Applied Utilitarianism and Global Climate Change

The extremely sharp Partha Dasgupta writes, apropos of the Stern Review, his Comments on it, and my take on those comments.

I had written:

Partha Dasgupta makes a mistake. This is a rare, rare, rare event.... In the "deterministic economy where the social rate of return on investment is, say, 4% a year" model that Dasgupta is using, the concept of "output" Y is Haig-Simons output--what you could consume and still leave the economy next year with the same productive capacity.... With that definition of output Y, with consumption level C, and with social rate of return on investment r, it is indeed the case that... the assumed values for r[=4%], δ[=0.1%], and η[=1] give us a 3.9% per year growth rate of consumption. If you impose the steady-state requirement that the growth rates of consumption and output be the same, you do indeed get a 97.5% savings rate--that consumption is 2.5% of Haig-Simons output:

C/Y = .025

because with r=4% per year that is the only way to get g(Y)=3.9%

But suppose that you use a different concept of output--GDP--and say that productive capacity increases not just because you save some of GDP but also because of improvements in knowledge and technology g(A), so that:

g(Y) = r(1 - C/Y) + g(A)

with worldwide g(A) equal, say, to 3% per year. Then our g(C) equation still gives us a 3.9% per year total economic growth rate, but our g(Y) equation is then:

3.9% = g(Y) = r(1 - C/Y) + g(A) = 4%(1 - C/Y) + 3%

which gives us a savings rate not of 97.5% of Haig-Simons output but rather of 22.5% of GDP, leaving 77.5% of GDP for consumption... far from absurd....

That being said, I agree with most of Dasgupta's major point: the action here is in the choice of the parameter η. I think it's appropriate to consider different ηs in the range from 1 to 5, and think the Stern Review should have done so.

Now Partha Dasgupta writes:

Partha Dasgupta:

Dear Professor DeLong,

I... fail to see in what way I made a mistake. In the classroom exercise I was considering, I assumed a constant-population/no-technological-change scenario, to get a sense of what low values of eta do in hypothetical instances. You could certainly counter that in conducting such exercises one should also consider technological change, as you do.

With a 3% per year figure for the residual, one gets much more satisfactory figures for the optimum saving ratio for the delta-eta values in the Stern Review. But my purpose, in what was a piece for non-economists, was to show how little prior intuition we all have for such important parameters as eta and delta. To suppose in a class room exercise that the rate of technological progress is zero is not a mistake, it's to field a parameter value so as to explore the implications of other parameter values.

And by the way, there is no obvious ethical reason why eta should be a constant.

I feel bad being having become involved in this debate. For the past thirty years I have tried to bring ecological concerns into contemporary economic thinking. I have believed for some time that climate change is the most all-embracing problem humanity faces today and would be happy to vote for a 1.8% of the GDP of rich countries on expenditure to confront the problem. On the other hand, I am too much of an academic economist not to force economic reasoning to bear on a document that is on the economics of climate change.

I wonder whether I could ask you for a favour. On having printed out your piece in your semi-daily journal, I find that people place their responses in it. I wonder whether you could do lift this letter and place it in your column....

I hope you and your readers will not mind if I were to elaborate on the need for classroom exercises to sharpen one's intuitive feel for such concepts as delta (the time/risk-of-extinction discount rate) and eta (the measure of inequality/risk in consumption). One can't obtain an intuitive feel from the huge computer models, because one can't track what's influencing what in any sharp way.

The exercise you conducted in your piece on my piece on the Stern Review is, like mine, a classroom exercise. To suppose that the rate of technological change is going to be 3% per year forever is also to assume something with weak support. Our experience of significant technological progress - in the sense of the g(A) in your notation - isn't much more than 250 years old. When taken in the context of a 11000 year sedentary history, that's not much to go on.

To take another, not implausible, classroom example, suppose the rate of technological change was taken to be, say, 1% a year. Keeping the values of the other parameters the same as before, the optimum saving rate jumps up to 72.5%, which is, again, a high rate of saving. My point in working with the parameter values in my piece was only to show that a figure of 1 for eta reflects scant interest in inequality among people and scant interest in avoiding risk. I had nothing else in mind.

With best wishes.

Partha Dasgupta

I agree with almost all of what Partha Dasgupta says. I agree that eta = 1 involves a judgment that risk is not very important and that inequality between the present and the (presumably richer) future is not something that carries much weight. I share his belief that delta = 0.1% per year and eta = 1 does not generate conclusions that correspond to our moral intuitions, and that eta = 3 or so creates a better match with at least my beliefs about how one should take risks to and inequality across persons into account.

I agree that finger exercises like the one he carried out--the consequences for optimal savings plans of delta =0 .1% per year, eta=1, and r = 4% per year--are very useful, and indeed indispensible if we are to control our models rather than having our models controlling us. And Dasgupta is perfectly correct that in a model with delta = 0.1% per year, eta = 1, and r = 4% per year together imply a savings rate of 97.5% of output. (Indeed, in this model eta=3 produces a savings rate of 25% of net output.) My only quarrel is that once one allows for technological progress the Haig-Simons output concept appropriate for the model economy is not output-understood-as-conventionally-measured-GDP.

But...

The problem I see lies in a perfect storm of interactions: in the assumption of a constant 4% per year rate of return on investment that requires that the underlying production function be of the knife-edge "AK" form, in Partha Dasgupta's use of "GDP" rather than "output," and in the interaction of those two with the fact that most readers are not going to be very careful or thoughtful or well-informed. All these mean that Dasgupta's true statements about the Platonic Forms becoming misleading in the eyes of those who can only see the shadows on the walls of the cave.

For example, go to the Cato Institute's website and you will find opinions attributed to Dasgupta which I think he would not approve of:

Cato-at-Liberty: Dasgupta thinks that Stern's moral admonition to treat generations the same across time is demonstrably ridiculous.... Assume, for instance, that we apply a 0.1% discount rate for future investment and assume a social rate of return on investment of 4% a year.

It is an easy calculation to show that the current generation in that model ought to save a full 97.5% of its GDP for the future! You should know that the aggregate savings ratio in the UK is currently about 15% of GDP. Should we accept the Review's implied recommendations for this country's overall savings? Of course not. A 97.5% savings rate is so patently absurd a figure that we must reject it out of hand. To accept it would be to claim that the current generation in the model economy ought literally to impoverish itself for the sake of future generations....

[A]nyone honestly concerned about equity would happily confiscate as much of the wealth from future generations that they could get their hands on...

Jerry Taylor of Cato makes his declaration that Dasgupta thinks "treat[ing] generations the same across time is demonstrably ridiculous" in spite of the fact that Dasgupta says exacty the opposite: "I have little problem with the figure of 0.1% a year the authors have chosen for the rate of pure time/risk-of-extinction discount (delta)." Why? Because Taylor believes that Dasgupta has shown that ""treat[ing] generations the same" entails cutting consumption to 2.5% of GDP not in one particular finger-exercise model but in the real world.

The problem is broader than just Dasgupta's comment. For example, Australian economist John Quiggin notices confusion out there--on the part of people who are by nowise dumb--between market discount rates and pure rates of time preference assumed in the Stern Review:

Crooked Timber: In yet another round of the controversy over discounting in the Stern Report, Megan McArdle refers to Stern's use of "a zero or very-near-zero discount rate."... Bjorn Lomborg refers to the discount rate as "extremely low" and Arnold Kling complains says that it's a below-market rate....

Stern... picks parameters that determine the discount rate... the pure rate of time preference (delta) which Stern sets equal to 0.1[% per year] and the intertemporal elasticity of substitution (eta) which Stern sets equal to 1.... Given eta = 1, the [market] discount rate is equal to the rate of growth of consumption per person plus delta.... A reasonable estimate for the growth rate is 2 per cent, so Stern would have a real discount rate of 2.1 per cent... a discount rate a little above the real [U.S. Treasury long-term] bond rate.

Arguments about discounting are unlikely to be settled.... There's a strong case for using bond rates.... There are also strong arguments against, largely depending on how you adjust for risk. But to refer to the [current long-term] US [Treasury] bond rate as "near-zero" or "extremely low" seems implausible, and to say it's below-market is a contradiction in terms....

[T]hese writers have confused the discount rate with the rate of pure time preference...

Yet they are--without understanding correctly how the benefit-cost analysis works--making strong negative statements about the Stern Review.

If we had Nicholas Stern here, I suspect that he would say that we should all look at http://www.hm-treasury.gov.uk/media/3DD/43/Technical_annex_to_postscript.pdf, and would say that it is extremely hard to set even semi-realistic parameter values for delta and eta that would would push expected discounted damages from global warming below, say, 4% of total world wealth.

Comments

[John Emerson]

I guess I'll concede that Megan McArdle, Bjorn Lomborg , and Arnold Kling are in nowise dumb, but I think that their misinterpretation of Dasgupta is systematic and predictable in a different way which has nothing to do with their relative IQs or the subtlety of Dasgupta's writing.

[MobiusKlein]

Perhaps the GDP / consumption ratio is the incorrect analysis metric.

If we can put a value on the current state of the Earth and all the improvements and degredations we cause, what would be the sensible rate of savings vs. consumption?

How do we count spending on durable endevors that can contribute to future generations? (Does a solar energy plant count as consumption, or an improvement to future generations with an added benifit of reducing CO2 emissions?)

For this model, seemingly rational inputs produce crazy outputs. So the answer is to make a better model, not tweak the inputs.

[Keith]

To put it simply, to the extent growth is exclusively a function of saving and capital formation, then you'll want to save a whole lot. But if growth is mostly a function of "stuff" that just "happens," then savings isn't nearly as important. Well, okay.

More precisely, changes in time preference, especially as time preference gets very low, REALLY tosses your optimal savings rate around the room when savings is the sole driver of growth.

[Slocum]

"I share his belief that delta = 0.1% per year and eta = 1 does not generate conclusions that correspond to our moral intuitions, and that eta = 3 or so creates a better match with at least my beliefs about how one should take risks to and inequality across persons into account."

We should judge the model's savings rate parameter based on whether or not it produces results that corresponds with our moral intuitions?

But if we tweak parameters to avoid results that conflict with our intuitions then -- what exactly does the model buy us (other than an unjustified impression that our moral intuitions have been 'objectively' demonstrated to be correct)?

[anne]

An exceptional post. Thank you so much, Brad.

[anne]

http://www.calvorn.com/gallery/photo.php?photo=7013&exhibition=7&ee_lang=eng&u=58522,0

Monk Parakeet
New York City.

Agreed, John. We are so fortunate.

[BillCross]

has there been any sort ofd sensitivity analysis of the input coefficients? In engineering these are often extremely useful in understanding models.

[RedCharlie]

I won't even begin to address the post above, but rather take the opportunity to post a response to Dasgupta's critique of Jared Diamond's "Collapse" (and to excuse my changing the subject I'll plead that a), to borrow from Dasgupta, I don't have the necessary "toolbox" to comment on the above, but at least I know that, and b) DeLong does at least link to the critique).

Shorter Dasgupta: Deforestation was the proximate cause of Easter Island's collapse, but it may also have been one of the ultimate causes of the industrial revolution in Britain, and thus helped contribute that nation's subsequent increase in wealth. "...scarcities lead individuals and societies to search for ways out, which often means discovering alternatives." So you shouldn't talk about environmental crises without discussing how technology is sometimes good too.

My Reply: As evidence of Diamond's lack of "a sympathetic understanding of economic mechanisms" Dasgupta cites Diamond's choice of Tokugawa Japan as opposed to 18th century Britain as an example of a society coping with deforestation.
But Diamond is not so much "unsympathetic" to economics and innovation as unimpressed by it. Moreover, I think he gives due credit to adaptation and innovatation in comparing the Greenland Norse to the Inuit, and in comparing the Anazazi to the surviving Hopi? culture of the American Southwest.
Diamond has a larger point that our survival so far doesn't guarantee our survival tomorrow, and we could all be nailing our planetary coffin as I write. But Dasgupta frets that Diamond offers no way of tallying up just exactly how bad things are, that he offers up only "one side of the balance sheet" and always replies "Yes, but..." to sceptics who point out the benefits received from technological advancements.
By Dasgupta's reasoning, it would be irresponsible to critisize Enron for hiding "unsustainable" debt under off-the books shady lease agreements and other financing deals with subsidiaries without also showing, at some length and in detail, how Enron also made real money thru plenty of above board and legitimate activities. And furthermore, we couldn't say that Enron was losing money unless we were an accountant and could produce a balance sheet to demonstrate that the company, as a whole, was in the red.
But does one really need to be an accountant to know or argue that Enron was a corrupt company that drove itself to bankruptcy?
Dasgupta writes, "To say that the societies that have survived have done so because they managed their habitats well, maintained profitable relationships with their neighbours and prevented their members from killing one another, isn’t really to say anything." But saying that we can't say how badly our development is unsustainable, or even if it is unsustainable (in the case of the first world) without appropriate metrics is also not really saying anything.
Of course we need a "correct way to determine whether contemporary economic development has been sustainable." Who would argue with that? And no, we won't find any of that in Diamond's book, because, ah, well, Diamond isn't writing about economics, not even environmental economics. "Collapse" no more leaves me "with the impression that there is still no intellectual toolkit with which to deliberate" envinronmental economics than reading about the chemistry of exothermic reactions and Boyle's Law makes me think there are no tools to fix the internal combustion engine in my car.
(Perhaps Dasgupta finds a failure to address economic topics to be a fatal flaw for any book.)
We ARE engaging in unsustainable activities, but obviously Diamond doesn't know what our overall environmental economic balance sheet is. This is not a failure or lack of rigor on Diamond's part but rather his main point. We really don't know what's going on, and we had better start paying some attention. Diamond shows us that the plague is real and that we are mortal and might catch it too, but Dasgupta is disappointed that he doesn't offer us a precise way of describing the etiology, pathogenisis, and progression of the affliction.
Yes, scarcity may result in innovation and adaptive technologies, not just deprivation and collapse, and yes, we need good economic theory and metrics to understand how societies cope. But that is hardly a good reason to remain complacent about bottlenecks, or much worse, rush towards them. Innovation and technology are not guaranteed to save the day. Would a pre-historic Easter Islander been better off embracing the Japanese model or the British Model of responding to deforestation?
Of course, Dasgupta is pointing to what needs to be done. We will have to be open minded, and willing to "do the math", to survive. A recent example is Lowell Wood's proposal to seed the statosphere with sulfur (ala Krakatoa) to cool the Earth and counteract global warming. (http://www.rollingstone.com/news/story/12343892/can_dr_evil_save_the_world
If we dismiss such propositions out of hand, and are not willing to contemplate possible treatments or cures because they are "unnatural", we may be left in the same situation as the Greenland Norse, who starved to death amidst streams and seas full of fish.

[RedCharlie]

I do want to make clear that I think that Diamond and Dasgupta are on the same side here. My problem with Dasgupta, to borrow from 12-step terminology, is that he critisizes Diamond for failing at step 4 (taking inventory) when Diamond is clearly working on step 1 (admiting the problem, as in convincing the sceptics that we have a problem).

Dasgupta's idea of environmental economics, however, is certainly helpful to environmental causes. It's a truism that gas is cheap in the U.S. because we don't pay the true cost of it. Dasgupta is simply advocating the next step of calculating that true cost. Which is a wonderful and necessary step to take. In Diamond's defense, however, if we fail in completing step 1, if we ignore the sceptics rather than answering them, then this may hinder our inventory taking and calculations of true costs including environmental charges.

In this light, Diamond's perhaps pessimistic lack of faith in technological solutions is in response to the over-optimism environmental sceptics place in innovation, markets, and technology as panaceas.

In other words, Diamond's position might be put as, just because a problem might be fixable doesn't mean it's not a problem, and it also doesn't guarantee that the fix might not have problems of it's own. In a world that is more and more interconnected, failures and collapses in one part have increasing repercussions around the world. It's only responsible to change our attitudes and behaviour in advance of projected scarcities instead of waiting to fall off the cliff with the assumption that we can invent a parachute on the way down. Otherwise pleas to be economically reasonable ala Dasgupta can be taken to justify, say, solving our polution problem with scrapping obsolete ships by outsourcing the task to India. Such a solution makes sense in current economic calculus, but actually worsens the actual pollution.

Dasgupta hints at it, but we have to unreservedly admit that current conventional economics is faulty before we can then turn to adapting economic analysis so that it can help solve the problem.

Finally, I have to give credit to Dasgupta to challenging the canard that developing natural resources is good for overall development. This should be obvious, but somehow most people don't understand this. A quick survey of rich nations and regions in the world shows a strong correlation between temperate but resource poor regions and wealth. Rich nations and regions that are poor in natural resources include the NE US, Japan, Korea, and Western Europe. Conversely, Nigeria, Saudi Arabia, Iran, Mexico, Libya, etc, have used their incredible oil wealth to foster their development as, well, oil exporting nations.

As pro-football players can truthfully say, "If'n it wehrunt fer footbaahl, Ah wud naht be playin' footbaahl tuhday."

[Hal Varian]

I don't have a problem with discounting the welfare of future generations, but let us leave that aside and focus on eta=1 (log utility).

This is entirely an assumption about intergenerational marginal rates of substitution. With log utility and (essentially) zero social rates of time preference, reducing the current generation's consumption by 1% and increasing any future generation's consumption by 1.01% increases social welfare, regardless of how much the future generation consumes. And in the Stern model, future generations have a lot more consumption (and utility) due to capital productivity.

Log utility (as convenient as it may be) is just not a good assumption in this context.

[Keith]

I see Varian's point. If you're assuming risk-neutrality, you are also assuming no diminishing marginal utility.

If we believe there is diminishing marginal utility, and if we believe that futre generations will be richer, as Stern assumes...and if we also believe utility in income is not inversely distributed according to actual incomes around the world, then...

The Stern report would then be biased towards future generations and biased towards richer nations.

So, take Stern with the following grains of salt:

1. The optimal amount of investment in C02 reduction is probably less than what Stern's calculations would imply.

2. The ratio of total investment in C02 reductions by economically developed nations should proably be higher than what Stern's calculations would imply.

Major point: It's difficult to favor both future generations and poorer nations in the present. This probably makes some oft-heard rhetorical combinations (caring simultaneously about poor people and future generations) mutually inconsistent.