More on annual climate change costs from the Stern Review

It always takes me twice* with numbers. Yesterday, I puzzled as to how the time path of climated costs simulated in the Stern Review could lead to annual costs of 5% and 20%. Richard Tol politely pointed out in the comments that this is an annuity. My mistake was to discount the costs at .01 instead of .01%. This is a common mistake made by dolts and idiots.

Anyway, discounting at .01% is about the same as not discounting at all. If you add up the red line costs in Figure 6.5d of the Stern Review (see my link above, or scroll down to yesterday's post) and average these over the 200 years of the analysis, the average cost is about 5%.

I still see two problems here:

1. The high end cost scenario in Figure 6.5d leads to an average annual cost of about 5%, the low end of the annual cost range offered by the Stern Review. Where does the additional costs, "up to 20%", come from?
2. The language of the Stern Review is still incorrect. The 5% loss of GDP that might result from climate change "now and forever" doesn't happen now, and doesn't last forever, ... unless we can annuitize those costs of climate change, and we can't. We (i.e., the living) can enjoy low costs for a long period of time and then, about 2100, the living must suffer as all heck breaks loose.

The "now and forever" language must be considered an intentional distortion designed to get everyone's attention, and it has. The problem is, these now and forever costs aren't correct.

Not discounting at all can be ethically correct but not economically correct. With our savings and investment decisions we all reveal that we take the future less seriously than the present. In order to balance sometimes competing social goals, equity and efficiency, it is always a good idea for an economist to present benefits and costs discounted at different rates. The Stern Review presents one rate as far as I can tell so I'll fill in the gaps. Based upon my reconstruction of the high cost scenario in Figure 6.5d (this one includes all costs excluding the higher weighting of low-income countries), the net present value of the net benefits of mitigation (benefits - costs) is:

• 4.43% of GDP (undiscounted)
• 4.37% of GDP (discounted at .01%)
• 1.03% of GDP (discounted at 1%)
• 0.25% of GDP (discounted at 2%)

The conclusions of the Stern Review must be clarified. We have simply got to do something about climate change if we think a $1 loss of GDP in 2200 is the same as a $1 loss of GDP right now. If we discount the future, at the real rate of long term borrowing (2%), this conclusion is not so clear.

Ethically, we can say that the appropriate discount rate is zero. Economically, we can't, and that's why the interpretations of this analysis presented to the media, and then repeated by the media is so troubling. 

Update: I just left this in response to a question in the comments section of yesterday's post:

My enthusiasm for climate change mitigation is dampened as the benefits approach the costs. Both estimates are point estimates and have large error bands around them. There is a good chance that the costs will actually outweigh the benefits, due to statistical uncertainty, even when the net benefits are positive.

But yes, I think we should be doing something. I'm an advocate of a higher gas tax, carbon trading and public research into alternative fuels. But, I think we should start slow and ramp up over time as the costs of climate change become more clear.

Another update: More than twice with numbers (see Tol's comment below).

Comments

[Charles Young]

Confusing that this debate is taking place in various different parts of the site....

It is a serious muddle to think that very low discount rates for welfare - or indeed anything else - can be justified ethically but unjustified economically. Normative economics is merely a branch of ethics. John would do well to read the chapter on discounting in "Ethics out of Economics" by John Broome, or any of the numerous economists cited in Chapter 2 of the Stern report and its technical appendix. You can find the lack of justification for intertemporal discounting of welfare discussed in books on ethics (for example, "Reasons and Persons" by Derek Parfit) as well as in books on economics like the one just mentioned, or the ones cited by Stern, or Tyler Cowen on "what is the correct intergenerational discount rate" at:
www.gmu.edu/jbc/Tyler/DISCOUNT.doc
Cowen has also collaborated with Parfit in work on this area.

It is true that many economists are unaware of these issues, and do not distinguish the different rationales for discounting, some of which are valid (and recognised as such by Stern, who discounts for future increases in income). So while, as far as I know, there is no writer on ethics who would justify discounting the welfare of future generations, perhaps the majority of economists do this in practice, though only a small minority ever seek to justify it in theory. (One of the latter is Kenneth Arrow, though he argued only for a very low rate, which he rather arbitrarily put at 1%). Usually the distinction between the valid reasons for discounting and the invalid ones is of no practical importance. But in this context it is clearly vital.

[John Whitehead]

Charles,

I choose to be clear about the source of my choice of discount rate. 2% comes from the long term cost of government borrowing.

All sorts of ethical arguments can justify all sorts of discount rates. In other words, there is no "correct intergenerational discount rate." Cowen's last line is this:

...the choice of discount rate typically falls into the realm of ethics, and requires more normative presuppositions than are found in the standard body of ordinal welfare economics.

Thanks for providing that reference.

So, you are correct to say that folks can try to justify 0% discount rates economically. The problem is that it is very difficult to do without ethical arguments. Why not simply go to the ethical arguments? It is much easier and more valid.

John W.

[John Whitehead]

And let's not forget the implications of the Petry Prize:

In their paper, the authors note that the rate at which the future impacts of climate change are discounted in benefit-cost analysis has a very large influence on the present value of mitigation efforts. The study asserts that acknowledging uncertainty about future interest rates leads to a higher valuation of the future benefits of reducing greenhouse gas emissions today--regardless of the initial rate one chooses. By ignoring this uncertainty, they conclude, current approaches used in economic modeling may consistently undervalue the future benefits of current climate change mitigation efforts. However, including the effect of interest rate uncertainty in climate models almost doubles the value of mitigation efforts relative to conventional discounting at a constant rate.

In other words, my 2% discount rate might be too low.

[Charles Young]

John

No, the Petry prize folk are saying the opposite - your 2% is too high. "By ignoring this uncerainty, current approaches..consistently UNDERvalue the benefits of climate change mitigation efforts". That is to say, most economic approaches place too low a value on the types of action - carbon taxes etc. - to avoid or mitigate the effects of climate change that have been advocated by Stern.

You say go straight to ethics, but there is only one issue at stake here. Whether you classify it as ethics or economics is irrelevant. The fact is that all those economists cited by Stern - Ramsey, Pigou, Sen, Harrod, Solow - have concluded that 0% is the correct rate for discounting welfare (though they would agree that positive rates are appropriate for other kinds of discounting). No doubt a few have disagreed with them, though I've yet to see any convincing arguments to that effect by either ethicists or economists.

[Charles Young]

By the way, John, it is quite appropriate to discount INCOME by the long term cost of government borrowing, since long-term interest rates are related to long-term growth rates. Stern would go along with that, and has done it in his report. I think we both agree that $100 is worth more when incomes are low. But the rate of interest on long-term government bonds - and by the way the index-linked variety seem to yield only 1.5% at the moment - has no connection with whatever with the appropriate rate, if any, for discounting WELFARE.

[Tim Haab]

My head is spinning. Bizarro John is arguing for economic rationale for discount rates and Bizarro Tim is arguing against gas taxes on distributional grounds.

[John Whitehead]

Arg! Right! 2% is too low (that's what I was thinking when I typed the opposite).

And, I'm confused. You pointed me to Cowen's paper and now you say to ignore it?

I must admit I'm a little confused by your hard distinction between income and welfare. In economics we try to measure most everything in dollars: statistical lives, threatened and endangered species, etc. Are you saying we shouldn't discount consumer surplus (i.e., consumer welfare)?

Also, if people behave as if they discount the long distance future, and oftentimes they do, are you arguing that we should disregard that behavior and the appropriate discount should be zero. If so, we're back to my intergenerational efficiency vs intergenerational equity distinction.

John

[John Whitehead]

Tim,

I'm also arguing that we ought to disregard the shaky benefit cost analyses of climate change mitigation and do something about the potential problem anyway!

Can we rename this the environmental equity blog?

John

[Dano]

Interesting comments discussion at RP Jr's place about the discounting in the Stern report and political economy-type considerations too.

IMHO it supports some of the excellent comments here and on the other thread, and informs some others. Richard Belzer's comment about GDP losses echoes some of Dano's broken-recording about projections vs predictions and why the IPCC chose projections [and 1) how this obviates policy problems in the RP Jr discussion 2) how we still aren't doing a good job with the projections thingy].

Best,

D

P.S. for some of our spelling-challenged commenters (absent thus far here), I'm using FF 2.0 and it has a spell-check feature as you type. Just a thought.

[Charles Young]

John

First, are we in agreement that the gist of the Petry Prize paper is that most people use interest rates that are too high? (In your last post you again said that 2% was too low, but that you had previously said the opposite - in fact you said earlier that it was too low).

With regard to Cowen, there is only one issue at stake here, and in that quote he is choosing to place that issue in the realm of ethics rather than economics. Which of the two faculties it properly belongs to can be disputed, but is ultimately unimportant. Essentially he is saying that there is nothing in economics that would justify a positive rate for discounting the welfare of future generations, and thus agreeing with all the other economists I cited earlier.

With regard to the distinction between welfare and income, I'm sure you don't really need me to remind you that, if income has a diminishing marginal utility, then utility, or welfare, cannot be measured in the same dollars that we use for measuring income.

When people value their future welfare lower than their present welfare, they are taking risks with their own future welfare. They are quite entitled to do that. They may not be entitled to take risks with other individuals' future welfare.

[John Whitehead]

Damnit! Arg! Right! 2% is too high (that's what I was thinking when I typed the opposite ... twice).

Charles,

I think the realm that we place the 0% discount rate does matter because it makes the "do-something" argument sound like economics instead of ethics. If people prefer a social scientific justification instead of a humanities (?) justification then they'll be more convinced.

I think saying that a 0% discount rate is justified by economics is marketing.

To be continued ... after class.

[Richard Tol]

John:

Sorry to keep correcting you.

The Stern Review uses a UTILITY discount rate of 0.1%; and a constant rate of risk aversion of 1. That implies that the MONEY discount rate is the rate of consumption growth plus 0.001.

The 5-20% is most peculiar. The range in the report is 0.3-33%.

See http://www.fnu.zmaw.de/fileadmin/fnu-files/reports/sternreview.pdf

[Charles Young]

I look forward to the continuation. But I don't think you'll find any justification in economics for valuing my welfare more than yours, or vice versa. The most we can say is that we'd both agree that if anybody is handing out $100, they would probably create more welfare by giving it to whichever of us is poorer. (Fortunately we are both behind a veil of ignorance about which one of us that is).

Equally, you won't find any justification in economics for valuing our welfare more than our children's - though we can discount their income to the extent that they are richer than we are.

I think we are both happy to agree with Tyler Cowen that discount rates for welfare belong in the field of ethics, though he is not the only economist to have discussed the issue and reached the conclusion that no positive discount rate can be justified. You seem to be looking to economics to provide some alternative "objective" answer to the same question. I don't think you will find one.

[John Whitehead]

Richard,

Thanks for correcting me! The problem is, as you put it, "the 5-20% is most peculiar."

John

P.S. Dano pointed me to your review of the review which I've printed out and am reading tonight.

[Charles Young]

Yes, Mr Tol's letter contains some interesting points, though I for one am prepared to forgive Stern for omitting to review "Tol(forthcoming)".

However, I am sure Mr Tol will agree that he makes a mistake in asserting that Stern doublecounts catastrophic risk by including a small probability that future generations will not exist (meteorite or bird flu or whatever) - and thus using a higher discount rate. The inclusion of this probability, by raising the discount rate, reduces the future cost of climate change damage, far from doublecounting it.

[John Whitehead]

Charles,

Here is how I think about it. Suppose we know that utility functions are:

u=y (for income up to 100k
u=.5*y (for income past 100k)

We have diminishing marginal utility of income since utility equals income up to a point and then additional income adds 50% to happiness after 100k.

Income losses to the rich and poor are valued differently (with an arbitrary 100k cutoff).

Once we know the value of utility (i.e., welfare), then we can discount those dollar values. It shouldn't matter whether the income disparities are across time or space.

If it is measured in dollars (% of GDP, etc) then, I think, it is economically appropriate to discount the stream of benefits and costs over time. If the analyst doesn't want some idiot to discount the future value of utility (i.e., welfare) then the analyst shouldn't measure welfare in dollars.

John

[John Whitehead]

To all,

I'm quite correctable.

John

[Richard Tol]

To Charles Young:

My main point is that Stern puts three risk measures on top of one another.

On catastrophe discounting (that is, adjusting the discount rate for the probability that humanity will go extinct), the issue is not that the discount rate is higher and therefore future impacts weighed less.

Rather, if you compare a stream of benefits with a high discount rate to the same stream of benefits with a low discount rate -- then the low discount rate is better. Therefore, introduction of catastrophe discounting leads to lower welfare.

By the way, Stern uses an annual probability of 0.1% for the extinction of Homo Sapiens. That amounts to a 10% probability that we will not be around in 2100.

[Dano]

I'm enjoying the conversation here and at RP Jr's. But as RT says there if we can adapt to 2 degrees higher (which modern ecosystems have never seen, so this statement is problematic as economies require ecosystems to exist) - and this being env-econ.net - how come we are not discussing calculations of disasters in less resilient ecosystems or ecosystems flipping in such a highly-managed world, and the costs of adapting to that? Surely there's some env- in addition to the econ.net in this conversation somewhere?

But several scientists challenged that prediction [by The National Fisheries Institute, (saying) that most wild marine stocks remain sustainable...(and)...its members could meet the rising global demand for seafood in part by relying on farmed fish] and questioned why humanity should pay for a resource that the ocean had long provided for free. "It's like turning on the air conditioning rather than opening the window," said Stanford University marine sciences professor Stephen R. Palumbi, one of the paper's authors.

Best,

D

[John Whitehead]

Dano,

Many environmental economists are embarrassingly ignorant about the environmental part.

John

[Charles Young]

I'm happy to go with John's suggestion. I'm sure we'd both agree to make it a continuous, not a step function. It's OK to measure utility in dollars, just as long as you don't muddle it up with income. That's what I mean when I said it is not measured in the same dollars.

On the other thread, Joshua Corning helpfully pointed to Lomborg's article. Lomborg says that "Mr. Stern admonishes that poor people count for less in the economic calculus, so he then inflates 15% to 20%" as though this were somehow improper.

No concept has a more venerable history in economics than the declining marginal utility of income. Once it came to be tested against the facts, none has been better established, in the massive literature relating subjective welfare to income. (The literature also found that above about $20,000, rises in income seem to increase subjective welfare only if they exceed that of the reference group. Once needs are met, it seems to be status rather than income that matters - a finding that surprised economists, though perhaps not primatologists. If you want to put a kink in your utility/income curve, John, this is where it belongs). It would have been a massive error by Stern if he had failed to discount for rising income, whether across time or at any point in time. Of course, many other analyses have made the error of not discounting current income losses to higher incomes, and thus seriously under-estimated the welfare costs of climate change.

Lomborg also notes the wide difference between Stern's and Nordhaus' valuation of carbon, but this discussion has revealed the reason for that - Nordhaus valued the current generation's welfare more than that of future generations.

We are all disposed to believe that "I" am more important than "You", and are endowed with brains capable of finding specious arguments to this effect. Discounting welfare at 2% is roughly the same as saying that my generation is twice as important as my children's, four times more important than my grandchildren's, eight...and so on. If you build that into your assumptions, you are bound to reach the conclusion that my generation can party as it pleases, and future ones can get *****ed.

Equally, if we counterfactually equate $100 of income for a wealthy gas-guzzler to $100 of costs imposed on an African farmer, then we again build into our assumptions that "our" - speaking on behalf of gas-guzzlers - welfare is more important than "theirs".

Both these pleasing assumptions have been incorporated into most past economic analyses. We have been enthusiastic about discounting future welfare, reluctant about discounting for present income differences. Stern does what a good economist should, and discounts where it is justified economically, and not where it isn't.

Once correctly treated, it is immediately apparent that the costs of dealing with climate change are far below those of leaving it unchecked. People can chip away at the various cost estimates - and doubtless as many will wish to adjust in one direction as in the other - but the gap is wide. The evidence that a large truck is bearing down on us is so great that we would do well to step out of the road rather than stand here while we go on figuring.

Richard Tol's letter extols the adaptability and flexibility with which future generations will adapt to the changes we are likely to impose on them, but as Dano points out does not show much evidence of any flexibility about altering the present habits that necessitate this adaptation.

Footnote to Richard Tol - I think we agree that catastrophe discounting implies a higher discount rate. The costs of measures to avoid or mitigate climate change are earlier than their benefits, so catastrophe discounting will reduce the justification for such measures. Yet his letter suggests that this is one of the ways Stern overestimates the benefits of mitigation measures. Incidentally the cosmologist Martin Rees' assessment of humanity's prospects till 2100 is less optimistic than Stern's, but I've no view on who is right - I'm just clear that the greater the likelihood of catastrophe, the more we are entitled to eat, drink and be merry - provided that it is not the merry-making that provokes the catastrophe.

[Richard Tol]

To Charles Young:

Catastrophe discounting is paradoxical.

For sure, a catastrophe discount rate reduces the value of the future. However, a catastrophe discount rate is not a parameter but a variable. If a policy intervention reduces the probability of the catastrophe, there is more future and net present welfare goes up.

The Stern Review compares a future with climate change and a 0.1% annual probability of human extinction to a future without climate change and a 0% probability of extinction. The latter scenario has a lower discount rate but in the difference between the scenarios, more weight is placed on the future.

[Charles Young]

To Richard Tol

The example Stern gives to justify catastrophe accounting are (p. 47 of the report) a meteorite hit or nuclear war - in other words events quite unrelated to climate change. Nowhere does he claim that the probability of a meteorite strike will be reduced by measures to cut GHG emissions.

We can argue about the level of this probability - though, as John noted earlier, it makes precious little difference to the calculations. But nowhere that I have found does Stern ever discount with a rate that embodies a zero percent probability of extinction. I may have missed some part of this long report, and if so Richard Tol will no doubt refer me to the part of the report that he has in mind.

[Richard Tol]

To Charles Young

I went back to the Stern Review. In fact, it does not specify what it did.

The report mentions catastrophe discounting at 0.1% per year, and utility discounting at 0.1% per year. The report does not say whether
a) 0.2% is used in both scenarios;
b) 0.2% is used in one scenario and 0.1% in the other: or
c) whether 0.1% is used in both scenarios.

I talked to Chris Hope (the modeller) and he suggested that c) is the right answer.

I talked to Nick Stern and he suggested that b) is the right answer.

If a) or c) is the right answer, then Charles is right and I am wrong.

[Dano]

John,

I'm just asking the implicit question in bold - why aren't we calculating the cost of the drag on the GDP by fixing stuff we let break vs continuing to enjoy free ecosystem services?

I'd be happy to yap on about bunnies and flowers to fill in the gaps, but I'm just pointing out what's not getting discussed. :o)

Best,

D