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HB31
M.415
working paper
department
of economics
WHY DID THE WEST EXTEND THE FRANCHISE?
DEMOCRACY, INEQUALITY AND GROWTH
IN HISTORICAL
PERSPECTIVE
Daron Acemoglu
James Robinson
No.
97-23
November 1997
,
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
WORKING PAPER
DEPARTMENT
OF ECONOMICS
WHY DID THE WEST EXTEND THE FRANCHISE?
DEMOCRACY, INEQUALITY AND GROWTH
IN HISTORICAL
PERSPECTIVE
Daron Acemoglu
James Robinson
No.
97-23
November 1997
,
MASSACHUSETTS
INSTITUTE OF
TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASS. 02139
JAN 1 9
1998
UBRABES
Why
Did the West Extend the Franchise?
Democracy, Inequality and Growth in
Historical Perspective*
James A. Robinson*
Daron Acemoglu^
First Version:
Revision:
August 1996
November 1997
Abstract
During the nineteenth century, most Western societies extended the franchise, a
decision which led to unprecedented redistributive programs. We argue that these
political reforms can be viewed as strategic decisions by political elites to prevent
widespread social unrest and revolution. Political transition, rather than redistribution under existing political institutions, occurs because current transfers do not
ensure future transfers, while the extension of the franchise changes the future
cal equilibrium
and acts
as a
commitment
to future redistribution.
Our theory
politi-
offers
a novel explanation for the Kuznets curve, whereby the fall in inequality follows redistribution due to democratization. We characterize the conditions under which an
economy experiences the development path associated with the Kuznets curve, as
opposed to two non-democratic paths; an "autocratic disaster" with high inequality
,
and low output; and an "East Asian Miracle", with low inequality and high output.
Keywords: Democracy, Enfranchisement, Growth,
Inequality, Political
Commit-
ment, Redistribution, Revolution.
JEL
Classification: D72, 015.
*
We would like to thank two anonymous referees, Claudia Goldin, Peter Lindert, Torsten Persson,
Dani Rodrik, John Roemer, Peter Ternin, Jaume Ventura, Michael Wallerstein and seminar participants
at Boston University, Cornell, Harvard, NBER, Universidad de los Andes, Singapore National University
and the World Bank for helpful comments and suggestions.
t Massachusetts Institute of Technology, Department of Economics, E52-371, 50 Memorial Drive, Cambridge, MA 02142; e-mail: [email protected]
t
University of Southern California, Department of Economics, Los Angeles, CA 90089; e-mail:
arobinsSusc
edu.
j
.
Introduction
1
The nineteenth century was a period
and unprecedented
of fundamental political reform
changes in taxation and redistribution. For example, British society was transformed from
an "autocracy" run by an
The
a democracy
elite to
franchise
was extended
in 1832, then
again in 1867 and 1884, a process which transferred voting rights to portions of the society
which did not previously have any
political representation.
The decades
after the political
reforms witnessed radical social reforms, increased taxation and the extension of education to the masses.
noted by Kuznets, inequality, which had previously been
Finally, as
increasing, started to decline during this period: the Gini coefficient for
in
England and Wales had
Two
1901.
skilled
risen
from 0.400
in
income inequality
1823 to 0.627 in 1871, and
fell
to 0.443 in
key factors in the reduction in inequality were the increase in the proportion of
workers (Williamson, 1985), and redistribution towards the poorer segments of the
society; for example, taxes rose
from 8.12% of National Product in 1867 to 18.8% by 1927,
and the progressivity
system was increased substantially (Lindert, 1989). During
of the tax
the late nineteenth and early twentieth centuries, the franchise was also extended in most
other Western societies. Those for which data exist
(e.g.
France,
Germany and Sweden)
show that democratization was followed by increased redistribution and the downturn
of
the Kuznets curve. 1
These events are hard to tmderstand with our existing models.
likely to lead to increased taxation
why should
the
political power,
In particular,
elite
and redistribution
extend the voting rights?
(e.g.
If
democratization
is
Meltzer and Richard, 1981),
Our answer
is
that the
elite,
who
held
were forced to extend the franchise because of the threat of revolution. 2
we argue
that democratization alters future political equilibria by changing
the identity of the median voter, thus acts as a commitment to future redistribution,
and prevents
social unrest.
In contrast to democratization, the promise by the elite to
redistribute in the future while maintaining political power
paradoxically,
we
find that in economies
promise of future redistribution
1
A
is
more
is
where the masses are
credible,
and so the
not credible.
Somewhat
politically organized, the
elite
can avoid a revolution
the U.S..
We
threat of revolution can intensify either because inequality increases (see for example Muller
and
country which exhibits a Kuznets curve, but some time after
full
democratization
is
return to this case in the concluding section.
2
The
on the strongly positive relation between income inequality and
because of some unusual event such as wars, depressions and famines.
Seligson, 1987,
political instability) or
without extending the franchise. This
may
why
explain
in the nineteenth century, while
Britain and France extended the franchise in the face of heightened social unrest and
inequality,
Germany which had
the most organized working class in Europe instituted the
much
welfare state, but did not extend voting rights until
First
later (after the turmoil of the
World War).
The second
contribution of our paper
and the Kuznets curve.
was an important
We
is
between democratization
to point out the link
argue that the increase in inequality in Western economies
which led to the extension of the fran-
factor in increased social unrest
Democratization, in turn, increased redistribution and was instrumental in reducing
chise.
inequality.
As predicted by our approach,
in Britain, France,
Germany and Sweden,
peak of the Kuznets curve coincides with the extension of the franchise.
model explains the Kuznets curve,
ture of
all
it
the
Although our
does not predict that this pattern should be a fea-
development processes (which accords with the empirical findings of Anand and
Kanbur, 1993;
Fields, 1995;
and Fields and Jakubsen, 1993). Instead we predict that a
Kuznets curve should be observed when a society democratizes due
to social pressure. Al-
ternative development paths, the "autocratic disaster" and the "East Asian miracle", do
not feature Kuznets curves.
In an autocratic disaster inequality
is
high, but there
democratization or redistribution because the masses are badly organized.
of the masses slows
down accumulation and
economy
leads the
of output. In an East Asian miracle initial inequality
is
is
no
The poverty
to stagnate at a low level
low, so the
economy accumulates
rapidly and converges to a high level of output, and because the gains from growth are
more equally shared,
reform
is
social pressure does not
until
much
later,
and thus
political
considerably delayed.
Our paper belongs
we
emerge
to the growing literature
on
political
economy and growth. However,
are aware of no other paper which shares our two key points: franchise extension as a
commitment
conflict.
device,
Among
provides the
and the Kuznets curve
the important contributions related to our work are
first
elite.
who
investigate a
Our paper
(1993)
Roemer
by
social
(1985)
who
economic model of revolution; Grossman (1991;1993;1995), who models
predation by the unprivileged against the
(1993),
as a result of political reform caused
is
rich;
model where there
also closely related to
is
and Ades (1995) and Ades and Verdier
concentration of power in the hands of an
Benabou
(1996), Galor
and Zeira (1993), Perotti
and Banerjee and Newman (1993) who model investment opportunities as
and thus show that distribution of income matters
for
indivisible
growth and development. In
fact,
our model in Section 3 builds on Galor and Zeira (1993). Finally, our contribution shares
a
common theme
with North and Weingast (1989)
who
also argue that political reform
can be a method of commitment, but in the context of the introduction of the English
Parliament in the seventeenth century.
The plan
power
is
of the paper
is
In Section
as follows.
concentrated in the hands of an
elite
we develop a model where
2,
and the masses can
political
a revolution to
initiate
We show that the elite can prevent a revolution either by redistributing,
the franchise. We characterize the conditions under which current and
contest this power.
by extending
or
promised future redistribution are not
commitment
3,
to future redistribution, the extension of the franchise,
we simplify
this
model
in a
number
that an increase in inequality can
of inequality
make
in
and output
of dimensions
make
we return
4,
in our analysis.
which a Kuznets curve
in this model.
A
is
Model
how a Kuznets
outline
and
curve, an autocratic
arise along the equilibrium path. In
many
justify
of the assumptions
than the U.S.)
some
extensions. Section 6 concludes.
of Democratization
consider an infinite horizon
economy with a continuum
while the remaining
—
1
A
of agents.
A form a rich
proportion A of
Throughout the
,
paper superscript p
denote poor agent and r
will
denote rich agent (or
poor agents as
and
all
We
elite).
identical.
that
if
asset,
will
will treat all
Initially, political
there
There
is
is full
power
is
1
identical,
"elite"
members
democracy, the median voter
will
.
member
of the
of the elite will also be
concentrated in the hands of the
elite,
but A
>
be a poor agent.
h (which should be thought as a combination of human and physical capital).
and each member
exogenous
(so
of the elite has
we drop time
t
first is
subscripts).
a market technology,
capital devoted to market production.
=
We
where each poor agent has human capital
h rQ > h% >
1.
In this section these stocks will be
Accumulation
There are two methods of producing the
The
\ so
a unique consumption good y with price normalized to unity, and a unique
begin our analysis of the economy at time
ital.
we
detected the peak coincides with political reform triggered by
these agents are "poor"
/iq
We show
The Environment
2.1
We
We
also argue in this section that for countries (other
social unrest. Section 5 briefly discusses
2
necessary. In Section
the revolution a threat, and analyze the dynamics
to the historical evidence,
We
is
and thus a firm
and add capital accumulation.
an East Asian miracle and a revolution may
disaster,
Section
sufficient to stave off a revolution,
final
is
investigated in Section
3.
good. Both techniques are linear in cap-
Y m = AH™
t
The second
is
where
H™
is
the
amount
of
human
an "informal", or home production
Y h = BH'
technology:
sector
is
,
where Hj*
H
=
Jh
l
of
human
We
di.
role of
l
t
t
for
,
=
i
p,r,
where r
/3
specific,
hence
T
6
(0,1).
by a
in our analysis
is
to
Post-tax income
We
t
m where we have
constraint therefore implies T = r AH
m can be taxed. 3
capital used in market production, H
t
given by,
is
T >
is
t
y\
=
the transfer
assume throughout that taxes and transfers
and r are not indexed by
t
t
linear indirect utility function
the tax rate on income, and
is
t
that the agent receives from the state.
cannot be person
B, so the market
not taxable.
is
over net income, and a discount factor
— T )Ah + T
A>
assume that
home production
All agents have identical preferences represented
(1
home produc-
capital used in
than 100%, because while taxes can be imposed on the
less
home production
sector,
amount
the
The only
always more productive.
ensure an equilibrium tax rate
market
is
+ H™ =
we have H^
Naturally,
tion.
l
t
t
,
i.
The government budget
used the fact that only
human
,
The "masses"
(A poor agents),
endowed with a revolution
though
excluded from the political process, are
initially
Since they form the majority, they can overthrow
technology.
the existing government and take over the means of production,
any period
t
>
We
0.
assume that
poor only retain a fraction
the previous
analysis,
nothing after a revolution). In particular,
agent receives a per period return of
total wealth in the
economy
between A agents.
A
whether
fi t _i
may be more
=
h
fi
attempted,
is
\x t
we assume,
if
there
AHj\
AH, and
it
always succeeds, but the
is
partially kept
is
a revolution at time
t,
This
in all future periods.
then each poor
is
of this
fi t
because the
and share
low value of y implies an ineffective revolution technology
h
and y
/j
or y}
.
The
l
=
0.
We
In particular,
fact that
\x
by
for simplicity, that the elite receive
they capture a fraction of
society in which the poor are unorganized).
between two values:
is
of the output (the rest gets destroyed or
fi t
though in the
elite,
a revolution
if
the capital stock in
i.e.
assume that
we have
/zis
Pr(// t
=
stochastic
h
fj,
)
—
(e.g.
it
a
and changes
q irrespective of
fluctuates captures the notion that
some periods
conducive to social unrest, and also that a promise to redistribute today
may
not materialize due to changes in circumstances tomorrow.
Finally, in each period the elite
it is
have to decide whether or not to extend the franchise.
extended, the economy becomes a democracy, and
sets the tax rate.
We
assume that
if
now the median
voter, a
If
poor agent
voting rights are extended, they cannot be rescinded.
So the economy always remains a democracy. 4
3
We think of time t <
as governed by a different model, for example with less inequality, so that there
for all t < 0.
redistribute by the elite, thus Tt — Tt =
This is not to deny that in many countries coups happen. It is nevertheless true that once voting rights
are extended and political parties are formed, it is relatively costly for any group to exclude the rest from
was no threat of revolution and no need to
4
the political process.
We
discuss
some reasons
for this in Section 5
The timing
of events within a period can
1.
the state
2.
the
elite
ji is
be summarized as
follows.
revealed.
decide whether or not to extend the franchise.
If
they decide not to extend
If
there
the franchise they also set the tax rate.
3.
the poor decide whether or not to initiate a revolution.
share the remaining output.
the tax rate
4.
there
the capital stock
(a
poor agent).
allocated between market
is
a revolution they
no revolution and the franchise has been extended,
is
by the median voter
set
is
If
is
and home production and incomes are
realized.
Analysis
2.2
The
analysis can be simplified by exploiting two features of the model. First, the capital
allocation decision takes a simple form.
capital to
home
best-response. It
attention to r£
Second,
use, thus
is
<
player. Also, all
0.
(
clear then that
H™ = H
f and
members
all
m =
if
t
,
If
If
r
t
> f = ^p,
then
on the other hand r
t
all
<
agents allocate their
f,then
H™ = H
no voter would ever choose r > f and we can
,
t
is
t
a
restrict
which reduces the number of actions to be considered.
of the elite have identical preferences, so
we can
poor agents have the same preferences, and when
not to participate in a revolution, there
is
no
"free-rider
it
treat
them
as one
comes to whether or
problem", because
if
an agent does
not take part in the revolution, he can be excluded from the resulting redistribution. So,
we can
treat all poor agents as one player. Therefore, this
a dynamic
game between two
In the text,
gies only
we
players, the elite
characterize the
non-Markovian equilibria
eral results.
The
Perfect Equilibria of this game, in which strate-
formally, let
a
(elite in
(fi,
explicitly
on time. Even though
natural in this setting, for completeness,
we
disciiss
Appendix, and show that they do not change our gen-
state of the system consists of the current opportunity for revolution,
represented by either
r
in the
is
as
and the masses.
depend on the current state of the world and not
the focus on Markovian equilibria
P=E
Markov
economy can be represented
l
\x
or
h
fi
,
and the
political state
P) be the actions taken by the
power) or
D
elite
(democracy or
when
the state
More
elite control).
is \x
=
pr or
1
p.
,
and
(democracy). This consists of a decision to extend the franchise
P = E, and a tax rate r when = (i.e. when franchise is not extended). Clearly,
= 0, P remains at E, and if = 1, P switches to D forever. Similarly, p (p, P\4>,T r
if
are the actions of the poor which consist of a decision to initiate a revolution, p (p — 1
representing a revolution), and possibly a tax rate rp when the political state is P — D.
4>
when
(j>
r
<f)
<r
)
These actions are conditioned on the current actions of the
elite
who move
before the poor
agents according to the timing of events above. Then, a (Markov Perfect) equilibrium
strategy combination,
each other for
We
priate
there
all \i
{a p
(fi,
P),a
r
r
(fi,P\(j),T )}
such that
Bellman equations. Let us
start
a revolution (starting in state
VP (R) —
never occur). Clearly,
and a are best-responses to
V P (R)
by defining
h
=
(X
fj,
xn-% which
is
this
game by
writing the appro-
we have
rich lose everything,
Next, suppose there
>
A
1/2)
V
(R)
=
the per-period return from revolution for
and wants
much
as
no allocative cost as long as r
<
lution, so in
=p
V>(pt, E)
we would have
((i
h
Vp
h
(/j,
,E)
a poor agent
t
as:
E).
is
balanced,
VP (D) =
The
h
(fi
T = (A — B)H. We
t
)H
Bhy
are in power
elite
and
\[tp*
=
and r
V
r
=
(D)
=
and there
=
0.
^jr-,
can then write
[^
)H
.
no threat of revo-
is
Therefore, the values of
,
= ,^,
(5 [(1
-
l
q)V'(fi
,
E). Suppose that the
.
The
+ gV V, E)\
E)
elite
play
revolution constraint
is
<fi
(1)
.
=
and r r
equivalent
=
to:
0.
Then,
V P (R) >
,E). In words, without any redistribution and franchise extension, the masses prefer
to initiate a revolution
Assumption
Revolution
is
1
g
more
when
That
this constraint binds.
fj,
= /A To make
the analysis interesting,
we assume
so that there
is
> $=£}.
attractive for the masses
sufficient
Assumption
when
1
wealth among the rich
ensures inequality
prefer revolution to the status
outcome
that
is:
inequality,
hT /hp
,
is
high so that they
have more to gain by taking control of the means of production, and when A
X)h r ).
=
Bhr+
{
r
f
are given by:
r,
= Ah? +
Finally, consider the state
Vp
,
ov
is
redistribution as possible, because redistribution has
any Markov Perfect Equilibrium,
poor and rich agents, j
median voter
.
1
(fj,
at the time of
f Therefore, the equilibrium tax rate will be r
the return to poor and rich agents
state
h
constant over time). Also, since the
is
In this case, the
and from the assumption that the budget
Now, consider the
\i
0.
a democracy.
is
if
since in the other state a revolution will
the revolution matters, hence the per-period return
T
poor agents
as the return to
the infinite future discounted to the present (note that only the value of
(since
a
and P.
can characterize the Markov Perfect Equilibria of
is
is
T
p
ct
for the elite,
is
(recall total
sufficiently
wealth of the rich
it.
is
low,
(1
—
high (and A low) that the poor
quo with no redistribution. Since the revolution
they will attempt to prevent
is
They can do
this in
is
two
the worst
different
ways.
0=1.
they can extend the franchise,
First,
V P (D).
under democracy,
Second, the
Then, the poor receive their return
can choose to maintain
elite
V
but redistribute through taxation: in this case, the poor obtain
With
the tax rate chosen by the rich.
either action
by the
elite,
political
h
p
(fj,
,E,T
the poor
=
power,
r
where r
)
may
T
0,
is
prefer
still
a revolution, thus:
V*(jm\ E)
Next,
we
= max {VP (R);
4>V P {D)
+
h
E, t
,
(fj.
t
)
=
(1
-
r
r )Ahp
+
t
t
AH + p [qVp
In words, the rich redistribute to the poor, taxing
—
therefore receive net income (1
next period we are
r T )Ahp from their
in state
still
=
\i
h
fi
the next period the economy switches to
V p (fi
l
>
}
.
)
,
all
E, r
T
)
income
own
+
- q)V p {fJ, E)]
(1
at the rate t t
capital
and
transfer
.
f,
r
<
f,
that
then each
is
(rich)
the
elite
(2)
The poor
T=
=
//',
redistribution stops
t t AH.
an
cannot tax themselves at a rate higher than f
all
in
commit
effective revolution threat.
agent would privately prefer to put
if
and the poor receive
,E). This captures the discussion in the introduction that the elite cannot
note that r
r
r
then redistribution continues. However,
,
//
h
(fj,
to future redistribution, unless the future also poses
if
0)^\ E, r
have:
Vp
If
-
(1
Also
= ^p;
their assets to the
home
sector, reducing aggregate tax revemies to zero.
Before proceeding further,
simplifies the exposition to restrict attention to the area of
it
the parameter space where democratization prevents a revolution, that
is
V P (D) > Vp (R).
Thus, we assume:
Assumption
Next,
Bhp + (A- B)H >
2
useful to calculate the
it is
extending the franchise,
utility is clearly
V p (fi
h
,
^f1
.
maximum
utility that
can be given to the poor without
E\q), as a function of the parameter
achieved by setting r r
=
f in
(2).
q.
This
maximum
Therefore, combining (1) and (2),
we
obtain:
0V,
Now,
is
if
Vp
m
h
(iJL
,
E\q)
=
W.
B, f )
< VP (R),
=
B* + (A
then the
-W-W -,X'- *><"-">
maximum
transfer that can
be made when
(3)
/j,
not sufficient to ensure that the poor receive enough to prevent a revolution.
clear that
?Y^)
<
Vp
h
(/j,
VP (R)
,E\q
=
1)
= VP (D) > VP {R)
by Assumption
1.
Moreover,
Vp
by Assumption
h
(/j.
,
E\q)
is
2,
and
Vp (fi h ,E\q =
=
h
\i
It is
0)
=
monotonically and continuously
,
increasing in
Therefore, there exists a unique q* G
q.
V
Finally, note that
This
(fi
,
E, r r )
because when there
is
in the
h
r
hand
is
E
of the elites, r
decreasing in r
is
=
a democracy, r
and
,
f in
=p
whenever p
(0,f]
r
such that
(0, 1)
=
but r
,
,
it is
1
(fj,'
,
= VP (R).
E\q*)
V
greater than
periods, whereas with the
all
h
rr
for all
Vp
when p
=
T
(D).
power
From
/J.
this
5
discussion the following characterization of equilibrium follows immediately:
Proposition
Suppose Assumptions
1
and 2
1
Then,
hold.
for all q
^
there exists a
q*,
unique Markov Perfect Equilibrium such that:
1.
If
< q\
q
then a r (fi ,E)
l
=
=
(cp
0),a r (p\ E)
=
(4>
=
<**
1,.)-
h
'(fi
,
E\<f>
=
= 0,t = f) and o*(jjl h D) = (r = f).
r
where f r G (0,f)
2. If ^ > g*, then a (p',£) = (0 = O,T = 0),a (p\ £) = (0 = 0,f
r
Also p (^,£;|0 = 0,t) = (p = 1) for all r < f
defined by 1/ p (#) = V p (p'\ £, f
=
0,r)
(p
=
a p (p'
1),
1
,
E\<f>
=
=
=
0,r
1, .)
(p
,
r
r
)
is
ap
r
ct
).
h
(fi
1, .)
,E\(f)
=
(
The
p
=
0,t)
= 0, r =
=
f)
(p
and
=
^(/A D) =
starts with the elite in power.
1
Now,
strategy of initiating a revolution
if
the franchise
>
(r
f
is
poor agent and sets the tax rate r
if
q
<
fi
=
h
fi
combination
,
in a
=
fi
.
=
fi
The poor play the optimal
ft
=
p',
when
>
q
q*,
the rich can prevent the
once again they set r
=
and
in the
the unique (Markov Perfect) equilibrium of the game.
even though the
is
elite face
may
this analysis:
a lower future tax burden with redistribution than
prefer to extend the franchise. This
is
because when q
<
q*,
not sufficient to prevent a revolution. With q low, the revolution threat
transitory, thus the
and then
when p
,
under democracy, they
is
game
they set a tax rate, f r just enough to discourage revolution. This strategy
is
redistribution
,E\(j)
p = p and the franchise has not been
the new democracy the median voter is a
In contrast,
p
p
h
There are three important conclusions to be drawn from
First,
(^
=
is
extended, in
f.
h
simple way: recall that the
then the rich set a zero tax rate
q*,
the state
=
the equilibrium path,
off
state switches to
if
cr v
= f).
revolution by redistributing. So in the state
state
and
,
can be expressed
and extend the franchise when the
And
r
0) for all
results of Proposition
extended.
,
r
poor realize that they
transfers will cease.
Redistribution
will only receive transfers for
when
noncredible promise of future redistribution by the
fj,
=
h
fi
elite.
a short while
can therefore be viewed as a
Unconvinced by
this promise,
5
When q ^ q* the equilibrium is no longer unique. In particular, there exists an equilibrium which
takes the form in part 1 of the Proposition, and one which is similar to part 2. Also, in the Appendix, we
,
allow for non-Markovian strategies and find that even
when
q
<
q*
,
there exist
with redistribution and no democratization, but there exists a cutoff q**
unique equilibrium has franchise extension in the state (/j, h ,E).
<
subgame
q* such that
perfect equilibria
when
q
<
q**, the
The
the masses would attempt a revolution.
revolution
only prevented by franchise
is
extension.
Second, perhaps paradoxically, a high value of q makes franchise extension
A
less likely.
high q corresponds to an economy in which the masses are well organized, so they
A
6
frequently pose a revolutionary threat.
case, democratization
is
more
However,
likely.
revolutionary threat, future redistributions
Germany, which had the most developed
may have been
naive intuition
this
is
become
that in this
not the case because with a frequent
This result
credible.
may
explain
why
socialist party, instituted the welfare state in
the nineteenth century without franchise extension, while Britain and Prance extended the
franchise.
We
Finally,
return to this issue in Section
4.
straightforward to see by comparing
it is
r
increasing in the extent of inequality, h /h p
V P (R)
and
A
3
Model
of
,
E\q*) that q*
more
The
role of inequality in
detail in the next section.
Growth and Inequality Dynamics
The Environment
3.1
The
previous section established
when they can use
why
the elite
may be
forced to extend the franchise, even
taxation and redistribution to reduce inequality.
We now
of the analysis to explore the implications of such political reform on growth
To
is
This implies that higher inequality enlarges
.
the area of the parameter space where democratization occurs.
franchise extension will be discussed in
Vp (fi h
simplify the analysis,
The same continuum
we
alter the focus
and
inequality.
consider a non-overlapping generations model with bequests.
of agents as in the last section
beget a single offspring. Technology
now
live for
only one period and each
identical to that in Section 2, but
is
human
capital
accumulates over time. This allows us to study how political transition interacts with the
dynamics of
inequality.
We assume that all agents have identical preferences defined over their own consumption
and "educational bequests" given
4+1 =
(cj,ej +1 =
ti'te,
u
for
i
—
period
r,p and 7 €
t,
and
l
e t+1 is
Alternatively,
v
would have t >
J
by:
(0, 1).
)
)
Here
(cj)
c\
"7
1
-7
(e\ +i
is
y
if
e\ +1
ife\+l
>
1
<\
the consumption of a
member
of group
i
alive in
the investment in the offspring's education. These preferences imply a
we could have assumed
0.
1
(ci)
l
fi
>
In this case, a high value of
so that even in this state with the elite in power,
l
fi
would
9
also lead to the
same
result.
we
constant savings rate equal to 7, and an indirect utility function which
Both the consumption and bequest decisions are made
as in the previous section.
end of the individual's
amount
of bequest,
The form
life.
=
e\ +l
income
linear in
is
a
minimum
amount, he
will leave
of the utility function implies that there
and when the agent cannot
1,
afford this
at the
is
nothing to his offspring. This non-convexity captures the feature that very poor agents will
not be able to accumulate assets (see Galor and Zeira, 1993).
The
human
offspring's
capital
given by:
is
=max{l;Zej + /}
^+1
where
Z>
and
1,
also
<
(5
The presence
indefinitely.
investment, there
The timing
is
a
1
which
will
(5)
guarantee that accumulation does not continue
of max{l;.} in (5) implies that even in the absence of any
minimum amount
of events within a period
of
human
now
would have.
capital that each agent
is:
1.
education bequests are received.
2.
the
3.
the poor decide whether to initiate a revolution.
decide whether or not to extend the franchise.
elite
there
If
is
a revolution they share
the remaining output of the economy. Otherwise, the political system decides the tax rate
a poor median voter
(i.e.
4.
the capital stock
if
there
democracy, and a rich agent
is
allocated between market
is
if
not).
and home production, and consumption
and bequest decisions are made.
Although the timing of events
Now, there
is
no
quite similar to Section
is
2,
there
is
a major difference.
possibility of choosing redistribution to prevent a revolution,
we
are set after the revolution decision within the period. This implies that
<
attention in the case of q
are focusing
terms of the analysis of the previous section.
Analysis
3.2
As noted above, the
and
q* in
because taxes
e\
+l
=
0,
if,
preferences in (4) imply a constant savings rate:
-)y\
<
1.
So
if
an agent can afford
he
it,
will
Assumption
The
agent
first
3
consume
7A <
1
all
of
it.
and {^B)
At
13
this stage
Z>
the
minimum
level of
when
we make the
7$,
his
income
if
7$ >
1
proportion
is
below a
following assumption:
1.
part implies that in the case where there
who has
=
will invest a fixed
of his post tax income in the education of his offspring, but
minimum, he
e\ +l
human
10
is
capital, h\
no taxation (rt
=
1, will
leave
=
T%
=
0),
an
no education to
his offspring, thus
=
h lt+l
accumulate while others do
accumulation of
is
B<
human
Therefore,
also.
1
The second
so.
capital takes place,
A, a steady state level of
human
possible for
is
it
some households not
when
part of the assumption guarantees that
and even
if
the rate of return on
than
capital greater
human
to
capital
can be reached. This second
1
part will not only enable accumulation by the rich in the absence of taxation, but also
ensure that taxation will never be severe enough to stop accumulation.
In
of our analysis,
all
we only
consider initial conditions such that:
hss
where h rss
>h
r
Q
>
(l
A
-l
)
human
the steady state value of the rich agents'
is
inequality ensures that
we
start with less than steady state
be growth (rather than decumulation of
human
The second
capital).
The
capital.
first
part of the
capital, thus there will
inequality ensures that rich
agents are beyond the point of non-convexity, and are able to leave positive educational
Once
bequests to their offspring.
different technology so that
first
no one accumulates and inequality
Autocracy and Only the Rich Accumulate
1:
control of the political system, rt
=
3 implies h%
Vt
1
>
0,
=
0.
<
as governed by a
stable.
=Z
T
h t+l
= Z (-yAhl)
(e[+1 )
human
.
Z>
1
by Assumption
Inequality in this
poor: yl/yt
=A
A
Case
2:
also
poor
still
r
t
_1
<
(7^)
capital
dynamics
for this
3,
= ((jAf Z)^
)
h\.
On
the
will also
Then we
rich
on the
group are given by:
and
A>
B, we have hss
>
way
to the steady state h\
i
is
1-
ratio of the rich to the
increasing, so inequality
income
in this
economy
is:
-i
Autocracy and All Agents Accumulate Suppose h rQ >
0.
The
(6)
Finally, the steady state level of aggregate
+ (1-A)(( 7 ^Z) T
=
then Assumption
.
economy can be measured by the income
= Ah\/A =
increasing too.
also that h%
elite in
This dynamic equation has a unique steady state:
h ss
Since ('fBy
Suppose
we have the
Since
so that the poor are unable to accumulate.
other hand will accumulate and the
loo
ss
is
t
analyze accumulation and inequality in the absence of the threat of revolution.
Case
is
of the periods
Equilibrium Dynamics without the Threat of Revolution
3.3
We
we think
again,
have: h{+1
= Z{^Ah\Y
be able to accumulate. Thus h\
>
converge to the same steady state, hss, given by
11
>
hp >
h$
(-fA)'
1
and
,
-1
for j
=
1 Vt.
This implies that both groups will
(6).
r and p. Since
(jA)
Since the poor start with less
,
the
human
capital
and converge
The steady
same
to the
income
state level of aggregate
Therefore, this
along this equilibrium path, inequality
level,
economy converges
more equal
to a
= A UjAf
Yg S
given by:
is
Zj
distribution of income
The reason
higher level of aggregate output than the previous case.
is
decreasing.
1_/
and
>
Yg S
.
also to a
for this is that in
Case
a fraction of the agents were unable to accumulate, causing a poverty trap.
1,
Case
Democracy We now
3:
We know
= f = ^=^-
consider the dynamics under democracy.
maximum
that in this case, the poor median voter will set the
tax rate: rt
.
Accumulation dynamics are then determined by:
= max jl, Z
h{+1
for j
T
ht >
=
1.
r
and
The second
p.
(7 [Bh{
(A -
+
part of Assumption
Z >
(jB)
3,
(7)
])^
ensures
1,
to accumulate
(7A)
-1
when they
Now
receive transfers.
may
so that the poor
If /iq
> (jA)'
1
/i[
+1
>
1
if
so that in the absence
,
would be able to accumulate, they
of redistributive taxation the poor
<
t
Therefore, taxation will not stop accumulation by the rich. This does not however
guarantee that the poor will be able to accumulate.
h,Q
B)H
consider the
be able
more involved case where
Suppose h p
not accumulate.
will also
=
1,
then equation
(7)
implies that the capital of the rich converges to the steady-state level:
D
h ss
It is
= 1Z
-
[{A{\
straightforward to see that hgS
A)
is
+ XB) h°s + (A-
strictly less
Condition
1
than Yg S and Yg S
7 [B
+ (A - B)
is
tax return
in this
/if
1;
thus Ygg
and
1
h\
A)
>
1
=
on
his
human
economy when
/if
=
accumulation by the poor.
level of
income (human
richer.
When
it is
capital,
1
and h
t
=A
X
hss-
+
(1
—
,
Let also Ygg
X)hg S which
=
hg S
If it holds, at
.
Condition
/i{j
some point the
=
1:
he receives an after
the total per-person transfer
is
1
necessary and sufficient for
is
rich will
have a high enough
capital) so that redistributive taxation will enable the
violated, there exists
no k[ < hg S that
to enable accumulation by the poor.
12
will
note that the term in square
this
and the second term
T
<
hgS the redistribution from taxation
the post tax income of a poor household with
B
.
consider:
- X)h§s +
=
=
poor to accumulate. To see
sufficient to enable the
brackets
Now
((1
This condition states that when
be
.
P
uniquely defined and hg S
denote the steady-state level of output when hp
is
B)X]
will
poor to grow
generate enough tax revenue
When
Condition
economy converges
holds, the
1
accumulating to hss, so inequality
when
hand,
to
Y$ s with both the poor and the
will also decrease as in the previous case.
the poor
do not accumulate, inequality,
given by
^
^
J to
J
'
'
% =
—
——
On
the other
—K—
\j-
(A-B)((l-A)/ir+A)+B
Vt
will increase despite the fact that there are also increased transfers to the poor. Also,
Condition
in
holds,
1
it is
also possible for the poor to start accumulating
which case inequality
this
will fall monotonically.
The necessary and
rich
from period
-,
'
when
t
=
0,
sufficient condition for
is:
p
7 [Bh
Condition 2
+
{A
which ensures that at time
than
(7) is greater
1,
- B)
t
=
thus 7^0
((1
0,
>
- X)h r + Xh p )} >
the after-tax income of the poor times the savings rate
We can now summarize equilibrium
be defined as
useful to notice that
1. It is
than Condition 2 because h
1 is less restrictive
1.
<
If h,Q
< hg S
whenever h^
<
1,
Condition
.
in (6):
controlled by the
is
T
dynamics without the threat of revolution. Let hss
Proposition 2 Suppose that Assumption
system
1,
(7/I)
-1
elite.
then h\
,
=
Then, we have r
t
1
>
V£
0,
E
3 holds, Hq
=
yA)~ l ,hss) and the
/
((
political
and:
h T monotonically converges to hss, aggregate
t
output converges to Yj 5 and inequality increases monotonically.
2.
> (jA)'
If h,Q
1
,
output converges to YgS
then both h\ and h r monotonically converge to h S s, aggregate
t
> Ys S and
inequality decreases monotonically.
Proposition 3 Suppose that Assumption
system
democratic.
is
1.
>
If /to
t
(jA)~ l
,
output converges to Y§s
2.
and
If
=
1
h,Q
Vi
>
4. If ho
i,
<
and h
/if
3. If
h\
ho
_1
(7^4)
r
such that h
and decreases
v
t
=
_1
1
> YgS and
inequality decreases monotonically.
and Condition 2
and Condition
holds, then inequality
1 fails
1
is
is
monotonically decreasing,
is
growing Vi
>
i.
Aggregate output converges to
no Kuznets curve: inequality
is
-
to hold, then inequality increases monotonically,
to
holds and Condition 2
Vi G (0,f), and h\
thereafter.
political
t
and h\ converges to h^s- Output converges
(7v4)
and the
hss),
,
f and;
There are a number of features to note.
there
-1
then both h v and h\ monotonically converge to h S s, aggregate
{^A)~ l and Condition
0,
<
h rQ G ((jA)
converge to hss, aggregate output converges to Yg S
t
<
=
Then we have r
3 holds,
First, in the
F55
fails
<
Y$g.
to hold, then there exists
Inequality
is
t
Y^.
absence of redistributive taxation,
always increasing or decreasing.
13
increasing until
A
Kuznets curve
is
however possible with a democracy (Proposition
sufficiently wealthy, the transfers
from them to the poor
But when the
inequality will increase.
become
rich
crucial threshold, the poor start accumulating,
redistributive taxation
Kuznets curve
Section
was
4,
is
key
when the
rich are not
not ensure accumulation, and
sufficiently wealthy, transfers reach
and inequality
Kuznets curve.
societies did not start out as
and there was no
will arise for a larger set of
franchise extension to an
more
for the
will
4):
falls.
However,
Thus
a
in this model,
this configuration of the
not totally compelling; as noted earlier and discussed in more detail in
Western
increasing,
is
Part
3,
democratic and were not so when inequality
redistributive taxation.
We will see that the Kuznets curve
parameter values when we add the possibility of revolution and
economy with the
elite in
we
power, and this
believe
is
a
much
plausible explanation for the Kuznets curve.
Second, inequality and especially the poverty of the masses are harmful to development.
When
the poor have h^
Y$ s whereas otherwise
,
Yg S
.
it
> (jA) -1
may
,
the economy converges to the higher steady state
get stuck in the lower steady state with per capita income
This relation between inequality and prosperity applies both to a democracy and an
autocracy.
This result
is
a direct consequence of the nonconvexity in the accumulation
technology as in Galor and Zeira (1993).
Finally, in this
lation
model democracy
is
good
for
economic performance
by the poor, but detrimental otherwise. In the absence
condemns the economy
much more
stringent.
On
enables accumu-
of democracy,
/iq
<
than Yg S
.
So the impact of democracy on performance
is
-1
,
the other hand,
if
democracy but the poor cannot accumulate, the economy converges to Yg S which
less
(jA)
Yg S but with democracy,
to the lower level of steady state output
the conditions for "stagnation" are
if it
there
is
is
even
ambiguous. With some of
the costs as emphasized by Alesina and Rodrik (1994) and Persson and Tabellini (1994),
democracy would have an ambiguous
effect
even when
enables the poor to accumulate.
it
Therefore, the empirical results that show no robust correlation between democracy and
growth should not be too surprising.
The Threat
3.4
We
will
now
of Revolution
analyze an economy which starts with the
constraint never becomes binding
of Proposition 2 will apply.
rich
If
(e.g.
if fi is
elite in
power.
If
the revolution
very small), then the equilibrium dynamics
on the other hand revolution becomes a
real threat, the
have to redistribute to the poor in order to prevent a revolution. However, given the
timing
we have assumed, a promise
to redistribute
14
by the
elite is
not credible, thus would
not prevent revolution.
power to the poor,
The only way
becomes binding, the franchise
is
when
general revolution constraint
Ah\ >
previous section:
when
AH /X.
t
to transfer political
is
the revolution constraint
extended and the dynamics of Proposition 2 are replaced
with those of Proposition 3 where the median voter
The
commitment
credible
extend the franchise. Therefore,
to
i.e.
make a
to
But now
a poor agent.
is
the rich are in power
constant and h Q /h^
fi is
same
is
the
is
changing over time.
r
as in the
Therefore, the revolution constraint becomes:
K < A(l-M)
^-Mi-A)When
revolution constraint are:
which
is
fairly intuitive.
benefit of the revolution
are fewer of
falls.
case, the
stuck at
1:
them with the same income
=
Condition 3
more
is
is less
2:
inequality
is
decreasing, so
Condition 4
inequality
is
it fails
The Threat
Condition 4
§
is
T
h
(i.e.
is
t
—
A)/i[)
given), the return
is
serious
(8); this is
when a
society has
because the
and when there
from revolution
more inequality
segmented (A relatively low).
When
Only The Rich Accumulate
In this
on the way with the poor
Thus we have:
Condition 3 holds, the threat of revolution
Case
the less tight
A,
> ^m=av
h ss
rich accumulate. If
the revolution constraint,
is
to Y§ s with increasing inequality
will never bind.
it
points to note about this
not binding at the point of steady state (which has maximal
If (8) is
1.
level
of Revolution
economy converges
/if
Two
the tighter
/z,
is
t.
to takeover the wealth of the rich ((1
is
The Threat
at time
is
Second, the higher
gap between h and h p ) and
inequality),
in
the higher
r
Case
If
first,
Therefore, the threat of revolution
(a larger
If
be no revolution
holds, there will
(8)
()
(8)
we can
to hold, then
of Revolution
it is
become
will
some point
as the
ignore the revolution constraint.
When
highest at time
effective at
t
All Agents
=
0.
Then we
Accumulate
In this case,
have:
< ^g=$.
satisfied,
then there
is
lower after this point, there
which both Conditions 3 and 4 hold
from the accumulation process,
themselves by force.
If in
at
no revolutionary threat
at
time
is
never any threat of revolution.
is
of interest. In this case,
some point they
will
if
t
=
and
since
The configuration
the poor are excluded
want to redistribute resources to
contrast they are also accumulating along the development path,
they will not see revolution as a worthwhile activity.
15
As discussed above, when the
revolution constraint binds, the elite have no choice
but to extend the franchise. However, we have to ensure that the extension of the fran-
The necessary condition
chise generates sufficient redistribution to stave off a revolution.
Assumption
for this is related to
—
X)h1
+ A/if] /A. The LHS
and the
RHS
is
Afi
[(1
what he
(A
2 in Section 2.
what a poor agent
is
We
gets with revolution.
- B)
((1
(8) implies
that h
T
t
=
A (A - /z) >
are particularly interested in whether
and the poor are not
we combine the
In this sxibsection,
Then the
critical
From
1
at t
Growth and Democratization
Throughout we assume that the
following result
Suppose the economy
—
starts in
is
Case
1,
elite start in
and Conditions
)
~v,
,
/i(l-A)'
the revolution constraint binds and the
on the poor also start to accumulate, inequality
converges to YgS
and outline
power
immediate from our previous analysis:
the rich accumulate and the poor do not. At
threshold
this point
to impose:
holds.
The Kuznets Curve The
Result
we need
analysis of the previous two subsections
possible paths of development.
and Assumption 3
ac-
- //).
Results: Implications For
3.5
some
B{\
+ A/if) + Bh\ >
S[Z\) at this point. So to ensure that in this
case franchise extension prevents a revolution,
Condition5
X)h\
gets after redistributive taxation,
this condition holds at the point the revolution constraint binds
cumulating. Equation
-
t
1,
3
and
5 hold.
inequality exceeds the
elite
falls
extend the franchise.
and aggregate output
.
In our view, this sequence of events corresponds to the experience of Britain, France,
Sweden and Germany, where,
as discussed in
more
detail in the next section, after a pe-
riod of increased inequality accompanied by wars and depressions, the threat of revolution
intensified.
This forced the extension of the franchise and increased redistribution. As a
result, inequality declined.
section,
we
This case
is
the main focus of our analysis. In the rest of this
outline alternative paths of development to contrast with the Kuznets curve.
Autocratic Disaster
Result 2 Suppose the economy
starts in
the rich start to accumulate at time
t
=
Case
1,
and Condition 3 does not hold. Then,
and the poor do
not.
The
revolution constraint
never binds, the economy remains an autocracy with high inequality and converges to
aggregate output Yg S
.
16
This
the path of an economy where
is
initial inequality is high,
but nonetheless, the
masses do not pose a revolutionary threat. This might be because the absence of a welldeveloped
other factors imply that
civil society or
/j,
is
small (that
hard time organizing, therefore a revolution would be very costly
r
high so that revolution
became a
not as beneficial at given h /h p
is
real threat, this
economy could democratize,
If \i
for
the poor will have a
them), or because A
is
were large so that revolution
redistribute to the poor,
and reach
Thus, contrary to conventional wisdom, political and social
a higher level of income.
instability
.
is,
may sometimes be good
for growth.
In particular, whether a
good "revolution
technology" hinders or enhances growth depends on which case the economy
is in.
East Asian Miracle
Result 3 Suppose the economy
accumulate starting at time
t
=
0,
starts in
Case 2 and Condition 4 holds. Then,
inequality declines
binds. Aggregate output converges to
Yg S
all
agents
and the revolution constraint never
.
In this case, along the development path the poor segments of the society are sharing
in the benefits of rising average per capita income,
to create social unrest.
and therefore do not
find
it
This case reminds us of Taiwan and South Korea.
worthwhile
In the early
post war period, both of these countries were in a situation very similar to that of the
Philippines except that inequality was
autocratic disaster).
elite,
7
In
much
three, political
all
higher in the latter (as in the case of the
power was concentrated in the hands of an
not unlike nineteenth century Britain. In Britain per capita income and inequality
grew and
political transition
took place. In the Philippines, aggregate income stagnated at
a high level of inequality, and there was no political transition. In contrast to these cases,
Taiwan and South Korea experienced
fast
somewhat. 9 Our model suggest that
fell
7
The Gini
coefficient
was 0.34
in 1965 in
growth but no democratization, 8 and inequality
this
may have been
because the gains of growth
South Korea and 0.31 in 1964
in
Taiwan whereas
it
was 0.45
in Philippines in 1957 (see Fields, 1995).
8
A
process of democratization
is
now
occurring rather rapidly in the Philippines, South Korea and
Taiwan. Nevertheless, for the purposes of the present study it is interesting to understand the prolonged
undemocratic regimes in these countries as opposed to the experiences of much faster democratization
in Britain and other developing countries such as India, Colombia and Turkey. It is also significant to
note, for example, that in the thirty years prior to
its
democratization, 1960-90, per-capita
GDP
in
Korea
increased by a factor of 6.89. This was considerably faster than British growth during the nineteenth
century. During the period 1820-1870, British income per-capita increased by a factor of 2.75 (all data
from Maddison, 1995). This motivates our claim that South Korea and Taiwan have experienced a period
of very rapid growth, but no democratization and no Kuznets curve. Section 5 discusses how a simple
extension of our model can account for delayed, rather than no, democratization in South Korea and
Taiwan.
9
for
For example, the average Gini coefficient over the period 1965-1970 was 0.34 for South Korea and 0.32
Taiwan, and these averages fell to 0.33 and 0.30 respectively for the period 1981-1990, see Campos and
17
were equally divided between different social classes in South Korea and Taiwan, so the
poor did not organize and the
until
much
did not have to extend political power to wider groups
elite
later (see also the discussion in Rodrik, 1994;
and Campos and Root, 1996;
in
support of such a view).
Revolution
Result 4 Suppose we are
Case
1,
the rich start to accumulate at time
t
binds at time i
The main
when
>
h^
in
:^~^
,
is
=
The
revolution threat
is
that
B
is
large relative to A.
only a limited ability to tax the rich in a democracy, and
place along the equilibrium path.
to
not.
place.
from the Kuznets curve
profitable for the masses to take over the
social unrest increased,
and the poor do
and a revolution takes
difference of this case
This implies that there
Condition 3 holds but Condition 5 does not. Then
means
This case
and attempts
is
to bring
it is
more
of production. Thus, a revolution will take
similar to pre-revolutionary Russia
more moderate groups, such
where
as Mensheviks,
power were unsuccessful.
Historical Perspective
4
Our theory
is
motivated by historical evidence. Here we
will
provide an overview, empha-
sizing the evidence in support of the following four features:
1.
Inequality was increasing before, and decreasing after, the extension of the franchise.
2.
The
as a strategic
3.
power before the franchise and extended the franchise
elite controlled political
move
to avoid a revolution or at least very costly political unrest.
Democratization was directly (redistribution) or indirectly (expanded education) a
key factor in the reduction in inequality.
4.
There are differences
in social conditions
which make some periods more conducive
to social unrest, and there are also differences in the level of organization of the masses
across countries which are important in determining political outcomes.
Our most
Germany
4.1
detailed evidence
is
from Britain, but evidence from Prance, Sweden and
also supports our model.
Inequality
Britain Data on income inequality
for the nineteenth
century are not extremely reliable.
However, a number of studies using different data sources on Britain reach the same conRoot (1996), Table
1.1.
18
elusion.
Inequality increased substantially during the
then started falling in the second
This picture
1870.
is
1
to
be sometime
is
and
after
of Lindert
not completely uncontroversial (see Feinstein, 1988).
taken from Williamson's (1985) Table 4.2 gives a representative picture:
Table
1
-
British
Income Inequality
Share of the Top 10%
Gini Coefficient
47.51
0.400
1830
49.95
0.451
1871
62.29
0.627
1891
57.50
0.550
1901
47.41
0.443
1911
36.43
0.328
1915
36.46
0.333
1823
A
The turning point appears
also consistent with the findings of Crafts (1989),
(1986) on wealth inequality, but
Table
half.
half of the nineteenth century,
first
similar pattern also emerges from earnings inequality data reported in Williamson
(1985) Table 3.2 where the Gini coefficient increases from 0.293 in 1827 to 0.358 in 1851
and
falls to
0.331 in 1901.
Other Countries While
tive survey, argues that
In
Germany
again the data are sparse, Morrisson (1997) in his authorita-
Germany, France and Sweden
inequality rose during the nineteenth century
peak around 1900. For example, Kuznets (1963)
per cent went from
declining to
31%
28%
in 1873-1880 to
in 1911-13.
1880, rising to 32.6% in 1900
inequality
all
fell
Dumke
and
rapidly during the
the income share of the top
the Kuznets curve in
32%
went through a Kuznets curve.
and most researchers place the
finds that the
in 1891-1900, stayed at
(1991) finds the
falling to 30.6
%
fallen
Germany peaked
32%
during 1901-1910,
same income share
to be
in 1913. Following the First
Weimar Republic. Kraus
5% had
income share of the top 5
28.4%
in
World War
(1981) records that
by 1926
by 6.2%. Overall, Morrisson (1997) argues that
in 1900,
went
flat
and started
to fall in the 1920's.
For France, Morrisson (1991, 1997) argues that inequality rose until 1870, with the income
share of the top 10 percent peaking at around 50%. However, inequality started to
the 1870's, and in 1890 the income share of the top 10 percent was
falling to
grew
in
36% by
1929.
Finally,
down
to
fall in
45%, further
Soderberg (1987, 1991) records that income inequality
Sweden, peaking just before the First World War,
during the 1920's and then falling rapidly thereafter.
19
levelling off or falling slightly
Franchise Extension and the Threat of Revolution
4.2
Britain In Britain, the franchise was extended
(and later in 1919 and 1928 when
women were
in 1832,
finally
and then again
allowed to vote).
in
1867 and 1884
When
introducing
the electoral reform to the British parliament in 1831, the prime minister Earl Grey said
"There
than
is
am
no-one more decided against annual parliaments, universal suffrage and the ballot,
The
I...
Principal of
my
reform
reforming to preserve, not to overthrow."
reform
is
is
to prevent the necessity of revolution... I
am
(quoted in Evans, 1983). This view of political
shared by modern historians such as Briggs (1959) and Lee (1994). For instance,
Darvall (1934) writes: "the major change of the
was the reform
of Parliament
Whigs. ..as a measure to stave
first
three decades of the nineteenth century
by the 1832 Reform Act, and
off
this
was introduced by the
any further threat of revolution by extending the franchise
to the middle classes." In fact, the years preceding the electoral reform
by unprecedented
political unrest including the
were characterized
Luddite Riots from 1811-1816, the Spa
Fields Riots of 1816, the Peterloo Massacre in 1819,
and the Swing Riots
of 1830 (see
Stevenson, 1979, for an overview).
The reforms
that extended political power from a narrow elite to larger sections of the
society were immediately viewed as a success not because of
or democracy, but because the threat of revolution
Lee, 1994).
some
ideal of enlightenment
and further unrest were avoided
(see
Before the 1832 Reform Act, the total electorate stood at 478,000 out of a
population of 24 million. Although the Act reduced the property and wealth restrictions
on voting and increased the electorate to 813,000, the majority of British people could not
vote. Moreover, the elite
contained
less
still
had considerable scope
for
patronage since 123 constituencies
than 1,000 voters (the so-called "rotten-boroughs"), and there
of serious corruption
and intimidation
of voters
which was not halted
is
evidence
in Britain until the
Ballot Act of 1872 and the Corrupt and Illegal Practices Act of 1883 which introduced
effective secret ballots at elections.
The
process of increased representation gained
momentum
with the Chartist movement
during the 1830's and 1840's. Consistent with our approach, leading chartists saw increased
way
representation as the only
growth
(see Briggs,
1959).
movement was again one
to guarantee a
more equitable distribution
of the gains of
In the meantime, the response of the elite to the Chartist
of preventing further unrest.
For example, during the 1850's
Lord John Russell made several attempts to introduce franchise reform arguing that
it
was
necessary to extend the franchise to the upper levels of the working classes as a means of
preventing the revival of political radicalism (Lee, 1994). In discussing the lead up to the
20
1867 Reform Act, Lee argues that "as with the
first
Reform Act, the threat
has been seen as a significant factor in forcing the pace; history was repeating
interpretation
is
supported by
many
of violence
itself."
This
other historians, for example Trevelyan (1937) and
Cowling (1967). The Act was preceded by the founding of the National Reform Union
in
1864 and the Reform League in 1865 and the Hyde Park riots of July 1866 provided the most
immediate catalyst
(see Harrison, 1965).
As a
result of these reforms, the total electorate
was expanded from
1.4 million to 2.52 million
and then doubled again by the Reform Act
of 1884
and the Redistribution Act
of 1885
removed many remaining
inequalities in the
distribution of seats (see Wright, 1970). Overall, in Britain the timing of franchise extension
corresponds quite closely to the peak of the Kuznets curve.
Other Countries
Weimar Republic
In Germany, democracy was established with the creation of the
in 1919.
There
is
no controversy amongst historians that
the threat of social disorder and conflict following the defeat in the
1943;
Abraham,
1986).
IV
coalition of "iron
rural areas
flat
and
to
Gerschenkron,
of Prussia
revolution,
had created a parliament, Germany was non-democratic
controlled by Junker landlords
rye" after the 1870's.
by the landlords
Even though, following the 1848
since 1900).
The 1848 parliament was
until 1919.
(see
was due
This date corresponds to the downturn of the Kuznets curve
(though inequality had been
Frederick William
War
this
and then by the
Moreover, voting was oral and controlled in
(see Gosnell, 1930
and Goldstein,
1983).
In France, before the revolution of 1848 property restrictions limited the electorate
to
about 241,000, about 0.75% of the population
(see
Cole and Campbell, 1989).
collapse of the regime led to a brief democratization which
of Louis
Napoleon
in 1852.
The
real spur to
The
was cut short by the coup
democracy was the defeat of the French
armies in the Franco-Prussian war of 1870, which created the Third Republic and the Paris
Commune
of the following year.
as Orleanist
emerged
in
is
and Legitimists
victorious,
this
tried to suppress worker parties.
is
In 1877, the Republicans
accepted to be the date for the establishment of democracy
France (see Carstairs, 1980, Cole and Campbell, 1989, Elwitt, 1975). Once again, this
approximately at the peak of the Kuznets curve.
Finally, in
til
and
This was followed by a seven year struggle for power
Sweden, while universal male suffrage was introduced in 1907
it
was not un-
1918 that true parliamentary government was introduced and the political power of the
Conservative Party and the monarchy curtailed. 1918, the year where democracy became
established,
is
once again at the peak of the Kuznets curve. Social unrest was again impor-
tant in these reforms.
The reform
in 1907
had been preceded by
21
strikes
and demonstrations.
In 1918, social unrest was
World War, the revohition
more
intense: while
in Russia
Sweden was not a participant
and the situation
in
Germany
in the First
forced the concession
of true democratic rights. Tilton (1974) records that in 1918 the Swedish Minister of
army and navy
characterized the sentiments of the
is
as "very revolutionary"
and
this
War
view
supported by Verney (1957), Castles (1973) and the essays in Strth (1988).
4.3
Redistribution
Britain The Reform Acts of the 1867-1884 were a turning point
state. In 1871
Gladstone reformed the
civil service,
opening
it
in the history of the British
and
to public examination
Liberal and Conservative governments introduced a considerable
making
it
amount
of labor market legislation fundamentally changing the nature of industrial rela-
meritocratic.
tions in favor of workers.
During 1906-1914, the Liberal Party under the leadership of
Asquith and Lloyd George introduced the modern redistributive state into Britain, including health
and unemployment insurance, government financed pensions, minimum wages,
and a commitment
to redistributive taxation.
As a
result of these fiscal changes, taxes
more than doubled
as a proportion of National Product
and then doubled again. In the meantime, taxation
also
in the 30 years following 1870
became highly progressive
Lindert, 1989). Consistent with these trends, Lindert (1994) has recently
ables measuring democracy, in particular voter turnout,
had a
shown that
(see
vari-
significant positive effect
on
the expansion of government expenditures on social programs (welfare and unemployment
compensation, pensions, health care and housing subsidies) in the period from 1880-1930,
again supporting the interpretation that democratization has been a key driving force of
the radical shift towards redistributive
fiscal
and
social policy.
Meanwhile the education system which was only open to the
elite
during most of the
nineteenth century became more and more open to the masses (see Schofield, 1973 and
Mitch, 1992).
First, school leaving
1899 and special provisions
age was set at 11 in 1893, then increased to 12 in
for the children of
needy families were introduced.
Finally,
the reform act of 1902 introduced public schooling as a duty of the government towards
its
people.
As a
result of these changes, the proportion of 10-year olds enrolled in school
which stood at a disappointing 40%
p. 207).
Many
in 1870, increased to
in 1900 (see Ringer, 1979,
educational historians argue that the democratization of British society was
the key driving force behind these changes
(e.g.
Simon, 1960).
Williamson (1985) sees the increase in the supply of
in inequality.
100%
skills as
the key reason for the
fall
Therefore, to the extent that mass schooling contributed to this increase,
22
the education policies were a key factor in reducing inequality.
Lindert and Williamson (1985) "the rate of
This
is
summed up by
deepening reached impressive
skill
levels in
the era following the educational reforms of the 1870's, coinciding with the drop
Britain's
Kuznets Curve." Moreover, the data already reported
down
in the previous subsection
suggests that the reduction in income inequality was faster than the compression in earnings
inequality which
is
consistent with the view that increased
and more progressive taxation
played a key role in reducing inequality.
Other Countries
In Germany, during the period where the Kuznets curve peaked,
primary school enrollments were
by the creation
of a welfare state
and Baldwin, 1990).
standards
While
this
by Bismarck
is
which began
well
known,
social conflict
in the early 1880's (see
was met
Tampke, 1981;
was a small amount of redistribution by contemporary
seems to have been enough to stop the
it
in inequality
initiated
10
However, as
flat.
rise in inequality.
Moreover, the
fall
in the 1920's coincides with the large increase in redistribution
by the Weimar state
(see Flora, 1983). In France, as in Britain,
coincided with important educational reforms
11
.
democratization
In 1881 the government abolished fees in
public primary schools, and in 1882, 7-year compulsory education was introduced.
primary enrollment rate increased from 66%
in 1863 to
82%
in 1886.
The
Moreover, central
GDP increased by one third from 9.4% in 1872
12.4 % in 1880 (Flora, 1983). For Sweden, as for
government expenditure as a percentage of
(a figure itself inflated
Germany, there was
by the war) to
little
impact of democratization on educational enrollments, however,
Lindert's (1994) data shows that before 1920 there
while after this date
4.4
An
jumped up
at all in
Sweden,
sharply.
Revolution Opportunities
important part in the timing of
as indicated
10
it
was no redistribution
political
reform was played by increased inequality
by the coincidence of democratization with the peak of the Kuznets curve.
which has received much recent attention in the context
Campos and Root, 1996). Whether or not land reform
is attractive to the elite, and acceptable to citizens depends on where revolutionary threats come from.
Typically it is urban workers who pose the biggest threat to regimes, and they were the target of Bismarck's
reforms, not rural peasants. In Germany the proportion of the labor force in agriculture in 1870 was around
45% (see Flora, 1983) while for Britain it was already down to 20% by this date (Michell, 1962). In South
Another possible method of
of the "East Asian Miracle",
is
redistribution,
land reform (see
was around 80%.
from the historical experience of the world's 25 largest nations, ...,
a major commitment to mass education is frequently symptomatic of a major shift in political power
and associated ideology in a direction conducive to greater upward mobility for a wider segment of the
Korea and Taiwan
u Easterlin
this percentage
(1981) notes:
"to judge
population."
23
Equally important in determining the timing of the extension of franchise were economic
depressions and wars.
In Britain, the
move towards democracy
a sharp business cycle downturn (Lee, 1994).
slump (widely recognized
into a prolonged
to
was spurred by
in 1867
Also after 1873, the world economy went
be the worst of the nineteenth century),
which caused increasing distress over the next decade. In France, the Franco-Prussian war
was
Commune and
of crucial importance in leading to social unrest, to the Paris
War appears
In Sweden, the end of the First World
Third Republic.
And
the revolutionary sentiment (Verney, 1957, and Castles, 1973).
War was
the defeat in the First World
to
to the
have increased
finally, in
Germany,
instrumental in creating social unrest and to the
founding of the Weimar Republic.
Social unrest
was
in
(a point stressed
Germany was by
predicts that
Germany during
as strong in
the mid nineteenth century as
and France. However, while there were no strong
in Britain
and France
was certainly
by Stephens, 1989,
elite
should have had more
by promising future redistribution.
This
socialist parties in Britain
example), the Social Democratic Party
party in Europe at that time.
far the largest left-wing
German
for
democratization in Britain and France, in Germany the
first
without a real transfer of political power to the working
classes.
Our model then
dealing with social unrest
flexibility in
While there was
consistent with the facts.
is
it
welfare state was instituted,
Extensions
5
In this section
we
will informally discuss
which are relevant
for the
Among
Heterogeneity
there
is
case,
H =
model
of Section 3.
the Rich
a distribution of asset levels,
A/if
t
except that
+
now
(1
—
A)
/
hdG
the tax rate
suppose that Gt(h)
is
t
some
{h).
G
t
{h)
The
may be
skewed to the
It is
extensions, focusing especially on those
12
straightforward to extend the model so that
among
the rich, with lower support h
rest of our setup
positive even
and
results
when the
right. In this case, the
elite
median
>
1.
In this
remain unchanged,
are in power.
rich agent
would
First,
like
a
zero tax rate, and none of our results need to be modified. In particular, given decreasing
human
returns to
However,
if
G
t
(h)
capital, all rich agents converge to the
is
skewed to the
left,
same
G
t
(h)
is
sufficiently skewed,
human
then this tax
may be
or not
depends on
We
are grateful to the referees for bringing out
some
24
this tax rate.
high enough to ensure accumulation
by the poor and avoid the revolution constraint. The interesting feature
12
capital, hss-
then the median rich will set a positive tax rate.
Now, whether the revolution constraint becomes binding
If
level of
is
that in this case
of the issues discussed in this section.
amount
the
of conflict
among
the elite has an impact on the conflict between the elite and
the poor.
Among
Imperfect Substitution
and the poor supplying unskilled
rich agents supplying skilled labor
substitution between these two types of labor. For example:
Y =
In this case, differences in A would have another, perhaps
more
When
likelihood of revolution.
would translate
A
income
Costs of Redistributive Taxation
see that
income
if
this
level
is
make our
be without
this inequality
.
A(Xh^) a ((l
—
A)h[)
1-Q
.
on the
intuitive, effect
point in the simplest model,
distortions. It
relaxed, then a democratic society
Yg S < Yg S Whether
labor, with imperfect
inequality.
In order to
redistributive taxation to
assumption
t
can think of the
high, unskilled wages will be depressed so a given h Tt /h pt
is
into a higher level of
we have assumed
We
the Rich and the Poor
is
strict or
is
straightforward to
would actually tend to an
not will depend on a number
of other features which are not crucial for our story but would strengthen the conclusion
that the lack of robust correlation between democracy and growth
Targeted Taxes and Transfers
We
have so
far
may
not allowed the transfer
lump-sum taxes used
want to use
their political
Laws
or
light).
power
Combination Acts which outlawed unions
However, in doing
this
when
to subsidize production, the elite,
to redistribute in their favor (one
to be
specific
would
can interpret the Corn
in the nineteenth century Britain in this
they have to respect the revolution constraint again: a high
this case the elite will often tax the
power and may
is
that in
masses just enough to make them indifferent between
the existing system and a revolution.
elite is in
t
in power,
tax on the poor would make a revolution worthwhile. The interesting implication
when the
T
With person
negative or person specific, so the elite preferred no intervention.
transfers or
not be surprising.
fit
This case makes increasing inequality more likely
the example of some African cases where state power
appears to have been used more often to redistribute from one group to another.
Why
is
Democracy
Irreversible?
franchise they cannot rescind
it.
coups which have restricted the
the question of
why
This
is
We
have assumed that once the
elite
clearly unrealistic, since there are
political participation of the masses.
extend the
examples of
This issue also raises
the poor are initially excluded from the political process. Part of the
answer appears to be that
political
power depends on wealth. The
elite initially
are
much
wealthier than the masses, and can use their wealth in order to control the political process.
Once the
and
franchise
is
extended, the distribution of income and wealth becomes more equal,
this implies that the
process,
and a return
masses now possess the resources to take part in the political
to autocracy
becomes much harder.
25
We could easily
introduce this in
our model by making
/x
a function of the income level of the poor, for example, n(y p ) (with
p
the restriction that
)
fj.(y
<
p,
so that democracies do not necessarily lead to a revolution).
In this case, once the franchise
organized, so even
if
inequality
is
extended and yp increases, the poor are much better
falls,
the threat of revolution does not totally disappear.
This reasoning also suggests a reason
why South Korea and Taiwan may have
Our simple model
the democratization process over the past ten years.
should remain an autocracy forever.
some point
to income, at
ji
However,
With
predicts that they
of political
will increase sufficiently so that the elite
franchise, despite the low level of inequality.
that, as in the case of
we think
if
this modification,
power
become
our approach predicts
South Korea and Taiwan, economies which start with relatively low
sufficiently wealthy, social unrest
Forward Looking
2),
as related
have to extend the
inequality should experience high growth and no democratization for a while
the masses
started
and then once
should force democratization.
Elites Finally, in the model of Section 3 (as opposed to Section
the agents are "myopic" because they live only one period and do not care about the
dynamics
after they die. If
we introduce more
general kinds of altruism or long horizons
for the agents this aspect will change. In this case,
accumulate slower than otherwise
the
members
A(l
—
some
fj)/fi,
of the elite
may
one might conjecture that the
realize that
H* However,
than
.
they collectively have assets worth
if
the important point to note
kind of coordination from the "state"
he would ignore
his
may
in order not to hit the revolution constraint. Intuitively,
the revolution threat will become active. So they
level less
elite
If
.
member
each
impact on the aggregate stock of
accumulating more. Such behavior by
all
the
may
is
of the elite
stop accumulation at
that this requires
is
some
deciding individually,
and thus would
assets,
H* =
"free-ride"
members would take the economy
by
to H*.
Concluding Remarks
6
This paper has offered a simple model of political transition and reform, and investigated
the implications for the dynamics of growth and inequality.
this
paper
are: (1) it explains
why
the rich
elite
may want
the fact that this implies higher taxation in the future; (2)
The two main
contributions of
to extend the franchise, despite
it
offers
a
new explanation
for
the presence of a Kuznets curve in the development experience of Western societies, which
appears to accord well with the data.
The emphasis
equilibria
in this
may have
paper on political reform as a way of changing future political
a number of other applications.
of franchise extension in our
model
is
that
it
26
changes
Recall that the important feature
who
the median voter will be in
the future, and thus commits the
elite to
future redistribution.
and
future political balances. For example, electoral systems
institutions influence political equilibria,
policies.
Also, programs differ in
countries, entitlement
of whether there
was a commitment motive
issues
when
it is difficult
commitments
as
to certain
This raises the question
these programs were instituted.
treated satisfactorily in this paper. First of
although Britain, Germany, France and Sweden
U.S.
relations with international
difficult to cut.
in play
we have not
affect
can be reversed. For example, in most
easily they
programs appear to be very
There are a number of
all,
how
and thus may act
Other reforms also
fit
our story, the U.S. does not. In the
to get a picture of the extent of suffrage because of a plethora of state
level restrictions (on the basis of wealth,
property ownership, race
etc.,
see Williamson,
1960; Crotty, 1977). Nevertheless, the best guess seems to be that by the 1850's, around
50%
Such a
of adult white males could vote.
The
was
sufficient to generate
Inequality, however, increased until
substantial redistribution in other countries.
1930 and then started declining.
level of suffrage
downturn of the Kuznets curve
fact that the
again related to increased redistribution, which followed the Great Depression,
aging for our theory, but
easy to determine.
We
why
around
is
encour-
is
redistribution started 80 years after democratization
number
conjecture, together with a
once
is
not
of historians, that the U.S.
was
exceptional, especially due to high levels of immigration.
Historical sociologists such as
Kaelble (1986b) argue that U.S. citizens saw themselves as very upwardly mobile, partly
because the lower ranks of the society were taken by migrants. This
may have changed
in
the late 1920s with the depression (and the fact that immigration was severely curtailed
in the 1920's).
fit
Even though these arguments may
the U.S., more research
more
likely
when
general,
when
inequality
is
is
inequality
required.
is
justify
why our
simple model does not
Second, our model predicts that democratization
however ignores another important
high. This
effect.
In
who
will
be
taxed more heavily. This implies that the impact of inequality on democratization
will
be
is
high, democratization
determined by the interplay of two offsetting
is
forces.
to use a "repression" strategy, such an extension
American and African
quite
damaging
Third,
may be
countries. Finally, there are
major
to the elite
we have not allowed the
relevant for a
number
differences in the
elite
of Latin
form of
redis-
tribution across countries. In Britain, education increased substantially after the franchise
due to increased government support. In contrast,
via the welfare state.
and whether the same
It is
in
Germany, early redistribution was
important to understand what might cause these differences,
forces are also important in shaping the differences in the extent
and form of redistribution we observe today.
27
Appendix
7
We now
More
analyze the model of Section 2 without the restriction to Markovian strategies.
we look
specifically,
for
cutoff probability of state
p
h
subgame
<
q**
,
such that when q
q*
We
perfect equilibria.
>
will find that there exists
q**,
there will be redistribution
without democratization which prevents a revolution. In contrast when q
when p = p
equilibrium will feature the extension of the franchise
note that
First,
V
ends with
P
a (p
h
,E\.,.)
1
E\.,
,
elite are
.)
game
=
=
(p
at time
=
=
1,.)
(p
t
without a revolution. 13
Next, note that after
0).
to their
minimum
=
only
1)
payoff, since r
if
=
(f> t
=
f in
VP (R) > V P (D).
and ignoring revolution, the
1,
all
perfect equilibrium,
irrespective of the history of the
game up
to this point.
and r
0,
by the masses other than
V p (p k
r
,
,
E\(f>
when they
=
0,
cr
p
(p
,
E\(f>
will play
=
p
Suppose q
1
<
play p t
2 ensures that this inh
p
(p
,
=
E\(p
Now
).
=
0.
ps
=p
f)
elite in state
h
where f
<
r
f.
and T (p s ) > f
(p
all
= 0)
of the
p
t
1 if
=
1 if
and only
V P (R) > V p (p h
t
,
if
E\<f>
VP (R) > V p
=
0,
h
(p,
at time
elite:
t.
=
h
al(p ,E)
p}, for all s
E\<p
=
0,
=
rr )
r r ).
t
Markov
be the tax rate
)
Consider the following candidate equilibrium
=
=
=
(<j> t
For the masses, a (pj ,E\(j)t
ps
,
that in this case, there were no
1
P
if
=
Then, in any subgame perfect equilibrium, a P (p ,E\4>
Recall from Proposition
strategy combination. For the
=
=
consider this.
T
0,t[
.)
So we have pinned down
r
Perfect Equilibria with redistribution and no democratization. Let T (p
chosen by the
1,
h
with probability
q*.
0,r
cr
Therefore,
t t ) be the continuation payoff of the masses, conditional on
t t ) will only put positive probability on p
and
=
h
future periods.
Assumption
subgame
Let
then effectively the game
t,
This immediately implies that
equality never holds, thus in any
strategies
.
t
down
aP (n h ,E\(j)
the only
q**,
= p AH/X(l — (3), Therefore, in any subgame perfect equilibrium,
= (p = 1) only if V P (R) > V p where V p is the payoff of the masses in
P (R)
the continuation
of (fjL
<
h
t
the masses initiate a revolution at time
if
a
<
t,
and
(p
=
= f) and al(p ,E) =
T
0,r[) = (p = 0) if T (p
> f if
= 1) otherwise. Then, the payoffs
0,r
r
l
(<fi t
£
s)
in this candidate equilibrium are given by:
Vj (ph
V j {p
for j
,
l
,
h
E)
= (l- r)Ah j + tAH +
[qVj (p
E)
= (l-
[qVj {p
f)Ah?
= p and r. Now define f
+ TAH +
such that
V p (p h
,
E)
,
h
,
E)
+ (l- q)V
E)
+ (l- q)V
— V P (R).
f
<
We
to time
,
l
(p
,
E)]
(9)
E)]
(10)
all
2.
subgames. Next, we
now using <Tj instead of er, which stands for a conditional on the public history of the game up
The public history includes all past actions (but not mixing probabilities when these are used).
are
t.
J
l
(p
r exists by Assumption
Therefore, the above strategies are best response for the masses in
13
j
28
need to check whether they are best response
h
tax rate in state
0,t[
for the elite.
Clearly,
if
the
,E), this will immediately cause a revolution, thus
(fx
elite
reduce the
=
h
T
a (n ,E)
t
((f) t
=
= f) is optimal conditional on the history up to time t characterized by r r (fi > f
= n h and T r ([i > f if
— ji for all s < t. In contrast, if the elite deviate from
= 0, t[ = 0), this will not cause a revolution
= 0, r r = f) to er[(//', E) =
E) =
s)
l
if fi s
(?l(fA
((f> t
,
immediately.
elite
cr
',
(ii
t
E)
,
=
E\(fi
t
((f) t
only do so
h
T
can play
,
f
It will
always a v (\i h
The
fi s
s)
l
1,
=
=
when the
state changes to
h
(fx
But
,E).
in this case, the
= 1) and as we saw above, the best-response of the masses is
(p = 0) irrespective of the history of the game up to this point.
((fit
.)
payoff to the elite from following this deviant strategy starting in the state (n ,E)
l
V3V
,
E)
= Ah r
+P
r
[qV (D)
+
(1
-
l
q)VJ(fi
,
E)
Therefore, the above candidate equilibrium strategy combination
equilibrium
and only
if
if
V r (^f,E)
given by
(9)
and
(10)
is
is:
is
a subgame perfect
greater than or equal to
P)
= ^-ffi-q)
lt is straightforward that if q = q*
V r (^i\E) > VJ(/i ,E) and
r
r
at q = 0, V (fi ,E) < VJ(fJ,E). Also, V (fi ,E) falls faster in q than Vj(ti ,E). So there
r
exists q**, such that for all q < q**, V (fi ,E) < VJ(fi ,E), and there exists no equilibrium
l
VJ((i ,E)
l
-
,
l
l
l
l
l
with redistribution and democratization.
Finally,
when
>
q
q*,
the
ratization continues to be a
the above,
and
fi t
we can
= n
indifferent
l
,
but
Perfect Equilibrium with redistribution
subgame
perfect equilibrium,
and no democ-
and with a similar reasoning to
construct others which feature some redistribution both in state
all
these equilibria have the
same structure
between revolution and no revolution
payoffs to the elite
8
Markov
in the state
fi t
=
1
f-i'
of keeping the masses just
(/x
h
,E), thus give the
same
and the masses.
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