Extended liability for environmental accidents: what you see is what you get

Journal of Environmental Economics and Management 49 (2005) 157 173 www.elsevier.com/locate/jeem Extended liability for environmental accidents: what you see is what you get Emma Hutchinson and Klaas van t Veld Department of Economics, University of Michigan, 611 Tappan St., Ann Arbor, MI 48109-1220, USA Received 18 July 2002; received in revised form 24 July 2003 Available online 7 July 2004 Abstract When a firm may be bankrupted by the liability from an environmental accident, current laws often allow for the extension of liability to third parties with whom the firm contracts, with the aim of inducing full internalization of social costs. We find that, when the firm can take both observable and unobservable care to reduce expected accident damages, extended liability indeed results in full cost internalization, but not in first-best levels of care. We also find that, whereas without extended liability there is excess entry into environmentally hazardous industries, introducing extended liability leads to exit that, while excessive relative to the first best, is second-best optimal given firms choice of care. Furthermore, we show that direct regulation of observable care, when combined with extended liability, further distorts firms incentives. However, when used alone, such regulation strictly dominates extended liability. r 2004 Elsevier Inc. All rights reserved. Keywords: Environmental risk; Judgment proof problem; Extended liability; Lender liability; Industrial accidents; Bankruptcy; CERCLA 1. Introduction Under many of the major US environmental laws e.g., the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), the Oil Pollution Act, the Clean Water Corresponding author. Fax: +1-734-764-2769 E-mail address: ehutchin@umich.edu (E. Hutchinson). 0079-610/$ - see front matter r 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jeem.2004.03.003

158 E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 Act firms face strict liability for damages from environmental accidents. From the law-andeconomics literature (e.g., [30]), it is well known that such ex post liability can provide firms with optimal incentives ex ante to take care i.e., to undertake safety measures that reduce expected damages because it induces firms to internalize the full costs associated with accidents. Because environmental cleanups are often very costly, however, it is not uncommon for environmental damages to exceed the market value of the firm responsible for an accident. In such cases, the firm is bankrupted by its liability, and is said to be judgment proof : because it cannot lose more than its market value in bankruptcy, it externalizes any residual damages in excess of this value. One way in which environmental laws attempt to remedy this judgment proof problem is by extending liability for residual damages to parties with whom a firm contracts. The argument for doing so (laid out for example by Segerson [28]) is that, using their contractual leverage, third parties will pass on their residual-liability costs to the judgment-proof firm, thereby restoring the firm s incentive to take optimal care. Formal analysis of this argument has shown that the degree to which it holds up in practice depends importantly on whether safety measures undertaken by the firm are observable to third parties ([6,7,9,15,18,22,23,25]). A standard assumption in the literature is that care is unobservable to third parties. 1 Equally standard and closely related is the assumption that care takes the form of safety measures that reduce the probability of an accident occurring. Because such care tends to be of a procedural nature for example, making sure that workers follow standard safety procedures it is reasonable to assume that it is difficult for third parties to observe. In reality, of course, firms can take measures to reduce not just the probability of an accident, but also the extent of damages if an accident occurs. Moreover, such damage-reducing measures tend to take the form of tangible investments, which are readily observable to third parties. In the oil-shipping business, for example, proper training and supervision of crews reduces the probability of tanker groundings or collisions, but is difficult to observe. On the other hand, fitting double hulls to oil tankers reduces the extent of oil spills in the event of an accident, and is readily observable. Similarly, in the hazardous-waste disposal business, day-to-day enforcement of procedures ensuring that hazardous waste is stored correctly reduces the probability of leaks, but is difficult to observe. On the other hand, installing monitoring wells reduces the extent of leaks (by enabling early intervention) and is readily observable. In this paper, we allow for both probability- and damage-reducing safety measures. In addition, we assume that damage-reducing measures are observable to third parties, while probabilityreducing measures are not. Sections 2 and 3 introduce the model and determine the socially optimal levels of care. Section 4 analyzes firms equilibrium choices of care in the absence of extended liability. Section 5 analyzes the effects of a specific form of extended liability, namely lender liability. 2 Section 6 discusses direct regulation of damage-reducing care as a possible complement to, or substitute for, extended liability. Section 7 concludes. 1 An interesting exception is Boyd and Ingberman [8], who abstract from the moral-hazard distortions that can result from care being unobservable to focus on a different issue, namely under what circumstances firms choose to dissolve rather than face their accident liability. 2 Much of the literature on extended liability (e.g., [9,18,25]) has focused on the specific example of lender liability. See [10] for an overview of the history of lender liability under CERCLA. See also [14] for a discussion of proposals to introduce lender liability in the European Union.

E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 159 2. The model The representative firm in our model is considering engaging in an activity that carries with it a risk of a costly environmental accident. The activity generates fixed profits P, defined as revenues net of non-accident-related variable costs. An accident occurs with probability p and causes damages D. The firm faces strict liability for all accident damages, but this liability is limited by the firm s financial assets. If accident damages exceed these assets, then the firm will be bankrupted, and will therefore externalize some of the damages. The firm can reduce p by incurring non-pecuniary costs cð pþ, and it can reduce D by undertaking investments that involve up-front capital costs of IðDÞ. 3 The function cð pþ has the following properties: (i) cð pþ ¼0 at p ¼ p, (ii) c 0 ð pþo 0; c 00 ð pþ4 0; 8p 2ð0; pþ, and (iii) cð pþ!1 as p! 0. Similarly, the function IðDÞ has properties (i) IðDÞ ¼0atD ¼ D, (ii) I 0 ðdþo 0; I 00 ðdþ4 0; 8D 2ð0; DÞ, and (iii) IðDÞ!1as D! 0. To start up the activity, the firm must incur up-front capital costs of K in addition to IðDÞ. We assume that the firm has no initial wealth and therefore has to borrow to cover all up-front costs. We assume that the lending sector is competitive and that L1 : the lender s loan is secured, with the firm s assets as collateral, L2 : the firm s assets are not damaged or otherwise diminished in value if an accident occurs. Assumption L1 implies that if a bankrupting accident occurs, the lender will have first claim on the firm s assets, before any claims by accident victims. Assumption L2 implies that after repossessing the assets, the lender can in principle re-lend them to a new firm under the same terms as before. 4 We further assume that the firm s probability-reducing effort is not observable to (or verifiable by) the lender or any other outside parties, including the regulator, but its damage-reducing investment is. Hence, we use unobservable care and observable care as short-hand terms. 3. The social planner s problem In this section, we consider the social planner s problem, which is to choose the accident damage level D and the accident probability p that maximize welfare. To keep the welfare analysis simple, we assume that the firm s activity generates no consumer surplus. The welfare generated by the firm is then W p ½cð pþþriðdþþpdš; ð1þ where p P rk represents the firm s profits P less the opportunity cost rk to society from having productive capital K tied up in the firm for the period of the firm s operation. Throughout the paper we refer to p as the firm s gross profits (i.e., gross of any accident-related costs). The bracketed term on the right-hand side of (1) captures the social costs related to the possibility of 3 We define probability-reducing care costs as non-pecuniary because this is the standard assumption in much of the literature. In a working paper, we show that our results go through also if all care costs are pecuniary. 4 Allowing for damages to capital significantly complicates the analysis, but does not materially affect our results.

160 E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 environmental accidents: the non-pecuniary cost of unobservable care cð pþ, the opportunity cost of investments in observable care riðdþ, and expected accident damages pd. Assuming that a unique interior solution to the social planner s problem exists, it will be characterized by the following first-order conditions: ri 0 ðdþ p ¼ 0; ð2þ c 0 ð pþ D ¼ 0: ð3þ The first condition equates the marginal costs ri 0 ðdþ of damage-reducing care to the marginal social benefit p. The second condition equates the marginal cost c 0 ð pþ of probability-reducing care to the marginal social benefit D. Fig. 1. Marginal costs ri 0 ðdþ of reducing accident damages and (inverse) marginal costs c 0 1 ðdþ zðdþ of reducing the accident probability.

E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 161 For reasons of exposition, we define a function zðþ that is equal to the inverse of the function c 0 ðþ wherever this inverse exists (i.e., for po p), and equal to p otherwise. Condition (3) can then be rewritten as p ¼ zðdþ. As shown in Fig. 1, defining the zðþ function allows us to represent the social optimum ðd S ; p S Þ graphically in ðd; pþ space as the point where the ri 0 ðdþ and zðdþ curves cross. Also shown in the figure are two further critical values of D and p, namely D, which is the damage level that would be socially optimal if probability-reducing care were zero, and p, which is the probability that would be socially optimal if damage-reducing care were zero. Additionally, we define a critical value of p, namely p S cðp S ÞþrIðD S Þþp S D S, to denote the level of net benefits that just equals minimized accident-related costs. Clearly, firms with p less than p S will not be in business at the social optimum, as they would generate negative social welfare. For firms with p greater than p S, social welfare is positive and given by Eq. (1) evaluated at ðd S ; p S Þ. 4. The firm s problem without extended liability The firm s problem differs from the social planner s in two respects. First, whereas the social planner takes into account all damages associated with environmental accidents, the firm only takes into account those damages for which it can be held liable. Second, the firm must borrow capital, in return for a loan fee that allows the lender to at least break even in expectation. By assumption, the lender can observe the firm s investment in damage reduction, so that the terms of the loan contract can be conditioned on D. In contrast, the lender cannot observe the firm s expenditure on probability reduction, so that the loan contract cannot be conditioned on p. As illustrated in Fig. 2, we capture these observability assumptions by modeling the firm s and the lender s decisions as a three-stage game, which is solved by backwards induction. In stage 1, the firm chooses the level of damages D. In stage 2, lenders observe D and the loan fee is determined competitively. In stage 3, the firm chooses the accident probability p conditional on its earlier choice of D and the now contractually fixed loan fee. In both stages 1 and 3, the firm s objective is to maximize its payoff V ¼ p maxfðp DÞ; 0gþð1 pþðp Þ cð pþ: ð4þ With probability p the firm experiences an accident, and, after paying the lender, has financial assets of P with which to compensate accidents victims. 5 A solvent firm, whose assets exceed damages, is therefore left with P D in the event of an accident, while a judgment-proof firm is left with nothing. With probability ð1 pþ there is no accident, and the firm is then left with P. Irrespective of whether or not an accident occurs, the firm must incur the non-pecuniary care costs cð pþ. Given our assumptions of a competitive lending sector, the equilibrium loan fee is given by the break-even condition r½k þ IðDÞŠ ¼ 0: ð5þ 5 Recall that by Assumption L1 the lender has first claim on the firm s assets.

162 E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 Fig. 2. Timeline of the model. Note that Assumptions L1 and L2 imply that the lender can repossess the firm s assets in order to recover the principal of the loan. Moreover, the lender does not incur any loss in the event of an accident. As a result, the loan fee need only cover the opportunity cost r½k þ IðDÞŠ of the loan, and does not depend on the firm s subsequent choice of accident probability. This in turn implies that, in the absence of extended liability, our assumption that p is unobservable to the lender is immaterial. We find that the solution to the firm s optimization problem in the absence of extended liability can be characterized as follows: Proposition 1. Without extended liability, the only locally optimal D and p values are (a) D S and p S for firms that are solvent at that combination, (b) D and p ¼ zðpþ for firms that are judgment proof at that combination. Proof. All proofs are given in Appendix A. & At ðd; pþ combinations where a firm is solvent, the firm fully internalizes all accident-related costs. As a result, only ðd S ; p S Þ can be optimal. At ðd; pþ combinations where a firm is judgment proof, it externalizes all damages in excess of its financial assets P ¼ p riðdþ. Because of this, there is no marginal benefit to reducing damages below D. Conditional on this damage level, the social planner would choose p ¼ zð DÞ, where the marginal cost c 0 ðpþ of further reductions in p just balances the social marginal benefit D. For the judgment-proof firm, however, the private marginal benefit of reducing p is only p rið DÞ ¼po D. As a result, it will choose a higher privately optimal accident probability p ¼ zðpþ. The result of Proposition 1 is only partial, in that it does not establish whether any given firm is in fact solvent at ðd S ; p S Þ or judgment proof at ð D; zðpþþ, or possibly both. Nor does the proposition establish how zðpþ compares to the socially optimal accident probability p S. In the Appendix, we establish formally the rather obvious fact that firms with low gross profits below a cutoff value that we denote p N are judgment proof in equilibrium, whereas firms with gross profits above p N are solvent. We show also, however, that, when accident damages are endogenous, the state of being judgment proof becomes for some firms namely those with intermediate profits endogenous as well: such firms can choose whether or not to keep damages at a level exceeding their financial assets. Moreover, some judgment-proof firms compensate for taking no damage-reducing care by taking more probability-reducing care than they would at the first best. 6 6 Beard [1], Craig and Thiel [12], Posey [26], and Dionne and Spaeter [13] also find that judgment-proof firms may take more than first-best probability-reducing care. In their models, this possibility arises for very different reasons, however, which moreover depend on treating care as pecuniary. A note expanding on this point is available from the authors upon request.

E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 163 The latter result is illustrated in Fig. 1, which shows in ðd; pþ space the situation of two judgment-proof firms, a relatively rich one with gross profits p r and a relatively poor one with gross profits p p. Being judgment proof, both firms choose damage level D. However, because the rich firm has financial assets p r at stake that exceed D S, it has a greater incentive to avoid accidents than does the social planner, and so chooses an accident probability lower than p S. 7 The opposite is true for the poor firm. More generally, the lower a judgment-proof firm s gross profits p, the higher the accident probability it chooses. In the extreme case, a firm that has zero gross profits chooses p, i.e., takes no unobservable care. Because it takes no observable care either, Eq. (4) reduces to V ¼ 0 for this firm. Thus, firms with gross profits px0 are viable (in the sense that they have a non-negative payoff ) in the absence of extended liability. Note, however, that some of these firms (those with po p S ) are viable only because they externalize damages. 4.1. Welfare without extended liability To evaluate the welfare loss resulting from the judgment-proof problem without extended liability, we compare the welfare generated by firms (as given by Eq. (1)) when they choose their privately optimal values of D and zðpþ to the welfare generated at the social optimum. Recall from Section 3 that firms with po p S would not be in business at the social optimum. It follows that the welfare loss resulting from these firms being in business in the absence of extended liability corresponds to the negative welfare they generate at ð D; zðpþþ. Richer judgment-proof firms, in contrast, would be in business at the social optimum. For these firms, the welfare loss is therefore just the deadweight loss resulting from their distorted care choices. Fig. 3 illustrates this deadweight loss for the judgment-proof firm with profits p ¼ p r from Fig. 1. At the social optimum, the firm s full accident-related costs are equal to cðp S Þþp S D S þ riðd S Þ. At its privately optimal choice of D and p N ¼ zðpþ, the firm s full accident-related costs (including the expected damages p N ð D pþ that it externalizes) are cðp N Þþp N D. The difference between these two costs corresponds to the shaded area in the figure labeled DWL N. To understand the somewhat odd shape of this area, consider the following thought experiment. Suppose that, while holding damages constant at D, we reduce the accident probability p from p N to its optimal value conditional on D, namely p ¼ zð DÞ. Doing so increases unobservable care costs by the area to the left of the zðdþ curve between p and p N, but reduces expected damages by the rectangle ðp N pþ D. Thus, the net welfare gain is equal to the triangle above the zðdþ curve. Suppose that we then reduce damages from D to D S, while keeping the accident probability at its conditionally optimal value p ¼ zðdþ. This increases costs by the area under the ri 0 ðdþ curve, but yields a benefit equal to the area under the zðdþ curve. 8 Thus the net welfare gain is equal to the sliver between the zðdþ and ri 0 ðdþ curves. 7 It is important to note however, that the socially optimal accident probability p S is defined conditional on damages having been reduced to the socially optimal level D S. As discussed above, the socially optimal accident probability conditional on judgment-proof firms privately optimal damage level D is p ¼ zð DÞ, which is always lower than the accident probability p ¼ zðpþ chosen by such firms. 8 Recall that the the height of the ri 0 ðdþ curve is the marginal cost of damage reduction. By the envelope theorem, if the accident probability is kept at its conditionally optimal value, the marginal benefit of damage reduction is equal to p, i.e., to the height of the zðdþ curve.

164 E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 Fig. 3. Deadweight loss of a judgment-proof firm with and without extended liability. 5. The firm s problem with extended liability In this section, we consider how extending liability for residual damages to lenders changes the incentives of the firm. 9 If lenders are liable for residual damages, then, all else equal, they will require a higher loan fee in order to break even. However, all else will not be equal: in anticipation of this response by the lender, the firm will in general choose a different level of damage-reducing investment. For solvent firms, the analysis of Section 4 goes through unchanged. Because such firms fully internalize all accident damages, there is no residual liability to pass on to lenders. For judgment- 9 Because the literature on extended liability has largely focused on the specific example of extending liability to lenders, we use this example in much of the remainder of this paper. However, so long as the third party to whom liability is extended passes back its residual-liability costs to the firm, the results of our model also carry through to other forms of extended liability.

E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 165 proof firms, the stage-3 problem of optimally choosing p conditional on any given damage level D and given loan fee is unchanged as well. The firms will therefore still optimally choose p ¼ zðp Þ. The stage-1 problem of optimally choosing D does, however, change under extended liability, because the lender s stage-2 break-even constraint becomes p maxfd ðp Þ; 0g r½k þ IðDÞŠ ¼ 0: ð6þ With extended liability, the loan fee has to cover not just the opportunity cost of the loan but also the expected residual liability. 10 Given the change in the lender s break-even constraint, the solution to the firm s optimization problem changes as follows: Proposition 2. With extended liability, the only locally optimal D and p values are (a) D S and p S for firms that are solvent at that combination, (b) D L o D S and p L 4 p S such that ri 0 ðd L Þ¼p L ¼ zðp Þ for firms that are judgment proof at that combination. With lender liability, both solvent and judgment-proof firms now fully internalize all accidentrelated costs. For a judgment-proof firm, this is because the loan fee now includes the expected residual liability that the firm was able to externalize in the absence of lender liability. An immediate implication of this full cost internalization is that, ex ante, all firms would prefer to choose D S and p S, which minimizes these accident costs. However, the moral hazard problem prevents any judgment-proof firm from credibly committing to the choice of p S in stage 3, once the loan fee has been set. Instead, such a firm will choose an accident probability p L ¼ zðp Þ4 p S. As a result, in stage 1 it will choose a damage level D L o D S, such that ri 0 ðd L Þ¼p L. In effect, in order to keep its expected damages down, the judgment-proof firm partially compensates for taking too little unobservable care ex post, by spending what would otherwise be too much on observable care ex ante. Overall, however, because the firm is not making first-best care decisions, its total accident-related costs will exceed those at the social optimum. Once again, Proposition 2 leaves unanswered the question of which firms are judgment proof and which are solvent in equilibrium. In the Appendix, we show that the cutoff value p L above which firms are solvent is lower than p N, the cutoff value without extended liability. To see why, recall from our discussion following Proposition 1 that in the absence of extended liability there exists a range of relatively rich firms that are judgment proof by choice: these firms have the option of being solvent by choosing ðd S ; p S Þ, but also the option of achieving a higher payoff by externalizing damages. Introducing extended liability effectively removes the latter option, thereby inducing these firms to become solvent. As a result, these firms switch to taking socially optimal levels of both damage-reducing and probability-reducing care. 10 Note that enters the residual-liability term in (6), and that p is a function of. This implies that, for judgmentproof firms, increasing the loan fee now has two opposing effects on lender returns: it increases the lender s receipts, but also increases the lender s expected residual liability pfd ðp Þg. So as not to unnecessarily complicate the exposition of our model, we assume the first effect always outweighs the second. An appendix showing exactly what assumption is needed to ensure this, and the (very minor) implications for our results if this assumption fails, is available from the authors upon request.

166 E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 We also show in the Appendix that firms with positive but low gross profits are driven out of business by extended liability. More specifically, we find that the cutoff value of p above which firms remain viable, which we denote p L, is higher than p S. Recall from Section 4 that firms with p 2½0; p S Þ are viable only because they externalize damages. These firms are driven out of business when extended liability is introduced, because they are now forced to fully internalize all costs. In addition, however, there is a range of firms with gross profits greater than p S that are driven out of business as well, because they internalize costs that exceed those at the social optimum. 5.1. Welfare effects of introducing extended liability The welfare effects of introducing extended liability again depends on firms gross profits: Proposition 3. (a) For firms with either low gross profits p 2½0; p S Þ or high gross profits p 2½p L ; p N Þ the welfare effect of introducing extended liability is unambiguously positive. (b) For firms with intermediate gross profits p 2ðp S ; p L Þ the welfare effect is ambiguous. (c) Without extended liability, there is excess entry of firms. Extending liability results in exit that is excessive relative to the first best, but that is second-best optimal. For firms with p 2½0; p S Þ, welfare unambiguously improves; these firms generate negative welfare in the absence of extended liability, and are driven out of business when extended liability is introduced. For firms with p 2½p L ; p N Þ, welfare unambiguously improves as well; these are the firms that switch from being judgment proof to being solvent, and thereby switch to making socially optimal decisions when extended liability is introduced. For firms with p 2ðp S ; p L Þ, however, introducing extended liability replaces one source of welfare loss with a different one. The net welfare effect turns out to be ambiguous, and depends on the shape of the cost curves. The interval ðp S ; p L Þ can be divided into two sub-intervals ðp S ; p L Þ and ½p L ; p L Þ. Consider first firms with p 2½p L ; p L Þ, i.e., firms that stay in business after extended liability is introduced. For these firms, introducing extended liability implies replacing deadweight loss DWL N with a new deadweight loss DWL L, illustrated in Fig. 3. We can again usefully divide this deadweight-loss area into two parts: a triangle to the left of D L and a sliver between D L and D S. Using a thought experiment very similar to that discussed in Section 4, it can be seen that the triangle represents the welfare gain from holding damages constant at D L but reducing the accident probability from p L to its conditionally optimal value zðd L Þ. It can also be seen that the sliver represents the welfare gain from then increasing damages from D L to D S, while keeping the accident probability at its conditionally optimal value zðdþ. To show that introducing extended liability may either decrease or increase welfare for these firms, it is sufficient to show that for some configurations of the cost curves DWL N will be zero and DWL L positive, while for other configurations the opposite will be true. This is easiest to establish for judgment-proof firms that have gross profits p4 D S. To see that the deadweight loss DWL N can be zero for such firms, note in Fig. 3 that what in Section 4 we called the triangle will be smaller, the closer to horizontal at p S the zðdþ curve is for all DXp (so that society gains little from changing the accident probability from p N to the conditionally optimal p). Moreover, what we called the sliver will be smaller, the closer the ri 0 ðdþ curve is to

E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 167 the zðdþ curve for all DXD S (so that society gains little from reducing damages from D to D S ). In the limit where both the zðdþ and ri 0 ðdþ curves become arbitrarily close to horizontal at level p S everywhere to the right of D S, the deadweight loss becomes vanishingly small. It is also clear from the figure, however, that DWL L will be positive as long as the zðdþ and ri 0 ðdþ curves diverge everywhere to the left of D S. Conversely, if the curves coincide to the left of D S, but not to the right, DWL L will be zero, but DWL N positive. 11 Similar arguments can be used to show that the welfare effect of introducing extended liability is ambiguous also for firms with p 2ðp S ; p L Þ, i.e., firms that are driven out of business when extended liability is introduced. More specifically, we prove in the Appendix that the welfare generated by these firms in the absence of extended liability can itself be either positive or negative, so that driving these firms out of business can either decrease or increase welfare. 12 As for part (c) of the proposition, recall that, in the absence of extended liability, firms with p 2½0; p S Þ are viable, but generate negative welfare. In this sense, the absence of extended liability results in excess entry. When extended liability is introduced, these firms are driven out of business, but so are firms with p 2ðp S ; p L Þ. These latter firms would be viable and generate positive welfare if the commitment problem discussed above did not prevent them from taking first-best levels of care. In this sense, extended liability results in excess exit. Note, however, that in the absence of any mechanism that can induce judgment-proof firms to take first-best levels of care, driving firms with p 2½p S ; p L Þ out of business is secondbest optimal. If the first best cannot be implemented, a relevant question is whether there exists a policy that is feasible and dominates extended liability, in that it allows a greater range of firms to both stay in business and generate positive (though not necessarily maximal) welfare. The next section discusses one such policy, namely direct regulation of damage-reducing investments. 6. Direct regulation of damage-reducing investments Given our assumption that lenders can observe a firm s effort to reduce accident damages, but not its efforts to reduce the probability of accidents, it is reasonable to assume that the same would be true of regulators. If so, a natural question to ask is whether direct regulation of damage-reducing investments might either (1) complement extended liability, or (2) be a superior alternative to it. Taking these two questions in turn, we find the following: Proposition 4. Given a regime of strict but limited liability, (a) direct D-regulation does not complement extended liability: if extended liability is in place any binding restrictions on firms choices of D can only reduce welfare, 11 For firms with gross profits po D S, the conditions are only slightly different. Specifically, for DWL N to be zero but DWL L positive, the zðdþ and ri 0 ðdþ curves must converge at p S to the right of p (rather than D S ), and diverge to the left. 12 This result (that extended liability may drive firms out of business that generate positive welfare with strict liability alone) lends some support to the often-made claim (e.g., [11,17]) that extended liability deters socially productive investments.

168 E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 (b) direct D-regulation is a superior alternative to extended liability if such regulation can be tailored to firms gross profit levels; if it cannot, then either policy may dominate the other. Part (a) of the proposition follows directly from the fact that the firm s choice of D is secondbest optimal under extended liability. Part (b) follows from the fact that direct D-regulation can replicate the damage levels chosen by all firms under extended liability, but can do so for judgment-proof firms at a lower loan fee. As a result, these firms will choose a lower accident probability, and social costs will therefore be lower as well. This unambiguous theoretical result, that direct D-regulation is superior to extended liability, of course depends importantly on the assumption that the regulator has the same information as the lender, and can therefore tailor the D-regulation to firms gross profits. 13 If this is not the case in practice, then we are back to welfare ambiguity. 14 7. Conclusions The model developed in this paper incorporates two stylized facts about real-world safety measures that firms may take to reduce expected damages from environmental accidents. One is that firms can usually reduce not just the accident probability but also the magnitude of damages. The other is that probability-reducing care tends to be of a procedural nature, and is therefore difficult for third parties to observe, whereas damage-reducing care tends to involve tangible investments, and is therefore readily observable. We find that under these conditions introducing extended liability for environmental accidents drives judgment-proof firms with low gross profits out of business, and induces judgment-proof firms with high gross profits to become solvent and choose socially optimal levels of care. For judgment-proof firms with intermediate gross profits, however, extending liability fails to induce socially optimal levels of care, even though it forces these firms to fully internalize accident damages. The first two results contrast with those of Pitchford [25], who considers only unobservable, probability-reducing care and shows that (with full debt financing) extending liability to lenders reduces welfare, because it exacerbates the moral-hazard problem. The same effect arises in our model as well, but we show that if firms can also take observable, damage-reducing care, they will increase such care in order to improve their contractual terms with the lender. Some firms will in fact reduce damages to the point where they become solvent, and then take socially optimal levels of both observable and unobservable care. Firms that remain judgment proof, however, end up taking more than first-best observable care to partially compensate for taking less than first-best 13 As discussed in the literature on relationship lending (e.g., [2 4]), banks may accumulate information about firms over time. In practice, therefore, they may know more than the regulator. 14 Furthermore, we are abstracting from any dynamic welfare effects that either extended liability or direct D- regulation might have, for instance by altering firms incentives to reduce costs of damage reduction through innovation.

E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 169 unobservable care. Extending liability to these firms merely replaces one distortion with another, with an ambiguous net effect on welfare. More specifically, the net welfare effect depends on the precise shape of the care cost functions. It follows that determining whether extending liability is a desirable policy in practice may be difficult in industries with a rich array of care technologies, requiring more information on the part of the regulator than is likely to be available. One can imagine situations, however, where the regulator does have the relevant information, for instance because there is only a limited set of technologies available for damage and probability reduction. In such cases, extending liability is likely to be welfare-improving if the damage-reducing technologies are cheap relative to the probability-reducing ones, in the sense of reducing expected damages by more for a given level of expenditure. We find also, however, that if the regulator has information about costs and firm profits, a policy of direct regulation of damage-reducing investment combined with strict liability dominates extended liability. This result is interesting in light of the literature on combining ex ante regulation with ex post liability (see, e.g., [19 21,27,29]). The seminal paper in this literature is Shavell [29], who shows that if (i) the regulator cannot observe firm profits, (ii) some firms may be judgment proof, and (iii) the probability of successful prosecution is less than one, then a policy combining an ex ante regulation with ex post strict liability dominates either policy alone. A recent contribution by Schmitz [27] expands on this result by showing that if the regulator can observe profits and can moreover impose punitive damages (a possibility that Shavell does not consider), then either regulation or strict liability always dominates a combination of the two. Our result contrasts with Schmitz s in that we find that regulation can complement strict liability if it is targeted at observable, damagereducing care. Although our paper focuses on extended liability, the literature has also considered financialresponsibility requirements such as mandatory insurance and bonding as alternative remedies to the judgment-proof problem ([9,15,16,24]). 15 Such remedies will have the same effects in our model as extended liability: the only difference is that, instead of the loan fee increasing to cover residual liability, the firm will now face an insurance premium or bond fee. Our paper has also focused exclusively on debt-financed firms. The results we derive also carry through to the case of equity-financed firms, as long as owner equity is insufficient to make the firm solvent in the event of an accident. Acknowledgments The authors thank Robert Innes, Matthew Kotchen, an anonymous referee, and participants at the Second World Congress of Environmental and Resource Economists and the First CIRANO- IDEI-LEERNA Conference on the Management of Major Industrial/Environmental Risks for useful comments. 15 See [5] for an excellent discussion of existing financial-responsibility requirements under US environmental statutes.

170 E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 Appendix A Proof of Proposition 1. Part (a): Immediate from the fact that a solvent firm s payoff V ¼ p riðdþ pd cð pþ coincides with welfare W. Part (b): The judgment-proof firm s stage-3 optimization problem, conditional on its earlier choice of D and on the fixed loan fee, is max V ¼ð1 pþ½p Š cð pþ s:t: ppp; p with solution p ¼ zðp Þ. After substituting p and the lender s break-even condition (5) into V, the firm s stage-1 optimization problem becomes max V ¼ð1 D p Þ½P rk riðdþš cð p Þ s:t: Dp D; with solution D ¼ D. Substituting this back into the expressions for and p and using p P rk yields p ¼ zðpþ. & The remaining results discussed briefly in Section 4 can be stated formally as follows: Lemma 1. There exist critical gross-profit values D S o p L o p N o D such that (a) Firms with p 2½p L ; DÞ can choose to be either solvent or judgment proof, in the sense that for these firms both ðd S ; p S Þ and ð D; zðpþþ are locally optimal. (b) Firms with p 2½0; p N Þ are judgment proof in equilibrium; firms with p 2½p N ; 1Þ are solvent. (c) Of the firms that are judgment proof in equilibrium, those with p 2½0; D S Þ take less than first-best unobservable care ðzðpþ4 p S Þ; those with p 2ðD S ; p N Þ take more ðzðpþo p S Þ. Proof. Part (a): A firm is solvent at D S if its resulting financial assets p riðd S Þ weakly exceed D S, i.e., if pxd S þ riðd S Þp L, and judgment proof at D if its resulting financial assets p fall short of D. Both are true for some range of firms, since by our assumptions on the IðÞ and zðþ functions, D S þ riðd S Þ¼D S þ Z D D S ri 0 ðdþ ddo D S þ Z D D S zðdþ ddo D S þ ¼ D: Part (b): Let V s ðpþ denote a firm s payoff if it chooses D S and p S and is solvent at that combination, and let V N j ðpþ denote a firm s payoff without extended liability if it chooses D and p ¼ zðpþ and is judgment proof at that combination. Since both functions are continuous in p, itis sufficient to show that V N j ðp L Þ4 V s ðp L Þ and lim p! D V N j ðpþo V s ð DÞ, because the V N j ðpþ function must then cross the V s ðpþ function from above at some intermediate value p N 2ðp L ; DÞ. That V N j ðp L Þ4 V s ðp L Þ follows from Z D D S 1 dd V s ðp L Þ¼ð1 p S ÞD S cðp S Þo ð1 p S Þp L cðp S Þo ð1 zðp L ÞÞp L cðp L Þ ¼ V N j ðp L Þ;

E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 171 using that p L D S þ riðd S Þ and that p ¼ zðpþ uniquely maximizes the value V ¼ð1 pþp cð pþ of a judgment-proof firm. That lim p! D V N j ðpþo V s ð DÞ follows from V N j ð DÞ ¼ D rið DÞ p D cðpþo D riðd S Þ p S D S cðp S Þ¼V s ð DÞ; using that ðd S ; p S Þ uniquely maximizes the value V ¼ p riðdþ pd cð pþ of a solvent firm. Part (c): Since z 0 ðþo 0, zðpþ4 ðo Þ zðd S Þ¼p S if po ð4 Þ D S. & Proof of Proposition 2. As noted in the text, extended liability changes only a judgment-proof firm s stage-1 optimization problem. For purposes of the proof, it is convenient to recast this problem as that of choosing both D and simultaneously, subject to the new lender break-even condition (6) and to Dp D. The Lagrangian associated with this problem is L ¼ð1 p Þ½P Š cð p Þþl ½ð1 p Þ rk riðdþ p fd PgŠ þ l D ½ D DŠ; where p ¼ zðp Þ. Differentiating w.r.t. and D yields @L @ ¼ ð1 p Þþl ð1 p Þ z 0 ðp ÞfD ðp Þg ¼ 0; ða1þ @L j1 @D ¼ l ½ ri 0 ðdþ p Š l D ¼ 0: ða2þ The only value of D consistent with condition (A2) and the first-order conditions involving l and l D is D such that ri 0 ðdþ ¼p ¼ zðp Þ. From the properties of the zðþ and IðÞ functions, this solution condition and the inequality P o D that defines a judgment-proof firm can hold simultaneously only at ðd; pþ combinations with Do D S and p4 p S. & The remaining results discussed briefly in Section 5 can be stated formally as follows: Lemma 2. There exists a critical gross-profit value p L 2ðp S ; p L Þ such that only firms with pxp L remain in business under extended liability. Of these, firms with p 2½p L ; p L Þ are judgment proof, while firms with p 2½p L ; 1Þ are solvent. Proof. Let V L j ðpþ denote a firm s payoff with extended liability if it chooses DL and p L such that ri 0 ðd L Þ¼p L ¼ zðp Þ and is judgment proof at that combination. The critical gross-profit level p L is defined implicitly by V L j ðpl Þ¼0. That p L o p L follows from the fact that V L j ðpþ is increasing in p, and that Z p Z p cðp S Þ¼ c 0 ð pþ dpo c 0 ðp S Þ dp ¼ D S dp ¼ðp p S ÞD S o ð1 p S ÞD S ; p S p S p S so lim p!p LV L j ðpþ ¼ð1 ps ÞD S cðp S Þ is strictly positive. That p S o p L follows from 0 V L j ðpl Þ¼p L riðd L Þ p L D L cðp L Þo p L riðd S Þ p S D S cðp S Þ ¼ p L p S ; Z p

172 E. Hutchinson, K. van t Veld / Journal of Environmental Economics and Management 49 (2005) 157 173 since ðd S ; p S Þ uniquely minimizes full accident-related costs riðdþþpd þ cð pþ. The remainder of the lemma follows by recalling from the proof of Lemma 1 that the conditions defining V s ðpþ hold iff pxp L, and checking that the conditions defining V L j ðpþ hold iff p 2½pL ; p L Þ. & Proof of Proposition 3. Part (a): Immediate from the text. Part (b): Divide the interval ðp S ; p L Þ into sub-intervals ðp S ; p L Þ and ½p L ; p L Þ. That the welfare effect of extending liability is ambiguous for firms with p 2½p L ; p L Þ is immediate from the text. To establish the same for firms with p 2ðp S ; p L Þ, let W N ðpþ denote the welfare generated by these firms in the absence of extended liability, at p ¼ zðpþ and D ¼ D. Also, let W S ðpþ denote the welfare generated by these firms at p S and D S. We must show that W N ðpþ can be either positive or negative, so that driving these firms out of business can either decrease or increase welfare. To show that W N ðpþ can be positive, note that W S ðpþ W N ðpþ is just the deadweight loss DWL N, and that the conditions identified in Section 5 under which DWL N is zero for firms with p 2½p L ; p L Þ apply equally to firms with p 2½p S ; p L Þ. If these conditions hold, so that DWL N is indeed zero, then, since W S ðpþ is positive all firms with p 2ðp S ; p L Þ, W N ðpþ will be positive also. To show that W N ðpþ can be negative, consider the limiting case where zðdþ!zðd S Þ¼p S for all D (so p is in effect fixed at p S and cðp S Þ¼0), and ri 0 ðdþ!0 for all D 2ðD S ; DŠ (so riðd S Þ¼0). In this limit, W N ðpþ reduces to p p S D, and the equation V s ðp N Þ¼V N j ðp N Þ that defines p N reduces to p N p S D S ¼ p N p S p N, or p N ¼ D S. It follows that lim p!p NW N ðpþ ¼D S p S D, which can clearly be negative for sufficiently large D. Since W N ðpþ is increasing in p, this in turn implies that W N ðpþ will be negative for all judgment-proof firms (i.e., all firms with p 2½0; p N Þ), including firms with p 2ðp S ; p L Þ. Part (c): Immediate from the text. & Proof of Proposition 4. Immediate from the text. & References [1] T.R. Beard, Bankruptcy and care choice, RAND J. Econ. 21 (4) (1990) 626 634. [2] A.N. Berger, G.F. Udell, Relationship lending and lines of credit in small firm finance, J. Bus. 68 (3) (1995) 351 381. [3] A.N. Berger, G.F. Udell, Small business credit availability and relationship lending: the importance of bank organisational structure, Econ. J. 112 (477) (2002) F32 F53. [4] A.W.A. Boot, Relationship banking: What do we know?, J. Finan. Intermediation 9 (1) (2000) 7 25. [5] J. Boyd, Financial responsibility for environmental obligations: are bonding and assurance rules fulfilling their promise? Discussion Paper 01-42, Resources for the Future, Washington, DC, August 2001. [6] J. Boyd, D.E. Ingberman, The polluter pays principle : should liability be extended when the polluter cannot pay?, Geneva Pap. Risk Ins. 21 (79) (1996) 182 203. [7] J. Boyd, D.E. Ingberman, The search for deep pockets: Is extended liability expensive liability?, J. Law Econ. Organ. 13 (1) (1997) 232 258. [8] J. Boyd, D.E. Ingberman, Fly by night or face the music; Premature dissolution and the desirability of extended liability, Amer. Law Econ. Rev. 5 (1) (2003) 189 232. [9] M. Boyer, J.J. Laffont, Environmental risks and bank liability, Euro. Econ. Rev. 41 (8) (1997) 1427 1459. [10] R. Burke, Sailing in safe harbors: recent developments regarding lender liability under CERCLA, Pace Environ. Law Rev. 16 (1998) 143 188. [11] J.J. Byrne, T.J. Greco, Comment: superfund reform needed to keep credit flowing, Amer. Banker (1994) 17. [12] B. Craig, S.E. Thiel, Large risks and the decision to incorporate, J. Econ. Bus. 42 (3) (1990) 185 194.

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