Haig-Simons Income vs. GDP

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.)