Remediation and self-reporting in optimal law enforcement

Journal of Public Economics 72 (1999) 379–393

Remediation and self-reporting in optimal lawenforcement

*Robert InnesDepartment of Agricultural and Resource Economics, University of Arizona, Tucson, AZ 85721,

USA

Received 9 September 1997; received in revised form 6 June 1998; accepted 8 August 1998

Abstract

Many environmental laws encourage firms to self-report their violations to governmentregulators, rather than subject themselves to probabilistic enforcement. This paper studiesself-reporting enforcement regimes when there are ex-post benefits of remediation orclean-up. Remediation benefits are shown to impart two advantages to the use of self-reporting beyond those identified elsewhere. Firstly, whereas non-reporting firms onlyengage in costly clean-up when they are caught by an enforcement authority, self-reportingfirms always engage in efficient remediation. Secondly, with self-reporting, the governmentcan costlessly impose stiffer non-reporter penalties that reduce the government enforcementeffort required to achieve a given level of violation deterrence. 1999 Elsevier ScienceS.A. All rights reserved.

Keywords: Law enforcement; Self-reporting; Remediation

JEL classification: K42; K32; D62; Q28

1. Introduction

Many environmental laws, including America’s Clean Air Act, Clean WaterAct, and Superfund law, require firms to self-report their compliance or violationstatus to government regulators. Penalties, both explicit and implicit, are leviedwhen a firm fails to accurately report its violation, over and above penalties that

*Tel.: 11-520-621-9741; fax: 11-520-621-6250.E-mail address: [email protected] (R. Innes)

0047-2727/99/$ – see front matter 1999 Elsevier Science S.A. All rights reserved.PI I : S0047-2727( 98 )00101-7

380 R. Innes / Journal of Public Economics 72 (1999) 379 –393

1may be assessed on a firm which accurately reports its behavior. State en-vironmental statutes also encourage self-reporting of violations (Anderson, 1996;Geltman, 1996). For example, recent Arizona legislation would have exempted acompany that violated an environmental law from civil enforcement action if thecompany reported the violation and took prompt corrective action to mitigate harmand avoid a recurrence of the violation. Environmental groups criticized the bill asa ‘polluter protection act’ that would provide polluters with little or no incentive to

2prevent the occurrence of environmentally damaging accidents.Although the study of self-reporting in the theory of optimal law enforcement is

not new, the literature on this topic is quite small and recent. In this paper, I buildon this literature, addressing issues that are most closely related to two key works

3by Kaplow and Shavell (1994) (KS) and Malik (1993) (M). Two genericquestions underpin these studies, and this paper as well: firstly, when is it efficientfor an enforcement regime to elicit self-reporting by violators? And secondly, what

4is the optimal structure of an enforcement regime with self-reporting?1The Comprehensive Environmental Response, Compensation and Liability Act (CERCLA, or

Superfund), for example, explicitly provides for non-reporting penalties (42 U.S.C., sec. 9603(b)).Beyond such explicit penalties, legal experts warn potential polluters that failure to accurately report anenvironmental violation can prompt the government to impose higher fines than it would impose on a‘cooperating’ firm; to use the failure to report as evidence in its case against the firm, increasing itschances of a successful prosecution; and prosecuting the firm more vigorously. Starr (1992) writes, forexample: ‘Companies should never conceal the violations they discover . . . When a company fails todisclose even the smallest of violations, . . . (w)hat was once a minor violation may serve as thecenterpiece of the government’s case in a major criminal prosecution . . . When the government piecestogether its case with the benefit of 20/20 hindsight, reports which are only partially accurate becomeparticularly damning . . . ’ Government sentencing guidelines and consumer product safety laws alsohave self-reporting provisions (Kaplow and Shavell, 1994). The US Consumer Product Safety Actrequires producers to report violations of product safety laws or face penalties if they do not. Similarly,federal sentencing guidelines stipulate stiffer sanctions for criminals who have not reported theiroffenses.

2See, for example, ADS (1996).3This work also builds on the generic public enforcement literature. See, for example, the classic

papers of Becker (1968), Stigler (1970), and the more recent work of Shavell (1991), Mookherjee andPng (1992), Polinsky and Shavell (1992). Important related work on environmental law enforcementincludes Grieson and Singh (1990), Harrington (1988), Harford and Harrington (1991), Russell et al.(1986), Garvie and Keeler (1994). (These citations are an abbreviated subset of the enforcementliterature, and I hope authors of the many excellent papers not cited will accept my apology for theiromission.)

4Two other important papers also consider self-reporting in environmental regulation, but withdifferent objectives than the present inquiry. Harford (1987) studies firm responses to an exogenousgovernment enforcement policy that includes self-reporting, penalties for misreports, and taxes onreported pollution; however, optimality in enforcement policy is not the object of Harford’s analysis.Swierzbinski (1994) studies a pollution regulation model in which firms have private information abouttheir costs of pollution abatement and the amount of abatement achieved; the incentive-compatibleregulatory regime entails firm reports of their abatement levels, ex-ante taxes and monitoringprobabilities based upon these reports, and an ex-post penalty / reward for those firms who aremonitored. This study, which bears an analytical resemblance to studies on optimal auditing, considersdifferent issues than are germane here. Like the optimal auditing literature, for example, the question ofwhether or not self-reporting is optimal is not at issue.

R. Innes / Journal of Public Economics 72 (1999) 379 –393 381

Without self-reporting, law enforcement occurs in two stages: (1) the invest-ment of government resources in the monitoring and detection of potentialviolations, with higher investments yielding a higher probability that a givenviolation will be discovered; and (2) the assessment of penalties on identifiedviolators. Penalties are valuable because they provide incentives for potentialviolators not to commit a harmful act, or to invest in measures that reduce thelikelihood that a violation will occur. Self-reporting permits the identification of aviolator without government monitoring. However, a firm will only be prompted toself-report if it is promised a penalty that is no greater than can be expectedwithout self-reporting; therefore, the government must still invest resources inmonitoring in order to penalize prospective non-reporters (even if there are none inthe equilibrium) and thereby provide firms with the needed incentive to self-report.

In studying models with this structure, KS and M identify a number of5economic advantages of self-reporting. First and foremost, both papers argue that

self-reporting may directly reduce enforcement costs. In KS, for example, self-reporting implies that fewer firms need to be monitored in order to achieve a givenprobability of government detection (for non-reporters) because the population ofpotential (non-reporting) violators is smaller. Self-reporting thereby enables thegovernment to achieve a given level of deterrence with less government moni-

6toring effort. Secondly, both papers argue that self-reporting may indirectlyreduce enforcement costs by either reducing regulators’ reliance on an imperfectauditing technology or, as KS note, permitting a given level of deterrence to beachieved without resort to the costly use of imprisonment as a sanction. Finally,KS point out that self-reporting can improve risk-sharing by confronting risk-averse violators with a non-stochastic penalty rather than the stochastic penaltylevied on non-reporters (equal to zero when the violator is not caught and apositive penalty otherwise).

On the other side of the coin, KS and M note that administrative costs ofassessing penalties may disadvantage self-reporting. Self-reporting, it is argued,leads to the imposition of penalties, and the bearing of penalty assessment costs,with probability one; without self-reporting, the administrative costs only need tobe borne a fraction of the time, the frequency with which a violation is detected.

This paper extends this work by studying prospective ex-post benefits fromremediation, or clean-up. To my knowledge, such benefits have not yet been

5Beyond similarities in their qualitative conclusions, there are important differences between the KSand M papers. For example, Kaplow and Shavell (1994) focus on models with heterogeneous agentsthat make binary harm prevention (or care) decisions and have private information about costs of care;Malik (1993), in contrast, focuses on a model with homogeneous agents and continuous harmprevention choices, as does the present paper.

6In Malik (1993), a similar argument is made. There, self-reporting implies that government ‘audits’only need to be performed on firms that report a low level of pollution (i.e. no ‘violation’), thus directlyeconomizing on auditing costs.


7studied in enforcement games. In practice, clean-up activity is a central com-ponent of environmental law enforcement, playing a particularly crucial role in themotivation of self-reporting. For example, a central function of America’sSuperfund law, as well as 22 State-level voluntary site clean-up programs(Anderson, 1996), is to achieve remediation. In this paper, benefits of remediationare shown to provide further economic weight to the case for self-reporting.Self-reporting permits clean-up benefits to be obtained with probability one,whereas non-reporters only clean-up when they are caught. Remediation benefitscan also impart a more subtle advantage to self-reporting, implicitly permitting thegovernment to exert less monitoring effort in order to achieve a given level ofviolator deterrence, even when self-reporting enjoys none of the direct cost-reduction benefits identified in KS and M.

2. The model

N identical, risk neutral and profit-maximizing firms engage in activities thatcan cause accidents. Accidents damage the environment, which is costly to thegeneral public. Each firm can exert non-negative accident-prevention effort (orcare) that reduces the risk that an accident will occur. With x [ [0, x] denoting afirm’s care level — and also (without loss of generality) its cost of care — theprobability that a firm will have an accident is p(x), where p9(x) , 0, p0(x) . 0, andp90(x) $ 0 (care reduces accident risk at a decreasing rate), p9(0) is arbitrarily

8large, and p9(x) is arbitrarily small.Damages from an accident can depend upon whether or not the firm engages in

post-accident clean-up. I will assume that clean-up either takes place, or does nottake place. If clean-up occurs, the firm bears the positive cost C and remainingdamages are D . If clean-up does not occur, damages are D , where D . D 1 CA B B A

(optimal clean-up cannot increase total damages).Each firm has private information about its level of care, x, and about whether

or not an accident has occurred. However, when the government invests G dollarsper firm in accident monitoring, it detects an accident with probability r(G) [ (0,1)where, for G below a finite threshold G, r9(G) . 0, and r0(G) , 0 (governmentmonitoring investments raise detection probabilities at a decreasing rate); r(0) is

7In their conclusion, KS suggest that remediation may provide an additional motivation forself-reporting, but do not develop the argument.

8A non-negative third derivative, p90(x)$0, is a strong sufficient condition for uniquely optimal2government enforcement decisions in this paper. A weaker sufficient condition is: p90(x)$2p0(x) /p9(x).

(See the Appendix proof of Proposition 4 for details.) If p90 is negative, the latter restriction merelyrequires that care has first derivative effects on the accident probability that are stronger than secondderivative effects in the following weak sense: marginal increases in x lead to proportionate reductionsin the magnitude of p0 that are no more than twice the corresponding proportionate reductions in themagnitude of p9.


arbitrarily small, r9(0) is arbitrarily large, and r9(G) 5 0 for G . G (ensuring thatpositive and bounded enforcement effort is undertaken). When the governmentdetects an accident, it can levy a fine that does not exceed the firm’s assets, y.However, even with accident detection, a firm’s care level remains hidden fromthe regulator.

This set-up gives us a standard accident regulation model augmented by apost-accident clean-up measure. Two types of enforcement regimes are possible inthis setting, one without self-reporting of accidents (NSR) and one with self-reporting (SR). In the first, the government monitors accidents (by investing G);for those firms caught creating an accident, a fine of f is levied and clean-up isc

mandated. In the second, a violating firm can self-report its accident, in which casethe government mandates clean-up by the firm and levies a fine of f ; if, however,s

the firm does not self-report and is ‘caught’ by the government, the firm faces afine of f , as before. For notational simplicity, the clean-up cost (though borne byc

the firm) is subsumed in the fines; thus, the actual fines levied are less than the9notional fines f and f by the amount C.c s

Throughout the analysis, I model the detection probability, r(G), as invariant tothe number of self-reporters. KS point out that, when some firms self-report, thegovernment needs to monitor fewer of the remaining firms in order to achieve agiven probability of detecting a non-reporter’s accident — spending less to achievea given level of r. I assume that this benefit of self-reporting is not present here in

10order to focus attention on other advantages of self-reporting mechanisms.

3. Analysis

Let F denote the expected penalty that a firm faces, given that an accident hasoccurred. In an NSR regime, for example, F equals the probability that thegovernment detects the accident, r(G), times the penalty that is levied whendetection occurs, f ; in an SR regime which sets the sanctions so as to elicitc

self-reporting, F simply equals the fine f . Given F, the firm will choose its cares

level to solve the following problem:

min x 1 p(x)F s.t. x [ [0, x] (1)x

9If the government (rather than the firm) bears the clean-up cost, then all that changes is theinterpretation of the fines as exclusive (not inclusive) of clean-up costs; the analysis and results remainentirely unaffected.

10This specification is also realistic when enforcement occurs by monitoring, which KS describe as‘the posting of enforcement agents to observe violations among any of a population, such as whenpolice are stationed at the roadside’. In such cases, self-reports have no affect on the number of — orinvestment in —monitoring posts that is required to achieve a given likelihood of detecting anon-reporter’s violation.


The firm minimizes the sum of its costs of care and the expected costs that itmust bear from prospective accidents. By the construction of p(x), problem (1) has

11an interior solution for all F [(0,D ]. This solution is unique (by convexity ofB

p(x)) and will be denoted by x*(F ).

3.1. The first-best

In a ‘first-best’ world with symmetric information and no costs of monitoringfirm behavior, a benevolent social planner would mandate clean-up whenever anaccident occurs (thus saving D 2(D 1C)$0 in accident damages) and set eachB A

firm’s accident penalty equal to the true social costs of the accident (givenclean-up), D 1C. Such a policy would elicit the first-best care level, x*(D 1C).A A

3.2. The no-self-reporting (NSR) optimum

When the government cannot costlessly monitor accidents, and there is noself-reporting of behavior, a benevolent (welfare-maximizing) government choosesits monitoring investment G and its penalty to firms caught creating an accident,f , to minimize total expected societal costs associated with accidents and accident-c

prevention activity:

min J (G) ; G 1 hx*(r(G)f ) 1 p(x*(r(G)f ))[r(G)(D 1 C)NS c c AG, fc

1 (1 2 r(G))D ]j s.t. f # y (2)B c

A firm that has caused an accident faces the expected penalty, F5r(G)f ,c

prompting the care choice, x*(F )5x*(r(G)f ). When an accident is not detected,c

the firm will not choose to clean-up (because clean-up is costly), leading to the12societal accident damages D . This logic yields the government’s choice problemB

in (2), minimizing the sum of the government’s per-firm monitoring costs, G; eachfirm’s accident prevention costs, x*(); and the expected damages from a firm’s

11A solution to (1) exists by the Weierstrass Theorem. Moreover, any solution is interior forF [(0,D ] because marginal firm costs of care, 11p9(x)F, are negative at x50 (with p9(0) arbitrarilyB

large) and positive at x5x (with p9(x) arbitrarily small).12Implicit in this argument is one of the following two premises: (1) enforcement occurs before

clean-up takes place, or (2) if clean-up can occur both before and after enforcement, then thegovernment is unable to condition its sanctions on the implementation of pre-apprehension clean-up(perhaps because it cannot verify the timing of clean-up activity, whether it is before or afterapprehension). In either case, a firm will have no incentive to engage in clean-up unless and until itsoffense (or accident) has been detected by government inspectors, as posited here. In Innes (1998), Iconsider an alternative specification in which the government can condition sanctions on levels ofpre-apprehension clean-up; in such an environment, an optimal NSR regime will often prompt firms toengage in pre-apprehension (voluntary) clean-up by offering a lower sanction to those that do so.


prospective accidents. The latter damages equal the probability that an accidentoccurs, p(x*()), times the average damages from an accident, given that theaccident has occurred, r(G)(D 1C)1(12r(G))D .A B

With remediation benefits, the standard logic that argues for always assessingthe maximum possible fine (the assets y in our model) no longer holds. This logic,due to Becker (1968), is as follows: if the government raises the fine f , it canc

lower its monitoring expenditures G and preserve the expected fine, r(G)f , thusc

achieving the same accident deterrence incentives at lower cost. Here, this logic isconfounded by the adverse effect of lowering G on the frequency with which

13socially beneficial clean-up occurs. In particular, consider problem (2) withoutthe constraint f #y. So long as ex-post benefits of cleanup are strictly positive,c

D 2(D 1C).0, and the marginal effectiveness of infinitesimal governmentB A

monitoring investments, r9(0), is sufficiently large (as assumed here), this problem*has a solution, ( f ,G*):c

*f 5 D(G*) /r(G*), where D(G) 5 r(G)(D 1 C) 1 (1 2 r(G))D (3a)c A B

G*: 1 2 p(x*(D(G)))r9(G)(D 2 (D 1 C)) 5 0 (3b)B A

Eqs. (3a) and (3b) sets the f fine so as to confront the firm with the averagec

damages caused, and sets government monitoring effort to equate its marginal cost(one) with its marginal benefit in increasing the frequency of clean-up. Clearly, if

*f is less than the firms’ asset level, y, the constraint in problem (2) will not bind;c

Eqs. (3a) and (3b) will describe the optimal enforcement policy without self-reporting; and the optimal fine will not be set maximally.

NSRProposition 1. An optimal enforcement regime without self-reporting, (G ,NSRf ), solves problem (2). If the following condition holds, the optimal fine for anc

NSRaccident, f , is set below the maximum possible level, y, with Eqs. (3a) andc

(3b) describing the optimum:

y . D(G*) /r(G*) (4)

Condition (4) is more likely to hold when: (a) the asset level y is larger; and (b)there is a higher optimal probability of accident detection, r(G*), which is favoredby larger ex-post benefits of cleanup, D 2(D 1C); a more effective accidentB A

13There is a rather extensive literature that identifies reasons for the failure of the Becker (1968)logic, and helps to explain observed practice of less-than-maximal fines. However, to my knowledge,none of this literature identifies ex-post benefits of apprehension as a possible explanation forless-than-maximal fines. See Bebchuk and Kaplow (1992) for a succinct and complete review of thisliterature.


detection technology (i.e. higher levels of r9(G)); and a greater likelihood thataccidents occur, p(x*(D(G*))).

3.3. Self-reporting

In order to prompt firms to self-report their accidents, the government mustprovide them with a self-reporting penalty that is no greater than the expectedpenalty they face when they do not self-report:

f # r(G)f (5)s c

Self-reporters exert care in response to their penalty, x5x*( f ). In addition,s

post-accident clean-up benefits are always obtained, because self-reporters neednot be ‘detected’ in order for clean-up to be mandated. The government’s policychoice problem thus becomes:

min G 1 hx*( f ) 1 p(x*( f ))(D 1 C)j s.t. f # r(G)f and f # y (6)s s A s c cG, f , fs c

Two sets of conclusions can be derived from the study of problem (6): (1)attributes of the optimal self-reporting regime, and (2) prospective benefits fromenacting a self-reporting mechanism in place of a non-self-reporting mechanism.On the first front, we have:

Proposition 2. In an optimal self-reporting enforcement regime, (i) self-reportersare given a penalty exactly equal to the expected penalty that they would facewhen not self-reporting, f 5r(G)f ; (ii) the fine levied on non-reporters is alwayss c

set maximally, f 5y; and (iii) the self-reporting penalty, f , is less than thec s

accident damages, D 1C, prompting a care choice that is less than first-best,A14x*( f ),x*(D 1C).s A

The logic underlying each of the Proposition 2 conclusions is as follows.

1. If the self-reporting penalty were lower than the non-reporter’s expectedpenalty r(G)f (and it cannot be higher by constraint (5)), then the governmentc

monitoring expenditures G could be unilaterally lowered without upsetting theself-reporting constraint or, therefore, the firms’ incentives for accident-preven-tion effort.

2. Because self-reporting permits ex-post clean-up benefits always to be realized,the Becker (1968) logic on maximal fines holds. By raising the non-reporters’fine f and lowering G to preserve the non-reporting expected penalty, r(G)f ,c c

accident-prevention and self-reporting incentives are preserved; ex-post benefits

14Proofs of Propositions, when not implicit in the text, are contained in Appendix A.


of clean-up continue to be derived; and the only efficiency effect is to lowerenforcement costs (by lowering G).

3. At the first-best fine level, f 5D 1C, a marginal reduction in the fine can bes A

achieved by an attendant reduction in G (recalling that f 5r(G)y). Such as

reduction has no affect on the societal costs of accidents and accidentprevention because the initial fine minimizes societal costs by setting themarginal societal cost of the fine to zero. Thus, by directly lowering thegovernment’s costs, G, this reduction raises social welfare.

Turning now to the relative benefits of self-reporting, consider the followingstrategy: (A) set the self-reporting penalty, f , equal to the optimal expecteds

NSR NSRpenalty in the NSR regime, f 5r(G )f ; (B) set the non-reporting penalty ass c

high as possible, f 5y; and (C) set government monitoring expenditures to justc

preserve firms’ incentives to self-report,

NSR NSRG 5 G : f 5 r(G )f 5 r(G )y (7)o s c o

This strategy achieves the same incentives for accident prevention effort, x, asdoes the optimal NSR regime, while reducing societal costs in two ways: firstly,the self-reporting regime achieves ex-post benefits of clean-up 100% of the time,

NSRcompared with r(G ) percent of the time under the NSR regime. And secondly,whenever the optimal NSR regime specifies a less-than-maximal accident penalty,

NSRf ,y, the self-reporting regime can provide the same level of accident deterrentc

incentive with a lower level of G by setting the non-reporting penalty maximally,NSR NSR 15at f 5y. That is, when f is less than y, G in Eq. (7) is less than G .c c o

Proposition 3. The optimal self-reporting regime is strictly superior to the optimalenforcement regime without self-reporting whenever there are positive ex-postbenefits of clean-up /apprehension, C1D ,D .A B

Note that self-reporting is welfare-enhancing here even though none of theself-reporting benefits that are identified in Malik (1993) or Kaplow and Shavell(1994) are present. Remediation also has a number of implications for enforce-ment design:

Proposition 4. When there are positive ex-post benefits of clean-up /apprehension,C1D ,D : (i) the optimal self-reporting fine is less than the optimal expectedA B

NSR NSRpenalty without self-reporting, f ,r(G )f ; (ii) optimal government enforce-s c

ment expenditures, G, are lower under self-reporting than without self-reporting;

15Both of these cost-reducing effects of self-reporting occur only when there are positive ex-postNSR NSRbenefits of clean-up; without any clean-up benefits, f equals y and, hence, G 5G .c o


and (iii) optimal accident prevention effort /care is lower under self-reporting thanwithout.

To understand Proposition 4, there are two cases to consider: (1) when theNSRoptimal NSR regime sets the ex-post sanction maximally, f 5y; and (2) whenc

NSRit does not, f ,y. Turning to the first case, note that there are fewer benefits ofc

monitoring and penalizing firms under a self-reporting regime, for the followingreasons: because clean-up always occurs when accidents are self-reported, ex-postdamages are lower. Therefore, other things the same, firms need to be penalizedless for their accidents in order to provide them with appropriate incentives foraccident prevention. In addition, increases in government monitoring expendituresdo not increase the frequency of ex-post clean-up under a self-reporting regime; incontrast, increases in G do increase ex-post clean-up under the NSR regime. As aresult, there are fewer benefits of government monitoring investments whenaccidents are self-reported, which favors lower levels of G and the associatedaccident penalty, f 5r(G)y. Faced with a smaller accident penalty, firms exert lesss

‘care’.NSRSimilar forces are at play in the second case, when f ,y. However, in thisc

case, marginal government monitoring investments have higher accident deterr-SRence benefits under self-reporting due to a higher non-reporter penalty, f 5y.c

NSRf . Despite the ‘greater bang for the government buck’, the following threec

observations imply that societal incentives for accident deterrence remain lowerunder self-reporting: (I) due to enforcement costs of deterrence, the optimal SRregime ‘underdeters’ accidents by levying a sanction that is less than post-clean-updamages (by Proposition 2): f 5r(G)y,C1D ; (II) post-clean-up damages ares A

NSRlower than average damages under the NSR regime, C1D ,D(G ); and (III)A

in this second case, the ex-post NSR penalty f is chosen freely so as to equate thec

average accident penalty with average accident damages (by Proposition 1):NSR NSR NSRD(G )5r(G )f . Together, the underdeterrence incentives and lowerc

damages that are experienced with self-reporting regimes lead to lower optimallevels of accident deterrence that are achieved with lower levels of governmentenforcement expenditure.

4. Conclusion

This paper has studied a simple model designed to shed light on the prospectiveefficiency benefits of using self-reporting enforcement regimes, and on the desiredstructure of such regimes. In prior work, Kaplow and Shavell (1994) and Malik(1993) identified economic advantages of self-reporting that include (i) directlyeconomizing on enforcement costs by making the detection of non-reportingviolators easier, (ii) improving risk-sharing by assessing non-stochastic penalties,and (iii) reducing regulators’ reliance on poor auditing technologies and the costly


use of imprisonment as a sanction. In this paper, I have argued that self-reportingenjoys additional economic advantages that have so far escaped academicattention: (iv) increasing ex-post benefits of clean-up/ remediation by increasingthe likelihood that clean-up occurs, and (v) often indirectly economizing onenforcement costs by permitting the costless imposition of stiffer non-reporterpenalties that reduce the government monitoring required for a given level of

16violation deterrence.Remediation benefits are also found to be important in enforcement design.

Without self-reporting, clean-up benefits often lead to the optimal imposition ofless-than-maximal fines. The reason is that minimal government monitoringinvestments, made possible by maximal fines, are often not optimal; higher levelsof government monitoring increase the likelihood of clean-up and thereby yieldeconomic benefits over and above those attributable to penalty assessment andattendant accident deterrence. With self-reporting, however, non-reporters areoptimally assessed maximal fines. Hence, an optimal self-reporting policy oftenentails a stiffening of non-reporters’ penalties, although it also entails a reductionin the average penalty that self-reporters face (Proposition 4).

In the US environmental arena, remediation benefits have largely motivatedrecent State-level legislation that provides clear clean-up standards and liabilityprotections to self-reporting violators of those environmental statutes under Statejurisdiction (Anderson, 1996; Geltman, 1996). However, State-level protections ofself-reporters may be ineffective in the absence of similar statutory protections atthe Federal level. Although policy statements of both the US EPA and theDepartment of Justice promise more favorable treatment of self-reporters whoengage in corrective remediation, neither agency has yet committed either tolimiting use of environmental self-audits in its prosecutions or to limitingprosecutions of self-reporters (Von Oppenfield, 1996; Starr and Cooney, 1996).Nor, at present, do promised protections necessarily extend to enforcement of allFederal environmental statutes (Geltman, 1996). Such limitations may discourageself-reporting in practice, at the prospective cost of lost remediation and reducedefficiency in enforcement.

Remediation benefits may also be important in other contexts. Voluntary recallsor customer notices may reduce damages from a defective product. Rehabilitationand monitoring may reduce an employer’s cost of an employee’s drug problem. Aparty to a traffic accident can reduce the injury caused to accident victims bypromptly calling for help and assisting at the scene. In these cases and others, thispaper suggests that remediation opportunities may impart efficiency advantages tolaws and contracts that elicit self-reporting.

16As noted above, these benefits of self-reporting are only present when there are strictly positiveex-post benefits of remediation or clean-up.


Acknowledgements

I am particularly indebted to Dennis Cory for inspiring my work on this topicand to an anonymous reviewer for two sets of insightful comments. I also owethanks to Roger Gordon, David Zilberman, Bill Boggess, Dhamika Dharmapala,Rohan Pitchford and seminar participants at the University of Arizona, AAEAmeetings, Australian National University, University of New England, Universityof Southern Queensland, and LaTrobe University for helpful discussions andremarks on earlier drafts.

Appendix A

Proof of Proposition 1

The following Observation suffices to prove Proposition 1 by showing that anysolution to (2) specifies an interior G, G[(0,G). G can therefore be restricted tothe compact set, [0,G], without loss of generality; and a solution to (2) thus existsby the Weierstrass Theorem.

Observation 1. In a solution to problem (2), G is non-zero, bounded, and solves:

9J (G) 5 1 2 p(x*(D(G)))r9(G)(D 2 (D 1 C)) 5 0NS B A

NSR *when f 5 f , y (Case(1)) (F1)(A)c c

9J (G) 5 1 1 r9(G)NS

3 hx*9(r(G)y)(1 1 p9(x*())D(G)y 1 p(x*())(D 1 C 2 D )j 5 0A B

NSRwhen f 5 y (Case(2)) (F1)(B)c

Proof of Observation 1. Because the derivatives in (F1) describe the marginalcost of G in any possible solution to (2), it suffices to show that they are (a)negative at G50 and (b) positive for all G$G. For Case (1), result (a)

9(J (0),0) is implied by (D 1C2D ),0 (a necessary condition for Case (1) toNS A B

9prevail) and an arbitrarily large r9(0). For Case (2), J (0),0 is implied by anNS

arbitrarily large r9(0), x*9().0 (higher fine levels yield higher levels of firm care,from problem (1)), (D 1C2D )#0, andA B

1 1 p9(x*(r(0)y))D(0) # 1 1 p9(x*(r(0)y))(D 1 C)A

, 1 1 p9(x*(D 1 C))(D 1 C) 5 0 (A1)A A

where the first inequality is due to D(0)5D $D 1C; the second inequality isB A

due to x*9().0, p0().0, and r(0)y,D 1C (because r(0) is arbitrarily small);A


and the final equality follows from the definition of x*(). For both Cases (1) and9(2), result (b) (J (G).0 for G$G) follows from r9(G)50 for G$G. QED.NS


Results (i) and (ii) follow from the arguments in the text. In view of theseresults, the optimal level of G must solve the following restatement of problem (6)(obtained by substituting f 5r(G)y):s

min J (G) ; G 1 hx*(r(G)y) 1 p(x*(r(G)y))[D 1 C]j s.t G $ 0 (A2)S AG

SRObservation 2. Problem (A2) has a non-zero bounded solution, G , that solves:

9J (G) 5 1 1 x*9(r(G)y)r9(G)y(1 1 p9(x*(r(G)y))(C 1 D )) 5 0 (F2)S A

9Proof of Observation 2. It suffices to show that J (G) in (F2) is (a) negative atS

G50, and (b) positive for all G$G. Result (a) follows from x*9().0, inequality(A1), and an arbitrarily large r9(0). Result (b) follows from r9(G)50 for G$G.QED Observation 2.

With x*9().0 and r9(G).0, condition (F2) requires that

1 1 p9(x*(r(G)y))(C 1 D ) , 0 (A3)A

Because 11p9(x*(C1D ))(C1D )50 (from problem (1)), condition (A3)A A

requires that p9(x*(r(G)y)),p9(x*(C1D )). With p0().0 and x*9().0, this lastA

inequality implies result (iii), r(G)y,C1D . QED.A


NSR *There are two cases to consider: Case (1) when f 5f ,y, as defined in Eqs.c cNSR(3a) and (3b); and Case (2) when f 5y. To compare SR optima with NSRc

optima in these two cases, I will use first order condition arguments that implicitlyrely upon Observation 1 above and the following result.

Observation 3. J (G) in (A2) is strictly convex for all G less than and in aSSR SR 9neighborhood of any G that solves (F2); hence, G is unique and J (G),0 fors

SRall G#G .Proof of Observation 3. Convexity: differentiating (F2) and simplifying:

2 299J (G) 5 x*9()h(r9(G) /r(G))y(1 1 p9()(C 1 D ))[( p9()p90() /p0() ) 2 2]S A

21 r0(G)y(1 1 p9()(C 1 D )) 1 x*9()(r9(G)y) p0()(C 1 D )j (A4)A A

where derivatives of p(x) are evaluated at x5x*(r(G)y). From the proof ofProposition 2, r(G)y,C1D for G less than, equal to, or in a neighborhood ofA

any solution to (F2); therefore, for such G values,


1 1 p9(x*(r(G)y))(D 1 C) , 1 1 p9(x*(D 1 C))(D 1 C) 5 0 (A5)A A A

(by x*9().0, p9(),0, and p0().0). With x*9().0, p0().0, and r0(),0, (A5)299implies that J (G).0 so long as ( p9()p90() /p0() )22,0. The latter inequalityS

2follows from p90()$0 or, less strictly, p90()$2p0() /p9().Uniqueness: suppose not. Then there are two levels of G, G and G .G , that1 2 1

99solve (A2) and (F2). However, because G solves (F2), J (G).0 for all G#G ;2 S 2

9hence, J (G ),0, a contradiction. QED Observation 3.S 1

*Case (1) ( f ,y). Here, the NSR optima are described by Eqs. (3a) and (3b)c

* * *and (F1)(A), ( f ,G*). Now define G : r(G )y5D(G*)5r(G*)f . With f ,y, Gc o o c c o

is less than G* and gives the government monitoring investment level which, in aself-reporting regime that satisfies the optimality requirements of Proposition 2,will yield the same expected accident penalty, r(G )y, as a firm would face in theo

*optimal NSR regime, r(G*)f .cSRTo derive results (i)–(iii), it suffices to show that the solution to (F2), G , is

9less than G . To this end, I will evaluate J (G) in (F2) at G by first subtractingo S o

9the zero-valued derivative in (F1)(A), J (G*)50, from the derivative in (F2),NS

9J (G ):S o

hx*9(r(G )y)r9(G )y(1 1 p9(x*(r(G )y))(C 1 D )o o o A

1 p(x*(D(G*))r9(G*)(D 2 (C 1 D ))j (A6)B A

Now note that, by the first order condition defining x*() (the solution to (1)), wehave:

1 1 p9(x*(r(G )y))(C 1 D ) 5 p9(x*(r(G )y))(C 1 D 2 r(G )y)o A o A o

5 p9(x*())(C 1 D 2 D(G*)) 5 2 p9(x*())(1 2 r(G*))(D 2 (D 1 C))A B A

(A7)

where the second equality is due to the definition of G , r(G )y5D(G*), and theo o

third follows from the definition of D(G*)5r(G*)(C1D )1(12r(G*))D .A B

Substituting (A7) into (A6) gives us:

9J (G ) 5 (D 2 (D 1 C))h p(x*())r9(G*)S o B A

2 x*9()r9(G )yp9(x*())(1 2 r(G*))j . 0 (A69)o

where the inequality follows from D .D 1C, r9().0, x*9().0, and p9(),0. ByB ASRObservation 3, (A69) implies that G ,G , the desired conclusion.o

NSRCase (2) ( f 5y). Given Observations 1–3, results (i)–(iii) of the Propositionc

9will follow if J (G) in (F2) is positive when evaluated at the optimal level of GSNSR NSR9for the NSR regime, G , as described in (F1)(B). Evaluating J (G ) (byS

adding (F1)(B) to (F2) and simplifying) gives us:

NSR NSR9J (G ) 5 r9(G )[D 2 (C 1 D )]h p(x*()) 2 p9(x*())x*9()yj . 0 (A8)S B A


where the inequality follows from D .C1D , p9(),0, r9().0, and x*9().0.B A

QED.

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Remediation and self-reporting in optimal law enforcement