- Email: [email protected]
Public insurance and accident prevention
International Review of L a w and Economics (I 982), 2 (67-80) © 1982 B u t t e r w o r t h s
PUBLIC I N S U R A N C E A N D ACCIDENT PREVENTION GORAN SKOGH*
University of Lund, Sweden In m a n y industrial countries there has been a trend towards more or less allinclusive, publically financed compensation for losses due to accidents. In Sweden, for instance, most accident-based health-care and income losses are covered by the social insurance system. A problem with such nearly complete and all-inclusive insurance, however, is that it reduces the economic incentive to prevent accidents. Public accident insurance is often combined, therefore, with measures aimed at accident prevention. To this end, Sweden has established extensive regulations concerning such matters as working conditions and traffic safety. Violations of the regulations lead to penal sentences (mainly fines). Economists and lawyers have argued against this form of administrative control.l A major argument has been that traditional tort liability for accident costs, in combination with private insurance, is more influenced by the market. Cost liability decentralizes decisions to those involved in accidents (who know best how to avoid accidents) and to insurers in the market. Tort liability has many weaknesses, however. For example, one argument for abandoning tort liability is that it has not been shown to prevent accidents. Another argument is that uniform, complete and speedy compensation is most easily administrated by public agencies. 2 Taxes, fines and damages can all be regarded as different Pigovian taxes that make it costly to individuals not to act carefully. 3 The theoretical welfare literature, however, gives no quick answer as to whether it is best to use taxes, damages or fines. One reason is that there have been no models attempting to compare the different measures. Also, whereas accidents often cause large and sudden losses, the Pigovian tax literature, as well as most of the liability models, neglect the insurance problem .4 In the present paper the insurance problem and the use of cost liability versus penal sanctions in accident prevention are analyzed. In Section I a model is presented which includes all-inclusive public insurance and the use of Pigovian taxes as well as punishments for optimal control of the number of accidents. This model is compared with a simple model of tort liability and private insurance. In Section II the models are applied to the prevention of traffic accidents in Sweden. Industrial accidents are studied in Section III and, finally, the work is summarized in Section IV.
* Financial support from the Swedish Council for Research in Humanities and Social Sciences is gratefully acknowledged. Thanks are due to Ingemar Hansson, Charles Stuart and to the participants at the Arne Ryde Symposium on Social Insurance in Lund, 1981, at which an earlier version of the paper was discussed.
68
Public insurance and accident prevention I. THE MODELS
A model which captures the essence of many accidents is one involving two agents, a 'victim' and an 'injurer', who may with some probability be involved in an accident. The victim is faced with a loss of size a if an accident occurs. This loss is expressed in terms of the numeraire good in the economy. The only way to reduce expected accident costs is seen as being to reduce the probability of the accident. Only the injurer is considered as able, via the control variable x, to influence the probability of an accident. The probability of an accident occurring is denoted by p and of not occurring 1 - p . The p(x) function is assumed to be continuously decreasing and twice differentiable. Increasing the control variable is costly. The unit cost of x is assumed to be constant and equal to o n e ) The benefit of the activity to the injurer is viewed as constant and sufficiently large that the injurer always takes the dangerous action. The parties involved are seen to be risk averse and to maximize expected utility. Since the benefit of the dangerous action is given, the problem for the injurer is simply to choose the control measure x that minimizes the disutility of the danger. This model can be applied to traffic and industrial accidents. An example from each area will serve to clarify this: I.
2.
A car drives off the road and injures someone who could not easily prevent this occurring. The control variable x here is represented by such aspects as the inverse of the driving speed, the mechanical quality of the brakes, the condition of the tyres, etc., all of which the injurer controls. A welder is injured in a gas explosion caused by a leaking tube. The probability of this accident's occurring was influenced by the employer in choosing the dimension of the tube.
Costless contracting When the injurer acts without any consideration of the effects for the victim and thus takes no preventive measures, this results in an externality, unless the parties are able to bargain costlessly and sign an enforceable contract. In this case, the victim is willing to pay the injurer for being careful. Similarly, if the victim has the right to stop the dangerous action, the injurer is willing to pay the victim for the right to act. Such costless negotiations result, through the logic of Coase, in Paretooptimal preventive measures. 6
The first best benevolent dictator control In many dangerous activities private contracting is prohibitively costly. For instance, drivers cannot bargain on speed and routes with all potential victims. Hence, the parties have to rely on external regulation of some sort. Suppose that the external regulation is done by a well informed controllerma benevolent dictator--who costlessly controls the dangerous behaviour in a Paretooptimal way. The problem of the controller is to maximize the expected utility for one party, e.g. the victim, given the expected utility of the injurer and a resource constraint. The following notations will be used: U the utility function for the injurer, EU the
GORAN SKOGH
69
expected utility, u initial wealth, un wealth when no accident occurs and ua wealth when the accident occurs. V is the utility function of the victim, E V the expected utility, v the initial wealth of the victim, v~ the victim's wealth if the accident occurs and v n if it does not occur. Inserting these terms into a model outlined by Shavell, 7 the injurer's expected utility is E U = p ( x ) U(ua) + (1 - p ( x ) ) U(un)
(1)
whereas the victim's expected utility is E v = p(x) v(va) + (1 - p(x)) v(v.)
(2)
The resource constraint states that expected resource use equals availability of resources. That is [(1 - p ( x ) ) v , , +p(x)v~] + [(1 - p(x))u,, +p(x)u,,] + Oo(x)a + x] = u + v
(3)
The controller chooses x, as well as the utility distribution u,,,ua, vn, va. Shavell shows that a first best solution is achieved if: 1. 2.
For any x , the risk averse parties are given the same wealth regardless of whether an accident occurs or not (un = ua, vn = va). s The control measure chosen minimizes the social costs of accidents Cs.
Here Cs includes the expected accident loss (p(x)a) and the resources used for prevention. Hence, given the wealth redistribution, the dictator will Minimize Cs = P(X) "a + x with respect to x
(4)
with the first order condition -p~a = l
(5)
Thus, to be efficient, the cost of taking marginal preventive measures must equal the benefit in terms of decreased expected accident costs. The intuitive explanation of this first best solution is that since the dictator fully controls the wealth distribution by a lump sum transfer, the optimal approach is to eliminate the riskiness for the risk-averse parties by complete insurance and by simultaneously minimizing the expected costs of accidents.
The tax The first best solution rests on the assumption that the dictator controls not only the distribution of wealth but also the control measure x. In principle the insurance system here may be designed to level out accident losses to potential parties completely, but in fact no dictator controls preventive measures that are (by definition) taken by the injurer. Since if all losses are compensated the injurer has no incentive to prevent accidents, the problem of how to control the injurer remains.
70
Public insurance and accident prevention
One option is to use a traditional Pigovian tax. Assume that the dictator introduces an all-inclusive insurance for accident losses. To obtain efficient accident control the dictator imposes a tax, t, on the injurer. Then t(x) is a non-increasing function of the control measure taken. In this case the injurer will Minimize t (x) + x with respect to x
(6)
which has the first order condition - tx = I
(7)
which means that the marginal cost of preventing accidents equals the marginal tax. Note that no risk is present for the risk averse parties due to the full insurance. The tax is a fee levied on the participation in a dangerous activity. The first best condition, Eq. (5), is achieved when the marginal tax equals the marginal impact on the expected accident cost at the efficient level of control, x*, i.e. when
tx, =px.a
(8)
Punishments In most models of Pigovian taxes identification of the taxpayer is without cost. Identification and policing costs for dangerous activities, however, are usually not negligible. Suppose, therefore, that the public controller uses y units of the available resource for policing. A particular detection rate d, lying between zero and one, can be chosen. Full detection (d= 1), as in the tax case above, is clearly too costly to be achieved. When d < 1, the expected cost for the payer of the fee is less than the fee charged when detection occurs. To correct for this, a larger (stochastic) fee--here termed a punishment--may be imposed. If, for instance, one out of ten is caught, the fine can be fixed ten times higher to make the expected cost of punishment equal to the tax. For punishments a legal standard, .~, that defines the outlawed activity, is needed. The punishment, or fine, f , is imposed when the identified control measure, x, is less than ~. First, the policing problem when the fine is fixed and is small relative to the initial wealth of the offender will be analyzed. In this case the fine is a transfer with negligible wealth distributional effects. Control of the offender here is effected by deterrence. The detection rate, d, is increased by increased policing, y, and decreased by increased preventive measures, x. It is assumed that, at any given level of policing, .9, d(x,fi) is continuously decreasing and twice differentiable in x. We also assume that increased policing increases the marginal impact of private control on the detection rate (i.e., dxy < 0). Finally, the detection rate and/or the fine is small enough to make crime a rational choice (x < x-). At a given level of policing, .9, the offender who maximizes expected utility would Maximize EU=(1 -d(x,.~))U(u-x)+d(x,.~)U(u-x-f) with respect to x
(1')
GORAN SKOGH
71
Since in the case considered the fine, f , is small relative to initial wealth, u, the offender will tend to minimize the expected cost of punishment. Thus, the problem simplifies to Minimize with respect to x d ( x , . ~ ) f + x
(6')
with the first order condition - dxf= 1
(7')
The offender should then choose a control in which the gain in terms of decreased expected marginal punishment equals the cost of additional control. From the assumption dxy < 0 it follows that increased policing increases private control. 9 For example, increased patrolling on roads increases the impact of speedy driving on the detection rate. Increased policing will then increase the marginal benefit of careful driving, which reduces the speed of rational, well-informed drivers. The probability of an accident can thus be indirectly controlled by policing efforts. The problem of the public controller is to Minimize Cs = p ( x ( y ) ) a + x ( y ) + y with respect to y
(4')
with the first order condition - p . ~ X y ' a = 1 + Xy
(5')
Hence, when policing is optimal, the marginal policing cost plus the marginal cost of control taken by the injurer (as a result of the deterrence, Xy) equals the marginal benefit in terms of reduced expected accident costs. When the potential injurer changes his degree of control, this not only influences the probability of an accident but also changes policing in accordance with the reaction function, Eq. (5'). Both expected accident costs and policing costs must thus be taken into account for deterrence to be optimal. At optimal deterrence + d x , f = + px," a + yx*
(8')
That is, the expected punishment of a marginal reduction in private control is equal to the increase in expected accident cost and the change in the cost of policing. Note the difference between the tax and punishment solutions. The optimal marginal tax equals the marginal expected accident cost, Eq. (8). For punishment, the impact on marginal policing cost is added. The tax is a fee (d= 1) for participation in the dangerous activity, while the fine is stochastic. To compensate for the limited degree of detection (d < 1) and the policing costs, the fine is thus made larger than the tax. It is assumed, however, that f is small compared with the inframarginal a. This holds as long as d x is large relative to Px. A numerical example can readily illustrate this. Suppose initial wealth u = 1500 and accident loss a = 1000. The marginal impact on the probability of an accident is at an optimum when Px = - 0.001. The optimal marginal tax would thus be tx. = 1, if it could be levied,
72
Public insurance and accident prevention
However, it is prohibitively costly to detect every change in x. A relatively small fine, f = 15 (1/100 of the initial wealth), is therefore used. The marginal impact on optimal policing when the individual increases his control will be assumed, for the purpose of illustration, to be - 0 . 2 5 . The optimal marginal detection rate is then dx.= 1/15 ( - 1/1000 x 1000+0.25)= - 1/20. In reality the public controls both the policing y and the punishment f . With the aim of increasing deterrence, f m a y thus be increased. When punishments are severe and risk aversion is present, however, a number of problems arise. 1. 2.
It is possible that increased policing and punishments fail to deter.l° Heavy punishments result in a welfare loss due to the offenders' risk aversion that the benevolent dictator must take into account.
Assume that the social cost of punishing the offender who is detected is known by the public controller and is equal to F(f). F increases with increasing f due to the offenders' risk aversion. An increase in the punishment costs can also be assumed, due to an increase in collection costs and the prevalence of bankruptcy problems when punishments are large. The expected cost of the punishments imposed is d-F. In this case the public controller simultaneously chooses y a n d f s o as to Minimize with respect to y , f
Cs =p(x(y,f))a + x ( y , f ) + y + d ( x ( y , f ) , y ) F ( f )
(4") II
The problem, however, is complex and quite restrictive assumptions are needed to derive definite results. 12 Tort liability An alternative to the 'benevolent-punishment' approach is to rely on tort liability and market insurance, which can also be analyzed with a model similar to the one presented above. The probability of an accident, p(x), depends here as before on only the control measures taken by the injurer. The accident loss a is constant and is settled without costs (see the introduction to section I). Negligence is defined by a legal standard g determined by a judge. If the injurer has been careful at the time of the accident (x >Jr), he does not pay damages. On the other hand, if he is found to be negligent (x < X'), he has to compensate the victim for the accident costs in full. If the negligence standard g equals the first best preventive control, x*, then the negligence rule here tends to result in a first best public control of accidents.13 The logic is as follows: the injurer can decrease his control measure to g without expected accident costs. At such a level, a marginal decrease in x results in an infra-marginal cost increase equal to the expected accident costs. The rational injurer here will therefore be just careful enough to avoid negligence and, since £ = x * , the control chosen is efficient. As a result, the risk-averse victim will have to pay the accident costs. Assume, however, that there is an actuarially fair (competitive market) insurance available. Under these conditions, the insurance premium, r, equals the expected accident cost p ' a (there is no profit and administrative costs are nil). The victim buys full insurance, which completely eliminates the burden of risk. If, because of administrative costs, r > pa, the victim will choose only partial insurance and the burden of
GORAN SKOGH
73
risk will not be fully eliminated. 14 Strict liability is an alternative to the negligence rule. Here the injurer pays the victim full compensation whenever an accident occurs. If the injurer is risk neutral, this results in a first best solution without insurance, since the injurer minimizes expected accident cost plus control effort (see Eq. (4)). The risk-averse victim is thus fully compensated. On the other hand, if the injurer is risk-averse and no insurance is available, total welfare can be increased at a compensation less than the accident loss, a. In this case risk remains, both for the victim and the injurer. 15 If liability insurance is available, the risk-averse injurer will purchase it. Just as with public insurance, this insurance reduces the incentive to prevent an accident. The moral hazard involved can be avoided, however, if the insurer costlessly identifies the control measure taken by the insured and varies the premium r with x. The competitive, actuarially fair premium here, r(x)=p(x)a, assumes zero administration costs. The insured will under these conditions Minimize r(x) + x with respect to x
(6")
with the first order condition -
rx
= 1
(7")
Thus, the marginal cost of increasing control equals the marginal impact on the insurance premium. Since the marginal premium rx equals the marginal expected accident cost, pxa, this all-inclusive, completely differentiated 'perfect' insurance results in a first best optimum (see Eq. (5)). The assumption of a perfectly differentiated market insurance thus eliminates the problem of risk aversion. It is interesting to note the similarities between this (hypothetical) perfect market insurance and the combined social insurance and tax analyzed above. Both systems eliminate risk completely; the tax and the premium alike are predetermined fees for participating in a dangerous activity; the tax agency and the insurer both need the same sort of information concerning the control function p(x). In any realistic case, the insurer has limited information regarding both the behaviour of the insured and p(x). An interesting alternative extreme to study is, therefore, the case where the insurer has no information concerning p(x) at all. Here market insurance will end up with a deductible. The partial insurance reduces the moral hazard. The expected utility of the insured is maximized through coverage being reduced to the point where the benefits from the lower premium rate just equal the disutility due to increased exposure to risk. The administrative costs included in the premium increase the tendency towards only partial insurance. 16 II. THE PREVENTION OF TRAFFIC ACCIDENTS For a tax to be efficient (see Eq. (8)), tax authorities need information concerning the expected marginal harm of the preventive measures taken by the potential injurer, which is, of course, an extreme assumption. Taxes with low collection costs, to be sure, may be useful where an acceptable standard is easily found. 1T For example, total traffic volume might be reduced by a tax on cars, petrol or roads. As
74
Public insurance and accident prevention
a side effect, accidents might likewise be reduced. Such a tax, however, would be a dull instrument for reducing accidents. One reason for this is that the accidentreducing effects of different preventive measures vary considerably. Another reason is that information on the behaviour of drivers is limited. Suppose, for example, that the efficient speed on a road varied between zero and 100km/h depending on curves, traffic intensity, slipperiness, darkness and the characteristics of cars. By a tax on speed (if this were possible to administer) it might be possible to arrive at an average car speed of, say, 50km/h. It might be possible to vary such a tax with the quality of the car but hardly with the other factors. The main characteristic of the fine as opposed to the tax is its stochastic nature and the indirect control of accidents it provides via deterrence. When penalties are involved, the public enforcer needs information on the effects which policing has on expected accident costs, where the deterrence of the offender is included in the accident costs (see Eq. (5')). Although there is insufficient knowledge about these matters, it appears that penal control of accidents may be superior to regulation by way of a tax. A differentiated tax, applied in all situations ( d = 1), is often too costly to administer. By choosing a detection rate less than 1 the policing cost can be kept relatively low. Note that the expected punishment can be differentiated in relation to the importance of the preventive measures taken. Since the incentive effect of regulation here is reflected in the product of the probability of apprehension and the fine is apprehended, it is possible to tailor either of these (as well as the exact form of the penalty) to meet the requirements of specific situations. For example, it is possible, on a stretch of non-uniform road, to vary not only speed-limits but also the intensity of policing and the magnitude ol' fines in order to exercise a differential control of driving intensity. Indeed, in practice policing usually is varied over time, for example, through having special checks at rush hours and practically no policing late at night. A problem with penal sanctions is the harm inflicted on the punished. Fines, however, are transfers which need not have any significant redistributional effects, as long as they are relatively small. In Sweden, for example, there is a system of fixed monetary fines for speeding offences, for failure to comply with the seat-belt law, etc., of between 100-600Skr, which is small relative to the yearly budget of most car owners. 18 For 'reckless driving' there are larger fines which vary with the income of the punished. The prosecutor chooses some number of 'day-fines', between 5 and 60, depending on the seriousness of the crime. This number is (roughly) multiplied by a per mill of the yearly income of the offender. Hence, as long as punishment is not increased to include jail-sentences and other restrictions on freedom (e.g., withholding a driver's licence or his permission to perform a profession), the social cost of punishment can be kept relatively low. For a negligence rule to be efficient, the judge needs information on the preventive measure to be taken by the injurer (x*). If the victim influences the expected cost of an accident, then efficient action by the injurer depends on the measures taken by the victim as well (see note 5). One reason why a judge possesses limited information on the behaviour of the parties to an accident is that they are not properly motivated to present correct information. As a result, the judge often has to rely on some established and measurable standard of due care, for instance the speed at the time of the accident, the quality of the car, the alcohol consumed by the driver, etc. These standards are more or less the same as the penal standards. There is a difference, however, in the method of identification. Speed controls and safety checks are designed to prevent accidents, while the tort case is ex
GORAN SKOGH
75
post. If judges can be expected to have detailed information on the behaviour of the parties to an accident, the possibility of accident-cost liability may influence a potential injurer towards more cautious and adequate behaviour than it is possible to engender with punishments alone. For a liability insurance to be perfectly differentiated, the insurer needs the same type of information as the perfectly informed tax authority. In practice, drivers' discounts, differentiation with respect to vehicles, etc. are only partially related to the preventive measures taken by drivers. Such insurance is also costly to administer. 19 Legal processes are costly as well. That may be a reason why cost compensations for accidents are settled out of court, mainly by the insurers. Thus, a system with only tort liability and market insurance can be high in cost and fail to eliminate riskiness. Indeed, certain behaviour, such as reckless or drunken driving, speeding and driving without a licence are usually excluded from coverage in private insurance policies. The bankruptcy problem is especially apparent with liabilities that are not insurable in the market, e.g. in connection with reckless or drunken driving. Such dangerous behaviour is therefore typically controlled by penal sanctions. Minor fines can usually be paid by the offender who is detected. Large punishments result in collection costs and bankruptcy problems. The preventive effects of cost liability depend on the ability of the liable individual to predict the possibility of an accident. With penal regulation of accident-prone behaviour, however, the chain of information becomes more indirect, though it may nevertheless be effective, for example through a regulator who is better informed of the risks inherent in certain activities than the individuals involved in these activities communicating this information via regulation, which has incentive effects if backed up by sanctions. A common argument against regulation (among economists at any rate) is that the individual involved in an accident knows best how to avoid an accident. However, it is not at all hard to find cases where a third party (an insurer or a public safety agency) can more easily foresee risks. Speed limits, for example, can have an informative value for drivers who cannot see the road beyond a curve. Similarly, differentiated insurance premiums communicate the actuarial information based on large numbers of cases. Models often assume utility maximization on the part of individuals, but this may not necessarily be the case. Psychological experiments and survey studies show that people tend to insure against low-loss hazards and reject insurance in situations where the probability of loss is low but the potential loss is large. 2° Such behaviour is understandable in view of the limitations of the human mind. Unless we ignore many low probability threats we would become so burdened that productive life might become quite impossible. Findings along these lines imply not only that people tend to 'underinsure' themselves for large but rare losses, but also that they 'underprotect' themselves against such accidents. Social insurance for rare but large losses, combined with fines and relatively frequent detection, may thus be advantageous, provided the possibility of being detected and fined is relatively easy for the individual to perceive. In order to be effective, a regulating authority must have sufficient information on the nature of the risky activities it wishes to control. This condition is often met as far as traffic regulation is concerned. The traffic process, despite its complexity, is relatively simple and well-understood, at least when compared with other forms of accidents. Most accidents are collisions. The damages possible are well-known and depend on speed, brakes, tyres, lights and other vehicle characteristics, as well as on
76
Public insurance and accident prevention
personal factors such as skill, reaction time, and perception, which can be fairly easily regulated and policed by speeding regulation, safety checks, licensing, restrictions on drunken driving, etc. 21 Most countries utilize a mixture of measures both to prevent accident-related damage and to ameliorate the distributional consequences of accidents. Risks are typically spread thinly by private and public insurance. Prevention is accomplished not only by provisions for the recovery of damages from liable parties but also by the use of deductibles, differentiated premiums and penal regulation. Without further empirical evidence and knowledge of the political trade-off between prevention and wealth redistribution, it is difficult to say anything about the optimal mix. 22 III. PUBLIC CONTROL OF INDUSTRIAL ACCIDENTS In Sweden, the policy for dealing with industrial accidents is similar to that applied to traffic accidents. That is, compensation is financed collectively and preventive functions are increasingly in the domain of central agencies. However, the differences between traffic and industrial safety are significant. These are of interest from both a theoretical and a practical point of view. The most important difference is that the relation between the parties causing industrial accidents (employer, producers of tools and machinery, and employees) is contractual. Contracting costs are apparently lower here than in the case of traffic accidents. It is thus possible to place the costs of accidents and illnesses (mostly income losses) on one of the involved parties without decreasing efficiency, since negotiations will internalize external effects. For example, an employer who is liable for costs due to gas explosions will influence the quality of gas tubes brought on the market and the preventive measures taken at the factory, for example through the instructions given and payment made to a welder. Except for small enterprises, the firm is, by virtue of its size, in a relatively good position to bear the risks of sudden losses arising from illness or accidents. Most enterprises can predict the average absence rate during a year fairly well (except when major catastrophes occur). The typical enterprise is thus a good potential insurer and, to the extent that it does insure its employees, insurance problems here tend to be less pressing. However, employees are presumably interested in carrying some deductibles if compensated through better salaries or other benefits. A third difference between traffic and work is that, whereas the traffic process is by comparison relatively simple and well-known by central authorities, the daily activities at the place of work which cause illnesses and accidents are much more diversified. Information about these processes are often present only at the level of the enterprise and are hard for central authorities to collect. Exceptions are information on dangerous chemicals, safety devices, etc., which are common in large sectors of the economy. Failure to take account of these differences can cause large misallocations. The Swedish experience with social insurance compensation for victims of industriallyrelated accidents may be a good example. Nowadays, 90°70 of income losses, as well as most other costs of accidents, are collectively reimbursed and paid via a payroll tax of roughly 10070. Given the high level of marginal taxes in Sweden, there is effectively no deductible for the individual employee. The payroll tax is the same for all enterprises, despite the fact that absence due to illness varies greatly. As a consequence, neither employer nor employee carries the costs of dangerous and/or
GORAN SKOGH
77
unhealthy production. Uncompensated suffering by employees and production delays for employers are hardly sufficient to induce efficient job safety. On the contrary, there is a mutual interest in increasing profits, wages, and other benefits, while the expenses of an unhealthy and accident-prone environment are neglected, since the costs of the latter are borne by the general public. This amounts to a subsidization of dangerous industries. Preventive measures in the form of increased central administrative regulation and policing can hardly be expected to counteract this as long as there is a mutual interest within the enterprise in escaping regulation and thus in maintaining the subsidy. 23 IV. SUMMARY Traffic and industrial accidents may be prevented by taxes, tort liability or penal sanction. The differences between these public controls are analyzed above. It is argued that whichever is used depends on the incentive structure it creates, its distributional effects and its differing transaction and enforcement costs, factors that have typically been disregarded in earlier economic studies. It is hard to see the usefulness of classifying regulations and penal sanctions as administrative measures and tort liability as a market-oriented solution. 24 Both function via judicial decisions. The proper implementation of such measures requires hard-to-gather information. To be optimal, a tax must be varied according to the marginal harm of the accident-causing activity. Since such taxes are costly to administer, an alternative is to use stochastic detection combined with larger payments (fines) when detection occurs. As regards tort, a judge (or a court) must settle the liability. For the solution to be optimal, the judge must know the efficient preventive measures to be taken by the injurer. For a 'perfect' all-inclusive market insurance the premium must be varied in relation to the dangerous behaviour of the insured. Here the insurer needs the same information as the (perfect) tax authority. In practice, market insurance is restricted by deductibles and limiting conditions. Consequently, in a world with only tort liability and market insurance a considerable burden of risk, including that of bankruptcy, will exist. Public compensation for losses due to traffic accidents, combined with regulations, sanctions and policing varied with the seriousness of the outlawed activity (e.g. speeding or reckless driving) may reduce distributional problems and improve accident prevention. Punishment has distributional consequences as well as damages. However, fines can be kept low (relative to the damage) because of the low expected cost of the outlawed activity and the relatively good means of apprehension. Regulation of traffic accidents in Sweden is compared with the regulation of industrial accidents there. The system of public compensation for losses and central control of accident-prone activities is about the same for the two. The externality, however, is of a different kind. As is indicated, if someone in 'the production process (e.g., the employer) is strictly liable for losses due to accidents, there will be a market bargain between producers, employees and consumers over the accident prevention and the burden of risk. In this case, there will be no externality. When the general public compensates for accident losses, on the other hand, no one who can influence the number of accidents is liable and externality is created rather than eliminated.
78
Public insurance and accident prevention REFERENCES AND NOTES
1. See, for instance, the seminal book in this area, G. Calabresi, The Cost o f Accidents. A Legal and Economic Analysis, New Haven (1970), and S. Peltzman, 'The Effects of Automobile Safety Regulation', (1975) 83 J. Pol. Econ. 677-725. 2. For a comprehensive survey of the problems involved in providing compensation for accidents, see P. S. Atiyah, Accidents, Compensation and theLaw. London (1980). 3. A basic idea in 'The Economics of Crime', founded by G. Becker in 'Crime and Punishment: An Economic Approach', (1968) 76 J. Pol. Econ. 169-217, is that punishments are used as stochastic fees to correct for negative externalities. 4. See, e.g., J. P. Brown, 'Toward an Economic Theory of Liability', (1973) 2 J. Legal Stud. 323-349; and, P. Diamond and J. Mirrlees, 'On the Assignment of Liability: The Uniform Case', (1975) 6 Bell J. Econ. 487-516. A recent exception is S. Shavell, 'Accidents, Liability, and Insurance', (1979) Harvard Institute of Economic Research. Discussion Paper Number 685. 5. It can also be argued that others, e.g., the victim, typically influence risk by their care and attention. This more general case can be included in the model by letting p(x,z), Pxz :~ 0, where z is a control variable of the victim. This assumption is made by Brown, op. cit. Here it would complicate the analysis somewhat without changing the general results, although strengthening them. 6. R. Coase, 'The Problem of Social Cost', (1960) 3 J. Law and Econ. 1-44. For a mathematical proof, see A. Gifford and C. C. Stone, 'Externalities, Liability and the Coase Theorem: A Mathematical Analysis', (1973) 11 Western Econ. J. 260-269. 7. Supra, note 4, pp. 5-10. 8. Note that u~ must not equal v~. The dictator may very well choose a different initial wealth by a lump-sum transfer. 9. Differentiation of Eq. (7') yi.'elds dx _
d y>O
dy
d=
d~ > 0 at a minimum and dxy < 0 by assumption. 10. If punishment is strong, it is possible that increasing f will not deter. The reason is that high marginal utility in the case of conviction makes additional control very costly. Increased punishment or policing may then reduce the control taken in order to increase utility in the case of conviction. Formally, the first and the second order conditions for maximized expected utility, Eq. (1 ') are d~(Uc- U,,)- ( 1 - d ) U ~ ' - d ' U ~ ' = O , and D = d=( Uc - U,) + 2dx( Un' - Uc') + (1 - d)u~" + d" Uc" < 0 respectively. Here Un = U ( u - x), the utility when there is no conviction, and Uc = U ( u - x - f ) , utility when there is conviction. Total differentiation of the first order condition with respect t o f a n d y yields: dx df-
dxUc' - d" Uc" -D
dx < O, d > 0 and U~' > O, Uc" < 0 at risk aversion. D < 0 at a maximum. Hence, dx - ~ > 0 only when [ d" Uc" I > t dxUc' I uj
the
GORAN SKOGH
79
Similarly dx dy
dxy(
Un) + dy( Un' -D
dxy < 0, (Uc- U,,) < 0, dy > 0 and ( U ~ ' - Uc') < 0. Hence,
dx
--S=. > O only if dxy( U~ - U~) > l dy( U," - U~')I uy
11. The social cost of accident function, Eq. (4") has much in common with the social loss function presented in Becker's pioneering paper, supra, note 3, p. 181. There are important differences, however. 'Crime' is in Becker's analysis an (unspecified) social 'evil', which the criminal justice system controls through the choice of the punishment and the detection rate. In our case crime is a standard (x < $) settled by the public, at which the fine is directed (when x > .~ there is no punishment and thus no crime). For an analysis of the social costs of property crimes, see G. Skogh and C. Stuart, 'An Economic Analysis of Crime Rates, Punishment and the Social Consequences of Crime', Public Choice (forthcoming). 12. The first order conditions for a minimum of Eq. (4") are apxxy + Xy + 1 + Sy = 0 and apxx: + xf
13. 14. 15. 16.
17. 18. 19. 20. 21.
22.
+ S: = 0
Here Sy=(dxxy+dy)F and S f = d x x f F + d F f . Since dx < 0, the sign of Sy and S: is ambigious. If xf+ Sf is negative throughout, an increase in punishment decreases both the expected cost of accident and the private and public cost of control. Punishment is then increased until all crimes are deterred (x=J~). Similarly, if xy + 1 + Sy is negative throughout it pays to increase the detection rate towards 1. For a mathematical proof, see Shavell, supra, note 4, pp. 22-24. For a mathematical proof, see A. Raviv, 'The Design of an Optimal Insurance Policy', (1979) 69 Am. Econ. Rev. 84-96. See Shavell, supra, note 4, pp. 11-21. For 'adverse selections', i.e. when the insurer is not able to identify differences among groups of insurers, there may exist no equilibrium in the insurance market. See M. Rothshild and J. Stiglitz, 'Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information', (1976) 90 Quarterly J. Econ. 629-649. For a discussion of taxation for reaching a standard, see W. J. Baumol, 'On Taxation and the Control of Externalities', (1972) 62 Am. Econ. Rev. 307-322. Svensk F0rfattningssamling (Swedish statutes) SFS 1981:716. The cost of administering third-party automobile insurance in Sweden is about 30°70 of the claims paid, or around 45 Skr for each policy in 1976. Enskilda Fi~rstikringsanstalter. Statens Offentliga Statistik (1977), p. 110. For a survey, see H. Kunreuther and P. Slovic, 'Economics, Psychology, and Protective Behavior', (1978) 68 Am. Econ. Rev. 64-69. The costs of policing traffic in Sweden were approximately 300Skr per vehicle in 1980, a figure which is low compared with many of the expenditures necessary to operate a vehicle. The figure includes the costs of the police traffic divisions and the compulsory yearly traffic safety check. Peltzman, supra, note 1, argues that the literature on traffic regulation ignores the fact that drivers will respond to mandatory safety devices by less careful driving. His empirical results indicate that savings of auto occupants' lives are at the expense of more pedestrian accidents. However, in a similar study based on Swedish data, B. Lindgren and C. Stuart,
80
Public insurance and accident prevention
'The Effects of Traffic Safety Regulation in Sweden', (1980) 88 J. Pol. Econ. 412-427, indicate that lowered speed limits and mandatory improvements in physical vehicle safety do not decrease careful driving. 23. In G. Skogh, Priser, Skadestand och Straff, Lund (1977), pp. 83-94, I argue for strict employer liability (with a corresponding decrease in the payroll) with the employer paying sickness compensation directly to the employee. Note that I am not advocating the type of system which existed previously in Sweden, where the costs of accidents in each branch were distributed among the firms in that branch. Such a system entails full insurance for the single firm and leaves few incentives for holding down accident costs, just as in the present system. Furthermore, if a firm were large enough to be able to reduce its branches' accident costs and thus reducing premiums by instituting costly preventive measures, it would also end up decreasing costs for its competitors in the branch. 4. There is a philosophical difference, however, between the two approaches. In the benevolent-punishmentapproach, social welfare is maximized by a central power, and the wealth of one person is compared with the wealth of another. This approach is utilitarian, while the tort-liability-private-insurance approach is contractarian. In the latter the central power is limited to the judge setting the legal standard for cost liability. There is no comparison there of the wealth of the different parties. Insurance levels out wealth expost, but only as a result of contracts in the market. Becker's (supra, note 3) theory on crime and punishment is utilitarian. A contractarian theory as regards penal sanctions is also possible. Private contracts concerning penal regulation and punishments exist. An example is the employee who freely accepts a system of parking fines within the firm. More serious punishments, however, are usually in the domain of the State. In theory it is possible to describe a social contract regulating the punishing power of the State, see G. Skogh and C. Stuart, 'A Contractarian Theory of Property Rights and Crime', (1982) Scand. J. Econ. (in press). In such a social contract, the right to tax, judge and punish is settled between independent parties. However, in solving the practical problem of accident control by penal sanctions or by cost liability in the modern Western world, it does not matter whether one starts from a utilitarian or a contractual approach. The public power judging, regulating, taxing and compensating accidents can be taken for granted.
PUBLIC I N S U R A N C E A N D ACCIDENT PREVENTION GORAN SKOGH*
University of Lund, Sweden In m a n y industrial countries there has been a trend towards more or less allinclusive, publically financed compensation for losses due to accidents. In Sweden, for instance, most accident-based health-care and income losses are covered by the social insurance system. A problem with such nearly complete and all-inclusive insurance, however, is that it reduces the economic incentive to prevent accidents. Public accident insurance is often combined, therefore, with measures aimed at accident prevention. To this end, Sweden has established extensive regulations concerning such matters as working conditions and traffic safety. Violations of the regulations lead to penal sentences (mainly fines). Economists and lawyers have argued against this form of administrative control.l A major argument has been that traditional tort liability for accident costs, in combination with private insurance, is more influenced by the market. Cost liability decentralizes decisions to those involved in accidents (who know best how to avoid accidents) and to insurers in the market. Tort liability has many weaknesses, however. For example, one argument for abandoning tort liability is that it has not been shown to prevent accidents. Another argument is that uniform, complete and speedy compensation is most easily administrated by public agencies. 2 Taxes, fines and damages can all be regarded as different Pigovian taxes that make it costly to individuals not to act carefully. 3 The theoretical welfare literature, however, gives no quick answer as to whether it is best to use taxes, damages or fines. One reason is that there have been no models attempting to compare the different measures. Also, whereas accidents often cause large and sudden losses, the Pigovian tax literature, as well as most of the liability models, neglect the insurance problem .4 In the present paper the insurance problem and the use of cost liability versus penal sanctions in accident prevention are analyzed. In Section I a model is presented which includes all-inclusive public insurance and the use of Pigovian taxes as well as punishments for optimal control of the number of accidents. This model is compared with a simple model of tort liability and private insurance. In Section II the models are applied to the prevention of traffic accidents in Sweden. Industrial accidents are studied in Section III and, finally, the work is summarized in Section IV.
* Financial support from the Swedish Council for Research in Humanities and Social Sciences is gratefully acknowledged. Thanks are due to Ingemar Hansson, Charles Stuart and to the participants at the Arne Ryde Symposium on Social Insurance in Lund, 1981, at which an earlier version of the paper was discussed.
68
Public insurance and accident prevention I. THE MODELS
A model which captures the essence of many accidents is one involving two agents, a 'victim' and an 'injurer', who may with some probability be involved in an accident. The victim is faced with a loss of size a if an accident occurs. This loss is expressed in terms of the numeraire good in the economy. The only way to reduce expected accident costs is seen as being to reduce the probability of the accident. Only the injurer is considered as able, via the control variable x, to influence the probability of an accident. The probability of an accident occurring is denoted by p and of not occurring 1 - p . The p(x) function is assumed to be continuously decreasing and twice differentiable. Increasing the control variable is costly. The unit cost of x is assumed to be constant and equal to o n e ) The benefit of the activity to the injurer is viewed as constant and sufficiently large that the injurer always takes the dangerous action. The parties involved are seen to be risk averse and to maximize expected utility. Since the benefit of the dangerous action is given, the problem for the injurer is simply to choose the control measure x that minimizes the disutility of the danger. This model can be applied to traffic and industrial accidents. An example from each area will serve to clarify this: I.
2.
A car drives off the road and injures someone who could not easily prevent this occurring. The control variable x here is represented by such aspects as the inverse of the driving speed, the mechanical quality of the brakes, the condition of the tyres, etc., all of which the injurer controls. A welder is injured in a gas explosion caused by a leaking tube. The probability of this accident's occurring was influenced by the employer in choosing the dimension of the tube.
Costless contracting When the injurer acts without any consideration of the effects for the victim and thus takes no preventive measures, this results in an externality, unless the parties are able to bargain costlessly and sign an enforceable contract. In this case, the victim is willing to pay the injurer for being careful. Similarly, if the victim has the right to stop the dangerous action, the injurer is willing to pay the victim for the right to act. Such costless negotiations result, through the logic of Coase, in Paretooptimal preventive measures. 6
The first best benevolent dictator control In many dangerous activities private contracting is prohibitively costly. For instance, drivers cannot bargain on speed and routes with all potential victims. Hence, the parties have to rely on external regulation of some sort. Suppose that the external regulation is done by a well informed controllerma benevolent dictator--who costlessly controls the dangerous behaviour in a Paretooptimal way. The problem of the controller is to maximize the expected utility for one party, e.g. the victim, given the expected utility of the injurer and a resource constraint. The following notations will be used: U the utility function for the injurer, EU the
GORAN SKOGH
69
expected utility, u initial wealth, un wealth when no accident occurs and ua wealth when the accident occurs. V is the utility function of the victim, E V the expected utility, v the initial wealth of the victim, v~ the victim's wealth if the accident occurs and v n if it does not occur. Inserting these terms into a model outlined by Shavell, 7 the injurer's expected utility is E U = p ( x ) U(ua) + (1 - p ( x ) ) U(un)
(1)
whereas the victim's expected utility is E v = p(x) v(va) + (1 - p(x)) v(v.)
(2)
The resource constraint states that expected resource use equals availability of resources. That is [(1 - p ( x ) ) v , , +p(x)v~] + [(1 - p(x))u,, +p(x)u,,] + Oo(x)a + x] = u + v
(3)
The controller chooses x, as well as the utility distribution u,,,ua, vn, va. Shavell shows that a first best solution is achieved if: 1. 2.
For any x , the risk averse parties are given the same wealth regardless of whether an accident occurs or not (un = ua, vn = va). s The control measure chosen minimizes the social costs of accidents Cs.
Here Cs includes the expected accident loss (p(x)a) and the resources used for prevention. Hence, given the wealth redistribution, the dictator will Minimize Cs = P(X) "a + x with respect to x
(4)
with the first order condition -p~a = l
(5)
Thus, to be efficient, the cost of taking marginal preventive measures must equal the benefit in terms of decreased expected accident costs. The intuitive explanation of this first best solution is that since the dictator fully controls the wealth distribution by a lump sum transfer, the optimal approach is to eliminate the riskiness for the risk-averse parties by complete insurance and by simultaneously minimizing the expected costs of accidents.
The tax The first best solution rests on the assumption that the dictator controls not only the distribution of wealth but also the control measure x. In principle the insurance system here may be designed to level out accident losses to potential parties completely, but in fact no dictator controls preventive measures that are (by definition) taken by the injurer. Since if all losses are compensated the injurer has no incentive to prevent accidents, the problem of how to control the injurer remains.
70
Public insurance and accident prevention
One option is to use a traditional Pigovian tax. Assume that the dictator introduces an all-inclusive insurance for accident losses. To obtain efficient accident control the dictator imposes a tax, t, on the injurer. Then t(x) is a non-increasing function of the control measure taken. In this case the injurer will Minimize t (x) + x with respect to x
(6)
which has the first order condition - tx = I
(7)
which means that the marginal cost of preventing accidents equals the marginal tax. Note that no risk is present for the risk averse parties due to the full insurance. The tax is a fee levied on the participation in a dangerous activity. The first best condition, Eq. (5), is achieved when the marginal tax equals the marginal impact on the expected accident cost at the efficient level of control, x*, i.e. when
tx, =px.a
(8)
Punishments In most models of Pigovian taxes identification of the taxpayer is without cost. Identification and policing costs for dangerous activities, however, are usually not negligible. Suppose, therefore, that the public controller uses y units of the available resource for policing. A particular detection rate d, lying between zero and one, can be chosen. Full detection (d= 1), as in the tax case above, is clearly too costly to be achieved. When d < 1, the expected cost for the payer of the fee is less than the fee charged when detection occurs. To correct for this, a larger (stochastic) fee--here termed a punishment--may be imposed. If, for instance, one out of ten is caught, the fine can be fixed ten times higher to make the expected cost of punishment equal to the tax. For punishments a legal standard, .~, that defines the outlawed activity, is needed. The punishment, or fine, f , is imposed when the identified control measure, x, is less than ~. First, the policing problem when the fine is fixed and is small relative to the initial wealth of the offender will be analyzed. In this case the fine is a transfer with negligible wealth distributional effects. Control of the offender here is effected by deterrence. The detection rate, d, is increased by increased policing, y, and decreased by increased preventive measures, x. It is assumed that, at any given level of policing, .9, d(x,fi) is continuously decreasing and twice differentiable in x. We also assume that increased policing increases the marginal impact of private control on the detection rate (i.e., dxy < 0). Finally, the detection rate and/or the fine is small enough to make crime a rational choice (x < x-). At a given level of policing, .9, the offender who maximizes expected utility would Maximize EU=(1 -d(x,.~))U(u-x)+d(x,.~)U(u-x-f) with respect to x
(1')
GORAN SKOGH
71
Since in the case considered the fine, f , is small relative to initial wealth, u, the offender will tend to minimize the expected cost of punishment. Thus, the problem simplifies to Minimize with respect to x d ( x , . ~ ) f + x
(6')
with the first order condition - dxf= 1
(7')
The offender should then choose a control in which the gain in terms of decreased expected marginal punishment equals the cost of additional control. From the assumption dxy < 0 it follows that increased policing increases private control. 9 For example, increased patrolling on roads increases the impact of speedy driving on the detection rate. Increased policing will then increase the marginal benefit of careful driving, which reduces the speed of rational, well-informed drivers. The probability of an accident can thus be indirectly controlled by policing efforts. The problem of the public controller is to Minimize Cs = p ( x ( y ) ) a + x ( y ) + y with respect to y
(4')
with the first order condition - p . ~ X y ' a = 1 + Xy
(5')
Hence, when policing is optimal, the marginal policing cost plus the marginal cost of control taken by the injurer (as a result of the deterrence, Xy) equals the marginal benefit in terms of reduced expected accident costs. When the potential injurer changes his degree of control, this not only influences the probability of an accident but also changes policing in accordance with the reaction function, Eq. (5'). Both expected accident costs and policing costs must thus be taken into account for deterrence to be optimal. At optimal deterrence + d x , f = + px," a + yx*
(8')
That is, the expected punishment of a marginal reduction in private control is equal to the increase in expected accident cost and the change in the cost of policing. Note the difference between the tax and punishment solutions. The optimal marginal tax equals the marginal expected accident cost, Eq. (8). For punishment, the impact on marginal policing cost is added. The tax is a fee (d= 1) for participation in the dangerous activity, while the fine is stochastic. To compensate for the limited degree of detection (d < 1) and the policing costs, the fine is thus made larger than the tax. It is assumed, however, that f is small compared with the inframarginal a. This holds as long as d x is large relative to Px. A numerical example can readily illustrate this. Suppose initial wealth u = 1500 and accident loss a = 1000. The marginal impact on the probability of an accident is at an optimum when Px = - 0.001. The optimal marginal tax would thus be tx. = 1, if it could be levied,
72
Public insurance and accident prevention
However, it is prohibitively costly to detect every change in x. A relatively small fine, f = 15 (1/100 of the initial wealth), is therefore used. The marginal impact on optimal policing when the individual increases his control will be assumed, for the purpose of illustration, to be - 0 . 2 5 . The optimal marginal detection rate is then dx.= 1/15 ( - 1/1000 x 1000+0.25)= - 1/20. In reality the public controls both the policing y and the punishment f . With the aim of increasing deterrence, f m a y thus be increased. When punishments are severe and risk aversion is present, however, a number of problems arise. 1. 2.
It is possible that increased policing and punishments fail to deter.l° Heavy punishments result in a welfare loss due to the offenders' risk aversion that the benevolent dictator must take into account.
Assume that the social cost of punishing the offender who is detected is known by the public controller and is equal to F(f). F increases with increasing f due to the offenders' risk aversion. An increase in the punishment costs can also be assumed, due to an increase in collection costs and the prevalence of bankruptcy problems when punishments are large. The expected cost of the punishments imposed is d-F. In this case the public controller simultaneously chooses y a n d f s o as to Minimize with respect to y , f
Cs =p(x(y,f))a + x ( y , f ) + y + d ( x ( y , f ) , y ) F ( f )
(4") II
The problem, however, is complex and quite restrictive assumptions are needed to derive definite results. 12 Tort liability An alternative to the 'benevolent-punishment' approach is to rely on tort liability and market insurance, which can also be analyzed with a model similar to the one presented above. The probability of an accident, p(x), depends here as before on only the control measures taken by the injurer. The accident loss a is constant and is settled without costs (see the introduction to section I). Negligence is defined by a legal standard g determined by a judge. If the injurer has been careful at the time of the accident (x >Jr), he does not pay damages. On the other hand, if he is found to be negligent (x < X'), he has to compensate the victim for the accident costs in full. If the negligence standard g equals the first best preventive control, x*, then the negligence rule here tends to result in a first best public control of accidents.13 The logic is as follows: the injurer can decrease his control measure to g without expected accident costs. At such a level, a marginal decrease in x results in an infra-marginal cost increase equal to the expected accident costs. The rational injurer here will therefore be just careful enough to avoid negligence and, since £ = x * , the control chosen is efficient. As a result, the risk-averse victim will have to pay the accident costs. Assume, however, that there is an actuarially fair (competitive market) insurance available. Under these conditions, the insurance premium, r, equals the expected accident cost p ' a (there is no profit and administrative costs are nil). The victim buys full insurance, which completely eliminates the burden of risk. If, because of administrative costs, r > pa, the victim will choose only partial insurance and the burden of
GORAN SKOGH
73
risk will not be fully eliminated. 14 Strict liability is an alternative to the negligence rule. Here the injurer pays the victim full compensation whenever an accident occurs. If the injurer is risk neutral, this results in a first best solution without insurance, since the injurer minimizes expected accident cost plus control effort (see Eq. (4)). The risk-averse victim is thus fully compensated. On the other hand, if the injurer is risk-averse and no insurance is available, total welfare can be increased at a compensation less than the accident loss, a. In this case risk remains, both for the victim and the injurer. 15 If liability insurance is available, the risk-averse injurer will purchase it. Just as with public insurance, this insurance reduces the incentive to prevent an accident. The moral hazard involved can be avoided, however, if the insurer costlessly identifies the control measure taken by the insured and varies the premium r with x. The competitive, actuarially fair premium here, r(x)=p(x)a, assumes zero administration costs. The insured will under these conditions Minimize r(x) + x with respect to x
(6")
with the first order condition -
rx
= 1
(7")
Thus, the marginal cost of increasing control equals the marginal impact on the insurance premium. Since the marginal premium rx equals the marginal expected accident cost, pxa, this all-inclusive, completely differentiated 'perfect' insurance results in a first best optimum (see Eq. (5)). The assumption of a perfectly differentiated market insurance thus eliminates the problem of risk aversion. It is interesting to note the similarities between this (hypothetical) perfect market insurance and the combined social insurance and tax analyzed above. Both systems eliminate risk completely; the tax and the premium alike are predetermined fees for participating in a dangerous activity; the tax agency and the insurer both need the same sort of information concerning the control function p(x). In any realistic case, the insurer has limited information regarding both the behaviour of the insured and p(x). An interesting alternative extreme to study is, therefore, the case where the insurer has no information concerning p(x) at all. Here market insurance will end up with a deductible. The partial insurance reduces the moral hazard. The expected utility of the insured is maximized through coverage being reduced to the point where the benefits from the lower premium rate just equal the disutility due to increased exposure to risk. The administrative costs included in the premium increase the tendency towards only partial insurance. 16 II. THE PREVENTION OF TRAFFIC ACCIDENTS For a tax to be efficient (see Eq. (8)), tax authorities need information concerning the expected marginal harm of the preventive measures taken by the potential injurer, which is, of course, an extreme assumption. Taxes with low collection costs, to be sure, may be useful where an acceptable standard is easily found. 1T For example, total traffic volume might be reduced by a tax on cars, petrol or roads. As
74
Public insurance and accident prevention
a side effect, accidents might likewise be reduced. Such a tax, however, would be a dull instrument for reducing accidents. One reason for this is that the accidentreducing effects of different preventive measures vary considerably. Another reason is that information on the behaviour of drivers is limited. Suppose, for example, that the efficient speed on a road varied between zero and 100km/h depending on curves, traffic intensity, slipperiness, darkness and the characteristics of cars. By a tax on speed (if this were possible to administer) it might be possible to arrive at an average car speed of, say, 50km/h. It might be possible to vary such a tax with the quality of the car but hardly with the other factors. The main characteristic of the fine as opposed to the tax is its stochastic nature and the indirect control of accidents it provides via deterrence. When penalties are involved, the public enforcer needs information on the effects which policing has on expected accident costs, where the deterrence of the offender is included in the accident costs (see Eq. (5')). Although there is insufficient knowledge about these matters, it appears that penal control of accidents may be superior to regulation by way of a tax. A differentiated tax, applied in all situations ( d = 1), is often too costly to administer. By choosing a detection rate less than 1 the policing cost can be kept relatively low. Note that the expected punishment can be differentiated in relation to the importance of the preventive measures taken. Since the incentive effect of regulation here is reflected in the product of the probability of apprehension and the fine is apprehended, it is possible to tailor either of these (as well as the exact form of the penalty) to meet the requirements of specific situations. For example, it is possible, on a stretch of non-uniform road, to vary not only speed-limits but also the intensity of policing and the magnitude ol' fines in order to exercise a differential control of driving intensity. Indeed, in practice policing usually is varied over time, for example, through having special checks at rush hours and practically no policing late at night. A problem with penal sanctions is the harm inflicted on the punished. Fines, however, are transfers which need not have any significant redistributional effects, as long as they are relatively small. In Sweden, for example, there is a system of fixed monetary fines for speeding offences, for failure to comply with the seat-belt law, etc., of between 100-600Skr, which is small relative to the yearly budget of most car owners. 18 For 'reckless driving' there are larger fines which vary with the income of the punished. The prosecutor chooses some number of 'day-fines', between 5 and 60, depending on the seriousness of the crime. This number is (roughly) multiplied by a per mill of the yearly income of the offender. Hence, as long as punishment is not increased to include jail-sentences and other restrictions on freedom (e.g., withholding a driver's licence or his permission to perform a profession), the social cost of punishment can be kept relatively low. For a negligence rule to be efficient, the judge needs information on the preventive measure to be taken by the injurer (x*). If the victim influences the expected cost of an accident, then efficient action by the injurer depends on the measures taken by the victim as well (see note 5). One reason why a judge possesses limited information on the behaviour of the parties to an accident is that they are not properly motivated to present correct information. As a result, the judge often has to rely on some established and measurable standard of due care, for instance the speed at the time of the accident, the quality of the car, the alcohol consumed by the driver, etc. These standards are more or less the same as the penal standards. There is a difference, however, in the method of identification. Speed controls and safety checks are designed to prevent accidents, while the tort case is ex
GORAN SKOGH
75
post. If judges can be expected to have detailed information on the behaviour of the parties to an accident, the possibility of accident-cost liability may influence a potential injurer towards more cautious and adequate behaviour than it is possible to engender with punishments alone. For a liability insurance to be perfectly differentiated, the insurer needs the same type of information as the perfectly informed tax authority. In practice, drivers' discounts, differentiation with respect to vehicles, etc. are only partially related to the preventive measures taken by drivers. Such insurance is also costly to administer. 19 Legal processes are costly as well. That may be a reason why cost compensations for accidents are settled out of court, mainly by the insurers. Thus, a system with only tort liability and market insurance can be high in cost and fail to eliminate riskiness. Indeed, certain behaviour, such as reckless or drunken driving, speeding and driving without a licence are usually excluded from coverage in private insurance policies. The bankruptcy problem is especially apparent with liabilities that are not insurable in the market, e.g. in connection with reckless or drunken driving. Such dangerous behaviour is therefore typically controlled by penal sanctions. Minor fines can usually be paid by the offender who is detected. Large punishments result in collection costs and bankruptcy problems. The preventive effects of cost liability depend on the ability of the liable individual to predict the possibility of an accident. With penal regulation of accident-prone behaviour, however, the chain of information becomes more indirect, though it may nevertheless be effective, for example through a regulator who is better informed of the risks inherent in certain activities than the individuals involved in these activities communicating this information via regulation, which has incentive effects if backed up by sanctions. A common argument against regulation (among economists at any rate) is that the individual involved in an accident knows best how to avoid an accident. However, it is not at all hard to find cases where a third party (an insurer or a public safety agency) can more easily foresee risks. Speed limits, for example, can have an informative value for drivers who cannot see the road beyond a curve. Similarly, differentiated insurance premiums communicate the actuarial information based on large numbers of cases. Models often assume utility maximization on the part of individuals, but this may not necessarily be the case. Psychological experiments and survey studies show that people tend to insure against low-loss hazards and reject insurance in situations where the probability of loss is low but the potential loss is large. 2° Such behaviour is understandable in view of the limitations of the human mind. Unless we ignore many low probability threats we would become so burdened that productive life might become quite impossible. Findings along these lines imply not only that people tend to 'underinsure' themselves for large but rare losses, but also that they 'underprotect' themselves against such accidents. Social insurance for rare but large losses, combined with fines and relatively frequent detection, may thus be advantageous, provided the possibility of being detected and fined is relatively easy for the individual to perceive. In order to be effective, a regulating authority must have sufficient information on the nature of the risky activities it wishes to control. This condition is often met as far as traffic regulation is concerned. The traffic process, despite its complexity, is relatively simple and well-understood, at least when compared with other forms of accidents. Most accidents are collisions. The damages possible are well-known and depend on speed, brakes, tyres, lights and other vehicle characteristics, as well as on
76
Public insurance and accident prevention
personal factors such as skill, reaction time, and perception, which can be fairly easily regulated and policed by speeding regulation, safety checks, licensing, restrictions on drunken driving, etc. 21 Most countries utilize a mixture of measures both to prevent accident-related damage and to ameliorate the distributional consequences of accidents. Risks are typically spread thinly by private and public insurance. Prevention is accomplished not only by provisions for the recovery of damages from liable parties but also by the use of deductibles, differentiated premiums and penal regulation. Without further empirical evidence and knowledge of the political trade-off between prevention and wealth redistribution, it is difficult to say anything about the optimal mix. 22 III. PUBLIC CONTROL OF INDUSTRIAL ACCIDENTS In Sweden, the policy for dealing with industrial accidents is similar to that applied to traffic accidents. That is, compensation is financed collectively and preventive functions are increasingly in the domain of central agencies. However, the differences between traffic and industrial safety are significant. These are of interest from both a theoretical and a practical point of view. The most important difference is that the relation between the parties causing industrial accidents (employer, producers of tools and machinery, and employees) is contractual. Contracting costs are apparently lower here than in the case of traffic accidents. It is thus possible to place the costs of accidents and illnesses (mostly income losses) on one of the involved parties without decreasing efficiency, since negotiations will internalize external effects. For example, an employer who is liable for costs due to gas explosions will influence the quality of gas tubes brought on the market and the preventive measures taken at the factory, for example through the instructions given and payment made to a welder. Except for small enterprises, the firm is, by virtue of its size, in a relatively good position to bear the risks of sudden losses arising from illness or accidents. Most enterprises can predict the average absence rate during a year fairly well (except when major catastrophes occur). The typical enterprise is thus a good potential insurer and, to the extent that it does insure its employees, insurance problems here tend to be less pressing. However, employees are presumably interested in carrying some deductibles if compensated through better salaries or other benefits. A third difference between traffic and work is that, whereas the traffic process is by comparison relatively simple and well-known by central authorities, the daily activities at the place of work which cause illnesses and accidents are much more diversified. Information about these processes are often present only at the level of the enterprise and are hard for central authorities to collect. Exceptions are information on dangerous chemicals, safety devices, etc., which are common in large sectors of the economy. Failure to take account of these differences can cause large misallocations. The Swedish experience with social insurance compensation for victims of industriallyrelated accidents may be a good example. Nowadays, 90°70 of income losses, as well as most other costs of accidents, are collectively reimbursed and paid via a payroll tax of roughly 10070. Given the high level of marginal taxes in Sweden, there is effectively no deductible for the individual employee. The payroll tax is the same for all enterprises, despite the fact that absence due to illness varies greatly. As a consequence, neither employer nor employee carries the costs of dangerous and/or
GORAN SKOGH
77
unhealthy production. Uncompensated suffering by employees and production delays for employers are hardly sufficient to induce efficient job safety. On the contrary, there is a mutual interest in increasing profits, wages, and other benefits, while the expenses of an unhealthy and accident-prone environment are neglected, since the costs of the latter are borne by the general public. This amounts to a subsidization of dangerous industries. Preventive measures in the form of increased central administrative regulation and policing can hardly be expected to counteract this as long as there is a mutual interest within the enterprise in escaping regulation and thus in maintaining the subsidy. 23 IV. SUMMARY Traffic and industrial accidents may be prevented by taxes, tort liability or penal sanction. The differences between these public controls are analyzed above. It is argued that whichever is used depends on the incentive structure it creates, its distributional effects and its differing transaction and enforcement costs, factors that have typically been disregarded in earlier economic studies. It is hard to see the usefulness of classifying regulations and penal sanctions as administrative measures and tort liability as a market-oriented solution. 24 Both function via judicial decisions. The proper implementation of such measures requires hard-to-gather information. To be optimal, a tax must be varied according to the marginal harm of the accident-causing activity. Since such taxes are costly to administer, an alternative is to use stochastic detection combined with larger payments (fines) when detection occurs. As regards tort, a judge (or a court) must settle the liability. For the solution to be optimal, the judge must know the efficient preventive measures to be taken by the injurer. For a 'perfect' all-inclusive market insurance the premium must be varied in relation to the dangerous behaviour of the insured. Here the insurer needs the same information as the (perfect) tax authority. In practice, market insurance is restricted by deductibles and limiting conditions. Consequently, in a world with only tort liability and market insurance a considerable burden of risk, including that of bankruptcy, will exist. Public compensation for losses due to traffic accidents, combined with regulations, sanctions and policing varied with the seriousness of the outlawed activity (e.g. speeding or reckless driving) may reduce distributional problems and improve accident prevention. Punishment has distributional consequences as well as damages. However, fines can be kept low (relative to the damage) because of the low expected cost of the outlawed activity and the relatively good means of apprehension. Regulation of traffic accidents in Sweden is compared with the regulation of industrial accidents there. The system of public compensation for losses and central control of accident-prone activities is about the same for the two. The externality, however, is of a different kind. As is indicated, if someone in 'the production process (e.g., the employer) is strictly liable for losses due to accidents, there will be a market bargain between producers, employees and consumers over the accident prevention and the burden of risk. In this case, there will be no externality. When the general public compensates for accident losses, on the other hand, no one who can influence the number of accidents is liable and externality is created rather than eliminated.
78
Public insurance and accident prevention REFERENCES AND NOTES
1. See, for instance, the seminal book in this area, G. Calabresi, The Cost o f Accidents. A Legal and Economic Analysis, New Haven (1970), and S. Peltzman, 'The Effects of Automobile Safety Regulation', (1975) 83 J. Pol. Econ. 677-725. 2. For a comprehensive survey of the problems involved in providing compensation for accidents, see P. S. Atiyah, Accidents, Compensation and theLaw. London (1980). 3. A basic idea in 'The Economics of Crime', founded by G. Becker in 'Crime and Punishment: An Economic Approach', (1968) 76 J. Pol. Econ. 169-217, is that punishments are used as stochastic fees to correct for negative externalities. 4. See, e.g., J. P. Brown, 'Toward an Economic Theory of Liability', (1973) 2 J. Legal Stud. 323-349; and, P. Diamond and J. Mirrlees, 'On the Assignment of Liability: The Uniform Case', (1975) 6 Bell J. Econ. 487-516. A recent exception is S. Shavell, 'Accidents, Liability, and Insurance', (1979) Harvard Institute of Economic Research. Discussion Paper Number 685. 5. It can also be argued that others, e.g., the victim, typically influence risk by their care and attention. This more general case can be included in the model by letting p(x,z), Pxz :~ 0, where z is a control variable of the victim. This assumption is made by Brown, op. cit. Here it would complicate the analysis somewhat without changing the general results, although strengthening them. 6. R. Coase, 'The Problem of Social Cost', (1960) 3 J. Law and Econ. 1-44. For a mathematical proof, see A. Gifford and C. C. Stone, 'Externalities, Liability and the Coase Theorem: A Mathematical Analysis', (1973) 11 Western Econ. J. 260-269. 7. Supra, note 4, pp. 5-10. 8. Note that u~ must not equal v~. The dictator may very well choose a different initial wealth by a lump-sum transfer. 9. Differentiation of Eq. (7') yi.'elds dx _
d y>O
dy
d=
d~ > 0 at a minimum and dxy < 0 by assumption. 10. If punishment is strong, it is possible that increasing f will not deter. The reason is that high marginal utility in the case of conviction makes additional control very costly. Increased punishment or policing may then reduce the control taken in order to increase utility in the case of conviction. Formally, the first and the second order conditions for maximized expected utility, Eq. (1 ') are d~(Uc- U,,)- ( 1 - d ) U ~ ' - d ' U ~ ' = O , and D = d=( Uc - U,) + 2dx( Un' - Uc') + (1 - d)u~" + d" Uc" < 0 respectively. Here Un = U ( u - x), the utility when there is no conviction, and Uc = U ( u - x - f ) , utility when there is conviction. Total differentiation of the first order condition with respect t o f a n d y yields: dx df-
dxUc' - d" Uc" -D
dx < O, d > 0 and U~' > O, Uc" < 0 at risk aversion. D < 0 at a maximum. Hence, dx - ~ > 0 only when [ d" Uc" I > t dxUc' I uj
the
GORAN SKOGH
79
Similarly dx dy
dxy(
Un) + dy( Un' -D
dxy < 0, (Uc- U,,) < 0, dy > 0 and ( U ~ ' - Uc') < 0. Hence,
dx
--S=. > O only if dxy( U~ - U~) > l dy( U," - U~')I uy
11. The social cost of accident function, Eq. (4") has much in common with the social loss function presented in Becker's pioneering paper, supra, note 3, p. 181. There are important differences, however. 'Crime' is in Becker's analysis an (unspecified) social 'evil', which the criminal justice system controls through the choice of the punishment and the detection rate. In our case crime is a standard (x < $) settled by the public, at which the fine is directed (when x > .~ there is no punishment and thus no crime). For an analysis of the social costs of property crimes, see G. Skogh and C. Stuart, 'An Economic Analysis of Crime Rates, Punishment and the Social Consequences of Crime', Public Choice (forthcoming). 12. The first order conditions for a minimum of Eq. (4") are apxxy + Xy + 1 + Sy = 0 and apxx: + xf
13. 14. 15. 16.
17. 18. 19. 20. 21.
22.
+ S: = 0
Here Sy=(dxxy+dy)F and S f = d x x f F + d F f . Since dx < 0, the sign of Sy and S: is ambigious. If xf+ Sf is negative throughout, an increase in punishment decreases both the expected cost of accident and the private and public cost of control. Punishment is then increased until all crimes are deterred (x=J~). Similarly, if xy + 1 + Sy is negative throughout it pays to increase the detection rate towards 1. For a mathematical proof, see Shavell, supra, note 4, pp. 22-24. For a mathematical proof, see A. Raviv, 'The Design of an Optimal Insurance Policy', (1979) 69 Am. Econ. Rev. 84-96. See Shavell, supra, note 4, pp. 11-21. For 'adverse selections', i.e. when the insurer is not able to identify differences among groups of insurers, there may exist no equilibrium in the insurance market. See M. Rothshild and J. Stiglitz, 'Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information', (1976) 90 Quarterly J. Econ. 629-649. For a discussion of taxation for reaching a standard, see W. J. Baumol, 'On Taxation and the Control of Externalities', (1972) 62 Am. Econ. Rev. 307-322. Svensk F0rfattningssamling (Swedish statutes) SFS 1981:716. The cost of administering third-party automobile insurance in Sweden is about 30°70 of the claims paid, or around 45 Skr for each policy in 1976. Enskilda Fi~rstikringsanstalter. Statens Offentliga Statistik (1977), p. 110. For a survey, see H. Kunreuther and P. Slovic, 'Economics, Psychology, and Protective Behavior', (1978) 68 Am. Econ. Rev. 64-69. The costs of policing traffic in Sweden were approximately 300Skr per vehicle in 1980, a figure which is low compared with many of the expenditures necessary to operate a vehicle. The figure includes the costs of the police traffic divisions and the compulsory yearly traffic safety check. Peltzman, supra, note 1, argues that the literature on traffic regulation ignores the fact that drivers will respond to mandatory safety devices by less careful driving. His empirical results indicate that savings of auto occupants' lives are at the expense of more pedestrian accidents. However, in a similar study based on Swedish data, B. Lindgren and C. Stuart,
80
Public insurance and accident prevention
'The Effects of Traffic Safety Regulation in Sweden', (1980) 88 J. Pol. Econ. 412-427, indicate that lowered speed limits and mandatory improvements in physical vehicle safety do not decrease careful driving. 23. In G. Skogh, Priser, Skadestand och Straff, Lund (1977), pp. 83-94, I argue for strict employer liability (with a corresponding decrease in the payroll) with the employer paying sickness compensation directly to the employee. Note that I am not advocating the type of system which existed previously in Sweden, where the costs of accidents in each branch were distributed among the firms in that branch. Such a system entails full insurance for the single firm and leaves few incentives for holding down accident costs, just as in the present system. Furthermore, if a firm were large enough to be able to reduce its branches' accident costs and thus reducing premiums by instituting costly preventive measures, it would also end up decreasing costs for its competitors in the branch. 4. There is a philosophical difference, however, between the two approaches. In the benevolent-punishmentapproach, social welfare is maximized by a central power, and the wealth of one person is compared with the wealth of another. This approach is utilitarian, while the tort-liability-private-insurance approach is contractarian. In the latter the central power is limited to the judge setting the legal standard for cost liability. There is no comparison there of the wealth of the different parties. Insurance levels out wealth expost, but only as a result of contracts in the market. Becker's (supra, note 3) theory on crime and punishment is utilitarian. A contractarian theory as regards penal sanctions is also possible. Private contracts concerning penal regulation and punishments exist. An example is the employee who freely accepts a system of parking fines within the firm. More serious punishments, however, are usually in the domain of the State. In theory it is possible to describe a social contract regulating the punishing power of the State, see G. Skogh and C. Stuart, 'A Contractarian Theory of Property Rights and Crime', (1982) Scand. J. Econ. (in press). In such a social contract, the right to tax, judge and punish is settled between independent parties. However, in solving the practical problem of accident control by penal sanctions or by cost liability in the modern Western world, it does not matter whether one starts from a utilitarian or a contractual approach. The public power judging, regulating, taxing and compensating accidents can be taken for granted.