What’s the Value of a Statistical Life?

What’s the Value of a Statistical Life?
Rebecca Goldin Ph.D and Cindy Merrick, June 27, 2011
To Oscar Wilde, a cynic knows the price of everything but the value of nothing; but when it comes to regulation, statisticians understand that we all have our price.

Recently, The New York Times covered a story about the value of life – the statistical value, that is (also known by the acronym VSL). This is the value that government agencies use to evaluate the importance of regulation or legislation. It is the “official” value that your life is worth to the agency. President Obama has recently increased this value across agencies, according to the Times. But the variety of VSL estimates across agencies (and by different economists and statisticians), as well as the political nature of the value itself, makes one wonder – where do these values come from, and what are they good for anyway?

Suppose you are a legislator, and before you is a bill proposing that automakers be required to double the roof strength of new cars. According to the research cited, doubling the strength would save as many as 135 lives per year. Alternatively, for a smaller incremental gain in strength, you could save 44 lives. Knocking at your door are car manufacturers and autoworkers, claiming that new regulation would cost jobs, and consumer products advocates who claim that saving lives should be the priority.

How do you decide whether to sign the bill? Does the number of lives involved make a difference? Perhaps any increase in safely seems like a good idea – but such regulations are not without economic cost. Stricter standards typically mean greater expenses to manufacturers, which translate into higher costs for car buyers.

Would the answer be more obvious if the number of lives saved by double-strength roofs were 1,035 – or 10,035? What if only one life might be saved? Surely at play here is some sense of overall benefit/cost to society based on a value in units of human lives, however vague that unit value may be?

Presidents, legislators, economists, and business leaders have in recent decades sought methods which would make such cost-analyses precise: when is an investment, regulation or subsidy “worth it” in terms of human lives? For such a comparison, one needs a means of conversion, for turning the “apples-to-oranges” (dollars-to-lives) into “apples-to-apples” – or, in this case, dollars-to-dollars. Thus, if we somehow arrive at a dollar value to affix to each life cost by not strengthening car roofs, we can compare the cost of the regulation to the dollar “equivalent” of statistical lives saved. Such a dollar value on lives is known as the Value of a Statistical Life, or VSL.

As appealing as such a solution may be to the sharp-pencils concerned with bottom-lines, the rest of us may squirm in our seats at the thought of being reduced to dollars and cents for the purpose of political negotiation. Just how does one arrive at such a dollar value? And while we’re going down that road, stickier questions inevitably arise: should every life have the same statistical value? Should numbers change based on age, income, education level, or health status?

Insurance companies have their own business-oriented approach, based on risks and pay-outs. If you are a teen driver, expect to pay more for auto insurance, and if you are an overweight smoker, expect to pay more for life insurance. Actuaries base prices on risk profiles, taking into account what they would have to pay if the worst should come to pass. From a business point of view, this is different from the haggling that goes on for VSL; for life insurance, the customer decides the amount of the desired payment in case of death; and for auto-insurance the rates are determined by the possible medical costs in case of accidents. No decision is made on what a life is “worth”. All decisions are based on the required pay-out. The smoking, overweight 65-year-old male, may want more life insurance than the nonsmoking normal-weight 25-year-old female, and he will pay for it.

In contrast, government regulations trump individual preferences. Car manufacturers will not make cars of varying roof strengths in order to allow individuals to choose how much they want to pay for the increased safety. It will be determined by the legal limits. There is no pay-out for an associated death –the price per head can take into account damages to society in a broad sense (such as lost wages to the family, lost tax revenue to the government, lost investment for the educational system, and health costs to insurance companies) but these damages vary dramatically from person to person.

Wage-Risk and Price-Risk Studies
Government regulatory agencies use economic data from various studies of society’s risk choices. Wage-risk studies reflect the relationship between a person’s income and the risk of injury, death, or other hazards on the job, while price-risk studies measure a person’s willingness to pay to reduce exposure to risks in their lives (for example, real estate prices increase with distance from a polluted river or hazardous waste dump).

Many factors affect wages besides on-the-job risk, such as an employee’s education level and a variety of market forces. Standard statistical models have been developed to “disentangle” these other factors from the wage-risk preference exhibited by a labor force. In 2003, W. Kip Viscusi and Joesph E. Aldy published a meta-analysis of market research worldwide that has sought, with a range of econometric methods, to establish useful measures of VSL and social behaviors with respect to risk, both in the world’s labor forces and in product markets. They describe the simple wage-risk dynamic this way:

The firm’s demand for labor decreases with the total cost of employing a worker. The cost of a worker may include the worker’s wage; training; benefits such as health insurance, vacation, child care; and the costs of providing a safe working environment. Because worker costs increase with the level of safety, for any given level of profits the firm must pay workers less as the safety level rises…For any given level of risk, workers prefer the wage-risk combination from the market offer curve with the highest wage level.

In one price-risk study evaluated by Viscusi and Aldy, the “cost” of using a seatbelt is measured. The study estimated that eight seconds of time are required to secure the seatbelt. This time can be monetized by using an individual’s wage rate: the fact that individuals are willing to spend the time to put on the seatbelt implies (to an economist) that the risk of death or maiming for riding without a seatbelt is “not worth” (to the individual in question) the additional wage that he or she would earn by being paid for those eight seconds. Over many pieces of data like this, economists are able to get a sense of what risks are worth the money by individuals.

In the studies reviewed by Viscusi and Aldy, there was a trend showing a positive correlation between income and what they called “premiums for bearing mortality risk.” In other words, controlling for other factors, jobs with increased occupational hazards tend to pay people more for the risk. In economist lingo, relating a change in income to a change in demand for some commodity (including such commodities as “lower risk”) is known as income elasticity. The research consistently shows positive income elasticity with respect to risk-reduction considered as a monetized commodity.

Where VSL numbers come from
Ultimately, such analysis can be used to generate a number in dollars for VSL, using something called the standard wage equation. In their meta-analysis of wage-risk studies, Janusz Mrozek and Laura Taylor give a straightforward explanation of the math behind the numbers. The wage equation is a statistical estimate of the breakdown of wages due to a worker’s profile. Variables in the equation account for demographic factors like age and education level, and job characteristics like risk of injury, as well as overall risk of death on the job. VSL is computed as the rate of change of a worker’s wage with respect to the change in risk of death.

For example, suppose that the increased risk of death on a job is 1 in 10,000 compared to a job with no observable job-related death, and that a worker is paid an additional $0.35 per hour for accepting this risk. Assume the worker works 2,000 hours per year (40 hours per week times 50 weeks), so that $0.35 x 2,000 = $700 per year in wages is paid to the worker for death risk. Since the expectation is that 10,000 people would be paid this additional $700 per year in wages per one death, the statistical value of life is given by the total marginal wages earned ($700 x 10,000 = $7,000,000) per death.

One agency’s VSL is not another agency’s VSL
Of course, not all methods produce the same monetary values for VSL, and many differ significantly. Some research generates its data across a workforce for a particular industry, while other research is collated from multiple industries. Most vexing is that various government agencies use VLS numbers that vary by millions of dollars. The US government’s Office of Management and Budget gives guidelines for evaluating the VSL (as it does in a 2003 Circular) but does not give any advice as to what the value should actually be.

When the National Highway Transportation Safety Administration proposed in 2009 that roof crush standards be upgraded so that, in a rollover, a passenger vehicle would be able to withstand up to 3 times the weight of the car before crushing, it estimated an extra cost to consumers of about $875 million to $1.4 billion per year. And by stating that about 135 lives would be saved from such a safety upgrade, it refers to a VSL of between $6.4 million and $10.4 million. Such an upgrade failed in popularity during the Bush administration for being far more costly than the value of human lives saved. In 2009, the Department of Transportation, of which the NHTSA is a part, updated the VSL to be used across the department for economic analysis to $6 million.

In 2004, the FDA proposed improvements in the bottled water industry, based in part on the risk of cancer due to arsenic sometimes found in bottled water. They used a VSL of between $5 million and $6.1 million to justify the cost of new regulations. In 2009, the FDA again used $5 million as their VSL in regulating the egg industry for the prevention of salmonella poisoning. Several other recent regulatory proposals use the same $5 million amount, indicating that for the FDA, your VSL has not changed since 2004.

The EPA by all appearances has put in the lion’s share of research on VSL among government agencies. They make available their own set of guidelines for evaluating VSL and doing other similar analysis, and make transparent their past and current VSL numbers, as well as the procedures they used to arrive at them, via their web site. They currently post a value of $7.4 million in 2006 dollars.

Government agencies are not the only people interested in using VSL to put a figure on human life. In their analysis of the burden of cost to the US caused by women who fail to adequately breastfeed newborns, Harvard researchers Melissa Bartick and Arnold Reinhold, used a VSL of $10.56 million in 2007 dollars, more than twice as high as the FDA numbers, and at the high end of the range suggested by the Office of Management and Budget and used in the majority of research on the topic ($1 million to $10 million, based on data from 2003).

And, in an interesting twist, West Virginia University researchers turned to the same Viscusi report used by the EPA in their analysis of mortality cost of coal mining in Appalachia. They adjusted Viscusi’s 2003 values to 2005 dollars (for the year the report was published), coming up with a VSL range between $4.6 million and $7.7 million.

But while the variation of VSL muddies the waters of honest cost-benefit analysis, an agreed-upon means of comparing our risks and costs as laborers and consumers could help make some decisions less politicized. We may not all be in agreement about whether we should pay for extra roof strength on a car, but if we agree on the VSL, we can argue about the cost associated with legislation in relation to the calculated benefit in terms of lives saved. It’s apples-to-apples, even when our lives are in the balance.

One thing we should be clear about: VSL is not about the actual worth of a life or about the monetary cost if that person dies (such as lost wages); it’s only about the (statistical) money that risk of death is worth to humans who take on those risks in exchange for wages. Its calculation is fraught with cultural bias and perception of risk as much as anything factual about the risk itself. It only pretends to put a number on our value as human beings.