What's the real cost of CO2?

The EPA relies on sloppy science in a new CO2 cost estimate

NOTE: This post was inspired by economist David Friedman, who alerted me to the issue. Also, more Covid coverage is coming soon!

The EPA has proposed a massive increase in the cost estimate of CO2

The EPA is considering dramatically increasing the estimated social harm from CO2 greenhouse gas emissions from $51/ton to $190/ton.

That would lead to stricter regulation across the board, because the higher estimate would lead cost-benefit analyses to come out in favor of all kinds of new regulations.

Some will think, “good — I want stricter regulation!” but in reality, it’s harmful to set a cost of carbon that’s either too high, or too low.

Setting a cost estimate that’s too low would lead to higher economic growth, but at the cost of too much warming.

Setting an estimate that’s too high would lead to less warming, but it would excessively deprive people of the things they want in life.

So ideally, regulators would be serious about this, and find something resembling the true cost.

Is the increase politically-motivated?

Here’s the history of the EPA’s estimate: The Obama administration set it at $51/ton.

Then the EPA under the Trump administration lowered that to $1/ton.

Now the EPA under the Biden administration has reverted to $51/ton, and is proposing raising it to $190/ton.

Those are some dramatic ups-and-downs! That’s what one would expect of politics — not of technocratic, science-based adjustments.

What happens when one really digs into the numbers?

First, what does the EPA base their proposed change on?

In a supplemental document attached to a major regulatory filing, the EPA proposes dramatically higher costs of carbon, ranging from $120/ton to $340/ton, with a midpoint of $190/ton.

The EPA’s $190/ton midpoint is right in line with a finding of $185/ton in a forthcoming Nature study by Rennert et al., which attempts to estimate the cost of CO2 all the way out to the year 2300 — nearly 300 years in the future. Most of the estimated costs come after the year 2100.

The EPA’s proposal to change their estimated cost of carbon leans heavily on the Rennert study, citing it 17 times, and it also cites a similar (but non-peer-reviewed) Brookings report by Rennert an additional 11 times.

Rennert calls the EPA’s proposal to adopt his paper’s estimate “an important milestone.”

So, does his study make good arguments?

David Friedman’s critique

Economist David Friedman, author of the classic books Machinery of Freedom and Hidden Order has done an analysis on Rennert’s study.

Friedman first summarizes where Rennert gets the $185/ton costs from warming.

$90 of is due to increased mortality from higher temperatures, $84 to reduced agricultural output, $2 to sea level rise and $9 to energy costs

Friedman then argues:

the numbers for mortality and reduced agricultural output are substantial exaggerations due to multiple unrealistic assumptions …

What are the unrealistic assumptions?

First, the paper ignores how, as the world gets richer, people can better protect themselves from extreme weather.

That’s a critical issue, Friedman writes, since global income has been growing dramatically:

The economic model in Rennert implies per capita [income] roughly tripling by 2100, increasing about eleven-fold by 2300 … Rennert ignores the effect of that increase on temperature-related mortality

Secondly, the Rennert paper also failed to consider that, according to the UN’s IPCC:

Increases in temperature due to [human-caused] climate change … are greater in winter than in summer.

I didn’t know that, but it is true. A major reason winters are warming faster than summers seems to be that when there’s some warming, there’s less snow/ice to reflect heat back up into the atmosphere — and so the reduction in snow/ice then creates an additional warming effect that doesn’t apply to summers.

Friedman notes that a more recent paper (Carleton et al. 2022) did take those factors into account, and it found a cost of $17.1/ton “for a moderate emissions scenario (RCP 4.5)” which is the closest scenario to what Rennert’s paper is about.

Friedman then further notes two other factors that Rennert fails to address: technological progress, and migration. It’s hard to pin down their effect, but intuitively, the study’s nearly three-century time period gives people a lot of time to mitigate costs by innovating and migrating closer to the poles.

Friedman’s second critique: exaggerated harm to agriculture

Having shown that the mortality cost estimated by Rennert is exaggerated, Friedman then goes on to consider the next-biggest harm the study claims to find:

Rennert bases its estimate of the effect of climate change on agriculture on Moore et al. 2017. I find two problems with its calculations.

First, Moore’s study (which is actually a meta-analysis of many small studies) fails to consider technological gains that will help agriculture to adapt. The word “technology” is never mentioned in Moore’s study.

Second, while higher temperatures can disrupt farm plans, CO2 itself is well-known to be good for plant growth, as plants “breath” CO2 for use in photosynthesis. Friedman notes that Moore appears to lowball its positive effect on agriculture:

Moore uses a figure of 11.5% increase in … yield [for most crops] with a doubling of CO2 … and footnoting the claim to Long et al. 2006. Long, however, found increases of 12%, 13%, and 14% (rice, wheat, and soybeans) from an increase to 550 ppm from the ambient concentration, which implies an increase of about 17.5% for a doubling.

So Moore’s study claimed that another study had a similar finding, but that study actually found about 50% more benefit to CO2.

Another study, Friedman notes, found a 23% increase in crop yield

Here, I wondered: “these numbers are about crop yield increase caused by a doubling of CO2 compared to pre-industrial levels. Are we really close to having doubled global CO2?” Answer:

(The Met Office is the United Kingdom’s national weather service)

So CO2 is already halfway to doubling, and it likely will double the pre-industrial levels in a few decades. On an intuitive level, that seems worrying. Then again, the doubled level will still be 10 times less than the CO2 concentration when dinosaurs lived.

Drawn by Artificial Intelligence (Midjourney v3). Prompt: “a jurassic-era forest with dense foliage”

Now, let’s turn back to crop growth aided by CO2. Friedman concludes:

Correcting the neglect of technological change and using a more realistic value for CO2 fertilization would reduce Moore’s estimate substantially, and might make the net effect of climate change on agriculture positive.¹

Friedman notes that there’s good intuitive reason to think that warming will be a net positive for agriculture, especially when considered over a timespan of multiple centuries:

Human land use is currently limited, almost entirely, by cold, not heat — the polar regions are empty, some of the hottest regions densely inhabited. Warming due to anthropogenic climate change will push temperature contours towards the poles, producing a large increase in the amount of land in the northern hemisphere warm enough for human use.

Because of these things, Friedman tells me that the cost of warming “could easily be negative — we just can't tell.”

Also, on an intuitive level, I noticed that Moore’s study claims that the former Soviet Union (that is, mostly Russia) would suffer agricultural losses as a result of warming.² That does not seem particularly plausible.

If we adjust the numbers per Friedman’s quantifiable points, we get:

Deaths: $90/ton → $17/ton

Agriculture: $84/ton → $0/ton - $84/ton (or the cost might even be negative, but we don’t have a good quantifiable handle on that.)

Sea level rise: $2/ton

Energy costs: $9/ton

New cost: $28/ton - $112/ton

Discount rate roulette

The difficulty in predicting something so far out can also be seen in how incredibly sensitive the EPA estimate is to discount rates.

The EPA offers a wide range of different new estimates, from $120 - $340, with $190 as the midpoint. I notice that wide range entirely comes down to differences in the “discount rate” used by the government (and Rennert.) $190/ton is based on a discount rate of 2% — meaning that the analysis considers a cost that takes place next year to be 2% less important than a cost that takes place this year.

Is 2% right? It’s not easy to know exactly what the discount rate should be.

Notably, in creating the older $51 estimate, the EPA used a 3% discount rate, which is no longer even in the EPA’s new considered range (1.5-2.5%.)

The exact interest rate picked makes a huge difference in global warming cost estimates, because the projected costs are so far away (often hundreds of years down the road) and because discount rates compound.

For example, if you project $1 billion in damages 100 years from now, a 3% discount rate would value that loss at $49 million in today’s dollars, whereas a 2% rate would put it at a $135 million.

So the EPA changing the the discount rate from 3% to 2% raises their estimate dramatically.

From the EPA’s three estimates ($120, $190, $340,) which differ only on discount rate, we can get a sense of what costs would be under higher interest rates.

Since everything is equal in EPA’s three estimates (time horizons, non-adjusted costs, etc) we can get a rough estimate of the impact of the discount rate from the data points they give. As we would expect, they fall neatly on a curve:

Using that exponential trend-line equation, we estimate:

So, if the EPA had stuck with their 3% interest rate, they’d be changing things from $51/ton to about $70/ton, not to $190/ton.

In other words, out of their ~$140/ton increase, $120/ton of it came merely from changing the interest rate from 3% to 2%, and just $20/ton came from actually estimating more warming damage in the future. 85% of the EPA’s proposed increase is from changing the discount rate.

Interestingly, it turns out that changing the discount rate is also how the Trump EPA justified setting the lower bound of their range at a mere $1/ton: They picked a discount rate of 7%!

That wasn’t entirely arbitrary. The 7% that Trump’s EPA used comes from a 2003 regulatory guidance stating that the discount rates used by government agencies in general should be between 3 and 7%.

So what should the discount rate be? In other words, how much more do people actually value a dollar today, over a dollar tomorrow? Inflation-adjusted treasury bond yields give us some sense, because they show how much return people need to exchange a dollar today for a future dollar:

The average across that whole dataset is 2.46%. The current level is 1.78%.

One can see why the regulatory guidance from 2003 called for a discount rate of 3-7%; that’s the range that, at that time, had prevailed over the preceding decades.

One can also see how EPA’s latest proposed adjustment can be plausibly justified; people’s implied discount rates have been falling over time (except for the last 2 years.)

But the enormous variability also should give room for caution. Perhaps sometime soon, things will be like the 1980s again, and people will be desperate to have dollars at that time, not 100 or 200 years later. But if regulators make hard-to-change rules, dollars at that time may already have already been “reallocated to the future” so to speak, via over-zealous regulation.

So perhaps the average discount rate over the whole period (roughly 2.5) is the more reasonable measure to go with.³

If we adjust Friedman’s quantifiable critiques to Rennert’s study for the 2.5% estimate, we get (120/190) * (28/ton to $112/ton) = $17.7/ton - $70.7/ton

If one were to go with $17.7/ton as a “best estimate”, that would not be far from the cost of relatively low-hanging-fruit ways of offsetting emissions, which many companies offer for $15/ton, per Scott Alexander. So it doesn’t rule out all concern for acting on climate — but it would certainly call for less heavy-handed regulation than what most bureaucrats have in mind.

Also, the cost of carbon could still be lower, since Friedman also makes technological points that aren’t easily quantifiable.

The impossibility of predicting ~300 years out

Friedman notes the absurdity of trying to count up costs nearly 300 years from now, given the pace of technological change.

He points out that jets have replaced ships, diseases have been cured, and that our smartphones are more powerful than any computer 50 years ago. One could write pages about additional major breakthroughs — agricultural advances, satellites, energy advances, and more.

Looking to the future, Friedman points to the unpredictability of artificial intelligence. As of today, humanity appears to be on the cusp of unlocking artificial intelligence, genetic engineering, and/or computer-brain interfaces.

Those all pose a real possibility of completely upending life as we know it in the next couple of decades. Should we really sacrifice our wealth today, with the far future so uncertain?

Friedman reminds readers that “Rennert sums costs over the next three centuries, with about two-thirds of the total coming after 2100.”

If world-shattering technology is around the corner, giving up wealth today for gains 100 years from now makes little sense.

We can imagine the uncertainty more directly. Let’s say one thinks there’s a 30% chance that by the year 2100, AI will have truly taken off and either made climate easily controllable, or have gone rogue and destroyed humanity. In that case, one should reduce after-2100 costs of climate change by roughly 30%, because that’s the chance that they’ll be moot.

Overall, the chance of major tech disruption means we should value money today relatively more, because there’s a chance it won’t even be relevant in the year 2100 (to say nothing of 2300, which is the year Rennert and the EPA end at.) In other words, we should use a relatively higher discount rate.

But the general public is not using a high discount rate — it’s been around 2.5% in the last few decades.

But those of us paying attention to the speed of AI advances might want to set our own discount rates higher. One could certainly argue for a high discount rate, which would move the present day cost of carbon to nearly zero.

Climate concerns not addressed here

There are some clear limitations to the above analysis. For one thing, it does not consider the distributional effects of climate change. Specifically, countries around the equator, which are already generally poorer, will get hit hardest.

Also, it only considers things that can be quantified in terms of economic output. But perhaps people value having a world that doesn’t have such major change, or necessitate mass migration and adaptation.

Finally, it does not consider the impact of warming on nature and animals (extremely hard to measure.)

Any of these reasons could justify an individual in picking a number on the higher end of the plausible ranges.

Conclusions: Carbon Costs are exaggerated

— Friedman demonstrates that the studies the EPA relies on exaggerate CO2 costs by failing to consider various factors.

— The EPA’s estimates are extremely sensitive to discount rate changes.

— Expected tech progress over the EPA’s ~300 year horizon suggests that far-away climate costs could easily become moot, and that people should live more for the moment and set relatively higher discount rates.

— There does exist an objective, true cost of CO2. With the information we have, I suspect the cost of CO2 is somewhere between $17/ton - $70/ton, and I’d lean towards the lower end.

— There’s a lot of uncertainty. The cost could even be near $0/ton, depending on one’s expectations for future tech. On the other hand, people may have their own non-economic reasons for going above the range — but the EPA’s proposed increase to $190 is based on sloppy science that is not justifiable.

For those who want to dig further into this, Friedman’s full analysis is here.

Finally, on a light note, here’s what AI draws if you ask it to imagine “global warming”:

Regarding the AI’s image on the right, it seems that the AI associates polar bears on icebergs with global warming (obviously) but it also associates cows/bison with warming (due to methane) and so it combined the two. AI has a bit to still develop, but for now it can produce pretty and amusing art

1. I (Maxim) went through the Moore paper, but unfortunately it does not describe what proportion of the net effect that each part (CO2 fertilization, warming) accounts for. So one cannot easily see how the overall number would change if the benefits of CO2 for plant growth, specifically, were updated.

2. That’s from Figure 8 here.

3. Another approach could be to look at, say, only Rennert’s damage findings for the next 40 years (under the logic that, past then, the world will be so technologically different that it’s useless to consider damages.) Only about 12% of Rennert’s damages come in the next 40 years. So we’d be looking at about $14/ton if limiting ourselves to the next 40 years, if otherwise taking Rennert’s numbers at face value, and using a 2.5% interest rate.