Social Culture and Economic Performance
By HANMING FANG*
The connection between obtaining higher paying jobs and undertaking some seem-
ingly irrelevant activity is interpreted as “social culture.” In the context of a society
trying to adopt a new technology, I show that by allowing the firms to give
preferential treatment to workers based on some “cultural activity,” the society can
partially overcome an informational free-riding problem. Therefore, social culture
may affect the economic performance by altering the effective production technol-
ogy of the economy. (JEL P17, Z13)
What is social culture? What is the role of
of the costly-to-acquire requisite skills, an
social culture in economic performance? In a
interesting informational free-riding problem
provocative article, Kenneth Arrow (1971) ar-
arises. To fix ideas, consider an extreme case:
gued that “norms of social behavior, including
suppose that every worker in the economy in-
ethical and moral codes, ... , are reactions of
vests in skills. Then, regardless of the observed
society to compensate for market failure.”
signal of whether a worker is skilled, the firms
Somewhat surprisingly, this idea of the role of
should rationally assign any worker to the new
social culture has not been further pursued in
technology; but then no worker will have incen-
the literature.
tive to incur the costly skill investment. Free-
In this paper I take Arrow’s viewpoint seri-
riding results because the firms’ perception of
ously, and construct a simple model to examine
the fraction of skilled workers in the population
the possibility that social culture may alleviate
is a public good. To convey my main idea, I
market failure. I consider a society that is de-
focus on environments in which the free-riding
ciding whether to adopt a new technology.
problem is so severe that the unique equilibrium
Three important assumptions are made about
involves nonadoption of the new technology,
the economy: first, adoption decisions are made
even though it could induce a rise in productiv-
by entrepreneurs (or firms), but the operators of
ity greater than the skill acquisition costs. Now
the new technology are workers; second, the
I introduce in such an environment an activity A
new technology can be successfully operated
with three properties: first, it is observable to
only when the worker has invested in some
firms; second, it is intrinsically irrelevant for
imperfectly observable requisite skills; and
production; third, workers are heterogenous in
third, it is costly for the workers to acquire the
their tastes toward undertaking activity A, but
skills.1 Because of the imperfect observability
the taste distribution is independent of workers’
skill investment costs. I show that by allowing
the firms to treat workers differently, based on
whether they undertake activity A, an equilib-
* Department of Economics, Yale University, 37 Hill-
house
Avenue,
New
Haven,
CT
06511
(e-mail:
rium in which a positive fraction of workers is
hanming.fang@yale.edu). This paper is based on chapter 3
assigned to the new technology can be sus-
of my dissertation at the University of Pennsylvania. I am
tained. The main insight is as follows: firms
deeply indebted to my advisor, Andrew Postlewaite, for his
now have to form separate perceptions about the
insights and guidance. I also thank two anonymous referees,
fractions of the skilled workers among those
V. V. Chari, John Morgan, Stephen Morris, Dan Silverman,
Yoram Weiss, and seminar participants at the University of
who undertake A and among those who do not
Minnesota and the “Summer in Tel Aviv” conference in
1999 for valuable comments and suggestions. Financial
support from Sloan Foundation Dissertation Fellowship is
gratefully acknowledged. Any remaining errors are mine.
expensive inputs that only entrepreneurs can afford due to
1 The last two assumptions are quite standard. The first
imperfect credit markets, or if the assembly of new ma-
one can be justified if the new technology requires some
chines requires some firm-level know-how.
924

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FANG: SOCIAL CULTURE AND ECONOMIC PERFORMANCE
925
undertake A and this makes the firms’ percep-
sibly interpret activity A as “social custom” or
tion for each group a local public good. In this
“tradition.” Indeed in the sociology literature
type of equilibria, the subpopulation that re-
the terms “social culture,” “social custom,” and
ceives preferential treatment has a higher frac-
“tradition” are sometimes interchangeably used
tion of low investment cost workers because the
(e.g., Gellner, 1988).
skilled and unskilled workers have different in-
I will call the seemingly irrelevant but so-
centives to join the preferentially treated group.
cially valued activity that underlies the “social
In other words, activity A becomes an endog-
culture” the cultural activity, and those workers
enously generated signaling instrument for
who undertake the cultural activity (who thus
skilled workers. The severity of the informa-
receive preferential treatment) elites. An equi-
tional free-riding problem is reduced when lim-
librium with social culture is called cultural
ited to this subpopulation of group A workers.
equilibrium. One concrete example of cultural
I would like to somewhat loosely interpret the
activities is norms of etiquette. Most European
connection between undertaking the seemingly
societies require social elites to master complex
irrelevant activity A, which serves as the defin-
etiquette. A second example is fashion. Fash-
ing characteristic of the preferentially treated
ions such as designer clothing, exclusive cars,
group, and obtaining higher-paying jobs on the
furniture, and electronic equipment are charac-
new technology, as “social culture.” I would
terized by being expensive and not particularly
argue that this interpretation is consistent with
more functional than standard items. Georg
prominent definitions of “culture” by scholars
Simmel (1957 p. 544) wrote that “[f]ashion is
in various fields. Suppose that an outsider ob-
merely a product of social demands. ... This is
serves the society previously described. In an
clearly proved by the fact that very frequently
effort to understand the connection between ac-
not the slightest reason can be found for the
tivity A and higher-paying jobs, the observer
creation of fashion from the stand-point of an
may interpret it simply “as rules of the game
objective, aesthetic or other expediency.” But
which provide the informal constraints on hu-
being fashionable is necessary to be considered
man interactions,” which is the “definition” of
as elites in many societies. Most people will
culture given by economist Douglas North
agree that whether one masters these norms of
(1990). Alternatively, the observer may think of
etiquette, or whether one is fashionable, is not
group A workers as social elites, and interpret
directly related to productivity, but nonetheless
undertaking activity A as “the set of standards
social elites often receive preferential treat-
and values held up and prized by some social
ments in their search for jobs.3,4 Some sociolo-
elite.” This is one of the two views of culture
gists such as Jon Elster (1989) have been
proposed by political scientist James Wilson
puzzled by the complexity of the norms of eti-
(1994).2 If the outsider takes this view, he may
quette for social elites, and argued that “norms
then, from the connection between activity A
of etiquette” and an “Oxford accent,” “if any-
and higher-paying jobs, form the opinion that in
thing, ... , seem to make everybody worse off,
this society social elites are preferentially
by requiring wasteful investments in pointless
treated by the labor market. Finally, he may
behavior.” This paper sheds some light on why
simply rationalize the connection between ac-
it might be necessary for cultural activities to be
tivity A and higher paying jobs as “a distinct
as complicated as they are. As we see in Section
way of doing things which characterizes [this]
given community,” which is the definition of
culture given by a leading sociologist and an-
3 See, however, Wolfgang Pesendorfer (1995) for an
thropologist Ernest Gellner (1988). However, as
alternative explanation of fashion as a signaling device in
dating games.
pointed out by a referee, one can just as plau-
4 Another example is personal beauty. Daniel Hamermesh
and Jeff Biddle (1994) find that good-looking workers
earn more in the labor market, and it is not because their
2 Wilson (1994) also refers to culture as “a widely shared
looks are more productive in their occupations. The
integrating perspective or world view by which people
availability of plastic surgery makes personal looks
interpret their experiences, a perspective that is passed on
changeable; thus the theory in this paper provides an
from one generation to the next by precept, myth and
explanation for their findings without resorting to taste-
ritual.”
based discrimination.

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THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2001
II, the efficiency role of social culture might not
The main idea in the current paper, that differ-
be fulfilled if the distribution of utility costs in
ential treatment of groups may enhance effi-
the economy does not satisfy certain conditions.
ciency, also appeared in Andrea Moro and Peter
Similarly, the characteristically high prices of
Norman (1999) and, more directly, in Norman
fashion goods can be explained as the way in
(1999). They study a model of discrimination
which a society creates a disperse disutility dis-
with exogenous groups based on specialization,
tribution in the population, so that fashion as a
and show that informational gains from special-
cultural activity can alleviate some market fail-
ization in a discriminatory equilibrium may out-
ure. A little less related, some corporate culture,
weigh the losses from increased investment
such as working long hours among junior in-
costs. In this paper I study differential treatment
vestment bankers on Wall Street, singing com-
of endogenously chosen groups, and the under-
pany songs, and wearing company uniforms,
lying force of the cultural equilibrium is pre-
can also be viewed as ways to alleviate incen-
cisely the different incentives that skilled and
tive problems within a firm.
unskilled workers have in joining the preferen-
This paper belongs to the emerging literature
tially treated group. Moreover, the simplicity of
on the microfoundations of cultural effects. In-
my model allows me to state my welfare results
stead of thinking of cultural differences as sim-
using a Pareto criterion, whereas Norman’s is
ply arising from differences in preferences
stated in terms of a utilitarian social welfare
and/or opportunities, this literature attempts to
function. There is a less-related literature in
derive the social norm, or culture, from standard
which authors directly put concerns for status
preferences and the fundamental economic par-
into agents’ utility function and then study the
adigm of individual maximization, and to ex-
implications of such preference on some aspects
plain how social norms or culture interact with
of agents’ behavior [see, e.g., Arthur Robson
the market to induce agents to have different
(1992); Chaim Fershtman and Yoram Weiss
preferences or outcomes.5 Harold Cole et al.
(1993); B. Douglas Bernheim (1994)] and I will
(1992) introduce in an otherwise standard neo-
refer the readers to Cole et al. (1992 p. 1097) for
classical growth model some nonmarket goods
a critical discussion of this approach.
and decisions (e.g., marriage partners). They
The remainder of the paper is structured as
show that different rules governing the match-
follows. Section I describes the basic structure
ing of marriage mates can be supported as equi-
of the model and establishes the conditions un-
libria, and different norms of marriage imply
der which a new superior technology will not be
different economic outcomes. My paper shows
adopted in the absence of social culture. Section
how social culture based on some seemingly
II introduces cultural activity and studies the
irrelevant activity can change the effective pro-
existence and welfare properties of cultural
duction technology by alleviating the market
equilibria. Finally, Section III concludes.
failure caused by informational free-riding. In
contrast, Guido Cozzi (1998) analyzes an over-
I. A Basic Model
lapping generations growth model in which
“culture” is assumed to enhance the production
In this section, I endogenize the wage offers
efficiency of future generations. His main con-
in a model similar to that of Stephen Coate and
cern is to characterize the balanced growth
Glenn C. Loury (1992) to illustrate how a su-
paths with “culture,” which are supported by
perior technology may fail to be adopted be-
rational bubbles. This paper complements Coz-
cause of informational free-riding.
zi’s in explaining how “culture” may increase
production efficiency, even though I use a very
A. Firms and Technologies
different setup. It should be noted that Cozzi’s
use of the term “culture” is more in line with
There are two (or more) firms, indexed by
Wilson’s (1994) second view (see footnote 2).
i
1, 2. They both have a traditional (old) and
a new technology at their disposal. Every
worker can produce 1 unit of output with the
5
traditional technology. Workers with some req-
I thank an anonymous referee for this concise summary
of the literature.
uisite skills can produce x
1 units of outputs
q

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FANG: SOCIAL CULTURE AND ECONOMIC PERFORMANCE
927
with the new technology, but those without the
firms. The signal
is distributed according to
skills will produce 0. We assume that the firms
probability density function f
for qualified
q
are risk neutral and maximize expected profits.
workers and f for unqualified ones. We assume
u
that f
/f
is strictly increasing in
. This
q
u
B. Workers
standard monotone likelihood ratio property
(MLRP) implies that skilled workers are more
There is a continuum of workers of unit mass
likely to receive higher signals than unqualified
in the economy. Workers are heterogeneous in
ones. MLRP captures the notion that the test is
their costs of acquiring the requisite skills for
informative of the worker’s qualification.
the new technology. For simplicity, I assume
that a worker is either a low cost type, whose
Stage 3: Wage Offer.—The firms compete in
skill acquisition cost is C , or a high cost type
the labor market for workers by simultaneously
L
with cost C , where 0
C
C . The
announcing wage schedules as functions of
H
L
H
fractions of low cost and high cost workers are
the test signal
.6 A pure action of firm i at
and
, respectively; of course
this stage is a Borel measurable function w :
L
H
L
H
i
1. A worker’s cost type is her private informa-
[0, 1] 3 R .7
tion. It is assumed that the workers are risk
neutral and that they do not directly care about
Stage 4: Offer Acceptance.—The workers ob-
the technology to which they are assigned.
serve wage schedules w and w announced in
1
2
To dramatize the market failure caused by
Stage 3, and decide for which firm to work.8 If
informational free-riding, I assume that it is
a worker is indifferent between two firms, I
socially optimal for every worker to invest in
assume that she will flip a coin.
skills and use the new technology:
Stage 5: Technology Assignment.—In this fi-
ASSUMPTION 1: x
C
1.
nal stage each firm allocates its available work-
q
H
ers between the old and new technologies using
Assumption 1 explains the need for the assump-
an assignment rule, which is a Borel measurable
tion that entrepreneurs have access to the new
function t : [0, 1] 3 {0, 1}, where t ( )
1
i
i
technology, whereas workers do not; otherwise,
(respectively, 0) means that firm i assigns all
social optimum will be trivially achieved.
workers with signal
to the new (respectively,
old) technology.9
C. Timing and Strategies
D. Bayesian Nash Equilibrium
The timing of the game and the strategies of
the players are described in five stages:
A Bayesian Nash equilibrium (BNE) of the
game is a list including the workers’ skill
Stage 1: Investment Decision.—A worker of
type C
{C , C } chooses an action from {e ,
L
H
q
e }, where e means that she invests in skills (and
6 I assume that the output level is not contractible.
u
q
7
becomes a qualified worker) and e that she does
To simplify the description of the firms’ strategy sets,
u
we assumed that the firms cannot observe the aggregate
not invest (and thus remains unqualified). She
distribution of the test signals. This assumption does not
pays a monetary cost of C if she chooses e , and
q
affect the equilibrium outcomes.
pays no cost if she chooses e . Write the invest-
8
u
I should in principle allow the acceptance rule to de-
ment decision profile as e : {C , C } 3 {e , e }.
pend on the worker’s investment decision e as well as her
H
L
q
u
It is assumed the firms do not perfectly observe a
characteristic C. But the worker’s sequential rationality
requires that e and C should not affect her offer acceptance
worker’s investment decision; instead they ob-
decision in equilibrium because in this stage her investment
serve some noisy but informative public signals
decision has been irreversible, and the firms’ wage offers do
(e.g., test scores, interviews, recommendation let-
not depend on e or C because of unobservability.
9
ters) of her qualification.
A more complete description should allow the firms’
assignment rules to be contingent on the wage schedules
offered in Stage 4. However, because firms do not behave
Stage 2: Test Signal.—Each worker receives
strategically in Stage 5, allowing for this will not affect any
a signal
[0, 1] that is observed by both
of the results.

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928
THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2001
investment decision profile e and offer accep-
investing only comes from the higher likelihood
tance rules, and the firms’ wage schedules and
of receiving better test signals. How firms in-
technology assignment rules {w
, t
} such
terpret a signal depends on the firms’ perception
i
i
that every player optimizes against other play-
of the fraction of skilled workers in the popu-
ers’ strategy profiles.
lation. Thus the private benefit of skill invest-
In Stage 3 firms decide what wage to offer to
ment depends on
and is given by
a worker with signal . The firms interpret sig-
nal
based on some perception about the frac-
1
tion of skilled workers in the population,
B
w
,
fq
fu
d .
denoted by
, which serves as the prior in the
0
application of Bayes’ rule. Because firms com-
pete for workers in “Bertrand” competition
That the private benefit is a function of
is the
(wage posting), standard arguments establish
source of informational free-riding. The func-
that in equilibrium firms will make identical
tion B will also determine the magnitude of free
offers to a worker with test signal
at her
riding. First, B is clearly continuous in
; sec-
expected productivity on her more productive
ond, B(0)
B(1)
0. If the firms’ perception
technology. In Stage 4 the rationality of the
is that a zero measure of workers is skilled,
worker dictates that she accept a higher wage offer
then all workers will be assigned to the old
with probability 1 and randomize only if the offers
technology regardless of their signals, which
are the same. In Stage 5, firms’ profit maximiza-
means that there is no point in getting better
tion implies that each worker will be assigned to
signals. In other words, w(0,
)
1 for all ,
her more productive technology. The following
hence B(0)
0. Analogously if the firms perceive
lemma, formally proved in the Appendix, summa-
all workers to be skilled, then all workers will be
rizes the preceding discussion.
assigned to the new technology regardless of their
signals, hence w(1, )
x for all
and B(1)
0.
q
LEMMA 1: Suppose that in some BNE the
The value of B will be positive when the firms’
fraction of skilled workers is
. Then:
perception of the population is neither too opti-
mistic nor too pessimistic. From the preceding
1. For almost all
[0, 1],
discussion, it is clear that
0 always corre-
sponds to an equilibrium of the economy.
(1)
w1
w2
w
,
To convey my main idea that introducing
cultural activity may compensate for market
fq
max 1,
x
failure, I will in fact focus on the set of the
f
q
;
q
1
fu
economies in which
0 is the unique equi-
librium outcome. To characterize the skill in-
2. For almost all
, t ( )
t ( )
t( ),
1
2
vestment decision of a worker, it is important to
where t( )
1 if and only if
know when the private benefit of investment
f
exceeds her cost. We define
and
to be
q
L
H
x
the sets of values of
that will respectively
f
q
1.
q
1
fu
induce low and high cost type workers to invest
in the skills, that is,
{
[0, 1] : B( )
L
The first element in the max operator of equa-
C };
{
[0, 1] : B( )
C }. It is
L
H
H
tion (1) is the worker’s productivity on the old
worth remarking that the sets
and
are
L
H
technology, and the second element is her ex-
completely specified by the primitives of the
pected productivity on the new technology. She
economy { f , f , x , C , C ,
,
} because
q
u
q
L
H
L
H
will be assigned to the technology on which she
the function B is well defined by them.10
is more productive.
Now I analyze the workers’ skill investment
decisions in Stage 1. It is obvious that the social
10 Although the function B is single peaked in many
benefit of skill investment is x
1, regardless
q
examples, I am unable to establish single-peakedness as a
of other workers’ decision. However, from an
general property of B. If B is indeed single peaked, then
individual worker’s viewpoint the benefit of
both
and
will be intervals.
L
H

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VOL. 91 NO. 4
FANG: SOCIAL CULTURE AND ECONOMIC PERFORMANCE
929
FIGURE 1. MAPPINGS
AND
WHEN
I
L
S AN INTERVAL
Obviously
is a subset of
. The following
To facilitate the comparison with cultural
H
L
two assumptions are sufficient, but by no means
equilibrium, it is useful to define a mapping
necessary, for the economy to have a unique equi-
: [0, 1] 3 [0, 1] as follows:
librium with
0.
0
if
L
ASSUMPTION 2:
A and min
L
L
0,
L
if
L
.
L
L
if
int
L ,
ASSUMPTION 3:
A.
H
where
and int(
) are respectively the
L
L
PROPOSITION 1: If Assumptions 2 and 3
boundary and the interior of
.
gives the
L
hold, then the economy has a unique equilib-
measure of workers who will find skill acquisi-
rium in which no workers invest in skills and the
tion worthwhile when the firms’ perception is
new technology is not adopted.
. In any equilibrium the firms’ perception must
be consistent with the workers’ investment de-
PROOF:
cisions. That is, any equilibrium is character-
To induce C type workers to invest, it must
ized by a fixed point of . Assumptions 2 and 3
L
be that
; however, because
min
imply that the unique fixed point of
is at
L
L
this can occur only if some C type workers
0 [see Figure 1(a)].
L
H
also invest, which is ruled out by Assumption 3.
II. Cultural Activity and Cultural Equilibria
The domino effect underlying Proposition 1
can be generalized to a model with more than
In this section, I introduce an activity, called
two cost types of workers. Suppose that there
“cultural activity,” into the basic model.
are n types with C
C
...
C . Assume
1
2
n
that the measure of C
type workers is
.
A. Cultural Activity
k
k
Define a sequence of sets {
} analogous to
k
L and
. If for k
1, ... , n
1, min
Suppose there is an activity A that workers
H
k
¥k
and
A, then the economy will
can undertake. Let V
R be a worker’s utility
j
1
j
n
have a unique equilibrium with
0. It is also
(or disutility if negative) in monetary terms
helpful to relate the preceding result to George
from activity A. Therefore each worker now has
Akerlof’s (1970) lemons problem. The exis-
two private characteristics (C, V). Let H(V C)
tence of high cost type workers—“lemons” be-
denote the cumulative distribution of V condi-
cause
they
never
invest
as
a
result
of
tional on the skill acquisition cost C. I assume
Assumption 3— dampens the incentives of the
that whether a worker undertakes activity A is
low cost workers to invest in skills.
observable to firms. The defining characteristic

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THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2001
of a cultural activity is that it is a priori completely
gent on whether activity A is undertaken. If
irrelevant to other economic fundamentals:
firms do use this type of contingent wage sched-
ules, then workers may undertake activity A for
ASSUMPTION 4 (Independence of C and V):
instrumental reasons. If A-workers are prefer-
H(V C )
H(V C )
H(V), and H is
entially treated (in a manner to be made precise
L
H
continuous and strictly increasing in V with
below), then some workers who intrinsically
support [V, V
¯ ]
R.11
dislike activity A may choose A to get the
preferential treatment. Of course in equilibrium
ASSUMPTION 5: A worker’s test signal, and
it must be rational for firms to give preferential
her qualification for the new technology, are not
treatment to A-workers.
affected by whether she undertakes activity A.
An A-cultural equilibrium is defined to be a
Bayesian Nash equilibrium of the augmented
Now I augment the basic model by adding a
model in which a positive mass of A-workers
stage 0:
are assigned to the new technology, whereas all
B-workers are assigned to the old technology.
Stage 0: Activity Choice.—A worker of type
A-workers will be called elites in any A-cultural
(C, V) chooses j
{A, B}, where j
A
equilibrium. B-cultural equilibrium can be anal-
means that she undertakes activity A and j
B
ogously defined.
that she does not. She derives from activity A
I will first characterize some properties of an
(dis)utility V if she chooses j
A, and zero
A-cultural equilibrium if it exists. Because B-
utility otherwise. Write the activity choice pro-
workers are never assigned to the new technol-
file as g : {C , C }
[V, V
¯ ] 3 {A, B}.
ogy, in this equilibrium the fraction of the
L
H
Workers who choose A will be called A-work-
skilled among B-workers, denoted by
B, must
ers, and those who choose B, B-workers. The
be zero. Furthermore, in order for some positive
description of the strategies for Stages 1–5 and
fraction of A-workers to be assigned to the new
the definition of Bayesian Nash equilibrium
technology, the proportion of the skilled among
should of course be appropriately modified.
A-workers, denoted by
A, must belong to the
set
. An A-cultural equilibrium exists if
L
B. Noncultural Equilibrium
and only if for some value
A
, the
L
population will self-select the activity choices
Because of the a priori irrelevance of activity
such that the fraction of C
types among A-
L
A we can suitably augment the equilibrium de-
workers is exactly
A.
cision rules of the basic model, and obtain an
It should be clear from the proof of Lemma 1
equilibrium of the augmented model in which
that workers will still be paid their expected
activity A plays no role in the firms’ wage offer
productivity. Therefore firm i’s sequentially ra-
schedules and technology assignments. We call
tional wage offer schedule to B-workers wB is
i
such an equilibrium a noncultural equilibrium.
The activity and skill acquisition choices in the
wB
wB
w 0,
1
1
2
noncultural equilibrium are pictured in Figure
2(a). It is obvious that in the noncultural equi-
for all
0, 1 .
librium no workers are skilled, hence the new
technology is not adopted.
Suppose that the proportion of the skilled
C. Cultural Equilibrium
among A-workers is
A. Then firm i’s equilib-
rium wage schedule to A-workers wA is
i
The introduction of the observable activity A
allows the firms to potentially offer wage sched-
wA
wA
w
A,
.
1
2
ules and technology assignment rules contin-
For every
A, the expected wage of a skilled
11
A-worker is WA( A)
1 w( A, ) f
For the general discussion I assume a sufficiently wide
q
0
q(
) d ,
support [V, V
¯ ] to avoid corner problems.
and that of an unskilled A-worker is WA( A)
u

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FANG: SOCIAL CULTURE AND ECONOMIC PERFORMANCE
931
FIGURE 2. ACTIVITY AND SKILL ACQUISITION CHOICES
1 w( A,
) f ( ) d . The following lemma
positive mass of A-workers assigned to the new
0
u
characterizes the activity and skill acquisition
technology, we have
choice profiles if there is an A-cultural equilib-
A
A
rium. It is proved by revealed preference argu-
(2)
V
˜ q
V
˜ u
0.
ments in the Appendix.
Inequality (2) establishes that in a cultural equi-
LEMMA 2: Suppose in an A-cultural equilib-
librium, a single-crossing property (SCP) of the
rium the proportion of the skilled among A-
cultural activity is endogenously generated.
workers is
A. Then the following must be true:
More specifically, let us denote the net benefit
to undertake activity A for a skilled and an
e C, V
unskilled worker with the same utility type V
by b(e , V;
A)
V
V
˜ ( A) and b(e , V;
q
q
u
A
e
A
A
)
V
V
˜ ( A), respectively. Inequality
q
if C
CL , V
1
CL
Wq
u
e
(2) yields that b(e , V;
A)
b(e , V;
A) for
u
otherwise
q
u
every type V. In other words, in any A-cultural
g C, V
equilibrium, a skilled worker is more willing
than an unskilled one to endure disutility from
A
if C
C
A
A
activity A to be an elite, which in turn justifies
L , V
1
CL
Wq
A-workers as elites. Undertaking activity A be-
A
if C
C
A
A
H , V
1
Wu
comes a signaling instrument for skilled work-
B
otherwise.
ers as a result of the endogenously generated
SCP, which differs from Michael Spence’s
The activity and skill acquisition choices in
(1973) educational signaling models where that
an A-cultural equilibrium are portrayed in Fig-
property has been assumed. It is not true that I
ure 2(b), where we have defined V
˜ ( A)
1
have simply replaced the SCP by assuming
q
C
WA( A) and V
˜ ( A)
1
WA( A) as
MLRP on the testing technology. Indeed, in the
L
q
u
u
the threshold disutility values that respectively a
noncultural equilibrium SCP does not hold,
skilled and an unskilled worker are willing to
whereas MLRP is still assumed. In this sense,
incur to be a member of the elites. Note that
SCP does not merely follow from assuming
WA( A)
WA( A)
C because
A
.
MLRP in this model.
q
u
L
L
Because WA( A)
1 whenever there is a
Now I will provide the necessary and
u

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932
THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2001
sufficient condition for the existence of A-
value of
A, I can then calculate the propor-
cultural equilibria. For any
A
, Lemma
tion of the skilled among A-workers. Specif-
L
2 tells us how workers make activity and skill
ically, we define a mapping
: [0, 1] 3 [0,
acquisition choices. For every postulated
1] by
A
L 1
H V
˜ q
if
A
A
A
A
L
L 1
H V
˜ q
H 1
H V
˜ u
0
otherwise,
where the numerator of the fraction is the total
The following proposition establishes that
mass of skilled A-workers [see the shaded area
economies that admit a cultural equilibrium can
in Figure 2(b)] and the denominator is the total
be readily constructed. It is proved in the
mass of A-workers [the area marked “A” in
Appendix.
Figure 2(b)]. Every fixed point of the mapping
will correspond to an A-cultural equilibrium.
PROPOSITION 3: Fix { x , C , C ,
, f ,
q
L
H
L
q
An illustration of
is provided in Figure
f } satisfying Assumptions 1–3. For any
A
u
1(b). The way
is defined highlights the local
int(
), there exists some continuous and
L
public good aspect of group reputation in cul-
strictly increasing distribution function H such
tural equilibria. That is, A-workers’ skill invest-
that
A is the proportion of the skilled among
ment choices depend only on the firms’
A-workers in some A-cultural equilibrium of the
perception of the proportion of the skilled
economy { x , C , C ,
, f , f , H}.
q
L
H
L
q
u
among A-workers. In contrast the firm’s percep-
tion is a public good in the basic model.
D. Welfare
Let
max A
[
( A)
A] be the
L
maximal difference between the function
and
In a cultural equilibrium, the new technology
the identity map. It should be clear that
is well
is adopted by a positive mass of workers. In the
defined in terms of the primitives of the model,
meantime, some workers are enduring the dis-
regardless of any equilibrium considerations.
utility of activity A to be members of the
The following proposition is proved in the
elites. The trade-off is in favor of welfare
Appendix.
improvement.12
PROPOSITION 2: There exists at least one
PROPOSITION 4: Any cultural equilibrium
A-cultural equilibrium if and only if
0.
Pareto-dominates the noncultural equilibrium.
When
0 holds, Proposition 2 establishes
PROOF:
that the economy admits at least one A-cultural
With no loss of generality consider an A-cul-
equilibrium. In fact multiple A-cultural equilib-
tural equilibrium. B-workers are exactly as well
ria may exist. Moreover, besides the noncultural
off as they are in the noncultural equilibrium.
equilibrium that we knew always exists, an
By revealed preference A-workers are strictly
economy may simultaneously admit A- and B-
cultural equilibria because an analogous neces-
sary and sufficient condition for the existence of
12
B-cultural equilibria does not necessarily ex-
If, instead of Assumption 4, the utility costs of under-
taking activity A are the same for every worker, then A-
clude
0. In this sense exactly which group
workers will be indifferent between the A-cultural and the
of workers will receive preferential treatment
noncultural equilibria. In this case the A-cultural equilib-
can be quite arbitrary.
rium involves mixed strategies by low cost workers.

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VOL. 91 NO. 4
FANG: SOCIAL CULTURE AND ECONOMIC PERFORMANCE
933
better off than they are in the noncultural equi-
consistent with many existing definitions of “cul-
librium.
ture.” I show that by allowing the firms to give
preferential treatment to workers based on some
Recall that in Spence’s (1973) signaling
“cultural activity,” the society can partially over-
model low ability workers are worse off in the
come an informational free-riding problem. There
separating equilibrium. This is attributed to the
are two useful ways to understand why social
assumed negative relationship between ability
culture may reduce the free-riding problem: first,
and investment cost, which is necessary for
the introduction of cultural activity changes the
signaling to arise in his model. I can dispense
firms’ perception of the proportion of skilled
with this negative relationship because the SCP
workers from a public good into a local public
is endogenously generated. This explains the
good; second, a single-crossing property is gener-
difference in welfare properties from Spence.
ated in a cultural equilibrium, which makes un-
In this paper social culture is always efficient.
dertaking the cultural activity an endogenous
However, this is only because I have chosen as the
signaling instrument for skilled workers.
benchmark economy where the informational
An important message of this paper is that the
free-riding problem is extremely severe (Assump-
distribution of the utility (or disutility) from un-
tions 2 and 3). In fact if Assumption 2 were not
dertaking an activity plays an important role in
satisfied, then the basic model might have an
determining whether it can be used as a cultural
equilibrium in which the new technology is
activity (see Proposition 2). It is entirely possible
adopted by a positive mass of workers. The intro-
that there is no single activity that alone can be
duction of the cultural activity will again make
used as a cultural activity, but by requiring the
cultural equilibrium possible, but then there will
elites to undertake more than one activity the
be no guarantee that it is Pareto improving. To be
society can nonetheless partially overcome the
more specific, suppose that the primitives of the
informational free-riding problem. This suggests
basic economy are such that 0
C
B(
)
that there may be some efficiency-enhancing ra-
L
L
C . Obviously this economy violates Assumption
tionale for the seemingly unnecessary complexity
H
2 because min
. It is easy to see that the
of the norms of etiquette.
L
L
benchmark economy admits an equilibrium in
This paper is only a step toward a better
which a worker invests in skills if and only if she
understanding of the role of social culture in
is of low cost type, and the firms will assign a
economic performance. In the preceding over-
worker with a high enough test signal to the new
simplified static model I can impose a stability
technology. Suppose now we introduce in such an
restriction only on what can be used as a cul-
environment a cultural activity A from which all
tural activity. This limited setting precludes me
workers derive negative utility. Analogous to the
from analyzing important issues of selection
earlier analysis, one can find conditions on the
and evolution of social culture. For example,
distribution H under which the augmented econ-
when there are many activities that qualify as
omy will admit an A-cultural equilibrium in which
cultural activities, which are more likely to
only A-workers are assigned to the new technol-
emerge? When technologies change, what kind
ogy with positive probability. It is easy to see that
of pattern can we expect in the evolution of
all the B-workers are worse off in this A-cultural
culture? The answers to these questions will be
equilibrium than they were in the noncultural
crucial to understand why a previously success-
equilibrium.
ful culture turns disastrous or a previously un-
successful one causes a miracle. These are
III. Conclusions
exciting topics for future research and can be
addressed only in dynamic models.
This paper presents an explicit model to illus-
trate Kenneth Arrow’s (1971) idea that social
APPENDIX: PROOFS OF LEMMA 1, LEMMA 2,
norms or social culture are reactions of the society
PROPOSITION 2, AND PROPOSITION 3
to cope with market failure. I interpret the connec-
tion between obtaining higher paying jobs and
PROOF OF LEMMA 1:
undertaking some seemingly irrelevant activity as
It is implied by the following three interme-
“social culture.” I argue that this interpretation is
diate lemmas.

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Document Outline

• Social Culture and Economic Performance
  • I. A Basic Model
    • A. Firms and Technologies
    • B. Workers
    • C. Timing and Strategies
    • D. Bayesian Nash Equilibrium
  • II. Cultural Activity and Cultural Equilibria
    • A. Cultural Activity
    • B. Noncultural Equilibrium
    • C. Cultural Equilibrium
    • D. Welfare
  • III. Conclusions
  • APPENDIX: PROOFS OF LEMMA 1, LEMMA 2, PROPOSITION 2, AND PROPOSITION 3
  • REFERENCES

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