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Article Excerpt
We incorporate the concept of evidentiary standard to the analysis of the negligence rule under liability insurance and court errors. When the postaccident evidence is privately contractible and not too noisy, efficiency is achieved by both strict liability and a negligence rule with appropriate due care and evidentiary standards. When the evidence is not directly contractible, trial outcomes represent useful contractible information for the risk-incentives tradeoff in the liability insurance policy. Strict liability is then inefficient and dominated by the negligence rule. The negligence rule can itself be improved upon by decoupling damages from the harm suffered by the victim.
1. Introduction
* We consider the negligence rule under liability insurance when precautions are imperfectly observable by both courts and insurers. An efficient negligence rule requires an appropriate due care standard. When assessing care is subject to error, courts also need to apply an appropriate evidentiary standard, which refers to the "weight of evidence" for proving negligence. We characterize the optimal evidentiary standard and the conditions under which the negligence rule is consistent with efficiency. We show that the negligence rule may or may not be socially preferable to strict liability. Moreover, there are cases where negligence with compensatory damages can be improved upon by decoupling damages from the victim's harm. Whether efficiency can be achieved through the standard negligence rule depends on the informativeness of the evidence and on the extent to which insurance contracts can condition on the same evidence as would be used by courts to assess behavior.
Shavell (1982) was the first to systematically explore the social desirability of liability insurance when victims and injurers are risk averse. In a model where effort is observed without error, he shows that strict liability leads to the first-best outcome. The insurer can then perfectly control the injurer's precautions through contract. With strict liability, the victim is made whole and therefore bears no risk. The injurer and liability insurer internalize the victim's loss, hence their joint incentives are aligned with society's objectives. Perfect internalization also holds when the injurer's precautions are not verifiable. Although the first-best is not obtained due to moral hazard, the insurance contract efficiently trades off risk and incentives through partial coverage. Thus, in either case, the outcome is socially desirable.
Shavell also argues that the negligence rule would lead to a first-best outcome. An appropriately chosen due care standard would induce the injurer to take efficient precautions, hence the injurer would face no risk because he would not be held liable at equilibrium. The victim would now face uncertain losses, but could efficiently insure against those losses through first-party insurance. In Shavell's analysis, however, precautions were perfectly observable at trial and there was no error or uncertainty in the application of legal rules. For this reason, there was no demand for liability insurance.
We extend this analysis to court error about the injurer's level of care. Risk-averse injurers then purchase liability insurance. We focus on two polar cases. In the first, all postaccident evidence is privately contractible. The evidence that emerges following harm can be used by the injurer and his liability insurer in their insurance contract. In the second case, the detailed evidence itself is not privately contractible. The injurer and his insurer can, however, base their insurance contract on the outcome at trial--that is, whether the injurer is held liable or not liable and by how much. For instance, courts may weigh many different testimonies to assess the injurer's care. Typically, it is not feasible to write down ex ante into the insurance policy all possible evidentiary outcomes. It may then be that the contract can only condition on court decisions.
Several results emerge. Consider first the case where the postaccident evidence is privately contractible. The second-best allocation is then achieved by strict liability. When the postaccident evidence is not too noisy, the second-best allocation also obtains under a carefully designed negligence rule. However, when the evidence is too noisy, the negligence rule fails to implement an efficient outcome and strict liability dominates. Consider next the case where the postaccident evidence is not privately contractible. Strict liability is then inefficient; in particular, if the evidence is not too noisy, strict liability is dominated by the negligence rule. However, the standard negligence rule with compensatory damages is then itself inefficient. An even higher level of welfare can be achieved by a rule decoupling damages from the victim's harm.
There is a simple intuition for our results. When the evidence is privately contractible, a separation property ensues between efficient legal liability and efficient liability insurance. Efficient legal liability provides the injurer-insurer pair with the incentives to design a contract inducing the socially warranted level of care. This is feasible with strict liability. It is also feasible under a negligence rule with the appropriate due care and evidentiary standards, provided the evidence is sufficiently informative. In turn, given the contractibility of the postaccident evidene, the insurance contract under moral hazard yields the second-best risk sharing between insurer and injurer.
When the evidence is not privately contractible, the separation property breaks down. The information generated by the trial outcome then becomes relevant for the risk-incentives tradeoff under the insurance policy. Negligence now has the potential to dominate strict liability because it yields a more informative contractible signal. The nature of the "liable-not liable" signal depends on the evidentiary standard for establishing negligence. For instance, it may be that a high standard (i.e., very convincing evidence) improves the risk-incentives tradeoff in the liability insurance policy. As strengthening the standard reduces the liability risk faced by the injurer-insurer pair, their joint incentives can then be kept aligned with society's objectives only if punitive damages are introduced. In an efficient rule, the evidentiary standard depends on the injurers' attitude with respect to risk--their risk aversion and prudence--and is such as to optimize the private risk-incentives tradeoff. A demanding evidentiary standard is associated with punitive damages, a weak one with undercompensatory damages.
An older strand of papers has dealt with court error under the negligence rule but in the context of risk-neutral injurers, thereby precluding a demand for liability insurance (Diamond, 1974; Craswell and Calfee, 1986; Shavell, 1987; Kolstad, Ulen, and Johnson, 1990; Edlin, 1994). Even in this simple framework, however, no simple conclusion has emerged regarding the efficiency of the negligence rule. One reason was the failure to introduce the concept of evidentiary standard. Courts were modelled as receiving an unbiased estimate of the injurer's precautions. When the estimate is less than due care, courts rule that the injurer was negligent irrespective of the risk of error. Depending on the precision of the estimate, this leads to under- or overcompliance with the due care standard. Another shortcoming is that these models usually did not distinguish between mistakes in assessing the injurer's care and judicial uncertainty about the relevant due care standard. In our analysis, the risk of court error is due solely to imperfect information about the injurer's behavior.
Closer to our own article, there is a small literature involving risk-averse injurers, liability insurance, and court error in the determination of negligence. Sarath (1991) examines the tradeoff between litigation costs (through incentives to sue) and incentives to exert care, in a setting where injurers face liability risks because legal standards are uncertain. The injurer's precautions are perfectly revealed expost during litigation, and hence moral hazard is not an issue in designing the liability insurance contract. Danzon (1985a) discusses the optimal liability insurance contracts under the negligence rule, moral hazard, court error, and costly legal defense. An important feature is that the copayment provisions under moral hazard may undermine the insurer's incentives for legal defense. This induces a tradeoffbetween loss reduction by prevention and by legal defense. However, court errors are taken as given and the role played by evidence about care is not made explicit.
Our contribution is to model how evidence, liability insurance, and judicial decision making under evidentiary uncertainty interact to affect the performance of the negligence rule. We characterize the minimal informational requirements for the negligence rule to result in an optimal allocation and the efficient evidentiary standard when these requirements are met. We show that the private contractibility of the postaccident evidence affects the performance of liability rules. For instance, the standard negligence rule with compensatory damages is shown to be inefficient when the evidence is not fully contractible.
Our analysis also provides a new rationale for punitive or undercompensatory damages. A well-known result is the need for punitive damages when injurers are not always identified or when victims do not always sue (Polinsky and Shavell, 1998, inter alia). Other reasons for decoupling damages from harm include limited liability problems (Lewis and Sappington, 1999) or the tradeoff between litigation costs and the incentives to exert care (Polinsky and Che, 1991). In our setting, the benefits from noncompensatory damages stem from the interplay between the provision of appropriate incentives to the injurer-insurer pair and the provision of useful contractible information by court decisions.
The article develops as follows. Section 2 presents the basic setup. Section 3 describes the equilibria under contractible evidence and characterizes the efficient liability rules. Section 4 considers the case of noncontractible evidence. Section 5 introduces the possibility that the amount of loss also provides information about care. Interpretations, policy implications, and extensions are discussed in the concluding section. Proofs are in the Appendix.
2. The model
* The basic framework is borrowed from Shavell (1982). There is a large population of identical potential injurers and an equal population of identical potential victims. An injurer can accidentally harm at most one victim. The following notation is used:
l = victims' monetary loss if there is an accident;
p = probability of accident;
e(p) = injurers' effort on accident prevention, e' 0;
[[upsilon].sub.0] = initial wealth of victims;
[w.sub.0] = initial wealth of injurers;
U(w, e) = utility function of injurers, [U.sub.w] > 0, [U.sub.ww] < 0, [U.sub.e] < 0, [U.sub.ee] [greater than or equal to] 0.
The precautions taken by a potential injurer--his level of care--are reflected in p or equivalently e(p) and are private information. We assume e(1) = e'(1) = and e(0) = [infinity] to ensure that accident probabilities are bounded away from zero and one.
To simplify the exposition, we first assume that the size of the loss does not depend on care and is nonstochastic. The restriction is relaxed in Section 5. As far as possible, notation and claims are consistent with the more general case. The expected harm as a function of care is denoted by [bar.L](p). For the time being, [bar.L](p) = pl. The function is strictly increasing and convex in p, which will also be true in the general case.
Injurers and victims are risk averse. The injurer's utility function encompasses both the separable and nonseparable forms with U(w, e) =/d(w) - e or U(w, e) = U(w - e). In the first case, precautionary effort is nonpecuniary and has disutility e; in the second case, e is the monetary cost of precautions.
* Evidence. Although care is not verifiable as such, some information about the injurer's behavior becomes available ex post following the occurrence of harm. It is represented by a signal x with density function f(x; p) on the support [0, 1] and corresponding cumulative F(x; p), that is, precautions determine the distribution of the signal. The random variable x is a "summary" of all the detailed evidence available ex post. (1)
Assumption 1. [f.sub.p](x; p)/f(x; p) is strictly decreasing in x.
The assumption is the monotone likelihood ratio property (MLRP) with the convention that small values of x constitute unfavorable evidence in the sense of suggesting low care. The condition implies [F.sub.p](x, p) > except at the boundaries of the support where the derivative is nil. In words, the probability of unfavorable evidence (realizations below any given threshold) increases as precautions decrease. Restricting the support to the unit interval simplifies notation and is without loss of generality.
Assumption 2. pF(x; p) is convex inp.
Assumption 1 implies that the probability pF(x;p) of "accident and unfavorable evidence" increases in p, that is, with lower levels of precautions. Assumption 2 means that this is so at a nondecreasing rate.
Liability rules. Injurers may be held liable for the harm imposed on third parties and have sufficient wealth to pay for a victim's loss. A liability regime is represented by a damage rule D(x) specifying the amount of damages paid to the victim by the injurer--or his liability insurer--when an accident occurs and the evidence is x. Strict liability and negligence are the two common tort rules....
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