The Total Offset
Rule in Damage Awards
The total offset
rule, or offset rule, as it is sometimes called, is based on the assumption
that expected wage rate growth will on average equal the nominal rate of
interest. This assumption allows a simplified calculation of damage awards,
particularly for personal injury and wrongful death cases. The offset rule
reduces the need for the courts to hear testimony concerning expected rates of
inflation, real rates of interest, growth in labour productivity, and expected
wage inflation. Simply put, if the assumptions of the offset rule are
applicable, then a loss of $10,000 per year expected to last for 25 years would
be appropriately compensated with $250,000; there would be no need for
discounting or other calculations to take interest rates or growth rates into
account.
These implications
of the offset rule have met with considerable resistance from many directions,
despite considerable empirical support for its underlying assumptions.
Nevertheless, courts are increasingly paying attention to the arguments of the
offset rule.
The basic argument
of the offset rule goes as follows: Suppose a tort victim is injured, suffering
personal injury losses of $10,000 this year. Suppose further that the court
finds these damages are reasonably expected to last for 25 years. At this
point, most people would think it unreasonably naïve to award the plaintiff $250,000.
Instead, they would argue, the courts should take into account the fact that
the plaintiff could invest the damage award at some interest rate, say 8%, and
thus purchase a 25year annuity that would amount to much more than $10,000
each year. This criticism of the naïve approach argues that the present
discounted value of $10,000 per year for 25 years should be calculated using a
reasonable interest rate, and it is this present value which should be awarded
to the plaintiff. At an interest rate of 8%, this present value would amount to
approximately $107,000, considerably less than the amount calculated with the
naïve method, and much more acceptable to the defendant. Critics of the naïve
approach point out that if the plaintiff were awarded this sum of approximately
$107,000, he or she could invest that amount at an interest rate of 8%, and
draw annual payments of precisely the amount of the loss, $10,000 per year for
25 years, from the interest and the principal, leaving a balance of zero at the
end of the 25 years.
While this approach
to damage awards was common during periods of low inflation rates, though
likely inappropriately so, as will become clear later, simple discounting of
awards became clearly inconsistent with most compensation goals when
comparatively high inflation rates occurred during the 1970s. It became clear
to even the most innumerate of courts that $10,000 received 25 years from now
would not have anywhere near as much purchasing power as $10,000 received today.
Put differently, an annual loss of $10,000 today would likely require a much
larger annual compensation in the future to take into account expected
inflation.
At this point,
historically, the courts began to hear considerable testimony about how to
compensate victims for lost purchasing power due to inflation. Economists
presented various forms of the Fisher (1896) equation, which states that the
nominal, or face value, interest rate is equal to the real rate of interest
plus the expected rate of inflation. Here, the real rate of interest is defined
to equal the nominal rate of interest that would prevail when general
expectations are that the rate of inflation will be zero. Algebraically, this
relationship is written:

(1)
where i is the
nominal rate of interest, r is the real rate of interest, and E(%ΔP)
is the expected rate of inflation.
With nominal
interest rates in the 1970s and 1980s soaring to over 15% in many jurisdictions
and over 20% in some, and with people expecting doubledigit inflation, early
court cases that tried to take inflation into account involved a considerable
amount of testimony concerning both nominal interest rates and expected rates
of inflation. This testimony and the use of the Fisher equation were
necessitated by the courts= desires to make
sure that victims would not be under compensated for their losses by the use of
too high an interest rate.
Unfortunately these
early attempts to take account of inflation had serious drawbacks. In some
cases, the testimony led the courts to apply real interest rates of four or
five percent, which in retrospect, seem much too high, to the detriment of the
plaintiffs (see, for example, Andrews v. Grand & Toy, 1978). In
other cases, the testimony and disagreements seemed to do more to enrich the
economists testifying than to assist the courts, with large awards at stake but
no clear guidance emerging for future cases. The continued wrangling in the
courts even led one to write: Athe average
accident trial should not be converted into a graduate seminar on economic
forecasting (Doca v. Marina Mercante Nicaraguense, SA, 1980, 1981).@ In some jurisdictions, such as Ontario, Nova Scotia,
and British Columbia, in Canada, the frustration with the wide range of
interest rates used by the courts became so serious that the legislatures codified the real rate of
interest, instructing courts to use a 2.5% interest rate to discount plaintiffs= awards. Australia set the real rate of interest at 3%
for the purposes of calculating personal injury awards.
The assumptions
underlying the offset rule imply that there is a more direct method of
calculating the losses suffered by victims; these assumptions also imply that
by setting the real interest rate at 2.5%, the legislatures have probably made
a mistake which biases awards downward.
The simple algebra
of the offset rule. This section develops the basic equation of the offset
rule. Later sections provide its history and a discussion of the problems and
exceptions with the rule. Finally, a summary of recent empirical tests of the
underlying assumptions is presented.
Assume that a plaintiff
has suffered a loss in the amount of $D and expects to suffer
this loss each year for the next N years. The naïve approach
would grant the plaintiff an award of
(2) A = N
x D.
The traditional, discounting
approach would discount the award as follows:

(3)
where D_{t} is the annual
amount of the damages, expected to remain constant in real terms for each year,
t. If the nominal rate of interest is represented by i,
then this approach can also be written as

(4)
As we have seen,
however, the nominal rate of interest can be broken down into the real rate of
interest and the expected rate of inflation. While the Fisher equation
presented in equation (1) is a good approximation to the correct relationship
between expected inflation rates and interest rates, the correct relationship
is multiplicative and should be incorporated as follows:

(5)
where r is the
real rate of interest, and f is the expected rate of inflation.
Typically, the courts tried to determine the real interest rate, r,
for determining the award, attempting to discount the awards only by (1+r)
instead of by (1+i) = (1+r)(1+f).
The major problem
with determining a plaintiff=s award according
to equation (5) is that doing so does not take into account the likelihood that
the plaintiff=s loss, D, would grow over time.
Particularly in cases involving the loss of wages, the plaintiff could
reasonably have expected the loss to grow due to wage inflation, w,
and due to growth in the productivity of labour, g. Taking these
additional influences into account yields an expression for the damage award of

(6)
where D
represents the loss in the first year.
Equation (6) allows
a direct demonstration of the offset rule. If the expected rate of wage
inflation, w, is equal to the expected rate of price inflation, f,
and if the rate of growth of labour productivity is equal to the real rate of
interest, then all the terms after the summation sign in equation (6) cancel
out, leaving the addition of one, N times, which is N. Hence, under these
assumptions, the correct award would be given by equation (2), A = N
x D, precisely the same result as that yielded by the extremely
naïve approach. Of course having w equal f, and g
equal r, is a sufficient condition for reducing equation (6) to A
= N x D, but not a necessary condition. An even weaker
sufficient condition is simply that the numerator equal the denominator.
The offset rule
received early exposition in Posner (1977) in his textbook on the economic
analysis of law. An early use of the principles of the offset rule appeared in Beaulieu
v. Elliot (1967). The rule reached a much more complete statement in O=Shea v. Riverway Towing Co. (1982). Early
empirical tests of the offset rule=s assumptions were
conducted by Brody (1982) and by Anderson and Roberts (1985).
Extensions and
revisions of the offset rule. In its simplest form, as presented in equation (6),
the offset rule leaves much to be desired. It doesn=t
take into account the possibility that expected interest rates or inflation
rates might vary from year to year; nor does it incorporate information about
the lifecycle pattern of labour productivity, differences in risk, and
distinctions between longrun and shortrun interest rates. In general,
however, the offset rule can be expanded and revised to account for these
problems.
Variable expected
interest rates and inflation rates are the easiest to incorporate into the
offset rule. Letting each of g, w, r, and f take on different values in each of the
N time periods, the award becomes

(7)
In this version of
the offset rule, once again, it is a sufficient condition that the numerator
equal the denominator; even more generally, especially if T is
large, differences between the numerator and the denominator in one time period
might even conceivably be offset by differences in the opposite direction in
other time periods. And certainly, if it can be shown that (1+g)(1+w) =
(1+r)(1+f) for each time period, then equation (7) will readily
simplify to the simple expression of equation (2).
It is a relatively
simple step to expand equation (7) to include the changes in productivity over
the life cycle, F(t), to adjust for changes in life expectancy, X(t),
and to incorporate potential changes in the expected employment of the plaintiff,
G(t). Including these variables in the equation yields

(8)
which, if the assumptions of
the offset rule hold, reduces to

(9)
Equation (9) does
not reduce nicely to equation (2), and so the offset rule in its simplest form
will not necessarily take account of these variables that require the
personalizing of awards. Nevertheless, the assumptions of the offset rule, if
empirically verified, do allow the courts to dispense with testimony about
interest rates and expected inflation and growth rates.
Posner (1992) has
suggested that one possible drawback to the offset rule is that it treats
labour income and the income from financial capital as having the same risk
premia. If, on the one hand, the rate of return on financial capital is less
risky than the expected growth in labour income, then the offset rule would
tend to overcompensate the plaintiff by granting damages that will earn a less
risky return than would the human capital of the plaintiff. If, however, due to
uncertainties about global monetary policies and expected rates of inflation,
the rate of return on financial capital is more risky than the return to
human capital, then the offset rule would systematically under compensate the
plaintiff. Which rate of return is more risky is clearly an empirical question
for the courts to answer; however, it has been demonstrated (see Carter and
Palmer, 1991) that differential rates of return can also be dealt with by
extending the offset rule to

(10)
where q_{t} represents an
annually variable risk adjustment to account for the differences in risk
between human and financial capital. Once again, as can be seen from equation
(10), application of the offset rule requires no information concerning the
rate of inflation, the rate of interest, or rates of growth in labour
productivity.
Empirical Results. One of the first
empirical tests of the underlying assumptions of the offset rule was conducted
by Brody (1982) who used US data on interest rates and the growth in labour
earnings to simulate the dollar value of an annuity that a plaintiff could
receive if the initial award had been calculated following equation (2), A
= N H D. His simulation
revealed that the offset rule, as described in Beaulieu v. Elliot (1967)
yielded the desired results: the plaintiff would be neither over nor
undercompensated.
This result created
considerable consternation among personal injury lawyers and consulting
economists because they had typically been discounting plaintiffs= awards by a net discount rate of between 1.5% and
2.5%. The standard had been to assume that the real rate of interest was higher
than the expected rate of growth in labour productivity, while the rates of
price and wage inflation did indeed offset each other. Brody=s results challenged this tradition, and, needless to
say, did not go unquestioned.
Early criticisms of
empirical tests of the offsetrule assumptions focused on the data. For
example, La Croix and Miller (1986) pointed out that if Brody had begun his
simulations in a year other than 1960, or if he had used a different interest
rate series, he would have obtained different results, not necessarily
consistent with the assumptions of the offset rule.
Other criticisms
argued that there is no compelling reason to believe that labour productivity
will grow by the same, constant amount in every occupation throughout the
economy. Productivity, it was argued, did not change at all in some
occupations, while it changed tremendously in others. This criticism hinged on
shortrun arguments, for in the longrun, labour and occupational mobility
would equalize wage rates for equivalent skill levels, regardless of the
different apparent rates of growth of labour productivity in different occupations.
Furthermore, empirical work by Anderson and Roberts (1985) provided additional
support for the offset rule by showing similar patterns of wage growth across
broadly defined occupational categories.
These early
studies, however, did not provide sophisticated tests of the underlying
assumptions of the offset rule, namely that (1+g)(1+w) = (1+r)(1+f) .
The first of these tests appeared in Carter and Palmer (1991), with
multinational confirmations of their results appearing in their later work
(1994, 1995).
One of the keys to
the success of the work by Carter and Palmer was their use of the holding
period rate of return as a measure of nominal interest rates in each time
period. Following the work of Mishkin (1981, 1984), they argued, using a
rational expectations model, that the important interest rate variable in
determining the correct damage award must have a maturity that matches the time
period for which the data were collected.
Satisfying this criterion meant that they would be limited to using only
shortterm interest rates (as did Brody); an alternative was for them to use
the interest rates of longerterm securities but to calculate the shorter term,
holding period rates of return for these securities (see Shiller, 1979, 1981,
and 1983). Doing so allowed them to match the maturity of the security with the
relevant time period for the data. It also allowed them to examine the
criticism of Brody=s work that his results
depended on which term of security was used to determine the size of the award.
With this
adjustment to the data, and using more precise econometric techniques, Carter
and Palmer found that the underlying assumptions of the offset rule were
consistent with the data from the US (1991), Canada (1994), and Australia,
Belgium, Denmark, Germany, and Spain (1995). In no instance did they observe
data inconsistent with the assumptions of the offset rule.
These results are
important. They tell us that the traditional approaches to calculating damage
awards by using a net (assumed to be real) interest rate of between 1.5% and
2.5% will consistently and significantly underestimate the award relative to
what it should be to provide full compensation.
But despite the
importance and the simplicity of these results, they provide only a starting
point for calculating plaintiff=s damages. It would
likely be incorrect to apply these results holus bolus to all personal injury
cases. First, the results hold on average, only with tests over fairly long
time periods. They would not likely hold for shorter time periods than five
years. Second, the results hold only on average. They may not hold for any
single particular person, occupation, industry, or loss. This latter criticism
of the offset rule is perhaps best made in the paper and presentation by
Vellrath (1989). An empirical form of this criticism appears in Pelaez
(1995). In other words, while the basic
assumptions of the offset rule may hold in general and on average, they do not
necessarily apply to any particular personal injury case.
This lack of
specific applicability has been taken by some as grounds for complete rejection
of the offset rule. In a vague, general sense, they are correct. However, the
same criticism can be made of any rules that are based on economywide
averages. Just as it is inadvisable not to discount (or multiply, for that
matter) an award at all, despite the CarterPalmer results, it is equally
inadvisable to discount all awards by 1.5% or 2.5% per year or to use some other
economywide rule of thumb. Instead the courts should normally be expected to
take personal circumstances into account.
The implications of
the research on the offset rule are, nevertheless, strong and important. They
are that the economywide variables such as the nominal rate of interest, the
real rate of interest, the expected rates of price and wage inflation, and the
expected rate of growth of labour productivity, should not be necessary in the
calculation of plaintiffs= damage awards.
Instead, because the offset rule should hold on average, it is reasonable to
use it as a starting point before personalizing an award. And it is certainly
more reasonable to use the offset rule than any other rule as a starting point.
List of cases:
Andrews v. Grand &
Toy Alberta Ltd., [1978] 2 S.C.R. 229
Beaulieu v. Elliot
434 P.2d 665 (Alaska 1967)
Doca v. Marina Mercante
Nicaraguense, S.A. 634 F2d 30, 39 (2d Cir. 1980), cert. denied, 451 US 971
(1981)
O=Shea v. Riverway Towing Co 6777 F2d 1194 (7th Cir
1982)
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