5 - Imperfect Performance Measurement

Question 1

What are the elements of a model in multitasking and imperfect performance measurement?

Answer 1

• eᵢ ≥ 0: A’s non‐observable effort in task i (i= 1, 2)
• c(e₁, e₂) = 1/2 e₁²+ 1/2 e₂²: A’s effort costs
• A is risk neutral and his reservation utility is zero
• y ∈ {0, 1}: tasks’ contribution to firm value
• p ∈ { 0, 1 }: verifiable performance measure

Question 2

What is y and what is problematic about it in the imperfect performance measurement model?

Answer 2

• y = tasks’ contribution to firm value
• y is non‐verifiable and thus cannot be part of an incentive contract

Question 3

How is y defined in a model of imperfect performance management?

Answer 3

y ∈ {0, 1}: tasks’ contribution to firm value

• Pr [y= 1 | e₁, e₂] =f₁e₁ + f₂e₂
• fᵢ ≥ 0 is task i′s expected marginal productivity

fᵢ (i = 1, 2) is such that all probabilities remain below 1 at the first‐best and second‐best solution

Question 4

How is p defined in a model of imperfect performance management?

Answer 4

p ∈ { 0, 1 }: verifiable performance measure

• Pr [p = 1 | e₁, e₂] =g₁e₁ + g₂e₂
• gᵢ ≥ 0 is task i′s expected marginal impact on the performance measure
• in general fᵢ ≠ gᵢ

gᵢ (i = 1, 2) is such that all probabilities remain below 1 at the first‐best and second‐best solution

Question 5

What is the timing of an imperfect performance measurement problem?

Answer 5

1. P offers bonus contract (a,b)
2. A can accept (-> stage 3) or reject (reservation utility 0)
3. A chooses effort e₁, e₂ in both tasks
4. Performance measure p is realized (y could be realized later)
5. A is paid

Question 6

What are remedies for problems of imperfect performance measurement?

Answer 6

a) Additional performance measures
b) Job design

Question 7

What are advantages and disadvantages of additional performance measurements?

Answer 7

• Additional performance measures can mitigate or even resolve multitasking problems.
• However, collecting performance measures is costly.

Question 8

Give examples of jobs & imperfect performance measures?

Answer 8

• Production worker: quantity + quality
• Performance measures: quantity + some form of quality control
• Sales agent: selling the product + customer service
• Performance measures: sales + customer satisfaction
• Professor: research + teaching
• Performance measures: Publication record + student evaluations

Question 9

How can job design help to solve imperfect performance measurement problems?

Answer 9

• Assume P can hire two identical agents k = I, II and separate tasks
• Agent I (II) performs task 1 (2); only one performance measure p

Assigning the tasks to different agents allows the principal to individually adapt incentives for each task, which solves the multitasking problem.

Question 10

What are potential pitfalls to separating tasks in response to imperfect performance measurement problems?

Answer 10

• Not all tasks can be separated (e.g., quantity and quality in production)
• Hiring additional agents is costly (e.g., positive reservation utilities, minimum wages)
• If tasks are complements, separating tasks increases effort costs (e.g., professor: research and teaching)
• Fairness concerns in case agents have social preferences (e.g., inequality aversion)
• Coordination problems

Question 11

Why do firms use relational contracts?

Answer 11

Main advantage: relational contracts can incorporate non‐verifiable performance measures that better reflect the worker’s contribution to the firm (e.g., y in our model)

Question 12

What are relational contracs?

Answer 12

• agreement that cannot be enforced by a court because it is based on non‐verifiable variables
• promises and understandings that cannot be formalized by legal documents, e.g., promotion or salary increase for a “job well done”
• only works when the parties find it in their own interests to adhere to the contract
• E.g., reputational concerns in a repeated relationship can make a relational contract self‐enforcing.

Question 13

What is the main change in modeling a relational contract in an imperfect performance measurement setting?

Answer 13

• that principal and agent can observe y, but no third party can (y is still nonverifiable)
• With probability y ∈ (0, 1) , P and A work together in the following period -> potentially repeated employment relationship

Question 14

Why are relational contracts self-enforcing with repeated employment?

Answer 14

• If the firm reneges on its current promises, it may find that its employees expect it to renege on future promises as well.
• Employees are unwilling to exert extra effort in the future.
• If the firm reneges on its promises it profits in the short term, but its damaged reputation will cost it in the long term.
• The relational contract is self‐enforcing if the (expected/discounted) long‐term losses exceed the short term profits.

Question 15

What are examples for relational contracts based on subjective performance evaluation?

Answer 15

• 360‐degree peer reviews: an employee’s supervisor, coworkers, and subordinates provide information on that employee’s performance
• Management by objective systems: employee and supervisor construct a set of (non‐verifiable) goals for the employee
  
  • at the end of some specified period, the two meet to review the employee’s performance on those goals
  • Supervisor can take into account (non‐verifiable) factors that may have made it easy or difficult to reach the goals
• Merit rating systems: employees are given numerical scores
  
  • Based on their subjective evaluations, supervisors are required to allocate a fixed pool of points among employees

Question 16

What are potential costs of subjective performance evaluation?

Answer 16

• random influences -> costly risk premium
• influence activities: subordinates may attempt to affect their evaluations in unproductive ways (e.g., by spending too much time establishing good personal relationships with their supervisors)
• supervisors may find it personally unpleasant to evaluate their subordinates (e.g., criticizing employees, reward some but not others), which can entail untruthful evaluations (-> centrality bias, leniency bias)

Question 17

Give an example of how poorly designed incentive systems can induce dysfunctional behavior?

Answer 17

• Some schools in the U.S. reward teachers with cash bonuses if their school’s test scores rise: Teachers Gaming Student Test Scores. However, such systems have spawned cheating among teachers to boost their ratings. Schools were rated on how well their students did: The essays were graded by the students’ own teachers. If a school’s rating dropped, sanctions were imposed. Schools performing well received rewards. Auditors found that grades assigned to the writing portion of the exam were too generous. eachers were found typing students’ essays. Students received advance copies of the test and tip sheets. Teachers explained questions to students during the exam. Teachers permitted students to use maps, reference sheets, and calculators during exams.
• At Dun & Bradstreet, salespeople earned no commission unless the customer bought a larger subscription to the firm’s credit‐report services than in the previous year. In 1989, the company faced millions of dollars in lawsuits following charges that its salespeople deceived customers into buying larger subscriptions by fraudulently overstating their historical usage.
• In 1992 Sears Auto Center abolished the commission plan in its autorepair shops, which paid mechanics based on the profits from repairs authorized by customers. Mechanics misled customers into authorizing unnecessary repairs, leading California officials to prepare to close Sears‘ auto‐repair business statewide.

Question 18

What is the condition for the firm to be able to impose the first best effort in imperfect performance management?

Answer 18

It needs to have a perfect performance measure which is

b = f₁/f₂ = g₁/g₂

with f₁/f₂ = g₁/g₂

Question 19

What does this imply about a performance measure:

f₁/f₂ = g₁/g₂

?

Answer 19

The performance measure reflects the true relative importance of the tasks! In this case, the performance measure is called perfect.

Question 20

What does 𝛿 represent in this cost function?

Answer 20

𝛿 represents whether two tasks are complements. if 𝛿<0, tasks are complements.

Question 21

With relational contracting, what happesn as γ gets smaller?

Answer 21

The lower γ, the less likely it is that the employment relationship continues - so the principal is more tempted to break his promises, as future losses are smaller (the principal will committ to a smaller bonus).

Question 22

What is the commitment constraint in relational contracting?

Answer 22

The self‐enforcing or commitment constraint ensures that P complies with the relational contract. It is the condition that

the short term gain ≤ the long term loss

from breaking the promise.

Question 23

How does discounting affect the relational contract?

Answer 23

The relational contract becomes less effective when discounting is less. As the discount factor increases, the importance of the future profit for the firm increases.

Question 24

In 1992 Sears Auto Centers overcharged customers for unneeded or unperformed repairs. Sears had compensated salespeople with commissions based on total sales. They went to a straight salary.

Sears now indicated that it is planning to reinstate commissions for salespeople. Sears says that it has taken steps to prevent a recurrence of past problems: The decision right to recommend repairs is granted to mechanics who are paid a straight salary. Sales consultants are paid commissions for selling repair services but are not authorized to recommend repairs.

Why do you think Sears wants to reinstall commissions for its salespeople?

Answer 24

They want to give salespeople incentives to exert more effort in making sales -> so they want to reinstate the commission to increase sales

Question 25

In 1992 Sears Auto Centers overcharged customers for unneeded or unperformed repairs. Sears had compensated salespeople with commissions based on total sales. They went to a straight salary.

Sears now indicated that it is planning to reinstate commissions for salespeople. Sears says that it has taken steps to prevent a recurrence of past problems: The decision right to recommend repairs is granted to mechanics who are paid a straight salary. Sales consultants are paid commissions for selling repair services but are not authorized to recommend repairs.

Do you think that the new safeguard that separates diagnosing problems from selling services will prevent a recurrence of past problems?

Answer 25

No:

• Sales people could pressure mechanics to recommend more repairs, which the mechanics could do because of (1) social ties to sales people or (2) fear of negative reciprocity - that the sales people might become their managers and retaliate
• Sales people could even bribe mechanics to diagnose more
• If customers only talk to Sales people, the sales people might overstate the recommendations from the mechanics

Question 26

The wage w offered to the student is a linear incentive contract which defines a fixed salary and an incentive parameter , i.e., w = s+BX, where X is a performance measure that is specified below.

How can you recognize a selling-the-firm contract in this example?

Answer 26

If B = 1, the incentives of the principal (given X is the observable utility of the principal) and the agent perfectly align

Question 27

For a commitment constraint (1-γ)/γ B ≤ π(B), how can you graphically illustrate the constraint?

Answer 27

with:

1. γ is large -> P can committ to optimal B
2. γ is medium -> P can only committ to suboptimal B
3. γ is small -> P cannot committ to any B

Question 28

What features should a “good” performance measure have? Explain.

Answer 28

1. Incentivize only those actions which the principal wants to be chosen
2. Incentivize all those preferable actions
3. State carefully which objectives should be maximized (e.g. long vs short term)
4. Not much randomness (e.g. if agent is risk averse)