# Economists Do It With Models

## How Do You Value A Life? Economists Are Happy To Show You…

#### July 1st, 2010 · 32 CommentsDecision Making · Fun With Math · Just For Fun

My friend Marty is convinced that he can’t possibly be the only person who follows both my site and Saturday Morning Breakfast Cereal. I’m not sure I agree, but I’m thankful that he is nice enough to send along relevant links anyway.

I can’t tell whether the creators of this realized how close they were to being correct. For example:

\$1.54 million. Exchange rate — 190 million yen, 980,000 British pounds or one human life. That is the statistical worth of a person, according to studies by economics professor Orley Ashenfelter GS ’70.

After years of conducting research on the effects of speed limit changes, costs involved and traffic fatalities, Ashenfelter and Michael Greenstone GS ’93, an assistant professor at the University of Chicago, calculated the statistical value of a human life.

You can read the whole article here. Ashenfelter and Greenstone’s reasoning was basically the following:

• When speed limits are increase, people drive faster, even though it’s more dangerous.
• These people drive faster because it saves them time.
• Time is money.
• Therefore, we can compare the monetary value of the time saved to the increase in the risk of death to figure out how much people value their lives. For example, if people make \$20 an hour and are willing to increase risk of death by 1 percentage point to save 3 hours, then they must value their lives at most \$60/1% = \$6000. (This of course assumes that people are aware of precisely what the risks of driving faster are.)

There are a number of variations on this general principle, but they usually center around questions of “how much are people willing (and able) to pay to avoid risk of death?” or “how much do people demand to be compensated in order to be willing to face increased risk of death?” Economists, for the most part, seem to be fine with this sort of approach, but the principle seems to be more than a little off-putting to the general public. Perhaps people’s discomfort comes from the fact that the aforementioned questions often result in higher life valuations for higher-income people, perhaps they don’t want to acknowledge that these sorts of tradeoffs exist in the world, or maybe they just hate anything having to do with numbers. Personally, I find it interesting that the objections to this type of estimation persist despite the fact that economists use people’s revealed preferences to determine how much THEY value their lives rather than trying to tell them how much their lives should be worth.

Palatable or not, such a valuation is necessary and very important in a policy context. If policymakers went with what our mommies told us when we were little, they would argue that we’re all priceless. The logical extension of this is that if people are priceless little flowers, then any amount of expenditure is justified if it brings about any reduction in risk of death. However, I’m guessing even those that hold tightly to the belief that we are all special snowflakes would agree that a society shouldn’t spend \$10 trillion to enact a change that will on average result in 2 fewer deaths per year. Those snowflake-defenders then need to realize that as soon as they make that judgment they’ve put an upper bound on the value of human life.

See, economists and normal people aren’t that different after all. And you, dear readers, really are special snowflakes.

### 32 responses so far ↓

• 1 Steve // Jul 1, 2010 at 6:00 pm

I wonder if there is some causation in this too. i.e. those on higher wages are more likely to speed. as in we all might value life the same, and therefore if we earn higher wages there is more justification to drive faster.

Also shouldn’t we account for risk aversion. i.e. people don’t speed by as much as they could if they were risk neutral.

• 2 tamara // Jul 1, 2010 at 6:59 pm

No, Jodie. You’re a special nerdie snowflake and I like nerds so there you go and you can put value a life… just ask any life insurance company xD

• 3 Marty // Jul 1, 2010 at 7:09 pm

This post made me think of a short story i’d read: The Cambist and Lord Iron”, In which, among other things, a moneychanger is asked to valuate the life of a king versus that of a prisoner.

Print version:
http://issuu.com/spectra/docs/cambistandlordiron

And audio version (With intro by M.K. Hobson):
http://podcastle.org/2009/05/06/pc051-the-cambist-and-lord-iron/

• 4 misterxroboto // Jul 1, 2010 at 7:33 pm

jodi, tell your friend marty not to worry.

i might be the only one who reads this, SMBC, and marginal revolution?

regardless, the entire history of tort law has already told us about this. damages are rewarded to bring the harmed party to the point of indifference. theoretically, there’s a dollar value where i am indifferent between losing a hand, having lots of money; and keeping my hand, but only as much money as i have now.

people don’t like thinking about it, but it’s definitely true.

• 5 David Welker // Jul 1, 2010 at 8:38 pm

This insistence by a subset of especially ridiculous economists that we MUST put ARBITRARY monetary values on human life BECAUSE otherwise we cannot make “optimal” policy, I think borders on so short-sighted that only an economist sucked far too deeply into theory would buy into it.

First of all, what is life? I think everyone would agree that a life lived in a bubble with no freedom to take risks would not be a life worth living. (And when I am talking about “worth” I am not talking about money.) That is, even if we had unlimited resources, we would still want to take risks that could cost our lives. (Anyone remember when Michael Kennedy died playing “ski football.”)

Indeed, whether someone takes these sort of risks or not is often much more a matter of personality than finances. Are we to say that the more adventurous amongst us value their life less? I think not. Maybe they value their lives more and take risks because they know that a life without some risk is not a life worth living.

Also, consider this fact that some economists do not want to accept. Some things just are not reducible to money. It is not that life has infinite monetary value. It is that life cannot be sensibly exchanged for money. For example, no reasonable person with all of their nerves in tact would be willing to be tortured continually for 5 years in the most severe manner, no matter the promise of monetary reward at the end. Money simply could not compensate for such a miserable existence for such a long period of time. That is, avoiding such torture cannot be priced. And it turns out, a lot of really important things cannot be priced. I guess that might diminish the role of economists in telling the rest of us what the “right” amount of torture is, but I for one think that is a good thing. Maybe economists should just admit they have no special expertise in advising the rest of us on the optimal level of torture our government should inflict upon criminals or terrorists. And they have no special expertise on the value of life. No reasonable person will exchange their life for any amount of money (unless they are very sick, very ill, or mentally distressed).

Second, the idea that we can look at people’s behavior to tell us how much they value their own life is also dumb. Most people have no clue whatsoever how whatever risks they take increase or decrease the probability of death with any degree of precision. Therefore, this is a useless measure of their preferences. This makes this measure of the value of life entirely ARBITRARY, because it measures exactly nothing; it certainly is not based on the “preferences” of the individuals in question for life.

Let us move beyond the question of whether people even know the risks they are taking, which they won’t. If I were willing to take a payment of \$10,000 for a 1% chance of death, this does not imply that I only value my life at \$1,000,000. A lot of people (especially young people) secretly believe they are invincible. Also, if one were willing to take \$10,000 out of desperation, well, after they had that money, they may not be very desperate anymore. You cannot assume that the price for taking a 2% risk is \$20,000 because the price for a 1% risk if \$10,000. Maybe to take the second 1% risk, the person will now require \$500,000. And for the third 1% of risk, they require \$100,000,000. (They really are very comfortable now they have \$500,000.) And after that, they aren’t willing to take any more risk at all. (And, lets not forget that some people actually pay to engage in activities that are much more exciting and interesting because there is risk involved.)

Jodi is right that the idea that those who make more money have more valuable lives is offensive and arbitrary. Valuable to whom? If a parent works a lot and makes more money and neglects their children, this makes their life more valuable than someone who devotes more time and energy to their children? That is nonsense.

Finally, note the argument that economists make. Oh, it is UNREASONABLE to not explicitly put monetary values on human life. After all, Jodi argues, we wouldn’t want to spend 2 TRILLION dollars to save 2 lives, would we? Well, last time I checked, before certain economist came around and said that we must put a value on human life, we did not do that. Hmm…. I wonder why. It is kind of absurd to say that putting explicit arbitrary monetary values on human values is necessary to avoid leading us to absurd decisions like this, isn’t it. Historically, we have never made any such decisions. Perhaps that is because we recognize that in fact, a life without risk isn’t a life worth living. At least for a lot of people. That has nothing to do with money.

I guess that society wouldn’t actually fall apart if we declined to put a value on human life after all. So we can neatly throw that silly argument out the door.

Ultimately, what actions society should do to protect human life is a matter of our values. A much more useful project for economists than trying to put values on human life would be to identify inconsistencies in the amount of expenditures that we put to reduce risk in different contexts where we assume that people do not gain any benefit from increased risk. (For example, risk from mistakes in different medical treatments.) We might also note whether society is spending a lot of money on reducing risk for certain individuals and then we can QUESTION whether or not such expenditures are justified.

So, economists can have a useful role in evaluating risk. But trying to come to impose what is an essentially normative value judgment on the rest of us (as economists who try to put a value on human life do) is beyond the economists proper role.

As a citizen, an economist can say that they think a life should only be valued at \$X. What they can’t say is that such a number and the entire idea that putting such a value on life at all is appropriate is anything other than a normative value judgment. That is, there really is not a lot of reason for the other economists or other citizens to listen to the opinions of such economists where our normative value judgments differ.

• 6 David Welker // Jul 1, 2010 at 8:49 pm

misterxroboto,

As a lawyer, the claim that one can derive “truth” from the particulars of tort law strikes me as a little off.

By the way, I was wondering how much someone would have to pay you to saw off your hand with an old rusty saw so that you would be indifferent.

For me personally, there is no amount of money that could compensate. I would never voluntarily agree to such a transaction.

• 7 misterxroboto // Jul 1, 2010 at 10:08 pm

fine, i’ll bite.

[First of all, what is life? I think everyone would agree that a life lived in a bubble with no freedom to take risks would not be a life worth living.]

well then why don’t we put dollar values on utility instead? that way, we can account for taste preferences.

[Also, consider this fact that some economists do not want to accept. Some things just are not reducible to money. It is not that life has infinite monetary value. It is that life cannot be sensibly exchanged for money.]

you are confusing unlike things. making pricing difficult does not mean there is no price. just like calculating my opportunity cost of writing this post is ridiculously difficult. should we therefore assume that all intro economics books are wrong?

[For example, no reasonable person with all of their nerves in tact would be willing to be tortured continually for 5 years in the most severe manner, no matter the promise of monetary reward at the end. Money simply could not compensate for such a miserable existence for such a long period of time. ]

this is a failure of your imagination. if i were to imagine that i have a large family, etc. if i could reasonably exchange my family’s safety for torture? i’d do it. i know that it looks like i’m switching safety for money, but in this scenario, it’s conceivable that i could use the \$4 trillion i got for torture to take extraordinary steps to save my family’s lives.

[And it turns out, a lot of really important things cannot be priced. ]

citation needed.

[Second, the idea that we can look at people’s behavior to tell us how much they value their own life is also dumb. ]

then kindly stop using people’s behavior as a justification for your argument.

[Maybe to take the second 1% risk, the person will now require \$500,000. ]

according to your argument, even a 1% risk should not have any monetary value because life itself has no monetary value, any risk to it cannot have value either.

[Well, last time I checked, before certain economist came around and said that we must put a value on human life, we did not do that.]

again, you suffer from the problem of ignorance. you not knowing that before economists, people traded other people by bartering doesn’t mean it didn’t happen.

[A much more useful project for economists than trying to put values on human life would be to identify inconsistencies in the amount of expenditures that we put to reduce risk in different contexts where we assume that people do not gain any benefit from increased risk.]

why are we making these assumptions about benefits from risk? either you think people’s preferences are vastly different and some people like different risks than others or everyone is similar enough that we can plan for it.

[I guess that society wouldn’t actually fall apart if we declined to put a value on human life after all. So we can neatly throw that silly argument out the door.]

your conclusion does not follow from your argument. you seem to be claiming that society would not fall apart if we applied no risk calculations to our behavior and acted randomly. you don’t appreciate that risk assessment is a value on human life.

[As a citizen, an economist can say that they think a life should only be valued at \$X.]

and here is the meat of your argument, a fallacy all too common. no economists are arguing that we should have 65 mph speed limits because lives are worth \$1mil. you place the cart before the horse. it’s “if and only if lives are worth \$x, we should set risk controls to y.” this is positive, not normative.

as for your comments about tort law and truth. check webb v. mcgowin and hawkins v. mcgee. i know you say you can’t derive things from the particulars of tort law, but that’s precisely its purpose.

• 8 David Welker // Jul 1, 2010 at 11:02 pm

misterxroboto:

First:

I accept your concession that some things cannot sensibly be reduced to monetary values. Your absurd price of 4 trillion dollars for you to continuously endure the most extreme forms of torture (that is not fatal) for 5 years illustrates that concession perfectly.

Second:

I find it amusing that you would equate the opinions of mere judges with some sort of deep universal truth. But who am I to argue with you if such judges are the high priests of your religion.

• 9 Jonatan Krovitsky // Jul 1, 2010 at 11:37 pm

While I’m generally inclined toward misterxroboto, here is a point to ponder:
Human life have no value… TODAY.
Thru ancient times, as long as slaves were a comodity, you had a differentiated market price for humans. Using it was common practice in various cultures – for instant the Talmud has a whole section- “Arachin”- discussing someone who wanted to donate ” his own worth” to the temple.

• 10 David Welker // Jul 1, 2010 at 11:48 pm

Mr. Krovitsky,

I found the argument that the price of slaves should be considered “the value” of human life sort of amusing as well.

• 11 Braden // Jul 2, 2010 at 1:50 am

@misterxroboto

I also read ediwm, smbc, and marginal revolution. Insofar as Google Reader alone reports respective follower counts of 341, 43,900, and 180,566, I expect we could throw a party of such readers. (I’m surprised Jodi isn’t better followed, given her interesting content, advertising on Facebook, links from Mankiw, and attractiveness.)

• 12 econgirl // Jul 2, 2010 at 3:45 am

@ Braden: FeedBurner and my traffic numbers do in fact suggest a higher number, but Google Reader could underreport numbers for all sites, so I can’t speak to the relative comparison that you give. That said, marketing suggestions are always welcome….oh, and thank you.

• 13 Jonatan Krovitsky // Jul 2, 2010 at 7:48 am

@Welker
Market price is never the value, but the equilibrium between “My family can pay you ransom” and “We do need someone to row the galley”.

• 14 misterxrotobto // Jul 2, 2010 at 2:06 pm

[I accept your concession that some things cannot sensibly be reduced to monetary values. Your absurd price of 4 trillion dollars for you to continuously endure the most extreme forms of torture (that is not fatal) for 5 years illustrates that concession perfectly.]

This isn’t an objection to my point. This IS my point. Your claim was that there is absolutely no value which would suffice, all I needed to do was find a number, even if it is larger than what is currently held by any individual.

[I find it amusing that you would equate the opinions of mere judges with some sort of deep universal truth. But who am I to argue with you if such judges are the high priests of your religion.]

As an attorney, I would expect you to know about hearsay. If my sister were to say “I have a pink elephant” it would be true for me to later tell someone “My sister said she had a pink elephant.” My claims (both about my sister and the history of tort law) have nothing to do with the truth of the original arguments. Whether my sister actually has a pink elephant or whether someone’s hairy hand is worth exactly that dollar amount are moot. I may disagree with Webb v. McGowin, but I can still state its facts. Those facts indicate that a person was wronged, due to bodily harm, and he was compensated with money in order to correct it.

• 15 misterxrotobto // Jul 2, 2010 at 2:08 pm

Good point on the weighting, I neglected that in my original probability scheme.

I’d love to see a bleg of EDIWM readers’ favorite econ vs. non-econ blogs. I feel like this would be a much more interesting set of readers than we’d normally get.

• 16 David Welker // Jul 2, 2010 at 2:28 pm

misterxrotobto,

First:
Actually, you have undermined your point. When you can only come up with a crazy value, that tends to show that non-crazy values are not possible to produce.

Let me be very precise about this though. If someone would agree to undergo 5 years of the most extreme torture at any price, they are by definition irrational or desperate. In neither case, would such transactions be good measures of the “price” that would compensate someone for involuntarily undergoing torture.

Second:
You can normatively assert that we should assign all things arbitrary monetary values. I can normatively assert that we shouldn’t because there is no non-arbitrary methodology for doing so and furthermore an ethical system that equated all things to money would be an extremely poor system.

Third:
That courts award people money for their injuries does not prove they are fully compensated. A tort victim who, for example, has had both of his or her eyes gauged out and whose face is burned beyond recognition by acid in a way not correctable by plastic surgery will never have be able to see again and will have an extremely difficult time finding a life partner.

Of course, they should be compensated with money. That would definitely be helpful to them. But to think that any amount of money could put that person in the position they were in before their eyes were gauged out or their face burned beyond recognition by acid is ridiculous.

A court cannot give the victim his or her eyes back nor can the court correct the now disfigured face. It can only give the person money. That a court in its helplessness only awards money does not prove that the victim has been truly fully compensated.

• 17 misterxrotobto // Jul 2, 2010 at 3:10 pm

[First:
Actually, you have undermined your point. When you can only come up with a crazy value, that tends to show that non-crazy values are not possible to produce.]
You presented a crazy situation and are trying to claim my response is irrelevant because it too, is crazy? I really don’t follow your argument here.
[Let me be very precise about this though. If someone would agree to undergo 5 years of the most extreme torture at any price, they are by definition irrational or desperate. In neither case, would such transactions be good measures of the “price” that would compensate someone for involuntarily undergoing torture.]
This is an abuse of the word “irrational.” They are not saying “I’m hungry. If I’m hungry, I should get some food. Therefore, I run a marathon.” Disagreeing with their choices does not make them irrational. They are able to string together the premises and conclusions.

Desperation does not nullify that they place value on something. It’s consistent with supply and demand.

[Second:
You can normatively assert that we should assign all things arbitrary monetary values. I can normatively assert that we shouldn’t because there is no non-arbitrary methodology for doing so and furthermore an ethical system that equated all things to money would be an extremely poor system.]

Again. You confuse “should” with “do.” I’m not saying we “should” do anything. I’m observing the behavior.

[Third:
That courts award people money for their injuries does not prove they are fully compensated.]

Expectation Interest. Q.E.D.

• 18 misterxrotobto // Jul 2, 2010 at 3:21 pm

as a lovely supplement:
http://en.wikipedia.org/wiki/Damages

“Damages in tort are generally awarded to place the claimant in the position he/she would have been had the tort not taken place.”

confirmation bias is alive and well!

• 19 David Welker // Jul 2, 2010 at 3:56 pm

misterxrotobto,

This conversation does not give me a lot of confidence in your intelligence. However, I think I will go with the alternative explanation that we are talking past each other.

First, the argument that we “should” as a society assign a monetary value to something is normative judgment. The fact remains, monetary values are not normally assigned to human life. That is, snuff films, even if the victim consents, are illegal.

Monetary values to transfer control of property do not “objectively exist.” Rather, monetary values are assigned by humans.

Now, money is more efficient than barter. So there is a good justification for allowing money. And money requires that people be allowed to assign monetary values (“prices”) at which they will exchange objects.

But there are some things that society does not allow to be exchanged for money. For example, in our society, you cannot sell your son or daughter into prostitution or slavery. We do not even allow someone to sell themselves into slavery. Nor would we allow Bill Gates to make snuff films (not that he would want to) no matter how much money he is willing to pay. Our normative judgment is that for certain things, monetary values should not be attached. You might individually believe that society should do the opposite. But that would merely be your own normative judgment. The idea that everything SHOULD be for sale or have a monetary price is a normative judgment that the majority of society rejects.

So, when certain economists assign a monetary value to human life, they are making a normative judgment that this is a proper thing to do. This is a normative judgment that they are justifiably morally condemned for making.

Now, of course the move by an economist who wishes to avoid such moral condemnation might be to deny that they are making a normative judgment. But of course that is false. There is no non-arbitrary value that you can assign to human life. Objectively, by assigning a value to a human life, they are making a normative judgment that (1) whatever methodology they have chosen for coming up with a particular value is reasonable and (2) it is reasonable to assign a value to human life in the first place.

Note, that this is a separate issue from having courts assign non-infinite damages for wrongful death. If we believe that human life is not adequately compensated money, it does not follow that such accidents should be compensated by an infinite amount of money. The whole point is that we are not under the illusion that a family can really be made truly whole by a wrongful death lawsuit; we provide such a remedy not because it is adequate, but because not providing any remedy at all would be even worse. (That is, we don’t make the perfect the enemy of the good.)

Now, as to the point that damages in tort place the claimant in the position they would have been had the tort not taken place, in many cases that is just false. In many cases, you could only do that if you went back in time and changed history. When someone’s hand is chopped off, or their face is disfigured after being burned by acid, or their eye is gouged out, this is not something that we humans have any ability to change. We cannot actually put the claimant in the position that they were in if the tort had not taken place.

Now, you can continue to argue. But I am going to assume that this is because you are approaching things from a different framework rather than that you are just plain stupid. I don’t really believe you are so stupid that you believe that someone whose eye is gouged out can be put in “the position he/she would have been had the tort not taken place.” It is pretty obvious that you have forever altered their life and that many people would reasonable prefer to keep their eye than be compensated with any amount of money.

• 20 Timmy // Jul 3, 2010 at 2:34 pm

“I can’t tell whether the creators of this [comic] realized how close they were to being correct.”

I think it should also be noted that the comic also got it correct that (most) economists are bald, ageing men with bizarre fashion sense (who would wear a puke green polo shirt with an olive green/gray jacket?!). All economists also wear glasses as well and have tilde-shaped eyebrows. The comic’s accuracy is remarkable.

• 21 econgirl // Jul 3, 2010 at 3:02 pm

Hmph. =P I suppose, in a way, that this fact benefits me, but still…hmph.

• 22 Scott Ritchie // Jul 6, 2010 at 12:27 am

When I explain the “value of a human life” concept to non-economists, I find it very helpful to instead describe it as a PRICE.

It is simply a calculation of how much money you need to pay society at large (helicopter drop, tax reduction, increased income) in order for them to, on average, save one of their own lives. They do this by all the means we estimate the price – buying safety equipment, being less likely to take dangerous jobs, and so on.

Once you describe it as a societal default price, you can then fairly make all the normative claims that economists do. So when an economist says “don’t build the guard rails because they will cost three times the value of a human life but only save two lives”, this is wrong.

Instead, we should say “don’t build the guard rails, because while they save two lives, if you simply refunded the money in reduced taxes, people would use it to save three lives instead.”

The second statement is superior simply because it doesn’t matter how much an individual values a life. Even if they value life as priceless, as your mother told you to, they will still agree with the latter policy because it can be shown to save more lives.

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