Monday, May 22, 2006

The Value Of A Statistical Life...

I was listening to NPR the other day and the talk show was about how insurance companies, auto makers, risk management companies, etc., calculate how valuable a human life is. The average cost/value of a human life is $6 million dollars...ONLY $6 million dollars. You and I are valued at $6 million dollars.

What this statistical value means is this:

Your insurance company, job, etc., weigh this $6 million dollar value figure into their cost analysis of what monetary loss they would incur if you were to die and it was their fault or they had to pay out for the loss of you (or anyone else who might die in a similar circumstance). If the cost of providing you with safety equipment which might lessen your risk of death on your job is more than that $6 million dollar figure, chances are you are NOT going to get that equipment! This is called "Risk Management". And here we all thought "Risk Management" was actually in place to PROTECT us on the job...well it's not...especially if that protection costs more than the statistical value of YOUR life!

I did a little research on this topic and was horrified and shocked to learn ALL COMPANIES who deal in any type of potential loss of human life use this statistical figure. Your car maker, your local transportation system, the makers of household products, etc.

For those of you who actually UNDERSTAND (and perhaps even ENJOY math/'re just plain sick if you do!) statistical calculations, I am including some cut and paste info for you to peruse. I'd say "enjoy", but that just sounds sadistic...

The Value of a Statistical Life

The value of a human life is the willingness to pay to avoid the end of life. It can be conceptualized as the following. Suppose utility (happiness) depends on income and health: U(H,Y), where U(.) is utility, H is health and Y is income.

The value of a change in health risk (from perfect health) is:
U(pH,Y) = U((1-p)H,Y-WTP)
Where H represents perfect health and p is the probability of good health, 0

The willingness to pay to avoid risk increases with the level of risk, DWTP/Dp > 0. The value of life (VL) is for someone in perfect health is:
U(H=1,Y) = U(H=0,Y-VL)

Market Studies
Information from people's behavior when faced with risk can be used to measure the WTP to avoid risk.

The hedonic price method uses information on people's job choices to estimate WTP for job risk changes. The WTP for a risk change is equal to the wage differential generated from labor markets

WTP = -dW
where -dW is the wage differential (dW <>

The value of a statistical life can be estimated from hedonic wage-risk studies. Suppose that a wage differential (dW) is associated with a job fatality risk change (dR) in the following way:

W = a - b*R

where a and b are parameters. The effect of b on W is negative because increases in risk leads to decreases in the wage rate. Suppose R = .0005; this means that there is a 5 in 10,000 chance of a job fatality (this is a high job risk, higher than for the mining industry). If there are 10,000 workers, there will be 5 random deaths. To reduce the job risk and the number of deaths by 20% (from 5 to 4) would make R = .0004 and dR = .0001. If dR > 0, then dW <>

-dW = b*dR = b*.0001

If the estimate of b = 2500, then WTP for dR is $2500*.0001 = $0.25. The individual is willing to accept a wage $0.25 lower per hour for the lower job risk. The annual value of the risk change is $0.25*2000 = $500 (assuming 2000 hours worked per year). With 10,000 workers, the value of a statistical life (VSL) is VSL = $500*10,000=$5,000,000.

Contingent Valuation Studies
Market studies are limited in that only those risks experienced by people can be used to infer the value of a statistical life. Stated Preference (contingent valuation, ranking, etc.) surveys can be used to estimate the benefits of policies that place people beyond the range of their choice making experience (eg, changes in job risk not experienced, new life saving drugs).

Consider the following survey question which asks for the willingness to pay for a private good (adapted from Johannesson, Johansson, and O'Conor, 1996).

"In the U.S., about 1 in 5000 people die annually in traffic. A possible measure to reduce the traffic risk is to equip cars with safety equipment, such as airbags. Imagine a new type of safety equipment. If this equipment is installed in your car, the risk of dying in a traffic accident will be cut in half for you and everyone else travelling in the car. This safety equipment must be tested and serviced each year to make sure that it is working correctly. Would you choose to install this safety equipment in your car if it will cost you $A per year?

[YES or NO]

Where A might take on values of $30, $150, $300, $750, $1500, or $3000 for each survey respondent. A similar question which asks for the willingness to pay for a public policy might read (again, adapted for Johannesson, et al.)

"In the U.S., about 1 in 5000 people die annually in traffic. The number of deaths can be reduced if we devote more resources to preventing traffic accidents. We can, for example, straighten out turns, build safer crossings, and increase the supervision of traffic. Imagine a program that cuts in half the risk of your and everyone elses risk of dying in a traffic accident. Are you willing to pay $A per year more in taxes on your car for this program?

[YES or NO]

With both questions, the value of a statistical life is equal to the average willingness to pay divided by the reduced risk of death (dR). In this case, the reduced risk of death is (in general, the reduced risk of death is equal to the number of lives saved divided by the affected population).

If the average WTP = $500 and dR = .0001 (1 in 10,000), then VSL = 500/.0001 = $5 million.

Additional Readings
Fisher, Ann, Lauraine G. Chestnut, and Daniel M. Violette, "The Value of Reducing Risks to Death: A Note on New Evidence," Journal of Policy Analysis and Management, 8, no. 1, pp. 88-100, 1989.

Differentiate the value of a statistical life based on the level of risk. Find that estimates of the value of a statistical life range from $1.6 million to $8.5 million.

Johannesson, Magnus, Per-Olov Johansson, and Richard M. O'Conor, "The Value of Private Safety Versus the Value of Public Safety," Journal of Risk and Uncertainty, 12, pp. 263-275, 1996.

Estimate that the value of private and public safety measures to reduce by half the number of fatal traffic accidents is about $712 and $590 (1996 dollars). The implied value of statistical life is $8.9 million and $7.4 million, respectively.

Viscusi, W. Kip, "The Value of Risks to Life and Health," Journal of Economic Literature, 31, no. 4, pp. 1912-1946, December 1993.

Finds that estimates of the value of a statistical life range from $0.07 million to $4 million in labor and product market studies (1990 dollars).

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