Relied upon by economists to calculate the loss of enjoyment of life damages in personal injury and wrongful death cases, value of life literature in economics serves to provide estimates for the loss of society and companionship as a result of the death of a close family member. Included in this article is an example letter sent to a client which breaks down the economic estimates for the hedonic valuation of life and calculates the loss of enjoyment of life.
This article originally appeared in: The New Hedonics Primer For Economists And Attorneys, Second Edition, 1996, Lawyers & Judges Publishing Company, Inc.
By Stan V. Smith
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 that 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 1 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 what is the 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."
An Example of Loss of Companionship Hedonic Valuation Estimates
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.
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-old, Caucasian, female child, who was born on January 1, 1978, and died on January I, 1990. Jane Doe's remaining life expectancy is estimated at 68.3 years. This data is from the National Center for Health 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:
- The depositions of Sue and Tom Doe.
- An interview with the Doe's.
- Statements from relatives and friends regarding Jane Doe.
- 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. DC.: 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 Ibbotson 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 arc net of 5.53 percent inflation based on the Consumer Price Index from 1974 through 1994, published in monthly issues of the U.S. Bureau of Labor Statistics, CPI Detailed Report (Washington, DC: 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 Life,” 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:
- Consumer behavior and purchases of safety devices
- Wage risk premiums to workers
- Cost-benefit analyses of regulations
For example, one consumer safety study analyzed the costs of smoke detectors and the lifesaving reduction associated with them. One wage premium study examined 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 regulation examined the lifesaving resulting from the installation of smoke stack 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 because of special qualities or circumstances that economists do not as yet have a methodology for analysis.
In each set of tables, the estimated losses are calculated from January 1, 1990, through an assumed trial or settlement date of January I, 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 1 - Loss 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 7 2,326 206,795
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 0.98066 $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 75,273 386,056
2001 23 83,559 0.88954 74,329 460,385
2002 24 64,136 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 68,040 955,216
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 0.71774 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 94,571 0.62613 59,214 1,649.583
2020 42 95,224 0.61403 58,470 1,708,053
2021 43 95,881 0.60217 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 1,934,688
2025 47 98,555 0.55696 54,891 1,989.579
2026 48 39,694 0.54620 21,681 $2,011,260
Jane Doe $2,011,260
Table 3 — Present Value of Net Relationship of Jane Doe to Survivors 1990-2026
Year Age Relationship Cumulate
1990 12 $65,646 $85,646
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
1996 18 79.174 518,423
1996 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 28 69.781 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 1,658,192
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
January 30, 1996
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: I.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, Re 26.9
Relationship
1990 = 60000 (1988 Base) * 5.71% 65646
1991 = 65483 * 4.84% = 68823
1992 = 68718 * 5.09% = 72326
1993 = 71294 * 3.62% = 74944 1
994 = 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%
References
Brookshire. Michael. L., Stan V. Smith and Charles de Seve, Economic/Hedonic Damages — 1991/2 Supplement, Anderson Publishing Co., Cincinnati, 1991
Brookshire, Michael. L., and Stan V. Smith. Economic/Hedonic Damages — 1992/3 Supplement, Anderson Publishing Co., Cincinnati. 1992
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, 75-89
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: JAI Press, 1993
Viscusi, Kip W., “The Value of Risks to Life and Health,” Journal of Economic Literature 31, 1993, pp. 1912-1946