Incentives and Behavior Prof. Dr. Heiner Schumacher KU Leuven 13. - - PowerPoint PPT Presentation

Incentives and Behavior

• Prof. Dr. Heiner Schumacher

KU Leuven

• 13. Pay for Performance
• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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Introduction

The moral hazard problem Imagine two individuals, a principal and an agent. The principal (the

• wner of a company) wants the agent (the manager) to work on a

project (maximize the company’s value). A moral hazard problem

• ccurs if the following attributes characterize the

principal-agent-relationship. Informational Asymmetry. The principal cannot observe (or evaluate) the agent’s behavior. Con‡ict of Interest. The principal and the agent have di¤erent preferences regarding the set of actions the agent can take. For example, the principal wants the agent to work hard on the project, while the agent would rather like to enjoy perks or increase the size of the company.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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Introduction

Many situations are characterized by moral hazard: Principal Agent Employer Employee Creditor Borrower Client Financial Advisor Patient Doctor People Government In this chapter, we ask to what extent monetary incentives (performance pay) can solve the moral hazard problem. We will see that monetary incentives work …ne in some circumstances, while in others, they have negative consequences for the principal.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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Introduction

Overview The Owner-Manager Con‡ict The First-Best Contract The Second-Best Contract Extensions

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Owner-Manager Con‡ict

We build a simple model to analyze the owner-manager con‡ict. Our goal is to …nd an incentive contract that maximizes the owner’s utility under the constraint that the manager exerts a certain level of e¤ort.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Owner-Manager Con‡ict

We call the owner of the company “principal” P, and the manager “agent” A. The possible pro…t levels (or “states of the world”) are x 2 fx1, x2, ..., xng, where x1 < x2 < ... < xn. A chooses between to actions, al and ah, where al represents low e¤ort and ah high e¤ort. The costs of action for A are given by C(ah) = c > C(al) = 0. If A does not work for P, he gets his reservation utility ¯ V .

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Owner-Manager Con‡ict

A’s action determines the probability distribution over the company’s pro…t x: a = ah ) ph = (ph

1, ph 2, ..., ph n), ph i > 0, n

∑

i=1

ph

i = 1,

a = al ) pl = (pl

1, pl 2, ..., pl n), pl i > 0, n

∑

i=1

pl

i = 1.

The expected value is larger under high e¤ort:

n

∑

i=1

ph

i xi > n

∑

i=1

pl

i xi.

P is risk-neutral and has the utility function π = x w, where w is the wage P pays to A. A is risk-averse and has the utility function V = U(w) C(a) with U0(w) > 0 and U00(w) < 0.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Owner-Manager Con‡ict

The sequence of events is as follows:

1

P o¤ers an incentive contract w(x).

2

A decides whether to accept or reject P’s contract. If A rejects the contract, P gets 0 and A gets ¯ V . Otherwise, the game continuous.

3

A chooses his action a.

4

The pro…t x is realized, P gets x w(x) and A gets U(w(x)) C(a).

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The First-Best Contract

Suppose that there is no asymmetric information and P can determine A’s action in the contract (for example, by imposing a huge …ne on A if he deviates to another action). What incentive contract w(x) then maximizes P’s expected pro…ts? We answer this question by going through two steps. First, we determine for each possible action the optimal incentive contract that implements the action at lowest costs. Second, we choose the action that P would like to implement (given the minimal costs from the …rst step).

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The First-Best Contract

We start with ah. The optimal contract solves the problem max

wi n

∑

i=1

ph

i (xi wi)

subject to A’s participation constraint (PC)

n

∑

i=1

ph

i U(wi) c ¯

V . In the optimum, PC must be binding (why?).

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The First-Best Contract

The Lagrangian function is L =

n

∑

i=1

ph

i (xi wi) λ

" ¯ V

n

∑

i=1

ph

i U(wi) + c

# . The …rst-order conditions are ∂L ∂wi = ph

i + λph i U0(wi) = 0,

∂L ∂λ =

n

∑

i=1

ph

i U(wi) c ¯

V = 0.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The First-Best Contract

The …rst-order conditions characterize the optimal contract. From the …rst equality we obtain 1 U0(wi) = λ for all i 2 f1, 2, ..., ng . This means w1 = w2 = ... = wn = ¯ w(ah), where ¯ w(ah) is A’s wage if he chooses ah. The constant wage o¤ers A full insurance!

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The First-Best Contract

From the second equality we obtain U( ¯ w(ah)) c = ¯ V . We can rewrite this as ¯ w(ah) = U1( ¯ V + c). Hence, A is compensated for his outside option and gets his reservation value!

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The First-Best Contract

As with high e¤ort, we can derive the optimal incentive contract that implements low e¤ort al. Again, we obtain a …xed wage w(al) = U1( ¯ V ) (why?). P then chooses the contract that o¤ers her the highest expected pro…t:

n

∑

i=1

ph

i xi U1( ¯

V + c) vs.

n

∑

i=1

pl

i xi U1( ¯

V ).

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The First-Best Contract

The optimal contract pays a …xed wage to A if he chooses the action prescribed in the contract. If he chooses another action, he pays a huge …ne so that deviation does not pay o¤. Note that under the optimal contract, both the allocation of risk (A has full insurance while the risk-neutral P absorbs all the risk) and e¤ort incentives (A chooses the optimal action) are e¢cient.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Second-Best Contract

We now consider the interesting case where P cannot observe A’s

• action. The contract no longer can condition on a. How does the
• ptimal incentive contract look like under asymmetric information?

Under a …xed wage, A would always choose al. A contract that implements ah has to pay more to A in a state of the world that is more likely after high e¤ort ah than after low e¤ort al.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Second-Best Contract

Again, we proceed in two steps. First, we determine for each possible action the optimal incentive contract that implements the action at lowest costs. Second, we choose the action that maximizes P’s pro…t.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Second-Best Contract

We start with ah. P’s maximization problem is max

wi n

∑

i=1

ph

i (xi wi)

subject to the participation constraint (PC)

n

∑

i=1

ph

i U(wi) c ¯

V and the incentive compatibility constraint (IC)

n

∑

i=1

ph

i U(wi) c n

∑

i=1

pl

i U(wi).

The incentive compatibility constraint ensures that it does not pay o¤ for the agent to accept the contract and then choose action al.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Second-Best Contract

The Lagrangian function becomes L =

n

∑

i=1

ph

i (xi wi) λ

" ¯ V

n

∑

i=1

ph

i U(wi) + c

# µ "

n

∑

i=1

pl

i U(wi) n

∑

i=1

ph

i U(wi) + c

# .

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Second-Best Contract

The …rst-order conditions are ∂L ∂wi = ph

i + λph i U0(wi) µ(pl i ph i )U0(wi) = 0,

∂L ∂λ =

n

∑

i=1

ph

i U(wi) ¯

V c = 0, ∂L ∂µ =

n

∑

i=1

(ph

i pl i )U(wi) c = 0.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Second-Best Contract

The …rst-order conditions characterize the optimal contract. We must have 1 U0(wi) = λ + µ

• 1 pl

i

ph

i

• for all i 2 f1, 2, ..., ng .

The Lagrange multipliers are positive constants (in a next step, we will explain why). This implies that the wage is not constant, but moves with the likelihood-ratio pl

i /ph i .

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Second-Best Contract

This allocation is ine¢cient. Although A is risk-averse and P risk-neutral, A has to bear some risk. P tries to motivate A to high e¤ort through a share in the pro…ts. At the same time, she tries to reduce the risk premium she has to pay A. The “second-best” optimal contract solves the trade-o¤ between an e¢cient risk allocation and optimal incentives.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Second-Best Contract

Under the optimal contract, the IC must be binding (why?):

n

∑

i=1

ph

i U(wi) c = n

∑

i=1

pl

i U(wi).

Hence, A is indi¤erent between high and low e¤ort. In equilibrium, he will choose high e¤ort. Under the optimal contract, the PC must be binding (why?):

n

∑

i=1

ph

i U(wi) c = ¯

V . A is indi¤erent between accepting or rejecting the contract. He is compensated for his outside option and e¤ort costs. The expected wage payment to A is larger under asymmetric than under symmetric information (why?).

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Second-Best Contract

How does A’s wage change, if the pro…t increases from xi to xi+1? The likelihood-ratio decreases: pl

i

ph

i

> pl

i+1

ph

i+1

) U0(w) decreases ) wi+1 > wi. The likelihood-ratio increases: pl

i

ph

i

< pl

i+1

ph

i+1

) U0(w) increases ) wi+1 < wi. Note that under the optimal contract A’s wage may decease when P’s pro…t increases!

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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The Second-Best Contract

How does the optimal contract look like if P wants to implement al?

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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Extensions

Additional Information Suppose that P can observe two signals, x and y. For example, x may be the companie’s pro…t and y the pro…t of P’s rivals. Should the optimal contract condition on both signals? The answer is yes if and only if the second signal contains additional information about A’s action. The more information P has about A’s action, the smaller is the risk-premium she has to pay to A.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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Extensions

Risk-neutral Agent What is the optimal contract if P cannot observe a, but both P and A are risk-neutral? Now it does not matter for e¢ciency who bears the risk. The following incentive contract implements the …rst-best allocation: wi = xi K, where K is chosen so that A gets his reservation utility. Interpretation: P sells the company to A at price K. This solution of course requires that A is not wealth constrained.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 13. Pay for Performance

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Extensions

Renegotiation Proofness Suppose that A has chosen her action, but the outcome is not yet

• realized. P and A can negotiate the allocation in the last period.

Would they want to change the contract? The answer is yes (why?). Fudenberg and Tirole (1990) show for a two-actions example that if parties anticipate the outcome of renegotiations, there does not exist a contract that induces A to choose high e¤ort with probability 1.1 Instead, the equilibrium will be in mixed strategies so that P does not know whether A has chosen high or low e¤ort. The optimal contract with renegotiation is strictly worse than the

• ptimal contract without renegotiation (commitment has positive

value).

1Fudenberg, Drew, and Jean Tirole (1990): “Moral Hazard and Renegotiation in

Agency Contracts,” Econometrica 58(6), 1279-1319.

• Prof. Dr. Heiner Schumacher (KU Leuven)

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• 13. Pay for Performance

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Extensions

Other Types of Incentives Multitasking Team Incentives Tournaments, Career Concerns Authority Intrinsic Motivation Fairness, Reciprocity

• Prof. Dr. Heiner Schumacher (KU Leuven)

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• 13. Pay for Performance

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