SUBJECTIVE PERFORMANCE MEASURES IN OPTIMAL INCENTIVE CONTRACTS

1
SUBJECTIVE PERFORMANCE MEASURES IN OPTIMAL
INCENTIVE CONTRACTS

• Contract Theory and Operation Management
• Luca Tiozzo Pezzoli
• University Ca Foscari (Venice)

2
The Problem

• How can we measure the performance of employees
  actions?
• It should reflect the employees contribution to
  firm value!
• Hence, it should include static externalities
  across business and dynamic effects on long-run
  firm value
• Objective (Measurable) vs. Subjective (Not
  Measurable) measures of Performance
• Only Objective measures of performance induce
  distorted incentives!

3

• We can distinguish two types of contracts

Subjective Measure of Performance
Objective Measure of Performance
IMPLICIT CONTRACT
EXPLICIT CONTRACT
Enforced by the firm it is concerned about its
reputation in the labor market
Enforced by a court
Two kind of Models
Substitute Nature of Contracts Objective measure
close to be perfect, no place for
Implicit
contract
Complement Nature of Contracts Combination of
the two kind of contracts
can generate a positive profit.
More accurate objective measure,
there is still place for Implicit
contract
4
Benchmark Models the Economic Environment
Framework Repeated Game between Firm and Worker
Worker chooses an action (a), that action
contribute to the firm value (y)
Firms value can be either y 1 or y 0 given
that Prob(y 1a) a a (0,1)
1) The contribution is complex y is not
objectively measurable!
Workers action affect a measure of performance p
2) The measure of performance p is objectively
measurable
Worker receive a signal before the action is
done such that Prob(p 1) a
Implicit comp.
s b
Compensation Contract
Salary
Explicit comp.
5
Benchmark Models The Dynamics
The Contract is offered
Firm
Individual Rationality
Accept
Reject
Worker
He observes and choose a
Firm and Worker observe y and p
If p 1 Firm pays (Explicit contract) If y
1 firm decides to pay or not b (Implicit
contract)
Firm Payoff
y - I
Worker Payoff I - c(a)
Total comp.
Total cost
Firm expected profit
6
Benchmark Models Explicit Contract
a is the best choice
if
High
if
a depends on
Convex cost function
increases
decreases
7
Benchmark Models Implicit Contract
Supposition worker trusts the firm
Firm Expected Profit, given the optimal worker
choice and individual rationality constraint
meet, is
Repeated Game adopting Trigger Strategies (firm
can renege the contract)

t 0
t 1
t 2
not pays the bonus
1 - s
0
0

if y 1 firm can decide
pays the bonus
1 - s - b
1 - s - b
1 - s - b

Bonus is paid if
where r is discount factor
8
r 0.10
r 0.07
r 0.05
b 0.89
9
Optimal Interplay between Implicit and Explicit
Contracts
Assumption - at the end of each period both firm
and worker observes y and p
- both implicit and explicit contracts are
available
Hence, the expected profit from honoring the
contract is given by so that in
absence of implicit contracts the expected payoff
is given by
Implicit Part
Explicit Part
Only Implicit Part
10
Case
The firm enters in the contract and pays b
From calculations we obtain
If
not need for explicit
and
and finally
1) The value of the discount rate is sufficiently
high
2) The level of distortion in the objective
performance measure is sufficiently low
1) The value of the discount rate is sufficiently
low
N.B. The highest discount rate at which the first
best can be achieved declines when
falls
11
Case
if incentive distortion caused by objective
performance measure are sufficiently high. If
firm renege implicit it shut down the overall
contract!
Ambiguous behavior for var! (see the figure in
the next slide)
we introduce imperfect objective perf. measure
such that
Suppose
and
for small value of
Thus, adding the explicit contract (objective
performance measure)
improves the ongoing relationship!
12

• - In absence of distortion for the objective
  measure of perf. the optimal explicit contract
• achieve its best!
• As the distortion increases the value of optimal
  explicit contract decreases ( )
• For sufficiently high level of distortion the
  explicit contract become unprofitable
• Distortions do not affect the optimal implicit
  contract

13
No implicit contract feasible, only explicit
contract is optimal
For this level of distortion the implicit
contract become feasible
Distortion increases,
increases,
decreases
For this level of distortion the explicit
contract gives 0 profits
exceeds
the presence of explicit contract enhances the
value of ongoing relationship
14
r is sufficiently high so that no implicit
contract is feasible on its own
Previously commented
As before, the presence of explicit contract
enhances the value of ongoing relationship, so
explicit and implicit contracts are feasible if
(and only if) used in combination!
The distortion is too high so no explicit
contract is feasible
15
Subjective Weight on Objective Perf. Measures

• The firm can assess the incentive distortion
  caused by the imperfect objective performance
  measure
• We assume that the firm and worker observe
  at the same time, namely for the firm after p is
  realized.

is noncontractible
can not be contingent on
The worker receive s
vary with
Worker believes the firm will honor the contract
Firm
if it honors the contract It receives
if it does not honor the contract It receives

It depends if
Worker
0
16
for
find minimum
for
Minimum level of for which the firm accept
the contract
Worker is at the first best, Firm does not renege
Worker is not at his first best, Firm is still
giving as maximum incentives
17
Second-best contract uses more explicit
incentives than the first-best contract
Implicit Incentives in 2nd-best contract
Explicit incentives in 2nd-best contract
Firm suffers for inadequate incentives but will
not renege on the implicit contract
The firm will suffer excessive incentives
18
Conclusions

• Firm has to evaluate the performance of a worker.
  It can assess in two ways subjectively of
  objectively.
• Objectively the firm observe the measure of
  performance and on this basis it evaluates the
  workers performance (Explicit Contract)
• Subjectively the firm does not observe the
  measure of performance but only the realization
  on its value. It can, in that case, renege the
  contract.
• A possible combination of both contract can
  improve the ongoing relationship
• By the use of Subjective weight on Objective
  performance measure, the firm can assess
  incentive distortion caused by
• imperfect objective measures of performance