Decision making under large uncertainty

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Decision making under large uncertainty

• Marie-Laure Guillerminet
• ZMK, University of Hamburg
• Atlantis Meeting
• January 24th, 2003

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• Uncertainty gives rise to two different issues
• One relates to risk aversion
• The fact that one cannot uninvest control
  capital or actively remove carbon from the
  atmosphere is irrelevant to the optimal
  regulatory strategy (Kolstad, 1996).
• One relates to uncertainty where that uncertainty
  is being resolved over time, i.e. information is
  being acquired over time
• The literature on irreversibilities tells us
  that with learning, we should avoid decisions
  that restrict future options.

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1. Literature of irreversible investment under
uncertainty

• Cf. Pindyck (2000), in Resource and Energy
  Economics Introduction to special issue on
  irreversibility.
• Consider a carbon tax to reduce global warming.
• The Net Present Value rule (classic theory,
  now-or-never strategy) responds as follows 
• The difference between the present values of the
  expected flow of benefits and the expected flow
  of costs required to implement this policy.
• If it is greater than zero, invest.

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• It ignores three important characteristics of
  most environmental problems and the policies
  designed to respond to them 
• Uncertainty over the future costs and benefits of
  adopting a particular policy
• The best you can do is to assess the
  probabilities of the alternative outcomes that
  can mean greater or smaller profits (or loss) for
  adopting this policy.

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• Important irreversibilities associated with
  environmental policy
• Policy adoption is rarely a now-or-never
  proposition and you have some leeway about the
  timing of adopting this policy
• You can postpone action to get more information
  about the future.

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• These three characteristics interact to
  determine the optimal decisions
• The Real Options Theory recognizes the important
  qualitative and quantitative implications of the
  interaction between irreversibility, uncertainty,
  and the choice of timing, unlike the Net Present
  Value rule.

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• The Real Options Approach stresses the analogy
  with options on financial assets
• The opportunities to acquire real assets are
  called real options.
• According to Henry (1974), Arrow - Fisher (1974),
  uncertainty creates new investment opportunities,
  i.e. some value.
• Call this value ?, defined as the Option Value
  Multiple.
• E.g. preserving from the submersion of countries
  or regions, the extinction of a species, a shift
  in the Gulf Stream.

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• Irreversibility and the possibility to delay are
  very important characteristics of most
  investments in reality.
• The ability to delay an irreversible investment
  expenditure can profoundly affect the decision to
  invest and also undermines the simple NPV rule
  (cf. Dixit - Pindyck, 1994)
• A firm with an opportunity to invest is holding
  an option
• It has the right but not the obligation to buy
  an asset at some future time of its choosing.

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• When a firm makes an irreversible investment
  expenditure, it exercises its option to invest
• It gives up the possibility of waiting for new
  information to arrive that might affect the
  desirability or timing of the expenditure
• It cannot disinvest should market conditions
  change adversely.
• This lost option value is an opportunity cost
  that must be included as part of the cost of the
  investment
• The NPV of exercise is large enough to offset the
  value of waiting for more information.

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• Illustration of the Option Value Multiple ?

NPV, Option Values
Waiting
Investing
Cost of Capital
Threshold under certainty MKVNPV
Threshold under uncertainty HV
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2. Application to our problem

• Environmental policy involves two kinds of
  irreversibilities which work in opposite
  directions 
• Sunk costs associated with an environment
  regulation policies aimed at reducing
  ecological damage impose sunk costs on society
• Sunk benefits of avoided environmental
  degradation environmental damage can be
  partially or totally irreversible. So adopting a
  policy now rather than waiting has a sunk benefit
  (a negative opportunity cost).

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• These irreversibilities interact with two kinds
  of uncertainties to affect optimal policy
  timing 
• Economic uncertainty, uncertainty over the future
  costs and benefits of an environmental damage and
  its reduction
• Ecological uncertainty, uncertainty over the
  evolution of the relevant ecosystems.
• We have to take them into account to choose the
  timing of adopting the policy.

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• Results
• The decision can be deferred
• Information about the evolving environmental
  impacts and values accumulates over time and can
  lead to a better decision.
• Why make an irreversible investment in reducing
  greenhouse emissions today if waiting a little
  while will reveal greater certainty what the
  outcome will be?
• Waiting entails a cost, the foregone benefits
  from the investment during the waiting period,
  but this may be much less than the benefits from
  the better decision that results.

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• On the other side, it is better to protect the
  environment from irreversible damage now
• It can be unprotected if new information
  suggests that the damage, through irreversible,
  will be minor.
• Pindyck (2000) An increase in uncertainty,
  whether over future costs and benefits of
  environmental protection or over the behavior of
  the environment, leads to a higher threshold of
  policy adoption
• Policy adoption involves a sunk cost associated
  with a reduction in the entire trajectory of
  future emissions, whereas waiting involves only
  continued emissions over the waiting period.

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• Pindyck (2000)
• This result depends on the extent to which the
  policy is indeed irreversible.
• It also implicitly assumes that emissions over
  the period do not increase the risk of a
  catastrophic impact.
• There is some possibility of essentially
  irreversible catastrophic impact, as would result
  for example
• from the disintegration of the West Antartic Ice
  Sheet and consequent rise in sea level of 5-6 m.

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• These global environmental risks are
  low-probability events with major, widespread
  (Cass and al., 1996) and possibly irreversible
  consequences.
• Classic theories underestimate low-probability
  events with major irreversible consequences.
• It seems plausible that the probability of such
  an event is positively related to the level of
  greenhouse gas concentrations in atmosphere
• The risk oughts to be endogenous in a model of
  the optimal control of greenhouse gas emissions.

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• We will assume that the social planners beliefs
  about a catastrophic event at an arbitrarily
  instant of time can be represented by a
  conditional probability rate, given that a
  catastrophe has not occurred at all earlier
  instants of time.