Interesting post on this over at James Empty Blog. So: Weitzmans basic thesis is: the PDF of the climate sensitivity has a long fat tail; the cost diminishes less quickly; so the “expected utility”, which is the integral of the two, is divergent. This has echoes of mt’s arguments, which he has been making for some time. But mt didn’t wrap his arguments up in a pile of maths, so of course he gets ignored.
There, I’ve given away what I think: this is a pretty piece of maths (or it may be: I can’t say I’ve read it all through in detail) but it has precious little relevance to the real world. For two reasons: we have no good evidence for high values of CS; and we have no real knowledge of the cost function for high temperature change either. So in fact this post isn’t really going to critique anything of substance about the paper itself, but merely ride a couple of my hobby horses.
On a technical point, I would have thought that the total cost would be bounded above by total destruction of the world, and would therefore be finite, so I can’t quite see how the integral would diverge anyway. Even if you allow us to expand into the entire galaxy and last for the expected lifetime of the universe the future value ought to be bounded above.
JAs main point, which appears to be true, is that CS actually has a value, we merely don’t know what it is. Thats his point though so read him for that.
Perhaps more interesting for me is JAs comment Notably, although he talks in terms of climate sensitivity, there is nothing in Marty’s maths that depends specifically on a doubling of CO2. A rise to 1.4x (which we have already passed) will cause half the climate change, but that would still give an unbounded expected loss in utility (half of infinity…). By the same argument, a rise even of 1ppm is untenable. Come to think of it, putting on the wrong sort of hat would become a matter of global importance (albedo effect).. This does seem to point up a confusion in the Marty paper: although it nominally talks about divergence of the integral due to long tails, in practice this can’t happen because the tail isn’t infinite. Its just about plausible to assert that the CS is 8 oC, it isn’t possible to believe there is even a eeensy-teensy probability of 80 oC, whatever pretty maths you may have put in to generating your PDF. And since most of these start from a uniform prior on [0,10] or perhaps [0,20], 20 oC is a hard upper limit even just from the maths point of view. So, yet another reason why the integral can’t diverge: all that he has done is put the wrong maths in.
But stepping back from the maths for a moment, I don’t think there is any possibility of sensibly characterising the “tail”: let us say, the bit above 6 oC. Of course, you’re entitled to say 6 oC is such a disaster that we should avoid it, but in that case the whole Marty thing becomes irrelevant. There is no observational evidence for CS above 6 oC, ie data points in that region (a bold assertion made mostly in ignorance apart from a skim of ar4 chapter 9). There isn’t really any good model evidence for it either (there are some runs with that high a value that could probably be discredited as implausible if looked at carefully…). So the idea that you can fit, mathematically, a reliable distribution to it is not true. Therefore, you cannot meaningfully attempt to integrate it. Similarly, the cost function for T > 6 oC has completely unknown form.
So perhaps you could attempt to say: aha, but with more research we could characterise the PDF better and maybe know its form better for high values and then we can justify divergence. But no, this is to miss JAs point: the PDF isn’t a property of CS, its a property of our knowledge of CS. More research (assu,ing its correct; and maybe allows us to throw out some old stuff) should narrow the PDF towards whatever the true value is.
The bottom line: the Marty analysis is fun maths, but of no relevance to the real world. It simply amounts to mt’s point, that high-damage low-probability events need to be weighted, but tells us nothing useful about how to do this weighing.
Oh dear, no, thats not the bottom line, since I just found Such a planetary experiment of an exogenous injection of this much GHGs this fast seems unprecedented in Earths history stretching back perhaps even hundreds of millions of years. Can anyone honestly say now, from very limited information or experience, what are reasonable upper bounds on the eventual global warming or climate change that we are currently trying to infer will be the outcome of such a first-ever planetary experiment? What we do know about climate science and extreme tail probabilities is that planet Earth hovers in an un-stable climate equilibrium , chaotic dynamics cannot be ruled out… which is all good well-meaning stuff, but its over the top. There is no good evidence that we’re hovering in an un-stable equilibrium (in fact its obvious that we aren’t, taking the words literally: if we were, we would have left it, that being the nature of unstable equilibria). So this is just hyperbole. Why is why ref  is to Hansen :-)