Lender liability for environmental harm: A model of environmental screening under double moral hazard and ex ante information

Transcription

1 Lender liability for environmental harm: A model of environmental screening under double moral hazard and ex ante information Joshua Okeyo Anyangah Department of Economics, University of Lethbridge, Lethbridge, AB, Canada TK 3M4 ( joshua.anyangah@uleth.ca) Abstract. We build a model where lenders employ an imperfect screening technology to elicit information about their borrowers environmental risk type prior to committing funds. Borrowers di er in terms of their net worth. They also exercise unobservable level of care. Under conditions we describe, introducing or increasing the lender s liability for environmental harm caused by its judgment-proof borrower unambiguously leads to a decrease in both the cost of capital and accident probability. It is shown that an increase in the liability of the lender triggers a shift towards high net worth borrowers and a contraction of the environmentally hazardous industry. This contraction may be welfare enhancing, however, if the regulatory environmental is characterized by a disproportionate share of low risk borrowers. JEL classi cation: K3, K32, D82, Q58 Keywords: Environmental regulation; Endogenous screening; Extended liability; Judgment proof problem.

2 Introduction The possibility that a rm protected by limited liability can cause an environmental damage and then declare bankruptcy (Shavell, 986 coined the term judgment-proof to describe such rms) appears to many to be ine cient in that it dilutes the injurer s incentive to be cautious ex-ante. Extending liability to third parties hereafter referred to as extended liability with deep pockets (they are not liable to bankruptcy), such as the rm s lenders, is viewed as an e cient regulatory response to the problem of judgment-proofness. Because they are held liable in the event of an injury, lenders subjected to extended liability will have the incentive to reduce their exposure to such environmental risks. The US Comprehensive Environmental Response, Compensation and Liability Act (CERCLA) was enacted largely against the background of this legal doctrine. 2 Other jurisdictions have apparently taken the cue from the US and enacted similar legislations (Richardson, 2002). The foregoing begs the question: how can extended liability a ect the frequency of accidents, the availability of credit to an environmentally hazardous industry, and social welfare? We attempt to answer this question by building a model in which the relationship between the lender and the borrower exhibits bilateral moral hazard and ex ante information. In the model, wealth-constrained entrepreneurs (or rms) have access to environmentally risky investment projects and must obtain external nancing from lenders. Each entrepreneur is characterized by its net worth and private information about its underlying risk. This creates an agency problem of the adverse selection type on the part of the entrepreneur. It is assumed that projects that are particularly environmentally risk have a negative present value and are therefore not credit worthy; the lender would like to minimize its exposure to such projects. Thus, the lender performs two key roles here: she not only provides the entrepreneurs with the requisite nancial resources. She also screens projects, by subjecting loan applicants to a creditworthiness test, in order to weed out bad environmental risks. The screening technology is imprecise, however, so the lender is able to spot and eliminate only some, but not all bad risks from the pool of loan applicants. Thus, the novelty of our analysis is that the probability that a funded project will cause a damaging accident does not only depend upon the project s intrinsic risk (or type) and the amount of care exercised by the entrepreneur, as has been postulated in the received literature. It also depends on how scrupulously the lender conducts the credit assessment (or screening). Another important new insight that our model brings to the fore is that the lenders credit o ering decisions determine the size of the environmentally hazardous industry, and therefore aggregate environmental damage. Screening and care are not observable and cannot, therefore, be directly contracted upon. Thus, in addition to the adverse selection problem mentioned above, there is also a bilateral moral hazard problem between entrepreneurs and their lenders. Our strongest result relates to the impact of extended liability on the availability of credit to the environmentally hazardous industry. We nd that introducing or increasing extended liability decreases the range over which lending is feasible. More concretely, increasing the lender s exposure to tort liability induces a shift away from low net worth borrowers to high net worth borrowers 2

3 and in this way decreases the proportion of projects that are nanced. As for the cost of capital, we nd, contrary to the conventional view, that legal reforms that introduce or increase lender liability unequivocally reduce the rate of interest. This lack of ambiguity is not found in the standard model without bilateral moral hazard, and it also cannot arise in settings without ex ante signals. Intuitively, extending liability to the lender increases environmental performance risks that are borne by the lender, and in this way generates two distinct e ects. First, it tightens the lender s participation constraint, which in turn worsen the moral hazard problem on the part of the borrower. Second, it slackens the lender s incentive compatibility constraint. This makes the moral hazard problem on the part of the lender less severe. The rst e ect is rst-order in magnitude, whilst the second e ect is only of second-order importance. Thus, the balance of these two e ects is to worsen the borrower s moral hazard problem. To best limit the borrower s moral hazard incentive, the lender lowers the rate of interest. This increases the borrower s reward in the no-accident state, which in turn leads to an increase in the level of care exercised by the borrower. And even though lowering the rate of interest has a deleterious e ect on the lender s incentive to incur expenditure on screening, the gain in expected surplus from the higher level of care more than o sets any losses resulting from the lower screening intensity. The other key comparative-static results are as follows: First, an increase in extended liability unambiguously increases the level of care. Intuitively, an increase in the lender s residual liability leads to a decrease in the interest rate, which in turn increases the marginal bene t of care. Since the marginal cost of care remains unchanged, the new optimal level of care must be higher than the initial one. Second, an increase in extended liability has an ambiguous e ect on screening intensity. This is because an increase in lender liability triggers two analytically di erent e ects. On the one hand, there is the interest rate e ect, which operates through changes in the interest rate. As explained above, an increase in the lenders tort liability ultimately pushes lenders to reduce the rate of interest and thus their screening e ort. On the other hand, there is the direct e ect, which works by relaxing the lender s incentive compatibility constraint. Third, legal reforms that increase extended liability unambiguously decrease expected damage, both at the individual and aggregate level. At the rm level, expected damage declines because an increase in extended liability lowers the accident probability; at the aggregate level, expected damage is lower because of the ensuing contraction of the environmentally hazardous industry. As for social welfare, we nd that the contraction of credit that accompanies any increase in the liability of the lender may actually enhance social welfare. More precisely, if the liability of the lender is increased in a regulatory environmental characterized by a disproportionate share of low risk entrepreneurs, then the ensuing contraction in the industry, because it squeezes out more bad risk than good risk, may actually enhance social welfare. Thus, credit rationing may be e cient. Our study is by no means the rst one to explore this area of environmental regulation. A number of studies have formally investigated the implication of extended liability as a regulatory instrument and yielded important insights on the e ects of this type of intervention. Their results have been somewhat mixed, however. Most prominently, Pitchford (995) has shown that when 3

4 lenders are held liable for environmental damages that arise from activities of their judgement-proof borrowers, social damages may actually increase. Obviously, this result is fundamentally at odds with the spirit of CERCLA. It also contrasts sharply with Boyer and La ont (997) and Heyes (996), who nd that lender liability may increase the incentive for accident prevention. It also warrants mentioning that Pitchford s key insights contradicts studies by Polinsky (993), Privileggi et al., (200), and Shavell (997), who analyze the problem of extended liability in the context of the relationship between a rm and its manager/employee. Balkenborg (200) focuses on the impact of bargaining power at the contracting stage in an imperfectly competitive world. The author shows that there is a cuto level of creditor bargaining power, below which increased lender liability increases accidents, and above which it does not. Lewis and Sappington (200) considers a setting with many di erent levels of damages rather than the binary-damage technology assumed by many studies, and nds that the lender s deep pockets can be valuable in mitigating the judgement-proof problem. Dionne and Spaeter (2003) use a framework in which investment in precaution a ects the distribution of environmental losses and operating revenue to show that extending liability may increase the level of precaution. Hutchinson and van t Veld (2005) build a model that allows for both probability and damage reducing safety measures on the part of the injurer. By assuming that damage reducing actions are observable whilst probability reducing measures are not, they show that extended liability results in the full internalization of social cost. Interestingly, and quite contrary to a principal argument of this paper, the authors show that introducing extended liability leads to excessive exit from environmentally hazardous industries as more projects become infeasible. The present study di ers from the studies cited above in two respects: First, all these formal analyses abstract away from or presume that the lender lacks the ability to perform extensive due diligence prior to committing her sunk investment. The standard assumption in all these investigations is that both parties are willing to deal and only the price of environmental risk is at question. Consequently, the control of a project s environmental risk is the exclusive preserve of the borrower. In other words, the probability of an accident depends solely on the level care exercised by the borrower. This depiction of the lender disregards a well known function performed by lenders; namely, the task of evaluating projects for their credit worthiness. 3 The present study endogenizes the screening activity of the lender. In so doing, we develop a model of entrepreneurial rm- nancing that directly links the lender s screening incentive to the probability of an environmental accident. Second, previous studies have tended to rely on rm-level results in order to make conjectures about the potential impact of liability rules at the industry level. But such a reasoning may not be adequate if regulatory reforms have a bearing on lenders credit o ering decisions and credit allocation. It is possible, for example, that as a result of these reforms, expected damage at the rm-level improves, but the industry expands (through the nancing of more project) su ciently to actually increase aggregate damage. We explicitly derive the expected damage, both at the rm and the industry level, by conditioning the intensity of environmental damage on the amount of capital employed, and by allowing for not one, but rather many borrowers who are, however, 4

5 heterogenous with respect to their nancial requirements. As a consequence, the aggregate damage function depends upon both the level of activity per project ( rm) and the proportion of projects that are actually nanced. This study is also closely related to the literature that has examined the economic application of double moral hazard. Demski and Sappington (99) examine the problem of double-sided moral hazard in the context of a rm with a risk neutral owner and a risk averse worker, and show that the problem can be completely and costlessly resolved if the principal has the option of requiring the agent to purchase the enterprise at a pre-negotiated price. Cooper and Thomas (985, 988), Emons (988) and Manns and Wissink (988) examine the nature of the optimal warranty when both the producer and the consumer of a product take privately observed actions that a ect the quality of the product. Agrawal (999), and Eswaran and Kotwal (985) examine double-sided moral hazard in the context of agricultural contract. Romano (994), and Bhattacharyya and Lafontaine (995) examine models of double-sided moral hazard to explain the prevalence of linear contracts. Kim and Wang (998) extend the same theme by examining the robustness of linear contracts and show that the optimal contract is generally not linear if the agent is risk averse. On a general level, this paper is related to studies that have examined how lenders control asymmetric information in the market for loans. Depending on the type of asymmetric information and agency problems that prevail, lenders can design contracts that induce self-selection among borrowers (Bester 985), they can employ ex-ante screening (Hauswald and Marquez 2003; Thakor 996), interim monitoring (Besanko and Kanatas 993), or ex-post veri cation (Townsend 979; Diamond 984). The rest of this paper is organized as follows. Section 2 develops the central elements of the model. Section 3 characterizes the solution to the borrower s problem. Section 4 derives comparative static results of the impact of regulatory reforms. Section 5 concludes. 2 The Model The model comprises three risk-neutral agents: entrepreneurs, lenders and a victim. All entrepreneurs operate in an environmentally hazardous industry and have access to business investment idea that requires I to undertake. However, entrepreneurs di er in terms of their initial wealth endowment wealth A. Denote by! = A=I the entrepreneurs net worth ratio. Thus, the set of entrepreneur in the industry is described by the cumulative distribution function F (!; I); that is, F (!; I) indicates the proportion of entrepreneurs with net worth ration less than!. This assumption allows us to explicitly determine the amount of aggregate damage and the magnitude of lending to the industry without the necessity to make any conjecture about the aggregate properties of the model. There are two important dates in the model: date 0 and date. For simplicity, assume a zero discount rate. At date 0, each entrepreneur starts a project. At date, the project return is realized. Since entrepreneurs have insu cient funds to undertake their projects, they must go 5

6 to the capital market and borrow I A = (!)I. Lenders operate in a competitive capital market and have access to an unlimited supply of capital at a constant gross rate of interest ~r. Following Bose and Cothlen (997), we assume that an entrepreneur can obtain funding from at most one lender, but a lender can fund several projects. We also stipulate that a lender can enter into a separate contract with each entrepreneur and that each contract is designed independently of the other. In what follows, therefore, we consider only a single representative relationship between a lender and an entrepreneur. A project generates a net cash ow v from which all nancing payments and accident-related costs are drawn. We assume v is costlessly veri able. In addition, each started project carries the risk of causing an environmental accident. The probability that a project will cause an environmental harm is given by '(; a) = a <, where 2 f H ; L g, L < H, a is the level of care undertaken by the injurer and the value of is private information to the entrepreneur. Thus, for any given level of a, an investment project of size k can be of two types : low-risk (or type L ) projects cause accidents with probability L a; high-risk (or type H ) projects cause accidents with probability H a. It is common knowledge that Pr( = L ) = P (L) =. Regardless of the project s environmental performance, the entrepreneur earns private bene ts (a), where the function (a) is strictly decreasing and concave in a. (a) is meant to capture the idea that, from the entrepreneur s perspective, committing resources to preventive activities entails an opportunity cost, and that this cost can be measured in terms of the foregone consumption of "perks" generated by the diversion of funds from the project s environmental investment. Put simply, if the entrepreneur wants to increase his private bene ts (e.g., perquisite consumption), he must divert resources away from the project (see, for example, Holmstrom and Tirole 997). We assume that the lender cannot share in the consumption of perks generated by the diversion of funds. For analytical simplicity, we posit the following speci c functional form for (a): (a) = 2 ( a2 )v. () Thus increasing the level of care entails a sacri ce of private bene ts. 5 Closely following Broecker (990), we assume that no self selection devices are available to the lender. Instead, the lender is endowed with a costly screening technology. Thus, prior to granting a loan, the lender performs environmental due diligence, which involves screening projects in order to uncover their environmental riskiness. 6 More concretely, by exerting screening e ort at rate s 2 [0; ], the lender can receive a noisy signal about an applicant s underlying riskiness. The signal takes on either a high (h) or low (l) value, 2 fl; hg. 7 Assume that the conditional distribution function of is P ( = lj L; s) = P (lj L; s) = P ( = hj H; s) = P (hj H; s) = + ( P ( = lj H; s) = P (lj H; s) = P ( = hj L; s) = P (hj L; s) = ( )s s). In other words, P (lj L; s) is the conditional probability that the lender will correctly recognize a low- 6

7 risk project when screening e ort s is employed, whilst P (lj H; s) is the conditional probability that the lender will erroneously evaluate a high-risk project as a low-risk one. Hence, the signal is correct with probability P (lj L; s), but is incorrect with probability P (lj H; s). 8 Note that the quality of the signal is increasing in screening intensity s: lim s! P (lj L; s) =, lim s! P (lj H; s) = 0, and lim s!0 P (lj L; s) = lim s!0 P (lj H; s) =. Thus, if screening is su ciently intense, the lender receives a perfect signal (i.e., there is a zero probability of committing a type II error). On the other hand, at the zero level of screening intensity, the signal reveals absolutely nothing about the rms environmental status. The cost of screening is given by g(s), where g(s) is assumed to be monotonically increasing and convex (g 0 (s) > 0 and g 00 (s) > 0). Assumption. g(s) = 2 s2. Assumption simply imposes a quadratic technology on g(s) that, as we show below, allows us to obtain closed-form solutions and sharp comparative static results. Throughout the analysis, it is assumed that s is not contractible. In the event of an accident, the victim su ers h harm. Denote by c 2 (0; h] the court s evaluation of the lender s liability for her borrower s environmental malfeasance. To capture the idea that the industry in which the entrepreneurs operate is a highly hazardous one, we assume that if an accident manifests itself, then bankruptcy is inevitable. An important consideration is how the realization of bankruptcy a ects the rm s asset value. In this paper, we assume that in the event of bankruptcy, the rm s assets are worth a lower value than vk. There are a number of reasons why this assumption is plausible: the lender may experience losses if she is forced to pay cleanup costs on a contaminated site; creditor s protection may not be adequate; the debt recovery process may be time consuming and costly. We make the following additional assumptions: Assumption 2. NP V L = [ ( L a)]v ( L a)c ~ri > NP V H = [ ( H a)]v ( H a)c ~ri < 0 Assumption 3. NP V L + ( )NP V H < 0 Assumption 2 says that nancing the high risk borrower has a negative net present value, whilst nancing the low risk borrower has a positive net present value, i.e., only the L types are creditworthy (Broecker 990). Hence, the nancial contract will be designed for only type L. Assumption 3 states that the expected net present value from a project that is not screened is negative; that is, it is not pro table to nance a cross section of projects. This assumption e ectively rules out a randomized loan granting strategy on the part of the lender. Taken together, assumptions 2 and 3 justify the restriction of the analysis only to cases where lenders screen all loan applicants. Upon receiving a good signal, the lender computes, via Bayes Rule, her posterior belief that the project s environmental risk is low, namely P (Lj l; s) = P (Lj = l; s) = P (lj L; s) = + ( )s 2 (0; ), (2) P (lj L; s) + ( ))P (lj H; s) 7

8 P (Lj h; s) = P (Lj = h; s) = ( )P (lj H; s) = ( )( s) 2 (0; ). (3) ( )P (lj H; s) + P (lj L; s) Remark. The probability of receiving a good signal is dependent neither on screening intensity s nor the level of care a. Proof. P (L)=P (Lj l; s) + ( )P (Lj h; s) =. The probability that a successful applicant, who exerts care level a, will cause an environmental accident is given by: (s; a) = ( L a)p (Lj l; s) + ( H a)p (Lj h; s) = (a) ( )s, (4) where (a) = ( L a)+( H a)( ) = L a is the unconditional probability of an environmental accident for a randomly selected entrepreneur and 0 < = H L <. Thus, a randomly selected entrepreneur is more likely to cause a damaging accident than the one subjected to a creditworthiness test. Equation (4) is crucially important because it delineates a direct link between the likelihood of a damaging accident and the lender s action choice in a manner that has not been explored previously. We model the interaction between the entrepreneur and the lender as a multi-stage game. In the rst stage, nature chooses the project s type and only the entrepreneur observes this information. In the second stage, lenders compete by simultaneously o ering loan contracts. A loan contract comprises a gross borrowing rate R. This o er is contingent on the screening s outcome at the next stage. In announcing the contract, each lender takes all the other lenders interest rates and screening e ort as given. In stage three, the entrepreneur makes an application for nancing; each entrepreneur can apply to only one lender. In stage four, the lender screens loan applicants and either accepts (A) or rejects (n) an application depending on the private signals. Thus, in our model, information about the borrower s type is revealed ex ante in that it becomes available before the project is endorsed by the lender. The game ends if the contract is rejected. If the contract is accepted, the rm undertakes the project. Payments are made once the outcome of the project is observed publicly. Formally, the lender s strategy at the fourth stage of the game is (s; O ), where each O 2 fn; Ag is the lender s credit o ering decisions based on signal 2 fh; lg. Any credit o ering decision O is either a rejection of the applicant represented by n, or an o er of k units of capital with a speci ed repayment obligation represented by A. Given that nancing the high risk borrower has a negative net present value, an important part of the lender s strategy is its decision when to turn down an application and when to o er credit. Let be the probability that the lender o ers credit when the signal 2 fh; lg is received. The following remark is a statement on the lender s decision to accept an application given any signal. Remark 2. Suppose that the lender receives the signal 2 fh; lg. A strategy that does not include h = 0 and l = is strictly dominated. 8

9 Proof. Suppose that the lender has undertaken the optimal level of screening. Then conditional on observing a signal, she can respond as follows: (i) play A if = l and play A if = h; (ii) play n if = l and play n if = h; (iii) play n if = l and play A if = h; (iv) play A if = l and play n if = h. The rst two rules are not optimal since they would not justify screening in the rst place. The third rule can also be ruled out because it is at odds with assumptions 2 and 3. Thus rule (iv) constitutes the only reasonable strategic response by the lender. Henceforth, we restrict the analysis to cases where h = 0 and l =. In other words, the optimal contract will be designed with only the low-risk type in mind. 3 Solution to the borrower s problem In this section we examine the characteristics of the optimal nancial contract and the induced level of a, s and. The borrower s expected payo can be written as U(s; a; R; k) = f[ ][v R] + minf0; v R cgg + 2 ( a2 )v. (5) where is de ned by (4). Equation (5) says that with probability ( ) the project causes no damage, in which case the borrower receives the residual v R after paying R to the lender, and with probability a damaging accident occurs, in which case the borrower gets nothing in the event of bankruptcy or the residual value v R c if the rm is solvent. As indicated earlier on, we focus on the interesting case where an accident inevitably leads to bankruptcy. Thus, in the accident state, v R c 0, implying that R + c v. The lender s expected payo is E[~(s; R; k)] = [( )R c ~r(!)i] 2 s2, (6) where E{.} is the expectations operator with respect to the prior probability distribution on. Equation (6) reports that with probability ( ) the project causes no damage, in which case the lender receives R from the borrower, and with probability a damaging accident occurs, in which case the lender pays compensation c to the victim. We assume that borrowers hold the balance of bargaining power. Hence, the lender s expected payo will be driven down to zero in equilibrium. One justi cation for this is that the lender operates in a competitive credit market, and therefore, as in Besanko and Kanatas (993), does not wield any monopoly power. The program of the entrepreneur, stated as EP, can be written as max [ fr;s;ag (H a)][v R] + 2 ( a2 )v (7) subject to: [( (s; a))r(k ) c ~r(!)i] 2 s2 = 0; (8) 9

10 ( ) [R + c] = s; (9) [v R)] = av; (0) v R 0; and () U(s; a; R; k) 0. (2) Expression (7) re ects the fact that the borrower s expected payo comprises the net surplus that he retains in the no accident state after repaying the lender, and private bene ts from diverting resources. Equation (8) is the lender s individual rationality or participation constraint. It says that perfect competition in the credit market drives the borrower s expected pro t to zero. Equation (9) is the lender s incentive compatibility condition. It guarantees that prior to signing the contract, the lender selects the optimal level of screening given the gross rate of interest R. Similarly, the entrepreneur determines the optimal level of care to undertake given the gross rate of interest R. His incentive compatibility condition is given by constraint (0). 9 Since the entrepreneur is protected by limited liability, she cannot be required to repay more that the project s residual cash ow vk in the state of the world in which the project is nondamaging. 0 Thus, the optimal rate of interest charged by the lender must satisfy constraint (). Finally, (2) gives the entrepreneur s participation constraint. It reports that in order for the entrepreneur to undertake the project, he must be promised a non negative expected payo. Problem EP can be considerably simpli ed by reducing the number of constraints. First, note that constraint (2) can be rewritten as v R + [ (s; a)] + 2 ( a2 )v 0. (3) Thus, if constraint () is satis ed, then constraint (2) must also hold. It follows that constraint (2) is redundant and can therefore be eliminated. Next, it is easy to see that if incentive compatibility constraint (0) is satis ed, then constraint () must also satis ed; hence, constraint () can also be eliminated. An equivalent representation of problem EP now comprises the objective function (7) and constraints (8), (9) and (0). Before laying out the solution to problem EP, it is worthwhile to consider the relationship among R, s, and a. Totally di erentiating equations (9) and (0), it is easy to see that whilst screening increases with R in equilibrium, the opposite is true when it comes to the relationship between care a and R: ds dr = ( ) > 0; da dr = v < 0 (4) The key features of the solution to problem EP are now reported in the following proposition. Proposition There exists a critical threshold! :! = ~ri + c L I~r 2 ( )2 2 v c c L ( ) 2 2 c 2 4I~r v 2 ( )2 2, (5) 0

11 such that borrowing for entrepreneurs with! <! is not feasible. The optimal contract for an entrepreneur with!! is to borrow exactly (!)I at interest rate ~ R(!): ~R(!) = ~r(! )I + c L 2 ( )2 2 c! 2 v 2 ( )2 2 + v ~r [!! ] I 2 ( )2 2! 2. (6) The corresponding screening intensity s(!), care a(!) and induced accident probability (!) are given, respectively, by s(!) = ( h i ) ~R(!) + c (7) a(!) = [v v ~ R(!)] (!) = L ( ) 2 2 c + v ( ) 2 2 (8) ~R(!). (9) Proof. See the appendix. Equation (5) gives the condition under which borrowing is feasible. It says that not all entrepreneurs are funded. More concretely, entrepreneurs who pass the creditworthiness test are sorted into two groups, according to the size of their projects and external nancial requirements: those below the threshold! and those between! and. Only the latter group qualify for nancing. Evidently! determines the size of the environmentally hazardous industry. [ F (! )] indicates the fraction of entrepreneurs with projects greater than!, and hence the initial size of the industry. This result parallels Heyes (996), and is reminiscent of Stiglitz and Weiss (98), and Williamson (987). In Heyes (996), the basis for credit rationing is the entrepreneur s wealth: poor borrowers are not able to o er lenders adequate return. In Stiglitz and Weiss (982), and Williamson (987), it is assumed that the supply of funds is inadequate to meet demand and that there is no way to elicit more funds by raising the (expected) return faced by lenders. Credit is therefore only given to borrowers with particularly risky projects, where risk is measured in terms of variability of returns. Next, the proposition suggests that an entrepreneur who accepts to undertake a project invests all her wealth and borrows just enough to execute the project. The reason for this is the following: The entrepreneur s utility is decreasing in the project s nancing gap I A and, therefore, the repayment obligations. The higher the amount borrowed, the higher the repayment amount and the smaller the residual surplus that the entrepreneur can retain in the event that no damaging accident materializes. Thus, among all contracts that provide zero expected pro t for the lender, the one most preferred by the entrepreneur must limit the debt repayment burden by requiring the entrepreneur to borrow just enough to undertake the project. Equation (6) gives the expression for the optimal rate of interest. Interestingly, it shows that the interest rate is monotone in!, i.e., R ~ 0 (!) > 0. This characteristic of the interest rate stems from the lender s need to ensure that each entrepreneur selects the correct loan size. The lender must make the selection of a small loan undesirable for an entrepreneur with a small net worth. It does this by making the interest rate fall with loan size, thus letting large borrowers (low net

12 worth borrowers) earn some rent. The lender must also ensure that small borrowers do not select loans designed for large borrowers. Such a possibility is ruled out, however, since it would impose an onerous repayment burden on the borrower. In our model, screening is valuable because it reduces the likelihood of an accident thereby increasing the amount (in expectation) that can be recouped in the event of bankruptcy. Thus, if the rm is potentially judgment proof, the lender will nd it optimal to invest in screening so long as it s worth the cost; that is, until the marginal bene t from the s th unit is just equal to the marginal cost. Equation (7) gives an explicit expression for the screening intensity. It indicates that net worth! has a positive incentive e ect (measured by s 0 (!) > 0). Equation (8) reports the characteristics of the optimal level of care that the borrower will undertake. As with the screening intensity, the amount of care exercised by the borrower increases with project size. Since the credit market is perfectly competitive, increasing project size unambiguously reduces the interest rate as already demonstrated. The lower rate of interest allows borrowers to keep some of their gains from trade, which in turn induces them to exercise more care ex ante. In studies that abstract from endogenous screening, the accident probability is generally dependent on the level of precaution exercised by the borrower. In this paper, however, the accident probability is determined by the risk parameter, the level of precaution and, more importantly, the intensity of screening, which is under the direct control of the lender. Equation (9) gives the accident probability, which is obviously endogenously derived in this model. Signi cantly, it indicates that there is a positive relationship between a borrower s net worth and the accident probability. In fact, the accident (or default) probability is strictly an increasing and concave function: 0 (!) > 0, 00 (!) < 0. Thus, an increase in the borrower s net worth (i.e., a decrease in loan size) leads to a decreases economic e ciency. Conversely, a decrease in borrowers net worth (i.e., an increase in loan size) bolsters economic e ciency. 2 This result appears to lend theoretical support to the evidence adduced by Jiménez and Saurina (2004). Intuitively, a higher loan size raises the lender s exposure and makes accurate screening more important; it also leads to a lower level of R, which in turn makes more intense care more rewarding. 4 Impacts of regulatory reforms We are now ready to examine the main positive results the comparative static impact of changes in policy parameter c. Our ultimate goal is to uncover how variations in c a ect aggregate lending, aggregate damage and social welfare. As an important transitional step, however, we need to determine the main channels through which changes in c a ect these variables; that is, we want to determine how changes in c a ect the minimum feasible size of the project!, the rate of interest R, screening intensity s, and care a, 2

13 4. Intermediate comparative statics Di erentiating equations (5), (6), (7) and (8) with respect to c = I~r L ( ) 2 2 c + 2 v c L ( ) 2 2 c ~ = 2 2 ~r(! )I + c L 2 ( )2 2 c! 2 v 2 ( )2 2 2 v c L ( ) 2 2 c v 2 ( )2 2 (2) v ~r [!! ] I 2 ( )2 2! 2 L ( ) 2 2 c = ( ) v R(!) ~ # v c L ( ) 2 2 c 2 ( )2 = R(!) ~. In words, equation (20) indicates that an increase in c decreases the range over which lending is feasible. Stated di erently, increasing the amount of tort liability to which the lender is subjected increases the severity of credit rationing by increasing the minimum net worth!. As explained in the following paragraph, an increase in c pushes lenders to lower the rate of interest R (equation (2)) in a rational attempt to preclude any moral hazard incentive on the part of the borrower. The e ect of this diminution in the rate of interest is to relax both the participation and limited liability constraints of the borrower and induce the entry of projects that were initially "too small" to be executed. Equation (2) reports that an increase in c unambiguously leads to a decrease in the cost of capital. The reason for this is that an increase in c slackens the lender s incentive compatibility constraint, which in turn makes the moral hazard problem on the part of the lender less severe. This result contrasts Heyes (996) who nds that an increase in c has an ambiguous impact on the rate of interest. In Heyes model, the screening function is not explicitly derived. Instead, the rate of interest charged to borrowers is used as a screening device. In our model, by contrast, screening is done ex ante, so R is designed to control the borrower and the lender s moral hazard incentives. Equation (22) shows that changes in c a ect the lender s screening incentives through two channels. First, there is the interest rate e ect, which operates indirectly through variations in R(!). From equation (2) this e ect is negative: by inducing more care on the part of the borrower (through a lower level of R), an increase in c pushes the lender to reduce her screening e ort. Second, there is the direct e ect: an increase in c slackens the lender s incentive compatibility constraint thereby inducing an increase in s. Hence, the sign is ambiguously. Equation (23) shows that an increase in c has a positive incentive e ect on care. Intuitively, an 3

14 increase in c leads to a decrease in R, which in turn increases the marginal bene t of care. Since the marginal cost of care remains unchanged, the new optimal level of care must be higher than the initial one. Finally, consider the impact of regulatory reforms on the accident probability. Taken together, equations (22) and (23) imply that an increase in c has a negative e ect e ect = ( ) R(!) ~ ( ) 2 2. The key features of these results are now summarized in the following proposition: Proposition 2 An increase in extended liability reduces the accident probability (!). 4.2 Aggregate lending Our next order of business is to evaluate the aggregate properties of the model. To begin with, we examine aggregate lending. 4 When lending is feasible; that is, when!!, the probability that a good credit risk yields a good signal is P (Lj l; s), which also represents the probability that such an applicant obtains a loan o er from the lender. Assuming that a loan applicant cannot receive a loan o er from any other source if the lender wrongly denies credit, the probability of receiving a loan o er for a low risk borrower is P (Lj l; s). The corresponding probability for a high-risk borrower is P (Lj h; s). It follows that the (expected) loan amount for a type-l entrepreneur is P (Lj l; s)( A similar expression holds for the high-risk borrower, whose expected loan amount is P (Lj h; s)(!)i. Thus the (expected) aggregate volume of lending to the environmentally hazardous industry is given by B(k) = Z Z! By remark, P (Lj l; s) + ( an entrepreneur endowed A reduces to ( 0!)I. [P (Lj l; s) + ( )P (Lj h; s)] (!)IdF (!; I). (25) )P (Lj h; s) = P (L) = ; hence, the expected quantity loan for!)i. In other words, the amount of loan received by an entrepreneur does not depend on the lender s screening e ort; it depends only upon the entrepreneur s net worth ration! and the probability that the entrepreneur is a low risk. Equation (25) can be rewritten as Z B(!) =! Z 0 (!)IdF (!; I) = Z! (!)E(Ij!)dF (!), (26) where E(Ij!) is the conditional expectation of I given! and F (!) is the marginal cumulative distribution function of!. We can now state the following result: Proposition 3 An increase in lender liability c increases the threshold level of project size below which borrowing is not feasible. As a result, the volume of lending to the industry decreases. Proof. 4

15 Di erentiating (26) with respect to c we obtain db(!) dc = (! )E(Ij! )F 0 (! ) d! dc < 0. (27) Proposition 5 indicates that an increase in extended liability unambiguously induces a contraction in lending to the environmentally hazardous industry. This result parallels Hutchinson and van t Veld (2005), and Heyes (996). In Hutchinson and van t Veld (2005), the introduction of extended liability eliminates the viability of those rms with particularly low gross pro ts because they are forced to internalize damages that they previously externalized. In Heyes model, an increase or the introduction of extended liability reduces the lender s expected return. This pushes the lender to raise the minimum wealth that the entrepreneur must contribute towards the project. As a result, entrepreneurs whose wealth fall below the new higher wealth threshold are rationed of credit. An implication of the foregoing is that extended liability can a ect rms access to credit. More precisely, an increase in extended liability may produce a shift away from low net worth entrepreneurs. 4.3 Damage function In this section we derive the damage function. In so doing, we explicitly di erentiate between project-level damage and industry (aggregate) damage, a distinction that we believe has been conspicuously overlooked in the received literature. Our assumption that the industry is teeming with projects of varying magnitudes allows us to achieve this objective. At the project level, the expected damage l(!) can be written as l(!) = h(!) = h L ( ) 2 2 c + h v ( ) 2 2 ~R(!). (28) Di erentiating l(!) with respect to! implies that l 0 = h v ( ) 2 2 ~R 0 (!). (29) Note that l 0 is positive by virtue of the fact that ~ R 0 (!) > 0. Furthermore, l 00 = h v ( ) 2 2 ~R 00 (!)<0, (30) since ~ R 0 (!) < 0. Taken together, equations (29) and (30) imply that l(!) is concave. More precisely, l(!) increases at a decreasing rate as shown in Figure 3. The result that increases in net worth increase expected damage is intriguing. At lower levels of!, increases in! do not lead to a su ciently strong increase in care or screening intensity since the expected damage is relatively modest. However, moving to some interior value of k implies an increase in the severity of any environmental damage. This makes accurate screening and expenditure on care more important, 5

16 thereby decreasing (!) and l(!). Now di erentiating l(!) with respect to our policy parameter = h( ) h v ( ) 2 ~ < 0. (3) Previous studies have tended to rely on the characteristics of activity at the rm-level in order to make qualitative predictions about the potential impact of extended liability on industry-level environmental quality. But such a reasoning may fail to adequately account for the fact that regulatory reforms have a bearing on lenders credit o ering decisions, credit allocation, and therefore the size of the industry. It is possible, for example, that as a result of these reforms, damage at rm-level improves, but the industry expands (through the execution of additional projects) su ciently to actually raise aggregate damage. At the industry level, the damage function, denoted by L(!), depends on both the size of individual projects and the proportion of projects that are actually undertaken. endogenously determined by the lenders credit o ering decisions. Hence, we have L(!) = Z! l(!)f(!)d! = h Di erentiating this equation with respect to c yields Z The latter is! = (33) From the right-hand side of the equation (33), we can delineate two channels through which changes in the policy parameter c a ect L(!): (i) the rst e ect works by changing (!) and is captured by the integral term on the RHS of equation (33). < 0, this e ect is clearly negative. The second e ect relates to how changes in c a ect the feasibility of nance for the smallest net worth project! and is represented by the second term on the RHS of equation (33). =@c > is unambiguously negative, i.e., an increase in extended liability will lead to a decrease in aggregate damage. The last two results are now formalized in the following proposition. Proposition 4 An increase in c unambiguously leads to a decrease in expected damage both at the project and aggregate level. 4.4 Social welfare It remains to determine the impact of changes in the policy parameters c on social welfare. Summing the expected payo s over all the entrepreneurs served by the lenders and the accidents cost borne 6

17 by the victim, we obtain the expected social welfare as Z SW = fp (Lj l; s)[( )v h ~r(a=!)] (34)! +P (Lj h; s)( )[( )vk h ~r(a=!)] + 2 ( a2 )v 2 s2 f(!)d! Note that any compensation received by the victim represents a pure wealth transfer and has no aggregate welfare implications. Using the fact that P (L) = Pr(L) = P (Lj l; s)+p (Lj h; s)( ) =, the social welfare function can be rewritten as SW = Z! [vk( ) h ~r(a=!)] + 2 ( a2 )v 2 s2 f(!)d!. (35) Equation (35) shows that any e ects on social welfare must stem from (a) the borrowers investment in care, (b) the lender s decision to invest in information acquisition and the use of this information in lending, and (c) the proportion of projects that are actually undertaken. The socially e cient level of care a (!) and screening intensity s (!) are identi ed by maximizing the utilitarian welfare function, not constrained by the feasibility condition, the lender s participation constraint and the incentive compatibility constraints: This yields Z max [vk( ) h ~r(a=!)] + s; a! 2 ( a2 )v Z Together, equations (37) and (38) imply that a satis es 2 s2 f(!)d!. (36)! f[v + h] a (a ; s ) + va g f(!)d! = 0 (37) Z! f[v + h] s (a ; s ) + s g f(!)d! = 0. (38) [v + h] va = 0 (39) whilst s satis es [v + h]( ) s = 0. (40) Comparing (39) and (40) with (8) and (7) it is easy to see that the optimal values of a(!) and s(!) that are generated through private contracting fall short of the socially e cient levels a (!) and s (!). This is because under the private optimum, the feasibility constraint imposes a limit on how much interest can be charged. Additionally, due to limited liability on the part of the entrepreneur, the marginal bene t from care is evaluated only over those states of the world in which the rm is solvent. As a result, the social cost of the accident are not fully internalized. The same logic can be used explain the suboptimal level of screening: the lender does not enjoy the full 7

18 reward from her e ort in the solvency state since R must be structured to evoke e ort from both parties; however, she must absorb any residual losses in the bankruptcy state. We can now state the following: Proposition 5 Suppose that the rm is judgment-proof and extended liability is the only regulatory tool in place. Then an increase in extended liability has ambiguous welfare e ects. Proof. The derivative of the social welfare function with respect Z + f[v + h] f(!)d! Z + f[v + h]( f(!)d!, where a and s are de ned by equations (7) and (8), and f:g is the term in curly brackets f:::g in equation (36). Equation (4) categorizes, at least, three distinct channels through which changes in c can e ect welfare. There is the threshold e ect, which is captured by the rst term on the right-hand side of equation (4). It shows that an increase in c induces the lender to increase the screening threshold! below which borrowing is not feasible. As a result, some projects that were initially feasible are not undertaken. Whether this industry expansion raises or lowers welfare depends, however, on the sign of the multiplicative term in the curly brackets f:g. It turns out that this term is actually the net present value of the project. Evidently, its sign depends on parameter, the proportion of projects that are low risk. For low levels of, it is likely that f:g is negative and therefore the threshold e ect is positive since most the projects that are rejected are high risk rms. On the other hand, when is high, it is likely that the overwhelming majority of the projects that become infeasible are type L, in which case f:g is positive, and so the threshold e ect is negative. The care e ect is represented by the rst integral term on the right-hand side of equation (4). This term is strictly positive by virtue of the fact that a(!) < a > 0. The screening e ect is represented by the last integral term on the right-hand side of equation (4). The sign of this term is ambiguous by virtue of the fact that the sign is ambiguous. In sum, cannot be de nitely signed. However, an interesting set of implications can be derived when f:g is positive; that is, when is su ciently large. In this case, the negative threshold e ect works at cross purposes with both the screening and care e ects, and the sign critically depend on the magnitude of =@c relative to the combined e ects of the screening and care e ects. Thus, equation (4) leads to the intuitively appealing conclusion that the e cacy of c as a regulatory instrument crucially depends on the proportion of high risk entrepreneurs in the industry. More precisely, if c is increased in a regulatory environmental characterized by a disproportionate share of low risk entrepreneurs, the the ensuing contraction in the industry may actually enhance social welfare. The foregoing result contrasts with Hutchinson and van t Veld (2005), Boyd and Ingberman (997) Pitchford (995) and Dionne and Spaeter (2003). In Hutchinson and van t Veld, extended li- 8

19 ability leads to excessive exit from the industry, as rms that were previously externalizing damages lose their viability. In Boyd and Ingberman, the welfare e ects of extended liability are ambiguous: whilst extended liability forces greater cost internalization, it also leads to distortions in capital investment decisions. Pitchford focuses on a single rm and argues that increasing the liability of lenders may actually increase the frequency of accidents and reduce social welfare if the premium that the lender can charge to compensate herself for bearing the risk of an accident is su ciently large. Dionne and Spaeter extend Pitchford analysis by showing that partial extended liability is welfare improving, but full lender liability is never optimal. 5 Conclusion This paper used a simple lending model to examine the implication of extending liability to a lender for the environmental harm caused by its borrower. In the model lenders and borrowers are informationally advantaged: lenders have an information advantage because the screening services (credit assessment) they provide are not observable and cannot therefore be contracted upon; borrowers undertake unobservable care and have private information about the environmental risk associated with their projects. Screening is valuable because it enables the lender to receive an imperfect signal about the borrower s risk type ex ante. By endogenizing screening activity in the manner described above, we generate a model in which the probability of an environmental accident depends the lender s action choices. This dependence of the accident probability on how diligently the lender pursues her gatekeeping role highlights an important dimension of the judgement proof problem that has hitherto not been investigated. We nd that the introduction or an increase in lender liability decreases the interval over which lending is feasible, and thereby leads to a reduction of credit to the industry. We also show that regulatory reforms that increase the lender s liability reduce the cost of capital, unambiguously increase the level of care, but has ambiguous e ect on screening intensity. Legal reforms that increase extended liability unambiguously decrease expected damage, both at the individual and aggregate level. As for social welfare, we nd that the contraction of credit that accompanies any increase in the liability of the lender may actually enhance social welfare. More precisely, if the liability of the lender is increased in a regulatory environmental characterized by a disproportionate share of low risk entrepreneurs, then the ensuing contraction in the industry, because it squeezes out more bad risk than good risk, may actually enhance social welfare. Thus, credit rationing may be e cient. While the model provides important insights on the impact of regulating environmental externalities, there remains some interesting extensions. To keep things simple, we have abstracted from modelling risk preferences presuming, instead, that all parties are risk neutral. A natural extension might admit alternative speci cation of risk preferences. A typical entrepreneur may not hold a large portfolio of projects and may therefore be unable to diversify away all risks associated with a project. Thus, it may be appropriate to model the entrepreneur as a risk-averse economic agent. 9