JOB MARKET SIGNALING *
MICHAEL SPENCE
1. Introduction, 355.-2. Hiring as investment under uncertainty,356.3. Applicant signaling, 358.- 4. Informational feedback and the definitionof
equilibrium, 359.- 5. Properties of informational equilibria: an example, 361.
- 6. The informationalimpact of indices, 368.- Conclusions, 374.
1. INTRODUCTION
The term"marketsignaling"is not exactly a part of the welldefined,technical vocabulary of the economist. As a part of the
preamble,therefore,I feel I owe the reader a word of explanation
however,to give a coherentand
about the title. I findit difficult,
comprehensiveexplanationof the meaningof the term abstracted
fromthe contentsof the essay. In fact,it is part of my purposeto
outline a model in which signalingis implicitlydefinedand to explain why one can, and perhaps should, be interestedin it. One
mightaccurately characterizemy problemas a signalingone, and
that of the reader,who is faced with an investmentdecision under
signals.
uncertainty,as that of interpreting
How the readerinterpretsmy reportof the contentof this essay
will dependupon his expectationconcerningmy stay in the market.
If one believes I will be in the essay marketrepeatedly,then both
the reader and I will contemplatethe possibilitythat I mightinvest
in my futureability to communicateby accurately reportingthe
contentof this essay now. On the otherhand, if I am to be in the
then the above-menmarketonly once, or relativelyinfrequently,
tioned possibilitydeserves a low probability. This essay is about
marketsin which signalingtakes place and in which the primary
insignalersare relativelynumerousand in the marketsufficiently
frequentlythat they are not expectedto (and thereforedo not) invest in acquiringsignalingreputations.
* The essay is based on the author's doctoral dissertation ("Market
Signalling: The Informational Structure of Job Markets and Related Phenomena," Ph.D. thesis, Harvard University, 1972), forthcomingas a book en-
in Hiringand Related Screening
Transfer
titledMarketSignaling:Information
Processes in the Harvard Economic Studies Series, Harvard University Press.
The aim here is to present the outline of the signaling model and some of its
conclusions. Generalizations of the numerical examples used for expositional
purposes here are found in ibid. and elsewhere.
I owe many people thanks for help in the course of the current study,
too many to mention all. However, I should acknowledge explicitly the magnitude of my debts to Kenneth Arrow and Thomas Schelling for persistently
directingmy attention to new and interestingproblems.
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I shall argue that the paradigm case of the marketwith this
type of informationalstructureis the job marketand will therefore
focus upon it. By the end I hope it will be clear (although space
limitationswill not permitan extendedargument)that a considerable varietyof marketand quasi-marketphenomenalike admissions
procedures,promotionin organizations,loans and consumercredit,
can be usefullyviewed throughthe conceptuallens applied to the
job market.
If the incentivesfor veracity in reportinganythingby means
of a conventionalsignalingcode are weak, then one must look for
othermeans by whichinformation
transferstake place. My aim is
to outlinea conceptualapparatus withinwhichthe signalingpower
of education,job experience,race, sex, and a host of otherobservable, personal characteristicscan be determined.The question,put
crudely,is what in the interactivestructureof a market accounts
forthe informationalcontent,if any, of these potential signals. I
have placed primaryemphasisupon (i) the definitionand properties
of signalingequilibria, (ii) the interactionof potentialsignals,and
(iii) the allocative efficiency
of the market.
2. HIRING
AS INVESTMENT
UNDER UNCERTAINTY
In mostjob marketsthe employeris not sure of the productive
capabilities of an individual at the time he hires him.' Nor will
this informationnecessarilybecome available to the employerimmediately after hiring. The job may take time to learn. Often
specifictrainingis required. And there may be a contractperiod
withinwhich no recontractingis allowed. The fact that it takes
time to learn an individual's productive capabilities means that
hiringis an investmentdecision. The fact that these capabilities
are notknownbeforehandmakes the decisionone underuncertainty.
To hire someone,then,is frequentlyto purchase a lottery.2In
what follows,I shall assume the employerpays the certainmonetary equivalent of the lotteryto the individual as wage.. If he is
1. There are,of course,otherinformational
gaps in the job market.Just
as employershave less than perfectinformation
about applicants,so also will
informedabout the qualitiesof jobs and workenapplicantsbe imperfectly
And in a different
vironments.
vein neitherpotentialemployeesnor employers
knowall of the people in the market.The resultingactivitiesare job search
and recruiting.For the purposeof this essay I concentrateupon employer
and the signalinggame that results.
uncertainty
2. The term"lottery"is used in the technicalsense,impartedto it by
decisiontheory.
3. The certainmonetaryequivalentof a lotteryis the amountthe individual would take, with certainty,in lieu of the lottery. It is generally
thoughtto be less thanthe actuarialvalue of the lottery.
JOB MARKET SIGNALING
357
the wage is taken to be the individual'smarginalconrisk-neutral,
tributionto the hiringorganization.
Primary interestattaches to how the employerperceives the
lottery,forit is theseperceptionsthat determinethe wages he offers
to pay. We have stipulatedthat the employercannot directlyobserve the marginalproductpriorto hiring. What he does observe
is a plethoraof personal data in the formof observable characteristics and attributesof the individual, and it is these that must
ultimatelydeterminehis assessmentof the lotteryhe is buying.
(The image that the individualpresentsincludeseducation,previous
work,race, sex, criminaland service records,and a host of other
data.) This essay is about the endogenousmarketprocesswhereby
the employerrequires (and the individual transmits) information
about the potential employee, which ultimately determinesthe
implicitlotteryinvolved in hiring,the offeredwages, and in the
end the allocationof jobs to people and people to jobs in the market.
At this point,it is usefulto introducea distinction,the import
of which will be clear shortly. Of those observable,personal attributesthat collectivelyconstitutethe image the job applicant
presents,some are immutablyfixed,while othersare alterable. For
example,educationis somethingthat the individualcan investin at
some cost in termsof time and money. On the otherhand, race and
sex are not generallythoughtto be alterable. I shall referto observable,unalterableattributesas indices,reservingthe termsignals
forthose observable characteristicsattached to the individualthat
are subject to manipulationby him.4 Some attributes,like age, do
change,but not at the discretionof the individual. In my terms,
these are indices.
Sometime after hiringan individual,the employerwill learn
the individual's productivecapabilities. On the basis of previous
experiencein the market,the employerwill have conditionalprobability assessmentsover productivecapacity given various combinationsof signalsand indices. At any pointof timewhenconfronted
with an individualapplicantwith certainobservableattributes,the
employer'ssubjective assessmentof the lotterywith which he is
confrontedis definedby these conditionalprobabilitydistributions
over productivitygiventhe new data.
From one point of view, then,signals and indices are to be redistinctionis borrowedfromRobert Jervis(The
4. The terminological
Logic of Images in InternationalRelations (Princeton,N.J.: PrincetonUniversityPress,1970)). My use of the termsfollowsthat of Jervissufficiently
closelyto warranttheirtransplantation.
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garded as parametersin shiftingconditionalprobabilitydistributionsthat definean employer'sbeliefs.5
3. APPLICANT
SIGNALING
For simplicityI shall speak as ifthe employerwererisk-neutral.
For each set of signals and indices that the employerconfronts,
he
will have an expectedmarginalproductfor an individual who has
these observable attributes. This is taken to be the offeredwage
to applicantswiththose characteristics.Potential employeesthereforeconfrontan offeredwage schedulewhose argumentsare signals
and indices.
There is not much that the applicant can do about indices.
Signals, on the otherhand, are alterable and thereforepotentially
subject to manipulation by the job applicant. Of course, there
may be costs of makingthese adjustments.Education, forexample,
is costly. We referto these costs as signalingcosts. Notice that the
individual,in acquiringan education,need not thinkof himselfas
signaling. He will invest in education if there is sufficient
return
as definedby the offeredwage scheduleA Individuals, then, are
assumedto select signals (forthe mostpart,I shall talk in termsof
education) so as to maximizethe difference
betweenofferedwages
and signalingcosts. Signalingcosts play a key role in this type of
signaling situation, for they functionallyreplace the less direct
costs and benefitsassociated with a reputationfor signalingreliability acquired by those who are more prominentin their markets
than job seekersare in theirs.
A CriticalAssumption
It is not difficult
to see that a signal will not effectivelydistinguishone applicantfromanother,unlessthe costsof signalingare
negativelycorrelatedwith productivecapability. For if this condition fails to hold, given the offeredwage schedule,everyonewill
investin the signal in exactlythe same way, so that they cannotbe
distinguishedon the basis of the signal. In what follows,we shall
make the assumptionthat signalingcosts are negativelycorrelated
with productivity.It is, however,most appropriatelyviewed as a
5. The shiftingof the distributions
occurswhen new marketdata are
receivedand conditionalprobabilitiesare revisedor updated. Hiringin the
marketis to be regardedas sampling,and revisingconditionalprobabilitiesas
passingfrompriorto posterior.The wholeprocessis a learningone.
6. There may be otherreturnsto education. It may be a consumption
good or serve as a signal of thingsotherthan workpotential(status for example). These returnsshouldbe added to the offered
wage schedule.
359
JOB MARKET SIGNALING
offered Wage Schedule
Employers Conditional
Probabilistic Beliefs
as a Function of
Signals and Indices
Hiring,Observationof
Signaling Decisions by
Relationshipbetween
Applicants; Maximization
Marginal Product and
of ReturnNet of Signal-
Signals
ing Costs
Signaling Costs
FIGURE
I
Feedback in the Job Market
Informational
prerequisitefor an observable,alterable characteristicto be a persistentlyinformativesignal in the market. This means,amongother
things,that a characteristicmay be a signal with respectto some
types of jobs but not with respectto others.7
Signalingcosts are to be interpretedbroadlyto includepsychic
and othercosts, as well as the directmonetaryones. One element
of cost,forexample,is time.
4. INFORMATION
FEEDBACK
AND THE
DEFINITION
OF EQUILIBRIUM
At this point it is perhaps clear that there is informational
feedback to the employerover time. As new market information
comes in to the employerthroughhiringand subsequent observation of productivecapabilitiesas theyrelate to signals,the employer's conditionalprobabilisticbeliefs are adjusted, and a new round
starts. The wage schedule facing the new entrantsin the market
generallydiffersfromthat facingthe previousgroup. The elements
in the feedbackloop are shownin Figure I.
It is desirableto finda way to studythis feedbackloop in the
7. The reason is that signalingcosts can be negativelycorrelatedwith
one typeof productivecapabilitybut not withanother.
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QUARTERLY JOURNAL OF ECONOMICS
marketover time. To avoid studyinga systemin a continualstate
of flux,it is useful to look for nontransitoryconfigurationof the
feedback system. The systemwill be stationaryif the employer
startsout with conditionalprobabilisticbeliefsthat afterone round
are not disconfirmed
by the incomingdata theygenerated.We shall
referto such beliefsas self-confirming.
The sense in whichthey are
is definedby the feedbackloop in Figure I.
self-confirming
A SignalingEquilibrium
As successivewaves of new applicants come into the market,
we can imagine repeated cycles around the loop. Employers' conditional probabilisticbeliefs are modified,offeredwage schedules
are adjusted, applicant behavior with respect to signal choice
changes,and after hiring,new data become available to the employer. Each cycle,then,generatesthe nextone. In thinkingabout
it, one can interruptthe cycle at any point. An equilibriumis a set
of componentsin the cycle that regeneratethemselves. Thus, we
can thinkof employerbeliefsbeing self-confirming,
or offeredwage
schedulesregeneratingthemselves,or applicant behavior reproducing itselfon the nextround.8
I findit most useful to think in termsof the self-confirming
aspect of the employerbeliefs because of the continuityprovided
by the employer'spersistentpresencein the market.9Thus, in these
termsan equilibriumcan be thoughtof as a set of employerbeliefs
that generateofferedwage schedules,applicant signalingdecisions,
hiring,and ultimatelynew marketdata over time that are consistentwiththe initial beliefs.
A furtherword about the definitionof equilibriumis in order.
Given an offeredwage schedule, one can think of the market as
generating,via individual optimizingdecisions, an empirical distributionof productivecapabilites given observable attributesor
signals (and indices). On the other hand, the employerhas subjectively held conditionalprobabilisticbeliefswith respectto productivity,given signals. In an equilibriumthe subjective distributionand the one implicitin the marketmechanismare identical,
8. In pursuingthe propertiesof signalingequilibria,we select as the obbut usuallyemployer
whateveris analyticallyconvenient,
ject forregeneration
wage schedules.
beliefsor offered
orientedwill realize that what is at issue here is
9. The mathematically
a fixedpointproperty.A mappingfromthe space of conditionaldistributions
givensignalsinto itselfis definedby the marketresponse
over productivity
mechanism.An equilibriumcan be thoughtof as a fixedpointof thismapping.
of thissubjectis containedin Spence,op. cit.
treatment
A mathematical
361
JOB MARKET SIGNALING
over the rangeof signals that the employeractually observes.' Any
in the marothersubjective beliefswill eventuallybe disconfirmed
ket because of the employer'spersistentpresencethere.
Indices continueto be relevant. But since they are not a matter of individualchoice,they do not figureprominentlyin the feedback systemjust described. I shall returnto themlater.
5. PROPERTIES
EQUILIBRIA:
OF INFORMATIONAL
AN EXAMPLE
I proposeto discuss the existenceand propertiesof marketsignalingequilibriavia a specificnumericalexample.2For the timebeing,indicesplay no part. The propertiesof signalingequilibriathat
we shall encounterin the exampleare general.3
Let us suppose that there are just two productivelydistinct
groupsin a population facingone employer. Individuals in Group
I have a productivityof 1, while those in Group II have a productivityof 2.4 Group I is a proportionq1 of the population; Group II
is a proportionof 1- q1. There is, in addition,a potentialsignal,say
education,whichis available at a cost. We shall assumethat education is measuredby an indexy of level and achievementand is subject to individual choice. Education costs are both monetaryand
psychic. It is assumed that the cost to a memberof Group I of y
units of education is y, while the cost to a memberof Group II is
y/2.
We summarizethe underlyingdata of our numericalexamplein
Table I.
TABLE I
DATA OF THE MODEL
Group
Marginal
product
Proportionof
population
I
II
1
2
1-q1
y,
Cost of educationlevel y
v
y/2
model one faces the possibilitythat certaintypes
1. In a multi-market
of potentialapplicantswill rationallyselect themselvesout of certainjob
may never appear in these
markets,and hence certainsignal configurations
markets.When this happens,the beliefsof the employersin the relevant
in a degenerateway. No data are forthcoming.
marketare not disconfirmed
based discrimination
This raises the possibilityof persistentinformationally
againstcertaingroups.The subjectis pursuedin detail in ibid.
2. Obviously,an exampledoes not prove generality.On the otherhand,
if the readerwill take reasonablegeneralityon faith,the exampledoes illustratesome essentialpropertiesof signalingequilibria.
3. See Spence,op. cit.
the readermay read "what the individualis worth
4. For productivity
here.
to the employer."There is no need to relyon marginalproductivity
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W(y
2
I
I
0
yy
Y
FIGURE II
Offered
Wages as a Functionof Level of Education
To findan equilibriumin the market,we guess at a set of selfconfirmingconditionalprobabilistic beliefs for the employerand
then determinewhetherthey are in fact confirmedby the feedback
mechanismsdescribed above. Suppose that the employerbelieves
that thereis some level of education,say y* such that if y < y*,then
productivityis one with probabilityone, and that if yay*, then
productivitywill be two withprobabilityone. If these are his conditional beliefs,then his offeredwage schedule, W(y), will be as
shownin Figure II.
Given the offeredwage schedule,membersof each group will
select optimal levels for education. Consider the person who will
set y <y*. If he does this,we know he will set y =0 because education is costly,and until he reaches y*, there are no benefitsto increasingy, giventhe employer'shypothesizedbeliefs. Similarly,any
individualwho sets y>y* will in fact set y=y*, since furtherincreases would merely incur costs with no correspondingbenefits.
Everyonewill thereforeeitherset y = 0 or set y = y*. Given the employer's initial beliefsand the fact just deduced, if the employer's
beliefsare to be confirmed,
thenmembersof Group I mustset y =0,
whilemembersof Group II set y = y*. Diagrams of the optionsfacing the two groupsare shownin Figure III.
Superimposedupon the wage scheduleare the cost schedulesfor
the two groups. Each groupselectsy to maximizethe difference
betweenthe offeredwages and the costs of education. Given the level
of y* in the diagram,it is easy to see that Group I selectsy = 0, and
Group II sets y=y*. Thus, in this case the employer'sbeliefs are
and we have a signalingequilibrium. We can state the
confirmed,
JOB MARKET SIGNALiNG
GroupI
363
Group11
Cl~~~~~~~~C
i
2(
0
ye 2
2eW(y)
r/W(y)
I
ly2y
yy*2C
OptimalChoice of y
OptimalChoice of y
FIGUREIII
ChoiceofEducationforBoth Groups
Optimizing
conditionson behaviorby the two groups,in orderthat the employin algebraic terms. Group I sets y=0 if
er's beliefsbe confirmed,
1>2-y*.
Group II will set y y* as required,providedthat
2y-*/2> 1.
Puttingthese two conditionstogether,we findthat the employer's
by marketexperience,providedthat the
initialbeliefsare confirmed
parametery* satisfiesthe inequality,
1 <y*<2.
It is worthpausing at this point to remarkupon some striking
featuresof this type of equilibrium. One is that withinthe class
of employerexpectationsused above, thereis an infinitenumberof
possible equilibriumvalues fory*. This means that thereis an infinitenumberof equilibria. In any one of the equilibria the employer is able to make perfect point predictionsconcerningthe
productivityof any individual,having observedhis level of education. The reader will realize that this propertyis special and depends,at least in part,upon the assumptionthat educationcosts are
perfectlynegativelycorrelatedwith productivity.However, even
in this case, thereare equilibria in whichthe employeris uncertain,
as we shall shortlysee.
The equilibria are not equivalentfromthe point of view of welfare. Increases in the level of y* hurtGroup II, while,at the same
time,membersof Group I are unaffected.Group I is worse offthan
it was withno signalingat all. For if no signalingtakes place, each
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QUARTERLY JOURNAL OF ECONOMICS
person is paid his unconditionalexpected marginal product,which
is just
q + 2 (
- q1)
--
2- q1.
Group II may also be worseoffthan it was with no signaling. Assume that the proportionof people in Group I is 0.5. Since y*> 1
and the net returnto the memberof Group II is 2- y*/2, in equilibriumhis net returnmust be below 1.5, the no-signalingwage.
Thus, everyonewould prefera situationin whichthereis no signaling.
No one is actingirrationallyas an individual. Coalitions might
profitablyformand upset the signalingequilibrium. The initial
proportionsof people in the two groupsq1 and 1- q1 have no effect
upon the equilibrium. This conclusiondepends upon this assumption that the marginalproductof a personin a givengroupdoes not
changewithnumbershired.
Given the signalingequilibrium,the education level y*, which
definesthe equilibrium,is an entrancerequirementor prerequisite
for the high-salaryjob -or so it would appear fromthe outside.
From the point of view of the individual,it is a prerequisitethat
has its source in a signaling game. Looked at fromthe outside,
education mightappear to be productive. It is productivefor the
individual,but, in this example,it does not increase his real marginalproductat all.6
A sophisticatedobjection to the assertion that private and
social returnsdiffermightbe that, in the contextof our example,
the social returnis not really zero. We have an informationproblem in the society and the problem of allocating the rightpeople
to the rightjobs. Education, in its capacity as a signal in the
model, is helping us to do this properly. The objection is well
founded. To decide how efficient
or inefficient
this systemis, one
mustconsiderthe realisticalternativesto marketsortingprocedures
in the society.7But noticethat even withinthe confinesof the market model,thereare moreor less efficient
ways of gettingthe sorting
accomplished. Increases in y* improvethe quality of the sorting
not one bit. They simplyuse up real or psychicresources. This is
5. Coalitionsto changethe patternsof signalingare discussedin Spence,
op. cit.
6. I am ignoringexternalbenefitsto educationhere. The assertionis
One
to productivity.
simplythatin the exampleeducationdoes not contribute
mightstill claim that the social productis not zero. The signalcost function
does, in principle,captureeducationas a consumptiongood, an effectthat
simplyreducesthe cost of education.
7. This questionis pursuedin Spence,op. cit.
JOB MARKET SIGNALING
365
just anotherway of saying that there are Pareto inferiorsignaling
equilibriain the market.
It is not always the case that all groupslose due to the existence
of signaling.For example,if,in the signalingequilibrium,y* <2q1,
then Group II would be better offwhen education is functioning
effectivelyas a signal than it would be otherwise. Thus, in our
example if q1> I so that Group II is a minority,then there exists
a signalingequilibriumin whichthe membersof Group II improve
theirposition over the no-signalingcase. Recall that the wage in
the no-signalingcase was a uniform2- q1 over all groups.
We may generalizethis bit of analysis slightly. Suppose that
the signalingcost scheduleforGroup I was given by a1y and that
for Group II by a2Y.5 Then with a small amount of calculation,
we can show that there is a signalingequilibriumin which Group
II is betteroffthan withno signaling,9
providedthat
q1 > a2/al.
How small a "minority"Group II has to be to have the possibility
of benefitingfromsignalingdependsupon the ratio of the marginal
signalingcosts of the two groups.1
Beforeleavingour educationsignalingmodel,it is worthnoting
that there are other equilibria in the systemwith quite different
properties. Suppose that the employer's expectationsare of the
followingform:
If y <y*: Group I withprobabilityq1,
Group II withprobability1- q1;
if y>y*: Group II withprobability1.
As before,the only levels of y that could conceivablybe selectedare
8. It is assumed that a2<aL.
9. Notice that the statementis that thereexistsa signalingequilibrium
in whichGroupII is betteroff.It turnsout thattherealwaysexistsa signaling
equilibriumin whichGroup II is worseoffas well.
1. The calculationis straightforward.
Given these signalingcosts groups
will make the requisitechoiceto confirm
the employer'sbeliefsprovidedthat
1>2 aly*
and
2-a2y*>1.
These translateeasilyinto the followingconditionon y*:
1
1
a2
a,
Now, if GroupII is to be betteroffforsome signalingequilibrium,then
- a2
2-
or
al
>2 - qi,
a2
a to
This is whatwe set out to show.
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QUARTERLY JOURNAL OF ECONOMICS
Return
Return
CZ
22
2-,ql
0
o
2q, yKly
Optimal
y forGroupI
2,y
Optimal
y forGroup11
FIGURE IV
OptimalSignalingDecisionsforthe Two Groups
y=O and y=y*. The wage for y=O is 2-qj, while the wage for
y = y* is simply2. From FigureIV it is easy to see that bothgroups
rationallyset y=O, provided that y*>2q1. If they both do this,
then the employer'sbeliefs are confirmed,and we have an equilibrium.
It shouldbe notedthat the employer'sbeliefsabout the relationship betweenproductivityand education for yCy* are confirmed
in a somewhatdegenerate,but perfectlyacceptable, sense. There
are no data relatingto these levels of educationand hence,by logic,
no disconfirming
data. This is an exampleof a phenomenonof much
widerpotentialimportance.The employer'sbeliefsmay drive certain groups fromthe market and into anotherlabor market. We
cannotcapturethis situationin a simple one-employer,one-market
model. But when it happens,thereis no experienceforthcoming
to
the employerto cause himto alter his beliefs.2
Education conveysno informationin this type of equilibrium.
In fact,we have reproducedthe wages and information
state of the
employerin the no-signalingmodel,as a signalingequilibrium.
Just as thereexists a signalingequilibriumin which everyone
sets y =0, thereis also an equilibriumin whicheveryonesets y =y*
forsome positivey*. The requisiteemployerbeliefsare as follows:
If y <y*: GroupI withprobability1;
if yby*: Group I withprobabilityq1,
Group II withprobability1- q1.
2. This is discussedin detail in Spence,op. cit.
JOB MARKET SIGNALING
367
Followingour familiarmode of analysis,one findsthat these beliefs
are self-confirming
in the market,providedthat
Y*<-q1.
Again,the educationlevel conveysno usefulinformation,
but in this
instance individuals are rationallyinvestingin education. If they
as individuals did not invest,they would incur lower wages, and
the loss would exceed the gain fromnot makingthe educational investment.The implicationof this versionof the signalingequilibrium is that there can be stable prerequisitesfor jobs that convey
no information
by virtueof theirexistenceand hence serveno function.
It is interestingto note that this last possibilitydoes not depend upon costs being correlatedwith productivityat all. Suppose
that the signaling costs for both groups were given by the one
scheduley. And suppose furtherthat employerbeliefswere as describedabove. Then everyonewill rationallyselecty=y*, provided
that
Y*<1q1.
The outcomeis the same. But the interesting
thingis that, because
of the absence of any correlationbetween educational costs and
productivity,education could never be an effectivesignal, in the
sense of conveyinguseful information,in an equilibriumin this
market.
We have dwelt enoughupon the specificsof this model to have
observedsome of the effectsthe signalinggame may have upon the
allocational functioningof the market. The numericalexample is
not important.The potential effectsand patternsof signalingare.
An alterable characteristiclike education,which is a potential
signal,becomesan actual signal if the signalingcosts are negatively
correlatedwith the individual's unknownproductivity.Actually,
the negative correlationis a necessarybut not sufficient
condition
forsignalingto take place. To see this in the contextof our model,
assume that the only values y can have are one and three. That
is to say, one can only get units of education in lumps. If this is
true,then thereis no feasiblevalue of y* that will make it worthwhileforGroup II to acquire an education. Three unitsis too much,
and one unit will not distinguishGroup II fromGroup I. Therefore,effectivesignalingdependsnot only upon the negativecorrelation of costs and productivities,but also upon there being a "sufficient"numberof signalswithinthe appropriatecostrange.3
3. In ibid. it is arguedthat many potentialsignalsin creditand loan
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QUARTERLY JOURNAL OF ECONOMICS
An equilibriumis definedin the contextof a feedbackloop, in
whichemployerexpectationslead to offeredwages to various levels
of education,which in turnlead to investmentin education by individuals. After hiring,the discovery of the actual relationships
betweeneducation and productivityin the sample leads to revised
expectationsor beliefs. Here the cycle startsagain. An equilibrium
is best thoughtof as a set of beliefsthat are confirmedor at least
not contradictedby the new data at the end of the loop just described. Such beliefswill tend to persistover time as new entrants
into the marketflowthrough.
Multiple equilibria are a distinct possibility. Some may be
Pareto inferiorto others. Private and social returnsto education
diverge.Sometimeseveryoneloses as a result of the existenceof
signaling. In othersituationssome gain,while otherslose. Systematic overinvestment
in educationis a distinctpossibilitybecause of
the elementof arbitrarinessin the equilibriumconfiguration
of the
market. In the contextof atomisticbehavior (which we have assumedthus far) everyoneis reactingrationallyto the marketsituation. Informationis passed to the employerthroughthe educational signal. In some of our examples it was perfectinformation.
In othercases this is not so. There will be randomvariationin signaling costs that prevent the employerfrom distinguishingperfectlyamong individualsof varyingproductivecapabilities.
In our examples,educationwas measuredby a scalar quantity.
With no basic adjustmentin the conceptualapparatus,we can think
of education as a multidimensionalquantity: years of education,
institutionattended,grades,recommendations
and so on. Similarly,
it is not necessaryto thinkin termsof two groupsof people. There
may be many groups,or even a continuumof people: some suitedto
certainkindsof work,otherssuitedto otherkinds. Nor need education be strictlyunproductive.However,if it is too productiverelative to the costs,everyonewill investheavilyin education,and education may cease to have a signalingfunction.
6. THE INFORMATIONAL IMPACT OF INDICES
In the educational signalingmodel we avoided consideringany
observable characteristicsother than education. In that model
educationwas a signal. Here we considerwhat role,if any,is played
marketseffectively
become indicesbecause the "signaling"costs swamp the
gains,so thatcharacteristics
thatcould be manipulatedin factare not. House
ownershipis an exampleof a potentialsignalthat,in the contextof the loan
market,failson thiscriterion
and hencebecomesan index.
JOB MARKET SIGNALING
369
by indices. For concretenessI shall use sex as the example. But
just as education can stand for any set of observable, alterable
characteristicsin the firstmodel, sex can stand for observable,
unalterable ones here. The reader may wish to think in terms of
race, nationality,size, or in termsof criminalor police recordsand
service records. The latter is potentiallypublic informationabout
a person'shistoryand is, of course,unalterablewhen viewed retrospectivelyfromthe present.4
Let us assume that there are two groups,men and women. I
shall referto these groupsas W and M. Withineach groupthe distributionof productivecapabilities and the incidence of signaling
costs are the same. Thus, withinM the proportionof people with
productivityone and signaling (education) costs of y is q1. The
remainderhave productivitytwo and signaling costs y/2. The
same is true forgroup W. Here m is the proportionof men in the
overall population of job applicants.
TABLE IV
DATA
Race
Productivity
W
W
M
M
1
2
1
2
OF THE
MODEL
Education
costs
Proportion
within group
Proportion of
total population
y
qi
1-q1
q1(1-m)
(1-q1)(1-m)
q1m
(1-q)m
y/2
yq
y/2
1-q1
Given the assumptionsthe centralquestion is, "how could sex
have an informationalimpact on the market?" The next few paragraphsare devotedto arguingthat indices do have a potentialimpact and to explainingwhy this is true. We begin by notingthat,
under the assumptions,the conditionalprobabilitythat a person
drawn at random fromthe population has a productivityof two,
giventhat he is a man (or she is a woman), is the same as the unconditionalprobabilitythat his productivityis two. Sex and productivityare uncorrelatedin the population. Therefore,by itself,
sex could nevertell the employeranythingabout productivity.
We are forcedto the conclusionthat if sex is to have any informationalimpact, it must be throughits interactionwith the
educationalsignalingmechanism.But here again we run up against
an initially puzzling symmetry.Under the assumptions,men and
women of equal productivityhave the same signaling (education)
4. It is, or oughtto be, the subjectof policydecisionsas well.
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QUARTERLY JOURNAL OF ECONOMICS
costs. It is a generalmaximin economicsthat people withthe same
preferences
and opportunity
sets will make similardecisionsand end
up in similar situations. We may assume that people maximize
theirincomenet of signalingcosts so that theirpreferencesare the
same. And since signalingcosts are the same, it would appear that
theiropportunitysets are the same. Hence, again we appear to be
drivento the conclusionthat sex can have no informationalimpact.
But the conclusionis wrong,foran interesting
reason.
The opportunitysets of men and womenof comparableproductivityare not necessarilythe same. To see this, let us step back to
the simple educational signalingmodel. There are externalitiesin
that model. One person's signalingstrategyor decision affectsthe
marketdata obtainedby the employer,whichin turnaffectthe employer'sconditionalprobabilities.These determinethe offered
wages
to various levels of educationand henceof rates of returnon education for the next group in the job market. The same mechanism
applies here,with a notable modification.If employers'distributions are conditionalon sex as well as education,then the external
impacts of a man's signalingdecision are felt only by other men.
The same holds forwomen.
If at some point in time men and women are not investingin
educationin the same ways, then the returnsto education formen
and womenwill be different
in the next round. In short,their opportunitysets differ.In what follows,we demonstraterigorously
that this sort of situation can persist in an equilibrium. The important point, however,is that there are externalitiesimplicit in
the fact that an individualis treated as the average memberof the
groupof people who look the same and that,as a result,and in spite
of an apparent sameness the opportunitysets facing two or more
groupsthat are visibly distinguishablemay in fact be different.
The employernow has two potential signals to consider: education and sex. At the starthe does not knowwhethereithereducation or sex will be correlatedwith productivity. Uninformative
potentialsignals or indices are discarded in the course of reaching
an equilibrium.As beforewe mustguess at an equilibriumformfor
the employer'sexpectationsand thenverifythat these beliefscan be
via the marketinformationalfeedbackmechanisms.
self-confirming
We will trybeliefson the followingform.
= 1 withprobability1.
If W and y < y*w,productivity
If W and y>y*w, productivity
=2 withprobability1.
=1 withprobability1.
If M and y <y*M, productivity
If M and y>y*M, productivity= 2 withprobability1.
371
JOB MARKET SIGNALING
WM(y
way)
2
2
I
l
I
l
I ...--o.I
Y*W
Y
Ym
Y
FIGURE V
Offered
Wages to W and M
These lead to offeredwage schedulesWw(y) and WM(y) as shown
in Figure V.
Because groupsW and M are distinguishableto the employer,
theirofferedwages are not connectedat the level of employerexpectations. Applyingthe reasoningused in the straightforward
educational signalingmodel,we findthat the requiredequilibriumconditionson y*w and y*Mare
1 <y*w <2
and
1 <y <2
No logical conditionrequiresthat y*w equals y*min an equilibrium.
Essentially we simply have the educational signaling model
iteratedtwice. Because sex is observable,the employercan make
his conditionalprobabilityassessmentsdepend upon sex as well as
education. This has the effectof makingsignalinginterdependencies
betweentwo groups,W and M, nonexistent.They settleinto signaling equilibriumconfigurations
in the marketindependentlyof each
other. But in the firstmodel therewas not one equilibrium,there
were many. Therefore,thereis at least the logical possibilitythat
men and womenwill settle into different
stable signalingequilibria
in the marketand stay there.
As we noted earlier,the signalingequilibria are not equivalent
fromthe point of view of social welfare. The higherthat y*w (or
Y M) is, the worse offis the relevantgroupor, more accurately,the
high-productivity
portionof the group. One example of an asymmetricalequilibriumwould be givenby y*M= 1.1 and y*m=1.9. In
this case high-productivity
womenhave to spend moreon education
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QUARTERLY JOURNAL OF ECONOMICS
Returns
21
Returns
'
IYW
r
/
t2
2
y
l
Y 2
y
FiGuREVI
MarketEquilibriumwithSex as an Index
and have less leftoverto consumein orderto convincethe employer
that theyare in the high-productivity
group.
Notice that the proportionsof high- and low-productivity
people in each groupdo not affectthe signalingequilibriumin the
market. Hence, our initialassumptionthat the groupswereidentical
with respect to the distributionof productivecharacteristicsand
the incidenceof signalingcosts was superfluous.More accurately,
it was superfluouswith respectto this type of equilibrium. As we
saw in the educational signaling model, there are other types of
equilibriumin whichthe proportionsmatter.
Since froman equilibriumpoint of view men and womenreally
are independent,
theymightsettleintodifferent
typesof equilibrium.
Thus, we mighthave men signalingy=y*m= 1.1 if they are also in
the higherproductivitygroup,while other men set y = 0. On the
otherhand, we may findthat all women set y = 0. In this case all
womenwould be paid 2- qj, and the upper signaling cutoffpoint
y*Mwould have to be greaterthan 2q1. Notice that all women,includinglower productivitywomen,would be paid more than lowproductivitymen in this situation.5 High-productivitywomen
would,of course,be hurtin termsof wages received. It is conceivable, however,that returnsnet of signaling would be higher for
womenwithproductivityof two. In otherwords,it is possible that
2 -q1 > W- Y*M12
5. I have not assumedthat employersare prejudiced. If they are, this
differential
could be wiped out. Perhaps more interestingly
laws prohibiting
if enforced,
would also wipe it out.
wage discrimination,
373
JOB MARKET SIGNALING
CX
YM Men
YW Women Y
Y
FIGURE VII
in the Market
AnotherEquilibriumConfiguration
This will occur when
2q < y*M.
Looking at this situationfromoutside,one mightconcludethat
women receive lower wages than some men because of a lack of
education,whichkeeps theirproductivitydown. One mightthengo
lookingoutside the job marketfor the explanationforthe lack of
education. In this modelthe analysisjust suggestedwould be wrong.
is in the informaThe sourceof the signalingand wage differentials
tional structureof the marketitself.6
Because of the independenceof the two groups,M and W, at
the level of signaling,we can generate many differentpossible
by taking any of the educational signalequilibriumconfigurations
and assigningit to W and thentakmodel
ing equilibriain our first
ing any educationequilibriumand assigningit to M. However,an
exhaustivelistingof the possibilitiesseemspointlessat this stage.
We have here the possibilityof arbitrarydifferencesin the
of two or more distinctgroups.
equilibriumsignalingconfigurations
Some of themmay be at a disadvantagerelativeto the others. Subsets of one may be at a disadvantageto comparablesubsets of the
others. Since the mechanismthat generatesthe equilibriumis a
feedback loop, we might,followingMyrdal and others,wish to
referto the situationof the disadvantagedgroupas a vicious cycle,
based one. I preferto referto the situalbeit it an informationally
6. Differential signaling costs over groups are an important possibility
pursued in Spence, op. cit.
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QUARTERLY JOURNAL OF ECONOMICS
ation of the disadvantagedgroupas a lower level equilibriumtrap,
whichconveysthe notionof a situationthat,once achieved,persists
forreasonsendogenousto the model. The multipleequilibria of the
educationmodel translateinto arbitrarydifferences
in the equilibrium configuration
and status of two groups,as definedas observable, unalterablecharacteristics.
CONCLUSIONS
We have looked at the characteristicsof a basic equilibrium
signalingmodel and at one possible type of interactionof signals
and indices. There remainsa host of questions,whichcan be posed
and partially answeredwithinthe conceptual frameworkoutlined
here. Amongthemare the following:
1. What is the effectof cooperativebehavior on the signaling
game?
2. What is the informationalimpactof randomnessin signaling
costs?
3. What is the effectof signalingcoststhat differsystematically
withindices?
4. How general are the propertiesof the examples considered
here?
5. In a multiple-market
setting,does the indeterminateness
of
the equilibriumremain?
6. Do signalingequilibria exist in general?
7. What kinds of discriminatorymechanismsare implicit in,
or interactwith,the informational
structureof the market,and what
in dealing withthem?
policies are effectiveor ineffective
I would argue furtherthat a range of phenomenafromselective
admissions procedures through promotion,loans and consumer
credit,and signalingstatus via conspicuousconsumptionlends itself
to analysis with the same basic conceptual apparatus. Moreover,
it may be as importantto explain the absence of effectivesignaling
as its presence,and herethe prerequisitesforeffectivesignalingare
of some use.
On the otherhand, it is well to rememberthat the propertyof
relativeinfrequencyof appearance by signalersin the market,which
definesthe class signalingphenomenaunder scrutinyhere, is not
characteristicof many markets,like those for consumerdurables,
and that,as a result,the informationalstructuresof these latterare
likely to be quite different.
HARVARDUNIVERSITY