States and
much
first set
of issues
it
is
nonetheless
the relative
In practice, there are exam-
have achieved high rates of economic
of
Western Europe during the postwar
era illustrate the potential economic success of democratic societies. In contrast,
Japan
both in the prewar and the postwar periods, and South Korea, Taiwan, and Singapore in
the postwar era are examples of ohgarchic societies that have pursued pro-business pohcies
and achieved successful economic performance.^ The development experiences of Brazil
and Mexico, on the other hand,
illustrate
both the potential gains and
oUgarchic regimes. Haber (2003), for example, explains
how
significant costs of
import-substitution pohcies
in these coimtries were adopted to protect the businesses of the rich ehte
the government.^
He
further documents
how
aHgned with
these import-substitution policies enabled
®A11 four countries approximate oligarchic societies. For example, in Japan, the pre-war era is commonly recognized as highly oligarchic, with the conglomerates known as the zaibatsu dominating both
politics and the economy (the title of the book on pre-war Japanese politics by Ramseyer and Rosenbluth,
1995, is Politics of Oligarchy). The postwar politics in Japan, on the other hand, have been dominated
by the Liberal Democratic Party (LDP), which is closely connected to the business elite (see, for example,
Ramseyer and Rosenbluth, 1997, and Jansen, 2000). In the Korean case, the close links between the large
family-run conglomerates, the chaebol., and the politicians are well-documented (see, for example, Kang,
2002). In both cases, government policy has been favorable to major producers and provided them with
subsidized loans and protected internal markets as well as secure property rights (e.g., Johnson, 1982,
Evans, 1995). For example, in Japan, the Antimonopoly Act of 1947 imposed by the Americans was
soon relaxed, and the LDP introduced various anticompetitive statutes to protect existing businesses.
Ramseyer and Rosenbluth report that in 1980 there were 491 cartels, and "almost half [of those] had been
in effect for twenty-five years and over two-thirds for more than twenty years" (1997, p. 132). However,
it should also be noted that inequality of income in both cases has been limited, most likely because of
other historical reasons, for example, the extensive land reforms in South Korea undertaken to defuse
rural unrest fanned by the Communist regime in the North (e.g., Haggard, 1990).
^For example, he describes the formulation of policies in early 20th-century Mexico as "Manufacturers
who were
part of the political coalition that supported the dictator Porfirio Diaz were granted protection,
War
rapid industrialization both before and after World
Beyond these
sMps
but also created significant
and economic problems.
distortions
show that
II,
in the
selective examples, cross-coimtry empirical analyses, e.g.,
postwar
era, electoral
Barro (1999),
democracies have not grown faster than dictator-
(wliich generally correspond to oligarchic societies in
terms of the model), despite the
weU-documented presence of disastrous dictatorships with very weak records of property
rights enforcement.
and oUgarchic
The model
is
consistent with this pattern, because both democratic
societies create distortions.
from democracies that are
Successful economic performances will
relatively less redistributive,
and from ohgarchic
societies
come
where
entry barriers are hmited or where heterogeneity of productivity in entrepreneurship
is
relatively imimportant.
Existing evidence
also consistent with the notion that democracies are
is
tributive, but introduce fewer entry barriers
(2002, Table 7)
cies.
show that there
than
more entry
are
oligarchies. For
more
redis-
example, Djankov et
barriers in non-democracies
al.
than democra-
Rodrik (1999) shows that labor share and wages are typically higher in democracies
than in dictatorships. Democracies also appear to tax more than non-democratic countries.
Figure
against the
1
shows a
significant positive correlation
Freedom House measure
of democracy, once the effect of log
has been taken out from both variables.
is
between tax revenue over
Appendix
B
GDP
GDP
per capita
demonstrates that this pattern
robust to controlling for education, population, continent dummies, and to excluding
former communist countries and federal countries.^
The second
set of questions that the
and dechne of nations.
A common
model might shed some Mght on
conjecture in social sciences
also lays the seeds of futme failures (e.g.,
is
relate to the rise
that economic success
Kennedy, 1987, Olson, 1982). The analysis in this
paper suggests a specific mechanism formalizing this conjecture: early success might often
come from providing
prevent entry by
security to
new groups,
major producers, who then use
creating d3mamic distortions. This
by the contrast between the economic
their political
mechanism
histories of the Northeastern
is
power to
illustrated
United States and the
Caribbean diuing the 17th, 18th, and 19th centuries.
everyone else was out in the cold"
(p.
18),
and during the
later era, "manufacturers could
lobby the
executive branch of government, which could then, without the need to seek legislative approval, restrict
the importation of competing products"
(p. 48).
^Moreover, at least part of the economic problems of some democracies also seem to stem from "antibusiness" policies. See, for example, Besley and Burgess (2003) for an interesting analysis of the economic
costs of pro-labor regulation in India.
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5
Residuals from Democracy Index
Figure
Residuals of tax revenues as a percentage of
1:
Freedom House democracy index
in 1997-98.
corresponding variables on log
The Northeastern United
GDP
Both
GDP
in 1998 vs. residuals of
residuals are from a regression of the
per capita in 1998. See Appendix B.
States developed as a typical settler colony, approximating
a democratic society with significant
political
power in the hands of smallholders
(e.g.,
Galenson, 1996).^ In contrast, the Caribbean colonies were clear examples of oUgarchic
with pohtical power in the monopoly of plantation owners, and few rights for the
societies,
slaves that
made up
the majority of the population
1972). In both the 17th
places in the world,
United States
1995,
and 18th
centuries, the
(see, e.g.,
Caribbean
Beckford, 1972, and Dunn,
societies
were among the richest
and almost certainly richer and more productive than the Northeastern
(see, e.g.,
Acemoglu, Johnson and Robinson, 2002, Coatsworth, 1993,
Engerman, 1981, and Engerman and
Sokoloff, 1997).
Eltis,
Although the wealth of the
Caribbean undoubtedly owed much to the world value of its main produce, sugar,
it
seems
that Caribbean societies were able to achieve these levels of productivity because the
planters
had every incentive to
But starting
^This
is
invest in the production, processing
in the late 18th century, the
and export of sugar.
Caribbean economies lagged behind the United
a relative statement, not meant to deny the significant power of rich industrialists and landown-
ers in the 19th-century United States (see, e.g., Beard, 1952).
States
and many other more democratic
opportunities, particularly in industry
Engerman and
2002, and
societies,
and commerce (Acemoglu, Johnson and Robinson,
Sokoloff, 1997).
and Western Eiu"ope invested
While new entrepreneurs
in these areas,
hands of the planters, who had no
which took advantage of new investment
power
in the
in the United States
Caribbean remained in the
interest in encoTiraging entry
by new groups. ^° Though
not as stark as the contrast between the Northeastern United States and the Caribbean,
the experiences of other ohgarchic societies, including those of Japan, South Korea, Brazil,
and Mexico, where
initial
growth supported by close relations between major producers
and the government has shown a tendency to come
to
an end, are also consistent with
the mechanism emphasized in this paper.
Many
studies
on economic growth and the pohtical economy
of development have
pointed out the costs of entry barriers, while others have emphasized the disincentive
effects of redistributive taxation.
fully articulates
For example, the classic by North and
Thomas
force-
the view that monopoly arrangements are the most important barrier
many
to growth,
and
joint stock
company, replacing the old regulated company" and "the decay of industrial
cite "the
ehmination of
of the remnants of feudal servitude,..., the
regulation and the declining power of guilds" as key foundations for the Industrial Revolution in Britain (1973, p.
155).
This point of view
is
also developed in Parente
and
Prescott (1999), and in the recent book by Raj an and Zingales, where they emphasize the
threat to successful capitahsm from the "incumbents, those
who
Ushed position in the marketplace and would prefer to see
remain exclusive." (2003,
18).
An
even larger
For example,
Romer
Tabellini (1994),
literature,
it
already have an estab-
on the other hand, focuses on the cost of
(1975), Roberts (1977), Meltzer
p.
redistribution.
and Richard (1981), Persson and
and Alesina and Rodrik (1994) aU construct models
in
which the median
voter chooses high levels of redistributive taxation, distorting saving, investment or labor
supply decisions (see also Benabou, 2000, on how, imder certain circumstances, democracy
may
not generate enough redistribution). Barro succinctly summarizes the costs of
a democratic regime as
"...the
tendency to enact rich-to-poor redistribution of income
(including land reforms) in systems of majority voting and the possibly enhanced role of
interest
groups in systems with representative legislatures." (1999,
am not
aware of any analysis that relates the distortions created by redistributive democ-
p. 49). Nevertheless, I
racy and those caused by entry barriers in oligarchy as the two sides of the trade-off over
^"Sokoloff
and Kahn (1990) and Kahn and Sokoloff (1993) show that many of the major U.S. inventors
were not members of the aheady-estabhshed economic ehte, but new comers with
in the 19th century
diverse backgrounds.
the "form of property rights", nor any analysis of the dynamic costs of oligarchy.
Other closely related papers include Krusell and Rios-Rull (1996), Acemoglu, Aghion
and
Zilibotti (2003), Learner (1998), Robiioson
and Vollrath
(2003).
The
and Nugent (2001), and Galor, Moav
result of potential cycles in oligarchy in the current
model
is
related to the political-economic cycles in Krusell and Rios-Rull (1994). In their model,
technology-specific investments create vested interests opposed to the introduction of new
technologies.
The pohtical power
of these vested interests
may lead
to growth cycles. Ace-
moglu, Aghion and Zilibotti (2003) develop a theory where protecting large firms at the
early stages of development
is
beneficial because
it
relaxes potential credit constraints,
but such protection becomes progressively more costly as the economy approaches the
world technology frontier and selecting the right entrepreneurs becomes more important.
That paper
also provides
some empirical evidence that economies with high
levels of en-
try and international trade restrictions suffer severe growth slowdowns as they approach
the world technology frontier. Finally, Learner (1998), Robinson and Nugent (2001) and
Moav and VoUrath
Galor,
vestment in
may
initially
human
(2003) discuss the potential opposition of landowners to in-
capital.
For example, Galor
et al.
emphasize how land abundance
lead to greater income per capita, but later retard
human
and economic development. None of these papers contrasts the
lation
democracy and oligarchy or
The
rest of the
paper
is
identifies the
dynamic
organized as follows.
capital
accumu-
trade-offs
between
costs of oligarchy.
Section 2 describes the economic en-
vironment, and characterizes the equilibrium for a given sequence of policies.
Section
3 analyzes the pohtical equiMbrium in democracy and ohgarchy, and compares the out-
comes. Section 4 discusses a simple model of changes of regime between ohgarchy and
democracy. Section 5 concludes.
2
The Model
2.1
I
The Environment
consider a non-overlapping generations
There
is
a rmique
agent has a single
final
economy consisting of a continuum
good which can be used
off'spring,
and
is
for
consumption or
1 of dynasties.
for bequest.
Each
imperfectly altruistic with the utility function:
u^^{i-py^'-^^p-^{ciY-'{b^,,y-4,
(1)
where
the consumption of agent j at time
is
cj.
and
offspring,
zj is the
6^^j is
t,
the bequest he leaves to his
(non-pecuniary) cost of effort that the agent incurs
if
he becomes
an entreprenem:.
This utihty function
convenient since
is
impHes a constant savings rule
it
for
each
agent of the form:
^+i=W,
where W^
is
the total income of the agent at time
utility function of agent j at
turn the
I
sum
e
—
>
0.
e of
The reason
can otherwise
=
0,
specific
new
there
is
demand
also exist other equilibria,
to
.
income
is
in
death
is
and
economy with
to avoid the case where the
a range of wage rates, which
In other words, in the economy with
in this case, the limit e -^
picks a
set of equilibria.
economy
distinction in this
up a firm
= Wl — z\ Total
i.e., Wl = Wl + h{.
1/^
for labor for
arise in the oligarchic equilibrium.
and capitalists/entrepreneurs on the
or set
implies that the indirect
with a small probability e in every period,
for introducing the possibility of
one from the
The key
(dies)
W^,
It also
dynasties are born. I will consider the Umit of this
exactly equal to the
may
t.
simply given by
t is
of earned income, VF/, and bequests,
supply of labor
e
time
assume that each dynasty disappears
and a mass
(2)
is
other.
between production workers on the one hand
Each agent can
become an entreprenem:.^^ While
all
either
be employed as a worker
agents have the
same productivity
as workers, their productivity in entrepreneiu-ship differs. In particular, agent j at time
t
has entrepreneurial talent
an agent needs to
set
G {A^,A^] with A^ <
al
up a
firm, or alternatively,
up a new firm may be
father. Setting
A^
To become an entrepreneur,
.
he could inherit the firm from his
costly because of entry barriers created
by existing
entrepreneurs.
Each agent
talent a[
a firm.
therefore starts period
G {A^ A^], and
si
,
I will
also refer to
G
t
{0, 1}
with a
level of
bequest (income)
h{
society,
he
an agent with
may be
=
s^
1
as a
member
politically
more
influential
Within each period, each agent makes the following
denoted by
c^,
In addition
if z^
(effort),
a bequest decision denoted by
=
1, i.e., if
of the "elite", since he
6^_,.i,
barriers),
wiU
and
in
than non-ehte agents.
decisions: a
consumption decision
and an occupation choice
%{
G
{0, 1}.
the agent becomes an entrepreneur, he also makes investment
employment, and hiding decisions,
^^See, for example, Banerjee
entrepreneurial
which denotes whether the individual has inherited
have an advantage in becoming an entrepreneur (when there are entry
an oligarchic
,
and
Newman
el,
ll
and
hi,
where
hi denotes
whether he
(1993) for a model of occupational choice of this type.
incurs an investment and operation cost of el
will refer to
profits of
+
With some abuse
K'.
as the profit function. Given a tax rate Tj
tt
an entrepreneur with talent
(r„
TT
li, ei,
ai w,)
i.e.,
=
hi
1,
and a wage rate Wt
>
0,
I
the net
a^ are:
= i^(a^)-(e^y-(/^)- -
as long as the entrepreneur does not hide his output,
output,
of terminology,
=
hi
i.e.,
he avoids the tax, but loses a fraction 5
^ - kX,
-
w^lj
0.
<
1
If
(4)
he instead hides his
of his revenues, so his
profits are:
TT
{ruli,ei,ai,wt)
The comparison
= ^{ainei)'-^{lir - wtli 1 —
ei
a
of these two expressions immediately impUes that
-
if tj
kX.
>
6, all
entrepre-
neurs will hide their output, and there will be no tax revenue. Therefore, the relevant
range of taxes
will
be
0<Tt<5.
Since, in the presence of entry barriers, entrepreneurship
additional cost Kt for agents with
an agent of type
si
=
0,
il
=
an
1) entails
the net gain to becoming an entrepreneur for
a function of the pohcy vector
(5^,0^) as
(i.e.,
(kt, Tt),
and the wage
rate, Wt,
is:
U(kt,Tt,Wt
where the
last
I
sl,al) =meiX-K(Tt,ll,el,al,Wt)
term indicates that
if
-
(1
-
sl)ktX
(5)
the agent does not inherit the firm from his father,
he will have to pay the additional cost imposed by entry barriers. ^^ Notice also that
11
the net gain to becoming an entrepreneur, since the agent receives the wage rate Wt
is
irrespective (either working for another entrepreneur
—thus having to hire one
himself
imphes that an agent
will
less
—when he
worker
become an entrepreneur
become an entrepreneur only
if
Il(^kt,Tt,wt
^^Private sales of firms from agents with
when he
s^
=
sl,al)
\
1
>
a worker, or working
for
an entrepreneur). This feature
i£ Tl (^kt, Tt,
Wt
\
si
,
al)
>
(and can
0).
to those with
equivalently assumed to be subject to the entry cost Kt). This
we
is
is
is
Sj
=
are not allowed (or they are
without
loss of generality, since, as
where the equilibrium wage is
do not have the funds to finance the purchase of existing firms from the
will see below, entry barriers exist only in the oligarchic equilibrium,
zero and agents with
s^
=
incumbents.
Note that private sales of firms without any entry barrier-related costs would circumvent the inefficienfrom entry barriers. The absence of such sales, and consequently the existence of real effects of entry
barriers, seems plausible in practice (see, for example, Djankov et al., 2002, on the relationship between
entry barriers and various economic outcomes).
cies
10
Labor market clearing requires the
demand
total
Since entrepreneurs also work as workers, the supply
for labor not to
is
equal to
exceed the supply.
1, so:
lldj<l,
iilldj=
(6)
Jjeit
where
It is
the set of entrepreneurs at time
useful at this point to specify the law of
It is also
which determines the "type" of agent
by equation
(2).
a firm, then
liis
The
transition rule for si
is
Sq
=
that there
is
straightforward:
offspring inherits a firm at time
for all j,
and
also s^
=
if
motion of the vector (6j,Sf,aj)
As already noted, bequests are given
j at time t}^
^^+1
with
t.
=
i
+
1
,
agent j at time
if
t
sets
up
so
^l
(7)
dynasty j
is
born at time
Finally, I
t.
assume
imperfect correlation between the entreprenemrial talents of different agents
within a dynasty, and assimae the following Markov structure:
{A^
with probability
A^
G
cfl
Here
(0, 1).
with probability
with probabihty
an
in entrepreneiuship conditional
is
on
is
is
his father
i.e.,
an <
1,
is
,
.
^'
'
having high productivity, and gl
It is
natural to suppose that
more hkely to be highly productive
important for the results
dynasty,
1 - (7jy
I- a^
al
the probability that an agent has high productivity
probabihty when his father has low productivity.
so that an individual
if
with probability ai
A^
A^
where aH^
= A"
if a{ = A^
ii 4 = A"
if Gj = A^
gh
if
his parent is
is
the
uh > ct/,,
so. What
imperfect correlation of entrepreneurial talent within a
so that the identities of the entrepreneurs necessary to achieve
productive efficiency change over time.
It
can be
verified easily that
M = --f^G (0,1).
^^In fact,
what
is
important for the purposes here
is
the subvector
I
Sj
,
a^
I
.
Bequests are introduced to
and the incomes of current elites, which plays a role in Section 4. For
most of the paper, there is no need to keep track of the distribution of bequests. It is also worth noting
that the model could be set up with infinitely-lived agents, with little change in the results, though the
analysis becomes somewhat more complicated, because agents would have to take into account the future
implications of setting up a firm and becoming part of the elite. Since these issues are not central to the
create a link between past profits
focus here,
I
opted
for the
non-overlapping generations setup.
11
the fraction of agents with high productivity in the stationary distribution
is
(1
— M) ai)-
Since there
a large number of agents,
is
I
(i.e.,
is
to
is
1,
so that, without entry barriers, high-productivity entrepreneurs generate
demand
any point
assmne that
MX >
ficient
— an)
a continuum of
agents), wliich implies that the fraction of agents with high productivity at
I
(1
appeal informally to the weak law
of large nimibers (ignoring comphcations related to the fact that there
M. Throughout
M
employ the
as large; in particular,
I
entire labor supply. Moreover,
assume A >
I
more than
svif-
M as small and A
think of
which ensures that the workers are always in the
2,
majority and simpUfies the pohtical economy discussion below.
Finally, the timing of events within every period
1.
Entrepreneurial talents,
2.
The entry
3.
Agents make occupational choices,
4.
Entrepreneurs make investment and employment decisions,
5.
The labor market
6.
The tax
7.
Entrepreneurs make hiding decisions,
8.
Consmnption and bequest
Note that
I
barrier for
rate
[a^], are
new
clearing
and similarly
:
[0, 1]
—> {A^
,
reahzed.
entrepreneurs
wage
on entreprenetus,
used the notation
the mapping sn
J,
is:
[zj]
[e], /j]
rate, Wt, is determined.
rt.,
is set.
decisions,
[a^]
kt is set.
[/ijl
[cj, 6^^;^]
are made.
to describe the whole set [a^]
.^ ^,
,
or
more formally,
>1^}, which assigns a productivity level to each individual
for [zj], etc.
Entry barriers and taxes wiU be
set
by
different agents in different political regimes
as will be specified below. Notice that taxes are set after the investment decisions, which
can be motivated by potential commitment problems whereby entrepreneurs can be "held
up" after they make their investments decision.
employment decisions are made,
it is
Once these investments
in the interest of the workers to tax
are simk:
and
and redistribute
entrepreneurial income.-'^
^^This timing of events
is
adopted to simplify the analysis and the exposition. Because there are only
12
2.2
Analysis
I start
with the "economic equilibrium" which
the (subgame perfect) equilibrium of the
is
economy described above given a policy sequence
more
formally, let
ocj.
=
(il,elJl,hl,cl,
{kt, Tt}t=o
Definition (Economic Equilibrium) {[5^]}.
type
ket,
(bPf.,sl,al), xl
i.e.,
equation
I
now
(2), (7)
and
(8)
j, (1),
and wt
given
characterize this equiUbriiim. Recall that Sq
entry barrier would create waste, but not affect
all
fixed costs of operation
entrepreneurs will hire the
where, recall that,
maximum amount
=
4=
can be written as
Cj
=
Now using the
=
n
(kt,
,
Tt,
Wt
I
=
(1
— fi)^/"ajA
= -^-(1 1
—Q
=
0,
any positive
scale technology
Given
this,
E
imply that
It,
investments will be:
(10)
where
fj is the
tax rate expected
Tt).
(9)
and
(10), the net
gain to entrepreneur-
equiUbrium wages, the status
can be obtained
si, a{)
t.
Ttf/^aiX.
=
ko
(9)
-
ship, as a function of entry barriers, taxes,
talent,
for all j,
X,
equihbrium factor demands,
and entrepreneurial
and suppose
for all j,
of labor. Thus, for all j
(1
at the time of investment; in equilibriimi, ft
Sj^xi "^t+i))
enters entrepreneiorship)
the set of entreprenemrs at time
/j is
(Alternatively, (10)
who
(&^_|.i,
mar-
[x^].
and the constant returns to
II
{tWfjj^Q
clears the labor
in the next period,
so that in the initial period there are no entry barriers (since Sg
The
t.
given poUcies kt,Tt, the wage rate Wt and his
if,
Each agent's type
then follows from equations
at time
and a sequence of wage rates
gi
maximizes the utihty of agent
(6) holds.
define this equilibrium
be the vector of choices of agent j
6^_,_j)
constitute an economic equihbritun
To
•
i
si of
the agent
si)ktX.
(11)
as:
TtY^'^aiX
- WtX - kX -
{1
-
two types of entrepreneurs, it turns out that if workers choose the tax rate before investment decisions,
they will set r^ =
(see Appendix A). The timing of events here implies that they cannot commit to
this tax rate, and consequently ensures a positive level of redistribution. In Appendix A, I show that
the main results generalize to an environment where there are more than two levels of entrepreneurial
productivity and where voters set taxes Tj at the same time as kt, i.e., before investment decisions. In
this case, voters choose Tt > 0, trading off redistribution and the disincentive effects of taxation, as in,
among others, the models by Romer (1975), Roberts (1977), and Meltzer and Richard (1981).
13
^
Moreover, since
=
Xdj
J. J
=
/j
and the
1,
A for
all j,
the labor market clearing condition (6) implies that
mass of entrepreneurs
total
it= [
<
dj
any time
at
is:
1/A.
Jjeh
Tax revenues
at time
Tt
and the per capita lump-sum transfers are given
t
=
E W = Y3^^*(l - rO'^A J]a^
jeit
Who
will
shows that
any
for
Sj
and
dl,
Wt
and the
= A^
agents with al
=
si
\
and
5^
1,
= A^) > U
al
first
=
Sj
We
=
will
depend on
can then define two
economy? Inspection
in this
term
will
[kt, Tt,
Wt
|
s^, Qf)
>
11
of (11) immediately
(A;^,
Tj,
1^(15^
=
0, a{
always strictly greater than the third term. So
is
choose
=
Zj
0,
= A^
the occupational choice of agents with al
and
(12)
jeit
become an entrepreneur
11 {kt,Tt,
as:
becoming workers.
and
=
si
On
the other hand,
and of those with
1
al
= A^
kt.
different types of equilibria:
1.
Entry equilibrium where
2.
Sclerotic equilibrium
all
entrepreneurs have al
where agents with
=
si
= A^
become entrepreneurs
1
irrespective of
their productivity.
An
n
entry equihbrium requires that
[kt,Tt,Wt
I
si
=
1,
"
1
ai
— a (1
=
-
A^) <
0,
TtY^'^A''
IT
that
(^kt,
Tt,
Wt\
=
si
0, al
= A^^ >
and
is:
-K-kt>Wt> -^(1
—
a
1
Therefore, there wiU be an entry equihbrium only
- tO'/"A^ -
/c.
if
-^-{l-rtY/^{A''-A'^)>kt,
1 — a
(13)
'
i.e.,
is
only
if
the net marginal product of labor of a high-productivity non-elite entrepreneur
greater than that of a low-productivity
the other hand, only
if
the converse of (13)
Moreover, in an entry equilibrium,
i.e.,
elite.
is
A
sclerotic
equihbrium
emerge, on
the case.
when
(13) holds,
we have
{^(l-r,)V">l^-K-A:,;0|.
14
will
(14)
=
A^)
This follows because, in eqiiilibrium,
If it
were
11
(fcj,
r^, lut
si
\
strictly positive, or in other words, if the
=
0, al
= A^)
wage were
less
must be equal
than w^,
all
would be "excess demand"
for labor.
This argument also shows that
it
=
agents with
MX
high productivity would enter entrepreneurship, and since, by assumption,
>
this
economy. Labor supply
ing as a function of the wage rate. This
holds, so that there exists
demand
portion
i.e.,
MX
supply at the wage given in
>
1
1,
while labor
demand
is
demand
decreas-
drawn under the assumption that
figiu:e is
first
(13)
portion of the curve shows the
= A^ and sj — 1, and the second
those with aj = A^ and si = 0. These two
agents with aj
high-productivity non-ehtes,
groups together demand
constant at
an entry equilibrium. The
of high-productivity ehtes,
is for
is
there
1
1/A.
Figure 2 illustrates the entry equilibrium diagrammatically by plotting labor
and supply in
to zero.
i.e.,
workers, ensuring that labor
demand
intersects labor
(14).
LS
k
1-tJ«^^-k
1
1
!!;(>-',)"*'-'
LD
"
l-a
k-TJaA^-K-k^
'
"
—
xu
1
Figmre
2:
Labor supply and labor demand when
(13) holds
and there
an entry
exists
equiHbrium.
who
In a sclerotic equilibrium, on the other hand, low-productivity agents
si
=
,r^{l - Ttf'^A^ -
k\
firm from their parents will remain in entrepreneurship,
deaths so that e
Wt e [max
=
0,
we would have
{j^{l - Ttf/'^A" - k -
exactly equal labor supply
supply of
1.
if
=
1/A and
kt\Q]
for
i.e.,
Sj_;^.
If
inherited a
there were no
any
,
labor
demand would
— 1/A agents demanding exactly A workers each, and a
Hence, there would be multiple equiUbrium wages. In contrast, when e
the measure of entreprenetirs
who
could pay a wage of Yr^(l
15
~
Tt)^l°'A^
—
k
is
total
>
it
0,
=
(1
—
at
any wage above the lower support of the above range. This imphes that the equihbrium
<
e) it_i
1/A for
wage would be equal
is
>
all t
thus there would be excess supply of labor at this wage, or
0,
al
economy where e
—
>
0,
=
it
In the remainder,
1/A.
which picks
I
t^^I°-A^
= A^
between entrepreneurship and working, in equilibrium a
entrepreneurship, and
—
{jz^{l
wage agents with
Since at this
identical to (14).
max
to this lower support,
and
sufficient
si
~k—
=
kf,
O},
which
are indifferent
number
of
them
enter
focus on the Umiting case of this
max {y3^(1 — TtY^^A^ —
wage even when labor supply coincides with labor demand
k
for
—
kt;0] as the equilibriimi
a range of wages. ^*
LS
^
ik
^Jl-.J«.^-.
LD
1-E
Figure
3:
1
Labor supply and labor demand when
(13) does not hold
and there
exists a
sclerotic equihbrium.
Because (13) does not hold in this
Figure 3 Ulustrates this case diagrammaticaUy.
case, the second flat portion of the labor
agents with
aj.
= A^
and
Sj
=
1,
demand curve
is for
low-productivity ehtes,
i.e.,
who, given the entry barriers, have a higher marginal
product of labor than high-productivity non-ehtes.
Finally, since at time
i
Wo
^^In other words, the
=
we have
ko
=
0,
will also give
initial
period equilibrium will feature:
= max |-^(1 - ro)^/°A^ -
wage max-^ 13^(1 ~ TtY^^'A^ — k — kt;0>
equilibrium set where the equilibrium correspondence
I
the
is
o|
at e
.
=
is
the only point in the
(lower-hemi) continuous in
the relevant expressions for the case where e
16
k;
>
0.
e.
For completeness,
In the remainder of the paper,
I
assume
-^^{l-Sfl'^A" >K,
<
so that, for any tax t
and
5
In addition, note that at
ically,
A;
=
f
=
(15)
the equihbrium wage
0,
is
positive.
entrepreneurs have high productivity.
0, all
More
specif-
define
^i,
=
Pr
{al
= A"
as the fraction of entrepreneurs at time
the economy starts with
^*
_
~
ixq
=
1.
CTHl^t-i
J
=
1?,
who
t
The law
+
=
1)
I
=
(g^'
A""
\j
G h)
are high productivity. In the initial period,
of motion of
- /^i-i)
0-^(1
Pr
/i^ is
then given by:^^
(13) does not hold
if
.
\
This law of motion also imphes that
(13) holds
if
(13) never holds, lim4_^oo
if
fJ-t
=
.
^^^^
•
1
^<
^i i-^-,
the frac-
tion of high-productivity entreprenexirs limits to the average fraction of high-productivity
agents in the population.
The
following proposition summarizes the
main
results in this subsection (proof in the
text):
Proposition
Given a policy sequence
1
equihbrium, there are
=
it
{kt,Tt}f.^Q-y
,
an equihbrium always
exists.
In
1/A entrepreneurs and each entrepreneur hires A workers, and
undertakes the investment level given by (10), and the equihbrium wage
is
given by (14).
In addition:
• if (13)
holds at
tivity, i.e.,
is Ait
=
Zj
=
i,
an individual becomes an entrepreneur only
= A^
=> Qj
1
does not hold at
t,
productivity entrepreneurs
with
19
For e
>
he has high produc-
and the fraction of high-productivity entrepreneurs
1;
• if (13)
• if (13)
,
if
the equihbrium has
is /Xj
=
anl-i-t-i
=
0, this
1
,
and
satisfies limt ^oo
equation
£
^*
I
1
is
+
modified
(1
fit
=
=
+ cl(1 —
never holds, then the equilibrium has
yUg
i-j.
M<
/i^
=
s-j.,
and the
fraction of high-
A't-i);
anj-i't-i
+
"^/-(l
1.
to:
e) (cTH^t't-i
+
crz,(l
1
—
Mt-i))
if
(13) does not hold
if
17
(13) holds
~
/^i-i)
starting
Political Equilibrium
3
To obtain a full political equilibrium, we need to determine the policy sequence
I will
1.
{kt, rt}^^Q
^
consider two extreme cases:
Democracy: the poUcies
and
kt
r^ are
determined by majoritarian voting, with each
agent having one vote.
2.
Oligarchy
among
voting
the policies
(elite control):
the ehte at time
t.
I
and
kt
take the ehte to be those
firm from their parents, or in other words those with
In this section, oligarchy
is
determined by majoritarian
tj are
St
assumed to be "technological"
=
who have
inherited a
1.
in the sense that irrespective
of the exact pohtical institutions, those with control of the productive resources of the
society
and greater income have more say
pohcy choices
reflect their preferences.
whether the society
in pohtical decision-making,
In the next section,
democratic or oligarchic
is
is
and consequently,
analyze a model where
I
determined in equiUbrium.
Democracy
3.1
The timing
of events imphes that the tax rate at time
decisions at time
decisions are
t,
t,
Tt, is
decided after investment
whereas the entry barriers are decided before. Both of these pohcy
made by
majoritarian voting.^° Recall also that the assumption A
>
2
above
ensures that non-elite agents are always in the majority.
At the time taxes are
set,
investments are sunk, agents have aheady
cupation choices, and workers are in the majority.
maximize per capita
transfers.
We
fj is the
voters.
tax rate expected by entrepreneurs and
output, and tax revenue wiU be
affect
n
U
This expression takes into account that
0.
Tt
is
if tj
their oc-
Therefore, taxes wiU be chosen to
can use equation (12) to write tax revenues
I
where
made
>
Tj is
5,
Tt
as:
>
the actual tax rate set by
entrepreneurs will hide their
a fxmction of the entry barrier,
kt,
since this can
the selection of entrepreneurs, and thus the X^,g/, al term.
At the time the entry
barrier, kt, is set, agents
choices. Low-productivity non-ehte agents,
^"Appendix
A
presents a
more general version
i.e.,
have not made their occupational
those with
s^
=
and
a^
=
A^, know that
of the model, which has both policy choices
simultaneously, and yields identical results to those in the text.
18
made
they will always be workers, and thus simply receive the equilibrium wage and transfers.
Therefore, the utihty of agent j with
t//
where
fej
is
=
Sj
= 6^+ <
al
= A^
+ Tt
[kt, Tt
and
ft)
{kt
I
the bequests he has inherited, and wl[kt
equation (14), but with the anticipated tax rate
is
f,)
\
equilibrium, naturally, Tt
wt
{kt\ ft)
=
ft)-
ft replacing
i.e.,
to
maximize
tUj {kt
same and they
the
also given
is
+
ft)
\
by
those with
Consequently,
(18).
Tt {kt,Tt
|
Sj
=
A
\
I
\
ft)
+
is
Tt {kt, Tt
\
Because taxes are set after investment decisions, workers prefer
redistribution of income
^^The
S
and w^
{kt
|
results are identical
does not depend on
when
^^
^^
such that:
ft)
-
=
Tt
T {kt, Tt
from the entrepreneurs to themselves
ft)
a pohcy sequence
is
Jt=o,i,...
L
{kt
as:
^^^^ ^^^^ {[^]}t=oi
and \kt,ft>
) t=o,i,...
(4, ftj e argmaxiWi
h,Tt
=
non-ehte agents are
all
democratic equihbrium
economic equilibrium given \kt,ftr
at Tt
,
non-elite agents will choose kt
and economic decisions {[^]}j^oi
'?'*(•
(fct,
al
shows that a democratic equilibrium can be defined
Definition (Democratic Equilibrium)
4,
all
= A^ may become
Tt, wt
sf = 0, al = A^)
and
11
(19)
are in the majority, the democratic equihbrium will maximize these
preferences. This analysis
I
conditioned on the expected
Since the preferences of
ft)-
is
Thus:
entrepreneurs, but as the above analysis shows, in this case,
so their utihty
is
the actual tax rate (this
= max S^^^il- ft)'/'' A''-i^-kt;o\.
High-productivity non-ehte agents,
0,
the equiUbrium wage given by
ft) is
because the labor market clears before tax decisions, so wl
tax; rate, fj; in
(18)
I
6 to
\
maximize the
ft) is
maximized
r^.^^
taxes are on income rather than output. In this case, the objective
[1 — Tt)wf{kt
ft)+Tt {kt,Tt fj), with Tj (A;t,Tt fj) unchanged
because tax revenues now include taxes from wage income, but this is offset by the lower tax
revenue from entrepreneurs, who are now paying taxes only on their net income, i.e., output minus wage
function of the median voter would be:
|
\
|
(this is
bill).
It
can be verified that this expression
derivative of this expression with respect to Tt
—
which
Y3^(l
is
maximized at
tj
=
S.
To
see this note that the
is
^
rv
always positive since, by definition, for
— Tt)~^ Xal >
is still
all
j
—
G
It,
we have t^(1 — 7"t)
°
Aa^
—wf >
wl, implying that voters would like as high a tax rate as possible,
19
0.
i.e.,
Therefore,
Tt
=
5.
-
Inspection of (17) and (19) shows that wages and tax revenue are both maximized
when
=
kt
so the democratic equihbrium will not impose any entry barriers.
0,
by protecting incimabents, and a
intmtive: workers have nothing to gain
is
since such protection reduces labor
demand and
= A^ The
and only
if
il
=
I
only
if
following proposition therefore follows immediately (proof in the text):
.
Proposition 2
if
lot to lose,
wages. Since there are no entry barriers,
only high-productivity agents will become entrepreneurs, or in other words
Qj
This
al
A democratic equilibrium always features Tt = 6 and kt =
= A^, and = 1. The equihbrium wage rate is given by
0,
and
il
=
1
/ij
a
-f = 1-Q (1 and the aggregate output
Y,^
-
sy/'^A"
K,
is
= Y^ = ^(l-J)V-A^ + 5iLJ)
1- a
1 - a
"
^^,
(20)
^
^
1-tt
Notice that in the
and the second term
equilibrium
is
first line
is
of (20), the
tax revenue at the rate
that aggregate output
is
term
first
Tt
=
is
total production net of taxes,
5^'^
An
important feature of this
constant over time, which wiU contrast with the
ohgarchic equilibrium.
Finally, note that since
n
{kt
=
0,Tt,wt
si
1
=
0,ai
= A")=U
{kt
=
0,rt,wt
\
= 1,4 = A^) =
sj
0,
high-productivity agents are indifferent between entrepreneurship and production work.
Nevertheless, entrepreneiirs earn greater incomes to compensate
costs of entrepreneurship. In fact, in
come
(net of bequests)
I
^^The expression above
have been subtracted.
^^To obtain
T
=
5.
periods, production workers have a post-tax in-
:^'^
W- = -^-(1
—
K,
all
them for the non-pecuniary
a
- 5Y^^A"
1
refers to total output,
Output net of these
-K + 5^^—^
—
"
A"",
before the costs of investment,
costs
is
(21)
a
given by q(1
—
e,
<5)-'/°j4^/ (1
and operation,
—
a)
+
aS{l
—
wage, (19) and tax revenues, (17), with r =
with equilibrium factor demands (9) and (10),
(21), use the expression for the equilibrium
To obtain
(22), use
the production function
(3)
and the fact that output is taxed at the rate t = f = 5, then subtract the
add W^ which is what the entrepreneur receives as a worker himself.
,
20
total
wage
bill
using (19), and
while each entrepreneur receives:
W^ = {1-
+ kX + W^ >
Sy/^'A^X
W"".
(22)
Oligarchy
3.2
In ohgarchy, only existing entrepreneurs (agents with
and
process,
elite is
=
1)
participate in the pohtical
determined by majoritarian voting among this
policies are
nature of the ohgarchic equilibrium
within the
si
is
set of agents.
The
simpUfied by the fact that the only heterogeneity
between high-productivity and low-productivity agents. This implies
that majoritarian voting wiU lead to the policies most preferred by whichever group
in
is
the majority within the ehte.
To
with
it
=
state this formally, let
=
St
This
1.
whereas
1,
an agent
at time
St
t,
=
1
j2t
fi^
from
is different
^j,
which
refers to the entreprenerus,
refers to the agents in the elite,
chooses
it
=
those with
i.e.,
St
=
and does not become an entrepreneiu, he
and thus takes part
wiU not be
be the fraction of high-productivity agents among those
in the determination of the tax rate,
i.e.,
1.
those with
Notice that
is still
though
if
in the elite
his offspring
in the ehte.^"*
In addition, note that the most preferred policies of an ehte agent with productivity
al are given
U^
where
=
6^ is
by
bi
kt
and
tj that
+ max {n
{kt,
maximize:
Tt,wt
the bequest the agent
I
=
l,a{)
;
hcis inherited,
the net return to entrepreneur ship,
Tt,
si
lUt,
O}
the
+ w\ (h
\
ft)
11 fiuiction,
given by (19),
is
+ Tt
{kt,Tt
from
(5)
\
ft)
above, denotes
the equilibrium wage rate and
given by (17), denotes transfers. This expression incorporates the fact that the agent
will
become an
Then
let
entrepreneiu- ordy
if
the net return to entrepreneurship
An
and economic decisions
<A;t,ft>
L
it
alternative modeling assumption
=
1. It
can be
characterized here
eqiuUbrimn
oligarchic
{ [2^] },^n
i
J t=o,i,...
would be to
I
a poUcy sequence
is
such that {[^]}j^oi
and \kt,ft\
economic equilibriiun given \kt,ft\
^*An
non-negative.
us define:
Definition (Oligarchic Equilibrium)
with
is
is
^^
^^
such that:
J t=o,i,...
limit the decision
on the tax rate only to agents
verified that the equilibrium in this case is identical to the non-cycling equilibrium
(i.e., it
does not contain cycles even
21
when
condition (24) holds).
*
>
if Jit
1/2, then
argmax {max (ll
[kt,ftj e
Wt\
{kt, Tt,
si
=
1,
si
=
l,a^
= A")
al
;
+
O)
Wt {k
\
ft)
+ Tt
ft)
+ Tt{kt,Tt
{kt, Tt
\
ft)]
kt,Tt
*
<
if /it
1/2, then
€ argmax {max
(kt.ft)
where
To
Tt {kt, Tt
\
ft) is
(n(fci,rt,ii;t
|
given by (17) and wf
{kt
characterize the oligarchic equihbrium, let us
productivity ehtes
(i.e.,
those with
=
si
and
1
al
=
\
=
A^) O)
;
ft) is
first
=
kt
G [ir^(l ~
0.
Equihbrium wage, given
ft)^^°'A^
—
in (19), will
Without
K, oo).
|
given by (19).
A^). Since these agents wiU remain as
to be as low as possible,
=
be minimized at wf
any generahty,
loss of
(/cj
consider the preferences of high-
an entrepreneur, they would always hke the wage and taxes
ft
+ iw"
0,
i.e.,
by choosing any
focus on a particular
I
point in this set,
kt
=
= -^{l-5)'/''A"-K.
—
k^
Next consider the pohcy preference
si
=
1
and
al
=
A^).
His payoff
is
he remains an entrepreneur, making
redistribution).
Or
it is
worker receiving income jz^{l
^
-
of a low-productivity ehte
maximized
=
kt
-
5)1/"
and
- k+
5)^^°'A^
[a{l
either
profits equal to
maximized by
(23)
a
1
Tt
yz^(1
by
kt
=
{jz^A^ —
=
-
S,
(i.e.,
k^ and
an agent with
X (plus
k)
when he chooses
6)'^^~°'^/"A^.
=
Tt
0,
when
wage and
become a
to
As long
as
+ 5{1 - (5)(i-°)/°] A" -K
1—
profits
tion.^^
from entrepreneurship are greater, and low-productivity ehtes prefer the
Therefore,
when
(24) holds,
both low-productivity and high-productivity
have the same preferences over pohcies, and vote
tion
is
for kt
=
k^ and
the ohgarchic equihbrium, and results in equihbrirun wages
In this equihbrium, aggregate output
Yt^
^^Note that
if
the pohcy of kt
= k^
and
Tj
=
when
= 0. This
wf = 0.^*^
tj
op-
elites
combina-
is:
= f^tj^A" +
1 — a
to remain in entrepreneurship. However,
first
is
(I
- pit)Y^A^
1 — a
(25)
elite would always prefer
between entrepreneurship
imposed, the low-productivity
deciding policies, the choice
is
with kt = k^ and Tt = 0, and production work with kt =Q and Tt = 5.
^^
This result also shows that even if taxes that only apply to labor income and transfers directed only
to the elite were allowed, there would be no need for the elite to use them, since wages are already at
their
minimum
value.
22
\
ft)}
;
where
^ij
=
an/J^t-i
M,
sequence converging to
aggregate output
Urn Yt^
The reason
^ given by (16), with
+ <^l{^ ~ A^t-i)
y^-^ is
/ig
=
Since
1.
/Xj
is
a decreasing
also decreasing over time with:^^
—^ (A^ + M{A" - A^))
= Y^ =
(26)
time goes by, the comparative advantage of the members
for this is that as
of the eUte in entrepreneiirship gradually disappears because of the imperfect correlation
between parents' and children's
talents.
Another important feature of
ings) inequahty.
Wages
this
are equal to
each entrepreneur earns
and
XYf.^,
equiUbrium
0,
is
that there
is
a high degree of (earn-
while entrepreneiKS earn positive profits
—
in fact,
their total earnings equal aggregate output.
This
contrasts with relative equahty in democracy.
when
Alternately,
preferences from high-productivity ehtes.
Therefore, the equilibrium depends on the
ratio of high-productivity vs. low-productivity ehtes,
i.e.,
on
When
/ij.
—
productivity ehtes are pivotal and the above characterization applies
=
ft
0.
poUcy
(24) does not hold, low-productivity elites have different
when
In contrast,
equihbriimi pohcies are
<
Jl^
—
kt
p.^.
i.e.,
>
1/2, high-
kt
=
k^ and
and
1/2, low-productivity elites are in the majority
and
=
fj
Therefore, at date
5.
the equilibrium will
t,
be identical to the democratic equihbrium. However, entry of high-productivity agents
when
into entrepreneurship
will
/ij_,_i
time
+
t
and the eqmlibrium
1,
alH <
and
t
satisfying
t
=
will revert
when
taxes. Therefore,
periodicity
gh <
implies that
/jj
be greater than 1/2 and high-productivity
k^ and
for
=
kt
1/2, then even at
will prefer
A;^
=
t-|- 1
and
Then provided
1.
elites will
:
<
^^
= mint
f
be
that
an >
1/2,
in the majority again at
back to the sclerotic one with entry barriers
(24) does not hold, the
mint E N
can be defined as
f, t
=
equihbrium wiU be cyclic with
1/2. Alternatively, using the fact that
N
e
:
u,
i
<
i/-=^.28
if
Jl^
=
/i^
on the other hand,
low-productivity agents will be the majority within the ehte,
r^
=
5,
so the ohgarchic equilibrium will be identical to the
democratic one.
Therefore,
we have the foUowing proposition (proof
Proposition 3
as given
by
E
(24) holds, then the oligarchic equilibrium has rj
and the equilibrium
(23),
^^For the case where e
-
(1
mJt^A^
and
be
less
than 1/2
/U£
=
1
>
r^ =
^*In other words, this
we have
is
0,
Jlf
<
we have
^
^^
is
=e+
=
and
always sclerotic and features wl
=
+ '^lO- ~
=
[\
—
e) [aiilJ-t-i
Mt-i)) ^"^
"^t^
0.
=
kt
k^
Aggre-
l^tT^-^^
"'"
(a^ + ,_,\%:l^^^J A" - A^)).
the level of
for the first
while
in the text):
time at
t
fJ-t-i
=
i.
such that were the equilibrium to remain
But because the equilibrium switches
1/2.
23
sclerotic,
/ij
would
to the entry equilibrium,
gate output
If (24)
economy
and
an >
does not hold and
starts with
=
/Xq
and
1,
satisfies
the law of motion
= i where i is defined as t = min i G N
kt = k^ as given by (23) lit ^ ni for any
:
=
/if
and jumps up
ni,
t 7^
/.ij
1/2, then the ohgarchic equilibrium
t
any n G N, and
If (24)
1 ii t
to
is
=
an <
t
The
=
ni
~J'^
n G N, and
nt for some n G N, so
iZ^A^ when
does not hold and
< ^
|l^_l
=
given by (25) with ^j
for
it
.
Tt
The
= anfJ-t-i + cl(1 — A^t-i)
The equilibrium has r^ =
= 5 and kt = if t = ni for
anlJ^t-i
+ "^/-(l ~ A^t-i)
declines during
all
if ^ 7^
ni
periods where
some n G N.
is
identical to the
2.
Comparison Between Democracy and Oligarchy
last
two subsections highlighted a number of
oligarchic equihbria. This subsection
differences
between democratic and
compares aggregate output and
democratic and ohgarchic equihbria.^^
To
simplify the discussion,
where (24) holds, so that the oligarchic equihbrium does not have
The first important
equihbritmi,
i.e.,
Y(f,
result
is
y^ =
>
Therefore, for aU 5
because
it is
is
its
I
dynamics in the
focus on the case
cycles.
that aggregate output in the initial period of the oligarchic
greater than the constant level of output in the democratic equi-
hbrium, Y^. In other words,
0,
5
>
—
if
0,
then
—
- sV-^A"" < Y.^ = -^A"".
-^(1
(i-*)-A"<n'
a
oligarchy initially generates greater output than democracy,
protecting the property rights of entrepreneurs.^*^ However, the analysis also
shows that Y^^ dechnes over time, while
economy may subsequently
depends on whether
(1
is cyclic.
jj.^.
1/2, then the ohgarchic equilibrixmi
democratic equihbrium in Proposition
3.3
with
given by (26).
some n G N. Aggregate output
for
= j^A^
given by (25) and decreases over time starting at Yff
Yf = Y^as
limt^oo
until
is
- 5)^ A"/
(1
-
Y^
q)
is
fall
Y^
is
behind the democratic
greater than
> {A^ + M[A" -
Y^
as given
A^)) /
Consequently, the ohgarchic
constant.
(1
-
society.
by
(26).
q), or
Whether
it
does so or not
This wiU be the case
if
if
l-c
(1-5)^>^ + m(i-^).
(27)
can be verified that all the results here also hold for the comparison of net output levels.
^°The result that the oligarchic equilibrium always generates greater output than the democratic equilibrium at time i =
is a consequence of the assumption that the only source of distortion in oligarchy
is the entry barriers. In practice, an oligarchic society could pursue other distortionary policies to reduce
wages and increase profits, in which case it might generate lower output than a democratic society even
at time f = 0.
^^It
24
If
condition (27) holds, then at some point the democratic society will overtake ("leapfrog")
the oligarchic society. (27)
words,
if
democracy
will
is
more
hold
likely to
when
The
economy
is
if
low and high-productivity entrepreneurs
average of high-productivity agents
of taxation in democracy
democratic
is
M are low.
In other
the cost of misaUocation of talent
low, then the oUgarchic equilibrium always generates greater output.
cost of misaUocation of talent will be low, in turn,
trepreneurship
A^/A^ and
pursue highly "populist" poUcies imposing high taxes on busi-
nesses in order to redistribute income to the poor, and
in the
5,
is
is
limited
is
limited
high
(M
and the
when
{A^/A^
high).
either the skiU
high) or
On
when
gap between
the population
the other hand,
if
failiue to allocate the right agents to en-
very costly, then societies stuck in oligarchy will ultimately
societies.
the extent
fall
behind
^^
Output
in
democracy
Output in oligarchy
Figure
4:
Comparison of aggregate output
curve depicts output in oligarchy
^'Notice that
if
(24) does not hold
income than the case discussed
when
and the
in the text.
in
democracy and
(27) holds,
and the
oligarchic equilibrium
More
is
oligarchy.
solid
The dashed
hne when
cyclic,
then
it
it
does not.
generates greater
formally; let Y^^ be the aggregate equilibrium output
time t, and Y^^ be the aggregate equilibrium output in the
Suppose that condition (24) holds as an equality, so that both the noncyclic and the cyclic equilibria exist. Then, we have that Y^^ = Yf.^ for all i < i and Y^^ > Y^^ for all
t > t. Nevertheless, democracy may still generate greater aggregate output than the cyclic oligarchic
equilibrium. In other words, Y^^ < Y^ is still possible, though more difficult (and naturally, this will
only be the case if Y^ < Y'-', where, by definition, Y-^ is the minimum aggregate output level reached
in the non-cyclic oligarchic equilibrium at
cyclic oligarchic equilibrium.
by the
cyclic oligarchic equilibrium).
25
Figure 4
shows the
both of these possibihties diagrammatically. The thick
illiistrates
for
the case where
or
Y^, which may
it
and
does not. Both of these curves asymptote to some hmit, either
Y^
below or above Y^. The dashed curve shows the case where
(27)
lie
l^-^,
holds, so after a while (in the figure after date
democracy.
When
(27) does not hold, the
oligarchy asymptotes to a level higher than
It is also useful
to point out that
both democracy and ohgarchy
a society
may
taxation,
and
may
restrict the
let
t'),
oligarchy generates less output than
sohd curve apphes, and aggregate output in
Y^.
some
alternative arrangements
would dominate
terms of aggregate output performance. For example,
in
amount
to redistribution by placing a constitutional Hmit on
the decisions on entry barriers be
made
democratically. Alternately,
it
prevent entry barriers constitutionally, and place the taxation decisions in the hands
of the ohgarchy.
The
perspective here
practice because of the inherent
power in
their
it is
is
that these arrangements are not possible in
commitment problem
hands make the poUcy
credible. Consequently,
decisions,
and previous promises are not necessarily
their political
power to erect entry
them not
poUtical power with the poorer agents and expect
What about
income
democracy than
in oligarchy.
To
barriers, or vest
to favor redistribution.
the preferences of different groups over regimes?
are always better off in
It is clear
that non-elites
see this, note that non-elites
born with bequest
bl is
comparison, Assimaption (15) guarantees that the wage rate in democracy,
W^,
receive
By
in pohtics: those with the poUtical
not possible to give political power to incumbent producers,
and then expect them not to use
fej.
other two curves depict the
.
as a function of time for the case where (27) holds
output in oligarchy,
level of
Y^ The
aggregate output in democracy,
level of
hne
flat
given by (21),
in ohgarchy, so the utihty of a non-elite agent
is positive,
so the
same agent
will
have utihty
bj.
+ W^ >
bj..
Therefore,
non-ehtes are always better off in democracy. In contrast, as long as condition (24) holds,
aU
elites prefer
kt
=
k^
(if
the ohgarchic solution, since, as shown above, they
vote for Tt
—
and
this condition does not hold, high-productivity ehtes prefer ohgarchy, while
low-productivity ehtes prefer democracy). There
and
all
is
therefore a confhct between the ehtes
non-elites over the type of pohtical regime.
Oligarchy also typicaUy generates more inequality relative to democracy. RecaU that in
democracy, workers' and entrepreneurs' incomes are given by (21) and
(22). In contrast, in
the non-cychc oligarchic equihbrirmi, entrepreneurs (ehtes) erect entry barriers to depress
labor
demand and wages, and consequently, workers earn wl =
26
0,
while entrepreneurs earn
Wf = XY/'.^'^
than
The
analysis also reveals that there
equihbrium
in oligarchy: in oUgarchy, the
firms,
whereas in democracy there
is
is
is
greater social mobility in democracy
sclerotic
and the same dynasties run the
continuous churning in the ranks of entrepreneurship
and production work.
New
3.4
Technologies
The Introduction discussed the possibihty of a more democratic society, such as the United
States at the end of the eighteenth century, adapting better to the arrival of
ment or
here also provides a potential explanation for this pattern.
Suppose that at some date
new
technology as a
i'
>
a new technology arrives exogenously.'^'^ Let us think
new production method,
1
where
ip
invest-
technological opportxmities than an oligarchy, such as those in the Caribbean.
The model
of this
new
>
1
and
enabling entrepreneur j to produce:
—a
al is the talent of this
entrepreneur with the
new
technology. Therefore,
entrepreneur j's output can be written as
—a
[l
The
I
cost of operating this technology
is
—a
J
assumed to be the same as the old technology,
kX. Also to simplify the discussion, assiune that the law of motion of al
is
similar to that
of al given by
,
^^The ratio of
elite to non-elite
income
is
always higher in oligarchy.
typically higher in oligarchy. This (absolute) income gap
—
is
The
equal to XY^^
difference in incomes
is
also
= n^j^A^ X + [l— fif)Y^A^X
A^ X + kX in democracy. The income gap in democracy, as we saw above,
compensates entrepreneurs for the costs of effort. It can be verified that as long as Y^^ > Y^, the
income gap is greater in oligarchy than in democracy. However, if Yf.^ is much smaller than Y^, the
converse may be the case. This happens only for extreme parameter values: when A^ is very low, so that
aggregate income and thus entrepreneurial profits are low in oligarchy, while 5 is low and k, is high so
that the compensating income differential that entrepreneurs receive in democracy is large. For example,
in oligarchy,
and
to (1
'"
5)
the condition
(1
is
-
a) ((1
- 5)i + kA) < A^/A" +
sufficient (but not necessary) to ensure that the
M
{l
- A^/A")
income gap between entrepreneurs and workers
always greater in oligarchy than in democracy (also note that this condition
"^^An interesting question
sities to
invent
new
is
,
is
compatible with (27)).
whether democratic and oligarchic societies would have different propen-
technologies, which
is
is
sidestepped here by assuming exogenous arrival of the
technology.
27
new
,j
''*+i
for all
>
t
and Pr
t'
in particular
is
a^,,
_
~
I
(a^
with probability
=
^-^
|
with probability
1
=
a|)
Af
for
It is
-
any
= A^
cjl
and create
is
if
a{
if
a^
'
This implies that
a^'s.
and
t',
reasonable since
new
= A^
a^,
In contrast, in oligarchy, the ehtes are in power at time
they would
do not have comparative advantage
condition
Y^
as given
not
is
new technology
by
(20) to
—a
1
is satisfied,
and
technologies exploit
agents with comparative advantage for the
become the entrepreneurs, so aggregate output jumps from
of condition (24)
'
comparative advantages than the old ones.
different
at the time
.
Sj,
straightforward to see that the structure of the democratic equiHbrium
affected,
,
^
M irrespective of the talent of
—
1
= A^
= A^
= ^^
= yl-^
and a^ In other words,
t,i
with probabihty
a-j.
if a{
l-an
independent of past and future
a^,
if
with probabiUty
the individual with the old technology. This
different skills
an
with probability gl
A^
A^
^
M and
with probability
A^
A^
t',
and as long as a modified form
remain the entrepreneurs even
like to
if
they
working with the new technology. This modified
for
is:
-1- [^(1
_
sy/-
+ 5{1 -
(5)(^-)/"]
i^A"
-
K
'
j^ma^{^PAL,Ai^}-K
It states that
^
'
remaining a low-productivity entrepreneur with the new teclmology, with
productivity ipA'^, or a high-productivity entrepreneur with the old technology, with productivity
A^
,
in
at the competitive
wage and receiving
(which gives an income of
is satisfied,
new
maximum entry barriers,
both cases protected by
j^
[a{l
-
preferable to working
redistribution at the rate S in the entry equihbrium
+ 5{1 -
Sy/"'
(5)(i-")/°]
i/jA"
-
k).
As long
as (29)
the oligarchic equilibrium will remain sclerotic even after the arrival of the
technology.
How
aggregate output in the ohgarchic equihbriim:! changes after date
whether ipA^
> A^
or not. If
it is,
Y^ =
and remains
^
{A^
at this level thereafter. This
weak law of
t'
depends on
then aU incumbents switch to the new technology and
aggregate output in the ohgarchic equilibrium at date
the
is
is
if
+ M{A^ -
jumps up
A^))
to
,
because al and al are independent, so applying
large numbers, exactly a fraction
M of the ehte have high productivity
with the new technology, and the remainder have low productivity.
28
If,
on the other hand, ipA^ <
A^
,
then those ehtes
who have
high productivity with
new technology
the old technology but turn out to have low productivity with the
to use the old technology, and aggregate output after date
^
Yf =
with
/i(
[MiPA" + /ijl - M)
+ il-
A^'
1.1,)
given by the same process as before, (16). Intuitively,
who have high
productivity with the
new technology and
motion
follows the law of
t'
(1
- M) M"-]
prefer
,
now the members of the
ehte
who have low productivity
those
with the old technology switch to the new technology, while those
Avith
high productivity
with the old and low productivity with the new remain with the old technology (they
switch to
new technology only when they
technology).
As a
result,
=
with limt^oo Y,^
jz^ [M^pA^
More important
Y^ — Y^
gap
or
Y^ — Y^
new technology
the arrival of the
M
{1
- M) A^ +
{1
-
is
decreasing over time,
Mf ipA^]
easy to verify that, as long as
it is
(or whichever is relevant) is always greater
new technology, Y^ —Y^
(for t
>
i').
Y^ < Y^,
was
Y^ — Y^ <
richer
In other words, the arrival of
makes
before the arrival of the
than the democratic
new technology
society immediately
0, i.e.,
full
at date
use of the
t'.
society,
the
than the output gap
creates a further advantage for the democratic society. In fact,
have been the case that
oligarchic society
+
that Y,^, just like Y,^ before,
for the focus here,
before the arrival of the
the
we have
with the old
lose their high-productivity status
new
but the ranking
Intuitively, tliis is
new technology by
it
may
technology, the
is
reversed after
because the democratic
allowing those
who have
a
comparative advantage to enter entrepreneur ship, while the oligarchic society typically
fails
to do so,
and therefore has greater
difficulty
adapting to technological
change.'^'*
Regime Changes
4
The
previous section characterized the political equihbrium under two different scenarios;
democracy and ohgarchy. Which pohtical system
as exogenous.
Why
prevails in a given society
are certain societies democratic, while others are
with the ehte in control of pohtical power? One possibility at
historical accident, while another
is
was treated
more ohgarchic,
this point is to
appeal to
to construct a "behind- the- veil" argument,
whichever pohtical system leads to greater efficiency or ex ante
utility
would
whereby
prevail. Nei-
ther of these two approaches are entirely satisfactory, however. First, since the prevailing
^''in practice, it
than
of
may
also
be the case that entrepreneurial talent matters more for new technologies
another reason for democratic societies to take better advantage
for old technologies, creating yet
new
technologies.
29
political
regime influences econoniic outcomes, rational agents should have preferences
over these regimes as well, thus boding against a view which treats differences in regimes
as exogenous. Second, pohtical regimes matter precisely because they regulate the conflict
of interest between different groups (in this context, between workers
The
behind-the-veil argument
is
unsatisfactory, since
it
and entrepreneurs).
recognizes and models this conflict
to determine the equihbrium within a particular regime, but then ignores
is
it
when
there
a choice of regime. Finally, neither of these two approaches provide a framework for
analyzing changes in regime, which are ubiquitous.
be to
let
consider an
racy, while ehtes
interests
satisfactory approach
make a prehminary attempt
economy where non-ehtes would Uke
would
be mediated?
whichever group
tive
more
would
the same trade-offs emphasized above also affect which regimes wUl emerge and
persist in equilibrium. In this section, I
I
A
adopted in
is
like to
A
preserve the ohgarchic system.
plai:isible
answer
politically or mihtarily
this section,
and the
fornas itself into a
that there
more powerful
conflict
is
from oligarchy to democ-
How wiU
no easy
these conflicting
compromise,'^'^
and
This
is
the perspec-
power of a group
is
hnked to
will prevail.
its
between the ehtes and the non-ehtes, the
increasing in their relative economic strength or in
elite will prevail is
their relative wealth. This
is
political or military
economic power. In other words, in the
Ukehhood that the
to switch
in this direction.^^
assumption
is
more democratic one
plausible: a non-democratic regime often trans-
in the face of threats or imrest,
and the degree
to which the regime wiU be able to protect itself depends on the resoiuces available to
(e.g.,
4.1
see the discussion in
Acemoglu and Robinson,
it
2003).
Basic Model
Suppose that the society starts as an
mains democratic
thereafter.
in a reduced-form way,
democracy
I
oligarchy,
model the
and
effect of
if it
switches to democracy,
economic power on
political
it re-
power
and assume that the probabihty that an ohgarchy switches to
is
Pt=p{ABt),
*^See Acemoglu and Robinson (2000, 2003) for a class of models of equilibrium political institutions,
with an emphasis on shifts in political power between poorer and richer segments of the society. These
models do not consider the economic trade-offs between distortionary taxation and entry barriers.
^^It may be argued that there should be room for compromise, since one of the regimes generates
greater aggregate income (efficiency), and this income can be redistricted in a way to make all parties
better off. This type of argument ignores the constraints that commitment problems place on feasible
redistributions (e.g., Acemoglu, 2003).
30
where
is
the per capita wealth difference between the ehtes and the non-ehtes (workers) at
the beginning of period
tP
I
the beginning of the period.
assume that regime change takes place immediately
Using Df
=
to denote oligarchy
and
£>t
=
1
at
to denote
democracy, the points emphasized above can be captured by the following law of motion
for
A:
with probabihty
{01
\-p {ABt)
with probabihty p {ABt)
1
The assumption
that economic power buys poUtical power
decreasing. In the analysis below,
Definition (Equilibrium
a policy sequence
is
II
[^1J l*_n
J f_U,l,...
is
L
-^
equivalent to
p
(•)
being
With Regime Changes) An equilibrium with regime changes
and economic decisions
A;t,ft >
{
[x{]
j^^^
^
such that
and
an economic equilibrium given \kt,Tt>
J j^o,l,...
• if
Dt
=
0,
then (kt^Ttj
is
the oligarchic equihbrium policy sequence, and
• if
A=
1;
then [kt^ftj
is
the democratic equilibrium pohcy sequence,
where Dt
is
given by (31) with
Dq =
and
ABt = P (ASi_i +
and
Y^^-j^ is
XYf_,)
if
A-i =
given by (25).
This definition makes
oligarchic equilibrium,
and the
is
(31)
.
1
allow p () to be non-increasing.
I
(^
an
A-i =
if A-i =
if A-i =
if
vise
of the fact that since Dj
B^ =
fact that in oligarchy
=
0, 6q
=
for all j
and
lyf
=
ABt = Bf. It then uses the savings rule in
each member of the the ehte earns an income of XY^^.
0,
thus
in
(2)
^^Note that an alternative would have been to make political power a function of the relative wealth
and workers. In the current model, this is not possible, since the long-run wealth level of
workers is even if they start with positive wealth. To accommodate this possibility, we can assume that
the minimum wage is positive, say w>0, for example because of an outside option. In this case, it can
be shown that if all agents also start with positive wealth, the ratio of elite wealth to worker wealth will
first increase and then decline. The result that there can be multiple steady-state equilibria derived in
Proposition 5 below generalizes irrespective of whether or not the relevant measure of inequality increases
monotonically in oligarchy it only relies on the feature that there is greater inequality in oligarchy than
in democracy.
levels of elites
—
31
Now
imagine the eqmlibrium path of this economy starting at
disciossion,
suppose that condition (24)
not
Since each agent
cyclic.
is
is
satisfied, so that
i
=
To
0.
simplify the
the oHgarchic equilibrium
is
imperfectly altnoistic, the possibility of regime change in
the future does not affect behavior, so the equiUbria characterized above as a function of
the political regime continue to apply. Therefore, at
equilibrium, with no redistribution and
=
t
we
0,
wages, and so Wq'
=
will
XY(f and
Wq' and Wq^ denote the per capita incomes of ehtes and non-ehtes
given by (25). Given the savings rule impUed by
is
Sf = ABi =
With the same argument,
if
more
we
Wq^ =
respectively,
0,
where
and Fq^
therefore have
pXYo^.
the society remains oHgarchic,
5f = AB2 =
or
(2),
have the oligarchic
I3XY^
we have
+ ^'AVq^,
generally,
t
Bf =
It is clear
that
ASj
is
and
Bf = AB, =
A
(32)
J] ^"^^-n-
an increasing sequence, and so pt
will
be a non-increasing sequence.
Therefore, the longer the society remains as an ohgarchy, the bigger the wealth gap
between the
elites
and the
non-elites,
and the more
difficult for
the society to transition
to democracy.
Moreover, note that
vyE
lunABt =
where
Y^
exists
AB
also exists
is
given by (26).
< ABoo such
t
Now two
that
such that for allt
to democracy before
t, it
will
AB^ =
-^,
can be
interesting cases
(33)
distinguished:'^^
(1)
There
p (AB) = 0. (2) p {AB^o) > 0. In the former case, there
> f, we have ABt > AB so ii the economy does not switch
,
be permanently stuck in oligarchy. In the second
case, as
time passes, the economy wiU switch out of oligarchy into democracy with probabiUty
The next
1.
proposition summarizes the equilibrium path with potential regime changes
(proof in the text):
Proposition 4 In the economy described above, the equilibrium with regime change
as foUows: the
economy
starts with
Dq =
and the
oligarchic equilibrium,
and
is
transitions
A third possibility is lim(_ooP (ASj) = 0, in which case the nature of the limiting equilibrium
depends on the rate at which p (ASj) converges to 0.
^'^
32
motion as given by
to the democratic eqioilibrium according to the law
ASj =
with
(31)
t
A V2/3"l^-?„, and remains democratic
thereafter. In addition:
n=l
AB
• suppose that there exists
by
then
i,
•
(33),
it
let i
will
= min t
G
>
Pr (limi_oo
A=
1)
0,
=
:
If
the
—
Dj
i.e., if
{AB) =
where ABco
is
given
economy remains
oligarchic until
=
for all
0,
=
then Dt
t
>
t;
then the society will become democratic at some point,
1-
Path Dependence and
Finally, consider
such that p
N ABt > AB.
always remain oligarchic
suppose that p (ABoo)
i.e.,
4.2
and
< AB^o
Instability
a generalization of the above framework where democratic societies can
switch back to oUgarchy, and to simphfy the discussion, assume that
oligarchy, the agents with s|
=
1 (i.e.,
the
initial eUte)
become the
if
there
is
a switch to
ehte.^^ In particular,
assume that when democratic, a society becomes oligarchic with probability
qt
where now q
(•) is
gap between the
si
=
0),
thus
=
q{ABt)
a non-decreasing function, q
initial elite (those
ABt =
X,,.=i
Kdj/X -
with
s\
/^,^.^o
(0)
=
=
1)
6^dj/ (1
0,
and ABt now
and the
-
initial
refers to the
wealth
non-ehte (those with
A).
Similar arguments to before establish that
1 — p (ABt)
with probabiUty p {ABt)
with probability q [ABt)
with probability 1 — q {ABt)
with probability
In addition, the law of motion of
which exploits the
numbers, a fraction
ABt
is
=
Dt-i =
if A-i =
if A-i =
if -Dt-i
if
(34)
1
1
given by:
fact that after the switch to
democracy, by the weak law of large
M of the previous eUtes and a fraction M of the previous non-eUtes
wiU become entrepreneurs and earn the higher income Wt given by
'^The alternative would be
for the agents
who
33
the average
= 1 to become the elite. This would
becomes quite involved.
currently have Sf
require us to keep track of the entire wealth distribution, which
(22), so
incomes of previous
differences
The
way by
among
and
elites
individuals
non-elites will
be equal, and the only source of wealth
differences in their bequests,
is
an equilibrium with regime change
definition of
i.e.,
"initial" conditions.
modified in a straightforward
is
replacing (31) with (34). In addition, in order to provide a simple example of path
dependence,
I
now aUow
the society to start as democratic,
Rather than providing a
on certain cases of
=
with Dq
1.
description of all potential types of equilibria, here
full
which are summarized
interest,
i.e.,
I
focus
in the following proposition:
AB
< ABoo such that p (Afi) = where AB^ is
given by (33) and let t = mini G N ABt > AB with ABt given by (32), and that there
such that q (aS^ = 0, and let i{t') = mini e N ABt < A5 where ABt
exists AB >
Proposition 5 Suppose there
exists
;
:
is
given by (35) starting at
• If
Do
=
=
then Df
1,
=
i
i'
ABf
with
1 for all i; i.e., if
given by (32). Then:
a society starts as democratic,
it
wiU remain
democratic thereafter.
• If
Do
=
A
then
and A'
=
1 for
democratic for
• If
Do
=
oligarchic
• If
Do
first
in
i
=
=
aU
the
1 for
i
>
i';
time in
first
i.e.,
=
for all t
and remains
=
and D^
time at time
t
>
t'
and non-decreasing
G
<
[f,
i'
t'
+ i{t')]
,
and remains
remain democratic thereafter.
i,
=
then Dj
oligarchic until
1,
1 for all i
a society becomes democratic at
if
i{1f) periods, it will
and Dt
A=
and
t',
i,
then
it
for
aU
i;
i.e.,
a society starts
if
always remain oligarchic.
will
then the probability of switching back to oHgarchy for the
after the switch to
in
i',
with
democracy
limt_+oo Qt\t'
=
—
at
i.e.,
i',
Qt\t' is
non-increasing
a society faces the highest
probability of switching back to oligarchy immediately after the switch from oh-
garchy to democracy, and this probability
is
higher
if it
has spent a longer time in
oligarchy.
The
why
first
three parts of the proposition foUow from the preceding discussion.
the last part
in oligarchy, so
A
greater
i
is
correct, note that
a greater
t'
i',
see
implies that the society spent longer
ABt, and hence the probability of switching back to ohgarchy,
given
To
on the other hand, corresponds
is liigher.
to the society having spent a longer
time in democracy, reducing the wealth gap between the
initial elites
and non-ehtes, and
consequently, the probability of switchback to oligarchy. Moreover, as t—t' -^ oo, equation
(35) implies that
AA ^
0,
so g
(AA)
^
0.
34
There are two interesting
sibility of
results contained in this proposition.
Of two
path dependence.
identical societies,
if
The
the pos-
first is
one starts oligarchic and the
other as democratic, they can foUow very different pohtical and economic trajectories.
With the assumption that
generate an income level
and therefore
q
=
0.
q (0)
Y^
On the
=
0,
the initial democracy will always remain democratic,
and an equal distribution
other hand,
if it
starts ohgarchic,
equilibrium, with an unequal distribution of income.
will enable
them
to have the
no transition to democracy
power to sustain the
tmtil
some
of income, ensuring that
The
it
wiU foUow the oligarchic
greater income of the elites
and
oligarchic equihbriimi,
point, date i (which
may be
t
=
0),
than workers to be able to sustain the ohgarchic regime
sufficiently richer
ABt =
if
there
is
they will be
forever.
This
type of path dependence provides a potential explanation for the different development
experiences in the Americas suggested by
Johnson and Robinson (2002).
originally
an
Engerman and
Sokoloff (1997)
Similar path dependence will also result
and Acemoglu,
if
a society
but then switches to democracy and remains democratic
oligarchy,
sufficiently long period of time, so that inequality created during the ohgarchic
is
for a
phase
diminishes significantly and democracy becomes fully consohdated.^°
Another interesting
result
collapse right after transition
previous ehtes are
gap wiU
decline,
still
is
that a democracy
is
predicted to be most susceptible to
from oligarchy to democracy, because,
substantially richer than the workers.
and democracy wiU become more
stable.
oHgarchy before the switch to democracy, the larger
and the workers, and the
less stable is
is
at this point, the
As time goes by the wealth
Moreover, the longer Uved
is
the wealth gap between the ehtes
democracy.
Conclusion
5
There
is
now
development.
a general consensus that "institutions" have a first-order effect on economic
But we
what these
are far from understanding
institutions are.
Many
economists and political scientists beheve that the extent of property rights enforcement
is
an important element of
this set of institutions,
but even here there are fundamental
unanswered questions. Most notably, whose property
question becomes particularly pertinent
when
there
is
rights should
be protected? This
a conflict between protecting the
property rights of various different groups.
""^See also
Benabou (2000)
and
policies that are
equality
for a model featuring multiple steady-state equilibria, one with high inmore favorable to the rich, and another with lower inequality and greater
redistribution towards the poor.
35
This paper develops a model where protectuig the property rights of current producers
comes
at the cost of
weakening the property rights of future producers. This
effective protection of the
is
because
property rights of current producers requires them to have
pohtical power, which they can use to erect entry barriers, violating the property rights
of future producers. This pattern of well-enforced property rights for current producers
and monopoly-creating entry
an oligarchic society contrasts with
barriers in
relatively
high taxes on current producers but low entry barriers in a democratic society.
I
develop a simple framework to analyze the trade-off between these two different forms
of property rights enforcement. I
efficiency,
who
because agents
show that an
oligarchic society first generates greater
are selected into entrepreneurship are often those with a
comparative advantage in that sector and oUgarchy avoids the distortion
tributive taxation. But, as time goes
shifts
by and comparative advantage
away from the inciunbents to new
effects of redis-
in entrepreneurship
agents, the allocation of resources in ohgarchy
worsens. Contrasting with this, democracy creates distortions because of the disincentive
effects of taxation,
but these distortions do not worsen over time. Therefore, a possible
path of development
for
more democratic/open
The model
of
many
an ohgarchic society
first rise
with ohgarchic
for
featiu'es,
why they
both
fall
relative to
a
historically
and
dxu-ing the
postwar
era,
often run into significant growth slowdowns. In
predicts that oligarchic societies
may fail to take advantage
of
new growth
op-
was the case with the highly ohgarchic and relatively prosperous Caribbean
portunities, as
plantation economies, which failed to invest in indvistry and
initially-less-prosperous
I also
and then
society.
but also suggests a reason
it
to
therefore provides a potential explanation for relatively high growth rates
societies
addition,
is
new
technology, while the
North American colonies industriahzed.
use this framework to discuss endogenous regime transitions, in particular,
to highlight the possibihty of path dependence.
Path dependence
arises
because those
enriched by the ohgarchic regime can use their resources to sustain the system that serves
their interests.
As a
pohtical regimes
may
two otherwise
result,
identical societies that start with different
generate significantly different income distributions, which in turn
sustain different political regimes and hence economic outcomes.
The paper
also suggests a
a number of questions are
number
left
of areas for future research.
On
open. First, the model assimies that
can only keep their status by managing their own firms, even
if
the theoretical side,
members
they have low-productivity.
In practice, delegating managerial positions to more productive agents
36
of the elite
is
an option.
In-
corporating this possibility into the current framework
there might also be
more
interesting angles to study.
ers are sufficiently liigh, high-skill individuals
may
is
relatively straightforward,
For example,
not start their
when
own
but
entry barri-
businesses, thus
creating a sufficient pool of managerial talent, and indirectly increasing the profitability
and durability
of
an oligarchic regime. Second,
in a world with innovations
destruction, sufficiently successful (creative) entrepreneurs
buy protection and entry
poUtical resources to
tween
initial
model of
success
and
politics in this
later stagnation.
paper
is
the economic and
barriers, thus creating another link be-
Finally,
and perhaps most importantly, the
rudimentary. More micro-founded models of
nomic power buys pohtical power need to be developed
side, it is
may possess
and creative
in future work.
On
how
eco-
the empirical
important to further investigate whether distortions in oligarchic societies are
introduced by entry barriers, while those in democracies are caused by anti-business and
redistributive pohcies,
and decUne of
and whether there are any systematic patterns related
oligarchies different
from the dynamics of democratic
37
societies.
to the rise
Appendix:
6
Here
I
briefly outline
A
More General Model
a simple generalization which ensures that even
at the beginning of the period,
tax rate, and
all
i.e.,
the results of the
we can dispense with the hiding
which trades
voter,
if
voters choose taxes
before investment decisions, they would set a positive
main
analysis generalize. In addition, in this model,
decisions, hi
,
by the median
since the tax rate preferred
off redistribution versus disincentive effects, is
always
less
than
1.
Consider an economy similar to the one analyzed above, with the same technology and
preferences, but with three levels of productivity,
productivity
is
a generaUzation of
agents in the society and
M^
(8)
.
Define
M^ as the fraction of very high-productivity
A
(M^ + M")
which imphes that the "marginal" entrepreneur
if
A^. The law of motion of
as the fraction of high-productivity agents.
XM^ < 1<
even
A^ > A^ >
is
(Al)
,
the high-productivity type, because,
there axe no entry barriers, the very high-productivity entrepreneurs
cannot hire the entire labor
Let us
now assume
1.
Entrepreneurial talents,
2.
The entry
3.
Agents make occupational choices,
4.
Entrepreneurs
5.
The labor market
6.
Consumption and bequest
[a^]
new
,
is
as follows:
are realized.
entrepreneurs
kt
and the tax
clearing
wage
rate, Wt, is
decisions,
taxes, Tj, are
the same time as the entry barriers,
now
kt.
rate, r^, are set.
[z^]
make investment and employment
Most importantly,
by themselves
force.
that the timing of events
barrier for
Assume that
decisions, [ej,/j].
determined.
[cf,6^_^]^]
are made.
set before the
Moreover, there
investment decisions, exactly at
is
no hiding decision
commitment problem).
Assumption (Al) implies
that, in democracy, the equilibrium
--^(l-r,)^/"/l^-«;Oy
1
—Q
i
~a
/
while tax revenues are:
38
wage
will
be
(in fact,
no
A
where
is
a weighted average of
J^ and A^
reflecting the ratio of very high to high
^
productivity entrepreneurs. In particular,
A = XM^A^ +
Next note that
in democracy,
A^
productivity equal to either
"
1
—a
i.e.,
(1
- XM^) A" > A^.
once entry barriers are
or
A^
+ -^r(l-r)'^A
—
given by the wage rate plus redistribution (plus
is
—agents with
al
they receive the same utility in this case. Since
maximize (A2). The
^(1 - tV-^A" -
1-a^
^
^
with complementary slackness. Inspection of
r
=
0,
which
justifies
made
the claim
solution to this problem
= A^ may
M^
first-order condition for this
- W-^A
—^(1
1-Q^
(A2)
a
1
the bequest they have inherited)
the preferences of agents with
by
are given
:i-r)i/"y4^-/c
because, in equiUbrium, their utility
0,
<
1/2, the democratic tax rate will
maximization problem
- tV-^-^A <
-t(1
a
this condition
set
>
A = A-^ then
as ^ > A^ the
shows that
if
However, as long
and voters
is
and r
^
^
in footnote 17.
is strictly positive,
become entrepreneurs, but
,
,
a positive tax
rate,
- A^
,^ <1,
,, — A"
A/a
A
r'=
to redistribute
The
income from the entrepreneurs to themselves.
rest of the analysis in the text applies,
with the democratic equihbrium tax rate
given by (A3), and the ohgarchic equilibrium unchanged.
is
(A3)
As a result, output
in
democracy
now:
Yf = Y^^-^{l-r,)'^A,
—
1
whereas output in oligarchy in the
initial
Y<f
=
a
period
is:
-^A
> Y^,
—a
1
but then limits to
lim
t->oo
Whether Y^
Yf = yf =
{A^ + M^iA"" T^
—a
A"^)
+ M^(A^ -
A^))
<
Yq^.
1
is
lower than
Y^
or not
is
determined by a similar analysis to that in
the text, with the only interesting twist being that
higher precisely
when
there
is
productivity. This impUes that,
greater inequality
somewhat
now
among
the equilibrium tax rate,
the entrepreneurs in terms of
paradoxically, ohgarchy
in societies with greater inequality in terms of productivity.
39
r'^, is
may
be more
efficient
7
Appendix B:
Here
I
shown
of
Revenues and Democracy
Tcix
briefly discuss the empirical relationship
in Figure
GDP
1.
in 1998
Appendix Table Bl includes regressions of tax revenues
on the democracy index and various
unless otherwise indicated, are from the
the democracy index
for 1998.
is
The Freedom House measure
1
is
shows a strong raw
indicates that a change in
is
is
variables,
transformed so that both indices assign higher
important to note that tax revenue as a percentage of
correlation.
government.
The magnitude,
democracy from the
score (1) would increase tax revenues over
that this relationship
AU economic
World Development Indicators 2002 dataset, and
refers only to the revenues of the central
Column
controls.
as a percentage
from the Freedom House for 1997-98 or from the PoUty IV dataset
scores to greater democracy. It
GDP
between tax revenues and democracy,
level of that in
GDP by
2.5 (standard error
Myanmar
15 percentage points.
=
0.3)
(7) to
the best
Column
2 shows
robust to using the Pohty index.
Since democracies are typically richer than nondemocracies the relationship in columns
GDP increase with economic
development. To control for this, colunms 3 and 4 add log GDP per capita. Even
though this reduces the coefficient on democracy a little, and log GDP per capita itself
may
1
and
is
significant, the
2
economicaUy
reflect
the fact that taxes as a percentage of
overaU relationsliip
significant correlation
is
unchanged, and there remains a statistically and
between democracy and tax revenues.
The remaining columns focus on the Freedom House index and add
additional controls,
including log of total population in 1998, average years of schooling in 1995 (from the Barro
and Lee dataset), continent dummies, and dummies
communist
The
countries,
finally,
relationship remains strong
continent
and
Handbook
and formerly
same
variables at the
and
though the addition of the
significant in all cases,
11 repeats the regression of
finally,
OPEC member
column 10 adds aU of these
dummies somewhat reduces the magnitude
Column
tries,
and
for
column 12 excludes
of Federal Countries, 2002).
time.
of the relationship.
column 3 excluding the formerly communist counall
federal countries (according to the
None
tax revenues and democracy.
40
of these
aff'ect
fist
from
that the correlation between
8
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44
Appendix Table B1
Dependent Variable Tax Revenues as Percentage
of
GDP
Excluding ex
(1)
Political rigtits
Polity
Log
(2)
(4)
(5)
(6)
(7)
(8)
1.566
1.591
1.266
1.345
1.679
1.315
1.697
1.612
(0.517)
(0.591)
(0.465)
(0.437)
(0.467)
(0.573)
(0.522)
(0.482)
1.292
0.717
(0.234)
(0.366)
2.515
3.466
2.506
2.119
2.069
3.088
2.694
1.511
2.274
3.420
(1.090)
(1.226)
(1.105)
(1.764)
(0.982)
(0.982)
(1.057)
(1.463)
(1.109)
(1.154)
-0.472
-0.319
(0.413)
(0.570)
0.395
0.182
(0.624)
(0.488)
America
Africa
Asia
Oceania
-9.725
-10.098
(1.874)
(2.571)
-3.566
-3.842
(3.081)
(4.899)
-9.835
-9.788
(2.474)
(3.657)
-4.902
-5.018
(2.899)
(4.301)
OPEC
-7.523
-1.474
(4.436)
(4.142)
Ex-communist
Political rights
Average years
4.510
0.351
(1.749)
(2.546)
100
91
97
89
97
62
97
97
97
62
75
82
0.347
0.285
0.375
0.357
0.383
0.403
0,571
0.408
0.416
0.598
0.365
0.449
Tax revenues, GDP per capita, and population are for 1998 and come from the World Bank's WDI 2002. Tax revenues are
1997-98 and Polity IV for 1998. between 1 and 7, with higher scores comesponding to more democratic countries.
the population over age 1 5 is for 1 995. from the Barro-Lee Data Set.
errors in parentheses.
from Freedom House
of schooling of
{12)_
1.714
Avg. years of sctiooling
Robust standard
(11)
(0.487)
Log population
R-squared
(10)
countries
2.537
per capita
N
(9)
federal
countries
(0.301)
democracy index
GDP
(3)
Excluding
communist
for
3837
ni
for central
government
only.
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