TT's Lost in Tokyo

[Note:  Although the giant snakes I mentioned in my preceding post may have fat tails, I didn't want my description of the discussion between Harvard`s Martin Weitzman and Yale`s William Nordhaus of the limits of cost-benefit analysis to be overlooked, so I have largely copied it below.  I've added an introduction, as well as a few links.]

"Fat tails" seem to be the rage these days, as Bill Safire noted last week in the NYT.  But what are "fat tails"?  Notes Safire,

To comprehend what fat tail is in today’s media wringer, think of a bell curve, the line on a statistician’s chart that reflects “normal distribution.” It is tall and wide in the middle — where most people and things being studied almost always tend to be — and drops and flattens out at the bottom, where fewer are, making a shape on a graph resembling a bell. The extremities at the bottom left and right are called the tails; when they balloon instead of nearly vanishing as expected, the tails have been designated “heavy” and, more recently, the more pejorative “fat.” To a credit-agency statistician now living in a world of chagrin, the alliterative definition of a fat tail is “an abnormal agglomeration of angst.”

In an eye-popping Times Magazine article last month titled “Risk Mismanagement,” Joe Nocera, a business columnist for The Times, focused on the passionate, prescient warnings of the former options trader Nassim Nicholas Taleb, author of “The Black Swan” and “Fooled by Randomness,” who popularized the phrase now in vogue in its financial-­statistics sense. Nocera wrote: “What will cause you to lose billions instead of millions? Something rare, something you’ve never considered a possibility. Taleb calls these events ‘fat tails’ or ‘black swans,’ and he is convinced that they take place far more frequently than most human beings are willing to contemplate.”

If I make quibble with Safire's description; "fat" refers not to the probabilty distribution ballooning on either tail, but refers to the case that the tail probability does not decline quickly to zero (viz., probability approaches zero more slowly than exponentially).

*   *   *

The size of the giant snakes and the much higher temperatures (and GHG levels) at their time (60 million years ago) and shortly after during the PETM (a perod 56 million years ago temperatures shot up by 5° Celsius / 9° F in less than 10,000 years) tell us no simply that climate is sensitive (on geological scales, sometimes rather short-term) to atmospheric levels of carbon and methane, but  remind us that there is a "fat tail" of uncertain climate change risks posed by mankind`s ramped up efforts to release as much as possible of the CO2 that has been stored up in the form of fossil fuels, methane and limestone over millions years.  

I have mentioned the issue of "fat tails" previously, in connection with attempts at applying cost - benefit analysis (CBA) to determine whether to tax CO2 emissions.  While economists like Yale`s William Nordhaus who have applied CBA to climate policy have been saying for decades that taxing carbon makes sense on a net basis, our own Bob Murphy has criticized Nordhaus`s approach on rather narrow (and decidedly non-Austrian) grounds.

But Nordhaus has also been strongly criticized by economists such as Harvard`s Martin Weitzman, who basically argue that Nordhaus has UNDERSOLD the case for carbon pricing or that the results of such CBA imply a greater certainty of knowledge (and complacency) than is deserved.  Weitzman points out basic difficulties inherent in applying CBA to policies addressing climate change, particularly where there seems to be a grave possibility that we do not understand how drastically the climate might respond to our influences.  Weitzman`s comments (scheduled to appear in the February issue of The Review of Economics and Statistics) were the focus of the lead essay by Jim Manzi in Cato Unbound`s August 2008 issue, which I reviewed.

Nordhaus has since responded to Weitzman in a comment that became available in January; this time with Bob Murphy stepped in as a defender of CBA!  I note that Ron Bailey, science correspondent at Reason online, has just published a piece examining Weitzman's paper last year and Nordhaus's recent comments.

Weitzman has now replied to Nordhaus, and has kindly permitted me to quote from a draft of his reply (which he has out for review).  It seems that Weitzman provides a compelling statement of some the limits of CBA, as applied to climate change.  (NB:  Weitzman`s draft response is a .pdf file that I cannot upload, though I have uploaded a version converted to .txt format.  I am happy to forward the .pdf to any interested readers.)

Weitzman`s criticisms of the limits of CBA ought to resonate with Austrian concerns about complexity, limits of knowledge and the difficulty of prediction -- even as Weitzman (and Nordhaus and, indeed, Bob Murphy) completely fail to consider the fundamental problems of conflicting preferences in the absence of property rights and of the likelihood that rent-seeking with corrupt governmental policy responses.

The rest of the post sets those of Weitzman`s key points that I consider most salient to a discussion among laymen:

"there is enormous structural uncertainty about the economics of extreme climate change, which, if not unique, is pretty rare. I will argue on intuitive grounds that the way in which this deep structural uncertainty is conceptualized and formalized should influence substantially the outcomes of any reasonable CBA (or IAM) of climate change. Further, I will argue that the seeming fact that this deep structural uncertainty does not influence substantially outcomes from the "standard" CBA hints at an implausible treatment of uncertainty."

"The pre-industrial-revolution level of atmospheric CO2 (about two centuries ago) was Normal 0 0 2 false false false MicrosoftInternetExplorer4 about280 parts per million (ppm). The ice-core data show that carbon dioxide was within a range roughly between Normal 0 0 2 false false false MicrosoftInternetExplorer4 ≈180 and Normal 0 0 2 false false false MicrosoftInternetExplorer4 ≈280 ppm during the last 800,000 years. Currently, CO2 is at Normal 0 0 2 false false false MicrosoftInternetExplorer4 ≈385 ppm, and climbing steeply. Methane was never higher than Normal 0 0 2 false false false MicrosoftInternetExplorer4 ≈750 parts per billion (ppb) in 800,000 years, but now this extremely potent GHG, which is thirty times more powerful than CO2, is at Normal 0 0 2 false false false MicrosoftInternetExplorer4 ≈1,780 ppb. The sum total of all carbon-dioxide-equivalent (CO2-e) GHGs is currently at Normal 0 0 2 false false false MicrosoftInternetExplorer4 ≈435 ppm. Even more alarming in the 800,000-year record is the rate of change of GHGs, with increases in CO2 being below (and typically well below) Normal 0 0 2 false false false MicrosoftInternetExplorer4 ≈40 ppm within any past sub-period of ten thousand years, while now CO2 has risen by Normal 0 0 2 false false false MicrosoftInternetExplorer4 ≈40 ppm in just the last quarter century.

Thus, anthropogenic activity has elevated atmospheric CO2 and CH4 to levels extraordinarily far outside their natural range - and at a stupendously rapid rate. The scale and speed of recent GHG increases makes predictions of future climate change highly uncertain.  There is no analogue for anything like this happening in the past geological record. Therefore, we do not really know with much confidence what will happen next."

"To keep atmospheric CO2 levels at twice pre-industrial-revolution levels would require not just stable but sharply declining emissions within a few decades from now. Forecasting ahead a century or two, the levels of atmospheric GHGs that may ultimately be attained (unless drastic measures are undertaken) have likely not existed for tens of millions of years and the rate of change will likely be unique on a time scale of hundreds of millions of years.

Remarkably, the "standard"CBA of climate change takes essentially no account of the extraordinary magnitude of the scale and speed of these unprecedented changes in GHGs - and the extraordinary uncertainties they create for any believable economic analysis of climate change. Perhaps even more astonishing is the fact that the "policy ramp" of gradually tightening emissions, which emerges from the "standard" CBA, attains stabilization at levels of CO2-e GHGs that approach Normal 0 0 2 false false false MicrosoftInternetExplorer4 ≈700 ppm. The "standard" CBA [of Nordhaus] thus recommends imposing an impulse or shock to the Earth's system by geologically-instantaneously jolting atmospheric stocks of GHGs up to Normal 0 0 2 false false false MicrosoftInternetExplorer4 ≈21/2 times their highest past level over the last 800,000 years - without even mentioning what an unprecedented planetary experiment such an "optimal" policy would entail."

"So-called "climate sensitivity" (hereafter denoted S1) is a key macro-indicator of the eventual temperature response to GHG changes. Climate sensitivity is defi…ned as the global average surface warming following a doubling of carbon dioxide concentrations. ... the median upper 5% probability level over all 22 climate-sensitivity studies cited in IPCC-AR4 (2007) is 6.4° C - and this stylized fact alone is telling. Glancing at Table 9.3 and Box 10.2 of IPCC-AR4, it is apparent that the upper tails of these 22 PDFs tend to be sufficiently long and heavy with probability that one is allowed from a simplistically-aggregated PDF of these 22 studies the rough approximation P[S1>10° C] Normal 0 0 2 false false false MicrosoftInternetExplorer4 ≈1%. The actual empirical reason why these upper tails are long and heavy with probability dovetails nicely with the theory of my paper: inductive knowledge is always useful, of course, but simultaneously it is limited in what it can tell us about extreme events outside the range of experience - in which case one is forced back onto depending more than one might wish upon the prior PDF, which of necessity is largely subjective and relatively diffuse. As a recent Science commentary put it: "Once the world has warmed by 4° C, conditions will be so different from anything we can observe today (and still more different from the last ice age) that it is inherently hard to say where the warming will stop."

"Exhibit C" concerns possibly disastrous releases over the long run of bad-feedback components of the carbon cycle that are currently omitted from most general circulation models. The chief worry here is a significant supplementary component that conceptually should be added on to climate sensitivity S1. This omitted component concerns the potentially powerful self-amplification potential of greenhouse warming due to heat-induced releases of sequestered carbon. ... Over the long run, a CH4 outgassing-amplifier process could potentially precipitate a cataclysmic strong-positive-feedback warming. This real physical basis for a highly unsure but truly catastrophic scenario is my Exhibit C in the case that conventional CBAs and IAMs do not adequately cover the deep structural uncertainties associated with possible climate-change disasters.  Other examples of an actual real physical basis for a catastrophic outcome could be cited, but this one will do here.  The real physical possibility of endogenous heat-triggered releases at high temperatures of the enormous amounts of naturally-sequestered GHGs is a good example of indirect carbon-cycle feedback effects that I think should be included in the abstract interpretation of a concept of "climate sensitivity" that is relevant here. What matters for the economics of climate change is the reduced-form relationship between atmospheric stocks of anthropogenically-injected CO2-e GHGs and temperature change. ... When fed into an economic analysis, the great open-ended uncertainty about eventual mean planetary temperature change cascades into yet-much-greater yet-much-more-open-ended uncertainty about eventual changes in welfare."

"Exhibit D" concerns what I view as an unusually cavalier treatment of damages or disutilities from extreme temperature changes. The "standard" CBA treats high-temperature damages by a rather passive extrapolation of whatever specification is assumed (typically arbitrarily) to be the low-temperature "damages function."  ... Seemingly minor changes in the specification of high-temperature damages can dramatically alter the gradualist policy ramp outcomes recommended by the "standard" CBA. Such fragility of policy to postulated forms of disutility functions are my Exhibit D in making the case that the "standard" CBA does not adequately cope with deep structural uncertainty - here structural uncertainty about the specification of damages."

"An experiment without precedent is being performed on planet Earth by subjecting the world to the shock of a geologically-instantaneous injection of massive amounts of GHGs. Yet the "standard" CBA seems almost oblivious to the extraordinarily uncertain consequences of catastrophic climate change."

"Almost nothing in our world has a probability of exactly zero or exactly one. What is worrisome is not the fact that extreme tails are long per se
(reflecting the fact that a meaningful upper bound on disutility does not exist), but that they are fat (with probability density). The critical question is how fast does the probability of a catastrophe decline relative to the welfare impact of the catastrophe. Other things being equal, a thin-tailed PDF is of less concern because the probability of the bad event declines exponentially (or faster). A fat-tailed distribution, where the probability declines polynomially, can be much more worrisome. ... To put a sharp point on this seemingly abstract issue, the thin-tailed PDFs that Nordhaus requires implicitly to support his gradualist "policy ramp" conclusions have some theoretical tendency to morph into being fat tailed when he admits that he is fuzzy about the functional forms or structural parameters of his assumed thin-tailed PDFs - at least for high temperatures. ... When one combines fat tails in the PDF of the logarithm of welfare-equivalent consumption with a utility function that is sensitive to high damages from extreme temperatures, it will tend to make the willingness to pay (WTP) to avoid extreme climate changes very large."

"Presumably the PDF in the bad fat tail is thinned, or even truncated, perhaps from considerations akin to what lies behind the value of a statistical life (VSL). (After all, we would not pay an infinite amount to eliminate altogether the fat tail of climate-change catastrophes.) Alas, in whatever way the bad fat tail is thinned or truncated, a CBA based upon it remains highly sensitive to the details of the thinning or truncation mechanism, because the disutility of extreme climate change has "essentially" unlimited liability. In this sense climate change is unique (or at least very rare) because the conclusions from a CBA for such an unlimited-liability situation have some built-in tendency to be non-robust to assumed tail fatness."

"Reasonable attempts to constrict the fatness of the "bad" tail can still leave us with uncomfortably big numbers, whose exact value depends non-robustly upon artificial constraints, functional forms, or parameters that we really do not understand. The only legitimate way to avoid this potential problem is when there exists strong a priori knowledge that restrains the extent of total damages. If a particular type of idiosyncratic uncertainty affects only one small part of an individual's or a society's overall portfolio of assets, exposure is naturally limited to that specific component and bad-tail fatness is not such a paramount concern. However, some very few but very important real-world situations have potentially unlimited exposure due to structural uncertainty about their potentially open-ended catastrophic reach. Climate change potentially affects the whole worldwide portfolio of utility by threatening to drive all of planetary welfare to disastrously low levels in the most extreme scenarios."

"Conclusions from CBA [are] more fuzzy than we might prefer, because they are dependent on essentially arbitrary decisions about how the fat tails are expressed and about how the damages from high temperatures are specified. I would make a strong distinction between thin-tailed CBA, where there is no reason in principle that outcomes should not be robust, and fat-tailed CBA, where even in principle outcomes are highly sensitive to functional forms and parameter values. For ordinary run-of-the-mill limited exposure or thin-tailed situations, there is at least the underlying theoretical reassurance that finite-cutoff-based CBA might (at least in principle) be an arbitrarily-close approximation to something that is accurate and objective. In fat-tailed unlimited exposure situations, by contrast, there is no such theoretical assurance underpinning the arbitrary cutoffs or attenuations - and therefore CBA outcomes have a theoretical tendency to be sensitive to fragile assumptions about the likelihood of extreme impacts and how much disutility they cause."

"My target is not CBA in general, but the particular false precision conveyed by the misplaced concreteness of the "standard" CBA of climate change. By all means plug in tail probabilities, plug in disutilities of high impacts, plug in rates of pure time preference, and so forth, and then see what emerges empirically. Only please do not be surprised when outcomes from fat-tailed CBA are fragile to specifications concerning catastrophic extremes.  The extraordinary magnitude of the deep structural uncertainties involved in climate-change CBA, and the implied limitations that prevent CBA from reaching robust conclusions, are highly frustrating for most economists, and in my view may even push some into a state of denial. After all, economists make a living from plugging rough numbers into simple models and reaching specific conclusions (more or less) on the basis of these numbers. What are we supposed to tell policy makers and politicians if our conclusions are ambiguous and fragile?"

"It is threatening for economists to have to admit that the structural uncertainties and unlimited liabilities of climate change run so deep that gung-ho "can do” economics may be up against limits on the ability of quantitative analysis to give robust advice in such a grey area. But if this is the way things are with the economics of climate change, then this is the way things are - and non-robustness to subjective assumptions is an inconvenient truth to be lived with rather than a fact to be denied or evaded just because it looks less scientif…cally objective in CBA. In my opinion, we economists need to admit to the policy makers, the politicians, and the public that CBA of climate change is unusual in being especially fuzzy because it depends especially sensitively on what is subjectively assumed about the high-temperature damages function, along with subjective judgements about the fatness of the extreme tails and/or where they have effectively been cut off. Policy makers and the public will just have to deal with the idea that CBA of climate change is less crisp (maybe I should say even less crisp) than CBAs of more conventional situations."

"The moral of the dismal theorem is that under extreme uncertainty, seemingly casual decisions about functional forms, parameter values, and tail thickness may be dominant. We economists should not pursue a narrow, superficially precise, analysis by blowing away the low-probability high-impact catastrophic scenarios as if this is a necessary price we must pay for the worthy goal of giving crisp advice. An artificial infatuation with precision is likely to make our analysis go seriously askew and to undermine the credibility of what we say by effectively marginalizing the very possibilities that make climate change grave in the first place."

"The issue of how to deal with the deep structural uncertainties in climate change would be completely different and immensely simpler if systemic inertias (like the time required for the system to naturally remove extra atmospheric CO2) were short (as is the case for SO2; particulates, and many other airborne pollutants). Then an important part of an optimal strategy would presumably be along the lines of "wait and see.” With strong reversibility, an optimal climate-change policy should logically involve (among other elements) waiting to see how far out on the bad fat tail the planet will end up, followed by midcourse corrections if we seem to be headed for a disaster. This is the ultimate backstop rebuttal of DT given by some critics of fat-tailed reasoning, including Nordhaus. Alas, the problem of climate change is characterized everywhere by immensely long inertias - in atmospheric CO2 removal times, in the capacity of the oceans to absorb heat (as well as CO2), and in many other relevant physical and biological processes. Therefore, it is an open question whether or not we could learn enough in sufficient time to make politically feasible midcourse corrections. When the critics are gambling on this midcourse-correction learning mechanism to undercut the message of DT, they are relying more on an article of faith than on any kind of evidence-based scientific argument.

"I think the actual scientific facts behind the alleged feasibility of "wait and see”policies are, if anything, additional evidence for the importance of fat-tailed irreversible uncertainty about ultimate climate change.

"The relevance of "wait and see”policies is an important unresolved issue, which in principle could decide the debate between me and Nordhaus, but my own take right now would be that the built-in pipeline inertias are so great that if and when we detect that we are heading for unacceptable climate change, it will likely prove too late to do anything much about it for centuries to come thereafter (except, possibly, for lowering temperatures by geoengineering the atmosphere to reflect back incoming solar radiation). In any event, I see this whole "wait and see" issue as yet another component of fat-tailed uncertainty - rather than being a reliable backstop strategy for dealing with excessive CO2 in the atmosphere.

Nordhaus states that there are so many low-probability catastrophic-impact scenarios around that 'if we accept the Dismal Theorem, we would probably dissolve in a sea of anxiety at the prospect of the infinity of infinitely bad outcomes.' This is rhetorical excess and, more to the point here, it is fallacious. Most of the examples Nordhaus gives have such miniscule thin-tailed probabilities that they can be written off."

"Nordhaus summarizes his critique with the idea there are indeed deep uncertainties about virtually every aspect of the natural and social sciences of climate change - but these uncertainties can only be resolved by continued careful analysis of data and theories. I heartily endorse his constructive attitude about the necessity of further research targeted toward a goal of resolving as much of the uncertainty as it is humanly possible to resolve. I would just add that we should also recognize the reality that, for now and perhaps for some time to come, the sheer magnitude of the deep structural uncertainties, and the way we express them in our models, will likely dominate plausible applications of CBA to the economics of climate change."

(emphasis added)