optimal statute of limitations for a strict liability rule, and Section 4 repeats the analysis for a negligence rule. Section 5 then offers some informal evidence in support of the theory
based on the enactment of statutes of repose for products liability cases, the emergence of the rule of discovery under negligence law, and differences in the statute of limitations for
trespass 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 both risk-neutral, and injurers alone can take care to reduce the likelihood of an accident i.e., the
model is one of unilateral care. For simplicity, the injurer’s care choice is dichotomous: either take care or no care. Let q be the probability of an accident if the injurer takes care,
and p be the probability if he does not, where p . q . 0.
The cost of care for injurers is denoted x, which varies across the population of injurers according to the distribution function Hx. Injurers know their own cost of care, but victims
do 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 the
court can observe whether or not an injurer took care as well as the injurer’s cost of care for purposes of applying a negligence rule if a case goes to trial.
Victims vary in their fixed damages in the event of an accident, denoted D. The distribution function of victims’ damages is FD. At the time they make their care choice,
injurers do not know the damage that an individual victim will suffer, but they know the distribution of victim damages. However, the court can observe D after the fact when
determining a damage award.
When an accident occurs, if the victim files suit, she incurs litigation costs of c
v
while the injurer incurs litigation costs of c
i
. In Hylton’s 1990 static model, all victims who find a suit
profitable file immediately. Here I allow the possibility that some victims will delay filing suit. For example, some injuries might not be immediately evident or some injurers might
avoid immediate detection or identification. To keep the model simple, I abstract from the specific reason for delay and simply treat the length of time after an accident that a victim
files suit, denoted t, as a random variable with distribution function Gt. Thus, for example, if the statute of limitations is set at L, then GL is the probability that a randomly chosen
victim will file suit by time L.
2
3. Strict liability
Under strict liability, all victims for whom D c
v
and t L will file suit. Thus, if an accident occurs, the probability of a lawsuit is gt[1 2 Fc
v
] at any t up to L where
2
Alternatively, GL can be interpreted as the number of suits filed by L. I assume that t is independent of the victim’s damages, D.
384 T.J. Miceli International Review of Law and Economics 20 2000 383–394
gt [ G9t , and zero thereafter. If a suit is filed, the injurer faces liability equal to the
damage suffered by the victim, D. For suits filed in the future t . 0, this amount should be discounted to the present the date when the injurer makes his care choice by the interest rate
r , yielding a present value of liability equal to De
2rt
for a suit filed at time t. I assume, however, that the court awards the victim interest on D at rate r, beginning at the accident
date t 5 0,
3
thereby exactly offsetting the injurer’s discounting. Thus, regardless of the date when a case is filed, the injurer bears expected liability of D as of t 5 0. In the absence of
this “prejudgment” interest, the injurer’s incentives would clearly be diluted merely by the victim’s delay in filing.
4
The same is not true of the injurer’s litigation costs. Specifically, a case filed at time t costs the injurer c
i
e
2rt
in present value terms. Thus, the injurer does gain from delay in this respect.
Given the above factors, the injurer’s expected costs of taking care under a rule of strict liability with a statute of limitations of L are given by
x 1 qG~L
E
c
v
`
DdF~D 1 1 2 F~c
v
E
L
c
i
e
2rt
g~tdt .
1 Similarly, the expected costs of not taking care are
pG~L
E
c
v
`
DdF~D 1 1 2 F~c
v
E
L
c
i
e
2rt
g~tdt .
2 Combining Eq. 1 and Eq. 2 yields the condition for the injurer to take care:
x ~ p 2 qG~L
E
c
v
`
DdF~D 1 1 2 F~c
v
E
L
c
i
e
2rt
g~tdt ; x
s
~L. 3
The right-hand side represents the highest cost injurer who chooses to take care under strict liability as a function of L. Taking the derivative of Eq. 3 with respect to L yields [Eq. 4]
x
s
L
5 ~ p 2 q g~L
E
c
v
`
~D 1 c
i
e
2rL
dF~D . 0. 4
Thus, increasing the statute of limitations increases the number of injurers who choose to take care, by increasing both expected liability and the present value of litigation costs. This
captures 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 no
care. 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 date
when a settlement is first offered. 385
T.J. Miceli International Review of Law and Economics 20 2000 383–394
x 1 qE~D 1 1 2 F~c
v
E
L
~c
i
1 c
v
e
2rt
g~tdt .
5 This differs from Eq. 1 in two respects: the inclusion of damages suffered by victims who
do not file suit, and the inclusion of the present value of the litigation costs of victims who do file. The social cost of not taking care are
pE~D 1 1 2 F~c
v
E
L
~c
i
1 c
v
e
2rt
g~tdt ,
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 qE~D 1
1 2 F~c
v
E
L
~c
i
1 c
v
e
2rt
g~tdt ; x
s
~L. 7
The right-hand side of Eq. 7 represents the highest cost injurer for whom it is socially desirable to take care under strict liability. Comparing Eq. 3 and Eq. 7 shows that x
s
L . x
s
L for any L, implying that strict liability underdeters Hylton, 1990. This is true because, as noted above, injurers ignore the damages imposed on victims who do not file suit
i.e., those with D , c
v
, 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 given by Eq. 5 weighted by the number of injurers who take care, H x
s
L, plus Eq. 6 weighted by the number of injurers who do not take care, 1 2 H x
s
L. The resulting expression, after rearranging, is given by
SC
s
~L 5 pE~D 1 1 2 F~c
v
E
L
~c
i
1 c
v
e
2rt
g~tdt 2 H~ x
s
~L~ p 2 q
3 E~D 1 1 2 F~c
v
E
L
~c
i
1 c
v
e
2rt
g~tdt 1 x
s
~L xdH~ x. 8
The optimal statute of limitations is found by minimizing Eq. 8. The first-order condi- tion, after rearranging, is given by
5
1 2 F~c
v
e
2rL
~c
i
1 c
v
g~L p~1 2 H~ x
s
1 qH~ x
s
5
S
x
s
L
D
h~ x
s
x
s
~L 2 x
s
~L. 9
5
I assume here and below that the second-order condition for a minimum issatisfied. 386
T.J. Miceli International Review of Law and Economics 20 2000 383–394
The left-hand side of Eq. 9 represents the marginal cost of an increase in L. It captures the increase in the present value of expected litigation costs when L is increased by one period,
where p1 2 H x
s
1 qH x
s
is the probability of an accident, and [1 2 Fc
v
] gL is the number of new cases filed in the event of an accident. The right-hand side captures the
marginal benefit of an increase in L in terms of increased deterrence. The term x
s
L represents the increase in the threshold for care when L is raised, which is weighted by h x
s
, the fraction of injurers with cost of care equal to x
s
. The bracketed term represents the net savings in social costs when one more injurer takes care, where this term is positive due to
the general underdeterrence under strict liability. According to Eq. 9, the optimal statute length balances the increased litigation costs from a longer statute against the increased
deterrence benefits.
4. Negligence
