Inequality and Growth

NBER

WORKING

INEQUALITY

AND

Ronald

NBER

NATIONAL

PAPER

GROWTH

B6nabou

Working

BUREAU

SERIES

Paper 5658

OF ECONOMIC

1050 Massachusetts Cambridge,

RESEARCH

Avenue

MA 02138

July 1996

This paper is forthcoming

in the NBER Macroeconomics

Jordi Gali and Julio Rotemberg

grateful for their detailed comments as well as to Alberto Raquel

Femandez,

Alesina, Herschel

for providing

assistance

from the C.V,

research program

Grossman,

1996

by Roland

Fluctuations

B6nabou.

Torsten

Persson

acknowledged.

and Growth.

All rights reserved. permission

Bertola,

I am also Rios-Rtill,

Patrick Bolton,

and Thomas

Piketty.

me with their data set, and Tim

the Luxembourg

Bureau of Economic

paragraphs, may be quoted without explicit is given to the source.

series from

to Jess Benhabib,

Perotti and Jos6-Victor

Bernard, Giuseppe

Newman,

Starr Center is gratefully

in Economic

Roberto

Andrew

Andrew

I am indebted

at early stages of this project.

and Lynn Squire for providing

me with specific

author and not those of the National O

to my discussants,

Abhijit Banerjee,

I also wish to thank Klaus Deininger Smeeding

Annual.

for helpful conversations

Income

Study.

Research

This paper is part of NBER’s

Any opinions

expressed

are those of the

Research.

Short sections provided

of text, not to exceed

that full credit, including

two

O notice,

NBER

Working

Paper 5658 July 1996

INEQUALITY

AND

GROWTH

ABSTRACT

Using

two unifying

main theories

linking

The first model for explicit

models

income

integrates

and an empirical

distribution

the political

of

simultaneously investment

redistribution depress

captures the essence

The second

accumulation.

groups’

rent-seeking

abilities,

political

power.

conflict,

the empirical Finally,

empirical

issue:

is surveyed

and discussed

the possibility

of multiple

steady-states

are cross-country

is there convergence

B6nabou of Economics

New York University and NBER

NY

10003

differences

in inequality

not only in first moments

the growth costs policies

the wealth

constraints

which

impede

of the prisoner’s

dilemma

which

reduces the security of property

rights,

rate is shown

to fall with interest

rich and poor.

in the relative

of political

It allows

such

growth

evidence

distribution?

New York,

but inequality

evidence.

schooling:

version

conflict

between

the

or public

as well as with the gap between

For each of the three channels

analysis.

Department

is a growth

The economy’s

per se that matters, however,

Equivalently,

and ameliorate

empirical

capital markets theories.

the tradeoff

land reform

of theories where sociopolitical

discouraging

as well as the relevant

and embodies

model

this paper presents and extends

and imperfect

taxes,

incentives

thereby

Roland

economy

through

savings

by the poor.

inequality

and growth,

departures from perfect democracy

and benefits

exercise,

It is not income

distribution

economy,

of earnings

capital markets

in conjunction

and

and social

with the theoretical

leads me to raise and take up a new permanent,

or gradually

(GDP per capita),

narrowing?

but convergence

in

1

Introduction

1.1

Korea

To introduw beginning respect

the theme

of his article.

to all major

In the early 1960’s,

-nomic

manufacturing,

but in exports

and manufactures, antury

the Philippines

The

enrollment.

Given

Korea

nearly

If one looks beyond

identical

population,

had a somewhat

starting

points,

growth

urbanization,

of primary

about

at the

primary

share of GDP

how can it be that

averaging

(1993)

were similar with

higher

had the same proportions

“miraculous”

at about

in

commodities over the next

6% per annum,

while

2%?

first moments,

shown by Table 1, the distribution lGini(%)ll

per capita,

Philippines

both muntries

experienced

stagnated

GDP

All

raised by Lucas

South Korea and the Philippines

aggregates:

school

Not So Similar After

I shall revisit the puzzle

of this paper

and secondary

quarter

circa 1960:

and the Philippines,

however,

initial conditions

of income was considerably

Q1 [

Q2

I Q3

I

Q4

I

Q5

were in fact quite different.

more unequal I Q3+Q4

As

in the Philippines:

I Q5/Ql

I Q5/(Ql+Q2)

1965

Korea

34.34

5.80

13.54

15.53

23.32

41.81

38.85

7.21

2.16

Philippines

51.32

3.50

12.50

8.00

20.00

56.00

20.50

16.00

3.50

Korea

33.64

7.39

12.29

16.27

21.81

42.24

38.08

5.72

2.15

Philippin=

45.73

5.20

9.10

13.30

19.90

52.50

33.20

10.10

3,67

1988

Table 1: Korea and the Philippines Sours:

Deininger

The Philippines’ seventeen

Ginis, or 2.5 among

points

higher,

East-Asian

top 2070 to the bottom

data set; Qi denotes

about

characterized

1The year

regime.

Ferdinand

1965 is the earliest

based on the same survey method

land ownership:

is for gross personal

income,

quintile.

in the world distribution

the ratio of the income

the Gini coefficient

be blamed

was first elected

one for which data household

for

was of

share of the

for farmland

was 38.7 for

in 1961 and 1960 respectively. 2 This greater concentration

Marcos

(gross

of the i–th

40% was about tloice m la~e in the Philippines,

and wealth, which persists to this day, cannot

the Marms

deviations

Most strikingly,

20Y0, or even to the bottom

the share

below that of Korea. ] The Gini coefficient

1.8 standard

countries.

Korea and 53.4 for the Philippines income

(1995a)

Lorentz curve lay everywhere

percentage

Similar disparities

and Squire

on the “kleptocratic”

president

of

nature of

in 1965, and declared

a state

both countries are available. Moreover, these figures were

income),

making

them comparable.

The 1988 Philippine

but very close to the 1985 figure which still [lsed household

number

income.

‘The sourm for land Ginis is Taylor and Hudson (1972). The twelvepoint gap corrwponds to about one standard deviation. While it is common knowledge that Korea implemented a land reform following World War II, it may be worth mentioning that the Philippin- al= had ib own around the end of World War I, during the American holdings

occupation

were purch~ed

was not as egalitarian became

r~ncentrated

period.

Following

the di=tablishernent

and redistributed. as in Korea, during

where

The relatively individual

the following

of the Catholic

Church,

high land Gini for 1960 suggests

holdings

forty years

1

were limited

to 3 hectarm,

a large part that either or that

of its land land reform

land ownership

of emergency period

ordy in 1972. Preceding

were two presidents

background

whose

him in power at the end of the US–assisted main policies

notis as seeking to “expand

reform programs, Of couw

and develop

Table

Philippine

and diversify

1 does not mnstitute

cert airily not the sole reason–

are described

in the US State

ties to its Asian neighbors,

Department’s

implement

domestic

the economy”. proof

that greater

why the “miracle”

But the facts which it documents

ranstruction

omurred

initial

equality

in one country

was the reason – and not the other.

do suggest that the answer to the puzzle may lie outside

the

represent ative agent framework.

1.2

Empirical

%gularit

ies

South Korea and the other Eas-Asian pines, but to Latin American ventional

wisdom

a significant

to formal empirical

evidence,

(1994),

Table 2 summarizes

typically

(twenty

include:

by mlumn

raises the annual growth

gap of about do=

not mme

and Korea, non–linear

rate of GDP

awith

to eontribute

negatively

(e.g.

is detrimental

for the growth

However,

result

(1996),

observed

several models

of equilibria.

that when male and female stock who also rliseusses

2

possible

(b) the

points.

regressions, distribution,

The magnitude

decrease

On one hand it amounts

differential

These

growth,

deviation

which is far from inconsequential,

These

ratios; as shown

measures of income

to long–run

a one standard

leading to a multiplicity

Barro

(1) mrresponds

and significant;

dummies.

per capita by .5 to .8 percentage

or East Asia and Latin America.

of the puzz]ing

and by

and several controls.

of growth rates found in most samples.

close to accounting

the ~xcePtion

(c) regional

with many different

initial inequality

25% after 30 years,

effect, possibly

Column

is always negative

positive;3

across most studies:

deviation

regressions

or proxies in the form of initial school enrollment

large or small may be in the eye of the beholder. 45% of the standard

growth

the paper.

on initial inequality

whose coefficient

run over a variety of data sets and periods

of this effect is mnsistent

(1994) ancl Persson

where the average growth rate of per capita GDP over some

(8) this effect is systematically

message:

from anecdotal

recent studies of the links from in-

I shall refer to it throughout

(a) initial inmme,

deliver a mnsistent

in the later

testing of the main theories.

years or so) is regressed

initial stock of human capital,

has moved

in cross-country

the main results from twent y–three

to the basic, reduced form regression,

con-

and land in the first group played

by the findings of Alesina and Rodrik

(1996) methodical

economists’

the high levels of wealth concentration

effect of inequality

equality to growth or investment.

long period

of income

In recent years the literature

impulsed

not to the nearby Philip-

It has long been part of development

whereas

to growth.

(1994) of a negative

(1992),

are usually contrasted

that the very equal distribution

were a serious impediment

Perotti’s

countries.

role in their take-off,

and Tabellini

“dragons”

in inequality

Whether

to between

this is

30% and

It also implies an income On the other between

hand,

the Philippines

in the literature

predict

In that case small differences are distinguished,

explanations).

this

the latter

a in

aPPears

initial inequality regressions,

can have marginal

and significantly

The inclusion Sometimes capital

is included,

sub-Saharan presenm

insignificant,

are added.

of these controls, negative

link between

long–inn

(c) typically

as in Benhabib and Squire

with inequality,

income distribution

in Africa

need to be explained, distributions

1.3

when dummies

on inequality,

for Latin America

remains

si~ificant

in and stocks of secondary

and in some of the theories through

education

discussed

have a

below

the

investment.

comes from the high levels

These persistent

in the direction

and

even in the

human capital

variation in inequality

Latin America.

and in fact point

mentioned

(1995b)

and growth arises precisely

and, particularly,

the coefficient

and Spiegel (1993) when the stock of human

In any case, enrollments

Note finally that a large part of the cross-country observed

redums

In most other studies inequality

correlation

by linear

outcomes.

(b) and especially

or in Deininger

Africa

substantial

influen~

of mntrols

it becomes

effects well in excess of the average slope estimated

inter–regional

of the models

differences

with multiple

long–run

above,

Overview

This paper presents well the evidence the empirical mnomy

and extends

on their relevance.

literature,

capital

the security of property

arise solely through Rodrik

can affect output

to inequality,

I start in Section

(1994),

theories.

the balance

Persson

The first model

and Tabellini

integrates

the political

of income

system

(Bertola

(1993),

The idea is that by lowering

the income

investment.

here, which combines mechanism

features of Persson and Tabellini

but also formalizes

there is a role for productive

departures public

with the degree of pr~wealth wit h a general aveat, differentially,

Compared

on redistribution

impact

in left–wing

4 See Fields

~owth

curve

democracy,

(1994) hypothesis.

The

one vote, ideal.

I also provide

affects democracies

income

disparities

model

(1995a),

in this class of models

system.

and growth only in right–wing

or populist

and Jakuhson

the Kuzneb

investment,

bias in the political

to a perfect

(1994) and B6nabou

from the one person,

on the issue of whether inequality

impact

support

discourages

effects

Alesina

the pressure

in turn,

to the

(whether

and distributional

average, greater inequality

This,

and

(1955) hypothesis.4

median voter or pivotal middle class relative to the national for rdstribution.

of

rather than on reverse effects from the level

in the political

(1994)).

as

a survey

are converging

on how the distribution

where asset markets are complete

of power

models,

section asks whether countries

growth,

and growth,

one deals with social conflict

It thus barely touches on the Kuznets

2 with theories

distribution

two unifying

The second

The paper focuses primarily

or endogenous)

of development

markets

income

through

exercise.

rights. The empirical

same level of inequality.

linking

This is done

and an econometric

and imperfect

exogenous

the main theories

and

of the

increases developed

displays this

Whether

or not

always increases

new results,

together

and non–democracies

are shown to have a lesser

or wealth–biased

regimes,

and a greater

ones. for a recent

review

of this issue w well as some new evicleuce,

which do=

not

In S~tion nomic

3 I turn to another

implications

but simply

set of theories,

due to imperfections

“turn off”

With decreasing

increase total output of land reform, to depressed

or growth.

public

Indeed, the main idea in this literature

incentives

the decentralized

equilibrium

Ades

(1993),

for which uninsurable

and Bolton

with the politics

paper

(1996),

(1994),

nomic effects of distribution

Fernandez

(Galor

immunities

and Rogerson

common

principle

equilibrium Section of property and poor

(1994), Maskin and Kremer

predatory

discouraging

at the expense of Grossman

(1994),

of the prisoner’s

dilemma

which captures

the essence

sustainable

seeking abilities,

per se, but inequality

CIWS, mntrary

disparities

to common

degTee of democracy

conflict

in con-

equilibria,

to explain

the

a variety of general

reduces the security

when the gap between to engage

of property

(1995),

Tornell

and Rustichini I propose

them.

and Velaco

(1996).

gTowth version The economy’s

to interest

groups’

It may then be profitable

and political

is not part of the story

interpretation,

As in the case of taxation,

(1992),

Only the lmt two

land reform, eclucat ion subsidies,

of earning

or

rights is the main

of this class of models. related

rich

in rent-seeking

here a simple

or uncertainty

4

I

above,

In particular,

between

distribution

in this

as well.

the analysis reveals that what really matters is not income

in the relative

instability

(1996b),

of new propositions

arise, through

to be negatively

transfer wealth to the poor through

More generally,

out that actual

rate is shown

as well as to in~me

rich to collectively protection.

growth

(1996a),

I then use this example

and Kim (1996) and Benhabib and growth.

Durlauf

long–run

Acemoglu

link inequality

sorting of agents into

can lead to multiple

The security

explicitly

and

the macroeco-

The results obtained

have a greater temptation

(1991),

Verdier

of credit constraints

accumulation.

of the former.

B6nabou

how the mmbination

mentioned

however,

maximum

(1994)).

based on the idea that sociopolitical

the latter presumably

Tornell (1994), Grossman

(1996b),

steady–st at e distributions

in several of the models

rights, thereby

activities

system

(1993),

class of models

a number

rates and levels of inequality.

4 turns to theories

focus of the models

papers,

political

by which multiple

feedbacks,

and Verdier

growth requi i-es some (interior)

democratic

(1993),

market incompleteness

by, the enciogenous (1993),

markets case. I also demonstrate

in growth

widens

(B6nabou

is

Some papers focus on

and Newman

In a related

of this entire set, and include

and a less than perfectly both

(1995a)).

costs due

issue in the literature

while others combine Saint-Paul

can

these growth benefits

and their traditional

Banerjee

arise from, or are magnified

explain for instance why maximizing

differing

(1996)),

or other “clubs”

between

The other central

(Perott i (1993), B6nabou

(1996),

are representative

trast to the complete

transfers,

(1993),

which starts with

the efficient amount of

shocks are of the essence.

and Z.ira Piketty

of redistribution

Saint-Paul

homogeneous

or other progressive

as before

is higher, so that redistributions

the tradeoff

for savings or labor supply.

mobility,

Aghion

prevent the poor from undertaking

My model embodies

schooling

of wealth has macroeco-

I use the very same model

returns their marginal product

intergenerational

(1996a),

in asset markets,

the loan market.

Loury (1981) is that credit constraints investment.

where the distribution

power.

told by most

rent– for the

or trade inequality

I also point models

growth is reduced

in this through

a decline in the expected Finally,

return on investment,

the possibility

of multiple

due to a higher threat of expropriation.

long–run

earlier leads me to raise in Section 5 an empirical are count riea converging Equivalently,

distributions question

model

once

new data set put together convergence

some interesting

puzzles,

The general strategy are thus stripped

it is enriched

by Deininger

in distribution.

Although

including adopted

2

Economy

to be developed

omy and imperfect generations

capital

the main ideas.

-

shocks?

Using

a

pass at this issue of uncovers

in Ginis.5 and unification.

The models

to the richness and realism of the literature, These are briefly discussd

for further research.

with Complete

markets theories.

distributions

to resolve the issue this exercise

in the concluding

All proofs are gathered

in the appendix.

Markets

here and in the next section

families, indexed

I make a fist

differences?

by most versions

idiosyncratic

of mean–reversion

which contribute

before turning to directions

The model

and Squire (1995a)

some evidence

of many elements

Political

as would be predicted

with uninsurable

it is insufficient

permanent

of their income

in this paper is one of simplification

but are not essential to conveying section,

or are there

not only in the first moments

GDP per capita– but also in the second one (and higher), of the neoclassical

discussed

which has not been taken up previously:

to the same level of inequality,

is there convergence

and history~ependenm

will bring together

There is a mntinuurn

by z E [0, 1]. The utility of a member

the political

of non–altruistic i in generation

econ-

overlapping t is

(1)

where ~ and d; denote consumption with resources

W;, distributed

invest in human or physical

when young and old respectively.

independently

capital according

This person is born endowed

across agents with mean wt = E[wj].

Agents

can

to the technolo~ (2)

where r is mnstant income.

and O < ~ S 1; k; is the amount

Note that individuals

can interpret through

face decreasing

investment.

The higher the general level of basic

quality.

sometimes income

Another

work on the general

used as an imperfect

which

technolo~

pretax

is linear.

One

which can be supplemented

skills, the easier it is to develop within a given generation,

or in

can be omitted.

5The paucity and sometim= poor quality of international of data

capital,

I shall focus for a while on what happens

which case time subscripts

as in all empirical

and y: is second-period

returns but the aggregate

w: as agent i’s basic level of skill or human

acquire new knowledge.

here,

invested

isues;

problem proxy),

see Deininger

data on income

is the lack of almost even

though

in mmt

is determinant.

5

distribution

and Scluire (1995a) any data

theories

remain

and Perotti

on the distribution

it is this distribution

binding constraints

(1 W)

for discussions

of wealth rather

than

(land

is

that

of

2.1

Savings and Intragenerational

There is a frictionless other,

credit market where agents in each generation

at some endogenoua

there is a government

inter~t

rate ?. The amount borrowed

who redistributes

case of linear taxes solutions

Growth

and focus

smnd-period

instead

by i is denoted

income.

on a simple

log-linear

borrow from and lend to each

I depart scheme

bi ~ O. Finally,

here from the standard which

will yield

explicit

and missing capital markets. G Let post–t ax and transfer income be

with both perfect

(3)

~i = (Yi)l-T(i)T! where the break-ven

income level ~ is defined by the balanced

~l(yi)l-T(j)7dz

=

I Note that the scheme the maximum

with free disposal

imperfectly

---

Z. Given an expected

everyone

democratic

regimes,

= p“ = p~(l

has the same second-period

GThis scheme

– ~)(w/k)l-D(w’

PP(l – ~)w

from the standard 70ne

markets.

scheme

but none of the essential

(lW5a)

one implies that –

+ bi – k).

condition

J: bi dz = O yields:

(6)

of aggregate

resources.

Consequently

take place

in equilibrium.

markets is the tltmat of expropriation

in a context

and lumpsum

levels would results

is

= y = j, and F = r~(l

to actual transfers of wealth.7

some multiplicative

invatment

problem

(5)

The second

so no actual transfers

here to complete

taxes

it to 7 >

= 5(T)W

s = s(~)

under complete

in Bdnabou Applied

of linear

could easily introduce

lated with wI. Optimal positive,

–7)

income,

w opposed

was introduced

and insurance

0;

then bmmes

thus invests the same fraction

of the return to investment,

I restrict

– Fbi]},

k* = k, hence ii = yi = rkDwl-d

_ fba — – pr~(l

The critical feature of redistribution

reasons

– ~) (ji/ki).

up over agents and using the loan market-clearing

individual

when 7
0.

the tax rate is the one

eficiency

requires more pro-wealth

bias in, a more uneqtLal count~:

A/2. of these results may lead one to think

taxation

They do not.

models

relative

With complete

are homothetic (1993)

~set

wealth,

markets.

(Persson

(Bertola

(1994)).

model

system.

with an elasticity

of political

I show there A, the pivotal

11

elites, ageut

but also

(1993))

or to fi-

that

intuitions

has no efficiency To equalize

and Bdnabou

in particular

not only

(1994))

The underlying

markets wealth heterogeneity

as-

features of most

and Tabellini

an externality

and Rodrik

reflect special

This includes

it does not even affect aggregates.

for a (lynamic

of the political

to correct

(Alesina

that they

These are in fact robust

with mmplete

are required

public investment

are indeed straightforward.

rather

of initial

(15)

be called

where there is no useful role for the government

12See Verdier

that the distribution

power

w.

intertemporal

nanm some productive

absolute

normal.

democracies

= AA – A2/2

rather than general insights,

of alternative

or the bargaining

to the wealth level w“ defined by @((w*

values of J muld

is maximized

those where taxes or subsidies

quences;

either the ideology

the more bimed against the poor is the political system:

very stark nature

sumptions

for the

2

(1) Growth h higher,

W“

(1991)

A2) .

and simply speak of positive

12 Substituting

Proposition

of a standard

But since even Western

“popuhst”.

power,

is log–normal:

voter or pressure group then corresponds

@-1(p).

to a system

lobbying

or Conway

bias reflecting

assume moreover

let it be the

have lower participation

of the proletariat”)

lnwi N N(m,

The pivotal

unequal

individuals

(e. g., Edsall (1984)

(“dictatorship

To get simple expressions,

in emh generation

franchise,

and less educated

p < 1/2 corresponds regime

voting

countries

being decisive,

The case p > 1/2 mrresponds

due to a wealth–restricted

even in industrialized

of a non–democratic

some more general points.

at the pth percentile.

or simply the fact that poor

rates in elections,

I shall

from the “one person, one vote” ideal, in a manner which

but allows me to demonstrate

agent or pressure group located

are and how they can be tested.

(199,5a)

if political

conse-

the social

for a discusion influence

has rauk AA and log–wealth

reflects

n~ + AA*.

marginal

costs and benefits

adopting

the point

markets

also imply

of taxation

of view of the individual that aggregate

state, the same applies to output return on capital, to other souras or regulations

of income.

rather

impact

problems

the perspective

on redistribution (1994)

his valuation

rate; in steady– the rate of

with highest wealth relative

of any complementarities,

public

shied away from the most direct

and taken up by Perotti

discussed

“non+emocracies”.

While

in Proposition it does

mndtion

or model.

the cmss–patiid

and regime.

in this instance

second

second-order

effect:

regimes.

(1992),

inputs

the differential

ancl others,

be stronger

to some

testable

The claim, first made

(1996)

1 should

relate

is that the

in “democracies”

valid intuitions,

cannot

criticism

involves

there

are two

on the direction

to political

inequality

restrictive

and Rodrik

whether

on these remarks,

and inequality,

order rendition:

(1994)

through

union.

are decisive,

= AA — A2/2,

Its crossfunction,

14

distribution

across political

who pointed

out that

What

should

regimes A similar

even diet ators matter

is how

of their constituency.

A and A, on redistribution

ln(l — p(r))

assumptions.

but

by the first-rder

elite or powerful

riots or bribes.

I shall now formally

at the pti wealth permntile

to inmme

of that agent or gToup’s objective

of income

Such

can be signed unambiguously,

lanclowning

functional

impact

affects the desire for realist ribution

Elaborating

with respect

in which one moves away from pure democracy.

by Alesina pressure,

rate,

no accident.

the tax rate) is determined

the third derivative

be signed without

was formulated

are subject

of the growth

a dictator,

its sign, any differential

must surely depend

this is probably

Not only is it rare when cross–partials

the gTowth rate (or equivalently,

thus inevitably

(b) Whatever

Upon reflection,

derivative

of the decisive agent –whether

and therefore

located

13 Complete

with this ar~ment.

distribution

stitution

of the individual

and growth across political

of inequality

concern

partial

rises with the interest

instead on a more indirect,

(a) I know of no formal proof claims

endowment.

growth thus means maximizing

seems to have somewhat

(1), focusing

and Tabellini

than

Maximizing

This includes

literature

effects of inequality

negative

growth

which means

which might affect the private return.

namely

by Persson

growth.

only look at averages,

with the ‘Representative”

consumption

thereby adopting

The empirical implication,

one need therefore

examine

the cross~ffects

and growth.

the equilibrium

When

of political

in-

voters or constituents

tax rate is given by their first–

where p was defined in (14).

This implies

(16)

ls~his

~e=oni~g

the same result

irnpli~itly

BUmes

even with progr=ive

matters is the threat of taxation). 14sakt_paul and Verdier (1993) show how r=tricting neither

paper

growth

(&~/~~~A

the political

provides and

r=ults

linear

‘=ation

taxation

because

and perwn rights

I

in all the literature

in equilibrium

and Tabellini

of different

on how the political

~2g/8~~A in my model),

u

in the working

class=

affects

regime

alters

under

everyone

growth

paPer

the same version

(an effect similar

the impact

of inequality

which is the issue of contention

12

discussion.

invests

here.

My model amount

of their to ~g/~A

yields

(all that

1994 here).

on reclistrihution

article But and

henw ==(l;,$;))(-1+’A-’’A((’)2+5:;~;w(-))))))) The first term in the smnd

bracket

ln(l – p).15 This is a complicated

is negative,

expression,

it numerically.

Alternatively,

first. Together

with similar derivations

version of the “democracy

’17) but the semnd

one depends

on the curvature

of

even for A close to zero. One could of course evaluate

observe that when A is small, the second term is dominated

by the

for the growth rate, this allows me to prove an amended

and inequalit y“ conjecture:

Proposition 3 As long as inequality on growth am weaker, 82g/8A8A

is not too la~e,

the less favomble

its positive

effect

to the poor is the political

to democracies,

in left–wing,

populist

inequality

shotid

have mom impact

regimes and less impact ordy in right-wing

also from (16) that in this latter case taxes first decline, A ~ ~. Distributional skeness

the poor.

~nflict

The regressive

which ensured link between

initially

of the income

~2r/8A8A

to

positive.

effect

0

redistribution

As seen in (10), the missing credit market does not affect him at all because

poorer

the agent

as everyone

the very rich (differential

the social losses from liquidity

or lend.

costs through

Now there are two opposite

savings but did not materialize

liquidity

now maximizes

The first is the progmssivii?y of the tax scheme,

in “soaking”

The opposite

policy

is the third result.

ti > w gain at the expense

With

level if

to A 2. The second one has a familiar ring, although

proportional

make him “un–repre=ntative”.

same amount.

tax

level.

now has not only efficiency

always chose the efficient policy.

threat which discouraged

is above this eflcient

wealth is below the eficient

given that redistribution

EWi [Ui (~)]. Most striking

all those below

W would set a positive

+ p), and above in the reverse case.

it should be noted that the median voter’s

especially

favor

in A.

5(7) but also efficiency

to borrow

with own income

results.

tax rate of the agent with avemge

to internalize

ideal

+ (1 + PB(l – T))(ln wi – n~).

(3) The prejemd

result).

each agent’s

to the social one, let us next rewrite:

tax mte of t}te agent with median wdth

individual

who prefer this

with the average endowment

(2) The prefemd

welfare,

– 1 was

5

(1) A social planner

The fist

> 2A2),

112
(pP)–l V’(Z)

in w; and increases

Proposition

+ (1 + P8(1 – ~))(lnwi

over all ~ 2 Z, where z = – (1 + l/p~)

tax rate ri is then given by the first-order

progressivity.

i’s welfare is equal to:

of all agents,

a similar

is his failure to (1 – ~)A2.

he does not want as both

richer and

(1 – ~) A2 is large enough or simply when ~ < 1/2 this

bias and the average agent chooses an inefficiently

20

low tax rate,

even less efficient than that of the median voter. 24 Democracy

~sibly

To explore in more detail the effects of political the pivotal agent or group correspond

institutions

and inequality

once again to the pt~ percentile,

in Wi = m + AA into (11) and setting U’i(7)

has its virtues,

after all.

on redistribution,

let

with p = O(A). Substituting

= O leads to the following

results:

Proposition 6 (1) Growth and intertempod in the political system, (2,) If the pivotal incmes

a~ hill-shaped with respwt

A. They are rntimized

(3) If the pivotal to inequality.

at Ac > A w >0. with inequality;

such

agent is of higher mnk than the median (A > O), taxes are U-shaped

with

and reduce growth.

Tax cuts induced

by rising inquality

duce

growth if ~ is not too close to 1. Tax incwes

eflmts

up to some

beomes

negative.

point,

a potential

am always inefficient

explanation

to intertemporal

for Barre’s

at some interrnediate

monotonic

relationship

me~uring

IAI rather than A. Note that asset market incompleteness

for this non–linear

Alesina and Rodrik

level of democracy,

(1996)

maximized

between

the two.

system

not change the fact that rest rict ing the political plained following

Proposition

non–distortionary

private expenditures. fore with –A,

markets

and potentially

political

taxes and we~am

~se. 25 The difference

import ant explanation

(1995a)

that model

of any

are both

In models

such as

or spillovers

as ex-

(1993) model where

supplementing

both

does

wealth0.

5.

in (25), in which case cr~it

cases accord efiect

8r/8A

with the claim in B6nabou >0

can be reversed.

In

Direct

3.4

and Indirect

Effects of Inequality

We saw earlier that for a given policy Does

this remain

the envelope

theorem

by an efficient

to (23)

planner,

arises through U’i(~)

true when policy

= O of the pivotal

responds

shows

process.

redu~.s

growth

endogenously?

and intertemporal

A straightforward

that such is the case when

r = 7P(A)

i.e.

the political

r, inequality

-

kt

arg max{W}.

The

application

redistribution

of

is determined

more interesting

r“ (A, A) denote this solution

efficiency.

case is when it

to the first-order

rendition

group:

(p~)-lV’(r)

+ (1 –~)A2

– AA = O.

(26)

We ean write :=%+(~).=..x

(~)

and similarly for W. The first term, which holds policy fixed, is always negative, were analyzed

in Proposition

with inequality;

moreover,

6. In a pure democracy the equilibrium

with respect to inequality.

a detrimental

to which agents fexcept

decreasing

taxes w g does.

Whether

effect on savings incentives

growth rises or falls thus depends

returns and have unequal resources.

that since it puts positive In particular,

(~ S O) taxes increases

With positive wealth bias, on the other hand, taxes are

Lower taxes have a positive

one on credit constraints,

system

rate is always above 7P, hence in the range where W

and a fortiori g decline with redistribution. U–shaped

or a populist

while the l~t two

weight on first-period

Proposition

on the extent

The effects on W are similar,

mnsumption

6 established

but

it does not “overvalue”

that where rising inequality

letis

low

to tax

cuts, these are never efficient. Proposition

7

(1) If the pivotal interternpod

agent is at or below the median (~ s O), inequality

mduc~s both growth and

eficiency.

(2) If the pivotal agent is of higher rank than the median (A > O), inequality long os ~ is not too large, thti can ody

inequality

co.se, inequality

incmes

with the indirect

between these variables. less be possible, calls attention wealth

intertempord

eficiency,

but

reduces growth if A is not too small and ~ not to close to 1. In the growth through a decmse

While the direct effect of inequality its interaction

may increase

occur through an incm~~e in mdisttibution.

(3) For A >0 opposite

For B close to 1 inequality

still lowers W m

on growth

one (policy

(through

response)

wealth constraints)

can generate

Sorting out the two channels through

and even appears

desirable.

to the fact that if political

and if capital

in tax rates.

market

imperfections

Particularly

a structural

correlated

are not too severe,

22

a fairly mmplex

interesting

power is sufficiently

often dominates,

greater

relationship

model should nonethe-

is the third result, with financial inequality

which

or human

may actually

increase growth through

a decline in redistribution.

social conflict

in Section

growth)

dscussed

is not income

of political

power.

former translate actually

3.5

inequality

Where

institutions

or the political

stability

(which promotes

relative

to the inequality

of income

technology

are such that increases

(or here, taxation)

Income

2: even though

pletely exogenous,

Distributions

distribution

ket outmme

need not rise, and may

Ravikumar

(1993),

Saint–Paul

itself from one

of the wealth distribution

policies

and Rogerson (1993),

(Loury

(1994))

Saint–Paul

(1995a)).

Aghion

Making

affects persistence,

in this paper

that intergenerational

mechanism

capital

spillover

is at the

and Bolton (1981),

mar(1996),

Glomm

and

and those which encioge-

and Verdier

(1993),

these distributional

The intergenerational

Verdier

dynamics persistence

as the level of inequality

both in theory and in practice,

largely

is easily amended

to deal with these issues.

linkages operated or through

of the form:

operates

are fairly homogeneous

onl y at the aggregate

universal

w~+l = c~+l y~. ht

public

education,

me now recognize

is therefore

level.

lJntil now Whether

they resulted

in socioeconomic

status:

school

districts,

in a

that the transmission

within the family or at the level of small communities

first the pure human capital spillover interpretation,

simply replaced

neighborhoods,

which

social networks,

under which wj+l = c:+ 1 yt is

by: W;+l = E;+l y:.

Under perfect

the

with the absence

will reproduce

is at least as relevant a social concern

of how policy

an economy-wide

etc. Consider

B6nabou

(1994)

those which focus on the decentralized

redistributive

(Perotti

is mm-

after period,

and Rodrik

of factor prices combines

Galor and Zeira (1993),

Fernandez

(1994),

of endowments

and Alesina

to address the issue of social mobility.

developed

it was assumed

of human

distribution

interest.

The model

transmission

(1993),

outmme

and wealth disparities

per se. The question

(1993)

evolution

This includes

(1996a),

as a political

is also necessary

through

the endogenous

and Newman

B6nabou

nize redistribution

of mnsiderable

In Bertola

the constancy

models.

markets models discussed

(1994) as here it simply reflects, period

those which analyze potential

(1992),

Mobility

to ensure that any initial distribution

markets

(Banerjee

(1996)),

of income

abilities.

By contrast,

core of incomplete

and Ades

of agents’

uncertainty

to the next.

Social

it plays a critical role, the pretax

of wealth is indeterminate:

of idiosyncratic

and

a feature inherited from the complete

In Persson and Tabellini

the fixed distribution

in~me

in the

fall.

in Section

explicit

for sociopolitical

per se, but the inequality

Up to this point I have maintained

Piketty

4 : what matters

into increases in the latter, instability

Endogenous

period

A similar insight will arise from the model of

capital markets this changes nothing,

because y~ = r (5L)P wt for all agents.

remains i.i.d., with variance A2 = Var[ln c] = s2. With imperfect

other hand, equation

(8”)

capital

markets,

(20) now implies that family income follows the law of motion:

23

Family on the

where ~t is the tax rate chosen in period distributed,

and its intergenerational

follows the autoregressive

t and tit is given by (19).

persistence

Income

remains log-normally

is given by ~(1 – ~t). As a result,

inequality

prouss:

(28)

The alternative

mechanism

vately or locally

funded.

1 – ~ of smnd the constant

period

of intergenerational With

the preferences

rwources

~mplete

but these retain the property

human capital.

Together

distortion

long–run

s’(~t)

that redistribution

reduces

and borrowing

constraints

also in dl future perioh: growth is maximized

now pri-

w~+l = ~~+1~,

different

the persistence

for aggregate

where

d: = y: so (27)

individual

dynamics,

of w;. From here on I

gTowth whereas the second one

that

benefit of redistribution

as before,

Therefore

markets lead to somewhat

with (28) this makes clear that once the dynamics

an additional,

investment,

to one. In the absence of credit markets,

shall focus on the first case, since it has implications does not. R,ecall in particular

is educational

( 1‘ ), agents all want to invest the same fraction

in their child’s

has again been normalized

and (28) remain unchanged.

t ranstission

of income distribution

appears.

A marginal

rise in ~t causes the same

but now the growth 1OSS- due to the combination are reduced not only in the current period A~f~ is lower, for all k. This homogenizing

at a higher level of redistribution

a lower deg-ree of wealth bias A in the political

system,

are endogenized,

of wealth inequality

((1 – ~t)2A~/2

is lower), but

effect means that long-run

than previously. ‘G This, in turn, requires which must therefore

be closer to pure

democracy. This brings me to the question bution,

which I will discuss both theoretically

in each generation Together, Proposition

by the preferred

~t and At then determine

ZGAwn~J

policy

behavior

myopic

tax rate,

infinite lives both

feedback

~referenc=

just

(I)

of the pivotal

next period’s

As before,

group:

distribution,

and its income

let taxes be determined

~t = ~“ (At, A), defined

according

distri-

to (28).

in At, so that endogenous

by (26).

Recall now from redistribution

on inequality,

or (I’)

imply

w they do not internalize

are internalized

of the economy

and empirically.

7 that when A s O, ~“ (At, A) is increasing

acts as a stabilizing

current

of the long-run

to an extent

that

they C1Onot internalize

the mean

which reflects

24

this variance

effect of yl on WL+I. With the [Iiseount

factor;

effect when setting

forwar[l-looking

see B&nabou

(1996a),

altruism

the or

Proposition 8 If the median voter

or some

per-iod (A < O), the ewnomy ‘r

~——r*(A,

agent located at a lower pementile

wnve~es

to a unique steudy-state

2 — Am —s 2/( 1 – ~2(1 – ~a)2)

Am),

chooses

the tax rate in eue~

growth path (Tm, Am, gm) when

and tile gmwtl~ rate is

(29)

As one would expect, tnbution

a stronger

Multiple

With

any positive

bng

Run

influena

so on. The feet-bzk Proposition

of wealth on the political

states.

from policy

to intergenerational

steady-state

dynamics

hence also ~~+1, and

is now potentially

through

markets:

a negative

which multiple

wage,

A more unequal

depressing

Conversely,

social mobility generates

wealthy

very unequally

distributions

feedback

lower.

(1993)

entrepreneurs

dynast ies benefit high inequality.

form of “mobility

if the economy’s

in turn, aggravate poor agents’ borrowing low total wealth and high dispersion and wealth vary negatively

this feedback

of labor,

the bequest

through

which

the interest

and make mobility

persist into the next period.

enough

with positive

idiosyncratic

This

rate.

probability;

the wealth

pro-

however,

a poor families

is then ergo[lic

25

makes for low (1996),

When

borrowers. low.

Across stewly–states,

and the long-run

wealth is

This implies

more difficult;

escapes

Piketty

High interest rates,

with the interest rate. In the present model,

uncertainty,

the real

they leave to their

and Bolton

total wealth is relatively

constraints

through

Instead they bemme

lower wages.

Builcling on Aghion

trap”

operates

of

who do not have the mllateral

or employers

from paying

capital

via a worsening

thus both aggregate

as in Saint–Paul

“Multiple equilibria can also arise from a non-convexity at tile level of iu(lividual families, With

true

the common

with imperfect

on mobility,

there are few lenders and a lot of would-be

high interest rates, especially

This is a fortiori

more generally

arise in models

of inequality

the wage and therefore

and persistently a related

higher and Am

of wealth means more people

either self–employed

mllectively

is

it is based illustrate

and Newman

distribution

steady-

be true for the growth rate gm.

long–run

general equilibrium

constraints .27 In Banerjee

required to bwme

Tm

(27) on whi&

credit

Zeira (1993).

destabilizing,

W incre~~es m one moves from a less redistnbutive,

to one where

9 and equation

ptinciple

distributed

eficiency

welfare Ewi [U=], and may &o

Proposition

children.

again. By (28) this tends to increase At+l,

interternporal

more inegditarian

workers,

on the other hand, taxes initially

agent i.s of higher rank than the median (~ > O) there can be multiple

In that cue,

for m-ante

process,

9

If the pivotal

thrmhold

greater redis-

Distributions

decrease with At, before increasing

income

towards

bias shifts this steady-state

and less inequality,

3.6

(1996)

populist

as in Galor

the poverty distribution

and

(no inv~tment) uni~lue.

(1994) and Wnabou of education

(1995a),

the feedback

serve M imperfect

leads to lower redistribution by worsening positively

the credit

mrrelated

substitutes

constraints

form of mtitiplicity

omurs through

In Durlauf

for instance,

of poor

more heterogeneous richer, more educated

neighbors

taxes and transfers or public funding

agents,

When greater inequality

and makes disparities

This is why transfers

in spite of savings distortions,

sufficient

disparities

more persistent,

and growth

as stated above,

in models of endogenous

communities ~t

population,

mobility

segregation

families to form small homogeneous

policy;

for the missing credit market.

this again reduces

across steady–states

(1996b)

is through

in wealth and/or

can be

A related

community

imposition,

education

cause well-off

rather than share the fixed rests with a larger,

off from the tax base and positive

would have provided,

local

spillovers

poor families again experience

which

no or little

upward mobility, 2s Are countries

all headed towards

8, or are there permanently Proposition broader

different

trajectories

9? I shall argue in Section

interest

direction.

4

the same long-run

distribution

in terms of both

empirically,

and Property

votes are aunted,

are models generally

impeding

praumed

that this becomes

of related

(1995),

productive,

to the majority

of property

or -nomic

and Kim

and defensive classes.

strategies,

(1996)

activities

occurs through rule.

an orderly

At the other extreme else’s wealth.

rich and poor

rights discourages

or coalitions.

Using “dynamic

It is

widens,

investment,

extract

and Rustichini

rents from others;

level of development,

also B6nabou effects,

(1993),

as well as Maskin

when segregation

focus on the allocation

commons

of one–shot

problem”

wnflict

thereby

occurs

of human

(1996 b),

interactions

efficient.

multiplicity

long-lasting

(lW6a)

and Fern andez

(1994)

on segregation

But

if one combined

COUIC1occur

once again.

26

(1994), between

between

in-

and Rustichini interest groups

groups’

deal with inequality. constrains

as well as on a form of inequality

Durlauf

and Kremer

it is always capital,

of resources

the role and sources of interest

the y do not directly

(1991),

games with either Markovian

between

(1996) show how the extent to which social conflict

on the economy’s

Grossman

Tornell and Velasco (1992), Tornell (1994) and Benhabib

The first two papers emphasize

opportunistically

in the literature.

in the context

(1996) study how growth is affected by distributional

accumulation

expropriation

more likely when the gap between

ideas have been formalized

and Grossman

predatory

or trigger–type

2sSee

and growth.

Rights

submits

decline in the security

is of even

growth,

A number Acemoglu

then everyone

as in

then take the first few steps in that

where agents or interest groups can simply grab part c)f someone

and that the resulting

sorting

in distribution

But first I turn to the last of the three main theories linking distribution

In the median voter model (at least when taken literally),

dividuals

as in Proposition

level and inequality,

5 that this issue of convergence

and merits to be investigated

Social Conflict

process:

of income,

Benhabib

growth may depend

which relates to equilib-

ancl Rogerson

(1996),

by skills in tile labor market. this ]]roduction

ability to

model

(1994)

for related

In tile latter

case,

with credit-constrained

rium selection

rather than initial conditions:

of their model,

of a very simple model,

ingredients

Dilemma

an mnomy

to the economic

constituted

with Capital

of the problem

(“deviate”).

The consumption

and Rustichini

In period

groups of agents, labelled

or try and extract

a disproportionate

of groups

61(1 –5), al(l

–5)

When both sides moperate,

its claims

at the expense

capital stock at the start of the

1 and 2 are given by the following

shares of kt :

D az(l

az(l

+p15,

1 and 2; allowing

amount,

c

D

(1996) but

t each can choose to either moderate

Formally, let kt be the economy’s

l\2

c

to a familiar object:

Accumulation

by two homogeneous

pie (“cooperate”)

of the other group

structure

from several of the others.

for n groups would be straightforward.

period.

equilibria

and make some new points by means

The model has close links to that of Benhabib

A Prisoner’s

Consider

the essence of this literature

which relates the underlying

dilemma.

also inmrporat=

4.1

of subgam~perfect

the one with fastest growth involves equal utility for all players.

I shall seek here to convey

the prisoner’s

among the continuum

–5)

–5)

al(l

–5)

– (~z ‘62)5’,

– (D1 – 61)5

~z(l

–5)

+~z5

717 ?2

a total of ct = (1 –~ ) k~ is consumed,

while

5k~

is reinvested

according

to the linear technolog: kt+~ = ‘r (k~ – Ct) . The parameters

CYl < CY2=

outcome,

can be thought

which

competitive

shares of capital

a Nash equilibrium: a fraction

1 – al

this opportunistic

s

gain, a fr=tion

opposite 29 or

side.

That

alternatively,

(1992).

~einvat~

fli5k~ could

and the reduction

in investment,

resource

allocation

and Gr=man technolo~

than

be strictly 6i~kl.

are of course

problems

and Kim (1996). and the 6i’s (more

between

pro(luctive,

[Jsing th= generally,

pal]ers’

from

and rlefeusive

terminology,

(net)

.X

Tornell

in expropriation,

by making spent

loss, say piskt, morlelling

as in Groxman

the private

or aggregate

and ‘ela=o

~i = pi + 6i. All costs

them WOUIC1re[luire

activities,

does not

gain (net of resources consumption

thus imposing

the ~i’s reflect

the bi + pi – pi ‘s) its social

27

side’s

can only

be seized back by the

abroad;

i’s private

Of

stock and ~i – 6i

than investment

costs of engaging

to endogenize

reinvested,

the rest of society

such as del]osits

the sum of the other

offensive

the

most of the literature,

they could

6i5kt. Thus deviator

exogenous]y;

reflect

(C, C) is never

have been

to expropriation

I shall not do m for simplicity, specified

however,

Following

extracted

with a lower return,

less than

otherwise

is that otherwise

(1 — s)k~ +

for instance

from raiding the capital

into the model direct or opportunity

on expropriation)

game

-t

could game,

consumption.

is less vulnerable

in ~me

payoffs sum to 1-

payoffs in the stage

1 comes

motivation

consumption

One could also introduce

non-cooperative

O < 6; s

in the non-conflictual

an extra share of the pie, equal to

s kt which would

or rents unilaterally

The underlying

They

solution.

i can appropriate

of the other group’s

that transfers

be mnsumed.29

group

1 of the resources

of income

In the singl~period

and labor.

~ O is at the direct expense it is resumed

the distribution

as the market

by deviating,

O < pi

capture

(30)

efficacy

“destructiven~”.

(1991),

and

agents’ (1994)

of the predation

mean that it is entirely

The possibility

safe, however.

of indirect

levies or outright

theft implies that not all of the deviator’s

is often assumed

in the literature;

have different

import

gain need come from investment,

pi and 6i are conceptually

distinct,

as

and will be seen below to

implications.

On net, a unilateral In a situation

deviation

of open mnflict

by some group z reduces the capital

where both

they will be lead to overconsume is consumed, represent

taxes and subsidies,

groups

try to appropriate

even more: for simplicity

~1 + 72 = 1, but this is not essential

each side’s strength

in the political

stock by a factor resources

from each other

I assume that under (D, D) all capital

for the nature of the results.

struggle,

1 – 8;.

that is, its power.

The shares 7;

They could be related

to the ~i’s and pi ‘s, as dscussed

later on, but in general need not be.30 Let me assume from here

on that ~i(l

< ~i for all i, which implies that the unique equilibrium

one-shot

– S) — (@_i — 6_i)5

game is (D, D), Consider,

however,

agents who are infini tely–lived,

of the

with preferences

m g=() where I/a

> 1 is the intertemporal

play the game described

of substitution

by the above payoffs.

which makes this a dynamic the “first–best”

elasticity

The capital

game, rather than simply

case where there is only one group,

carry out lump–sum

transfers.

intertemporal

U = u(5) kl–a/(l

utility

Starting

and p rl ‘a < 1. In each period stock kt constitutes

a repeated

or equivalently

with k. = k, playing

one.

a state variable

I begin

a central

they

by focusing

planner

(C~,(~) in every period

on

who can yields the

– a), where (1-~)1-a U(5) =

The growth mte is constant entire capital

and equal to r5.

stock is consumed

immediately,

case r = 3, p = .4, a = .25, the function

(31)

1 – p(7”5)l-a” This strategy

is preferable

to (D, D),

if u(s) > u(O) = 1. As depicted

u(.) is strictly concave

and maximized

where the

on Figure 1 for the at s’ ~ pll” rl/”-l.

This is the value which the planner would choose if he could select the savings rate continuously, One could let s = 5*, but more generally

I will simply require that s belong

to the interval (Z, 1)

over which u(s) > 1, so that T5 is indeed the best of the two growth rates achievable mnomy.

The main question

is whether

it can be sustained

when groups have the ability to behave opportunistically share from the mmmon

30For instanm, 31were agenb

as a subgame

and extract

in our simple

perfect

equilibrium

more than their cooperative

pool of resources. 31

Benhabib and Rustichini (1996) impose a symmetry restriction similar to 7, = 1/2. alm allow~ to ~on~ulne l=S t]]au ~i (1 – 5), SUCII deviations could be shown to be unprofitable

long ass

is not too far below the optimal

s(s/s*)”)

is a decreasing

function

savings

with j(s”)

rate 5* (specifically,

= 1).

28

aij(s)

~ 1 where

f(5)

-(1

–s)(5/5’)”

~

/ (1 –

1.6:

as~iiai

Vi(s),

oryi/ai

increases

1.4;

1.2: 1.

I

I

I I I I

0.8:, 0.6:

0.4: 0.2 00

0.2

0.6

0.4

I I I

I

1

: I i

: I

/“

0.8 5’

Figurel:

Income

4.2 Playing

Inequality,

behavior.

These

This high-mnflict,

to which players

trigger strategies

> (~i(l

(Qi)l-aU(5)

on growth

and Growth

is always an equilibrium.

serve as the punishment

from cooperative

wnstraints

Power Inequality

(D, D) in every period

will naturally

incentive

1 3

revert whenever

equal to a fr~tion

in the following condition

period

- 5) + ~i5)1-a

has deviated

+ ~(T5 (1 - 6i)~i)’-a.

~i~ of the capital stock.

where both

someone

outcome

will sustain the first best if, for all i,

The first term on the right hand side is group i’s current consumption extra rmour-

low–growth

when it deviates

The second term measures

groups play D, liquidating

the capital

stock,

and grabs its payoff

Rewriting

this

leads to:

Proposition

10

If the incentiue

compatibility

U(5)

> (1 – 5 + (~i/0!i)5)1-a

b satisfied jor both groups, equilibrium.

If it is tiolated,

Several interesting

comtraint

continued

+ P(T5 (1 – 6;)(~i/CYi))l-a

cooperation

the only equilibrium

and growth at the mte rs is sustail~able 0s an ti the non-woperatiue

results can now be obtained

trated on Figure 1.

29

(32)

~ ~i(5)

by examining

one with no growth.

condition

(32),

which is illus-

(1)

Incentive

compatibility

typically

holds

when s is low enough,

enough values, This implies that there is a maitnu?n by confict

over the distribution

growth rate rs~= (2)

Growth

other through economic s~~

of income,

falls as maxi {~i/a;

becomes

stainable

as in Benhabib

} or maxa{~i/ai}

opportunistic

deviations

at high

growth rate which is constrained

and Rustichini

(1996).

This maximum

rise. 32

harder to sustain when some (or both)

unilateral,

and is violated

group’s

is dispmpotiio?~ate

pie: for any given 5, (32) ceases to hold as ~i/ai

ability to expropriate

to its “normal”

becomes

large enough.

the

share of the Gnsequently,

declines. (3)

Inwrne

inquality

and expropriating mnstraint

ability.

is binding

the poor,

also limits the emnomy’s For instanm

transfer

al.

group

This scenario,

here from the desirability (4)

However,

the incentive

compatibility

2 is better

formalized

be the poor

~1 /al

< T2/a2,

for instance,

model

thus makes clear that what

land reform,

education

subsidies,

a minimum

off if its own share a2 can be permanently

by Grossman

(1994),

who are relatively

reduced

(1995) in a static context,

earning and political power:

more vulnerable

versus large. landowners.

it is the rich’s threat to deviate

of income per se, as often claimed sin~

is 1. 33 Note

payoffs is a potential

come from

arises

of growth.

it could

growth,

1/2,

of power

they are. In this case it may be in the interest of the rich

one can think of small peasants

exploitation;

maximizes

if @l = ~z and ~ =

wealth to the poor through

wage, or trade protection: to increase

rate, for a given allocation

for the group with the smaller income share, al < a2. Deviations

and are more likely the poorer

to voluntarily

growth

problem

matters

If PI/al

which reduces

is not inequality

in the literature,

to expropriation = ~2/a2

but inequality

in the relative

that the important

for the empirical

role played by off-the

implementation

The

distribution distribution

al + a2 = ~1 + 72 = 1, the minimal value of maxi {~i/ai}, also

but

accumulation,

in the (equilibrium)

or

of

which

equilibrium–path

of such gametheoretic

models.

I

shall return to it below. (5) The more of the expropriation

comes from capital,

tion, the easier it is to sustain cooperation:

32For instance 6i)(~i/~) described




=

– 6~)(~i/~~))’

1 < ~i(i)

here there are only two sustainable growth rates, rs and zero.

continuum

of such games,

indexed

by s, which

can be played;

consump-

in d;.

1 + p(rs(l

and u@)

to other people’s

all other

But

‘a

whenever suppose

parameters

x

vi(s)

fli/~i

>

now that

are invariant.

as long as (1 – 1. In the game there

is in fact

Among

a

values

which cooperation can be sustained, both groups will prefer the one with the constrained-optimal growth rate, 5“’ S min{s” ,5ma. }. They will also be unanimous in preferring the s’” game to any other with a single,

of 6 for

uncooperative both

the s’*

33 Deviations with stochastic

equilibrium

if u(s’”)

> m~i{(~;/~i)

and the zero-growth

by the rich also occur endowments

enter

and fight over the appropriation

1‘“}.

If this condition

is not satisfied

the Pareto

frontier

includes

outcomes. in Barbosa,

into an ex–ante

of total

r-urces.

Jovanovic

and Spiegel (1996),

efficient Their

income

decisions

30

sharing

but the context

agreement.

are based

on current

Ex–post,

is different.

Agents

they may renege

payoffs only.

Empirical

4.3

The findings

Evidence

from most studies which have examined

property

rights,

m-ures

of “instability”

sociopolitiml turnover,

political

constructed

violence,

and Poole

(1996)).

are summarized

or “insecurity”

instability

Londregan Perotti

and growth

Because

Alesina

fires

investors,

risk, rule of law, enforceability Keefer and Knack of security

deteriorate

that both

greater

and growth, property

(1995),

of contracts,

turmoil

(1993) or Barro

to be clearly

identified,

hand, greater political

equation,

I also wrote support the latter and intuitive

through

formalized

thus appears

regressions,

(1995)

instability

report

that

becomes

or empirical

notions

In turn,

rights decrease

“friction” model

or resource

with symmetric

sassinations,

etc.

information

about

effect).

information,

the extent of agents’

GDP

in the

is still somewhat

of the story.

The leads,

spread in the return to investment and thus leads, ve~

equilibrium

muclt

or the threat thereof. is achieved

without

in Alesina

struggles along the equilibrium of income

any

in a bargaining

for strikes, riots, coups,

as for instance

over what this distribution

ten-

First, note that contrary

is not one where greater inequality

It has no up-side

information,

31

on the other

because the link between

above.

there is no role in these models

incomplete

remain

and property

for initial

instability

will reflect not so much the distribution

uncertainty

however,

instability

is really not pati

ancl payoffs,

(1991), will generate delays and resource-dissipating extent to which these occur

by the evidenm;

Just as there is no reason for delay to occllr

dissipation,

Incorporating

actions

investment

which in turn makes

well supported

m in the voting modeZs, to a lower mean return due increased expropriation, with perfect

(10) shows

rights, as does a more equal income

model presented

to a mean–preserving

(and even this is known to have an ambiguous

Second,

column

types

insignificant.

here and in most of the literature conflict,

and so on; see

(9) shows that both

when one controls

unurt aint y or unpredictability

more acute political

a

or nationalization

only the latter are significant;

of social or political

uous. This can be seen from the representative

mechanism

Column

for “the general idea” rather than “the models”

interpretation,

(1996),

corruption,

social conflict,

implies more secure property

and Knack political

and Roubini

risk” sold by specialized

(1993) finds that when both political

in investment

stability

Keefer

growth

of

is more directly linked to the

of property

exacerbates

of indices

(1986),

risk, expropriation

inequality.

broad

and Gupta

The specific channels through which this occurs,

Svensson

rights variables are included

to mmmon

income

Two

most studies estimate

of “country

(1996).

and lower protection

and reduces

plausible.

default

Olzer

quality of the bureaucracy,

The general idea that inequality

indeed it is eminently

investment

such as sovereign

as a result of increased

rights less secure

distribution.

by various indicators

2.

over

strikes, government

Venieris

problem

The other form of “instability”

Svensson

political

of protests,

Alesina,

of the potential] y serious simultaneity

rights. It is measured

to international

(1996),

mnflict

The first consists

and the like (e.g.,

and Perotti

inequality,

(9) and (10) of Table

have been considered.

revolutions,

joint model of growth and instability. issue of property

in columns

from various mmbinations

mups,

(1990),

the links between

as-

and Drazen path; but the

(and power)

as

is. Why the two should be related

is not obvious, politiml

Given imperfect

economy

models:

information,

resources

would be dissipated

the voter who turns out to be pivotal

have his way, but only after costly political

campaigns,

lobbying

as well in standard

(say, median)

and legislative

will eventually maneuvers.

will make the two types of model a little more similar yet, as would the incorporation dynamic

mncerns

strategies

5

into the voting model:

reputation

on the part of the private sector,

Convergence:

Are muntries

muntries

to the same level of inequality?

on-.

Similarly,

than European

and minimum

wages.

may seem unusual,

Yet it is important,

It is common

knowledge

ones, themselves

the specter of U, S.–style inequality

of redistribution

(and Higher)

This question

literature.

the facts is in itself of interest.

tend to be more unequal

trigger

and so on.

indeed it has not been taken up by the empirical First, ascertaining

of strategic,

of the pivotal class for fiscal restraint,

On to Second Moments

mnverging

This

and

on several counts,

that Latin American

less equal than East–Asian

is often used in Europe

to justify

But are all these gaps really permanent,

high levels

or inexorably

narrowing?34 %nd,

it can shed light on the relevance of models

dependence

of the inmme

distribution,

mechanisms

of credit market inmmpleteness

bility which underlie these theories, Third,

tion.

conve~ence

i~l distn”bution:

for equity

gree of inequality

at OECD

~oun~ri=

and chang=

had the highest

initial

incre=

low inequality

from inequality

international

steady=tate.

during

by Proposition

should

persistent

rationing wealth

in Piketty (agents

distribution

exogenously, Departing probably

can

(1996) borrow

and Smeeding

the 80’s.

If anything,

9. The largest

(1995)

occurred

may be converging and Denmark;

this exercise

provides

valuable

find no relation

there is some evidence

incre~s

Portugal

to credit

less than constraints

or as the economy from homothetic

grows

preferences

lead to history dependence,

of this ergodicity

what

they

discussed it becomes

muld

in the dereturn or

in Section

with

Some

could

it suffers

too weak to generate

by introducing

a minimum

but the stochastic

version

of these

absent

multiplicity

consumption of that

one)

model

but

because

being

without

still remains

credit

from

the

are specified

and Bolton

level w in Cbatterjee

on a

credit–

even include

the latter

to a

based

the feedback

(Aghion

at

steadyatate.

be converging

from

models

initial

and the [JS, which

to a high inequality

probability

3.6 is either

between

of polarization

in the UI{

thus Denmark

information,

property.

repay

32

differences

of some form of increasing

France,

for examples

tend towards

differences

small number of eountri~, several of which are observed over a very short interval of time. qssee for instanm Banerjee and Newman (1991), Ayagari (1994), Bertola (1995) or the c= constraints

growth model

structure.

that these countri=

in Italy,

While

the presence

l~gO’S, Gottscllalk

levels, su~-ting occurred

of innate abilities,

in per

income distribu-

income. 35 Barring unexplained

or politioeconomic

in the

to social mo-

convergence

with the same fundamentals

indicate

in inequality

of the type suggested

The small~t

test of the joint

shocks, most versions of the neoclassical

countries

mnversely

and history–

3.6.

examining

of wealth and pretax

in the mnornic

levels of inequality the extremm,

an indirect

feedback

in Section

literature

or in the distribution

would

mmplementarity 34~k~g

and negative

as explained

with idiosyncratic

the same invariant distribution in “tmtes”

it provicles

steady–states

This variable is after all only the first mo?nent of each collntry’s

Once augmented

imply

In particular,

there is now a vast empirical

capita incomes.

with multiple

(19M)).

(1994)

to be studied.

could

Having raised the question

of mnvergence

in higher moments,

I shall make here a first pass

at trying to answer it. Ideally, one would apply to an international the same tests which are now standard regressing

rates of change

over time (Barro

(1991),

on initial Barro

by Deininger

(1995).

period.

missing wlls.

I start with a bird’s for which Deininger

Middle

High Income,

and Eastern Europe.

these numbers

I computed

each inequality

measure,

summary

East and North Africa,

by averaging

I

countries

eye view of the issue, by comparing

Africa,

I Gini (%)

the coverage

but considerable

and Squire (1995a) provide

measures,

tests of Quah

is data:

no such panel

is a new data base recently

expands

of previous

falls

put together

data sets, both

from the Luxembourg

effort has been devoted

Income

to making

across countries.

Sub-Saharan

inequality

dispersion

to the extent that one can think of it as a panel with (still many)

far fewer observations

comparable

cross–sectional

however,

measures

of first moments:

or the more complex

constraint,

I shall also use data for a sample of OECD

Study (LIS). It mntains the numbers

(1992)),

The binding

It significantly

on the mnvergence whether

The closest substitute

and Squire (1995a).

over time and over countries,

values, examining

and Sala–i-Martin

(1993) and Durlauf and Johnson exists over a long enough

in the literature

panel of inequality

statistics

on inequality:

East Asia/Pacific,

For each region they constructed all available observations

both

the seven main regions of the world Latin America,

South Asia, OECD

and

decaclal averages of various

from the 1960’s to the 1990’s.

the world average and the cross-regional

standard

From

deviation

of

These are report ed in Table 3.

Aclj. Gini (%) I Bottom 20% I 3d+4’h Quiutilfi

Top 20%

Top 20 / Bottom20

Mean 1960!s

39.99

41.52

6.18

35.65

47.84

9.03

1970’s

39.34

40.92

6.03

36.49

47.24

8.89

1980’s

37.47

39.92

6.52

37.56

44.73

8.31

1990’s

38.28

41.63

6.43

37.24

45.47

8.46

Standard

Deviation

1960’s

10.03

10.77

2.17

4.29

8.91

4.52

1970’s

10.54

11.23

2.77

3.74

8.76

4.29

1980’s

8.33

9.43

1.50

2.97

5.97

3.73

1990’s

7.79

9.46

1.58

3,52

6.66

3.82

Table 3: inequality Regions: South

Latin

Asia,

America,

OECD

and

Sub-Saharan

computed

While

these are somewhat

36 One would want column

from Deininger

level of inequality

and Squire

in the world

to weigh regions

than income

seven main regions East

surveys.

(1995a),

crude statistics,

and North

Tables

Africa

, East

Asia / Pacific,

typically

to some interesting

is one of relative

or income,

made by Deiuinger

The former

5 to 7.

they point

the picture

by population

of Table 3 refers to an adjustment

ture rather

acrm

Middle

High Income, Eastern Europe.

Source:

mean

Africa,

for instance.

and Squire (1995a)

bias the Gini coefficient

33

The

stability; “adjusted

to observations downward.

facts.36 some Gini” bawd

For the

small and in the second on expendi-

The adjustment

consists

gradual

improvement

Cross-regional of variation

is visible until the 1980’s,

variations

in inequality,

after which the situation

starts to deteriorate.

on the other hand, show a clear decline.

falls by 1970 for the Gini mefficients,

The coefficient

30% for the shares of the bottom

quintile,

for the shares of the third and fourth quintiles and 37% for the share the top quintile. that almost all of this “convergent”

occurred

between

shar=

to the extent permitted

or share ratios because

directly ewh

countries,

to the transition

muntry

I then ran a regression

I Sample

1 (N=69)

Gini

of this variable on a constant

The first sample

II Sample

for which

muntries;

(4.49)

(1.48)

-.017

-.036

-.060

(-3.04)

(-2.54)

(-4.75)

(-1.34)

.061

.262

.480

,050

tesh

using using Ginis’ average

To redua of adding

and Squire data set (1995a);

surveys;

Sample

3: subset

of the 69 countries

one is perhaps

Sample

of OECD

2: subset

countrim;

the negative

having

it restricts

been

obtained

and generally

significant

in Table

observations

in eac]l c=,

3 are, unsurprisingly,

set.

and Squire

tbe differences

not statistically

the rate of

to the 25 countries

from similar countries

types

of surveys

in the full sample.

the same regression

The results are consistent

signs indicate

size of the bias, which Deininger

are onlY ~ven

documented

using gro~

4: LIS data

attention

of the 19 OECD

that these results were due to measurement

to the Gini the average there

of countri-

Saml)le

for which I was able to compute

the most reliable:

The third one consists

rate of change

in parenthesis)

by the LIS data set, where I was able to perform

the chanm

data set. 3TGiven that of variation

t=tatistics

the typical time interval is much shorter, however.

four columns:

4 (N=16)

(2.65)

income),

It is complemented

Sample

3 (N=19)

-.015

the data are most comparable,

(gross household

I Sample

2 (N=25)

(3.07)

consists

change, 39 The second

and the initial value

2.56

1: Deininger income

the first and last

1.22

4: convergence

for

in Table 4, for four samples.

(heteroskedasticity-consistent

household

between

.755

R2

Table

it relates more

.641

c

Sample

and because

model, 3s In the first test I computed

(28) in the formal

of the Gini. The results are reported

across

by the data. I chose the Gini rather than particular

the average yearly rate of change in the Gini coefficient

available observations.

initial

tests for the Gini coefficients

it was available for more observations,

equation

Note also

the 1970’s and 1980’s.37

I next went to the full sample and ran simple convergence individual

22%

mean–reversion

on 16

across the

in inequality.

error on the first observation compute in standard

significant.

to be about deviations

6.6 Yo in their ‘r coefficients

In my view this does not make

them any less intriguing, especially in the light of tbe other eviclence discussed below. 38For a log_normal, the Gini is a monotonic function of the variance of the 10gs A?. I also ran manY of ‘lle regressions with the logarithms of the Ginis instead of the levels. This led to similar results. 39~tncting the sample to thcountri~ where at le~t ten years sel]arate the first and last oblsemations to throwing

out nine data

points,

with essentially

unchanged

34

rcsu]ts.

leads

(which bias-

the wefficient

right–hand–side the s~ond virtually

towards

negative

variables but replacing

the left–hand

and last available observations. unchanged

positive

and insignificant;

points

(with the trend often mmputed

betw~n

18 and 62 for the Deininger

standard

cross–sectional

panel it is nassary observations

to interpolate

mnvergence

the basic regression is negative

in the regression

data and net inmme

smnd

mlumn

(“dginires”,

muntries

(Table 5c, 25 countries).

gross inmme,

for observations

income

for both dates.

Some numbers income,

come others

from expenditure

First, I include data,

personal

the results are reported

then run the regression

in the

on the residuals

on the subset of countries

These results, given in the “Sample ones.

Once again there. is significant

3“ column evidence

of

from 1970 to 1980, much less so from 1980 to 1990 and none at all for the

with and without

or by interpolation).

dummies,

The results are presented

are all negative,

to the semnd,

and Squire

(1995a)

in both d~u=

when moving these problems,

between

the first two results and

subsets of countries,

on yet another

subsample

consisting

“Sample

but not in magnitude to the full twenty–years

2“.

of the 24

Once again the

from the first decade period.

of wllicll tile first one is tile most serious.

35

I therefore

were available (either from the original data

under the heading

with a drop in significant

and a drop

discrepancy

are for different

for which 1970, 1980 and 1990 observations

40Deininger

of concern

but some are for net (after tax) figures.40

and netdum);

years),

which might explain the puzzling

the regressions,

estimates

comparable.

Finally, I run the regression

the last one is that the data for ewh subperiod

muntries

One sourw

only at

1970 to 1990.

One problem

reran

The coefficient

I first regTess both the initial and final Gini coefficients

at the relevant

of each table).

198&

The first mlurnn presents

for 1970–1 990.

generated

perdum

are very similar to the previous

mnvergence

a usable

5a, 33 countries),

ways, all of which lead to similar results.

data (expdum,

(evaluated

which used gross family

whole period

1970–1 980 (Table

may not be directly

of Table 5. Alternatively,

third column

of each table,

To generate

for 1970, 1980 and 1990. I was then able to

and small and insignificant

variables

inmme

on these dummies

over different

This is what I did, using neighboring

data,

for the periods

finally, most concern

dummy

to

of the data set does not permit one to run the

some missing

I deal with this issue in three different

inequality

and i ts rate of change are computed

surveys, others from income surveys; some pert ain to household

income;

12 data

at the 5% level for 197&l 980, similar in size but significant

is that the data from different

to personal

only

by just a few years) as opposed

over a fixed, ten or twenty year period.

and 1970-1990

the 107o level for 1980-1990,

from expenditure

contained

of the change in the Gini on the initial value and a constant.

and significant

remained

and Squire data set.

regressions

1990 (Table 5b, 38 muntries)

that regression

over dates separated

when required to obtain Gini coefficients

run inequality

the inefficient

(t–stat ist ics ranged from 1,9 to 3, O). For the LIS

The incompleteness

regression

with the exact same

side by the average rate of change between

however,

with this test is that inequality

periods for different countries.

I ran the regression

For the first three subsamples

and st artistically significant

data set, it bmme

One problem

values),

A possible

explanation

would for some countries

to go from above to below the mean (say) during the first

decade,

then move back above during the second one, In the fourth,

OECD

countries,

magnitude

and stability

insistently periods

by wntrast, across

periods.

of mean-reversion

across major

regions

koking

between

1970 and 1980, but the picture

no virtually

in Tables

countries,

most of its decline

however,

deviation

(sdev),

between

of inequality

the 1970’s and the

one sees no evidenw

reported

5a to 5C

for the other

to recall that in Table 3, the dispersion

of the world experienced

the range of Ginis. The standard

reported

of

in terms of both

the regressions

It is interesting

across individual

seems stronger

Overall,

point to some mean–reversion

is much less clear.

1980’s.

the evidence

much smaller subsample

of any narrowing

in

in the last two lines of Table 5, shows

no change during any of the two decades under considerate ion.

The general picture general stability experiencing

which emerges

at the end of this empirical

in the world distribution

some non–negligible

actual convergence awaits a definite

answer.

of Ginis, within which countries

amount

or whether countries

of relative

oscillate

This is perhaps

for empirical

research.

data (looking

is thus a mixed one:

and regions seem to be

The question

around dist inet long–run

of whether

given the rather preliminary

as an important

across states or regions as in Barro and Sala-i-Martin

nature of

however,

and essentially

future studies with more sophisticated

there is

levels of inequalit y still

of the data.41 My main purpose,

in distribution

Hopefully,

mobility.

not surprising

the analysis and, above all, the limitations forward the issue of convergence

exercise

was to put

unexplored

econometrics

(1992))

topic

and better

will help resolve the

issue. Two related ticular

empirical

by Proposition

countries,

questions

9, is whether

or even industrialized

or are there permanent by Lindert

(1996)

differences

suggests

broad

xtually

increase

mobility,

a

capital

markets.

Recent

of education answer.

41In particular,

‘*See

Piketty

Are

Evidence

formal

on OECD

countries

tests on larger samples

(27) and suggested (1996)

studying

provided

are needed.42 redistribution

by most

models

with

the effect of state financing

of families in poor communities

suggests

that borrowing

a positive constraints

of inequality.

hypothesis)

of mean income (1995)

in par-

in redistribution”.

fiscal, or other forms of progressive

work by Cooper mobility

One, motivated

to the same relative size of the welfare state,

in equation

I have only looked at unconditional

the Kuznets

the dynamics

formalized

“convergence

(1995), on the other hand, finds only mixed evidence

affect the transmission

ity (e.g.,

but more

educational,

on the intergenerational

Mulligan

converging

in the social contr~t?

the latter,

issue is whether

serious investigation.

there is so to speak

countries,

Another

imperfect

also deserve

and the reverse

and income

and B6nabou

inequality

(l995A)

convergence.

The l]otential

links from inequality should

for models

be examined

studied

on inequal-

in this pal)er sugg=t

jointly.

which seek to explain

36

effects of develo]]ment

to growth

such persistent

differences.

that

6

Conclusion

Non representativ~agent

growth

is necessarily

First, I focused

growth,

incomplete.

theory

rather than the reverse.

response

to credit mnstraints

technology

and policy

abstracted

from the Kuznets

This choim

reflects both

model

The first model’s

and policy

precluded

(1955)

sp=

income

outmmes,

hypothesis,

Another

except

when discussing

whether

formalized domestic

by Murphy, market

growth regressions

distribution

in their data.

Keefer

and interacted

An empirically

distribution,

of the middle

fertility,

profitable,

mnsidered

these mrrelations,

out theory

Perotti

on fertility,

Among

the models

3 often play a critical

a number

of simplifications.

altruism, occupational as from spillovers the literature, Where

do we go from here?

43 See for instance and B6nabou

impede

consumption=rno

rather

(1995b)

Quadrini

to trade,

for the theory

the links between share

and because

to formalize

investment

some of these

which were extensively

role (e.g., Galor and Zang (1993)). in some depth, the analysis necessarily

I abstracted

from i nheritecl ability, dynastic as well

have been incorporated

in

at various points in the paper.

The political

economy

and imperfect stage. 43

the quantitative

and Rfos–Rfill

in the WOnd.

in

and grcjwth which can robustly

ties of any kind. All these elements

and have reached

Krusell,

(1994)

by including

and this in turn has a significant

which have begin

For ancision

and their role mentioned

of

even with

choice and effort decisions of workers, ent reprenellrs or rent–seekers,

and non~onvexi

now well understood

concerns

large

is the absolute

finds that a greater income

fertility

Even for the three main theories which were examined involved

however,

due to space constraints

on educational

theory

concentration

total GDP, and openness

(1996)

rent-

and Rustichini

mechanism

of research

of distribution,

the kind of wealth constraints

in Section

direction

effect

in the

They find no support

I did not discuss this mechanism

there is yet no well worked

links, moreover,

negative

properties

like Inclia is considerable

with income distribution.

and development.

arising

and extensive

excessive

test the “big push”

(1995)

curve,

requires a sufficiently

The relevant constraint,

more successful

CISSShas a strong

impact on growth.

generate

and Knack

conflict

If industrialization

technologies

to growth.

the role of fixed rests.

arises in the ‘(big push”

measures of market size such as population,

both by themselves

positive

an obstacle

returns

I thus entirely

or rich ones (see Benhabib

weight of the middle class, which in a large country

very high inequality.

income

Shleifer and Vishny (1989).

to make increasing

wealth may represent mnomic

effect of income

in

of preferences,

in the Kuznets

sociopolitical

on

endogenously

Similar homogeneity

in most remnt studies,

level-dependent

evolved

level of development.

and a waning interest

me from examining

or wealth inequality

but due to the homotheticity

seeking are diseases more likely to afflict poor countries (1996)).

distribution

by the economy’s

constraints

support

so rapiclly in recent years that this tour

only on the effects of income

it WM not affected

from its lack of empirical s-rid

has developed

There

othing but not invmtment

(l W), also

(1995)

many

(e. g., Ayagari

different.

37

capital While

in the first

quantitative (1994),

Bertola

further

case,

models

market models

(1995)),

developments

Fern andez

where

are

ancl Rogerson

liquidity

constraints

hut their ]]roperties

are

(perhaps swpe

in relation

to fertility

of the theoretical

work a high priority: put it mildly),

or technolog)

literature

will surely prove valuable,

and the scarcity

of direct

evidence

signs of the adverse effects of redistribution

and inferences

about

the gap between

makes further

on growth

the role of credit constraints

empirical

remain elusive

far too indirect.

With

(to

respect

to sociopolitiml

conflict,

there remains

room for theoretical

to one another.

Existing

models provide

many valuable insights but few robust results about the

effects of income inequality path),

fully predictable

on mfiict,

whether mnflict

or uncertain.

rights variables should be included

between

mnomic

open ~tict

in the regressions,

considered

and the Philippines?

pure political

economy

through

average

it

mnsumed

and

broadly deed

1.97%

more: with

in secondary

education

Philippines.

Similarly,

Philippines’

between factors ity

and

207.

by

very

government

the ~nmdotal

elit=.

GDP,

from

42%

versus

(1989).

1992

roles

puzzle

in 1960

were

is the the

extent

with

now

to theories

of social

on the phi]i~Pinm

ducation

and

changes.

(1W5))

and low growth,

and Wolf (1989)

are from the World

that

su~~t

Bank’s

38

1986

to

rate and

much

less,

numbers

are

50%

28%

to

65%

was

political

instabil-

high

Korea more

went

the tyl]e of l)ath analyzed

rights and to the richest

in Proposition

(1 993)

model

over 1-1985;

Development

3.6070

similarly

Their indices of political 40% of hea] th subsidies

An-

to cultural

assassinations,

here are averages

the

behind

versus

experienced

and Ades’

rate

respectively.

(5.55%

rights,

in-

for

far

as opposed

property

and 1995 World

and

enrollment

of 6%

rate

economic

or even Verdier

data mentioned

the

GDP shares

hypothesis,

as opposed

fertility

of

with

These

Philippines:

and political

and the fact

is cited by Alesina

to the wealthy

Most of the Barro

conflict

1.46%

pattern,

Korea.

of 42%

it reflects

had more revolutions

crises and constitutional

(this number

rates

from the poor,

redistributed

in this inst ante, as the two countries

relevant

evidence

same

enrollment

higher

which

Once again, the

versus

accumulation

of the

1965

much

to

South

in 1985,

Korea’s

Philippines’

although

that

to 95%

reversed,

in

capital

past

3.71% the

to clearly

transfers in Korea were

government

1.58%

human

education

show

Korea

(see for example

pressure emanating

Philippines’

skyrocketed

tertiary

by redistribution

given below for tertiary

of

the

creditwnstrained

The Philippines

of the population

renta=king

for

1985),

appear

riots, coups,

characterized

of

linking distri-

of South

csse studies

by Barro and Wolf

expenditures

While

investment

Turning

levels of turmoil.

44Both

the occurrence

the most relevant mechanisms

redistributive

~ucation

44

1.66%

the

of the

is unclear. not

of excessive

1980.

went

19Yo;

piece

1965

does

and

educational

likely

one would expect

such as those compiled

respectively.

wnsistent

other

for detailed

half times higher than in the Philippines:

1970

a little

Korea’s

the

the interaction

which of the theories

the ballot box or the street, does not fare well. Public

between

5,13%

and property it is instability

Examining

power in determining

by asking:

this is not a substitute

hypothesis

low but still two-and-a

of

whether

in this paper best shed light on the experiences

While

show up in basic indicators

on

that matters.

of political

to conclude

(1995) on Korea and Taiwan),

whether

of policy

so as to determine

redistribution

and inequality

full circle, it is tempting

and growth

Rodrik

side, the vatiances

also seems desirable.

Coming bution

inequality

work to move closer

will be open or latent (off the equilibrium

On the empirical

or just the average level of extra–legal

and empirical

the

9,

of purely the figures

Reports.

civil liberties protection

were also virtually

similar. 45 The more discriminating

discussed earlier (rule of law, enforceability

instrumental

in inducing banking

system,

government,

45 Barro are Sttie

not only in creating

Korean households

without

and Wolf’s

excessive

(1989)

= (0.00, 0.00),

data

expropriation

a favorable

climate

for business

to entrust much of their considerable

which in turn channeled

(2.1,

enforceability

2.3, 2.6)

last ten years.

of contracts

and the Philippines The averages

2.2 and 1.7 respectively.

number

of th=

Rwt = (2.12, 1.00),

and ~.3,

and nationalization

potential.

(1 .5, 1.9, 2.2).

]]attern

of these three BERI

The

average

on a scale of zero to 50.

ICRG

See Keefer

rights was

investment,

deemed

events

l)er year

for Korea

Assass= (0.12, 0.73),

= (0.38,0.08), Constih = (0.22, 0.09), Polr-ight = (4.80, 4.7), CiVlib = (5.0, 4.5). dGThe earliat available data are BERI’s (BusinH Environmental Risk Intelligence) delays,

risk, mrruption,

but also

strategic

by the

along the way.

on the average

Revel= (0.31, 0.46),

rights

savings to a stat~controlled

credit towards the industries

dissipation

of property

ahead. 46 This general security of property

etc. ), on the other hand, put Korea distinctly probably

of contracts,

indicators

This xores

computed

(International and Knack

by Keefer

Country (1995)

39

1972 scor=

On a scale of O (worst) is confirme(l

and Knack

for sourc=

scores

(1995) over

and definitions.

data

Crisis

for bureaucratic

to 4 (best),

by the additional

Risk Guirle)

and the Phili])pines

CoILp= (0.09, 0.00),

Korea

available

over 198&l 1986–1995

scored for the

995 were were 36.7

Appendix Proof of Proposition

1

Let us first study the properties

of the function

that it has a unique, global maximum

‘—= PP

1 +pp(l (1 -T)2(1

is positive

if and only if 72 < 1 + l/p~.

where z -

–~~.

+pp(l

~early,

(13) implies

(Al)

-T))2 concave

i’s utility function

also strictly concave

claims which follow equation

by (12).

– 72)

Thus V is strictly

By (11), individual and therefore

defined

at ~ = O. Moreover,

v“(T)

p) ln(A + Bi~)

V(7)

on the policy

U;(7)

(z, 1),

is of the form V(~)

on (z, 1). The envelope

(11 ), as well as Proposition

domain

theorem

+ (1 +

then yields the

1.

Proof of Proposition 3 The result for taxation

For A small enough,

was proved in the text.

~2r/~A~A

to A makes the second apply to intertemporal

Next, note from (9) that

was seen to be negative,

term again dominated efficiency

and the fact that

dT/dA

by the first; hence the result,

is proportional

Similar derivations

V.

Proof of Proposition 4 The first claim follows impli-

directly

from

(22).

Differentiating

that

this equation

and using

(6) also

. (A.2)

Since the left side is increasing This maximum

is interior

in ~, g increases with r up to some 79(A)

(and increasing

in A) if and only if

(1- P)A2> (1 As z < –1,

it suffices for instance

rate is positive

E [z, 1), then decresses.

-Z)2;1

(A,3)

+PP)’

that (1 – @)A2

> 1/(4 + 8p~).

>0~(1–~)A2

1 > ~+pP.

The growth-maximizing

tax

if 79(A)

(A.4)

Proof of Proposition 5 Because W(7)

is the sum of V(T)

on (z, 1). The same statements social and (interior) the planner’s

and a concave,

hold for individual

private optima

quadratic preferences

function

of 7, it is strictly concave

ZJi(T), now given by (24).

are thus respective] y defined by W’(~)

case, (23) implies that V’(~p)

= –p@(l

40

– D)(1 – 7P)A2.

The

= O and ZJ’i(7) = O. In

The fact that V is strictly

mncave

and maximized

in the first-order

at zero then yields Claim 1, while Claim 2 follows from setting in w; = m

condition

U’i (~) = O derived

the agent with average wealth, which by (25) is equivalent ~tivalently,

W’(I

7P >1

– (2p)-1

+

in w = m + A2/2.

to W’(rP)

- (29)-1)

from

>0,

Clearly,

Next,

let ra be the preferred

tax of

~“ < Tp if and only if U’a(~p)

+ [p~2(l – 7P) – p~/2]A2

‘

CZaim 3. Finally, let us show that when ~ < 1/4 there exists an interval where the tax rate

Tm set by the median voter is less inefficient zero the median

mnverges

to the mean, and both Tm and To converge

which is 7P(O) = O. Therefore, and W’(rm)/p~ W’(~”) W(r”)

= –~(1

than that set by the average agent, ~a. As A goes to

from (25):

– 7~)A2

W’(~a)/p~

= –@A2

= (1/2 –Q(l

+ 0(A2).

to the planers’

–T”))A2

optimum,

= (1/2 –@)A2

+O(A2)

Thus if ~ < 1/4 and A is small enough,

> –W’ (~m), which implies (using Taylor expansions)

that

Tp – r“

>

rm

– Tp

and therefore

< w(~m).

Proof of Proposition 6 Strictmncavity of individual preferences U’(7) implies that the equilibrium defined by the fist~rder

rendition

as long as there is an interior strictly

increasing

(26), or

solution

~“ (A, J) > Z. Since WA < 0 < —Vr it is clear that ~“ is

in A. Proposi tion 5 showed that maximizing

Aw < A because for J > A, V(O, A, J) Aw is obvious;

W requires

implying conversely,

value which makes 7* (A, ~) equal to Z, T* (A, A) falls below ~g (A), ~G is interior,

as long as (A. 3) is satisfied.

the effects of A on equilibrium

tax rate is uniquely

taxes r*(A,

This concludes

W’(~*)

J w > O; conversely >0

since 7P(A)

>0.

as ~ increases towards the

implying

g’ (~”) > 0. Therefore

the proof of Claim 1, which concerns

A).

I now turn to the effects of A on ~“, and the resulting contributions to (A,5) is interior for all A if and only if maxA{(P@)-lV’(l)

to W and g. The solution

+ (1 – Z)A2

– AA}

>0,

or

(A.6)

which will be assumed ~uations

(A.5)

from here on (since z < – 1, a sufficient

condition

is ~ 2 0 and W’(7*)

< 0, hence

g’(~’)

0 if and only if ~“ S 1 – J/(2 A),

(13) into (A.5),

or

this means

‘%-’A~(’::?;:4)

that p~A2/4

=*m

< 1, hence

~

from r’ (O, A) = O to a minimum

the ~ = O axis at A = A. Finally,

to one with 1 – ~“ = O/A,

> 0. Therefore 7“ 0, ~7*/~A

+ pO~/2A)

(A.6)

0 for each A. For further

O~O–

reference

l/0=

A,

(All)

note also that this limit is

reached from below: V(A, ~) E n:, ~t

us now turn to the efficiency

and only if ~’ 21

– A/~A.

consequences

Equivalently,

–T*(A,A))A @2/(1

– ~) then W’(~*)

where taxes decre=e

with inequality,

taxes

inequality,

increases

limA+w[A(l A2 > p2/(1 Cue

with

– 7P(A))]

=

> 0 for all A. Therefore

these reductions

although

(1 – ~)-112,

never which

on the interval

in ~“ are always inefficient.

sufficiently is less than

fast.

Indeed,

6 defined

[0, A]

On [A, +aI)

one can show

in (All)

that

if and only

if

–p).

(ii):

if A2 < ~2/(1

– ~) then W’(r*)

>0

on [0, A) and W’(T*)

A > A. This implies that W’(r*)

T“ decreases subsidized

with inequality,

>0

over the whole interval

[0, A] where

and even over a strict superset of the interval [0, A] where capital is

(~ < O). This is intuitive,

as the planner

42

always wants to set ~P(A)

> 0. Only once

inequality

has reached

This mncludm

taxes ~“ (A, A) > 0 to excessively

the proof of Claim 3, u far as intertemporal

It only remains (A.2)

A does it drive equilibrium

and (A.5)

to mnsider

AA

-

< (1

7“(1 – 7*)

–@)A2

T*[A/A – (1

@

sinm the losses from heterogeneity

tax effects on savings are of first order.

A))

>

0 e

20 e

the growth

efficiency

high levels.

>0.

(A.14)

is never sat isfiecl.

order in A2, whereas the induced

the condition

in the neighborhood

of A

1, > 1. This inequality

holds if and only if ~ is not too close to

one, in which case there exists a range of A’s satisfying parameter

configuration,

tax cuts induced

(A.6)

by rising inequality

such that g’(~*(A,

A)) >0.

In this

just below A reduce growth,

while

tax increases which occur as A rises just above A tend to improve it. To show that this last result is not specific to the region regressive of tipi tal subsidies A = A. Sin~

7“(A, A) = O, (A.2)

A)) >0 e A2>

it can be shown that the right-hand

some fied

upper bound.

in the neighborhood

is compatible

of A = A+ generate

asymptotically: of maximizing increwe

(1-B):l+PP)”

side is greater than of (A.6)

tax increases

(A. 14) as A ~

1) is equivalent

with (A.6)

at

as long as ~ is below

In that case there exists a range of A’s such that increases in inequality

growth rate, Finally, let us mnsider A ~ ~19, which by (Al

g’ (7”)

shows that:

g’(7*(A,

Again

(~” < O), let us next examine

to A2 2 ~2/(1

to positive

levels which still improve

m and 1 – ~“ s O/A,

– ~). When this condition

if and only if ~ is s not too close to one) holds,

equilibrium

taxes increase with inequality,

not only W but even g. men

too fast with rising inequality,

The condition

the

becomes

(which once more

g’(~*(A,

A)) > 0 even

but too slowly from the point of view

A2 < ~2/ (1 – ~), on the other hand, taxes eventually

whether from the point of view of welfare or from that of

growth,

43

Proof of Proposition 7 CZaim 1 immediately A >0,

results from Propositions

4 and 6, or directly

from

(A.7)-(A.8),

For

let us write out:

(pPA)-’

-(1

=

_

~

-Q)(I

(~ -PA(1

-T”)’+

of the second

D)(l – ~*) A]2/4.

(1-9)

(1-W

Therefore, V“(T*)

(2 - B)2 4 +

) by (Al).

term is a qutiatic (dW/dA).=T*

polynomial

greater than 6-2 (1+ p~(l – Z) ) -2. Provided

-~”)

-A)

+ A2

(A.16)

“

in A whose maximal

value is [(2 –

as long as: –v//(T*)

~’ 4(1 –~)

Now, recall from (A. 12) that A(l

(2A(1

–V’’(7*)/p~

T—T’ The numerator

-T*))


A and ~g/~A

for A large enough in this c~e,

~

and W’(~*)

>0,

-p)(l

which

3) (in which ~

the proof of Claim 2.

to make clear the role played by @ 0

First, we showed earlier that if ~2 < ~2/( 1 – ~), g’ (~”) becomes

large enough.

A, for which polynomial

in ~ whose maximal

T*

>0.

The numerator

value is (1 –7’)2(1

of the second

+ (1 –~)~*)2A2/4.

term is a quadratic

Therefore,

(dg/dA),=T.

A as long as: (1-

V“(T*)

B)(l-W

> (1 +(1 )

As A tends to infinity, 1 + 6-2>

(1 – @/2)2/(1

1 – T’ H 13/A and –V’’(~*)/(p~A2)

complete

>0.

markets we,

= 6-2,

– ~). This holds if and only if ~ is below

hence the first part of Claim 3. Conversely, A2Q limA+o[–A/~*]

-p)T*)2 47.

Indeed as A -0 where ~g/ar

so the rendition

some critical

bmmes

value in (O, 1),

one can show from (A. 18) that lim~+O[(dg/dA)T=T. (or also as ~ -

~j+l,

By Proposition

at some 7P (A ~) > 0. Since W(7, Aj)

–z)2)).

and let W(~j,

5, each W(-, Aj)

Aj,)

is strictly

is decreasing

in its second argument,

~(~j) Aj,),

(A.19)

this allows us to write:

W(Tj+I,

Aj+I,)

hence the result that intertemporal state.

The same holds a fortiori

efficiency

~(~j+l,

Aj,)

declines

from Tj to ~j+l

A ranking similar to (A. 19) obtains for gowth

such is the case in particular all j, implying

A;

> s2/(1