The AREA Journal 1997
Over the past two decades, the value-of-life literature in economics has developed to the point where it can provide useful guidance to jurors in assisting them in the valuation process. Hence, it has been used by economists to calculate the loss of enjoyment of life damages in personal injury and wrongful death cases.
This literature can also serve to provide estimates for the loss of society and companionship as a result of the death of a close family member.
This evidentiary approach to measuring the loss of enjoyment of life, often called hedonic damages, is arrived at by subtracting human capital values from whole life values. The whole life values are obtained using the value-of-life results based on the willingness-to-pay approach. This approach measures the costs of investing in safety equipment and safer consumer behavior, as well as inducements provided to workers who undertake risk in the workplace.
The literature on the willingness-to-pay and the willingness to accept payment is extensive and well-reviewed by Viscusi (1993) and Miller (1990). Measurement problems are not fully resolved but are no more acute than in most other areas of forensic economics.
The details of the methodology for calculating the loss of enjoyment of life are rather well-known by now and can be found in Smith (1993, 1990, and 1987), Brookshire and Smith (1992 and 1990), Miller (1990) and elsewhere.
Value of life estimates are frequently based on what members of a family spend to save a life. If a person places a smoke detector in his own bedroom, he is expressing a lower-bound to the value of his life in an amount equal to the cost of the detector (purchase price, installation, batteries, etc.) divided by the reduction in the risk of death. If, for example, the detector costs $25 dollars and reduces the risk of death by I chance in 100,000, then the value of life expressed is $2.5 million.
Now, suppose that a detector is placed in the bedroom of a child by a parent who seeks to preserve the society and relationship with that child? What value of life is expressed? The same value, $2.5 million. But this is the value to the family of the child’s life.
This conclusion has been arrived at by Miller (1989):
“When … individual’s survivors may recover for their own loss of enjoyment, whole life costs can again be used to estimate the appropriate level of compensation.”
Chestnut and Violette (1990) come to a similar conclusion:
“We conclude that the WTP estimates are potentially useful when the definition of compensation involves putting a dollar figure on non-financial losses to the deceased or to survivors.”
The following report shows the loss of Society and Companionship due to the death of 12-year-old girl, Jane Doe, survived by her parents. The losses are calculated from the date of death, January 1, 1990, through to the life expectancy of the parent expected to live the longest, Jane’s mother, when Jane would be 48 years old.
The basis for the value of life is a $2.3 million-dollar average value of life in 1998 dollars for a statistically average person. (See Brookshire and Smith, 1990 and 1992 for details). Past growth rates and an assumed future growth rate of 0.69 percent in this value are based on the growth in wages as a proxy for long-term increase in the average ability-to-pay. A discount rate of 1.97 percent is applied.
Value Of Life Compensation Report
January 1, 1996
Mr. Paul Barrister
456 Justice Ave, Ste 50
Chicago, IL 60000
Re: Jane Doe
Dear Mr. Barrister:
You have asked me to calculate the value of relationship or society and companionship sustained by Jane Doe’s surviving family as a result of her death.
Jane Doe was a 12-year-o1d Caucasian, female child, who was born on January 1, 1978, and died on January 1, 1990. Jane Doe’s remaining life expectancy is estimated at 68.3 years. This data is from the National Center for Hearth Statistics, Vital Statistics of the United States, 1991, Vol. II, Sec. 6, Life Table, Washington: Public Health Service, 1995.
I have reviewed certain materials provided to me including: (1) the depositions of Sue and Tom Doe; (2) an interview with the Doe’s; (3) statements from relatives and friends regarding Jane Doe; and (4) the Case Information form.
I have made a number of assumptions for the purposes of calculating these losses, which are explained below. Aside from specific studies cited, my methodology is based on general economic studies on past growth rate and interest rate behavior, as well as studies regarding the value of life.
My estimate of the real growth factor per year is 0.69 percent. This growth rate is based on wage growth data published in monthly issues of the U.S. Bureau of Labor Statistics, Monthly Labor Review (Washington, D.C.: U.S. Government Printing Office), for the real increase in wages from 1974 through 1994.
My estimate of the real discount rate is 1.97 percent. This discount rate is based on the real rate of return on U.S. Treasury bills from 1974 through 1994, published in the Economic Report of the President. This rate is consistent with a projection of the long-term future rate on these instruments published by lbbotson Associates, Chicago, in its series Stocks, Bonds, Bills and Inflation. This publication, which I originated, is generally regarded as the most widely accepted source of statistics on the rates of return on investment securities, relied upon by academic and business economists, insurance companies, banks, institutional investors, CPA’s, actuaries, benefit analysts, and economists in courts of law.
Real growth and discount rates are net of 5.53 percent inflation based on the Consumer Price Index thorn 1974 through 1994, published in monthly issues of the U.S. Bureau of Labor Statistics, CPI Detailed Report (Washington, D.C.: U.S. Government Printing Office).
Economists have long agreed that life is valued at more than the lost earnings capacity. My model of the value of life provides an estimate based on many economic studies on what we, as a contemporary society, are willing to pay to preserve the ability to live a normal life. The studies examine incremental pay for risky occupations as well as a multitude of data regarding expenditure for life savings by individuals, industry, and state and federal agencies.
My estimate of the value of life is consistent with estimates published in other studies that examine and review the broad spectrum of economic literature on the value of life. Among these is, “The Plausible Range for the Value of Lite,” Journal of Forensic Economics, Vol. 3, No. 3, pp. 17-39 (1990), by T. R. Miller. This study reviews 67 different estimates of the value of life published by economists in peer-reviewed academic journals. The results, in most instances, show the value of life to range from approximately $ 1.6 million to $2.9 million dollars in 1988 after-tax dollars, with a mean of approximately $2.2 million dollars.
The underlying studies fall into three general groups: (1) consumer behavior and purchases of safety devices; (2) wage-risk premiums to workers; and (3) cost-benefit analysis o£ regulations. For example, one consumer safety study analyzes the costs of smoke detectors and the lifesaving reduction associated with them. Wage premium studies examine the differential rates of pay for dangerous occupations with a risk of death on the job. Just as workers receive shift premiums for undesirable work hours, workers also receive a higher rate of pay to accept an increased risk of death on the job.
A study of government regulations examines the lifesaving results from the installation of smokestack scrubbers at high-sulfur, coal-burning power plants. As a hypothetical example of the methodology, assume that a safety device costs such as airbag costs $460 and results in lowering a person’s risk of premature death by one chance in 5,000. The cost per life saved is obtained by dividing $460 by the one in 5,000 probability, yielding $2,300,000.
Tables 1 through 3 show the loss of relationship sustained by Jane Doe’s surviving family. The value of preserving the ability to live a normal life is also a measure of the value placed on the loss of relationship or society and companionship by all of society, the great majority of which is captured by close loved ones.
Thus, it is an estimate of their value of the relationship with the deceased. Close family members place at least the same or greater value on their relationship with the deceased as compared to statistically unknown persons with whom they have no relationship and for whom the concern for lifesaving is less tangible.
Based on Sue Doe’s remaining life expectancy of 36.4 years, my opinion of the loss of the relationship to survivors as a result of the death of Jane Doe is $2,450,509 (Table 3). The loss of the relationship is expected to last until the death of the family member with the longest remaining life expectancy, which in this instance is Sue Doe. This relationship loss includes the pecuniary value of companionship, advice, and guidance. This loss is premised upon a statistically average relationship.
A trier-of-fact may weigh other factors to determine if these estimated losses should be adjusted. Due to special qualities or circumstances, economists may not as yet have a methodology for these analyses.
In each set of tables, the estimated losses are calculated from January 1, 1990, though an assumed trial or settlement date of January 1, 1996, and from that date thereafter. The last table in each set accumulates the past and future estimated losses. These estimates are provided as an aid tool and guide for the trier-of-fact.
If there is additional data which I have not yet taken into account, please let me know so that I may incorporate new information into a supplement of this analysis.
Sincerely,
Stan V. Smith
President
Table I
Lost of Past Relationship of Jane Doe to Survivors
1990 – 1995
| Year | Age | Relationship | Cumulate | |
|---|---|---|---|---|
| 1990 | 12 | $65,646 | $65,646 | |
| 1991 | 13 | 68,823 | 134,469 | |
| 1992 | 14 | 72,326 | 206,795 | |
| 1993 | 15 | 74,944 | 281,739 | |
| 1994 | 16 | 77,329 | 359,068 | |
| 1995 | 17 | 80,181 | $439,249 | |
JANE DOE: $439,249
Table 2
Present Value of Future Relationship of Jane Doe to Survivors
1996 – 2026
| Year | Age | Relationship | Discount Factor | Present Value | Cumulate |
|---|---|---|---|---|---|
| 1996 | 18 | $80,734 | 0.98068 | $79,174 | $79, 174 |
| 1997 | 19 | 81,291 | 0.96173 | 78,180 | 157,354 |
| 1998 | 20 | 81,852 | 0.94315 | 77,199 | 234,553 |
| 1999 | 21 | 82,417 | 0.92493 | 76,230 | 310,783 |
| 2000 | 22 | 82, 986 | 0.90706 | 75,273 | 366,056 |
| 2001 | 23 | 83,559 | 0.88954 | 74,329 | 460,385 |
| 2002 | 24 | 84,136 | 0.87235 | 73,396 | 533,781 |
| 2003 | 25 | 84,717 | 0.85550 | 72,475 | 606,256 |
| 2004 | 26 | 85,302 | 0.83897 | 71,566 | 677,822 |
| 2005 | 27 | 85,891 | 0.82276 | 70,668 | 748,490 |
| 2006 | 28 | 86,484 | 0.80687 | 69,781 | 818,271 |
| 2007 | 29 | 87,081 | 0.79128 | 68,905 | 887,176 |
| 2008 | 30 | 87,682 | 0.77599 | 66,040 | 955,216 |
| 2009 | 31 | 88,287 | 0.76100 | 67,186 | 1,022,402 |
| 2010 | 32 | 88,896 | 0.74630 | 66,343 | 1,088,745 |
| 2011 | 33 | 89,509 | 0.73188 | 65,510 | 1, 154,255 |
| 2012 | 34 | 90, 127 | 0.71714 | 64,688 | 1,218,943 |
| 2013 | 35 | 90,749 | 0.70388 | 63,876 | 1, 282,819 |
| 2014 | 36 | 91,375 | 0.69028 | 63,074 | 1,345,893 |
| 2015 | 37 | 92,005 | 0.67694 | 62,282 | 1,408,175 |
| 2016 | 38 | 92, 640 | 0.66386 | 61,500 | 1,469,675 |
| 2017 | 39 | 93,279 | 0.65104 | 60,728 | 1,530,403 |
| 2018 | 40 | 93, 923 | 0..63846 | 59,966 | 1,590,369 |
| 2019 | 41 | 94,511 | 0.62613 | 59,214 | 1,649,583 |
| 2020 | 42 | 95,224 | 0.61403 | 58,470 | 1,708,053 |
| 2021 | 43 | 95,881 | 0.60 217 | 57,737 | 1,765,790 |
| 2022 | 44 | 96,543 | 0.59053 | 57,012 | 1,822,802 |
| 2023 | 45 | 97,209 | 0.57912 | 56,296 | 1,879,098 |
| 2024 | 46 | 97,880 | 0.56794 | 55,590 | 1,934,68 8 |
| 2025 | 47 | 98,555 | 0.55696 | 54,891 | 1,989,579 |
| 2026 | 48 | 39,694 | 0.54620 | 21,681 | $2,011,260 |
JANE DOE: $2,001,260
Table 3
Present Value of Net Relationships of Jane Doe to Survivors
1990 – 2026
| Year | Age | Relationship | Cumulate |
|---|---|---|---|
| 1990 | 12 | $65,646 | $65,646 |
| 1991 | 13 | 68,823 | 134,469 |
| 1992 | 14 | 72,326 | 206,795 |
| 1993 | 15 | 74, 944 | 281,739 |
| 1994 | 16 | 77, 329 | 359,068 |
| 1995 | 17 | 80, 161 | 439,249 |
| 1996 | 18 | 79,174 | 518,423 |
| 1997 | 19 | 78,180 | 596,603 |
| 1998 | 20 | 77,199 | 673,802 |
| 1999 | 21 | 76,230 | 750,032 |
| 2000 | 22 | 75,273 | 825, 305 |
| 2001 | 23 | 74,329 | 899,634 |
| 2002 | 24 | 73,396 | 973,030 |
| 2003 | 25 | 72,475 | 1,045,505 |
| 2004 | 26 | 71,566 | 1,117,071 |
| 2005 | 27 | 70,668 | 1,187,739 |
| 2006 | 26 | 69,701 | 1,257, 520 |
| 2007 | 29 | 68,905 | 1,326,425 |
| 2008 | 30 | 68,040 | 1,394,465 |
| 2009 | 31 | 67,186 | 1,461,651 |
| 2010 | 32 | 66,343 | 1,527,994 |
| 2011 | 33 | 65,510 | 1,593,504 |
| 2012 | 34 | 64,688 | 1,658,112 |
| 2013 | 35 | 63,876 | 1,722,068 |
| 2014 | 36 | 63,074 | 1,785,142 |
| 2015 | 37 | 62,282 | 1,847,424 |
| 2016 | 38 | 61,500 | 1,908,924 |
| 2017 | 39 | 60,728 | 1,969,652 |
| 2018 | 40 | 59,966 | 2,029,618 |
| 2019 | 41 | 59,214 | 2,088,832 |
| 2020 | 42 | 58,470 | 2,147,302 |
| 2021 | 43 | 57,737 | 2,205,039 |
| 2022 | 44 | 57,012 | 2,262,051 |
| 2023 | 45 | 56,296 | 2,318,347 |
| 2024 | 46 | 55,590 | 2,373,937 |
| 2025 | 47 | 54,891 | 2,428,828 |
| 2026 | 48 | 21,681 | 2,450,509 |
JANE DOE: $2,450,509
November 23, 1997
WORK NOTES
BASIC FACTS: 12 YEAR OLD GIRL KILLED IN AUTO ACCIDENT.
NAME: JANE DOE
DATE OF DEATH: 1-1-90
DATE OF TRIAL: 1-1-96
DATE OF BIRTH: 1-1-78
AGE AT DATE OF DEATH: 12.0
REMAINING LIFE EXPECTANCY AT DATE OF DEATH: 68.3
TOTAL LIFE EXPECTANCY AT DATE OF DEATH: 80.3
RACE/GENDER: WHITE FEMALE
GROWTH RATE: 0.69%
DISCOUNT RATE: 1.97%
FAMILY BACKGROUND
SUE DOE-MOTHER, BORN 1-1-45, AGE 45, RLE 36.4
TOM DOE-FATHER, BORN 1- 1 -40, AGE 50, RLE 26.9
RELATIONSHIP
1990 = 60000 (1988 BASE) * 5.7I% 65646
1991 = 65483 * 4.84% = 68823
1992 = 68718 * 5.09% = 72326
1993 — 71294 * 3.62% = 74944
1994 = 74567 * 3.18% = 77328
1995 = 77328 * 3.69% = 80181
THRU MOTHER’S RLE OF 36.4 YEARS (AGE 48.4 FOR JANE)
FUTURE GROWTH AT .69%
About the Author
Dr. Stan V. Smith,. Ph.D. is President of Corporate Financial Group, Ltd.at 1165 N. Clark. Suite 650, Chicago, IL. In 1984, in Sherrod v Berry, he introduced the term “Hedonic Damages,” and presented his model on the value of life the first time in U S. Courts.
REFERENCES
- Brookshire, Michael. L., Stan V. Smith and Charles de Seve, 1991. Economic Hedonic Damages – 1991‘2 Supplement, Anderson Publishing Co., Cincinnati.
- Brookshire, Michael. L., and Stan V. Smith, 1992. Economic Hedonic Damages – 1992’3 Supplement, Anderson Publishing Co., Cincinnati.
- Chestnut, Lauraine G., and Daniel M. Violette, “The Relevance of Willingness-To-Pay Estimates of the Value of a Statistical Life in Determining Wrongful Death Awards,” Journal of Forensic Economics, Vol. 3, No. 3, 1991, pp. 73-89.
- Miller, Ted R., “Willingness to Pay Comes of Age: Will the System Survive?“ Northwestern Law Review, Vol 83, 1989, pp. 876-907.
- Miller, Ted R., “The Plausible Range for the Value of Life: Red Herrings Among the Mackerel,” Journal of Forensic Economics, Vol. 3, No. 3, 1990, pp. 17-39.
- Smith, Stan V., “Hedonic Damages in Wrongful Death Cases,” ABA Journal, Vol 74, Sept 1988, pp. 70-74.
- Smith, Stan V., “Hedonic Damages in the Courtroom Setting – A Bridge Over Troubled Waters,” Journal of Forensic Economics, Vol. 3, No. 3, 1990, pp. 41-49.
- Smith, Stan V., ”Hedonic Damages in Personal Injury and Wrongful Death Litigation,’ in Gaughan, Patrick A. and Robert J. Thornton (Eds.), Litigation Economics, Greenwich: JAl Press, 1993.
- Viscusi, Kip W., “The Value of Risks to Life and Health,” Journal of Economic Literature 31, 1993, pp.1912-1946.