Bengt Holmström Prize Lecture: Pay for Performance and Beyond

420 

The Nobel Prizes

Conversely, if l(x,y) does not depend on y the optimal scheme is of the form 

s

H

(x). We can in that case write

 

f(x,y|e) = g (x|e)h(y|x), for every x, y and e = L, H. 

(5)

On the left is the density function for the joint distribution of x and y given 

e. On the right, the first term is the conditional density of x given e and the 

second term the conditional density of y given x. The key is that the conditional 

density of y does not depend on e and therefore y does not carry any additional 

information about e (given x). In words we have the following: 

Informativeness Principle (Holmström, 1979, Shavell, 1979). —An 

additional signal y is valuable if and only if it carries additional 

information about what the agent did given the signal x.

Stated this way the result sounds rather obvious, but it only underscores the 

value of using the distribution function formulation.

7

 One can derive a charac-

terization similar to (4) using the state-space formulation x(e,ε), but this char-

acterization is hard to interpret because it does not admit a statistical interpreta-

tion. The reason is that there are two ways in which y can be informative about e 

given x. It could be that y provides another direct signal about e (y = e + δ, where 

δ is noise) or y provides information about ε (y = δ, where δ and ε are correlated), 

which is indirect information about e. Both channels are captured by the single 

informativeness criterion.

As an illustration of the informativeness principle, consider the use of 

deductibles in the following insurance setting. An insured can take an action to 

prevent an accident (a break-in, say). But given that the accident happens, the 

amount of damage it causes does not depend on the preventive measure taken by 

the insured. In this case it is optimal to have the insured pay a deductible if the 

accident happens as an incentive to take precautions, but the insurance company 

should pay for all the damages, regardless of the amount. This is so because the 

occurrence of the accident contains all the relevant information about the pre-

cautions the agent took. The amount of damage does not add any information 

about precautions.

B.  Implications of the Informativeness Principle

Several implications follow directly from the informativeness principle.

1.  Randomization is suboptimal. Conditional on signal x, one does not 

want to randomize the payment to the agent, because by eliminating the 

---

Pay For Performance and Beyond 

421

randomness without altering the agent’s utility at x gives the principal a 

higher payoff. Randomization may be optimal if the utility function is 

not separable.

8

2. Relative performance evaluation (Baiman and Demski, 1980, Holm-

ström, 1982) is valuable when the performance of other agents tells 

something about the external factors affecting the agent’s performance, 

since information about ε paired with measured performance x is infor-

mative about the agent’s action e. The important tournament literature 

initiated by Lazear and Rosen (1981) studies relative performance evalu-

ation in great depth.

3. The controllability principle in accounting states that an agent’s incen-

tive should only depend on factors that the agent can control. The use of 

relative performance evaluation seems to violate this principle, since the 

agent does not control what other agents do. The proper interpretation 

of the controllability principle says that an agent should be paid based 

on the most informative performance measure available. Since x already 

depends on outside factors (captured by ε) anything correlated with ε

can be used to filter out external risk, making the adjusted performance 

measure more informative.

4. A sufficient statistic in the statistical sense is also sufficient for design-

ing optimal incentive contracts. For instance, the sample mean drawn 

independently from a normal distribution with known variance is a suf-

ficient statistic for mean effort and can be used to evaluate performance 

(Holmström 1982).

5. Optimal incentive pay will depend on lagged information if valuable 

information comes in with delay.

Bebchuk and Fried (2004) among others have argued that CEOs should not 

be allowed to enjoy windfall gains from favorable macroeconomic conditions. 

Appealing to the informativeness principle, they advocate the use of relative per-

formance evaluation as a way to filter out luck. In many cases this is warranted, 

but not without qualifications. In a multitasking context relative performance 

evaluation may distort the agent’s allocation of time and effort. When agents that 

work together are being compared against each other, cooperation is harmed or 

collusion may result (Lazear 1989). Filtering out the effects of variations in oil 

prices on the pay of oil executives will in general not be advisable (at least fully) 

because this would distort investment and other critical decisions.

Longer vesting times, causing lagged information to affect pay, are unlikely 

to negatively distort CEO behavior. On the contrary, too short or no vesting 

---

422 

The Nobel Prizes

aggravate problems with short-termism and strategic information release. Allow-

ing executives to sell incentive options so quickly in the 1990s was clearly 

unsound and the current vesting periods may still be too short.

C. Puzzles and Shortcomings

The informativeness principle captures the central logic of the basic one-dimen-

sional effort model. In doing so it helps explain some puzzling features of the 

basic model and also its main shortcomings.

Surprisingly, the optimal incentive scheme need not be nondecreasing even 

when x = e + ε. The reason is that higher output need not signal higher effort 

despite first-order stochastic dominance. The characterization (4) shows that 

the optimal incentive scheme is always monotone in the likelihood ratio l(x) 

and therefore monotone in x if and only if the likelihood ratio is monotone, in x. 

Suppose the density has two humps and the difference e

H

− e

L

 is small enough so 

that the two density functions will cross each other more than once (the humps 

are interlocked). This creates a likelihood ratio that is non-monotone, implying 

that there exist two values x such that the larger value has a likelihood ratio below 

one, speaking in favor of low effort, while the lower value has a likelihood ratio 

above one suggesting high effort. In line with inference, the agent is paid more 

for the lower value than the higher value. One can think of the two humps as two 

states of nature: bad times and good times. The higher outcome suggests that the 

good state obtained, but conditional on a good state the evidence suggests that 

the agent slacked.

9

One can get around this empirically implausible outcome by assuming that 

the agent can destroy output, in which case only nondecreasing incentives are 

relevant (Innes 1990). Or one can assume that the likelihood ratio is monotone, a 

common property of many distribution functions and a frequently used assump-

tion in statistics as well as economics (Milgrom 1981). But the characterization 

in (4) makes clear that the basic effort model cannot explain common incentive 

shapes. The universal use of piece rates for instance cannot be due to similar 

likelihood ratios.

The inference view also helps us understand a troubling example in Mirrlees 

([1975]1999). Mirrlees studies the additive production function x = e + ε where 

ε is normally distributed with mean zero and a constant variance. In other words, 

the agent chooses the mean of a normal distribution with constant variance. He 

analyzes the problem with a continuous choice of effort, but the main intuition 

can be conveyed with just two actions.

---