Arnold Kling  

Valuing Life

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Robert H. Frank writes.


Mr. Landsburg's argument finesses the important distinction between a "statistical life" and an "identified life." The concepts were introduced by the economist Thomas C. Schelling, who observed the apparent paradox that communities often spend millions of dollars to save the life of a known victim - someone trapped in a mine, for example - yet are often unwilling to spend even $200,000 on a highway guardrail that would save an average of one life each year.

This disparity is not economically irrational, Mr. Schelling insisted, because the community values what it is buying so differently in the two cases. It is one thing to risk one's own life in an unlikely automobile accident, but quite another to abandon a known victim in distress.


Frank refers to an article by Steven E. Landsburg arguing that it was cost-effective to disconnect the ventilator of a terminally ill woman who apparently wanted to live to see a relative. I did not find Landsburg's thought-experiment concerning insurance at all persuasive. That does not mean that I believe that the woman should have been kept alive.

However, I find the claim by Frank (or by Schelling?) that it is rational for "the community" to pay more to save an identified life than a statistical life to be highly suspect. Even assuming that I have no personal relationship with the people involved, I can see where I might instinctively prefer saving an identified life to saving statistical lives. However, if I thought about it, I probably would conclude that this instinct is not rational on my part. If my instinctive valuation is irrational for me as an individual, then why is not also an irrational valuation for "the community" to make?


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COMMENTS (14 to date)
spencer writes:

Yes, but life is full of different values.

But as economists we usually refer to it as consumer demand.

The sum you will pay for many, many things is different then I would pay.

Moreover, the sum you will pay at different times is also different. For example I bet you would pay more for air conditioning in Washington in August then in Jan.

These differences are not irrational.

Doesn't the entire concept of consumer surplus depend on this?

Forgive an amateur's question, but ...: Why do economists get so hung up over the question, "Is this behavior rational or not?" It seems like a childish obsession. In this case: Maybe it's rational in some sense and irrational in another. Who cares? Which doesn't make the observation (about how a community might be willing to pay skillions to save a known life, etc...) uninteresting , or unworthy of being poked-around-in from an economic point of view.

Bill Stepp writes:

I have not read Schelling's example, so this comment should be interpreted in that light, but I do think some institutional context would shed some light. In the mining example, the mine is likely to be privately owned and the owner(s) might be subject to a lawsuit. Therefore, he/they are going to invest quite a lot to free the trapped miner, if only to curry favorable public opiinion, which could be important in a lawsuit, and to alleviate any fear held by other employee-miners about a callous employer.

In the case of spending $200,000 to save some statistical lives, the road is probably owned by the State (which means it's actually owned by no one), so who cares?

Communities don't spend money--individuals do, in Frank's example, either mine owners/shareholders or non-owner- taxpayers. Which group has more incentive to maintain the property in question and prevent accidents?

daveg writes:


I would like to see some more examples of this.

Staying off the shoulder of the road arguably involves skill. Many hold a high opinion of there own skills and therefore conclude that they don't need a guardrail, and that the guardrail is only to help someone else.

Someone in a well or mine is there through no fault of their own (in theory) and therefore there is more of a "but for the grace of god" feeling?

As to being rational, I think the point is that rational action will save the most lives given a fixed amount of money, which is a good thing.

Lord writes:

Economists tend to think of rational as an objective fact rather than the judgement of facts within the context of a theory or theories and the assumption of a number of premises. People may hold different theories and and different premises and come to different conclusions and still both be rational. Is it rational? Not to me. It is emotional.

Lauren writes:

Hi, Michael.

Why do economists get so hung up over the question, "Is this behavior rational or not?" It seems like a childish obsession. Who cares?

An excellent question! The answer is that almost all fundamental matters in economics turn out critically to depend on whether or not people have and tend to make reasonable use of information. Depending on which way one leans on this matter, one can justify results as divergent as pro- or anti-free markets, pro- or anti- government interventions in matters from daily life, to borrowing and lending, to taxation, redistribution, and welfare, to government borrowing and debt, to international finance, and even monetary policy (which is fundamental with regard to inflation, employment, interest rates, and the value of fixed-rate debts).

Some economic models make an assumption tantamount to asserting that people do not have information about the future, or do not use or know how to use it even if they have it, or do not use it to best advantage. Other models make the assumption that people have all possible information about the future, or put whatever information they have to good advantage, or use market mechanisms to help take advantage of it. The latter kind of model, which came to the fore in the 1970s and 1980s simultaneous with the demise of the original Keynesian model (which demonstrably failed because it forceably assumed people couldn't foresee inflation or government behavior even when it was affecting every minute of their lives), came to be called "rational expectations." Models that lean toward assuming people make good use of available information are called "rational."

Since such important matters ride on whether or not people are "rational"--that is, if somehow or other efficient use is made of available information--the prevalence and relative effectiveness of rational behavior is hotly contested. Even when the term "rationality" is not used, it is often only a layer below the surface of economic debates. It is possible to trace many popular arguments about economics back to whether or not the individuals in the speaker's model are being assumed at the margin to be smart or stupid--rational or irrational.

Debates that are explicitly about rationality are often really about other matters entirely--matters that ultimately hinge on whether or not, and if so, when and how, people make full use of available information. Anomalies in rationality are interesting to both camps: are they important at the margin, or merely curiosities? It is not the goal of economics to explain the behavior of every individual any more than it is the goal of physics to explain the behavior of every atom. The question is: which assumptions provide more reliable predictions in general?

ptm writes:

Michael,
Good question, and what Lauren said.

Your question, and Lauren's "are people rational?", are a lot of what's studied in behavioural economics. BE is basically the border of psychology and econ - looking at how people's human non-computerness results in rational or irrational decisions.

resigned writes:

How is rationality quantified in a model?

Tom writes:

If the woman's family was unwilling to pay to keep her alive, why
should complete strangers be forced to pay to keep her alive. Obviously,
there are numerous people who believed this decision was wrong and the
woman should have been kept alive on a ventilator. But of these people,
how many put their money where there mouth is and actually sent in money
to keep her on a ventilator? How many have ever sent money to keep someone on
a ventilator? People are very ethical as long as it comes at someone
else's expense or out of someone else's wallet!

J Klein writes:

(1) It is rational to be more involved in saving the life of a relative, an aquaintance, a "significant" one (in a wide sense), than a complete stranger or a potential enemy or competitor.
(2) Any person whose fate is discussed in the papers, in TV or in the office, becames a celebrity and its image occupies a certain place, a certain number of neurons, in one's brain.
(3) As the celebrity of the person grows and it is more heard about and commented, he or she becomes part of me and it is rational to care for him.

Therefore, the miner trapped in the mine and his wife and family become part of my circle and worth saving.

Lauren writes:

resigned asked:

How is rationality quantified in a model?

One method is to embed in the model a probability function on which future outcomes depend, and to give the agents (people, businesses, government officials, etc.) the ability to learn about the parameters of the function. (This is called Bayesian updating.) That sounds eye-glazingly complicated, but it's not as complex as it sounds.

Here's a simple example of how it works out:

You don't know what inflation is going to be next year, but I bet you do weigh the probabilities when you make decisions important to you. You can guess pretty well at the mean expected inflation (say, you might guess it's going to equal 2005's plus maybe 1%). You can also guess a range around that (say, plus or minus 3%), perhaps a slightly bigger range than you would have put on it a year ago, say because you know the Chairman of the Fed is changing, or because you are worried based on newspaper reports or because you remember what happened in the 1960s-1970s when inflationary policy was leaned upon to help finance the Vietnam War. Based on your guesses, even if you don't pin the exact numbers down, you still know enough to make some decisions. For example, depending on your circumstances, you might sensibly refinance your adjustable rate mortgage to a fixed rate mortgage.

An economist who builds rationality into his model does so not by surveying what people expect (though that might be a perfectly good method, but it's costly, and responders don't always answer truthfully), but by guessing that people are reasonably good at using past history to predict things like inflation or interest rates. He approximates what millions of people like you do by running regressions and statistical analyses to figure out the statistically-predictable mean and variance of the inflation rate, and then uses those estimates in his model as if they are what people expect. His actual assumption is that at the margin, the agents in his model can use history just as well as he can. He's no smarter--if anything he's less smart!--than the sum total of all the people in the economy.

By assuming rational behavior and rational expectations in this way, it's very likely that that economist's numbers will be somewhat like yours. He'll come up with some exact numbers, and while they may not be identical to yours, his will be based on millions of folks just like you--in fact, literally including you because you are a contributor to the statistical bases supplied by the government and used by economists! It's also likely you are quite typical. So, assuming you are typical, one thing this economist's model will predict is that interest rates on fixed rate mortgages will rise relative to interest rates on adjustable rate mortgages, because individuals will tend to demand more fixed rate mortgages and fewer adjustable rate mortgages.

An economist who doesn't take this kind of rational, probability-oriented behavior into account might build into his model that the inflation rate for 2006 will be the same as for 2005, with an expected variance of 0%. He is implicitly assuming that people think next year's interest rates will stay the same and they do not expect any risk surrounding inflation. He will predict that the gap between ARMs and fixed-rate mortgages will not change. For, why would it?! According to his model, no one has any incentive to substitute a fixed-rate mortgage for an ARM.

(A third kind of prediction often comes from someone who makes up numbers altogether, based perhaps on his own personal experience, guesses, or personal surveys. For example, someone in the press or financial industry who claims inflation in 2006 will rise by 1% and inflation risk will increase to between 3-6%, without supplying either documentable survey information or published, replicable statistical analysis to back up his claim, is not generally recognized as an economist. All the same, his made up numbers may express an attempt to approximate rational thought and behavior, and may be an improvement over assuming no rationality whatsoever.)

Which economist makes better predictions--not only about mortgage interest rates but about hundreds of other prices and quantities, from heating oil to the redevelopment of New Orleans to the cost of eggs in the face of bird flu? So many things depend on whether or not people account rationally for the future that economists are still hotly in debate.

Daveg writes:

Not just people, but identified whales to:

The northern bottle-nosed whale, which is 16-18ft long and is usually found in deep sea waters, has passed Parliament and is moving upstream.

A rescue boat has been sent to protect the whale and rescuers have been trying to keep it away from the river banks.

Specialist equipment, including inflatable tubes to re-direct the animal downstream, are being sent.

The whale has come within yards of the banks and has crashed into an empty boat causing slight bleeding.

[Per various news sources, including Radio New Zealand online--Econlib Ed.]

Tom writes:

"Therefore, the miner trapped in the mine and his wife and family become part of my circle and worth saving."

J Klein, when does your flight to West Virginia leave?

Bob Knaus writes:

I think Lauren should write her own blog entries, and have her picture posted at the top along with Arnold & Brian.

One of the cool things about the work I do (teaching boy scouts how to sail in the Bahamas) is that I get to meet a lot of talented adult leaders from all walks of life. Last summer, one of my leaders told me he worked as an economist for the IRS. I asked him if he was a behaviorist or a rationalist. He paused in thought for a good bit longer than I expected and replied that he was an "empiricist".

If there is a 3rd way, seems to me that might qualify :-)

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