Risk Sharing and Incentive Contracts

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Risk Sharing and Incentive Contracts
Chapter 7
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Incentive Contracts as a response to Moral Hazard
The essence of incentive contracts are that they
attempt to Solve moral hazard problems by
balancing the cost of risk bearing against the
incentive gains that result
Insurance polices are essentially incentive
contracts
Deductible payments
Co-payments
Efficient contracts balance the costs of risk
bearing against the gains from incentives
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Principle-Agent Framework and Employment
Incentives
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Using incentives to create responsible behavior
on employees requires they bear some degree of
risk
Sources of risk
Factors external to, and independent, of job
effort and performance that impact measured
output
Performance measurement that include random or
subjective elements
Events beyond the control of the employee that
may affect their ability to perform as contracted
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Balancing Risks and Incentives
Risk Aversion and Risk Sharing
A risk-averse person prefers a safe outcome to a
risky one with the same expected value (r gt 0)
A risk-neutral person is indifferent between a
safe outcome an a risky one with the same
expected value (r 0)
A risk-seeking person prefers a risky outcome to
a safe one with the same expected value (r lt 0)
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An Example
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Certainty Equivalent and Risk Premium
The certainty equivalent is the amount of income
that makes a decision maker indifferent between a
safe and risky outcome
In the previous example the certainty equivalent
is 80,000
The risk premium is the difference between the
expected value of the risky alternative and the
certainly equivalent
In the previous example, the risk premium is
100,000 - 80,000 20,000
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Certainty Equivalent and Risk Premium
Assume that income received, I, is random with
E(I) I and variance Var(I). The certainty
equivalent is defined as
CE I - ½ r(I )Var(I)
where r(I ) is the coefficient of absolute risk
aversion
The certainty equivalent is merely expected
income, I , minus the risk premium, ½ r(I
)Var(I)
Value maximization implies that efficient
arrangements maximize the certainty equivalent of
all parties involved.
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Basing Pay on Measured Performance
In an ideal situation all risk can be spread,
performance can be perfectly measured and
efficient incentive contracts can be developed
However, in reality this is not possible and
tying pay to incentives requires employees to
bear risk and hence can create some inefficiencies
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Principles of Incentive Pay
The basic model
Let C(e) denote the personal cost of effort, e,
that is devoted to serving the interests of the
principle
P(e) denote the profit resulting from the
employees level of effort. This can be thought
of as the principles subjective evaluation of
agent productivity
Note that C(e), P(e) and e may be difficult to
objectively know or observe, but compensation can
vary systematically only with something the
principle can observe
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A Model of Incentive Compensation
Assume that the amount of actual effort (e) put
forth by the agent, cannot be directly observed,
but some other indicator say, z, that is subject
to error can. Then observed effort is measured
as
z e x
where x is a random variable with E(x) 0.
Additionally, there may be a second indicator y,
that is not affected by e, but correlated with x
and is such that E(y) 0.
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Linear Compensation Formulas
w a ß(e x ?y)
a denotes the base salary and ß is known as the
intensity of incentives.
? capture the weight given to y in determining
compensation
Employee CE a ße C(e) ½ ß2 Var(x ?y)
Employers CE P(e) (a ße)
Note the employer is assumed to be risk neutral
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Incentives for Effort and Contract Feasibility
Note the maximizing the employees CE
CE a ße C(e) ½ ß2 Var(x ?y)
yields the marginal condition
ß C(e)
ß C(e) is termed the incentive constraint and
contracts that satisfy this condition are called
incentive compatible
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Efficient Incentive Contracts
An incentive contract is efficient if and only if
the choices of (e, a, ß, ?) maximize the total
certainty equivalent
CE P(e) C(e) -½ ß2 Var(x ?y)
among all incentive compatible contracts (i.e.
those that satisfy the incentive constraint
Implementation problem fix e, and then try
and optimally choose (a, ß, ?)
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Four Key incentive Principles
The Informativeness Principle
The incentive-Intensity Principle
The Monitoring Intensity Principle
The Equal Compensation Principle
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The Informativeness Principle
In designing compensation formulas, total value
is always increased by factoring into the
determinant of pay any performance measure that
(with the appropriate weighting) allows reducing
the error with which the agents choices are
estimated and by excluding performance measures
that increase the error with which effort is
estimated (e.g. because they are solely
reflective of random factors outside the agents
control)
? should be chosen to minimize Var(x ?y). This
implies ? -cov(x,y)/Var(y)
Comparative performance evaluation
Insurance deductibles (comprehensive versus
collision)
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The incentive-Intensity Principle
The optimal intensity of incentives depends on
fours factors
The incremental profits created by additional
effort
The precision by which the desired activities are
assessed
The agents risk tolerance
The agents responsiveness to incentives
The optimal level of incentive intensity is given
by
ß P(e)/1 rVC(e)
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The Monitoring Intensity Principle
Comparing two situations, one with ß set high and
another with ß set lower, we find that V is set
lower and more resources are spent on measurement
when ß is higher when the plan is to make the
agents pay very sensitive to performance it will
pay to measure that performance carefully
Monitoring and incentive intensity are
complementary activities
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The Equal Compensation Principle
If an employees allocation of time or attention
between two different activities cannot be
monitored by the employer then either the
marginal rate of return to the employee from time
or attention spent in each of the two activities
must be equal, or the activity with the lower
marginal return receives no time or attention
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Mathematics of the Equal Compensation Principle
Employees certainty equivalent is given by
CE a ß1(e1 u1) ß2(e2 µ2) C(e1
e2) -½ rVar(ß1 x1 ß2x2)
The marginal conditions for choosing ß1 ß2 are
ß1 C(e1 e2) ß2 C(e1 e2)
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Two Examples of the Equal Compensation Principle
Teachers and Standardized Tests
Incentive Effects of Asset Ownership
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Intertemporal Incentives The Ratchet Effect
A fundamental problem with incentives is setting
standards
Time and motion studies
Comparative performance evaluation
Past performance-can lead to disincentives by
ratcheting up performance standards
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The Big Picture
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Examples of conditions, mechanisms and managerial
transaction costs
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