chapter 3 the moral hazard problem stefan p. schleicher university of graz economics of information...
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Chapter 3
The Moral Hazard Problem
Stefan P. SchleicherUniversity of Graz
Economics of InformationIncentives and Contracts
1. Introduction (1)
Asymmetric information creates incentive to use information advantage
Moral hazard problemAgent has information advantage since his effort is not observable
1. Introduction (2)
P designsthe contract
A accepts(or rejects)
A suppliesnon-verifiable effort
N determinesstate of the world
Outcomeand
pay-offs
Agent’s action is not verifiable oragent receives private information after the relationship has been initiated Informational asymmetry after the contract has been signed Examples
Labor market, research projectAutomobile insurance
1. Introduction (3)
))((1 MINMIN evUuw
Under a fixed wage contract the agent will always choose the smallest possible effort.
Therefore the principal will choose a wage which exactly compensates the agent for this effort.
2. The Moral Hazard Problem (1)
Asymmetric information with respect to effort
Effort is not verifiable
Solution concept
Subgame perfect equilibrium
2. The Moral Hazard Problem (2)
Stage 3: Agent chooses his effort
Incentive restriction or
Incentive compatibility constraint
n
i iie evxwuepMaxe1ˆ )ˆ())(()ˆ(arg
2. The Moral Hazard Problem (3)
Stage 2:Agent decides about acceptance of thecontract proposed by the principal
Participation constraint or
Individual rationality condition
n
i ii Uevxwuep1
)())(()(
2. The Moral Hazard Problem (4)
Stage 1:Principal designs the contract,anticipating the agent’s behaviour
n
i iiixwe xwxBepMaxnii 1])}({,[ ))(()(
,...,2,1
n
i iie evxwuepMaxe1ˆ )ˆ())(()ˆ(arg
[P3.1]
n
i ii Uevxwuepts1
)())(()(..
3. Agent chooses between two effort levels (1)
Risk-averse agent can choose between only two effort levels,
H high
L low
LH eee ,
)()( LH evev
Efforts and disutilities
3. Agent chooses between two effort levels (2)
nxxx ...21
Ordered set of results
Probability of outcome i under high or low effort
)( Li
Li epp )( H
iHi epp
pH first order stochastically dominates pL
(bad results are more likely under lower effort)
1...,,111
nkpp
k
i
Li
k
i
Hi
n
i
Li
n
i
Hi pp
111
3. Agent chooses between two effort levels (3)
(1) Principal demands low effort eL
Wage that guarantees reservation utility sufficient
)()()()( HLLL evwuevwu
)((1 LL evUuw
No true moral hazard problem exists.
Symmetric information contract continues to be optimal.
3. Agent chooses between two effort levels (4)
(2) Principal demands high effort eH
Wage needs to depend on outcome
Expected utility gain for agent must be greaterthan the implied increase in disutility.
n
i
Li
Ln
i
Hi
H evxwupevxwupii 11
)())(()())((
n
i
HLi
LH evevxwuppii1
)()())(()(
3. Agent chooses between two effort levels (5)
Principal solves
n
i
HLi
LH evevxwuppii1
)()())(()(
n
i iiH
xw xwxepMaxinii 1)}({ ))()((
,...,2,1
n
i
Hi
H Uevxwuptsi1
)())((..
3. Agent chooses between two effort levels (6)
Lagrangean
n
i
HLi
LH
n
i
Hi
H
n
i iiH
i
evevxwupp
Uevxwup
xwxpxwL
ii
i
i
1
1
1
)()())(()(
)())((
))((),,)((
3. Agent chooses between two effort levels (7)
First-order conditions
nixwupp
xwupp
iLi
Hi
iHi
Hi
...,,1,))((')(
))(('
0,0))(('1
n
ii
Hi
xwu
p
Hi
Li
i p
p
xwu1
))(('
1
3. Agent chooses between two effort levels (8)
Shadow price of participation restriction
0
Hi
Li
i p
p
xwu1
))(('
1
0))(('1
n
ii
Hi
xwu
p
Shadow price of incentive restriction
Wage will be larger the smaller the likelihood ratioand this will induce larger effort
3. Agent chooses between two effort levels (9)
Hi
Li
i p
p
xwu1
))(('
1
Wage will be larger the smaller the likelihood ratioand this will induce larger effort
Hi
Li
i
p
puxw
1
1)'()( 1
4. Solution using the first-order approach (1)
replaced by first-order condition
n
i iie evxwuepMaxe1ˆ )ˆ())(()ˆ(arg
n
i ii evxwuep1
0)('))(()('
Attempt to handle effort as a continuous variable
4. Solution using the first-order approach (2)
Modified optimization problem of the principal
n
i iiixwe xwxepMaxnii 1])}({,[ ))(()(
,...,2,1
[P3.2]
n
i ii Uevxwuepts1
)())(()(..
n
i ii evxwuep1
0)('))(()('
4. Solution using the first-order approach (3)
First-order conditions w.r.t. w(xi)
nixwuep
xwuepep
ii
iii
...,,10))((')('
))((')()(
i
i
i p
p
xwu
'
))(('
1
4. Solution using the first-order approach (4)
Wages increiase with increasing likelihood quotient(with high probability a good effort was exerted)
i
i
i p
p
xwu
'
))(('
1
5. A simple case with continuous effort
Probability function of the agent’s effort
Li
Hii pepeep )1()(
Condition of linearity of the distribution function
Can be solved by the first-order approach
6. Moral Hazard with hidden information
After contract is agreed upon the agent obtains informationon the environment that will determine which effort level isthe most adequate.
This information is not observable or not verifiable by the principal.
P designsthe contract
A accepts(or rejects)
N determines state of the world
which is onlyobserved by A
A supplieseffort
Outcomeand
pay-offs
7. Some comments on simpleMoral Hazard models (1)
7.1 The value of information
Loss of informtion about the agent’s effort impliesa cost to the principal-agent relationship.
Principal is interested in any signals that revealinformation on the agent’s effort.
Therefore, the contract can contain many contingencies, e.g. state of nature.
The sufficient statistic result.
7. Some comments on simpleMoral Hazard models (2)
The sufficient statistic result.
A contract should exploit all available informationin order to filter out risk optimally.
Principal may want to pay for control activities.
7. Some comments on simpleMoral Hazard models (3)
7.2 Mechanisms based on severe punishments
For results that are a perfect signal that the demanded effort was not excerted.
The threat should be sufficient.
Should lower the costs of controls.
7. Some comments on simpleMoral Hazard models (4)
7.3 The stratigic effects of contracts
Relevant, if contract effects third parties.
Then the contract is not only an incentive devicebut also an instrument to influence the behaviorof third parties.
7. Some comments on simpleMoral Hazard models (5)
7.4 What happens when it is the agent who offersthe contract
If the agent designs the contract, he must take intoaccount the fact that the pricipal will only accept believable contracts.
The only difference – the pricipal instead of the agent – is put at her reservation utility level.
B.1 Incentives for managers (1)
Objective of the shareholdes is to maximize profits,and this depends on the effort of the managers.
Shareholders hire managers.
The shareholders cannot control the effort ofthe managers.
B.1 Incentives for managers (2)
Manager’s utility
)()(),( evwuewU 0)('',0)(' wuwu 0)('',0)(' evev
Shareholder’s profits
wxcxpwxB ),(
Density distribution of sales
),( exf
B.1 Incentives for managers (3)
(1) Symmetric information
X
Xxw
Uevdxexfxwuts
dxexfwxcxpMax
)(),())((..
),()()(
Shareholder problem
B.1 Incentives for managers (4)
0),())(('),( exfxwuexf First-order conditionj w.r.t. w(x)
w(x) is constant
)((1 evUuw
Xe evUudxexfxcxpMax ))((),()( 1
B.1 Incentives for managers (5)
Xe evUudxexfxcxpMax ))((),()( 1
Rewritten shareholder problem
First-order conditionj w.r.t. e
X e evUuu
evdxexfxcxp
))(('
)('),(')(
1
B.1 Incentives for managers (6)
(2) Asymmetric information
X e
X
Xxw
evdxexfxwu
Uevdxexfxwuts
dxexfwxcxpMax
0)('),('))((
)(),())((..
),()()(
Shareholder problem