A new indicator of economic development: How many years would you work to buy your life?

Although most people find it distasteful to put a dollar value on human life, people have been doing it for centuries and these judgements have always had a big impact on people.   Before the 1960s, the motivation for putting an economic value on human life was for buying and selling human beings either as slaves or as payment to compensate a family for a member’s death as documented in Alfred Hofflander’s short history (1966). This motivation led to the oldest methodology for for putting a dollar value on people’s lives.  It is to simply estimate how much income a person would earn if he or she had lived or perhaps just the net income after subtracting personal consumption.  As primitive and ethically questionable as this methodology might seem, it is still widely used in legal cases of wrongful death today.  It doesn’t seem fair that the US legal system literally judges the life of a high-income vulture capitalist to be thousands of times more valuable than the life of a full-time homemaker taking care of young children.  Most people’s lives are pretty cheap by this method because a majority of Americans don’t work for wages at any given point in time and many of the Americans who are working, don’t earn very much.

In the 1950s, RAND corporation economists developed a new methodology for valuing life because they had a new kind of motivation: how much to spend on saving lives. They were trying to help the US military make decisions using cost-benefit analysis and one of the major costs of warfare is the value of lives lost.  Two RAND economists, Jack Carlson, and his advisor, Thomas Schelling, developed the idea of evaluating the monetary value of life based upon the individual choices that people make every day.  For example, when there are two equivalent jobs like driving a skid steer in an underground coal mine versus in an ordinary highway project, workers will only choose the riskier job if it pays higher wages.  If the coal miners require $2,000/year higher wage to accept a slightly higher probability of death (say, 0.0002/year), then it is easy to calculate their value of life:

(Probability of death)*(Value of life) = (Expected value of taking on the additional risk)

Plugging in the numbers we get:

(0.0002)*(Value of life) = $2,000

Solve for the Value of life and you get:

(Value of life) = $2,000/(0.0002) = $10,000,000

This is basically how economists calculate the value of a life.  Assuming people are risk neutral, then those who do not take the coal-mining job must value their lives above $10m and the coal miners must value their lives at less than $10m.  It is a crude estimate, but perhaps it is better than nothing.  The same sort of calculation has been done for all sorts of risks that everyday people pay to avoid.  For example, airbags used to be an optional safety feature in cars, so economists could calculate how much people value their lives at when they buy airbags.  The same can be done for the purchase of fire alarms and a whole slew of choices that we all make.  Similarly, economists also take surveys to ask how much people would be willing to pay for safety equipment and use that information in the same manner.

Unfortunately, people’s choices vary widely in different scenarios and that makes it difficult to pinpoint the average statistical value of a life.  Some studies value life at orders of magnitude greater than other studies.  Policymakers need a value of life because it provides guideline for how much government money to spend cleaning arsenic out of our water and keeping mad-cow disease out of our food supply.  Without some kind of rule, they will waste both money and lives.  For example, if we spend $12.5 million per life cleaning up paper-mill pollution instead of spending $3 million per life on air travel precautions, then we would be wasting money on paper mills that could have saved four times more lives if it had been spent on airlines.  Unfortunately, our policymakers have not been able to agree upon a single statistical value of a life, so different government agencies spend different amounts on our health and safety.

One of the huge problems with both methodologies for estimating the economic value of life is the fact that they value the lives of rich people as being worth more than the less fortunate.

This is obvious in the old methodology that judges a rich vulture capitalist’s life as being more valuable than a homemaker, but it is also true for the new methodology because richer people are able to spend a lot more money on safety and are not willing to work at risky jobs. For example, Donald Trump talks a lot about how he wants to create a lot more American coal mining jobs, but imagine what wage it would take to get him to work in one of those dangerous coal mines.  He probably wouldn’t even do it for $1,000/hr because that would only earn $2 million per year.  The mmutilitarian logic of economics thus judges that Donald Trump’s life is worth many times more than coal miners’ lives.  Fortunately, most economists are loathe to take their own logic to its natural conclusion and make these kinds of controversial judgements.  Instead, they usually switch to a remarkably egalitarian recommendation.  First they estimate an average value of life for a population (including Trump and the coal miners) and then they treat all lives in the population as being worth the the average.  As A. Markandya says, “different values attached to the deaths of the rich and the poor …would, rightly, be seen as immoral. …no one even thinks of taking different values for the deaths of the rich and the poor citizens” when making policies that affect a nation.

That is the logic in the chart above.  Different government agencies don’t agree on a single value, but each agency treats all American lives equally.  The EPA treated every American’s life as being worth $9.1 million in 2010 and the CPSC treated everyone as being worth about $5 million.

Although economists have avoided political controversy by valuing every life in a given population the same, there is no controversy in economics to the idea that different populations have vastly different values of life.  For example, the literature uniformly agrees that each American life is worth more real dollars today than life was worth in 1970.  Everyone agrees that life has been getting more valuable because nobody complains about that optimistic judgement which implies economic progress. Similarly, there is only a little more controversy over the idea that lives in rich countries are worth more than lives in poor countries because we aren’t sharing government expenditures internationally.

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Economists like A. Markandya have roughly estimated that the average American life is worth somewhere around double the value of the average Mexican life which is worth more than twice as much as the average Malawian life.  There is little controversy in making these comparisons because there is little political consideration about the tradeoff of whether to spend more on saving Malawian lives versus saving Americans. In comparing the average value of life between two different populations, the reasoning is the same as the reasoning behind the idea that Donald Trump’s life should be worth more than the average American’s.  Richer people are willing and able to pay more for their own safety and security and therefore their ‘revealed preference’ is that their lives are worth more. Similarly, American lives are worth more today because the average American is richer than Americans in 1970, and the same reason explains why American lives are judged to be much more valuable than poor Malawians.

Economists have also suggested that the value of life changes over the lifecycle in an arch-shaped relationship between age and value of life (Jones-Lee et al., 1985).  This arc also happens to describe earning power at different ages.  Young people have the lowest value of life, mainly because they are relatively poor.  Then as people get older, their careers take off and as earnings grow, people value their lives more and more until it peaks around the age of 50 and then begins to decline again as average earnings start declining.

The idea that rich people value life higher than everyone else comes from the mmutiltarian philosophy that the dollar is a constant standard of value against which all other things should be judged, but this is a ridiculous assumption.  Mmutilitarianism is a peculiar mutation of utilitarianism which considers money to have a constant value for all people.  (Mmutilitarianism is an abbreviation of money-metric utilitarianism.) Before the rise of mmutilitarianism in the 1940s, almost nobody accepted this idea because most economists and philosophers believed in the idea of diminishing marginal utility of money.  This is the idea that giving an additional dollar to a rich guy like Donald Trump would give him less utility (or wellbeing) than giving an additional dollar to a poor guy like a homeless Malawian.

An alternative interpretation of the value-of-life literature is that it gives strong evidence for the diminishing marginal utility of money.  It is much more plausible that all people value their lives the same.  Instead of using money as the universal numéraire against which to value all other things, we should use human life as the universal constant against which to judge all else.  After all, poor and rich alike are willing to give a similar percentage of their wealth to survive a life-threatening crisis.  Rich people just have much lower value of money and are willing to spend vast amounts for relatively trivial purposes that won’t buy significant additions to their lives whereas poor people demand many more years of life per each dollar that they spend.

The newer method for valuing life is based on what people spend (or say they would spend) for safety or healthcare that reduces their risk of dying whereas the older method for valuing life is based on how much money people are expected to earn during their life.  Both methods reach the same conclusion that rich people’s lives are worth more than poorer people’s lives.  One of the interesting differences between the two methods of estimating the value of life is that the newer method typically gives much higher estimates of the value of people’s lives.  How could people pay more money per hour of life gained than the average amount that they earn per hour?  Nobody could even afford to buy the whole life they are living!

The answer  is the same reason why people typically spend more money on a week-long vacation than they earn in a typical week.  They only buy a little bit of vacation every year, so they can afford to spend a lot of money on it.  Similarly, our choices don’t buy very big increases in lifespan.  When Americans spend $100 on safety equipment, they don’t expect to gain very many hours of additional life expectancy.  Wouldn’t you spend even more money to extend your life by a week than you would spend on a week of vacation?

Perhaps value of life estimates could even be used to develop a new kind of measurement of economic development.  If people hate the time they spend working, and don’t enjoy life much, then they shouldn’t spend much money on safety just to extend their lives.  However, if people enjoy their work, then they should be willing to give up a lot of wages in order to buy healthcare and safety improvements that only yield a relatively small increase in lifespan.  The latter tends to be true in rich countries and it should be a goal of economic development.  Since people spend a lifetime total of about 80,000 hours working, it should be as meaningful as possible.  What better way to measure it than by comparing expected wages to value of life.

For example, if the median American values life at $5 million, and earns $25,000 per year, then the median American is willing to spend 200 years working to earn enough money to buy their life!  Too bad we get old well before that time and cannot accomplish this goal.  The standard economic analysis suggests that people in poor nations value their lives less than people in rich nations.  By this logic, poor people should be willing to work fewer years to be able to pay for their lives and this makes some intuitive sense. If poor people have less pleasant work than rich people and less meaningful leisure time too, then they shouldn’t want to work as many years to pay for their meagre existence.  This is what the happiness (subjective wellbeing) literature suggests.  Poor people express less satisfaction in both their work and in their lives than richer people.

Charles Jones and Peter Klenow made the same assumptions in calculating how much consumption people would give up to save their life.  This is Table A1 from their Online Appendix.

Value of Life at Age 40:

Ironically, some of the value of life literature actually gives exactly the opposite conclusion.  For example, Markandya cited a 1986 estimate by Mitchell and Carson that the elasticity of value of life is 0.35 with respect to income.  Markandya used this idea to estimate the value of life for about 100 countries.  The result is that people in poor nations are willing to many more years to be able to afford their lives.  Markandya’s model would estimate that the average American is only willing to spend 155 years working to buy her life whereas the average person in Rwanda was willing to spend over 2,633 years working to buy his life!  If Markandya’s model is correct (which I doubt it is), then poor people really value their lives exponentially more than rich people.

Here is a graph of the mean years of work per life value according to Markandya’s model:

It turns out that rich people really do value their lives less than poorer people.  Here is a graph of actual empirical studies:

This contradicts economic theory.  Why would poorer people be willing to sacrifice more hours of work than rich people to gain another year of life?  It deserves more study.

Jones-Lee, M..; Hammerton, M. And Philips, P.  The value of transport safety: results of a national sample survey. The Economic Journal, n.95, Mar. 1985, p.49-72.