Problems with Performance-Based Incentives • 409

chooses effort so that additional sales revenue from extra effort exactly equals the marginal cost. But a worker equates the additional sales revenue multiplied by the commission rate, to marginal cost. Total value is therefore maximized if the commission rate is 100 percent. In our example, if the firm offers a 100 percent commission, the employee will exert 140 units of effort, yielding sales of $14,000 at an effort cost of $5,000. Since the commission equals total sales, the firm can require the worker to pay the firm $8,000 and still make the employee’s total payoff (commission less effort costs less payment to the firm) equal $1,000.6 The firm makes a profit of $8,000, which is the best the firm can do with any contract offer. Commission rates approaching 100 percent and “negative” salaries are observed in practice; franchising (which we discussed in Chapter 4) is a good example where the agent (the franchisee) pays a fixed fee to the principal (the franchiser) and keeps most of the revenues.

4.Performance-based pay can help resolve hidden information problems as well. Suppose, for example, that the salesperson receives better information than the firm regarding a hot sales prospect. Clearly, it is in the firm’s interest to have the salesperson spend relatively more time with clients who are somewhat likely to buy and less time with those who are unlikely to buy. When paid a fixed salary, the salesperson has little reason to quickly move on from clients who are unlikely to buy. A salesperson paid on commission, however, will have an incentive to make effective use of information about the likelihood of making a sale.

PROBLEMS WITH PERFORMANCE-BASED INCENTIVES

Using high-powered incentives such as large commission rates invites two potentially big problems. The first arises if the performance measure is affected by random factors that are beyond the employee’s control and therefore subjects the employee to unwanted risk. The second arises if the measure fails to capture all aspects of desired performance. Employees might focus attention on the measured aspects of performance at the expense of other aspects that may be equally or more important for profitability.

To understand how random factors in performance measures affect the cost of providing incentives to employees, we take a short detour to examine individuals’ preferences over risky outcomes.

Preferences over Risky Outcomes

Consider a freshly minted MBA graduate who is presented with two job opportunities. The jobs are identical in every way except compensation is “safe” in the first job and “risky” in the second. At the safe job, the employer will pay the graduate $100,000 at the end of the first year of employment. At the risky job, the employer will flip a coin at the end of the first year. If the coin comes up heads (which happens with probability one-half), the employer will pay $40,000. If it comes up tails, the employer will pay $160,000. Note that the expected values of the two jobs are identical—$100,000. Putting yourself in the shoes of this graduate, which job would you prefer?

Most people would prefer the safe job because most people are risk averse.8 A riskaverse person prefers a safe outcome to a risky outcome with the same expected value. People are risk averse because they tend to have diminishing marginal utility for wealth. This would imply that the inherent value of the “stuff” they can purchase from earnings between $40,000 and $100,000 is more than the inherent value of the “stuff”

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TABLE 12.1

An MBA Graduate’s Preferences over Jobs

they can purchase from earnings between $100,000 and $160,000. An income of $40,000 puts a family at about 200 percent of the poverty line, forced to avoid all of life’s luxuries. Moving from $40,000 to $100,000 allows the family to live in a modest home, buy some new clothes, take a decent vacation, and drive a new family sedan. Most families would welcome even these modest luxuries. Moving up to $160,000 buys a bigger home, fancier clothes, an overseas vacation, and maybe even a luxury car. Faced with these prospects, risk-averse individuals would not give up a certain income for $100,000 for a gamble that nets them $100,000 on average, but puts them at risk for a much lower standard of living.

The same MBA graduate would definitely prefer the risky job if the safe job paid only $40,000, as there would be no downside to the risky job. There must be some salary between $40,000 and $100,000 at which the graduate is indifferent between the two jobs. To locate this indifference point, consider reducing the payment associated with the safe job in $10,000 increments. As shown in the first row of Table 12.1, the safe job is preferred to the risky job when the safe job offers the same expected value. Suppose that the graduate would prefer the risky job when the safe job pays $70,000, but prefers the safe job at a salary of $90,000. Suppose that the indifference point between the safe job and the risky job occurs when the safe job pays $80,000.

We define $80,000 to be this decision maker’s certainty equivalent for this risk. It is the certain amount that makes the decision maker indifferent between taking the risk and taking the certain payment. Put another way, the certainty equivalent is the smallest certain amount the decision maker would be willing to accept in exchange for the risky payoff. We define the difference between the expected value of a risk and the decision maker’s certainty equivalent as the decision maker’s risk premium. In this case, the expected value of the risk is $100,000, while the graduate’s certainty equivalent is $80,000. Hence, the risk premium is $20,000. The risk premium can be thought of as the cost to the decision maker of having to bear the risk of an uncertain outcome.

The notions of certainty equivalent and risk premium have three key properties:

1.Different decision makers will have different certainty equivalents for the same risk. Ask yourself what safe wage (i.e., what certainty equivalent) makes you indifferent between the safe job and the risky job. If you reached a higher certainty equivalent than did our graduate, you are less risk averse than our graduate. If you reached a smaller certainty equivalent, you are more risk averse.

Problems with Performance-Based Incentives • 411

2.For a given decision maker, the certainty equivalent is lower (and the risk premium higher) when the spread or variability in payments is greater. Consider an even riskier job that pays either $180,000 or $20,000. Because of risk aversion, this job is less attractive than the one offering either $160,000 or $40,000. Hence, the riskier job has a lower certainty equivalent and thus a higher risk premium.

3.In choosing between two risky outcomes, a decision maker will select the one with the higher certainty equivalent.

Risk Sharing

Risk-averse individuals can often make themselves better off by sharing their risks. To illustrate this principle, consider two risk-averse homeowners. Each owns a wooden frame house worth $200,000, and each faces the possibility that the house may be destroyed by fire. Suppose the probability that a house burns down in a given year is 10 percent. If a house burns down, the entire value is lost, and the homeowner will have to pay $200,000 to rebuild. Hence, a homeowner’s rebuilding costs will be

Home burns down: Cost 5 $200,000 with probability 5 0.10

Home does not burn down: Cost 5 $0 with probability 5 0.90

A homeowner’s expected rebuilding cost is $20,000, but the uncertainty makes the house a risky asset.

Suppose that the first homeowner approaches the second and makes the following contract offer: if either home burns down, the two homeowners will share the cost evenly. We will assume that the events under which the houses burn down are independent, so that the probability that both burn down is (0.10)2 5 0.01.

Each homeowner now faces the following “gamble”:

Both homes burn down: Cost 5 $200,000 with probability 5 0.01

One home burns down: Cost 5 $100,000 with probability 5 0.18

Neither home burns down: Cost 5 $0 with probability 5 0.81

Each homeowner’s expected rebuilding cost is therefore:

(0.01 3 $200,000) 1 (0.18 3 $100,000) 1 (0.81 3 $0) 5 $20,000

In other words, each homeowner faces the same expected cost whether or not the second homeowner accepts the offer from the first. Note, however, that the probability of the worst outcome (that is, incurring rebuilding costs of $200,000) has fallen from 0.10 to 0.01. Similarly, the probability of the best outcome (incurring $0 costs) has fallen from 0.90 to 0.81. While this contract does not change expected rebuilding costs, it does reduce the variability in these costs by making the extreme worst and best outcomes less likely. Being risk averse, the second homeowner will gladly accept the offer. By sharing their risks, the two homeowners reduce the variability in their payoffs and both are made better off.

Some of the earliest insurance companies were organized on precisely this principle. The great Fire of London in 1666 destroyed property worth £10 million, a figure estimated to be around one-quarter of the total gross domestic product of England at the time. In its aftermath, Londoners searched for ways to protect their wealth against these risks. In 1696, a total of 100 subscribers joined together to form the Amicable Contributorship, a mutual insurance organization whose subscribers

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pledged their personal wealth to rebuild the homes of other subscribers in the event of damage by fire. Although most modern insurance firms do not rely on the personal wealth of a group of subscribers to pay claims (with Lloyd’s of London being a notable exception), the principle of risk sharing nonetheless continues to underlie the demand for insurance of all forms. Furthermore, the insurance industry is only one of a number of modern institutions that facilitate the sharing of risks. Financial markets serve a similar purpose. In an initial public offering, an entrepreneur sells ownership shares, which are an uncertain claim on the firm’s future cash flows, to investors in exchange for a certain, upfront payment. This transaction shifts risk from the entrepreneur to the investor.

An immediate corollary to the logic of risk sharing is the following. If one party is risk averse and another is risk neutral, the efficient allocation of risk places all risk with the risk-neutral party and gives a certain payoff to the risk-averse party. The reason is that the risk-neutral party values the gamble at its expected value, but the risk-averse party values it at a certainty equivalent that is less than the expected value. The risk-neutral party can offer the risk-averse party an amount of money somewhere between the expected value and the risk-averse party’s certainty equivalent, and both will be better off by accepting this transaction.

Risk and Incentives

We are now ready to incorporate our discussions of risk aversion and risk sharing into the theory of incentives. As noted earlier, the main costs of basing pay on measures of performance stem directly from difficulties in measurement. For example, measured performance depends in part on the agent’s actions, but it also depends on random factors that are beyond the agent’s control. Tying pay more closely to observed performance therefore links the agent’s pay to these random factors. A risk-averse agent dislikes random variations in pay, and the principal must compensate the agent for the cost of bearing this risk.

To illustrate, we adapt an agency model developed by Bengt Holstrom and Paul Milgrom.9 Consider a firm that selects a commission rate a for a salesperson working in a retail store. We assume that the salesperson is risk averse. We also assume that the firm is risk neutral. This is reasonable because a firm has many salespeople and is likely not greatly concerned about variation coming from the sales of any one salesperson. Also, if the firm’s stock is publicly traded, its shareholders can easily diversify any risk that is idiosyncratic to the firm.

It stands to reason that a salesperson who works harder will generate more sales. But the dollar value of goods sold by a salesperson will also depend on a number of factors beyond the salesperson’s control. The local economy may suffer a downturn. The store’s buyers may bet on the wrong merchandise to stock in the store. In a given week, the salesperson may also be unlucky; perhaps an unexpectedly large fraction of the customers are “just looking.” Building on a previous agency model supposes that sales depend on both effort, e, and a random variable, |e:

Sales 5 $100e 1 |e

Let |e be a random variable with expected value zero and variance 2. A positive realization of |e causes the employee’s sales to be higher than they otherwise would have been. This can be interpreted as resulting from a good local economy, a favorable selection of merchandise, or just good luck. Conversely, a negative realization of |e means that sales are unexpectedly low.

Problems with Performance-Based Incentives • 413

Suppose that our salesperson is risk averse and has certainty equivalent for an uncertain wage outcome of

E(Wage) 2 [1/2 3 Var(Wage)]

where E(Wage) is the expected value of the wage payment and Var(Wage) is the variance of the wage payment.10 The parameter , known as the coefficient of absolute risk aversion, is indicative of how risk averse the employee is. Larger values of imply greater risk aversion, since as increases the employee applies a greater discount to the uncertain wage due to its variability. Following our earlier agency example, the employee’s cost of effort is 0 up to 40 units of effort and 1/2 3 (e 2 40)2 thereafter, and the employee’s next-best job opportunity offers a certainty equivalent of $1,000, net of effort costs.

Suppose that the firm pays its sales force a fixed salary F per week and a commission of on sales. For an effort level e and random variable realization |e, the employee’s actual pay will therefore be F 1 (100e 1 |e). Given that the random variable |e has an expected value of zero, the employee’s expected pay is F 1 (100e), while the variance is 2 2. Hence, the employee’s certainty equivalent minus effort costs is

F 1 (100e) 2 12(e 2 40)2 2 12 2 2

This expression consists of the employee’s base salary (F ), the expected commission ( 100e), less costs from effort ((1/2)(e 2 40)2) and the cost of bearing risk (2(1/2) 2 2). If the firm hopes to attract the employee to this job, this amount must be greater than $1,000. If the firm asks the employee to bear more risk or exert more effort, it must compensate by offering a higher base salary and/or commission rate. This corresponds to the intuitive notion that people are willing to take jobs that are risky or difficult only if they are well compensated for doing so.

The employee gets a marginal benefit of 100 for each additional unit of effort expended. The employee incurs a marginal cost of exerting additional effort equal to (e 2 40). Equating the two, we find that the employee will exert 40 1 100 units of effort.11 As in the earlier agency example, effort increases with the commission rate. However, it is no longer optimal for the firm to set 5 100 percent (i.e., “sell” the business to the employee). This is because any increase in will increase the employee’s cost of bearing risk, which the firm must offset by offering a higher base salary.

The mathematical analysis can be summarized as follows. As the firm ties pay more closely to performance, it provides stronger incentives. This leads to more effort and, hence, more revenue. However, since the performance measure is subject to random factors, tying pay more closely to measured performance also increases the variability of the employee’s compensation. This makes the job less attractive to the employee and means that the firm has to pay higher overall wages in order to attract the employee. This leads to higher costs for the firm. The optimal strength of incentives is determined by a balancing of these two forces.

We can compute how the firm’s profit changes when it offers various compensation plans. For concreteness, we assume that the employee’s coefficient of absolute risk aversion, , is equal to 3 and that the variance of sales, 2, is 10,000.12 Suppose first that the firm offers a job without commissions. Since this job motivates no extra effort and places no risk on the employee, the firm can pay a salary of $1,000. As shown in Table 12.2, the employee will put in 40 units of effort, and the firm’s expected profit will be $3,000.

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TABLE 12.2

The Tradeoff between Risk and Incentives

If the firm offers a commission rate of 5 10 percent, the employee will put in 50 units of effort (leading to effort costs of $50) and earn expected commissions of $500. Because the pay now depends on output, which, in turn, is affected by random factors beyond the employee’s control, the employee is subject to risk. The employee discounts the value of the job because of this risk, applying a risk premium of $150. The firm must ensure that the certainty equivalent minus effort costs is greater than or equal to $1,000. Thus, in order to overcome the increased risk and effort costs, the firm must offer a fixed salary F of $700. The firm’s total expected wage bill goes up to $1,200, which is just enough to compensate for the increased risk and effort costs associated with the commission-based job. Here, the increase in expected productivity ($5,000, compared to $4,000 for the salary-only job) more than compensates for the increase in expected wages. Thus, the firm’s expected profit is higher if it offers the commission-based job than if it offers the salary-only job.

Filling in the remaining rows of Table 12.2, we see that further increases in the commission rate have similar effects. As the firm increases , the employee exerts more effort but bears more risk. The extra effort leads to additional revenue for the firm, but the extra risk leads to a larger risk premium and thus to higher expected wages. The optimal commission rate is determined by a trade-off between these benefits and costs. In our example, the firm’s profit-maximizing choice of is 25 percent.

To summarize this analysis, we have shown that if a firm wants to tie pay to a performance measure that is affected by random factors, the firm must compensate employees for the resulting increase in the variability of their pay. In determining how closely to tie pay to performance, the firm must weigh the costs of imposing risk onto risk-averse employees against the benefits of providing additional incentives. There is, therefore, a trade-off between risk and incentives.

Firms rarely have detailed information regarding employees’ risk preferences and effort costs c. Therefore, they cannot solve precisely for an optimal commission rate as we have done here. However, our model does yield a number of insights into the factors that favor the use of incentives. Without going into the mathematical details, the model shows that stronger incentives are called for if:

•The employee is less risk averse.

•The variance of measured performance is lower.

•The employee’s marginal cost of effort is lower.

•The marginal return to effort is higher.

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The model also shows that a firm’s profits are higher when there is less random variability in measured performance. When there is less variability, the firm can reduce its wage costs by paying a smaller risk premium for a given strength of incentives; it can also increase its revenues by using stronger incentives. Firms can reduce the risk that employees are exposed to by selecting performance measures that are subject to as little randomness as possible and investing in reducing the randomness in available measures.

PERFORMANCE MEASURES THAT FAIL

TO REFLECT ALL DESIRED ACTIONS

In the retail sales model developed earlier, the performance measure (sales) is a reasonably complete summary indicator of the various aspects of job performance. In other jobs, however, the available measures may not cover all aspects of job performance. Use of pay-for-performance incentives in this case will cause employees to focus on aspects of performance that are reflected in the measure and to neglect aspects that are not reflected in the measure. In Chapter 10 we called this multitasking.

A well-known example of multitasking is commonly called “teaching to the test.” We will use primary school teaching to illustrate the problem.14 Let’s think about dividing the various activities of teachers into two types: (1) activities that develop students’ test-taking skills and (2) activities that enhance students’ higher-order thinking skills. For skills like multiplication, reading comprehension, and spelling, it is easy to devise a standardized test to measure students’ progress. However, it is considerably more difficult to design a tool that assesses whether a student can reason effectively or think creatively. Hence, while both of these teaching activities build students’ ability to think, only the first can be measured effectively.

If teachers are rewarded on the basis of their students’ test scores, then they will devote more time to teaching test-related skills like multiplication. So far, so good. But if teachers have increasing costs of effort, when they devote more time to teaching multiplication, the marginal cost of making an effort to teach reasoning skills will increase. As a result, they will devote less time to the latter. If compensation is not at all tied to reasoning skills, then teachers will devote 100 percent of their effort to teaching test-taking skills. This reasoning is an application of the multitask principle developed in Chapter 10, which states that when allocating effort among a variety of tasks, employees will tend to exert more effort toward the tasks that are rewarded.

Our conclusion—that in the presence of test-based incentives teachers will allocate all effort toward test-taking skills—is clearly subject to a number of caveats.15 Most seriously, perhaps, we have ignored the fact that teachers self-select into their profession. A person who becomes a teacher is likely one who cares directly about student achievement. Such nonpecuniary benefits from student progress offer a counterweight to the pecuniary incentives derived from bonuses. Nevertheless, it is clear that the use of such test-based incentives will shift teachers’ effort choices in the direction of test-taking skills at the potential expense of reasoning skills.

A performance measure will sometimes reward activities that the firm does not want the employee to undertake. Consider the case of Lantech, a small manufacturer of packaging equipment based in Louisville, Kentucky.16 Hoping to increase productivity, the firm implemented employee bonuses based on the profits recorded by each of the firm’s five manufacturing divisions. The employees quickly discovered, however, that there is more than one way to increase a division’s profits. Increasing productivity is one, but fighting to have overhead charges allocated to other divisions