Bengt Holmström and the black box of the firm

Kevin Bryan

Bengt Holmström has been jointly awarded the 2016 Nobel Prize in Economic Sciences with Oliver Hart “for their contributions to contract theory”. This column outlines his key contributions.

The Finnish economist Bengt Holmström, who has been jointly awarded the 2016 Nobel Prize in Economic Sciences with Oliver Hart, did his PhD in operations research at Stanford, advised by Robert Wilson.

He spent his early career at the tiny department of Managerial Economics and Decision Sciences (MEDS) at Northwestern’s Kellogg School. To say MEDS struck gold with their hires in this era is an extreme understatement: in 1978 and 1979 alone, they hired Holmström and his classmate Paul Milgrom (another Wilson student from Stanford), hired Nancy Stokey, promoted 2007 Nobel laureate Roger Myerson to associate professor, and tenured Mark Satterthwaite. This list doesn’t even include other faculty in the late 1970s and early 1980s, such as eminent contract theorist John Roberts, behaviouralist Colin Camerer, mechanism designer John Ledyard, and game theorist Ehud Kalai.

This group was essentially put together by two senior economists at Kellogg – Nancy Schwartz and Stanley Reiter – who had the incredible foresight to realise both that applied game theory was finally showing promise of tackling first-order economic questions in a rigorous way, and that researchers with the proper mathematical background to tackle these questions were largely going unhired since they often did their graduate work in operations or mathematics departments rather than traditional economics departments.

This market inefficiency, as it were, allowed Schwartz and Reiter to hire essentially every young scholar in what would become the field of mechanism design, combining operations, economics, and mathematics in a manner unlike any other place in the world. In a theoretical milieu like that, it should be no surprise that Holmström was able to bring new mathematical tools to bear on some of the most classic questions in microeconomics.

Formal contract design

Holmström’s contribution lies most centrally in the area of formal contract design. Imagine that you want someone – an employee, a child, a subordinate division, an aid contractor or, more generally, an ‘agent’ – to perform a task. How should you induce them to do this?

If the task is ‘simple’ – meaning that the agent’s effort and knowledge about how to perform the task most efficiently is known and observable – you can simply pay a wage, cutting off payment if effort is not being exerted. When only the outcome of work can be observed, if there is no uncertainty in how effort is transformed into outcomes, knowing the outcome is equivalent to knowing effort, and hence optimal effort can be achieved via a bonus payment made on the basis of outcomes.

All straightforward so far. The trickier situations, which Holmström and his co-authors have analysed at great length, are when neither effort nor outcomes are directly observable.

Consider paying a surgeon. You want to reward the doctor for competent, safe work. But it is very difficult to observe perfectly what the surgeon is doing at all times, and basing pay on outcomes has a number of problems:

First, the patient outcome depends on the effort of not just one surgeon, but on others in the operating room and prep table. Team incentives must be provided.

Second, the doctor has many ways to shift the balance of effort between reducing costs to the hospital, increasing patient comfort, increasing the quality of the medical outcome, and mentoring young assistant surgeons. So paying on the basis of one or two tasks may distort effort away from other harder-to-measure tasks. There is a multitasking problem.

Third, the number of medical mistakes, or the cost of surgery, that a hospital ought to expect from a competent surgeon depends on changes in training and technology that are hard to know, and hence a contract may want to adjust payments for its surgeons on the performance of surgeons elsewhere. Contracts ought to take advantage of relevant information when it is informative about the task being incentivised.

Fourth, since surgeons will dislike risk in their salary, the fact that some negative patient outcomes are just bad luck means that you will need to pay the surgeon very high bonuses to overcome their risk aversion. When outcome measures involve uncertainty, optimal contracts will weigh ‘high-powered’ bonuses against ‘low-powered’ insurance against risk.

Fifth, the surgeon can be incentivised either by payments today or by keeping their job tomorrow, and worse, these career concerns may cause the surgeon to waste the hospital’s money on tasks that matter to the surgeon’s career beyond the hospital.

Holmström wrote the canonical paper on each of these topics. His 1979 paper shows that any information that reduces the uncertainty about what an agent actually did should feature in a contract, since by reducing uncertainty, you reduce the risk premium needed to incentivize the agent to accept the contract.

It might seem strange that contracts in many cases do not satisfy this ‘informativeness principle’. For example, CEO bonuses are often not indexed to the performance of firms in the same industry. If oil prices rise, essentially all oil firms will be very profitable, and this is true whether or not a particular CEO is a good one. Bertrand and Mullainathan (2001) argue that this is because many firms with diverse shareholders are poorly governed.

Justifications for simple contracts

Much of Holmström’s work in the 1980s and 1990s tried to square the gap between theory and empirics by finding justifications for the simplicity of many real world contracts that can be rationally justified.

Written jointly with Paul Milgrom, the famous ‘multitasking’ paper published in 1991 notes that contracts shift incentives across different tasks in addition to serving as risk-sharing mechanisms and as methods for inducing effort. Since bonuses on task A will cause agents to shift effort away from hard-to-measure task B, it may be optimal to avoid strong incentives at all (just pay teachers a salary rather than a bonus based only on test performance) or to split job tasks (pay bonuses to teacher A who is told to focus only on mathematics test scores, and pay salary to teacher B who is meant to serve as a mentor).

That outcomes are generated by teams also motivates simpler contracts. Holmström’s 1982 article on incentives in teams points out that if both my effort and yours is required to produce a good outcome, then the marginal product of our efforts are both equal to the entire value of what is produced, hence there is not enough output to pay each of us our marginal product. What can be done?

Alchian and Demsetz had noticed this problem in 1972, arguing that firms exist to monitor the effort of individuals working in teams. With perfect knowledge of who does what, you can simply pay the workers a wage sufficient to make the optimal effort, then collect the residual as profit.

Holmström notes that the monitoring isn’t the important bit; rather, even shareholder-controlled firms where shareholders do no monitoring at all are useful. The reason is that shareholders can be residual claimants for profit, and hence there is no need to distribute profit fully to members of the team.

Free-riding can therefore be eliminated by simply paying team members a wage of X if the team outcome is optimal, and zero otherwise. Even a slight bit of shirking by a single agent drops their payment precipitously (which is impossible if all profits generated by the team are shared by the team), so the agents will not shirk. Of course, when there is uncertainty about how team effort transforms into outcomes, this harsh penalty will not work, and hence incentive problems may require team sizes to be smaller than that which is first-best efficient.

A third justification for simple contracts is career concerns: agents work hard today to try to signal to the market that they are high-quality, and do so even if they are paid a fixed wage. This argument had been made less formally by 2013 Nobel laureate Eugene Fama, but Holmström in a 1982 working paper (finally published in 1999) showed that this concern about the market only completely mitigates moral hazard if outcomes within a firm are fully observable to the market, or the future is not discounted at all, or there is no uncertainty about agent’s abilities. Indeed, career concerns can make effort provision worse; for example, agents may take actions to signal quality to the market that are negative for their current firm.

A final explanation for simple contracts comes from Holmström’s 1987 paper with Milgrom. They argue that simple ‘linear’ contracts, with a wage and a bonus based linearly on output, are more ‘robust’ methods of solving moral hazard because they are less susceptible to manipulation by agents when the environment is not perfectly known. Michael Powell, a student of Holmström’s now at Northwestern, has a great set of PhD notes providing details of these models.

These ideas are reasonably intuitive, but the way Holmström answered them is not. Think about how an economist before the 1970s, like Adam Smith in his famous discussion of the inefficiency of sharecropping, might have dealt with these problems. These economists had few tools to deal with asymmetric information, so although economists like George Stigler (1961) analysed the economic value of information, the question of how to elicit information useful to a contract could not be discussed in any systematic way.

These economists would also have been burdened by the fact that the number of contracts one could write are infinite. So beyond saying that under a contract of type X does not equate marginal cost to marginal revenue, the question of which ‘second-best’ contract is optimal is extraordinarily difficult to answer in the absence of beautiful tricks like the revelation principle, partially developed by Holmström himself.

To develop those tricks, a theory of how individuals would respond to changes in their joint incentives over time was needed; the ideas of Bayesian equilibria and subgame perfection, developed by 1994 Nobel laureates John Harsanyi and Reinhard Selten, were unknown before the 1960s. The accretion of tools developed by pure theory finally permitted, in the late 1970s and early 1980s, an absolute explosion of developments of great use to understanding the economic world. Consider, for example, the many results in antitrust provided by 2014 Nobel laureate Jean Tirole.

Agency costs and innovation

Holmström’s work is brilliant in how it clarifies many puzzles that are tricky to understand without thinking about incentives within a firm. For example, why would a risk-neutral firm not work enough on high-variance moonshot-type R&D projects? This is a question Holmström asks in his 1989 paper. Four reasons:

First, in Holmström and Milgrom’s 1987 linear contracts paper, optimal risk-sharing leads to more distortion by agents the riskier the project being incentivised, so firms may choose lower expected value projects even if they themselves are risk-neutral.

Second, firms build reputation in capital markets just as workers do with career concerns, and high-variance output projects are more costly in terms of the future value of that reputation when the interest rate on capital is lower (for example, when firms are large and old).

Third, when R&D workers can potentially pursue many different projects, multitasking suggests that workers should be given small and very specific tasks so as to lessen the potential for bonus payments to shift worker effort across projects. Smaller firms with fewer resources may naturally have limits on the types of research a worker could pursue, which surprisingly makes it easier to provide strong incentives for research effort on the remaining possible projects.

Fourth, multitasking suggests that agent’s tasks should be limited, and that high-variance tasks should be assigned to the same agent, which provides a role for decentralising research into large firms providing incremental, safe research, and small firms performing high-variance research. A deep understanding of how these types of internal incentives aggregate into explanations for why firms appear the way they do can best be achieved by a thorough reading of Holmström and Milgrom’s beautiful 1987 paper, “The Firm as an Incentive System”.

References

Alchian, A and H Demsetz (1972), “Production, Information Costs, and Economic Organization”, American Economic Review 62(5): 777-95.

Bertrand, M and S Mullainathan (2001), “Are CEOs Rewarded for Luck?“ The Ones without Principles Are”, Quarterly Journal of Economics 116(3): 901-32.

Holmström, B (1979), “Moral Hazard and Observability”, Bell Journal of Economics 10(1): 74-91.

Holmström, B (1982), “Moral Hazard and Teams”, Bell Journal of Economics 13 (2): 324-40.

Holmström, B (1989), "Agency Costs and Innovation", Journal of Economic Behavior and Organization 12: 305-27.

Holmström, B (1999), “Managerial Incentive Problems: A Dynamic Perspective”, Review of Economic Studies 66(1, Special Issue): 169-82.

Holmström, B and P Milgrom (1994), “Aggregation and Linearity in the Provision of Intertemporal Incentives”, Econometrica 55(2): 303-28.

Milgrom, P and B Holmström (1987), “The Firm as an Incentive System”, American Economic Review 84(4): 972-91.

Milgrom, P and B Holmström (1991), “Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design”, Journal of Law Economics and Organization 7(Special Issue): 24-52

Stigler, G (1961), “The Economics of Information”, Journal of Political Economy 69(3): 213-25.