What is Your Life Worth?
Price theory as a tool for pricing the priceless
It is common to hear the phrase: “you cannot put a price on that.” Sometimes the phrase is meant more as a normative statement. To put a price on particular things is considered verboten.
Other times this phrase is meant to be taken literally. In that context, the phrase is meant to evoke the idea that whatever is being described is not something that you could purchase. It is often used to describe an experience or a moment or something of natural beauty.
For a price theorist, this use of the phrase is confusing. For example, as Thomas Sowell writes in Knowledge and Decisions:
To say that we “cannot put a price” on this or that is to misconceive the economic process. Things cost because other things could have been produced with the same time, effort, and material. Everything necessarily has a price in this sense, whether or not social institutions cause money to be collected from individual consumers.
Nonetheless, one often hears people use the phrase in reference to things like the value of human life. This is often meant to convey the idea that a human life is in some sense priceless. It is understandable why people might use the phrase in that context. Often this is attached to religious belief. There is a saying from the Talmud, for example, that “whoever saves one life, it is as if he saved the whole world.” Christians believe in the inherent dignity of man, that man was created in the image of God, for a purpose, and that human life is sacred and must be protected.
At the same time, one can think of many everyday experiences in which people are tasked with estimating the value of human life. Insurance companies must make such determinations. Legislators create rules designed to save lives and regulators must decide how and when to to enforce rules. This requires making a determination about whether the cost of saving an additional life would be worth the cost. The legal system allows the families of victims to seek compensation in the event of a wrongful death.
In this week’s newsletter, I want to focus on estimates of the value of life. In cases where one needs to put a value of human life, how does one do so? As always, price theory can be our guide.
The Statistical Value of Life
If we are trying to estimate the value of a life, we can get estimates from the economic decisions that people make. In this respect, we need to differentiate between two types of behavior. The first is the decision to purchase insurance. Someone who purchases insurance is someone who is trying to smooth out consumption. Absent insurance, a major health issue will shift a lot of consumption towards health care. During those times, the marginal value of a dollar spent on other goods is much higher. Insurance effectively transfers dollars from times when the marginal value of the dollar spent on those goods is lower to a time when the marginal value is higher.
A second type of behavior is the decision to invest in one’s health. These types of expenditures are designed to increase the probability of survival. This isn’t about reallocating disposable income over time. This is about living for a longer period of time.
It is important to note that there is feedback between both of these objectives. A longer lifespan has implications for consumption smoothing. There is also a moral hazard problem associated with health insurance. A person that has health insurance might not invest as much in health as the person would have if he or she had not purchased insurance.
Price theory can help us sort all of this out. Divide one’s life into two periods. Suppose that the consumer has actuarily fair insurance. The consumer would like to consume in both periods. The consumer must divide income between consumption goods (in both periods) and health expenditures. Greater health expenditures increase the probability of survival (with diminishing returns; the maximum probability is one, after all), but reduce consumption on other goods. The consumer has to decide how much to spend on health expenditures relative to other goods.
Price theory tells us that the consumer will choose health expenditures such that the marginal benefit of the last dollar spent is equal to the marginal cost. It is this marginal condition that gives us insight into the value that people put on their life. When you invest in health, this increases the likelihood of survival. This increases one’s average utility. At the same time, this increases the expected benefit from insurance since it increases the expected value of smoothing consumption over time.
Recall from my previous post on the price level that even though we cannot measure utility directly, we can use price theory to determine what observable variables make it possible to measure average utility. It is straightforward to show that we can capture average utility by measuring the value of consumption and leisure in the second period. Recall, however, that there is an additional benefit from being able to smooth consumption over time. Nonetheless, we can use price theory to show that the total effect is just some multiple of average utility, where the multiple depends on one’s willingness to substitute consumption across time.
There is still a challenge here. The multiple that I referenced above is a function of a parameter that measures the curvature of the utility function. It is possible to estimate that parameter. We have estimates. We can estimate the statistical value of life by calculating the present value of the product of that parameter and our measure of average utility.
However, there is also an equivalent measure of the value of life if we ignore this curvature. In fact, if we ignore the curvature of the utility function, it turns out that the marginal condition described above is equivalent to the marginal condition that one gets by choosing health expenditures to maximize lifetime wealth. This should make some intuitive sense since expenditures on health are made to extend one’s life. There is a natural correlation between increasing one’s lifespan and increasing one’s lifetime wealth.
This alternative measure gives us an easy way to measure the statistical value of life. The marginal condition from the wealth maximization problem measures the marginal benefit as the change in the probability of survival from an additional dollar spent on health multiplied by one’s wage.
What makes this alternative measure attractive is that one can back out such calculations by estimating wage regressions for workers. Dangerous jobs can result in death. People who work in those jobs know this in advance. They also know that they have alternatives. Dangerous jobs therefore require a wage premium.
Since the wage premium communicates something about how the person evaluates risk, one can use information in the wage premium to figure out the statistical value of life.
It might be easiest to do this by way of example. Back in 2004, Dora Costa and Matt Kahn estimated wage premia for workers between ages 18 and 45 based on the probability of dying on the job. They found that for 1980, one death per million hours of work in a profession led to a wage premium of about $5.34 per hour (in 1990 dollars). The price per change in probability is $5.34 million (in 1990 dollars), which is the implied statistical value of life.
This estimate is important. Going back to the discussion in the introduction, another common phrase you hear from people is that “if it saves just one life, it would be worth it.” That might be true in a certain metaphysical sense — and is certainly true to the family of person saved. However, in a world of finite resources, policymakers face trade-offs. How much should policymakers be willing to spend to save one life? The answer we have provided is about $5 million (in 1990 dollars). The figure is ultimately important for evaluating workplace safety rules, for deciding how much to spend on medical research, environmental regulations, etc.
The Statistical Value of Life Over Time
Since the statistical value of life is priced in terms of dollars, one might be interested to know how that value changes over time. Their estimates are in 1990 dollars. Changes in the purchasing power of a dollar certainly would affect these estimates. Nonetheless, this isn’t all that price theory has to say.
If we can estimate the statistical value of life using wage premia, then the statistical value of life might change in predictable ways over time. For example, if the quality of life improves over time, then workers will demand a higher wage premium. Changes in life expectancy matter as well. If non-job-related mortality declines, the wage premium should rise as well (this reflects a higher value of life because there is more life to live). At the same time, the demand for safety is likely a normal good. That means that as incomes rise, on average, the demand for safety will rise along with it. This is likely to lead to fewer workplace deaths. Yet, this effect could be somewhat ambiguous. Typically, we would expect workers would pay for this increase in safety with a lower wage premium. Nonetheless, people could create more safety is by moving out of risky sectors and into less risky sectors. All else equal, to attract more workers into the dangerous jobs, this would tend to push the premium higher.
In their paper, Costa and Kahn estimate the statistical value of life for 1940, 1950, 1960, 1970, and 1980. They find that workplace fatalities did indeed dramatically decline over this period. The trends were particularly dramatic in industries like mining and construction. They also find that the wage premium associated with fatality risk increased pretty significantly over that time.
For 1940, their linear model implies a statistical value of life of around $1 million (in 1990 dollars). This estimate more than doubles by 1960 and rises to $5.3 million for 1980. Thus, even though fatality risk declined pretty dramatically, the wage premium (and thus the statistical value of life) rose over this period.
Another important conclusion is that they find that the statistical value of life rises by approximately $1.50 to $1.70 per $1 increase in real GNP per capita. As people see their income rise, the value of their life rises faster than their income.
The implications are important. Costa and Kahn point out that many treat estimates of the statistical value of life as a constant, at least in real terms. Even those that update it over time with income, consider it relatively unresponsive to income compared to their estimates. Their argument is that this is not only incorrect from a theoretical point of view, but also that it has important implications for policymakers. Relying on old estimates can therefore lead to a significant underestimation of the value of life thereby adversely influencing rule-making and enforcement.
Concluding Thoughts
The main implication here is that price theory can be used as a tool to put a price on something even if that something does not have a market price. This is important. To argue that we cannot put a price on something ignores what economists mean by price. A price is a measure of cost. Even when things aren’t formally priced in markets, people’s actions still reveal the value they place on them. Decisions to work in a risky job and the compensation received for doing so tell us a lot about the value that people place on their life. Price theory allows us to take those actions and translate them into dollar values. In fact, a pretty basic formula for estimating the statistical value of life follows directly from price theoretic insights.