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Chapter 5
Signalling
Stefan P. SchleicherUniversity of Graz
Economics of InformationIncentives and Contracts
1. Introduction
How relevant is a university degree and the content of the degree?
Formal education acts as a signal.
This chapter analyzes situations in which one of the perties of a contract it interested in signalling some characteristic before the contract is signed.
2. The Value of Private Informationand of Signalling (1)
Private information distorts contracts since the agent attempts to take advantage of it.
Moral HazardAgent chooses an effort that maximizes his own expected utility, not the surplus of the relationship.Principal therefore offers a contract that gives the agent only the expected value of his reservation utility.
Adverse SelectionPricipal offers contracts that ikmprove the average utility of those agents who are most likely to take advantage of the relationship.
2. The Value of Private Informationand of Signalling (2)
Because of the design of the contracts offered by the principal, some agents may be worse off under asymmetric information.
Phenomen of signallingAgents may therefore have an interest to reveal their private information to the principal.
The story of Bruce the Bold.
In the same way firms search for workers with an ability to learn.
2. The Value of Private Informationand of Signalling (3)
SignalSome activity or some decision tht proves that the agent concerned has a certain ability or characteristic or possesses certain information, or – in other words – that the agent concerned belongs to a certain subset of the entire population.
3. Education as a Signal (1)
Spence (1973)Education is used as a means of signalling good worker characteristics among candidates for some job.
Agent2 types – differ w.r.t. productivity
productivity profitsType 1 (G for good) 2 2 - wType 2 (B for bad) 1 1 - w
Firms can’t distinguish the agent’s type
3. Education as a Signal (2)
Educationy time dedicated to education
costs of educationType 1 (G for good) y/2Type 2 (B for bad) y
ASS.: Education has no effect on productivity
3. Education as a Signal (3)
Firms’ beliefs as to the worker’s productivity, given an educational level
Level of education wageType 1 (G for good) y y* w = 2Type 2 (B for bad) y < y* w = 1
3. Education as a Signal (4)
Firms’ beliefs will be self-confirming
Level of educationType 1 (G for good) y = y* 2 – y*/2 1 - 0Type 2 (B for bad) y = 0 1 – 0 2 – y*
therefore 1 y* 2
5. The Informational Power ofContracts
Signalling effect of contracts.
Principal has private information about two types of jobs
)()(),(
)(),(1
1
evwuewU
weewB
Type 1
Type 2
)()(),(
)(),(
evkwuewU
wekewBk
k
5.1 Symmetric Information (1)
Optimal symmetric information contract for type 1 job
Uevwuts
weMax we
)()(..
)(],[
)('
)(')('
)()(
*1
*1*1
*1*1
wu
eve
Uevwu
Participation constraint
Efficiency constraint
),( *1*1*1 ewC
5.1 Symmetric Information (2)
Optimal symmetric information contract for type k job
Uevkwuts
wekMax we
)()(..
)(],[
)('
)(')('
)()(
*
**
**
k
kk
kk
wu
eve
Uevkwu
Participation constraint
Efficiency constraint
),( *** kkk ewC
5.1 Symmetric Information (3)
5.2 Agent is uninformed as to the difficultyof the job (1)
Both types of principals prefer C1*
If an agent reveives this offer, he does not know the typeof agent and therefore will not accept it.
5.2 Agent is uninformed as to the difficultyof the job (2)
Contracts can transmit information which changes theagents beliefs about the probability q that the principal isof type 1.
5.3 Seperating equilibria (1)
A seperating equilibrium is one in which the contract offered perfectly identifies the principals type.
0)(
1)(
),(1
*1*1*1
kCq
Cq
ewC
0)(
1)(
),(
1
***
Cq
Cq
ewCk
kkk
Agent receives contracts and and adjusts his beliefsabout the type of principal
5.3 Seperating equilibria (2)
Contract of principal k:
Result 5.6:In a perfect Bayesian separating equilibrium it must alwaysbe true that
),(),( *** kkkkkk eweworCC
5.3 Seperating equilibria (3)
Restriction for contract of principal 1:
),( 111 ewC
**11
*1*1**
11
)()(
)()(
)()(
kk
kk
wewe
wekwek
Uevwu
Participation constraint
Efficiency constraints
5.3 Seperating equilibria (4)
5.3 Seperating equilibria (5)
Further restriction for contract of principal 1:
Uevkwuts
wekMaxB we
)()(..
)(' ],[
Profits of a pessimistic type-1 principal
5.3 Seperating equilibria (6)
6. Comments
Companiessignals for profitability
New consumer goodsguarantee periodmoney-back guarantee
Governmentscredible announcements
The crucial role of believability
