Chapter 13 Irreversibility risk and uncertainty

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Chapter 13 Irreversibility risk and uncertainty
13.1 Individual decision making in the face of
risk 13.2 Option price and option value 13.3 Risk
and irreversibility 13.4 Environmental
cost-benefit analysis revisited 13.5 Decision
theory choices under uncertainty 13.6 A safe
minimum standard of conservation
In this chapter you will learn about the
difference between risk and uncertainty find out
how risk affects environmental decision making
and have the concepts of option value and option
price explained see how irreversibility affects
environmental decision making and learn about
quasi-option value consider decision making in
the face of uncertainty be introduced to the safe
minimum standard and the precautionary
principle learn how environmental performance
bonds could work
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Risk and uncertainty
Risk where all possible consequences of a
decision can be completely enumerated and
probabilities assigned to each possible state of
the world, state of nature, state Uncertainty
where where all possible consequences of a
decision can be enumerated, but probabilities
cannot be assigned Radical uncertainty - where
all possible consequences of a decision cannot be
enumerated Risk/uncertainty distinction not
always made in economics Lack of objective
probabilities (gambling, insurance) sometimes
dealt with by assigning subjective
probabilities In many environmental contexts,
probabilities are assigned on the basis of
modelling urban air pollution, nuclear
accidents The climate change problem exemplifies
radical uncertainty
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The St Petersburg paradox
A fair coin will be tossed repeatedly until it
lands tail up. If it falls head up at the first
toss, the gambler gets 1. If it falls head up at
the second toss, the gambler gets 2, at the
third toss 4, at the fourth 8, and so on.
Tossing continues until the coin falls tail up.
How much would somebody be willing to pay for
such a gamble? The answer might appear to be an
infinite amount because the expected monetary
value of the gamble is infinite. The expected
value is the sum of the probability-weighted
possible outcomes, which in this case is the
infinite series which has an infinite sum.
That anybody would be prepared to pay a very
large amount of money for such a gamble violates
everyday experience, and the example is known as
the Bernoulli, or St Petersburg, paradox. The
paradox can be resolved by assuming that
individuals assess gambles in terms of expected
utility, rather than expected monetary value, and
that the utility function exhibits diminishing
marginal utility. The relevant outcome is then
the infinite series which has a finite sum, so
long as there is some upper limit to U, which is
what diminishing marginal utility implies. In
economics, the basic approach to the analysis of
individual behaviour in any kind of risky
situation is to assume the maximisation of
expected utility and diminishing marginal
utility.
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Basic concepts for risk analysis 1
Expected value Expected utility Risk neutrality,
aversion, preference Certainty equivalence Cost
of risk bearing
The expected value of gamble with income outcomes
Y1 and Y2 probabilities p1 and p2 is
(13.1)
The expected utility of the gamble is
(13.2)
The certainty equivalent of the gamble is the
value for Y that solves
The cost of risk bearing is the difference
between the expected value of the gamble and its
certainty equivalent
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Basic concepts for risk analysis 2
For U Ya, 0ltalt1, expected utility is
(13.3)
and the certainty equivalent is the solution for
Y in
(13.4)
Y is the expected value of the gamble Y is the
certainty equivalent of the gamble For UYa,
0ltalt1, Y lt Y This individual is risk averse
and CORB Y - Y (13.5) For a 1, get
risk neutrality For risk preference arc ADEB
would lie below straight line ACB, with ?U/?Y gt 0
and ?2U/?Y2 gt 0
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Option price and option value 1
Consider an individual and a national park
wilderness area.
A available, the park is open N the park is
closed U(A) utility for income YA, park open and
wants to visit U(N) utility for income YA, park
closed and wants to visit. p1 probability of
N, 1-p1 of A NCA as p1 varies
Y is the expected value of the outcome Y is
the certainty equivalent
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Option price and option value 2
YA Y is the expected value of the
individuals compensating surplus, ECS. YA Y
is option price, OP, the maximum that the
individual would be willing to pay for an option
that guaranteed access to an open park. For
Figure 13.2 U function, risk aversion, Y gt Y
has OP gt ECS. OP ECS OV (13.6) with
OV, option value, positive. With risk neutrality,
NCA and arc NA coincide and OV would be zero.
Option value is a risk aversion premium ECS
understates the benefit of keeping the park open
as risk averse individuals would be willing to
pay a premium to avoid risk
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Option price and option value 3
Risk also attaches to whether the individual
wants to visit The weather determines whether or
not the individual wants to visit on a given
weekend fine wants to go, not otherwise. With
park open for free WTP for entry on a fine
weekend is 10 Probability of fine weather
0.5 ECS 5. Individual told park might be
closed next weekend, and offered ticket
guaranteeing access. With no risk aversion,
ticket is worth ECS, 5. If the risk averse
individual, in order to avoid risk of wanting to
go but not being able to get in, is WTP 6 then
option price is 6 and option value is 1.
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Risk and irreversibility
For a risk averse individual, option price
exceeds expected compensating surplus by option
value. If social decision making adopts consumer
sovereignty, given observed actual risk aversion,
option price should be used in ECBA. With
respect to wilderness development this implies
that the level of net development benefits
required to justify development needs to be
greater than in a world where the future is
certain. There are arguments that work in the
same direction require larger net development
benefits to justify development that do not
require the risk aversion assumption. These use
imperfect knowledge of the future and
irreversibility. Wilderness development ( also
nuclear power ) can reasonably be regarded as
irreversible, given the timescales typically
involved in any regeneration. The decision not to
develop is reversible.
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Identification of maximum net benefit
A is flow of wilderness services, decreasing with
extent of development. Costs and benefits are
functions of A A - wilderness service flow that
corresponds to allocative efficiency A can be
represented as MC(A) MB(A) Maximum NB(A) MNB(A)
0
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Irreversibility future known
1 is now. 2 is the future Future net benefits in
present value terms Following Krutilla-Fisher
arguments, future MNB2 higher than MNB1 for given
A Without irreversibility get A2NI gt A1NI With
irreversibility A2 cannot be larger than A1
Myopia would mean A1NI and A2 It means period 1
gain abc, period 2 loss edhi. Taking account of
irreversibility would mean A1I and A2I ab
de. Cost of irreversibility in period 1 is
abc Cost of irreversibility in period 2 is def
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Irreversibility in a risky world
At start of period 1 can assign probabilities p
to MNB21 and q (1 p) to MNB22. Working with
the expected value for period 2 leads to A1IR and
A2IR Adding risk to irreversibility leads to
lower A more development than irreversibility
alone But, to less development than if
irreversibility were ignored.
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Quasi-option value 1
Where there is the prospect of improved
information the expected benefits of an
irreversible decision should be adjusted to
reflect the loss of options that it entails
Arrow and Fisher Even if the decision maker is
risk-neutral The size of the adjustment is
quasi-option value All or nothing development to
simplify. Decision to be taken at start of period
1 when period 1 conditions fully known and period
2 outcomes listed and probabilities attached. At
the end of period 1, complete knowledge about
period 2 will become available The decision at
the start of period 1 is whether to permit
development
Table 13.1 Two period development/preservation
options
D development P preservation Ri return to
option i Bpt preservation benefits Bdt
development benefits Cdt development
costs period 2 costs and benefits as present
values
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Quasi-option value 2
The return to proceeding immediately with
development is
(13.20)
The return to the decision to preserve at the
start of period 1 is
(13.21)
Suppose for moment that decision maker had
complete knowledge at start of period 1. Decision
would be to develop if RdgtRp, Rd Rpgt0, which
from 13.20 and 13.21 is
(13.22)
which can be written
(13.23)
with N1 (Bd1 Cd1) Bp1, that which would
actually be known at the start of period 1 The
other terms in (13.23) could not be known at the
start of period 1, so it is not an operational
decision rule. But, by assumption the decision
maker does at the start of period 1 know the
possible outcomes for Bd2, Bp2 and (Bd2 Cd2)
and can attach probabilities. Question - ? use
the rule develop at start of period 1 if
(13.24)
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Quasi-option value 3
Answer no, using this rule would ignore the
fact that full information will become available
at the start of period 2. The decision maker does
not have full information at the start of period
1, but she does know the possibilities and
probabilities. The proper decision rule is go
ahead with development at the start of period 1 if
(13.25)
Whereas in 13.24 the decision maker uses the
maximum of of the expected values of period 2
preservation and development benefits, in 13.25
she uses the expectation of the maximum of period
2 preservation benefits and net development
benefits. The left hand side of 13.25 will be
larger than the left hand side of 13.24, so the
former, ie 13.25, is a harder test to pass at the
start of period 1. The difference between the
left hand sides of 13.25 and 13.24 is
quasi-option value. Quasi-option value is the
amount by which a net benefit assessment which
simply replaces outcomes by their expectations
should be reduced, given irreversibility, to
reflect the pay-off to keeping options open by
not developing until more information about
future conditions is available.
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Quasi-option value a numerical example
Two possible period 2 situations, A and B, are
differentiated only by what preservation benefits
in the future will turnout to be. For A and B,
(Bd2 Cd2) 6 For A Bp2 10, for B Bp2 5 pA
pB 0.5 Then, for 13.24 the third term on the
lhs is. For 13.25 we have two possible
outcomes
Hence
so the development gets the go-ahead if
(13.26)
and following this decision rule, the development
gets the go-ahead if
(13.27)
Suppose N1 EBd2 7.75. Then, using
13.24/13.26 development would be decided on at
the start of period 1, while using 13.25/13.27
the decision would be to preserve in period 1.
The test based on 13.25 is harder to pass than
the 13.24-based test. The 13.25 test adds a
premium to the 13.24 test Quasi-option value
which is 0.5 here.
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Quasi-option value 4
Positive quasi-option value is a general result
Arrow and Fisher 1974 If, as in the numerical
example EBp2 gt E(Bd2 Cd2) then 13.24
becomes
(13.28)
Now consider maxBp2, (Bd2 Cd2) from 13.26,
which is either Bp2 or a larger number.So long as
decision maker entertains the possibility that
(Bd2 Cd2) gt Bp2, EmaxBp2, (Bd2 Cd2) will
be greater than EBp2 and 13.25 which is
will be a harder test to pass than 13.28, with

where QOV stands for Quasi-option value
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Environmental cost-benefit analysis revisited 1
How should ECBA take account of risk? For risk
neutrality instead of
use
(13.29)
However, individuals are risk averse and if this
is to be reflected in ECBA, it should use
(13.30)
for the test, where CORBt is the cost of risk
bearing at time t.
It is sometimes suggested that risk can be dealt
with by using expected values and an a higher
discount rate
(13.31)
where b is the risk premium. This implies that
the cost of risk bearing is decreasing
exponentially with time
which is not generally the case. CORBt should be
estimated over the project lifetime and used as
in 13.30.
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Environmental cost-benefit analysis revisited 2
Environmental services are typically public
goods, so that the risk spreading argument cannot
be used to exclude consideration of CORBt. ECBA
that does not ignore risk should use either13.30
with EB(P)t replaced by ECSt and CORBt
replaced by OVt, that is
(13.32)
or replace both EB(P)t and CORBt with OPt and
use
(13.33)
where CS is compensating surplus, OV is option
value, and OP is option price. Putting numbers to
option values and quasi-option values is
difficult. Often judgemental allowance is made
and sensitivity analysis conducted.
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Decision theory choices under uncertainty 1
A game against nature
Table 13.2 A pay-off matrix
Two strategies A - Preservation B -
Development Three states of nature C High
Preservation Benefit Low return to mine D
Intermediate Preservation and
development E Low Preservation Benefit
High return to development
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Decision theory choices under uncertainty 2
Maximin - select the strategy with the least-bad
worst outcome is A Maximax select the best of
the best outcomes is B Minimax regret form
the regret matrix with entries that are the
difference between the actual pay-off and what it
would have been under the best strategy for the
given state of nature minimax on regret by
selecting for the lowest of the largest regret -
outcome is B Subjective probability assignment
on basis of principle of insufficient reason
assign equal probabilities to each outcome and
select for largest expected value pay-off
outcome is A for 60 (B is 58.33)
Table 13.2 A pay-off matrix
Table 13.3 A regret matrix
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A safe minimum standard of conservation
Table 13.4 A regret matrix for the possibility of
species extinction
Radical uncertainty cannot list all possible
outcomes If mine goes ahead, possibly unique,
plant population will be destroyed. Project
includes attempted re-establishment of plant
population at new location. With no previous
experience. No way of assigning probability of
success to possible prevention of species
extinction. F state of nature favourable,
relocation successful U state of nature
unfavourable, relocation unsuccessful A - do not
develop B develop
z is an unknown number. Safe minimum standard -
use minimax regret assuming z large enough to
make A the right strategy. Because species
extinction involves an irreversible reduction in
the stock of potentially useful resources, of
unknown future value. There are two kinds of
ignorance Regarding future preferences, needs
and technologies About the characteristics of
existing species as they relate to future
circumstances Presume z is large enough to make A
do not develop the correct strategy with
minimax regret
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A modified safe minimum standard
SMS is a very conservative rule. Any project that
entailed the possibility of species extinction
would get stopped. However large, current gains
would be foregone for possible avoided future
costs, presumed larger. A modified SMS would
adopt the strategy that ensures survival of the
species provided that it does not entail socially
unacceptably large current costs. How to
determine what is currently socially
unacceptable? A modified SMS can be applied to
target setting for pollution policy set
standards according to efficiency criteria
subject to SMS constraints accord efficiency a
lower priority than conservation except where the
two conflict, provided that the opportunity costs
of conservation are not excessive.
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Box 13.1 Stern climate change review 1
Economic activity
A schematic representation of the structure of
the enhanced greenhouse effect. Dotted lines
represent feedback effects. Examples methane
release, weakened carbon sinks. Our knowledge of
all of the links is highly imperfect. The climate
change problem is characterised by uncertainty
Emissions
Sinks
Concentrations
Climate
Biosphere
Humans
Figure 13.6 The enhanced greenhouse effect
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Box 13.1 Stern climate change review 2
The 1992 United Nations Framework Convention
on Climate Change adopted a Safe Minimum Standard
approach to the problem. Article 2, Objectives,
states that   The ultimate objective
of this Convention and any related legal
instruments that the Conference of the
Parties may adopt is to achieve, in
accordance with the relevant provisions of the
Convention, stabilization of greenhouse
gas concentrations in the atmosphere
at a level that would prevent dangerous
anthropogenic interference with the
climate system.   This is actually a modified
SMS in that Article 2 goes on to say that this is
subject to enabling 'economic development to
proceed in a sustainable manner'. The role
of uncertainty is explicitly recognised in
Article 3, Principles, where it is stated that  
3. The Parties should take
precautionary measures to anticipate,
prevent or minimize the causes of climate change
and mitigate its adverse effects.
Where there are threats of serious or
irreversible damage, lack of full
scientific certainty should not be used as a
reason for postponing such measures,
......... The EU also adopts a precautionary
approach, and it has operationalised it as
meaning that the change in global average
temperature should not be more than 2oC above the
pre-industrial level. A number of NGOs have
endorsed this objective. (It was endorsed at the
Copenhagen UNFCC COP December 2009)
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Box 13.1 Stern climate change review 3
The review notes the distinction between risk and
uncertainty, and that the fact of the latter
suggests a precautionary approach to decision
making, which is different from risk aversion. In
its formal analysis of the costs of climate
change the review actually uses the standard
expected utility framework with risk aversion. An
integrated assessment model, IAM, projects global
GDP under business as usual with and without the
effects of climate change. The difference gives a
trajectory of GDP loss on account of climate
change, which is converted to utility and
expressed in BGE loss terms as per Box 3.1
here. For each climatic parameter, Stern
constructed a subjective probability
distribution. For a given scenario IAM run 1000
times with climatic parameters drawn randomly
from their distributions. So, for each scenario
get 1000 BGE losses, reported as means across
1000 runs together with 5th and 95th
percentiles.
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Box 13.1 Stern climate change review 4
Table 13.4 Losses on BAU across six scenarios
High climate IAM includes feedbacks from methane
release and weakened carbon sinks as temperature
increases.
Utility discount rate 0.01 Elasticity of marginal
utility of consumption 1
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Box 13.1 Stern climate change review 5
Mitigation costs Bottom-up 1 of of GDP (range
1 to 3.5) for cutting to 75 of current level
by 2050 consistent with stabilisation at 550
ppm CO2e. Top-down 1 of GDP (/- 3) for an
emissions trajectory leading to stabilisation
around 500-550 ppm CO2e. Target setting in terms
of concentrations. Stern does not try to
optimise. Looks ( chapter 13) at dis-aggregated
impacts and costs, and supports with IAM scenario
results. the stabilisation goal should lie
within the range 450-500 ppm CO2e 550 ppm CO2e
would be a dangerous place to be, with
substantial risks of very unpleasant
outcome aiming below 450 CO2e would impose very
high adjustment costs in the near term for
relatively small gains, and might not even be
feasible Stern argument is based a modified safe
minimum standard a target of 550 ppm CO2e is
affordable and would avoid the worst that can be
envisaged. A target of 450 ppm CO2e would be
safer, but would cost a lot more, and may already
be infeasible.
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The precautionary principle
The precautionary principle is closely related to
the modified safe minimum standard and is gaining
widespread acceptance, at the governmental and
intergovernmental levels, as a concept that
should inform environmental policy. Statements of
the precautionary principle have been made by a
number of governments, by individuals, and as
part of inter-national agreements. Thus, for
example, Principle 15 of the June 1992 Rio
Declaration is that 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. Like the SMS, the
precautionary principle can be taken as saying
that there is a presumption against going ahead
with projects that have serious irreversible
environmental consequences, unless it can be
shown that not to go ahead would involve
unacceptable costs. The question which arises is
whether there are any policy instruments that are
consistent with this approach to irreversibility
and uncertainty, which could constitute a
feasible means for its implementation in such a
way as to avoid an outcome that simply prohibits
such projects.

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Environmental performance bonds 1
Environmental performance bonds have been
suggested as a response to the problem of
devising a means of project appraisal which takes
on board the ideas behind the SMS and the
precautionary principle. Some firm which wishes
to undertake a project involving major
technological innovation, so that there is no
past experience according to which probabilities
can be assigned to all possible outcomes. In so
far as genuine novelty is involved, there is
radical uncertainty in that not all of the
possible outcomes can be anticipated. An example
of such a project would have been the
construction of the first nuclear power
plant. Assume an environmental protection agency
(EPA) without permission from which the firm
cannot go ahead with the project. The EPA takes
independent expert advice on the project, and
comes to a view about the worst conceivable
environmental outcome of the projects going
ahead. Approval of the project is then
conditional on the firm depositing with the EPA
(posting) a bond of x, where this is the
estimate of the social cost of the worst
conceivable outcome. The bond is fully or
partially returned to the firm at the end of the
projects lifetime (defined by the
longest-lasting conceived consequence of the
project, not by the date at which it ceases to
produce output) according to the damage actually
occurring over the lifetime. If there is no
damage the firm gets back x, plus some
proportion of the interest. The withheld
proportion of the interest is to cover EPA
administration costs and to finance EPA research.
If the damage actually occurring is y, the
firm gets back x y, with appropriate interest
adjustment. For x equal to or greater than y,
the firm gets nothing back, forfeiting the full
value of the bond.
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Environmental performance bonds 2
The advantages claimed for such an instrument are
in terms of the incentives it creates for the
firm to undertake research to investigate
environmental impact and means to reduce it, as
well as in terms of stopping projects. Suppose
that the EPA decides on x as the size of the
bond, and that the firm assesses lifetime project
net returns to it as (x 1), and accepts that
x is the appropriate estimate of actual damage
to arise. Then it will not wish to go ahead with
the project. If, however, the firm took the view
that actual damage would be (x 2) or less, it
would wish to go ahead with the project. The firm
has, then, an incentive to itself assess the
damage that the project could cause, and to
research means to reduce that damage. If it
does undertake the project it has an ongoing
incentive to seek damage-minimising methods of
operation, so as to increase the eventual size of
the sum returned to it, x y. At the end of
the projects lifetime, the burden of proof as to
the magnitude of actual damage would rest with
the firm. The presumption would be that the bond
was not returnable. It would be up to the firm to
convince the EPA that actual damage was less than
x if it wished to get any of its money back.
This would generate incentives for the firm to
monitor damage in convincing ways, as well as to
research means to minimise damage. In the event
that damage up to the amount of the bond, x,
occurred, society would have received
compensation. If damage in excess of x had
occurred, society would not receive full
compensation. x is to be set at the largest
amount of damage seen as conceivable by the EPA
at the outset. A socially responsible EPA would
take a cautious view of the available evidence,
implying a high figure for x, so that society
would not find itself uncompensated.