Decision making under large uncertainty

1. Decision making under large uncertainty Marie-Laure Guillerminet* * ZMK, University of Hamburg Atlantis Meeting January 24th, 2003

2. 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 isirrelevant 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. NPV, Option Values • Illustration of the Option Value Multiple  : Waiting Investing Cost of Capital Threshold under certainty M=K=V*NPV Threshold under uncertainty H=V*

11. 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).

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. We will assume that the social planner’s 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.