holmstrom(1979)_ppt.pdf

Moral Hazard and Observability

Bengt Holmstrom

The Bell Journal of Economics (1979)

Overview

Studies Moral Hazard problem when agents effort is unobserved.

Shows the optimal sharing rule is second best.

Using signals other than payoff improve welfare.

The signal has positive value regardless of its noise.

Findings have wide-ranging implications.

2/23/2015 Goizueta Business School 2

Introduction

Consider an agent A works for a principal P.

Outcome determined by As effort and a shock.

Agents wage depends on the outcome.

Effort brings disutility to agent, wage paid brings disutility to principal [principal-agent problem].

If effort observed along with outcome, can be contracted away.

Usually called the first-best solution.


Introduction

If not observed, we have info asymmetry. Optimal solution is second-best.

Solution: Use (imperfect) signals to estimate effort.

In this paper: Derive optimal sharing under asymmetry.

Optimal solution with additional signal.

When is additional information useful?


Parameters

a - Agents action

random state of nature

x = x(a,) monetary outcome/payoff

F(x) cdf of x induced by

G(w) Principals utility function over wealth

H(w,a) Agents utility function

H Agents reservation utility

s(x) Share of x that goes to Agent


Assumptions

Additively separable utility of agent: H(w,a) = U(w) V(a), V > 0.

Payoff increases in agents effort: xa >= 0.

Above assn. => Fa(x,a)

Timeline

Principal offers a contract s(x).

If agent accepts, he puts an effort a before known.

a and one realization of determine outcome x.

Agent gets his share s(x), principal gets x-s(x).

If contract specifies other contingencies y, then agent gets s(x,y).


Payoff Alone Observed

Principals utility maximization:

Using the distribution of x:

Without this, we have

the first best

optimum. If effort not

observed perfectly,

we assume Agent

maximizes his utility.


Payoff Alone Observed

Usual optimization yields:

The paper shows that > 0 (Prop 1), second-best solution is strictly inferior to first-best (Cor 2)

Need to provide incentives for increased effort, so deviation from first-best.

x is used as signal to infer a, so dependence on x!

If a is better observed, can move towards first-best!

Second best

solution.

When = 0, we

get the first best.


An Example

a is repairmans effort, x monetary payoff = length of time the machine remains operative.

G w =w, U w =2 w, V a =a2, x~exp(1a

)

Optimal sharing rule: = [ +

2]2

And, = a3, a given by 4a3 + 2a = 1

First best solution: s(x)= 2, a = (2)

-1

Taking = , we get the following graph:


An Example

Marginal return

from effort < 0

Marginal return

from effort > 0

Welfare measure=0.75

Welfare measure=0.56


With Additional Information

y is a signal observed by both parties.

Optimal sharing rule s(x,y) given by:

For the same outcome x, different realizations of y give different payoff to Agent.

For a given y, if we infer less about a from x, deviation from first-best should be minimum.

Dont penalize for actions beyond control of Agent.


Example

Prob(failure) outside repairmans control ~ exp(1/k)

x ~ exp(1/a) and independent of above

If we cannot identify failure source, then:

If we can:

1 > 2 => costly to induce a particular action a when y cannot be observed.


When is information valuable?

Can we use some r.v. y always to improve contracts?

Signal y is valuable if following is false:

Equivalently,

Above condition => x is a sufficient statistic for (x,y) w.r.t parameter a.

x has all info about a and y adds nothing to it.

Prop 3: If y is informative, s(x,y) strictly Pareto dominates s(x).

Efficiency gains independent of noisiness in y.2/23/2015 Goizueta Business School 14

Summary

When only payoff is observed, contracts are less efficient.

Adding informative signal improves the contract. Provides same incentives for effort with less loss of risk-

sharing benefits.

Explains complexity of real world contracts

Further improvement possible by using y only when outcome really bad. (Conditional Informative)

Results robust when agent adjusts a based on expectation about .


Implications

Managers are not held responsible for events one can observe are outside their control.

Their performance is always judged against information about what should be achievable given the current economic situation (this is the additional signal here).

Similarly, when a natural disaster destroys the crop, farmers should not be held responsible for the outcome (beyond optimal risk sharing).


holmstrom(1979)_ppt.pdf

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