9 July 2014

Why is Aversion Unaccounted for in Environmental Policy Evaluations?

By Dr. Noah Kaufman Government regulations can reduce the associated with large environmental , such as catastrophic events caused by climate change, hydraulic fracking and The final version of this nuclear power plant meltdowns. Individuals dislike large risks—insurance companies publication appeared in earn profits because of the risk premiums that are paid to avoid risks such as sickness, Climatic Change Volume fires, floods and car wrecks—so there are considerable benefits to society associated 125, Issue 2, July 2014, with regulations that reduce or remove environmental risks. In welfare assessments, pp 127-135. The final typically use concave functions and estimate “option ” to publication is available account for risk aversion. at http://rd.springer.com/ article/10.1007/s10584-014- Nevertheless, environmental policy evaluations in the U.S. customarily disregard these 1146-8. risk-reduction benefits. Environmental regulations are increasingly influenced by cost- benefit analyses that are performed based on the guidance of the Office of Management and Budget (OMB).1 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 benefits of all potential outcomes). Unlike a rigorous economic analysis, policy evaluations that follow this OMB guidance do not account for the effects of risk aversion.2

This essay offers two potential explanations for why risk aversion is typically unaccounted for in environmental policy evaluations. First, there is an extensive public literature on conditions whereby governments should behave in accordance with risk neutrality (i.e. zero risk aversion) when evaluating public 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 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 ” of a policy.

www.nera.com 2 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 by a concave welfare function.3 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) Societal Welfare Utility Function

Risk Averse (RA) URN(Lucky) = URA(Lucky) Utility Function

URA(Safe)

Ignored Risk- Reduction Benefit

URN(Safe) = EURN = EURA

URN(Unlucky) = URA(Unlucky)

Unlucky Safe Lucky

Consumption

www.nera.com 3 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 reducing uncertainty are unaccounted for under the assumption of risk neutrality.4 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 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 cost- benefit 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:

www.nera.com 4 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 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 pre-existing uncertainty.5

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 this result holds6, 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 of carbon, which is an estimate of the marginal social cost of an additional ton of carbon dioxide emissions. In its 2010 report,7 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

www.nera.com 5 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 chosen primarily for their nice computational properties8 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 arbitrarily- selected 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 to different individuals and different types of risk.9 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 an uncontroversial manner.10

www.nera.com 6 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 accepted that a strictly positive number is appropriate11, 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 -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 qualitatively discuss the changes that may result from an assumption of risk aversion.12

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.

www.nera.com 7 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 Decisions, , 60(3): 364-378.

Bantwal V, Kunreuther H (2000). A cat bond premium puzzle? J Psychol Financ 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. 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

www.nera.com 8 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

www.nera.com 9 Notes

1 Executive Orders 12866 (signed September 1993) and 13563 8 For example, in the case of the constant of substitution (CES) (signed January 2011) direct government agencies to assess all costs utility function, King et al. (1990) shows that as long as preferences and benefits of available regulatory alternatives and, if regulation is are time separable and geometrically discounted, a representative necessary, to select regulatory approaches that maximize net benefits. agent must display a constant elasticity of intertemporal substitution The Circular A-4 is a document that provides “best practices” for a balanced growth path to exist. In the context of economic guidance to Federal agencies on the development of regulatory analysis of climate change policies, various commenters (e.g. analysis and aims to standardize the way benefits and costs of Federal Weitzman 2009, Pindyck 2013) have noted lack of justification for regulatory actions are measured and reported the chosen functional forms of the social welfare functions. (www.whitehouse.gov). 9 Halek and Eisenhauer (2001) summarized the state of the literature 2 Note that risk aversion does affect the discount rate, which (a characterization which remains accurate today): “There is determines the relative value of costs and benefits over time, but little consensus and few generalizations to be drawn from the this issue is separate from how uncertainty directly affects the existing literature regarding the magnitude of relative risk aversion, valuation of costs and benefits in any static timeframe, which is the its behavior with respect to wealth, or its differences across topic of this essay. demographic groups.” In addition, laboratory experiments on risk tend to focus on small gambles, but individuals are far more risk 3 The risk aversion of individuals has been shown in the empirical averse when faced with potentially catastrophic events (see Ogaki literature (see Mayer and Mayer, 2005) and by the existence of an 2001, Bantwal and Kunreuther 2000). Finally, Rabin (2000) shows insurance industry that profits from individuals’ willingness to pay that within the expected utility theory framework, the welfare premiums (i.e. accept lower expected values) to avoid uncertain functions typically used by economics are incapability of displaying outcomes. Economists therefore use concave social welfare functions reasonable risk preferences with respect to both small and large risks. when evaluating benefits and costs. 10 A similar debate exists in the economic literature over the appropriate 4 Note that accounting for risk aversion in this context is distinct from discount rate to use in welfare analyses that affect multiple the influence of risk aversion on the discount rate. It is also distinct generations. Proponents of a “revealed preferences” approach from the risks associated with the costs and benefits of the policy support the use of empirical data on individual preferences to itself; instead, it is pre-existing environmental uncertainty that is being select the appropriate discount rate. In contrast, proponents of a reduced by this hypothetical policy. “normative approach” generally support the use of lower discounts 5 The Green Book is the United Kingdom’s official guidance for rates that implicitly value all future generation equally (for an conducting proper regulatory impact analysis, similar to the OMB overview, see U.S. Government 2010). Circular A-4 in the U.S. While the Green Book appropriately notes 11 In other words, neither risk neutrality (i.e. the assumption of no risk that risk-averse decision-makers are willing to pay for certainty aversion) nor a 0% annual discount rate (i.e. the assumption of no (referred to as “the cost of variability”), the formula provided for preference to receive benefits earlier rather than later) would properly estimating this cost of variability addresses only the uncertain costs reflect individual preferences. and benefits of the policy itself: 12 The danger of this approach is that “supplemental qualitative Fraction of income worth paying for certainty = - ( of net discussions” to a quantitative analysis are often disregarded in additional income resulting from the project) / (2 x Total expected practice. For example, the U.S. Government’s report on the social income of those impacted by the project). cost of carbon (2010) includes numerous qualitative statements The Green Book concludes the following: “Given the size of national implying that it may not be providing unbiased estimates, and yet the income relative to the scale of most individual projects, the cost report’s quantitative estimates of the social costs of carbon are used of variability for projects that benefit the community as a whole is by other agencies in policy evaluations and discussed by the public as usually negligible.” No supplemental guidance is provided on how to the bottom-line results of the analysis. 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 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. About NERA

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Dr. Noah Kaufman Senior Consultant +1 617 927 4586 [email protected]

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