1 Introduction

Liability rules are important tool of environmental risks management in Canada, United States and Europe. The major legislations are CERCLA (Comprehensive Environmental Response, Compensation and Liability Act) adopted by the American Congress in 1980 and the Directive of the European Parliament and the Council on Environmental Liability with regard to the Prevention and remedying of environmental Damages which came into force in April 2004. A *E.J.L. & E. 78 liability rule induces correct incentive for risk prevention only if information is symmetric and the potential injurer has sufficient wealth to cover his liability. Indeed, it is well known from the previous literature that when the injurer’s wealth is not sufficient to pay liability judgments ex post (the injurer is said to be judgment-proof) this leads to underprovision of care ex ante (Summers 1983; Shavell 1986). In the case of environmental risks, on the one hand, perfect control of firm’s actions in prevention is not possible, and on the other hand, the wealth of the polluter may be small relative to the clean-up costs and victims’ compensation.

There are many policies to alleviate the judgment-proof problem. The first one is to extend liability to the parties who have a contractual relationship with the risky firm, the case under CERCLA which imposes extended liability to lenders. The economic analysis of the extended liability has given raise to mitigated results. Pitchford (1995) considers a one-period moral hazard model with two states of nature (accident or not). Since the loan fee fixed by the lender included his expected liability costs, the more the lender is liable, the more he charges the firm in the no-accident state. Then, the state of the nature “no-accident” becomes unfavourable for the firm and the full liability of the lender2 leads to a suboptimal level of effort whereas partial lender’s liability allows achieving the optimal level of prevention. In a two-period model, Boyer and Laffont (1997) show that partial liability of lender is optimal. Consequently, these authors conclude that the society has to make a tradeoff between prevention and compensation. In an alternative setting in which environmental damages are stochastic and prevention cost is a monetary investment that needs external funding, Dionne and Spaeter (2003) show that lender extended liability has a positive effect on the firm’s prevention level if and only if an increase in the face value of the debt implies an increase in prevention investment. Moreover, Balkenborg (2001) and Lewis and Sappington (2001) show that the benefits of extending liability to lenders depend on the observability of the firm’s prevention level by the lender, the bargaining power of each party and the nature of environmental damages. Finally, Hutchison and Van’t Veld (2005) consider a model with both observable damage-reducing activities and non-observable probability-reducing measures and show that introducing extended liability to lender induces judgement-proof firms with high gross profits to take socially optimal levels of care, those with intermediate gross profits to take suboptimal level of care and drives those with low gross profits out of business.

Financial responsibility is another remedy for the judgment-proof problem. Under a regime of financial responsibility, the firm is required to demonstrate that the cost of the harm she can cause is covered. The most common instrument of financial responsibility is the insurance contract. But as it is well known, the compulsory liability insurance induces the efficient level of prevention only when the insurer is able to observe the prevention level performed by the firm (Shavell 1986; Jost 1996; Polborn 1998). Following the analysis of Jost (1996), Feess and*E.J.L. & E. 79 Hege (2000, 2003) consider a model with monitoring-based incentives and show that the mandatory liability coverage for total harm leads to an allocation that is closed to the first-best.

In this paper, we investigate how the socially optimal allocation can be implemented through ex ante financial responsibility and ex post strict liability rule. We do not restrict our analysis to insurance contract but on contrary analyze financial guarantee contract. Indeed, in the Directive of the European Parliament and the Council on environmental liability there is a focus on a future legislation that imposes financial responsibility on the polluting firms. Then we analyze the consequences of financial responsibility on the incitation to prevention in a context of asymmetric information and show that the first-best allocation may be attainable. This follows from the fact that the level of damages provides a signal of the firm’s prevention level (Lewis and Sappington 1999) and can be used to design an optimal contract. But contrary to Lewis and Sappington (1999), in our setting, prevention measures do not only involve a disutility for the firm but also reduce the funds available for compensation and clean-up (Beard 1990; Lipowsky-Posey 1993; Dionne and Spaeter 2003; Dari-Mattiaci and De Geest 2005).

We consider a firm which activity yields a non-random gross profit and generates random environmental damages. The firm can improve the distribution of damages by an investment in prevention at the beginning of the period and safety measures during the production process. At the end of the period, only the damages and the resources of the firm net of the prevention cost are observable. Moreover, it is assumed that the firm’s wealth is lower than the highest amount of damages its activity can generate. We establish a necessary and sufficient condition for the implementation of the socially optimal allocation in spite of moral hazard when the firm is mandated to cover the highest amount of damages its activity can generate. We also demonstrate that the set of contracts that implement the socially optimal level of prevention includes a particular contract of the form “reward or maximal penalty” which is closed to a finite risk product referred to as spread loss treaty. The rest of the paper is organized as follows. The following section presents the firm’s optimal choice in the absence of the financial responsibility regime. Section 3 investigates the impact of financial responsibility on the firm’s prevention level. Finally, Section 4 concludes.

2 The optimal choice of the firm without financial responsibility

Consider a risk-neutral firm which activity generates a fixed profit P and creates a possibility of environmental damages ## ]0, L[. The firm can improve the distribution of damages by an investment in prevention at the beginning of the period and safety measures during the production process; these two measures are represented by a single prevention variable denoted e. However, the reduction of risk generates a cost c(e) when the firm chooses a level of prevention e. Moreover we assume that before engaging in its activity, the firm has initial wealth (equity) Rwhich can be partially used to cover the cost induced by prevention measures. Let f(##/e) and F(##/e) be respectively the density and the distribution function of the damages; the following is assumed:

*E.J.L. & E. 80 Assumption 1 ##e, f(##/e) > 0, decreases with ##.3 This means that the observation of a lower level of damage is relatively more likely if a higher level of prevention has been adopted. This assumption implies the first order stochastic dominance: ## ]0, L[,Fe (##/e) > 0. Moreover, Fe (0/e) = Fe (L/e) = 0.

Assumption 2 ## ]0, L[, Fee (##/e) < 0. This distribution function is strictly concave in e. 4

Assumption 3 ce (e) > 0 and cee(e) > 0. The prevention cost is strictly convex in e.

Assumption 4 If the amount of damages is very high, the firm’s assets may be insufficient for compensation; then the firm will be pushed into bankruptcy. Assume that the discount rate is null so that the firm’s net value without investment in prevention noted ## equals R + P.Formally, this liability assumption can be written as L > ##.

What about the optimal level of prevention from the firm’s point of viewThe intuition suggests that a firm facing limited liability will underinvest in prevention. But, as stated by the following lemma this is not always true.

Lemma 1 A judgment-proof firm does not always choose a suboptimal prevention level.

Proof: See the “Appendix”.

The social welfare criterion is assumed to be the minimization of the total cost which is the sum of the expected damages and the prevention cost. We assume that the regulator observes the prevention level. At the social optimum, the expected marginal benefit of prevention equals the expected marginal cost.

The objective of the firm is to maximize its net revenue which equals to the sum of its profit and equity minus the expected liability payments (compensation and clean-up costs). The firm can only pay up to her assets. Hence the private expected marginal benefit is lower than the social one because of the partial internalization of environmental damages by the firm. Moreover, the private expected marginal cost of prevention is lower than the social one because the funds invested in prevention are not available for compensation and clean-up. At the private optimal level of prevention, the private expected marginal benefit of prevention equals the private expected marginal cost. Consequently, the optimal private level of prevention may be lower or higher than the socially optimal one, depending on which effect dominates. However, the judgment-proofness of the firm may result in a partial remediation of damages. One can think about compulsory liability insurance which covers the highest amount of damages as a solution to this problem. But it is well known from economics literature that when care is non-observable, a full insurance leads to underprovision of care by the insured. In the following section we demonstrate that under a guarantee structure, incentives work well even if it is *E.J.L. & E. 81 impossible to observe the care by the polluter. The reason is that under the guarantee the polluter receives a return on investment in prevention. Moreover, this scheme provides the full coverage of damages: prevention and compensation are both satisfied.

3 Financial responsibility

This section is devoted to the economic analysis of a hybrid regime of ex ante regulation through financial responsibility requirement and ex post strict liability. More precisely, in our setting the financial responsibility takes the form of a guarantee provided by another party that has deep pockets. Then the hybrid regime can be viewed as a regime of vicarious liability in which the guarantor and the firm are joint liable. As we know, in this setting, the victims generally choose to collect from the guarantor because the later has deep-pockets. Then, in what follows, we will assume that the firm and its guarantor are jointly liable and that it is the guarantor who has to compensate for the damages generated by the firm.5,6

The analysis is based on the principal-agent paradigm. In this framework, the firm is the limited liability risk neutral agent and the guarantor is the risk neutral principal. The prevention level performed by the firm and consequently the cost of such a measure are not observable by the principal. Moreover, the amount of damages and the net resources of the firm at the end of the period are observable. The timing of the model is as follows. First, the guarantor and the firm sign a contract which stipulates the state-contingent-payments (transfers) that the firm has to make to his guarantor. Secondly, the firm performs a level of prevention and bears the associated cost which is unobservable by the guarantor. Then, the profit is realized and the damages occur and finally the transfer is made to the guarantor. Moreover, it is assumed that the guarantor has all the bargaining power and his objective is to design a scheme of transfers that maximizes his profit. However, the guarantor has to take into account some constraints. The first one is the participation constraint of the firm which reflects the fact that the financial guarantee must yield expected revenue at least equals to what the firm would have obtained without contracting (condition 1). The second one is the firm’s limited liability constraint (condition 2). The third constraint reflects the fact that the transfer is bounded below in such a way that the firm could be rewarded (condition 3).7 The last condition is the incentive compatibility constraint which reflects the optimal behaviour of the firm in choosing the prevention level (condition 4).8

*E.J.L. & E. 82 Formally, if we denote t(##) the transfer made by the firm when the amount of damages equals ##, the guarantor’s problem (P1) can be written as:

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subject to

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The existence of schemes of transfers that solve the problem above is not guaranteed. Then it is essential to characterize the conditions under which the problem (P1) admits a solution for a given utility u (expected firm revenue) and a given prevention level e. We can establish the following result:

Proposition 2 The problem (P1) admits a solution, i.e. the levels of utility u and prevention e can be implemented if and only if:

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Proof: See the “Appendix”.

The intuition underlying the proposition 2 is the following. For a given level of prevention e it is not possible to find a scheme of transfers that gives a level of utility u if the marginal cost of such a measure is greater than the marginal benefit. Let us remark that the marginal benefit of prevention is reflected by the reduction of the expected transfers that the firm has to pay to her guarantor. We have demonstrated (see the “Appendix”) that there is a scheme %23t(##) that gives the maximum marginal benefit of prevention, which equals [## – c(e) – B]Fe (##). If this upper limit of the marginal benefit of prevention is lower than the marginal cost of prevention for a given e, then any scheme of transfers cannot implement the prevention level e.

From the analysis above we can derive the following result:

Proposition 3 The social optimum (u, e*) can be implemented with the financial responsibility if and only if:

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*E.J.L. & E. 83 Proof: See the “Appendix”

The left-hand-side term of the condition (5) represents the rate of change of the marginal benefit of prevention at the point e* with a transfers scheme %23t(##), whereas the right-hand-side represents the rate of change of the marginal cost of prevention at the same point. Consequently if there is a level of damage ## such that the rate of change of the marginal benefit is at least equal to the rate of change of the marginal cost of prevention then the social optimum can be implemented.

The last step of the analysis is devoted to the characterization of a scheme of transfers that implements the first-best level of prevention. We can establish the following proposition:

Proposition 4 The set of transfers that implement the socially optimal level of prevention contains a scheme of the following form:

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Proof: See the “Appendix”

The scheme of transfers 23t(##) is such that if at the end of the period, the actual damage is lower than the target level ##, then the firm is rewarded by receiving the bonus payment B, so her net revenue at the end of the period equals ## Conversely if the actual damage is greater than the target level ##, then the payment made by the firm to the guarantor equals ## – c(e*) and the firm net revenue at the end is null.

This form of contract can be approached to a spread loss treaty. It is an alternative risk transfer (ART) solution, more precisely a finite risk product. By this contract, the financial responsibility of the firm is transferred to her guarantor (that can be a bank or an insurer).9,10 At the beginning of the contract, the firm pays either annual or single premium into a so-called experience account. Furthermore, the two parties contractually agree on an investment return. The funds are used to compensation and the rest is returned to the client. But if the claims payments exceed the funds available, the client has to pay the remainder.

In this paper, we consider a one-period model. Consequently, the model can be viewed as if we have aggregated the periods of the spread loss treaty. Moreover, if the realized damages are low, the funds into the experience account are sufficient for compensation whereas in the bad states of nature (high realized damages), the funds *E.J.L. & E. 84 are not sufficient. Hence, because of its limited liability, the firm cannot pay back the claims payments of the guarantor. Then, the guarantor takes this fact into account by penalizing the firm in the intermediate states of nature [those such that the amount of damages is between the target level ## and ## – c(e*)]. Consequently, the reward is used as an incentive device.

4 Concluding remarks

A potentially judgment-proof firm may not internalize the social cost of its activity and then may have insufficient incentives to choose the socially optimal level of prevention. Whereas most of papers studied the incentive effect of extending liability to the lenders of the injurer-firm, this paper on contrary considers another remedy to the problems generated by the judgment-proofness. I demonstrate that a full financial responsibility (operation licence subject to the demonstration of a financial guarantee which covers the highest remediation cost) is compatible with the socially optimal level of prevention and establish a necessary and sufficient condition under which this is realized.

Furthermore, I have shown that when the socially optimal outcome is attainable, a contract of the form “reward or maximum penalty” is included in the set of first-best solutions. Such a contract rewards the firm when the actual damages are lower than a target level because the guarantor infers that the firm took an adequate prevention level. Conversely, if the amount of the damages exceeds the target level, then the firm is maximally punished. This particular contract can be approach to an alternative risk transfer product referred to as spread loss treaty. Consequently, the alternative risk transfer solutions seem suited not only for the hedging of environmental risks, but also for incentive purpose.

Finally, recall that the Directive of the European Parliament and the Council on Environmental Liability has a special focus on a future legislation which imposes financial responsibility on the polluting firms. It is necessary that before the promulgation of such legislation, European authorities help insurance and banking sectors to develop the market for environmental guarantees.

Acknowledgments I am very grateful to an anonymous referee and to the editor for helpful remarks on a previous version of the paper. I would like to thank Jean-Marc Bourgeon, Georges Dionne, Marie-Cecile Fagart, Mahamadou Fall, Claude Fluet, Bruno Jullien, Anne Lavigne, Remi Moreau, Pierre Picard, Sandrine Spaeter, Jean-Marc Tallon and Daniel Zajdenweber. The paper also benefited from the comments of session participants of the 2005 SCSE congress in Charlevoix, 2005 AFSE congress in Paris and seminar participants at HEC Montreal, Universite d’Orleans, Universite de Sherbrooke and Universite du Quebec a Montreal. Financial support by CREF-HEC and the hospitality of the Canada Research Chair in risk management are acknowledged.

Appendix

Proof of lemma 1

The social optimum e* is the solution of the following problem:

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*E.J.L. & E. 85 The associated first-order condition is given by:

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The firm’s problem can be written as:

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The left-hand-side term of Eq. 6 (7) represents the social (private) expected marginal cost of prevention and the right-hand-side represents the social (private) expected marginal benefit. From the comparison of (6) and (7) eP can be lower or higher than e*.

Proof of proposition 2

Part 1: u ## [u,## – c(e) – B]

Every level of utility u is given by the following expression:

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Taking into account this expression, the objective function of the guarantor becomes:

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Moreover, (2) and (3) imply: ## – c(e) ? ## t(##)f(##/e)d## ? B; thus 0?u ? ## – c(e) – B

Consequently, the existence of a transfers scheme verifying (1), (2) and (3) implies that the utility of the firm is bounded: u ## [u,## – c(e) – B]. Note that the principal’s objective function depends only on the expected transfer (by u). Therefore, all solutions that verify the agent’s incentive constraint and that have the *E.J.L. & E. 86 same expectation are equivalent from the principal’s point of view. However, the existence of such solutions is not guaranteed. Indeed, if the problem does not admit a solution, then it is not possible to implement a given level of prevention e for a given level of utility u.

Part 2: [## – c(e) – B]Fe (##/e) ? ce(e)

Let us assume that u ## [u,## – c(e) – B], then the next step consists to establish conditions under which the incentive constraint (4) is satisfied. Let ## = {t(##)/B ? t(##) ? ## – c(e)##}, be the set of admissible transfers. Let us define:G[t(-)] = ## t(##)fe(##/e)d##; m = min ## t(##)fe(##/e)d## and M = max ##t(##)fe(##/e)d##.

We can establish that m is strictly negative and M strictly positive.11 Thus the function G [t(.)] is bounded in the set of admissible transfers. Then the validity of the incentive constraint depends on the value taken by m as follows.

Lemma 2 the incentive constraint is satisfied for a given e and u if and only if:

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Lemma 3 the scheme of transfers %23t(##) which minimizes the function G [t(-)] = ## t(##)fe(##/e)d## has the following form 12:

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The second part of proposition 2 follows from lemmas 2 and 3.

Proof of proposition 3

From proposition 2, we can derive that when the guarantor’s problem (P1) admits at least one solution, it is equivalent to the following problem (P1bis):

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Conditions (9) and (10) imply proposition 3.

*E.J.L. & E. 87 Proof of proposition 4

From the proposition 3 we know that the socially optimal prevention level can be achieved if Fe(##/e*)/F(##/e*) ? ce(e*)/u. Moreover, we can demonstrate that the function Fe(##/e*)/F(##/e*) is not increasing in ##.13 Consequently, if Fe(##/e*)/F(##/e*) ? ce(e*)/u, there is a level of damages ## > ## such that Fe(##/e*)/F(##/e*) = ce(e*)/u.

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E.J.L. & E. 2010, 30(2), 77-87