faculdade de ciências económicas e empresariais universidade católica portuguesa...

04/11/23 Ricardo F [email protected]

Faculdade de Ciências Económicas e Empresariais

Universidade Católica Portuguesa

2nd session:Principal – Agent Problem

Performance Evaluation

IMSc in Business Administration

October-November 2007

Ricardo F [email protected]

Session 02 - 2/3604/11/23Performance Evaluation



Principal Agent Model

This lecture is mostly based on:

Richard A. Lambert , Contracting Theory and Accounting,

Journal of Accounting & Economics, Vol. 32, No. 1-3, December 2001

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=284162





Agency theory and Accounting

1. How do features of information, accounting and compensation systems affect incentive problems?

2. How does the existence of incentive problems affect the design and structure of information, accounting, and compensation systems?



Setup of the basic agency model

s(x,y) denotes the compensation function and it is based on some outcome x and some vector of performance measures y

a denotes the vector of actions x(a) defines the outcome as a production function of the

vector of actions a chosen by the agent y=y(a) the vector of performance measures y is also a

function of the vector of actions a chosen by the agent

Contract s(x,y) agreed upon

Agent selects actions (a)

Performance measures (x, y) observed

Agent is paid s(x,y) Principal keeps x-s(x,y)





Extensions of the basic model

The outcome x may be unobservable, which makes information signals on x critical

Or it may be the case that the information signals are themselves produced by the agent: moral hazard problems on the agent

reporting truthfully





Extensions of the basic model The information signal might also be

generated by a third party (an auditor, for instance), the incentives of such an independent third

party to be modelled too Finally the performance measures may

be the stock price trust the market to aggregate all the

relevant information What information is available on the

market?





Extensions of the basic model Allowing agent and/or the principal to

obtain information prior to the agent selecting his actions Information on the productivity of different

actions, on the general setting, information on the agent’s type





Extensions of the basic model Include multiple periods

Repetition of the same action or interdependent actions

Include multiple agents Team work or competitive work Relative Performance Evaluation!





Single-period, single-action

Principal’s problem is a constrained maximization problem in which he chooses the compensation function to

maximize the principal’s expected utility

subject to agent’s acceptable utility constraint

agent’s incentive compatibility constraints.





Principal’s utility

Utility derived from the net proceeds generated

Let G[x-s] denote the utility function G’>0, meaning the principal prefers more

to less G’’≤0, meaning that the principal is risk

averse or risk neutral. If the principal is risk neutral, then:

G[x-s]=x-s





Principal’s utility

The impact of the compensation on the utility of the principal is twofold:

1. Each dollar paid to the agent is one dollar less to the principal

2. But the compensation mechanism affects the action selection of the agent and consequently the outcome





Production technology

Outcome and performance measures are affected randomly by the actions, among other exogenous variables.

f(x,y|a) is the pdf of outcome x and the performance measures y given the selection of actions a.





Compensation function Individual Rationality Constraint

The principal must ensure that this function is attractive enough to offer an acceptable level of expected utility. The agent must want to take part!

Minimal level to be guaranteed must beat the next best employment opportunity.





Compensation function Incentive Compatibility Constraints

These represent the link between the contract and the actions choice.

These constraints will condition the compensation function such that the agent will choose the actions in accordance to the principal’s objectives.





Agent’s utility

The agent’s utility is defined over two sets of variables: The increasing utility he derives from the monetary

compensation he receives, denoted by s. The disutility he suffers from the added effort of

undertaking actions a.

Most models assume the agent’s utility is additively separable: H(s,a) = U(s) – V(a). Some models ignore the disutility of effort, V(a)=0.





First-best solution

Benchmark case, where the actions are chosen cooperatively with all parties’ interests in mind and everyone tells the truth…

The principal chooses the action set that maximizes his utility.

The agent simply guarantees that he will participate.





Model for first best solution

maximize ∫∫G[x-s(x,y)] f(x,y|a) dx dy

subject to ∫∫U[s(x,y)] f(x,y|a) dx dy – V(a) ≥ H

s(x,y),a





Optimal contract

Differentiate the objective function with respect to s for each possible (x,y) realization to deliver the following first-order condition:

OPTIMAL RISK SHARING CONDITION

G’[x-s(x,y)] U’[s(x,y)]

=λ





Optimal contract

If the principal is risk-neutral and the agent is risk averse, then the optimal risk sharing indicates that the agent will be paid a constant s(x,y)=k.

The principal will then be bearing all the risk, completing shielding the agent.

If the principal is risk-averse and the agent is risk neutral, then the optimal risk sharing condition will be satisfied by the agent receiving s(x,y)=x-k.





Possible First-Best Solutions

Two conditions must hold: Principal designs a contract that induces first best actions Agent is imposed only the amount of risk under the pure risk sharing

condition

Agent is risk neutral Agent will bear all the risk and principal

receives a constant amount This means that the agent actually “bought

the firm” from the principal and now chooses the action to maximize his own objective function






Agent’s actions are observable Principal can offer a “compound” contract :

Agent paid according to the first best contract if principal observes the first best actions

Agent is penalized substantially, if principal observes otherwise

This type of contract is called FORCING CONTRACT.






No uncertainty in the outcome If the principal can infer from the outcome

if the first best action was undertaken. If the outcome distribution exhibits

MOVING SUPPORT: If the set of possible outcomes changes

with the actions selected.





Second best solution

Now the principal has no way to observe (directly or indirectly) the agent’s choice of action.

We focus on the simplest case: One single dimensional action or effort: a Effort is a continuous variable Outcome is also a continuous random

variable No other performance signal is available.





Production function

f(x|a) is the probability density function of outcome x given effort a.

More effort turns higher output more likely. No moving support:

If f(x|a)>0 for some a, then f(x|a)>0 for all feasible effort levels.

Increasing cost for higher efforts at increasing rate: V’(a)>0 and V”(a)>0.





Model

maximize ∫G[x-s(x)] f(x|a) dx

subject to (Individual Rationality Constraint)

∫U[s(x)] f(x|a) dx – V(a) ≥ H

and to (Incentive Compatibility Constraint)

a=argmax( ∫U[s(x)] f(x|a) dx – V(a) )

s(x),a





Incentive Compatibility Constraint

In order to make the ICC more tractable, this constraint is often replaced by the FOC of the agent’s problem:

∫U[s(x)] fa(x|a) dx – V’(a)=0





Optimal contract

Differentiate the objective function with respect to s for each value of x to deliver the following first-order condition:

G’[x-s(x)] fa(x|a) U’[s(x)]

= λ + μ f(x|a)





What if μ=0?

We reach the first best solution. Holmstrom [1979] shows that μ>0, as

long as the principal wants to motivate more than the lowest possible level of effort.





FOC revisited

This new condition implies that we analyze the term:

We can look at this term from the classical statistical inference. Think of the maximum likelihood function, where x is the sample outcome and the probability distribution f(x|a) and a is the parameter to be estimated.

The principal rewards those outcomes that indicate the agent worked hard.

fa(x|a) f(x|a)





If additional Performance Measures are available?

The FOC turns into:

Holmstrom’s informativeness condition: optimal contract is based on performance measures, iff the term fa(x,y|

a)/f(x,y|a) also depends on y

G’[x-s(x,y)] fa(x,y|a) U’[s(x,y)]

= λ + μ f(x,y|a)





If additional Performance Measures are available? Holmstrom’s informativeness condition:

implies that contracts will be based on many variables.

“While it is not surprising that a variable is not valuable if the other variables are sufficient for, it is more surprising that a variable is valuable as long as the other available variables are not sufficient for it.

“In particular, it seems plausible that a variable could be slightly informative, but be so noisy that its use would add too much risk into the contract.” The question, however, is how this variable will be ultimately used in the contract.





If additional Performance Measures are available?

“When the signals are independently distributed, any signal which is sensitive to the agent’s action is useful in the contract”, even variables not controlled by the agent.

What about when the performance measures are correlated?





What about when the performance measures are correlated?

It may be the case that the correlation is such that the additional variable does not add anything to the contract.

But there can also be performances measures completely unrelated to the agent’s effort that become relevant. Think of two employees affected by the same

random shock. You are the principal of one of them, and yet the performance of the other may be informative about what your agent is doing.

Relative Performance Evaluation





Relative Performance Evaluation Used in several contexts:

Grading on the curve, Employee of the month, Sports tournaments

Not so often in executive compensation: First problem: controlability Second problem: why compensate in a situation of

disaster, just because your disaster was smaller than others...

Third problem: destructive competition... Fourth problem: choose easy competitive path... Fifth problem: may provide a safety to the agent

you don’t want him to have.





Other problems to be considered Window dressing and how incentives may be

harmful Agent can take actions to improve performance

measure, but not the outcome Myopic performance measures

Performance measures not sensitive to long term effects

Divisional versus firm-wide performance Depending on the interconnection of the divisions,

should we use more or less firm-wide performance. Aggregation of information for valuation or for

compensation is different

faculdade de ciências económicas e empresariais universidade católica portuguesa...

Documents

agent slide

performance evaluation

performance evaluation

accounting slide

outcome slide

actions information

agent y

xs slide