Job market signaling

Michael Spence

1. Introduction

This essay is about markets in which

• signaling takes place

• signalers are

– relatively numerous

– in the market sufficiently infrequently

that they are not expected to invest in acquiringsignaling reputations

• If the incentives for veracity are weak

⇒ other means by which information transfers

take place.

• Aim is to outline a conceptual apparatus within

which the signaling power of the observable

personal characteristics can be determined.

• What in the interactive structure of a market

accounts for the informational content of these

potential signals.

2. Hiring

• Hiring: Investment decision under uncertainty ⇒

purchasing a lottery

• Assumption: the employer pays the certain monetaryequivalent as wage.

• Certain monetary equivalent depends on the observable characteristics of the individual:

– Indices: unalterable attributes (race, sex, age…)

– Signals: are subject to manipulation by the individual (education…)

3. Applicant signaling

• Offered wage has as arguments signals and indices.

• Individuals select signals so as to maximize thedifference between offered wages and signalingdifference between offered wages and signalingcosts.

• Assumption: signaling costs are negativelycorrelated with productivity– Prerequisite for an observable, alterable characteristic

to be a persistently informative signal in the market.

4. Definition of equilibrium

The system will be stationary if the employer

starts out with conditional probabilistic beliefs

that after one round are not disconfirmed by

the incoming data they generated.the incoming data they generated.

– Beliefs are self-confirming

5. Properties of informational equilibria:

an example

Guess a set of self-confirming conditional probabilistic beliefs:

– If y<y*: Group I with probability=1

– If y≥y*: Group II with probability=1

• Group I sets y=0 if 1>2-y*

• Group II sets y=y* if 1<2-y*/2⇒1<y*<2

• Infinite number of equilibria

• Equilibria not equivalent in welfare– Increases in y* hurt Group II.– Increases in y* hurt Group II.

– Signaling makes Group I worse off and can make Group II worse off too (it depends on q and the relative signalingcosts).

• Education does not increase the marginal product buthelps to allocate the right people to the right jobs.

Other equilibria: assume– If y<y*: Group I with probability q1 and Group II with

probability 1-q1

– If y≥y*: Group II with probability 1

• Group I sets y=0 if 2-q1>2-y*

• Group II sets y=0 if 2-q1>2-y*/2

⇒y*>2q1

• No data for y≥y*, so no disconfirming data

• Education conveys no information in this type

of equilibrium.

• There is also an equilibrium where everyone

sets y=y*.

• Employer beliefs are

– If y<y*: Group I with probability 1

– If y≥y*: Group I with probability q and Group II – If y≥y*: Group I with probability q1 and Group II

with probability 1-q1

⇒y*<1-q1

• Education level conveys no useful information.

• The negative correlation is a necessary but not

sufficient condition for signaling to take place.

• Example: y={1,3}

No value of y* that will make it worthwhile for

Group II to acquire an education.Group II to acquire an education.

• Effective signaling depends upon there being a

“sufficient” number of signals within the

appropiate cost range.

6. Informational impact of indices

• Sex and productivity are uncorrelated.

• The opportunity sets of men and women of

comparable productivity are not necessarily

the same.

• If at some t men and women are not investing

in y in the same way, then the returns to y will

be different in the next round.

Assume the following beliefs:

• Possibility that men and women in differentstable signaling equilibria and stay there.

• Example: – Men signal y=y*=1.1 if in Group I and y=0 if in Group

II.

– All women set y=0 and yw*>2q1. – All women set y=0 and yw*>2q1.

– All women would be paid more than lowerproductivity men.

• From outside: “women receive lower wagesbecause of lack of education, which keepsproductivity down”

Conclusions

A further range of phenomena from selective

admissions procedures through promotions,

loans and consumer credit lends itself to

analysis with the same basic conceptual analysis with the same basic conceptual

apparatus.