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Critique of Marty Weitzman on uncertainty
Here is a long post, criticizing Marty Weitzman's view that we should regard a small chance of a catastrophic event as reason to buy "insurance protection" against that event.
I am not persuaded by Jim Manzi's major point of rebuttal, namely: "the heart of Weitzman's paper revolves around the first point: the probability of extreme disaster is larger than current models assume." My reading of Weitzman (which may not exactly be Weitzman's own view) is the following: raising the discount rate doesn't choke off our worries of future dangers. In many plausible models, a higher discount rate means a higher degree of risk aversion as well, and thus we are back to worrying.
(For one simple version of this intuition, imagine a person near starvation. That person has both a high discount rate -- he wants to eat more now -- and he is very risk averse, for fear of losing his remaining food and dying. A billionaire in contrast can be more patient and bear risk more readily. The discount rate and the degree of risk aversion thus often move together, admittedly there are great complications here.)
Manzi also argues that: "There is No Good Reason to Think That the Probability Distribution for Estimates of Climate Sensitivity Fits Any Functional Form." Fair enough, there is only one world and ultimately the meaning of probability is murky, Bayesian or not. But we still have to act on probability estimates in an "as if" way and indeed we all do in a personal context.
If you want to know where Manzi is coming from, here is his critique of the Pigou tax on carbon.
The most serious critique of Weitzman, in my view, is simply that governments are bad at getting people to bear large costs to insure against low probability events, especially when the costs accumulate each year and there is little positive feedback in the interim. ("Reelect me, our costly tax held back global warming for yet another four years! Things didn't get worse!" does not thrill.) Our government does persuade its voters to support a large defense budget, but this is done in part by a) periodic conflict and invasions, and b) people holding deeply irrational views of America's proper place in the world (e.g., "my country, right or wrong"). On other foreign policy issues these irrational attitudes sometimes become very costly. So we might get people to support a Weitzmanesque insurance policy, but to do so they probably would have to be overworried about the relevant problems, and those overworries would lead to other policy mistakes. As a general rule of thumb, when it comes to risk the alternative is public overworry or public underworry, don't ever expect to hit that sweet spot in between or even get close.
Thanks to Reihan for the pointer.
Posted by Tyler Cowen on January 6, 2008 at 07:50 AM in Economics | Permalink
Comments
It's easy these days to view global warming risk through a subprime filter. We are not (as many writers have maintained) so good at risk, and we have an excellent example staring us in the face.
So given flawed humans, and flawed perceptions, we probably will have flawed attempts at "insurance."
Is there actually anything wrong with that?
The other human answer, that we should do nuthin' and hope it all works out, obviously has flaws of its own.
Posted by: odograph at Jan 6, 2008 9:23:27 AM
It seems to me that young people (teenagers and the like) often have a high discount rate and low risk aversion. That would seem to be a more common example than starvation - though maybe this particular phenomenon is confined to western cultures, whereas starvation is not. But risk aversion and low discount rate stem from a concern for the longer-term future, no?
Posted by: Ansel F at Jan 6, 2008 10:31:13 AM
In an earlier MR thread I brought up James Annan's work; I didn't quite understand the technical discussion on what it meant, but doesn't it still strongly undermine conclusions like "5% chance of climate sensitivity over 10 degrees"?
Also, this isn't right: "For example, if this is the PDF for the cost impact of AGW, then the area under the curve is equal to the total cost I expect it to create."
Posted by: steven at Jan 6, 2008 10:31:48 AM
It seems to me that young people (teenagers and the like) often have a high discount rate and low risk aversion. That would seem to be a more common example than starvation - though maybe this particular phenomenon is confined to western cultures, whereas starvation is not. But risk aversion and low discount rate stem from a concern for the longer-term future, no?
Posted by: Ansel F at Jan 6, 2008 10:31:54 AM
I think the best reason for a discount rate is the increasing chance that the problem will be made irrelevant by either technological fixes or the demise of civilization. How does that lead to greater risk-aversion?
Posted by: steven at Jan 6, 2008 10:37:33 AM
Steven, I'm not sure how we untangle such technological optimism from status quo bias, or for that mater, utopianism.
Posted by: odograph at Jan 6, 2008 10:51:44 AM
Tyler:
Thanks for your detailed and thoughtful comments on my article.
I tried to make the point in the post that Weitzman’s arguments about: (1) the relationship of risk aversion to discount rate, and (2) a fat-tailed PDF for climate sensitivity, are logically separate issues. I addresses the first point in another (mercifully for readers, much shorter) post that I referenced in this one.
The short form of the argument around the second point is that unless one makes a numerical (as opposed to functional form) argument that “uncertainty” may reasonably make the “true” PDF for some risk fat-tailed, then you have merely made a trivially true statement, since it is always possible that we have incorrectly specified a PDF. In the article I then go through three reasons why I think Weitzman has not made this empirical case.
You address the third (and most conceptual) of these three arguments when you say:
“Manzi also argues that: "There is No Good Reason to Think That the Probability Distribution for Estimates of Climate Sensitivity Fits Any Functional Form." Fair enough, there is only one world and ultimately the meaning of probability is murky, Bayesian or not. But we still have to act on probability estimates in an "as if" way and indeed we all do in a personal context.”
I may be missing something, but I don’t think you are addressing the point I was trying to make. Yes, we have to act on “impure” probability estimates all the time, but Weitzman makes a much more specific claim relevant to this part of the argument: that we have evidence that we should accept a PDF as a valid method of making probability estimates for extreme values for climate sensitivity. In this third point, I review the logic for why I think this is a mistaken claim in this case. If this claim is mistaken, then we have not promoted uncertainty about the possibility of extreme outcomes to reliably quantified (i.e., probabilistic) risk about extreme events, even in the limited sense in which Weitzman agues.
Finally, the worry you describe in you last paragraph is highly related what I describe in a lot of detail in the second post of mine concerning the Pigou tax argument.
Once again, thanks for your comments.
Posted by: Jim Manzi at Jan 6, 2008 11:50:04 AM
Steven / Odograph:
Thanks for your very thoughtful exchange about discounting.
I think that while comparing current vs. future costs and benefits of a proposed policy is critical, debates about discount rates or functions over centuries are sterile “angels dancing on the head of a pin” arguments. I explain why I believe this in this post: http://theamericanscene.com/2007/12/31/discounting-discounting
I think that it is very sensible to “discount” the far-future very heavily because of, in essence, humility. As far as I can see, our track record in predicting the evolution of human society over centuries is pretty poor, and I see no compelling evidence that we have now uncovered a reliable causal model for global civilization that makes me believe our go-forward capability is much better.
Posted by: Jim Manzi at Jan 6, 2008 12:20:07 PM
we should regard a small chance of a catastrophic event as reason to buy "insurance protection" against that event.
Seems fine. Of course, those sorts of insurance protections can come in different ways (I highly doubt people would want to reverse the Clean Air Act in an effort to get more pollutants in the atmosphere to lower the temperature, for example) and, worst of all, can be contradictory. Some of the best insurance against one catastrophic event may well increase the severity and chance of another-- to use the previous example, the Clean Air Act was at least partially motivated by worries of global cooling. It does become important to estimate the relative probabilities, naturally, of catastrophes of various sizes when deciding if, e.g., increasing the risk of a glacial period is worth decreasing the risk of ending the current ice age.
Posted by: John Thacker at Jan 6, 2008 1:36:36 PM
The argument hinges on whether it is possible to predict future climatic conditions **at all** given our models, and more specifically whether we are justified in believing that there are "fat tails", or disaster scenarios with finite probabilities associated with them. I would note:
1. The forecasts all depend on understanding of various feedback mechanisms related to water vapor and cloud formation. We really don't understand these very well. Absent these feedbacks you'd expect about a 1 degree C rise in temperature for a doubling of CO2. You'd expect about a 2 degree C rise with a constant relative humidity assumption. I don't know of any fundamental assumptions about physical processes that lead to the types of fat tails Weitzman describes. Estimating these tails by averaging error bounds from various types of published studies is very silly...
2. We've seen about a 35% increase in CO2 levels since the advent of the industrial age. We have not seen anything resembling runaway climate feedbacks generating disastrous outcomes. This is probably the best reason to assume that the climate is not wildly unstable with respect to CO2 concentrations.
3. Even so, it's reasonable to be concerned about C02 impacts on the climate. Much more research and other types of precautionary measures are prudent as a low cost insurance policy. Much as asteroid tracking is a sensible idea.
Posted by: JPC at Jan 6, 2008 1:40:31 PM
The other part of Weitzman's argument, which I hope I am summarizing correctly as:
"The correct discount rate is lower for extremely bad events than for ordinarily bad events"
This is not entirely irrational. IE you can afford to self-insure certain types of risks, but not others.
Posted by: JPC at Jan 6, 2008 1:48:51 PM
What Weitzman is trying to do is to show that benefit-cost analyses of climate change are seriously flawed if they do not account for substantial uncertainty about the socio-economic effects (including the possibility of low- or negative-growth)resulting from climate sensitivity models. He wants to model small probability, high magnitude climate consequences without resorting to what he considers to be unrealistically low discount rates. What his model shows is that even using observable discount rates (that is, even if we don't make the kind of ethically-based assumptions promoted by the likes of Ramsey, Arrow, Sen, Lind, and Stern), it is possible that a reasonably risk averse society should take additional (but not heroic) precautions to move the probability of extreme climate change consequences toward zero.
Empirically, Weitzman's analysis is based on the various climate sensitivity models underlying the IPCC's Fourth Assessment Report (2007). Those studies, in the aggregate, suggest a 5% chance of global mean temperature increases at or above 7 degrees Celsius by 2150. Five percent is, of course, a small risk. But what might be the consequences of a 7 degree C GMT increase, should that 5% chance materialize? As Weitzman correctly notes, we cannot possibly know because such a great temperature increase over such a short period of geological time has not been experienced in the entire history of human life on earth. But the effects could well be severe for any or every country, including possibly the end of human civilization. This is not doomsaying, but a realistic appraisal of both the magnitude and probability of catastrophic harm resulting from uncertainties in the "bad fat tails" of PDFs.
Most benefit-cost analyses of climate change (such as Nordhaus's) simply ignore those fat tails, focusing only on the mean expected damages from climate change PDFs. Weitzman thinks that ignoring potential climate catastrophes is a mistake, and the model he provides indicates a useful way of incorporate them into benefit-cost analyses of climate change without manipulating the social discount rate. He buttresses his normative argument in favor of incorporating potential climate catastrophes into climate change BCAs by reference to Aumann's experimental studies showing that individuals typically do not ignore low-probability, high magnitude harm situations when they purchase insurance.
Prof. Cowen's "most serious critique" of Weitzman is misplaced. Weitzman is not purporting to provide a political-economic prediction of what governments will in fact do; he is only attempting to make a marginal improvement to existing EU theory and the methodology of benefit-cost analyses. In other words, he is saying what governments should do; not what they will do.
Finally, it is entirely possible that the climate sensitive studies on which Weitzman relied were flawed, so that the change of a climate change catastrophe is far less than 5%. If so, it could affect Weitzman's conclusion about how much, if any, climate change insurance socities should purchase. It would not, however, invalidate his model, which is robust. Indeed, what his model shows most of all is that we need to work to reduce the uncertainty (the bad fat tails) to the extent practicable.
With best regards of the new year to all.
Dan
Posted by: Dan Cole at Jan 6, 2008 5:31:56 PM
John Thacker / JPC:
You are pointing out many of the difficulties, as I’m sure you know, with decision-making in the face of an unquantifiable risk of catastrophe.
Weitzman has made the argument that a reasonable person should accept a statement stronger than an AGW disaster COULD happen – he argues that we should believe that there is a PDF of possible AGW cost outcomes that is fat-tailed. As I mentioned in earlier comments, I go through three reasons in the long post for why I don’t think he has made his case.
To get practical about this, he claims in his paper that there is a quantifiable 1% chance that the average year-round temperature of the Earth will go to about 100F in the foreseeable future (roughly the summertime temperature in Death Valley). I’ll note that you can’t find any consensus statement of, say, actual climate scientists who believe this. If I were to accept this premise, I wouldn’t need a lot of fancy math to support fairly aggressive action to reduce emissions. If I don’t accept this premise, or something like it, his argument that he has made any progress in quantifying the distribution of possible future temperature changes falls apart (as far as I can see). That is, we end up right back where we were with the Precautionary Principle.
Posted by: Jim Manzi at Jan 6, 2008 5:36:02 PM
Dan:
I go into this in more detail in the long post, but Weitzman goes way, way beyond anything that the IPCC-AR4 report asserts about the likelihood of extreme events. As an example, Weitzman says that there is a 5% chance that what he calls “S1” climate sensitivity is greater than 7C (which is already more aggressive than anything you will find in AR4), but he extends this to what he calls “S2” climate sensitivity, and asserts that there is a 5% chance that S2, or true, climate sensitivity is greater than 11.5C (and a 1% chance that it is greater than 22.6C).
Posted by: Jim Manzi at Jan 6, 2008 5:44:22 PM
To argue that the distribution is **that** fat-tailed [which very few/almost no physical processes are] you need to posit a underlying mechanism that produces that type of distribution. Weitzman clearly hasn't/can't do that. To make his case with a straight face you can't simply say, well it's prudent to assume it could be possible, because it would be really bad if it happened. You need to at least posit some physical mechanism which would allow that type of extreme behavior - that would be some really strong positive feedback mechanism that I don't think has been identified, even in principle. In fact, the actual historical experience argues otherwise.
All that being said, paying attention to "realistic" extreme events is prudent risk management. If you can't formulate a smooth distribution you can use scenario analysis.
Posted by: JPC at Jan 6, 2008 6:15:05 PM
JPC:
Just to make sure I'm communicating clearly, we are in violent agreement about this.
Posted by: Jim Manzi at Jan 6, 2008 7:26:16 PM
I am not sure what you mean by "governments are bad at getting people to bear large costs to insure against low probability events".
If we were talking about something akin to insurance, i.e. the government sets funds aside to be spent in case of the event, then I can see the pressure on politicians to spend the funds anyway. If the government uses tax money to invest in clean energy soruces, and if those sources actually get developed, I would say the situation is very similar to current science spending through for example the NSF, but with benefits to the people that are better to explain. If the government manages to keep up NSF spending, and the people at large believe cleaner energy sources are important, I don't see why it couldn't also keep up the spending on clean energy for decades.
And why would a pigouvian tax be unstable in the long term? As long as people oppose the CO2 tax less than they oppose other taxes, and it is clear that it used to lower the other taxes, there will be relatively little pressure on politicians to lower it.
The only thing that would be really difficult to keep up for a long period would be, in my opinion, a pigouvian tax ( or some auction system) where the proceeds are exclusviely earmarked to be spend on CO2 reduction, instead of being used to lower other taxes.
At first this makes it unclear that these taxes are primarily meant as incentive for industry to increase efficiency.
Second, it would limit the amount of CO2 tax to the amount that people think reasonable to spend, by the goverment, on CO2 reduction. This amount can be much lower than the amount that would lead to the needed CO2 reductions.
Third, it would put CO2 heavy industries in direct conflict to the government-funded research programs. After all, if they can discredit those, the CO2 tax is likely to get lowered. A good policy on the other hand would make especially these industries in favour of CO2 reducing technology development.
Posted by: Great Zamfir at Jan 7, 2008 6:40:46 AM
Government can reward climate stability and raise revenue to do so, but it doesn't have to know all the probabilities before it does so: risk can be borne by those who want to bear it. Climate Stability Bonds [http://socialgoals.com/ieakyototext.html] would transfer the risks to those willing to bear it - voluntarily and with a continuing incentive to get the cost-benefit calcuations correct. Climate Stability Bonds would contract out the achievement of climate stability to the most efficient operators. If they fail to perform, then it is they who would lose out, not taxpayers the world over. It would be in their interests to do the calculations correctly, and to continuously refine them in line with our rapidly expanding knowledge and technology. They would have incentives to spend resources immediately on the most effective climate-stabilising projects, while bearing all the risk of failure. They certainly wouldn't delay doing anything until catastrophe becomes imminent and obvious to recalcitrant taxpayers...by which time it's also likely to be inevitable. [from: http://socialgoals.com/blog/2008/01/avoiding-catastrophic-climate-change.html]
Posted by: Ronnie Horesh at Jan 7, 2008 6:42:28 AM
The only thing certain is uncertainty, and even that's uncertain. - Joe Nye, 2007
Posted by: PJ at Jan 7, 2008 6:43:27 AM
There are other ways to insure against truly catastrophic global warming than by lowering atmospheric CO2 levels.
The first best is simply to become as wealthy a planet as we can be. Note that this also provides insurance against any other unforeseen eventualities that might arise in the coming centuries. But it does cut directly against high-cost CO2 reduction efforts.
The second, backup insurance policy against truly catastrophic global warming is geoengineering. There are a number of mechanisms known today that could be exploited, and certainly our richer progeny a century hence will know many more. Compared to the costs of reducing atmospheric CO2, these are essentially free. If and when it turns out that the effects of global warming are worse than the effects of geoengineering, then geoengineering will be used.
These alternate forms of insurance argue for our handling global warming by (1) capturing the known externalities of carbon emission as cheaply to the economy as possible and (2) continuing research into knowing the unknowns.
Posted by: MikeP at Jan 7, 2008 8:27:36 AM
What Weitzman's extraordinary paper has done is simply to show that there is NO plausible economic model which allows us to exclude bad fat tails in the analysis of potential catastrophes; and that in a wide range of such situations (including anthropogenic global warming)fat tails are probable in the economic analysis. The onus is therefore on anyone who excludes the low probability very high impact outcomes to provide valid reasons for excluding these cases.
This is a general result, not limited to climate change. Weitzman's remarks on climate change policy can only be treated as possible implications of his approach. Any worthwhile challenge to the paper must focus on the general result, not the policy asides.
Posted by: Diversity at Jan 7, 2008 9:27:49 AM
MikeP, how is getting as rich as possible going to help us against global warming? If in 2050 all people on earth have Cadillac Escalades with solid gold rims, and the food runs out, what are we going to do? Sell them?
Posted by: GreatZamfir at Jan 7, 2008 10:54:16 AM
I'd be able to better answer that question if I knew by what mechanism the food would run out. But I assure you that a wealthier world would be better able to handle whatever the mechanism is -- caused by global warming or not -- than a poorer world would.
Wealth means opportunity. Wealth means choice. Wealth means robustness.
Wealth apparently also admits the alchemy required to hold up a three-ton truck on rims made of solid gold.
Posted by: MikeP at Jan 7, 2008 11:22:26 AM
Tyler,
I agree with Dan Cole that your argument about public policy is positive,
not normative. That governments are short-sighted for political reasons
and therefore unlikely to carry out or sustain a policy recommended by
Weitzman is quite different from saying what he is proposing is unwise.
Jim Manzi,
I guess you have addressed this elsewhere, but clearly what one thinks should
be done has a lot to do with how risk averse one is, especially regarding possible
fat tails, to the extent they can be estimated or known.
Regarding the fat tailed issue, two points. One is that there are indeed good,
scientific reasons to think that the distribution is likely to be more fat-tailed
than Gaussian normal. These are the various nonlinear positive feedback effects that
are known to be operating in the global climate system, including water vapor and
albedo. These are hard to model, so most do not do so, but pretending they are not
there because we find them hard to model is unwise, especially when there do not seem
to be some equal set of well-known offsetting effects.
This then gets to the more serious issue of whether or not there is any functional form
or, if you prefer, underlying probability distribution. It is certainly possible to
argue against it on Bayesian or other grounds. However, there is past data, even if it
is fuzzy, hence the possibility of estimating some kind of distribution, and even if one
disavows that on climatic "Lucas critique" grounds (the system just keeps changing, etc.),
even a Bayesian would say there is some currently relevant distribution.
In any case, regarding both the past and its relevance to the "current Bayesian" distribution,
there is a serious literature, some of it by "global warming skeptics" such as Reid Bryson,
who have argued based on various data sources, mostly ice cores, that the periods of transition
into and out of ice ages occurred very rapidly, at least in terms of global temperature. We
have evidence of periods in the past when global temperature appears to have changed quite
rapidly in geological perspectives.
Now, of course we do not know what was causing those
apparently rapid shifts (which would be the fat tailed events), possibly totally exogenous
factors like changes in solar radiation or volcanic activity. But they may well also have been
the result of the sort of endogenous nonlinear feedback effects that we know are possible, even
likely, which suggests that indeed the possibility of fat tails in the relevant current
Bayesian distribution should be taken seriously, even if we are not able to estimate them very
well. What we do about them is, of course, another matter.
Posted by: Barkley Rosser at Jan 7, 2008 6:17:50 PM
Jim:
You are right that Marty goes beyond anything in the IPCC's Fourth Assessment Report (FAR) in modeling catastrophic climate change. In fact, Marty is quite explicit that he is going behind the Report to look at the 18 or so climate sensitivity studies on which the IPCC itself relied in compiling the FAR. His close reading of those 18 studies, in the aggregate, leads him to his determination of a 5% chance of GMT increases of 7 degrees C or higher.
Dan
Posted by: dan cole at Jan 7, 2008 7:43:55 PM
