Using Risk Assessment, Benefit-Cost Analysis, and Real Options to
Implement a Precautionary Principle
Scott Farrow
U.S. General Accounting Office and Carnegie Mellon University
Prepared for the Second World Congress of Environmental
And Resource Economists
Scott Farrow
U.S. General Accounting Office
441 G. St., N.W. MS 2040
Washington, DC 20548
Contact numbers: 202-512-6669; farrows@gao.gov
Appreciation is extended to Elizabeth Casman, Hiroshi Hayakawa, Ruchika
Kumar, Benoit Morel, Eva Wong, Felicia Wu and the Precautionary Principle working
group at Carnegie Mellon. Thanks are also due Graham Davis, Elaine Faustman, Charles
Mason, Klaas van't Veld, Richard Zerbe, participants at the North Carolina State
University Workshop on New Developments in Benefits Transfer and the Association of
Environmental and Resource Economists workshop on Assessing and Managing
Environmental and Public Health Risks (this paper is a revised and updated version of
material presented at the latter conference). This work was primarily completed while
the author was at Carnegie Mellon University where funding was provided through the
Center for the Study and Improvement of Regulation. The views expressed here are those
of the author and do not necessarily reflect the views of the U.S. General Accounting
Office.
1
Abstract
Risk assessment is a growing presence in the evaluation of environmental and
public health issues. However, economist's core approach to both risk assessment and
risk management for public policy, benefit-cost analysis, often fails to transparently
evaluate uncertainty.
Concurrently, environmental advocates are proposing a new
management criteria based on a vaguely framed "Precautionary Principle". This
manuscript demonstrates how risk assessment techniques, benefit-cost analysis, and
decision-making criteria under uncertainty and irreversibility can be combined. The result
is to augment standard benefit-cost techniques and define a quantifiable "precautionary"
threshold for action compared to standard economic approaches.
An application is
provided to the Clean Air Act.
Key words: risk assessment, benefit-cost analysis, real options, Precautionary Principle.
2
I. Introduction: Risk Assessment, Benefit-Cost, and Real Options
The distinction between risk assessment and risk management is relatively well
understood in concept (President's Commission on Risk Assessment and Risk
Management [26]) even if the practical line between them tends to be blurred.
Objectively addressing uncertainty is a core task of risk assessment while value
judgements are incorporated to drive risk management. In contrast, benefit-cost analysis
serves both assessment and management (roughly positive and normative) functions as
typically practiced in economics. Benefit-cost analysis is first a structure for assessing
and aggregating the impacts of alternative actions.
Second, it is associated with
management decision criteria for choosing an "optimal" public policy action that is
variously linked to measures of net benefits. However, uncertainty is seldom considered
in detail in a benefit-cost analysis. Numerical methods to obtain statistical distributions
are infrequent (unless in an econometric application) although they are the trademark of
people working in risk assessment.
In the absence of an explicit treatment of the
uncertainty of intermediate impacts
(which are of great importance to some risk
managers) and economic outcomes, advanced methods for decision making under
uncertainty such as options analysis cannot be implemented. And yet policy problems
analyzed using benefit-cost analysis are typically rife with uncertainty. What is to be
done?
This manuscript addresses problems of both risk assessment and risk management
in the use of benefit-cost analysis for pubic policy. It first addresses the use of uncertain
information in benefit-cost assessments, and secondly demonstrates how such
information can be used to implement what has been called a Precautionary Principle for
managerial decision-making under uncertainty. The relatively mundane usefulness of
incorporating statistical distributions into benefit-cost analysis is demonstrated through
Monte-Carlo simulation and the use of a statistical type of meta-analysis. This approach
provides a risk assessment as an intermediate step and a stochastic benefit-cost analysis
3
as a final step. Model diagnostics and sensitivity analysis results are demonstrated for
controlling criteria air pollutants.
The management of risk under uncertainty is then addressed which often, though
not always, involves irreversibilities in implementation. As financial economists
consider long term capital commitments to be "irreversible" it seems that at least chronic
illness, mortality, and many ecological impacts could be considered irreversible. Though
Arrow and Fisher [1] were among the first to note that an expected value maximizer
may have a different decision rule under uncertainty and the potential for new
information, which they discussed as quasi-option value, related insights have gained
fruitful empirical ground in financial economics as the topic of real options (Dixit and
Pindyck [7]; Trigeorgis [27]; Copeland and Antikarov [5]). A large body of literature,
though with only minimum attention to externalities and public policy (Dixit [8]), now
exists for real options (an action in which a real asset such as the environment has option
like characteristics for use, non-use or other alternatives). Fisher [13] discusses some
parallels between the two related concepts. The real option theory is investigated here as
a structure for a quantitative approach to descriptive calls for a Precautionary Principle
(EU [9]) as in Principle 15 of the 1992 Rio Declaration on Environment and
Development:
“In order to protect the environment, the precautionary approach shall be widely
applied by States according to their capabilities. Where there are threats of serious
or irreversible damage, lack of full scientific certainty shall not be used as a reason
for postponing cost-effective measures to prevent environmental degradation.”
Real options, as with quasi-options, can contain an element of caution depending on
how information may arrive and in the definition of the continuing activity (Farrow and
Morel [10]). The value of the option will be identified here as the value of "precaution"
and the multiplier between benefits and costs that induces that value as a quantitative
measure of precaution1. The empirical challenge is how to operationalize the tools of
option theory in policy settings where there is a lack of market data such as that used so
extensively by financial economists.
4
This paper proceeds in Section II by demonstrating the use of risk assessment
techniques in a relatively standard benefit-cost analysis. A flexible approach to metaanalysis is incorporated that allows sampling from multiple studies. The Precautionary
Principle and a theoretical approach to its measurement through a real options analysis is
investigated in Section III. Section IV develops an empirical method to merge the risk
assessment approach of Section II with the managerial model of real options and the
Precautionary Principle from Section III. Section V concludes.
II.
Risk Assessment and Benefit-Cost Analysis
Simulation methods have been used extensively to generate distributions of risky
outcomes (Morgan and Henrion [23]; Judd [17]). There is nothing inherent in the
methods which restrict their application to bad outcomes or to non-economic dimensions.
In fact, reductions of bad outcomes typically become the benefits of environmental,
health, and safety policy. One could stop here and simply state that statistical approaches
to the characterization of risk apply equally to questions of beneficial impact and
valuation for benefit-cost analysis. However, as a necessary component of an empirical
options analysis and because of its infrequent use in applied welfare economics, this
section summarizes both an application of simulation methods to a benefit-cost analysis
of the Clean Air Act and a flexible meta analysis methodology.
FERET: A Benefit-Cost Template with Integrated Uncertainty Analysis2
FERET, the Fast Environmental Regulatory Evaluation Tool, is a template to
produce a benefit-cost and impact analysis consistent with advanced practice (Arrow, et
al., [2]) for a regulatory design to reduce air pollution or accidents. It is designed to
mimic, and to allow departures from, the larger analytical efforts of EPA to evaluate the
costs and benefits of the Clean Air Act3 (U.S. EPA [28, 29]; Farrow, et al., [11]).
FERET has several sections and databases: a health section, whose purpose is to estimate
the change in disease incidence from a change in baseline air pollutant concentration, and
an economics section, whose purpose is to value the benefits of reducing disease. In both
5
sections, quantitative databases of the research literature are provided. FERET then
estimates the health impacts, the present value of benefits, costs, net benefits and
provides access to diagnostic and reporting capabilities. Standard risk analysis software,
Crystal Ball, is used to generate simulations and statistical distributions within a broader
spreadsheet tool.
Basic Structure of FERET: Certainty
FERET is a simple benefits transfer (Desvouges, Johnson, and Banzhof [6]) net present
value model. The present value benefits are the avoided external costs. The annual
benefits of impact i, Bi, are estimated as:
Bi  yi * Vi where yi are changes in impacts (cases for health) valued at Vi while
the present value of benefits is the sum over all impacts (I) and time periods (T):
PVB  
T
t 0

I
i1
Bit (1 g)t
where PVB is the present value of benefits, g is any rate
t
(1 r)
of growth in real benefits (e.g. due to increased population growth) and r is a real
(excluding inflation) discount rate. Bt may be zero in some early years if there is a
latency period or a delay in implementation.
As a default and following EPA [28, 29], FERET uses health impacts estimated in the
epidemiology literature based on concentration response functions. These functions are
typically of the form yi  y(eX 1) where y is the health impact (cases), X is the
change in concentration of a pollutant, and  is the concentration response coefficient
(percentage change in cases per unit change in concentration). The EPA cost and benefit
studies (US EPA [28,29]) and McClellan [20] also contain discussions.
The present value costs (PVC), are typically compliance costs by industry and
any non-market costs (external costs) to consumers. These costs are context specific to
the regulatory design. Some analysts may have their own models of costs in which case
they can enter their own cost distribution directly. FERET also provides an EPA model
(PROJECT) used in courts for over a decade. Intermediate information is obtained on all
environmental and health impacts considered in the model as well as the economic endpoints of interest.
6
Basic Structure of FERET: Uncertainty
There is uncertainty over a variety of model input parameters often including the
change in concentration (X), the concentration-response function for adverse health
impacts (y), compliance costs (C), and the value of impacts (V). If there is only one
source of a distribution for each variable, the simulation procedures directly use this
information. This is the approach used for X (concentration) and C (cost) in the Clean
Air Act example to follow.
However, for y (health response) and V (valuation) there are numerous studies
that can provide input data, each with a distribution. This is the compounded problem of
benefits transfer: not only must the analyst decide if a study is applicable to the problem
at hand, but there is an entire set of studies that may be applicable. FERET allows the
user to select one or many studies for sampling. The software has a study selection
algorithm which, on each trial, first selects one study and then samples from its parameter
distribution. The process is repeated so that different studies may be selected and the
information in each study sampled. The resulting “meta” distribution takes into account
the uncertainty across all included studies.
FERET provides the EPA default list of studies (US EPA [29]) but the user can
easily "turn off” any study from the bibliography and it will not be sampled during model
simulations4. Alternatively, the user can select non-EPA studies or even add their own
studies.
The output of FERET is familiar to risk assessors.
It is the “empirical”
distribution of the variables of interest which in FERET includes health outcomes,
valuations, costs, benefits, and net present value. It is an uncertainty augmented benefitcost analysis. Of importance in this paper, the information on the mean and variance of
the annual costs and benefits will be used as model based data in the options model for
risk management developed in the following section.
7
III.
Risk Management under Irreversibility and Uncertainty:
Real Options and the Precautionary Principle
A current topic in environmental risk management is the Precautionary Principle.
To date it is more a statement of a principle for risk management than a replicable,
implementable guidance for action although the European Union [9] has released a
communication that suggests that the Principle is a vague extension of risk assessment.
Recent debates over the Precautionary Principle have existed for a decade, while even
earlier discussions about margins of safety, safety factors, and a safe minimum standard
could be viewed as precursors.
Discussed here are some of the elements of the Precautionary Principle as viewed
by various authors5. Regarding "What is the Precautionary Principle?" Weintraub [30]
suggests that it is a regime that departs from the traditional, tort-oriented approach in
which no harm is presumed to result from the activity of another until damage and
causation can be demonstrated. Advocates suggest there is a need for the Precautionary
Principle because action cannot wait for conclusive scientific evidence when inaction
could lead to potentially irreversible or large costs. There is often a tone of mistrust
toward those doing analysis and a sense that the burden of proof should be shifted from a
demonstration that some action could cause harm to a demonstration that the action will
not cause harm.
In spite of growing support for the Principle by some policy makers, scientists,
and the legal community, the Precautionary Principle has its critics. Gray [15] denies the
Principle any role in scientific research, since it’s a principle which does not rely on
scientific evidence and which should be viewed at best as an "environmental
philosophy." Economists like Pearce [24] worry that there are no proper rules for
incorporating economic trade-offs or scientifically manageable uncertainties into
precautionary guidelines. Implementing the Principle may thus incur costs when such
funds could be more efficiently elsewhere.
In practice, precautionary approaches have been adopted into international
instruments and national legislation in a confusing variety. The Precautionary Principle
came into international prominence during the 1980s, as part of a significant shift in
8
European marine environmental policy (MacGarvin [18]). Until then it had been
assumed that the North Atlantic was so vast that it would be little affected by human
exploitation and chemical contamination. In the 1960s and 70s environmental policy
treated the marine environment as a resource, whose exploitation was considered mainly
in the context of whether the levels of contamination posed a threat to human consumers.
This 'Permissive Principle' was shaken by a series of unpredicted events - the ozone hole,
a drop in fishing stocks, and contaminants such as pesticides, PCBs, and CFCs.
Under customary international law, countries have the right to regulate activities and
substances that may be harmful to human health even if no conclusive or overwhelming
evidence is available as to whether the activity actually causes harm, the precise degree
of harm or the process by which it occurs. However, the Permanent Court of International
Justice has held that a treaty provision must take precedence over a general rule of
international law (Wimbledon [31]). In a case brought before a World Trade
Organization (WTO) panel by USA and Canada against EC’s ban to import beef, which
was raised on growth hormones, from USA and Canada, the panel concluded that the
EC’s import ban was violating WTO law. They held that the Precautionary Principle
could not be used to override the explicit wording of the treaty obligations (WTO [32]).
Canonical real options and the link to the Precautionary Principle
A challenge for analysts is to consider whether standard analytical models capture
the concerns of those who advocate such a principle. The focus here is on an empirical
method to incorporate uncertainty and irreversibility into the risk management criteria for
policy analysis.
A substantial literature has developed for such conditions but its
empirical application has been infrequent (Arrow and Fisher [1]; Fisher and Hanemann
[12]; Coggins and Ramezani [4]). In contrast, a second substantial literature in finance
(Merton [21]; Hull [16]) and with respect to real assets (Dixit and Pindyck [7], Trigeorgis
[27]) has emerged with a strong empirical as well as theoretical orientation. In a two
period model, such dimensions have also been shown to be a component of precaution
although other elements may exist depending on individual preferences (Gollier et al.
[14]).
9
Here we set out what has become a canonical continuous time real options model
to determine the threshold for action in the presence of uncertainty, irreversibility, and
delayability. This structures a problem in which empirical estimation of policy issues is
likely to rely on uncertainty augmented benefit-cost analysis as described in the previous
section.
In contrast to the standard benefit-cost prescription that an action be taken when
the net benefits or expected net benefits are positive, the threshold in a real options
approach can differ significantly. That difference is investigated here and identified as a
quantifiable measure of precaution.
Define the following terms for a canonical model (Dixit and Pindyck [7]) as:
Irreversible cost: I
Discount rate: r
Stochastic present value benefit of the action (benefit net of reversible
costs), represented by Geometric Brownian motion with drift
dV = Vdt + Vdz
where dz is the increment of a weiner process,  (> 0, <r) is a drift
parameter and  is the volatility of the process
The risk management problem is framed as one of expected value optimization:
when to optimally stop the existing (continuing) action and undertake the action with
present value, V. The existing action might be polluting or providing a given level of
safety. The proposed action might be a regulation that incurs irreversible capital costs or
health costs of I. A solution is obtained here through stochastic dynamic programming6.
The solution for the maximum value of continuing the current activity, the option value
F(V), is a function of the benefits of the new activity. The problem is to find a boundary
(stopping) value V* where it is optimal to exit the continuation activity (status quo) as
defined by the Bellman equation for the canonical model that maximizes expectations (E)
such that :
Ft (Vt )  max E (Vt  I )e  rt
s.t. dV  Vdt  Vdz
10
The solution is now well known such that the risk management action is to be
taken if the observed value of the project, Vt, passes a decision threshold, V*:
V* 

 1
I where

 1
  1
(1)
In equation 1,  is obtained from the positive root of the quadratic equation with
parameters , , and r (Dixit and Pindyck [7], pp. 140-144) . Of importance to this paper
is that the option value multiplier,  defined as /-1, is larger than one (unless there is
no uncertainty in which case it equals 1). This is the usual result for investment with
irreversibility, delayability and uncertainty.7 It can be shown that the multiplier increases
with uncertainty, /> 0. In other words, if the volatility of the benefit increases, then
the multiplier increases and the project must pass a higher threshold to take action.
At the optimal time of making a decision, a boundary condition defines the value
of the option as the difference between the value of the project and the irreversible cost.
The value of the option to delay the new activity (continuing the old activity) becomes an
added cost that the decision must bear and can be calculated as a function of the value of
the project as:
F(V)=AV
where "A" is a parameter determined from the boundary conditions and parameters of the
problem.
Interpretation as an analytical Precautionary Principle
How might the above risk management threshold for action, V*, be interpreted as
an analytical approach to a “Precautionary Principle?” First, the decision threshold in
this canonical model is more cautious than that of standard economic criteria where V*
need merely equal I. The decision-maker in the canonical case will delay taking action
until the benefits significantly exceed the costs with an amount of precaution defined by
11
 –1. Through this revised rule, the decision-maker takes into account the irreversible
aspect of the cost and the possibility that the currently observed value of the project may
be anomalously positive.
As the degree of precaution increases with increasing
uncertainty, it seems to follow the ad-hoc concerns of Precautionary Principle advocates-that greater caution be exercised with larger uncertainty and when irreversibility is
present. The degree of precaution thus becomes an empirical question investigated in the
next section.
However, several issues exist in the use of the real options approach to economics
based policy analysis. First, there is concern for externalities in a social setting compared
to a private investment setting. While this has been little discussed in the real options
literature, (e.g. Dixit [8]), in general the benefit and cost terms can be suitably redefined
to include social benefits and costs. Second, among other modeling concerns is the fact
that the irreversible costs may be stochastic as well as the benefits. Dixit and Pindyck
([7]; also Morel, Farrow, Wu, and Casman [22]) solve a model in which the solution is
homogenous of degree 1 in the benefits and costs. The result is that the canonical model
becomes even closer to a benefit-cost terminology as the benefit-cost ratio must exceed
the (gross) precautionary multiplier , (V/I)> (V/I)*= , to take action.
Finally, there is an interesting ambiguity in the risk management decision rule
depending on which party to the decision has the continuation right. In environmental
policy this may often be problematic as industry may view itself as holding a right to
continue to pollute while environmentalists may view themselves as holding a right to a
continued level of environmental services. While the structure of the decision rule
remains the same, the role of the variables and the size of the multiplier changes (Farrow
and Morel [10].) The legal or perceptual framing of the problem matters between the
industrialist and the environmentalist. One could imagine society deciding who has the
right to the continuation activity, such as emitting greenhouse gases or environmental
services. Until such a time, each stakeholder is likely to view their activity as having the
right to continue. The result is a Precautionary Principle whose applications are
dramatically different as the role of benefits and costs are reversed and the precautionary
multiplier is not independent of this reversal. These results demonstrate what has been
termed the "hysteresis" phenomenon in investment. In the standard investment context,
12
the decision threshold differs whether one is exiting or entering the industry because the
continuation activity differs. New firms are slower to enter the industry and old firms are
slower to exit in the presence of uncertainty and irreversibility (Mason [19].) Here that
difference between "enter" and "exit" has been assigned to stakeholders who have
different continuation rights in environmental services, such as the assimilation of
greenhouse gases or to provide a level of environmental services. The form of equation 1
continues to hold, but the "precaution" is taken with respect to whomever has the
continuation right.8 In the numerical example to follow, the decision criteria will be
investigated from both the "industrialist" and "environmentalist" perspective.
IV Implementing a Public Policy Real Options Analysis:
The Case of the Clean Air Act
This sections demonstrates the simulation and real option methods discussed in
sections II and III to empirically assess whether the anticipated impact of the Clean Air
Act meets an analytically based Precautionary Principle for regulating pollution.
Data
The FERET model discussed in Section II is calibrated to EPA’s data in the year
2010 of the Clean Air Act for the annualized benefits, costs, and discount rate (5 percent).
Although the EPA model is not framed as being dynamic, the benefits of the act are
projected here to grow at the rate of population growth, one percent per year ( of one
percent). This is because the benefits are driven by the value of premature deaths
averted. As this number can be viewed as the product of a geometric Brownian motion
process (population growth) and two random variables (proportion saved and value per
life saved), it is itself a geometric Brownian motion process. The real cost of control is
projected not to change. Table I presents the mean and standard deviations from the
FERET model of the national impact of the Clean Air Act in the year 20109.
[Insert Table I about here]
13
On first inspection, the data in Table I indicate the economic desirability of the
Clean Air Act (expected benefits minus costs are positive) under standard criteria10. The
variances appear large, particularly for the benefits.
Would a different decision be
reached using a real options Precautionary Principle from either an industrialist's or an
environmentalist’s perspective? The option decision from the industrialist’s perspective
is whether to delay implementation of controls due to uncertainty about the benefits of
pollution control and the irreversible costs of control. The option decision from the
environmentalist’s perspective is whether to delay the release of pollution due to
uncertainty about control costs avoided and the irreversible public health cost (Farrow
and Morel [10].) The definitions of V and I change in each case and are discussed below
in connection with Table II.
In finance or other applications, data may be available from observed activity. In
the context of policy oriented benefit-cost analysis, the data are likely to be generated by
a model, possibly informed by some observational data. In the case at hand, estimation
of Equation 1 requires values for V, I, r, , and 2. The values of V, I, , and r are
available immediately by construction11. The empirical challenge is the estimate of 2,
the instantaneous variance of the rate of change of the benefits.
Estimation of the instantaneous variance or volatility from static data has been an
issue in the finance literature (Campbell, Lo, and MacKinley [3]) in which the static
variance has sometimes been substituted incorrectly for the variance of the diffusion
process. It can be shown that while dV and V are lognormally distributed, the logarithm
of V and dlnV are normally distributed (Dixit and Pindyck [7] p. 81). In particular, dlnV
yields a variance stabilizing transformation (see also Campbell, Lo, and Mackinley [3] p.
362) as in equation 2.
1
d ln V  (   2 )dt  dz
2
(2)
The implication is that the sample standard deviation of dlnV (for a unit interval
of time) provides a maximum likelihood estimator of the volatility12.
14
An important complication is introduced when it is recognized that error exists in
the measurement of the dynamic process. Results from Childs, Ott and Riddiough (4A)
indicate that when the noisy measurement process is mean reverting, then the revealed
variance is the appropriate expected value estimator, although errors can of course be
made compared to knowing the true value13.
The FERET model, augmented with an estimated value of the drift parameter, ,
is an example of how model based values can be used to generate pseudo-data values for
Vt that can be transformed to compute dlnV and the sample variance of that time series.
Table II reports the results of using this method combined with the earlier data for V, I, r,
and  to compute the Precautionary multiplier of Equation 1 for the prospective
evaluation of the Clean Air Act.
[Insert Table II about here]
The results in Table II indicate that the EPA analysis of the future costs and
benefits of the Clean Air Act not only passes a standard benefit cost test for risk
management, but it also passes a Precautionary Principle based risk management test
regardless of who has the continuation right--environmentalists or industrialists, although
with less confidence from the industrialist’s perspective.
Rows one and two, the variable definitions and thresholds, identify several
different real option models depending on who has continuation rights, the industrialists
to emit pollution or environmentalists to a level of environmental services. Further
complexity is included in column 4 where both V and I, in the general context, are
stochastic. Row three presents the value of the precautionary multiplier for each case.
The multipliers range from 1.54 to 4.20 depending on which uncertain variable(s) is used
in the computation. Row 4 uses the expected value of the appropriate variables to test the
precautionary modified benefit-cost threshold. In each case the threshold for action is
exceeded and the risk management decision according to this framework is to control the
emissions. However, there is nothing in the theory to indicate what happens when repeat
15
observations are available for a single time period. In fact, the whole distribution of
outcomes are available with some observations exceeding the threshold and some not
exceeding. It is straightforward to define a null hypothesis of continuing with the status
quo (the continuation activity) and to ask, "What is the probability that the hypothesis
fails?" This form of the hypothesis test is consistent with Precautionary Principle
advocates suggesting that the usual "null hypothesis" be reversed to test against a null of
not allowing a risky activity. Row five formalizes the null hypothesis and reports the
cumulative probability that the null is not exceeded (the complement is the probability
the null is exceeded.) A low value indicates there is little probability that the null is
accepted; i.e. a high probability that the null is rejected14. In that case the continuation
activity is stopped and the proposed activity is started. A high value indicates failure to
reject the null hypothesis.
The last two rows summarize the results of the precautionary test.
Environmentalists, in columns 3 and 4, strongly fail to reject the null and so do not allow
further emissions beyond those allowed in the Clean Air Act. Industrialists, in column 2,
are asking a different question (see row 1) such that their relatively small chance of
accepting the null hypothesis leads to taking the action of controlling pollution. Both
sides are in agreement (although at different levels of confidence.)
These results demonstrate an implementable path from the integration of
uncertainty into benefit-cost analysis through to the empirical parameterization of a
formalized model of precaution based on a real options analysis. A model has been used
in place of observed data to parameterize the risk management threshold for a
precautionary analysis.
Incorporating Science and Model uncertainty
While an important part of uncertainty can be captured in the parameter
uncertainty of a model, another important part is not yet addressed, that of model
uncertainty. The results above assume that the model is a true representation of the
world. Especially for policy issues, there is likely to be debate about such a
representation. The software used here, FERET, provides at least one way to investigate
model uncertainty. Using FERET’s capability to allow alternative studies to be selected
16
and thereby generate a different meta analysis, the FERET model was exercised using
only short term studies for the link between particulate emissions and mortality15. Some
of the reason for this can be investigated by looking at Figures 1 and 2. They each order
the studies available in FERET in order of publication. For the dose-response functions,
there are clearly two separate classes: short term and long term studies. While the short
term results appear relatively stable over time, such a conclusion is less obvious for the
few long term studies, which are based on different populations. Figure 2, showing the
time arrival of information on the value of a statistical life also shows very large
variations (note that some "runs" are due to variations of the same study by a common
author.)
[Insert Figures 1 and 2 about here.]
As an example of model (and parameter) sensitivity, FERET was exercised using
only the short-term dose-response functions16. The results, when substituted into the
precautionary benefit-cost framework are presented in Table III.
[Insert Table III about here.]
The results in Table III indicate the importance of model uncertainty as well as parameter
uncertainty. In contrast to results in Table II, here the results are mixed with the
industrialist’s model rejecting the control of emissions (ie. accept allowing emissions) but
the environmentalist’s rejecting the release of additional pollution as indicated in the last
two rows17. This is an example of the importance of who has the continuation rights and
of model, as opposed to simply parameter, uncertainty.
V. Conclusions and Further Research
This paper focuses on an implementable path from the risk based augmentation of
benefit-cost analysis through to the empirical implementation of a Precautionary
Principle for risk management that incorporates uncertainty and irreversibility.
17
Numerous issues remain for both conceptual and empirical research. Among them are: 1)
consideration of other aspects of flexibility that yield option values, such as adaptive
regulation, 2) alternative estimators for the volatility parameter including stochastic
volatility, 3) investigating alternative data sources such as those involving perceptions, 4)
integrating a Bayesian approach to updating the state of knowledge at any particular time,
and 5) the investigation of the empirical application of third derivative or related
precautionary models.
In conclusion, this paper demonstrates that the risk assessment and risk
management paradigm can be applied to an extended form of benefit-cost analysis. The
tools of uncertainty analysis can enhance standard benefit-cost as demonstrated for a
model of the benefits and costs of the Clean Air Act. Additionally, debate about a
Precautionary Principle for risk management can often be cast as a risk management
choice to optimize the timing of action when uncertainty and irreversibility exist. The
results of this framing can be implemented with statistical information from an
uncertainty augmented benefit-cost assessment. When applied to EPA’s analysis of the
Clean Air Act, the Act passes a Precautionary test for either industrialist's or
environmentalist's although at a rather weak level if the industrialist is viewed as having
the continuation rights. The degree of precaution estimated for this problem is roughly
consistent with that represented as typical in the private investment literature (Dixit and
Pindyck [7]; Copeland and Antikarov [5]).
The augmentation of a benefit-cost
assessment to incorporate uncertainty provides an empirical path to risk management that
allows the practical implementation of a Precautionary Principle.
Such an
implementation can substantially alter what are considered the default criteria for action
in a benefit-cost analysis.
18
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19
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(ed.), Resources for the Future Press( 2002).
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Precautionary Principle T. O’Riordan and J. Cameron (eds.), Cameron May,
London (1994).
20
25. R. Pindyck, Irreversibilities and the Timing of Environmental Policy, Resource
and Energy Economics 22, 233-259 (2000).
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Commission
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Risk
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and
Risk
Management, Risk Assessment and Risk Management in Regulatory Decision
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Allocation, MIT Press, Cambridge (1996).
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Air and Radiation, Washington, D.C. (1997).
29. US EPA, The Benefits and Costs of the Clean Air Act, 1990 to 2010, Office of
Air and Radiation, EPA-410-R-99-001, Washington, D.C. (1999).
30. B. Weintraub, Science, International Environmental Regulation, and the
Precautionary Principle: Setting Standards and Defining Terms N.Y.U.
Environmental Law Journal, (1)173-178 (1992).
31. Wimbledon P.C.I.J. Rep., Ser. a, No. 1, (1923)
32. WTO Panel Report No. WT/DS26/R/USA (18 August) at page 202 (1997).
21
Table I: Mean and Variance of Clean Air Act Forecasts
Year
2010
Mean:
Benefit
(Damages
Avoided)
1.10*1011
(110 billion)
Variance:
Benefit
1.43*1021
22
Mean:
MitigationCost
2.70*1010
(27 billion)
Variance:
Cost
4.12*1018
Table II: Precautionary benefit-cost analysis: EPA base case
Row definitions
(dollars in billions)
Management Threshold
(Yes, act if true;
otherwise, no)
Empirical Precautionary
Multiplier
Test Value using mean
(adjusting for present value,
see endnote. 9)
Probability of null
(continuing the status
quo)
Result
Industry
Should Pollution be
controlled?
V=D Damages avoided
through pollution control
I=C Cost of control
Only D stochastic
D>D*=C
Environmentalists (A)
Should Emissions be
allowed?
V=C cost of control
(mitigation costs avoided)
I=D Environmental
damages
Only C stochastic
C>C*=AD
Environmentalists (B)
Should Emissions be
allowed?
V=C cost of control
(mitigation costs avoided)
I=D Environmental
damages
Both D and C stochastic18
(C/D)>(C/D)*= B
4.20
1.54
3.76
110>4.20*.8*27
110>91
27<1.54*1.25*110
27<212
(27/110)<3.76*1.25
.24<4.70
Ho: D-C<0
P(D-C<0)=.31
Ho: C-AD<0
P(C-AD<0)=0.99
Ho: (C/D)< B
P((C/D)< B)=1.00
Yes, control emissions
No, do not allow
emissions (i.e. control)
No, do not allow
emissions (i.e. control)
(A): Uncertainty only in the benefits; (B): Uncertainty in both the benefits and the costs
23
Table III: Precautionary Benefit-Cost Analysis: Short Term Mortality Only
Row definitions
(dollars in billions)
Management Threshold
(Yes, act if true;
otherwise, no)
Empirical Precautionary
Multiplier
Test Value using mean
(adjusting for present value,
see ftn. 11)
Prob of null (continuing
status quo)
Result
Industry
Should Pollution be
controlled?
V=D Damages avoided
through pollution control
I=C Cost of control
Only D stochastic
D>D*=C
Environmentalists (A)
Should Emissions be
allowed?
V=C Cost of control
(mitigation cost avoided)
I=D Environmental
damages
Only C stochastic
C>C*=AD
Environmentalists (B)
Should Emissions be
allowed?
V=C Cost of control
(mitigation cost avoided)
I=D Environmental
damages
Both D and C stochastic
(C/D)>(C/D)*= B
18.31
1.54
15.10
29<18.3*.8*27
29<395
27<1.54*1.25*29
27<58
(27/29)<15.10*1.25
.93<18.88
Ho: D-C<0
P(D-C<0)=1.00
No, do not control
emissions (i.e. allow
emissions)
Ho: C-AD<0
P(C-AD<0)=.89
No, do not allow
emissions
(i.e. control emissions)
Ho: (C/D)< B
P((C/D)< B)=1.00
No, do not allow
emissions
(i.e. control emissions)
(A): Uncertainty only in the benefits; (B): Uncertainty in both the benefits and the costs
24
Figure 1
Concentration-Response Parameter: Ordered by Date of Study
0.025
0.02
Long Term
0.015
0.01
Study used by
0.005
Short term
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Lines cover mean, plus and minus 2 standard deviations
-0.005
25
15
16
17
18
19
20
21
22
Figure 2
Value of a Statistical Life: Studies from 1972 to 1992
20000000
15000000
1990 Dollars
10000000
EPA Mean
5000000
0
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67
Lines cover mean, plus and minus
2 standard deviations or range
-5000000
Studies ordered by Publication Date
26
1
There is a literature in finance where "prudence" is related to the ratio of the third derivative of the utility
function to the second (see for instance, Gollier, et al. [14]) as well as cautionary actions due to
irreversibility.
2
This section is based on Farrow, Ponce, Wong, et al. [11].
3
FERET is presumably similar to but more aggregate than the consultant's model that underlies EPA
reports [28, 29].
4
The results of assumptions different from that of the EPA are reported in Farrow, et al. [11].
5
The history of the Precautionary Principle is based on work by Ruchika Kumar.
6
Private sector applications often focus on risk neutral applications based on an ability to hedge
investments. It is not clear that such opportunities are available in a policy setting and so the optimization
approach is used here (see Coggins and Ramezani [4], footnote 12).
7
Alternatively, other stochastic forms in place of geometric Brownian motion, such as mean reversion, can
also lead to positive option value.
8
This is a different issue than that of sunk “benefits” as investigated by Pindyck [25] where the “sunk”
nature of the benefits refers to the present value of a sequence of benefits that are committed to (or
foregone) by an action today.
9
As these values are for a year, the present value for the assumed regulatory action of infinite duration
adjusts the annual values by an annuity factor, 1/(discount rate –growth rate), where the denominator is the
net discount rate. In terms of the decision rule of equation of Equation 1, the Precautionary multiplier is
itself multiplied by the appropriate ratio. If the growth rates of V and I are the same, there is no
adjustment.
10
The entire statistical distribution is available as output in place of the more frequent practice of
identifying the mean, and a high and low value, among which policy users may be tempted to infer a
uniform distribution.
11
EPA used a 5 percent real discount rate which is used for r although other values can be investigated
parametrically while  is the growth rate of the benefits, modeled as the rate of population growth. While
not investigated here, there appear to be interesting possibilities to elicit perceptions of key data, such as the
parameters of the stochastic equation for benefits. Different stakeholders may perceive the dynamics to be
different and so the degree of precaution can change with the data being used. Note also endnote 9.
12
Copeland and Antikarov [5] suggest a different estimator involving two adjacent time periods without
investigating its statistical properties.
13
As Childs, Ott, and Riddiough [4A] investigate, this opens up the issue of deliberate investment in
information to reduce the measurement error in the revealed variance.
14
The probabilities are based on a normal distribution and a second order approximation to the expected
value and variance for the third, ratio, test.
15
These studies were reviewed by the EPA and considered in earlier drafts but in the final report, only a
single long term mortality study was used based on a advisory committee recommendation.
16
As reported in Farrow, et al. [11], there is no significant difference when contingent valuation studies are
dropped from the set of valuation studies in a parallel manner to focusing on health studies.
17
Note that incorporating multiple models has substantially increased the volatility (measured by the
variance of dlnV).
18
The formula for the parameters change somewhat, see Farrow and Morel [10].
27