ESTIMATION OF THE SOCIAL DISCOUNT RATE FOR
NON-MARGINAL ENVIRONMENTAL DAMAGES
Conor Parrish and David Courard-Hauri
Drake University Environmental Science and Policy Program
Abstract
When estimating the costs and benefits of programs to address
long-term environmental challenges like climate change, the
choice of discount rate often drives the results. The Pure Rate of
Time Preference (PTP) used in major analyses have ranged
from 0.1% (Stern) to 3% (Nordhaus) or higher. In many studies,
high values of PTP are supported by revealed preference
information based on marginal changes. However, many of the
expected effects of climate change are likely to be non-marginal,
including extinction, loss of entire habitat types, and inundation
of small nations. We report on efforts to measure PTP for nonmarginal changes by asking individuals to choose between
protecting all of a particular type of habitat for a fixed number of
years, versus a fraction of the habitat indefinitely. Presenting
individuals with this trade-off provides a way to assess
preferences that is easy for the participant to understand,
potentially realistic, and not subject to many of the confounding
factors that plague current techniques.
Social Discount Rates used in the literature
and government assessment vary widely:
•Office of Management and the Budget: 3 to 7%
•EPA: 2 to 7%.
•Australian government: Generally 7%
•Harrison (2010): 8%
•Nordhaus (2007): 4.3%
•Stern (2007): 1.3%
•Gollier and Weitzman (2009): Declining over time to lowest possible
rate in long term
•Fleurbaey & Zuber (2012): For climate, probably negative (see also
Daly and Farley, 2010)
This variation is due to the lack of an objective measure of what
the SDR should be. Our goal is to estimate the SDR people use
in making real tradeoffs when decisions involve long-term, nonmarginal environmental impacts.
Methods (continued)
Discussion
Multiple variants of the survey were sent out in which both the
question order in regards to ecosystem type varied, as well as
the fraction of habitat being saved changed between 50%, 25%,
10%, and 5%. Four variations of the question order were sent
out for each fraction, for a total of 16 unique variations. For each
survey variation we calculated a mean indifference point based
on direct responses, which are the respondent supplied
numbers. This yielded four indifference points for each fraction
(Figure 1), which allowed us to calculate the SDR for each
fraction (Figure 2). We attribute the variation with fraction of land
protected to be due to non-marginality considerations, so by
fitting an exponential trendline to the data series and calculating
the y-intercept of its equation we determined the single value
that should be used as the SDR.
The SDR value of 0.51% we calculated is much lower than the
value currently used by decision makers. As indicated by the
cost of carbon example, the choice of discount rate can have
dramatic impacts on decision making. By using a rate that is too
low, a decision will be made that is too costly for the present
generation, but one that is too high could result in increased
costs in the future (Table 1).
Results
Methods
Introduction
Table 1. Net Present Values of future damages of $1 trillion using multiple
discount rates.
1000
950
The SDR works like reverse interest, allowing analysts to
compare the value of expected future income/expenses with
money today, according to the equation:
U = ò e u ( c(t))dt
- rt
where U is the net present value of a future consumption path
c(t), u is the utility of that consumption (denoted in real dollars),
and r is the SDR.
Small changes in the SDR can have profound impacts on the
assessment of policies with implications to the distant future. For
example, estimates of the social cost of carbon (the correct level
for a carbon tax, for example):
•$360/ton at 1.4% discount rate (Stern)
•$35/ton at 4.3% discount rate (Nordhaus)
Other workers have used surveys to investigate these questions
(e.g., Evans 2005), but our methodology differs by prompting
respondents for answers that are not in monetary terms, but that
instead compare different quantities of ecosystem services over
different periods of time, allowing the respondents to consider
tradeoffs without prior economic training in valuation.
Mean Years
850
800
750
700
650
600
References
550
500
0
0.1
0.2
0.3
0.4
0.5
0.6
Fraction of Land in Question
Evans (2005) The elasticity of marginal utility of consumption:
Estimates for 20 OECD countries. Fiscal Studies. 26 (2): 197224
Figure 1. Mean indifference points by fraction of land saved for each survey variation.
0.006
Sample question:
Fleurbaey and Zuber (2012) Climate policies deserve a negative
discount rate. FMSH-WP-2012-19.
0.005
Imagine that a company has just purchased a piece of land that
contained 50% of the remaining ancient redwood forest in
California, and proposes to use the land to build a series of
housing developments. They propose to state regulators one of
two options: they could build developments on half of the land,
donating the other half to the Nature Conservancy to be
protected forever, or they could allow the Nature Conservancy to
use all of the land for the next 40 years, after which they would
develop the entire plot. Which scenario do you believe is
preferable?
Implied Social Discount Rate
Benefit-cost analysis (BCA) is a vital tool used worldwide to help
with policy assessment. When considering policies with longterm impacts, like those addressing climate change or habitat
loss, few parameters are as important as the social discount rate
(SDR). The SDR represents the value at which society prefers
money (or other benefits) today with money or benefits at a
particular time in the future. The SDR allows analysts to
compare costs and benefits that will be occurring at different
times in the future.
We emailed an electronic survey to 2,000 random members of
the Drake University Community, asking respondents to consider
different quantities of ecosystem services over varying periods of
time.
As you can see (Table 1), the 0.51% discount rate we calculated
has the potential to radically alter the decision making process. If
further analysis of the survey data produces similar results, we
could not justify standard benefit-cost analysis practices (use of
mid-range discount rates and valuation based on marginalist
techniques) from a consumer choice perspective.
900
0.004
Gollier and Weitzman (2009) How should the distant future be
discounted when discount rates are uncertain? CES Working
Paper 2863.
0.003
0.002
Harrison (2010) Valuing the Future: the social discount rate in
cost-benefit analysis. Visiting Researcher Paper, Productivity
Commission, Canberra Australia.
0.001
0
0
a.Development of half of the land now, saving the other half
forever.
b.Save all of it for 40 years before losing all of it forever to
development.
Progression from this point depends on which of the two options
the respondent selects.
0.1
0.2
0.3
0.4
0.5
0.6
Fraction of Land in Question
Figure 2. Implied social discount rates by fraction of land saved for each survey variation.
Fitting an exponential trendline to the data in Figure 2 yielded
the equation, y = 0.0051e-3.674x, with an R2 value of .983. We
calculated the underlying SDR by setting the fraction of land to 0,
the y-intercept of the trendline. This yielded a SDR of 0.51%.
IPCC; Intergovernmental Panel on Climate Change (2007)
Fourth Assessment Report, Cambridge University Press, New
York.
Nordhaus (2007) Critical assumptions in the Stern Review on
Climate Change. Science, 317, 201-202
Stern (2007) Stern review on the economics of climate change.
H.M. Treasury, UK.
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ESTIMATION OF THE SOCIAL DISCOUNT RATE