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 T1K 3M4 (e-mail:
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: K13, K32, D82, Q58
Keywords: Environmental regulation; Endogenous screening; Extended liability; Judgment proof
problem.
1
1
Introduction
The possibility that a …rm protected by limited liability can cause an environmental damage and
then declare bankruptcy (Shavell, 1986 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.1 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
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 (1995) has shown that when
3
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 (1997) and Heyes
(1996), 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 (1993), Privileggi
et al., (2001), and Shavell (1997), who analyze the problem of extended liability in the context of
the relationship between a …rm and its manager/employee.
Balkenborg (2001) 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 (2001) 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
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 (1991) 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 (1985, 1988),
Emons (1988) and Manns and Wissink (1988) 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 (1999), and Eswaran and Kotwal (1985) examine double-sided
moral hazard in the context of agricultural contract. Romano (1994), and Bhattacharyya and
Lafontaine (1995) examine models of double-sided moral hazard to explain the prevalence of linear
contracts. Kim and Wang (1998) 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 1985), they can employ ex-ante screening (Hauswald and Marquez 2003; Thakor
1996), interim monitoring (Besanko and Kanatas 1993), or ex-post veri…cation (Townsend 1979;
Diamond 1984).
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 1. For simplicity, assume a
zero discount rate. At date 0, each entrepreneur starts a project. At date 1, the project return
is realized. Since entrepreneurs have insu¢ cient funds to undertake their projects, they must go
5
to the capital market and borrow I
A = (1
!)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~
1.
Following Bose and Cothlen (1997), 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 < 1, where
care undertaken by the injurer and the value of
2f
H ; L g,
L
<
H
1, a is the level 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
with probability
H
L
a; high-risk (or type ‘H’) projects cause accidents
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 1997). 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):
1
(a) = (1
2
a2 )v.
(1)
Thus increasing the level of care entails a sacri…ce of private bene…ts.5
Closely following Broecker (1990), 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; 1], the lender can receive a noisy signal
takes on either a high (h) or low (l) value,
function of
is
about an applicant’s underlying riskiness. The signal
2 fl; hg.7 Assume that the conditional distribution
P ( = lj L; s) = P ( lj L; s) = P ( = hj H; s) = P ( hj H; s) =
+ (1
P ( = lj H; s) = P ( lj H; s) = P ( = hj L; s) = P ( hj L; s) = (1
)s
s).
In other words, P ( lj L; s) is the conditional probability that the lender will correctly recognize a low6
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: lims
lims
!0 P ( lj L; s)
= lims
!0 P ( lj H; s)
=
!1 P ( lj L; s)
= 1, lims
!1 P ( lj H; s)
= 0, and
. 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 (g0 (s) > 0 and g 00 (s) > 0).
Assumption 1. g(s) = 21 s2 .
Assumption 1 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. N P V L = [1 (
Assumption 3.
NPV
L
+ (1
L
a)]v (
)N P V
H
L
a)c r~I > N P V H = [1 (
H
a)]v (
H
a)c r~I < 0
<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 1990). 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)
=
P ( lj L; s) + (1
))P ( lj H; s)
7
+ (1
)s 2 (0; 1),
(2)
P ( Lj h; s) = P ( Lj
= h; s) =
(1
)P ( lj H; s)
= (1
)P ( lj H; s) + P ( lj L; s)
(1
)(1
s) 2 (0; 1).
(3)
Remark 1. 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) + (1
)P ( Lj h; s) = .
The probability that a successful applicant, who exerts care level a, will cause an environmental
accident is given by:
where (a) = (
(s; a) = (
L
a)P ( Lj l; s) + (
L
H
a)(1
a) +(
)=
L
H
a)P ( Lj h; s) = (a)
(1
) s,
(4)
a is the unconditional probability of an environmental
accident for a randomly selected entrepreneur and 0 <
=
H
L
< 1. 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
1. 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
1 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
credit when the signal
be the probability that the lender o¤ers
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
h
= 0 and
l
= 1 is strictly dominated.
8
2 fh; lg. A strategy that does not include
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
‘n’if
= l and play ‘n’if
and play ‘n’if
= h; (iii) play ‘n’if
= l and play ‘A’if
= l and play ‘A’if
= h; (ii) play
= h; (iv) play ‘A’if
=l
= 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
= 1. 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) =
where
f[1
][v
R] + minf0; v
1
cgg + (1
2
R
is de…ned by (4). Equation (5) says that with probability (1
damage, in which case the borrower receives the residual v
with probability
a2 )v.
(5)
) the project causes no
R after paying R to the lender, and
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)] =
[(1
)R
c
r~(1
!)I]
1 2
s ,
2
(6)
where E{.} is the expectations operator with respect to the prior probability distribution on .
Equation (6) reports that with probability (1
) 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 (1993), does not wield any monopoly power.
The program of the entrepreneur, stated as EP, can be written as
max [1
fR;s;ag
(
H
a)][v
1
R] + (1
2
a2 )v
(7)
subject to:
[(1
(s; a))R(k
1)
c
9
r~(1
!)I]
1 2
s = 0;
2
(8)
(1
v
)
[R + c] = s;
(9)
[v
R)] = av;
(10)
R
0;
and
(11)
0.
(12)
U (s; a; R; k)
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 (10).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.10 Thus, the optimal rate of
interest charged by the lender must satisfy constraint (11). Finally, (12) 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¤.11
Problem EP can be considerably simpli…ed by reducing the number of constraints. First, note
that constraint (12) can be rewritten as
v
R+
1
(s; a)]
[1
+
1
(1
2
a2 )v
0.
(13)
Thus, if constraint (11) is satis…ed, then constraint (12) must also hold. It follows that constraint
(12) is redundant and can therefore be eliminated. Next, it is easy to see that if incentive compatibility constraint (10) is satis…ed, then constraint (11) must also satis…ed; hence, constraint (11)
can also be eliminated. An equivalent representation of problem EP now comprises the objective
function (7) and constraints (8), (9) and (10).
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 (10), 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
(1
)
da
=
dR
> 0;
v
<0
(14)
The key features of the solution to problem EP are now reported in the following proposition.
Proposition 1 There exists a critical threshold ! :
1
! =
r~I + c
I r~
L
1
(1
2
2
)
2
1
c
1
vc
4I r~
10
L
1
v
)2
(1
1
2
(1
)2
2
2c
2
,
(15)
such that borrowing for entrepreneurs with ! < ! is not feasible. The optimal contract for an
~
entrepreneur with ! ! is to borrow exactly (1 !)I at interest rate R(!):
~
R(!)
=
r~(1
! )I + c
1
v
L
1
2 (1
1
2
)2
)2
(1
2c
2
!1
2
+
! ]I
1
(1
)2
2
1
v
!1
2
r~ [!
2
.
(16)
The corresponding screening intensity s(!), care a(!) and induced accident probability (!) are
given, respectively, by
s(!) = (1
a(!) =
(!) =
L
(1
)2
)
[v
2
c+
h
i
~
R(!)
+c
(17)
~
R(!)]
v
1
v
(18)
(1
)2
2
~
R(!).
(19)
Proof. See the appendix.
Equation (15) 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 1. Only the latter group qualify for …nancing.
Evidently ! determines the size of the environmentally hazardous industry. [1
F (! )] indicates
the fraction of entrepreneurs with projects greater than ! , and hence the initial size of the industry.
This result parallels Heyes (1996), and is reminiscent of Stiglitz and Weiss (1981), and Williamson
(1987). In Heyes (1996), 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 (1982), and Williamson (1987),
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 (16) gives the expression for the optimal rate of interest. Interestingly, it shows that
~ 0 (!) > 0. This characteristic of the interest rate stems
the interest rate is monotone in !, i.e., R
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
11
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 sth unit is just equal to the
marginal cost. Equation (17) gives an explicit expression for the screening intensity. It indicates
that net worth ! has a positive incentive e¤ect (measured by s0 (!) > 0).
Equation (18) 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 (19) 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.
12
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,
12
4.1
Intermediate comparative statics
Di¤erentiating equations (15), (16), (17) and (18) with respect to c we obtain
@!
1
=
@c
I r~
~
@R
=
@c
1
2
r~(1
L
)2
(1
! )I + c
1
2
)2
L
1
v
1
2 (1
! ]I
1
)2
2 (1
!
2
(1
1
c
v
1
1
2
c +
)2
2c
2
!
1
2
L
1
2
1
vc
1
)2
(1
L
1
v
2
(20)
c
)2
(1
1
2 (1
)2
2c
2
(21)
1
2
r~ [!
1
v
2
1
2
L
)2
(1
2c
+
1
2
1
v
@s(!)
= (1
@c
)
"
1
1
2 (1
1
vc
L
)2
)2
2
#
~
@ R(!)
+1
@c
~
@ R(!)
.
v @c
@a(!)
=
@c
(1
(22)
(23)
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
(21)) 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 (21) 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 (1996) 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 (21) 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 of @s=@c is ambiguously.
Equation (23) shows that an increase in c has a positive incentive e¤ect on care. Intuitively, an
13
2c
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 on (!):
@ (!)
=
@c
)2
(1
2
1
v
+
)2
(1
2
~
@ R(!)
.
@c
(24)
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.14 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)(1 !)I.
A similar expression holds for the high-risk borrower, whose expected loan amount is P ( Lj h; s)(1
!)I. Thus the (expected) aggregate volume of lending to the environmentally hazardous industry
is given by
B(k) =
Z
Z
1
!
By remark 1,
1
[ P ( Lj l; s) + (1
)P ( Lj h; s)] (1
!)IdF (!; I).
(25)
0
P ( Lj l; s) + (1
)P ( Lj h; s) = P (L) = ; hence, the expected quantity loan for
an entrepreneur endowed A reduces to
(1
!)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
B(!) =
Z
1
!
Z
1
(1
!)IdF (!; I) =
Z
1
(1
!)E( Ij !)dF (!),
(26)
!
0
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.
14
Di¤erentiating (26) with respect to c we obtain
dB(!)
=
dc
! )E( Ij ! )F 0 (! )
(1
d!
< 0.
dc
(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 (1996). 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
(1
2
c +h
1
v
(1
)2
2
~
R(!).
(28)
Di¤erentiating l(!) with respect to ! implies that
1
v
l0 = h
(1
)2
2
~ 0 (!).
R
(29)
~ 0 (!) > 0. Furthermore,
Note that l0 is positive by virtue of the fact that R
l00 = h
1
v
)2
(1
2
~ 00 (!)<0,
R
(30)
~ 0 (!) < 0. Taken together, equations (29) and (30) imply that l(!) is concave. More
since R
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,
15
thereby decreasing (!) and l(!). Now di¤erentiating l(!) with respect to our policy parameter c
yields
@l(!)
=
@c
)2
h (1
2
1
v
+h
)2
(1
2
~
@ R(!)
< 0.
@c
(31)
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. The latter is
endogenously determined by the lenders credit o¤ering decisions. Hence, we have
L(!) =
Z
1
l(!)f (!)d! = h
!
Z
1
(!)f (!)d!.
(32)
!
Di¤erentiating this equation with respect to c yields
@L(!)
=h
@c
Z
1
!
@ (!)
f (!)d!
@c
h (!)
@!
@c
(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). Since @ =@c < 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). Since @! =@c > 0,
@L(k)=@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
16
by the victim, we obtain the expected social welfare as
SW =
Z
1
fP ( Lj l; s) [(1
!
+P ( Lj h; s)(1
)v
)[(1
h
)vk
r~(A=!)]
(34)
1
r~(A=!)] + (1
2
h
a2 )v
1 2
s f (!)d!
2
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)(1
)=
, the social welfare function can be rewritten as
SW =
Z
1
[vk(1
)
1
r~(A=!)] + (1
2
h
!
1 2
s f (!)d!.
2
a2 )v
(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:
max
s; a
This yields
Z
1
[vk(1
)
!
Z
h
1
r~(A=!)] + (1
2
a2 )v
1 2
s f (!)d!.
2
(36)
1
!
Z
f [v + h] a (a ; s ) + va g f (!)d! = 0
(37)
f [v + h] s (a ; s ) + s g f (!)d! = 0.
(38)
1
!
Together, equations (37) and (38) imply that a satis…es
[v + h]
va = 0
(39)
whilst s satis…es
[v + h](1
)
s = 0.
(40)
Comparing (39) and (40) with (18) and (17) 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
17
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 to c
@SW
=
@c
+
Z
@!
f:g
+
@c
1
!
Z
1
!
f [v + h]
f [v + h](1
)
sg
vag
@a
f (!)d!
@c
(41)
@s
f (!)d!,
@c
where a and s are de…ned by equations (17) and (18), and f:g is the term in curly brackets f:::g in
equation (36).
Equation (41) 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 (41). 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 (41).
This term is strictly positive by virtue of the fact that a(!) < a and @a=@c > 0. The screening
e¤ect is represented by the last integral term on the right-hand side of equation (41). The sign of
this term is ambiguous by virtue of the fact that the sign of @s=@c is ambiguous. In sum, therefore,
@SW=@c 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 of @SW=@c critically
depend on the magnitude of
f:g @k =@c relative to the combined e¤ects of the screening and
care e¤ects. Thus, equation (41) 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
(1997) Pitchford (1995) and Dionne and Spaeter (2003). In Hutchinson and van ’t Veld, extended li18
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.
19
The paper assumed that the borrower had all the bargaining power. This was based on the premise
that capital markets were competitive and that lenders competed with each other in the provision
of both credit and screening services. A useful extension might consider how these results would
change if lenders did not compete in their role as …nanciers and could dictate the terms of the
…nancial contract. Another important caveat concerns our assumption that the information that
is correlated with the entrepreneur’s risk type becomes available before a contractually speci…ed
transaction takes plane. A useful extension might consider a setting where the signal is revealed ex
post. We hope that such extensions will enhance rather than undo the insights presented here.
Notes
1. The following additional arguments have also been advanced to justify this policy: lenders
may have pro…ted from the damaging activity and it is only fair that they share the costs
occasioned by the activity; lenders have deep pockets (they can never plead bankruptcy);
lenders are in a good position to investigate and require environmental compliance from their
borrowers.
2. This act empowers courts to subordinate a lender’s entire claim against the borrower if the
lender exercised control over the borrower …rm.
3. Although the …nancial intermediation literature boasts of an avalanche of studies on project
screening by lenders (see, for example, Manove et al. 2001), we are not aware of any treatment
of ex ante screening of projects in the context of environmental risk mitigation.
4. Throughout, we use “…rm,” “entrepreneur,” "agent" and “borrower” interchangeably.
5. The function (a) can also be interpreted more simply as the opportunity cost of expending
on care.
6. In Feess and Hege (2002) the lender’s intervention is in the nature of interim monitoring, which
is performed after funds have been advanced. Another important di¤erence between Feess
and Hege, and our study is that there is no moral hazard problem on the part of the lender.
Heyes (1996) also examines an entrepreneurial …nancing situation that involves screening,
but the model structure is di¤erent. In particular, the screening technology is not explicitly
modelled. Rather, it is assume that the lender can use the rate of interest as a screening
mechanisms. In our model, the optimal screening intensity is endogenously determined.
7. The signal could be interpreted as any evidence of an increase in the level of the environmental
risk to which the project is exposed, such as: (a) corporate report disclosing the accrual of an
environmental liability; (b) a citation for an environmental infraction; (c) warnings or …nes
for environmental o¤enses; (d) the release of environmentally information, such as the USA
Toxic Release Inventory (TRI).
20
8. Assume, for example, that m= actual level of screening e¤ort selected by the lender and
m = the level of screening required to induce a perfect signal. Then, the screening intensity
is s = (m=m ) 2 [0; 1]. Note that limm
!m
(m=m ) = 1 and limm
!0 (m=m
)=0
9. Previous studies have taken the view that only the borrower possesses an informational advantage (Pitchford 1995; Boyer and La¤ont 1997; Heyes 1996; Balkenborg 2001; Dionne and
Spaeter 2003).
10. Throughout, we use the feminine pronoun “she”to refer to the lender and masculine pronoun
“her” to refer to the borrower.
11. This is standard way of setting up bilateral moral hazard problems of this kind. For an
excellent exposition on this subject see, for example, Bhattacharyya and La¤ontaine (1995).
12. If a higher loan size corresponds to a lower net worth, then this result is strikingly di¤erent
from Bernanke et. al., (1996). They show, in an entirely di¤erent context, that lowering
borrower net worth can increase agency costs and therefore decrease e¢ ciency.
13. Note that pricing the increased liability risk by enhancing the rate of interest charged to
the borrower cannot be an e¢ cient strategy. Indeed, given the presumed technology, such a
strategy would reduce the borrower’s expected return, and sti‡e the borrower’s incentive to
exercise care, thereby reducing the expected total surplus.
14. The term aggregate, as used in this paper, refers only to the environmentally hazardous
industry, and not the entire economy.
Appendix: Proof of proposition 1
From the participation constraint (8), the equilibrium gross interest rate is
R=
(s; a)
c+
(1
(s; a))
(1
1
r~(1
(s; a))
!)I +
(1
1
s2 .
(s; a))2
(A1)
Substituting for s and a in equation (A1) using the incentive compatibility conditions (9) and (10),
we obtain the polynomial
1
1
c
v
L
(1
)2
2
c
This equation has real solutions if !
1
! =
r~I + c
I r~
L
1
(1
2
1
v
R
1
(1
2
)2
2
1
(1
2
(A2)
L
R2 r~(1 !)I c
0, where
2
)
2
1
c
1
vc
4I r~
21
L
1
v
)2
(1
1
2
(1
)2
2
2c
2
.
(A3)
)2
2
c
= 0.
For ! > ! , A2 has two solutions, but the relevant one is (16). Next, note that @U / @(I
@U
=
@(I A)
=
[
a (s; a)][v
[1
(s; a)]R
[1
R] + va]
@a
@(I A)
[1
(s; a)]
(s; a)]R,
@R
@(I A
A) < 0:
(A9)
(42)
since the term in square brackets [:::] in line 1 of equation (A9) equals to zero, from the …rst-order
condition associated with (10), and @R=@(I
A) = 0. Thus, if the entrepreneur is able to start a
project, she will …nd it optimal to borrow no more than (I
A). Equations (17) and (18) are now
obtained by substituting for R in (9) and (10) using equation (A8).
References
Agrawal, P., 1999. Contractual structure in agriculture. Journal of Economic Behavior and Organization 39, 293-325.
Balkenborg, D., 2001. How Liable Should a Lender Be? The Case of Judgment-Proof Firms and
Environmental Risk: Comment. American Economic Review 91, 731-738.
Bhattacharyya S., and La¤ontaine, F., 1995. Double sided moral hazard and the nature of share
contracts. RAND Journal of Economics 26, 761-781.
Bernanke, B. S., Gertler, M., Gilchrist, S., 1996. The …nancial accelerator and the ‡ight to quality.
Review of Economic Statistics 78, 1-15.
Besanko, D., Kanatas, G., 1993. Credit market equilibrium with bank monitoring and moral hazard.
Review of Financial Studies 6, 213-232.
Bester, H., 1985. Screening vs. rationing in credit markets with imperfect information. American
Economic Review 75, 850-855
Bolton, P., Scharfstein, D., 1990. A theory of predation based on agency problems in …nancial
contracting. American Economic Review 80, 93-106.
Boyd, J., Ingberman, D., 1997. The search for deep pockets: Is ”extended liability” expensive
liability? Journal of Law Economics and Organization 13, 232-258.
Boyer, M., Lafont, J-. J., 1997. Environmental risks and bank liability, European Economic Review
41, 1427-59.
Broecker, T., 1990. Credit-Worthiness test and Interbank competition. Econometrica 58, 429-452.
Cooper, R., Ross, T.W., 1988. An intertemporal model of warranties. Canadian Journal of Economics 21, 72-86.
22
Cooper, R., Ross, T.W., 1985. Product warranties and double moral hazard. RAND Journal of
Economics 16, 103-113.
Demski, J., Sappington, D., 1991. Resolving double moral hazards problems with buyout agreements. RAND Journal of Economics 22, 232-40.
Diamond, D., 1984. Financial intermediation and delegated monitoring. Review of Economic Studies
51, 393-414 .
Dionne, G., Spaeter, S., 2003. Environmental risk and extended liability: The case of green technologies. Journal of Public Economics 87, 1025-1060 .
Emons, W., 1988. Warranties, moral hazard, and the lemons problem. Journal of Economic Theory
46, 16-33.
Eswaran, M., Kotwal, A., 1985. A Theory of contractual structure in agriculture. American Economic Review 75, 352–367.
Feess, E., Hege, U., 2002. Safety regulation and monitor liability. Review of Economic Design 7,
173-85.
Gorton, G., Kahn, J., 2000. The design of bank loan contracts. The Review of Financial Studies
13, 331-364.
Hauswald, R., Marquez, R., 2003. Information technology and …nancial services competition, Review of Financial Studies 15, 901-926.
Heyes, A. G., 1996. Lender penalty for environmental damage and the equilibrium cost of capital.
Economica 16, 259-76.
Hutchinson, E., van ’t Veld, K., 2005. Extended liability for environmental accidents: what you see
is what you get. Journal of Environmental Economics & Management 49, 157–173.
Holmstrom, B., Tirole, J., 1997. Financial intermediation, loanable funds, and the real sector.
Quarterly Journal of Economics CXII, 663-91.
Jiménez, G., Saurina, J., 2004. Collateral, type of lender and relationship banking as determinants
of credit risk. Journal of Banking & Finance 28, 2191–2212.
Kim, S.K., Wang, S., 1998. Linear contracts and the double moral-hazard. Journal of Economic
Theory 82, 342-378.
Lewis, T.R., Sappington, D., 2001. How liable should a lender be? The case of judgement-proof
…rms and environmental risk: comment. The American Economic Review 91, 724-730.
Mann, D.P., Wassink, J. P., 1988. Money-back contracts with double moral hazard, RAND Journal
of Economics 19, 285-92.
23
Manove, M., Padilla, A. J., Pagano, M., 2001. Collateral versus project screening: a model of lazy
banks. RAND Journal of Economics 32, 726-744.
Pitchford, R., 1995. How liable should a lender be? The case of judgement-proof …rms and environmental risk. The American Economic Review 85, 1173-1186.
Polinsky, A. M., 1993. Should employees be subject to …nes and imprisonment given the existence
of corporate liability? International Review of Law and Economics 13, 239-257.
Privileggi, F., Marchese, C., Cassone, A., 2001. Agent’s liability versus principal’s liability when
attitudes toward risk di¤er. International Review of Law and Economics 21, 181-195.
Richardson, B.J. Environmental Regulation Through Financial Organizations.
Romano, R., 1994. Double moral hazard and resale price maintenance. Rand Journal of Economics
25, 455–466.
Shavell, S., 1986. The judgement proof problem. (1986). International Review of Law Economics
6, 45-58.
Shavell, S., 1997. The Optimal level of Corporate liability given the limited ability of corporations
to penalize their employees. International Review of Law and Economics 17, 203-213.
Stiglitz, J. E., Weiss, A., 1981. Credit rationing in markets with imperfect information. American
Economic Review 71, 393-410
Thakor, A. V., 1996. Capital requirements, monetary policy and aggregate bank lending: Theory
and empirical evidence. Journal of Finance 51, 279-324.
Townsend, R., 1979. Optimal contracts and competitive markets with costly state veri…cation.
Journal of Economic Theory 21, 265-93.
Williamson, S. D., 1987. Costly monitoring, loan contracts, and equilibrium credit rationing. Quarterly Journal of Economics 102, 135-145
24