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1、distortion and risk in optimal incentive contracts.george bakerforthcoming, journal of human resourcesabstract:performance measurement is an essential part of the design of any incentive system. the strength and value of incentives in organizations are strongly affected by the performance measures a

2、vailable. yet, the characteristics of valuable performance measures have not been well explored in the agency literature. in this paper, i use a multi-task model to develop a two-parameter characterization of performance measures and show how these two parameters distortion and risk affect the value

3、 and use of performance measures in incentive contracts. i show that many complex issues in the design of real world incentive contracts can be fruitfully viewed as trade-offs between these two features of performance measures. i also use this framework to analyze the provision of incentives in seve

4、ral specific environments, including r&d labs and non-profit organizations.1. introduction the provision of incentives to individuals and groups in organizations is one of the central problems in the economics of the firm. a long and varied literature considers the question of what optimal incen

5、tive contracts look like (see gibbons 1998, for a review). most of this literature examines the use of "risky" performance measures, and as a result focuses on what gibbons calls "the much studied trade-off between incentives and insurance." yet, in most incentive contracts in th

6、e real world, risk is not a central issue: with the exception of stock-based plans for top executives, most compensation arrangements in fact impose very little risk on employees. in addition, as predergast (2000) points out, the data do not confirm the existence of a trade-off between risk and ince

7、ntives.in many incentive contracts, the central issue is not risk, but what steven kerr calls "the folly of rewarding for a while hoping for b”(kerr 1975). consider the incentive plan tried by lincoln electric to motivate typists in its secretarial pool: they paid a piece rate for each key stro

8、ked. (fast and berg 1975) the plan was abandoned when it was discovered that secretaries were spending their lunch hours tapping the same key over and over. understanding this aspect of incentive contracting has been the objective of the so-called "multi-tasking" literature. this literatur

9、e has been concerned not with risk, but with "distortion." the papers in this literature get the same result as those in the insurance literature: the firm reduces the strength of the incentive contract. but the reason is not to avoid imposing risk on the agent, but to avoid rewarding the

10、wrong behavior.the multi-tasking literature has evolved along two almost independent paths, one in economics and one in accounting. in economics, holmstrom-milgrom (1991) and baker (1992) each develop models that show why principals avoid strong incentives for agents who face many effort margins. ho

11、lmstrom-milgrom shows that the principal distorts incentives when differences in measurement accuracy lead them to focus risk averse agents more on some tasks than others. baker shows that even when agents are risk neutral, the constraint that the principal generally cannot pay for what she really c

12、ares about leads to effort distortion.in accounting, feltham-xie (1994) build a model (very similar to the one developed in this paper) that demonstrates how the incompleteness of most managerial compensation contracts leads to distorted incentives. in their model, the fact that agents take many mor

13、e actions than the firm can measure leads to inefficiency in agent effort levels across all tasks. they also show how additional performance measures can mitigate, but generally not eliminate, this problem. a recent paper in this literature, datar, kulp and lambert (forthcoming) asks explicitly abou

14、t how principals should weight multiple, distorted performance measures. in this paper, i build on both strands in this multi-tasking literature to develop a simple two-parameter characterization of performance measures that captures many of the problems, and clarifies much of the intuition, in the

15、use of incentive contracting in organizations. the contribution of the paper is twofold. one is an intuitive geometric interpretation of and trigonometric expression for distortion in performance measures. the second contribution is to show how this two-parameter characterization and its interpretat

16、ions can capture and explain many of the issues that plague actual incentive plans.2. distortion relative to what? in order to characterize a distorted performance measure, it is necessary to define an undistorted performance measure. one particular performance measure plays a crucial role in this p

17、aper: the total value of the organization. this performance measure (labeled v) should be thought of as capturing the present value of all future net benefits to the residual claimant of the organization. for publicly traded companies, v represents the market value of equity; in this case, firm valu

18、e is an observable, contractible, and frequently used performance measure in incentive contracts. all types of stock-based compensation plans, including bonuses based on stock price, as well as executive stock grants, option grants, employee stock ownership plans, phantom stock, and stock appreciati

19、on rights are examples of incentive plans based on firm value. i make two assumptions about the nature of firm governance and equity markets that affect the performance measure v: (1)the objective of a publicly traded firm is to maximize the value of the firm to shareholders; and (2) the stock price

20、 accurately reflects this value. thus, in this paper, incentives plans based on equity value are undistorted: by definition they provide incentives that are perfectly aligned with the organization's objective.in many organizations the total value of the organization cannot be used in an incentiv

21、e plan. in privately held firms, not only is the financial value of the organization unknown, it is likely not be the owner's objective. rather, the objective is to maximize the owner's utility, and her utility is clearly not a contractible performance measure. this problem of non-contractib

22、le organization value is even more acute in non-profit organizations and government agencies. in organizations of this type, it may not even be possible for managers to agree on and specify the organization's objective. such organizations are often characterized by particularly difficult incenti

23、ve problems; they cannot use stock based incentive devices, and the absence of a well-articulated organizational objective hampers the design of an efficient performance measurement system. if the top level objectives are not known, then how is the organization to measure the performance of individu

24、al employees? i will argue below that the difficulty in defining "good" performance measures in non-profit organizations is one reason for the weak incentives that so often characterize organizations of this type, and for the dysfunctional consequences that often arise when these types of

25、organizations try to use strong incentives.the paper is organized as follows. in section 2, i develop the model and derive the optimal slope first for a risky but undistorted performance measure, and then for a risky and distorted performance measure, when no other performance measure is available.

26、the main intuition of the model is evident from this derivation: incentives are optimally weaker when performance measures are either riskier or more distorted. in section 3, i derive the optimal incentive contract when both a distorted performance measure and a risky but undistorted measure are use

27、d. i derive many of the same results as in the single performance measure case, along with some new results on relative performance evaluation. section 4 examines the trade- off presented by the choice between risky and distorted performance measures, showing how many issues in the design of incenti

28、ve contracts are fruitfully viewed as a choice between distortion and risk in performance measurement. section 5 concludes with a discussion of future work, as well as a discussion of incentives for innovation and the design of incentive programs in organizations without well-defined objectives, suc

29、h as non-profit institutions.3. the trade-off between distortion and risk it is a contention of this paper that the trade-off between distortion and risk modeled here is at the core of the problem of incentive design in many organizations. viewed in this way, the objective of incentive system design

30、 is to discover or create low distortion, low risk performance measures. in what follows, i discuss several examples of incentive plan design problems, showing how the choice of performance measures can be usefully viewed as a trade-off between distortion and risk.a. timing of measurementdecisions a

31、bout performance measurement often revolve around issues of timing: should employees be evaluated on short run or long run results? two examples help to illustrate how this choice involves trading off distortion and risk. the typical incentive plan for loan officers in a bank involves "originat

32、ion fees," in which the loan officer is paid for lending money. a feature of this type of incentive is that it gives the loan officer no incentive to search for and write "good" loans that is high interest rate loans that are likely to be repaid. instead, loan officers have incentives

33、 to make any loan, and banks typically have credit committees (made up of higher-level bank officers) whose job it is to determine the credit-worthiness of the potential debtor, and approve or deny the loan. the question in this scheme is why loan officers are not paid on the eventual profitability

34、of the loan, rather than on its origination.'4 bonuses based on loan profitability would have the advantage of giving loan officers incentives to search out good credit risks, and sell loans with higher expected value. in other words, such a performance measure would provide less distorted incen

35、tives to the loan officers. however, such a scheme would also give the loan officers greater risk, since many things can happen to debtors that are essentially unknowable when a loan is written. in this case, it appears, the trade-off between risk and distortion is made in favor of lower risk and hi

36、gher distortion. the opposite choice is often made in the design of bonus plans for project managers in large construction projects. construction managers often leave one project and move to a second before the first project is completed. frequently, the project manager will be paid a bonus based th

37、e final profitability of the project when it is completed. thus the project manager might have two or three "contingent" unpaid bonuses to his credit, whose payment awaits the completion of a project that he worked on months or even years earlier. the problem with such a bonus plan is clea

38、r: the project manager's bonus for a particular project depends on many factors over which the project manager has no control, not the least of which is the performance of his successor(s). yet the benefits are also clear: such a scheme gives the manager incentives to be concerned about the long

39、 run profitability of his decisions. trying to evaluate the project manager on the profitability of the project when he leaves would encourage him to (perhaps literally) bury problems that would not become clear until long after he had left the project. in this case, the benefits of low incentive di

40、stortion outweigh the costs of high risk for the project manager. in both of these examples, the choice of performance measures involves trading off risk and distortion. in both cases, the choice is between a higher risk, lower distortion performance measure (loan performance, final profitability) v

41、ersus a lower risk, higher distortion measure (loan origination, short term profitability). which measure is chosen depends on the relative costs of distortion and risk. b. level of aggregation compensation design problems frequently involve choosing the level of aggregation at which to measure perf

42、ormance. i examine two examples, one involving the choice of the group size over which to measure performance, and the other involving responsibility accounting. a key decision in determining an employee's incentive package is the weight to place on individual versus group performance, and if gr

43、oup performance, how large a group. consider the design of a performance measurement system for a worker who is a member of a work group. each worker engages in tasks that affect his own measured performance, as well as engaging in cooperative activities that improve the performance of the entire gr

44、oup. attempts to reward the worker for individual performance may thus reduce teamwork and destroy cooperation. on the other hand, rewarding individuals on the basis of group performance makes their rewards dependon the performance of the entire group, including all of the uncontrollable events (and

45、 actions of others in the group) that affect group output. once again, the choice of whether to use group or individual performance in the incentive contract depends on the trade-off between risk and distortion. group rewards subject group members to risk by making their rewards depend on uncontroll

46、able events; individual rewards distort incentives to cooperate. how this trade-off gets resolved depends mainly on the value of cooperation (and thus the distortion induced by an individual reward scheme) and the riskiness of group (relative to individual) output. 4. extensions and conclusions this

47、 paper provides a simple and intuitive structure for understanding the choices organizations face in the design of incentive contracts. i argue that a performance measure's usefulness in an incentive contract will depend on its distortion and risk: the more distorted and the riskier the measure,

48、 the less valuable it will be to the organization and the less it will be used in an incentive contract. furthermore, organizations rarely have available low risk, low distortion measures, and so are generally making trade-offs between measures that are high risk and low distortion, or low risk and

49、high distortion. as discussed above, many problems in incentive system design can be fruitfully analyzed using this framework.of course, much work remains to be done. questions raised by this analysis include: 1. what is the underlying structure (of information, incentives, etc.) that requires organ

50、izations to choose between distortion and risk in performance measures? is there some sort of "performance measurement possibility frontier? if so, what determines its efficiency? how do organizations choose where to locate on this frontier? 2. how do distorted, risky measures combine into &quo

51、t;portfolios?" what are the characteristics of linear combinations of performance measures? how should firms combine them?answers to these questions are important for developing a fuller understanding of the forces that drive the use of different performance measures in incentive contracts. oth

52、er extensions of this framework permit analysis of some specific incentive problems that organizations face. consider first the problem of designing incentive contracts to encourage innovation in technology-based firms. large firms often struggle to deliver incentives to scientists and engineers inv

53、olved in research and development. on what objective basis can such contracts be based? at the root of the difficulty in designing such an incentive contract is the problem that, in general, the desired outcomes cannot be known in advance, and the value of any given breakthrough is extremely hard to

54、 predict. the value of the breakthrough to the firm may not be known for many years, or perhaps may never be distinguishable from other causes of firm success or failure. in this context, how can research scientists be rewarded?firms (and economies) have several solutions to this performance measure

55、ment problem, none of them ideal. one is to pay research scientists flat wages, with modest rewards (in the form of career advancement and prestige) for good work as determined by subjective evaluations and peer recognition. while this solution is quite common it relies, to a large extent, on the in

56、trinsic motivation of scientists to do interesting and personally rewarding research, and often results in weak incentives to invent profitable products. a second solution is to reward researchers with significant stock-based compensation, so that they will share in their value creation to the exten

57、t that it increases the value of the firm. the efficacy of this second solution, of course, is highly dependent on the size and diversity of the firm. the larger and more diverse the firm, the lower will be the signal-to-noise ratio of the stock price with respect to the scientist's actions. in

58、very large firms, this type of reward is likely to have little effect on the scientist's behavior, since the optimal weight on such a noisy performance measure is quite small.one other solution is to have the r&d done outside the firm, in small companies whose only activity is r&d. in th

59、ese small companies, the total value of the firm (the current stock price, or the future price in an ipo or buyout) will be quite sensitive to the actions of the research staff, making it a more powerful incentive instrument than an equity stake in a large firm. such firms are common in technology-i

60、ntensive industries, and the high incentive strengths made possible by their small size is often cited as an important reason for their success in generating innovation. large firms, whose only choice is to rely on distorted performance measures or very noisy stock prices, cannot replicate these small firm incenti

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