People Care About Social Status

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Why Do People Care about Social Status?

Mary Rege


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Journal of Economic Behavior & Organization

Vol. 66 (2008) 233242

Why do people care about social status?

Mari Rege

University of Stavanger, 4036 Stavanger, Norway

Received 7 March 2005; accepted 27 April 2006

Available online 12 December 2006

Abstract

This paper shows that complementary interaction can induce people to care about social status because it

serves as a signal of non-observable abilities. There is a unique separating equilibrium in which everyone

cares about social status. In this equilibrium a persons social status perfectly reveals his abilities, and

everyone matches with a person of like ability. The analysis shows that peoples instrumental concern for

social status has important welfare and policy implications. Indeed, peoples efforts to keep up with the

Joneses may be welfare enhancing.

2006 Elsevier B.V. All rights reserved.

JEL classification: C72; D11

Keywords: Complementary interaction; Instrumental conspicuous consumption; Matching; Social status

1. Introduction

Several economists have maintained that consumers concern for social status has important

economic consequences. Veblen (1899) argued that a concern for social status induces people

to engage in conspicuous consumption in order to signal wealth. Similarly, Duesenberry (1949)

argued that a concern for status causes people to imitate the consumption standard of those above

them in the income hierarchy. More recently, several economists have shown that an incorpora-tion of a concern for social status alters results of traditional growth models (Cole et al., 1992;

Konrad, 1992; Fershtman et al., 1996; Rauscher, 1997; Corneo and Jeanne, 1999; Brekke and

Howarth, 2002). It has also been demonstrated that peoples concern for social status has impor-

tant implications for tax policy (Ng, 1987; Ireland, 1994, 1998; Bagwell and Bernheim, 1996;

Corneo and Jeanne, 1997). Moreover, several analyses suggest that a concern for social status can

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0167-2681/$ see front matter 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.jebo.2006.04.005


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234 M. Rege / J. of Economic Behavior & Org. 66 (2008) 233242

sustain different social norms (see e.g. Akerlof, 1980; Lindbeck and Snower, 1988; Hollander,

1990; Bernheim, 1994; Lindbeck, 1997; Lindbeck et al., 1999). A recent paper by Hopkins and

Kornienko (2004) analyzes how peoples concern for social status interacts with the distribution

of income.

In the literature referred to above it is typically assumed that people care for social status.1

As one explanation why people seem to care about social status, this paper demonstrates that a

certain type of interaction between people, referred to as complementary interaction, can induce

people to care about social status because it serves as a signal of non-observable abilities. Indeed,

there is a unique separating Nash equilibrium in which everyone cares about social status. In this

equilibrium a persons social status perfectly signals his abilities, and everyone matches with a

person of like ability.

Peoples concern for social status is analyzed in a game in which each person seeks to maximize

utility from consumption of non-status goods. Moreover, each persons income is determined by

his payoff from complementary interaction. In a complementary interaction a persons marginal

payoff with respect to his own abilities increases with the abilities of the person with whom heis interacting. Complementary interactions are common in both private and professional environ-

ments. Business interactions, for example, can be complementary: a businessman can better utilize

another persons high business skills if he has high business skills himself. In accordance with

the theory presented in this paper, the prominence of Rolex watches, Armani suits and BMWs

in certain business environments may be due to complementary business interactions. A busi-

nessman invests in such status goods because they serve as a signal of his abilities. By investing

in social status he thus increases his chances of making business connections with high ability

people. This argument is similar to Spence (1974), in which more productive agents make costly

but unproductive investments in education.2

By interpreting status consumption as an ability signal, the present paper provides new insightto the status literature. Indeed, the model shows that peoples concern for social status may be

welfare enhancing. This welfare result is important because thus far the economic literature on

social status has focused entirely on the inefficiency problems connected with peoples status

concern.3 In a well-known article by Frank (1985a), for example, peoples status concern leads to

an under-consumption of non-positional goods while everybody over-consumes positional goods

in order to keep up with the Joneses. Similarly, in another well-known paper by Cole et al. (1992)

peoples status concern leads to a rat race of the rich in the form of competitive over-saving. In

contrast to this literature, the present paper shows that a concern for social status also involves a

benefit in the form of more efficient matching, in addition to the cost of status consumption. If

interactions are sufficiently complementary, the benefit exceeds the cost.

A signaling interpretation of peoples status concern has important policy implications. The

analysis shows that a tax on status consumption cannot reduce peoples investment in social status.

Peoples total spending on status goods is independent of tax rates on status consumption. The

only thing a person cares about is how much money he is burning on status consumption relative

to other people. A tax on status consumption will, however, reduce net status investments. Thus, if

the status goods prevailing in a society have no user value, it is possible to increase social welfare

1 Exceptions are Cole et al. (1992) and Corneo and Jeanne (1999) in which people care about relative wealth because

it affects mating.2

See Frank (1985a), Fang (2001) and Pesendorfer (1995) for other models of money-burning as an ability signal.3 It is, however, well known in the signalling literature that wasteful ability signaling can be welfare improving (Stiglitz,

1975).


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M. Rege / J. of Economic Behavior & Org. 66 (2008) 233242 235

by taxing status goods and spending tax revenues on goods that have user value. Such a policy

may make status signaling less wasteful, thereby decreasing the cost of efficient matching.

This paper is in line with the work of several authors who have argued that people care about

social status because it is instrumental to their payoff (see e.g. Veblen, 1899; Frank, 1985a; Cole

et al., 1992). The differences between the present analysis of peoples desire for social status andprevious analyses are elaborated in Section 5.

2. The model

In society people engage in different types of interactions with each other. In many interactions

a persons payoff is dependent on the abilities of the person with whom he interacts, as well as

his own abilities. Let the abilities of person i be denoted by ri [0, 1]. Moreover, let person is

payoff from interacting with person j be denoted by:

mi = m(ri, rj) 0. (1)

The following analysis will show that the existence of a certain type of interaction, referred to

as complementary interaction, can induce people to care about social status. In a complementary

interaction m is strictly increasing and complementary in (ri, rj); that is, m1, m2 and m12 > 0.

Business interactions, for example, can be complementary: person i can better utilize person js

high business skills if he has high business skills himself.

People can acquire social statusby investing in status goods.Status goods are costly, observable,

and easily identifiable with the owner. Since the purpose of this paper is to explain why people

care about social status, it will be assumed that people have no direct preferences for social status,

nor for status goods. The last assumption implies that a status investment has no user value for the

consumer. For example, if a person buys a Rolex watch, then his investment in status goods is theadditional money paid for this watch relative to an equally well-functioning watch of a cheaper

brand.

Each person tries to engage in a complementary interaction. People cannot observe each others

abilities before engaging in a complementary interaction; they can only observe each others social

status. The timing of the game is as follows. Each person first chooses how much to invest in

social status. Thereafter, each person engages in complementary interaction with a random person

having the same social status as himself. If there is no person with the same social status as person

i, then person i matches with someone of lower status. Assume there is a continuum of people of

each type r [0, 1]. Let the strategy profile k(r) denote how much a person with ability rchooses

to invest in social status.Each person seeks to maximize his non-status consumption, ci. Let Idenote person is exoge-

nous income, which he receives in addition to the payoff mi. Then each person is consumption

constraint is given by:

I+mi = k(ri)+ ci. (2)

Assume that the payoff from complementary interaction is zero for a person with ability r = 0

(i.e. m(0, rj) = 0). Then, in a Nash equilibrium, a person with ability r = 0 will always choose

not to invest in status (i.e. k(0) = 0).

Lemma 1. Ifk(r) is a separating Nash equilibrium (i.e. k(r) = k(r) for all r = r), then k(r) is

strictly increasing.


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Proof. Assume that the statement does not hold. Then there exists a separating Nash equilibrium

k(r) and a r and r [0, 1] s.t. k(r) k(r) and r

> r. In this equilibrium a person with ability

r earns payoff = I+m(r, r) k(r). If a person with ability r deviates to strategy k(r) his

payoff is d = I+m(r, r) k(r). Note that d > , since k(r) k(r) and r > r. Thus,

k(r) cannot be a separating Nash equilibrium. This is a contradiction, so the statement must hold.

Now look at a strictly increasing strategy profile k(r). Ifk(r) is a Nash equilibrium, then the

following condition must hold:

I+m(r, r) k(r) I+m(r, r) k(r) for all r [0, 1]. (3)

If this condition does not hold, a person can increase his utility by deviating to an alternative

strategy. Eq. (3) implies that:

limrr

k(r) k(r)

r r= lim

rr

m(r, r)m(r, r)

r r= m2(r, r). (4)

Since k(r) is non-decreasing in r, k(r) must be differentiable (Royden, 1988, Theorem 3, p. 100).

Thus, Eq. (4) implies that:

k(r) = m2(r, r). (5)

Assume that m(r, r) is absolutely continuous in r. Then Eq. (3) implies that k(r) is absolutely

continuous. Furthermore, assume that m2(r, r) is Lipschitz continuous. Then, it is possible to

solve the differential equation in (5) by integrating both sides of this equation, since an absolutely

continuous function is the integral of its derivative (Royden, Corollary 15, p. 110). Since k(0) = 0,

the unique solution of this differential equation is given by:

k(r) =r

0m2(s, s) ds. (6)

It is now easy to prove the following proposition.

Proposition 2. If m(ri, rj) is absolutely continuous in rj and m2(r, r) is Lipschitz continuous,

then there exists a unique separating Nash equilibrium k(r) =r

0 m2(s, s) ds.

Proof. Clearly k(r) =r

0 m2(s, s) ds satisfies Lemma 1 as a candidate to be a separating Nash

equilibrium. The derivation in Eqs. (3)(6) shows that this candidate is unique. Finally, Eq. (5)

assures that k(r) is a best reply to itself.

Proposition 2 shows that people care about social status because social status is instrumental

to their payoff in complementary interactions. A persons social status serves as a signal of his

ability. By signaling high ability, a person can improve his chances to engage in a complementary

interaction with a high ability person. In the unique separating Nash equilibrium a persons

ability is positively correlated with his social status. On the one hand, if a person decreases his

investment in social status, he will experience a benefit in the form of decreased expenditures on

status consumption and a cost in the form of a lower payoff from complementary interaction. On

the other hand, if a person increases his investment in social status, he will experience a cost in

the form of increased expenditures on status consumption and a benefit in the form of a higher

payoff from complementary interaction. In both cases, the cost will exceed the benefit.

Note that the most efficient matching is clearly one in which every person matches with a

person of like ability (see Durlauf and Seshadri, 2003). Thus, Corollary 3 follows directly from

Proposition 2.


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Corollary 3. Status consumption can lead to efficient matching.

This benefit from status consumption in the form of efficient matching has not been captured

by previous economic models of social status. The focus has typically been on the cost of status

consumption in terms of decreased non-status consumption, and how this opportunity cost raises

as everyone tries to keep up with the Joneses (see e.g. Frank, 1985b, 1999).Note also that in the unique separating Nash equilibrium a persons total spending on status

goods is independent of consumer prices. The only thing a person cares about is how much money

he is burning on status consumption relative to other people. Thus, Corollary 4 follows directly

from Proposition 2.

Corollary 4. A tax on status consumption will not reduce peoples total spending on status goods.

3. Welfare analysis

This section analyses whether status investments are good for society. The reference pointin the welfare analysis is the Nash equilibrium in which nobody invests in status goods4

and people match randomly. In the welfare analysis it is assumed that a status good has no

user value for society.5 In many societies there exist status goods that do have a user value

for some people, such as publicly announced donations to public goods and volunteer work.

The existence of such status goods do, however, reinforce the results derived in this welfare

analysis.

Eqs. (1) and (2) and Proposition 2 imply that in the unique separating equilibrium social welfare

is given by U =1

0 (I+m(r, r) k(r)) dr. Moreover, in the Nash equilibrium with no status

investments, social welfare is given by U= 10 10 (I+m(r, s)) ds dr. Thus, status investmentsincrease social welfare by:

U= U U=

10

m(r, r) k(r)

10

m(r, s) ds

dr. (7)

Eqs. (6) and (7) imply that:

U=

10

m(r, r)

10

m(r, s) ds

dr

10

r0

m2(s, s) ds

dr. (8)

The first integral represents the benefit of status investments in terms of more efficient matching.

The larger the degree of interaction complementarity, the larger the benefit. The second integralrepresents the cost of status investments in terms of higher expenses to status consumption. Indeed,

depending on the functional form, m(ri, rj), the benefit of a more efficient matching may exceed

the cost of status consumption. It is, for example, easy to show that if m(ri, rj) = ri r

j , then

status investments increase social welfare if2 1 > 0, and decrease social welfare if

2 1 < 0.

4 k(r) = 0 for all ris a Nash equilibrium because deviating by investing in status will not increase payoff from comple-

mentary interaction.5

Recall that in the model a status good has no user value for the consumer. For example, if a person buys a Rolex watch,then his investment in status goods is the extra money paid for this watch as opposed to an equally well functioning watch

of a cheaper brand.


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If the status goods prevailing in a society have no user value, then Corollary 4 implies that it

is possible to increase social welfare by taxing status goods and spending tax revenues on goods

that do have a user value. Such a tax policy will make the status signaling less wasteful, thereby

decreasing the cost of efficient matching.

Note, however, that status consumption implies a decrease in welfare for those with low ability.This is because status signaling decreases the expected ability level of the people with whom low

ability people interact.

4. Binding income constraint

In the model presented in Section 2, the income constraint was non-binding. This could be either

because income is sufficiently high such that I > k(r) for all r, or because of a well-functioning

credit market. The following analysis will relax this assumption by allowing the income constraint

to be binding. Moreover, it is assumed that income varies across individuals.

Assume that individuals are uniformly distributed on [0, 1] [0, ], with ability r [0, 1] andincome I [0, ]. Let the strategy profile k(r, I) denote how much a person with ability r and

income Ichooses to invest in social status. Each person is income constraint is given by:

Ii k(ri, Ii). (9)

Apart from these changes, everything is the same as in Section 2.

The following analysis will show that there exists a Nash equilibrium of the form:

k(r, I) =

k(r) ifk(r) I

I ifk(r) > I.

where k(r) is strictly increasing. Individuals with k(r) I will be referred to as individuals

with a binding income constraint and individuals with k(r) > I will be referred to as individuals

with a non-binding income constraint. Note that this equilibrium is very similar to the Nash

equilibrium in Section 2. It is similar in the sense that all individuals for whom the income

constraint is non-binding are perfectly separated from each other with respect to ability (recall

that in Section 2 the income constraint was non-binding for all individuals). Individuals with a

binding income constraint spend their full budget on status consumption. These individuals are,

however, separated from each other with respect to income. Thus, in this equilibrium those with

social status corresponding to k(r) either have ability rand income I k(r), or they have ability

r > r and income I= k(r).First, look at an individual for whom the income constraint is non-binding. Then the payoff

from playing k(r) when everybody else is playing k(r, I) is given by:

= ( k(r))m(r, r)+ s(r, rj)+ I k(r), (10)

where

s(r, rj) =

1rj=r

m(r, rj) drj. (11)

In Eq. (10), the first term denotes expected payoff from matching with an individual with status

k and a non-binding income constraint, whereas the second term denotes expected payoff from

matching with an individual with status kand a binding income constraint.


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Similar to Section 2, if k(r, I) is a Nash equilibrium and k(r) is strictly increasing, then the

following condition must hold for any individual with k(r) I and for any r s.t. k(r) < I:

( k(r))m(r, r)+ s(r, r)+ I k(r) > ( k(r))m(r, r)+ s(r, r)+ I k(r). (12)

Eq. (12) implies:

limrr

(k(r))(m(r, r)+ 1) (k(r))(m(r, r)+ 1)

r r= lim

rr

(m(r, r)m(r, r))+ s(r, r) s(r, r)

r r.

(13)

Note from Eq. (11) that:

s2(r, r) =d

dr

1rj=r

m(r, rj) drj

= m(r, r).

Thus, since k(r) is strictly increasing, and hence differentiable, Eq. (13) implies that:(k(r))(m(r, r)+ 1)+m2(r, r)k(r) = m2(r, r)m(r, r). (14)

Eq. (14) is a differential equation, which together with the condition k(0) = 0, has a unique

solution.6 Let the solution to (14) be denoted by k(r). Moreover, let:

k(r, I) =

k(r) ifk(r) I

I ifk(r) > I. (15)

Assume now that k(r) is strictly increasing in r. The above analysis has established that k(r)

is a best response tok(r, I) for an individual with Iand rsuch that I

k(r). It is now necessaryto show that I is a best response to k(r, I) for an individual with Iand rsuch that I < k(r). Let r

denote the corresponding ability level for those investing I who are not constrained by income

(i.e. I= k(r)). An individuals payoff from investing I in social status is then given by:

I = I+ ( k(r))m(r, r)+ s(r, r) k(r). (16)

Note thatIis a best response to k(r, I) for an individual with I < k(r) i f (/r)I > 0 for all r < r.

Differentiating Eq. (14) with respect to r yields:

rI = k

(r)m(r, r)+ ( k(r))m2(r, r)+m(r, r) k(r). (17)

Moreover,

2

rrI = (1 k

(r))m1(r, r)+ ( k(r))m12(r, r) > 0, (18)

if7 < (2m(r, r)+ 1)/m2(r, r). Eqs. (14) and (17) imply that (/r)I = 0 for r = r. Thus, Eqs.

(18) and (17) imply that if < (2m(r, r)+ 1)/m2(r, r), then (/rj)I > 0 for all r < r.

The above analysis has established that k(r, I) denotes a best reply to itself given that

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