Saturday, May 30, 2009

Carbon Taxes, Cap and Trade, and All That

Suppose something some people do has substantial, widely dispersed, negative effects on other people; the standard example is air pollution. Since I am not bearing the cost of my actions, I may do things, such as light a fire in my fireplace, even when the net cost, to me and others, is larger than the benefit, and fail to do things, such as install a scrubber in the smokestack of my power plant or switch to low sulfur coal, even when the benefit of doing them would be larger than the cost. The obvious solution is direct regulation. Have some government agency tell power plants to install scrubbers, use low sulfur coal, and in various other ways modify their acts to take account of external effects.

There are at least two things wrong with this solution. The first is that the agency is very unlikely to know enough to do it right. How is it to figure out what the lowest cost way is of reducing pollution—scrubbers, low sulfur coal, both, or one for some power plants and some for others? How, indeed, is it to figure out when pollution ought to be reduced and when the cost of the reduction is more than the benefit? Carbon dioxide, after all, is said to be a pollutant via global warming; it does not follow that we should all stop breathing.

The second problem is that even if the agency had the information, it might not be in its interest to use it correctly, to require reductions of pollution if and only if they are worth their cost and by the least costly means. Such an agency is run, after all, not by philosopher kings but by bureaucrats appointed by elected politicians. If states that produce high sulfur coal are politically influential, it might be wise to impose regulations designed to discourage utilities from switching to low sulfur coal even when that is the lowest cost way of reducing the amount of air pollution they produce (a real world example, as it happens; see Regulation Magazine Vol. 14 no.4). If the steel industry has made generous campaign contributions to the majority party, perhaps it should be spared, in the national interest, the rigors of regulation of its emissions.

An alternative which many economists prefer is a "Pigouvian Tax," named after the economist who came up with the idea. Let the agency determine the external cost imposed by each ton of sulfur dioxide released into the atmosphere. Firms are free to pollute as much as they want, provided they pay for their pollution. It is then in the private interest of each firm to find the lowest cost ways of reducing its pollution and implement them, provided that the cost of the reduction is less than the benefit.

This does not eliminate all of the problems, since the agency still has to measure cost and still may be biased in its estimates of the differing costs of different effluents in different places by political considerations. But it looks like a considerable improvement on direct regulation.

A very similar alternative is currently being discussed under the label of "cap and trade." The government sets the total amount of effluent that may be emitted—say 80% of the pre-regulation level. Each firm is issued permits for its share of that amount, 80% of the sulfur dioxide it produced last year. A firm that reduces its emissions below that level can sell the excess permits to other firms; a firm that pollutes above the level it has permits for must buy additional permits. In effect, the price of the permit is the equivalent of the effluent fee under Pigouvian taxation. A firm that pollutes more than its share must pay that price for each additional ton of effluent. A firm polluting less than its share gives up, for each ton it emits, the opportunity to sell a permit for that price. Once the level of emissions is set, the market determines the cost of reducing emissions to that level and sets the required tax.

In a system run by philosopher kings, there is one important difference between the two alternative versions. A straight Pigouvian tax requires the agency to estimate the damage done by an additional ton of the pollutant. A cap and trade system requires it to estimate what the optimal amount of the pollutant is, how far it is worth reducing it. One can imagine some situations where the former information is more readily available, some where the latter is.

In a system run by elected politicians, there is another large difference—who gets the money. With an effluent fee, the tax goes to the government. With cap and trade, the payments are by one firm to another. Firms that can easily reduce their output of effluent end up richer than they would be without the scheme, since they can sell their excess permits to other firms for whom reduction is more difficult. Indeed, the regulated industry as whole may end up richer as a result of the regulation. Depending on the details of the situation, the increased income from the higher price for (say) electric power due to the higher cost due to the regulation might be more than the cost to the firms of reducing their emissions to meet the limit.

Which brings us to current proposals for cap and trade of carbon dioxide as a solution to problems of global warming. In a system run by philosopher kings, the only important difference between that and a carbon tax is the information required to set the level of emissions or amount of tax. In the real world, cap and trade has the (political) advantage of getting large parts of the regulated industry in favor of the regulation and thus eliminating a lot of potential opposition. The cost, possibly more than a hundred percent of it, is shifted to the customers, which is to say the general public—a dispersed and politically impotent interest group. And if the government retains considerable flexibility in just how emission permits get allocated, it can use some of them to buy political support from other groups or to reward them for past support.

Cap and trade has a political disadvantage as well, of course; a carbon tax would bring in lots of money. But that money would show up in the budget, get labelled taxation, and so make it harder for the administration to deny that it is raising taxes to pay for its programs. And much of it might end up spent to get the carbon tax passed by buying off organized interest groups that were potential opponents.

Think of the cap and trade version as eliminating the middle man.


G-Man said...

Hansen's proposal on a carbon tax is to have the revenues passed back to taxpayers as a refund - it wouldn't add one cent to the government.

I prefer a carbon tax because it's transparent.

Constant said...

The government sets the total amount of effluent that may be emitted—say 80% of the pre-regulation level. Each firm is issued permits for its share of that amount, 80% of the sulfur dioxide it produced last year.Could you clarify? "That amount" refers, grammatically, to 80% of pre-regulation level, but then the sentence completes by saying "80% of... produced last year". But pre-regulation is only "last year" for one year. So which is it?

Related to that question, going by your description, if, the year before cap-and-trade is implemented, I create a factory which produces nothing but emissions, then I will be issued a permit for 80% of that. I can then sell these permits. What, if anything, blocks this from happening? Is it that the permits will not be worth very much, so it would not be worth my while to produce pure emissions?

Also, how are my emissions measured? Can I easily lie, claiming to have produced more emissions prior to regulation than I actually produced, thereby getting permits for 80% of my falsely claimed emissions?

David Friedman said...

G-Man mentions Hansen's proposal to make a carbon tax revenue neutral. His proposal is for a per capita refund. Is that better described as a tax reduction or as a demogrant--a welfare payment in the form of a fixed amount to each individual--funded by a carbon tax?

In any case, Hansen isn't the President.

Constant makes a couple of good points about practical difficulties with a cap and trade system, ones I didn't discuss since I wanted to focus on other points. In response to one of his points, I think the permits for CO2 emissions are likely to be worth a great deal.

He may want to look at an old piece of mine which looks at a general issue he raises in a broader context. When the law changes, how does one treat those who would be disadvantaged by the change--consider, for example, the freeing of slaves. Possibilities range from compensating them at one end to holding them liable for costs they imposed before the change (on the theory that the change implements principles that were always correct)--letting slaves sue their previous owners for back wages.

happyjuggler0 said...

Both Pigouvian taxes and the cap and trade tax* simply suck when the negative externalities are global, as opposed to mostly domestic pollution.

There is another option. Do nothing until it is dirt cheap to do so. Announce to the world that if someone comes up with a way to get rid of "enough" of a certain type of pollution (e.g. reducing mercury emissions from coal by 98%) at a cheap enough cost (e.g. x+10%), then the US government will enact regulations requiring such an emissions cut (by any means), with the proviso of course that they aren't being "overcharged" by the provider(s) of the new technology.

We then get the benefits of massive reductions in emissions over time as the technology allows (as opposed to massive economic pain as some industries get decimated due to not-ready-for-prime-time emission reduction technologies), while providing a huge financial incentive for all and sundry to come up with such innovations.

This also has the huge benefit of not engaging in a trade war with the entire developing world, noting that they are currently, from a multi-year perspective, ramping up their economies at a rapid rate, which at market prices for energy and many materials which don't account for negative externalities, necessitates massive emissions increases (beucase that is cheapest) which would be mindboggingly expensive for them to avoid.

If we don't engage in such a trade war with them, or alternatively pay them humongous amounts of money to grow "greenly", then we'll see a massive shift of "polluting" activity engage in regulatory arbitrage between nations. If the latter happens, then all the talk of emissions reductions in the US or the EU or wherever will be mostly illusions with no real gain in reality.

* It is poor framing not to use the word "tax" at the end of cap and trade.

Kodjo said...

What is perhaps more interesting is the idea of auctioning the total volume of CO2 allowed to be released under the cap.

This takes away the discretion politicians have to allocate carbon allowances & raises substantial revenues which could be used to reduce an inefficient tax, eg, payroll taxes.

The effect is the same as an optimal Pigouvian tax so long as the cap is optimally set, but in any case is the same as a carbon tax of some specific level.

dWj said...

In re cap-and-trade as an off-the-books tax, note that, as you describe it, the permits (viz. the revenue) are granted to the incumbent polluters. That is not entirely what the Waxman bill proposes; it grants some permits specifically to "green energy" interests. This serves nothing to promote what, in your link from the comments, you call "continuity" over "retroactivity"; it is pretty transparently (to all but accountants and those who rely on stated accounting) a government subsidy paid for by the consumer. It is also a mad combination of command-and-control with a more market-driven system that privileges government-certified alternative energy over conservation or non-government-certified alternative energy, while doing nothing to improve the overall level of emissions beyond what paying off government debt with those revenues would do.

Raphfrk said...

The meta rule issue could also be framed in converting a commons to private property.

If the commons is open to all, at least in theory, then how much should each person/business be compensated.

In practice, (presumably), when commons were converted to private property, it was the locals who each were given a share of the commons for their private usage (even if others were also entitled to use them).

You could add a rule that all current polluters should be uneffected. They could be given permits so that all of their plants continue to yield the same return on investment.

This would mean that they receive less permits than pollution they emit. The assumption being unless they are the most efficient plants in the country, they can reduce output and sell some permits.

In the EU, milk quotas were based on output 2 year before the decision to issue them was made. This prevented farms from ramping up production during the test period.

Another option would be to give notice that the cap and trade rule is coming in at a later date and the slots will be auctioned.

This allow businesses to just not enter the market. The effect being to reduce competition for the ones that are already in the market and compensate them for losses.

Ofc, the government would find it hard to commit to "Cap and Trade will kick in on date 1st Jan 2016".

amiga said...

Altogether missing from the discussion, of course, is definitive proof that reducing CO2 emissions would have any measurable effect on global climate. It is becoming increasingly obvious that the "precautionary principle" is merely newspeak for increased control.

G-Man said...

Altogether missing from the discussion, of course, is definitive proof that reducing CO2 emissions would have any measurable effect on global climate.Sigh.

jimbino said...

More effect than a carbon tax or carbon cap & trade would be a tax or cap & trade on breeding. Let every American have the right to one kid; after that, he would have to buy the right to another kid from someone who chose to have none.

If a breeding cap were instituted, problems of pollution and other burdens on the planet would diminish. Such a plan would have an advantage over the Chinese breeding regulations in that the kids could have brothers, sisters, cousins, aunts and uncles.

Indeed, in the absence of tax, cap & trade or regulation of breeding, those who hold off on the breeding should be compensated with extra pollution rights!

Hammerhead said...

Exactly, Amiga. It's the most important question to be asked wrt to the taxing of CO2. Unfortunately, I think the issue is a runaway train under the Obama administration, so we will, short term anyway, be paying some sort of CO2 tithe. Perhaps in 30 years people will recall fondly, the fads of this time, 'carbon footprints' will be a retro thing, like 'hula hoops' and 'home bomb shelters'. Actually, a home bomb shelter nowadays might make more sense than paying a CO2 tax, given the North Korean and Iranian nuclear programs.

Anonymous said...

Amiga is partly right; it is true that

"a definitive proof that
reducing CO2 emissions would have any measurable effect on global climate"

doesn't exist.

IPCC provide a probability distribution function for the climate sensitivity (=how much hotter it gets per each doubling of CO2 concentration). This distribution ranges all the way from 0 to about 6 degrees C. With a maximum at about 3degC.

CO2 concentration is now at 390, growing by 2 per year. Pre-industrial value is 270 (ppm).
(Human contribution is now 4 per year; nature removes 2 per year; net result is 2 per year.)

Uncertainty doesn't preclude decision-making.

David Friedman said...

Alexei writes: "Uncertainty doesn't preclude decision-making."

The problem in the case of global warming is that the costs of reducing CO2 output are certain--not in detail but in general--and the benefits are not. The costs occur immediately, the benefits over a century or more--and we may never know how large they were, or even if they exist, since we don't get to observe both what happens with a carbon tax (or whatever) and without.

That doesn't preclude decision making, but it does heavily weight the calculation against doing things we know are very expensive to avoid costs we are very uncertain of.

Anonymous said...

"I may do things, such as light a fire in my fireplace, even when the net cost, to me and others, is larger than the benefit"

How do you know the cost is greater than the benefit? Sounds like you believe that value and cost are objective and comparable. If you burn a log of wood, is that 1.7093 happiness points, and for me it's -0.000000092 happiness points?

In fact there is no objective value, and pretending to sum things up this way is an exercise in false accounting.

Anonymous said...

David, I strongly disagree -- not so much with your assertions individually, as with your implication that the issue of GW as it stands now -- what's the right level of carbon tax? -- is helped along by such generalities as you offer.

(I'll go through them anyway. But I would much rather have a real argument -- with numbers.)

1. [implied:] Costs are large, benefits small.
Maybe. So let's count them, not just talk. And besides, what are the MARGINAL costs of CO2 reduction, as of now?

2. "Costs occur immediately, the benefits over a century or more."
Let's just choose the appropriate discount rate... *IF* we can agree on one...
As to the implied uncertainty -- see "4" below.

3. "...we may never know how large [the avoided GW damages] were..."
Unsatisfied curiosity will be killing us. (Sarcasm intended).

4. " [the presence of uncertainty] does heavily weight the calculation against doing things we know are very expensive to avoid costs we are very uncertain of."
But it is also true, that for a given MEAN value of anticipated damages, extra uncertainty only makes them WORSE.
Whereas you appear to conclude, extra uncertainty makes these damages BETTER.
Why the contradiction? My guess, you're talking about a peculiar sort of uncertainty -- the kind that DECREASES THE MEAN VALUE. Your statement is really not about uncertainty, but about the MEAN. For which, see "1" above.


Anonymous said...

Sorry if I made it sound, in my first sentence in the comment above, as if Prof. Friedman's "Carbon Taxes, Cap and Trade, and All That" was the target of my comment. No. Only his most recent comment was.

That comment purported to be about uncertainty. But it was not.

Uncertainty - as distinct from the MEAN - should cause us to care MORE, not LESS about climate change. Prof. Friedman was only able to suggest otherwise by mixing together three things: the uncertainty, the mean, and the time lag.


David Friedman said...

I think there is an important point Alexei is missing--although not one I made in the comment he is responding to.

Uncertainty decreases over time. Suppose there is a .5 chance that the problem will turn out to be serious, .5 it won't. Further suppose that, ten years from now, we'll know which it is. Finally suppose that solving it ten years from now costs 50% more than solving it now.

Looking at expected value of damage it may be worth solving it now. But waiting ten years has, on average, only .75 of the cost.

This is aside from the fact that, ten years later, we may know more about how to solve the problem and so be able to do it in a less expensive way.

Anonymous said...

I agree with Prof. Friedman's last comment; I'd like to formulate its 1st point as

Expectation that uncertainty shall decrease tends to favor the decision to "wait and see".

I do not know whether the existing economic analyses of climate change had taken this point into account. I would presume that they did -- or if they didn't, that they had considered it off-record and judged it to be insignificant.

What I can say with near certainty from my reading, is that such analyses normally do take into account the following facts, mentioned in Professor's two latest comments:

ten years later, we may know more about how to solve the problem and so be able to do it in a less expensive way.

The problem in the case of global warming is that the benefits [of action] are not [certain].

as well as
The costs occur immediately, the benefits over a century or more.

Regrettably, we keep talking about generalities. Whereas the real question is, What should be the level of the carbon tax NOW, with the knowledge we have NOW.

What's the current MARGINAL cost of CO2 emission avoidance?
What's the current MARGINAL damage from CO2 emissions, per tonne?

David Friedman said...

Alexei writes:

Whereas the real question is, What should be the level of the carbon tax NOW, with the knowledge we have NOW.

That's one interesting question. But as I argued in a post some time back, answering it doesn't tell you whether you should be for a carbon tax, because we probably don't have the option of having a carbon tax that will be set at the optimal level.

The option is having a carbon tax which will be set at whatever level it is in the interest of political actors setting it to choose. That might easily be worse than no carbon tax, even if the right carbon tax was better. Looking at the current controversy, I see no evidence that the decision will be based on the sort of calculation Alexei imagines. Indeed, I can see no evidence of anyone even doing the necessary calculation, unless you count people who first decide what answer they want and then design their calculation to produce it--for instance assuming a discount factor of about zero so as to magnify the weight of distant costs.

What's the current MARGINAL cost of CO2 emission avoidance?
What's the current MARGINAL damage from CO2 emissions, per tonne?

I don't know what the "current marginal damage" means. If you mean damage that actually occurs this year from this year's emissions, the answer is surely very close to zero. If you mean the total from now to infinity of damage due to this year's emissions, that calculation gets us into the sorts of uncertainties I just raised.

Anonymous said...

Mr Friedman,

How about writing a post on the relationship between crime and economy?

Something like you did with the subject of global warming.

I wonder if the current times are anything like past decades with economic hardships and crime. The situation displayed on the news seem to me pretty unusual. And nobody seems to care, but rather be amused, or see it as entertainment.

I suggest this to you because you seem to know many things, and gather people on your blog.

Anonymous said...

In this comment, I argue against Prof. Friedman's last comment.
I also offer my carbon-tax-related estimates---Alexei

The option is having a carbon tax which will be set at whatever level it is in the interest of political actors setting it to choose.
Just like any other issue. And no, public opinion won't be ignored, not on this one!

That might easily be worse than no carbon tax.
Not "easily", no.

I see no evidence that the decision will be based on the sort of calculation Alexei imagines. Indeed, I can see no evidence of anyone even doing the necessary calculation.

Whatever we do in life is based on a calculation, often a sub-conscious one. Whatever are our GW-related calculations, let us bring them into the open.

Professor Friedman's preferred option -- to do little/nothing for now -- must needs be based on a calculation. I would like to check his calculation against mine.

General talk is not enough.
Each side can name many factors in its favor. It is time we were arguing in terms of estimates and PDFs (probability distribution functions).

I can see no evidence of anyone even doing the necessary calculation [except for faulty calculations based on wrong assumptions]
Great! Let's fix those calculations up! Maybe your students would do that as an assignment?
Where there's a will, there's a way.

What's the current MARGINAL cost of CO2 emission avoidance?
(My question, unaddressed by Professor.)
My answer: ZERO, or zero-ish. Based on common sense.

What is the total, from now to infinity, of damage due to this year's emissions?
(My question, commented upon but not answered.)
My answer: a few tens of dollars per tonne of CO2. Based on Wikipedia.

What should be the level of the carbon tax NOW?
(My question, commented upon but not answered.)
My answer: initially 10 U.S. dollars per tonne of CO2. (Subsequently to be adjusted--upwards, unless new evidence suggests otherwise.)

Which translates into:
1 cent per kg of CO2.
4 cents per litre of gasoline
4 cents per kg of coal
1 cent per 1 kWh of coal-derived electricity;
half-cent per 1 kWh of gas-derived electricity.
(Caveat: only direct contribution to CO2 emissions factored in.)

What are the overheads of collecting the tax?
My estimate: under 0.1% of the tax value. (Based on 1 clerk employed full-time per amount consumed by 1 big coal station.)


Anonymous said...

Continuing from above---Alexei.

1. To clarify, a tax of $10-per-tonne-CO2 is much too small, I only propose that INITIALLY.

2. David refers in his argument to a "post some time back". I think I found it: the one of March 14, 2007.

The core argument goes:
[Taxes] would not be based on a realistic estimate of the marginal costs; [...] they would be based on some target level of emissions. If, as seems likely, the level of taxes needed to substantially slow global warming was much higher than the marginal damage done, the result would be [net economic loss].

However, this wouldn't be a problem if the "target level of emissions" was set correctly -- right?

Reasonable people, looking to set the target level, would choose it to minimize the net economic loss (suitably defined to accommodate things like disappearing species and resentful nations.)

So where's the problem? The problem is, that the matter may not be decided by reasonable people:
I offer as further evidence [my] arguments at Brian's "Backseat Driving" blog with people who are absolutely convinced that global warming would have catastrophic consequences but [cannot substantiate] that conviction...

I am not persuaded. Bloggers will be bloggers! Whereas politicians will be politicians, and lobbyists will be lobbyists! A level of tax set BELOW OPTIMUM is guaranteed to be better than ZERO TAX. And considering the lobbying power of coal/oil/steel/auto industries, how big the chance for that level to be set ABOVE OPTIMUM?


Anonymous said...

Above, I proposed a tax of $10 "initially". But, what should it really be?

Here's an estimate.

IPCC 2007 report found, that published studies estimated the social cost of carbon between 3 and 95 USD per tonne CO2, $12 on average. Note: in 2005 dollars, and according to pre-2005 studies.

The lower estimates are suspect. Most of them reportedly didn't even explore a range of temperature trajectories, just looked at "best guess". (Sorry, can't substantiate that. Just saw that claim somewhere. Seems credible.)

Can we trust the higher estimates? I tend to trust them more because of what I learned from the arguments over Stern's 2006 report. Stern was treated by many as an alarmist.

The controversy was mostly about one parameter called "social discount rate" (and other names). Stern had it at 0.1%. Nordhaus would have it at 3%.
Weitzman agreed with Nordhaus. However he also thought that Stern failed to properly value extreme outcomes (also called low-probability high-impact outcomes), and ***that these two wrongs made right.***

Someone who agrees with Weitzman about extreme events (as I tentatively do) while choosing a social discount rate below 3% (as I do), must conclude that Stern was not even alarmist enough!

Thus my higher trust in the upper end estimates.

Since 2005 temperature projections became higher. Stern recently doubled his 2006 recommendation: not 1%, but 2% of global GDP. Which PROBABLY means, the results of those pre-2005 studies would also double with the new knowledge. That yields 6-190 with an average of $24. (Still in 2005 dollars.)

Adjust that for inflation, put (as I do) more faith in the upper end -- and $50 looks reasonable.

So, maybe $50. Per tonne CO2.

This estimate probably does not include those less-material, harder-to-value things, like disappearing species and resentful nations.


Paul Martin said...

Ross McKitrick proposed the best carbon tax scheme I've heard to the Canadian government about two years ago. It uses the most widely agreed leading indicator of changes in global temperature as an adjustor to find the "right" tax rate.

I include a couple of paragraphs from a review of his write up on the topic.


Under McKitrick's proposal, the carbon tax would be, in dollar terms, 20 times the three-year moving average of tropical troposphere temperatures above the 1979-1998 average. In other words, with tropical troposphere temperatures currently 0.235ยบ Celsius above the 1979-1998 average, a current carbon tax would be $4.70 per ton.

The formula was deliberately chosen at 20 times the three-year moving average, McKitrick explains, because the best economic estimate of the cost to society of carbon emissions is currently about $4.70 per ton.

If temperatures continue to rise, as many scientists predict, the carbon tax automatically rises, providing economic incentives for carbon emitters to cut their emissions. If temperatures level off or rise only slightly in coming decades, as many other scientists predict, carbon emitters are not unjustly punished for their benign or minimally harmful emissions.

Noting "most economists who have written on carbon dioxide emissions have concluded that an emissions tax is preferable to a cap-and-trade system," McKitrick argues that under a temperature-linked carbon tax, "the regulator gets to call everyone's bluff at once, without gambling in advance on who is right. If the tax goes up, it ought to have. If it doesn't go up, it shouldn't have. Either way we get a sensible outcome."


The beauty of this approach is that it will do just what you want if you expect humans to bake the planet, and it will also do pretty much what you want if you believe humans are passengers, not drivers, of the global climate.

Of course no tax that applies to only one country can do anything about the rest of the world, but if you want a carbon tax, what's not to love about McKitrick's?

Anonymous said...

Paul --
To me, the level of the tax NOW is all that matters.

Let any plans for the future be made -- when future comes, we'll amend those plans if need be.

you quote a tax rate of $4.70. (Presumably per tonne CO2.)

$4.70 is said on the 'net to arise from the MEDIAN estimate from Tol's 2005 meta-study.

Looking into that study (actually into a follow-up study), MEAN estimate is roughly 20+, i.e. 4 times higher.
(Note that Tol's numbers are per tonne carbon. Divide by 3.7 to convert to "per tonne CO2".)

Which do we trust more? The mean or the median?

Worse, what does it all mean?
Reading Tol, I get the impression that each study he looks at provided him with one number. Tol then does statistical analysis on those numbers, deriving mean, median and mode.

But those individual studies -- don't they recognize uncertainty? In which case, don't some of them already provide a mean, a median, and a mode?

When they do, which number Tol uses?

When they don't, and only give one number, are we to understand their value to be the mode (best guess), median, or mean?


Anonymous said...

Ouch. I made a mistake, assuming that IPCC 2007 report's $12 average for the social cost of carbon applies to the future as we anticipate it to be. It could be BAU (business-as-usual) -- IPCC doesn't clarify.

If indeed that was BAU, the optimal level of carbon tax is LESS.

How much less? On one hand, could be a lot, as we see by comparing these two estimates from Stern:

For BAU: SCC = $85.
For the future limited to 450-550 ppm: SCC = $25-30.

On the other hand, Stern is an "outlier" according to Tol. In studies other than Stern's, BAU might be comparatively tame. And the difference, smaller.

My $50 estimate ought to be revised downward. Maybe to $30. (Same as Stern's for 450-550 -- but, note, that's Stern as of 2006!)

Same applies to Tol's numbers (referred to in my comment above). Some or most of the estimates he aggregates might be BAU.