Why “extremely unlikely” climate events matter

by John Quiggin on January 5, 2018

I’ve just been advised that my latest article “The importance of ‘extremely unlikely’ events: Tail risk and the costs of climate change” has come out online in The Australian Journal of Agricultural and Resource Economics. For those who can use it, the DOI is 10.1111/1467-8489.12238. For everyone else, here’s a link to a pre-publication version. The main points are

  • The IPCC convention is to use the phrase “extremely unlikely” to refer to outcomes (in particular, values of climate sensitivity) in the range of 0–5 per cent.
  • Most of the risks against which we act to protect and insure ourselves (for example, car crashes, premature death in any given year) are “extremely unlikely” by this definition
  • Around half, or even more, of the expected welfare loss from climate change arises from the worst-case 5 per cent of high values for climate sensitivity.

Nothing really startling here, but it’s the other side of the coin to the contrarian suggestion that since there’s a 5 per cent probability that global warming will turn out not to be a problem, we should do nothing.



JK 01.05.18 at 8:33 am

You could say that the world is like a single individual trying to insure themselves. It might or might not be rational, but you can’t say that it obviously makes sense because it’s the same as paying in to an insurance pool.

When you look at things from the point of view of social resources as a whole there is a big difference between most of the risks we insure against, such as your examples of car crashes and premature death, versus a 5% risk of high climate sensitivity.

The car crashes have a low risk of happening to any individual, but they are virtually guaranteed to happen to someone, and we can estimate how many people fairly accurately.

So the probability that the social resources will be well spent is not 5%, it is better than 99%.

But in the case of climate sensitivity we have one earth that either has high sensitivity or it does not. The chance that resources allocated on the basis that sensitivity is high will be well spent is 5%.

I’m surprised your policy implications don’t include a massive hike in resources for research on climate sensitivity.


ozajh 01.05.18 at 9:32 am

From the paper:

All of these [direct CO2 reduction] options are problematic in one way or another. Perhaps the most problematic is geoengineering. This term is used to encompass a variety of strategies involving radical human-induced changes in atmospheric and oceanic
systems, aimed at offsetting the warming effects of greenhouse gas emissions.

Unfortunately I have the very strong impression the world will stay in business-as-usual mode until well past the point where a harmful temperature rise is obviously underway. Politics will then dictate a “quick fix”, and geoengineering will offer the illusion of this, so that’s what we’re likely to get.


bruce wilder 01.05.18 at 4:23 pm

One thing I am a little confused about is the interplay between an individual and a global perspective on climate change, its consequences and when it is proper to say, “risk” or “insurance”.

If an individual chooses to own and drive an auto, there is some very small risk that operating the auto will have as a consequence someone’s death or serious injury in an accident, a risk that may be meliorated by, say, careful driving and insured by pooling the financial consequences with the very large number of drivers, most of whom will not have serious accidents in any finite, discrete period of time. If a society chooses to have a system of automotive transportation, there is some calculable expectation of some rate of accidental death and injury, a rate that may be controllable within limits by policies of safety promotion. It is sensible for the individual to buy insurance for the foreseeable but remote chances of catastrophic consequences to self or others. It may be sensible for the government to mandate that auto owners and drivers maintain insurance. And, certainly sense in having policies for safe highways, safe vehicles, enforcement of traffic laws, etc. But, is there any sense in the government buying insurance for the risk of having an auto system?

Climate change has the foreseeable consequence that extreme weather events become more common and more extreme. Those weather events may constitute insurable risks (allowing that actual large weather events stretch the capacity of actual insurance facilities) and subject to control by policy in the sense of mitigating consequences (e.g. flood control, building codes, weather forecasting, etc) But, I am a bit unclear about where the global and general effects of climate change are insurable. “global climate change” is global after all. And, “climate”! Climate is not an event — it subsumes weather events, no?

Whatever is meant metaphorically by talking prospectively about the “probability” that the climate might change faster than the consensus point estimate rate projection, that metaphoric “risk” lacks the discrete and repetitive qualities of something one can usefully bet on. Who is going to take the other side of the bet? How would anyone assemble a portfolio of such wagers? There is only one “global climate”.

Moreover, is there a control response, a means of enhanced mitigation? When we talk about “risk” that the processes of climate change might accelerate beyond the pace projected, where exactly does that put the efficacy of policy response? (The equivalent of driving more carefully in hazardous circumstances, say, or cracking down on drunk driving?) If the world collectively proves suboptimal in its ability to constrain carbon emissions (if! Ha!), and the natural forward forcings accelerating the rise in climate-temperatures (e.g. the melting of ice caps, methane releases from melting permafrost, etc), isn’t the “risk” that policy loses all traction? In projecting that a rate of carbon emission is associated with a level of ppm CO2 equivalent in the atmosphere and that corresponds to a climate state in 2050 and 2100, the false certainty of projection seems to be suggesting a continuous function relating additions of carbon to the carbon cycle to a rise in climate-temperatures. The actual science says something else, says that the direct, functional relationship between CO2 concentration and greenhouse effect is very modest almost minor, but that minor direct and functional effect will trigger forward forcings that will amplify and accelerate somewhat chaotically both the changes in climate and the consequences. Chaotic, as in not neatly and continuously functional. The uncertainty in the underlying science is about the nature and magnitudes, on balance, of these chaotic forcings positive and negative. The “risk” metaphor has been applied as a label for the possibility that climate change takes off on its own, so to speak, launched by past human additions of carbon to the carbon cycle, but forced by natural processes running out of human control and taking the climate to some new equilibrium climate state of much higher temperatures.

That is the science. But, what is the economics? “Insurable risk” seems like bad translation for what is meant when the IPCC tries to characterize the uncertainty of what are complex chaotic processes in inherently chaotic systems. In economic terms, I am not seeing how ideas like a portfolio applies, making sense of insurance concepts. But, I am also wondering whether proper attention is being paid to the potency and effectiveness of control responses in this frame of analysis.


Omega Centauri 01.05.18 at 9:47 pm

Its pretty tough to have something that works like insurance when the sample size N is one.
Now, one could do some partial things, that might to some degree mitigate the consequences, funded presumably by something like a carbon tax. The easiest would be to use the proceeds of such a tax to subsidize traditional insurance pools (but this risks a suboptimal response because
insured parties are not then responsible for the full costs of their local economic decisions). Also we could use the funds for infrastructure projects, like the hardening cities against sea level rise. But
these maybe shouldn’t be described by the term “insurance”.


Janda Beeston 01.05.18 at 9:50 pm

I read JQ’s three points on the attendant risk arising from climate change not as an imprecation to find some “insurance” (whatever that might be) but as a accurate restatement of the human tendency to significantly under-estimate the risks of events with which we’re familiar and wildly over estimate those with which we’re unfamiliar.

Governments have a disappointing track record of exploiting this weakness, attempting to frighten the citizenry with what are very low-risk probabilities and, conversely, sooth citzens’ concerns about what are, on rational analysis, evidently high-risk probabilities. They consequently devote substantial fractions of tax revenue on remote but apparently scary risks and, to pay for these, cut back investment on mitigation of genuine high-risk issues.

If the risk of certain events associated with climate change are approaching the 5% domain, these are not by any valid reasoning “extremely unlikely”, a phrase most carefully chosen and, self evidently, not for the purpose of properly informing the populace. Politics, writ large.


Mike Furlan 01.06.18 at 12:35 am

In a sane universe anyone wanting to dump large amounts of any gas into the atmosphere would have to prove that it was safe before they were allowed to do so.

Trying to prove that Carbon Dioxide emissions might be dangerous is and has been a losing game.

And, btw I think the discussed probabilities are bunk. The false precision of those numbers opens the entire argument up to attack.

If stating that a possible outcome of burning fossil fuels is an extinction event doesn’t make the case, then adding more significant digits to the estimate certainly will not convince.


Bernard Yomtov 01.06.18 at 12:59 am

Is the sample size one? Suppose we take the view that the nasty effects of climate change will not be evenly distributed, but will hit some people and places much harder than others. Then why is it wrong for everyone to have some insurance?

Bruce Wilder asks :

But, is there any sense in the government buying insurance for the risk of having an auto system?

Well, suppose the government simply paid the cost of auto accidents, adding it on to the tax system. Single-payer, you might call it. There are some obvious flaws with that, but in the absence of auto insurance companies it might be the best we can do. Is the climate change scenario vastly different?


Faustusnotes 01.06.18 at 2:07 am

John I read the prepublication draft and it appears you use an assumption of normality for the distribution of the equilibrium sensitivity Lamba – I infer this from your estimate of standard deviation of 1.95. is this correct? Assuming I’m correct about this then 95% of values lie between approximately 0.05 and 7.8. But this implies something like 2% of values imply cooling (a lambda less than 0). This is aphysical- cooling is not going to happen – and surely messes with your theory since the tail risks at the top are offset by equally likely risks of improvement in temperatures due to very mild cooling at the bottom of your inferred distribution. That bottom 2% or so of the distribution leads to a better world with almost equal probability to your catastrophic future.

Shouldn’t you instead have based your model on a distribution that was more like a gamma distribution of some kind, with most of the probability weight lumped near the median and only the right tail extreme? Because the distribution you seem to have inferred creates a problematic counter argument that you don’t seem to have considered. Am I wrong?


John Quiggin 01.06.18 at 2:51 am

@2 It really doesn’t matter how you treat the bottom 0-5 per cent of the distribution. The effect of zero change is, obviously, zero, and the effect of small changes is small. It’s true that the top 5 per cent and the bottom 5 per cent have equal probability, but the expectation of two equiprobable events, with outcomes huge disaster and zero is still disaster.


Faustusnotes 01.06.18 at 3:10 am

But John if the outcome of the bottom say 2% is actually positive then it does matter. “I could lose all my money or just a bit of money” is a very different scenario to “I could lose all my money or I could win a metric fuckton of money”. It’s the difference between an insurance analogy and a gambling analogy, for starters. If the bottom 2% of your distribution is very mild cooling then there are huge benefits to massive CO2 releases – all the benefits of uncontrolled growth in fossil fuel energy use combined with all the benefits of very mild cooling, which are likely huge (eg reversal of desertification, improved ocean environments, more habitable marginal land masses, less tropical storms, potentially greater crop productivity). This is also likely true if you have a large probability mass near zero, since very very mild warming is also possibly beneficial. I’m not sure why you would risk your argument with this arbitrary choice of (aphysical) distribution. Why did you do this?


John Quiggin 01.06.18 at 6:04 am

I haven’t explained that very well. First, we can ignore the benefits of (present day) fossil fuel burning since these benefits are invariant with respect to climate sensitivity .

Looking at the climatic effects, there simply aren’t huge benefits to mild cooling. Obviously the benefits of zero change are equal to zero, and there is probably a small benefit to very modest warming. Changing the probability distribution around these values for the bottom tail (say from -1 per cent of income to +1 per cent, with a probability of 0-5 per cent) makes essentially no difference (<0.05 per cent) to the estimated loss from warming overall.


Charles S 01.06.18 at 7:49 am

In section 4, there is a description of 0.5 C in a century being an acceptable “rate of change”. Wouldn’t it be more accurate to say that 0.5 C change is an acceptable “amount of change”? If the global mean temperature keeps increasing by 0.5 C/century, temperature change would reach a disastrous 5 C in a geologic eye-blink of 1000 years, and a largely human uninhabitable +15 C in only 3000 years.

Never mind what it would look like in 10,000 years!


Tim Worstall 01.06.18 at 10:13 am

Situations akin to those we insure against justify insurance against them.

Say, a revenue neutral carbon tax rather than the dismantling of industrial capitalism (I know JQ agrees with the first and not the second).


Mike 01.06.18 at 11:35 am

John, do you cite in your article any of the contrarians who say that the probability of no adverse climate change is 5% so no action is needed? Or do you have links?


Faustusnotes 01.06.18 at 12:08 pm

Oh dear. Tim you aren’t going to solve this crisis with a tax. How silly to think that’s all it takes. An even sillier to think anyone wants to dismantle industrial capitalism.

Though good luck finding a solution to the plastic waste problem that doesn’t involve reforming capitalism significantly.


Layman 01.06.18 at 12:16 pm

Why does anyone believe that a revenue neutral carbon tax would help? For it to be revenue neutral, it will be paired with tax cuts, and it seems likely to me that politics will dictate that the entities hit by the carbon tax will benefit from the other tax cuts, else it will be politically impossible to pass them.

My taxes will go up by X because I drive a conventional car, and down by X to offset that. Why should I pop $60k for a new electric car? Duke Energy’s taxes will go up by Y because it operates fossil-fuel-fired electrical plants, and down by Y to offset the increase. Why would Duke Energy spend any money to build renewable energy plants?


John Quiggin 01.07.18 at 7:02 am

Mike @14 This is a terse bloggers summary of the position taken by most lukewarmers, such as Lomborg. I didn’t mention this position in the paper, only in the blogpost.


Tim Worstall 01.07.18 at 12:59 pm

Revenue neutral carbon tax? Well, just that most economists, you know, the people who study incentives and economies, think that would be the solution. Sure, arguments about the rate, but the principle seems generally agreed. From Greg Mankiw through JQ here to Nick Stern and so on.

Pigou taxes on externalities, pretty standard stuff.


James Wimberley 01.07.18 at 1:13 pm

We can’t have a revenue-neutral carbon tax. The first claim on the revenues has logically to be an equal and opposite subsidy for carbon sequestration. As time goes on, this absorbs an ever-growing share of the revenue. Eventually we hit zero emissions, and zero revenue from the carbon tax, but will still need the sequestration subsidies to get back to 350-400ppm of CO2 in the atmosphere, the only levels we know we can live with.


J-D 01.07.18 at 9:29 pm

Nobody’s going to arrange a package which involves collecting extra tax and then paying back to each taxpayer individually the exact same amount that was individually paid in extra tax — what would be the sense in that? When a package is described as ‘revenue-neutral’, the description is intended to apply in the aggregate, not to each individual taxpayer. If a package is revenue-neutral, some individual taxpayers can expect to get back from it as much as they contribute in extra tax, or even more in some cases, but only if their pattern of behaviour is of a kind favoured by the package; hence the hope that such a package can motivate change in behaviour.


derrida derider 01.07.18 at 11:31 pm

The merits of a carbon price (whether the price should be a tax or an ETS is a separate argument) versus direct regulation is a bit OT for this post. But I must say the comments by the “banning cars is the only way to stop AGW and besides it would punish people I don’t like” faction are pretty unconvincing here. They show no evidence of having thought through the respective full effects (including political economy, as well as straight economics) of either a carbon price or of heavy direct regulation.

James Wimberley @19 in particular – why on earth would “the first claim on the revenues … logically … be an equal and opposite subsidy for carbon sequestration”? That is simply a straight non-sequitur.


Faustusnotes 01.08.18 at 12:40 am

The economists are wrong Tim, it won’t be enough. I have made this point again and again and shown the calculations on my blog. You can raise the tax to huge amounts and it still won’t get us to carbon zero. Consider any industry and you’ll see that while it will have some initial effect it’s long term impact will not be sufficient. Consider tobacco as an example – even with taxes on tobacco at 75% of the price we can’t stamp it out and we need a wide range of additional non tax based measures to control it.

You can’t tax your way out of a civilization ending crisis. Anyone who thinks you can doesn’t understand the science and doesn’t understand the urgency of the crisis.


faustusnotes 01.08.18 at 1:41 am

I’ll back that comment up with a typical example: A low income US family considering replacing their gas-guzzler car. For this family the car is essential and their primary issue is not low- vs. high fuel efficiency, but second hand vs. new. Faced with a new renault leaf or a secondhand nissan march they will choose the latter because it will be much cheaper and much more fuel efficient than their current car. You could force them to buy the new leaf by putting a huge licensing cost on second hand combustion cars but that is not a carbon tax. Your carbon tax will only encourage them to buy the leaf over the march if it is so incredibly high that it causes the annual fuel cost to significantly exceed both the annual fuel cost of their previous gas guzzler and the financing costs of the nissan leaf (and remember a low-income family will be getting this car on hire purchase so the financing costs will be huge).

Instead you will be left using your cabon tax to try and get them to use the car less, but they have a fixed amount of use they have to put it to – the daily work commute. If you raise the tax enough they will simply offset the increased commute costs with some other cutback which may be carbon intensive (e.g. heating) or may not (cinema tickets). But whatever happens, the carbon tax is not going to reduce this family to carbon zero.

A better way to make this family reduce its carbon footprint is to recognize that they need to buy the secondhand combustion car, and implement policies that ensure they never need to use it – so that either they decide not to buy any new car, or they only use it for very rare, short trips. The best policy in this case is to ensure they have access to a reliable electrified public transport network (as we have here in Tokyo) that ensures they never need to use the car. But this policy option has nothing to do with a carbon tax.

The same considerations also apply to any low-margin carbon-intensive industry with high financing costs – taxis, fisheries, trucking, you name it. It is simply ridiculous to think that these industries can be made carbon zero through a tax. It misunderstands the balance of their costs and the decisions they have to make, and it shows you aren’t seriously considering the full balance of the economic changes we have to make, or the speed at which we have to make them. A proper response to the economy fully considered is a rich mix of subsidies, bans, and heavy-handed interventions that force industries to change on the one hand, and help them change on the other.

Your small government ideas are bullshit and completely unsuited to this task.


Omega Centauri 01.08.18 at 2:37 am

Thanks, J-D, I don’t have to explain to layman, that a tax that ts revenue neutral in the aggregate doesn’t have to be revenue neutral for all economic units.

And I bought a new electric car last year for about half of your strawman $60K. Less than half counting tax incentives… It is in fact a choice that some make based purely upon economics.


Asteele 01.08.18 at 4:29 am

As ex commenter Rich would now point out here, taxes won’t work because as soon as they start to cost real money they get repealed. You have to change over the infrastructure to a carbon free form.


faustusnotes 01.08.18 at 4:58 am

John, just coming back to our unfinished (on my side!) discussion of your choice of distributions, I don’t think your explanation covers all the issues. If you allow a negative sensitivity in your distribution then there is the problem that we have already witnessed 1C of warming that has a small chance of not being anthropogenic (due to the negative sensitivity). That means we need to emit more carbon to cool the planet to offset whatever unidentified source (Russian steam-pipes? Insects?) is causing it. So the benefits of warming now need to include the prevention of all the potential catastrophe that appears to be on the verge of happening. I concede that this is an argument from your distribution that is too subtle for denialists to make but it’s there if you care to dig.

I appreciate that if you use a physically representative distribution your calculations are harder because you can’t describe the asymmetric, bounded distribution as conveniently as you have – instead you would need to do simulations from an empirical distribution (I guess), which is harder work. But it opens up a secondary argument that I have seen made informally on blogs but never formally stated – it dismisses the issue of low positive sensitivities. As you are no doubt aware there are a few published papers by people connected to the GWPF that use a Bayesian analysis with carefully constructed priors to show that sensitivity is much lower than 3.5. If you were using hte actual formal distributions of sensitivity in a simulation-based study you could compare the IPCC’s distribution with those (dodgy) alternative lower-median distributions and show that it doesn’t matter in either case, the insurance argument still holds, and thus even if those (dodgy) studies are correct and the ECS is lower than 3.5 there is still a need to act.

Also as a further aside you used all-cause mortality to identify an approximate 1% tail of a distribution as something to insure against (if I’m understanding your argument properly), based on US data. But much of the US mortality is death we don’t insure against (mostly old age). If you use mortality from causes that most countries mandate insurance against – motor vehicle and occupational – then you are talking about a much smaller % tail – perhaps 0.1% or 0.01% – which makes your case much much stronger, since the damages in the 0.01% tail of the climate sensitivity distribution are ridiculously extreme.


ph 01.08.18 at 6:03 am

@ 23 “Your small government ideas are bullshit and completely unsuited to this task.”

This seems unhelpful, both in terms of tone and substance.

We can be confident that any one size fits all approach is going to have it’s detractors. Individual transport is essential in areas where population densities do not justify large capital investments to set up electrified rail systems, or the costs of their maintenance. This is particularly true in larger nations, such as Canada, where all passenger rail services outside of densely traveled corridors are irregular and subsidized by the taxpayer. But is also true in Japan; where the concentration of employment opportunities and the benefits of cheap, effective transport, have had a crushing impact on the tax-base of smaller cities and communities outside large urban centers. This phenomena is not unique to Japan.

Individual consumption rates matter and shifting people away from carbon combustion transportation is an excellent short-term goal. Paris is doing what it can, as are other cities. Subsidizing new car purchases is one of the solutions in place in Japan. The older the vehicle, the greater the cost of having the vehicle inspected as roadworthy.

Imagining the end of capitalism and private property is fun, but individual choice – the choice to smoke, get fat, think bad thoughts, and drive cars is part and parcel of a free society.

When people are given beneficial choice a/ and less beneficial choice b/ many will in fact choose choice a/. Reduced tobacco consumption is a good case in point. Removing choices from people tends to make them grumpy and hostile. Hence the need to respect others, even small government types. Warning labels on

I’m sure you’ll agree that the need to protect the environment supersedes petty tribalism and point-scoring. Think of the children and the spotted owl, if that helps.


Faustusnotes 01.08.18 at 11:43 pm

Vintage kidneystones: you spend most of your comment saying nothing, write as if you’re disagreeing with me when in fact in paragraph 4 you agree with me; then having agreed with me without admitting it, accuse me of trying to dismantle capitalism (an impossible conclusion from my comment); co pketely fail to engage with the specific content of my comment at all; then patronize me at the end.

You really are a piece of work, kidneystones.

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