Session 4: Agency Theory I: Basic theory

Question 1

Principal-agent relationship basics

Answer 1

Three ingredients in a PA problem:
1. Surplus: The basis for the relationship is generated when the principal is willing to pay more for the execution of the task than it will cost the agent, i.e., a surplus is generated (An in-/decrease in the salary will be at the cost/benefit of the other)
2. Conflict of interest: How much effort should the agent supply? How much risk should the agent bear?
3. Asymmetric information: Unforeseen and hard-to-observe circumstances often hinder the observation of the effort of the agent (Agent has superior information compared to the principal)

Question 2

Assumptions about P and A

Answer 2

The principal:
* Is uninformed and risk neutral. His utility (income, profit) depends on A’s effort.
* Has all the bargaining power (there are many A).

The agent
* Is informed and risk averse.
* Has “disutility of effort.”
* Has a “reservation utility” (opportunity cost of working for the principal)
* Can choose between different effort levels (lazy or work hard)
* Effort imperfectly observed by the principal (level of output)

Question 3

Behavioral assumptions (Contracts and observable/verifiable + oppurtunism)

Answer 3

Is everything observable to everyone?
Complete contingent contract: Yes
Complete contract: No
Incomple contract: No

Is the observable information also verifiable?
Complete contingent contract: Yes
Complete contract: Yes
Incomple contract: No

Opportunism: The ingredient conflict of interests will be analyzed with the opportunistic behavioral assumption, i.e., the principal will take into account in the design of the contract the fact that the agent will use his or her superior information to his own benefit

Question 4

Hidden action problem

Answer 4

If both parties have the same information during the contract design stage, but the decisions of the agent are known only to the agent once the contract has been accepted. The principal can only observe the level of output (not effort)
* Moral hazard: Another word for hidden action problem. The informational asymmetry can be used by the agent in determining his or her investment decision, because the cause of a bad result cannot be discovered exactly by the principal.
* Ex-post information asymmetry: The hidden action problem entails an ex-post information asymmetry because there is asymmetric information during the contract design stage, but the agent has superior information once the contract and a level of effort is chosen.

Question 5

Hidden characteristics problem

Answer 5

Definition: When the agent already has more information than the principal during the contract design stage.
* There is then an ex-ante information asymmetry. A certain proposal by the agent to the principal is observable for both parties, but certain characteristics of the agent are not
* Is also labelled as adverse selection problem.

Question 6

Difference between hidden characteristics and hidden action problem

Answer 6

Hidden characteristic problem is in the design of the contract phase. Hidden action is in the execution phase.

Question 7

The profit-maximizing contract

Answer 7

In designing the contract, the principal takes the considerations of the agent into account:
1. Participation constraint: The requirement of voluntary participation. It implies that the principal must design the contract in such a way that the agent earns at least his or her opportunity costs when the contract is accepted
2. Incentive compatibility constraint: The behavior the principal desires the agent will be chosen by the agent because the rules of the contract are such that it yields the highest payment for the agent
3. Equilibrium: The behavior of the principal and the agent in equilibrium is not exactly clear. In equilibrium, the principal chooses the incorporate incentives in the contract in such way that the self-interest of the agent is aligned with the self-interest of the principal and/or to gather additional information

Question 8

HA PROBLEM: Solutions to hidden action problem

Answer 8

• Change the choice possibilities (i.e., job descriptions, tasks, what can be done with corporate resources) – “change the rules of the game”.
• Engage in monitoring – “change the information in the game”.
• Provide incentives – “change the payoffs in the game”.

Question 9

Contract design under complete information

Answer 9

Agent payoff: Denoted as the valuation of the salary minus the level of effort by the agent: payoff_agent= ÷w-e

Principal payoff: Denoted as the value of output given the agent’s effort minus the salary: payoff_principal=P(e)-w

Complete contingent contract: Can be written such that the level of effort can be specified which is required for a certain salary: (see picture in notes)

When the contract is chosen by the principal, and the agent has agreed to the contract, he must choose his level of effort
Nature (artificial player), meaning the effect of external circumstances, is added based on the effort level, where:
If agent chooses e=0, the probability of a bad result is 2/3; and if the agent chooses e=1, the probability of a good result is 2/3.
Principal pays agent according to the contract (NB: The level of effort is observable for the principal)

Constraints:
Incentive compatibility constraint: The payoff of the agent in the e=1 block must be higher than the payoff in the e=0 block in order for the agent to put forward a higher level of effort (√b-1≥√a-0)
Participation constraint: The principal must also consider the fact that the agent has opportunities elsewhere (√b-1≥1)
 High effort result: Is achieved when the two constraints are met

Risk allocation: Pareto optimal when the principal bears all the risk, because the risk-neural carries the risk and is better able to do so than the risk averse agent

Question 10

Contract design under incomplete information

Answer 10

Assumptions:
Only the agent knows the choice of e.
The principal observes only the final result (P=10 and P=30)
The principal cannot distinguish what part of payoff is determined by the agent’s effort level and what part is determined by nature.

Complete contract: Complete contingent contract is not possible anymore since the principal cannot observe effort. Now, the two numbers [y,z] in the complete contract are geared towards the two levels of output (not effort) (See picture in notes)

Implication: The agent can risk receiving a low salary despite that fact that he has provided a high effort (The agent payoffs differ under incomplete information)

Loss of efficiency: The agent continues to earn their reservation wage, but the principal experiences a decrease in income due to the higher average wage required to attract the agent as an employee.

Risk allocation: The agent receives part of the surplus (informational rent) which is due to superior information that is at the disposal of the agent. This is necessary because the risk-averse agent has to be compensated for bearing risk

Question 11

THE LINEAR AGENCY MODEL: Information asymmetry

Answer 11

Output: The result/output (z) is the sum of the effort and a stochastic variable representing uncertainty
z=e+x

X is “noise” in the output level since it makes it impossible to observe what part of the output comes from the agent’s effort

Question 12

THE LINEAR AGENCY MODEL: Salary

Answer 12

Agent’s salary: Based on a fixed salary base, α, and a variable part, β, based on the amount of production:
w=α+β(z)

Agent’s utility: The salary minus the personal cost of providing effort
U=U(W)-C(e)

Question 13

THE LINEAR AGENCY MODEL: Risk premium

Answer 13

Agent risk averse: he will request a risk premium, which depends on
* The degree of risk-aversion of the agent r
o 0: Risk neutral. <0: Risk loving. >1: Risk averse
* The degree of uncertainty of the wage, Var (W)

Question 14

THE LINEAR AGENCY MODEL: Certainty equivalents

Answer 14

To transform the agent’s utility to payoffs, use “certainty equivalents”

The certainty equivalent of any “gamble” is the sure outcome (payoff) that result in the same expected utility as the “gamble”

The agent’s certainty equivalent: See picture in notes

The principal’s certainty equivalent: See picture in notes

Question 15

LINEAR AGENCY MODEL: Maximization

Answer 15

See picture in notes

Question 16

LINEAR AGENCY MODEL: Implications

Answer 16

The risk premium is a ”cost”; reduce it and created value goes up.
β has to solve two tasks: providing incentives to work hard and insurance against uncertainty (but usually impossible under information asymmetry to handle both tasks optimally (“second best solution”))

Question 17

LINEAR AGENCY MODEL: Intensity of incentives (Size of β)

Answer 17

Multitasking problem: When an agent performs multiple activities, this creates contractual externalities. If strong incentives are given it might result in the agent only performing high piece-rate activities

Inaccurate performance measurement: When the performance measure deviates from firm value. Requires an adjustment of the incentive intensity principle –> The optimal incentive intensity has to be multiplied by the correlation between the marginal effect of an agent’s effort on what matters for the principal

For:
- Fine when effort has high incentive elasticity
- “Self-selection”: Laggards, shirkers stay away!
- Can foster upgrading of skills and knowledge

Against:
- What is “z”?
- Heterogeneity in the measure
- Multi-tasking problem: e.g., reduction of helpfulness
- How to decide the “normal” effort level (for which β* = 0)

Tradeoff:
1. Stronger incentives → Agent works harder but he faces more risk which he does not like (wants a risk-premium) (P is happier, A is less happy)
2. Weaker incentives → he works less hard but faces less risk (smaller risk-premium) (P is less happy, A is happier)

Question 18

LINEAR AGENCY MODEL: Intensity of monitoring

Answer 18

Monitoring reduces the variance Var(x) on the estimate of the agent’s effort –> The agent knows that his risk has declined –> He will demand a smaller risk premium –> More value is created in the relation.

Given costly monitoring, increase monitoring until MB_monitoring= MC_monitoring

Monitoring intensity principle: When the plan is to make the agent’s pay very sensitive to performance (high β), it will pay to measure that performance carefully (low V)

Question 19

LINEAR AGENCY MODEL: Monitoring and incentives

Answer 19

Optimal incentive system: Can be found at the intersection of the two principle lines: See picture in notes

Question 20

LINEAR AGENCY MODEL: Types of incentive pay

Answer 20

• Gainsharing / group incentives: Pay tied to gains in measures of group “success” (productivity, costs, quality, etc.)
• Profit-sharing: Pay tied to profits of firm
• Efficiency wages: Paying employees a “premium.”
• Piece rates: Pay tied to amount of output produced. E.g., sales commissions