Partha Dasgupta Makes a Mistake in His Critique of the Stern Review

Partha Dasgupta makes a mistake. This is a rare, rare, rare event. Dasgupta writes, criticizing the Stern Review:

http://www.econ.cam.ac.uk/faculty/dasgupta/Stern.pdf: To give you an example of what I mean, suppose, following the Review, we set delta equal to 0.1% per year and eta equal to 1 in a deterministic economy where the social rate of return on investment is, say, 4% a year. It is an easy calculation to show that the current generation in that model economy 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. A 97.5% saving rate is so patently absurd 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 starve itself so that future generations are able to enjoy ever increasing consumption levels...

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 as it has this year. 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 growth rate g(Y) of a zero-population-growth economy is:

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

Take the expression for the rate of growth of consumption g(C) as a function of the parameters δ and η:

g(C) = (r - δ)/η

And see that the assumed values for r, δ, and η 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.

A consumption-to-output ratio of 77.5% is far from absurd, and so Dasgupta's critique of Stern fails. His mistake is in failing to remember that in his model Haig-Simons output is very, very different indeed from standard reported GDP.

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.

(I'm also enough of a utilitarian fundamentalist to believe that the right value for δ is zero, and that Nordhaus's δ of 3% per year is unconscionable--it means that somebody born in 1960 "counts" for twice as much as somebody born in 1995, who in turn "counts" for twice as much as somebody born in 2020; somebody born in 1960 "counts" for 256 times as much as somebody born in 2160. That's not utilitarianism.)

Comments

[Bruce Wilder]

Not to unnecessarily complicate the analysis, but wouldn't it make sense in the context to model explicitly the relationship between the energy required to support productivity and the co-production of pollution with useful output, not to mention the disposal problem presented by deterioration of past productive capital (such as the iPods that we eventually throw away)?

[rekniht]

Does the Stern review also include a g(A) term? If it doesn't, wouldn't including a term like that reduce the % of GDP that should be used to prevent (or reduce) global warming by a similarly drastic amount?

[Eric Crampton]

Doesn't a zero discount rate imply a preference for a massive regressive transfer from the poor (today) to the rich (tomorrow)? If we don't have the discount rate, then we'd want people in 1960 to invest a dollar to prevent a two-dollar loss to a person in 1995, by your numbers. The 1995 person is about 2.25 times richer than the 1960 person.

Would you really argue for for a within-period efficient transfer that had this kind of distributional implication?

[rwoqiw]

nb, Eric, DeLong is talking about the *discount rate*, δ, not η, the factor which looks at declining marginal utility of consumption. I don't think utilitarian fundamentalists are committed to a particular value of η, are they?

[Eric Crampton]

Rwogiw: not committed to any particular value on diminishing marginal utility of consumption, but would prefer ones that don't lead to really odd implications when combined with really low discount rates. Note Nordhaus' discussion around page 12...

[Alex M Thomas]

This is to point out a typo in the heading.

"Partha Dasgaptu Makes a Mistake in His Critique of the Stern Review"

It is Dasgupta.

[rwoqiw]

Well, let's go there. I'm unclear what on p. 12 you see as outlining a good argument concerning combinations of delta and eta... are you thinking of p. 10? I'm concerned that that paragraph is wrong, but anyway: what do *you* take his point to be?

[Professor Sir 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.

With best wishes.

Partha Dasgupta

[Professor Sir Partha Dasgupta]

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

[Agreed: a figure of 1 for eta reflects a judgment that risk (faced by any one person) and that inequality across people are not very important. And I agree with you that it is an unsupported judgment, and probably a faulty judgment. I would be much happier with the Stern Review if it considered three scenarios: eta = 1, eta = 3, and eta = 5.]

[anne]

Brad and Partha:

A fine debate to further clarify and expand and present to students and generally. Nice.

[joshb]

2 questions

First, i guess i'm just not understanding why the parameter that Dr. Gasputa calls "eta" (the elasticity of of the marginal utility of consumption) necessarily says anything about our attitudes towards here-and-now inequality?

I gather by setting eta relatively low (as the Stern report does) you're implicitly saying that extra consumption doesn't translate particularly strongly into higher utility. This is true for Donald Trump, i guess, and definitely not true for subsistence farmers in the developing world, so, is the argument that we're weighing the former far too high in our choice of eta?

It seems to me that for the macro-level at which this exercise is conducted, however, a single value of eta just can't be very informative one way or the other, since we just don't know to whom extra consumption accrues.

As a lefty, my gut feeling is that social utility in the US in the past 30 years has gone up less than one would imagine tracking total consumption, for the simple reason that a large chunk of this extra consumption is happening at the top end, where presumably the elasticity of marginal utility wrt to consumption is pretty low. If the same increase in consumption had been concentrated on the lower end, utility would be much higher today.

So, a choice of a low value of eta in a macro-modeling exercise may mean that i *expect* future consumption growth to be disproportionately enjoyed by the rich, but, does it necessarily follow that this represents an approval of this?

If somebody could explain this i'd be grateful.

Second, and quicker, I gather that Nordhaus doesn't choose 3% as the social discount rate on purely ethical grounds, rather, he argues that this is the rate that is consistent with observable macroeconomic data. One may wish that the social discount rate wasn't that high, but, I don't really think you can read all that much into his ethical outlook from him citing this.

joshb

[Carola]

Dr. Dasgaptu...Dr.Gasputa?? come on it's Dr. DAS.GUP.TA

[joshb]

oops

sorry about the mis-spell.

it's true, it's not that hard.

joshb

[Michael Sullivan]

Dr. Dasgupta:

Doesn't it make sense in looking at what people actually save, that they would base their decisions on what they expect the rate of technological change to be over the next 20-30 years? The more growth they expect, the less they will bother to save in the hopes of maintaining steady consumption growth. It's intuitively obvious that if there is *no* technological growth, (i.e. no wealth whatsoever is created by technological improvements and efficiencies in the use of resources), then the total level of wealth creation in the economy and the rate at which the economy can expect to grow must be extremely small, much smaller than the rate we've seen over the last 250 years.

So consumption would never grow by 3.9% in the world economy with expectation of maintaining a steady state. In the past that kind of increase in consumption or capacity has never happened without a corresponding increase in technology.

So it seems that eliminating technology growth as a parameter makes for a model of purely academic interest, not one where it is at all useful to compare the actions of real people in the physcial world for a sanity check. Because real people are expecting some level of technology growth, and they are probablyl expecting to experience roughly what we've seen for the last 250 years, not what we saw for the 11,000 years before that.

You could certainly make an argument when doing long projections that the certainty of that projection over 100 years is much weaker than over the next 10-30 (as will show in most people's present value calculations leading to save v. spend decisions). But when comparing to people's actual saving rates for a model sanity check, you must use the epectations that those people would have, and that would be for 2-3% tech growth.

I'm still having some trouble wrapping my head around the consumption growth equation and deciding exactly what the discount rate and eta represent in that equation to make things work. I wonder if anyone has a pointer to a good explanation of this that's publically available. A quick bit of web searching did not turn up anything useful to me.

Michael

[Dave Parker]

I read the discount rate as an estimate of the declining impact of present-day policy changes on future (richer) populations' conditions - so it seems devoid of ethical grounds, though its proper value might be debated.

I think (?)I'm beginning to understand Brad's seemingly curious point, if he means that a 3% rate suggests we can just shunt the problem on to future generations because they'll be better able to bear the cost. But Nordhaus talks of reduction in payoffs, so I'm still pretty bemused.

Idiot's guide, please.

[Barkley Rosser]

Partha and Brad,

Does neithr of you favor the green golden rule discounting of Chichilnisky in which higher discount rates are used for shorter time horizons and lower ones for longer time horizons?

[baileyman]

On discount rates, in the context of the economy as contained in the ecology, where discounts in the economy are bounded by conventional GDP growth, so perhaps also long term discounts should be bounded by long term ecological growth. Perhaps this would be, say, the rate of accumulation of ecological surplus compared with the total stock of ecological assets. That is, growth in soils, biomass, geological hydrocarbons, beneficial atmoshperic gasses, etc. Would this rate be, just guessing, on the order of 1/4% or so?

[Hal Varian]

1) I don't buy the claim that the appropriate social discount rate is 0. Here's an argument:

Suppose that according to your favorite welfare function, it is ethically neutral to transfer $1 from Hal to Brad. Furthermore, Hal is just willing to give up $1 today in order to receive $1.10 more next year. Should your welfare function not find taking $1 from Hal today and giving Brad $1.10 next year ethically neutral?

2) Here's one way to describe the implication of zero social discount rate and log utility. Together they imply that reducing consumption by 1% today and increasing consumption by slightly more than 1% 200 years from now inceases welfare, regardless of how much more people consume in 200 years. (According to Nordhaus, the Stern model implies that per capita consumption will grow from $7,000 today to $94,000 in 2200.) Doesn't it seem strange that taking $70 from today and giving $940 to that future generation is ethically neutral?

[Yes, it seems strange. But the thing I think is wrong is log utility, rather than delta=0. eta seems to me to be considerably bigger than one

And, of course, there are the weak foundations of utilitarian-adding-up as social justice of any kind, but we won't get into those here.

Sorry we missed Carol's work at the Veterans Center. We were serving Christmas dinners yesterday, and didn't get over there until this afternoon...]

[Woodstock]

I am confused by this:

"(I'm also enough of a utilitarian fundamentalist to believe that the right value for δ is zero, and that Nordhaus's δ of 3% per year is unconscionable--it means that somebody born in 1960 "counts" for twice as much as somebody born in 1995, who in turn "counts" for twice as much as somebody born in 2020; somebody born in 1960 "counts" for 256 times as much as somebody born in 2160. That's not utilitarianism.)"

You're talking about a discount rate of zero? Or is there a difference between the "social discount rate" and the regular definition of a "discount rate?" Could someone clarify what δ represents and how it differs, if at all, from a regular discount rate? Seems to me that if you are saying the discount rate is zero, that means people don't need any incentive to give up happiness today for happiness tomorrow. Maybe that would be true if happiness today and tomorrow were equally certain, but clearly people in the real world need to be persuaded to give up happiness today.

And especially when talking about such a risky investment as preventing global warming, (where there is almost certainly a benefit, but quantifying it is difficult), it seems like the risk-adjusted discount rate should be higher than zero.

And if someone explained what this equation means, maybe it would make more sense: g(C) = (r - δ)/η

Saying that the rate of growth in consumption is a function of the rate of return on investment minus the discount rate, divided by a factor for the diminishing utility of consumption? Aren't the rate of return and discount rate the same thing in an economy at equilibrium?

[alkead]

Woodstock, it sounds to me like you are confusing the discount rate as an empirical phenomenon (what rate people actually do "discount," when we pretend that their behavior is best understood as discounting in some systematic fashion), and the discount rate as an element in decision theory. It is a dogma of rational choice theory and sister methodologies that these two things are the same, but it ain't necessarily so. Or have I misunderstood your confusion?

[Woodstock]

Have I understood the Consumption growth function correctly then?

I still don't see why discount rates and rates of return would ever be different if you believe in the concept of opportunity cost. This is far from believing that people are not perfectly rational, it states that they are perfectly stupid. This I don't believe.

I think I'm missing something more that hasn't been clarified.

[Hal Varian]

Brad, I agree with you that log utility isn't appropriate. But I think time discounting is fine, using the argument that I should treat the future utility of other people the same way I treat my own future utility --- i.e., discount it to some degree.

But I'm the first to admit that many intelligent people disagree with me.

[Pure time discounting is something we do do. Is it something we should do? I'm more inclined to reason the other way: to take as convincing the argument that when we happen to be born is not a reason to give us more or less weight in the SWF, and to draw from that the implication that I should treat my future selves on the same basis as I treat my present self (taking account, of course, of risk, declining marginal utility of income, and uncertainty).

Thus I tend to come down on the side of thinking that the fact that we do discount the utility of our future selves is a myopic mistake that we make.]

[anne]

http://www.nytimes.com/2006/12/14/business/14scene.html?ex=1323752400&en=f752c2197a4bfc0a&ei=5090&partner=rssuserland&emc=rss

December 14, 2006

Recalculating the Costs of Global Climate Change
By HAL R. VARIAN

The Stern Review on the Economics of Climate Change was released Oct. 30 and became front-page news because of its striking conclusion that we should immediately invest 1 percent of world economic activity (referred to as global gross domestic product in the report) to reduce the impact of global warming. The British report warned that failing to do so could risk future economic damages equivalent to a reduction of up to 20 percent in global G.D.P.

These figures are substantially higher than earlier estimates of the costs of global warming, and environmental economists have studied the 700-page report to try to figure out why the numbers are so large.

Recently two noted economists, William D. Nordhaus of Yale and Sir Partha Dasgupta of the University of Cambridge, have written critiques of the Stern report that try to solve this puzzle. The reports are available at http://nordhaus.econ.yale.edu/SternReviewD2.pdf and http://www.econ.cam.ac.uk/faculty/dasgupta/Stern.pdf.

The two critiques emphasize different but related aspects of the Stern Review's economic model.

Mr. Nordhaus's major concern is with the Stern Review's choice of the "social rate of time discount," the rate used to compare the well-being of future generations to the well-being of those alive today.

The choice of an appropriate social time discount rate has long been debated. Some very intelligent people have argued that giving future generations less weight than the current generation is "ethically indefensible." Other equally intelligent people have argued that weighting generations equally leads to paradoxical and even nonsensical results.

The Stern Review sides with those who believe in a low discount rate, arguing that the only ethical reason to discount future generations is that they might not be there at all — there could be some cataclysmic event like a comet hitting the earth that wipes out all life. The report assumes that the probability of extinction is 0.1 percent per year. For all intents and purposes, this implies a social rate of discount that is effectively zero, implying almost equal weight to all generations....

[Larry Karp]

The debate surrounding Stern’s choice of discounting parameters arises because of the attempt to use too few parameters to convey too much information. We would like discounting parameters that give proper concern for the distant future, and also reflect a reasonable opportunity cost for public funds. It is hard to achieve both goals with two parameters (the pure rate of time preference, delta, and the elasticity of marginal utility, eta) -- hence the debate.
One resolution to this problem is to recognize that the pure rate of time preference varies with the time horizon, i.e. to use hyperbolic discounting. We are better able to distinguish amongst people living at different points in time in the near future, compared to the distant future. (Time differences become “blurry” in the distant future.) Therefore, we discount utility in the near future at a higher rate compared to utility at a distant future.
Hyperbolic discounting can reconcile the competing demands placed on discounting. We can also use this sort of model to construct a “constant equivalent” discount rate, defined as the constant pure rate of time preference that would give the same (or a similar) decision as the hyperbolic discount rate. Some recent works shows that reasonable assumptions lead to constant equivalent discount rates similar to Stern’s.
A common objection to models of hyperbolic discounting is that they give rise to a “time inconsistency problem”: the continuation of the planned trajectory that is optimal today may not be optimal tomorrow. Another view is that the time-inconsistency of optimal plans is a central fact of life, one that we should deal with in modeling climate policy.