Transcript

Deterrence, litigation costs, and the statute of limitationsfor tort suits

Thomas J. Miceli

Department of Economics, U-63, University of Connecticut, Storrs, CT 06269-1063

Received May 1999; received in revised form October 1999

1. Introduction

The conventional justification for a statute of limitations on tort suits (or any otherlegal claim) is that evidence deteriorates over time, thereby increasing the likelihood oflegal error.1 The optimal statute balances this cost of a longer statute length against thedilution in deterrence that results from a shorter length. In this paper I develop a formalmodel to show that a finite statute length is optimal even in a world without thepossibility of legal error. The trade-off involves only litigation costs and deterrence:while a shorter statute reduces deterrence, it also saves on litigation costs by limiting thenumber of suits that can be filed.

I examine this trade-off under both strict liability and under negligence, and show that theoptimal statute length is (probably) shorter under strict liability than under negligence.Intuitively, the marginal benefit of lengthening the statute is higher under a negligence rulebecause, by increasing the length of time over which victims can file suit, deterrence isenhanced, which in turn reduces the likelihood that a given injurer will be found negligent.Thus, fewer victims file suits at each point in time because their chances of winning arereduced. As a result, litigation costs fall, which partially offsets the extra litigation costswhen the statute is lengthened.

The paper is organized as follows. Section 2 sets up the basic model, Section 3 derives the

Tel. 860-486-5810; fax: 860-486-4463.E-mail address:[email protected] (T.J. Miceli).1 See, e.g., Cooter and Ulen (1988: p. 155), Landes and Posner (1987: p. 307), and Epstein (1986). Despite

(or possibly because of) the wide acceptance of this argument, there has been almost no formal analyses ofstatutes of limitations in the law and economics literature. An exception is Baker and Miceli (2000).

International Review of Law and Economics 20 (2000) 383–394

0144-8188/00/$ – see front matter © 2000 Elsevier Science Inc. All rights reserved.PII: S0144-8188(00)00038-7

optimal statute of limitations for a strict liability rule, and Section 4 repeats the analysis fora negligence rule. Section 5 then offers some informal evidence in support of the theorybased on the enactment of statutes of repose for products liability cases, the emergence of therule of discovery under negligence law, and differences in the statute of limitations fortrespass versus nuisance cases. Finally, Section 6 concludes.

2. The model

The model is based on the one developed by Hylton (1990). Injurers and victims are bothrisk-neutral, and injurers alone can take care to reduce the likelihood of an accident (i.e., themodel is one of unilateral care). For simplicity, the injurer’s care choice is dichotomous:either take care or no care. Letq be the probability of an accident if the injurer takes care,andp be the probability if he does not, wherep . q . 0.

The cost of care for injurers is denotedx, which varies across the population of injurersaccording to the distribution functionH(x). Injurers know their own cost of care, but victimsdo not observe the costs of individual injurers (though they know the distribution function),nor do they know if an injurer actually took care in a given case. However, I assume that thecourt can observe whether or not an injurer took care as well as the injurer’s cost of care (forpurposes of applying a negligence rule) if a case goes to trial.

Victims vary in their (fixed) damages in the event of an accident, denotedD. Thedistribution function of victims’ damages isF(D). At the time they make their care choice,injurers do not know the damage that an individual victim will suffer, but they know thedistribution of victim damages. However, the court can observeD after the fact whendetermining a damage award.

When an accident occurs, if the victim files suit, she incurs litigation costs ofcv while theinjurer incurs litigation costs ofci. In Hylton’s (1990) static model, all victims who find a suitprofitable file immediately. Here I allow the possibility that some victims will delay filingsuit. For example, some injuries might not be immediately evident or some injurers mightavoid immediate detection or identification. To keep the model simple, I abstract from thespecific reason for delay and simply treat the length of time after an accident that a victimfiles suit, denotedt, as a random variable with distribution functionG(t). Thus, for example,if the statute of limitations is set atL, thenG(L) is the probability that a randomly chosenvictim will file suit by time L.2

3. Strict liability

Under strict liability, all victims for whomD $ cv and t # L will file suit. Thus, if anaccident occurs, the probability of a lawsuit isg(t)[1 2 F(cv)] at any t up to L (where

2 Alternatively,G(L) can be interpreted as the number of suits filed byL. I assume thatt is independent of thevictim’s damages,D.

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g(t) [ G9(t)), and zero thereafter. If a suit is filed, the injurer faces liability equal to thedamage suffered by the victim,D. For suits filed in the future (t . 0), this amount should bediscounted to the present (the date when the injurer makes his care choice) by the interest rater, yielding a present value of liability equal toDe2rt for a suit filed at timet. I assume,however, that the court awards the victim interest onD at rater, beginning at the accidentdate (t 5 0),3 thereby exactly offsetting the injurer’s discounting. Thus, regardless of the datewhen a case is filed, the injurer bears expected liability ofD as of t 5 0. In the absence ofthis “prejudgment” interest, the injurer’s incentives would clearly be diluted merely by thevictim’s delay in filing.4 The same is not true of the injurer’s litigation costs. Specifically, acase filed at timet costs the injurercie

2rt in present value terms. Thus, the injurer does gainfrom delay in this respect.

Given the above factors, the injurer’s expected costs of taking care under a rule of strictliability with a statute of limitations ofL are given by

x 1 q$G~L! Ecv

`

DdF~D! 1 @1 2 F~cv!# E0

L

cie2rtg~t!dt%. (1)

Similarly, the expected costs of not taking care are

p$G~L! Ecv

`

DdF~D! 1 @1 2 F~cv!# E0

L

cie2rtg~t!dt%. (2)

Combining Eq. (1) and Eq. (2) yields the condition for the injurer to take care:

x # ~ p 2 q!$G~L! Ecv

`

DdF~D! 1 @1 2 F~cv!# E0

L

cie2rtg~t!dt% ; xs~L!. (3)

The right-hand side represents the highest cost injurer who chooses to take care under strictliability as a function ofL. Taking the derivative of Eq. (3) with respect toL yields [Eq. (4)]

­ xs

­L5 ~ p 2 q! g~L! E

cv

`

~D 1 cie2rL!dF~D! . 0. (4)

Thus, increasing the statute of limitations increases the number of injurers who choose totake care, by increasing both expected liability and the present value of litigation costs. Thiscaptures the impact of the statute of limitations on deterrence.

Socially, care is desirable when the social costs of care are less than the social costs of nocare. The social costs of care are

3 I ignore the problem of possible differences between the discount rate and the interest rate.4 See Ross and Goelz (1985) on the calculation of prejudgment interest. Some states allow it to begin accruing

at the date of the accident (the assumption here), while others use the date that the complaint is filed or the datewhen a settlement is first offered.

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x 1 q$E~D! 1 @1 2 F~cv!# E0

L

~ci 1 cv!e2rtg~t!dt%. (5)

This differs from Eq. (1) in two respects: the inclusion of damages suffered by victims whodo not file suit, and the inclusion of the present value of the litigation costs of victims whodo file. The social cost of not taking care are

p$E~D! 1 @1 2 F~cv!# E0

L

~ci 1 cv!e2rtg~t!dt%, (6)

which differs from Eq. (2) by the same factors.Combining Eq. (5) and Eq. (6) shows that care is socially desirable when

x # ~ p 2 q!$E~D! 1 @1 2 F~cv!# E0

L

~ci 1 cv!e2rtg~t!dt% ; xs* ~L!. (7)

The right-hand side of Eq. (7) represents the highest cost injurer for whom it is sociallydesirable to take care under strict liability. Comparing Eq. (3) and Eq. (7) shows thatxs*( L). xs(L) for any L, implying that strict liability underdeters(Hylton, 1990). This is truebecause, as noted above, injurers ignore the damages imposed on victims who do not file suit(i.e., those withD , cv), and the litigation costs of victims who do file.

We are now in a position to derive the optimal statute of limitations under strict liability.To do so, we first need to write down the expression for expected social costs. This is givenby Eq. (5) weighted by the number of injurers who take care,H( xs(L)), plus Eq. (6)weighted by the number of injurers who do not take care, 12 H( xs(L)). The resultingexpression, after rearranging, is given by

SCs~L! 5 p$E~D! 1 @1 2 F~cv!# E0

L

~ci 1 cv!e2rtg~t!dt% 2 H~ xs~L!!~ p 2 q!

3 $E~D! 1 @1 2 F~cv!# E0

L

~ci 1 cv!e2rtg~t!dt% 1 xs~L! xdH~ x!. (8)

The optimal statute of limitations is found by minimizing Eq. (8). The first-order condi-tion, after rearranging, is given by5

@1 2 F~cv!#e2rL~ci 1 cv! g~L!@ p~1 2 H~ xs!! 1 qH~ xs!#

5 S­ xs

­L Dh~ xs!@ xs* ~L! 2 xs~L!#. (9)

5 I assume (here and below) that the second-order condition for a minimum issatisfied.

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The left-hand side of Eq. (9) represents the marginal cost of an increase inL. It captures theincrease in the present value of expected litigation costs whenL is increased by one period,wherep(1 2 H( xs)) 1 qH( xs) is the probability of an accident, and [12 F(cv)] g(L) isthe number of new cases filed in the event of an accident. The right-hand side captures themarginal benefit of an increase inL in terms of increased deterrence. The term­ xs/­Lrepresents the increase in the threshold for care whenL is raised, which is weighted byh( xs),the fraction of injurers with cost of care equal toxs. The bracketed term represents the netsavings in social costs when one more injurer takes care, where this term is positive due tothe general underdeterrence under strict liability. According to Eq. (9), the optimal statutelength balances the increased litigation costs from a longer statute against the increaseddeterrence benefits.

4. Negligence

Negligence differs from strict liability in that a victim will not recover against the injurer, evenif she files in a timely manner, if the injurer took due care. Following Hylton (1990), we definedue care by the Hand Rule,6 which, in the current context, says that an injurer is negligent if hefailed to take care andx , (p 2 q)E(D) [ xH; that is, if his cost of care is less than the socialbenefit of care (xH) in a world of zero litigation costs.7 The court can apply this rule because weassumed that it can observe the injurer’s care choice and cost of care after the fact.

Victims, however, cannot observe injurers’ costs of care, nor can they observe whether agiven injurer has taken care at the time that they make their filing decision. Thus, they canat best calculate the probability that an injurer will be found negligent, given that an accidenthas occurred. Let this probability bew, which we will define below. Thus, victims for whomwD $ cv and t # L will file suit under negligence. The probability of a suit, given that anaccident occurs, is thereforeg(t)[1 2 F(cv/w)] for any t # L, and zero thereafter.

Given the above, note that an injurer withx . xH will never take care because he willnever be judged negligent by the court. Thus, only injurers withx # xH are “potentiallynegligent” in the sense that they will be judged negligent if they failed to take care and thevictim files suit following an accident. A potentially negligent injurer who takes care incursexpected costs of

x 1 q@1 2 F~cv/w!# E0

L

cie2rtg~t!dt. (10)

Thus, he incurs only the cost of care plus his expected litigation costs, given that he will befound non-negligent at trial. In contrast, when a potentially negligent injurer does not takecare, his expected costs are

6 SeeU.S. v. Carroll Towing, 159 F.2d 169 (2d Cir. 1947).7 The results would be qualitatively the same if the due standard were based on the optimal standard in the

presence of litigation costs. See note 9infra.

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p$G~L! Ecv/w

`

DdF~D! 1 @1 2 F~cv/w!#E0

L

cie2rtg~t!dt%, (11)

which includes expected liability plus litigation costs. Combining Eq. (10) and Eq. (11) givesthe condition for the injurer to take care:

x # pG~L! Ecv/w

`

DdF~D! 1 ~p 2 q!@1 2 F~cv/w!# E0

L

cie2rtg~t!dt ; xN~L!, (12)

where the right-hand side is the highest cost injurer who chooses to take care undernegligence.

We can now calculate the equilibrium value ofw, which, recall, is the probability that agiven injurer will be found negligent, given that an accident has occurred. Since victimscorrectly anticipate the likelihood of a negligent verdict, we can use Bayes’ Rule to calculate

w~L! 5p@H~ xH! 2 H~ xN~L!!#

p@1 2 H~ xN~L!!# 1 qH~ xN~L!!. (13)

The numerator is the probability of an accident when the injurer does not take care times theprobability that the injurer is both potentially negligent and fails to take care, while thedenominator is the overall probability of an accident. Note thatw is positive if and only ifxH . xN(L), implying that there are some injurers who are potentially negligent and fail totake care. Although this need not be true in general, it must be true in a negligenceequilibrium.8

Assuming that an equilibrium exists, we can totally differentiate Eq. (12) and Eq. (13) andsolve simultaneously to find the impact of varyingL on the equilibrium [Eq. (14)]:

­ xN

­L. 0,

­w

­L, 0. (14)

Intuitively, an increase in the statute of limitations increases the expected liability of injurers,thereby causing more injurers to take care (xN(L) increases), but because more injurers takecare, the probability that a given injurer will be found negligent by the court (w(L))decreases.

We now turn to social costs. When the injurer takes care, expected social costs are given by

x 1 q$E~D! 1 @~1 2 F~cv/w!# E0

L

~ci 1 cv!e2rtg~t!dt%, (15)

8 The intuition is as follows. If all potentially negligent injurers take care, thenw50 and no victims will filesuit. But then injurers have no incentive to take care since they face no threat of a suit. For more details, seeOrdover (1978) and Hylton (1990).

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which is equivalent to (5) except thatcv/w replacescv as the lowest value ofD that resultsin a suit. When the injurer does not take care, expected social costs are

p$E~D! 1 @1 2 F~cv/w!# E0

L

~ci 1 cv!e2rtg~t!dt%, (16)

which similarly differs from Eq. (6). Combining Eq. (15) and Eq. (16) yields the conditionfor care to be socially desirable [Eq. (17)]:

x # ~ p 2 q!$E~D! 1 @1 2 F~cv/w!# E0

L

~ci 1 cv!e2rtg~t!dt% ; xN* ~L!, (17)

wherexN*( L) is the highest cost injurer for whom care is socially desirable under negli-gence. Note thatxN*( L) . xH due to the absence of litigation costs fromxH. Further, sincexH . xN(L) for existence of a negligence equilibrium, it follows thatxN*( L) . xN(L), orthat negligence, like strict liability,underdetersin equilibrium (Hylton, 1990).9

As above, the optimal statute of limitations under negligence minimizes expected socialcosts, which is given by Eq. (15) multiplied by the fraction of injurers taking care,H( xN(L)),plus Eq. (16) multiplied by the fraction not taking care, 12 H( xN(L)). After rearranging,this becomes

SCN~L! 5 p$E~D! 1 @1 2 F~cv/w!# E0

L

~ci 1 cv!e2rtg~t!dt% 2 H~ xN~L!!~ p 2 q!

3 $E~D! 1 @1 2 F~cv/w!#E0

L

~ci 1 cv!e2rtg~t!dt% 1 E

0

xN~L!

xdH~ x!.

(18)

where, recall,w is a function ofL. Minimization of Eq. (18) yields the first-order condition

@1 2 F~cv/w!#e2rL~ci 1 cv! g~L!@ p~1 2 H~ xN!! 1 qH~ xN!# 5 S­ xN

­L D h~ xN!

3 @ xN* ~L! 2 xN~L!# 2 S­w

­LD f~cv/w!~cv/w2!E

0

L

~ci 1 cv!e2rtg~t!dt

3 @ p~1 2 H~ xN!! 1 qH~ xN!#. (19)

9 The results of the analysis would therefore be unaffected if the due standard applied by the court is set atxN* rather than atxH. However, use ofxH greatly simplifies the model becausexH is independent ofL, whereasxN* is not. Moreover, there is no reason to believe that courts usexN* rather thanxH as the due standard of care.

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Note that the first two terms of this condition resemble the two terms in Eq. (9) and havethe same interpretation. Specifically, the term on the left-hand side of Eq. (19) is themarginal cost of a longer statute length in terms of increased litigation costs, while thefirst term on the right-hand side is the marginal deterrence benefits of an increased statutelength. As was true under strict liability, greater deterrence is socially desirable becausein equilibrium, negligence underdeters (as captured by the fact thatxN*(L) 2 xN(L) . 0).

What is different here compared to strict liability is the second term on the right-hand sideof Eq. (19), which is positive given that­w/­L , 0. This term captures an additionalmarginal benefit of increasing the statute length under negligence in the form of fewerlawsuits being filed ineach periodup to t 5 L. Intuitively, an increase inL lowers theprobability that any given injurer will be judged negligent (given that­w/­L , 0), therebymaking lawsuits less profitable for victims. Note that this effect was absent under strictliability because that rule did not require victims to prove negligence by injurers as acondition for recovery.

The extra marginal benefit term in Eq. (19) suggests that the optimal statute length shouldbe longer under negligence as compared to strict liability. This result cannot be establisheddefinitively because a comparison of the corresponding terms in Eq. (9) and Eq. (19) for anyL is ambiguous. However, if these common effects are roughly offsetting, one would expectthat the additional term in Eq. (19) would dominate, resulting in a longer statute length undernegligence.

5. Applications of the analysis

The foregoing analysis suggests that one might try to test the model by asking whetherthe statute of limitations is longer in areas of tort law governed by negligence ascompared to areas governed by strict liability. There are several problems in testing themodel in this way. First, statutes of limitations are costly to change and therefore mayrespond only sluggishly to changes in relative costs and benefits. Second, economictheory maintains that the legal rule is itself an endogenous variable that should respondto changes in some of the same variables that affect the statute of limitations (e.g.,litigation costs). Third, most torts are grouped under a single statute of limitations. Thus,for example, the shift in produces liability law from negligence toward strict liabilityduring the twentieth century may have had no effect on the general statute length forpersonal injury cases. Despite these problems, I offer some evidence that the statute oflimitations does in fact differ depending on whether a given area of the law is governedby strict liability or negligence. This evidence takes the form of variation in the rules thatdetermine when the statute begins to run.10

10 I thank a referee for suggesting the second and third applications in this section.

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Statutes of repose for products liability

As noted, one area of tort law that has shifted from negligence to strict liability is productsliability.11 In response to this change, many states enacted “statutes of repose” for productsliability suits (Peacock, 1993).12 In contrast to a statute of limitation, which begins to run at thetime an accident occurs, a statute of repose begins to run at the time the product in question wassold (Martin, 1982: p. 749). Thus, a statute of repose puts a predictable upper bound on the lengthof time that a manufacturer is at risk of suit from the sale of a particular product. A statute oflimitation alone provides no such bound because it allows suits for accidents that occur long aftersale as long as they are filed in a timely manner after the accident.

In the context of the model, it is easy to show that enactment of a statute of repose servesto reduce the expected number of suits that an injurer faces. In this sense, it is equivalent toa reduction inL. To see this formally, suppose that consumers purchase a dangerous productat timet 5 0, and it causes an accident at timet0 . 0, which varies across consumers basedon differences in use and random factors. Victims then file suit after a delay oft as describedin the above model (i.e., a victim of an accident at timet0 files at t0 1 t). Figure 1 showsall possible combinations oft0 and t, where each point represents a potential lawsuit.

In this amended model, the statute of limitations applies only to the delay in filing afteroccurrence of the accident. Thus, any suit witht # L is allowed to proceed, regardless oft0.Graphically, the statute of limitations permits all suits to the left ofL in Figure 1 (i.e., areas A andB). In contrast, a statute of repose of lengthR applies to the length of time following sale of theproduct, and therefore allows only those suits for whicht0 1 t # R. Thus, victims in area B ofFigure 1 will no longer be allowed to proceed, leaving area A as the set of products liability casesthat satisfy both the statute of limitations and the statute of repose.

What this argument shows is that adding a statute of repose on top of a statute oflimitations has the same effect as simply shortening the statute of limitations. Thus, theenactment of these statutes following the shift from negligence to strict liability for productsliability suits seems to be consistent with the predictions of the model.

The discovery rule for negligence

Historically, a cause of action under negligence law began to run at the time that an injuryactually occurred, or timet0 (the “damage rule”). Beginning in the area of medical mal-practice, however, courts and legislatures began to replace this with the “discovery rule,”under which “the statute does not begin to run until the negligent injury is, or should havebeen discovered.”13 This rule has now become the majority rule for negligence cases.

The impact of the discovery rule is clearly to lengthen the statute of limitations by starting

11 This evolution has been gradual, but Landes and Posner (1987: p. 307) roughly date the shift toHenningsenv. Bloomfield Motors, Inc., 32 N.J. 358, 161 A.2d 69 (1960).

12 Also see Martin (1982), who notes that as of 1982, as many as twenty-two states had enacted statutes ofrepose, ranging from six to fifteen years in length. Since then, however, many of these statutes have either beenrepealed or found unconstitutional (Warfel, 1991; Werber, 1995).

13 SeeTeeters v. Currey, 518 S.W.2d 512 (1974). Also see Keeton, et al. (1984: pp. 166-167).

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it at a later date relative to the time of the injury. It therefore works in the opposite directionof a statute of repose, which we saw above begins the statute prior to the time of the injury.(Indeed, Keeton, et al. (1984: pp. 166–167) observe that the enactment of statutes of reposewas in part a response to the widening use of the discovery rule.) In combination, therefore,these two rules work in the predicted direction of effectively lengthening the statute oflimitations for cases governed by negligence as compared to strict liability.

Trespass versus nuisance

The final application concerns the distinction between the torts of trespass and nuisance.Under trespass, the plaintiff is entitled to strictly enforce his or her right to exclusivepossession of a piece of property. In contrast, the plaintiff can only assert a claim undernuisance law if the harm is both substantial and unreasonable, where the latter is based ona balancing of “the gravity of the harm and the utility of the conduct” (Keeton, et al., 1984:p. 630). Thus, trespass is governed by strict liability and nuisance by a negligence standard(Landes and Posner, 1987: p. 49).

Fig. 1. The effect of a statute of repose.

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It follows from the theory that the statute of limitations should be shorter for trespass ascompared to nuisance, and this in fact appears to be the case. Specifically, under trespass, thestatute of limitations begins to run “from the time of unlawful entry”14 and “without regardto harm” (Keeton, et al., 1984: p. 70), whereas under nuisance, the statutory period does notbegin to run “until some injury has been sustained.”15 Once again, the law seems to conformto the predictions of the theory.

6. Conclusion

This paper has developed a formal model of statutes of limitations for tort suits based on thetrade-off between deterrence and litigation costs. While a longer statute enhances deterrence byconfronting injurers with more lawsuits, it increases litigation costs. The optimal statute lengthbalances these effects at the margin. A notable feature of the model is that, in contrast toconventional arguments in favor of statutes of limitations, it does not rely on arguments aboutstale evidence and legal error as a basis for imposing a finite statute length.16

A key prediction of the model is that the optimal statute length appears to be longer undera negligence rule as compared to a strict liability rule. The reason is that, when the statuteis lengthened, it increases incentives for care (deterrence), thereby making it harder forplaintiffs to prove negligence at trial. Thus, fewer cases are filed at any point in time, whichlowers expected litigation costs. Since this benefit partially offsets the extra litigation costsincurred by lengthening the statute, the optimal statute is longer.

The paper concluded by suggesting that this prediction is consistent with variations inactual statutes of limitations. We first argued that the enactment of statutes of repose in the1970s, which effectively shortened the statute of limitations for products liability suits, wasa response to the shift from negligence to strict products liability. We next argued thatadoption of the rule of discovery effectively lengthened the statute of limitations fornegligence suits by delaying the start of the statutory period until the plaintiff discovers (orshould have discovered) her injuries, rather than when she actually sustains them. Finally, weargued that the statute of limitations is longer for nuisance as compared to trespass actions,reflecting the reliance on negligence principles under the former and strict liability under thelatter.

Acknowledgment

I acknowledge the helpful comments of an anonymous referee.

14 See Am Jur 2d, Trespass, § 200 (1986).15 See Am Jur 2d, Nuisance, § 308 (1986).16 Though these factors are not inconsistent with the model, their omission makes it more parsimonious.

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Quarterly, 64,667–722.Hylton, K. (1990). The Influence of litigation costs on deterrence under strict liability and under negligence.

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Publishing Co.Landes, W. & Posner, R. (1987).The Economic Structure of Tort Law, Cambridge, MA: Harvard Univ. Press.Martin, M. (1982). A statute of repose for product liability claims.Fordham Law Review, 50,745–780.Ordover, J. (1978). Costly litigation in a model of single activity accidents.Journal of Legal Studies, 7,243–261.Peacock, M. (1993). An equitable approach to products liability statutes of repose.Northern Illinois Univ. Law

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Liability, 8, 79–87.Warfel, W. (1991). Tolling of statutes of limitations in long-tail product liability litigation: the transformation of

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