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The Human Life Value: A Theoretical Model Author(s): Alfred E. Hofflander Source: The Journal of Risk and Insurance, Vol. 33, No. 4 (Dec., 1966), pp. 529-536Published by: American Risk and Insurance AssociationStable URL: http://www.jstor.org/stable/251227Accessed: 28-10-2015 05:15 UTC

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THE HUMAN LIFE VALUE: A THEORETICAL MODEL ALFRED E. HOFFLANDER

The human life value concept is generally associated with life insurance. The concept, however, is not limited to insurance in its application and has been used in many other areas of economic theory and practice. Estimates of the value of human beings as capital are useful for a variety of purposes.' An analysis of popu- lation and migration could well include a consideration of the value of the people involved. Public policies and projects regarding health, highway construction, flood control, education,2 and rehabilita- tion should reflect the extent to which human life values are increased.3

The desirability of using per capita human capital values as a welfare index has been suggested.4 Such an index would reflect present and future mortality, health, employment, and earnings. Since all of these factors affect the general wel-

fare of the people, it might be a better measure of welfare than current per capita income which is often used. The main drawback to using per capita human capital values is the lack of data and difficulty of computation. On the other hand, it might be argued that future changes in mortality should be not be included in a welfare index attempting to measure present welfare. In this paper an attempt has been made to outline some of the problems involved in defining the human life value concept, developing some theoretical definitions, and showing how the concept might be applied to different fields.

The effect of various social and economic programs upon the value of a human life is an important area and deserves further work, but no effort will be made in this paper to cover this aspect of the problem.

The Concept of Value

There are many factors involved in setting the value of specific property at any given moment. Because of this multi- plicity of elements, it is extremely difficult to obtain any degree of unanimity among appraisers. These disagreements are not due solely to the inherent difficulties of all economic estimates involving prophecy. They are more frequently due to a lack of agreement as to the very meaning of the word "value." In an attempt to make its meaning more exact, many have placed a modifier before the word "value," (e.g., fair market, exchange, taxable, etc. ). These efforts have frequently led to more, rather than less, confusion because the

Alfred E. Hofflander, Jr., Ph.D., is Assistant Professor of Insurance in the University of Texas. Prior to going to Texas in 1963, Dr. Hofflander taught at North Florida Junior College and at Florida State University. He was a Fellow in the Huebner Foundation and was formerly Editor of the North Florida Business Review and a Director of the North Florida Small Business Institute. Dr. Hofflander is Business Manager of the Journal of Risk and Insurance and is an Associate of the Financial Advisory Associates. This paper was ac- cepted for publication in March, 1965.

' Burton A. Weisbrod, "The Valuation of Hu- man Capital," Journal of Political Economy, Vol. LXIX (October, 1961), p. 425. The introduction of this article offers an excellent discussion of the many uses of the concept.

2 An examination of the change in human life values due to increased schooling is one way of determining the monetary value of increased schooling.

3 Weisbrod, op. cit., pp. 425-426. 4 Ib;.

( 529 )



530 The Journal of Risk and Insurance

meaning of the modifier often varies from one area of economic endeavor to another. This problem exists not only in insurance (what do we mean by "human life value"?), but in law, business, accounting, an economics. The word "value" is a word of many meanings.5

To complicate the problem further, the various meanings are often intertwined and closely related. In an effort to find work- able definitions of the concept of value, court decisions and statutes have at- tempted to define various types of value. Many times this only further complicates the problem because such definitions are usually suited to the specific situation at hand and hence do not really help to clarify the general concept.

Lawyers once argued that there is only one value and that this value suited all purposes. To them it was fallacious to as- sign different values to the same item for different purposes. They contended that the "value" or "fair value" of an item was a definite "fact to be found" and not a function of the purpose of the evaluation." In recent years there has been a trend away from this line of thinking. As Justice Holmes observed, "A word is not a crystal, transparent and unchanged; it is the skin of a living thought, and may vary greatly in color and content according to the circumstances and the time in which it is used."7

In insurance it is also difficult to get agreement regarding the definition of the terms involved, hence there are misunder- standings and committees on terminology. In discussing the money value of a man the term "human life value" is often used. Just as in the case of the word "value," "human life value" can have many mean-

ings. Unfortunately, the human life value of an individual is not a "fact to be found." As in other areas of economic endeavor, the definitions and methods are dependent upon the use of the resulting figures. Thus, instead of one definition of the "human life value," there are many, and each is usually applicable to only one usage.

Definitions of Human Life Value

It appears that while many authors do not define exactly what they mean by the human life value, their ideas regarding the concept are similar. They would attempt to determine the present value of future earnings, but some would use gross earnings, and some would subtract self- maintenance. What factors they would consider in discounting, however, seem vague. In fact, one of the most interesting things about the human life value is that few authors have bothered to define the concept. Most of those who deal with the subject explain it in terms of an example, or simply state that it is the capitalized value of a man.

Dr. Huebner, in The Economics of Life Insurance, defined the human life value in two different places. Both definitions are similar, but they are not identical. He first defined the human life value as ". . . the capitalized monetary worth of the earning capacity resulting from the economic forces that are incorporated within our being."8 This is essentially a philoso- phical rather than a practical definition. In a later section he states that it is ". . . the capitalized value (at the prevailing rate of interest) of the current earning power of the insured devoted to the support of family dependents."9

One of the problems with these definitions is that they are somewhat ambigu-

5 Southwestern Bell vs. Public Service Commis- sion, 262 (U.S.), 276.

6 Robert S. Cline, "Valuation of Life Insurance Assets," (unpublished Ph.D. dissertation, Insur- ance Department, University of Pennsylvania), pp. 15-16.

7 Towne v. Eisner, 245 (U.S.), 418 (1918).

8 S. S. Huebner, The Economics of Life Insur- ance, (3rd ed., New York: Appleton-Century- Crofts, Inc., 1959), p. 5.

9ibid., p. 18.



The Human Life Value: A Theoretical Model 531

ous. In capitalizing the current earning power, no indication is given as to what factors other than interest are to be considered. Because of this, it is impossible to know exactly what the author had in mind when he defined the human life value in this manner.10

Purpose of the Definition

The human life value concept can be used for diverse purposes, and even within one area of usage it may have more than one application. But unless the human life value is unaffected by tlhe purpose for which it is to be used, it is not one value, but many values. The question then is whether the human life value for an individual is fixed, or whether it is a function of its purpose. An example will show that the latter is the case.

In determining the human life value of an individual for inclusion in national wealth (assuming the inclusion is proper), one would discount the earnings for many factors, including mortality. If, on the other hand, one is interested in determining the human life value of a member of this group to his wife for life insurance purposes, the discounting factors would not include mortality. One would not discount for mortality because the object of the insurance is to replace that portion of a man's income that would normally go to his wife and family had he lived. To discount for mortality, then, is to discount for the very factor which is being insured against.

Assume that a man is earning $12,000 per year and consumes $2,000 on self- maintenance. If his probability of death

for this year is 0.2, the question arises whether his wife should insure him for this year for $8,000 or for $10,000 (ignor- ing the other discounting factors). If she is interested in insuring the contribution he would have made had he lived, she would insure for $10,000, not $8,000. This is an example of the same individual hav- ing two human life values at the same time.

Obviously, this problem can be viewed as one of semantics. Does this individual have two different human life values or are they two different concepts, one, or both, or neither of which is the human life value? It is possible, but perhaps not feasi- ble, to call the first concept "human capital," and then to give other names to the different modifications in order to distin- guish one from another. Because of its long association with the life insurance field, the "human life value" would no doubt be used when referring to the life insurance concept.

The purpose of determining the human life value for life insurance (for this work) is to find that single sum which, on the average, represents the amount necessary to replace that which an individual would normally have provided for his family had he lived. The sum is the present value of an individual's stream of income (less self- maintenance) .

Since this sum is to be used as a guide in determining the amount of life insurance to be purchased, it will be discounted for interest and all factors (except mortality) which might prevent the earning of the income. Thus, if only ninety-six per cent of a certain homogeneous group (as to profession, age, health, locality, etc.) are employed, then the average future gross earnings of this group should be discounted for this factor in determining the human life value of a member of this group. This is done because there is only a .96 probability of an individual's earning this wage. The four per cent may not

1 Griffin Lovelace did not define the human life value, but an example which he used is such that he apparently was considering a concept which was similar to Dr. Huebner's original definition. For a fuller discussion of the history of the Human Life Value Concept, see A. E. Hoff- lander, "The Human Life Value: An Historical Perspective," Journal of Risk and Insurance, September, 1966, p. 381.



532 The Joturnal of Risk and Insurance

be working due to a number of causes; there is no way of predicting which members of this homogeneous group will be unemployed in any further year.

In the area of disability income insurance, the human life value will be used to compare the present value of future bene- fits for individuals who are disabled, to the present value of future earnings if they had not been disabled. The present value will be found by discounting for all factors, except disability, which might prevent the earning of the income. The probability of becoming disabled is ignored in this instance because the purpose of the end result is to determine what the individtial would have earned if he never became disabled. Thus, there is no discounting for the probability of becoming disabled.

In applying the human life value to company underwriting of life insurance, the same techniques will be used which were employed as a guide in determining the amounts of life insurance to purchase. This is because the two are in reality only different facets of the same problem. The company is interested in the "correct" amount of insurance so that it may be able to reject applications for amounts which represent overinsurance. The insured, on the other hand, is (or should be) interested in determining the "correct" amount of insurance so that he will not be unprotected.

The same is true when attempting to establish the money value of an individual in cases of recovery for wrongful death. In this situation, however, one would discount for mortality as well as other factors because here account should be taken of the chance that the individual would not have lived to earn future income.

A Simple Mathematical Model

For the individual whose human life value we seek to define, let us presume a large homogeneous group of individuals,

to which he belongs. Assume that these individuals are all of age x nearest birthday and that their average age is x (an integer). Analogous to this group is a mathematical model called a survivorship group, S, formed by Ix persons entering it-all at one time-at exact age x and subject to prescribed mortality rates. Let:

x attained age of a life in S (an integer); this is an exact age, i.e., age on a birthday; similarly y

(x) a life aged x in S w limiting age; youngest integral

age to which there are no survi- vors in S

lx the number of persons in S aged exactly x; lx + 1/2, ly + ?2 are defined analogously

fX(e) the fraction of the lx persons in S assumed to be gainfully employed at exact age x

wy estimated wages of each person in S who is alive and employed throughout the year of age y to y + 1 (whether wy is an estimate

for healthy lives or an average for all employed lives depends on the purpose)

my-= estimated cost of maintaining each person in S who is alive throughout the year of age y to y + 1

vt (1 + i)-t the present value, under compound interest at an- nual rate i, of a unit sum due in t years

The wage, maintenance, mortality and interest rates are selected so as to reflect expected future experience of the homog- neous group. Let Hx n) denote human life value of (x) according to assumption (n).

What form should a mathematical model take so that it could be used to analyze the need for life insurance, disability income insurance, recovery in cases of wrongful death and the underwriting




problems of life insurance companies? Four possibilities are:

w-1 (l) w 1 ( +(e) y+l 12-

H, = x (w-y+12 fy+1/2 v y=x

w-1

(III) (e) ~~~(e) y+1/2-x

(II L (W,y my) y+i 12 fy+1/2 V

W-1

(III) v ~~(e) y+1ll2-x

H,, = (Wy fy+1/2-My) ly+l12 v y =x

w-1

(IV) (e) y+1/2-x

Hx = 1 (wy fy+1/2- my) lx v y =x

(I)

Definition for Life Insurance. H x represents the present value of the future gross earnings of the group. If this figure

(v)

is divided by lx, the result H. , is the present value of the estimated future gross earnings of any member of this group.

w-1 /

H1 L (WY ly+l/2 fy+1/2 v /) (Ix y =x

If the purpose of life insurance is to replace the average future gross earnings of the group, then this would be, on the average, the correct amount of life insurance to purchase."1 While this figure has the advantage of simplicity, it ignores many factors, including the cost of self- maintenance.

(II)

Hx is the present value of the future gross earnings of the gainfully employed, less the cost of their self-maintenance.

(e)

This figure divided by fx w-1 1

(VI) ( (Y,f2 (e) y+1 /2-x

H,, = , (W - my) (1y+l1 2fy+l1 2V (e)

y=x f,,

is essentially the present value of the net future surplus of those continually employed. If the assumption is made that

11 At this point the decreasing protection under permanent forms of life insurance is ignored.

(e) the group represented by fy?+ is always

(e) composed of those in the fy+ l group, plus additional members added from the

(e)

(1 i - ~f,Ml) class, then there might be (II)

some validity in using H. as the definition of the human life value under certain circumstances. Unless special information exists to the contrary, however, one can- not assume that those who are unemployed in one period are the same as those who are unemployed in the subsequent period. The given assumption regarding the homogeneity of the group prohibits such an assumption in this case. Since there is no way to determine in advance which of the members will be in the unemployed group, one must consider the total class.

(III)

Hx rectifies this by taking the present value of the gross future earnings of all those who are working, less the cost of maintenance of all those who are alive (including some who are not working, but are, of course, consuming). This appears to be the concept being aimed at, for here those who are not working are consuming either past surplus (savings), or future surplus (borrowing). This surplus is not available to dependents and hence should not be included in the individual's human life value. This expression

(VI)

divided by lx, H. w-1 1

(VI) ( (e) +l /2-x H,= X wY fy+1/2-my) '1y+1/2 vy1)

y =X

would be the average human life value for life insurance purposes except that over time the wages and self maintenance reflect the mortality of the original group.

(IV)

Hx corrects this defect by providing a net wage figure regardless of mortality.




w-1 1 (VI) (e) A ( y+l/2-wx

Hx = X- wy fy+1/2-my) k1y+1/2 V Y /

y =x

(IV) (VIT) Dividing Hx by l, yields Hx

w-1 (VII) (e) A /2-x

Hx = X (wY fy+l /2-my) V

y = X

Using this expression, values for all ages from zero upward can be obtained, but are these figures meaningful for the purposes for which the expressions were derived? Apparently not. During child- hood (from x=O to about x=18) there is no one who is dependent upon the individual for support. Usually the only ones with an economic interest in the child are his parents. The economic interest of the parents is generally limited to their investment in raising the child. (This, of course, ignores the prospect of future support of the parents by the child. Where such future support seems realistic, some measure of the value of the prospective support should be allowed.)

Because of this, the amount of life insurance (or the amount recoverable for wrongful death) may not bear any relationship to the human life values at the early ages. This is especially true due to the problem of determining the type of profession that the child might have fol- lowed in later years.

During those years after retirement, the human life value is negative. At this time, the human life values and the amounts of life insurance may bear no relationship to each other. Hence, the restriction that

I x < r

where: x - initial age of the survivorship group

1 age at which dependency ceases

r - retirement age 12 The equations developed in this section are

also applicable to employer's liability.

Definition for Wrongful Death'2

(III)

If H, is divided by the number living at age x ( ,), then the result is

w-1 1 H I L (Wy fy+l/2-my) (1y+1/2 VY )+

y=x

or

w-1 (VII)( (e)

Fi Y (Wy fy+l /2 1y+1 /2i /l y=x

{ \ 1 y+l~~+ /2-x

-(my ly+1/2) /lx] V

Now through a term by term examina-

(VIII) tion of Hx (e) ,

a better understanding of

(e)

its meaning may be obtained. (fy + %ly + ) Ilx is the probability that an individual

in year of age x will be alive and working in year of age y + 1/2. From this is sub- tracted the cost of self maintenance in year of age y + ?/2. When discounted it is

(VII) (VIII) identical to Hx except that Hx dis-

(VIII) counts for mortality. Hx is the mathematical expression for the human life value for recovery from a third party for wrongful death'3 (the range of x dis- cussed above is still pertinent).

Definition for Disability Income

The case of disability income is similar to recovery for wrongful death in that the discounting factor includes death. It is different, however, in that those who are unemployed due to disability are not included among the unemployed. Thus

(VIII) Hx is adjusted to

13 One theoretical consideration which may be ignored in practice should be pointed out. When Equation (9) is applied to tort liability situations, the mortality statistics used should be "net" of the probability of being killed by a third party. If this is not done, then one will be discounting for the factor that is being isolated.




w-1 (IX) (e) i)

H.= X WY lyy+l'2 (fy+1/2+fy+1/2/

y =x

I y+1 /2-x

-my 1y+1 /2 V

where: (i)

fn is the fraction of the In persons assumed to be (i)

disabled at age n. Where fy+1 2 is very small, (VIII) (IX)14

H. may be used as an approximate to Hx

Human Life Value and Dependence

In the previous section there has been shown the development of several matJie- matical expressions for the human life value. They are lacking, however, in that there is no discussion of the primary issue, viz., "value to whom." Thus the value will be different depending upon whose benefit is being considering. The expression developed for life insurance represents the present value of all of an individual's net future earnings. It may not be necessary, however, for a man to purchase this amount of insurance cover- age, because the use of this total implies that there will be someone continuously dependent upon his wages until retirement, and possibly thereafter.

It follows from the above that a man whose only dependent is a wife aged 20 would not purchase the same amount of insurance as a man who has a mother of 66 as his sole dependent. To consider the probability of the dependent being alive adds a new dimension to this analysis. Up to this point, the discussion has re- volved around the question of what the wage earner would have contributed to his family, but the family by its very existence affects his value.'5

The human life value of a person to his dependent is contingent upon (1) the

factors inherent in the human life value itself; and (2) the existence and dependence of the beneficiary.'6 Thus, to purchase the same amount of insurance regardless of the age of the beneficiaries ignores the probability that the dependents might not be alive to need the income of the breadwinner. This may be taken into account in two ways: (1) proj- ject the self-maintenance figures so that they reflect the age of the beneficiary; or, (2) adjust the human life value equation to reflect the probability that the dependent may not be alive to need the income.'7

(VII)

For the latter case, H, can be adjusted to

w-1

Hx:z,= (Y -my) (y+1/2-xPz) y =x

where y+1/2-xPz = probability that a wife aged z survives y+1/2-x years (not necessarily according to the same mortality rates to which her hus- band is subject. Thus y+1/2_xPz = lz+y++1/2-x/lz

(from the mortality table for wives.) A simpler method when there is more than one dependent would be to use a series of summations, one for each dependent, and based upon the proportion of the breadwinner's income which goes to that dependent.

In life insurance programing, the probability of the dependent's living until the death of the breadwinner is generally assumed to be certainty, the one notable exception to this being the survivorship annuity which promises to pay a life income of a specified amount to a desig-

14 Unfortunately data are not available to apply either modell

15 The existence of the family was also noted and accounted for in determining what portion of the man's income was consumed by him and what portion by his family.

16 The necessity of such dependence has been recognized in the doctrine of insurable interest.

17 While this discussion is couched in terms of life insurance, the same principle is also valid in the application of the concept to underwriting and cases of recovery for wrongful death. Cf. A. E. Hofflander, "Loss of Income Due to Wrong- ful Death: A Method of Measurement," Insur- ance Law Journal (February 1965), pages 92- 101.




nated beneficiary if the beneficiary survives the insured. The probability of the dependent's continuing to live after the death of the breadwinner is considered in programing through the use of settlement options based upon life contingencies.

While he may be aware of this distinc- tion, there are two reasons why a prospective insured might wish to ignore the life contingencies of his dependents. He may wish to purchase an amount of insurance equal to his human life value, making the assumption that his dependents will still be alive and be in need of his support. This would be a conservative approach, and considering the importance of the undertaking, it is not completely unlikely. On the other hand, he may be aware of the fact that the funds provided by his insurance will be more than are needed by his dependents, but may wish that the excess, if any, be left to some charity or similar organization.

Summary

Very little effort has been expended in investigations into the meaning(s) of the human life value concept, most authors being content with a general statement regarding its usefulness. The human life value is not one value or concept, but rather it is many values. Each value must be defined carefully in order to be appro- priate for its expected use. This paper develops four models or mathematical definitions of the human life value.

Unfortunately these models are at the moment, only theoretical because the data necessary to use them are unavailable.'8 As in most fields of endeavor, abstraction precedes realization.

18For a discussion of the problems involved in obtaining data on age, income, and occupation, see A. E. Hofflander, "Salary Scales: An Aggre- gate Approach," Journal of Risk and Insurance, Vol. XXXII, No. 4 (December, 1965), pp. 571-8.



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