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HB31
f.'\
noo2-
Massachusetts Institute of Technology
Department of Economics
Working Paper
Fairness
U.S.
and
Series
Redistribution:
versus Europe
Alberto Alesina
George-Marios Angeletos
Working Paper 02-37
First draft: October 2002
Revised: January 2003
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MASSACHUSEHS
INSTITUTE
OF TECHNOLOGY
FEB
2 1 2003
LIBRARIES
Fairness and Redistribution:
US versus Europe*
George-Marios Angeletos
Alberto Alesina
Harvard University, IGIER,
NBER & CEPR
First draft:
MIT & NBER
October 2002. Revised: January 2003
Abstract
Different beliefs about
how
fair social
competition
is
and what determines income
inequality, influence the redistributive policy chosen democratically in a society.
the composition of income in the
first
place depends on equilibrium tax policies. If
a society believes that individual effort determines income, and that
to enjoy the fruits of their effort,
In equilibrium,
be quite
fair,
eff'ort will
and
it
will
be high, the
social beliefs will
role of luck limited,
be
all
have a right
chose low redistribution and low taxes.
self-fulfilled.
If
market outcomes
will tax
it
thus distorting allocations and making these beliefs self-sustained as well.
this interaction
US
a
lot,
We show
between social beliefs and welfare policies may lead to multiple
equilibria or multiple steady states.
explain
will
instead a society believes
that luck, birth, connections and/or corruption determine wealth,
how
But
vis a vis continental
We
argue that this model can contribute to
European perceptions about income
inequality
and
choices of redistributive policies.
*This project was initiated by a lively discussion
we had with
Olivier Blanchard
and Xavier Gabaix
in
February 2002. For helpful discussions and comments, we thank Daron Acemoglu, Robert Barro, Roland
Benabou, Olivier Blanchard, Peter Diamond, Glenn
Ed
Ellison,
Roberto Perotti, Thomas Philippon, Jim Poterba, Andrei
Glaeser,
Shleifer,
Jhon Gruber, Eliana La Ferrara,
Guido
Tabellini, Ivan
Werning, and
seminar participants at MIT, Warwick, Trinity College, Dublin, ECB, and IGIER Bocconi.
Arnaud
Devleeschauer provided excellent research assistance. Email: cialesina@har\'ard.edu, angelet@mit.edu.
A. Alesina
and G.M. Angeletos
Introduction
1
In the United States the redistribution of income from the rich to the poor
Mmited than
in continental
Western Europe ("Eiirope"
due to lack of
is
and entrepreneurship; and, given that
poor could raise out of poverty
trap, which unlucky people
effort
they really
if
fall in.
because
Many more Americans
effort rather
than bad luck or
Americans perceive wealth as the outcome of individual
"social injustice".
much more
in short), at least in part
of different perceptions about the sources of income inequality.
than Europeans believe that poverty
is
talent, effort,
determines success, they believe that the
tried.
Europeans instead view poverty a
According to the World Value Survey, 71 per cent
of Americans versus 40 per cent of Europeans believe that the poor could
become
rich
if
they just tried hard enough; and a larger proportion of Europeans than Americans (25
per cent versus 16 per cent) believe that income and success
who
is
who
think that
right, the
Americans who think that
effort
is
mostly due to luck.^ So,
determines success, or the Europeans
mostly luck?
it is
This paper shows that both Americans and Europeans can be correct in their beliefs
about what determines income, even
fundamentals between the two places.
luck
is
more important
even
if
preferences, technologies,
the variables "luck"
,
in
if
there are no intrinsic differences in economic
That
is,
Europe, while effort
"talent"
,
and
"natvire"
in equilibrium it
is
(i.e.
more important
can be the case that
in the
United States,
the exogenous statistical properties of
and "willingness to work" ) are the same
Different levels of government redistribution can then
be the
in the
two
places.
result of different beliefs that
are unbiased and truly reflect the actual relative weights of luck and effort in the income
distribution, beliefs that are actually self-fulfilling.
The key element that
With
these terms
drives our results
we capture a
is
the idea of "social justice" or "fairness".
social preference for reducing the degree of inequality
induced by luck while rewarding individual talent and
that a
common
desire for fairness
preferences for granted;
ences.
is
embedded
here,
In this paper
in individual preferences
we show emprical evidence
While we take them as given
effort.
in support of this
we can think
we assume
and take these
type of prefer-
of such preferences either as an
^For a comprehensive discussion of these points, see Alesina, Glaeser and Sacredote (2001).
Fairness and Redistribution
evolutionary-stable behavioral attribute,^ or as a social
a
socially preferable
outcome.^
For example,
if
norm
that attempts to support
individuals are risk averse and expect
uncertainty ("luck") in their lives but also differ in their talent, patience, or willingness to
work,
all
but not
A
individuals will favor a social
all
mechanism that provides insurance against
individuals will favor redistribution across different levels of talent
may
preference for fairness
thus
reflect
main motivations
in fact, one of the
to the extent that talent and
theft, fraud,
past investment decisions (such as education
skill reflects
skill.
On
the other
represent the effect of corruption, rent seeking, political subversion,
and the
like
are naturally treated
As the
is,
of the welfare state (e.g., Rawls, 1971). Moreover,
,
may
effort.
a demand for social insurance - insurance
or entrepreurship) there are efficiency gains in rewarding talent and
hand, "luck"
and
luck,
-
activities that involve large private
but no social benefits,^ and
by society as "unjust".
socially desired level of taxation
and redistribution depends on the perceived
sources of income inequality (luck versus talent and effort), and the actual composition
of income in turn depends on anticipated tax and redistribution policies, two stable equilibria
may
coexist for the
same "fundamentals". In the one equilibrium, taxes
are high,
individuals choose to invest and/or work less, and a relative large share of total income
due to
luck,
is
which in turn makes high redistribution and high taxation socially desirable.
In the other equilibrium, taxes are lower, effort and investment in productive activities
are higher, and a larger fraction of final income
in turn sustains the lower tax rates as
in terms of aggregate welfare.
"good" regime
is
and
due to
effort rather
than
luck,
which
The two regimes can be ranked
eqiiilibrium.
Conditional on preference and ability heterogeneity, the
unambiguously the one in which tax distortions are lower, a larger share
of total income variation
limited,
an
is
overall
is
due to
than
effort rather
economic outcomes are more
ever, the high-tax regime
may dominate when
luck, the
"fair"
.
need
Behind a
for redistribution is
veil of
ignorance, how-
the variation in innate talent
is
sufficiently
^See Bowles and Gintis (2000) and Sethi and Somananthan (2001) for the evolutionary origins of
reciprocity.
^Cole, Mailath
and Postlewaite (1992) show that
different social
norms may indeed
result in different
reduced-form preferences.
^For example, Murphy, Shleifer and Vishny (1991, 1993) and Angeletos and Kollintzas (1997) discuss
how
corruption and rent seeking are detrimental for economic growth.
A. Alesina and G.M. Angeletos
high.
We
emphasize that the observed differences in pohtical outcomes between the two
Where Americans and
continents could not be explained by differences in preferences.
Europeans
differentiate
most
in their perceptions
is
preferences for fairness.^ This paper explains
cies
how
different perceptions
preferences, fundamentals, or shocks
political
The
benchmark
static
different poli-
model) or different
dynamic extension); or similarly how small
self-sustained histories (in the
we
and
their
can be consistent with the same preferences and the same fundamentals, as the result
of either different self-fulfilling expectations (in the
and
about market outcomes, not in
differences in
may have resiilted to large difierences in
social beliefs
outcomes.
interaction of economic
and
political choices
and the consequent multiplicity that
identify in this paper are novel in the literature. In Piketty (1995), multiplicity orig-
inates in the inability of agents to learn the true costs
Different initial priors about the costs
and
benefits of redistribution.
and benefits of redistribution
steady-state beliefs, which support different optimal levels of taxation.
ilar
multiplicity arises in the recent
result to different
A
somewhat sim-
work of Benabou and Tirole (2002). Different
beliefs
are possible, not because people are unable to learn the truth, but rather because they
find
it
optimal to deliberately bias their
genetic bias,
own perception
namely procrastination.^ In Benabou
ity originates in
which
in turn results to high efficiency
^Actually, experimental studies
perhaps more
in the
(2000),
imperfect credit and insurance markets.
strong political support for redistribution as a
tions,
of the truth so as to offset another
altruistic that
way
on the other hand,
When
inequality
low, there
is
to correct for capital-market imperfec-
and low
inequality;
when instead
inequality
and the evidence on charitable donations suggest that Americans
Europeans, which alone would predict more rather than
are
less redistribution
United States.
^Benabou and Tirole (2002) endogenize the choice of political ideology and more
of whether to "believe to a just world"
and lack of self control. At the
distort their
own
optimal effort
their
is
multiplic-
own
is
beliefs
same
beliefs regarding
inefficiently
.
time, they have the ability to repress past experiences
what are the returns to individual
and maintain a more
more
the choice
In their model, but not in ours, people suffer from procrastination
effort.
low from an ex-ante perspective, people find
their future selves into putting
specifically
it
and thereby
Given that the ex-post
optimal ex ante to distort
"rosy" picture about the benefits of effort in order to "deceive"
effort
ex post.
Fairness and Redistribution
is
high, the rich strongly oppose redistribution, in which case low redistribution, low ef-
and high inequality are also
ficiency
In our paper, instead, multiplicity
self-sustained.
originates merely in the social desire to implement "fair" economic outcomes, even
beliefs are fully rational
and there are no important
differences in capital markets or
other economic fundamentals. Furthermore, our focus on fairness - which
by the empirical and experimental evidence we review
knowledge,
The
income
new
rest of
the paper
is
organized as follows.
is,
to the best of our
Section 2 reviews some evidence on
which justifies our mod-
Section 3 introduces the basic static model.
Section 4 analyzes the
interaction of economic
and
and voting choices and derives the two regimes as multiple
Section 6 concludes.
static
dynamics and derives the two regimes as multiple steady
equilibria. Section 5 introduces
unworthy
-
motivated
social preferences,
inequality, redistributive policies,
noise; in the
in Section 2
is
to the public-economics literature.^
elling approach.
states.
when
Throughout the main
Appendix, we consider
how
"luck" can
text,
we model
"luck" as exogenous
be reinterpreted
terms of socially
in
activities.
Evidence on Inequality, Redistribution and Fair-
2
ness
2.1
Income
After-tax income
fact,
inequaJity
is
inequality
According to the data
coefficient for pre-tax
in
much
higher in the United States than in Europe. This
however, reflects partly the different levels of redistribution.
the politics of redistribution
tion.
is
and redistribution
is
set
income
What
really matters for
the variance and skewness of the pre-tax income distribu-
by Deiniger and Squire (1996),
in the
in the
mid nineties the Gini
United States was 38.5 versus an average of about 29
Europe. Indirect measures of pre-tax income inequality, such as wage dispersion,
skill
premia, and returns to education, reveal a similar picture. In overall, before-tax income
in the United States has
'^Complementary
is
both higher variance and more skewness.
also the evidence
on the role of
As
for poverty,
fairness concerns in labor relations
Knetsch, and Thaler, 1986, Agell and Lundborg, 1995, Bewley, 1999).
the
(Kahneman,
and G.M. Angeletos
A. Alesina
fraction of population that receives
income
less
about 3 times higher in the United States than
than half of the country's median
in continental
Europe.^
Redistributive effort and support for the poor, on the other hand,
United States than in Eiirope. This
side of the
government budget.
the tax biirden of the rich
of government
is
is
is
much
Income taxation
is
more progressive
in Europe,
The
GDP). Table
1
is
OECD. The
indeed in transfers and other social benefits, where Europeans spend
about twice as much as Americans. Table 2 summarizes
OECD.
overall size
summarizes the composition of
government spending in Europe and the United States, using data from the
by the
and
about 50 per cent larger in Continental Europe than in the United
States (about 55 versus 30 per cent of
largest difference
lower in the
evident in both the revenue and the expenditure
relatively lower in the United States.^
is
level is
According to this measure as
"social spending", as
well, continental
measured
European countries spend
about twice as much the United States. ^° Note that a large fraction of transfer to families
is
pensions with pay-as-you-go systems, which imply a redistribution from the young to
the old. However, as documented by Alesina and Glaeser (2003), the poor retirees receive
proportionally
more than the
much
Europe than
larger in
rich,
and the rich-poor
redistributive role of pensions
is
one category
in
United States, hiterestingly, there
in the
which Americans spend just as much as Europeans, namely health
An
important dimension of redistribution
tion of labor
wage
is
and product markets.
legislation,
and
benefits.
in particular the regula-
and Layard (1999) report that the minimum
39 per cent of the average wage in the United States, whereas
the European Union. Table
(2001),
Nickell
is
3,
which
is
summarizes the large difference
is
it is
53 per cent in
reproduced from Alesina, Glaeser and Sacerdote
in
regulation, using data again from Nickel
employment protection and other labor-market
and Layard (1999) and Nickel
(1997).
We
note
that Europeans and Americans differentiate by a factor of five in the duration of un-
employment
benefits,
but not in the replacement
ratio; that
is,
Americans appear to be
protected relatively well against short-term unemployment, but not against long-term
*Ln the 1980s, that
number was
18 per cent in the United States versus 5 to 8 percent in Europe. See
Atkinson (1995) for more details.
®For more details, see Alesina, Glaeser and Sacerdote (2001).
^°Note that the two measures of social spending in table 2 and of transfers
to coincide because they
come from tow
different types of clsissification.
in table 1
are not supposed
Fairness and Redistribution
unemployment.
The
last
observation and the point on health benefits suggest that in the United
States there are
many programs
family, such as disease, disability,
designed to help certain characteristics of an indigent
number
there are very few programs to help those
of children, or short-term
who
are poor per
unemployment, but
Using evidence from the
se.
Liixembourg income study, Alesina and Glaeser (2003) indeed show that the poor are
generally
States
is
more protected
more limited
in Europe, but the difference
in cases were clearly identifiable sources of poverty are evident, like
disease, children to support, etc.
Evidence on tax systems and the regulatory environment
confirm that European countries try to protect those
An
United States. ^^
contribute
is
between Europe and the United
who
are poor per se
observation which goes in the same direction
much more than Europeans
to charitable contributions.
is
more than the
that Americans
One
interpretation
that they prefer to give to charities rather than being taxed because with a private
redistributive channel one can better choose the deserving recipients. ^^
2.2
Social mobility
and redistribution
As noted above, most Americans believe that the poor have a
fair
chance of getting out of
poverty, while Europeans believe that they are stuck in poverty. According to the World
Values Survey, 71 per cent of Americans versus 40 per cent of Europeans believe that the
poor have a chance of escaping poverty
believe that social mobility depends
for their
The
uals
own
they tried hard.
effort
In other words, Americans
much more than what Europeans
believe
society.
probability of
when ranking
between
on
if
upward mobility
redistributive policies
social mobility
to be taken into consideration by individ-
is likely
(e.g.,
Benabou and Ok,
and individual demand
2001).
The
for redistribution is studied
relationship
by Ravallion
and Lokshin (2000) on Russian data, by Corneo and Gruner (2002) using an international
survey on several
Whether or not
OECD
coimtries,
and by Corneo (2001)
certain types of regulation
are overprotected minorities
is
an important
do
for
in fact protect the very
issue which
we do
^^See Alesina, Glaeser and Sacerdote (2001) for data and
Germany and the United
poor or certain categories which
not explore here.
more
discussion.
A. Alesina and G.M. Angeletos
States. ^^ All these papers use cross-sectional
on the
ion
desirability of redistributive policies
likelihood of being upwardly mobile,
rather than self-assessed mobility
live in
The
more mobile
on individual
how
latter significaxitly affect
and La Ferrara (2001) study the
places or times, are
question remains of
and their self-assessments about their
and they conclude that the
attitudes towards redistribution. Alesina
who
data containing both the respondents' opin-
preferences,
more
and they
effect of actual
find that individuals
averse to redistribution.
compare on the two
in fact social mobility
sides of
the Atlantic. Measuring social mobility, and especially comparing measures across countries,
is
extremely
difficiilt.
A
by
recent survey
Fields
and Ok (1999) finds that the
evidence regarding observed social mobility in the United States and Europe
clusive,
even though in most estimates the United States
Europe. Gottshalck and Spolaore (2002) note that there
sibility
and
availability of means of social mobility
people move in the social ladder.
class
and the upper
differences are quantitatively small.
and Rustichini (1999)
a
slightly
more mobile than
between the pos-
diflFerences
social mobility
between the middle
United States than
in
Germany but the
Looking at educational attainment, Checchi, Ichino
find that the United States
is
more mobile than
education system that, on paper, should be more egalitarian in
Italy, despite
than the difference in inequality. Therefore,
it
is
seems rather implausible that
explain the dramatic difference in political outcomes.
What
is
an endogenous outcome and thus may not be used as an explanatory
fact,
measured
and investment
for effort
(either
and investment,
redistributive effort
is
it
own
both the
or parental).
might be that
higher, not the other
effect of luck
and the
As higher taxation
social mobility
way round.
is
much
it
lower
could help
more, social mobility
itself
social mobility reflects
^^In the paper by
is
is
In
variable.
effect of ability,
distorts the incentives
lower in Europe because
In our model, taxation
and
mobility are both endogenous, and the relation between the two can be ambiguous, as
depends on whether mobility
an
Italy.
In any event, the difference in social mobility across the two continents
effort,
incon-
and the actual observation of how much
They argue that
class is slightly higher in the
is
is
is
driven mostly by luck or mostly by
Corneo and Gruner (2002), other motivations of the demand
effort.
And
it
in the
for redistribution, along
with the political-economic channel, are taken into account, and the results are shown to differ between
Eastern and Western European countries.
Fairness and Redistribution
data, the decomposition of measiired social mobility to "luck"
and
"effort"
components
remains an open question.
2.3
Experimental evidence on fairness
The key assumption
"fair"
for
our results
demand
outcomes; they
is
that agents have a desire for "social justice" and
that individual effort
is
rewarded by society; and they
expect the government to intervene and "correct" economic outcomes when they
social competition
is
feel
that
"unfair".
Fehr and Schmidt (2001) provide an extensive review of the experimental evidence on
and
fairness, altruism,
endowment to
reciprocity. In dictator
others, even
games, people give a small portion of their
though they could keep
hi ultimatum gam,es, people
it all.
are ready to suffer a monetary loss themselves just to punish behavior that
"imfair".
In
in order to
gift
considered
exchange games, on the other hand, people are willing to suffer a loss
reward actions that they perceive as generous or
gam,es, cooperators tend to punish free-riders.
in the size of
is
fair.
Finally, in public good
These findings are very robust to changes
monetary stakes or the background of
players.
In short, there
is
plenty
experimental evidence that people have an innate desire for fairness, and are ready to
punish unfair behavior.
What
is
more, the existing evidence rejects the hjrpothesis that
altruism takes merely the form of absolute inequity aversion.
desire equality relative to
outcome, which
is
some reference
what we assume
point,
People instead appear to
namely what they consider as a
"fair"
in our model.
Further support in favor of our concept of fairness
is
provided by the evidence that
experimental outcomes are sensitive to whether the roles or the
initial
endowments of the
experimental subjects are assigned randomly or as a function of previous achievement. In
ultimatum games, Hoffman and Spitzer (1985) and Hoffman
who make
proposals are
to reject unequal offers,
trivia
more
likely to
make unequal
offers,
et
al.
(1998) find that those
and responders are
when the proposers have outscored the respondents
in a preceding
qmz or game, and even more if they have been explicitly told that they have
their roles in the
ultimatum game on the basis of
action market experiments, Ball et
al.
less likely
"earned"
their preceding performance. In double
(1996) report a similar sensitivity of the division of
A. Alesina and G.M.
Angeletos
surplus between buyers and sellers on whether market status
in a public
is
random
or earned. Finally,
good game where groups of people with unequal endowments vote over two
alternative contribution schemes, Clark (1998) finds that
likely to vote for the
scheme that redistributes
the same group, when
less
members
relative
performance in a
general-knowledge quiz rather than been randomly assigned. In short, there
between
conflict
self interest
and
fairness concerns,
more
from the rich to the poor members of
endowments depend on previous
initial
of a group are
but how this
whether experimental subjects regard any given inequality
always a
is
conflict is resolved,
in final
and
outcomes as justifiable
or unfair, seems to depend strongly on whether such inequality derives from achievement
random
or
luck.
Last but not least, psychologists, sociologists and political scientists have long stressed
the importance of a sense of fairness and justice in the private, social and political
men. People enjoy great
satisfaction
when they know
(or believe) that
world, where hard work and good behavior will ultimately pay
off;
they
live in
life
of
a just
they strongly believe
that one should get what he deserves and, conversely, that one should deserve whatever
he
gets;
prevails.
that justice
and
political
outcomes
not only experimental and psychological studies that support our modeling approach.
We now
The
provide direct evidence on the effect of fairness on political outcomes. ^^
effect of social beliefs
policy choices
1
demand
^^
Fairness
2.4
It is
they are outraged in the face of unfair behavior and they
is
about what determines income (luck or
on actual
not limited to a comparison of the United States versus Europe. Figure
shows a strong positive correlation
of social spending over
GDP
determined mostly by luck
and the
(as
in
the cross-section of coxmtries between the share
fraction of the popvilation
who
for the Gini coefficient
think that income
is
measured by the corrsponding fraction of the respondents to
the World Value Survey). In Table 4 we show that this correlation
^''For
effort)
and continent dummies. The
is
robust to controlling
correlation looses significance
if
one
a detailed discussion and more references, see Lerner (1982) and Benabou and Tirole (2002).
is also the evidence that fairness concerns affect labor relations (Kahnemcin, Knetsch,
^^Complementary
and Thaler,
1986, Agell
and Lundborg, 1995, Bewley,
10
1999).
Fairness and Redistribution
controls for the share of the old; this
this variable.
is
much
are paid to the old
shows,
if
because the
size of
pensions depends heavily on
However, as pointed out above, the redistribution in favor of the poor old
larger in continental
Europe than
much more
is
Europe than
continental
is
in the
in the
redistributive
US
US; that
way
the
is,
in
which pensions
from the rich young to the poor old in
(Alesina and Glaeser, 2003). Furthermore, as Table 5
one excludes pensions, the correlation between transfer payments and
beliefs in
luck remains very strong. These tables also control for two political variables, the nature
of the electoral system and Presidential versus parliamentary regime, which
may influence
the size of transfers, as argued by Persson and Tabellini (2003).^®
A covmtry's social spending is, of course, only an aggregated measure of final outcomes,
not a direct measure of individual preferences over possible political outcomes.
measure, however,
is
Such a
provided by the World Value Survey for a large sample of individuals
from each surveyed country. One of the questions asks the respondent whether he
being on the
identifies himself (herself) as
"leftist political
we then
of the political spectrimi.
left
We
regress this variable against the individual's
belief that luck determines
own
belief
income has a large and very
about what determines
significant efi'ect
Again, the
on the probability
leftist.-'^
Further survey evidence in support of the desire for fairness
They use the General
rara (2001).
individuals
who think
that income
is
comparable form, this
is
why
is
in Alesina
Social Survey for the United States
and La
social
spending was available only
the number of observations
is
different in the
two
for
OECD
leftist; leftists
less leftist
tend to
than
all
own
belief.
live in cities
and have fewer
children;
The dummy
and the oldest (above 65) are
for being a
that the concept of "left" and "right" might differ between Europe
mean
We
belief
US
significantly
citizen allows for the possibility
and the United
States; the results are
removing that indicator variable. Relative to the specification of Alesina, Glaeser
and Sacerdote (2001), we added the Gini
other hand,
countries
Income and education influence negatively the probability of being
the other age groups.
totally insensitive to
etc..
tables.
^^Similar results are reported in Alesina, Glaeser and Sacerdote (2001) using the country's
instead of the individual's
Fer-
and show that
determined by luck, connections, family history,
'^The breakdown between pensions and other
in a
take such
orientation" as a proxy for being in favor of redistribution. In Table 6,
income, together with a series of individual- and country-specific controls.
of being
(she)
we omitted
coefficient, to control for
ethnic fractionalization, because
report Probit estimates, but
OLS
it is
insignificant
results are very similar.
11
the effect of inequality per
and does not
affect
se.
On
the
the results.
A. Alesina
and G.M. Angeletos
rather than individual effort, education, ability,
ment
redistribution, even after controlling for
etc.,
much more
are
an exhaustive
favorable to govern-
set of other
determinants of
preferences for redistribution. These controls include the respondent income, his gender,
marital status, race, age, various characteristics of where he or she
lives,
employment
by
status, education, personal experience of social mobility. Similar results are reported
Fong
(2002) using a different data set for the United States.
3
The Basic Model
Consider a non-overlapping generation model, in which each generation consists of a large
number
of agents (a
[0, 1]
continuum),
who
two periods. In each period
live for
of
life,
agents engage in investment and productive activities, such as accumulation of physical
or
human
capital, work, entrepreneurship, etc..
In the middle of their
over the tax and redistributive policy of their government.
agents consume
economy
is
their disposable income.
all
essentially static,
As
there are
no
And
at the
life,
agents vote
end of
their
life,
links across generations, the
and we can characterize economic conditions and outcomes
in
one generation without reference to any other generation. (We consider inter-generational
links later, in Section 5.)
3.1
Heterogeneity, technologies, and preferences
The investment and productive
activities of the first
period of life require
the combined outcome of inherent talent, investment during the
diiring the second period of
life,
Vi
y,
denotes the income agent
he makes in the
life.^^
^*If
a G
we
[0, 1]
interpret
first
is
fc^
and
=
first
period of
A,[aki
life,
period of
Income
life,
is
effort
luck:
+
(1
-
a)e-\
+
and
e,
(1)
77^.
receives in the second period of
i
effort.
life,
ki
the investment
the effort he exerts in the second period of
a technological constant, which can be interpreted as the share of
£is
a form of
human
capital, ki
and
e^
are likely to be complements; such com-
plementarities would complicate the algebra but would not matter for our results.
12
Also, the case that
Fairness and Redistribution
income that represents return to past investment and that
fixed.
Ai represents the inherent talent and
which we interpret as pure random
of agent
skills
sunk when the tax rate
is
Finally,
i.
In the Appendix,
luck.
influence his "luck" by engaging in "bad effort"
that
,
is,
how
we
is i.i.d.
r]^
is
noise,
how one can
discuss
be reinterpreted
"luck" can
as corruption, rent seeking, political subversion, theft, fraud, or other forrns of socially
unworthy
activities.
Consumption
in the second period of life
Q <
r denotes the
represents a
lump sum
Romer
to model.
The
given by
r)2/,
+
G.
(2)
G
income tax the government imposes in the second period and
flat-rate
following
-
(1
is
This redistributive scheme
transfer.
is
widely used in the literature
and Meltzer and Richard (1981), because
(1975)
qualitative natiire of our
message
it is
the simplest one
not unduly sensitive to the precise
is
nature of this scheme.
Individual preferences are given by
=
Ui
The first term represents
= d-
Ui{ci,ki,ei,Q)
—ip{ki,ei)
Pi
the utility of consumption.
of first-period investment and second-period
-
-yD..
(3)
The second term
represents the costs
P^ parametrizes the willingness to
effort.
postpone consiomption and work hard: a low ^^ captures impatience or laziness, a high
captures "care for the future"
and hyperbolic discounting,
.
or "love for work"
loss of generality,
^{ki,e,)
and history of
In that case,
could
let
Pi
=
human
his family,
I
examined
we would need
for all
i
= ^k^ +
capital reflects, not only one's
is
agents suffered from procrastination
If
could also be interpreted as the degree of
/3j
For simplicity, and without serious
productivity and
.
we
let ip
(4)
choices during his
life,
but also the wealth
in Section 5.
to distinguish between ex ante
ex ante, whereas P^
<
\
and ex post preferences. For example, we
and Var{Pi) >
try to offset the temptation to procrastinate
which would decrease the incentive to
tax,
ex post. Such a modification would
A
"sophisticated"
when choosing the optimal tax
rate,
but the possibility of multiple equilibria would remain. For an
elegant model where the anticipation of procrastination
and
^^
be quadratic:
complicate the algebra but would not change fundamentally our equilibrium analysis.
median voter would
self control.
-^el
own
/5j
Tirole (2002).
13
aff'ects also
the choice of ideology, see Benabou
A. Alesina and G.M. Angeletos
The
coefficients
a/2 and
"social injustice"
— q)/2
are merely a normalization. Finally,
and 7 measures the strength of the
,
we capture aversion to
that with this term
and
Fairness
3.2
(1
social
demand
Q
is
a measure of
for "fairness"
.
unfairness, not aversion to inequality.
social injustice
Following the evidence in Section 2 that most people share a
common
concern for fairness
and a common perception that one should get what he deserves and deserve what he
we
Note
gets,
define
Q = E [{a -
Cif
(5)
and
Ci
=
=
Vi
A^\aki
+
(1
-
a)ei]
The
latter represent the "fair" or "ideal" levels of
that
is,
what the agent should enjoy on the
Q
In the absence of taxation,
distribution;
now Q measures how
are private information to agent
i.
effort or the
outcome of
fair levels
E appears in fi because
piire luck (or
(^4^)
"fair" levels of
effort. Q,
is
environment,
home
tell
whether
and thus
this
characteristics
as there
is
income
is
the fruits of talent
the outcome of corruption).
and/or willingness to work
income.
From a normative
specification
and willingness to work
(more resistance to fatigue or
both a
"fair"
and an
"imfair"
(fc,, e^, ci),
society as a whole observe
For instance, differences in Ai
location, etc.;
then gives an
the pre-tax income
(/3j)
stress).
component
Our
in
may be
may be
/3j
results,
income
generates en-
perspective,
debate endlessly about what source of income variation should be consider
should be treated as "unfair".
i,
of consumption in the
(/!,, /5j, 77,),
The government and the
Remark. Heterogeneity in talent
dogenous variation in the
and
basis of his talent
for agent
economic outcomes remain after redistribution.
the total income of each agent, but can not
and
(6)
7?^
would measure how unfair
vinfair
Note that the expectation operator
-
y,
consumption and income
aggregate measure of the distance between actual and
society.
=
"fair"
we may
and what
related to family
affected
by physical
however, survive as long
inequality.^° Moreover, our
seems most appropriate from a positive perspective, to the extent we think of
^°See also Section
5,
and
in particular 5.4,
where we examine how
difFerencies in family history
parental investment can be treated partly as "fair" and partly as "luck"
14
and
Fairness and Redistribution
variation in Ai
and
as ex ante heterogeneity
/3j
and variation
in
77^
as ex post heterogeneity.
Risk-averse agents woiild agree ex ante on a social institution that moderates the effect
of ex post heterogeneity, but not the effect of ex ante heterogeneity,
and
ability reflect differences in past investment choices, redistributing across
different levels of talent
explain
why
specification
Moreover, to the extent that differences
appears to proxy exactly such a social norm.
in talent
and our
it is
and
"fair" to
ability
would involve important
reward such
efficiency losses,
which
may
differences.
The Government
3.3
The government chooses the tax
rate r
and the
level of redistribution or
spending G,
subject to the following budget constraint:
G<
We
assume that the policy
theorem holds. There
for the effect of luck
will
is
jryi =
rEyi.
chosen with one person one vote rule and the median voter
be two motivation
for redistribution.
on income because of the demand
the event that the median of the population
"selfish" redistribution
a
la
(7)
is
One
for fairness.
is
to partly correct
The second
poorer than the mean,
is
one, in
the standard
Meltzer and Richard (1981).
The Politico-economic Equilibrium
4
The
general equilibriiim of the
Definition 1
such that
rate
r
{i)
An
equilibrium
the plan {ki, Ci)
economy
is
(2), (6)
and
(7), (5)
naturally defined as:
a tax rate r and a collection of individual plans {ki,
maximizes the
maxivfiizes the utility of the
Using
is
median
utility
of agent
i
for every
i,
and
{ii)
ei}i^[o,i]
the tax
voter.
reduces to
Q=E
/"{[(l-r)^/,
15
+ r%,]-y^}^
(8)
and G.M. Angeletos
A. Alesina
Suppose that
only
if
luck
we assume
—
yi
77^
yi is
independent of
this will turn to
yi;
be true
in equilibrium
independent of talent Ai and willingness to work or patience
is
for simplicity.
Then, from
(8)
we obtain
/3j,
if
and
which
social injustice as a weighted average
of the "variance decomposition'.' of income inequality:
n=
Note that the weights depend on the
Q.
+
T^Var{y{)
- TfVar{y, -
(1
yi).
(9)
namely
level of redistribution,
If
r.
minimizing
were the only purpose of taxation, and the income distribution were exogenous, the
equilibrium tax rate would be given simply by:
r
The right-hand
side represents
distribution
as they
is
-
y^)
a kind of signal-to-noise ratio in the income distribution;
and as the goal of redistribution
the optimal tax rate
Variyi
is
decreasing
and the corresponding
to eliminate the effect of noise on income inequality,
this signal-to-noise ratio.
is
signal-to-noise ratio are
depend on the investment and
effort choices
However, the income
endogenous in the economy,
made by
all
agents, which
we now
examine.
4.1
Investment and
effort choice
Consider the investment and effort decisions of agent
i.
He
chooses
ki
and
e^
so as to
maximize
^,
=
taking r, G, and
is
fi
(1
-
r)A[«fc.
+
(1
-
+G-
a)e.]
as given. Since agents choose ki before
a function of the anticipated tax rate and
is
tax and the investment the
in
made
before.
To
-
r is
^^^e| - 7^,
Cj
.
(11)
fixed, first-period investment
simk when the actual tax rate
the other hand, agents choose second-period effort
realized one,
^k\
is
chosen.
On
ex post, contingent on the realized
distinguish the anticipated tax rate from the
we henceforth denote the former by r and the
any perfect-foresight eqiiilibrium, but we adopt the
clarity.
16
latter
by
r.
Of course, t = r
different notation for the
shake of
Fairness and Redistribution
The
first
order conditions Avith respect to
k,
Substituting into (6)
=
-
(1
and
6i
=
=
(1
-
and
i.
Prom
r)y,
+ TEy =
(1
-
Substituting the above into
On the
-
(1
a)r]<5i,
(13)
in investment
and
effort (fcj,ei)
Moreover, and an increase in the tax
(yi),
and actual income.
fair
(2)
and
(13),
+
[a(l
-
r)
+
(1
- rf +
(1
-
a)(l
T)r],
t)t]-
+^
[l
-
=
^
-
a)(l
-
-
n=
- rf]
we conclude that equilibrium
(3),
ar^
[a{l
(1
-
other hand, social injustice
Var{rji),
(12)
t)][6,
+ t{E6 -
6^)].
(12),
<f>{h, e,)
= {l-
T)p^Ai.
voter and the optimal tax
Consider an arbitrary agent
u^
-
endogenous heterogeneity
and thereby reduces
The median
(4)
- ar -
[1
component of income
in the fair
rate distorts incentive
From
(1
P^Af. Therefore, exogenous heterogeneity in either talent {Ai) or impatience
and thereby
Q =
=
e,
imply
e^
we conclude
,
laziness (/3J translates to
4.2
and
T)^iAi
yi
where
and
ki
a)T^]
5,
+
[1
- ar -
+
(1
-
r)^Var{r]^).
(1
-
6,P,
utility is given
a)r]r(E5
-
6i)
by
- 7Q.
(14)
is
T^Var{y,)
which measiires the contribution of luck,
sures the contribution of talent, effort
is
(15)
exogenous, but Var{yi), which mea-
and investment,
is
endogenous.
Using (13) we
obtain:
Var{yi)
=
[1
Therefore, equilibriiim social injustice
Q=
r^fl
- ar is
- ar -
(1
-
a)T]'^Var{5i).
given by
(1
-
a)r] V^
17
+
(1
- rfv^
(16)
Angeletos
A. Alesina and G.M.
where
a"^
From
is
=
Var{5i)
and
(14)
=
Var{PiA'j) and
(5), it follows
a decreasing function of
the distribution of
any
rj^
is
5i
that Ui
is
single-picked in r
i
such that
6i
applies with respect to
= 6m
and
t]^
where k
=
(1
—
simplicity,
=
6i
u,
assume that
77^
for
and the median voter
where 6m denotes the median of
0,
6i.
Following (14), the utility of the median voter
Um =
and the r that maximizes
symmetric and a law of large numbers holds with respect to
corresponds to an agent
the distribution of
Var{r]i).
and an increasing function of t]^. For
The median- voter theorem then
6i.
=
v'^
K--{l- a)T^6m +
aT'^)6jn/'2.
Note that n
meaning that the median voter does not
past investment choices.^'
- ar -
[1
On
is
given by
is
(1
-
Q;)r]r(E(5
6m)
- 1^,
(17)
when r
perceived as a constant
is
chosen,
internalize the adverse effect of the tax rate
on
the other hand, the median voter does take into account
the distortion of contemporaneous effort; this efficiency cost
term above. The third term
-
in (17) is the net transfer the
is
reflected in the second
median voter receives from the
government, reflecting the fact that a positive tax rate effectively redistributes from the
mean
median of the income
to the
for redistribution, as in
"altruistic"
motive
distribution. This
term introduces a
"selfish"
motive
Meltzer and Richard (1981), whereas the last term captures an
for redistribution, originating in the social
concern
for fairness.
In order to focus on the implications of fairness, in the remainder of this section
6m =
restrict
We
E5i, so that the
mean and
the median of the income distribution coincide.
extend our results to the more general case, 6m
then 6m
=
2,
n
<
EJ^, in Section 4.4.
Normalizing
the median voter's utility reduces to
Um =
with
we
K—
{1 -- a)T'^
— 7^,
(18)
given by (16).
The ex post
"optimal" tax rate r maximizes the utility of the median voter, Um, taking
the ex ante anticipated tax rate r as given.
^^Ln other words,
we have assumed
It follows:
that the median voter
reasonable eissumption in 4.5.
18
leicks
commitment.
We
explain
why
this
a
Fairness and Redistribution
Lemma
V
to work,
a G
a >
1 Let
>
mean and
amount
the exogenous
the portion of
(0, 1)
the
median of
= arg
/(r)
measure the exogenous variation in
min {r^
income that
is
7 >
the desire for social justice,
sunk when the tax rate
and
Suppose that the
is voted.
income distribution coincide and define
the
[(1
of pure luck,
or willingness
talent, patience,
-
a)
+
{ja^)
- ar -
(1
(1
- a)Tf] +
- rfiW)}
(1
(19)
tG[0,1]
/ represents the best-response function of the median voter against market
That
//
'y
T G
when
is,
=
0,
[0, 1]
The
tax
the ex-ante anticipated tax rate is r, the ex-post optimal tax rate is r
=
/(r)
and
for
all
r G
intuition
// instead
a and increasing
decreasing in
is
[0, 1].
simple. If there were
is
median voter (who is
outcomes (7
>
0),
also the
7 >
in v
0,
>
the optimal tax is f{T)
=
/(r).
for
all
and a.
no concern about
zero, as redistribution has only costs
is
expectations.
fairness (7
=
0),
the optimal
and no benefits from the perspective of the
mean agent). When instead
the society desires
the optimal tax vnll trade less efiiciency for
more
economic
fair
fairness.
If
there
is
a concern for fairness, then society chooses a positive level of redistribution in order to
on income
correct for the effect of "luck"
income variation
due to luck, and the higher
is
consideration holds for larger
and
effort.
The
inequality.
v,
as this implies
is
As a
increases,
is
more income
variability
increase in r has two opposite effects.
"fair"
On
component of income
the one hand,
variation, as
it
is
due to
ability
unambiguous
the case of
distorts effort.
hand, a higher r redistributes more from the poor to the rich and
When r
opposite
distorts investment, but
like in
it
The
and the ex-post
generally non-monotonic. In fact an increase in r has an
adverse effect on the fairness of the income distribution, as
the effect of luck.
of the observed
the optimal tax rate.
relationship between the ex-ante anticipated tax rate (f)
optimal rate (r)
r reduces the
more
small, the second effect dominates;
may
r,
On
an
a higher
the other
thus "correct" for
r increases with r
in
order to expand redistribution and thus "correct" for the relatively larger effect of luck.
When
more
instead r
effort
is
high, the
first effect
and thus "substitute"
dominates; r
falls
with r in order to encourage
for the adverse effect of a higher r.
19
A. Alesina
General equilibrium
4.3
From
and
and G.M. Angeletos
(13),
is
the "signal-to-noise" ratio in the income distribution
decreasing in the anticipated tax rate as long as part of income
chosen (that
ta:x is
given
is
is,
a >
0).
On
by
is
simk when the
the other hand, minimizing social injustice
interpreted as minimizing the effect of "noise" on consumption variation.
optimal tax
Q
can be
The ex post
thus higher the lower the higher the signal-to-noise ratio in the income
is
distribution. It
is
this interaction
opens the door to multiple
between the signal-to-noise ratio that the tax rate that
equilibria.
In any eqmlibrium, expectations must be validated; the ex-post optimal and the exante anticipated tax rates must thus coincide. Following
Proposition
r
fixed point
If instead
when 7
1 Suppose that the
=
7 >
/(r), where
0,
f
is
the tax rate is
is sufficiently
median and
the
given by (19). If
r G
(0, 1)
small or when v/a
mean
'y
=
1,
we
conclude:
coincide.
An
equilibrium
unique equilibrium
0, the
in any equilibrium; the equilibrium
is either sufficiently
but there are two stable equilibria (and one unstable)
when 7
is
is
is
r
any
=
0.
unique
small or sufficiently large;
is sufficiently
high and v/a
takes moderate values.
Therefore, provided that part of the effort and investment choices are simk
the tax rate
economy
talent
is
and
is
when
chosen and the society cares about the fairness of economic outcomes, the
prone to multiple equilibria,^^ unless the amount of exogenous heterogeneity in
willingness to
work
is
either too high (in which case only a low-tax equilibrium
survives) or too small (in which case only a high-tax equilibrium survives).
of multiple equilibria
is
easy to see
when v/a
fa
and a
^^In light of the recent critique by Morris and Shin (2000), one
would break down
if
we were
to relax the
~
1,
may worry
in
The possibility
which case both the
that our multiplicity result
common-knowledge assumption and introduce
idiosyncratic
noise in the observation of economic fundamentals. However, Angeletos, Hellwig and Pavan (2002) show
that, in coordination environments with endogenous policy, multiplicity survives in the form of "policy
traps"
.
Besides, in the
dynamic extension we consider
in Section 6, the
two tax regimes re-emerge as two
stable steady states of a unique equilibrium path, in which case the Morris-Shin critic
20
is
simply irrelevant.
Fairness and Redistribution
exogenous amount of luck and the ex-post cost of taxation are almost
then two stable equilibria, one in which r
~
and one
in
which r
Figure 2 illustrates an example of multiple equilibria.
best-response function (19) for an economy in which 7
(meaning
that, in the absence of taxation,
differences in talent
and
effort
predetermined when the tax
is
70%
of the
=
.
fa 1.
The
solid curve depicts
a=
1/2,
a =
luck,
[US and EU) correspond
2.5,
and v
it
=
1
is
This curve has three intersection points with the
The two extreme
to stable equilibria, while the middle one corresponds to
an -unstable one. In point EU, the anticipation of a high tax induces agents to exert
effort.
the
and that half of income
45° line, each corresponding to a different politico-economic equilibriiim.
points
There are
income variation would be due to
and 30% due to random
chosen)
1,
zero.
This in turn implies that the bulk of income heterogeneity
is
little
due to luck and makes
ex post optimal for society to undertake large redistribution programs by imposing high
taxes, thus vindicating initial expectations.
low tax induces agents to exert high
outcome
of heterogeneity in talent
effort
and
In point US, instead, the anticipation of a
and implies that income variation
effort,
which
in turn
makes a low tax
is
mostly the
self- sustained
in the political process.
As long
amount
as there
of luck
is
in talent, a high-
is
both a desire and a cost
for redistribution,
neither too large nor too small as
compared to exogenous heterogeneity
and a low-tax regime are boimd to
was so large that the
effect of luck
and the exogenous
coexist.
On
the other hand,
is
illustrated
by the upper dashed
very small, so that either there
is
no
redistribution, or the cost of taxation
survive.
Such a situation
is
illustrated
Remark: Even in the cases that the
line in Figure 2.
And
may
if
is
Such a
7, v/a, or
social desire for fairness, or there
is
a were
no need
for
too high, then only the low-tax regime would
by the lower dashed lined
in Figure
2.
eqiiilibriiim is unique, the politico-economic
plementarity we have identified in this paper introduces a miiltiplier
differences in fundamentals
v/a
always dominated the effect of talent and effort in
shaping the income distribution, then only the high-tax regime woiild survive.
situation
if
effect.
That
is,
result to large differences in equilibrium outcomes.
21
comsmall
A. Alesina and G.M. Angeletos
Self-interested redistribution
4.4
We now
Sjn
<
allow the median of the income distribution to be lower than the mean, namely
E5, and thus introduce a selfish motive for redistribution, as in Meltzer and Richard
(1981).
Let
A=
— 5m
FiS
mean and
parametrize the distance between the
the median of the
pre-tax income distribution, which can be interpreted as a measure of pre-tax income
inequality.
As
6m =
before, normalize
From
2.
the median voter's utility
(17),
is
now
given by
Wm =
while social injustice
for the
/(r)
is
'^
—
—
(1
Oi)T'^
again given by
— 7^ +
(16).
We conclude
{ja')
(1
(1
—
a)T]A,
that the best- response function
median voter becomes
= argmin.e[0,ii
{ r^ [(1
-
- rfiW)
.^^.
the last term, which captures the Meltzer-Richard
effect.
a)
+
- ar -
-r[l-ar-(l The only
And
— ar —
r[l
difference
from (19)
is
(1
a)T]A
-
«)r)']
+
(1
}
again, a politico-economic eqviilibrium corresponds to any fixed point
A
Note that /(r) increases with
point of /
is
locally increasing in A.
median voter
is
relatively to the
for
any r G
This
[0, 1].
By
increases, the optimal tax rate trades less of the public
motive dominates, or 7
is
/{r).
simply the fact that, the poorer the
reflects
When A
=
implication, any stable fixed
mean, the higher the incentive to
private good (self-interest redistribution).
t
is
close to zero, so that there
good
As
redistribute.
(fairness) for
more
A
of the
sufficiently large, so that the selfish
is little
concern for fairness, a unique
eqmlibriiim siirvives. But otherwise, the possibility of multiple equilibria remains.
The above
redistribution:
results highlight that there are
The
two forces driving the equilibrium
absolute extent of income inequality (as measured by
level of
A) and the
social
value attributed to the fairness of economic outcomes (as measured by 7). Provided that
the latter
is siifficiently
strong,
it is
perfectly possible that the observed level of taxation is
lower in a coiintry with more income inequality, even
if
there
is
no
difference in underlying
fundamentals. Such an observation cannot be explained by a pure Meltzer-Richard model,
as in the absence of a social
demand
for fairness a
22
unique equilibrium survives, in which
Fairness and Redistribution
redistributive effort
is
higher the higher the income inequahty.^^
Comments
4.5
First, the
two eqmlibria can
easily
namely the one with lower taxes
be ranked from the perspective of the median voter,
always superior:
is
There are
investment, and more aggregate income; and the ex-post heterogeneity in income
relatively
ranking
is
more
(before learning either {Ai, P^) or
preferable
if
risk neutrality. In fact,
r;^),
is, if
is siifficiently
you do not know whether you
willingness to work,
due
clear-cut Pareto
behind the
you may prefer to be
bom
in
large
veil of
will
and agents are
ignorance
sufficiently risk
be born with high or low talent or
Europe rather than the United
European regime provides more insurance against such genetic
as the
is
the equilibrium with high redistribution might be
the idiosyncratic variation
That
averse.
The
to ability than to luck, a socially desirable outcome.
due to our assumption of
more
less distortions,
risk.
States,
In fact, an
extension considering risk aversion sheds additional lights on cross- Atlantic differences.
Equation
(3)
imposes that agents are
For instance, we
strictly
E\I'(.),
re-specify preferences as ui
concave function. Once agent
maximizing q
before.
may
risk neutral,
—
(p{ei,ki)
To rank the two
—
7Q.
i
knows
but
=
—
{Ai,ei,r]j),
The equilibrium
<f{ei, ki)
—
maximizing
7^), where
is
over the distribution of (A,
^i, Vi)-
is
sufficiently large, the
preferred to the American equilibrium.
is
a
Ui is equivalent to
compare
The concavity of
more insurance against
and willingness to work or random
concave, and idiosyncratic risk
^
analysis thus goes through exactly as
introduces risk aversion, and higher taxation provides
may
'i{ci
equilibria behind the veil of ignorance, agents
where the expectation
variation in either talent
easy to introduce risk aversion.
it is
luck.
If
^
Eaii
"I'
=
then
idiosyncratic
is
sufficiently
European equilibrium
will
be
Differences in risk aversion across the Atlantic
then provide additional explanatory power regarding the differences in welfare states.
Since Americans were immigrants, and self-selection of those
origin in search of "fortune"
that Americans
may favor the least risk
may have been
less risk averse
For cross-country evidence which also gives
little
redisitribution, see Perotti (1996).
23
who
averse people,
and thus
less
leave their country of
it is
reasonable to argue
prone to social insurance.
support for a pure Meltzer- Richards model of
and G.M. Angeletos
A. Alesina
imply different degrees of attitude toward
Second,
it is
risk in the
perfectly possible that the "good" eqmlibriiim
has more inequality than the "bad" eqioilibrium (EU):
and Var{ci)
be
will
more
will
be
^^
two sides of the Atlantic.
If
a
is
(i.e.,
what we
labelled
US)
high relative to v, Var{yi)
larger in the "good" equilibrium, but the "variance decomposition"
Thus, and contrary to the simple Meltzer-Ri chard model, one can have
fairer.
inequality and less redistribution in the United States relative to Etirope.
Third, the agents in our model dislike unfair distribution, not inequality per
Adding
se.
a concern for inequality per se would increase the incentives to redistribute, but would
not affect the qualitative nature of our
results.
any equilibrium, but multiplicity would
In particiilar, taxation wovild be higher in
On
siirvive.^^
the other hand,
if
the voters cared
only about the overall level of inequality, and were indifferent about the decomposition
and
of inequality between fair
disappear
median
all
unfair components, the multiplicity of equilibria would
together. This, in fact,
coincide,
and
in the case that the
Fourth, our paper could offer some
of taxation.
would be true both
median
is
in the case that the
mean and
poorer than the mean.
new insights on
the normative and positive analysis
Consider, for example, the taxation of capital.
On
the one hand, fairness
introduces an additional incentive for taxing capital income, to the extent that variation
in investment
and
retiirns reflects
a representative-agent economy
capital levy once capital
is
the effect of "luck".
it is
On
the other hand, while in
ex post optimal to impose the
maximum
sunk, a fairness concern in a heterogeneous-agent economy
limits the ex post optimal tax, to the extent that variation in investment
reflects
may
both the characterization and the time inconsistency of
affect
fiscal policy.
Fifth, our analysis highlights the
post heterogeneity.
(like
and returns
the effect of talent, entrepreneurship, and past hard work. In other words, a social
preference for fairness
optimal
possible
what we
When
call "luck" )
^''See Alesina, Glaeser
importance of the distinction between ex ante and ex
agents are risk averse, the anticipation of
generates endogenously a
demand
ea;
post heterogeneity
for redistribution as a
form of
and Sacerdote (2001) and the references cited therein for more discussion of the
question of attitudes and self selection.
^^The relationship between changes
in inequality
and tax
addressed in Galasso (2002).
24
levels
would then be more complex, an
issue
Fairness and Redistribution
But ex ante heterogeneity
risk sharing.
may
to work" )
what we
(like
call
-
"innate talent" or "willingness
significantly limit the levels of redistribution that are socially preferable
or politically sustainable,
hi other words,
individuals are risk averse and expect un-
if
certainty ("luck") in their lives, but also differ in their talent, patience, or willingness to
work,
all
individuals will favor insurance against luck, but not
all
individuals will favor
redistribution across different levels of talent or effort. Moreover, to the extent that talent
and
ability reflects past
investment decisions, such as education or entrepreneurship, re-
distributing across different levels of talent
and
ability involves
important efficiency
losses.
However, both the distinction between ex ante and ex post heterogeneity and the accumulation of
human
from the recent research
capital are absent
of optimal taxation and social insurance.
We
in the Mirrlees
paradigm
believe that such considerations may, not
only generate endogenously the kind of fairness preferences that we took for granted in
this paper,
Finally,
but also produce further important
it is
unrealistic to think that
insights.
an economy could "jimip" from one tax regime to
another by simply revising eqmlibrium expectations from one day to another. In the next
section,
we consider a dynamic extension,
steady states.
society holds
History then plays an important role in determining what beliefs the
and what
redistributive policies
regime would survive in the static economy
tax and redistributive policies before agents
decisions, such
and income are
5
which the two regimes emerge as multiple
in
commitment
will
be of
largely determined
little
it selects.
if
Similarly, while only the low-tax
the society could credibly commit on
make
their early-in-life investment
value in the dynamic economy,
by family
and
its
effort
when wealth
history.
Intergenerational Transfers and History Dependence
One important determinant
of wealth
In order to explore this issue,
parental investment
(e.g.,
and success
in
life is
being born in a wealthy family.
we now introduce intergenerational wealth
transfers
and
bequests, education, status, etc.) that link individual income
to family history and birth. ^^
In order to concentrate
on
beliefs
For a recent discussion of the intergenerational transfer of wealth and
entrepreneurship, see Caselli and GennaioiU (2002).
25
about the history of
its effect
on
effort choices
and
A. Alesina
and G.M. Angeletos
the wealth distribution rather than expectations about future taxation, we abstract from
investment choices
made
the source of multiple
The optimal
self-fulfilling equilibria
that
and redistribution
rate of taxation
generation, but
5.1
within a generation before the tax
is
we had
now
is set,
in the
and thus shut down
benchmark
static model.
imiquely determined for any given
depends on the whole history of the decomposition of wealth.
it
The environment
Consider an economy of non-overlapping generations indexed byt G {..,—1,0,
Within each generation, there
generation lives for one period.
made after the tax
voted on. Parents enjoy
is
by "bequests" we mean, not only monetary
investment. ^^ Let
c]
utility for leaving
but also
transfers,
denote the consumption of family
i
is
1,...}.
Each
a single effort choice,
a bequest to their children;
all
other sorts of parental
in generation
t,
and
kl
the bequest
the family leaves to the next generation. In the benchmark model, k denoted the effort
or investment
made by
the individual himself early in his
the bequest or parental investment of
same notation
is
not accidental;
component of wealth that
component of wealth that
ui
The
first
=
fixed
is
is
it
made by
/3f
instead denotes
The
use of the
emphasizes that, in either case, k corresponds to the
when the tax
is
chosen, whereas e corresponds to the
U'{4,ki,el,n^)
utility
is set.
Preferences are
now given by
= V{cl,kr>-^^{ei)-jnt.
(22)
from consumption and bequests, the second term
the disutility of effort, and the last term captures the
benchmark model,
now k
the individual's family.
determined after the tax
term represents the
life;
parametrizes "laziness" and
(f is
demand
for fairness.
As
is
in the
quadratic:
For simplicity, we also assume a Cobb-Douglas aggregator over consumption and bequests:
y{cl K)
^"^This
is
of course a short cut, which
=
1
7
is eeisier
T^
/
i\l-a
(cj)
{KT-
(23)
to model than adding the utiHty function of the children
into that of the parents.
26
Fairness and Redistribution
The constant
(1
—
an innocuous normalization. As the fraction of wealth
Q;)"^~°a° is just
a can be
allocated to bequests will turn to equal a, the coefficient
interpreted as an
intergenerational discount factor.
The budget
constraint for household
e^
i
in generation t
+ kl<{l-Tt)yl + Gt,
while the budget constraint for the government
Gt
Pre-tax income (or wealth)
is
given by
is
now
=
(24)
is
TtJyi.
(25)
.
given by the stun of effort, luck, and parental invest-
ment:
= Ai4 + 4 +
yl
Al represents, as before, innate talent, which
is
J4_,.
(26)
To the
independent of family history.
extent that productivity reflects child-rearing, education, and other shorts of parental
investment, we capture
i.i.d.
5.2
its effect
on income through
which captures exogenous luck within the
noise,
Market outcomes and
Household
i
in generation t chooses
maximize
utility (22) subject to
outcomes
{Tt,Q,t) as given.
life
not
A].'^^
r]l
is
again
of the agent.
consumption, bequest, and
effort (cj,fcj,e^) so as to
the budget constraint (24), taking political and social
Therefore, the optimal consumption and bequests are
ki
= a[{l-n)yi +
'
rty,],
(27)
Tty,],
(28)
is
ei
=
il-Tt)AiPi.
(29)
Introducing a production complementarity between parental investment,
e],
Finally,
social injustice
ci^{l-a)[{l-Tt)yl +
while the optimal effort
fcj_j,
would complicate the algebra, but would not alter our qualitative
27
fcj_j,
findings.
and individual
effort,
A. Alesina
and G.M. Angeletos
Since wealth depends on parental investment (bequests) from the previous generation,
and bequests
turn depend on contemporaneous wealth, the wealth of any given indi-
in
vidual depends on the level of effort
lifetime,
but also along his whole family
outcomes and
fair
and the
realization of luck, not only during his
tree.
We
thus need to adjust our measures of
social injustice for the propagation of luck
transfers. In the absence of taxation, iterating (26)
y^
own
and
(28)
through intergenerational
backward would give
=
=
{Ai4
+ r^ +
kl_,
=
{Aiel
+ ri]) +
a{Al_,el_,+r,i_,)
(30)
.
+
akU =
=
...
= X^ a^-M^ei + J^ a- v..
s<t
s<t
Assiiming that bequests and parental investments are considered
fair
only to the extent
that they reflect effort and talent, not pure luck or iindeserved privileges, the "fair" level
of wealth
is
the cumulative effect of effort and talent,
yl^Y.a^-^jV^el,
(31)
s<t
while the residual
yj-y^ =
J]a-V3
(32)
s<t
represents the cumulative effect of luck throughout the family's history.
wealth would result to
and
kl
=
ayl,
of consumption and bequests equal to
which in turn woirld imply a
bequests equal to
instead V{cl,
fair levels
k]).
V (cj,
fcj).
The
Our measure
fair levels of utility
The
fair level of utility
c^
fair level of
=
(1
—
from consumption and
actual level of utility from consumption and bequests
of social injustice
is
now
(27)
and
from consumption and bequests:^^
(28),
V{4,
kf)
=
(1
-rt)yj + r(E?/j) and similalry F(cj,
social injustice is equivalently the distance
^^An
is
the distance between actual and
nt=El [V{cl,ki)-V{c'ji)y.
By
Q:)yJ
(33)
fcj)
=
g. Therefore,
between actual disposable income and
alternative specification that gives identical results
the disutility of effort would also not alter our results.
28
is fit
= E J HcJ + /Cj] —
[cj
+
fcj]
!>
.
fair
Including
Fairness and Redistribution
income, exactly
income
like in
the benchmark model (see condition
By
(8)).
(29)
and
(31), fair
is
% = Y, a-M:4 = Y. a-*(l - r;)5\,
3<t
where
§1
=
P\{A\Y.
(34)
S<t
Hence, the signal-to-noise ratio in the income distribution
is
now-
given by
and
is
in turn decreasing in past tax rates. Finally, assiiming that SI
and y\~yl
lated with each other, which ensures that yj
other,
The above is identical
is
-
(1
T,)VaT[yl
benchmark
i
<t—
and
t,
and
1.
The
let
t.
To
if
simplify
Var{6l)
=
r^
=
r
(36)
y]).
model; once again
static
for all generations s
we assume
that
o^ and Var{rf^
signal-to-noise ratio in generation
-——
::—
=
1
=
t
- ar -
51
= 0l{Aiy
v^ for all i,t.
it
implies
signal-to-noise ratio
is
<t —
and
1,
tjI
then
are
Suppose r^
Tj
=
r
is
i.i.d.
across
=t
for all
reduces to
(1
-
a)Tt\
Var{yl -y\)
now
-
Multiple steady states
optimal for generation
This
are uncorre-
are also uncorrelated with each
bound to be a decreasing function of the
look for fixed points such that,
both
t]1
income distribution.
5.3
s
= nVar{%) +
to condition (9) in the
that the optimal tax rate
We
and
we obtain
Q,
in the
\^
Var {j:^^,a^-%)
Var{y\-y^,)
—.
.
(37)
v^
identical to the analogous condition (20) in the
benchmark model, with only r
representing an average of past tax rates rather than the ex-ante anticipated conrate.
To
we again assume 6m =
IB5.
temporaneous tax
abstract from the Meltzer- Richard motive for redistribution,
Normalizing EJ
the median voter in generation
t
=
2(1
—
a),
a)T\
-
jQt,
we can show that the
reduces to
<=K-
(1
29
utility of
A. Alesina
=
where k
— r) + (1 — a)- n
2a[l
is
and G.M. Angeletos
historically given for generation t
represents the efficiency cost of taxation.
to
we
Tt,
Q.t
and maximizing with respect
conclude:
Lemma
2 Let
to work,
V
and Q G
Substituting
and the second term
>
cr
>
measure the exogenous variation in genetic talent or willingness
Q the exogenous amount of pure luck, 7
>
the desire for social justice,
the relative importance of intergenerational transfers in shaping the wealth
(0, 1)
Suppose that the mean and the median of the income distribution coincide
distribution.
and define
f{T)
= argmin (r^
-
[(1
+
a)
(7(7^) (1
- ar -
(1
-
a)r)^]
+
(1
- rfiW)}
f{T) represents the best-response function of a given generation against a stationary his-
That
tory.
generation
when
is,
is
r
=
all
previous generations have chosen t, the optimal tax for the current
/(r).
Comparing the above with Lemma
to that in the
1
,
we
see that the functional
benchmark model. Therefore, om:
form of /
is
identical
earlier result of multiple equilibria in
the static economy directly translate to a result of multiple steady states in the d3Tiaraic
economy:
Proposition 2 Suppose
fixed point r
rate
is
t E
is
in
=
the
mean
0,
the unique steady state
any steady
state; the steady state is
fir).
(0, 1)
or when v/a
states
=
median and
that the
7/7
is
coincide.
r
=
0.
A
steady state
If instead
unique when 7
7
>
0,
is
any
the tax
is sufficiently
small
either sufficiently small or sufficiently large; but there are two stable steady
(and one unstable) when 7
is sufficiently
high and
v/a
takes moderate values.
Therefore, the example of Figure 2 can be directly reinterpreted in the context of a
dynamic economy with intergenerational
some given generation and r
transfers, provided
we read r
as a weighted average of tax rates in
all
as the tax rate in
past generations.
Multiple steady states again exist
when the
social desire for fairness is sufficiently high
and the
moderate
values.
US
relative effect of luck takes
and EU, correspond to the two stable steady
30
The two extreme
states.
intersection points,
Different initial conditions, or
Fairness and Redistribution
diiferent
exogenous aggregate shocks, would lead the economy to converge to either of
these two steady states.
fairer
US
is
characterized by lower taxation, lower distortions, and
outcomes as compared to EU.
Income inequality and
social mobility
can be higher
both inequality and mobility are mostly the
of luck in
other.
EU. Moreover, mobility and
It is
inequality
in either steady state. Nonetheless,
inequality need not
quite possible that the superior steady state
and yet higher
US
effect of effort in
social mobility. This will indeed
be
{US)
and mostly the
tightly related with each
is
associated with higher
be the case
cross-generation variation in talent or willingness to work
is
if
the within-family
sufficiently large, for
mobility will be mostly the effect of differences in effort and productivity in
it will
be mostly the
effect of
luck in
effect
then
US, whereas
EU.
Equalizing opportunities for children
5.4
In writing (31),
we assumed that the
society wishes to correct the cmnulative effect of
pure luck, but otherwise parents are fully entitled to make different transfers to their
children deriving
from
different levels of effort.
However, the society
may
not want to
keep children born by imworthy parents responsible for their parents' laziness and lack of
There
care.
is
then a conflict between what
is
considered
fair vis-a-vis cliildren.
As a
is
considered fair vis-a-\as parents and what
result, the society
may
like to
only partly entitled to leaving different bequests to their children, even
if
make
parents
these differences
reflect different levels of effort or parental care, so as to further equalize opportunities
across children.
This possibility
is
easy to incorporate in our model, as follows. Let A G
fraction of effort-driven parental bequests that children are entitled to; that
level of
wealth
(0, 1)
the
is,
be the
"fair"
is
yl
=
Aie\
+
A
J^
«^"'44-
3<t-l
1
—
A can be interpreted as a measure of the social desire
across children.
The
analysis goes through as before, with simply replacing
Assuming again that the mean and the median
we conclude
for equalizing opportrmities
coincide,
that the optimal tax rate in generation
31
t
and normalizing EJ
a
=
with aA.
2(1
— aA),
when past generations have chosen
A. Alesina and G.M. Angeletos
T
given by r^
is
=
/(r)
It follows
=
where
/(t),
argmin{r2
[(1
-
aX)
+
(7^^)
(1
- aXr -
{1
- aXyf] +
-
Tf{-fv'^)}
that the possibility of multiple steady states remains as long as A
Moreover, the tax rate in any (stable) steady state
small.
(1
is
is
.
not very
decreasing in A; that
is,
redistribution increases with a higher desire to equalize opportunities across children.
Remark.
We
have considered only one kind of taxation and redistribution, namely
income taxation coupled with lump sum
instriiments. For example,
A
society
may
Different redistributive goals given a
be achieved by using a mixture of
desire for fairness could
tax.
transfers.
we can introduce an
different
tax and redistribution
inheritance tax in addition to the income
then consider an inheritance more or less
"fair"
depending on whether
higher bequests are or are not due to higher ability and effort by the previous generation.
Our model would
Similarly, one could consider public provision of education.
an attempt to correct
that, in
Europe adopts a
larger
more unfair variation
for the
predict
in children's opportunities,
government intervention in education.
Conclusion
6
More Americans than Eruopeans think
rich);
that the poor are lazy (or at least lazier than the
and fewer Europeans than Americans think that market outcomes
gue that
in their
ket allocations, increases the effect of luck,
in turn, vindicates the
We
Europeans'
beliefs
in equilibriiun, distorts
and makes economic outcomes
and
justifies their policy choices.
occurs in the United States, where lower distortions imply a more
ution and therefore
need
less
inequality
is
for redistribution. ^°
ar-
fair
unfair.
marThis
The opposite
income
distrib-
These considerations help explaining
higher in the United States than in continental Europe, and
nevertheless redistributive policies are
^°It is
fair.
attempt to improve the fairness of economic outcomes, Europeans choose
more redistribution and more government intervention which,
why income
are
much more
limited.
A
different
way
of saying this
worth mentioning an interesting difference with respect to Benabou and Tirole (2002). In their
model
it is
mostly an "illusion" that
model
it is
a fully rational belief.
in
American
effort is
32
more important than
in
Europe, while in our
Fairness and Redistribution
is
that Europeans favor redistribution because they (correctly) perceive income inequahty
as largely the effect of luck, whereas Americans are willing to tolerate inequality because
they (also correctly) perceive
it
^^
as largely justified.
between the United
Interestingly, the biggest differences in redistributive policies
States and continental Europe reside in the support for poverty per
sick, old, or disabled,
do get
predict
if
That
is, if
you are
have dependent children, or have suffered an accident at work, you
substantial support in the United States; but
much support
se.
if
you are merely poor, you do not get
in the United States. ^^ This stylized fact
we allowed two kinds
of "luck"
,
is
exactly what our model would
observed and unobserved. Since accidents at
work, sickness, and disability are mostly beyond the control of the individual and are easily
observed and verified by society, the social desire to correct for their effect on income
and consumption should be equally strong
in the United States
on the other hand, can be the outcome of unobserved choice
exogenous luck.
poverty
We
will
If this is
more the case
in the United States
and
in Em-ope. Poverty,
(lack of effort) rather
than
than in Europe, support
for
indeed be lower in the United States.
have focused on income taxation and redistribution, but the demand
may have similar implications for many other policy choices as well.
for fairness
Consider, for example,
the regulation of the labor market. Unemployment can be the outcome of either bad luck
(e.g., inefficient
match) or lack of
shrinking while employed).
society
may
If
"everybody who
must protect anybody who
emerge:
One
in
willing to
work deserves a job" and the
"unjustly" laid-off, two politico-economic regimes
and high imemployment
in which limited regulation
("United States"). Moreover,
larger than that of long-term
European
is
is
which extensive employment protection, generous unemployment
benefits, low turn over,
and another
low job search while unemployed, or high
effort (e.g.,
if
and
rates reinforce each other ("Europe"),
efficient allocations
are self-sustained as well
the exogenous component of short-term unemployment
is
unemployment, the model would predict that American and
policies diverge Avith respect to long-term
unemployment support but converge
with respect to short-term imemployment support. This prediction
''^We are of course not arguing that this
additional factors, see Alesina, Glaeser
is
the only explanation.
and Sacerdote
consistent with the
For an exhaustive discussion of
(2001).
^^See Alesina, Glaeser and Sacerdote (2001) for more detailed evidence.
33
is
and G.M. Angeletos
A. Alesina
fact that the duration of benefits
ratio
is
as high as in
Europe
This paper has shown
is
much
shorter in the United States but the replacement
(see Table 3).
how the complementarity between political and economic choices
that emerges in the presence of a concern for fairness can lead to multiple equilibria or
same "fundamentals" More
multiple steady states for the
.
we can think
generally, however,
of this complementarity as an amplification and propagation mechanism, via which small
and persistent
differences in fundamentals or initial conditions result to large
may relate
in political outcomes. This
and continental European
States
are
to the different historical experiences of the United
"idol"
;
history,
born
in the right family.
The
its
its history, class differences
privileges,
which we can interpret as
"self-made
and aversion to nobility and birth-related
from
due to
countries. In Europe,
more rooted and wealth more associated with
"luck" of being
man"
and
very
is
much an American
privileges are deeply rooted in
American
very beginning. At the time of the extension of the franchise in Europe,
the distribution of income was perceived as unfair because
birth
differences
nobility
than by
ability
and
effort.
The
was generated more by
it
unfairness of market outcomes has
hence been a strong argument for aggresive redistributive policies and other forms of
government intervention
instead that those
in
Europe. In the "land of opportunities," the perception was
who were
successful
and wealthy had "made
it"
on
their
own, at
least
to a quite larger degree than in Europe.
As a consequence, Americans have chosen low
redistribution, strong property protection,
and limited regulation, resulting to much lower
inefficiencies
and a much smaller
effect of "luck".
Exogenous "shocks" that may have also pushed the two
different politico-economic equilibria are the
two disastrous wars fought in
its
sides of the Atlantic towards
major wars of the
last century.
territory created devastation
and misery
In Europe,
for
a large
nvimber of Europeans. The aftermath of the wars witnessed a major growth of socialist and
communist movements, with the
natiiral implications in
terms of redistributive
policies,
viewed especially with vavor in these periods of devastation. The United States did not
loose a war, nor fought a war
on its
territory,
devastation in any comparable magnitudes.
''^Interestingly,
examples of
eis
nor experienced civilain deaths and domestic
^^
Skocpol (1992) discusses, the American Civil
social welfare
programs
in the
War prompted one
US, namely veteran pensions.
34
of the few early
Fairness and Redistribution
Finally, a
steady state
word on welfare and regulation reforms
is
in Eiirope.
Since the "European"
locally stable, small "shocks", such as incremental policy reforms,
may
not be enough to move Europe away from the politico-economic regimes that sustains
the existing system.
Only
and persistent reforms may switch the
large, bold,
economic equilibrium to the one with low taxes, limited regulation, and more
outcomes.
In practice, this
means that a
people that market outcomes
efficient
successful welfare reform needs to convince
eventually
will
politico-
become more
"fair"
with lower taxes and
narrower government intervention.
Appendix: "Bad"
We now consider the
is
effort,
case in which the socially undesirable source of income inequality
due to various kinds of
socially
unworthy
rent seeking, etc. In order to focus
disutility of effort
not luck
on
this
activities, or
new
"bad
effort"
such as corruption,
,
channel, in this section
we abstract from
and cost of investment.
The environment
The agent has one
unit of time or capital diiring the first period of
allocate in either "production" or "corruption
activities as in the previous section: If
period of his
tion",
life,
agent
i
and rent seeking."
We
life,
which he can
model productive
allocates ki in production during the first
he receives Aiki during the second period. "Rent seeking" or "corrup-
on the other hand, represent
activities
which do not create any new social product
but merely affect the distribution of a given social product among the different agents
in the
(1
—
economy; they are a zero-srmi game.
fei)
of his resources to corruption
Specifically, if agent
i
allocates a fraction
and rent seeking, then he receives
Ri
-I.
35
J
G,
(38)
A. Alesina
and G.M. Angeletos
where
=
Zi
\B,{l-h)\^
(39)
li^.
represents the level of rent-seeking activity by agent
Zi
in rent-seeking activities;
let
=
i/'
life.
G
ij)
for agent
i
(0, 1)
we do so only to ensure an
i
in rent seeking, his
=
J.
R^
=
0.
Total income and
by
are given
y,
introduces diminishing returns
interior solution and, for simplicity,
game,
1/2- Since corruption is a zero-sum
consumption
the aggregate rent
/. Zj
with bureaucrats and lobbying with politicians, or his indifference
towards the moriality of his own business
we
and
Bi measures the productivity of agent
seeking in the economy.
ability in negotiating
i
+
A,k,
=
R,
A,ki
+
[2,
-
Ez^] G,
(40)
Q = (l-r)y, + G.
The
"fair" levels of
consumption and income
ci
Suppose that
if
Ai and
bi
=
yi
and Ri
play the
budget
same
=
yi
are:
A^ki
= Vz-
are independent; which will
Ri,
be true
Bi/Ai are independent, which we assiime
n
By comparing
=
(41)
j{ci
-
the above with (15),
role that luck
t/j
=
Cif
it
r''VaT{y{)
becomes
+
(1
(42)
in equilibrium
for simplicity.
if
and only
Then:
- TfVar{R,),
clear that rents Ri in the present
(43)
economy
played in the benchmark economy. Finally, the government
is
G=
T fyi=-Ety„
'
(44)
and individual preferences are given by
Mi
The
last
= Q - 7O-
(1
-
a)r^.
(45)
term captures any contemporaneous cost of taxation; we cut through the micro-
foundations only for the shake of expositional simplicity.
Equilibrium allocations, corruption, and redistribution
36
Fairness and Redistribution
The FOC with
respect to
ki
reduces
to^'*
^x2
l-k, =
It follows
that
Zi
=
Bi{^]
=
2(J{Bi/Ai) and Ez^
increasing with the size of government. Let
of agent
i
(46)
.
2G¥i{Bi/Ai). Rent-seeking activity
=
hi
are independent. Using (46) together with (38), (40) and (41),
and from "good"
Ri
It
follows that ¥iRi
Eyj
=
Eyi
=
E/l^
—
=
effort is
=
2G[hi
-
thus
Bi/Ai denote the relative productivity
in rent seeking and, without serious loss of generality,
rent seeking
is
we
assume that
infer that
hi
and Ai
income from
given by
m = Ai- Gh.
and
E6i]
(47)
(reflecting the fact that corruption is
=
GE6j. Normalizing WtAi
E6j
=
1
and using
a zero-sum game) and
G = rEt/j,
we
infer that
aggregate output and the size of government aie given by
Eyi
=
^—
G=
and
where r again denotes the anticipated tax
rate.
^—
(48)
Note that the negative dependence of
aggregate output on the tax rate reflects not the usual tax distortion, as
we have assumed
(only for simplicity) that total resources are in fixed supply, but rather the waste of
resources in rent seeking, which
From
(47), the "variance
is
proportional to the size of government.
decomposition" of income
Var{yi)
= V ar{Ai)+G'^Var{hi).
G from
(48),
Letting
ct^
=
is
Var{Ri)
Var{Ai) andu^
=
=
Var{bi),
4G'^Var{bi) and
and substituting
we conclude
Var{y,)
Var{R,)
i
^2
a
T
y2
2
1
- +
4
^
(49)
Therefore, as the incentives to engage in corruption and rent seeking are increasing in
the expected size of government, the "signal-to-noise ratio" in the income distribution
is
decreasing in the anticipated tax rate. Note that this relation between the "variance
decomposition" of income inequality and the anticipated tax rate
To avoid corner solutions
in
for
any equilibrium, Bi{G/Ai)^
<
is
isomorphic to that
any agent, we assume that the parameters of the economy are such that,
1 for all i.
This
is
obviously without any loss of generality.
37
A. Alesina
its
Now
benchmark model.
in the
it
and G.M. Angeletos
reflects the effect of corruption rather
implications for multiplicity are essentially the same.
If
arise.
Two
than luck, but
may
stable eqioilibria
again
agents anticipate a high tax rate, then they allocate a large portion of their
resources in corruption rather than production, as they anticipate the private benefits of
the corruption
game
to be large. But then most of income heterogeneity
of socially imdesirable means, which in turn
in
makes
it
other hand,
if
the outcome
optimal to impose a high tax rate
an attempt to redistribute from the corrupt rich to the
On the
is
politically
disadvantaged poor.
agents anticipate a low tax, they allocate most of their resources in
production rather than consumption. In this case, most income heterogeneity
desirable
and the ex post optimal tax rate
is
is
socially
small, once again vindicating agents' initial
expectations.
This version of the model implies that a "benevolent" government
some corruption that
itly
is
present somewhere in the system.
is
we are
In a sense
implic-
viewing government activities and interaction with the public as a combination of
benevolent and corrupt.
A
more
cynical interpretation would be that
some
programs are introduced to placate the electorate letting corruption run
tailed modelling of corruption is
of corruption
even some
cient
in
trying to correct
beyond our scope
and redistribution may
OECD
countries
well capture the case of
(e.g., Italy,
and well-functioning as that
here. ^^ The
European
de-
contemporaneous presence
many
countries.
developing countries,
is
not as
These are welfare
which redistributive programs are often mis-targeted, or favor special
attempts at correcting inequities end up creating even more
But a
wild.
Greece), in which the welfare state
of other
redistributive
states
interests,
injustice. In other
effi-
and
words, in
the previous sections we considered a redistributive system in which redistributive flows
were as well targeted as possible. In this section we have considered a case in which
flows are a combination of favoritism
more
"fair"
and corruption
in addition to
fiscal
an attempt at creating
economic outcomes.
^^For insightful models of corruption, see Shleifer and Vishny (1993), Tirole (1993), and Banarjee
(1997).
38
Fairness and Redistribution
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Table
1
Composition of General Government Expenditure, 2000 (Percent of GDP)
Social
Consumption
benefits
Goods and
Wages and
and other
Gross
TotaF
Services
salaries
Subsidies
transfers^
investment
United States
29.9
5.3
9.2
0.4
10.6
3.3
Continental Europe'^
44.9
8.3
12.4
1.5
17.6
2.5
France
48.7
9.7
13.5
1.3
19.6
3.2
Germany
43.3
10.9
8.1
1.7
20.5
1.8
Sweden
52.2
9.8
16.4
1.5
20.2
2.2
Country
Source: Authors' calculations based on data from
OECD Economic Outlook Database
(No. 71, Vol. 2002,
Release 01, June 2002).
a.
Totals also include interest payments
and some categories of capital
outlays.
b. Includes social security.
c.
Simple average for Austria, Belgium, Denmark, Finland, France, Germany, Greece,
Norway, Portugal, Spain and Sweden.
Italy,
Netherlands,
Table 2
Government Expenditure on Social Programs, 1998 (Percent of GDP)
disability
Unemployment
and labor
and
market
Old-age,
Total
survivors^
Family^
programs
Health^
Other"
United States
14.6
7.0
0.5
0.4
5.9
0.9
Continental Europe'^
25.5
12.7
2.3
2.7
6.1
1.7
France
28.8
13.7
2.7
3.1
7.3
2.1
Germany
27.3
12.8
2.7
2.6
7.8
1.5
Sweden
31.0
14.0
3.3
3.9
6.6
3.2
Country
Source: Authors' calculations based on data from the
OECD
Social Expenditure Database for 1980-1998 (3rd
Edition, 2001).
a.
Includes cash benefits and in kind services.
b. Includes,
c.
among
other things, inpatient care, ambulatory medical services and pharmaceutical goods.
Includes occupational injury and disease benefits, sickness benefits, housing benefits and expenditure
low-income households.
d. Simple average for Austria, Belgium, Denmark, Finland, France, Germany, Greece,
Norway, Portugal, Spain and Sweden.
on other
contiilgencies (both in cash or in kind), including benefits to
Italy,
Netherlands,
Table 3
Labor markets
in the
US and
in
Europe
Minimum
Benefit
replacement
Benefit
duration
Labor
Employment
annual leave
standards
protection
(weeks)
ratio (%)
(years)
1985-93
1990
1992
1989-94
1989-94
France
6
14
5
57
3
Germany
6
15
3
63
4
Sweden
7
13
5
80
1.2
38
4
58.7
2.6
50
0.5
Country
Great Britain
7
European Union^
United States
4.8
13.5
1
3.8
Source: Reproduced from Alesina, Glaeser and Sacerdote (2001). Original sovirces: NickeU and Layard (1999)
and NickeU (1997). The labor standard index is produced byt the OECD and extended by Nickell and Layard. It
refers to the strenght of legislastion with regards to five different aspects fo the labor market:working hours,
employment protection and employees' representation rights. The score ranges from to
is measured by an OECD index referrring to the legal framework concerning hioring
and firing restrictions (frome OECD Jobs Study 1994). The amximum value iks 20. Minimum annual leave is
from the same OECD source and includes pubic holidays. The benefit replacement ratio is the share of income
replaced by unemployment benefits and it is from US Socuial Security Administration Socail Security Programs
Troughout the World 1999. benfit duration si from the same source.
fixed terms contracts,
10.
a.
Employment
protection
European Union includes Austria, Belgium, Denmark, Finland, France, Germany, Ireland,
Sweden and Great Britain.
Portugal, Spain,
Italy,
Netherlands,
Table 4
Effect of belief that luck determines income on total social spending
(cross-country data)
Dependent variable: Total
1
social
spending
2
3
4
5
-0.306*
-0.238*
-0.115
-0.041
(0.347)
Gini coefficient
Mean
belief that luck
(1.724)
(1.739)
(0.613)
32.728"'
32.272"*
36.430'"
31.782"
13.758
(2.925)
(3.064)
(3.305)
(2.521)
(1.345)
-6.950*"
-4.323
-2.992
0.413
2.344
(3.887)
(1.472)
(0.941)
(0.098)
(0.832)
-9.244"*
-6.075**
-0.808
4.657
0.774
(6.684)
(2.153)
(0.142)
(0.618)
(0.314)
determines income
Latin America
Asia
GDP per capita
3.148
4.754
-1.202
(1.348)
(1.548)
(0.742)
1.430*"
Population above 65
(3.833)
Popub/w
0.079
15 and 64
(0.337)
0.493
0.031
(0.184)
(0.011)
Majoritarian
-4.24
Presidential
(1.392)
-3.088
7.907
-25.207
-41.401
-3.937
(0.590)
(1.396)
(1.152)
(1.425)
(0.215)
29
26
26
26
26
Adjusted R-squared
0.431
0.494
0.495
0.496
0.7
Source: Total social spending
is social
Constant
Observations
spending as a percentage of
GDP, from Persson and
Tebellini (2000);
IMF. Majoritarian, presidential, and age structure are from Persson and Tabellini (2002). Ethnic
fractionali2ation is from Alesina et al (2002). Mean belief that luck determines income is constructed using
World Value Survey data for 1981-97 from the Institute for Social Research, University of Michigan. This
variable corresponds to the response to the following question: "In the long run, hard work usually brings a
better life. Or, hard work does not generally bring success; it's more a matter of luck and connections." The
answers are coded 1 to 10. We recoded on a scale to 1 with 1 indicating the strongest behef in luck.
original source:
,
Robust
/
statistics in parentheses. * significant at
10%; **
significant at
5%; ***
significant at
1%.
Tables
The
effect of mean belief that luck determines
income on
social spending,
excluding old age, disability and survivors' benefits (cross-country data)
Dependent variable: Social spending excluding old age,
disability
and survivors' benenefits
1
2
3
-0.232
-0.014
-0.242*
Gini coefficient
Mean
belief that luck
determines income
(1.617)
(0.129)
(1.824)
29.817"
22.085*
27.686"
(2.552)
(2.026)
(2.317)
7.156*"
10.162*"
7.005"
(3.868)
(5.893)
(2.811)
GDP per capita
0.529*
Population above 65
(1.857)
-0.631*
Population
1
5-64
(1.832)
-0.895
-1.85
(0.490)
(1.143)
Majoritarian
-6.924'"
Presidential
(3.536)
-59.411"'
-89.823***
-22.528
(3.057)
(5.394)
(1.190)
20
20
20
0.511
0.644
0.609
Constant
Observations
Adjusted R-squared
Source: The dependent variable reports authors' calculations using data for 1980-1998 from the
OECD
Social Expenditure database.
benefits,
farcdly
imemployment
AU
cash
benefits,
benefits
It is
and
defined as the
services,
active
sum of occupational
labor
pubUc health expenditures, housing
market
injury and sickness
programs
expenditure,
benefits, other contingencies benefits.
other variables are as in Table 4.
Robust
t
statistics in parentheses. * significant at
10%; **
significant at
5%; ***
significant at
1%.
Table 6
The
effect of individual belief that luck determines
Dependent variable: Being
left
income on individual
on the
political
political orientation
spectrum
1
2
3
-0.428"*
-0.468'"
-0.354'"
(12.50)
(5.02)
(3.50)
-0.031"'
-0.038***
-0.039'"
(4.86)
US resident
Income
(7.19)
(4.65)
-0.013*"
-0.003
0.005
(3.78)
(0.43)
(0.76)
0.032'"
0.04*"
0.03*"
(4.23)
Years of education
City population
(7.38)
(4.89)
0.109'"
0.134"
0.112
(4.72)
(2.16)
(1.88)
-0.079"*
-0.093"
-0.104*"
White
Married
(3.20)
(2.42)
(2.71)
-0.03'"
-0.041*"
-0.046"*
No. of children
(3.66)
(3.25)
(3.46)
-0.135*"
-0.109*"
-0.09"
Female
(6.93)
Individual belief that luck
determines income
(2.79)
(2.57)
0.482***
0.512"*
(9.02)
(8.61)
-2.562"*
Gini Coefficient
(2.70)
0.352"*
0.182"'
0.205**
Age group 18-24
(6.43)
(2.22)
(1.96)
0.414*"
0.321"*
0.324***
Age group 25-34
(11.77)
(5.81)
(5.93)
0.396*"
0.389***
0.392"*
Age group 35-44
(12.00)
(8.63)
(8.32)
0.276"*
0.242***
0,25"'
(5.15)
Age group 45-54
(8.18)
(5.29)
0.125*"
0.08
0.077
(3.59)
(1.60)
(1.42)
-0.392"*
-0.761*"
0.025
(5.90)
(5.26)
(0.07)
20269
12488
11514
0.03
0.04
0.04
Age group 55-64
Constant
Observations
Pseudo R-squared
Source: The dependent variable
on the
left
is
a 0-1 indicator for whether the respondent classifies himself/herself as being
of the pohtical spectrum.
It is
constructed using data from the World Value Survey. The question
formulated as follows: "In pohtical matters, people talk of
this scale, generally
speaking?" The respondent
is
left
given a scale
and
1
right.
to 10,
1
is
How would
you place your views on
being the most leftist. To avoid small
We classified as
leftist (indicator value 1) anyone who
answered with a score of 5 or below and rightist (indicator value 0) anyone with a score of 6 or above. All other
individual characteristics are also from World Value Survey. The table reports Probit estimates; OLS gives very
differences,
we
transformed this score to a 0-1 indicator.
similar results.
Absolute value of?
statistics in
parentheses. * significant
at
10%; **
significant at
5%; ***
significant at 1%.
1
1
1
1
Belgium
20%
-
SwedeNetherlands
y^
France
Austria
15%
Denm^
Germany
-
laly
?Pu^^av
Norway >•
1/^
Ireland
RnlandUnitedKifl^om
10%
Switz^H^
-
CanadaujK^lf'^
Chile
Fbrtugal
Brazil
U.S.A/«rtjstrana
>^
5%o
00
^
0-
Iceland
Argentina
Dominican Republi(yene2uela
Turkey
VBxn
Rnilippines
20%
40%
80%
60%
percentage who believe that luck determines income
Figure 1
Reproduced from Alesina, Gleaser and Sacerdote (2001). This
cross-country correlation between the percentage of
fraction
of respondents
to the
GDP
scatterplot illustrates the positive
allocated to social spending and the
World Value Survey who believe
that luck
determines income.
-
'
~/^^
/
0.8
/^
-
'
-
-
-
^^
/
"<;
^^^
1
/
2
^ff
5*
0.2
~
-
'
/-^/
0.
o
/"'
Jl
/
0.6
^^^^
--'
—
-
y
"•'
iS^^^^^^^^^""""'''^
^
^
--
,-
r
0.4
0.2
.
0.6
ex-ante anticipated tax rate,
.
.
I
,
.
.
1
0.8
t
Figure 2
The above
between the tax rate that agents anticipate ex ante, and the tax
(median voter) finds optimal ex post. The solid curve represents an economy
where the exogenous noise (luck) in the income distribution is moderate as compared to the
exogenous heterogeneity in talent, patience, or willingness to work. A politico-economic equilibrium
corresponds to any intersection of this curve with the 45-degree line. In this case, there are two stable
equilibria, one with low injustice and low taxation (US), and one with high injustice and high taxation
(EU). The lower dashed line, on the other hand, represents an economy where the noise in the income
distribution is very small, the social desire for fairness is very week, or the cost of taxation is very
high. In this economy, only the low-tax regime survives. Finally, the upper dashed line represents an
economy where both the desire and the ability to redistribute are high, in which case only the high-tax
regime survives.
figure depicts the relation
rate that the society
^ji^lb^
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