Let’s Be Careful With “Spreading Out” Damages
Lately at his blog, David Friedman has been doing a great job challenging the “the science is settled, we need a big carbon tax NOW” dogmatism. However, in a recent critique of an older piece by William Nordhaus (which I myself criticized at IER when it came out), Friedman makes a move that seems rather dubious. It doesn’t necessarily flip Friedman’s overall point, but I just want to point it out since I see people on both sides of the debate using this technique. So here’s Friedman talking about Nordhaus’s study of the climate change issue:
[Nordhaus] finds that the net cost of waiting fifty years instead of taking the optimal actions now is $4.1 trillion dollars. Spread out over the rest of the century, that comes to about $48 billion/year, or about .06% of current world GNP. Which position is that closer to, that there is a need to panic and take drastic action or that there is not?
I claim that Friedman’s move here is really fishy, and I am pretty sure I complained when Krugman used a similar trick to show why cap-and-trade was also really “cheap.” (I’m not going to bother looking it up.)
What Nordhaus looked at was the present discounted value of the flows of costs and benefits from various strategies regarding climate change. If governments around the world imposed the “optimal” (in a Pigovian sense) carbon tax immediately, it would reduce conventional economic growth but it would mitigate climate change damages. Humanity would be richer by $X trillion, where X>4.1. Instead, if humanity did nothing for 50 years and then implemented the optimal carbon tax worldwide, from today’s vantage point this would still be better than the status quo of no controls on emissions, but the gains would be smaller; humanity would only be richer by $(X – 4.1) trillion.
Now to say a policy decision has a cost of $4.1 trillion in today’s terms (actually back in 2012 when the piece came out, since Nordhaus at that point was updating his 2008 numbers), is a pretty big deal. As Nordhaus himself points out, that’s how much major wars can cost. If somebody tried to say the Iraq and Afghan invasions and occupations weren’t a big deal because they only reduced world GNP by 0.06% through 2100, that would be a bit weird wouldn’t it?
It’s not clear why Friedman picked the end of the century, either. If we’re not going to use a single number today for the cost, then the only non-arbitrary “spreading out” period would be the 50 years where we’re delaying. To put the point differently, why not spread the cost of “doing nothing for 50 years” out until the year 2400? Then it would be virtually zero percent of world output per year.
But there’s another problem. Friedman isn’t doing the conversion properly. He apparently came up with his number by taking $4.1 trillion and dividing by 85 years, since we’re already into 2014 and so “through the rest of the century” means another 85 years. (Note that $4.1 trillion / 85 = $48.2 billion.)
But that’s just plain wrong. You can’t ignore interest on an 85-year amortization schedule. At a 3% interest rate (which might be what Nordhaus used himself, when discounting the flows of costs and benefits from various policies–I can’t remember off the top of my head), you would have to make 85 annual payments of about $134 billion in order to knock out an initial debt of $4.1 trillion (assuming no midnight Excel mistakes on my part). That’s almost triple the number Friedman came up with; you really can’t ignore discounting if you’re going to “spread the costs out” over 85 years.
Anyway, you can either view my post here as a wonderful display of intellectual honesty, in criticizing someone who’s on “my side” of an issue. Or, you can think I’m still sulking about my debate with Friedman last Porcfest (which now has more than 21,000 views!). Either way, kids, be careful about turning lump sums into annual amounts.
UPDATE: After posting I realized I should clarify two things, especially for the casual reader:
(1) I am a HUGE CRITIC of Nordhaus’ entire approach. Indeed, I have an article at The Independent Review going methodically through Nordhaus’ DICE model and his case for a carbon tax. All I’m saying in this post is that Friedman was trying to use Nordhaus’ own calculations against him, and I think Friedman didn’t make a good move on this minor rhetorical point.
(2) If we’re going to pick discount rates for this type of thing, I think 3 percent is too low. But I wanted to be generous with Friedman (since the bigger the discount rate we use, the worse his estimate of $48 billion would look compared to the “true” number). Also, perhaps more relevant, Nordhaus himself was using a discount rate to turn the flows of costs and benefits into a PDV of $4.1 trillion. So to turn that lump sum back into annual flows, it seemed to me more reasonable to pick a discount rate like 3 percent, since a lot of the economists in this field use lower discount rates than I personally think are appropriate. But like I said in the original post, I can’t remember which discount rate Nordhaus used; for all I know he picked 5 percent in these model runs.
“It’s not clear why Friedman picked the end of the century, either. If we’re not going to use a single number today for the cost, then the only non-arbitrary “spreading out” period would be the 50 years where we’re delaying.”
Because the costs Nordhaus is talking about are costs distributed from now to the end of the century. Fifty years is how long, on one option, we wait before doing anything, but 86 years is the period over which he is summing costs. If we are asking by how much poorer it makes us, the relevant ratio isn’t between the cost and a year’s GNP, it’s between the cost and 86 years GNP. That’s what we will have to pay the cost out of.
“You can’t ignore interest on an 85-year amortization schedule. ”
The cost is $48 billion present value as of 2012 per year. I have no reason to expect the 2012 present value of world GNP in (say) 2050 to be lower than the 2012 present value of world GNP in 2013–do you?
If I put it in current value year by year I would also have to use current value of world GNP year by year. My way of describing it seems to me simpler and clearer.
I don’t think you are sulking. Just wrong.
So far as discount rates, my own inclination would be to use the real interest rate, which I believe historically runs at about two percent. But I wasn’t redoing Nordhaus’ calculations, I was pointing out their implication.
David Friedman wrote:
“Because the costs Nordhaus is talking about are costs distributed from now to the end of the century. Fifty years is how long, on one option, we wait before doing anything, but 86 years is the period over which he is summing costs. If we are asking by how much poorer it makes us, the relevant ratio isn’t between the cost and a year’s GNP, it’s between the cost and 86 years GNP. That’s what we will have to pay the cost out of.”
David, what makes you say that? If you go to Nordhaus’ manuscript, he has results of temperature change, carbon emission trajectories, etc. through the year 2200. I didn’t spend that long looking at it, and I can’t pin down him saying it explicitly, but I am pretty sure that his runs here are summing the damages through the year 2200. (I know for a fact that when the Obama Working Group used DICE as well as two other models, they summed the damages through the year 2300.)
So where are you getting the claim that Nordhaus is only summing damages through 2100? I mean, in his tables he’s reporting what the Social Cost of Carbon in the year 2100 is. It would be $0 if he stopped the damage calculations at 2100.
[UPDATE: No David, he is clearly going out further than the year 2100. Look at Table 5-1. One of the line items is a 50-year delay, and the one before it is a 250-year-delay, which he is taking as equivalent to “no controls baseline.” Obviously that only makes sense if his period of analysis is 250 years (at least).]
Also, on the discount rate to be used, Nordhaus says in footnote 10 of his New York Review piece that he used 6 percent per year. But, in context he is saying how he updated his published 2008 estimates into 2012 terms (to get the $4.1 trillion figure), so I don’t know if that means he used 6 percent in his model when taking future climate change damages and turning them into present value terms.
David Friedman wrote:
I don’t think you are sulking. Just wrong.
Eh, I disagree, on both counts.
You could be correct. Looking at the beginning of the Nordhaus manuscript you link to, which I think is the one I looked over some time back, I find:
” Although economic studies in this area are subject to large uncertainties, the best guess in this book is that the economic damages from climate change with no interventions will be on the order of 2.5 percent of world output per year by the end of the twenty-first century. ”
On the other hand, you are correct in pointing out that at various points in the manuscript he gives numbers well past 2100. Aside from what I just quoted, I can’t find any place where he specifies how long a period he is summing costs over.
If his costs are over a period longer than to the end of the century, that strengthens my argument, since it means that we should divide his $4.1 trillion by a number larger than 86.
I also find: “The estimated discount rate in the model aver-
ages 4 percent per year over the next century.”
DF wrote:
Aside from what I just quoted, I can’t find any place where he specifies how long a period he is summing costs over.
David, did you see my update above? I wrote:
[UPDATE: No David, he is clearly going out further than the year 2100. Look at Table 5-1. One of the line items is a 50-year delay, and the one before it is a 250-year-delay, which he is taking as equivalent to “no controls baseline.” Obviously that only makes sense if his period of analysis is 250 years (at least).]
If he’s comparing the costs/benefits of a 50-year delay with a 250-year delay, he is clearly going out at least 250 years with his evaluation, right?
We don’t know what the cost of doing nothing is.
The cost of the only thing to do is easy. It’s basic research.
Bob,
Is there any evidence…har har…that carbon taxes actually will “save” carbon in the long-term?
Here’s what I mean. If something costs more, maybe it just costs more. Maybe’ you’ve just raised the incline on the treadmill. Now we have to rev up the economy (our pace on the treadmill) to keep the same quality of life (not falling down and being perpetually banged up against the wall behind the treadmill).
If the government who collects the revenues from this carbon tax is less than 1, this is very easy to imagine. So, one must assume that then we will substitute other technologies that don’t burn carbon.
The problem is, they don’t exist yet. So…we might reduce our standard of living…reduce resources available to do basic research to create those technologies…AND…drumroll…burn all the carbon!
“government MULTIPLIER…less than 1” I meant to say.
Also, I should add that people need a more Hayekian view of “technology” to understand my point. Yes, coal gasification or corn ethanol may exist as a chemical engineering professor’s grant portfolio, but such technologies don’t exist as ready for mass rollout.
Coal gasification was widely used to supply gas to cities before natural gas – but this is not carbon reducing technology, so irrelevant. Corn ethanol is actually used in fuel, not just in a professor’s grant portfolio, but also not a solution to carbon reduction, so a red herring in my view. However, nuclear power is currently a reality for large scale power generation. This could be scaled up quite quickly. I don’t understand environmentalists worried about carbon dioxide rejecting nuclear. Wind, wave and tidal are actually in use, but these will never supply all our needs. Large scale solar is technologically available, but it will require infrastructure investment. Carbon capture and storage could be implemented without too much trouble, but there is no incentive to do so if simply emitting the carbon is free. It is not true to say the alternatives are not there.
Means to an end, my friend. Does that make it easier to understand?
No, sorry. Can you elucidate the end? I think they are just mistaken about the dangers of nuclear. Whilst there are clearly hazards, the evidence says the hazard is not that great.
The end is globally enforced socialism/communism. The entire ethos of environmentalism is a means.
Those who aren’t rabid socialists and really do just want to “protect mother Earth” are patsies and dupes, being used by the powers that be to help them achieve the real goal.
http://upsidedownworld.org/energyquestionthree.htm
Interesting site, rambles a bit (as do I) but lot’s of heartfelt theory. Would be interesting debate against Bob Murphy, but probably better as a short essay debate than a live debate.
Hey, there are vested interests on all sides. Some may want to use energy policy to promote global socialism, but there is no reason why the rest of us should let them. Some may want to stifle changes in energy sources to maintain their own industries, but we should not let them get away with it.
Lets put the proper arguments out there instead of following vested interest. Anyone that thinks local biomass generators, wind turbines and solar panels are going to get us out of this on their own is in cloud cuckoo land, although they all have a part to play. We will need big scale generation to maintain our society, and I reckon it is better to maintain and improve this one than start from scratch, since this one is generally pretty good.
So yeah, there are some that want to stifle nuclear because it is “big business”, but I do not think that is the general opinion. I think most people have been misled into thinking it is more dangerous than it is, just as I think many people have been misled into thinking global warming is less dangerous than it is.
Out of interest , what do you think of the Montreal Protocol?
Harold,
You didn’t catch my drift. No matter.
Take nuclear, for example. A carbon tax will not magically produce a politically acceptable nuclear plant design approval.
Here is the hypothesis: to many progressives reducing our standard of living is an equality move. It’s a feature rather than a bug. So they have no real reason to care to look into nuclear power.
The power elite will be fine with nuclear getting a bad rap (partly due to government regulations) so that the solution is top-down regulation rather than a technological workaround.
Exactly, Andrew. Don’t let the government fool you. The LAST thing they want is for some scientific genius to figure out a zero-cost way to either eliminate CO2 emissions and replace them with clean energy or to scrub CO2 from the atmosphere so emissions don’t matter.
That would totally interfere with their desires to control us.
Winston Churchill
Tel, that brought this article to mind:
The Real Churchill
http://mises.org/daily/1450
Churchill the Socialist
Churchill made a name for himself as an opponent of socialism both before and after the First World War, except during the war when he was a staunch promoter of war socialism, declaring in a speech: “Our whole nation must be organized, must be socialized if you like the word.” Of course, such rank hypocrisy was by now Churchill’s stock-in-trade, and not surprisingly, during the 1945 election, Churchill described his partners in the national unity government, the Labour Party, as totalitarians, when it was Churchill himself who had accepted the infamous Beveridge Report that laid the foundations for the post-war welfare state and Keynesian (mis)management of the economy.
As Mises wrote in 1950, “It is noteworthy to remember that British socialism was not an achievement of Mr. Attlee’s Labor Government, but of the war cabinet of Mr. Winston Churchill.”
Even if the “real” number is triple Friedman’s number, I think his point still essentially stands.
The alarmists carry on as if “doing nothing” will represent the end of civilization as we know it. Even if the true damages of waiting 50 years were say, 1% of world GDP per year, that’s still an incredibly minuscule number compared to what most “men on the street” probably believe.
Like, if you roamed down the streets and asked random people the question, “Waiting 50 years to take action on climate change would result in costs that represent X percent of global GDP” and asked people to estimate X, I’m guessing most people would answer 20% or higher.
I agree with you on this point, Matt M.
“The alarmists carry on as if “doing nothing” will represent the end of civilization as we know it. Even if the true damages of waiting 50 years were say, 1% of world GDP per year, that’s still an incredibly minuscule number compared to what most “men on the street” probably believe.”
To me, a much more important point is that the “1% of world GDP” is actually bringing back future costs to the present. The actual damages occur in the future…when people will be much better off.
For example, if people in the year 2100 have 5x the income that they do today, but global warming costs them 10% of that income, they still have an income of 5 x 0.9 = 4.5 times the present. So why in the world does *anyone* think it’s moral for the people of the present to sacrifice for the people of the distant future?***
***P.S. That’s actually a rhetorical question. I don’t think *anyone* thinks it’s moral for the people of the present to sacrifice for people of the distant future. I base this on the fact that, despite repeatedly inviting people who advocate action on global warming to provide estimates of such things as GDP/capita, life expectancy, malaria deaths, etc. for the year 2100, no one has ever done it:
http://markbahner.typepad.com/random_thoughts/2013/03/my-entry.html
Mark,
Excellent point. I felt it sort of went without saying that one obvious benefit of “doing nothing for 50 years” is the non-zero chance that within 50 years, technology will have progressed to the point where CO2 emissions would become totally irrelevant, either due to advances in energy generation that make carbon emissions unnecessary, or perhaps due to some sort of CO2 scrubbing device that can easily remove it all from the air.
I can’t think of a great analogy here, but it generally seems strange to demand people sacrifice and lower their quality of life now in order to solve a problem that might end up being no problem whatsoever in the future.
Hi Matt,
“I can’t think of a great analogy here, but it generally seems strange to demand people sacrifice and lower their quality of life now in order to solve a problem that might end up being no problem whatsoever in the future.”
Yes, there’s the possibility that it won’t be a significant problem in the future. In fact, I would go so far as to say it’s “more likely than not” as the IPCC would put it.
But let’s even assume that global warming is a HUUUUGE problem…consuming even 30 percent of the GDP in the year 2100. But if the people of 2100 are even making double what we are now (I think it’s much more likely to be 10 times more, or greater)…then with global warming they would still be be making 2 x (1-0.3) = 1.4 times what we are. And that’s just income. Their life expectancies will likely be much greater also.
To me, it’s morally acceptable to say that we should leave future generations no worse off–on the whole–than we are now. But it’s virtually inconceivable that global warming could make them worse off, on the whole, than we are now.
Consider this analolgy. Suppose one smokes. Heavily. One dies, and leaves one’s heirs a house. It’s worth less money than it would be if one didn’t smoke (because they’d probably have to repaint and replace the carpeting and curtains). But they’re still unquestionably better off for getting the house for free. There’s no moral imperative for one not to smoke just to leave one’s heirs a slightly better house.
We may owe future generations a better world than we have, but we definitely don’t owe them a perfect world.
Mark
P.S. There’s a completely separate issue, which is that I think there’s clearly a cap on the amount of damage that people in the distant future can incur, because they will be able to reduce atmospheric CO2 concentrations to the pre-industrial level of 280 ppm if they really want to:
http://markbahner.typepad.com/random_thoughts/2013/04/global_warming_is_not_irreversible-1.html
But that’s a separate issue from the morality of the less-well-off sacrificing for the better-off.
“Like, if you roamed down the streets and asked random people the question, “Waiting 50 years to take action on climate change would result in costs that represent X percent of global GDP” and asked people to estimate X, I’m guessing most people would answer 20% or higher.”
Matt, your giving the average Joe and Jane way too much credit. The most likely response would be “what’s GDP?”
No, I think YOU’RE giving them too much credit! The average American wouldn’t hesitate to make a stupid guess anyway, even if they didn’t know what the term meant. Most people believe that you look smarter offering a guess than saying “I don’t know.”
Since I was born in 1951, Global Warming will certainly kill me by 2070.
No way. Now that we have Obamacare, you’ll live forever.
That’s true, but I need to eat more brocolli too.
Does having to buy more brocolli, in order to eat it, count against the concept of a “living wage”? Because, surely, that’s not really living.
#ProgressivesBiteThemselves