Thoughts on the Social Rate of Discount
Dr. Bruce Stram
Introduction
Two recent evaluations of potential global warming policy are starkly at odds. The “Stern
Review” (Nickolas Stern for the British Treasury) and “A Question of Balance” (William
Nordhaus) are nearly an order of magnitude apart on what level of current resources should be
directed toward reducing carbon emissions. This difference is all the more striking because
careful examination of the two documents reveals that both use very similar estimates of
future damages from warming. The difference almost entirely boils down to one number: the
rate of discount applied to those future damages. Nordhaus uses a discount rate comparable
to that used for most benefit cost analyses which are based on market rates of return. Stern
uses a very low rate, a choice driven by the fact that this analysis is intergenerational in
nature, which per Stern requires a very low discount rate to avoid generational bias.
Social rate of discount has been a theoretical issue for economists for many years, beginning
at least with Ramsey (1928). Its application circumscribes many important policy issues
associated with economic evaluation of long term consequences versus actions that might be
taken today. Unquestionably, however, the dialogue regarding global warming has given
substantial new impetus to the discussion.
Much of the dispute about the “social rate of discount” centers on the fear that the current
generation will be selfish with regard to preventing future damage to the environment,
consuming now and leaving great costs for future generations. And this despite the fact that a
market like rate of discount applied to both private and public cost benefit analysis
encourages deferral of current consumption in favor of investment and provision for the
future.
Models optimizing long term economic and environmental consequences of human activity
seem to yield, at least for some observers, acceptance of too much environmental harm. Since
market based rates of discount seem to reduce the present value of dire environmental
consequences to very low values over very long time periods, such observers logically
question whether this discounting applied to time periods extending well beyond current
generations has inherent flaws. The hypothesis here is that such flaws, if they exist, are
occasioned by more mundane shortcomings in the valuations placed on environmental
damage in the future.
Discounting Costs and Benefits
Cost benefit analysis (CBA, public sector) or discounted cash flow (private sector) follows the
same general methodology. Values with occur in the future are factored by a compounded
discount rate which resembles a rate of interest (i.e. 1.06). These discounted values are then
compared to current values.
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The basic rationale for such discounting is that economic resources which are withheld from
current consumption can be diverted to projects or activities which on average provide for
greater future benefit. Such “diversions” include investments in physical capital, research and
development of technology, and education.
Economists point to the markets for savings and lending to provide guidelines for establishing
criteria for selecting desirable investments. These markets in effect aggregate willingness to
defer consumption versus receiving future reward. Investments which do not yield returns at
least equal to these rates diminish overall welfare (for public investments) or reduce the value
of a private sector business or activity. Both governments and businesses borrow funds which
are repaid with interest (i.e. a discount rate). Businesses also raise equity capital for projects
with the expectation that there will be a positive return, also an implicit discount rate.
Earning a positive return on invested capital is part of an amazing and highly distinct period
of economic development in relatively recent history.
“Was Malthus Right? Economic Growth and Population Dynamics, Jesus FernadezVillaverde, University of Pennsylvania, Dec. 1, 2001
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Economists strongly believe that the notion of a focus on capital formation and the
concomitant formalization of a market for capital is an integral part of the foundation of this
economic growth. This development, along with entrepreneurship, vision, risk taking, and
“animal spirits” has created an engine of economic growth. CBA and discounted cash flow is
a methodology that is a codification of this process in order to provide criterion for efficient
investment. This methodology is used almost universally for evaluating governmental and
business investments.
Objections have arisen, however, regarding very long term evaluations. It begins simply as a
matter of arithmetic. Typically a discount rate is estimated in the range of 4% to 6% in real
terms. Thus a project “paying off” in 10 years must retrun 1.8 times its cost. Alternately, an
asset valued at 1.8 10 years from now would be valued at 1 today.
Longer term compounding has a much more dramatic effect. Firty years from now,
something valued at 18 would be deemed to be worth 1 today. For 100 years the ratio to
current value would be 340:1, and for 200 years, an astonishing 115,000:1.
Needless to say, applying such discounts to the value of hypothesized adverse effects from
global warming (or other environmental damages) is viewed with some substantial concern.
That has led to a vigorous renewal of the social rate of discount analysis.
A Brief Examination of Social Rate of Discount Theory
Much thought has been devoted to this fundamental issue of weighing the value of the future
to value in the present. These include the following: The Stern approach; various rationales
for declining discount rates (over time, DDR), and a “Fat Tails” approach. These will be
outlined in turn, followed by an alternative approach.
Stern
The Stern Report justifies the use of a very low (relative to a typical 4.5% to 6% real often used for
cost benefit analysis (CBA)), numerically 1.4%. The rationale is based on moral grounds. It devolves
from a well known mathematical and highly theoretical economic model depicting economic growth
based on capital formation and population growth and optimization of welfare over tiime. An end
result is a simple formula:
r =ρ +θg=δ
the letter r represents the marginal rate of return to capital, ρ “the pure rate of time
preference, i.e. human’s preference for gratification now as opposed to the future, θ is the
elasticity of utility (or welfare) with respect to income, g per capita income growth, and δ the
social rate of discount.
This may be interpreted as follow: societies’ future welfare should be discounted according to
the marginal rate of return to capital (r and δ being equal), and in addition by decline in the
value of future income increase fostered by growth in per capita income. (Given the abstract
nature of the analysis, many real world conditions (taxes, externalities, etc) that would disturb
the equality are ignored.)
From this foundation, the Stern Report makes the following assertion: the pure rate of time
preference observed for the current generation should not be visited on future generations to
their disadvantage. Therefore that component of the formulation should be set to zero. Since
it is take to be 3%, the social discount rate is appropriately 1.4% rather than say 4.5% which
would represent the marginal return to capital.
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In this, the Stern Report follows a number of eminent British (and other) economists—
Ramsey, Harrod, etc.
However, this formulation would have the current generation defer consumption to achieve
much greater benefit for future generations than would be the case applying the standard
methods. Such an approach seems to ignore the fact that a high discount rate implies
continued economic growth such as has occurred over the last few hundred years. Thus
those future generations for whom greater sacrifice is deemed appropriate will be much
wealthier than we currently. Equivalently, this is akin to asking that our ancestors alive in
1800, and much poorer than we today, be compelled to reduce consumption in order to
additionally benefit us. By this formulation, future generations are to be treated better than
we have been by our ancestors, and better that we treat ourselves.
Uncertainty as to Future Growth Rates
It is certainly the case that for at least the last two hundred years, “Western” economies have
enjoyed historically very high growth rates driven in significant part by a high marginal
productivity of capital. Much of the rest of the world (weighted by population) seems finally to
be catching on and achieving this by similar means. But this growth is not axiomatic. There
is no certainty this effect will continue in the future, and the less so the farther off the future.
Such uncertainty has given rise to several analyses which seem to imply that use of DDR is
appropriate.
Financial markets are often looked to find measures that reflect a rate of return to capital and
hence a CBA discount rate. But forward markets, which are not perfect predictors of the
future, do not extend to the future being contemplated in very long term analyses and
therefore provide very limited guidance.
Martin Weitman tries to capture this effect roughly as follows: he defines future states of the
world which embody different returns to capital and hence appropriate discount rates. He
then proposes to evaluate the future in total by summing these weighted by their probability
and discounted by their own return to capital. As time goes to infinity, the future world with
the “smallest possible” discount rate dominates the weighted average.
This hoisting of high discount rates on their own petard certainly deserves a smile. However,
some objections come immediately to mind. What is the smallest possible discount rate,
zero? Certainly this and even negative discount rates are contemplated in the literature on
this subject. An infinite time horizon makes no sense. If nothing else, the earth and the
universe have a limited life. And finally there is a certain circularity to the result: if the
conclusion of the analysis is that the “lowest possible” discount rate is the one appropriate,
shouldn’t it be applied to all the future states, obviating the conclusion?
But these objections don’t apply to a more mundane point. Given uncertainty as to potential
future growth rates and hence appropriate discount rates, a normal probability distribution of
such would suggest that an expected value is a reasonable measure to use for determining
expected future income. However, the marginal value of that income will be higher in lower
growth situations then higher. That is, even if uncertain future income is normally distributed,
future welfare is not. Further, one can demonstrate that there is a DDR which captures the
welfare effect of this asymmetry. (Whether using a DDR to reflect this is the best practice is
another matter and will be considered below.)
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Weitzman also raises a “Fat Tails” argument. The supposition is that the probability of a
catastrophic outcome, i.e. representing near infinite loss from global warming remains high
enough so as to more than offset cumulative exponential discounting. This really amounts to
a strong suggestion that cost benefit analysis cannot be reasonably applied to global
warming concerns given potential catastrophic impacts. But a resource allocation problem
remains: there are many unknowable probability catastrophic events (meteor, hadron collider
creating a black hole on earth, nano technology gone wild, etc.), But only finite resources
are available now to be allocated toward avoiding possible infinite outcomes in the future.
Perhaps a more useful approach to such concerns is to these dangers in terms of
“backstops”. That is, instead of evaluating the consequences of the hypothesized events,
examine the actions that might be taken to avert them. For global warming these might
include the cost of chemical carbon capture and storage, genetic engineering of carbon
eating and sequesting plants (Dyson) and/or geoengineering. CBA is clearly appropriate for
evaluating such alternatives.
Substitutability
CBA or discounting makes sense because the flow of reproducible or manufactured goods
can be increased by deferral of consumption and comcommitant capital formation. But
environmental assets are not generally reproducible. That natural endowment can be and
demonstrably is being reduced by human activity. If it is reasonable to suppose that future
generations will benefit from high economic growth rates (with appropriate high discount
rates), the availability of environmental assets will diminish both in a relative sense and
absolutely. Therefore, the value of such assets will logically increase relative to reproducible
goods. Further, one may readily observe that richer societies spend a greater proportion of
income on environmental protection and the enjoyment of such amenities. One can posit
that as environmental assets diminish and reproducible goods increase, that an increase in
value of the former could outweigh the growth rate of the latter, and even be greater than the
discount rate. Such circumstances potentially provide for an additional offset for the discount
of potential environmental damages in the distant future. (Krutilla and Fisher)
Conclusion
No one believes that economic analysis of the far off future necessary to evaluate the potential
dangers of global warming (or any other very long term situations) is anything but
problematic. Straightforward use of a “standard” discount rate yields a devaluation of future
environmental damages which is disturbing to many. That has led to much reevaluation of
standard CBA methods and in particular, analysis of the appropriate social rate of discount.
Various methods have been proposed to revise this rate to reflect various concerns. These
have been briefly considered in this paper and are certainly in whole, worthy of consideration.
However, there is no inherent need to incorporate such adjustments in a singular discount rate
number. At best, doing so is simply an analytical convenience. Each of the adjustments
considered here could be incorporated into an overall analysis as a separate item in an overall
analysis.
Such an approach would be eminently more functional than relying on a single discount rate
factor. The logical need for such adjustments remains open to question. Further in
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application, the elements of these adjustments are themselves highly uncertain. For example
the long term decline of the marginal utility of income at much higher per capita income
levels is highly speculative. So too is any uncertainty in long term rate of economic growth
and the return to capital. Including any such adjustments explicitly rather than subsuming
them into a single discount rate provides for much more clarity and transparency.
This analysis very strongly implies that collaborative action between environmental scientists
and economis to get more correct answers resulting from more careful examination of
potential future income levels, their impact on environmental amenities and systematic
estimation of how the valuation of environmental benefits changes with income level.
References
Gollier & Koundouri & Pantelidis, 2008. "Declining discount rates: Economic
justifications and implications for long-run policy," Economic Policy, CEPR & CES &
MSH, vol. 23, pages 757-795, October
Krutilla, J. and A. C. Fisher (1975), The Economics of Natural Environments. Baltimore:
Johns
Hopkins University Press.
Nordhaus, William, A Question of Balance: Weighing the Options on Global Warming
Policies, Yale University Press, New Haven, CT, 2008
Ramsey, F. P. (1928), New Haven, CT, 2008s on Global Warming Policies,long-run policy
Stern, N.H. (2006). ‘The Economics of Climate Change’, available at:
http://www.hm-treasury.gov.uk/independent_reviews/stern_review_economics_climate_
change/stern_review_report.cfm
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