Bengt Holmström Prize Lecture: Pay for Performance and Beyond

436 

The Nobel Prizes

increases future sales. We assume that the latter returns can only be transferred 

through ownership. This is a reduced-form way to introduce a role for owner-

ship (Grossman and Hart 1986). An independent sales agent owns the long-term 

returns; a sales employee does not. The remedy for the loss of long-term incen-

tives is to pay the sales employee a fixed wage. This makes the sales employee 

willing to allocate attention to tasks in whatever way the firm desires, at the cost 

of weaker overall initiatives.

We have, then, two coherent incentive systems as found by Anderson and 

Schmittlein. An independent contractor (sales representative) owns the long-

term returns, is paid high commissions for direct sales and is free to represent 

other firms. A sales employee does not own the long-term returns, is paid a 

fixed wage, and cannot represent other firms. And consistent with the evidence, 

employment is favored if direct selling is hard to measure or if non-selling activi-

ties are valuable.

Another way to introduce a distinction between employment and contracting 

is to assume that a firm can restrict the tasks of a sales employee more easily than 

it can for an independent representative (Holmström 1999b). Both alternatives 

show that the theory of incentive contracts and the theory of property rights are 

complementary. Together they can provide a richer perspective on organization.

VII. CONCLUSION

Let me close with a summary of the intellectual journey I have described. When I 

started to study moral hazard, the main paradigm was the basic one-dimensional 

effort model. Despite the seeming simplicity of this model, it behaved in ways 

that were perplexing at times. The Informativeness Principle revealed the basic 

logic of the model, providing useful insights about the value of information at 

the same time as it made clear that the basic model cannot explain the shape of 

common incentive schemes.

22

 This led Paul Milgrom and me to ask why incen-

tive schemes are linear. Our willingness to listen to the basic agency model intro-

duced us, rather serendipitously, into the world of multitasking, which opened 

up a rich set of issues and opportunities. The value of low-powered incentives 

in the context of multitasking explains why firms make so little use of explicit 

bonuses and instead use alternatives like job design and bureaucratic rules to 

construct coherent incentive systems that are very distinct from the way incen-

tives are designed in the market.

The firm’s comparative advantage relative to markets rests partly with its 

unique ability to use low-powered incentives combined with constraints. This 

explains why bringing the market inside the firm is such a misguided idea, 

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Pay For Performance and Beyond 

437

something I failed to understand at Ahlström and advocates of market-like 

incentives in firms seem to miss today.

APPENDIX

A1. The General Multitask Lab

In Holmström and Milgrom (1987) we study a multi-dimensional Brownian 

process in which the agent can choose drift rates independently, at a cost that 

depends on the rates chosen. This model features an optimal solution that is 

linear in the different dimensions of the Brownian process, and just as in the 

one-dimensional case the optimal coefficients can be solved through a static 

model where the agent has several tasks to perform, each one corresponding 

to one of the dimensions of the Brownian process. In its most general form the 

static multitask model has the following elements:

•  The agent chooses “inputs” e = (e

1

,. . .,e

n

).

•  There are m measures of performance x

i

 = k

i

(e) + ε

i

, i = 1,. . .,m. The 

measurement errors follow a joint normal distribution with mean vector 

0 and variance-covariance matrix Σ. The “production” functions k

i

 deter-

mine how the agent’s choices map into the mean of the corresponding 

performance measure.

•  The principal’s benefit function is B(e) and the agent’s cost function is C(e).

•  The optimal incentive scheme is linear: s(x) = Σ

i

α

i

x

i

 + β, with commis-

sion rates α

i

 and salary β.

The agent’s behavior is characterized by the first order conditions

 

Σ

i

α

i

∂k

i

(e)/∂e

j

 = ∂C(e)/∂e

j

 for every j.

It is readily seen that the misalignment model is a special case of this model. 

The model also encompasses cases where a risk neutral agent observes a random 

signal θ before acting as in Baker (1992).

See Holmström and Milgrom (1991) for further details on the solution and 

variations.

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NOTES

1. It is common to see companies pay executives a bonus that is linear within a perfor-

mance interval, but capped both at the top and the bottom; see Murphy (1999). On 

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Pay For Performance and Beyond 

441

the other hand, real estate agents and sales people are paid commissions without an 

upper bound. Stiglitz’s (1975) paper on sharecropping was the first to study linear 

incentives.

2. Mirrlees ([1975]1999) was the first to use this formulation. It avoids taking deriva-

tives of the endogenous incentive scheme s(x), which may well be non-differentia-

ble a priori.

3. Holmström (1977) proves existence by assuming that s(x) has to be chosen from a 

finite interval. A more instructive existence proof is provided by Grossman and Hart 

(1983) when the number of outcomes is finite. The key assumption is that probabili-

ties have to be strictly bounded away from zero for all action choices.

4. This equation is the first-order condition of the Lagrangian with respect to s(x) 

for each x.

5. If μ = 0, the formula implies a constant s

H

(x) in which case the agent would choose 

L, violating the incentive constraint; so μ > 0. If λ = 0 constraint (2) is slack and the 

principal can do better by reducing all utility levels by a constant; so λ > 0.

6. Typically s

λ

 does not correspond to optimal risk sharing for the reservation value of 

U in the agent’s participation constraint (3), because that problem will have a differ-

ent λ value. I thank Jörgen Weibull for pointing this out.

7. The informativeness principle as stated applies when there is just one binding 

incentive compatability constraint (2). If the agent is indifferent among several 

actions, there will be a Lagrange multiplier μ

j

 for each binding incentive constraint 

j. One can extend the inference interpretation to this situation by evaluating the 

outcome against the likelihood of the agent randomizing across actions of indif-

ference with the Lagrange multipliers providing the (relative) weights of this ran-

domized strategy. I am grateful to Paul Milgrom for suggesting this extension.

Gjesdal (1982) and Grossman and Hart (1983) provide a weaker ordering using 

Blackwell’s Theorem, which applies regardless of the number of binding incen-

tive constraints. For other variations, see Kim (1995) and Chaigneau, Edmans and 

Gottlieb (2014).

8. See Gjesdal (1982).

9. Grossman and Hart (1983) show that the only thing one can say in a general model 

with discrete outcomes x is that the optimal incentive scheme cannot be such that 

whenever the agent is paid more, the principal is paid less. There must be one incre-

ment in x such that payments co-move.

10. This nonexistence result violates Grossman and Hart’s (1983) assumption that prob-

abilities are bounded strictly away from zero.

11. For every x, there is a separate control s(x). The space of all possible functions s is 

infinite-dimensional.

12. The agent’s utility function is u(m, e) = 1 − exp[−r(m − c(e))], where r is the agent’s 

absolute risk aversion, c(e) is the opportunity cost of effort and m is money. This util-

ity function is multiplicatively rather than additively separable. The reason we chose 

this function is that income levels do not affect the agent’s choice.

13. This seems to violate the informativeness principle: the timing of sales is not used. 

The reason is that it is optimal for the principal to implement a constant action and 

for this implementation the timing of sales is irrelevant.

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442 

The Nobel Prizes

14. See Holmström and Milgrom (1987) for an intuitive derivation and Hellwig and 

Schmidt (2002) for a rigorous analysis.

15. When the agent can observe his progress and make his choice of effort contingent 

on the current state, the agent can generate essentially any distribution over the final 

position of the process at time 1 using a Brownian bridge (which takes the process 

from its starting point at t = 0, to an arbitrary point at time t = 1). I am grateful to 

Michael Harrison for showing me this.

16. So the second activity e

2

 actually cost the principal a lot and should therefore enter 

B(e), but with a big negative sign, reflecting the costs of the reputation loss.

17. There are also examples where firms implement aggressive piece rate plans success-

fully. Safelite, the dominant firm in the windshield replacement market, is one case in 

point (Lazear 2000). Lincoln Electric, a welding equipment manufacturer, is another 

(Milgrom and Roberts 1995). In each case, the introduction of piece rates required 

a number of matching changes in the organizational structure to avoid the kind of 

problems described above.

18. A formal treatment of this example can be found in Holmström and Milgrom (1991).

19. Comparative statics results like this one, involving several endogenous variables, will 

in general require a more complex analysis using monotone methods (see Milgrom 

and Roberts 1990 and Holmström and Milgrom 1994). Because the exclusion of 

private tasks only depends on the commission rate, but not directly on the measure-

ment error, this case is straightforward. If instead the value of the principal’s task 

increases, there is a negative direct effect on exclusion, and it is therefore possible 

that fewer private tasks will be allowed even though the commission rate goes up. 

There are two ways of increasing the agent’s attention to the principal’s task: raise the 

commission rate or exclude private tasks. Both instruments may be used together.

20. In an important paper,  Prendergast (2002) observes that empirically we often see 

that higher risk go together with stronger, not weaker, incentives as just described. 

The reason for changing conclusion is that risk in his model concerns productivity, 

not measurement error, and there is therefore value in having the agent respond to 

changing circumstances. This case can be incorporated in the multitask model by 

replacing the additive output function with a multiplicative one. The agent’s action 

will then be a contingent strategy and the single measure will be a weighted average 

of the possible states of nature. Prendergast’s model as well as the multitask model 

can explain the positive co-movement (see Baker and Jorgensen 2003).

21. The related literature on relational contracting studies the scope of informal con-

tracts that can support rules and practices; see e.g. Levin (2003); MacLeod and 

Malcomson (1988); and Baker, Gibbons and Murphy (1994, 1999).

22. Much attention was paid to problems with the First-Order Approach—the fact that 

one cannot in general replace the agent’s incentive compatibility constraint with a 

first-order condition. Rogerson (1985) provided a sufficient condition for the first-

order approach and efforts continue to refine his work. But it is evident by now that 

the one-dimensional effort model as such has serious shortcomings.