Comparing Fault-Based & Strict Liability Offenses in Law Enforcement: An Economic Analysis, Study notes of Law

Download Comparing Fault-Based & Strict Liability Offenses in Law Enforcement: An Economic Analysis and more Study notes Law in PDF only on Docsity! Social Norms and Legal Design: Fault-Based vs Strict Liability Offences Bruno Deffains∗ Claude Fluet† October 2014 Abstract The framing of offences is an important issue in legal or regulatory design. Should offences be fault-based, for instance involving consid- erations of recklessness or negligence, or should the doing of an act constitute an offence per se? We compare the performance, from a de- terrence and enforcement cost perspective, of fault-based versus strict liability offences in the economic model of public enforcement of law, extended to incorporate informal motivations and social norms of con- duct. We show that fault-based offences are generally more effective in harnessing social or self-image concerns for the purpose of inducing compliance. However, this need not always be the case and depends in a complex way on the salience of social norms and on enforcement costs. An optimal legal regime and enforcement policy entails fault- based offences when detected violations of the law would seldom occur and strict liability offences otherwise. KEYWORDS: Normative motivations, regulatory offences, other-regarding behavior, law enforcement, strict liability, fault, compliance, deter- rence. (JEL: D8, K4, Z13) ∗Université Panthéon Assas and Institut Universitaire de France. E-mail: Bruno.Deffains@u-paris2.fr †Université Laval and CIRPEE. E-mail: Claude.Fluet@fsa.ulaval.ca 1 Introduction Illegal behavior ranges from crimes of great antiquity, such as murder or rape, carrying strong moral opprobrium down to lesser ‘quasi-crimes’, e.g., false or misleading advertising, income underreporting in tax filings, dis- charges of pollutants, fishing out of season, and the like. An important issue in legal or regulatory design is the categorization of offences. Should they be criminalized or qualified as mere violations punished at most by a fine? The issue is one which legal systems have been dealing with since the mid 19th century owing to the multiplication of “modern”regulatory offences, e.g., in factory legislation, food and drug laws or sanitary and public health regula- tions. More recently, from the 1960s onwards, there has been a resurgence of the debate in the wake of the criminal law reforms in many countries. To give but one example, the Model Penal Code of the American Law Institute rejected the principle of strict liability in criminal law. Whether some of- fences should be criminalized has also been contentious in the development of new fields of law, in particular competition law, financial regulations and environmental protection legislation. The issue is in some respects related to the classical dichotomy between malum in se and malum prohibitum1. Malum in se means wrong or rep- rehensible in itself. The expression refers to conduct viewed as inherently wrong independently of regulations or laws governing the conduct. For ex- ample, murder and theft would be wrong regardless of the law. By contrast, malum prohibitum refers to conduct that is wrong only because it is prohib- ited by law. Some acts are crimes not because they are inherently bad, but merely because they have been declared illegal by statute law. The distinc- tion is important in most penal systems, if only implicitly. Obviously, many 1Another way to describe the underlying conceptual difference between malum in se and malum prohibitum is iussum quia iustum and iustum quia iussum, namely something that is commanded (iussum) because it is just (iustum) and something that is just (iustum) because it is commanded (iussum). 1 prosocial individuals with some incentives to mimic the virtuous. The issue is how this influences the design of offences and the enforcement policy, i.e., resources spent on detecting violations of the law. A basic result is that fault-based offences tend to be more effective in harnessing reputational concerns. The reason is that being found guilty of an offence is then more informative. A strict liability offence merely ascertains that the violator committed a potentially harmful action and says nothing about the circumstances in which the action was committed. By contrast, a fault-based offence unambiguously reveals reprehensible behavior, thereby providing more precise information about the individual’s character. When the social norm is a strong one, with potentially strong stigmatization of violators, socially useful incentives are therefore provided by the signaling role of “fault”, allowing greater deterrence or lower enforcement costs when ascertaining “fault” involves negligible additional costs. When the social norm is non-existent and legal sanctions are restricted to socially costless fines (pure transfers), fault-based and strict liability offences are equally effi cient. However, in intermediate situations with weak social norms, it is not always the case that fault-based offences do better than strict liability offences in harnessing reputational concerns. Which regime is better depends in a complex way on the underlying situation. We show that the optimal legal regime and enforcement policy are interdependent and entail fault- based offences when detected violations of the law would seldom occur and strict liability offences otherwise. The dichotomy between fault-based and strict liability offences captures an important distinction between “criminalized” offences and purely “reg- ulatory” offences. In our analysis, the legal design problem is approached from a standard utilitarian perspective, in the sense that opprobrium and the reputational effects of legal sanctions are only considered for their in- centive effects. When offences are fault-based, social sanctions tend to be harsher because of more precise reputational effects. It follows that fault- 4 based offences do better for acts that are clearly bad from a moral and/or social point of view. By contrast, when there is no pre-existing norm, strict liability does as well. The analysis therefore provides an economic interpre- tation of the usefulness of the distinction between malum in se and malum prohibitum for the purpose of legal design and for deriving the optimal en- forcement policy. Section 2 reviews some of the relevant litterature. Section 3 presents the basic setup. Section 4 compares the incentives under different legal regimes and enforcement policies. Section 5 derives the implications for effi cient legal design. Section 6 concludes. Proofs are in the Appendix. 2 Literature review A recent microeconomic literature has emphasized that one’s actions may signal something about unobservable predisposition and that some predis- positions are socially valued (see e.g. Bernheim, 1994; Bénabou and Tirole 2006, 2011; Daughety and Reinganum, 2010; Deffains and Fluet, 2013). Numerous experimental or field studies have also shown that social image concerns are major motivators of prosocial behavior (Masclet et al. 2003, Dana et al. 2006, Ellingsen and Johannesson 2008, Andreoni and Bernheim 2008, Ariely et al. 2010, Funk 2010, Lacetera and Macis 2010, among others). Relatedly, there is a growing literature on the interaction between formal legal sanctions and informal nonlegal sanctions. Much of this literature an- alyzes the substituability of legal and nonlegal sanctions, pointing out that various nonlegal sanctions, such as stigma or loss of standing in a commu- nity, may deter undesirable behavior just as or more effectively than formal legal sanctions (Macauley 1963; Ellickson 1991; Bernstein 1992). Other as- pects of the literature focus on the potential complementarity of informal and formal sanctions, noting that legal penalties may influence the existence and impact of informal sanctions (Kahan, 1998, Posner 2000; Cooter 2000a, 5 2000b; Teichman 2005). A specific field of the literature studies the relation- ship between morality and law. Cooter (1998) analyzes how law promotes individual incentive to acquire morality and self-control. Posner (1997) ex- plains how law complements or substitutes for social norms. Shavell (2002) compares the two in terms of the social costs of enforcement and the ef- fectiveness in controlling behavior. He argues that, if the expected private gain from undesirable action and the expected harm due to the conduct are large, it is optimal to have law supplement morality and, if morality does not function well, law alone is optimal. In a civil law context, Deffains and Fluet (2013) analyze how liability rules (under the form of damages paid to the plaintif) for misbehavior and social pressure interact to provide incentives to take care and what are the impacts of those interactions on the structure of the legal system. The main point made is that the negligence rule tends to be more effi cient than strict liability. The logic is that under the negligence rule, courts assess a person’s level of care. Hence, if he is found to be negligent, it will be impossible or unlikely that he is a prosocial person. Thus, for people who want to be viewed as prosocial, the negligence rule provides a reputational incentive to take optimal care. Under strict liability, however, no direct information is provided by the legal system about the level of care– a person who is truly prosocial and took care could have caused an accident nevertheless and be found strictly liable. Hence, the reputational incentive provided by strict liability to take more care, for people who value their reputation, is muted. The focus of that paper is the extent to which formal legal sanctions crowd-out or crowd-in informal motivations under different liability rules. The question of the interaction between law and (moral or social) norms is also important in criminal law. For instance, McAdams and Rasmusen (2007) and Shavell (2002) provide a general discussion of legal sanctions versus informal motivation as regulators of conduct. Fault-based offences also bear a relation to the concept of “expressive law”. According to this 6 that conduct jeopardising public safety and health may be punishable in the absence of any blameworthy mental state, it sends a strong deterrence mes- sage ((Schaeffer and Muller-Langer, 2008). Secondly because, as a practical matter, it would be so extraordinarily diffi cult to prove that a person ac- tually intended to act so as to jeopardise public safety or health, successful prosecutions would be so unlikely that the law would be meaningless. One of the most common forms of strict liability offences of this kind are simple motor vehicle laws. These are intended to underpin public safety, and their utility depends upon the absence of a need to prove “fault”when they are contravened. Civil aviation safety regulations are strict liability offences for essentially the same reasons. Consequently, the debate between strict liability and fault in criminal offences is a complex one. The legal doctrine sometimes looks for a compro- mise and tries to define the appropriate degree of fault according to different categories of crimes. For instance, Thomson (1994) explains how the Cana- dian Suprem Court relies on the notion of stigma as the primary factor to be considered in determining the constitutionally required degree of fault for crimes such as murders. These debates certainly shed some light on the fault-based vs strict liability controversy for criminal offences. However, one needs to go further by identifying the signaling effects of the different legal mechanisms when individuals are influenced by social norms of conduct and concerns about social approval and self-image. 3 Set-Up We start by reviewing the basic public law enforcement model, borrowing from Polinsky and Shavell (2000, 2007). Next we extend this model to in- corporate other-regarding behavior. The purpose of the model is to analyze the use of public agents to detect and to punish violators of legal rules. In this context, an individual will commit a harmful act if and only if his gain 9 from doing so exceeds the fine that is imposed by the public authority in case of violation. The standard model. Risk-neutral individuals can obtain a private gain g from committing an act causing an external harm of amount h. The gain – equivalently the opportunity cost of not committing the act – varies among individuals and depends on the circumstances. The probability dis- tribution is F (g) with density f(g) on the support [0, g], where g > h. Social welfare is the sum of the gains individuals obtain from committing the act less the harm they cause to others. Denoting the individuals’behavior by e ∈ {0, 1}, where e = 1 means commission of the act2, and interpreting e(g) as behavior in the circumstance g, social welfare is∫ g 0 e(g) (g − h) f(g) dg. Socially optimal behavior is therefore e∗(g) = { 1 if g ≥ h, 0 otherwise. (1) The harmful act is a strict liability offence if it is illegal irrespective of circumstances. We refer here to offenses such as traffi c violations, fraudulent advertising, income tax underreporting, illegal parking... The sanction for violating the law is a fine s, a socially costless transfer of money. The en- forcement policy is summarized by the probability p of detecting violations. The per capita enforcement expenditure is c(p) with derivatives c′ > 0, c′′ ≥ 0. An individual will commit the harmful action if his gain from doing so exceeds the expected fine, g ≥ ps. For a given enforcement policy, welfare is therefore ∫ g ps (g − h) f(g) dg − c(p). 2Observe that we could intrepret the acts in different perspectives: acts of "omis- sion" (not complying with some regulation, e.g. fire detectors) vs "positive" acts (driving through red light). 10 An optimal policy maximizes this expression with respect to the value of the fine and the probability of detection. As is well known, in such a framework the fine should be set at the maximum possible level, say the in- dividuals’wealth or some given upper bound on allowable fines. Accordingly, I take s to be exogenous. Maximizing welfare with respect to the probability of detection and assuming an interior solution, the optimal probability of detection satisfies the first-order condition (h− ps)dF (ps) dp = c′(p). (2) Thus ps < h, implying that the optimal enforcement policy entails un- derdeterrence compared with first-best behavior. Some individuals, those for whom ps ≤ g < h, will commit the harmful act even though it is not so- cially warranted. The optimal policy trades-off some ineffi ciency in behavior against savings in enforcement expenses. Now consider fault-based offences, wereby an individual who causes harm is sanctioned only if he failed to obey some standard of behavior. In the present framework, legal standard of behavior is in terms of the circum- stances under which the harmful act is committed. If an individual commits a harmful act, his gain must equal or exceed some threshold in order for him to avoid liability; otherwise, he is considered to be at fault. The legal standard is therefore defined by a threshold level of gain ĝ. Committing the harmful act is illegal when the circumstances are g < ĝ, in which case the violator is subject to a fine if he is detected. An individual will therefore commit the harmful act if g ≥ min(ps, ĝ). The optimal policy consists in choosing the probability of detection and the fault standard so as to maxi- mize ∫ g min(ps,ĝ) (g − h) f(g) dg − c(p). It is easily seen that an optimal policy requires ĝ ≥ ps, otherwise enforce- ment costs could be reduced with no detrimental effect on deterrence. The 11 Individuals can both cause harm or suffer harm caused by others. Con- sider an omniscient regulator who can directly impose the action profile e(g), g ∈ [0, g] on all individuals. The average net material payoff is then w = w0 + ∫ g 0 e(g) (g − h) f(g) dg. (5) where w0 is initial wealth. Let the action profile ê(g) be welfare maximizing and suppose that the regulator has the option of either publicizing or pre- venting any information about the individuals’types. If an optimum entails that no information is disclosed, then ê(c) maximizes W subject to the re- source constraint (5) and to beliefs satisfying tI = λ, where λ is simply the prior belief about types. Clearly, this implies ê(g) = e∗(g) as defined in (1). Welfare then equals W ∗ = w0 + ∫ g h (g − h) f(g) dg + βλ. (6) Now, the same result would also obtain when full or imperfect information about types is disclosed because the reputational benefits and losses would then simply cancel out.7Benabou and Tirole (2006, 2011): esteem is a zero sum game Public information and branding. Society at large – equivalently an individual’s relevant reference group – does not directly observe the circumstances faced by an individual nor his behavior. However, public enforcers are assumed to be able to ascertain the circumstances when they detect a harmful act. In other words, they are able to apply the law when the offence is fault-based. Legal proceedings against an individual constitute public information from which inferences can be made. Specifically, I assume that the only information “publicly” available about an individual – by which I mean in society at large – is either G for “guilty”, in which case the individual is known to have been found guilty of an offence, or N for “no 7This follows from the law of iterated expectations, E(E(t | I)) = E(t) = λ. 14 news”. The latter means that either the individual did not commit an offence or that he did but was not detected. In terms of the previous notation, the publicly available information affecting one’s reputation is therefore the binary signal I ∈ {G,N}. The significance of the signal will depend on the legal regime, in particular whether offences are strict or fault-based, and on the enforcement policy. We adopt here an interpretation of self- image that is developed by Bodner-Prelec (2003) and Benabou-Tirole (2006). These authors have incorporated concern for image into models of individual decisions by formalizing them as preference-signaling games and by applying the concept of signaling equilibrium to analyze behavior. These models feature a decision-maker with unobservable preferences over outcomes, who also derives value from the endogenously determined beliefs of an observer about those preferences. 4 Equilibrium under a Given Regime This section describes the equilibria under given legal regimes and enforce- ment policies. A (perfect Bayesian) equilibrium is characterized by the indi- viduals’action profiles and the beliefs about individuals’type conditional on the “guilty”and “no news”events. The legal regime is defined by the stan- dard of fault when committing the harmful act. The regime is fault-based if the legal standard is less the upper bound of possible gains, otherwise the regime involves a strict liability offence. The enforcement policy is char- acterized by the fine for unlawful conduct and the probability of detecting such behavior. We proceed in three steps. First we derive the action profiles taking the posterior beliefs as given. Next we derive the beliefs as a function of action profiles. Finally we solve for the equilibrium wherein action profiles and beliefs are consistent with one another. Incentives. Let the sanctioning rule be denoted by δ(g, ĝ), where 15 δ(g, ĝ) = 1 if g < ĝ and is otherwise zero. The expected utility of a type-t individual in the circumstance g is ut = w + e [g − pδ(g, ĝ)s]− tγmax(e− e∗(g), 0) + β [ peδ(g, ĝ)tG + (1− peδ(g, ĝ)) tN ] , e ∈ {0, 1}, t ∈ {0, 1}. The first term, w, is the part of the individual’s wealth that he takes as given. This consist of initial wealth minus the average harm caused by others plus the per capita tax to finance the enforcement policy (surveillance expenditures minus fines collected). The second term is the expected net material payoff from committing or not committing the harmful act. The third term is the guilt disutility from committing the harmful act when it is socially unwarranted. The fourth term is the expected reputational utility. If the individual does not commit the harmful act, e = 0, or if he would not be legally at fault when he does, δ(g, ĝ) = 0, the belief about his type will be tN for sure, the posterior probability that he is a good citizen given “no news”. If he unlawfully commits the harmful act, he is detected with probability p and the belief about his type is then tG, the posterior probability conditional on “guilty”. If he is not detected, the belief is again tN . These beliefs are determined at equilibrium but are taken as given by the individual. Consider a non prosocial individual. If the harmful act is not committed, expected utility is ut = w + βtN . If it is committed and it is lawful, that is g ≥ ĝ, expected utility is ut = w+g+βtN . Hence it will then be committed. In circumstances where the act is unlawful, expected utility is ut = w + (g − ps) + β(ptG + (1− p)tN ) and the act is then committed if g ≥ p(s+ β∆), where ∆ ≡ tN − tG will be referred to as the reputational penalty from being found guilty of an offence. Altogether a non prosocial commits the harmful act if and only if g ≥ min[ĝ, p(s+ β∆)] ≡ g0, (7) 16 Figure 1 provides examples of the reputational penalty as a function of the bad citizens’ compliance rate under two different legal regimes, given y1 = 1. The enforcement policy is the same under both regimes. In case A, the standard of fault is the first-best ĝA = h, equivalently ŷA = 1. The reputational penalty is then bounded below by λ. In case B, the standard of fault is above the first best, ŷB > 1. The reputational penalty then goes down to zero when all the non prosocial comply perfectly. For compliance rates suffi ciently close to unity, the reputational penalty under regime A is therefore larger than under B. As depicted, the curves intersect. This need not occur but it is a possibility at suffi ciently small compliance rates. I will discuss this further when we turn to legal design. Figure 1 about here Equilibrium. From the foregoing discussion, both types behave the same if they overcomply, so that the reputational penalty is then nil. Be- cause reputational concerns then provide no incentives, overcompliance can arise only if the expected fine ps > h as in the standard model with no in- formal motivations. We disregard policies with ps > h because they would serve no purpose. In the cases considered, good citizens therefore always perfectly comply with the social norm of conduct. An equilibrium consists of a compliance rate for the non prosocial and of a reputational penalty that are mutually consistent, given that good citizens perfectly comply. Proposition 1 Let the enforcement policy and legal regime satisfy ps ≤ h and ĝ ≥ ps. Then there is a unique equilibrium with y0 ≤ y1 = 1. (i) If ps = h, y0 = 1 as well. (ii) If ps < ĝ ≤ h, the equilibrium y0 is increasing in p as long as p(s+βλ) < ĝ, otherwise y0 = F (ĝ)/F (h); in either case, y0 is increasing in ĝ. (iii)If ps < h < ĝ, the equilibrium y0 is increasing in p and may be increasing or decreasing in ĝ. 19 Different equilibria are illustrated for the case ps < h. In the Figures 2 to 5, yS = F (ps)/F (h) denotes the compliance rate that would obtain in the standard model; ∆(y0) is the reputational penalty as a function of the compliance rate under a given legal regime and enforcement policy; y0(∆) is the compliance rate as a function of the reputational policy under the same regime and enforcement policy. The perfect Bayesian equilibrium is the intersection of theses curves (point E). Consider first the case ŷ < 1. An individual found guilty of an offence is then for sure non prosocial. In Figure 2, the compliance rate of the non prosocial is increasing in the reputational penalty up to the upper bound ŷ entailed by the fault standard. Figure 3 depicts the case where ŷ does not bind. In either case, relaxing the fault standard (that is, increasing ĝ or equivalently ŷ) yields an increase in the equilibrium compliance rate. The effect is obvious if the fault standard binds. When it does not, the effect follows from the fact that relaxing the standard shifts the reputational penalty curve to the right (the curve also rotates upwards, while remaining bounded below by λ when y0 = ŷ). The intuition is that relaxing the fault standard increases the significance of the “no news” event, so that reputational incentives have more bite. In Figure 4, the standard of fault is the first-best ŷ = 1. In the case represented, all individuals comply perfectly. This arises if reputational concerns are suffi ciently important (β is large) or if the expected fine is suffi ciently large even though ps < h. Figure 2 to 5 about here In Figure 5, ŷ > 1 and both types can be found guilty. Further relaxing the fault standard then has an ambiguous effect on the reputational penalty curve which may rotate upwards or downwards, so the equilibrium compli- ance rate may go either way. As before, relaxing the standard increases the significance of “no news”. However, it also reduces the significance of an 20 offence because more good citizens are found guilty, so the net effect on the reputational penalty is ambiguous. Increasing the probability of detecting harmful acts increases the signif- icance of “no news”, with no effect on the significance of the “guilty”event. In the figures, the reputational penalty curve therefore rotates upwards. Because offenders are now more likely to be apprehended, a larger proba- bility of detection also shifts the positively sloped portion of the compliance curve to the right (and reduces the slope). Thus, compliance unambiguously increases except at corner solutions where y0 = 1.9 5 Optimal Legal Regime and Enforcement When the enforcement policy satisfies ps ≤ h, welfare reduces to the first best W ∗ as defined in (6) minus the loss from undercompliance on the part of the non prosocial and the per capita enforcement expenditure: W = W ∗ − (1− λ) ∫ h g0(ŷ,p) (h− g) f(g) dg − c(p) (9) where g0(ŷ, p) is the equilibrium threshold for the non prosocial, given the legal regime and enforcement policy. An optimal policy sets ĝ and p so as to maximize the above expression. This is equivalent to maximizing V (ŷ, p) ≡ (1− λ) ∫ h g0(ŷ,p) (g − h) f(g) dg − c(p). (10) The structure of the problem is the same as in the standard model except that one now takes into account that different policies may be more or less effi cient in harnessing reputational motivations.10 9When ŷ > 1, the effect on the equilibrium reputational penalty is ambiguous. A negative effect may be interpreted as greater formal legal enforcement partially crowding out informal motivations. 10The maximum sanction principle still holds for the usual reasons. Thus we take s as given. 21 different fault standards determine different signals which cannot be ranked in the sense of one binary signal being more informative than the other.12 If the reputational sanction curves intersect, one can show that they do so at13 y0 = 1 2(1− λ) ( 1− 2λ− 1− p F (h)p ) . (11) The right-hand side of (11) is positive only if λ < 1/2 and p > 1 1 + (1− 2λ)F (h) . For instance, if λ = 1/4, F (h) = 2/3 and p = 9/10, then the intersection is at y0 = 4/9. When under strict liability the equilibrium compliance rate is less than the value at which the curves cross, as in situation L of Figure 6, one can check that the per capita frequency of detected offences will be greater than one half. As shown below, this turns out to be a necessary condition for a strict liability offence to be optimal. The optimal legal regime and enforcement policy depend on the under- lying situation and both must be jointly chosen. The underlying situation includes the importance of reputational concerns, the proportion of prosocial individuals, the severity of the harmful act, and the probability distribution of possible circumstances. Moreover, whether a fault-based or a strict lia- bility regime performs better also depends on enforcement possibilities, as defined by the permissible fine and the enforcement cost function. Proposition 3 Suppose the legal regime and enforcement policy are opti- mal. If the legal regime is fault-based, then detected offences constitute a rare event, pF (h)(1− λ)(1− y0) < 1 2 . (12) 12There is an exception: for ĝ < h, relaxing the fault-standard increases the infor- mativeness of the binary “guilty-no news” signal, which explains why ĝ < h cannot be effi cient. 13Solve (17) and (18) in the Appendix for y0 yielding the same ∆ under both legal regimes. 24 If the legal regime involves a strict liability offence, then detected offences constitute a frequent event, p [1− F (h) + F (h)(1− λ)(1− y0)] ≥ 1 2 . (13) The left-hand side of (12) is the frequency of detected violations under the fault-based regime with standard ĝ = h and enforcement policy p, given the equilibrium compliance rate on the part of the non prosocial. The left- hand side of (13) is the frequency of detected violations under a strict liability regime given the equilibrium compliance rate under that regime. Everyone then commits the harmful act when g ≥ h; when g < h, a fraction 1− y0 of the non prosocial do. The condition (12) is more likely to hold when the permissible fine is large, as this allows deterrence with a relatively small probability of de- tection. It is also more likely if detecting violations is very costly so that the probability of detection is small. Thus, the choice between fault-based and strict liability offences will depend on enforcement considerations. In particular, the following condition is suffi cient. Corollary 1 The optimal legal regime is fault-based if socially unwarranted acts would constitute a rare event in the absence of legal sanctions, F (h)(1− λ) < 1 2 . (14) The condition is satisfied if the harmful act is usually socially warranted (i.e., 1 − F (h) is greater than one half) or if good citizens constitute a majority. 6 Discussion and Extensions In many situations, socially unwarranted behavior will be a rare event be- cause most individuals are socially minded. Hence illegal behavior will also 25 be rare. It may also be that detected illegal behavior is rare because sub- stantial deterrence is achieved with a large fine and a low probability of apprehension. A legal regime that seeks to harness reputational incentives should then seek to reduce apparent unlawfulness. This is achieved by a fault-based regime. Not finding fault may then be banal, therefore posteri- ors conditional on “no news”do not differ too much from the prior. But then to be found guilty of an offence yields substantial disesteem. By contrast, when detected illegal behavior would be a frequent event under a fault-based regime, offences are banal and not finding fault may yield significant esteem. It will then be better to switch to a strict liability regime, as this increases the salience or visibility of offences, thereby increasing the significance of “no news”. Our results are reminiscent of Bénabou and Tirole’s (2006, 2011) dis- cussion of how acceptable behavior arises from the interplay of “honor”and “stigma”. High stigma is attached to a behavior that “is just not done”, only the worst type will do it. Alternatively, when “everyone does it”, the same behavior carries little stigma. But then “not doing it”yields prestige. In the case of legal regimes, whether being guilty of an offence imposes sig- nificant stigma or whether not having been found guilty confers significant honor depends on the underlying situation but also on the legal regime itself together with enforcement possibilities. 7 Concluding Remarks Violating the law does not have the same social meaning under strict liabil- ity and fault-based offences. A fault-based offence is a stronger signal about one’s character than a strict liability offence. Fault-based regimes will there- fore often perform better in harnessing reputational concerns for the purpose 26 (i) Let ps = h. If ŷ = 1, obviously y0 = 1. For ŷ > 1, Lemma 2 implies ∆(y0, ŷ, p) > 0 for all y0 < 1 and ∆(1, ŷ, p) = 0, hence y0 = 1 is again the unique solution to (20). (ii) Let ps < ĝ ≤ h, equivalently yS < ŷ ≤ 1. I show that the equilib- rium y0 ∈ (yS , ŷ]. Obviously ϕ(yS) > 0. By Lemma 2, ∆(ŷ, ŷ, p) = λ. If p(s+βλ) ≥ ĝ, ϕ(ŷ) = 0 and the equilibrium satisfies y0 = ŷ. If p(s+βλ) < ĝ, ϕ(ŷ) < 0 and the equilibrium satisfies y0 < ŷ. In the latter case, differenti- ating (19) totally with respect to ŷ and p yields ∂y0 ∂ŷ = pβf(g0)∆ŷ F (h)− pβf(g0)∆y0 , (21) dy0 dp = f(g0)(s+ β∆ + pβ∆p) F (h)− pβf(g0)∆y0 , (22) where g0 = p(s+β∆(y0, ŷ, p)). The reputational penalty is decreasing in y0, hence the denominator is positive. From (17), ∆(y0, ŷ, p) is increasing in ŷ and in p. Hence (21) and (22) are both positive. To complete the argument, when p(s+ βλ) ≥ ĝ, y0 = ŷ and is then also increasing in ŷ. (iii) Let ps < h < ĝ, equivalently yS < 1 < ŷ. The argument is similar except that the solution now satisfies y0 ∈ (yS , 1). As before, ϕ(yS) > 0. By Lemma 2, ∆(1, ŷ, p) = 0 and therefore ϕ(1) < 0. Differentiating (19) totally with respect to ŷ and p again yields (21) and (22). However, the reputational penalty is now defined by (18). The signs of ∂∆/∂y0 and ∂∆/∂p are positive but that of ∂∆/∂ŷ is now ambiguous (see the proof of Proposition 2). Thus y0 is increasing in p but may now be increasing or decreasing in ŷ.  Proof of Proposition 2. Let y0(ŷ, p) and g0(ŷ, p) denote equilibrium values as derived in Proposition 1, y0(ŷ, p) ≡ F (g0(ŷ, p))/F (h). An optimal legal regime and enforcement policy maximizes V (ŷ, p) := (1− λ) ∫ h g0(ŷ,p) (g − h) f(g) dg − c(p). (23) The partial derivatives are Vŷ(ŷ, p) = (1− λ) ( h− g0(ŷ, p) F (h) ) ∂y0(ŷ, p) ∂ŷ , 29 Vp(ŷ, p) = (1− λ) ( h− g0(ŷ, p) F (h) ) ∂y0(ŷ, p) ∂p − c′(p). From the proof of Proposition 1, the function y0(ŷ, p) may be discontinuous at ŷ = 1; even when the function is continuous, the derivative ∂y0(ŷ, p)/∂ŷ is discontinuous at ŷ = 1. Moreover, for ŷ < 1, ∂y0(ŷ, p)/∂p is discontinuous when p(s + βλ) = ĝ. As need be, derivatives will be understood to mean left or right derivatives. Let (ŷ∗, p∗) denote an optimal policy, assuming p∗ > 0. I consider the possibilities that ŷ∗ ≤ 1 or ŷ∗ > 1. Let y = F (g)/F (h), so that ŷ = y amounts to strict liability. Case 1: ŷ∗ ≤ 1. For ŷ ≤ 1, the function y0(ŷ, p) satisfies part (ii) of Proposition 1. When ŷ < 1, g0(ŷ, p) < h and ∂y0(ŷ, p)/∂ŷ > 0, hence Vŷ(ŷ, p) > 0. If ŷ∗ ≤ 1, it must therefore be that ŷ∗ = 1, equivalently ĝ∗ = h. When p(s + βλ) ≥ h, g0(1, p) = h so that Vp(1, p) < 0. The optimal p∗ must therefore satisfy p∗(s+ βλ) < h, implying underterrence, i.e., y0(1, p∗) < 1. Case 2: ŷ∗ > 1. For ŷ > 1, the function y0(ŷ, p) satisfies part (iii) of Proposition 1, im- plying g0(ŷ, p) < h whenever ps < h. I first show that the optimal p∗ must satisfy p∗(s+ βλ) < h as in Case 1. Suppose not. Then, for all ŷ > 1, V (ŷ, p∗) = (1− λ) ∫ h g0(ŷ,p∗) (g − h) f(g) dg − c(p∗) < − c(p∗) = V (1, p∗) where the right-hand side is the welfare level reached by setting the standard ŷ = 1 instead and inducing the first-best behavior because p∗(s+ βλ) ≥ h. When p∗(s + βλ) < h, y0(ŷ, p∗) < 1 in the closed interval [1, y] and the function is then continuous on this interval. The latter follows from the fact that, when y0 < 1, the reputational penalty is continuous in ŷ at ŷ = 1. It follows that lim ŷ↓1 ∆(y0(ŷ, p ∗), ŷ, p∗) = λ 1− p∗F (h)(1− λ)(1− y0(1, p∗)) , 30 where the right-hand side is the penalty as defined in (17). Thus we may look for an optimal policy ŷ∗ ∈ [1, y]. If ŷ∗ 6= 1, then either ŷ∗ = y or ŷ∗ is an interior solution. In the latter case, the solution must satisfy the first-order condition Vŷ(ŷ ∗, p∗) = 0, implying ∂y0(ŷ, p ∗) ∂ŷ ∣∣∣∣ ŷ=ŷ∗ = 0, (24) and the second-order condition Vŷŷ(ŷ ∗, p∗) ≤ 0 which, when (24) holds, implies ∂2y0(ŷ, p ∗) ∂ŷ2 ∣∣∣∣ ŷ=ŷ∗ ≤ 0. (25) From (21), the condition (24) requires ∆ŷ(y ∗ 0, ŷ ∗, p∗) = 0, (26) where y∗0 = y0(ŷ ∗, p∗). Differentiating (21) with respect to ŷ, given (24) and (26), yields ∂2y0(ŷ, p ∗) ∂ŷ2 ∣∣∣∣ ŷ=ŷ∗ = pβf(g∗0)∆ŷŷ(y ∗ 0, ŷ ∗, p∗) F (h)− pβf(g∗0)∆y0(y ∗ 0, ŷ ∗, p∗) . Therefore (25) requires ∆ŷŷ(y ∗ 0, ŷ ∗, p∗) ≤ 0. (27) The reputational penalty as defined in (18) can be rewritten as ∆(y0, ŷ, p) = λ(1− λ)(1− y0) (ŷ − λ− (1− λ)y0) [1− pF (h)(ŷ − λ− (1− λ)y0)] so that ∆ŷ(y0, ŷ, p) = − λ(1− λ)(1− y0) [1− 2pF (h)(ŷ − λ− (1− λ)y0)] {(ŷ − λ− (1− λ)y0) [1− pF (h)(ŷ − λ− (1− λ)y0)]}2 . (28) Given (26), it is then easily seen that ∆ŷŷ(y ∗ 0, ŷ ∗, p∗) = λ(1− λ)(1− y∗0)2pF (h) {(ŷ − λ− (1− λ)y∗0) [1− pF (h)(ŷ − λ− (1− λ)y∗0)]} 2 , 31 [14] Cooter, R. and A. Porat (2001), Should Courts Deduct Nonlegal Sanc- tions from Damages? Journal of Legal Studies 30, 401—22. [15] Dal Bó, E. and M. Terviö (2013), “Self-Esteem, Moral Capital and Wrong-Doing.”Journal of the European Economic Association 11, 599- 633. 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