Voluntary Environmental Investment and Responsive Regulation

Voluntary Environmental Investment

and Responsive Regulation

JOHN W. MAXWELL1,* and CHRISTOPHER S. DECKER2

1Kelley School of Business Indiana University, 1309 E. 10th St, Bloomington, IN, 47405, USA;2Department of Economics, University of Nebraska at Omaha, Omaha, NE, USA; *Author forcorrespondence (e-mail: [email protected])

Accepted 20 October 2005

Abstract. Instances of corporate voluntary environmental investments have been rising inrecent years. Motivations for such activities include corporate image building, regulatorypreemption, and production cost savings. While some of these investments arise from industry

attempts to set environmental standards where none currently exist, many investments seem tobe aimed at reducing the costs of complying with existing regulations. Using a simple game-theoretic model, we investigate firm motivations for, and welfare consequences of, these types

of voluntary investments by focusing on the role regulatory enforcement might play. We findthat such investments unambiguously increase when an enforcement regulator acts as aStackelberg follower (a regulatory structure we refer to as responsive regulation) in setting its

monitoring and enforcement strategy. These additional investments may be socially undesir-able, necessitating a restructuring of non-compliance penalties.

1. Introduction

There is a growing academic literature discussing voluntary investments bycorporations aimed at improving environmental performance.1 The expla-nations for these voluntary actions include green consumerism, regulatorypreemption by industry, and the so called ‘‘win–win’’ hypothesis of envi-ronmental investment.2 While these explanations have merit, each is aimed atexplaining environmental investments that are independent of existing reg-ulations. However, many environmental programs focus on providingincentives for firms to voluntarily increase compliance activities with respectto existing environmental regulations.3 In this paper, we investigate thephenomenon of voluntary environmental investments (such as investments inself-audit programs or direct investments in cleaner technologies) by focusingon the behavior of the regulator as an enforcer of existing environmentalregulations.

In our model, regulatory actions prompt the firm to raise its level ofenvironmental investment voluntarily. Specifically, the regulator offersto respond to these investments by reducing the frequency with which it

Environmental & Resource Economics (2006) 33: 425–439 � Springer 2006DOI 10.1007/s10640-005-4992-z

monitors the firm. The firm is motivated to take action because the regula-tor’s response will lead to a reduction in the firm’s expected fine. While thefirm is motivated by the reduction in its expected fine, we show that the firm’saction works to raise its compliance probability. This makes it optimal forthe regulator to lower its monitoring frequency, which in turn makes its offercredible.

Our model is driven by two key assumptions. First, the regulator’s offerinduces the firm to make a sunk investment and, second, that these invest-ments lower the firm’s marginal compliance cost, committing the firm to raiseit compliance probability. These two assumptions arise from an examinationof a number of recent U.S. EPA voluntary programs, and changes to itsauditing practices. For example, under the EPA’s StarTrack program, par-ticipating firms are rewarded with being considered ‘‘a lower inspection pri-ority’’ if they establish a self-auditing compliance program, conduct periodicaudits, institute plans, and submit progress reports to the EPA and thepublic.4 The StarTrack program is very much in the spirit of the EPA’s recentchanges in its audit practices contained in the publication Audit Policy:Incentives for Self Policing (EPA 1998a). According to this document thechanges include encouraging regulated entities to seek monitoring andenforcement relief by voluntarily discovering, disclosing, and correcting vio-lations of existing environmental statutes by investing either in the estab-lishment of self-auditing procedures, or in some cases by investing in newequipment.

There is little doubt that a great proportion of these investments are sunkin the sense that documentation of the investments must be made by programparticipants prior to the granting of any regulatory relief.5 Do these invest-ments commit firms to higher levels of compliance? Firms could installequipment, but fail to operate it. They could also establish self-audit pro-cedures, but fail to follow them. However, the fact that the EPA grantsenforcement relief to its voluntary program participants illustrates that itbelieves that the associated sunk environmental investments do indeed raisecompliance rates. Participant reaction to the program is suggestive of the factthat participation does raise compliance. For example, according to a envi-ronmental engineering manager at Spalding Sports Corporation, a StarTrackparticipant, the program provided an opportunity for the company to furtherdevelop the system requirements necessary for continuous environmentalperformance improvement.6

Our model is most closely related to the literature on regulatory responsesto environmental capital investments. Stranlund (1997) examines howoffering technological aid to encourage installation of superior pollutioncontrol equipment reduces enforcement costs. Most EPA voluntary pro-grams, however, offer little in the way of concrete aid. Moreover, in our

JOHN W. MAXWELL AND CHRISTOPHER S. DECKER426

model, we demonstrate that a credible commitment to reduce monitoring andenforcement can achieve this same effect without the need for a side-payment.Amacher and Malik (1996, 1998) examine cooperative bargaining between afirm and a regulator in which the firm agrees to adopt a cleaner technology inexchange for more lenient enforcement. They assume, though, that the reg-ulator precommits to an audit probability. However, as the authors them-selves state, it is unclear how this commitment is achieved. In our model thefirm and regulator simultaneously and non-cooperatively determine theirrespective optimal compliance and monitoring decisions, so precommitmentis not an issue. In this setting we show that the firm will raise its level ofenvironmental investment when faced with the regulator’s offer, and fol-lowing through on the offer is credible.

The remainder of this paper proceeds as follows. In Section 2 we firstprovide an overview of the model, and discuss issues related to timing. Wethen present the model in detail. In Section 3 we examine the regulator’s offerof responsive regulation and examine social cost issues. In Section 4 we offersome concluding remarks and discuss avenues for future research.

2. The Model

2.1. OVERVIEW AND TIMING

We present a two-stage game consisting of two players: a risk neutral regu-lated firm, motivated to minimize its expected compliance costs, and a riskneutral regulator, motivated to minimize environmental damage. The firmhas two choice variables. The first is a level of environmental investment,z 2 [0, 1), that reduces compliance effort costs (e.g., investment in a newtechnology or the creation of an environmental audit department). Thesecond is an investment in compliance effort that captures labor resourcesdevoted to conducting an internal compliance audit, or making sure thatabatement technologies are kept in working order, and is reflected through achoice of compliance probability, p 2 [0, 1]. The crucial difference betweenthe firm’s two choice variables is as follows. The environmental investment isassumed to be fixed and observable prior to the regulator’s choice of moni-toring resources, while the compliance probability is not observable prior tothe regulator’s decision.

We examine two different policy regimes. In the first, the firm minimizes itscompliance costs by choosing its compliance effort and an observable envi-ronmental investment. At the same time, the regulator chooses its optimallevel of monitoring and enforcement effort, reflected through a choice ofmonitoring and enforcement probability, m 2 [0, 1]. Thus, the regulator doesnot, by construction, subsequently respond to the firm’s investment decision.We characterize this regulation as unresponsive. The second regime, which we

VOLUNTARY ENVIRONMENTAL INVESTMENT AND RESPONSIVE REGULATION 427

characterize as responsive, is modeled as a two-stage game. In Stage I, the firmdetermines an optimal level of environmental investment taking into consid-eration the regulator’s optimal Stage II response. In Stage II, the regulatorestablishes its monitoring and enforcement effort, taking into account thefirm’s Stage I choice, and the firm determines its optimal compliance effort.

Since the primary motivation for the firm to undertake voluntary invest-ments is the offer of responsive regulation, it is worth noting that we do notexplicitly model the regulator’s decision to adopt such regulation. As we shallsee, in our model the regulator benefits from offering a responsive enforce-ment policy. To be sure, the regulator may incur some costs to make suchresponsiveness credible (e.g., establishing and promoting such a program). Ifthese costs exceeded the expected benefits (e.g., higher firm compliance andlower environmental damage), then a responsive policy would not be offered.

2.2. MODEL DETAILS

2.2.1. The Firm’s Objective

As stated, our regulated firm minimizes expected environmental compliancecosts by choosing p and z:

minp;z

EðCfirmÞ ¼ ð1� pÞmfþ wðp; zÞ þ z: ð1Þ

These costs are simply the sum of the expected fine, the costs of complianceeffort, and the cost of the environmental investment. The fine, f=F+c,embodies both a pure monetary component, F (assumed to be set exoge-nously by the legislative or judicial branches of government) as well ascleanup costs, c. Indeed, many penalties require that, in addition to monetaryfines, violating firms pay for remediation and restoration which can be quitecostly (see, e.g., EPA 1998b) .7 The firm’s compliance cost function, w(p, z), isassumed to be twice differentiable with: wp> 0, wpp>0, wz<0, wzz> 0,wpz<0 " p, z>0.8

2.2.2. The Regulator’s Objective

We assume the regulator wishes to minimize both the expected cost to theenvironment resulting from violations and its costs of monitoring andenforcement. This assumption implies that the regulator is not a social costminimizer since it is not concerned about the firm’s compliance cost. Thishighlights the separation between the legislative and regulatory enforcementbodies of government.

While some may also doubt that the legislature is a true social cost min-imizer, it is more likely to be subject to direct political pressures, which maycause it to take firm compliance costs into account.9 Since environmental


damages will persist without detection and enforcement, expected environ-mental cost are (1) m)(1) p)c, where c reflects the environmental cost orharm caused by noncompliance. It is important to note that implicit in thisconstruction, which is consistent with structure of f, is that a violating firmfound noncompliant is required to remediate any damage to the environ-ment. In addition to minimizing expected environmental costs, the regulatoris also concerned with its monitoring and enforcement costs, c(m), wherecm>0,cmm> 0. Thus, the regulator’s objective is given by:

minm

EðCregÞ ¼ ð1�mÞð1� pÞcþ cðmÞ: ð2Þ

2.3. UNRESPONSIVE REGULATION

we first examine a benchmark case in which the firm chooses p and z, and,simultaneously, the regulator chooses m. Solving (1) yields the following first-order conditions:

�mfþ wp ¼ 0; ð3Þ

wz þ 1 ¼ 0: ð4Þ

The first condition states that the marginal cost of compliance effort equalsthe expected penalty from noncompliance. The second condition states that zis chosen such that its marginal benefit, compliance effort cost reduction,equals its marginal cost (which is one dollar). Equation (4) is of particularinterest because it illustrates that in the benchmark case the benefits toenvironmental investment are non-strategic in nature; that is, they do notarise from changes in regulatory behavior. For this reason we label this caseunresponsive regulation.

Optimization of the regulator’s objective (2) yields:

�ð1� pÞcþ cm ¼ 0; ð5Þ

which states that the marginal cost of monitoring and enforcement effort, cm,equals the marginal benefit of increased monitoring (a reduction in theexpected environmental cost of noncompliance, (1)p)c). Solving (3)–(5)simultaneously yields Nash equilibrium solutions for p, z, and m in theunresponsive game: pur(f, c), zur(f, c) and mur(f, c).

2.4. RESPONSIVE REGULATION

Under responsive regulation, the timing of the game is as follows: In Stage Ithe firm chooses z, in Stage II the firm chooses p and, simultaneously, the


regulator chooses m. We seek a subgame perfect Nash equilibrium for m andp by solving the model from its second stage.

2.4.1. Stage II

The Firm. In Stage II the firm selects its effort level to minimize its expectedcosts of compliance (1). This yields the first-order condition (3), which definesthe firm’s ‘‘compliance effort’’ best response function: p̂ðm; z; fÞ. Totallydifferentiating (3), we obtain the following results:

@p̂

@m¼ f

wpp

> 0;@p̂

@f¼ m

wpp

> 0;@p̂

@z¼ �

wpz

wpp

> 0: ð6Þ

These results are quite intuitive, but the last result is worth nothing. It statesthat an increase in environmental investment will raise compliance effort,since z reduces compliance costs.

The Regulator. The regulator’s Stage II objective is to choose monitoringresources to minimize (2), which yields (5). Using (5) to define the regulator’s‘‘effort’’ best response function, m̂ðp; cÞ, it is straightforward to derive thefollowing comparative static results:

@m̂

@p¼ � c

cmm

<0;@m̂

@c¼ 1� p

cmm

> 0: ð7Þ

The first result in (7) characterizes the regulator’s best response to achange in the firm’s compliance probability. The greater the firm’s proba-bility of compliance, the less likely the firm will be in violation. The less likelya violation, the lower will be the expected cost to the environment. Hence, theexpected return from monitoring the firm is decreased, and the regulator willrespond optimally by decreasing its (costly) monitoring effort. Analogousreasoning holds for the second result in (7).

The Stage II Nash Equilibrium. The simultaneous solution of the firm’sand regulator’s best response functions determines a stable Nash equilibriumin compliance and monitoring probabilities, p*(z, c, f) and m*(z, c, f). Noticethat, in contrast to the equilibrium under unresponsive regulation, theequilibrium levels of p and m are functions of z. Totally differentiating (3)and (5), and applying Cramer’s Rule, we see that:

@m�

@z¼

�wpzc

�ðfcþ cmmwppÞ<0; and

@p�

@z¼

wpzcmm

�ðfcþ cmmwppÞ> 0: ð8Þ

This first result illustrates that responsive regulation is credible. Because itreduces the marginal cost of compliance, an increase in z increases the firm’scompliance probability for any given level of m. This, in turn, reducesexpected environmental costs. Since monitoring is costly, the regulator will


find it optimal to reduce its monitoring probability. The second result showsthat an increase in z increases the probability of compliance since the cost ofcompliance falls in z.10

2.4.2. Stage I

Subgame perfection implies that the firm can see through to the Stage IIequilibrium outcome. Therefore, in Stage I the firm will choose a level ofenvironmental investment, z, given p* and m*. Thus, the Stage I objective forthe firm is:

minz

E �ðCfirmÞ ¼ ð1� p�Þm�fþ zþ wðp�; zÞ: ð9Þ

This results in the following first-order condition:

ð�m�fþ wpÞdp�

dzþ wz þ 1þ ð1� p�Þf dm

�

dz¼ 0: ð10Þ

Using (3) and rearranging we get:

wz þ 1 ¼ �ð1� p�Þf @m�

@z> 0: ð11Þ

Defining the optimal solution to (11) as z*, analysis of this condition leadsdirectly to the following two-part proposition.

Proposition 1. (A) Under responsive regulation, the firm realizes additionalbenefits to environmental investments relative to unresponsive regulation,ceteris paribus. (B) Responsive regulation induces the firm to increase itsenvironmental investment relative to its optimal investment under unresponsiveregulation, i.e., z*>Zur, ceteris paribus.

Proof. See the appendix.Proposition 1 implies that the firm, when faced with a credible offer of

responsive regulation, will increase its environmental investment activity.Since the regulator’s best response function is downward sloping in (m, p)-space, its strategic response is to reduce its monitoring probability. As in thestrategic investment literature, the firm raises its investment in z relative tothe level it would have chosen were there no strategic response, since theregulator’s strategic response is favorable to the firm.

3. Regulatory Credibility and Social Cost

3.1. REGULATORY CREDIBILITY

We have shown that a switch to responsive regulation will induce the firm toincrease its level of voluntary investment. In this section we confirm, in light


of the firm’s behavior, that the regulator’s offer of responsive regulation iscredible. To see this we examine the impact of the firm’s decision on theregulator’s payoff. That is,

dEðCregÞdz

¼ �ð1�m�Þc @p�

@zþ ½cm � ð1� p�Þc� @m

�

@z<0: ð12Þ

Noting that the final term in (12) is zero from (5) and using (8), we see thatthe regulator benefits from offering responsive regulation because regulatorycosts are decreasing in z.

Of course, prior to the decision to offer responsive regulation, the regu-lator may encounter certain fixed setup costs.11 However, once any costsassociated with offering responsive regulation are incurred (sunk), the regu-lator will not want to renege on its offer since doing so would raise itsexpected costs.

3.2. SOCIAL COSTS

We have established that, given a credible offer of responsive regulation, thefirm will increase its level of environmental investment and that this actionbenefits the regulator. Thus, the two parties most directly involved in thisregulatory change benefit from it. However, does the switch benefit society asa whole? In this section we examine how a switch to responsive regulationimpacts the social cost of the firm’s activities. We record two interestingobservations. First we find that it is possible for the regulator to offerresponsive regulation when it is not socially desirable to do so. In these casessocial cost minimization would dictate that the firm reduce its investment inz, something it will never do. This observation is part of the broader resultthat the firm’s choice of z will in general differ from its social cost minimizinglevel. We then demonstrate that to insure the firm chooses the desired level ofz under responsive regulation, there must be an adjustment of the fine, spe-cifically the monetary portion of the fine: F=f ) c. These observations areimportant because the EPA and its regional offices appear to be actingindependently in switching to more responsive regulation, but the results wederive below suggest judicial or legislative oversight (aimed at monetary fineadjustment) is in order.

To derive the observations just outlined, we begin by examining whetheror not the additional environmental investment that responsive regulationinduces is in fact socially desirable. Expected social costs are:

EðSCÞ ¼fð1� pÞmfþ wðp; zÞ þ zgþ fð1�mÞð1� pÞcþ cðmÞg � ð1� pÞmF: ð13Þ


The term contained within the first set of braces on the right-hand side of(13) represents the firm’s expected costs, while the term in the second set ofbraces represents the regulators costs. From these two costs we subtract theexpected monetary fine since it constitutes a social benefit.12

Solving this expression for the social cost minimizing level of z underresponsive regulation results in the following proposition.

Proposition 2. Under responsive regulation, the social cost minimizing level of zmay be larger or smaller relative to the social cost minimizing level of z underunresponsive regulation.

Proof. Minimizing (13) with respect to z under unresponsive regulation yieldswz+1=0. Under responsive regulation, minimizing (13), with respect to zyields:

wz þ 1 ¼ �ðwp � cÞ @p�

@z� cm

@m�

@z: ð14Þ

While �cm@m�

@z and @p�

@z are positive, the term )(wp)c) is ambiguous in sign,making the right-hand side of (14) is ambiguous in sign. Hence, there is apossibility that the social cost minimizing level of z may be lower underresponsive regulation than under unresponsive regulation. This will occurwhen the firm’s marginal cost of compliance, wp, is not only larger than theenvironmental cost of noncompliance, c, but also larger than then cost sav-ings associated with reduced monitoring. h

With this result in mind, recall from Proposition 1 that the firm will raiseits environmental investment to reduce its expected fine. We also know from(12) that the regulator will offer responsive regulation to save on its moni-toring and enforcement costs. These observations lead directly to the fol-lowing corollary of Proposition 2.

Corollary 3. Ceteris paribus, the regulator may offer responsive regulationwhen it is socially costly to do so.13

The above results show that, for a given monetary fine, the firm willgenerally not pick the socially optimal level of z when the switch is made toresponsive regulation. We now show that in general the switch to responsiveregulation should be accompanied by an adjustment in the monetary fine inorder to induce the firm to pick the social cost minimizing level of z.

First we determine the optimal fine under unresponsive regulation underthe assumption that the regulator has full control of its choice of m and thefirm has full control over it choices of p and z. That is, we assume a setting inwhich a social cost minimizing actor (such as the legislative or judicial


branch of government) has control of the monetary fine F. In this case theoptimal fine will arise from the minimization of (13) subject to the followingconditions governing firm and regulatory behavior under unresponsiveregulation

�mfþ wp ¼ 0

�ð1� pÞcþ cm ¼ 0

wz þ 1 ¼ 0:

This minimization yields

ðmurf� cÞ @pur

@Fþ ð1� purÞc @m

ur

@F¼ 0: ð15Þ

While a closed form solution for F cannot be found without the use ofspecific functional forms it is noteworthy that when F is set according to(15) there is no need to switch to responsive regulation from the socialcost minimizing point of view. However, even when the optimal fine ischosen we see from (12) that the regulator, driven by the desire to reduceits monitoring costs, will still desire to offer responsive regulation to thefirm.

With (15) serving as a benchmark, we next derive the cost minimizing levelof F under responsive regulation. Unlike the optimal F under unresponsiveregulation, the social cost minimizer now must take into account the firm andregulator behavior under responsive regulation, that is:

�mfþ wp ¼ 0

�ð1� pÞcþ cm ¼ 0

ðwz þ 1Þ þ ð1� pÞmf@m

@z¼ 0:

This minimization yields:

ðm�f� cÞ @p�

@z

@z�

@Fþ @p

�

@F

� �þ ð1� p�Þc @m�

@z

@z�

@Fþ @m

�

@F

� �

þ �ð1� p�Þf @m�

@F

� �@z�

@F¼ 0: ð16Þ

Again, it is not possible to solve the optimal monetary fine without specificfunctional forms. However, it is clear from a comparison of (15) and (16)that, in general, the optimal monetary fine under the two regimes will differ.Thus, it is clear that when regulators switch to responsive regulation anadjustment of the fine is in order. This observation is important because


programs aimed at responsive regulation, such as StarTrack, do not explicitlylink these offers to changes in monetary fines.

4. Conclusion

We have shown that, under reasonably general firm and regulatory objec-tives, responsive regulation can give rise to voluntary environmental invest-ments. In addition, we found that, despite the fact that all agents in the modelact voluntarily, their actions may lead to a suboptimal level of environmentalinvestment. Importantly we illustrate that the switch to responsive regulationshould be accompanied by an adjustment of the fine structure. This suggestsjudicial or legislative oversight of EPA offers of responsive regulation thatcurrently do not exist.

Our model offers several extensions. For example, currently the damagedone to the environment, c, is exogenous. If c were considered in the contextof a policy variable measuring, say, an optimal pollution standard, then aswitch to responsive regulation may offer policy makers an opportunity totighten the pollution standard. Hence, the additional investment generates apositive externality, a result which might further mitigate the potential forover-investment in z. In addition, it may be interesting to study responsiveregulation in a multi-firm setting. Firm interactions might lead to strategicenvironmental investments designed to shift regulatory scrutiny on to rivalfirms. In this case, product market competition (Bertrand or Cournot) mightaffect firm investment behavior and may have associated welfare implica-tions. We leave these extensions for future research.

Acknowledgements

Both authors thank Sjak Smulders, Thomas P. Lyon, and two anonymousreferees for their comments.

Notes

1. Two recent surveys of voluntary self-regulation are Lyon and Maxwell (2004) andSegerson and Li (2000).

2. The green consumerism literature suggests that voluntary environmental investmentsdifferentiate products, weaken price competition, and draw high-valuation greenconsumers to the investing firms (Arora and Gangopadhyay 1995). The reemption

literature (Maxwell et al. 2000; Segerson and Miceli 1998) posits that firms voluntarilyabate pollution to preempt threats of future regulations. The ‘‘win–win’’ literature (see,e.g., Porter and van der Linde 1995) suggests that firms undertake voluntary environ-mental investments because these investments actually lower production costs (i.e.,

environmental improvements are a natural by-product of cost minimization).


3. In examining firm motivations for the adoption of environmental plans, which are natural

precursors to environmental investments, Henriques and Sadorsky (1996) found that theoverwhelming motivation was compliant with existing and future regulations.

4. See EPA (1998c, p. 2).

5. For example, there are nine conditions that participants in EPA’s Audit Policy must meet,Prominent among these requires that firms establish a systematic management plan toachieve and maintain compliance (see EPA 2000, p. 17). Participants under StarTrack arerequired every year to prepare and publicize a comprehensive environmental performance

report. Moreover, every 3 years they are required to engage in third-party verification toreview and certify compliance efforts (see EPA 1998c pp. 2–3).

6. William W. Sweetman, manager of Environmental Engineering, Hazardous Materials

Management, Safety, and Health at Spalding Sports (see http://www.epa.gov/region1/pr/2000/0509001.html).

7. Most major environmental statutes such as the Clean Air Act (CAA) and Clean Water

Act (CWA) establish maximal penalties that regulatory authorities can assess forenvironmental violations. The Water Quality Act of 1987, for instance, authorized theEPA and state environmental authorities to issue administrative fines of up to $10,000 perviolation per day for violations of CWA regulations. Civil penalties under the CWA can

reach $25,000 per day per violation (Sullivan, 1995, p. 165–66). In addition to the civilpenalties assessed, Pacific Gas & Electric Co. was required to spend over $6 million forenvironmental enhancement and restoration (see EPA 1998b).

8. An explicit functional form illustrating these characteristics is w=p2/(z+1). This functionalso exhibits the following third-order cross partial effects: wppz=wpzp=wzpp<0 andwzzp=wzpz=wpzz< 0. Note that when p=0 all derivatives are zero. We assume this is also

a property of our generic w function, which implies that when the firm’s optimalcompliance probability is zero, then its optimal investment in z is also zero. This would bethe case if the firm faces an expected fine of 0.

9. Our choice of regulatory objective function is motivated by three factors. First, the statedmission of the EPA is to ‘‘protect human health and to safeguard the natural environment– air, water, and land – upon which life depends,’’ which suggests a greater concern forenvironmental costs than for firm compliance costs (see http://www.epa.gov for the EPA’s

mission statement). Second, the EPA must operate within a budget constraint, suggestinga concern for its own monitoring and enforcement expenses. Finally, our objectivefunction is similar in spirit to Amacher and Malik’s (1996, 1998). In their model, the

regulator minimizes the weighted sum of regulatory costs (environmental harm plusenforcement costs) and firm compliance costs. We highlight the regulator’s incentives tobe responsive by implicitly applying a weight of zero on firm compliance costs. Note that

placing a positive weight on firm compliance costs in our regulator’s objective, will notchange any of our qualitative results as long as the regulator cares more than the firmabout the cost that noncompliance imposes on the environment.

10. Other results from the application of Cramer’s rule include the fact that higher penalties

induce a higher probability of compliance as do higher environmental costs. This lattereffect is true because monitoring and enforcement intensifies with higher levels of c. Theseresults are available from the authors upon request.

11. For instance, the regulator must be able to verify that the firm’s investment does result in acredible commitment to increase its compliance efforts. Verification will likely include thecollection and review of proposals submitted by the firm.

12. Consistent with the existing literature we model the monetary component of the fine asrepresenting a benefit to society in that these fines are typically paid into a state or federalgeneral fund that can be used to finance environmental cleanup, natural resource


reclamation projects, or be used in other ways to enhance social welfare (see Kleit et al.

1998). We do not include the fill fine f because the benefit of full remediation is alreadyaccounted for in the regulator’s cost function. To see this suppose that the firm, uponbeing found in violation, is required to remediate only a percentage / of its environmental

cost c, so that f=F+/ c. In this case the regulator’s costs would be(1)m)(1)p)c+m(1)p)(1)/)c+c(m). Thus, we can see that the benefits of full remediationwhere /=1 are accounted for by the regulator in that its costs are lower.

13. Note from (12), that the benefits to the regulator from more z are increasing in (1)m*)c. If

the fixed costs associated with responsive regulation are high, then it is more likely to beoffered when (1)m*)c is large, and thus when z is likely to be socially desirable.

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Standards’, Journal of Environmental Economics and Management 34, 228–239.

Appendix

Proof. Proposition 1(A). Examining (4) and (11), and noting that wzz>0, we see that as ¶m*/¶z<0, the firm has an additional incentive to make additional investments in z since with it

comes a reduction in m. h

While the incentive to increase investment is clear from this part of the proposition, onecannot in general directly compare optimal environmental investment levels between unre-sponsive and responsive regulation because doing so involves making comparisons across two

different models. However, following Brander and Spencer, 1983, we can make such a com-parison.

Proof. Proposition 1(B). Our proof will make use of the mean value theorem.

The mean value theorem. Let f(x) be a continuously differentiable function defined over the

set of real numbers R2 and let x* and xur be two points on this function. Then there exists apoint xc such that

Df ¼ fðx�Þ � fðxurÞ ¼ @f

@xjx¼xcðx� � xurÞ; ðA1Þ

where xc=xur+h(x*) xur) and h 2 (0,1).Using this theory, we first define Dz=z*) zur where z* and zur are environmental invest-

ments in the responsive and unresponsive cases, respectively. Let f(x) be ¶E*(Cfirm)/¶z for bothz* and zur. Then we can apply (Al) as follows (dropping the Cfirm argument for notationalconvenience):

D@E�

@z¼ @E

�

@zjz¼z� �

@E�

@zjz¼zur ¼

@2E�

@z2jz¼zcðz� � zurÞ: ðA2Þ

Re-arranging terms we can get

ðz� � zuÞ ¼@E�

@z jz¼z� � @E�

@z jz¼zur@2E�

@z2jz¼zc

: ðA3Þ

From (11) we know that @E�=@zjz¼z� ¼ 0 and @E�=@zjz¼zur ¼ ð1� pÞð@m�=@zÞf<0.

Therefore, the numerator of (A3) is positive. Since cost minimization requires that@2E�=@z2jz¼zc > 0, we can conclude that z*)zur>0. h

As Brander and Spencer (1983) note, since existence and uniqueness are difficult toestablish in stage games, second-order partials derived from such games are difficult to sign in

practice. In our case, when expanded, we find that

@2E�

@z2¼ wzz �

@m�

@z

@p�

@zfþ ð1� p�Þf @

2m�

@z2: ðA4Þ

Note that the first two terms in (A4) are positive, which works towards the cost minimizing

result. But the third term is indeterminate because ¶2m*/¶z2 cannot, in general, be signed.


However, straightforward differentiation shows that each component of ¶2m*/¶z2 involves

third-order cross partial derivatives from our w(p, z) function. As a result ¶2m*/¶z2 isambiguous. In practice, such third and higher order effects are reasonably assumed to berelatively small. Since the first two terms in (A4) are higher order effects of the correct sign, we

follow Brander and Spencer, 1983 and reasonably conclude that overall ¶2m*/¶z2<0.


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