The Development of an actuarial approach to calculate damages for loss of future earnings

Abstract

1. Introduction

Personal injury and fatal accident may arise as a result of various accidents such as motor vehicle accidents, accidents at work, acts or omissions of another person, defective products and industrial disease cases. In Malaysia, more than half of the litigation works handled by lawyers arise out of motor vehicle accidents commonly called running down cases (Ramasamy, 2000).

In the case of a personal injury or fatal accident results from the negligent acts or omissions of another responsible party, the injured party may be entitled to fair and appropriate compensation for the injuries suffered by having the court award of damages. Generally, there are two major categories of damages awarded in personal injury and fatal accident claims—compensatory and punitive. Court awards for compensatory damages provide a plaintiff a sum of money which will restore the individual to the status quo ante—as nearly as possible to the original position, at least financially. Compensatory damages are divided further into special and general damages.

Special damages refer to pre-trial economic losses that the plaintiff has incurred from the date of the accident occurred to the date of trial. Various pre-trial economic losses under special damages which are claimable as a result of the negligent act of another include medical expenses, cost of repairs to motor vehicle and pre-trial loss of earnings. Special damages need documentary proof and must be pleaded and proved.

General damages represent post-trial economic losses and non-economic losses. In Malaysia, general damages for personal injuries and fatal accident claims are assessed under four categories or heads: post-trial economic losses include, (I) loss of future earnings, (II) loss of earning capacity and (III) future care expenses; and non-economic losses associated with (IV) pain and suffering and loss of amenity. Post-trial economic losses can be estimated, but non-economic losses are generally viewed as subjective and the amount of such damages differs from case-to-case basis.

According to Balan (2004), the category or head that needs critical examination and reform is the category concerning loss of future earnings. Therefore, this article focuses only on the actuarial approach to model loss of future earnings in general damages (post-trial economic loss) that are far more complicated to assess. Calculating pre-trial loss of earnings under special damages is relatively easy to estimate and may be calculated precisely—which is the amount of the actual loss. Non-economic losses are subject to individual circumstances and should be undoubtedly at the judicial discretion of the courts, and as such are not the subject of this study. Punitive damages or what is usually termed as exemplary damages will also not be considered in this article.

2. Actuarial assessment of damages: international comparison

In the USA, when it comes to personal injury and fatal accident litigation, actuaries are usually needed to provide forensic economic analysis and various financial calculations to assist lawyers with their cases. In a court case involving personal injury and fatal accident claims where calculations of future loss of earnings over the duration of the working life of the plaintiff are necessary, an actuary will be required to give expert testimony to assist the court in the quantification of the amount of compensatory damages. The concept of human life value, which is a concept developed by Huebner (1927) is most often used in court cases involving personal injury and fatal accidents claims when determining damages. In fact, this was the method the United States Department of Justice used to determine benefits for the September 11 Victims Compensation Fund to beneficiaries of those killed in the terrorist attacks.

In the UK, actuaries have long been involved in advising lawyers who are representing the plaintiff or defendant in personal injury and fatal accident litigation in assessing damages. The role of actuaries also has long been valued by the courts through membership of the interdisciplinary working party of actuaries, lawyers and accountants that prepares the Ogden Tables, named after Sir Michael Ogden (Government Actuary’s Department, 1984). The Ogden Tables or the Actuarial Tables with Explanatory Notes for Use in Personal Injury and Fatal Accident Cases issued from time to time by the Government Actuary’s Department, provide figures in terms of years (multipliers) to assist in calculating the appropriate period of loss. The multiplicand (the plaintiff’s net annual loss in the case of losses; or annual cost in the case of expenses, as at the date of trial) is then multiplied by the multiplier found in the relevant table to produce the present value of the future loss of earnings. Judges in the UK were not required to use the Ogden Tables in calculating damages until year 1999, where in the case of Wells v. Wells,¹ the House of Lords approved actuarial technique as the primary method of calculating future losses and made it compulsory to utilize the Ogden Tables when assessing an award of damages. The use of Ogden Tables has undoubtedly improved the transparency and consistency of the calculation of awards (Wass and McNabb, 2009).

In Malaysia, the Civil Law Act 1956 (CLA 1956) is the primary legislative provisions which deals with all civil litigation involving personal injury and fatal accident claims. The amendments to CLA 1956 made by the Amendment Act No. 602 came into force on 1 October 1984. It amended section 7 which governs the assessment of damages for loss of dependency; section 8 deals with claims by deceased’s estate and introducing a new section 28A which governs claims for personal injuries. Prior to these amendments, the law for loss of dependency and personal injury claims was largely governed by the common law principles based on English law and judicial precedents.

The current practice of courts in Malaysia in the determination of compensation awards uses the conventional multiplier–multiplicand approach without admitting any actuarial evidence. There are some issues, obviously arising when using the conventional approach in choosing multipliers. In almost all cases the determination of the multiplier can be described as arbitrary (Tan, 1998). For instance, the courts do not incorporate mortality rates which are omitted in the prevailing use of the multiplier–multiplicand approach. Also the courts do not make explicit any allowance for the income taxation in the calculations of the plaintiff’s future loss of earnings and prospective increase in income, e.g. by job promotion, is ignored. Another issue of current practice is that the award of interest for damages is discretionary. Section 11 of the CLA 1956 makes provision about powers of courts to award interest on damages. This will lead to inconsistency in the court’s choice of interest rate. Therefore, a proper choice of interest rate that is used for discounting should be determined. It is significant that even in the UK, which now adopts the actuarial approach, the interest rate is fixed by the Lord Chancellor at 2.5%.

In some Asian countries, for instance in Hong Kong, the Hong Kong version of the Ogden Tables have been constructed—Personal Injury Tables Hong Kong by Chan et al. (2013) which were first published by Sweet and Maxwell in 2003. These actuarial tables, also known as the Chan Tables, have now been recognized by the Hong Kong courts, as in the case of Yuen Hiu Tung v. Hospital Authority,² the court acknowledged an actuarial approach in assessing damages.

I agree that the Chan Tables should be accepted as the starting point in Hong Kong, just as the Ogden Tables are accepted as the starting point in the UK. In future, there should be less need to refer to previous case law of multiplier precedents, particularly if those cases were decided without reference to actuarial tables by way of a cross-check.

Another version of Ogden Tables which have been constructed in Singapore is the Personal Injury Tables Singapore 2015: Tables for the Calculation of Damages by Chan et al. (2014).

3. Research objectives

In Malaysia, there is no scientific method in calculating the award of damages in personal injury and fatal accident claims. Current practice shows that courts use the conventional multiplicand–multiplier approach in the quantification of the amount of compensatory damages.

As was mentioned above in Section 2, the obvious drawback of using the current method of multiplier is that there is no actuarial evidence in support of the method. Although there was a marked reluctance on the part of Malaysian courts to accept actuarial assessment dealing with personal injury and fatal accident cases, for instance in the case of P.S. Lum v. H.H. Lim;³ we should quickly move forward to adopt actuarial methods in assessing damages. Otherwise, Malaysia will continue to lag behind compared to other countries which are far ahead of us, that have long been using actuarial methods in assessing damages for personal injury and fatal accident claims.

Therefore, this article attempts to develop actuarial models using the concept of human life value that can be used as a guide to determine the amount of loss of future earnings in general damages (post-trial economic loss). We believe this is where actuaries and actuarial scientists need to play a role in developing a new scientific model in assessing damages in personal injury and fatal accident claims in Malaysia, which is relevant and satisfy both plaintiff and defendant. Unlike the Hong Kong’s Chan Tables and the Singapore version of the tables—both adopted the methodology used in constructing the Ogden Tables in the context of local circumstances; this article provides a standard formula which is more flexible to use.

4. Modelling of loss of future earnings

The principle of compensation for loss of future earnings is to measure damages and restore the victim nearly as possible to their pre-injury financial position, which is the position they would have been in if the negligent acts had not been committed. This article uses the same principle, but also to consider other important factors such as personal income taxes that the plaintiff would have been required to pay and the amount that would have been used for personal consumption expenditures (only in the case of fatal accident claims).

In the USA, for instance in Norfolk and Western Railway Company v. Liepelt,⁴ the Supreme Court ruled that the loss of earnings should be computed after deduction for amounts that would have been paid as income taxes rather than gross income before taxes. Similarly, in the UK, following the decision of the House of Lords in British Transport Commission v. Gouley,⁵ damages for loss of future earnings in personal injury should be net of tax—setting a legal precedent known as the ‘Gourley Principle’ that remains important in English law. The Court of Appeal confirmed that the same principle applied in fatal accidents cases, for instance in Parsons v. BNM Laboratories,⁶ whereby damages must be reduced by an amount equal to the taxes that the plaintiff would have been payable on the earnings.

Another important factor needs to be considered is personal consumption expenditures. In personal injury cases, the plaintiff’s personal consumption expenditures do not need to be estimated because the plaintiff is still alive and continues to require expenses such as food, clothing, health expenses and housing. However, for fatal accident cases, the decedent’s personal consumption expenditures need to be estimated and then to deduct from the future earnings. These are the expenses that a deceased person would have spent over the period of time that the earnings were received.

As was already mentioned in the research objectives, this article uses the concept of human life value—a concept in life insurance, to model loss of future earnings. The concept of human life value can be defined quantitatively as the present value of future earnings after deducting expenditures and income taxes over the estimated working life (Leimberg and Doyle, 2006). Therefore, the methodology to develop the loss of future earnings model in this article uses, with some modifications, the previously developed actuarial models—a revision method of human life value by Hasim and Service (2013). The modifications are in the terms of bringing the life insurance industry’s consideration of human life value concept in estimating the amount of life insurance a person need, to actuarial models that can be used to determine the amount of loss of future earnings in court cases.

4.1 Modelling of income

The first step in developing the loss of future earnings model began with a projection of income for each year over the remaining years of working life and income after retirement such as retirement benefits. The model also considers the mortality risk that allows discount to be made for the risk of a premature death. We use the life annuity method where it calculates the probability of each future income by reference to the probability of survival in each remaining year of working life. An actuarial notation, $tPx$ is used which means the probability that a person age x survives to at least age x + t.

In estimating income of a person in the context of Malaysia, we need to consider other important factors such as the Employees Provident Fund (EPF) and the Social Security Organisation (SOCSO) contributions. The EPF is the only scheme to provide retirement benefits for all employees and it is compulsory for all Malaysian employees to contribute towards this fund. Therefore, the salary, denoted by S, is subject to a certain percentage set by the EPF as a statutory contribution rate. The accumulated amount of contributions from both employee and employer, with compounded dividends—we name it as the projected EPF Savings—can be withdrawn upon retirement. Besides that, a person employed under a contract of service and earns a monthly income of RM2000 and below must compulsorily contribute to SOCSO. The employee’s SOCSO contribution is deducted as a percentage of salary.

4.1.1 ‘Loss of Chance’ in the modelling of income

The modelling of the loss of future earnings brings with it considerable uncertainty. In some cases the calculation of loss of future earnings is further complicated where it is the plaintiff’s contention that they would have followed a particularly progressive and lucrative career path if the accident had not happened. The ‘loss of chance’ doctrine acknowledges the hypothetical financial outcome that may have been foregone.

The total income of a person age x + t, denoted by I_x+t as in equation (1), can be regarded as the ‘baseline’ for the loss of total income. If there is a possibility of a career path that allows high income potential in the future, this will be considered on a loss of chance principle, providing that the claim must be sufficiently substantive rather than being merely speculative. The case of Dixon v. Were⁷ is a good example of a claim in which the loss of chance of higher income was considered to be too speculative.

In order to establish the loss of chance calculations, the probability of a number of possible paths, which the plaintiff’s career could potentially have progressed, is estimated. One of the leading cases which sets out the approach to the loss of chance calculation is Langford v. Hebran⁸—a world champion kick boxer who adduced factual evidence as to how his career would have progressed, had he not been injured. In this case, four possible outcomes were put forward based on escalating success in his fighting career. Another court case which requires estimating the probabilities of having been promoted over time is Brown v. Ministry of Defence.⁹ This case worked out the percentage chances of reaching a certain level of career advancement, and various lengths of service and ranks. However, the statistical method of valuing probability in the loss of chance claims is beyond the scope of this article. Pan and Gastwirth (2013) and Miller (2005) provide some probability models in loss of chance claims.

In estimating income of a person in the context of loss of chance claims, we use the method of expected value or weighted average as in King (1981). Expected value is the chance of something occurring in the future given various possible outcomes. Probabilities are assigned to the various outcomes. This method then computes a weighted average of all possible outcomes based on the probability of its occurrence.

Subsequently, the present value of the expected total income can be derived as in equations (5) and (6).

4.2 Modelling of income taxes

4.3 Modelling of personal consumption expenditures for fatal accident cases

As discussed above in Section 4, personal consumption expenditures of the decedent, in fatal accident cases, would need to be subtracted from the projected earnings. However, to model personal consumption expenditures is not straightforward since the customary data source to estimate the expenditures is the household expenditure survey conducted by the Department of Statistics Malaysia. In fatal accident damages, personal consumption expenditures represent the portion of total household expenditures that are exclusive to the decedent. Therefore, we need to convert household expenditures data to an adult male or female equivalent basis.

In this survey, known as the 2009–2010 Malaysian Household Expenditure Survey, household consumption items are classified based on Classification of Individual Consumption According to Purpose (COICOP) into 12 main categories. The data is delineated by the number of persons in the household regardless of family relationship or life activity. We know that personal consumption expenditures vary with respect to a person’s age and gender, and their food and non-food requirements also differ. Children require less food than adults, and females require less food than males in order to maintain an adequate nutritional standard. Similar to the Patton and Nelson (1991) and other forensic economists’ studies (Gilbert, 1991; Krueger, 2008) in estimating personal consumption expenditures in a fatal accident claim, we have divided consumption across adult males and females, and broken down the average household expenditures into categories in order to determine the amount of direct personal consumption of an adult male or female. This method, known as adult-equivalent scales are useful tools in identifying the consumption of various household members to the overall household expenditures.

1. The first category in the Household Expenditure Survey is food and non-alcoholic beverages, E₁. To allocate food personal consumption expenditure, we use the ‘food basket’ method—a method which has also been used by economists in measuring poverty—to estimate the calorie requirement for each member of the household based on the food component. The measurement of the food component is based on the dietary requirements of Malaysians by age and gender. The method defines the ‘food basket’ that will provide a balanced diet consisting of a variety of Malaysian foods.¹⁰ We rely on the data provided by the National Coordinating Committee on Food and Nutrition (2005) on recommended daily energy requirements for Malaysians—an adult male needs on average 2276 kilocalories per day; 1984 kilocalories for an adult female; and 1615 kilocalories for a child on average regardless of age and gender. Next, we need to find adult male-equivalent scales for weighting food consumption for different persons composing the household to adult male equivalent. The adult-equivalent scale for each individual in the household is determined by the ratio between the calorie requirements and the adult male calorie requirement as a reference value. These equivalence scales give a weight of 1 to the adult male (2276/2276 kilocalories), 0.8717 for an adult female (1984/2276 kilocalories) and a weight of 0.7096 (1615/2276 kilocalories) for each child. For the purpose of this research, we then develop models to calculate the proportion of household expenditure for food and non-alcoholic beverages for a male adult at age x, $E1(x)male$ and a female adult at age x, $E1(x)female$ in the household. In these models we assume a household, h consists of a couple and α children.

   $E1(x)male=E1(x),h[1(1+0.8717+α·0.7096)]$

   (10)

   $E1(x)female=E1(x),h[0.8717(1+0.8717+α·0.7096)]$

   (11)

   where $E1(x),h$ is the annual household expenditure for food and non-alcoholic beverages at age x based on the number of individuals in the household (⁠$h=2+α$⁠) and α is the number of children in the household. We use an inflation rate on food and non-alcoholic beverages published by the Department of Statistics Malaysia (2014) to reflect the future cost of food in order to estimate future expenditures in this category for a male adult age x + t, subject to t = 0, 1, 2, 3… t < e_x^o,

   $E1(x+t)male=E1(x)male(1+ΠF)t$

   (12)

   where $E1(x)male$is a household expenditure for food and non-alcoholic beverages for a male adult at age x as in equation (10) and $ΠF$is a constant inflation rate on food and non-alcoholic beverages, x is a current age and e_x^o is a life expectancy at current age x. For a female adult,

   $E1(x+t)female=E1(x)female(1+ΠF)t$

   (13)
2. The second household expenditure category is alcoholic beverages and tobacco, E₂. These expenditures are regarded as adult-related expenses and are treated as personal consumption expenditures for adults in the household. A research by Cheah (2014) shows that the majority of smokers and alcohol drinkers in Malaysia are males with 77.19% and only about 22.81% are females. Therefore, we can estimate the proportion of alcoholic beverages and tobacco expenditures for a male adult age x in the household as,

   $E2(x)male=0.7719E2$

   (14)

   For a female adult,

   $E2(x)female=0.2281E2$

   (15)
   We then estimate future expenditures on alcoholic beverages and tobacco by using a non-food inflation rate, $Π$⁠. Therefore, the household expenditure in this category for a male and a female adult age x + t, subject to t = 0, 1, 2, 3… t < e_x^o are given by the following equations (16) and (17), respectively.

   $E2(x+t)male=E2(x)male(1+Π)t$

   (16)

   $E2(x+t)female=E2(x)female(1+Π)t$

   (17)
3. The total amount of household expenditures under the clothing and footwear category, E₃ is divided equally among household members (Martin, 1988; Patton and Nelson, 1991). Therefore, the annual household expenditure for this category at age x based on the household size, $E3(x),h$ to be divided by the number of individuals in the household, h.

   $E3(x)male=E3(x)female=E3(x),hh$

   (18)
   Equation (18) is then multiplied by $(1+Π)t$ to derive the household expenditure in this category for a male and a female adult age x + t, subject to t = 0, 1, 2, 3… t < e_x^o.

   $E3(x+t)male=E3(x+t)female=E3(x),hh(1+Π)t$

   (19)
4. For housing, water, electricity, gas and other fuels category, E₄, we follow the Patton and Nelson (1991) method in treating this category. One-half of the total household expenditures are divided equally among the household members. The other half of the amount is considered to be undividable and is treated as consumption cost for adults in the household. Therefore, the proportion for both a male and a female adult is given by the following equation,

   $E4(x)male=E4(x)female=E4(x),h(0.5h+0.52)$

   (20)
   Next, we estimate the household expenditure in this category for a male and a female adult age x + t, subject to t = 0, 1, 2, 3… t < e_x^o is given by,

   $E4(x+t)male=E4(x+t)female=E4(x),h(0.5h+0.52)(1+Π)t$

   (21)

5. Expenditures under categories of furnishing, household equipment and routine household maintenance, $E5$⁠; health, $E6$⁠; transport, $E7$⁠; communication, $E8$⁠; recreation services and culture, $E9$⁠; education, $E10$⁠; restaurants and hotels, $E11$ and finally, miscellaneous goods and services, $E12$⁠, are jointly consumed by and benefit all family members. Therefore, these expenditures are all divided equally among household members, h. We then derive the household expenditure for a male and female adult age x + t, subject to t = 0, 1, 2, 3… t < e_x^o for furnishing, household equipment and routine household maintenance, $E5(x+t)male$⁠, $E5(x+t)female$⁠; health, $E6(x+t)male$⁠, $E6(x+t)female$⁠; transport, $E7(x+t)male$⁠, $E7(x+t)female$⁠; communication, $E8(x+t)male$⁠, $E8(x+t)female$⁠; recreation services and culture, $E9(x+t)male$⁠, $E9(x+t)female$⁠; education, $E10(x+t)male$⁠, $E10(x+t)female$⁠; restaurants and hotels, $E11(x+t)male$⁠, $E11(x+t)female$ and miscellaneous goods and services $E12(x+t)male$⁠, $E12(x+t)female$ by multiplying with $(1+Π)t$⁠.

5. Model to calculate loss of future earnings

We develop actuarial models to calculate damages for loss of future earnings, which derive from the human life value concept. There are two models: (I) loss of future earnings model in personal injury cases and (II) loss of future earnings model for fatal accidents.

6. Conclusions

In Malaysia, the current practice in the determination of compensation awards in personal injury and fatal accident cases uses the conventional multiplier–multiplicand approach without admitting any actuarial evidence. Most judges select the multipliers by reference to past court decisions and have little scientific basis.

In personal injury and fatal accident claims, the object of valuation is the value of a life. This article proposes models for the calculation of loss of future earnings using the human life value concept which have actuarial evidence in support of the models. Four major areas are emphasized in the calculation—(I) to estimate the plaintiff’s or decedent’s total income that would have been received at some point in the future, (II) the plaintiff’s or decedent’s income taxes are calculated using the existing tax tables and rules produced by the Inland Revenue Department in Malaysia and (III) in the case of fatal accident claims, the personal consumption expenditures of the decedent that would have spent exclusively on himself, calculated using the data published by the Department of Statistics, Malaysia. These models therefore could be a guide to determine the appropriate amount of damages in personal injury and fatal accident claims.

References