The Value of Life to Close Family Members: Calculating the Loss of Society and Companionship

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:

  1. The depositions of Sue and Tom Doe.
  2. An interview with the Doe's.
  3. Statements from relatives and friends regarding Jane Doe.
  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. 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:

  1. Consumer behavior and purchases of safety devices
  2. Wage risk premiums to workers
  3. 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

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