The Managerial Compensation Responding to Earnings Manipulation

Ruoyu Zhang** August 10, 2012

Abstract

When the true earning in each period is private information to the agent, then the performance based pay provides the agent with incentive to misallocate the earnings to get more compensation. To address the concern of earnings manipulation problem, SEC imposed a strict disclosure regulation in 1993. An optimal managerial contract should be designed not only to provide the agent with an incentive to take actions that enhance the actual profitability of the firm, but also to minimize the agent’s incentive to falsify earnings reports. This paper uses a two-period model to demonstrate that the compensation scheme contingent on reported earnings cannot provide the agent with the incentive both to maximize earnings and to report earnings honestly. In the optimal contract, the principal must still tolerate some degree of earnings management. In addition, with the increase of the misrepresentation penalty, the principal would rather lower the incentive to make the agent work less but report earnings truthfully.



I thank Professor Jean-Etienne De Bettignies and Professor Olena Ivus for valuable comments and suggestions. All errors are my own. ** MSc Candidate in Business Economics, Queen’s School of Business. Email: 11rz3@queensu.ca

Table of Contents
Abstract ........................................................................................................................................... 1 1. INTRODUCTION............................................................................................................................ 3 2. THE MODEL.................................................................................................................................. 7 2.1 Basic Setup ............................................................................................................................ 7 2.2 Information............................................................................................................................ 8 2.3 Contracting ............................................................................................................................ 8 2.4 Payoffs ................................................................................................................................. 10 2.5 Timeline ............................................................................................................................... 12 2.6 The First-Best Solution ........................................................................................................ 12 3. CONTRACT RESPODING TO ONE TYPE OF AGENCY PROBLEM .................................................. 13 3.1 Moral Hazard ....................................................................................................................... 13 3.2 Misrepresentation ............................................................................................................... 17 4. EARNINGS MANIPULATION ....................................................................................................... 19 4.1 The Agent’s Optimal Reactions ........................................................................................... 19 4.2 Contract Responding to Both Moral Hazard and Misrepresentation Problem ................... 22 4.3 Comparative Statics ............................................................................................................. 28 5. CONCLUSION ............................................................................................................................. 31 REFERENCES .................................................................................................................................. 32 APPENDIX A ................................................................................................................................... 34 APPENDIX B ................................................................................................................................... 41

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1. INTRODUCTION
In order to align the incentives of agents with the interest of the principal, a growing number of firms have adopted performance-based executive compensation in the late twentieth-century (Frydman, 2008). The advantage of performance-based pay is to encourage the agent to exert more efforts. However, accounting scandals of the early twenty-first century point to a darker side of performance-based compensation plans. A bonus plan provides agent with incentive to misrepresent the company’s true performance to benefit him/herself (Crocker and Slemrod, 2006). For example, agents may change the revenue and cost recognition method to achieve certain goals such as greater earnings per share (EPS) or low variance of EPS to enhance perceived performance. Hence, accounting data sometimes lead to financial statements that provide less relevant and less accurate information of actual financial performance (Healy and Wahlen, 1999). Earnings manipulation is possible when auditing is inadequate. If the regulator and the regulated organization do not have equal access to information (Baron and Besanko, 1984), then there is an opportunity for agents to manipulate earnings at will. The agent’s abuse of such reporting manipulation schemes as big bath restructuring charges and premature revenue recognition threaten the credibility of financial reporting (Healy and Wahlen, 1998) and have led to the Securities and Exchange Commission (SEC) imposing strict regulation on disclosure in 1993 1 . As a result, investigators in United States can now require detailed corporate proxy statements on the compensation of a company’s top executives, including the agent’s base pay, bonus pay, the value of stock options and etc. (Main, Bruce and Buck, 1996). This strict
1

SEC (1993) Securities Act Releases No. 6962 and No. 7009. 3

regulation is expected to eliminate the incentive for earnings manipulation to some degree. The traditional principal-agent model, such as the one presented in Holmstrom (1979), ignores a critical feature of the principal-agent relationship: if the agent privately possesses information of the firm’s true earning in each period and could falsify that information in his/her report to the principal, then the agent may manipulate the earnings allocation over periods to benefit him/herself. My paper will focus on the earnings manipulation problem between a principal and an agent. I will examine the managerial compensation scheme in an environment where the agent may manipulate earnings that affect the principal’s payoff. Because the principal bears the burden of punishment imposed by SEC if his/her agent falsely reports earnings, the optimal managerial contract should be designed not only to provide the agent with an incentive to take actions to enhance the actual profitability of the firm, but minimizes the agent’s incentive to falsify earnings reports. This paper characterizes the optimal bonus compensation contract and demonstrates that compensation schemes contingent on reported earnings do not provide the agent with the incentive both to maximize profits and to report those profits truthfully. Consequently, in the optimal compensation scheme, the principal’s payoff will be always less than the first-best level and some degree of earnings management must be tolerated. With the increase of the expected misrepresentation penalty, the principal would rather lower the bonus amount to make the agent works less but reports earnings truthfully, the optimal contract will provide decreased incentives to the agent, in an attempt to favor

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accurate performance reporting rather than effort exertion. We can therefore expect that if the principal’s penalty of agent misreporting tended toward infinity, in order to eliminate any temptation to misreport, the optimal contract should always be no bonus at all. However, if the expected penalty for misrepresentation is low, the principal will prefer the agent to exert a relatively high level of effort. Although the principal knows the agent may misreport excessively, the relatively low penalty for doing so may still be to the principal’s financial benefit. Many previous works empirically test the problem of agents’ earning manipulation. Stolowy and Breton (2004) define accounts manipulation as “the use of management’s discretion to make accounting choices or to design transactions so as to affect the possibilities of wealth transfer between two parties” (Stolowy and Breton, 2004). In their paper, accounts manipulation is divided into three categories. Manipulation affects the wealth transfer between the company and (i) society (political costs), (ii) funds providers (cost of capital) and (iii) its agents (compensation plans). In the first two categories, the firm’s agent manipulates the account for the firm. The underlying motivation could be the desire maximize reported income and minimize income variance (Moore 1973). Most papers examining account manipulation fall into these two categories. For example, Libby and Kinney (2000) examines the earnings management decision to minimize the cost of capital to meet analysts’ forecasts; Cormier, Magnan and Morard (2000) reveals that earnings manipulation problem is partly caused due to satisfying investors’ emphasis on dividends payment, and etc. The transfer between the firm owner and its agent is different from the transfer between the company and society or between society and fund providers. In this case, the
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agent no longer misreports performance for the firm and instead acts against the firm: the agent manipulates earnings only to benefit him/herself. Most past works in this area have empirically tested the manager’s misrepresentation behavior to either maximizing short term total compensation or changing of control, such as Holthausen, Larcker and Sloan (1995) and J. Gaver, K.M. Gaver and Austin (1995). One of the most famous papers in this area is Healy (1985). Healy (1985) shows that the agent of a firm has incentive to manipulate accounting policies to maximizing his/her own total compensation amount. The paper claims that agents are more likely to choose income-decreasing accruals when their bonus plans’ upper or lower bounds are binding, and income-increasing accruals these bounds are not binding. There are few papers that theoretically test the influence of manager’s misrepresentation behavior on compensation scheme 2 . My work is most close to the theoretical paper by Crocker and Slemrod (2007), which assumes that the firm’s agents are required to buy a certain amount of equity stake. Hence, the agent has incentive to always over-report firm performance in order to receive more compensation. Crocker and Slemrod (2007) use a one period model to characterize the optimal compensation scheme in responding to over reporting problem, while I am dealing with the earnings misallocation problem in a two-period setting, and examine the effect of misreporting penalty on the compensation scheme.

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There is a series of paper theoretically testing the coordination of financial reporting system (flexible: allows earning management, or inflexible: truth telling only) and contracting system in a principal-agent model, such as Evans and Sridhar (1996). But there are few theoretical papers testing the influence of manager’s misrepresentation behavior on compensation scheme directly.

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The paper proceeds as follows. In the next section, I outline the basic model setup and present the first-best solution. In section 3, I develop a model of managerial compensation in an environment in which an agent may take one type of hidden action that impacts in the principal’s payoff (either moral hazard or misrepresentation) and show how these cases reach the first-best condition. In section 4, I will examine the optimal compensation scheme in response to both moral hazard and misrepresentation problems and discuss the intuition behind the primary results. The final section concludes this paper.

2. THE MODEL
2.1 Basic Setup Consider the firm with the following properties. The principal of the firm hires an agent to implement a project and the agent generates earnings for the principal through that project. The agent faces a two-period employment horizon. Both the principal and agents are risk-neutral and maximize their expected payoffs. The agent has zero wealth. The actual earnings generated by the agent in period is denoted by Xi, .

The amount of earning generated is an increasing function of the effort level exerted by the agent. Assume , where ai ≥ 0 is agent’s effort level, and ε is a random

term which is uniformly distributed [-z, z], with z sufficiently small so that earnings is always greater than or equal to zero. The pdf of ε is
.

.

,

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2.2 Information Assume that the principal does not observe earnings in each period, but observes the total earnings over two periods. In other words, the agent could manipulate the earnings allocation over two periods, but the total earnings over two periods are fixed, and verifiable by the principal. The agent’s effort level is also unobservable to the principal. 2.3 Contracting Bonuses are a widely used form of incentive pay in firm organization 3 . The purpose of my study is to identify certain agency problems that organizations will face in practical life given a specific bonus plan setting. In this paper, I will establish a specific compensation scheme to address the agency problems. I will not explain whether bonus contracts are optimal or not; instead, I will assume a bonus contract form and derive the optimal contract within that contract space. The compensation scheme in this paper includes two parts: basic wage t and bonus Bi. The bonus in each period is based on the agent’s reported earnings Ri. The compensation in each period is denoted by Wi, summarized in the following graph: . The compensation structure is

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Many academic researches point to a growing use of bonus payments by organizations. A survey by the Hay Group reveals that many firms in the highly competitive high-tech industry have made annual bonuses a part of the compensation package for an increasing number of their employees. This study also predicts that firms in other industries are likely to follow suit and offer bonuses to employees at lower levels in the organization (Comp flash, 1985). A firm level survey by Joseph and U. Kalwani reveals that 72% of the firms in their sample report using bonus payments in their compensation plans3 (Joseph and U. Kalwani, 1998). Also, there are a lot of papers empirically testing the effect of bonus plan adoption, such as Healy (1985), Watts and Zimmerman (1978), Tehranian and Waegelein (1985), etc. 8

If the reported earnings generated in one period are below the bonus threshold, denoted by β, agent will only get the basic wage, which is t. If the agent generates earnings greater than the threshold β, then the agent will get basic wage t plus a bonus B. Thus, the compensation scheme can be expressed as:

, where i=1, 2

With this compensation structure, the agent will always have an incentive to manipulate earnings to get more bonus awards: for example, if the specified minimum target β is not met, the agent has an incentive to further reduce the current earnings by deferring earnings to the next period. By doing this, the probability of meeting target in the next period is higher. Or, the agent can also choose to over-report earnings in the first year in order to receive the bonus for that year, and make up the difference in the second year by underreporting. The key assumption in this paper is that the earnings amount in each period is private information to the agent, but the total earnings over two periods are verifiable by
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the principal. Thus, if the agent chooses to misreport earnings, this verifiability prevents the agent from further conducting other malfeasance behavior, such as underreporting earnings and then keeping the earnings for him/herself, or over-reporting earnings in the first period but not making up the difference in the second period, etc. The agent must make up the difference carried over to the second period by under reporting the exact amount he over reported in the previous year. That is R1 + R2=X1 + X2 must be satisfied. 2.4 Payoffs The principal’s objective is to maximize his profit by maximizing the total expected earnings over both periods net of compensation costs, while the agent attempts to maximize his total expected compensation net of effort costs over both periods. The return for the risk neutral agent is given by

where

is the cost of exerting effort in period i. In this paper, I assume . If the agent exerts no effort, the cost of effort is zero: . The cost

of effort

is an increasing function of ai: > 0.

> 0. The marginal cost of exerting

more effort is also increasing:

In this paper, I assume the principal of the firm faces a financial punishment imposed by Securities and Exchange Commission (SEC) if the agent is caught misreporting earnings. The cost to the principal of falsely reported earnings, including the expected value of any penalties imposed by the SEC on the principal, is The function is convex so that , , and . . The
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parameter

is the probability of being caught by SEC,

is the

difference between actual and reported earnings; and P ≥ 0 is the unit cash punishment. Both λ and P are exogenously. The given cost is increasing in the magnitude of the falsification d. If the agent correctly reports earnings, d=0 and the cost on the principal is zero. If the agent misreports in the first period, he must make up the difference in the second by misreporting the same amount; hence, the expected penalty over both periods is the same. Hence, for purpose of simplicity, in this paper, I assume the probability of being caught in period two is zero, which means the penalty on misrepresentation only counts once. This simplified setting yields the same inference since the only change is the penalty halved (see proof in Appendix B). The profit maximization problem for the principal can be expressed as below:

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2.5 Timeline

2.6 The First-Best Solution To offer a benchmark for future comparison, I first consider the case where there is no information asymmetry (no agency problem) between the principal and the agent. If there is no any information asymmetry between the principal and the agent, the contract can be designed based on the actual state, then first-best solution can be induced. Given that the actual earnings in each period are observable, the misrepresentation problem is nullified. The effort level exerted by the agent is assumed to be contractible. The contract must satisfy the participation constraint; i.e., in each state, it offers each agent at least the base utility, which is zero. Let [FB] be the principal's problem under full information: [FB]
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Subject to the binding participation constraint4: [PC] The solution to the maximization problem is:

Principal’s payoff:

Agent’s payoff:

RESULT 1. In the first best solution, (i)

, and (ii) the principal extracts

all rents from the agent, U=1, leaving the agent with the base utility, V=0.

3. CONTRACT RESPODING TO ONE TYPE OF AGENCY PROBLEM
3.1 Moral Hazard In this section, I consider the case where there is only a moral hazard problem. The earnings in each period are still observable, so the agent does not have the chance to misreport, but his/her effort level is private information to the agent. Since the effort level is unobservable now, in order to control the agent’s incentive, the principal could manipulate the value of β and B to motivate the agent to exert more effort. Let [PMH] denotes the principal's problem under moral hazard problem:

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The binding [PC] implies that the agent’s utility is always held at the base level, which is zero.

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[PMH]

As in the standard agency model in literature, the contract is subject to the following constraints: Incentive Constraint ensures that the contract maximizes the agent’s expected payoff. [ICPMH]

Participation Constraint ensures that the agent keeps working for the firm; the expected profits in each period have to be greater or equal to zero. [PCPMH] Limited Liability Constraint [LLPMH] Solve the maximization problem:

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The IC constraint [ICPMH] can be rewritten as

Taking

:

It is clear that in any solution to problem [PMH], [LLPMH] must be binding:
PMH

PMH

Substitute these two binding constraints (

and

) into the principal’s

objective function [PMH], we obtain the following explicit version of principal’s objective function, denoted as [ ]:

[ Notice that the principal’s objective function [

]

] is an increasing linear function of β,

so the principal could set the value of β as large as possible to get more rents, and the maximum value of β makes the [PCPMH] binding.

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Substituting the binding [PCPMH] into [PMH], we can get:

Principal’s payoff:

Agent’s payoff:

RESULT 2 If the principal faces ONLY a moral hazard problem, then

(i)

(ii) The principal extracts all rents from the agent, leaving the agent at base utility. The solution to [PMH] reaches the First-Best condition. Part (i) in RESULT 2 suggests that the optimal effort level in case [PMH] is equal to first-best effort level, and depends on the value of B. Consequently, the optimal effort
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level is increasing with the value of B: high bonuses motivate agents to exert more effort. The marginal effect on effort level is a constant with respect to B. In this particular problem [PMH], the solution reaches the first-best level. This result is due to my particular compensation structure setting: in my specified compensation structure, there are two variables that could be manipulated by the principal (the bonus amount B and bonus threshold β). Just as I showed above, the agent’s effort level depends on variable B only, so the principal could induce first-best effort level by offering enough incentive by adjusting only the bonus amount B. As for the other variable in the compensation scheme, β, the value of β does not affect the agent’s action, so the principal could manipulate the value of β to any value to benefit himself. When the value of β makes the PC constraint binding, the solution to the problem [PMH] reaches the first-best condition. 3.2 Misrepresentation In this section, I consider the case where there is only a misrepresentation problem. In this case, the effort level is no longer private information to the agent, but the earning in each period becomes unobservable, so the agent has a chance to misreport. Recall that, the motivation for the agent to misreport earning is to get more bonuses, so as long as the principal offers bonus to the agent, the agent will have incentive to manipulate the earning allocation over two periods. So in this case, the wise choice for the principal is to cancel the bonus award and offer the agent a flat wage t only. Since the agent’s effort level is now observable, the principal can sign upon effort level directly.

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The flat wage also leaves the agent with no misrepresentation incentive, so that the principal no longer needs to pay for agent’s misrepresentation behavior. Now let [PM] be the principal's problem under only misrepresentation problem: [PM] Subject to [PCPM] The solution is determined by binding [PCPM]:

Solve the maximization problem:

Principal’s payoff:

Agent’s payoff:

RESULT 3 If the principal faces ONLY a misrepresentation problem, then (i) It is optimal for the principal to cancel the bonus award and offer the agent a flat wage only. The solution to [PM] reaches the First-Best condition.

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4. EARNINGS MANIPULATION
In practice, both the agent’s effort level and earning in each period are unobservable to the principal. Consequently, an optimal contract between the principal and the agent should be designed not only to provide the agent with an incentive to take actions that enhance the actual profitability of the firm, but also to minimize the agent’s incentive to falsify earnings reports. In this section, I examine the optimal compensation scheme in response to both moral hazard and misrepresentation problems. In order to examine the influence of the agent’s misrepresentation behavior, we need to find out how the agent makes misrepresentation decision first, so in Section 4.1, I am going to show the agent’s optimal misrepresentation decision under different circumstances first, and in Section 4.2, I will show how the agent’s misrepresentation behavior affects the principal’s benefits. 4.1 The Agent’s Optimal Reactions If the agent has private information about the actual earnings in each period, he/she will manipulate earnings over two periods to benefit him/herself. Therefore, in this case, the actual earning in each period might be different from reported earnings .

Intuitively, if the first period earnings are high enough, greater than threshold β, it is always optimal for the agent to report β and to defer all extra earnings in the probability of meeting threshold earning in the second period. But if the first period earning is low, the agent could either under-report earning to zero or over report earning to β to maximize the expected total compensation over two periods.

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In order to examine the agent’s exact reaction under different circumstances, here I use backward induction: The first point of inquiry is to decide the agent’s reporting decision in period two. According to my assumption that total earnings over both periods are observable by the principal, the agent must report what he gets in the second period and the difference carried over to the second, which is R1 + R2=X1 + X2 must be satisfied. Therefore, the agent’s reporting decision in period two can be expressed as the following equation: IN PERIOD 2:

Now I assume function compensation in the second period is:

stands for expected value, hence the expected

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The second step in the backward induction is to look at the reporting decision for the first period. In the first period, we know the agent only has two options, either underreporting earning to zero ( ) or over reporting earning to β ( ), so the

compensation in the first period can be expressed as:

Hence, the total compensation over two periods would be:

The agent makes reporting decision to maximize his/her total compensation over two periods. The agent chooses the max of the two options. RESULT 45 (i) If , it is optimal for the agent to choose ; if ; if , it is

optimal for the agent to choose choosing from .

, the agent’s payoff will be the same in

RESULT 4 suggests that the agent’s reporting decision in the first period depends on the value of β. If the value of β is relatively low, the agent will choose then the agent will choose
5

; if β is high, . Consider the

. The boundary case is when

We can determine the agent’s optimal reaction by subtracting the two total compensation from each option one from the other.

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following situation: if the principal changes the value of β from a low level to a high level, then the agent will change the reported earnings from to to respond.

During this process, the compensation for the agent in the first period drops by B, but in the meantime, the earnings carried over to the second period increase the expected compensation in the second period by

Hence, if from

, that is ; if

, the agent’s payoff will be unaffected in choosing , the loss in the first period compensation exceeds the gives the agent

gain in expected compensation in the second period, so choosing more expected total return; if

, the loss in the first period compensation is less gives

than the gain in expected compensation in the second period, so choosing the agent better total return.

4.2 Contract Responding to Both Moral Hazard and Misrepresentation Problem So far I examined the agent’s reaction under different circumstances (when and when ), now it’s time to figure out how the principal would be affected by

agent’s misrepresentation behavior. Recall that the SEC imposed a financial punishment on the principal of the firm if his agent’s misrepresentation behavior is caught. The cost to the principal of falsely reported earnings is , where , and P ≥ 0.

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Now let [EM] denote the principal’s maximization problem under both moral hazard and misrepresentation problem: [EM] The optimal contract must satisfy the following constraints: [IC2EM]

[IC1EM]

[LLEM] [PCEM] Where

In the last section, I already showed the agent’s optimal reactions under different scenarios: If If , it is optimal for agent to choose , it is optimal for agent to choose

Anticipating the agent's reactions in both scenarios, now the principal can estimate how much his payoff will be if he imposes a high/low value of β. Subsequently, the

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principal can choose the β from either scenario that will maximize his own expected payoff. Let [EMB] denote the principal’s problem when β takes a relatively high value (i.e. ), and let [EMS] denote the problem when β takes a relatively small value (i.e. ). The detailed derivation for the solution to problem [EMB] and [EMS] are provided in Appendix A. Here I present the results directly. RESULT 5 If the principal chooses a high β ( ), for any value of z and λP, it is

always optimal for the principal to use the following compensation scheme, denoted by CEMB:

Consequently, the agent’s effort level will be:

Principal’s payoff: Agent’s payoff: If the principal decides to set a relatively high threshold β, the principal will expect the agent report zero in the first period. To respond the high β, the agent has two choices: the agent can both evenly spread his effort over two periods to receive bonus in the second period, or concentrate effort in one period and receive bonus in the other. In

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this paper, I assume the agent will concentrate his/her effort in the first period6. From the principal’s perspective, concentrated effort exertion is not preferred. Because the principal knows the agent will report zero earning in the first period, therefore, if the agent still generates a lot of earnings, the principal will face a high misrepresentation penalty. Hence, the principal’s contract should encourage the agent spread effort over two periods to save more on misrepresentation cost. Consequently, the principal lowers the bonus award B and also the threshold β to offer less effort incentive and narrow down the difference between actual and reported earnings. Although the agent will exert more effort if he/she chooses to concentrate effort in one period, the gains from relatively high effort exertion still not enough to cover the extra misrepresentation penalty (see appendix A for the detailed compensation schemes). We can also see that the effort level, bonus award and bonus threshold in responding to earnings manipulation problem are lower than the first-best level. The only explanation is the principal’s compromise for misrepresentation penalty. The optimal contract provides less effort incentives to the agent, in an attempt to favor truthtelling rather than effort exertion. RESULT 6 If the principal chooses a low β ( ), then the principal has two choices:

(i)

For any value of P and z that satisfies the following conditions:

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Here I assume the agent will concentrate effort in the first period. Actually, it is indifference for the agent to concentrate effort to either period, but the agent’s choice will affect the principal’s payoff. If the agent works hard in the first period but reports zero, the principal will face a high misrepresentation cost. However, if the agent concentrates effort in the second, there would be no misrepresentation problem. In this paper, I choose to consider the worse situation. Therefore I assume the agent exerting effort in the first period instead of exerting effort in the second period.

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It is optimal for the principal to use the following compensation scheme CEMS(i):

Then the agent’s effort level would be:

Principal s payoff: Agent s payoff: (ii)
Otherwise, it is optimal for the principal to use the following compensation scheme CEMS(ii):

Then the agent’s effort level would be:

Principal’s payoff: Agent’s payoff:

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If the principal decides to set a relatively low threshold β, then the principal will expect the agent report β in the first period. To respond the low β, the agent also has two choices: (i) the agent can evenly spread his/her effort over two periods and receive bonus in the first period, (ii) the agent also can denote a very high effort in the first period, high enough to generate enough earnings to receive bonus in both periods. When the agent spreads effort over two periods, the total effort exerted is higher than the effort exerted when the agent concentrates his/her effort in the first period. However, in the optimal contract in responding to the evenly spread effort, the bonus threshold is also high; therefore, if the agent spreads effort over two periods, the principal will face a high effort exertion, as well as a high or low misrepresentation penalty. Hence, the agent’s evenly spread efforts do not necessarily make the principal better off. Regardless which compensation scheme the principal chooses, the effort level, bonus award and bonus threshold responding to earnings manipulation problem are also lower than the first-best level due to the principal’s compromise for misrepresentation penalty. Contracts tend to provide less effort incentives to the agent, in an attempt to favor truthtelling rather than effort exertion. As we can see from RESULT 5 and RESULT 6, the principal’s payoff will be always less than the first-best level7, which means the principal is worse off if he does not have enough observability regarding the agent’s effort level and true earnings in each period. However, the principal’s payoff under compensation scheme CEMB, CEMS(i)

7

Here I assume the value of z is sufficiently small. In particular,

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and CEMS(ii) is still different, the principal can choose the one with relatively high payoff. RESULT 7 In this particular model setting, for any values of z and λP that satisfy the condition: It is optimal for the principal to use the compensation scheme CEMB, otherwise, it is optimal for the principal to use the compensation scheme CEMS(i).8 4.3 Comparative Statics The principal’s objective is to choose the compensation scheme which gives the best payoff for himself. We already showed that the principal tends to provide less effort incentives to the agent to encourage truthtelling rather than effort exertion, so the main tradeoff for the principal is between the loss on expected earnings generated and the saving on misreporting penalty. In this section, I examine how the misrepresentation penalty λP affects the contract and the principal’s payoff. RESULT 8 Regardless of which compensation scheme the principal chooses (CEMB or CEMS(i)) the comparative statics are the same9:

(i) (ii) (iii) (iv)
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For any value of z and λP , the principal’s payoff under CEMB is always greater than the payoff under CEMS(ii). So the principal’s choice is between CEMB and CEMS(i). 9 Here I assume the value of z is sufficiently small. In particular,

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(v)
According to RESULT 5 and RESULT 6, we could derive the according expected amount of earnings the agent is going to misreport under the compensation scheme CEMB and CEMS(i):

Hence, with the increasing expected financial penalty, the principal will narrow the difference between the expected actual earning and reported earning to avoid some costs by inducing proper effort level .

The comparative static (ii) also suggests that the optimal effort level in the presence of misrepresentation and moral hazard problems is always decreasing with the expected unit financial penalty λP. If the value of λP is equal to zero, then the effort level in the presence of misrepresentation reaches the first-best level.
10

Therefore, we can

conclude that if the expected financial penalty is high, then the compensation scheme will induce ‘lazy’ but relatively honest agent; if the expected financial penalty is low, the agent will work hard but misreport a lot at the same time.

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In compensation scheme CEMB,

, the effort level decreases with λP and equal to , since I

one when λP=0. Similarly, in compensation scheme CEMS (i),

assumed that the value of z is sufficiently small (z