Saturday, November 25, 2006

Present Discounted Value Calculations and the Benefits of Fighting Climate Change

The Stern Report has generated world wide headlines. A leading economist argues that climate change will be quite costly perhaps costing us 5% of world GNP each year in the future. In this interesting report on the Stern Review, Bill Nordhaus argues that many of the Stern Report's findings are driven by its implicit assumption of a 0% interest rate in calculating the present discounted value of flows of benefits and costs associated with climate change.

While I give you the Nordhaus piece, I apologize for the strange way the footnotes get embedded in the text.

This issue of discounting returns to the "old" Robert Solow question on sustainability concerning whether physical capital and human capital substitutes for natural capital. If innovation (new ideas) and physical capital (better New Orleans Levees) can protect natural capital then it is important from a sustainability perspective to think about the next best alternative (i.e opportunity cost) for resources we spend on fighting climate change today.

The Stern Review on the Economics of Climate Change1

William Nordhaus
November 17, 2006

Opposite ends of the globe

It appears that no two global warming policies on earth are farther
apart than the White House and 10 Downing Street. In 2001, President G.W.
Bush announced his opposition to binding constraints on greenhouse gas
(GHG) emissions. In his letter of opposition, he stated, “I oppose the Kyoto
Protocol because it exempts 80 percent of the world, including major
population centers such as China and India, from compliance, and would
cause serious harm to the U.S. economy.” This policy, much like the war in
Iraq, was undertaken with no discernible economic analysis.2
In stark contrast, the British government in November 2006 presented a
comprehensive new study, the Stern Review on the Economics of Climate Change
1 The author is grateful for helpful comments by Scott Barrett, William Brainard,
Partha Dasgupta, Robert Stavins, Nicholas Stern, and John Weyant.
Text of a Letter from the President to Senators Hagel, Helms, Craig, and Roberts, March
13, 2001,
(downloaded November 13, 2006). There is no record of a fact sheet or other
economic analysis accompanying the letter. The Bush Administration’s economic
analysis was contained in the 2002 Economic Report of the President and the Council of
Economic Advisers, published almost a year after President Bush’s letter to the
Senators. The Economic Report’s analysis suggests that the Kyoto Protocol is costly,
but its analysis does not show that binding action is economically unwarranted.
(hereafter the Review).3 Prime Minister Tony Blair painted a dark picture for
the globe at its unveiling, “It is not in doubt that if the science is right, the
consequences for our planet are literally disastrous…. [W]ithout radical
international measures to reduce carbon emissions within the next 10 to 15
years, there is compelling evidence to suggest we might lose the chance to
control temperature rises.”4
The summary in the Review was equally stark: “[T]he Review estimates
that if we don’t act, the overall costs and risks of climate change will be
equivalent to losing at least 5% of global GDP each year, now and forever. If a
wider range of risks and impacts is taken into account, the estimates of
damage could rise to 20% of GDP or more.… Our actions now and over the
coming decades could create risks … on a scale similar to those associated
with the great wars and the economic depression of the first half of the 20th
These results are dramatically different from earlier economic models
that use the same basic data and analytical structure. One of the major
findings in the economics of climate change has been that efficient or
“optimal” economic policies to slow climate change involve modest rates of
emissions reductions in the near term, followed by sharp reductions in the
3 All citations in this note were from the online version at http://www.hmtreasury.
sternreview_index.cfm (downloaded various dates, November 2006).
4 PM's comments at launch of Stern Review, http://www.number- (downloaded November 13, 2006).
5 Review, Summary of Conclusions.
medium and long term. We might call this the climate-policy ramp, in which
policies to slow global warming increasingly tighten or ramp up over time.6
While seemingly counterintuitive, the findings about the climate-policy
ramp have survived the tests of multiple alternative modeling strategies,
different climate goals, alternative specifications of the scientific modules, and
more than a decade of revisions in integrated assessment models. The logic of
the climate-policy ramp is straightforward. In a world where capital is
productive, the highest-return investments are primarily in tangible,
technological, and human capital, including research and development in
low-carbon-emissions technologies. As societies become richer in the coming
decades, it becomes efficient to shift investments toward policies that intensify
the pace of emissions reductions and otherwise slow GHG emissions. The
exact mix and timing of emissions reductions depends upon details of costs,
damages, and the extent to which climate change and damages are
While scientists have sounded many somber warnings about the longterm
peril of unchecked climate change,7 the Review attempts to justify strong
6 This strategy was one of the major conclusions in a review of integrated-assessment
models: “Perhaps the most surprising result is the consensus that given calibrated
interest rates and low future economic growth, modest controls are generally
optimal.” David L. Kelly and Charles D. Kolstad, Integrated Assessment Models For
Climate Change Control,” Henk Folmer and Tom Tietenberg (eds.), International
Yearbook of Environmental and Resource Economics 1999/2000: A Survey of Current Issues,
Cheltenham, UK, Edward Elgar, 1999.
For a recent warning, see James Hansen, Makiko Sato, Reto Ruedy, Ken Lo, David
W. Lea, and Martin Medina-Elizade Global temperature change, Proceedings of the
National Academy of Sciences (US), 103, 2006, pp. 14288-14293.
current action in a cost-benefit economic framework.8 Because it has
conclusions that are so different from most economic studies, the present note
examines the reasons for this major difference. Is this radical revision of
global-warming economics warranted?
Overview of the Review
I will not summarize the basic findings of the Review – a clear summary
is found on its website. Instead, I begin with five summary reactions. First, the
Review is an impressive document, buttressed by more than a dozen
background studies. There is little new science or economics here, but it
provides many new syntheses of the extensive and rapidly growing literature.
While not as balanced and ponderously reviewed as the reports of the
Intergovernmental Panel on Climate Change (IPCC), it is much more current
than the latest IPCC report, published in 2001.9 For those seriously interested
in global warming, it is worth a few days’ study.
Second, while I question some of the Review’s modeling and economic
assumptions, its results are fundamentally correct in sign if not in size. The
approach taken in the Review – selecting climate-change policies with an eye
to balancing economic needs with environmental dangers – is solidly
grounded in mainstream economic analysis. By linking climate-change
policies to both economic and environmental objectives, the Review has
8 The early precursor of this Review is the study by William R. Cline, The Economics
of Global Warming, Washington, Institute for International Economics, 1992.
9 Contribution of Working Group I to the Third Assessment Report of the
Intergovernmental Panel on Climate Change, Climate Change 2001: The Scientific Basis,
J. T. Houghton, Y. Ding, D.J. Griggs, M. Noguer, P. J. van der Linden, and D. Xiaosu,
eds., Cambridge, Cambridge University Press, 2001.
corrected one of the fundamental flaws of the Kyoto Protocol, which had no
such linkage. By contrast, the parallel analysis of the Bush Administration,
cited in footnote 2 above, provided no support for the Bush Administration’s
rejection of binding emissions constraints on GHG emissions.
Third, the Review should be viewed as a political document. Its chief
author is Sir Nicholas Stern, who has had a distinguished career in academic
and government positions. Until 1993, he was a public-finance economist in
British universities specializing in taxation and economic development; today,
he is Head of the Government Economics Service and Adviser to the
Government. The disciplinary background of a public-finance economist is the
leitmotiv running through the chapters. However, it is not an academic study.
Like most government reports, the Review was published without an appraisal
of methods and assumptions by independent outside experts. But even the
analysis of HM Government needs peer review.
The fourth comment concerns the Review’s emphasis on the need for
increasing the price of carbon emissions. The Review summarizes its
discussion here as follows, “Creating a transparent and comparable carbon
price signal around the world is an urgent challenge for international
collective action.” In plain English, the Review argues that it is critical to have a
harmonized carbon tax or similar regulatory device both to provide incentives
to individual firms and households and to stimulate research and
development in low-carbon technologies. Carbon prices must be raised to
transmit the social costs of GHG emissions to the everyday decisions of
billions of firms and people. This simple yet inconvenient economic insight is
virtually absent from most political discussions of climate change policy
(including the marathon slide show by Al Gore in An Inconvenient Truth).
But these points are not the nub of the matter. Rather, and this is the
final comment, the Review’s radical revision arises because of an extreme
assumption about discounting. Discounting is a factor in climate-change
policy – indeed in all investment decisions – which involves the relative
weight of future and present payoffs. At first blush, this area would appear a
technicality that should properly be left to abstruse treatises and graduate
courses in economics. Unfortunately, it cannot be buried in a footnote, for
discounting is the central to the radical revision. The Review proposes using a
social discount rate that is essentially zero. Combined with other assumptions,
this magnifies enormously impacts in the distant future and rationalizes deep
cuts in emissions, and indeed in all consumption, today. If we were to
substitute more conventional discount rates used in other global-warming
analyses, by governments, by consumers, or by businesses, the Review’s
dramatic results would disappear, and we would come back to the climatepolicy
ramp described above. The balance of this discussion focuses on this
central issue.
The social discount rate: concepts and assumptions
Discounting involves a concept called the pure rate of social time
preference – I will call this “the social discount rate” for short. The social
discount rate is a parameter that measures the importance of the welfare of
future generations relative to the present. It is calculated in percent per year,
like an interest rate, but refers to the discount in future “utility” or welfare,
not future goods or dollars. A zero social discount rate means that future
generations into the indefinite future are treated equally with present
generations; a positive social discount rate means that the welfares of future
generations are reduced or “discounted” compared to nearer generations.
Philosophers and economists have conducted vigorous debates about how to
apply social discount rates in areas as diverse as economic growth, climate
change, energy policy, nuclear waste, major infrastructure programs such as
levees, and reparations for slavery.10
Discussions about discount rates need to respect the distinction
between the social discount rate and the discount rate on goods. The former
refers to the relative weights on different people or generations and is the
major source of concern in this note. The latter refers to discounts on bundles
of goods and is measured as a “real interest rate.” I discuss the connection
between these two concepts below.
The sections that follow examine the philosophical arguments about
intergenerational equity, how discounting affects the measurement of
damages, the role of discounting in economic modeling of climate change,
saving behavior, and behavior under uncertainty.
10 Many of the issues involved is discounting, particularly relating to climate change,
are discussed in the different studies in Paul Portney and John Weyant, Discounting
and Intergenerational Equity, Resources for the Future, Washington, D.C., 1999. Note
that the pure rate of social time preference differs from the real interest rate or the
discount rate on goods and services, which is in principle observed in the market
place. A useful summary is contained in K. J. Arrow, W. Cline, K.G. Maler, M.
Munasinghe, R. Squitieri, and J. Stiglitz, “Intertemporal equity, discounting and
economic efficiency,” in Climate Change 1995—Economic and Social Dimensions of
Climate Change, edited by J. Bruce, H. Lee, and E. Haites, 1996, Cambridge:
Cambridge University Press, pp. 125–44.
Philosophical questions about the social discount rate
At the outset, we should recall the warning that Tjalling Koopmans
gave in his pathbreaking analysis of discounting in growth theory. He wrote,
“[T]he problem of optimal growth is too complicated, or at least too
unfamiliar, for one to feel comfortable in making an entirely a priori choice of
[a social discount rate] before one knows the implications of alternative
choices.”11 This conclusion applies with even greater force in global warming
models, which have much greater complexity than the simple, deterministic,
stationary, two-input models that Koopmans analyzed.
The Review argues that it is indefensible to make long-term decisions
with a positive social discount rate. The conclusion of the approach is the
following, “The argument … and that of many other economists and
philosophers who have examined these long-run, ethical issues, is that [a
positive social discount rate] is relevant only to account for the exogenous
possibility of extinction.” (Annex to Chapter 2, p. 52) The argument is that a
high social discount rate would lead societies to ignore large costs that occur
in the distant future. The actual social discount rate used in the Review is 0.1
percent per year, which is only vaguely justified by extinction estimates; for
our purposes, it can be treated as near-zero.
11 Tjalling C. Koopmans, “On the Concept of Optimal Economic Growth,” in
Pontificiae Academiae Scientiarum Scripta Varia 28, 1, Semaine D'Etude sur Le Role de
L'analyse Econometrique dans la Formulation de Plans de Developpement, 1965, pp. 1-75
(available for download at
Zero discounting leads to deep mathematical problems such as non-convergence of
the objective function and incompleteness of the functional. For the analytical
background, see also Frank Ramsey, “A Mathematical Theory of Saving,” Economic
Journal, 1928, 38, pp. 543–559; David Cass, “Optimum Growth in an Aggregative
Model of Capital Accumulation,” Review of Economic Studies, 1965, 32, pp. 233–240.
The logic behind the Review’s social welfare function is not as conclusive
as it claims. The Review argues that fundamental ethics require
intergenerational neutrality using an additive separable logarithmic utility
function. Quite another ethical stance would be to hold that each generation
should leave at least as much total societal capital (tangible, natural, human,
and technological) as it inherited. This would admit a wide array of social
discount rates. A third alternative would be a Rawlsian perspective that
societies should maximize the economic well-being of the poorest generation.
Under this policy, current consumption would increase sharply to reflect likely
future improvements in productivity. Yet a fourth perspective would be a
precautionary (minimax) principle in which societies maximize the minimum
consumption along the riskiest path; this might involve stockpiling vaccines,
grain, oil, and water in contemplation of possible plagues and famines.
Without choosing among these positions, it should be clear that alternative
ethical perspectives are possible. Moreover, as I suggest below, alternative
perspectives provide vastly different prescriptions about desirable climatechange
Even if a low social discount is chosen, a second issue arises in the
calibration of the social discount rate to actual macroeconomic. Behind the
Review’s modeling is the assumption that the world economy is in long-run
equilibrium of a Ramsey optimal growth model. In a Ramsey equilibrium
with stable population, there are two observables – the rate of return on
capital and the rate of growth of consumption; and there are two normative
parameters – the social discount rate and the curvature of the utility function
(more precisely, the elasticity of the marginal utility of consumption). A
realistic analysis would also need to account for distortions in the tax system,
for uncertainties and risk premiums, and for the equity-premium puzzle, but
these complications can be ignored in the present context.
The Review assumes a relatively low curvature parameter (the
logarithmic utility function) along with the near-zero social discount rate.
However, in calibrating a growth model, the social discount rate and the
curvature parameter cannot be chosen independently if the model is designed
to match observable variables. A low curvature (such as in the logarithmic
utility function) implies a relatively high social discount rate. A high
curvature (represented by a high degree of risk aversion or a high aversion to
intergenerational inequality) implies a low or even negative social discount
rate. It turns out that the calibration of the utility function makes an enormous
difference to the results in global-warming models, as I show in the modeling
section below.
Measuring impacts with near-zero discounting
With these analytical points behind us, I next discuss the Review’s
estimates of the aggregate economic impacts. The Review concludes, “Putting
these three factors together would probably increase the cost of climate
change to the equivalent of a 20% cut in per-capita consumption, now and
forever.” This frightening statement suggests that the globe is perilously close
to driving off a climatic cliff in the very near future. However, this is an
unusual definition of consumption losses, and when the Review says that there
are substantial losses “now,” this does not mean “today.” The measure of
consumption used is the “balanced growth equivalents” of consumption.
Roughly speaking, with low discounting, this is the certainty equivalent of the
average annual consumption loss over the indefinite future. The measure is
akin to an annuity. In fact, the Review’s estimate of the output loss now, as in
“today,” appears to be zero.
If we look inside the impact boxes, we find some strange things. The
damage estimates are much higher than the standard estimates in the impact
literature. This probably occurs because of assumptions that tilt up the
damage curve: rapid economic growth forever, high economic damage
estimates, high climatic impacts of GHG accumulation, catastrophic risks,
adverse health impacts, yet higher sensitivity of the climate system, and an
adjustment for inequality across countries. Additionally, the Review drew
selectively from studies, emphasizing those with high damage estimates,
some of which are highly speculative. For example, the Review used estimates
from the study of Nordhaus and Boyer (see footnote 12 below) that projected
damages way beyond 2100; however, those authors noted that projections
beyond 2100 were particularly unreliable.
However, the major point is that these impacts are far into the future,
and the calculations depend critically upon the assumption of low
discounting. Take as an example the high-climate scenario with catastrophic
and non-market impacts. For this case, the mean losses are less than 1 percent
of world output in 2050, 2.9 percent in 2100, and 13.8 percent in 2200 (see
Figure 6.5d). Yet this somehow turns into a mean annual impact of 14.4
percent shown in Table 6.1, and after a few other gloomy ingredients are
stirred in, it becomes the “20% cut in per-capita consumption, now and
How do damages, which average around 5 percent of output over the
next two centuries turn into a 14.4 percent reduction in consumption now and
forever? The answer lies in the way that near-zero discounting magnifies
distant impacts. With near-zero discounting, the low damages in the next two
centuries get overwhelmed by the long-term average over many centuries. We
can illustrate using the Review’s model discussed in Box 6.3. Suppose that
scientists discover that that a wrinkle in the climatic system will cause
damages equal to 0.01 percent of output starting in 2200 and continuing at
that rate thereafter.
How large a one-time investment would be justified today to remove the
wrinkle starting after two centuries? The answer is that a payment of 15 percent
of world consumption today (approximately $7 trillion) would pass the
Review’s cost-benefit test. This seems completely absurd. The bizarre result
arises because the value of the future consumption stream is so high with
near-zero discounting that we would trade off a large fraction of today’s
income to increase a far-future income stream by a very tiny fraction. This
bizarre implication reminds us of Koopmans’s warning quoted above to
proceed cautiously to accept theoretical assumptions about discounting before
examining their full consequences.
Hence, the damage puzzle is resolved. The large damages from global
warming reflect large and speculative damages in the far-distant future; the
impacts now, as in today, are small; and, as I will suggest below, the 20
percent cut in consumption from global-warming might be reduced by an
order of magnitude if alternative assumptions about discounting are used.
Economic modeling with low discount rates
I next apply these points in an empirical model of the economics of
global warming. To foreshadow the result, these calculations show that the
assumption of a near-zero social discount rate drives most of the economic
results in the Review.
It is virtually impossible for mortals outside the group that did the
modeling to understand the detailed results of the Review. It would involve
studying the economics and geophysics in several chapters, taking apart a
complex analysis (the PAGE model), and examining the derivation and
implications of each of the economic and scientific judgments.
The alternative approach followed here is to use a small and welldocumented
model of the economics of climate change to estimate the optimal
policy, and then to make parameter adjustments to parallel assumptions made
in the Review. For this purpose, I use the “DICE model,” which is an acronym
for a Dynamic Integrated model of Climate and the Economy. This model,
developed in the early 1990s, uses a simple dynamic representation of the
scientific and economic links among population, technological change, GHG
emissions, concentrations, climate change, and damages. The analytical
structure of the DICE model is identical to that in the Review. DICE calculates
the paths of capital investment and GHG reductions that maximize a social
welfare function, where the social welfare function is the discounted sum of
population-weighted utilities of per capita consumption. The DICE model
assumes a pure rate of social time preference starting at 3 percent per year and
declining slowly to about 1 percent per year in 300 years. The social discount
rate was chosen to be consistent with a logarithmic utility function, market
interest rates, and rates of private and public saving and investment. 12
For this analysis, I have updated the DICE model to 2005 data,
economics, science, and 2006 prices.13 I then make three runs, which are
explained as we proceed:
Run 1. Optimal climate change policy in the DICE-2006 model
Run 2. Optimal climate change using the Stern Review zero discount rate
Run 3. Optimal climate change using a recalibrated zero discount rate
Run 1. Run 1 is the Optimal climate change policy in DICE-2006. This run
takes the DICE-2006 model and calculates the optimal trajectory of climate
change policies as described above. This calculation leads to an optimal
carbon price in 2005 of $17.12 per ton C, rising over time to $84 in 2050 and
$270 in 2100. (The “optimal carbon price,” or carbon tax, sometimes called the
“social cost of carbon,” is the calculated price of carbon emissions that will
balance the incremental costs of reducing carbon emissions with the
12 Results and documentation of the DICE model are provided in William Nordhaus,
“An Optimal Transition Path for Controlling Greenhouse Gases,” Science, vol. 258,
November 20, 1992, pp. 1315-1319; William Nordhaus, Managing the Global Commons:
The Economics of Climate Change, MIT Press, Cambridge, Mass., 1994; William
Nordhaus and Zili Yang “A Regional Dynamic General-Equilibrium Model of
Alternative Climate-Change Strategies,”, American Economic Review, vol. 86, No. 4,
September 1996, pp. 741-765; William Nordhaus and Joseph Boyer, Warming the
World: Economic Modeling of Global Warming, MIT Press, Cambridge, Mass, 2000;
William Nordhaus, “Global Warming Economics,” Science, November 9, 2001, vol.
294, no. 5545, pp. 1283-1284.
13 Documentation of the changes in the DICE-2006 model and the GAMS computer
program for the DICE-2006 model are provided in William D. Nordhaus,
“Documentation for DICE-2006, November 2006 round,” November 17, 2006,
available at , under “Recent Stuff.”
incremental benefits of reducing climate damages.) The optimal rate of
emissions reduction is 6 percent in 2005, 14 percent in 2050, and 25 percent in
2100.14 This optimized path leads to a projected global temperature increase
from 2000 to 2100 of around 1.8 degrees C. While the findings of such
mainstream economic assessments may not satisfy the most ardent
environmentalists, if followed they would go far beyond current global
emissions reductions and would be a good first step on a journey of many
Run 2. The results of the standard DICE model just discussed are
completely different from those in the Review. The Review recommends a
social cost of carbon of $311 per ton C. This number is almost 20 times the
DICE model result. Based on calculations made in earlier publications (see
footnote 12), it seems likely that the major reason for the Review’s sharp
emissions reductions and high carbon price is the low social discount rate. I
therefore calculated run 2, Optimal climate change using the Stern Review zero
discount rate. The assumptions are the same as Run 1 except that the social
discount rate is changed to 0.1 percent per year. This dramatically changes the
trajectory of climate-change policy. The 2005 optimal carbon price in the DICE
model rises from $17.12 in Run 1 to $159 per ton C in Run 2.15 Efficient
emissions reductions in Run 2 are much larger – with emissions reductions of
14 The future numbers are the solutions to the model based on current information
and provide estimates of optimal future policies under current estimates of
parameters. They are not decisions that are taken today. They should be revised over
time as new scientific and economic information becomes available.
15 The social cost of carbon estimated in the Review is approximately two times
higher than the number calculated in Run 2. Because different models are used, it is
not possible to identify reasons for the discrepancy. Modeling results are extremely
sensitive to parameter changes when the discount rate is near-zero.
50 percent in 2015 – because future damages are in effect treated as occurring
today. The climate-policy ramp flattens out.
Run 3.An earlier section noted that alternative calibrations of the social
welfare function are consistent with observable variables. So the final run is
one in which assumes a low social discount rate but where the curvature
parameter is calibrated so that the economic growth path conforms to
observable variables. Some history might be helpful here. When the DICE
model was constructed fifteen years ago, I assumed logarithmic utility for
computational reasons – alternative utility functions would not converge
numerically. This calibration led to a social discount rate of 3 percent per year,
which was calibrated to match the growth of consumption, savings rates, and
market rates of return on capital. Because of improvements in computers and
software, we can now easily calibrate alterative utility functions. Experiments
with the DICE-2006 model indicate that a social discount rate of 0.1 percent
per year is consistent with a utility curvature parameter of 2.25. However, the
Review’s social discount rate of 0.1 percent per year is inconsistent with its
utility curvature assumption of 1.16 The Review’s calibration gives too low a
rate of return and too high a savings rate compared to macroeconomic data,
16 The discussion in the text assumes zero population growth. More generally, the
Ramsey-Cass-Koopmans steady-state optimal growth equilibrium equation is
r = ρ + αg + n, where r = the marginal product of capital, ρ = social discount rate,
α = elasticity of the marginal utility of consumption, g = growth of per capita
consumption, and n = rate of growth of population. Conceptually, the marginal
product of capital has the same units as the real interest rate, but entirely different
units from the social discount rate. To apply this equilibrium condition, assume that
the observable variables (in rates per year) are r = 0.05, n = 0.00, and g = 0.02. For this
simplest equation, if we assume that the social discount rate is ρ = 0 per year, then α
= 2.5. If we take the log-linear utility function of the Review together with the
observable variables in this footnote, then this implies that ρ = 0.03 per year. The
calibrations in DICE-2006 are slightly different from these equilibrium calculations
because of positive population growth and non-constant consumption growth, but
these equilibrium calculations given the flavor of the results.
but the alternative calibration proposed here fits the macroeconomic data
underlying the DICE model.
We can now rerun the DICE-2006 model with the near-zero social
discount rate and the associated calibrated curvature parameter derived in the
last paragraph. This is Run 3, Optimal climate change with recalibrated zero
discount rate. Run 3 looks very similar to Run 1, the standard DICE-2006 model
optimal policy. The first-period social cost of carbon in Run 3 is $19.55 per ton
C, slightly above Run 1. The recalibrated run looks nothing like Run 2, which
is the run that reflects the Review’s assumption. How can it be that Run 3, with
a near-zero social discount rate, looks so much like Run 1? The reason is that
the recalibrated social discount rate in Run 3 maintains the assumption of
productive capital, with a relatively high real interest rate in the near term.
This high return means that the logic of the climate-policy ramp continues to
hold even though the social choice function has been recalibrated to a zero
social discount rate. This calibration removes the cost-benefit dilemmas just
discussed as well as the savings and uncertainty problems discussed in the
next two sections.
Implications for saving and investment
I return for the balance of this note to the Review’s assumptions on both
social discount rate and utility curvature (the assumptions that underlie Run
2). One surprising implication of the Review’s social discount rate is the effect
on consumption and saving. If the Review’s philosophy were adopted as a
general policy, it would produce much higher overall saving as compared
with today. In Run 2 (Optimization with Stern discount parameter), the global net
savings rate almost doubles compared to the historical numbers or Run 1. This
implies that global consumption would be reduced by about 14 percent,
requiring a reduction of $6 trillion per year in current consumption.
Where would the consumption cuts come from? From India and Africa?
That hardly seems equitable. The higher investment would be more than five
times total overseas development aid of all countries today. Perhaps the
consumption should come from the wasteful Americans? This would be fourfifths
of current levels of consumption and many times the decline in the
Great Depression.
Aside from the question of who pays, we might wonder whether such a
large decline in current consumption today is desirable in a world where
average consumption is growing rapidly. The Review projects that per capita
consumption will grow at 1.3 percent per year over the next two centuries (p.
162). In 2006 dollars, this means that today’s per capita consumption of $7,600
would grow to $94,000 in 2200. Here perhaps is a shard of hope for the globe.
However, this growth also means that future climatic damages will
come out of a much higher level of income. For example, the high-damage
case is associated with a 13.8 percent decline in consumption in 2200 as
discussed above. This means that per capita consumption would grow from
$7,800 today to only $81,000 in 2200. Hence, the Review advocates reducing
current consumption to prevent the decline in consumption of future
generations that it projects to be much richer than today. While this might be
worth contemplating, it hardly seems ethically compelling.
Faced with these implications of the discounting assumption, advocates
of the Review policy might propose a “dual-discounting” approach – limiting
the scope of the low social discount rate to climate policy. In other words,
perhaps countries should choose global-warming policies assuming the nearzero
social discount rate, but leave the rest of the economy to operate with the
present high social discount rate. While this seems an attractive possibility, it
is in fact a roundabout way to slow climate change sharply. In effect, we are
using a low social discount rate to “prevent dangerous interference with the
climate system” (in the language of the Framework Convention on Climate
Change). If that is the reason, why not impose the limit directly? Instead of
using the near-zero social discount rate as an analytic subterfuge to slow
climate change, why not simply adopt policies that will directly keep climate
change below the dangerous threshold? Limiting climate change directly is
more efficient as well as more transparent.
Hair triggers and uncertainty
A further unattractive feature of the Review’s near-zero social discount
rate is that it puts present decisions on a hair-trigger in response to far-future
contingencies. Under conventional discounting, contingencies many centuries
ahead have a tiny weight in today’s decisions. Decisions focus on the near
future. With the Review’s discounting procedure, by contrast, present
decisions become extremely sensitive to uncertain events in the distant future.
We saw above how an infinitesimal impact on the post-2200 income
stream could justify a large consumption sacrifice today. We can use the same
example to illustrate how far-future uncertainties are magnified by low
discount rates. Suppose that we suddenly learn that there is a 10 percent
probability of the wrinkle in the climatic system that reduces the post-2200
income stream by 0.01 percent. What insurance premium would be justified
today to reduce that probability to zero? With conventional discount rates, we
would probably ignore any tiny wrinkle two or three centuries ahead. If we
did a careful calculation using conventional discount rates, we would
calculate a breakeven 0.0002 percent insurance premium to remove the year-
2200 contingency, and a 0.0000003 percent premium for the year-2400
contingency. Moreover, these dollar premiums are small whether the
probability is large or small.
With the Review’s near-zero discount rate, offsetting the low-probability
wrinkle would be worth an insurance premium today of almost 2 percent of
current income, or $1 trillion. We would pay almost the same amount if that
threshold were to be crossed in 2400 rather than in 2200. Because the future is
so greatly magnified by a near-zero social discount rate, policies would be
virtually identical for different threshold dates. Moreover, a small refinement
in the probability estimate would trigger a large change in the dollar premium
we would pay. We are in effect forced to make current decisions about highly
uncertain events in the distant future even though these estimates are highly
speculative and are almost sure to be refined over the coming decades.
While this feature of low discounting might appear benign in climatechange
policy, we could imagine other areas where the implications could
themselves be dangerous. Imagine the preventive war strategies that might be
devised with low social discount rates. Countries might start wars today
because of the possibility of nuclear proliferation a century ahead; or because
of a potential adverse shift in the balance of power two centuries ahead; or
because of speculative futuristic technologies three centuries ahead. It is not
clear how long the globe could long survive the calculations and machinations
of zero-discount-rate military powers. This is yet a final example of a
surprising implication of a low discount rate.
Summary verdict
How much and how fast should the globe reduce greenhouse-gas
emissions? How should nations balance the costs of the reductions against the
damages and dangers of climate change? The Stern Review answers these
questions clearly and unambiguously: we need urgent, sharp, and immediate
reductions in greenhouse-gas emissions.
I am reminded here of President Harry Truman’s complaint that his
economists would always say, on the one hand this and on the other hand
that. He wanted a one-handed economist. The Stern Review is a Prime
Minister’s dream come true. It provides decisive and compelling answers
instead of the dreaded conjectures, contingencies, and qualifications.
However, a closer look reveals that there is indeed another hand to
these answers. The radical revision of the economics of climate change
proposed by the Review does not arise from any new economics, science, or
modeling. Rather, it depends decisively on the assumption of a near-zero
social discount rate. The Review’s unambiguous conclusions about the need for
extreme immediate action will not survive the substitution of discounting
assumptions that are consistent with today’s market place. So the central
questions about global-warming policy – how much, how fast, and how costly
– remain open. The Review informs but does not answer these fundamental