Incentive Contracts, Optimal Penalties And Enforcement

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Incentive Contracts, Optimal Penalties and Enforcement by

Joshua S. Gans University of Melbourne First Draft: 13 August, 1997 This Version: 31 January, 2001

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. In this circumstance, it is always 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.

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I thank Stephen King, Rohan Pitchford, Bob Officer and Philip Williams and two anonymous referees for their helpful comments. Responsibility for all views expressed remains my own. Please forward any comments to Joshua Gans, Melbourne Business School, 200 Leicester Street, Carlton Victoria 3053, Australia; E-mail: [email protected].

2 This paper considers the optimal level and configuration of penalties and optimal degree of enforcement in situations where harmful acts are committed by people who act as agents for a principal. For instance, the agent might be an employee of a corporation who does not take sufficient care in preventing environmental or consumer harm. Or, alternatively, the agent might be a divisional manager who engages in anti-trust violations. A previous literature on penalties in the context of principal-agent relationships has confirmed that many of the conclusions of the optimal penalties literature apply in this situation. This includes the results that penalties for unambiguously harmful acts should be set equal to the benefit the principal and agent receive from the socially harmful act and that it is better to raise penalties in order to economise on enforcement expenditures (Posner, 1977; Garoupa, 1997; Polinsky and Shavell, 2000). But that literature goes further. First, it has been demonstrated that, whe n agents are wealth-constrained, penalties should be imposed on the principal who would impose internal sanctions on the agent, making the penalty effective (Sykes, 1981, 1984). In addition, if a non-monetary penalty (such as imprisonment) can be imposed on the agent this would reduce the penalty that would need to be imposed on the principal (Polinsky and Shavell, 1993). In this paper, I challenge each of these conclusions by examining a principal-agent relationship where the principal can observe profits but cannot observe the precise source of those profits. That is, profits might arise from “good” activities such as cost reductions or product innovation, or, alternatively, “bad” activities such as anti-competitive acts or environmental pollution. This imperfection in information differs from the previous literature that concentrated solely on the principal’s information regarding the agent’s choices that might impose social harm.

3 In this environment, in the absence of penalties, a principal will write an incentive contract with a wealth-constrained agent based on profit (an observable measure). Consequently, the agent will endeavour to maximise this by any means – including harmful as well as socially beneficial acts. The previous literature suggests that one should impose a penalty on the principal in this situation equal to the benefit they would receive in profits from the socially harmful act. This would motivate the principal to alter the terms of the incentive contract in a way that causes the agent to refrain from that act. However, in this environment, this creates an additional, social cost in that the way in which the principal reduces the agent’s incentives for ‘bad’ actions also reduces its incentive to undertake good actions introducing an additional social cost to the imposition of penalties. As such, it is better to apply a Pigouvian logic to penalties – setting them equal to expected social harm – rather than for complete deterrence as would normally be the case for acts that are unambiguously socially detrimental. 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. Forcing the principal to internalise the only social harm also motivates them to restructure the agent’s incentives in a socially desirable manner. To do otherwise may cause the principal to be too aggressive in reducing the agent’s overall incentives or perhaps removing the agent’s right to undertake desirable activities altogether (i.e., through an organisational restructure).1

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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), Arlen (1994), 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 wh ile 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.

4 This perspective is also challenges existing conclusions on the optimal enforcement of harmful acts. When enforcement costs are taken into account, Becker (1968) has argued that the optimal penalty structure is to set penalties equal to the wealth of the individual concerned. This economises on enforcement resources.2 This result is no longer true in the principal-agent 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 profit-making 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 profitmaking 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. The model below also allows the agent to face some sanction as a result of the harm being caused. When a fine can be imposed on the agent, it is demonstrated that both principal and agent penalties 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 contrast to

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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 offence is detected and an individual punished (Becker, 1968). In reality, however, actual penalties rarely come close to an agent’s wealth. Previous analyses

5 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 caused. They argue that sanctions on the agent reduce the need for principal liability. Once again, this is because, in their model, the socially harmful action is the only one undertaken by the agent. These results below 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 demonstrating that when the principal has complete information and agent effort is contractible, standard results on penalties hold. Section II then turns to consider the implications of incomplete information and incentive contracts based on realised profits. It is demonstrated that each of the standard results does not hold with this change in the environment. A final section concludes and offers directions for future research.

I.

Penalties Under Complete Information

To begin, I consider a first best case where the principal can observe the level and type of effort undertaken by the agent. In particular, the agent can engage in two sorts of

have focussed on difficulties in distinguish among different crimes and wealth levels of individuals as well as the role of risk aversion. See the surveys of Garoupa (1997) and Polinsky and Shavell (2000).

6 activities – cost reduction (e) and socially harmful behaviour (a). More of each type of effort can increase divisional profit according to the following stochastic equation:

e+a 3 1 π (e,a) =  with probability 1−e− a 0 In addition, action a will, with probability a, realise a social bad of value H (> 1) while no social harm comes from additional effort, e. Finally, it is assumed that agent effort cost is quadratic and separable in the two effort types, i.e., c(e,a) = γ 12 (e 2 + a 2 ) .4 Moreover, as in Baker (1992), the agent is assumed to be risk-neutral. The agent’s reservation utility is u and competition among agents ensures that, in equilibrium, its expected payoff is driven to this. In the absence of any penalties, the principal will contract with the agent so that the agent expends effort levels eˆ and aˆ that solve:

max{e ,a } π (e ,a) − c(e ,a ) or max{e ,a} e + a − γ 12 (e2 + a2 ) . This yields: eˆ = aˆ = γ1 .5 This contrasts with the social optimum of e* = γ1 and a * = 0 that solve: max {e ,a } π (e , a) − aH − c (e ,a ) or max {e ,a } e + a (1 − H ) − γ 12 ( e2 + a2 ) .

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The idea that profits take on two discrete values only is a simplification designed to economise on technicalities (as in Baker, 1992). The model here can easily be generalised to the more conventional case where each type of effort shifts the distribution of realised profits (see Athey, 2001). 4 The specification here assumes that the agent incurs positive costs in undertaking the socially harmful action. Once again, this assists in economising on notation although it is not unreasonable to expect that an agent’s time to undertake both types of activities is limited. Nonetheless, even if a does not explicitly give rise to private costs for the agent, so long as the probability of social harm generated is bounded below one, all of the qualitative results to follow will apply for this case. 5 Where, of course, the agent is paid at least α = u + 1γ to compensate them for their costs and outside opportunity.

7 Notice that, in the absence of any penalty for social harm caused, the private level of the good activity (e) equals its social optimum while too much of the socially harmful activity (a) is undertaken. The planner’s problem is to determine a policy towards penalties that improves social welfare. It is assumed that the social planner 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. In this instance, the planner could impose penalties, f and F, on the agent and principal respectively. This transforms the principal-agent contracting problem to:

max{e ,a} e + a(1 − σ ( f + F )) − γ 12 ( e2 + a2 ) with solutions eˆ =

1 γ

and aˆ =

1−σ ( f + F ) 6 γ

. Therefore, so long as, f + F = 1/ σ , the socially

optimal levels of both types of activities are implemented. So, as in standard models of penalties, the sum of the expected penalties on the principal and agent is set just high enough to ensure that the harmful activity is completely deterred; this is optimal given that a is purely socially harmful. Notice also that this means that penalties on the principal and agent are perfect substitutes; that is, it is the total penalty that matters.7 Finally, suppose that the planner can choose the level of enforcement activity – for example, to choose a probability (σ ) has social costs of λσ 2 . In this case, the logic of Becker holds and that probability should be set as low as possible; consequently, raising the expected penalties on the principal and agent. In summary, when the principal can observe the agent’s effort choices, all of the standard results of the economic literature on penalties continue to apply. That is, penalties

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If any penalty is imposed on the agent, the principal must pay the agent at least α = u − σγ (1 + ( f + F )(1 − σ − σ 12 ( f + F ) ) to satisfy their participation constraint.

8 are set to deter the socially harmful activity, the penalties on the principal and agent are substitutes, and the level of resources devoted to enforcement should be kept low and the imposed penalties are raised in turn. In the next section, this benchmark case is compared to the situation where the principal cannot observe the agent’s effort allocation. It is demonstrated that this small change alters each of the standard results presented above.

II.

Incentive Contracts and Optimal Penalties

Suppose now that the principal, like the social planner, cannot directly observe the agent’s allocation of effort. However, division profit, π , remains observable and verifiable. In this situation, the principal can set the agent an incentive contract based on the realisation of profit rather than directly contracting for a given level of effort. 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. I continue to assume that the agent and principal potentially face fines if social harm is realised and it is enforced. In

(a + e)β − γ

this 1 2

(a

situation, 2

the

agent

chooses

effort

levels

to

maximise:

+ e2 )− aσf , which results in eˆ = βγ and aˆ = β −γσ f . 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 ) = eˆ + aˆ (1− σ ( f + F )) − γ

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1 2

(eˆ2 + aˆ 2 )− u

Such substitutability is in line with traditional intuition regarding penalties (see Polinsky and Shavell, 1993).

9 This results in β * = 1 − 12 σ (F − f ) . Note that in that absence of any penalties, the incentive intensity chosen for the agent is β * = 1 . Moreover, 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. As is demonstrated below, this means that imposing some penalty on the principal is always socially desirable; regardless of whether penalties can be imposed directly on the agent or not. The social planner takes into account the impact of penalties on the incentive contract set by the principal. Hence, it chooses f, F and σ to maximise: V = eˆ( β * ) + aˆ( β * )(1 − H ) − γ

1 2

( eˆ( β

) + aˆ ( β * )2 ) − 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 f * = F * = H / σ . That is, both the principal and the agent are penalised an amount such that the expected penalty equals the expected harm. The intuition here is that a penalty designed to completely deter the harmful action carries an additional social cost – that of dampening the principal’s incentives for the agent to undertake good actions. Hence, there exists an optimal set of penalties, balancing the benefits of reducing the probability of social harm and the costs of reducing desirable profit making activities. There are several additional things to note about this outcome. First, it 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.

10 Second, consider a situation where only the principal can be held liable for the harm done. In these situations of vicarious liability, the optimal penalty, even for purely socially harmful acts, should reflect the level of harm caused rather than the benefit the principal receives. So, in contrast to traditional results in the literature, the penalty structure is more akin to Pigouvian thinking on externalities than the use of penalties to simply deter behaviour. Finally, notice that both the principal and the agent have penalties imposed that are unrelated to each other. To see this more clearly, suppose that the agent has limited but verifiable wealth, w, and hence, f ≤ w . Then it is easy to show that under this constraint the social planner continues to set F * = H / σ while f * = min[ w, H / σ ] . Hence, setting the principal’s penalty is always desirable as it forces the principal to internalise the externality it imposes when setting incentives for the agent. In addition, where possible it is also desirable to set a separate penalty on the agent equal to expected social harm. Again this forces the agent to internalise the social costs of their actions that remain even when the principal is motivated to set incentives in a more socially desirable manner. In effect, both the agent’s action (a) and the principal’s choices (β ) have external social impacts. Only by setting penalties such that each internalises their respective externalities can a social harm be minimised. 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:

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 w2 + 4γλ   wH  * F * = max  H ,  and σ = min 1, 2 . w    w + 4γλ  Thus, the Beckerian logic regarding enforcement levels does not apply with the level of enforcement being positive. The reason for this is that reduced enforcement has a direct impact on the incentives the principal sets the agent. In particular, when the agent is wealth constraint, a lower σ, raises β*. This increases the agent’s incentives to undertake the harmful action counteracting the cost minimising properties of penalties as opposed to enforcement. The end result is that it is optimal for some resources to be devoted to enforcement.8

III

Conclusions

When employees of a firm commit socially harmful acts, 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 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).

12 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, it was 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. While a specific model was used in this paper, these principles would likely carry over into more general structures. Specifically, consider more general analyses of principalagent relationships. Much for the literature focuses on the type of incentives when the agent is risk-averse. Basing incentives on observables stochastically related to effort, places additional risk on the agent; representing a cost of providing incentives. In this situation, penalties by placing additional risks on the agent will further dilute the incentives the principal will give for the agent; reducing further any effort devoted to productive activitie s. While this will not change the principle that the principal’s penalty equal expected harm, it will change the penalty imposed directly on the agent as this now creates uncertainty there (as in Polinsky and Shavell, 1979). Nonetheless, risk aversion could restore the type of trade-offs between principal and agent penalties as analysed by Polinsky and Shavell (1993) and Shavell (1997). A complete analysis is left to future research. In addition, generally, principals can set a richer set of incentives than described by the model of this paper. This includes both monitoring activities and also internal punishments

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An earlier version of this paper (available at www.ssrn.com) demonstrated that it would also be optimal

13 directly aimed at penalising the agent in the event some social sanction is imposed on the principal. The purpose of this paper was to focus upon how observability impacted on standard results regarding penalties and hence, provided the simplest model possible to demonstrate these. Nonetheless, a more complex model is likely to still preserve the policy that the principal be penalised based on expected harm as this would cause it to internalise any externalities in setting any incentive policy. However, the precise interaction between such policies and both agent penalties and the level of enforcement is an open issue; again left to future research.

to devote resources to enforcement if the agent faced some costs imposed by the principal in the event the planner detects them undertaking the socially harmful action.

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References

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Sykes, A.O. (1981), “An Efficiency Analysis of Vicarious Liability Under the Law of Agency,” Yale Law Journal, 91, pp.168-206. Sykes, A.O. (1984), “The Economics of Vicarious Liability,” Yale Law Journal, 93, pp.1231-1280.