9 July 2014
Why is Risk Aversion Unaccounted for
in Environmental Policy Evaluations?
By Dr. Noah Kaufman
The final version of this
publication appeared in
Climatic Change Volume
125, Issue 2, July 2014,
pp 127-135. The final
publication is available
at http://rd.springer.com/
article/10.1007/s10584-0141146-8.
Government regulations can reduce the uncertainty associated with large environmental
risks, such as catastrophic events caused by climate change, hydraulic fracking and
nuclear power plant meltdowns. Individuals dislike large risks—insurance companies
earn profits because of the risk premiums that are paid to avoid risks such as sickness,
fires, floods and car wrecks—so there are considerable benefits to society associated
with regulations that reduce or remove environmental risks. In welfare assessments,
economists typically use concave utility functions and estimate “option prices” to
account for risk aversion.
Nevertheless, environmental policy evaluations in the U.S. customarily disregard these
risk-reduction benefits. Environmental regulations are increasingly influenced by costbenefit analyses that are performed based on the guidance of the Office of Management
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and Budget (OMB). The guidance of OMB for benefit-cost analyses is to estimate
expected benefits and costs in monetary terms (i.e. a weighted average is calculated
using the probabilities and monetary net benefits of all potential outcomes). Unlike a
rigorous economic analysis, policy evaluations that follow this OMB guidance do not
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account for the effects of risk aversion.
This essay offers two potential explanations for why risk aversion is typically unaccounted
for in environmental policy evaluations. First, there is an extensive public economics
literature on conditions whereby governments should behave in accordance with risk
neutrality (i.e. zero risk aversion) when evaluating public investments with uncertain
costs and benefits. Arrow and Lind (1970) showed that when populations are relative
large, the risk premiums for small public investments with uncertain effects converge
to zero because they can essentially be “spread out” among constituents. Indeed, both
the U.S. and U.K. government documents that provide the official guidance on proper
regulatory analysis specifically reference the uncertain costs and benefits of a regulation
when recommending risk neutrality as the default assumption.
A second rationale for ignoring risk aversion is computational and theoretical difficulties.
Any attempt to quantify “societal risk premiums” will run into significant computational
and theoretical problems. There is no well-accepted level of societal risk aversion, and no
generally accepted methodology for converting monetary values into estimates of societal
well-being that account for risk aversion. The choices of these modeling parameters would
be controversial in any policy evaluation.
Neither of these two rationales stands up to scrutiny. First, computational and theoretical
difficulties are of course not a valid justification to disregard risk-reduction benefits. Second,
Arrow and Lind (1970) is an endorsement for risk neutrality only for regulations that have
uncertain costs and benefits, not for regulations that reduce uncertainty that exists in the
absence of environmental policy (“baseline” or “business-as-usual” uncertainty). Policies
that reduce pre-existing environmental uncertainty will provide risk-reducing benefits to all
affected risk-averse individuals, and in no sense is the risk “spread out” across constituents.
Policy evaluations should therefore account for risk aversion in situations when pre-existing
uncertainty is significant. The implications of not doing so can be dramatic, as shown by
Anthoff and Tol (2009) in sensitivity analysis on estimates of the social costs of carbon
dioxide emissions.
However, given the computational and theoretical difficulties of estimating risk premiums,
each policy evaluations cannot be tasked with determining an appropriate methodology
for estimating risk premiums. Instead, general guidance should be provided on how
to incorporate risk aversion into policy evaluations, as has been done in the case of
discounting future benefits and costs to present value terms. Despite the contentious
ongoing academic debates surrounding the appropriate “social discount rate,” most U.S.
policy evaluations follow the guidance of the Office of Management and Budget without
controversy. Similarly, an expert panel could provide guidance on when and how the
uncertainty-reducing benefits of regulations should be incorporated into environmental
policy evaluations.
The remainder of this essay is structured as follows. The next section provides an overview
of the benefits of regulations that reduce pre-existing environmental uncertainty. The
following section discusses potential reasons that risk aversion has not been accounted for
in these policy evaluations. The final section provides recommendations for a way forward.
The Benefits of Reducing Pre-existing Uncertainty
In U.S. environmental policy evaluations, benefits and costs are nearly always calculated by
estimating expected net benefits in monetary terms. Specifically, the net benefits for each
potential resolution of uncertainty are estimated and assigned probably weights. Economic
theory supports a different approach. The proper measure of a policy’s impact on social
welfare is the willingness to pay of individuals prior to the resolution of uncertainty
(Boardman et al., 2001). Economists often refer to this ex-ante calculation for measuring
welfare impacts under uncertainty as the “option price” of a policy.
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A key difference between the option price of a policy and an ex-post estimate of the
policy’s expected net benefits is that the option price will account for preferences toward
uncertainty. In other words, option prices account for risk aversion, whereas ex-post
expected net benefit calculations typically assume a risk neutral society. If a risk cannot be
eliminated by the purchase of insurance (at an actuarially fair price), then society will benefit
from a public policy that reduces the risk (Boardman et al. 2001). Clearly, insurance is not
available to protect against certain large-scale environmental risks, such as catastrophic
climate events.
A simple example may be useful. Suppose there are two potential states of the world that
are equally likely in the absence of government regulation: (1) the Lucky state, in which the
negative effects of a pollutant are relatively small and the consumption level is relatively
high; and (2) the Unlucky state, in which the negative effects of the pollutant are relatively
large and the consumption level is relatively small.
Suppose further that public policy can be enacted that removes the pre-existing
uncertainty. In this scenario, the negative effects of the pollutant are avoided, but
consumption is decreased due to the cost of the regulation (to the Safe state, at the
midpoint of Lucky and Unlucky).
Figure 1 illustrates this example for two different assumptions on risk: (1) a risk neutral
society, represented by a linear welfare function; and (2) a risk averse society, represented
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by a concave welfare function. Consumption levels are on the horizontal axis and societal
welfare (i.e. utility) levels are on the vertical axis.
Figure 1: Risk Reduction Benefits for Risk Neutral and Risk Averse Societies
Risk Neutral (RN)
Utility Function
Societal Welfare
Risk Averse (RA)
Utility Function
URN(Lucky) = URA(Lucky)
URA(Safe)
Ignored RiskReduction Benefit
URN(Safe) = EURN = EURA
URN(Unlucky) = URA(Unlucky)
Unlucky
Lucky
Safe
Consumption
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To a risk neutral society, the expected welfare in the absence of regulation is EURN, which
is the midpoint between “URN(Lucky)” and “URN(Unlucky).” This is equal to the expected
welfare with the regulation, URN(Safe). In other words, this regulation provides zero benefits
under risk neutrality.
To a risk averse society, the expected welfare in the absence of regulation is EURA. With the
regulation, expected welfare is higher, equal to URA(Safe). The benefit of the regulation to a
risk averse society is the vertical distance between EURA and URA(Safe).
Of course, the net benefits of environmental regulations in the real world will be a
combination of the changes in the expected outcome and the changes in uncertainty.
By holding constant the expected outcome, this example has shown that the effects of
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reducing uncertainty are unaccounted for under the assumption of risk neutrality. This
problem will arise for any regulation that decreases pre-existing environmental uncertainty.
Why Risk Aversion is Unaccounted for in Environmental
Policy Evaluations
Given how well-accepted risk aversion is as a preference trait, it is somewhat surprising that
risk neutrality is typically assumed in environmental policy evaluations. There are at least
two potential explanations:
1. A lack of distinction between regulations that reduce uncertainty versus regulations that
cause uncertainty;
2. The computational and theoretical difficulties of incorporating risk aversion in costbenefit analyses.
Regulations that cause uncertainty versus regulations that reduce uncertainty
There are two distinct types of uncertainty associated with most environmental regulations:
1. Baseline uncertainty, in which there is pre-existing uncertainty about environmental
outcomes, independent of (or prior to) policy choices; and
2. Effectiveness uncertainty, in which the benefits and costs of an environmental
regulation are uncertain (i.e. the regulation causes uncertainty).
For important environmental issues such as climate change, it is unknown precisely how
dangerous our current trajectory is, so there is considerable baseline uncertainty. However,
the guidelines of the U.S. government for regulatory policy analysis only contemplate
effectiveness uncertainty.
The Circular A-4 was developed by the U.S. Office of Management and Budget to provide
guidance to government agencies on how to estimate the benefits and costs of regulatory
actions (OMB 2003). The following is the lone reference in the Circular A-4 to the
appropriate assumptions related to societal risk aversion:
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It is a common practice to compare the ‘best estimates’ of both benefits and costs
with those of competing alternatives. These ‘best estimates’ are usually the average
or the expected value of benefits and costs. Emphasis on these expected values
is appropriate as long as society is ‘risk neutral’ with respect to the regulatory
alternatives. While this may not always be the case, you should in general assume
‘risk neutrality’ in your analysis (OMB 2003, p. 42, emphasis added).
This passage clearly relates to regulations with uncertain costs and benefits, and it instructs
policy evaluators to assume society is “risk neutral” with respect to such uncertainty.
No separate guidance is offered for handing baseline uncertainty. The United Kingdom
provides similar guidance to policy evaluators, referring to the benefits of reducing
the uncertainty related to a policy’s costs and benefits, with no mention of effects on
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pre-existing uncertainty.
The assumption a risk neutral society in the face of effectiveness uncertainty has support
in the economic literature. In particular, there is an extensive literature on the conditions
under which governments should behave in accordance with risk neutrality with respect
to risky public investments (i.e. regulations that cause uncertainty). Arrow and Lind (1970)
are generally credited with the key contribution, showing that the riskiness of public
investments is essentially “spread out” across members of society. If the population is
sufficiently large, not only do individual risk premiums converge to zero, but—contrary to
intuition—the sum of all risk premiums converges to zero as well. In the situations in which
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this result holds , the effects of risk aversion can safely be ignored.
However, this rationale for ignoring risk aversion when evaluating risky public investments
does not provide any basis for ignoring risk aversion in the presence of pre-existing
environmental uncertainty, when risk cannot be “spread out” across the population.
Nevertheless, separate guidance is not provided to policy evaluators for situations in which
baseline uncertainty is affected by a regulation.
The implication is that regulatory policy evaluations have mistakenly applied the guidance
for risk neutrality to all situations in which uncertainty is present, regardless of whether the
regulation causes uncertainty or reduces uncertainty.
One notable consequence of this guidance can be seen in the U.S. Government’s
estimates of the social cost of carbon, which is an estimate of the marginal social cost of an
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additional ton of carbon dioxide emissions. In its 2010 report, the government recognized
that individuals are risk averse, and states that “it is possible that regulatory policy should
include a degree of risk aversion” (U.S. Government 2010, p. 30). However, risk aversion
is unaccounted for in the estimates of the social cost of carbon, with the following
explanation: “assuming a risk-neutral representative agent is consistent with OMB’s
Circular A-4” (p. 30).
Of course, the costs and benefits of climate change policies are uncertain. However, the
major source of uncertainty is in the effects of climate change itself, such as the levels of
global temperature change and economic damages for a given emissions trajectory. This
baseline uncertainty is improperly ignored on the basis of the Circular A-4 guidance.
Incorporating just a modest level of risk aversion can vastly increase the social cost of
carbon, perhaps by a factor of four or five (see, for example, Anthoff and Tol 2009,
Ackerman et al. 2013, Kaufman 2012). If the social cost of carbon was increased to such
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an extent in the roughly 20 U.S. government rulemakings for which it was used between
March 2010 and February 2012 (Kopp et al. 2012), the estimated net benefits of these
regulations could have been vastly different, and different regulatory options may have
been selected.
Computational and Theoretical Difficulties
The omission of risk-reducing benefits has led to incomplete policy evaluations, but
there is no “easy fix” to this problem. Indeed, the various unavoidable theoretical and
computational difficulties associated with risk aversion are likely an important reason why
it is typically unaccounted for in policy evaluations.
First, when uncertainty is present, costs and benefits to a risk averse society must be
translated into measures of well-being (or “utility”). Economists commonly use concave
utility functions to represent—among other preference traits—the preference of risk averse
individuals for certainty over uncertainty.
Aside from the computational difficulties of substituting a non-linear utility function for a
linear utility function (which implicitly assumes risk neutrality), there are various theoretical
problems that come along with introducing the concept of utility. Utility functions are
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chosen primarily for their nice computational properties rather than because of any
widespread agreement that they accurately represent individual or societal preferences. It
would not be wise to make policy decisions based on a utility function with an arbitrarilyselected functional form. Various functional forms would need to be tested to ensure the
robustness of results, placing subjective judgments and computational burden in the hands
of policy evaluators.
A second difficulty is the absence of a “correct” risk aversion level. It is clear from
empirical evidence that individuals are risk averse, but there is no consensus on how much
individuals benefit from reductions in uncertainty. Risk aversion varies widely with respect
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to different individuals and different types of risk. Given this heterogeneity, a single level
of risk aversion cannot easily be chosen to represent a society. To properly account for risk
aversion in an environmental policy evaluation, a wide range of risk aversion levels would
need to be used, placing additional computational burdens on policy evaluators.
Finally, even if all individuals shared a common “risk aversion” level toward all risks, it
does not necessary follow that government regulations should be based solely on the
risk preferences of current constituents. When public policies have the potential to
affect the welfare of future generations, the risk preferences of the current generation
may imply taking large gambles and passing forward the consequences of these gambles,
but policymakers may want to shield future generations from potential injustices.
The acceptable amount of risk to place on the shoulders of future generation is a
philosophical question that would be difficult for any policy evaluation to resolve in
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an uncontroversial manner.
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A Way Forward
Economic theory supports the inclusion of risk-reduction benefits in environmental policy
evaluations. However, whether due to misstated guidance, misapplied guidance, or the
desire to avoid complication and controversy, these policy evaluations have generally used
the assumption of risk neutrality.
There is no easy solution to this problem because of the controversial assumptions required
to factor the effects of risk aversion into cost benefit analyses. However, if policy evaluators
were provided with default guidance on which they could safely rely, it would not be overly
burdensome to add risk aversion to an environmental policy evaluation.
A template for accomplishing this objective can be seen in the guidance on the discount
rates used in U.S. regulatory impact analyses. Discount rates convert future cost and
benefits into present value terms. There are considerable similarities between choosing
a “correct” discount rate and a “correct” level of risk aversion. In both cases, it is widely
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accepted that a strictly positive number is appropriate , but there is no consensus on the
precise value to use.
Despite the ongoing debate and controversy over the appropriate discount rate, it has
been recognized that some guidance is better than no guidance at all. OMB’s Circular
A-94 (1994) and Circular A-4 (2003) direct government agencies to use 3 percent and
7 percent annual discount rates in regulatory evaluations, despite weak justifications for
these precise values. Most policy evaluations have followed this discount rate guidance
without controversy.
Similar guidance could be provided for when and how to factor risk aversion into policy
evaluations. This essay does not presume to have the answers. In any case, the answers
should come from a source that can be reliably cited by government agencies and other
policy analysts. To this end, the government could convene a panel of experts with a
mandate to provide this guidance.
This expert panel would ideally undertake two tasks. First, it would describe the conditions
under which it is appropriate to quantitatively account for risk aversion in policy evaluations.
The objective of a policy evaluation should be to quantify as many costs and benefits
as possible without sacrificing an excessive amount of precision. For costs and benefits
that are not easily quantifiable, there is an inherent trade-off between completeness and
precision. Is it preferable to have a “complete” analysis that contains imprecise estimates of
risk premiums or an incomplete analysis that recognizes its bias due to the lack of estimated
risk premiums? It depends on the situation. For some regulations, the difficulties of
estimating risk premiums may imply that the best approach is to assume risk neutrality and
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qualitatively discuss the changes that may result from an assumption of risk aversion.
Second, if conditions are such that risk aversion should be factored into the analysis, the
expert panel would provide guidance on how these calculations should be undertaken.
This may include the use of social welfare functions or the calculations of option prices
or risk premiums.
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Given the regulatory proceedings forthcoming on climate change and other environmental
issues, it is more important than ever that environmental policy evaluations are conducted
based sound economic theory, so that the results can be used by policy makers to make
well informed decisions. For regulations that reduce pre-existing environmental uncertainty,
risk-reduction benefits should be taken into account.
References
Ackerman F., Stanton E. and Bueno R. (2013). Epstein-Zin Utility in DICE: Is Risk Aversion
Irrelevant to Climate Policy? Environment and Resource Economics. 56:73-84.
Anthoff, D. and R.S.J. Tol (2011). The Uncertainty about the Social Cost of Carbon: A
Decomposition Analysis Using FUND, ESRI Working Paper 404.
Arrow, K., and R. Lind. (1970). Uncertainty and the Evaluation of Public Investment
Decisions, American Economic Review, 60(3): 364-378.
Bantwal V, Kunreuther H (2000). A cat bond premium puzzle? J Psychol Financ
Market 1(1):76–91
Boardman, A.E., Greenberg, D.H., Vining, A.R., Weimer, D.L. (2001). Cost-Benefit Analysis:
Concepts and Practice, second ed. Prentice Hall, Upper Saddle River, NJ.
Halek M, Eisenhauer J (2001). Demography of risk aversion. Journal of Risk
and Insurance 68(1).
Kaufman, N (2012). The Bias of Integrated Assessment Models That Ignore Climate
Catastrophes. Climatic Change 110 (3): 575–595. doi:10.1007/s10584-011-0140-7.
King R, Plosser C, Rebelo S (1990). Production, growth and business cycles: technical
appendix. Comput Econ 20:87–116
Kopp, Robert E.; Mignone, Bryan K. (2012). The US government's social cost of carbon
estimates after their first two years: Pathways for improvement, Economics, No. 2012-15,
Economics: The Open-Access, Open-Assessment E-Journal, Vol. 6, Iss. 2012-15, pp.1-41,
doi:10.5018/economics-ejournal.ja.2012-15 , http://hdl.handle.net/10419/57823
Meyer, Donald J. and Meyer J (2005). Relative Risk Aversion: What Do We Know?" Journal
of Risk and Uncertainty 31(3):243-262.
Ogaki M (2001). Decreasing relative risk aversion and tests of risk sharing.
Econometrica 69(2).
Pindyck RS (2013). Climate Change Policy: What Do the Models Tell us?
NBER WORKING PAPER SERIES. Working Paper 19244. July 2013.
Rabin M. (2000). Risk aversion and expected-utility theory: A calibration theorem.
Econometrica, 68(5):1281-92
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US Office of Management and Budget (OMB) (2003). Circular A-4, Regulatory analysis.
HM Treasury (2011) Green Book: Appraisal and Evaluation in Central Government, 2003,
2011. Annex 5. http://greenbook.treasury.gov.uk/
US Regulatory Impact Analysis (2010). Appendix 15a. Social cost of carbon for regulatory
impact analysis, under executive order 12866.
Weitzman, M.L., 2001. Gamma Discounting. American Economic Review 91(1), 260-271.
Weitzman M (2009) On modeling and interpreting the economics of catastrophic climate
change. Rev Econ Stat 91(1):1–19
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Notes
1
Executive Orders 12866 (signed September 1993) and 13563
(signed January 2011) direct government agencies to assess all costs
and benefits of available regulatory alternatives and, if regulation is
necessary, to select regulatory approaches that maximize net benefits.
The Circular A-4 is a document that provides “best practices”
guidance to Federal agencies on the development of regulatory
analysis and aims to standardize the way benefits and costs of Federal
regulatory actions are measured and reported
(www.whitehouse.gov).
2
Note that risk aversion does affect the discount rate, which
determines the relative value of costs and benefits over time, but
this issue is separate from how uncertainty directly affects the
valuation of costs and benefits in any static timeframe, which is the
topic of this essay.
3
The risk aversion of individuals has been shown in the empirical
literature (see Mayer and Mayer, 2005) and by the existence of an
insurance industry that profits from individuals’ willingness to pay
premiums (i.e. accept lower expected values) to avoid uncertain
outcomes. Economists therefore use concave social welfare functions
when evaluating benefits and costs.
4
Note that accounting for risk aversion in this context is distinct from
the influence of risk aversion on the discount rate. It is also distinct
from the risks associated with the costs and benefits of the policy
itself; instead, it is pre-existing environmental uncertainty that is being
reduced by this hypothetical policy.
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For example, in the case of the constant elasticity of substitution (CES)
utility function, King et al. (1990) shows that as long as preferences
are time separable and geometrically discounted, a representative
agent must display a constant elasticity of intertemporal substitution
for a balanced growth path to exist. In the context of economic
analysis of climate change policies, various commenters (e.g.
Weitzman 2009, Pindyck 2013) have noted lack of justification for
the chosen functional forms of the social welfare functions.
9
Halek and Eisenhauer (2001) summarized the state of the literature
(a characterization which remains accurate today): “There is
little consensus and few generalizations to be drawn from the
existing literature regarding the magnitude of relative risk aversion,
its behavior with respect to wealth, or its differences across
demographic groups.” In addition, laboratory experiments on risk
tend to focus on small gambles, but individuals are far more risk
averse when faced with potentially catastrophic events (see Ogaki
2001, Bantwal and Kunreuther 2000). Finally, Rabin (2000) shows
that within the expected utility theory framework, the welfare
functions typically used by economics are incapability of displaying
reasonable risk preferences with respect to both small and large risks.
10
A similar debate exists in the economic literature over the appropriate
discount rate to use in welfare analyses that affect multiple
generations. Proponents of a “revealed preferences” approach
support the use of empirical data on individual preferences to
select the appropriate discount rate. In contrast, proponents of a
“normative approach” generally support the use of lower discounts
rates that implicitly value all future generation equally (for an
overview, see U.S. Government 2010).
11
In other words, neither risk neutrality (i.e. the assumption of no risk
aversion) nor a 0% annual discount rate (i.e. the assumption of no
preference to receive benefits earlier rather than later) would properly
reflect individual preferences.
12
The danger of this approach is that “supplemental qualitative
discussions” to a quantitative analysis are often disregarded in
practice. For example, the U.S. Government’s report on the social
cost of carbon (2010) includes numerous qualitative statements
implying that it may not be providing unbiased estimates, and yet the
report’s quantitative estimates of the social costs of carbon are used
by other agencies in policy evaluations and discussed by the public as
the bottom-line results of the analysis.
5The
Green Book is the United Kingdom’s official guidance for
conducting proper regulatory impact analysis, similar to the OMB
Circular A-4 in the U.S. While the Green Book appropriately notes
that risk-averse decision-makers are willing to pay for certainty
(referred to as “the cost of variability”), the formula provided for
estimating this cost of variability addresses only the uncertain costs
and benefits of the policy itself:
Fraction of income worth paying for certainty = - (Variance of net
additional income resulting from the project) / (2 x Total expected
income of those impacted by the project).
The Green Book concludes the following: “Given the size of national
income relative to the scale of most individual projects, the cost
of variability for projects that benefit the community as a whole is
usually negligible.” No supplemental guidance is provided on how to
estimate benefits for a regulation that reduces baseline uncertainty
(see HM Treasury 2011, pp. 88-89).
6
The literature has also noted many instances when this result of
Arrow and Lind (1970) does not hold. In particular, Fisher (1973)
shows that environmental externalities or irreversible outcomes
provide a basis for the inclusions of risk premiums in the evaluations
of risky public investments.
7
A revised version of this report was published in 2013, but the
methodology of the U.S. Government’s Interagency Group on the
Social Cost of Carbon was left unchanged from the 2010 report.
Only the underlying models from the literature were updated.
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Contact
For further information and questions, please contact the author:
Dr. Noah Kaufman
Senior Consultant
+1 617 927 4586
[email protected]
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