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Abstract

This chapter discusses the theory of the public enforcement of law - the use of

public agents (inspectors, tax auditors, police, prosecutors) to detect and to

sanction violators of legal rules. We first present the basic elements of the

theory, focusing on the probability of imposition of sanctions, the magnitude

and form of sanctions, and the rule of liability. We then examine a variety of

extensions of the central theory, including accidental harms, costs of imposing

fines, mistake, marginal deterrence, settlement, self-reporting, repeat offenses

and incapacitation.

JEL classification: K14, K42

Keywords: Law Enforcement, Crime, Deterrence

 

1. Introduction

 

In this chapter we consider the theory of the public enforcement of law - the use

of public agents (inspectors, tax auditors, police, prosecutors) to detect and to

sanction violators of legal rules. Of course, private parties also play an

important role in law enforcement, by providing information to public

authoritiesand also by initiating their own legal actions (notably, tort suits), but

to maintain focus we restrict attention here to public enforcement activity. (On

private enforcement, see generally Landes and Posner, 1987, and Shavell,

1987c; and on private versus public enforcement, see Becker and Stigler, 1974;

Landes and Posner, 1975, and Polinsky, 1980a.)

 

In Sections 2 through 4, we present the basic elements of the theory of

public enforcement of law. Our concern is with the probability of imposition of

sanctions, the magnitude and form of sanctions, and the rule of liability. In

Sections 5 through 16 we then examine a variety of extensions of the central

theory, including accidental harms, costs of imposing fines, mistake, marginal

deterrence, settlement, self-reporting, repeat offenses and incapacitation.

Before proceeding, we note that economically-oriented analysis of public

law enforcement dates from the eighteenth century contributions of

Montesquieu (1748), Beccaria (1770), and, especially, Bentham (1789), whose

analysis of deterrence was sophisticated and expansive. But, curiously, after

Bentham (1789), the subject of enforcement lay essentially dormant in

economic scholarship until the late 1960s, when Becker (1968) published a

highly influential article, which has led to a voluminous literature.

 

2. The Basic Framework

 

An individual (or a firm) chooses whether to commit an act that for simplicity

is assumed to cause harm with certainty (see Section 5 on uncertain harm). If

he commits the act, he obtains some gain, and also faces the risk of being

caught, found liable and sanctioned. The rule of liability could be either strict -

under which the individual is definitely sanctioned - or fault-based - under

which he is sanctioned only if his behavior fell below a fault standard. The

sanction that he suffers could be a monetary fine, a prison term, or a

combination of the two.

 

Whether an individual commits a harmful act is determined by an expected

utility calculation. He will commit the act if that would raise his expected

utility, taking into account the gain he would derive and the probability, form,

and level of sanction that he would then face. We will usually first examine the

assumption that individuals are risk neutral with respect to sanctions, that is,

that they treat an uncertain sanction as equivalent to its expected value; but we

will also consider alternative assumptions.

 

Social welfare generally is presumed to equal the sum of individuals’

expected utilities. An individual’s expected utility depends on whether he

commits a harmful act, on whether he is a victim of someone else’s harmful

act, and on his tax payment, which will reflect the costs of law enforcement,

less any fine revenue collected. If individuals are risk neutral, social welfare

can be expressed simply as the gains individuals obtain from committing their

acts, less the harms caused, and less the costs of law enforcement. (The

assumption that individuals’ gains always are credited in social welfare could

be relaxed without affecting most of our conclusions. The principal difference

that altering the assumption would make is that more acts would be treated as

socially undesirable and that optimal sanctions and enforcement effort would

increase.)

 

We assume, as is conventional, that fines are socially costless to employ

because they are mere transfers of money (but in Section 6 we consider fines

that are costly to impose), whereas imprisonment involves positive social costs

because of the expense associated with the operation of prisons and the

disutility due to imprisonment (which is not naturally balanced by gains to

others).

 

The enforcement authority’s problem is to maximize social welfare by

choosingenforcement expenditures or, equivalently, a probability of detection,

the level of sanctions and their form (a fine, prison term, or combination), and

the rule of liability (strict or fault-based).

 

3. Optimal Enforcement Given the Probability of Detection

 

We consider here optimal enforcement given the assumption that the

probability of detection is fixed (the probability will be treated as a policy

instrument in the next section). Thus, we ask about the optimal form and level

of sanctions under strict and fault-based liability, and about how the two

liability rules compare.

 

Strict Liability

Assumeinitially that fines are the form of sanction and that individuals are risk

neutral. Then the optimal fine is the harm h divided by the probability of

detection p, that is, h/p; for then the expected fine equals the harm (observe that

p(h/p) = h). If, for example, the harm is $1,000 and the probability of detection

is 25 percent, the optimal fine is $4,000, and the expected fine is $1,000. This

fine is optimal because, when the expected fine equals the harm, an individual

will commit a harmful act if, but only if, the gain he would derive from it

exceeds the harm he would cause. Essentially this basic and fundamental

formula was noted by Bentham (1789, p. 173) and it has been observed by

many others since.

 

If individuals are risk averse with regard to fines, one would expect the

optimal fine to be lower than in the risk-neutral case for two reasons. First, this

reduces the bearing of risk by individuals who commit the harmful act. Second,

because risk-averse individuals are more easily deterred than risk-neutral

individuals, the fine does not need to be as high as before to achieve any desired

degree of deterrence. (However, for subtle reasons that we will not address here,

the optimal fine could, in principle, be higher when individuals are risk averse.)

 

Next assume that imprisonment is the form of sanction, with social costs

incurred in imposing sanctions. In this case, there is not a simple formula for

the optimal imprisonment term (see Polinsky and Shavell, 1984). The optimal

term could be such that there is either underdeterrence or overdeterrence,

compared to socially ideal behavior. On one hand, a relatively low

imprisonment term, implying underdeterrence, might be socially desirable

because it means that imprisonment costs are reduced for those individuals who

commit harmful acts. On the other hand, a relatively high term, implying

overdeterrence, might be socially desirable because it means that imprisonment

costs are reduced due to fewer individuals committing harmful acts, even if

some of these deterred individuals would have obtained gains exceeding the

harm. (The possible optimality of overdeterrence strikes us as more theoretical

than real, however.)

 

 

Now consider the combined use of fines and imprisonment. Here, the main

point is that fines should be employed to the maximum extent feasible before

resort is made to imprisonment. In other words, it is not optimal to impose a

positive imprisonment term unless the fine is maximal. (The maximal fine

might be interpreted as the wealth of an individual.) The rationale for this

conclusion is that fines are socially costless to impose, whereas imprisonment

is socially costly, so deterrence should be achieved through the cheaper form

of sanction first. This point is noted by Bentham (1789, p. 183) and Becker

(1968, p. 193); see also Polinsky and Shavell (1984). To amplify, suppose that

the fine f is less than the maximal fine fmand that a positive prison term t is

employed. Raise f toward fmand lower t so as to keep the disutility of the

combined sanctions constant. Then deterrence and the amount of harm will not

change, but the cost of imposing the imprisonment sanction will fall, raising

social welfare. Hence, it must be optimal for the fine to be maximal before

imprisonment is used. (Observe that this argument holds regardless of

individuals’ attitudes toward risk of either fines or imprisonment.)

 

Fault-Based Liability

Assumeagain that fines are the form of liability. Then the same formula for the

fine that we said was optimal under strict liability - namely, h/p, the harm

divided by the probability of detection - will lead to compliance with the fault

standard (assuming that the fault standard is optimally selected). For example,

suppose that the harm is $1,000, and that an individual would be found at fault

if he failed to take a precaution costing less than $1,000 that could have

prevented the harm. Furthermore, suppose such a precaution exists that costs

$700. If the probability of detection is 25 percent, then a fine of $4,000 for

beingat fault would induce the individual to take a precaution costing less than

$1,000; in particular, he would prefer to spend $700 on the precaution and

escape liability than not to take the precaution and bear an expected fine of

$1,000.

 

Observe that the optimal fine of $4,000 in the preceding example is not

unique. Any higher fine also would induce compliance with the fault standard,

as would some lower fines (as long as the expected value of the fine exceeds

$700, or whatever is the expense of the precaution that costs less than $1,000).

Note that higher fines do not lead to a problem of overdeterrence because

parties can escape fines by complying with the fault standard. (However, if

mistakes occur in the legal process, they might be induced to spend excessively

on precautions; see Section 8 below).

 

If individuals are risk averse, they are more easily deterred than if they are

risk neutral, so the fine does not need to be as high to induce compliance with

thefault standard. Moreover, assuming that compliance occurs, no one actually

is sanctioned because no one is found at fault (assuming, as we do here, that

there are no mistakes). Thus, fault-based liability has the attractive feature that

it can accomplish desired deterrence of harm-creating conduct without

imposing risk on risk-averse individuals (Shavell, 1982).

 

Next, consider imprisonment as the sanction; see Shavell (1987a). Here, for

essentially the reasons given in the case of fines, any sanction above a threshold

level will ensure compliance with the fault standard, and the minimum sanction

necessary to induce compliance is higher the lower is the probability of

detection. Also (Shavell, 1985), fault-based liability again can accomplish

deterrence without the actual imposition of sanctions, which would be socially

costly.

 

Finally, consider the joint use of fines and imprisonment. In this case, it

does not matter what the combination of sanctions is, provided that the

sanctions achieve compliance with the fault standard. In particular, it is not

advantageous for society to employ maximal fines before resorting to

imprisonment because compliance means that sanctions are never imposed.

 

Comparison of Liability Rules

Because sanctions are not imposed under fault-based liability (in the absence

of mistakes), this form of liability has an advantage over strict liability when

the sanction is the fine and individuals are risk-averse, or when the sanction is

imprisonment. However, fault-based liability is more difficult to administer.

Namely, to apply fault-based liability, the enforcement authority must have

more information than under strict liability: it must be able to calculate optimal

behavior to determine the fault standard and it must ascertain whether the fault

standard was met. Under strict liability, the authority need only ascertain harm.

(Moreover,for reasons we discuss in Section 7 below, strict liability encourages

better decisions by injurers regarding their level of participation in

harm-creating activities.)

 

4. Optimal Enforcement Including the Probability of Detection

 

We now consider the optimal system of enforcement when expenditures on

enforcement, and hence the probability of detection, are allowed to vary.

Consideration of this issue originated with Becker (1968); the early writers on

enforcement(including Bentham, 1789) did not examine the issue of the choice

of enforcement effort.

 

Strict Liability

Assume first that the sanction is a fine and that individuals are risk neutral.

Then the optimal level of the fine is maximal and the optimal probability is low

 (in a sense to be described). The basic explanation for this conclusion is that if

the fine were not maximal, society could save enforcement costs by

simultaneously raising the fine and lowering the probability without affecting

the level of deterrence. Suppose, for example, that the fine initially is $4,000

and that the probability of detection is 25 percent. Now raise the fine to

$10,000, presuming that the maximal fine is at least this high, and lower the

probability of detection to 10 percent. Then the expected fine remains equal to

$1,000, so that deterrence is maintained, but expenditures on enforcement are

significantly reduced, implying that social welfare rises. This process can be

continued, and social welfare augmented, as long as the fine is below the

maximal level fm. Becker (1968) suggested this result (although much of his

analysis implicitly presumes that the fine is not maximal); Carr-Hill and Stern

(1979, pp. 280-309) and Polinsky and Shavell (1979) note it explicitly.

 

The optimal probability is low in that there is some underdeterrence; that

is, the optimal p is such that the expected fine pfmis less than the harm h

(Polinsky and Shavell, 1984). The reason for this result is that if pfmequals h,

behavior will be ideal, meaning that the individuals who are just deterred

obtain gains essentially equal to the harm. These are the individuals who would

be led to commit the harmful act if p were lowered slightly. That in turn must

be socially beneficial because these individuals cause no net social losses

(because their gains essentially equal the harm), but reducing p saves

enforcement costs. How much pfmshould be lowered below h depends on the

saving in enforcement costs from reducing p compared to the net social costs

of underdeterrence that will result if p is lowered non-trivially.

 

If individuals are risk averse, the optimal fine generally is less than

maximal, as first shown in Polinsky and Shavell (1979) (and elaborated upon

in Kaplow, 1992). This is because the use of a very high fine would impose a

substantial risk-bearing cost on individuals who commit the harmful act.

Another more particular explanation involves reconsidering the argument that

we used in the risk-neutral case. If the fine f is less than fm, it is still true that

f can be raised and p lowered so as to maintain deterrence, but because of risk

aversion, this implies that pf falls, meaning that fine revenue falls. The

reduction in fine revenue reflects the disutility caused by imposing greater risk

on risk-averse individuals. If individuals are sufficiently risk averse, the decline

in fine revenue associated with greater risk-bearing could more than offset the

savingsin enforcement expenditures from reducing the probability of detection,

implying that social welfare would be lower.

 

Next,assume that the sanction is imprisonment and that individuals are risk

neutral in imprisonment, that is, the disutility of imprisonment is the same for

each additional year. (We did not discuss individuals’ attitudes toward the risk

of imprisonment in Section 3 because the points we made there did not depend

on this consideration.) Then the optimal imprisonment term is maximal

 (Shavell, 1991b). The reasoning behind this result parallels that used to show

that the optimal fine is maximal when individuals are risk neutral in fines.

Specifically, if the imprisonment term is raised and the probability of detection

lowered so as to keep the expected sanction constant, neither individual

behavior nor the costs of imposing imprisonment are affected (by construction,

the expected prison term is the same), but enforcement expenditures fall.

 

Suppose instead that individuals are risk averse in imprisonment. In other

words, the disutility of each year of imprisonment grows with the number of

years in prison, perhaps because imprisonment becomes increasingly difficult

to tolerate. In this case there is a stronger argument for setting the

imprisonment sanction maximally than when individuals are risk neutral

(Polinsky and Shavell, 1997). This is because, when the imprisonment term is

raised, the probability of detection can be lowered even more than in the

risk-neutral case without reducing deterrence. Thus, not only are there greater

savings in enforcement expenditures, but also the social costs of imposing

imprisonment sanctions decline because the expected prison term falls.

 

Last, suppose that individuals are risk preferring in imprisonment, that is,

the disutility of each year of imprisonment falls with the number of years in

prison. This assumption seems particularly important: the first years of

imprisonment may create special disutility, due to brutalization of the prisoner,

or due to the stigma effect of having been imprisoned at all. Additionally, the

fact that individuals discount the future disutility of imprisonment makes

earlier years of imprisonment more important than later ones. If individuals are

risk preferring in imprisonment, the optimal sanction may well be less than

maximal (Polinsky and Shavell, 1997). In particular, the type of argument used

above does not necessarily apply. When the sanction is raised, the probability

that maintains deterrence cannot be lowered proportionally, implying that the

expected prison term rises. Because the resulting increased cost of imposing

imprisonment sanctions might exceed the savings in enforcement expenditures

from lowering the probability, the optimal prison term might not be maximal.

When the probability of detection is set optimally, together with the

imprisonment term, underdeterrence may well result, not only to save

enforcement expenditures, but also to reduce the costs of imposing

imprisonment sanctions. (In theory, however, overdeterrence could be optimal

for the reason mentioned in Section 3 - that overdeterrence could reduce the

costs of imprisonment.)

 

Now consider the situation when both fines and imprisonment are employed

as sanctions. Recall that under the optimal enforcement policy, the fine must

be maximal, for otherwise it cannot be desirable to employ imprisonment. The

main point we wish to make is that, unlike when imprisonment is used alone,

the optimal imprisonment term may not be maximal even if individuals are risk

neutral or risk averse in imprisonment. Suppose that individuals are risk

neutral in imprisonment and fines. Then if the imprisonment term is raised and

the probability of detection is lowered so as to keep the expected imprisonment

term constant, deterrence declines because the expected fine falls (due to the

reduction in the probability). Hence, to maintain deterrence, the probability

cannot fall proportionally. But this implies that the expected prison term, and

the costs of imposing imprisonment, are higher than previously. Only if the

savings in enforcement costs are sufficiently large, therefore, is it socially

desirable to raise the imprisonment sanction.

 

Fault-Based Liability

The least expensive way to accomplish compliance with the fault standard is

to use the highest possible sanction and, given this sanction, the lowest

probability of detection that deters individuals who would be at fault. The

reason is that, if all individuals who would be at fault are deterred, the only cost

incurred is associated with the setting of the probability; this cost is minimized

by using the maximal sanction and a correspondingly low probability. Note that

this is true regardless of whether the sanction is a fine or imprisonment and

regardless of individuals’ attitudes toward the risk of fines or of imprisonment.

 

Comparison of Rules

As we emphasized earlier, under fault-based liability sanctions are not actually

imposed (in the absence of mistakes), which is an advantage over strict liability

when the sanction is a fine and individuals are risk averse, and is always an

advantage when the sanction is imprisonment. Moreover, this advantage of

fault-based liability implies a second advantage: it may allow a further savings

in enforcement expenditures over that under strict liability. For example,

suppose that the sanction is a fine and that injurers are risk averse. Then, as we

have emphasized, the optimal fine under strict liability generally is not

maximal, due to risk-bearing by injurers. This implies that the probability of

detection needed to achieve any given level of deterrence is higher than if the

fine were maximal. Under fault-based liability, however, the optimal fine is

maximal despite the risk aversion of injurers (because the fine is not actually

imposed), meaning that a lower probability can be employed. However, to

decide which liability rule is preferable, these advantages of fault-based liability

would have to be weighed against the disadvantages of this rule relative to strict

liability that we mentioned at the end of Section 3 (one of which, as noted, will

be discussed in Section 7).

 

This concludes the presentation of the basic theory of public enforcement of

law. We now turn to various extensions and refinements of the analysis.

 

5. Accidental Harms

 

As we noted at the outset, we assumed that individuals decide whether or not

to commit acts that cause harm with certainty, that is, they decide whether or

not to cause intentional harms. In many circumstances, however, harms are

accidental - they occur only with a probability. For instance, if a driver speeds,

he only creates a likelihood of a collision; or if a firm stores toxic chemicals in

a substandard tank, the firm only creates the probability of a harmful spill.

 

Essentially all that we have said above applies in a straightforward way

when harms are accidental. If individuals are risk neutral, sanctions are

monetary, and the expected sanction equals harm, then induced behavior will

be socially optimal; further, the optimal magnitude of sanctions is maximal if

individuals are risk neutral because this allows enforcement costs to be saved;

and so forth. Our general conclusions from above can thus be interpreted to

apply both when harms are intentional and cause harm for sure, as well as

when actions alter the risk of harm.

 

There is, however, an additional issue that arises when harm is uncertain:

a sanction can be imposed either on the basis of the commission of a dangerous

act that increases the chance of harm - storing chemicals in a substandard tank

- or on the basis of the actual occurrence of harm - only if the tank ruptures

and results in a spill. In principle, either approach can achieve optimal

deterrence. To illustrate, suppose that the substandard tank has a 10 percent

chance of rupturing, in which case the harm would be $10 million; the expected

harm from using the tank therefore is $1 million. If injurers are risk neutral and

sanctions are imposed only when harm occurs, deterrence will be optimal if, as

usual, the expected sanction equals the harm of $10 million. Alternatively, if

sanctions are imposed on the basis of the dangerous act of using the

substandard tank, deterrence will be optimal if the owner of the tank faces an

expected sanction equal to the expected harm due to his use of the substandard

tank, $1 million.

 

Several factors are relevant to the choice between act-based and harm-based

sanctions (Shavell, 1993). First, act-based sanctions need not be as high to

accomplish a given level of deterrence, and thus offer an underlying advantage

over harm-based sanctions because of limitations in parties’ assets. In the

example in the preceding paragraph, the owner of the storage tank might be

able to pay the $1 million required if sanctions are act-based but not the

$10 million required if sanctions are harm-based. Second, and closely related,

because act-based sanctions need not be as high to accomplish deterrence, they

offer an advantage over harm-based sanctions when parties are risk averse.

Third, act-based sanctions and harm-based sanctions may differ in the ease

with which they can be applied. In some circumstances, act-based sanctions

maybe simpler to impose (it might be less difficult to determine whether an oil

shipper properly maintains its vessels’ holding tanks than to detect whether one

of the vessels leaked oil into the ocean); in other circumstances, harm-based

sanctions may be easier (a driver who causes harm might be caught without

difficulty, but not one who speeds). Fourth, it may be hard to calculate the

expected harm due to an act, but relatively easy to ascertain the actual harm if

it eventuates; if so, this constitutes an advantage of harm-based liability.

 

6. Costs of Imposing Fines

 

We inquire in this section about the implications of costs borne by enforcement

authorities in imposing fines. Our principal observation is that such costs

should raise the level of the fine.

 

We assume for simplicity that the probability of detection is fixed, that

liability is strict, and that individuals are risk neutral. In this setting, recall

from Section 3 that the optimal fine is h/p, the harm divided by the probability

of detection.

 

Now let there be a public cost k of imposing a fine. The optimal fine then

becomes h/p + k; the cost k should be added to the fine that would otherwise be

desirable (Becker, 1968, p. 192 and Polinsky and Shavell, 1992). The intuition

behind this result is that, if an individual commits a harmful act, he causes

society to bear not only the immediate harm h, but also, with probability p, the

cost k of imposing the fine - that is, his act results in an expected total social

cost of h + pk. If the fine is h/p + k, the individual’s expected fine is p[(h/p) +

k] = h + pk, leading him to commit the harmful act if and only if his gain

exceeds the expected total social cost of his act.

 

For example, suppose the harm is $1,000, the probability of detection is 25

percent, and the cost of imposing the fine is $500. An individual’s harmful act

causes society to bear expected total social costs of $1,125 - the harm of $1,000

plus a 25 percent chance of the $500 cost of imposing a fine. If the fine is set

equal to $4,500, the individual’s expected fine also will equal $1,125.

 

Additionally, observe that, not only does the state bear costs when fines are

imposed, so do individuals who pay the fines (such as legal defense expenses).

The costs borne by individuals, however, do not affect the formula for the

optimal fine. Individuals properly take these costs into account, because they

bear them.

 

7. Level of Activity

 

We have been assuming that the sole decision that an individual makes is

whether to act in a way that causes harm when engaging in some activity. In

many contexts, however, an individual also makes a choice about his activity

level - that is, not only does he choose whether to commit a harmful act when

engaging in an activity, he also chooses whether to engage in that activity or,

more generally, at what level to do so. For example, besides deciding how to

behave when driving (whether to exercise care in changing lanes), an

individual also chooses how many miles to drive; the number of miles driven

is the individual’s level of activity. Similarly, not only does a firm decide how

toconduct its operations during production (whether to pollute), it also chooses

its level of production; the output of the firm is its level of activity.

 

The socially optimal activity level is such that the individual’s marginal

utility from the activity just equals the marginal expected harm caused by the

activity. Thus, the optimal number of miles driven is the level at which the

marginal utility of driving an extra mile just equals the marginal expected harm

per mile driven. The determination of the optimal level of activity presumes

that individuals act optimally when engaging in the activity - for example, that

they drive with appropriate care. Thus, in determining the optimal level of

activity, an individual’s marginal utility from the activity is compared to the

expected harm that results when he acts appropriately when engaging in the

activity. Often this expected harm is positive even when a party acts optimally,

because the cost of precautions (or, equivalently, the gain or savings from not

taking precautions) exceeds the expected reduction in harm that taking the

precautions would bring about.

 

Will parties’ choices about their activity levels be socially correct under the

two major forms of liability? The answer is that under strict liability, their

choices about activity levels will be correct, but under fault-based liability, they

generally will participate in activities to a socially excessive extent. Under strict

liability, parties will choose the optimal level of activity because they will pay

for all harm done. They will choose the optimal number of miles to drive

because they will pay for all harm per mile driven. Under fault-based liability,

however, parties generally do not pay for the harm they cause because, as we

have discussed, they will be induced to behave so as not to be found at fault.

Consequently, when deciding on their level of activity, they will choose an

excessive level. They will not take into account the harm that each additional

mile of driving causes, and therefore they will drive too much.

 

The interpretation of the preceding points in relation to firms is that under

strict liability the product price will reflect the expected harm caused by

production, so that the price will reflect the full social cost of production.

Hence, the amount purchased, and thus the level of production, will tend to be

socially optimal. However, under fault-based liability, the product price will not

reflect harm, but only the cost of precautions; thus, the amount sold, and the

level of production, will be excessive.

 

 

A related comment is that safety regulations and other regulatory

requirements are often framed as standards of care that have to be met, but

which, if met, free the regulated party from liability. Hence, regulations of this

character are subject to the criticism that they lead to excessive levels of the

regulated activity. Making parties strictly liable for harm would be superior to

safety regulation with respect to inducing socially correct activity levels.

 

The tendency of parties to choose an excessive level of activity under

fault-based liability, but not under strict liability, constitutes a fundamental

advantage of strict liability; it was first emphasized in Shavell (1980) and

Polinsky (1980b). This advantage, note, is stronger the greater is the harm

engendered by engaging in the activity (given that behavior is optimal when

engaging in the activity). Thus, for activities for which expected harm is likely

to be substantial, the disadvantage of fault-based liability will be significant.

 

8. Mistakes

 

Errors of the two classic types can occur in public enforcement of law. First, an

individual who should be found liable might mistakenly not be found liable - a

Type I error. Second, an individual who should not be found liable might

mistakenly be found liable - a Type II error. For an individual who has been

detected, let the probabilities of these errors be 01and 02, respectively.

 

Given the probability of detection p and the chances of Type I and Type II

errors, an individual will commit the wrongful act if and only if his gain g net

ofhis expected fine if he does commit it exceeds his expected fine if he does not

commit it, namely, when g·p(1··1)f > • p·2f, or, equivalently, when g >

 (1• • 1• • 2)pf.

 

The first point to note is that, as emphasized in Png (1986), both types of

error reduce deterrence: the term (1 • • 1• •2)pf is declining in both •1and •2.

The first type of error diminishes deterrence because it lowers the expected fine

if an individual violates the law. The second type of error, when an individual

is mistakenly found liable, also lowers deterrence because it reduces the

difference between the expected fine from violating the law and not violating

it. In other words, the greater is •2, the smaller the increase in the expected fine

if one violates the law, making a violation less costly to the individual.

 

Because mistakes dilute deterrence, they reduce social welfare (see generally

Kaplow and Shavell, 1994a). Specifically, to achieve any level of deterrence,

the probability p must be higher to offset the effect of errors. It should also be

noted that, were one to take into account an individual’s decision whether to

engage in an activity (like driving), Type II errors have the additional effect of

discouraging socially desirable participation in the activity.

 

Now consider the optimal choice of the fine. Given any probability of

detection, the dilution in deterrence caused by errors requires a higher fine to

restore deterrence. If the probability and the fine are variable, then, as

explained in Section 4, the optimal fine is maximal. Somewhat surprisingly, the

optimal fine remains maximal despite mistakes, by essentially the argument

used previously: if the fine f were less than maximal, then f could be raised and

the probability p lowered so as to keep deterrence constant, but saving

enforcement costs.

 

Now consider the possible risk aversion of individuals. As we emphasized

in Section 4, the optimal fine under strict liability generally is less than

maximal when individuals are risk averse, because lowering the fine from the

maximum level reduces the bearing of risk. Introducing the possibility of

mistakes may increase the desirability of lowering the fine because, due to

Type II errors, individuals who do not violate the law are subject to the risk of

having to pay a fine (Block and Sidak, 1980). Indeed, because the number of

persons who do not violate the law often would far exceed the number who do,

the desire to avoid imposing risk on the former group can lead to a substantial

reduction in the optimal fine.

 

Next, consider imprisonment and mistake. In this regard, our conclusions

parallel those with respect to fines in several respects. Notably, mistakes of both

types dilute the deterrent effects of imprisonment; and the optimal

imprisonment term is maximal if individuals are risk neutral or risk averse in

imprisonment but generally is not maximal if they are risk preferring in

imprisonment.

 

We have not yet commented on fault-based liability. Here, an important

implication of mistake is that some individuals will bear sanctions even if they

comply with the fault standard. Hence, the results regarding the optimal

probability of detection and the sanction under strict liability apply to some

extent under fault-based liability as well. Moreover, as stressed by Craswell and

Calfee (1986), individuals will often have a motive to take excessive

precautions in order to reduce the chance of being found erroneously at fault.

 

Finally, observe that, although we have treated the probabilities of error as

fixed, they can be influenced by procedural choices. For example, prosecutorial

resources can be increased in order to reduce the probability of a Type I error,

or the standard of proof can be raised to reduce the chance of a Type II error

(although this presumably increases Type I errors). Because the reduction of

both types of error increase deterrence, expenditures made to reduce errors may

be socially beneficial (Kaplow and Shavell, 1994a).

 

9. General Enforcement

 

In many settings, enforcement may be said to be general in the sense that

several different types of violations will be detected by an enforcement agent’s

activity. For example, a police officer waiting at the roadside may notice a

driver who litters as well as one who goes through a red light or who speeds,

and a tax auditor may detect a variety of infractions when he examines a tax

return. To investigate such situations, suppose that a single probability of

detection applies uniformly to all harmful acts, regardless of the magnitude of

the harm. (The contrasting assumption is that enforcement is specific, meaning

that the probability is chosen independently for each type of harmful act.)

 

The main point that we want to make is that in contexts in which

enforcement is general, the optimal sanction rises with the severity of the harm

and is maximal only for relatively high harms; this point was first made in

Shavell (1991b) (Mookherjee and Png, 1992a is closely related). To see this,

Assume that liability is strict, the sanction is a fine, and injurers are risk neutral.

Let f(h) be the fine given harm h. Then, for any given general probability of

detection p, the optimal fine schedule is h/p, provided that h/p is feasible;

otherwise - for high h (all h such that h/p > fm) - the optimal fine is maximal.

This schedule is obviously optimal given p because it implies that the expected

fine equals harm, thereby inducing ideal behavior, whenever that is possible.

 

The question remains whether it would be desirable to lower p and raise

fines to the maximal level for the low-harm acts for which h/p is less than

maximal. The answer is that if p is reduced for the relatively low-harm acts

(and the fine raised for them), then p - being general - is also reduced for the

high-harm acts for which the fine is already maximal, resulting in lower

deterrence of these acts. The decline in deterrence of high-harm acts may cause

a greater social loss than the savings in enforcement costs from lowering p. To

express this point differently, p must be sufficiently high to avoid significant

underdeterrence of high-harm acts (for which fines are maximal). But since this

p also applies to less harmful acts, the fines for them do not need to be maximal

in order to appropriately deter them.

 

The result that, when enforcement is general, sanctions should rise with the

severity of harm up to a maximum also holds if the sanction is imprisonment

and if liability is fault-based. The underlying reasoning is the same as that

given above.

 

10. Marginal Deterrence

 

In many circumstances, a person may consider which of several harmful acts

to commit, for example, whether to release only a small amount of a pollutant

into a river or a large amount, or whether to kidnap a person or also to kill the

kidnap victim. In such contexts, the threat of sanctions plays a role in addition

to the usual one of attempting to deter individuals from committing harmful

acts: for individuals who are not deterred, sanctions influence which harmful

acts individuals choose to commit. Notably, such individuals will have a reason

to commit less harmful rather than more harmful acts if expected sanctions rise

with harm. Deterrence of a more harmful act because its sanction exceeds that

for a less harmful act is sometimes referred to as marginal deterrence (it

apparently was so named by Stigler, 1970).

 

Other things being equal, as observed by Beccaria (1770, p. 32) and

Bentham (1789, p. 171), it is socially desirable that enforcement policy creates

marginal deterrence, so that those who are not deterred from committing

harmful acts have a reason to moderate the amount of harm that they cause.

This suggests that sanctions should rise with the magnitude of harm and,

therefore, that sanctions should not generally be maximal. However, fostering

marginal deterrence may conflict with achieving deterrence generally: in order

for the schedule of sanctions to rise steeply enough to accomplish marginal

deterrence, sanctions for less harmful acts may have to be so low that

individuals are not deterred from committing some harmful act.

 

We have two additional observations to make about marginal deterrence.

First, marginal deterrence can be promoted by increasing the probability of

detection as well as the magnitude of sanctions. For example, kidnappers can

be better deterred from killing their victims if more police resources are devoted

to apprehending kidnappers who murder their victims than to those who do not.

(But in circumstances in which enforcement is general, the probability of

detection cannot be independently altered for acts that cause different degrees

of harm.) Second, marginal deterrence is naturally accomplished if the expected

sanction equals harm for all levels of harm; for if a person is paying for harm

done, he will have to pay appropriately more if he does greater harm. Thus, for

instance, if a polluter’s expected fine would rise from $100 to $500 if he dumps

five gallons instead of one gallon of waste into a lake, where each gallon causes

$100 of harm, his marginal incentives to pollute will be correct. For formal

analyses of marginal deterrence, see Shavell (1992), Wilde (1992), and

Mookherjee and Png (1994).

 

11. Principal-Agent Relationship

 

Although we have assumed that an injurer is a single actor, injurers often are

more appropriately characterized as collective entities, and specifically as a

principal and the principal’s agent. For example, the principal could be a firm

and the agent an employee; or the principal could be a contractor and the agent

a subcontractor.

 

When harm is caused by the behavior of principals and agents, many of the

conclusions of our prior analysis are not fundamentally altered; they simply

carry over to the sanctioning of principals. Notably, if a risk-neutral principal

faces an expected fine equal to harm done, he will in effect be in the same

position vis-à-vis his agent as society is vis-à-vis a single potential violator of

law (see Newman and Wright, 199• on a closely related point). Consequently,

the principal will behave socially optimally in controlling his agents, and in

particular will contract with them and monitor them in ways that will give the

agents socially appropriate incentives to reduce harm (but see Arlen, 1994).

Another result that carries over to the principal-agent context is that it often

will be desirable for society to tolerate some degree of underdeterrence in order

to conserve enforcement resources.

 

A question about enforcement that arises when there are principals and

agents is the allocation of financial sanctions between the two parties. It is

apparent, however, that the particular allocation of sanctions does not matter

when, as would be the natural presumption, the parties can reallocate the

sanctions through their own contract. For example, if the agent finds that he

faces a large fine but is more risk averse than the principal, the principal can

assume it; conversely, if the fine is imposed on the principal, he will retain it

and not impose an internal sanction on the agent. Thus, the post-contract

sanctions that the agent bears are not affected by the particular division of

sanctions initially selected by the enforcement authority.

 

The allocation of monetary sanctions between principals and agents would

matter, however, if some allocations allow the pair to reduce their total burden.

An important example is when a fine is imposed only on the agent and he is

unable to pay it because his assets are less than the fine (see Sykes, 1981, and

Kornhauser, 1982). Then, he and the principal (who often would have higher

assets) would jointly escape part of the fine, diluting deterrence. The fine

therefore should be imposed on the principal rather than on the agent (or at

least the part of the fine that the agent cannot pay).

 

A closely related point is that the imposition of imprisonment sanctions on

agents may be desirable when their assets are less than the harm that they can

cause, even if the principal’s assets are sufficient to pay the optimal fine (see

Polinsky and Shavell, 1993). The fact that an agent’s assets are limited means

that the principal may be unable to control him adequately through use of

contractually-determined penalties, which can only be monetary. For example,

a firm may not be able, despite the threat of salary reduction or dismissal, to

induce its employees never to rig bids. In such circumstances, it may be socially

valuable to use the threat of personal criminal liability and a jail sentence to

better control agents’ misconduct.

 

12. Settlements

 

Although we have thus far assumed that when a liable injurer is discovered he

is sanctioned in some automatic fashion, in practice he must be found civilly

or criminally liable in a trial, and before this occurs, he commonly settles in

lieu of trial. (In the criminal context, the settlement usually takes the form of

a plea bargain, an agreement in which the injurer pleads guilty to a reduced

charge.) Given the prevalence of settlements, it is important to consider how

they affect deterrence and the optimal system of public enforcement, and

whether settlements are socially desirable.

 

There are two general reasons why parties might prefer an out-of-court

settlement to a trial (see generally the survey by Cooter and Rubinfeld, 1989;

and for some recent discussions of plea bargaining, see, for example,

Reinganum, 1988, and Miceli, 1996). First, a trial is costly to the parties in

terms of time and/or money. Second, settlements eliminate the risks inherent

in the trial outcome, a benefit to parties who are averse to such risks. These

advantages of settlement to the parties suggest that settlement is socially

valuable, but the effect of settlement on deterrence is a complicating factor.

 

Specifically, settlements dilute deterrence: for if injurers desire to settle, it

must be because the expected disutility of sanctions is lowered for them (see

generally Polinsky and Rubinfeld, 1988). The state may be able to offset this

settlement-related reduction in deterrence by increasing the level of sanctions;

if so, settlements need not compromise the overall level of deterrence.

Settlements may have other socially undesirable consequences. First, they

mayresult in sanctions that are not as well tailored to harmful acts as would be

true of court-determined sanctions. For example, if injurers have private

information about the harm that they have caused, settlements will tend to

reflect the average harm caused, whereas trial outcomes may better

approximate the actual harm. Thus, the distribution of sanctions meted out

through settlements will not be as good in terms of inducing injurers to take

proper precautions (high-harm injurers will be underdeterred, and vice versa).

 

Second, settlements hinder the amplification and development of the law

through the setting of precedents, a factor of occasional relevance; and

settlements also sometimes allow defendants to keep aspects of their behavior

secret, which can reduce deterrence. Third, settlements for prison terms can

result in increases in public expenditures on jail if defendants are risk averse

in imprisonment. On the social desirability of settlement, see, for example,

Shavell (1997a) and Spier (1997).

 

13. Self-Reporting

 

We have assumed that individuals are subject to sanctions only if they are

detected by an enforcement agent, but in fact parties sometimes disclose their

own violations to enforcement authorities. For example, firms often report

violations of environmental and safety regulations, individuals usually notify

police of their involvement in traffic accidents, and even criminals occasionally

turn themselves in.

 

We explain here why it is generally socially desirable for the structure of

Enforcement to be such as to encourage self-reporting (see Kaplow and Shavell,

1994b). Self-reporting can be induced by lowering the sanction for individuals

who disclose their own infractions. Moreover, the reward for self-reporting can

be made small enough that deterrence is only negligibly reduced.

 

To amplify, assume for simplicity that the sanction is a fine f, that the

probability of detection is p, and that individuals are risk neutral. If an

individual commits a violation and does not self report, his expected fine is pf.

Suppose the fine if an individual self-reports is set just below pf, say at pf • •,

where• > • is arbitrarily small. Then the individual will want to self-report but

the deterrent effect of the sanction will be (approximately) the same as if he did

not self-report. For example, suppose that the fine if an individual does not self

report is $1,••• and that the probability of detection is 1• percent, so the

expected fine is $1••. If the fine for self-reporting is slightly below $1••, such

as $95, or even $99, individuals will self-report but deterrence will barely be

reduced.

 

Given that self-reporting can be induced essentially without compromising

deterrence, why is self-reporting socially advantageous? There are two basic

reasons. First, self-reporting reduces enforcement costs because, when it occurs,

the enforcement authority does not have to identify and prove who the violator

was. If a company reports that it caused pollution, environmental enforcers do

not need to spend as much effort trying to detect pollution and establishing its

source. Second, self-reporting reduces risk, and thus is advantageous if injurers

are risk averse. Drivers bear less risk because they know that if they cause an

accident, they can (and will be led to) report this to the police and suffer a

lower and certain sanction, rather than face a substantially higher sanction (for

hit and run driving) imposed only with some probability.

 

14. Repeat Offenders

 

In practice, the law often sanctions repeat offenders more severely than

first-time offenders. We explain here why such a policy may be socially

desirable.

 

Note first that sanctioning repeat offenders more severely cannot be socially

advantageous if deterrence always induces first-best behavior. If the sanction

for polluting and causing a $1,••• harm is $1,•••, then any person who

pollutes and pays $1,••• is a person whose gain from polluting (say the savings

from not installing pollution control equipment) must have exceeded $1,•••.

Social welfare therefore is higher as a result of his polluting. If such an

individual polluted and was sanctioned in the past, that only means that it was

socially desirable for him to have polluted previously. Raising the current

sanction because of his having a record of sanctions would overdeter him now.

 

Accordingly, only if deterrence is inadequate is it possibly desirable to

condition sanctions on offense history to increase deterrence. But deterrence

often will be inadequate because, as we emphasized in Section 4, it will usually

be worthwhile for the state to tolerate some underdeterrence in order to reduce

enforcement expenses.

 

Given that there is underdeterrence, making sanctions depend on offense

history may be beneficial for two reasons. First, as developed in Polinsky and

Shavell(1996), the use of offense history may create an additional incentive not

to violate the law: if getting caught violating the law implies not only an

immediate sanction, but also a higher sanction for any future violation, an

individual will be more deterred from committing a violation presently. Second,

as studied, for example, in Rubinstein (1979) and Polinsky and Rubinfeld

(1991), making sanctions depend on offense history allows society to take

advantage of information about the dangerousness of individuals and the need

to deter them: individuals with offense histories may be more likely than

average to commit future violations, which might make it desirable for

purposes of deterrence to impose higher sanctions on them.

 

There is also an incapacitation-based (see Section 16) reason for making

sanctions depend on offense history. Repeat offenders are more likely to have

higher propensities to commit violations in the future and thus more likely to

be worth incapacitating by imprisonment.

 

15. Imperfect Knowledge about the Probability and Magnitude of

Sanctions

 

Although we have implicitly assumed that injurers know the probability and

magnitude of sanctions, this is not always the case. Individuals frequently have

imperfect knowledge of these variables; that is, they have estimates, or more

likely, subjective probability distributions, describing the true probability of a

sanction and its true magnitude. They might not know the true probability of

a sanction for several reasons: because the enforcement authority refrains from

publishing information about the probability (perhaps hoping that individuals

will believe it to be higher than it is in fact); because the probability is variable,

depending on factors that individuals do not fully understand (the probability

of a tax audit, for example, is influenced by a large number of considerations);

and because probabilities seem to be difficult for individuals to assess. Also,

individuals may have incomplete knowledge of the true magnitude of sanctions,

particularly if the magnitudes of sanctions are not fixed by law, but are to some

degree discretionary.

 

The implications of injurers’ imperfect knowledge are straightforward.

First, to predict how individuals behave, what is relevant, of course, is not the

actual probability and magnitude of a sanction, but the perceived levels or

distributions of these variables.

 

Second, to determine the optimal probability and magnitude of a sanction,

account must be taken of the relationship between the actual and the perceived

variables (on which, see, for instance, Bebchuk and Kaplow, 1992, and see

Kaplow, 199•b, on learning about sanctions). For example, suppose that there

is a delay of at least a year before individuals fully comprehend a change in the

probability of enforcement. Then if enforcement resources are increased so as

to make the probability, say, 15 percent rather than 1• percent, there might not

be a significant increase in deterrence for some time, making such an

investment less worthwhile. Or, for instance, suppose that the sanction for some

act, such as robbery, is variable (say from one month of jail time to 1• years),

and that individuals’ perceptions are quite rough, not based on true averages

but more on the possible range. Then increasing the average sentence might

have very little effect on deterrence, but increasing the probability substantially

might still augment deterrence. The psychology and learning process (see Sah,

1991) by which individuals assimilate and formulate perceived probabilities of

sanctions and their magnitude are important, therefore, to determining how

deterrence works and what optimal policy is.

 

16. Incapacitation

 

Our discussion of public enforcement has presumed that the threat of sanctions

reduces harm by discouraging individuals from causing harm - that is, by

deterring them. However, an entirely different way for society to reduce harm

is by imposing sanctions that remove parties from positions in which they are

able to cause harm - that is, by incapacitating them. Imprisonment is the

primary incapacitative sanction, although there are other examples: individuals

can lose their drivers licenses, preventing them from doing harm while driving;

businesses can lose their right to operate in certain domains, and the like. We

focus here on imprisonment, but what we say applies to incapacitative sanctions

generally; on the economic theory of incapacitation, see Shavell (1987b).

 

To better understand the role of public enforcement when sanctions are

incapacitative, suppose that the sole function of sanctions is to incapacitate; that

is, sanctions do not deter. (Deterrence might not occur if, for instance,

individuals’ gains from harmful acts exceed the expected sanctions, given the

relevant range of the probabilities and magnitudes of the sanctions.) We assume

that the social goal is as before, to maximize gains from acts less harm, and less

the costs of enforcement and sanctions, including the costs of keeping

individuals in prison.

 

The optimal sanction to impose on an individual who is apprehended is

determined by comparing the expected harm, net of gains, he would cause if

not in prison to the private and public costs of imprisonment. If the expected

net harm exceeds the costs of imprisonment, he should be put in prison and

kept there as long as this condition holds. Thus, the optimal sanction as a

function of expected net harm is zero up to a threshold - the point at which

expected net harm equals the costs of imprisonment - and then rises

discontinuously to the length of time during which the person’s net expected

harm exceeds imprisonment costs. Jail should only be used to incapacitate

individuals whose net harm is relatively high.

 

Two points about the incapacitative rationale are worth making. First, there

is evidence that suggests that the expected harm caused by individuals declines

with their age. Thus, from the incapacitative standpoint, individuals should be

released from jail when their dangerousness falls below the cost of

incapacitation. Second, as a matter of logic, the incapacitative rationale might

imply that a person should be put in jail even if he has not committed a crime

- because his danger to society makes incapacitating him worthwhile. This

would be true, for example, if there were some means accurately to predict a

person’s dangerousness independently of his actual behavior. In practice,

however, the fact that a person has committed a harmful act may be the best

basis for predicting his future behavior, in which case the incapacitation

rationale would suggest imposing a jail term only if the individual has

committed an especially harmful act.

 

Last, we comment on the relationship between optimal enforcement when

incapacitation is the goal versus when deterrence is the goal. First, when

incapacitation is the goal, the optimal magnitude of the sanction is independent

of the probability of apprehension. In contrast, when deterrence is the goal, the

optimal sanction depends on the probability - the sanction generally is higher

the lower is the probability. Second, when incapacitation is the goal, the

sanction rises discontinuously with the magnitude of harm (from zero to a

positive amount), but when deterrence is the goal the sanction rises

continuously with harm. Third, when deterrence is the goal, the probability and

magnitude of sanctions depend on the ability to deter, and if this ability is

limited (as, for instance, with the enraged), a low expected sanction may be

optimal. However, a high expected sanction still might be called for to

incapacitate.

 

17. Conclusion

 

It may be worthwhile summarizing the main points that we have made in this

chapter:

 

(a) When the probability of detection is for some reason fixed, the

benchmark level of the optimal fine is the harm divided by the probability of

detection, for this results in an expected fine equal to the harm. However, costs

incurred by the public in collecting the fine should be added to the benchmark

level of the fine, and risk aversion of injurers should usually lower the level of

the fine.

 

(b) When the probability of detection may be varied, high sanctions may

be optimal, for this allows a relatively low probability to be employed and

thereby saves enforcement costs. Indeed, the optimal fine is in principle

maximal for this reason if individuals are risk neutral in wealth, and the

optimal imprisonment term is maximal if individuals are risk neutral or risk

averse in imprisonment. More realistically, optimal sanctions are not maximal

when individuals are risk averse in wealth or risk preferring in imprisonment

(as well as for the general enforcement reasons discussed in Section 9),

although the motive to set sanctions at relatively high levels in order to reduce

enforcement costs still applies.

 

(c) Optimal enforcement tends to be characterized by some degree of

underdeterrence relative to first-best behavior, because this conserves

enforcement resources. More precisely, by lowering the probability of detection

from a level that would lead to first-best behavior, the state reduces

enforcement costs, and although more individuals commit the harmful act,

these individuals do not cause social welfare to decline substantially because

their gains are nearly equal to the harm.

 

(d) The use of fines should be exhausted before resort is made to costlier

sanctions, notably imprisonment.

 

(e) An advantage of fault-based liability over strict liability is that costly

sanctions - fines when individuals are risk averse, and imprisonment - are

imposed less often: under fault-based liability, injurers generally are induced

(in the absence of mistakes) to obey fault standards, and therefore ordinarily do

not bear sanctions. Under strict liability, however, injurers are sanctioned

whenever they are caught.

 

(f) An advantage of strict liability over fault-based liability is that it is

easier to apply. Another advantage is that injurers’ activity-level decisions

generally will be better: under strict liability, injurers’ activity levels will tend

to be optimal because injurers will pay for harm that they cause. But under

fault-based liability, their activity levels will tend to be excessive because they

generally will not pay for harm that they cause (because they will be led to

behave without fault).

 

These and other basic conclusions about the public enforcement of law that

we have described in this essay are now, for the most part, well-established in

the economic literature on enforcement. However, an important aspect of this

subject that has received relatively little attention is the behavior of public

enforcers themselves. Because our focus was on deriving socially optimal public

enforcement policies, we assumed, as is conventional, that public enforcers act

so as to maximize social welfare. A logical step to take next would be to

re-examine optimal enforcement policies when public enforcers behave in a

self-interested manner. Although some effort already has been devoted to this

inquiry, much remains to be done.



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