Month: September 2005

Autumn 2005 issue of the Expert Witness newsletter (volume 10, issue 3)

Posted on By economica

Contents:

  • Claims by Elderly Parents for Loss of Caregiving by Adult Children
    • by Hugh P. Finnigan
    • The article addresses the fact that many adult children accept at least some responsibility for the provision of care to their aging parents. This leads to a possible claim by elderly parents for the loss of caregiving services, if an adult child is seriously injured or killed. The purpose of his article is to review some recent research that examines the factors that determine whether an adult child will care for an elderly parent.
  • The Impact of Disability on Earnings: Pitfalls in the Use of Average Data
    • This article appeared in our newsletter but has been removed from our web site at the author’s request.
  • Death and Retirement: Allowing for Uncertainty
    • by Christopher Bruce
    • In this article Christopher Bruce explains how experts deal with situations in which there is uncertainty about the plaintiff’s future income path – such as when it is not known whether the plaintiff will recover from his or her injuries. He also comments on an error that experts often make when dealing with such uncertainty.

Death and Retirement: Allowing for Uncertainty

Posted on By economica

by Christopher Bruce

This article first appeared in the autumn 2005 issue of the Expert Witness.

Assume that a plaintiff has begun to recuperate following a serious accident. If her injuries stabilize at their current level, she will suffer a loss of earnings of $20,000 per year. If, however, she has a relapse, her losses will increase to $40,000 per year. Her doctors tell you that there is a 50 percent chance that there will be a relapse (and a 50 percent chance that there will be no relapse).

How should the annual value of her loss be calculated? If damages are set equal to $20,000 per year, there is a 50 percent chance that she will be under compensated; whereas if she is paid $40,000, there is a 50 percent chance that she will be over compensated. (And if she is paid some amount between $20,000 and $40,000, there is a 100 percent chance that she will be incorrectly compensated.)

This conundrum, in which there is uncertainty about the outcome of future events, is common in the assessment of personal injury (and fatal accident) damages. Not only is there uncertainty about the future course of the plaintiff’s injuries, as in the example above, we also face uncertainty concerning the age at which the plaintiff will retire, the plaintiff’s life expectancy, the probability that the plaintiff would have (and will be) unemployed, and a host of other factors.

The general approach that virtually all financial experts take in such cases is to calculate the average outcome that would arise from the uncertain event, if the event could be repeated a large number of times. For example, if the injury described above was to be repeated 100 times (for example, if there were 100 plaintiffs with that same injury), we would expect that the plaintiff’s injuries would remain stable in approximately 50 cases, leading to a loss of $20,000 per case. In the other 50 cases, the plaintiff would suffer a relapse and her loss would rise to $40,000. Thus, the total annual loss, across all 100 cases, would be ((50 × $20,000) + (50 × $40,000) =) $3,000,000. The average annual loss would be $30,000; which could also be calculated by multiplying 50% times $20,000 and adding 50 % times $40,000. That is, the average value of a loss can be calculated by multiplying each of the possible losses by its probability and then adding the resulting numbers together.

But, as was noted above, $30,000 is guaranteed to be the “wrong” amount in 100 percent of cases. How, then, can it be justified? One simple answer is this: if the event in question is truly uncertain, the plaintiff should be able to use the $30,000 to purchase insurance that will compensate her fully regardless of which value turns out to be her true loss – either $20,000 or $40,000. The reason for this is that if the insurer issues, say, 100 such policies, it can expect to pay out $20,000 in 50 cases and $40,000 in the other 50, for an average of $30,000. (It will have collected $3,000,000 [= 100 × $30,000] and will have paid out $3,000,000 [= 50 × $20,000 + 50 × $40,000].)

Risk of Mortality

This type of calculation is most commonly used when dealing with the uncertainties associated with mortality. Take the extreme case in which there is a ? probability that a plaintiff will live exactly one year (and then die), a ? probability that he will live exactly two years, and a ? probability that he will live exactly three years. If he would have earned $60,000 per year but has now been left unable to work, his loss can be calculated using the technique described above. That is, there is a ? chance that he has lost one year’s income ($60,000), a ? chance he has lost two years’ income ($120,000), and a ? chance he has lost three years’ income ($180,000); for an average of $120,000 (=? × $60,000 + ? × $120,000 + ? × $180,000).

Alternatively, in such cases, it is sometimes possible to use a “rule of thumb” to estimate the loss. Given the probabilities in the preceding example, it can be shown that, on average, the plaintiff will live two more years before dying. (2 = ? × 1 + ? × 2 + ? × 3) That is, his life expectancy is two years. His expected loss can then be calculated as the sum of his losses over that life expectancy, or $120,000 (= 2 × $60,000). Note, however, that this approximation works best if the losses are approximately the same in each year, as it was here. (If the annual loss is significantly different in the first year than, say, the third year, this approach yields a biased estimate.)

What is clear is that it would be inappropriate to mix together the two calculation techniques. It is not appropriate, for example, to estimate the loss by multiplying each of the first two years’ losses by their associated probabilities and assuming that the loss continues for only two years. That would produce an “estimated” loss of only $60,000 (=? × $60,000 + ? × $120,000), $60,000 less than the true loss.

Retirement Age

The techniques described here can also be used to estimate the effect of uncertainties about the plaintiff’s retirement age. Assume, for example, that there was a ? probability that a 63 year-old plaintiff would have worked for exactly one year (i.e. to his 64th birthday) and then retired, a ? probability he would have worked two years, to his 65th birthday, and a ? probability he would have worked three years, to his 66th birthday. If he would have earned $60,000 per year while working, his loss, again, can be found from the formula: ? × $60,000 + ? × $120,000 + ? × $180,000 = $120,000; or by multiplying the average number of years to retirement by his annual earnings, to produce $120,000 = 2 × $60,000.

As with the mortality example, it would clearly be incorrect to multiply each year’s earnings by the probability it would occur and assume the individual would have retired at the average age, of 65. That would produce an “estimate” of, (? × $60,000 + ? × $120,000 =) $60,000, again, only half of the correct estimate.

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).

Claims by Elderly Parents for Loss of Caregiving by Adult Children

Posted on By economica

by Hugh P. Finnigan

This article first appeared in the autumn 2005 issue of the Expert Witness.

Advancements in medical technology have prolonged the lives of individuals and dramatically increased their costs of care. As a result, many adult children accept at least some responsibility in the provision of such care to their aging parents. This leads to a possible claim by elderly parents for the loss of caregiving services, if an adult child is seriously injured or killed.

Before such a claim can be made, however, some determination must be made of the probability that an adult child will offer such care, especially if the parent had not been in need of assistance before the child was injured. In this article I shall review some recent American research that examines the factors that determine whether an adult child will care for an elderly parent.

In an early study, Stone, Cafferata, and Sangl (1987) examined 1982 data to develop a profile of caregivers by their relationship to the care recipient. The researchers found that the average age of these caregivers was 57.3. Moreover, one-third of these caregivers were still employed and having to make adjustments to their work schedules. One-third of the caretaker’s families were near or below the poverty line. Finally, one-third of the care providers were themselves in only fair to poor health.

Several researchers have examined opportunity cost as a possible motivation. That is, children might find that the expense of caring for their elderly parents exceeds what they themselves could earn in the workplace. Thus, they might be economically better off to care for their parents in lieu of working a traditional job. Supporting this theory, researchers have found that adult women in particular tend to reduce their hours of paid work (or leave the labour force altogether) to provide care for their parents. This finding is consistent with the persistent wage differentials found between women and men. If women tend to earn less than men, on average, they face a lower opportunity cost when deciding to care for their parents.

It has also been argued that children might feel differently towards their parents, depending on the latter’s marital status. Pezzin and Schone (1999), for example, found that divorced men were less likely to receive care or financial assistance from their children than were divorced women. Moreover, if the divorced father does receive care the number of hours is often lower than that received by mothers or widowed fathers. These findings were later confirmed by Pelkowski (2005).

Pelkowski also found a number of other determinants that had not been measured by other researchers. Most importantly, she found that if the children lived within close proximity (within 10 miles) to their parents there was a far greater chance they would provide care. Also, males with living sisters tended to have a low propensity to provide assistance to their parents. Finally, Polkowski is able to answer a question posed earlier by Folbre and Nelson (2000): in her survey the expectation of a bequest was found not to be an important determinant of a child’s willingness to provide care to an elderly parent.

References

Levit, Katharine R.; Cowen, Cathy A.; Lazenby, Helen C.; McDonnell, Patricia A.; Sensenig, Arthur L.; Stiller, Jean M. and Won, Darlene K. “National Health Spending Trends, 1960-1993.” Health Affairs, Winter 1994, 13(5), pp. 14-31.

Nancy Folbre & Julie A. Nelson, 2000. “For Love or Money-Or Both?,” Journal of Economic Perspectives, American Economic Association, vol. 14(4), pages 123-140.

Pelkowski, Jodi Messer, 2005. “Adult Children’s Propensity to Care for an Elderly Parent: Does the Marital Status of the Parent Matter? The Journal of Economics, 31(1), pp.17-38.

Pezzin, Liliana E. and Schone, Barbara Steinberg. “Parental Marital Disruption and Intergenerational Transfers: An Analysis of Lone Elderly Parents and Their Children.” Demography, August 1999, 36(3), pp. 287-97.

Stone, Robyn I.; Cafferta, Gail L. and Sangl, Judith A. “Caregivers of the Frail Elderly: A National Profile.” The Gerontologist, October 1987, 27(5), pp.616-626.

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From 2003 through 2005, Hugh Finnigan was a consulting economist at Economica, with a Master of Arts degree from the University of Calgary.