Incentive Contracts, Optimal Penalties And Enforcement*

Incentive Contracts, Optimal Penalties and Enforcement* by

Joshua Gans University of Melbourne First Draft: 13 August, 1997 This Version: 22 January, 1998

This paper re-examines the literature on optimal penalties and the allocation of resources to enforcement from the viewpoint of incentive theory. It is assumed that an agent might perform a socially harmful act. In contrast to previous analyses, the agent might also perform profit enhancing actions for the principal. The principal cannot distinguish between the good and harmful acts, but can set incentives based on observed profits. When the agent is wealth constrained, it is demonstrated that it is optimal to hold the principal liable for the agent’s actions and to set the optimal penalty equal to expected harm caused. This is because the imposition of high penalty levels causes the principal to dilute incentives for the agent, resulting in a reduction in productivity. The same logic also means that it optimal to devote some resources to enforcement and to impose penalties on both principal and agent if that is feasible. Journal of Economic Literature Classification Numbers: K14, K42. Keywords: optimal penalties, law enforcement, agency theory, incentive contracts, vicarious liability.

*

I thank Rohan Pitchford, Bob Officer and Philip Williams for helpful discussions. Responsibility for all views expressed remain my own. Please forward any comments to Joshua Gans, Melbourne Business School, 200 Leicester Street, Carlton Victoria 3053, Australia; E-mail: [email protected]. The latest version of the paper is available at http://www.mbs.unimelb.edu.au/home/jgans.

2 When some socially harmful act might be undertaken by an economic agent, the imposition of penalties can potentially deter such activities. If the action has no redeeming consequences, it is usually argued that the optimal penalty should reflect the benefit the agent receives from the socially harmful act. On the other hand, when the action has a redeeming side, the optimal penalty should reflect the magnitude of the harm imposed on others. This usually arises in cases concerning the level of care employed to prevent a harmful accident. As care is costly, too high a penalty might lead to too much care being taken. In antitrust cases, it is possible that anti-competitive behaviour might allow a cartel or firm to engage in investments to reduce production costs. In situations in which the social consequences of an action are ambiguous, the logic applied to penalties is that same as the Pigouvian logic applied to externalities. The penalty should force the agent to internalise the potential social harm thereby alligning private and social interests. In this paper, I present an analysis of a set of situations in which an act might unambiguously result in a social detriment but that the principle that expected penalties should equal actual harm is optimal. These situations are those where the act is committed by an employee or agent of a corporation but where some decisions are in the hands of the agent because they either possess superior information or, alternatively, their effort allocation is difficult to observe and verify.

That is, they involve principal-agent

relationships. The rationale is as follows: in these environments, if there were no penalties imposed, a principal might optimally write an incentive contract with the agent that bases their expected pay on observable performance measures such as divisional profit. The agent would then be free to pursue profit by any means they would find optimal. This could involve “good” activities such as cost reductions or product innovation, or, alternatively, “bad” activities such as anti-competitive acts or environmental pollution. When the principal is liable for the “bad” activities of its employees, however, the observable measure, such as profit, does not reflect the actual measure that the principal might wish to base their activity on, such as profit less expected penalties. As a result, if

3 they are liabile for damage caused, the principal might choose to lower the power of incentives in general so as to reduce the probability that they incur the penalty. Thus, higher penalties are associated with a social cost in that incentives for “good” activities are reduced. The optimal expected penalty is for the principal to pay an amount equal to the harm caused. This is because, while the act under scrutiny is a pure social bad, controlling the act has the side effect of reducing incentives for, potentially unrelated, socially beneficial acts. This result complements the literature on vicarious liability (Sykes, 1981; 1984). Like the present paper, that literature views agents as wealth constrained and hence, somewhat judgment proof. It then asks whether principals should be vicariously liable for the level of harm caused. Newman and Wright (1993), Pitchford (1996) and Shavell (1997) all note that vicarious liability can result in a distortion of incentives. In each of these papers, agents can undertake socially harmful acts while principals can provide incentives based on the level of harm caused. Hence, in those models, optimal penalties may be above or below the level of harm caused. In the model below, incentives are based on profits and hence, could motivate beneficial as well as harmful acts. In this situation, the optimal penalty on the principal is equal to the expected level of harm. The model below also allow the agent to face some sanction as a result of the harm being caused. Initially, the sanction is non-monetary while in a later section, an actual fine is imposed (subject to the agent’s wealth constraint). It is demonstrated that both principal and agent penalities are optimally set equal to expected harm. This is because each is taking actions that influence the probability of harm. In particular, if only the agent is liable for harm, the principal will create more incentives for the agent to undertake the harmful act. Hence, it is optimal to hold both the principal and agent liable. This stands in constrast to results of Polinsky and Shavell (1993) who show how the use of state imposed sanctions on the agent (such as imprisonment) can compensate for some of the incentive distortions

4 caused. They argue that sanctions on the agent reduce the need for principal liability. Once again, this is because the socially harmful action is the only one undertaken by the agent. This perspective is also informative for the literature on the optimal enforcement of harmful acts. When enforcement costs are taken into account, it is often argued that the optimal penalty structure is to set penalties equal to the wealth of the individual concerned. This economises on enforcement resources. The basic reasoning is that agents are deterred from an activity if their expected penalty exceeds the net benefit they receive. However, having determined this expected penalty, a government concerned about enforcement costs can always achieve this sanction by raising the actual penalty while lowering enforcement costs and the probability that an offense is detected and an individual punished (Becker, 1968). In reality, however, actual penalties rarely come close to an agent’s wealth. Therefore, research has been directed towards trying to explain why the optimal penalty structure might involve greater enforcement effort and a lower penalty. Stigler (1970) introduced the concept of “marginal deterrence,” that argued that if all penalties for all acts were high, an individual contemplating committing a less harmful act might be tempted to escalate harm given that this may raise their benefits without lower their expected costs.1 Polinsky and Shavell (1979) argued that risk aversion was the key to the puzzle. A risk averse agent, contemplating commiting a harmful act, takes into account the uncertainty surrounding being caught. A more uncertain but higher sanction, therefore, imposes more costs (in terms of utility) on them compared with a more certain but low sanction. Hence, the social planner, who takes into account the utility of all agents and the costs of enforcement, might choose a high enforcement effort and lower penalty so as to improve the social allocation of risk bearing. Polinsky and Shavell (1991) also argue that when 1

This effect has found modern expression in recent objections to the “three strikes” policy in the U.S.. It is argued that this policy has resulted in greater enforcement costs, as alleged criminals who might face mandatory life imprisonment for a relatively mild marginal crime, drug possession, will expend as much effort in avoiding being caught as those accused of more harmful acts such as murder. The result is an increase in costly activities such as high speed police car chases.

5 individuals differ in their wealth, the optimal penalty might be lower than the wealth of some individuals at the expense of greater enforcement effort.

This is because lower

enforcement effort saves the costs of deterring high wealth agents but actually raises the incentives of lower wealth individuals to act inappropriately. Finally, Shavell (1991) argues that while the original Becker style logic holds for specific enforcement effort (e.g., issuing parking tickets), it does not hold when enforcement effort is general (e.g., a police force). With general enforcement effort, the probability of detection is the same for more and less harmful acts, therefore, the less harmful acts do not require as extreme sanctions. The result that, if enforcement is a costly activity, expected damages should be composed of a high penalty and low enforcement level, is no longer true in the principalagent environment of this paper.

When agents are wealth constrained, in that their

appropriable wealth is less than the level of social harm they could cause, lowering the probability of detection reduces their incentives to refrain from socially harmful profitmaking activities. Hence, the principal is forced to reduce their overall incentives to compensate. Thus, even though the expected penalty might remain the same, the principal is concerned about the intensity at which the agent might engage in the harmful act and hence, will lower incentives overall. This, in turn, reduces the level of effort toward socially beneficial profit-making outcomes. The social planner takes this into account when choosing the level of enforcement and hence, chooses a high enforcement level when the costs of so doing are relatively low. These results are presented using a very simple principal-agent model, based on Baker (1992). That model is based on a distinction between performance measures that more or less reflect the principal’s objective. Since there is a distinction between what the principal cares about when it is liable for an agent’s acts and the measurable performance of the agent, this represents an appropriate framework to cast the main issues of the paper. The basic model is introduced and analysed in section I. Section II then turns to consider the effect of allowing costly monitoring by the principal of the agent’s activities. Section

6 III then looks at the optimal structure of penalties when fines can be imposed both on the principal and the agent. A final section concludes.

I.

Incentive Contracts and Principal Liability Suppose that an agent engages in effort that can improve division profit, π, the level

of which is observable and verifiable. Effort can increase profit through two sorts of activities -- cost reduction (e) and socially harmful behaviour (a).

Suppose that the

principal cannot observe what sort of activities generated any realised profit.

That is,

profits are determined by: e+a 1 π (e, a) =  with probability 1− e − a 0 The principal observes the realisation of profits but not its source. Action a will, with probability a, realise a social bad of value H > 1 while no social harm comes from additional effort, e. Agent effort cost is quadratic and separable in the two effort types, i.e., c(e, a) = γ 12 (e 2 + a 2 ) . The agent’s reservation utility is u . As in Baker (1992), attention is restricted to linear wage contracts. The agent receives a base salary, α. In addition, the agent receives a bonus, β, if profits are 1 and 0 otherwise. Therefore, the agent chooses a and e to maximise (e + a)β − γ 12 (e 2 + a 2 ) , which yields: e* =

β γ

and a* = γβ . The principal adjusts the base salary, α of the agent so

that the agent’s expected utility equals u . Taking this into account the principal chooses β to maximise: Π(α , β ) = ( a* + e* ) − γ

1 2

(a

*2

)

+ e* − α . Under these assumptions it can be 2

readily shown that the principal will choose β * = 1 and α * = u − γ1 . The contribution of this paper is to consider how these chosen incentives change when the principal is potentially liable for the harm the agent causes. Initially, I assume

7 that the agent does not have any verifiable wealth that can be appropriated by the social planner in the event it detects socially harmful behaviour. The principal, however, does have sufficient wealth and so it is possible for the planner to impose a penalty on them. The interesting question concerns what amount, if any, the planner will extract from the principal if it catches the agent engaging in the socially harmful activity. It is assumed that the social planner, like the principal, cannot actually observe a. However, if the social bad occurs, the planner can, with probability σ , detect the agent’s harmful activity and attribute it to them. The principal can, in that event, receive a penalty of F. In order to determine the (socially) optimal penalty, I work backwards, considering the principal’s incentive policy for any given σ and F. As the agent cannot be held liable for socially harmful activity, their effort choice problem is unchanged and they choose e* =

β γ

and a* = γβ . The principal, however, takes into account the possibility of receiving

a fine when it determines the agent’s incentives (α, β). Now the principal maximises: Π(α , β ; F ) = ( a* + e* )(1 − β ) − a*σF − α , subject to the agent’s participation constraint that ( a* + e* )β − γ

1 2

(a

*2

)

+ e* + α ≥ u . In 2

this case,

β * = 1 − 12 σF and α * = u − γ1 (1 − 12 σF ) . 2

Incentives are muted relative to the situation in which the principal is not liable for the harm caused by the agent. However, while this reduces the level of the socially harmful activity (a) it also reduces beneficial cost reduction (e). The planner will take into account the effects of the penalty on firm profits as it wishes to maximise social surplus and not simply minimise the probability of the harmful act. It, therefore, chooses F to maximise:

8 V ( F ) = ( a * + e* ) − a * H − γ

1 2

(a

*2

)

+ e* . 2

As α is determined entirely by the participation constraint, the only difference between the government’s objective and the principal’s is what they suffer as a result of the social harm actually being realised. The planner suffers the social harm, H, while the principal only suffers σ F. Therefore, by setting F * = H / σ , the government can make the principal’s objective identical to its own. This is the optimal penalty as it forces the principal to internalise the external harm in setting incentives for the agent. Notice that this is not a first best outcome. The social optimum involves a* = 0 and e* = γ1 .

However, given that the agent’s actual effort choices are not observable,

incentives are distorted to reduce the probability of social harm. As a result, even with an optimal penalty, too much of the socially harmful activity and too little of the socially beneficial one are undertaken relative to the first best. The key point here is that in situations in which the principal is held vicariously liable for the actions of its agent, the optimal penalty, even for purely socially harmful acts, should reflect the level of harm caused rather than the benefit the principal receives. So the penalty structure is more akin to Pigouvian thinking on externalities than the use of penalties to simply deter behaviour.

II.

Incentives and Optimal Enforcement In the previous section, the probability (σ) that the socially harmful activity was

actually detected by the planner was held fixed. However, it is possible that this might be increased by devoting more resources to enforcement. As noted earlier, the conclusion of the previous literature on optimal enforcement focused on the basic result that enforcement effort should be as low as possible. That is,

9 given that the optimal penalty always equals expected harm divided by the probability of detection, one could achieve any given penalty with less resources devoted to enforcement. This result also applies to the model presented in section I where the optimal penalty was shown to equal H/σ . Given this, a change in σ has no effect on the incentive contract chosen by the principal. Hence, reducing enforcement effort, i.e., lowering σ , achieves the same social outcome while economising on enforcement costs. In this section, I demonstrate that this conclusion relies on the assumption that the agent suffers no cost if social harm is detected by the government. In reality, however, this is not a reasonable assumption. Even if the principal themself cannot extract any wealth from the agent, the government can. Indeed, further costs in terms of imprisonment or restrictions on future employment could substitute for a lack of verifiable wealth. As such, it is likely to be the case that the agent suffers some cost if there is a judgement brought against the principal. To consider the effect of this, suppose that the agent bears a cost, c, if the principal is held liable for their socially harmful act. This involves an implicit assumption that the principal can commit to imposing these costs in the event the harmful act is detected. Not surprisingly, this possibility causes the agent to undertake less of the harmful act. That is, the agent maximises (e + a)β − aσc − γ 12 (e 2 + a 2 ) resulting in choices of a* =

β − σc γ

and

e* = γβ . Substituting the agent’s new participation constraint into the principal’s problem, i.e., with α * = u − ( a* + e* )β + a*σc + γ

1 2

(a

*2

)

+ e* , the principal chooses β to maximise: 2

Π( β ; F, σ ) = ( a* + e* ) − a*σ (c + F ) − γ

1 2

(a

*2

)

+ e* − u . 2

This yields β * = 1 − 12 σF . This is the same level of incentives as chosen earlier (see Section I). The fact that the agent now faces some costs from the socially harmful act does

10 not concern the principal. They are concerned only about the penalty they face and hence, take this into account when setting overall incentives. Turning to the planner’s problem, as c represents real resource costs, it must take them into account when choosing its penalty and enforcement policies. Let λσ 2 be the costs of choosing an enforcement level, σ. The planner chooses F and σ to maximise: V ( F, σ ) = ( a* + e* ) − a* ( H + σc) − γ

1 2

(a

*2

)

+ e* − λσ 2 , 2

as c are only incurred if the harmful act is detected. For this case, the optimal policy becomes:

[

F * = max H , HH−1 2γλc− c

2

] and σ

*

[

]

( H − 1) = min 1, 2cγλ , −c2

assuming that 2γλ > c 2 . In effect, the optimal penalty is set according to the same principle as in Section I, i.e., F * = H / σ . What differs is that σ is now a variable and, indeed, is not set as low as possible.2 This is because while the magnitude of the penalty has only an indirect effect on agent incentives, the enforcement level has a direct effect. A higher enforcement level reduces the agent’s incentives to undertake the harmful activity. Hence, despite the fact that the planner is concerned about the level of the agent’s punishment, it still chooses to engage in a positive and perhaps high level of enforcement. This directly reduces the probability that the social bad occurs.

III

Penalties for the Agent In the previous section, it was assumed that the agent suffered a socially costly

penalty as a result of being detecting undertaking the harmful act. In this section, the question of agent penalty is considered in greater detail. Here we suppose that the agent 2

It is worth noting that if the social planner did not care about the agent’s cost, c, then the optimal policy

[

would be F = max H , *

4 γλ c

] and σ

*

[

]

= min 1, 4 γλcH+ c . 2

11 has a verifiable wealth, w , that can be appropriated by the social planner in the event the harmful act is detected. This is done by the government imposing a penalty of f on the agent. Here I will consider what the optimal penalty policy is when this is possible. That is, what penalties are imposed on the firm in this instance and what level of enforcement is chosen? When a fine of f is imposed on the agent, its chooses effort levels to maximise: ( a + e)β − γ

1 2

(a

2

+ e 2 ) − aσf , which results in e* =

β γ

and a* =

β − σf γ

. Taking into account

the participation constraint, the principal maximises expected profit as before. This results in β * = 1 − 12 σ ( F − f ) . Note that the existence of direct penalty on the agent allows the principal to increase incentives. Indeed, if F were 0, β would exceed 1, the level chosen in the absence of any penalties. It will be demonstrated below that this feature means that, even in the absence of binding agent wealth constraints, imposing some penalty on the principal is socially optimal. In this environment, the social planner chooses f, F and σ to maximise: ( a * + e* ) − γ

1 2

(a

*2

)

+ e* − a* H − λσ 2 . 2

As penalties are transfers only, they do not enter directly into the planner’s problem. With this it is straightforward to show that: H H f * = min  , w  and F * = . σ σ  That is, both the principal and the agent are penalised an amount such that the expected penalty equals the expected harm; i.e., the Pigouvian solution. If this amount exceeds the agent’s wealth, then the penalty is capped. However, this does not alter the penalty on the principal. The intuition behind this result is as follows. It is probably easiest to compare the situations of no principal liability and no agent liability respectively. In the former case, the penalty imposed on the agent is still proportional to expected harm. Such a policy forces

12 the agent to internalise the social costs of their actions. As noted in section I, the same is true for the no agent liability case. In that situation, the penalty forces the principal to internalise social costs when setting incentives. Because the agent is still choosing the level of a and the principal is still setting incentives, when they are both liable, the optimal penalty is the same way as when only one is liable. What level of enforcement will the planner choose in this environment? If w is infinitely high, the Beckerian logic applies and the enforcement level is set arbitrarily close to zero. This is because both the principal and agent are forced to internalise the social consequences of their actions and hence, the planner saves on enforcement costs by raising the penalty arbitrarily high. In general, however, the level of penalties will be constrained by the agent’s wealth. In this case, f * = w , so that: F* =

w 2 + 4γλ wH and σ * = 2 . w w + 4γλ

If the planner reduces enforcement levels, they alter the principal’s decision regarding the level of incentives given to the agent. However, this now reduces the agent’s incentives to refrain from the harmful act. As a consequence, the principal would be forced to dampen the agent’s incentives by a greater amount than would be socially optimal.

IV

Conclusions When socially harmfuls acts are committed by employees of a firm, it is often the

case that that firm is responsible for setting incentives for that employee to engage in profit enhancing activities. This paper has demonstrated that, when the incentive setter cannot distinguish between profits generated by “good” or “harmful” acts, there is a cost associated with setting penalties simply to deter harmful acts. High penalties imposed on a firm might cause it to dilute incentives for profitable activities and hence, might be socially

13 costly. In such situations, it was demonstrated that the optimal penalty should be set equal to the expected level of harm.

This would force the firm to internalise the social

consequences of incentive contracts and hence, result in a second best outcome for society (the first best being precluded by the information asymmetry between the firm and its employee). While a specific model was used in this paper, this principle would carry over into more general structures. Looking at penalties from this perspective has implications for many aspects of penalty setting. These include the level of resources devoted to resources and the interaction between penalties imposed on a principal and those imposed on its agent. In contrast to previous results, we found that the rationale for imposing liability on principals is independent of whether liability is, or should be, imposed on agents. This is because principals’ incentive setting decisions will always influence agent choices as to whether they engage in harmful acts. If there are agent wealth constraints, then these effects will be to the detriment of society.

14

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