Law and economics scholars have written extensively about how insurance markets affect the tort system. They have noted the beneficial cost-spreading function of insurance, as well as the detrimental incentive-distorting affects of insurance, stemming from the problems of adverse selection and moral hazard. Surprisingly, however, scholars have overlooked one of the most important salutary functions that insurance serves for the tort system: it provides much of the information that courts need to apply the marginal Learned Hand formula in negligence cases. The Learned Hand formula is an algebraic formula (B = PL), according to which liability turns on the relation between investment in precaution (B) and the product of the probability (P) and magnitude (L) of harm resulting from the accident. If PL exceeds B, then the defendant should be liable. If B equals or exceeds PL, then the defendant should not be held liable. This paper explains precisely how insurance markets collect and disseminate information about the expected values of all three variables in the Hand formula: the probability of accidents, the level of harm and the burden of precaution. This information is available to everyone, including those who choose not to purchase any insurance. Most importantly, in the absence of the information insurance markets provide, parties in many cases would have no way of cost-effectively determining, ex ante, the proper level of care to avoid liability/harm. Consequently, the Learned Hand formula could not effectively operate. This is not to say that the insurance markets provide complete information for making ex ante calculations of the expected value of accidents and avoidance measures. But in many (if not most) cases, insurance provides the best information available. Indeed, as a normative matter, judicial determinations of liability in accident cases might be improved by setting the burden of precaution using insurance market values as a baseline.
Since Judge Learned Hand first penned the famous algebraic expression, B = PL, that came to bear his name,1 judges, lawyers, legal scholars and economists have debated its meaning, significance and limitations.2 The formula instructs potential tort parties to base their levels of precaution on three variables: (1) the probability, P, that an accident will occur; (2) the magnitude, L, of resulting harm, if any accident occurs, and (3) the cost of precautions, B, that would reduce the expected harm.3 Parties are supposed to factor these variables into a comparative benefit-cost analysis, prior to engaging in activities that might result in costly accidents, to determine efficient levels of care.
When the cost of an accident—the monetary cost of harm, L, times its probability of occurring, P—exceeds the costs of prevention, B, then the accident should be prevented. When B exceeds PL, however, the accident should not be avoided. Society's net wealth or welfare is maximized by preventing only those accidents where B is less than PL.4 Thus, the Learned Hand formula is designed to maximize a social welfare function.
The formula assumes, however, that courts are in a position to compare, ex post, the risks of accidents and the costs of avoiding them. If judges or juries cannot accurately compare these risks and costs, they may be unable to assess liability in a way that induces efficient behaviour. According to Judge Richard Posner, the Learned Hand formula has ‘greater analytic than operational significance’ because ‘the parties do not give the jury the information required to quantify the variables that the Hand formula picks out as relevant’.5 Consequently, juries are ‘forced to make rough judgments about reasonableness, intuiting rather than measuring the factors in the Learned Hand formula’.6
Judge Posner does not explain, however, ‘why’ parties do not give juries the requisite information to perform ex post the same calculations that the parties are supposed to have performed ex ante.
The first purpose of this paper is to supply that explanation which is simple enough: parties often cannot provide juries with detailed information about probabilities and magnitudes of expected harm and costs of ex ante precautions because the parties themselves do not possess that information. Before the fact of an accident, individuals often do not know, even within a rough approximation, the probability that they will have an accident. Nor do they know the likely harm should an accident occur. That is to say, they do not possess the information the Learned Hand formula requires them to possess in order to perform the requisite ex ante calculations. Consequently, court-imposed liability rules that depend on the formula are unlikely, by themselves, to create the necessary incentives to reduce risk-generating behaviour to efficient levels.
Parties will not modify their behaviour unless they comprehend the consequences of their actions in advance. And the Learned Hand formula for negligence fails precisely because it treats the various cost factors unrealistically, as certain and known by parties before they engage in risk-creating behaviour. In fact, such information tends to be significantly uncertain, ex ante, to any potential individual plaintiff, who might also have to estimate whether or not a defendant has taken proper precaution. This creates an obvious problem: What utility does the Learned Hand formula have, if the information it depends upon concerning probabilities and magnitudes of harm is always uncertain and costly to obtain?
The second purpose of this paper is to show that, while individuals (and the courts also) may be incapable of providing information to satisfy the Hand formula, insurance markets are able to provide approximations of that information at least over the population as a whole. Because any given individual may fall randomly across the probability distribution, insurance market information may lead some people to spend too much on precaution and others to spend too little. But the investment of insurers in specialized knowledge about the average probability and liability of accidents gives a readily available market signal to potential defendants, plaintiffs, judges and juries. Even if tort plaintiffs and defendants do not know the factors the Learned Hand formula requires them to know and assess, they do know the price they pay, e.g. for automobile insurance coverage.
Many scholars have discussed how insurance spreads the costs of accidents (e.g. Calabresi, 1970, chapter 4) and distorts the incentives of potential accident causers and victims (Shavell, 1987, chapters 8 and 10; Shavell, 2004, chapter 11). No one seems to have noticed, however, that insurance also supplies crucial information to the tort system about the expected values of the costs of accidents and accident-avoidance measures, thereby permitting a reasonable application by the courts of the Learned Hand formula.7 Essentially, insurance allows potential injurers and victims to substitute the expected value of the harm, EVL, as calculated by the industry that specializes in that information, for the court-determined PL that the parties are expected to know ex ante. This information thereby accounts for some of the uncertainty surrounding the information that a court needs in order to assess whether a defendant in a tort case has fulfilled the duty of care expressed through B. Although insurance is, to be sure, an imperfect measure, for reasons that will be discussed later, the substitution of insurance market values for B allows potential injurers and victims to approximate the economically efficient level of precaution.
Section 2 explains why the formula fails to achieve efficient outcomes when the values of any of its elements are substantially uncertain. Section 3 recasts the model to include valuations available from insurance markets. Replacing PL in the Learned Hand formula with a measure of the insurance market's expected value of harm (EVL) improves the formula's effectiveness and achieves a stable equilibrium solution. Section 4 recognizes some limitations on the abilities of insurance markets to solve the information constraints of the Learned Hand formula, but notes that market signals and regulatory action might provide actors with information about EVL and create incentives to lower social costs in the long run. The article concludes with some implications from the analysis.
Why the marginal Learned Hand formula fails to achieve economic efficiency when PL is uncertain
An automobile driver has a lot of decisions to make: what brand and model of car to drive, what performance and safety equipment to purchase, what routes to take, what time of day to drive (or not to drive), how quickly or slowly to drive under various weather conditions and how to drive given the perceived behaviour of other drivers and non-drivers (e.g. pedestrians). Each of these decisions can bear on the probability of accidents, P, and the magnitude of harm, L, resulting from an accident. It is doubtful that the tort system, by itself, provides individual drivers with the information they would need to make such choices efficiently.
The biggest problem is that the liability factor, L, of the Learned Hand formula is an independent and random variable, which is generally incapable of accurate assessment.8 The independent aspect of the variable indicates that neither party to an accident can control the various aspects of the liability element of the formula. In laymen's terms, when selecting the level of care, neither the potential injurer nor the victim can account for all the elements that affect liability, including elements such as income, health or age of the victim, which are independent of the level of care. In mathematical terms, the liability term is defined as L = f(Y, A, H, B, T), where Y is the income, A is the age, H is the health, B is the burden and T represents the technological change component of the formula. Note that the burden B is the only factor under complete control of the party (although, B's impact on L will be uncertain). A party while attempting to reduce the probability, P, of an accident may also reduce the liability component, L, to some degree. However, the burden, B, is just one component of the formula and the other factors are outside the party's control. The randomness of the liability component means that its value is difficult to predict. These two characteristics—independence and randomness—imply that neither party can select the appropriate level of care when applying the Learned Hand formula. To the extent that a party cannot control or predict one of the variables of the formula, it is unlikely that tort law liability rules based on the formula will create the appropriate incentives to prevent the harm or avoid the accident. Since the potential injurer and victim cannot know the potential liability factor, L, they cannot select the socially efficient level of care, B.
Consider, e.g. the case of Vaughan v. Taff Vale Ry. Co.,9 where the defendant Railroad Company's locomotive sparked a fire that burned the plaintiff's woods. The court ruled that the defendant was not liable for the harm because the expected harm (PL) was less than any additional precaution (B) the defendant might have undertaken.10 But what if the plaintiff's woods had been occupied by a group of campers all of whom died in the fire? In that case, assuming it was foreseeable that campers would be in the plaintiff's woods, the defendant's B would likely have been less than PL, with the consequence that defendant would have been liable under the Learned Hand formula. Thus, the defendant's burden of precaution would depend on facts that could not have been known to the defendant before the fact of the accident. And the same might well be true for the plaintiff. To achieve the efficient level of care, the injurer must have some degree of certainty about the probability and the magnitude of harm. This degree of certainty will not exist with an uncertain liability factor, L.11
After relaxing the assumption that the level of liability is known, the Learned Hand formula no longer appears as a socially maximizing function with a stable equilibrium solution. If liability, L, is substantially uncertain, parties are likely to either over-invest or under-invest in precaution, B.
Table 1 is based on the following assumptions: First, P falls at a diminishing rate with each additional increment of care. Meanwhile, the marginal cost of B rises at an increasing rate. For simplicity, we assume that the increments of care do not change L, which in this case is highly uncertain regardless of the level of care chosen. It is not simply that L is uncertain, but the possible values of L are completely random. That is, L may be at any of its listed values, from $100 to $10 000, for any of the given levels of P and B. Before the fact of an accident, there is no way of knowing where within that range the actual level of harm will fall. There is ex ante uncertainty and no convergent equilibrium. So, the Learned Hand formula cannot provide an efficient solution, i.e. it cannot specify the efficient level of precaution. A potential injurer or victim will not know what level of investment to make in harm avoidance. As the table indicates, increasing the level of care would not necessarily lead to a reduction in the expected harm. That is, increasing the burden of precaution, B, may not reduce the expected liability, PL. Moreover, there is no mechanism to ensure the correct level of investment in harm prevention. In effect, potential injurer and victims cannot make the correct level of investment (except by accident) because they cannot account for all the factors that could affect the liability variable L of the Learned Hand formula.12
Units of care
Units of care
The liability column in Table 1 can be viewed as an after-the-fact determination of the realized level of harm. In effect, the courts will assess the actual harm L, make an assumption about P and then compare PL to B for each case to determine negligence. Therefore, based on the court's determination of how much care ‘should’ have been taken, the court will assess liability for the accident. The important point, however, is that the determination of negligence will not provide an incentive to increase the investment in care, B, in subsequent cases because making liability dependent on elements not known to the parties when they choose their actions cannot affect their behaviour (see Kaplow & Shavell, 1996). In a sense, the defendant's liability, or lack there of, is just a matter of the ‘luck of the draw’ with respect to which liability, L, occurs at the time of the accident.
It might be argued that a plaintiff will always know the level of potential injury, L, or at least a close approximation. After all, he is the one being injured. But there is reason to doubt that individuals always, or even very often, understand the risks they face as potential accident victims. In addition, plaintiffs may not be aware of the potential injury that others might suffer from the same or similar type of accident. For example, the plaintiff in Vaughan was well aware of his potential injury—the destruction of some or all of his forest—but he might not have known the potential harm others, e.g. campers, might suffer from the fires created by the railroad. Therefore, he might have assumed that such potential harms were much greater than his own, and that the railroad properly accounted for them when operating its trains. Thus, the plaintiff's injury, L, in Vaughan was just one point on a continuum of potential injuries and not sufficient to provide the knowledge necessary for him to make efficient investment decisions in care, B.
The key problem is that individuals—both potential plaintiffs and defendants—in many cases have a limited interest in investing in protective measures when the potential liability is extremely uncertain or the probability of its occurrence indeterminable, so that PL is unknown.13 After all, an injurer's or victim's decision to adopt a protective measure depends on a comparison of the investment in care, B, with the expected reduction in the liability losses, PL. However, individuals may perceive the potential liability of an accident to be so uncertain that the investment in protective measures will not be justified.14 Alternatively, high discount rates may result in the extreme, but highly remote, potential liabilities reduced in subjective value to near zero.15 Indeed, accidents where the risk is considered unknowable produce a low willingness to pay to avoid them.16 Individuals, when faced with uncertain liability, may not adopt cost-preventive measures in spite of known court-imposed liability. In effect, individuals are not willing to invest in care if they are uncertain about whether or not such investment will avoid liability. The hypothetical version of the Vaughan case illustrates this point. Why would a railroad increase its level of care if it was uncertain about whether or not the new level of care would exonerate it from liability? Therefore, individual injurers or victims would not be willing to pay any burden, B, to avoid an uncertain potential liability, PL.
There may well be practical considerations with this strategy. Even though the investment in care may be set to the absolute minimum, that investment might still be considerable. For example, automobile accidents may have a minimum expected liability of $2000 property damage and $4000 personal injury. The level of care that potential injurers and victims should be expected to account for when establishing the level of care should then reflect the expected value of this minimum expected liability, i.e. ($2000 + $4000) × P. However, the expected accident costs could conceivably exceed this minimum by a considerable margin.
Since damages are based on the harm received by the victim/plaintiff, regardless of how extremely unlikely that such a harm will occur, it is conceivable that the potential injurer/defendant will not invest in a sufficient level of care in situations where the harm is foreseeable but extremely unlikely. Consider the classic strict liability case of Grimshaw v. Ford Motor Co.,17 where Ford decided not to invest in a device to prevent the gas tank of a Ford Pinto from rupturing and exploding after a rear-end collision. In reaching this decision, Ford determined that the liability component of the Learned Hand formula of $200 000 per death and $67 000 per injury did not justify the additional investment.18 Ford reasoned that the additional investment $11 per vehicle outweighed even this level of expected harm.19 In effect, the company decided to run the risk of potential injury, even death, rather than pay the additional per-unit costs.20
There are two possible explanations for Ford's decision: (1) the level of liability was uncertain and the level of care was not; therefore, it was better to run the risk of potential liability than to risk paying too much to avoid it or (2) substantial errors existed in measuring the true value, i.e. expected judicial valuation of human life or potential injury. Therefore, it was better to run the risk of not accounting for the true liability than to risk paying too much to avoid it. The issue was whether Ford's estimate was grossly inadequate or was the range of potential harm so great that Ford could not account for it?
First, consider whether the variance was so great that the original estimate of the harm becomes meaningless.21 Ford assumed, in its liability calculation, that the cost of injury from the fire hazard was $67 000. The ultimate jury award for Grimshaw was $2 516 000 plus $3 500 000 in punitive damages.22 This damage figure was approximately 37 times greater than Ford's original estimate of the harm (90 times greater if punitive damages are included). Simply put, it was not cost justified to invest in the device to prevent gas-tank ruptures and ensuing fires when the estimated cost of prevention, B, of $11 per vehicle greatly exceeded the estimated cost of the harm, PL, which, before the Grimshaw case was settled, was only $1.23 Clearly, the $11 per vehicle investment would have an impact on the plaintiff's injury and is certainly cost justified in that extreme case. However, this is an ex post evaluation. Ex ante investment would not have been justified, where the potential cost of an injury was so much less than that suffered by the plaintiff in Grimshaw. Table 2 illustrates the problem of extreme variance in the range of actual values.
Accident probability (%)
Ex ante PL
Ex post PL
|1||$11.00||$67 000||$2 500 000||0.0015||$1.00||$37.50|
|3||$11.00||$67 000||$200 000||0.0015||$1.00||$3.00|
|5||$11.00||$67 000||$70 000||0.0015||$1.00||$1.05|
|6||$11.00||$67 000||$10 000||0.0015||$1.00||$0.15|
|7||$11.00||$67 000||$5 000 000||0.0015||$1.00||$75.00|
|8||$11.00||$67 000||$500 000||0.0015||$1.00||$7.50|
|9||$11.00||$67 000||$50 000||0.0015||$1.00||$0.75|
Accident probability (%)
Ex ante PL
Ex post PL
|1||$11.00||$67 000||$2 500 000||0.0015||$1.00||$37.50|
|3||$11.00||$67 000||$200 000||0.0015||$1.00||$3.00|
|5||$11.00||$67 000||$70 000||0.0015||$1.00||$1.05|
|6||$11.00||$67 000||$10 000||0.0015||$1.00||$0.15|
|7||$11.00||$67 000||$5 000 000||0.0015||$1.00||$75.00|
|8||$11.00||$67 000||$500 000||0.0015||$1.00||$7.50|
|9||$11.00||$67 000||$50 000||0.0015||$1.00||$0.75|
Note that in four out of the nine possible outcomes, the expected value of PL is greater than the actual probability-adjusted value of the accident. In these cases, expenditure of $1 in precaution would have more than satisfied the Learned Hand formula and exonerated Ford from liability. In three other cases, $1 would have been insufficient but $11 would have sufficed. In cases 1 and 7, however, even $11 would have been insufficient.24 Where does this table leave us? Uncertain to be sure. But in a negligence regime governed by the Hand formula, no precautionary measures should be taken unless the expected value of the injury PL is greater than the burden B. If Ford did not expect there was a chance that case 1 or 7 in the table was possible, then it would have made no economic sense for the company to have invested $11 to prevent Grimshaw's accident.
We can, of course, assume that a potential tort defendant will learn from experience. That is, the range of values of L will converge on the value a court is likely to place on the harm. It will never be perfect—all estimates are less than perfect. However, over time, new information may indicate that the original estimate is significantly erroneous. For example, accident reports may indicate that the original estimate is significantly less than the true expected value. Consider the possibility that Ford is able to cost-effectively observe that tort awards in all cases of accidents due to automobile manufacturer negligence are higher than those they originally expected. As a result, the company decides the actual value of L is $675 000 (an increase in the cost of harm by more than a factor of 10). However, given the same accident probability, the expected cost of the accident rises only to $10. This value is extremely close to the $11 cost of avoiding the harm B.25 If the device will prevent all injuries including the extreme cases, then it may become cost effective to make the investment based on this reassessment of the expected harm.26
However, in the face of uncertainty of low probability, extreme accidents at the appropriate level of precaution cannot be determined, since neither the injurer nor the victim knows the consequences of her action in advance. Therefore, imposing liability in extreme liability situations has the effect of reducing the incentive to avoid potential harms. Since potential injurers or victims cannot select which harm to prevent, they will set their level of precaution so that it will not exceed any potential liability. This implies that an individual will invest in care in some, but not other, situations to avoid liability. From the injurer's or victim's perspective, it is better to run the risk of liability than to pay too much to avoid it.
The insurance market as a partial solution to the information constraints of the Learned Hand formula
From the foregoing discussion, it is clear that there are informational barriers to the application of the Learned Hand formula that create inefficient incentives for potential plaintiffs and defendants. The Learned Hand formula does not create an incentive to invest in efficient care because of the uncertainty surrounding PL.
A solution to the informational problems lies in markets where potential victims and injurers, as well as the courts, can gain some insights into valuations of both the probabilities and the liabilities of accidents (i.e. the expected value of accidents) and therefore the required value of B. Insurance markets (along with regulatory measures and precedent) provide data that can guide the courts in understanding the appropriate level of investment in care and thus the determination of B. However, as we will discuss in Section 4, insurance is only a partial solution to the information problem of the Learned Hand formula.
Many scholars have written about the relation of insurance to the tort system, but mostly about how insurance spreads the costs of torts and, in doing so, distorts the incentives of injurers and accident victims.27 We do not dispute those problematic affects of insurance.28 However, scholars have overlooked the valuable contribution insurance markets make to the operation of the Learned Hand formula, by providing (if only implicitly) potential tort plaintiffs, defendants and courts with the information about (a) the probabilities and magnitudes of harm from various kinds of accidents and (b) the expected benefits of various precautions in reducing probabilities and magnitudes of harm.29
Because insurance firms invest in acquiring precisely the information that establishes the probabilities and costs of accidents—information that is too costly for individuals to acquire on their own, for reasons having to do with economies of scale and cost spreading—insurance markets partially solve the problems connected with the tort system's inability on its own to gather and process that kind of information. Moreover, the insurance industry, along with the legislative process, creates a system of incentives and fines, i.e. carrots and sticks, to induce potential injurers and victims to reduce the likelihood of harm over time and thus lower social costs.
An insurance firm gathers the data it believes narrow the uncertainty surrounding the probability of any given type of accident and its likely cost in terms of harm. It calculates the expected value of harm—which we will term EVL to distinguish it from court estimates of PL—then charges a premium based on this information, which it offers to a largely competitive insurance market. If, in this market, the cost of insurance from Firm A is high relative to that of the other insurance companies, no one will buy A's insurance, but will instead choose from other competitors, assuming they are of equal reliability. The market price will converge on a supply–demand equilibrium price that will be stable, and which would under certain assumptions (that are oversimplified to be sure) provide a sufficient determination of the value of B.
Consider a model in which insurance is strictly ‘fair’, i.e. where it is always known to be precisely equal to the expected value of harm (EVL), and the market is perfectly competitive so that the premium will converge on a price and quantity based on the forces of supply and demand. The premium cannot be supplied at a rate lower than EVL as this would represent a loss for the firm, but it will converge on that price on the assumption that the ‘cost of harm’ for the firm represents the marginal cost of providing protection to the insurance buyer. The price of insurance might be temporarily higher than EVL in the event that demand increases, but it would return to the marginal cost price since the higher return would induce entry, causing prices to fall.
Indeed, in a competitive market with complete and symmetrical information, consumers would know that the value of EVL represents fair insurance—the precise cost of the expected value of harm—and no one would buy a policy at a price above EVL. The equilibrium would be stable. Furthermore, since the courts would observe the premium and understand that it represents the cost of harm, it would also represent the value of B. A defendant who spent less than EVL (i.e. the insurance premium I), whether by purchasing insufficient insurance or providing insufficient precaution through other means, would be liable for harm; any defendant who spent I or more would be deemed not liable since the level of precaution would clearly have been sufficient.
Assuming that the premium I does reflect the EVL and the premium is used as a proxy for B, the result may be sufficient, but does it result in an ‘efficient’ level of investment in care? Table 3 is constructed so that the economically correct level of investment occurs where the burden, B, is equal to the expected value of the loss.
Units of care
Cost of harm L
EVL P × L
Units of care
Cost of harm L
EVL P × L
In Table 3, the correct level of precaution is 4 units of care with B = I = PL = $65. This illustrates the case where, given the assumption that EVL = I = B, the static equilibrium will be stable at $65, and B can be determined at negligible administrative cost by the court. Additional units of care would reduce the probability of accident though at a decreasing rate, but at an accident probability of 6.5% the EVL would equal the total burden B and, assuming a fair insurance premium, would equal I as well at $65. Moreover, the marginal burden of $12.50 would equal the marginal benefit, satisfying the marginal Learned Hand formula.
An interesting result of insurance markets is that for social costs to be minimized, both potential victim and injurer should take precautions equal to EVL. That is, both face the same expected value of harm with the cost distributed according to who is deemed liable. If the victim knows that the injurer has invested $60 in precaution, she will have to pay for any injury. But this implies that the same injury is insured twice. In theory, the lowest cost solution for the potential victim and the injurer would be to contract and jointly pay one premium I. The contract would satisfy the court that the parties, between them, have undertaken a sufficient level of B.30
Limitations of insurance markets as sources of information for the Learned Hand formula
The model of insurance markets and their effects described above gives an idea of how insurance markets can provide at least a starting point for a solution to the informational constraints of the Learned Hand formula. But the stylized model in Section 2 does not correspond to actual insurance markets. It neglects some important considerations that necessarily enter into the calculation of B.
First, the price of insurance is not equal to fair insurance, i.e. the expected value of harm. It is expected that I > EVL, so that the insurance will be purchased by those who are risk averse or who have, for other reasons such as their own reckless behaviour, calculated their expected value of an accident to be higher than the standard measure of EVL. However, given the great uncertainty attached to the outcome of accidents (as discussed in Section 3), many will choose to insure so long as the gain in expected utility from owning insurance is greater than the expenditure of that money on all other alternatives.31 But it is important to note that the price of insurance in the market is not precisely equal to an insurer's EVL. Consequently, premium prices, though they provide information to potential victims and injurers at low cost, cannot be used as perfect substitutes for the cost of harm and thus do not tell a court the exact value of B.
Another characteristic of insurance markets makes a market premium a less than perfect proxy for the level of B. As noted, insurance markets are intended to spread the risks to insurance firms across a pool of insured—both potential victims and injurers—so that the average value of harm represents a real number that when translated into premia allows for both claim satisfaction and company profits. However, this means that an insurer's EVL (and market premium) represents the ‘average’ cost of harm over a particular type of accident across a universe of insured individuals. This information, while clearly of great value, does not identify the specific range of harms or the factors that might make one sub-group of insured, e.g. those in particular occupational categories, to have a higher or a lower accident probability. Undoubtedly, the variance could be more completely understood if insurers would provide market segment data. Although these data exist, they are not publicly disseminated.
Moreover, reliance on insurance data would not satisfy the conditions set by Judge Hand in the ‘Carroll Towing’ ruling, even if premia were fair and so precisely equal to EVL. Judge Hand was explicit that the potential injurer needed to consider the particular circumstances that raised or lowered his liability: “[T]he likelihood that a barge will break from her fasts and the damage she will do, vary with the place and time; for example, if a storm threatens, the danger is greater; so it is, if she is in a crowded harbour where moored barges must be constantly shifted about.”32 Under these strictures, a level of care set at the market rate for insurance, which is greater than the EVL, might nevertheless be too low for the circumstances. In such cases, potential injurers would have to rely on precedent to understand the disposition of the court in the event that an accident occurs. Judicial precedents may raise or lower the burden, though the baseline for judging sufficiency of care should be the market premium. This implies, of course, that the reasonable person of tort law would have knowledge of insurance premia. We believe this to be a fair implication, as the search costs for insurance premia generally are quite low.
Another question that arises with respect to insurance markets is the long-term effect. If the insurance industry can insure both parties and derive twice the expected value of harm through premium payments by both potential victim and injurer, it may seem that the insurance industry itself has no incentive to reduce the accident costs. Where the injurer or victim supposedly has this incentive, i.e. to pay the cost of avoiding the accident or pay the damages, the insurance company merely collects the premiums from all, injurers and victims alike, and then in the event of claims, redistributes the proceeds between the two. In effect, the insurance industry will make its profit regardless of the value of the expected harm.
In fact, there may be incentives for insurers to seek reductions in EVL and for consequent reductions in I, but whether or not these reduce social costs is not entirely clear. Assume that, e.g. in Table 3 the insurance premium I is equivalent to EVL and that the premium represents the actual expected cost of the potential accident.33 Moreover, we can assume that this functional relationship is a one-to-one transformation, because any change in the expected harm EVL will result in a direct and proportionate change in the premium I.34 But what about the functional relationship between the burden B and the premium I? While they are set equal to one another, at the equilibrium point in the static model in Table 3, long-run social efficiency may be achieved by shifting part of the burden onto potential defendants allowing the premium to go down, but only as overall B rises. Since B is functionally related to P and L which, in turn, are valued by insurance markets as EVL, and since EVL is directly related to I, B is functionally related to I as well. So, as P or L changes in an insurer's calculation because of new information, I changes and so should B.
However, the direction of the effect is unclear in this instance. It might be the case that insurers will try to induce additional expenditures on precaution outside of the insurance premium, raising B by at least as much as I falls. That is, the insurance industry will attempt to influence the injurer's and victim's behaviour in order to reduce accident costs.35 The industry will either persuade the injurer and the victim through monetary incentives and disincentives—lower rates or higher deductibles—or seek government action through increased regulatory requirements, e.g. automotive passive restraint systems, to reduce the accident cost EVL and the corresponding premium I, by increasing the actual cost of B.36
The increase in cost may, however, be only a short-run phenomenon. Reducing the EVL may cause overall long-run social costs to fall, and B will likely fall over time. Consider the following hypothetical case from Table 3: Insurer A forces potential injurers to internalize an additional $15 in precaution, so that B rises to $75. But as already noted, an increase in B will have an impact on P and L. Thus, the probability of an accident decreases over time by one-third, from 6% to 4%. The new EVL is $40, and the total burden equals $55. If an insurer attempts to maintain premia at $60, a competitive market will lead to entry and a decline in the price to $40. Thus, even if this presupposes a continuation of $15 that a potential injurer must internalize, the social cost of accidents has fallen; specifically, the marginal benefit has increased by $20—the reduced expected costs of an accident—at a cost of $15, for a net social gain of $5.
Though there may be dynamic efficiency gains from insurance markets, the fact that insurance markets may achieve them by forcing costly changes in the behaviour of the insured complicates the value of insurance market prices as a solution to the information problem of the Learned Hand formula. The court must understand the degree to which the burden has been removed from the calculation of I and distributed directly to those who buy insurance. This may not be an easy calculation. Consequently, while insurance can provide a measure of EVL, the degree to which that measure diverges from B still must be determined by the court.
The need for the insured to internalize at least some of the costs apart from the value of EVL also helps reduce a persistent problem for insurance markets generally: moral hazard. As economists have shown,37 if one insures and knows that insurance constitutes a sufficient measure of precaution, the individual will be less cautious in her behaviour actually raising the probability (and so the EVL) of accidents. It is one reason why the insurance industry would not charge the fair premium that would correspond directly to the EVL.38 Since the insured knows her own level of risk, she will be more likely to indulge in risky behaviour knowing that the value of an accident will be completely covered. In this instance, a potential injurer has an informational advantage over the insurance company, which can only know the average EVL and not the specific mindset of any individual.
Assume, hypothetically, that the market premium is $100 and this represents the EVL exactly so that the insurance is fair. Person 1, however, buys insurance knowing that her expected cost is $125 because she is more prone to engage in risky behaviour and that is the amount she would spend on her own precautions in the event she could not insure. The fact that she can buy insurance from the market at a discount means that she will be more likely to indulge in risky behaviour, since the market is bearing a disproportionate amount of her risk. Insurance contracts are not fair, however, and so she buys insurance but may have a deductible or a variable premium that will rise in the event she has ‘too many’ accidents. This forces her to raise the size of her burden of which the premium is only a base, not the full measure of her reasonable level of precaution.
The variability of deductibles and premium levels also means that insurers will reward those who take on extra burdens of precaution, such as purchasing especially safe automobiles or purchasing alarm systems for their homes, with lower premium payments. The opportunity of insured individuals to gain benefits from internalizing a greater share of the cost of precaution may also lead to a further reduction in accident probabilities and/or levels of harm, further reducing social costs as well. Of course, the fact that insurance premia are neither identical to the burden of potential injurers (or victims for that matter) nor identical across insurance buyers complicates the problem of using insurance market prices to solve the dilemma of the Learned Hand formula as a means of resolving tort cases.
There are still other issues that limit the utility of insurance premia as information for B. Most property and casualty (P&C) insurance markets—the branch of insurance that provides most accident-related data—are notoriously cyclical. In one part of the cycle, insurance companies will drop premium rates in order to gain market share. As the Insurance Information Institute explains, ‘A dominant factor in the property/casualty insurance cycle is intense competition within the industry. Premium rates drop as insurance companies compete vigorously to increase market share. As the market softens to the point that profits diminish or vanish completely, the capital needed to underwrite new business is depleted’.39 In other phases of the cycle, premium rates rise to such an extent that the market may become highly constricted as insurers try to rebuild profits by raising premium rates. During this phase of the P&C cycle, it might be difficult for potential victims and injurers to find insurance at acceptable prices.
This complicates the task for courts in attempting to utilize the insurance market data to solve the informational constraints of the Learned Hand formula. If the P&C cycle is in the competitive phase,40 the premium may be lower than EVL and so expenditures of that level by a defendant on precaution might be insufficient. On the other hand, rates may be held so high during rebuilding phases that premiums overstate considerably the expected value of harm.
The insurance cycle does not negate the value of insurance information in the effort to calculate B. But again, it means that the numbers are imprecise and require an understanding of where in the cycle the market is at the moment, and therefore whether the numbers should be scaled up or down with respect to the burden a defendant should have been expected to bear.
Nevertheless, a court might reasonably expect that the level of the burden must correspond with the market rate for P&C insurance, plus or minus. Clearly, if insurance is offered in a particular case at a given rate, a defendant would have the responsibility to demonstrate that any amount spent on the precaution that was less costly than the premium satisfied the Hand formula nonetheless. Expenditures substantially less than the premium—behavioural changes monetized to reflect their costs—would need to be justified by the defendant, as warranted by the circumstances. The court can stand on the premium as a baseline datum that, absent defenses for insufficiency, constitutes a reason to impose liability on him. This reduces the court's problem and shifts the requirement to the defendant to show that he or she took adequate care, wherever the cost was lower than the premium. Where, a defendant assumed costs greater than or equal to the premium, the plaintiff would need to demonstrate that these expenditures were not sufficient under the circumstances. This also reduces the administrative costs for the courts and consequently should lower overall social costs and raise economic efficiency.
While P&C markets are cyclical, medical malpractice insurance markets have been quite predictable. However, they embody other informational problems for prospective tort parties and courts. Indeed, premia have risen steadily even as claims have fallen. This segment of the industry, so far from facing competitive pressures along the lines of P&C, has been according to some arguably cartel-like, since the McCarran–Ferguson Act exempted insurance companies from most Federal antitrust laws (see King, 2003). In that case, premium rates might well be distorted, and especially problematic as a proxy for B in malpractice cases.
The problem of medical malpractice and the role of the McCarran–Ferguson Act in affecting market behaviour show how government regulation can lead to increased information costs that would likely reduce the ability of courts to use price signals as a means of solving informational constraints in negligence cases. However, regulatory action can work both ways. That is, it can both make court estimates more reliable and provide impetus for increases in dynamic efficiency, reducing accident costs and probabilities.
Consider the case of a government regulation requiring the installation of airbags in automobiles.41 This requirement was generally expected to lead to an overall reduction in the cost of harm, not by reducing the probability of accidents but by reducing the resulting harm.42 Essentially, such government regulation induces others to invest in technology that will reduce the liability component of the Learned Hand formula. As noted above with respect to investment that is shifted by insurers to the insured, it is not immediately clear that such redirection of resources lowers social costs. Government regulatory action can be considered a kind of technology shock. This will raise costs on certain margins in the hope of lowering them on others. But while government can induce change, it cannot ensure that those changes will be efficiency enhancing.43
The Learned Hand formula is an algebraic function that will result in accident cost minimization when the variables are known by the various actors engaged in risk-creating behaviour. The problem is that the tort system, by itself, often fails to provide the potential victims or injurers with the information they need to make rational decisions about the levels of precaution. Fortunately, insurance markets provide some of that information, and, indeed, provide a baseline around which the burden of precautionary behaviour can be determined. This eases the task of the courts. Insurance markets provide imperfect information to be sure, but it is highly useful information that can be accessed at low cost.
It is important to recognize that insurance markets provide a number of other benefits to the resolution of negligence cases. One key benefit of insurance is that neither the injurer nor the victim is shackled with the burden of ‘take your victim as you find him’. The insurance industry internalizes the problem of extreme liability situations and spreads it among the insured. This allows the individual injurer or victim to consider first the market-determined expected value of the harm (EVL) when establishing the desired level of care, B, and potential injurers or victims can economically account for all potential liabilities above EVL through additional insurance; i.e. from a market standpoint, they may ‘over’ insure, but in recognition of their own particular circumstances and the likely consequences of tort action, they can obtain insurance to cover the full value of their B.44 The benefit of this arrangement is that the insurance industry is required to foresee the average harm and the individual injurer or victim can take this as a datum. The individual is then required only to foresee whether conditions warrant a departure from the average. This arrangement enhances economic efficiency because the insurance industry is in a better position to analyse the costs and benefits of levels of care across cases. Simply stated, the sheer number of claims processed allow the insurance industry to better evaluate the benefits of increased levels of care on average and change premia accordingly. Further, these processed claims provide the industry with a continual stream of information about the probability curve surrounding the liability variable, L, of the Learned Hand formula, which permits continual updating of EVL. That information, which is not possessed by the individual injurers and victims because of diseconomies of scale, increases the general foreseeability of the harm. In other words, the insurance industry has the necessary information to reasonably anticipate the potential harm for a selected type of accident.
Foreseeability in torts is crucial to the calculation of the defendant's burden, but without considering the function of insurance, the court's situation is highly problematic because the courts often fail to account for the individual injurer's and victim's inability to foresee the consequences of their actions when establishing liability. Foreseeability is not viewed as a functional relationship but rather is seen as a condition to be determined after the fact of accidents. From a logical standpoint, ‘any’ injury is foreseeable regardless of how remotely related the injurer's or victim's activity is to the harm. But to impose liability, under these circumstances, has the effect of reducing the investment in care because neither the injurer nor the victim has the power to control the various elements that affect liability. Therefore, to avoid investing too much, the potential injurer or victim will make the minimum investment in care and not insure against the unforeseen consequences of incurring higher levels of liability.
The problem with viewing foreseeability as a functional relationship is that high transaction costs impede a party's ability to foresee the array of potential harms. Further, it is unlikely that an individual will comprehend the expected liability of any potential accident. In effect, high transaction costs impede individuals from seeking information on the strength of this relationship. Insurance can be viewed as a mechanism designed to reduce the high transaction costs associated with foreseeability. The insurance industry is an efficient means of gathering information on the nature and costs of accidents. The industry uses this information to influence the injurer's or victim's behaviour and establish the appropriate level of care.
Insurance companies do not influence the behaviour of their clients only by altering premia and deductibles; in some cases, insurance providers directly regulate their customers‘ activities. For example, hazardous waste facilities, which are required by federal law to obtain insurance,45 find that the cost of coverage includes environmental assessments, site inspections and improved safety and security measures (see, e.g. General Accounting Office, 1994, p. 22). These contractual preconditions to coverage are designed to limit insurance company losses from hazardous waste spills and contamination. According to some commentators, it was Congress's intent in imposing liability insurance requirements on hazardous waste facilities to draft the insurance industry as a surrogate regulator (see, e.g. Nixon, 1986, p. 143; Kunzman, 1985, p. 470). That is, Congress expected insurance companies to impose their own regulatory restrictions on hazardous waste facilities, in addition to federal government regulations. Apparently, policy makers possess a fairly sophisticated understanding of how insurance can provide potentially liable parties with information about PL.46
Finally, it should be noted that negligence is not a relevant issue with insurance. The insurance industry is not concerned with who is at fault, if it insures both parties to the accident.47 It simply prorates the premium between the parties to account for the possibility that one of them will be at fault. This freedom from negligence allows the industry to account for the unique characteristics of the insured. That is, the industry will consider characteristics such as the age, sex, income or health which affect both the probability and the liability of the Learned Hand formula when establishing the premium for each insured.48 Therefore, the EVL can be factored into the premium independent of the tort system's determination of negligence. Insurance data are, therefore, as close as we have to an objective measure upon which the court can rely. Plaintiff and defendant are self-interested and their data inevitably are biased. For a court to base a determination of liability in negligence cases, insurance data may provide the most solid foundation. These data do not solve the dilemma of the Learned Hand formula, but they can provide a starting point, a partial solution to a problem that would otherwise remain unsolved.
United States v. Carroll Towing Co., 159 F.2d 169 (2d Cir. 1947).
See, e.g. McCarty v. Pheasant Run, Inc., 826 F.2d 1554, 1557 (7th Cir. 1987), Posner (1998, pp. 179–183) and Brown (1973). This paper assumes a law and economics perspective on negligence. More specifically, we assume that the goal of the negligence system of tort law is not corrective justice but, as Calabresi (1970, pp. 26–29) has put it, to minimize the sum of the costs of accidents, accident avoidance and judicial administration. In the context of this article, we believe that the law and economics perspective is implicit in the Learned Hand formula itself. Under that formula, liability does not turn on notions of corrective justice or any other moral basis but on the respective costs of precaution and accidents. For more on the law and economics approach to negligence theory and tort law generally, see, e.g. Cole & Grossman (2005, pp. 212–215), Shavell (1987) and Posner (1998, pp. 179–235).
159 F.2d at 173.
This standard analysis is fundamental to all law and economics texts discussing the Learned Hand formula, see, e.g. Cole & Grossman (2005, p. 215). Law and economics scholars generally agree, however, that Judge Hand's original version of the formula was deficient because it was premised on total, rather than marginal, costs, see, e.g. Posner (1998, pp. 180–181). Throughout this article, references to the ‘Learned Hand formula’ should be read as references to the economically refined version of that formula known as the ‘marginal Learned Hand formula’.
McCarty v. Pheasant Run, Inc., 826 F.2d 1554, 1557 (7th Cir. 1987).
The only existing reference in the literature to this function of insurance is by two of this article's co-authors, based on the analysis appearing in this article. Cole & Grossman (2005, pp. 223–225).
A random variable is predictable in that each and every event in the sample space has an associated probability. Court cases provide some information as to the predictability of these events. For example, if in 5 out of 10 court cases the liability variable is determined to be $100, then it is 50% likely that the L factor of the Learned Hand formula is $100. Of course, the remaining 50% probability is important as well. However, courts generally are not interested in the fact that the liability factor (L) is random or has a large variance, they operate according to the theory that the defendant ‘takes your victim as you find him’. Hart & Honoré (1985, pp.173, 343)
5 H.&N. 679, 157 Eng.Rep. 1351 (Ex.Ch. 1860).
The court also suggested that B < PL for the plaintiff.
It should be noted that each P and each L mathematically represents a discrete point on a continuum. P and L should actually be represented as Li and Pi, where i ranges from 1 to n. The question is which P and which L are selected from the range of values? But this is really the wrong question. All values for P and L are in fact encapsulated in the insurance company's premium calculation, which is based on the expected values, as we will discuss in detail inter alia.
The large variance tends to create the non-convergence of the formula. If there is only a slight variance of the L factor, then the formula will still tend towards a convergent solution. However, cases where the L factor exhibits slight variance may be rare.
This issue is discussed in Kunreuther (1996, pp. 403) (arguing that homeowners in disaster prone areas lack the interest to adopt loss-reduction measures). For example, a 1974 survey of more than 1400 homeowners in hurricane-prone areas in the United States revealed that only 22% of the respondents had voluntarily adopted any protective measures, i.e. 78% of the homeowners did not invest in any loss-preventive measures. Even after Hurricane Andrew, most residents in hurricane-prone areas along the Atlantic and Gulf Coast appear not to have invested in loss-reduction measures. The reasons given are (a) underestimation of the probability of the disaster and (b) high consumer discount rates. By analogy, we assume that the majority of injurers or victims will not adopt a harm-prevention measure because they are not capable of estimating the probability of the harm realized in an accident.
A decision to adopt accident-avoidance measures involves a comparison of up-front investment in care costs, B, to the reduction of potential liability costs, PL. Individuals may perceive the probability of the accident to be so low or uncertain that an investment in protective measures, B, will not be justified. Therefore, individuals will adopt a minimum level of care instead of maximizing the costs avoidance measures. Of course, some extremely sensitive minority group may adopt measures above the minimum, e.g. in hurricane-prone areas, 22% of the population adopted disaster costs avoidance measures.
Evidence for high annual discount rates has been observed in studies evaluating the reluctance of consumers to invest in energy-saving equipment. See, e.g. Ruderman et al. (1987, pp. 101).
Savage (1993) contends that ‘[h]azards about which the risk is considered unknown engender a lower willingness-to-pay to avoid the hazard’.
119 Cal. App. 3d 757 (1981).
Even though this is a strict liability case, it is illustrative of the determination of the liability component of the Learned Hand formula, where the possibility of the accident, even though extremely remote, is still within the range of reasonable foreseeability. These values are presumed to be expected values because they were the potential liability for each of 180 possible deaths and 180 potential burns, i.e. no two accidents have identical liability values. The $200 000 life value figure might appear to be low but it is the value the National Highway Transportation Safety Administration placed on human life. As such, Ford adopted a value for human life set by a government agency. See Schwartz (1991).
Ibid at 1024.
In the algebraic terms of the Learned Hand formula, it is better to pay the potential injury, i.e. PL, than to pay for a measure of prevention, i.e. B, which might exceed the expected value of the injury.
The variance is a measure of the spread or dispersion from the expected value. It is a measure of the tendency for observations to depart from a central value. The greater the spread, the less likely the expected value will represent the actual cost incurred by any potential victim/plaintiff.
Grimshaw, 119 Cal. App. 3d 757.
$1.00 is the projected value of a burn injury per automobile $12 000 000 = $67 000 × 180 burns per 12 500 000 vehicles sold. Schwartz (1991, p. 1020).
We assume here that the probability of an accident is unchanged by the increase in B.
This analysis excludes the expected cost of potential fatalities.
If the investment will not prevent all types of injuries, then the original problem of insufficient allocation of resources associated with the Learned Hand formula remains.
But see Grayston (1973) (finding empirically that liability insurance actually added to the tort system's deterrent effect with respect to automobile accidents).
To his credit, Posner (1998, p. 222) recognizes that insurance premia can affect activity levels of potential injurers. He notes the ‘accident-prevention effect of liability insurance’.
Assume a prorated premium.
See Shavell (2005).
159 F.2d at 173.
Other costs of insurance are not represented for the sake of simplicity. Those costs would include administrative and marketing costs that insurance companies will, to the extent permitted in competitive markets, include in the premium. To some extent, these administrative costs include information that is of value to consumers, tort parties and the courts.
We assume that the industry is competitive and the change in expected value will result in a corresponding change in the premium.
According to Shavell (1987, p. 195) ‘[i]nsured will be induced by the terms of insurance policies that maximize expected utility to take risk-reducing actions when the cost of the actions is less than the decrease in expected losses due to the actions’.
One potentially complicating factor is that some precaution costs are up-front, one-time costs, whereas insurance premia cover longer periods of time, e.g. a year. The court would need to come up with an amortization schedule, which courts certainly can do, to match the one-time cost of precaution with the longer-term cost of insurance coverage.
See, e.g. Philips (1988).
See, e.g. Layard & Walters (1978, p. 382).
Insurance Information Institute, ‘Facts and Statistics’. Available at http://www.iii.org/media/facts/statsbyissue/pcinscycle/.
Though we refer to P&C as competitive, it should be noted that it is far from the ‘perfect’ competition model of economics textbooks. All insurance markets are subject to a significant amount of regulatory oversight and direction. However, it is clear that P&C firms do compete with each other and premium rates are affected by that competition.
See 49 CFR Ch. 5, Part 571, Standard # 208.
According to the National Highway Traffic Safety Administration (1996), airbags have significantly reduced overall deaths and injuries resulting from automobile collisions. At the same time, however, airbags actually have increased the probability, P, of accidents because driving safer cars has led drivers to exercise less care. See, e.g. Harless & Hoffer (2003).
It is worth noting that significant legislation with respect to highway safety has utilized insurance industry data through the Insurance Institute for Highway Safety.
See Shavell (1987, p. 193 Example 8.4).
The Resource Conservation and Recovery Act Amendments of 1984, 49 U.S.C. Section 6925, impose on hazardous waste treatment, storage and disposal facilities (TSDFs) substantial financial responsibility requirements. Pursuant to this statutory requirement, the Environmental Protection Agency promulgated regulations requiring TSDFs to possess adequate insurance coverage for any injuries caused to third parties or their properties. 40 C.F.R. Sections 261.147 and 265.147.
This is not to argue that compulsory insurance laws necessarily are effective. The General Accounting Office, ibid, suggests that mandatory insurance coverage has been very difficult for many hazardous facilities to obtain. However, some analysts believe that such compulsory insurance laws can, at least in some areas, provide a useful complement to, or even substitute for, regulation. See, e.g. Richardson (2002) and Kehne (1986). Even when insurance is not compulsory, the existence of insurance markets, which create market prices for risk, provides useful information to potential injurers and victims about PL, ‘regardless of whether they actually purchase insurance’.
The industry can also account for the uninsured through premia. Also, responsibility for the harm created by the negligence formula is accounted for in the premium. That is, the non-negligent party as well as the negligent party can insure against the potential loss of the accident.
This differentiation of the insured results in segmentation of the insurance market, i.e. 22-year-old single males pay more for automobile liability insurance. This market differentiation and segmentation is far from complete, however. We do not know the proportion of a premium that goes to a specific harm or set of harms from a particular kind of accident. The insurance companies may or may not have that information, but it is generally not provided to the market, except on an aggregated basis; specifics are lost in the aggregation.