Ed Hopkins

Tatiana Kornienko

English

Research Papers in Economics

Inequality and Growth in the Presence of
Competition for Status∗
Ed Hopkins†
Department of Economics
University of Edinburgh
Edinburgh EH8 9JY, UK
Tatiana Kornienko‡
Department of Economics
University of Stirling
Stirling FK9 4LA, UK
August, 2005
Abstract
We investigate a simple endogenous growth model where agents care about
their social status. As greater equality tends to provide greater incentives to dif-
ferentiate oneself, redistribution may increase wasteful competitive consumption
and lead to lower growth.
Journal of Economic Literature classiﬁcation numbers: C72, D11, D31, D62, D90
Keywords: Status, relative standing, income inequality, growth, consumption
externalities.
∗We are grateful for the comments of Maria Rosaria Carillo, John Duﬀy, Chris Papageorgiou, and
participants at the conference on “Economic Growth and Distribution” in Lucca, Italy. Errors remain
our own. Ed Hopkins acknowledges support from the Economic and Social Research Council, award
reference RES-000-27-0065. Kornienko acknowledges support from the Faculty of Management of the
University of Stirling.
†E.Hopkins@ed.ac.uk, http://homepages.ed.ac.uk/ehk
‡Tatiana.Kornienko@stir.ac.uk, http://staﬀ.stir.ac.uk/tatiana.kornienko1 Introduction
For a long time there has been an active debate over the relationship between inequal-
ity and growth, fuelled further by more recent cross-country empirical studies (Forbes
(2000), Banerjee and Duﬂo (2003)). Aghion, Caroli and García-Peñalosa (1999) (hence-
forth ACG) provide an excellent survey of the theoretical side of the argument, where
there is little consensus either. They also discuss an important theoretical argument
in favour of growth-enhancing redistribution. In an endogenous growth model, where
output is produced at the household level and depends on accumulated production
experience, if the production technology exhibits decreasing returns, endowment redis-
tribution is unequivocally growth-enhancin g .T h i si sb e c a u s er e s o u r c e sa r es h i f t e df r o m
the “low-return” rich to “high-return” poor individuals.
In this paper we explore whether the above argument that redistribution enhances
growth holds in the presence of competition for social status. We investigate a variant of
A C G ’ se n d o g e n o u sg r o w t hm o d e lw h e r ea g e n t sh a v eac o n c e r nf o rs t a t u sa sd e t e r m i n e d
by their ordinal rank in the distribution of (conspicuous) consumption. Here, each indi-
vidual’s problem is strategic as her utility depends on the consumption choices of others,
so that equilibrium consumption and investment choices depend on the distribution of
endowments. As greater equality provides greater incentives to diﬀerentiate oneself, it
tends to promote greater consumption. As in ACG’s argument, what is crucial here is
the behaviour of the relatively less-endowed individuals. In a society where low social
status leads to complete social exclusion, redistribution leads to lower investment by
those relatively poor as any extra resources are diverted to conspicuous consumption.
However, in the societies where social competition is relatively “mild”, the argument of
ACG may still hold, and redistribution lead to faster growth.
The eﬀects of status concerns on savings and growth have been considered recently
by Cole et al. (1992), Corneo and Jeanne (1998), Cooper et al. (2001). Here we integrate
the model of status concerns in Hopkins and Kornienko (2004) with the growth model
of ACG. However, here we develop a new technique which allows us to explore how a
linear taxation scheme aﬀects decisions of the same individual, or of individuals with
the same rank (rather than of individuals with the same endowment as was done in
Hopkins and Kornienko (2004)), and thus show that in an even in ACG’s growth model,
shifting wealth from the rich to the poor may not always generate higher growth.
2 Endogenous Growth with Concerns for Status
Consider the simple overlapping-generations model with endogenous growth and market
imperfections found in Aghion et al. (1999) (ACG). There is only one good that serves
both as capital and consumption good. Each period, there is a continuum of agents,
indexed by i ∈ [0,1], each living for two periods. Each agent i upon birth at date t is
r a n d o m l ye n d o w e dw i t he n d o w m e n tzi,t, an independently and identically distributed
1random variable with mean µ, distribution G, and density g, that is strictly positive on
the support [z, ¯ z].
We assume that when agents are young, their consumption is observable and confers
social status. This may be because, as Veblen (1899) suggested, status may bring
intrinsic satisfaction, or because, as Postlewaite (1998) argues, some goods (such as
marriage partners) are not supplied by the market but are allocated according to one’s
social status. We follow the later, instrumental, explanation for concerns with status,
and thus assume that when young, individuals attempt to build up their status and
hence, implicitly, marriage opportunities. In their old age, they are only interested in
consumption (the result would be very diﬀerent if instead individuals cared about their
status when old - c.f. Corneo and Jeanne (1998)).
For expositional purposes, we consider an extreme case where agents when young,
rather than being concerned with the absolute level of their consumption, they only care
about their social status as determined by their relative consumption (allowing agents
also to care about their absolute level of consumption when young complicates the
argument without changing its qualitative outcome). Thus, the utility of an individual
i born at date t is given by:
Ut,i =l o gS(ci,t,F t(ci,t)) + ρlogci,t+1 (1)
where ci,t and ci,t+1 denotes consumption when young and when old, respectively, and
Si,t = S(ci,t,F t(ci,t)) is this individual’s status when young. We assume that an agent’s
status will be determined by her position in the distribution of visible (conspicuous)
consumption, with higher consumption meaning higher status. Following Hopkins and
Kornienko (2004), status is deﬁned as
S(c,F(·)) = δF(c)+( 1− δ)F
−(c)+S0 (2)
where c is individual’s consumption, δ ∈ [0,1), F(c) is the mass of individuals with
consumption less or equal to c,a n dF−(c) = limc0→c− F(c0) is the mass of individuals
with consumption strictly less than x. The parameter S0 ≥ 0 is a constant representing a
guaranteed minimum level of status, and it represents the “mildness” of social pressures.
Each individual can either consume her endowment, or invest it into the production
of the future consumption good. In the extreme case of capital market imperfections,
when borrowing is not possible, each individual faces the following constraints: ci,t +
ki,t ≤ zi,t, ci,t+1 ≤ yi,t, ci,t ≥ 0 and ci,t+1 ≥ 0. When individual i invests an amount
of physical or human capital ki,t at date t, production of the future consumption good
takes place according to the technology
yi,t = Atk
α
i,t (3)
where 0 <α<1. At is the level of human capital or technological knowledge available
in period t, and it is common to all individuals.
The fact that, in each time period, the young are in competition for status implies
that their choice of consumption is strategic. We look for a symmetric equilibrium where
2all agents adopt the same strategy, a strictly increasing consumption rule c(z).I f a l l
other agents do adopt the strategy c(z), the status for an individual with consumption
ci,t will be S = S0 + G(c−1(ci,t)). Maximising with respect to choice of consumption
gives ﬁrst order conditions that implicitly deﬁne a diﬀerential equation. Its solution (see
Hopkins and Kornienko (2004)) gives the symmetric equilibrium choice of consumption
c(zi,t) from which we can derive equilibrium investment:
k(zi,t)=zi,t − c(zi,t)=
R zi,t
z (S0 + G(z))νdz + zSν
0
(S0 + G(zi,t))ν (4)
where ν =( αρ)−1. Note that the choice made by the least endowed agent with endow-
ment z is of crucial importance here, and it depends on the “mildness” of concern with
status, S0.I n p a r t i c u l a r ,i f S0 =0 ,t h e nc(z) ≤ z with limz→z+ c(z)=z,t h ep o o r e s t
consume nearly all their endowment when young, but if S0 > 0, the individual with the
lowest endowment z does the opposite and consumes nothing. That is,
(c(z);k(z)) =
½
(z;0) if S0 =0
(0;z) if S0 > 0 (5)
The point is that in a symmetric equilibrium, the individual with lowest endowment
will have the lowest expenditure and so will have status equal to S0.F o r S0 close to
zero, this speciﬁcation of preferences (1) implies very low utility even if second period
consumption is well above zero. That is, S0 =0represents complete social rather than
material exclusion. For example, in polygamous societies low ranked men are unable
to marry even though their consumption is above subsistence levels. This gives very
strong incentives to avoid low social position and low ranked individuals spend heavily
on visible consumption.
Following ACG, we will now consider a pure linear redistributive taxation scheme,
whereby everyone is taxed at a ﬂat rate τ ∈ [0,1), and the tax revenue is redistrib-
uted back equally, so that zτ
i,t(zi,t) is the post-tax endowment of an agent with pre-tax
endowment zi,t:
z
τ
i,t(zi,t)=( 1− τ)zi,t + τµ⇒ zi,t =
zτ
i,t
1 − τ
−
τµ
1 − τ
(6)
As the result, the initial before-tax distribution G is a mean-reserving spread of the
after-tax distribution Gτ. Being a lump-sum tax, the policy does not change the returns
to investment. However, it aﬀects the incentives to invest insofar as it changes the
individual’s endowment, as well as changing the return to status as this is determined
by the endowment distribution. To see that, observe that the after-tax distribution
of endowments Gτ(zτ) is t h es a m et y p eas the before-tax distribution G(z),s ot h a t
Gτ(zτ)=G(z) and gτ(zτ)=g(z)/(1 − τ) (see, for example, Feller (1968)). That is,
while the linear redistributive tax scheme preserves individual social rank, the density
of individuals is, however, increased at every social rank which, in turn, increases the
returns to conspicuous consumption.
3We analyse the eﬀects of redistribution on consumption and investment decisions by
taking an individual i,b o r na tt i m et, with before-tax endowment zi,t and comparing
her equilibrium choices before and after tax. In what follows, kτ(zi,t)=k(zτ
i,t(zi,t))
denotes equilibrium after-tax investment for individual i born at time t with before-tax
endowment zi,t.F o re a c hp e r i o dt, and each individual i,w ec o m p a r et h ee q u i l i b r i u m
choices given by the equation (4) for the pre-tax distribution of endowments G(z) and
for the post-tax distribution of endowments Gτ(zτ).
Proposition: When individuals care about status when young, the relationship between
the before-tax and after-tax symmetric equilibrium investment decisions of a ﬁxed indi-
vidual i born at time t with before-tax endowment zi,t is described by:
k
τ(zi,t)=( 1− τ)k(zi,t)+τµ
Sν
0
(S0 + G(zi,t))ν (7)
In turn, this implies that:
(i) if S0 =0then kτ(zi,t) <k (zi,t) for all zi,t >z ,a n d
(ii) if S0 > 0,t h e nt h e r ee x i s t sˆ z ∈ (z,µ) such that, for all zi,t < ˆ z, kτ(zi,t) >k (zi,t),
and for all zi,t > ˆ z, kτ(zi,t) <k (zi,t).
Proof: Since before-tax and after-tax endowment distributions are of the same type,
one can write (4) as follows:
k
τ(zi,t)=k(z
τ
i,t(zi,t)) = (1 − τ)k(zi,t)+τµ
Sν
0
(S0 + G(zi,t))ν
Substituting into (4), the investment schedules cross at ˆ z such that
Z ˆ z
z
µ
1+
G(z)
S0
¶ν
dz = µ − z
Finally, deﬁne Q(G(z)/S0,ν)=( 1+G(z)/S0)ν − 1 > 0, and rewrite the above as:
Z ˆ z
z
µ
1+Q
µ
G(z)
S0
,ν
¶¶
dz = µ − z ⇒ µ − ˆ z =
Z ˆ z
z
Q
µ
G(z)
S0
,ν
¶
dz > 0
which implies that ˆ z ∈ (z,µ).
The above proposition says the following. Fix an individual i with endowment zi,t
and note that redistribution increases endowments of all below average individuals. Yet,
if the competition is “cut throat”, i.e. S0 =0 , after-tax investment is lower at all levels
of endowment. However, if S0 > 0, redistribution results in higher investment by the
poor, and lower investment by the relatively rich - including some “lower middle class”
agents (endowments between ˆ z and µ) who have higher endowments after redistribution.
We further explore how these equilibrium investment choices translate into economic
growth. Following ACG, we assume that the output of each individual productive unit
yi,t is aggregated into aggregate production yt simply as yt =
R
yi,tdi.F u r t h e r m o r e ,
4learning-by-doing and knowledge spillovers are captured by the following dynamics of
productivity parameter: At =
R
yi,t−1di = yt−1. That is, accumulation of knowledge re-
sults from past aggregate production, but because of learning-by-doing, growth depends
on individual investments. Thus, the rate of growth is
γt =l n
µ
yt
yt−1
¶
=l n
R
Atkα
i,tdi
At
=l n
Z
k
α
i,tdi (8)
When status concerns are present, redistribution may or may not lead to faster growth.
This is because relatively poor individuals may consume, rather than invest, their higher
post-redistribution endowment. To see that, write the equilibrium before-tax growth
rate as:
γt =l n
Z ¯ z
z
k(z)
αg(z)dz
and the equilibrium after-tax growth rate is:
γ
τ
t =l n
Z ¯ z
z
k
τ(z)
αg(z)dz =l n
Z ¯ z
z
µ
(1 − τ)k(z)+τµ
Sν
0
(S0 + G(z))ν
¶α
g(z)dz
For S0 =0the above expression becomes simply:
γ
τ
t =l n
Z ¯ z
z
((1 − τ)k(z))
α g(z)dz = αln(1 − τ)+γt <γ t
so that the after-tax economy unambiguously grows slower than the before-tax economy.
However, if S0 > 0, we have seen that investment by the poor may increase. The
diminishing marginal returns to investment imply that it is possible that the fruits of the
increased investment by the relatively poor outweigh the consequences of the decreased
investment by those in the middle and at the top of the distribution. Whether this
happens or not, depends on the “mildness” of social pressures, S0. The “milder” is
social competition (i.e. the higher S0), the greater rate of economic growth, and if S0
is small so that social competition is “cut throat”, linear taxes are harmful for growth,
but if the “mildness” S0 is suﬃciently high then linear taxes bolster growth. Thus, the
growth-maximising tax rate is zero for small values of S0, but positive for higher values
of S0.
3C o n c l u s i o n s
The present paper joins the growing body of literature that emphasizes the importance
of social arrangements. We show here that the same redistributive taxation scheme may
have opposing eﬀects on economic growth in societies that diﬀer only in their social
norms. In a simple model of endogenous growth where agents, when young, compete
for status in terms of visible consumption, the eﬀects of greater equality on economic
growth is ambiguous and is determined by how society treats its lowest ranked members.
When low social rank leads to complete social exclusion, redistribution diverts resources
to wasteful consumption rather than productive investment and leads to lower growth.
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6

Inequality and Growth in the Presence of Competition for Status

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