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 nave 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 25-year annuity that would amount to much more than $10,000 each year. This criticism of the nave 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 nave method, and much more acceptable to the defendant. Critics of the nave 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 double-digit 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 nave 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 Dt 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 nave 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 life-cycle pattern of labour productivity, differences in risk, and distinctions between long-run and short-run 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 qt 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 under-compensated.

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 offset-rule 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 short-run arguments, for in the long-run, 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 short-term interest rates (as did Brody); an alternative was for them to use the interest rates of longer-term 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 economy-wide averages. Just as it is inadvisable not to discount (or multiply, for that matter) an award at all, despite the Carter-Palmer results, it is equally inadvisable to discount all awards by 1.5% or 2.5% per year or to use some other economy-wide 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 economy-wide 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)


Bibliography

 

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Brody, M.T. 1982. Inflation, productivity, and the total offset method of calculating damages for lost future earnings. University of Chicago Law Review 49: 1002-36.

 

Carter, R.A.L. and J.P.Palmer 1991. Real rates, expected rates, and damage awards. Journal of Legal Studies 20:439-62.

 

Carter, R.A.L. and J.P.Palmer 1994. Simple calculations to reduce litigation costs in personal injury cases: additional support for the offset rule. Osgoode Hall Law Journal 32:197-223.

 


Carter, R.A.L. and J.P.Palmer 1995. The offset rule: some multinational evidence. Unpublished paper presented at the 8th annual Law and Economics Workshop, Maastricht.

 

Fisher, I. 1896. Appreciation and interest. Publications of the American Economic Association (3d) 2:341 - 368.

 

LaCroix, S.J. and H.L.Miller 1986. Lost earnings calculations and tort law: reflections on the Pfeiffer decision. University of Hawaii Law Review 8: 31-40.

 

Mishkin, F.S. 1981. The real interest rate: an empirical investigation. In The Cost and Consequences of Inflation, ed. K. Brunner and A. H. Meltzer, Carnegie-Rochester Series on Public Policy, 15: 151 - 183.

 

Mishkin, F.S. 1984. The real interest rate: a multi-country empirical study. Canadian Journal of Economics 17:283 - 299.

 

Pelaez, R.F. 1995. Calculating awards for lost earnings: an empirical assessment of Beaulieu. Journal of Legal Economics 5(1):49 - 62.


Posner, R.A. 1977. Economic Analysis of Law. 2nd edn. Boston: Little Brown & Co; 4th edn, 1992.

 

Shiller, R.J. 1979. The volatility of long-term interest rates and expectations models of the term structure. Journal of Political Economy 87:1190 - 1222.

Shiller, R.J. 1981. Alternative tests of rational expectations models. Journal of Econometrics 16:71 - 94.

 

Shiller, R.J., J.Y. Campbell and K.L. Schoenholtz 1983. Forward rates and future policy: interpreting the term structure of the interest rates. Brookings P