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 Reviewshould have done so.

Now Partha Dasgupta writes:

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.