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Here is a chart by Johannes Ruf (using a bibliography prepared by Bernhard Ganglmair), listing a number of papers that list the value of life as estimated by such trade-offs:
So, allowing some tolerance for inflation and deflation, and taking the average of all of the above, we arrive to about 4 million dollars. If we assume that the average life expectancy is 78 years, and that half of the day is waking time, the value comes down to about $12 for a waking hour of life - arbitrary, but the right order of magnitude. Additional complexity can be entered into this model to improve it.
I will now address what we can do with these numbers.
Bilmes and Stiglitz estimate cost of the Iraq war to 3 trillion, while the US military casualties currently number 4250. So, the cost of lives lost is 17 billion, but the economic cost borne by the United States is 3 trillion. What is the true cost of the Iraq war in human lives? 3 trillion divided by 4.2 million comes down to over 720,000 lives. This is the true casualty count, which accounts for people having to work on stuff that explodes instead of spending time with their families. On the Iraqi side, there were about 100,000 civilian lives lost, but it's hard to estimate the full cost of war to Iraq - the Lancet study claims numbers considerably larger than this.
Andrew Gelman has also written about this - when is one's risk of radon to health sufficient to justify the cost of measurement or remediation. I'd again like to acknowledge Johannes and Bernhard's help with the research, but all flaws are solely my own. The difficulties of estimation shouldn't stop us from studying the problem - maybe better awareness of this will help save a million lives in the future.
I don't understand the point about the "true casualty count" being the result of "people having to work on stuff that explodes instead of spending time with their families". Do we consider the "true casualty count" of automobile accidents to include people "having to work on stuff that drives" rather than spending time with their families? The war in Iraq was and is a terrible mistake, but I can't see that this way of thinking about it is valid.
Wait a second, just because we value lives at four million dollars each doesn't mean we can save them at that price. The valuation above is like an average demand for saving lives, but if you want to know the opportunity cost in saving lives, you need to divide the price of the war by the cost of saving lives, not by our willingness to pay.
Dave, you can improve the model by including other factors. The book does attempt to do this for the war cost estimate itself.
TheOEMan, could you develop your argument in more detail?
The cost of saving lives is much smaller than 4M at least at the margin. However, if we had the total budget for the Iraq war, we'd be in territory where the margin is not as big a factor, the average cost of saving many lives should be near the statistical value of a life due to equilibrium. If we could save many lives at substantially less than 4M we'd be taking advantage of that mechanism and those lives would already have been saved... plus or minus the information related issues such as any way in which we can save lives cheaply that we are not currently aware of or institutional factors such as methods that we are not allowed to use by government decree. At least that's one argument. I'd be happy to hear alternate arguments.
My understanding is that the lancet study has been repeatedly discredited, but I don't know all of the details.
The ugly question I'd like to pose instead is, do all of the estimation studies listed assume that all human life is equally valuable? What happens to the accounting if you remove this restriction?
Interesting to see, given that this is a blog about statistics, that you quote the Iraq body count number of about 100k Iraqi civilian deaths as being "the number of civilian lives lost" rather than relying on any of the statistical estimates that have been made. To my eye, the Lancet studies are the most reliable casualty count we have available and is many times greater than the Iraq body count project number. Indeed, the Iraq body count project makes no claims to be anything other than a count of reliably documented civilian deaths by violence which clearly makes it a biased estimate of the total civilian casualties. Also, why only count the civilian toll? Are Iraqi combatants less worthy of counting than US combatants?
The Lancet studies have been repeatedly attacked, but whether they have been discredited is quite another story.
Also, it is incorrect to compare the Lancet figures with the Iraq Body Count estimates, as they measure very different things. The Lancet studies estimate all excess mortality using a survey approach, while the IBC counts violent deaths of civilians that are reported in the media. The IBC figures are thus a very conservative lower-bound estimate.
Thanks, Daniel!
This relates to the point raised by "pwyll": the 4M figure probably relates to a working-age adult. In the list, the figure for a young child was 0.5M (not accounting for inflation). In many hospitals, they stop life support for terminally ill patients when the hope is sufficiently low - life support can technically save a life every second, but that life is very fragile.
It's tremendously hard to generalize, but as scientists we have no right to state what ought to be done, we can merely observe and study what is being done. We can observe the trade-offs families make when lives are at stake, and we can infer the values that would be understood to guide people's behavior.
So, in summary, 4M is the cost of an average life tragically lost. The full cost of the war for the US comes to 720,000 lives tragically lost.
David - I listed both a source of data and an estimate. I can't judge the estimate, but I do provide links that allow readers of this blog to form their own opinion. I was unable to find figures on Iraqi combattants, and I'd appreciate useful pointers.
Aleks, I appreciate that you did provide links to both sources. My main point is that the Iraq body count project doesn't claim to be an estimate of the total number of iraqi lives lost due to the war, or even of the total number of civilian lives lost. It is, as Brendan points out, a lower bound (and not a very good one).
I'm surprised that you state you can't judge the estimates given - if we can't rely on statisticians from one of best universities in the world for such judgments, who can we rely on?
Lancet study was the subject of a debate at the 2007 JSM meeting - there are a few names who would be credible sources on the topic. Perhaps you can invite them to post comments on this blog or otherwise. I served at another session.
It's really crazy to think about things in these types of terms. I really don't think we can ascribe a value to a human life in any way/shape/form.
I think that we've become cold to numbers. Using numbers like "billion" and "trillion" so many times removes our perception of them and nobody has a true comprehension of what they mean. While translating the value of human lives into dollars and cents does has some value, I feel more confused after my brief study than enlightened.
[SEO link to "noadapterneeded" deleted from Brian Kurtz's name, this might not be a valid comment.]
See my blog for more than you would have ever wanted to know about the controversy over the Lancet studies. (Short version: Johns Hopkins and AAPOR have sanctioned one of the lead authors. The authors refuse to make the data available to their most serious critics.)
But my issue with this original post is the somewhat sloppy thinking about the counterfactual world. Assume that Bush in 2003 decides not to invade Iraq. What else happens in that world? Does the oil embargo against Iraq continue? (On what basis?) Do US planes continue to violate Iraqi sovereignty? (On whose authority?)
Now, none of us can ever be sure of what would have happened in that counterfactual world, but given Saddam's history, there is at least a chance that he would have killed as many people in the 15 years after 2003 as he did in the 15 years prior. Maybe he would have killed more. Maybe fewer.
But the true cost of the Iraq war is not simply the deaths that we have. It is the difference between the deaths we have and the deaths we would have had.
David Kane's blog is an exciting read - thanks for the link!
Regarding the counterfactual argument: If I understand it correctly, there is reality A (Bush attacks) with the cost of 720,000, and reality B (Bush does not attack) with an unknown cost. So, it would be sloppy to claim that reality B has the cost of 0, but I have not done that. Instead, one should employ a similar value-of-life calculation for reality B.
My goal is to treat the economic cost of war and death on an equal footing.
To balance David Kane's blog, have a look at Tim Lambert's Deltoid blog, under the "LancetIraq" category. Note also that David has been on the receiving end of censorship on this issue, when the IQSS blog (in your blog-roll) suppressed a post he made there, which was read as alleging fraud on the part of the Lancet authors (link).
As for the AAPOR sanctioning Burnham, it seemed rather extraordinary to me that a trade association should attempt to sanction someone who is not a member, not even a member of the same profession (on the grounds of not responding to their demands for clarification). It seems to me there was an element of opportunistic posturing going on (but not being in Pol Sci I have no idea if that organisation has any credibility).
How many people could we have expected to die at the hands of Saddam, and later Uday or Kusay? How many lives (and lifetimes) would have been lost intervening in future conflicts had the war not occurred?
Subtract that answer from whatever you think the cost of the war was.
Don't forget that life in a relatively free and stable society is more valuable than life under a brutal totalitarian regime ruled by a psychopath.
Funny (or not really), the other day I was watching National Geographics about aircraft desasters, and that one accident was caused because a recommendation for retrofitting the stock of aircraft with some device was voted down (I think it was fire alarm and sprinklers in the luggage rooms), because it would cost about 350m US-$. Some rough calculation with lifetime-GDP got me to about 5m per person. This example showed me that a single aircraft accident can cause an economic loss far in excess of the proposed savings. Additionally, it shows that it makes sense to do these calculations of economic value of lifes, even if it is terribly cynical.