Nordhaus, Tol, and Climate-Change Economics: Turning Around the Conventional Wisdom
By Robert Murphy -- July 11, 2012“The scientific modeling of climate change, and its possible impacts on human welfare, are very technical…. When experts try to summarize the fields for the layperson, they sometimes present matters in misleading ways, however inadvertent. William Nordhaus’s treatment of the economics literature, and RealClimate’s discussion of the accuracy of climate models’ temperature predictions, are good examples.”
At the Institute for Energy Research (IER) blog, I rebutted Yale economist William Nordhaus’s New York Review of Books criticism of a Wall Street Journal editorial by 16 “global warming skeptic” scientists, including MIT’s Richard Lindzen.
To understand the full point-counterpoint, the interested reader should consult the above links chronologically. Elsewhere I have challenged the entire case for a carbon tax. However, in the present post I want to focus on just two issues in the overall debate, that were raised in the wake of my initial IER post:
(1) the timing and amount of net damages from climate change, according to the best economic models, and
(2) what the climate scientists mean when they talk of a “confidence interval” in temperature projections.
The casual reader in these areas may be very surprised at what I have to report.
Richard Tol: Climate-Change Damages
There were several things that Nordhaus had written in his piece that bothered me. One, in particular, was misleading and a disservice to the debates. When talking about the economic approach to classifying greenhouse gas emissions, Nordhaus wrote (bold added):
In economics, a pollutant is a form of negative externality—that is, a byproduct of economic activity that causes damages to innocent bystanders. The question here is whether emissions of CO2 and other greenhouse gases will cause net damages, now and in the future. This question has been studied extensively. The most recent thorough survey by the leading scholar in this field, Richard Tol, finds a wide range of damages, particularly if warming is greater than 2 degrees Centigrade. Major areas of concern are sea-level rise, more intense hurricanes, losses of species and ecosystems, acidification of the oceans, as well as threats to the natural and cultural heritage of the planet.
I hope the reader will agree with me that Nordhaus is certainly inviting the reader to infer that now and in the future, the best available studies (as summarized by leading scholar Richard Tol) show that emissions of GHG will cause net damages.
The above quotation is not taken out of context; this is all the information Nordhaus provides on the topic. The only ambiguity the reader can imagine concerns just how much damage GHG emissions will cause, now and in the future.
Yet if we consult Tol’s paper—the very one cited by Nordhaus in support of the above quotation—we find that most economic studies find global warming will confer net benefits on humanity at least through the years 2050 – 2060. Only after we get at least another 2 degrees Celsius of warming (and that is compared to a recent baseline, not a preindustrial benchmark), do most studies in this literature say that the damages to certain parts of the world begin to overwhelm the benefits to other parts of the world.
As I mentioned in my IER post, I hope the average reader will agree with me that Nordhaus’s summary of Tol’s findings was extremely misleading (perhaps unintentionally). I daresay the average person, relying on mainstream media treatment of the issue, has been led to believe that “the consensus” of experts believes climate change is right now causing incredible damage and will only get worse as time passes.
And yet, the very person Nordhaus singled out as the leading scholar in the field, shows that the majority of the best available studies show global warming leading to net benefits at least for another four decades.
Tol Clarification—Global Warming’s “Sunk Benefits”
Now when I made the above point in my IER post, I got some pushback from various critics, saying I was misrepresenting Tol’s work. Indeed, Richard Tol himself made the following clarification in the comments of my post:
It’s easy to misinterpret Figure 1 from [my paper] Tol (2009).
Initial warming is indeed likely to be beneficial: CO2 fertilization of crops, reduced spending on heating homes, and fewer cold-related deaths are the main factors.
However, totals do not matter. The incremental impact turns negative around 1.2K. If we were able to control climate, we would warm the planet by 1.2K and stop there. However, the momentum of the climate system and the energy system is such that, if you accept the mainstream view of the workings of the climate, we cannot avoid 1.2K warming, or 2.0K warming for that matter.
The initial benefit is thus a sunk benefit: We will enjoy it regardless of what we do.
This is a very interesting and subtle point. I rush to mention that I made this very point myself in my original IER post footnote:
I note that just because global warming might arguably confer net benefits on the world for the next sixty years, doesn’t by itself mean that no mitigation efforts should be undertaken beforehand. If the standard climate models are correct, then the trajectory of global temperatures will only respond sluggishly, even with drastic changes in emissions down the road.
Thus, Tol’s clarification in the comments is perfectly consistent with my take in the original post. I wasn’t trying to draw conclusions about climate policy from that one graph from Tol’s 2009 paper. Rather, I was showing that Nordhaus had misleadingly summarized what the literature says on the impacts of global warming.
Now I am not here trying to be coy. We all recognize that the political battles over climate change can become downright nasty, and it is understandable that Tol was concerned his work might be used by “deniers” to say that no government intervention is needed. In that light, I probably should have amplified the caveat (which I had only put in a footnote) to make sure Tol’s own position were clearly stated.
A Very Crucial Point
With this straight, let me emphasize why I think this is so critical: The general public has no idea that the “consensus” (if we wish to use such terminology) of economic studies shows net benefits from anthropogenic climate change for decades.
If the general public did know that, it is undeniable that public opposition to a massive new carbon tax or cap-and-trade scheme would be that much greater.
Restated: It is one thing to tell the average citizen, “We are currently doing damage to everyone on Earth, particularly people who live in tropical and coastal regions. Emitting CO2 is exactly analogous to dumping poisonous chemicals into a river and polluting drinking water downstream, which is why the government ought to penalize the activity.”
It is a far different thing to tell people, “Unrestricted GHG emissions are currently hurting some people, but benefiting others. In fact, considering humanity as a whole, the gains to the winners from a warmer planet outweigh the losses to the losers. We estimate this situation will continue for the next 50 years or so, if governments do nothing and let businesses and individuals emit GHG as they please. However, according to our best computer simulations, about the year 2060 our grandchildren—who will be far richer than we are now—will, on net, be made poorer, and will wish we had restricted our own economic growth in order to keep the planet cooler for them.”
We have very little idea what the relevant tradeoffs and technologies will be 50 years from now, and it’s also not nearly as obvious how to properly evaluate the “social utility” of our grandchildren against our own. The case for climate activism does indeed become much more dubious when people learn the true state of the economics literature.
Yes, it is true that many of the scholars working in this field still think there is a case for (initially modest) government mitigation efforts such as a global carbon tax, but the confidence we should have in their recommendations is much lower once the time element is highlighted.
To repeat my main point, and to underscore why I was so upset with his original article: The innocent reader of William Nordhaus’s treatment in the New York Review of Books would have absolutely no idea that the second description above, is the more accurate picture of what the economics literature has to say about the impacts on human welfare from anthropogenic climate change.
Climate Trends: Models vs. Reality
Now we have seen just how important the accuracy of the computer simulations are. After all, Nordhaus is asking us to go along with a massive new tax to eliminate a “negative externality” that won’t manifest itself for at least half a century.
In assessing the predictive power of the standard suite of models, in my IER post I linked to climate scientist Chip Knappenberger’s MasterResource discussion of the following chart from Santer et. al’s 2011 survey article:
Fig. 2. A comparison between modeled and observed trends in the average temperature of the lower atmosphere, for periods ranging from 10 to 32 years (during the period 1979 through 2010). The yellow is the 5-95 percentile range of individual model projections, the green is the model average, the red and blue are the average of the observations, as compiled by Remote Sensing Systems and University of Alabama in Huntsville respectively (adapted from Santer et al., 2011).
Looking at the above chart, Knappenberger concluded that the standard suite of climate models was “on the verge of failing.” (Note that Santer et al. did not come to this conclusion in their paper.)
Knappenberger’s reasoning was straightforward enough: In the chart above, the green line is the average model prediction of global temperatures. The red and blue lines are actual observations (from three different sources) of the global temperature trend from 1989 through 2010, and they have been consistently below the model’s projected trend. In fact, unless observed temperatures begin rising fairly quickly in the next few years, the observed trend will breach the lower boundary of the yellow envelope. If the suite of models were accurately capturing the true climate system, we would only expect natural variability to generate such a breach (on the low side) 5% of the time.
A Different View: Are the Climate Models Doing Just Fine?
Regarding the above, a critic pointed me to this February 2012 RealClimate blog post, which produces a graph and analysis that seems to give an entirely different accounting of the success of the climate models:
Indeed, this graph appears to give a much different picture from the Santer et al. graphic that Knappenberger discussed. The climate models look to be right on the money, predicting a bit too much warming in recent years but well within the uncertainty bounds.
Counterintuitive Confidence Intervals With Climate Models
The resolution of this conundrum relies on two things. First, the confidence interval is tighter in the first graphic from Santer et al. In other words, the yellow envelope in the first chart shows the range in which the actual observations need to remain, if we only want to have a “false negative” 10 percent of the time, whereas the second chart’s gray region is more generous and will only allow researchers to incorrectly reject a correct model 5 percent of the time.
The second crucial difference is that the Santer et al. graph (with the yellow band) looks at temperature trends, whereas the RealClimate graph (with the gray band) looks at single-year observations. Yes, it is true that “natural variability” and other noise can keep the suite of climate models from being “falsified” in any given year. Yet if we look at a 30-year trend, the noise should largely cancel out, with the underlying predicted trend being quite dominant. On this score, the climate models have indeed overpredicted warming, such that they are on the verge of being falsified.
While contemplating “confidence intervals” in the context of climate models, something just didn’t sit right in my mind. In my personal discussions with Chip Knappenberger, it was hard to convey why this procedure seemed so counterintuitive to me. Let me elaborate on the point, because this may be an area where economists and climate modelers come with different preconceptions.
In a standard economic regression analysis, we typically approach things the way one is taught in high school when learning basic statistics. Namely, you set up a null hypothesis that is the opposite of the causal relationship you (the researcher) actually think exists. Then, if there is an apparent relationship in the data (such that you get a positive value on the coefficient for a certain term in a least-squares regression, say) you can see if the result holds up at a 90 percent, 95 percent, or 99 percent confidence interval.
In this normal context, the higher the confidence interval, it means the more confident you are that the apparent relationship between two measured variables isn’t spurious. You are in effect saying, “If there really weren’t any relationship between variable X and variable Y, then I wouldn’t be getting this type of result 99 percent of the time. Therefore, I reject the null hypothesis—which says there is no relationship—and think that there really is a relationship.”
Yet in charts of climate model projections, the “confidence interval” works the other way around. Here, the higher the number, the less confident we can be that an apparent match between the model and nature is due to the underlying accuracy of the model. To put it in other words, here the null hypothesis is that “this suite of climate models is accurately simulating global temperature.” Thus if we make it harder to reject the null (by ramping up the confidence level), then it gives more wiggle room for the models.
Specifically, the “95% range” in the second graph above comes from looking at all of the observed “runs” of the suite of climate models, and then plotting the gray boundary that captures the realizations of 95% of the runs centered around the average. Ironically then, the less agreement there is between the individual climate models, then the wider the gray zone would be, and the harder it would be for Nature to “falsify” the suite of climate models.
Now to be fair, there are rational vetting procedures that the IPCC uses, to determine which climate models are included in the set, the various runs of which are used when constructing these graphics. But to make sure the reader understands the crucial point I am making: Suppose for the sake of argument that one particular model accounted for 3% of the total simulated runs, and it predicted global temperature anomalies of 20 degrees Celsius from the year 2010 forward, while another particular model accounted for a different 3% of the total simulated runs, and it predicted global temperatures of minus 20 degrees C from 2010 forward.
In this (absurd) situation, the RealClimate post would show a massive gray zone covering the “95% confidence interval,” and (barring an asteroid collision or a massive change in the sun), it would be inconceivable that temperature observations would fall outside of this range. Yet that would hardly shower confidence on the suite of models.
To repeat, I am not claiming that there are models included in the IPCC suite, which are palpably absurd and generate the high/low ranges yielding the gray confidence interval. I am simply trying to ensure that outsiders understand exactly what climate researchers mean when they talk about a “95% confidence interval.”
Their interpretation is almost the exact opposite of the statistical tests performed in other disciplines, such as economics. This difference isn’t because the climate researchers are charlatans; it flows from the nature of their task. Even so, it’s crucial for everyone to be aware of this difference.
Conclusion
The scientific modeling of climate change, and its possible impacts on human welfare, are very technical areas requiring years of study to master. When experts try to summarize the fields for the layperson, they sometimes present matters in misleading ways, however inadvertent. William Nordhaus’s treatment of the economics literature, and RealClimate’s discussion of the accuracy of climate models’ temperature predictions, are good examples.
Thanks, Robert, for the clarification.
To amplify your point about future technologies: People have worried about the impact of climate change on malaria for two decades. There is indeed reason to believe that malaria would be more prevalent and more intense in a warmer and wetter world. At the moment, though, malaria incidence is falling rapidly because of a heavy investment in primary health care. That does not mean we need not worry. Malaria numbers fell in the 1960s too, but then the powers that be lost interest. This time, though, there is a promise of a malaria vaccine.
[…] Green News Source- Click to read full article […]
One further instance of “reductio ad absurdum”, mentioned but not pursued above.
A carbon tax, in any form, does not directly reduce carbon emissions, it merely negatively incentifies the emitters. Carbon emissions are reduced by replacing carbon emitting facilities and equipment with facilities and equipment which do not emit carbon, or emit substantially less carbon; or, by capturing some or all of the carbon emitted by facilities and equipment. Carbon emissions can also be reduced marginally by conservation (doing less with less) and efficiency (doing the same with less).
Replacing facilities and equipment with low/no emissions facilities and equipment requires significant capital investments. A carbon tax, in any form, merely adds cost on top of the investment requirement, thus increasing the total expenditures required to reduce emissions; and, thus, the increased costs imposed on consumers of the products or services provided by the emitters.
A carbon tax, in any form, enriches government at the expense of the governed. From the perspective of government, that is a desirable outcome; from the perspective of the governed, not so much.
Richard Tol,
Keep up the good work. You’re the only person I’ve seen that has tried to estimate the economic impact of greenhouse gases in a non-biased manner. I cite your 2009 meta-article a lot, so I’m glad that you were able to publish it in a journal.
Nordhaus’s worst mistake, IMAO, is assuming that the “ideal policy” calculating from some economic theory, is the same thing as the best possible policy in the real world. This is no minor point: Nordhaus argued that the climate skeptics were wrong to point to the fact that according to his analysis, a policy of doing nothing for several decades is very close to the “ideal” carbon tax (which is quite small. Nordhaus insists that the small “improvement” is good enough reason to advocate doing something rather than nothing. This is politically very naive. In the real world, the ideal policy is not possible. Nordhaus’s argument would only make sense if the government policy was going to be determined by angels that decide what level to set a carbon tax exactly at the level it has been determined to be “optimum”, rather than at whatever level politicians feel is appropriate for their actual agendas as human beings, not angels. So the skeptics were actually being sensible in pointing out that doing nothing is better than real world (not academic fantasy game) proposals that politicians might actually consider.
If one took this into account, advocates of the “ideal policy” of “doing a little, not too much, but not nothing” would be wrong even if there were going t0 be as much damage as Nordhaus assumes.
[…] have a long post up at MasterResource, revisiting the issues that came up in my earlier response to Nordhaus. If you […]
Robert / Bob (I followed the link here from your blog),
” (..) However, according to our best computer simulations, about the year 2060 our grandchildren—who will be far richer than we are now—will, on net, be made poorer, and will wish we had restricted our own economic growth in order to keep the planet cooler for them.”
Silly question, but is it really necessary to restrict growth? Would it not be possible to substitute income taxation with carbon taxation without loss of future wealth? Would the efficiency gain of lowering income taxes not offset the temporary efficiency loss of carbon taxation or is that empirically utterly implausible?
[…] einem umfassenden Beitrag auf dem amerikanischen Energie-Blog “MasterRessource” setzt sich der amerikanische […]
Martin-“Silly question, but is it really necessary to restrict growth? Would it not be possible to substitute income taxation with carbon taxation without loss of future wealth? Would the efficiency gain of lowering income taxes not offset the temporary efficiency loss of carbon taxation or is that empirically utterly implausible?”
One cannot say that the effects of taxes on the economy may be equivalent to one another simply by design one to bring in similar revenue to the other, so one cannot make the two equal and then exchange them and have no effect on the economy. Similarly, one can’t really design the exchange of the two to be a certain “net benefit”. Both taxes have different effects on the redirection of investment from the place that the market would otherwise tend to have it go. Both then encourage malinvestment but there is no real way to compare the economic losses from one redirection of investment from the other, no way to construct a perfect policy where we have no net negative impact on the economy by trading one bad policy for another. Even if prefect economic calculation were possible-it’s not-for it to be practical would again require that politicians were angels who would carry out the fantasy “perfect policy” were by the harm of a carbon tax is exchanged for the benefits of eliminating income taxation to some extent, leaving everything perfectly balanced.
And anyway, there is something quite perverse about replacing the government’s primary revenue raising measure with what constitutes a “Sin Tax”-such taxes are designed for the purpose of limiting the action they are taxing (in this case, emitting CO2) and thus, if they worked as intended, would eliminate their own revenue.
Climates changes net benefits? You are kidding, right? The statiststical connection between extreme weather, not a benefit, and climate change is pretty well established by NOAA and other groups.
“Malaria numbers fell in the 1960s too, but then the powers that be lost interest. This time, though, there is a promise of a malaria vaccine.”
A vaccine, genetically altered mosquitoes, treatment drugs, indoor residual spraying, bed nets. There are a host of reasons why it can be predicted with virtual certainty that the number of deaths in the year 2050 or 2100 from malaria will be a small fraction of those in the year 2000, regardless of how much the world warms between 2000 and 2050 or 2100.
In fact, it is probable that malaria will be eradicated by 2050 or 2100, regardless of how much warming occurs by 2050 or 2100.
[…] […]
“Malaria numbers fell in the 1960s too, but then the powers that be lost interest. ”
Liar, nobody “lost interest.” Malaria numbers fell in the 1960s, but a gang of left-wing hysterics convinced policy-makers that DDT was a greater danger than malaria. And perhaps it was, to them.
[…] comment on Econlog, discussing an article here. I hope the reader will agree with me that Nordhaus is certainly inviting the reader to infer that […]
[…] MasterResource Share this:PrintEmailMoreStumbleUponTwitterFacebookDiggRedditLike this:LikeBe the first to like this. This entry was posted in Cap & Tax, Climate Change, Economics and tagged carbon tax, climate hysteria, climate models, co2 emissions, dioxycarbophobia, PlayStation® climatology, weather superstition. Bookmark the permalink. ← Bursting at the Seams: America’s Energy Potential […]
Malaria outbreaks occurred north of the Arctic Circle in Finland. It is not a direct function of temperature, but of malaria control, which Western nations began to implement even before the recognition of DDT as an insecticide. Around 1950, British colonial doctors discovered malaria could be controlled in the tropics by the indoor spraying of huts with DDT. In 1972-73, the EPA banned its use in the US on the false claim DDT caused cancer. The powers that be demanded it be banned world-wide. The tropical nations that did so, witnessed malaria cases soar. Tens of millions of humans have died, hundreds of millions reduced to misery, all based on false science.
[…] Robert Murphy: Nordhaus, Tol, and Climate-Change Economics: Turning Around the Conventional Wisdom […]
[…] http://www.masterresource.org/2012/07/nordhaus-tol-climate-economics-reconsidered/#more-20736 […]
[…] Murphy has a first-rate piece on global warming in which he covers some important new ground. First, here’s ground he and I (in a post on […]
The one thing I find missing from both this and Nordhaus’ discussions is the economic growth impact of climate change. For instance, if-for simplicity’s sake-we assume the predicted rate of AWG as correct, there appears consensus on the following broad statement:
“AWG will generally” benefit” the near future, but “hurt” the far future”
This creates an inter-generational negative externality whose resolution requires some wealth transfer (Coase Theorem). The specific question is: how much benefit to transfer from the near future to compensate the far future for their hurt? This appears a relatively straightforward non-renewable resource issue.
However, there is a huge catch: economic growth is cumulative, and-unlike most non-renewable resources-there is no substitute for air. Thus, any carbon tax is broad-based and will likely decrease economic growth. Just like a savings account, the longer the time frame the greater the impact of a lower interest rate on the balance. Thus, a large part of the true cost of a carbon tax targeting the near future will “paid” by the far future in terms of accumulated lost economic growth.
One could argue that, if properly designed, such a tax could encourage investment in and substitution toward new technologies. This would “spur” economic growth in a different direction. However, these arguments ignore the counter-factual. They are simply a clever re-packaging of the broken-window fallacy.
[…] For example, the “consensus” (if we want to use that term) of economic studies shows that climate change will confer net benefits on humanity for another fifty years. Is Inglis’ educational outfit going to spread that message […]
20-Thomas
“This creates an inter-generational negative externality whose resolution requires some wealth transfer (Coase Theorem). ”
I don’t agree that people who are worse off (the present generation) need to transfer wealth to people who will be better off (the future generation).
There is no obligation on the present generation to make the world perfect (as if that’s even possible) for the future generation.
Indur Goklany has a good analysis that shows how less-well-off present generations compare to more-well-off future generations, even after subtracting the costs of global warming that the future generations will incur.
http://www.cato.org/pubs/regulation/regv32n1/v32n1-5.pdf
From Figure 3 of that paper, in the A1F1 scenario (which has the greatest global warming of the IPCC scenarios), the welfare per capita of the Industrialized countries in 1990 is $14,000, and the Developing countries in 1990 is $1,000.
In the year 2100, the welfare per capita of the Industrialized countries $99,000, and the Developing countries is $62,000.
In other words, even in the A1F1 scenario which has the highest global warming, the welfare of the Developing countries in 2100 ($62,000) is higher than the welfare of the Industrialized countries in 1990 ($14,000). So even to require the Industrialized countries of 1990 to sacrifice for the Developing countries in 2100 is to have the poor sacrificing for the benefit of the rich.
Again, no generation has any legitimate claim that they should be born into a perfect world…that previous generations should solve all the future generation’s potential problems.
An additional item that isn’t even covered by Indur Goklany’s article (and there’s no reason it should have been) is that the future generation could fairly easily, with their vast wealth, remove carbon dioxide from the atmosphere to get back to the pre-industrial level of ~400 ppm…and still have a higher per-capita income than we have today.
Oops. That should have been “…the pre-industrial level of ~280 ppm…”
Hi,
Here’s an analogy about why I think the present generation is not morally responsible for eliminating global warming, so that future generations don’t have to deal with it.
Suppose I have a house that I got from my parents. And suppose I added a lot of new rooms and appliances, new carpeting, and other good things.
Suppose I give it to my chidren when I die. And suppose that right before I die, I crash the lawnmower into the air conditioning compressor outside the house, and totally destroy the compressor.
Do I have a moral obligation to spend my money to fix the compressor before I give the house to my children when I die? No, I don’t think I do…and I think most people would agree with me.
Global warming is analogous to that broken air conditioning compressor. We’re going to give our children and grandchildren a house (earth) and it will be better than the one we got from our parents (new rooms, new appliances, new carpeting)…except for that broken air conditioning compressor.
We don’t have any moral obligation to give our children and grandchildren a perfect world. Simply giving them a better world than we inherited should be enough.
[…] worthwhile discussion of climate models, confidence, […]
[…] different groups are given platforms to speak to (and sometimes for) the church. Robert Murphy has a lengthy and worthy entrance into this broader discussion, which includes this critical observation about the insights of economists on the climate […]
[…] to me that warmer (and higher atmospheric CO2 levels) isn’t in many ways better. Robert Murphy pointed to recent economic analyses that found this to be the case, at least for some additional warming. And […]
One of many things that are missing in all of this is that a large percentage of CO2 comes from Coal. And almost all the Mercury in the environment is from Coal. Women are now advised to keep their tuna consumption to one can a week at the most.
Here is a fact that no one seems to wish to discuss. ALL energy production has costs. You can get cheap energy ONLY by stealing it from your neighbors (see various african countries), or from the futre, by poisoning the environment in ways both known and unknown.
Perhaps we should look at attempting to live in ways that to not involve poisoning the air and water. Or is someone here about to argue that all that airborne Hg is not a problem? Or that all those refineries and coal plants do not poison the local air, land and water?
Doug:
First, thanks for the comment.
The modern energy era, where carbon-based energies substituted for 100% renewables, has been a boon for mankind. Benefits have been far greater than costs, and the last billion people without modern forms of energy need to complete the revolution. We need far more dense energy, not less.
Alex Epstein is making an ethical case for fossil-fuel energy against Bill McKibben et al. His posts at MasterResource are here: http://www.masterresource.org/category/epstein-alex/. Your evaluation of his arguments would be of interest.
Finally, what are the trends with pollution and resource availability? Human ingenuity has and will make energy more sustainable, not less, in market settings. Energy statism, to me, is the number one threat against energy sustainability.
I believe that
[…] so. However, this beneficial warming is already baked into the cake. As Tol describes it, these are “sunk benefits.” Thus, you wouldn’t (in this framework) subsidize carbon emissions now. The marginal emissions […]