It is time to stop quivering in our boots in pointless fear of the future and just roll up our sleeves and build it.
- Ray Pierrehumbert

Friday, September 13, 2013

The Wrongest Denial Ever

A fellow by the name of Topher Field, who prefers to go by "Topher", has created a very polished piece of propaganda, which claims to make the case that "avoiding climate change" costs fifty times what the avoided climate change would cost. He takes the position that he accepts IPCC numbers, and has come up with this "game changing" analysis.

Here it is:

You can also see it on his website


In a sense, this is good news. If the deniers drop their pseudo-science and retreat to economics, at least science can be left to go about its business; all the post-normal science will end up centered around economics, which to my way of thinking, they well deserve.

But that doesn't mean that Topher's argument should be left unchallenged. 

In fact, the usual sources of rebuttals of denialism come up empty here. So somebody needs to step up to the plate and go through it. 

It turns out that, despite its superficial credibility, it is about the worst thing that has ever been produced on the climate issue. There are several tricks along the way.  In the end, we will see that he is not just wrong, he is demonstrably wrong by a factor of over a thousand.

Please watch the whole thing and then come back here for the analysis, leaving it cued up for reference.


Topher wants to convince us that avoiding climate change is fifty times as expensive as enduring it.

Clearly, in extremis this is nonsense. Suppose climate change became so severe as to lead to human extinction. (This is not likely in practice, but if we did nothing to suppress human alteration of the climate as Topher suggests, it's not totally off the table.) 

According to Topher's style of argument we should do nothing to avoid the end of humanity and the end of multicellular life, because doing something about it would be fifty times worse.

This reductio ad absurdum applies to the argument at a smaller scale. You simply can't just take a small sample of this system and extrapolate it to the system as a whole. 

But supposing you could. Topher is still woefully wrong.


Topher works backwards from the common wisdom in the Australian right that the soon-to-be abandoned carbon tax there was pointless. That argument is based on three stipulated facts:
  1. The tax would cause Australian net emissions over a decade to be reduced by 5 %.
  2. The tax would amount to $160B over ten years
  3. The impact on global temperature would be immeasurable at the end of the ten years
(An Australian dollar is close enough to a US dollar or a Canadian dollar nowadays that for the present purposes of rough approximation we can consider them interchangeable. We will be dealing with much bigger inaccuracies than that! For clarity, from here on, by dollars, we mean Australian dollars.)

Topher then tells a compelling tale of how wasteful this is. What did the $160B gain us? Nothing measurable! What a failure!

This argument seems solid, but is based on a couple of common misapprehensions.

First of all, there is confusion about the cost of the tax. Second, there is confusion about the way the benefits accrue. Third, there is confusion about the costs of inaction. These errors multiply together.


To decide if a tax is worth doing, you have to evaluate the cost of the tax and compare it to its intended benefit. But the cost of the tax is not the total moneys collected! 

In fact, a revenue neutral tax arguably has no aggregate cost at all. Australia did not structure its revenues that way, but indeed much of the collected money was returned as a very large increase in the amount of federal tax-exempt income. From the first $6000 of income being tax-free the sheltered amount went to $18200.

In any case the increase in public funds that is not rebated is presumably is 100% wasted. So the total funds collected is not actually the cost. 

" The plan sets out to achieve to these targets by encouraging Australia's largest emitters to increase energy efficiency and invest in sustainable energy. The scheme is administered by the Clean Energy Regulator. Compensation to industry and households is being funded by the revenue derived from the charge."
All else equal, taxes are suboptimal in allocating resources in a perfect market, yes, but it is simply nonsense to presume that taxes have the same net effect as burning money. A tax is not the same as the government taking your money and burning it! If it were, the most successful societies would have no taxes at all!

Let us suppose that some of the money is rebated, some replaces other taxes, some is used to support useful energy-related infrastructure, and fully a quarter of it is utterly wasted. So we very generously ask Topher to give us back no more than a factor of four:

If the Australian government does better than that, well, the cost becomes that much smaller, and that much more of the 50:1 evaporates.

So we're not at 50 to 1. We're at 12.5 to 1 already.


On the other side of the ledger, the benefit which Topher is eager to minimize, we have a more complicated calculation.

Let's follow his lead and divide this into the amount of carbon to be reduced per dollar, and the temperature decrease per unit of carbon avoided.

Topher asserts that under the tax, Australian cumulative emissions would be reduced by 5% over ten years. 

Thus, every dollar expended on the tax is presumed to reduce a specific amount of carbon. But that's not the point of the tax at all.

The main error on the impact side of the ledger is the casual presumption that if a $20 tax per ton on carbon reduces emissions by 5%, that it would require twenty times that much to cause the 100% reduction, i.e. a $400 tax. 

Back to Wikipedia:
"The pricing is part of a broad energy reform package called the Clean Energy Plan, which aims to reduce greenhouse gas emissions in Australia by 5% below 2000 levels by 2020 and 80% below 2000 levels by 2050."
It is in fact the case that the 80% reduction in emissions in advanced countries is about the most we can get away with shy of driving the climate well past the 2 C "dangerous" target. So, Australia has been joining a few European countries in trying to play fair, even in the absence of a treaty.

But the purpose of the price increase is not to punish the carbon user. Rather it is to make non-carbon-emitting energy competitive and thus reduce the amount of carbon you use. This could well be in the vicinity of a sustained $20/ton to eliminate most emissions, but some propose as high as $160. 

Let's be generous to Topher. We'll use $160. Note that $160 is still less than $400 by a factor of 2.5 .

So let's ask Topher, generously, only to give back a factor of 2.5 here:

So it's not 12.5 to 1, but 5 to 1.


The whole point of this is to actually reduce the emissions! 

And we have a four-fold cut in total emissions by definition!  

The total cost is not proportional just to the tax rate, but also to the amount of carbon we are emitting. And the reason we raised the cost was to reduce the emissions.

Let's limit our goal to an 80% reduction, because if we get to 100% reduction, the net amount spent on the tax becomes zero! 

The ratio of 20% to 95% is 4/19; we'll only be paying the $160 tax 4/19 as often as today. That's the whole point. 

So, we're down to 20/19 to 1 or 1.05 to 1.

Now, even though we have been extremely generous with Topher's errors, we are already close to breaking even. But wait! There's more!

ASIDE - The 3.4 quadrillion dollar cheat

Before we actually move the calculation to the other side of the ledger, let's focus on the scale-up at 2:48 in the video. 

Topher is taking the benefit of the Australian tax as being not its reduction of emissions, but as the cumulative amount of emissions over an arbitrary period of a decade, which is not long enough for them to add up to much. Then he is scaling that up to reduce warming by a degree, over ten years, and getting a ridiculous number.

But the scenario is completely ridiculous. The background warming rate is a sixth of a degree C per decade; he is proposing the value of a carbon tax that would remove six times more carbon from the air than we produce, over the next decade! 

Now, whatever the prospects for carbon sequestration, we are not going to do it over a decade.

(You could suggest credits for sequestered carbon, but then, if a tax is counted as pure cost to the economy, shouldn't a sequestration rebate be a pure benefit?)

No, the scenario is silly and meaningless. He is scoffing at a fantasy of his own concoction. The column of coins going to Neptune and back is definitely silly. 


But wait, there's more. I promised you more, and we've already passed it? Remember the little bit of math at the one minute mark? Well, as promised it follows IPCC convention. But then at 1:42 we multiply by the "ten-year climate sensitivity parameter". But that's a switch! Are we interested in how much climate changes as a result of our actions? Or only in how much it changes instantaneously?

While some criticize climate economics for not discounting the future enough to match economic practice, this is the opposite. The factor of 0.33 is being used to convert from watts to temperature. But the usual factor converting watts per square meter to degrees C is close to 1, taking 3.7 W of top-of-atmosphere forcing to 1.5 to 4.5 degrees C.

So at the very least the right multiplier is 0.4, not 0.33, but on the consensus best estimate sensitivity (which he is using) it should in fact be 0.67.

That is, if we don't care what our behavior over a decade does at the end of a decade, but rather, what our behavior does in the long run, we get another factor of just over two.

So now the calculation is 2 to one in favor of mitigation!

But the biggest error of all is yet to come! And yet he makes it twice!


At 4:40, he uses his multiply flawed calculation to get 80% of annual GDP to remove the 0.17 degree warming over the decade. Then he makes this equivalent to an 80% cut in GDP! But it is spread over ten years by his own construction! So it should only amount to 8% of present-day GDP. 

But since he makes the mistake twice, going in his own favor both times, it would be repeating his mistake in reverse to double count it.  This is just meant to point out that all the rhetoric about an 80% cut is bogus. It's an 8% cut, with all his exagerrations.

However, tempted though I am to throw in an extra factor of ten, I won't. Because it ties in with the last factor of twenty-five (see below) that would be double counting. Suffice it to say that Topher happily conflates annual costs and total costs to his convenience throughout the whole presentation.


Without the exagerrations counted to this point, he is off by a factor of almost exactly 100. So the actual impact we are talking about is 0.08 %. (*)


At 6:01, he refers to the Stern report's conclusion that climate change would cost between 0 and 3% of GDP by the end of the century. In order not to compare to zero, Topher kindly splits the difference and takes 1.5 %.

But this seems pulled out of his rear; if it makes any sense at all this is about the wrong side of the ledger
· Unabated climate change could cost the world at least 5% of GDP each year; if more dramatic predictions come to pass, the cost could be more than 20% of GDP.
· The cost of reducing emissions could be limited to around 1% of global GDP; people could be charged more for carbon-intensive goods.
Splitting the difference between 5% and 20% we get 12.5 %, rather than 1.5 % So we immediately get a factor of 8.3 in our favor. Let's be kind and round it down to 8.

(By the way, Stern now thinks his number is an underestimate.)

So now we are to 16 to 1 in favor of mitigation.


Topher misses the point. Stern delivers not a one-time cost as a percentage GDP. It is a perpetual loss of GDP.

So given that this is over a century, we could arguably be multiplying this by something like 100. But the impacts are loaded toward the end of the century, so let's say it ramps up linearly after 2050. 

This gives us another factor of 25 going the other way!

The result is 400 to 1 in favor of mitigation!


Comparing costs over a century is a complicated problem, and much of the criticism of Stern revolves around it.  This is a favorite critique by right-wing economists, who think the discount rate is set by banks. That would slant the result against mitigation. It's also a point that I complain about, though in my estimation it goes the other way. What if growth stops or reverses? What's the discount rate then?

Fortunately, Topher's simplistic argument is based on a very simpleminded idea of what a dollar is anyway, so it ignores this issue altogether. So we don't have to take it up here.


On Topher's own terms, just fixing his numbers up, and being generous to him at every turn, he has gone from 50 to 1 in his favor to 400 to 1 against him, an error factor of 20,000.

He achieves this by combining six errors: 4 * 2.5 * 4 * 2 * 8 * 25

But what's a factor of 20 thousand among friends, eh? Hey, Topher, lend me a fiver, would you?


Not really, just following Topher's flawed argument and fixing the numbers up.

Stern comes up with 1 % of GDP, so we seem to have lost a factor of twelve. I think that is because the cost of a tax is not really related to the amount of money spent on the tax at all, but itself must be processed through the economy.

But still, the risk/benefit is nothing like 50 to one against.

If we trust Stern for a number, why not trust him for both numbers? Stern 2006 comes out at

12.5 to 1 in favor of mitigation.

As such, Topher's result is only off by a factor of 625. It's his flawed calculation that is off by a factor of 20,000. The difference is because his calculation is based on bad reasoning in the first place.


The point of the denial movement is not that it's going to unnecessarily cost us all 1% and so they need to protect us from that. Clearly, we can put up 1% to avoid an existential threat.

You can see it in how systematically they exaggerate the costs of mitigation. (The 80% nonsense that Topher spins.)

Much more than 1% of the net worth of the incumbent fossil fuel industry is going to be transferred to a playing field where they have less of an advantage.

The denial movement is not, despite its pretensions or delusions, defending anything but a narrow private interest. And even that interest is deluded. The Koch brothers' kids themselves will have to live on whatever world their parents built for them. They may be better off having only a couple of billion dollars (instead of tens of billions) on a healthy world that doesn't blame them for its troubles.

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