Optimal Liability With Stochastic Harms, Judgement-Proof Injurers, and
Asymmetric Information
R
OBERT
I
NNES
University of Arizona, Tucson, Arizona, USA E-mail: innesag.arizona.edu
This paper studies the use of ex post liability to regulate unilateral accidents when injurers have 1 different probability distributions for accident damages and, as a
result, different optimal levels of accident prevention effort, 2 private information about their damage distributions, and 3 liability that is limited to the injurer’s
available assets. When the asset bound on liability is in a plausible range, an optimal damage-contingent legal rule is shown to take a threshold form, assessing maximal
liability when ex post damages are above a given threshold and zero liability otherwise. © 1999 by Elsevier Science Inc.
I. Introduction
In many cases, parties who potentially cause injuries have better information than others about the risks and consequences of accidents that they may cause. Often, they
also have financial resources that are insufficient to cover victims’ damages from particularly harmful accidents. Examples include medical product failures e.g., , Tha-
lidamide and the Dalcon Shield, industrial disasters e.g., chemical releases such as the one that occurred at the Union Carbide plant in Bhopal, India, and hazardous
substance releases of the sort covered by the U.S. Comprehensive Environmental Response, Compensation and Liability Act CERCLA e.g., leakages from under-
ground petroleum storage tanks or mine tailing ponds. In practice, such problems are regulated by both ex ante safety standards [e.g., citing and technology standards for the
production and disposal of toxic wastes, as specified in the U.S. Resource Conservation and Recovery Act 1982] and ex-post liability [e.g., as assessed under tort law and
CERCLA 1980, 1986, 1990].
I want to thank an anonymous reviewer and Rohan Pitchford for inspired comments on this paper. I am also indebted to Dennis Cory, Edna Loehman, John Antle, and seminar participants at Brigham Young University, the
University of Arizona, and American Association of Agricultural Economics meetings in San Diego for valuable encouragement and comments on earlier versions. The usual disclaimer applies.
International Review of Law and Economics 19:181–203, 1999 © 1999 by Elsevier Science Inc.
0144-818899–see front matter 655 Avenue of the Americas, New York, NY 10010
PII S0144-81889900004-6
This paper studies these types of accident situations. In the analysis, injurersfirms reduce accident risks by taking “care” and have different optimal levels of care because
they have different accident damage distributions. The injurers have private informa- tion about their damage distributions and liability that is limited to their available assets.
Because firms’ assets are sometimes exceeded by accident damages, the government cannot implement a liability rule under which injurers pay exactly the damages that
they cause and which thereby elicits the care choices that most efficiently mitigate accident risks.
1
Moreover, asymmetric information rules out heterogeneous govern- ment standards on care that would be required to prompt efficient behavior by the
different firms. In an important paper, Shavell 1984 argued that asymmetric information and
limited liability may together motivate joint use of liability regulation and government “safety” standards on permissable levels of care. In doing so, he fixes the liability rule in
a model with nonstochastic damages. The present paper, in contrast, posits stochastic damages, whether because of imperfections in the damage assessment process, inherent
randomness in damage creation, or both. Moreover, the liability rule is endogenized to address the following key question: Given that asymmetric information and limited
liability rule out simple resolutions to the problem of optimal accident regulation, what is the most efficient design— or form— of a liability rule?
Despite a rich literature on liability rules in tort law, these design questions have not yet been studied.
2
Recent work, for example, has focused on the problem of providing appropriate incentives for a plaintiff victim suit when there is both a costly court
process and a desire to achieve a given level of injurer precaution incentive. Such plaintiff incentive considerations lead to optimal award levels [Polinsky and Rubinfeld 1988],
optimal decoupling of plaintiff and defendant liability [Polinsky and Che 1991], and optimal penalties to losing plaintiffs [Polinsky and Rubinfeld 1996]. Other work has
been concerned with injurer precaution incentives, but not with their implications for the design of liability rules [e.g., Png 1987]. An interesting paper by Spier 1994
studies how to design a liability rule that balances the benefits of efficient precaution and the benefits of cost-saving settlements, but it does not consider the problem of
heterogeneous injurers.
3
In sum, despite recent strides in the analysis of legal games, there remains the unanswered question posed for this paper: How, in view of liability
limits, can liability be tied to stochastic damage realizations in a way that confronts different injurers with optimal precautionary incentives?
An injurer’s liability may depend on realized measured damages and, in principle, his care level. Because care choices are often complex combinations of precautionary
measures that are difficult to observe and measure ex post [e.g., see Rose-Ackerman 1991 and Viscusi 1989], this paper focuses on non-care-contingent liability rules
that can take any functional form consistent with limited liability.
4
1
The implications of limited liability for accident regulation are studied in a number of illuminating papers, including Summers 1983, Shavell 1986, Schwartz 1985, Beard 1990, and Boyd and Ingberman 1992.
However, to my knowledge, only Shavell 1984 analyzes accident regulation under both limited liability and asym- metric information.
2
This literature dates back to the classic papers by Brown 1973, Diamond 1974, and Green 1976, among others. Thorough surveys of the field can be found in Shavell 1987 and Landes and Posner 1987.
3
The papers cited here are only a few of the many excellent studies on settlement and trial games, the few that are most closely related to the arguments made in this paper.
4
In an expanded version of this paper available from the author on request, optimal care-contingent liability rules are also characterized. There it is found that a first-best can often be achieved with a care-contingent legal rule that
182 Optimal liability
Under conditions that often hold for the industrial and environmental accidents that are of interest here, this setting gives rise to the following optimal liability rule: If
damages are above a given threshold, injurers are assessed maximal liability; otherwise, when damages are below the threshold, injurers have zero liability. For example,
suppose that firms each have assets of 100,000 and that the threshold is 40,000. Then, if damages are below 40,000, a firm will pay nothing; and if damages are 40,000 or
more, a firm will pay 100,000.
5,6
The presence of stochastic damages is crucial to the optimality of this damage threshold liability rule. For example, consider a world with nonstochastic damages, in which the
accidents of different firms cause different levels of harm, but the harm caused by each firm is deterministic once an accident has occurred. In this case, it will be optimal to
fine firms for the actual damage they have caused. Low-damage firms will be able to pay their fines, and high-damage firms—those with damages above their assets—will only be
able to pay their assets. This strict liability rule is efficient because it induces the lower damage firms to exert the optimal amount of care, and it prompts the higher damage
firms to take as much care as they can be induced to take, even though it is too little. Moreover, the damage threshold rule described above will elicit too little care by firms
with damages below the liability threshold e.g., 40,000 because these firms pay nothing for their accidents; in contrast, firms with damages between the threshold e.g.,
40,000 and the asset limit e.g., 100,000 will be prompted to exert excessive care.
With stochastic damages, these arguments no longer hold. For instance, suppose that the harm from a firm’s accident is continuously distributed in the interval from 1 to
150,000 according to a positive density, with the distribution of harm being “higher” for some firms high-damage than for others low-damage. In this situation, strict
liability always prompts too little care by sometimes assessing too little liability when damages are above the 100,000 asset limit and never assessing too much. A damage
threshold liability DTL rule helps to cure the problem of too little care by sometimes imposing liability that is higher than harm. For some firms, however, the above-harm
liability—if unmatched by a relaxation of liability for other levels of harm—will prompt excessive levels of care. The DTL rule mitigates this problem by requiring no payment
for harms below the threshold. Although low-damage firms gain most from the zero- liability portion of the DTL rule because they are more likely to cause damages below
the threshold, they also pay their assets when the realized harm is above the threshold; indeed, because they are more likely to have harms between the threshold e.g.,
40,000 and the asset level e.g., 100,000—whereas high-damage firms are more likely to have harms above the asset level, when accidents are necessarily underpenal-
ized—low-damage firms are often more subject to the overdeterrence problem created by the above-harm liability than are high-damage firms. In sum, although a DTL rule
will clearly underpenalize low-damage firms when damages are deterministic, it often
resembles a rule of comparative negligence, wherein a firm’s proportionate liability declines with its care level. These results build upon the important insights of Rubinfeld 1987.
5
This liability rule has a simple negligence interpretation. When liability does not depend explicitly on ex ante care levels, negligence may be thought to have occurred when damage realizations are sufficiently high; in this event, a court
or government may conclude that the prospective damages from an accident were sufficiently large that the injurer was negligent in allowing the accident to have occurred. Such negligence calls for the assessment of liability, while the
absence of negligence exempts a firm from liability.
6
In a model with legal error and costs of court care, Rasmusen 1995 shows that optimal liability may sometimes be discontinuous in the damage level, jumping from a low level of liability to a high level of liability when harm rises
only slightly. The optimal liability rule in this paper has a similar property, but is optimal for entirely different reasons.
183 I
NNES
overpenalizes these firms when damages are stochastic. It is precisely when this occurs— when the damage threshold rule tends to overpenalize low-damage firms and under-
penalize high-damage firms—that this rule will be optimal. In general terms, a DTL rule is distinguished from other liability functions by the
property that it maximizes liability when damages are high and minimizes liability when damages are low. Among liability rules that deliver a common level of precautionary
incentive to some low-damage firm, DTL penalizes higher damage firms—those firms that have higher probabilities of creating high damages—as much as possible. More-
over, limited liability often precludes the assessment of sufficient accident penalties on the high-damage injurers—those that have higher probabilities of creating accident
damages above the asset bound. In such cases, care-exertion incentives can be enhanced by the use of a DTL rule that, although providing a requisite precaution incentive to
low-damage firms, gets the high-damage injurers expected liability as high as possible and, hence, as close as possible to their expected damages.
In practice, there are many examples of liability rules akin to that characterized in this paper. For instance, in the United States, both federal and state environmental laws
require firms to report their own violations, providing liability protections when they do and imposing nonreporting penalties when they do not. In general, however, the
liability protections are only available when the violations do not involve serious harm to public health or to the environment; in essence, the self-reporting laws exempt “small
damage” violations from liability and do not exempt “large damage” violations.
7
Simi- larly, CERCLA distinguishes between “major” and “minor” accidents when it assesses
liability for hazardous substance releases. Major accidents are subject to more onerous damage assessments that include lost passive use values; minor accidents are exempted
from both exhaustive damage assessments and from liability for passive-use damages that often represent the bulk of environmental harm.
8
In regulating agricultural pol- lution, Arizona laws also distinguish between “egregious violations” that are subject to
asset-liquidating penalties and nonegregious violations that are exempted from the penalties, with an “egregious violation” judged by the extent of harm that it causes
[Cory 1997]. In all of these cases, liability assessments exhibit the central qualitative attribute of this paper’s damage threshold rule, subjecting violators with damages above
a threshold to large liability, while treating violators with damages below the threshold to much lower, and often negligible, penalties.
The balance of the paper is organized as follows. Section II develops the model framework and is followed by derivations of the paper’s main results in Section III.
Section IV discusses a variety of extensions and implications of the analysis, including the scope for ex ante safety standards to improve on liability regulation alone.
II. The Model
