Risk, uncertainty and irreversibility

Transcription

1 Risk, uncertainty and irreversibility Kine Josefine Aurland-Bredesen Guest lecture ECN275, Motivation Do we live in a certain world where all choices are reversible? Incorporating risk, uncertainty and/or irreversibility may change policy recommendations Sub-optimal policies Welfare cost My focus: The basics of decision making in the face of risk and uncertainty. 1 1

2 Risk versus uncertainty Probability Known Risk Risk: Gambling, coin toss, dice game. Uncertainty: Urban air pollution, level of NOx in Oslo Unknown Radical uncertainty (ignorance) Uncertainty Radical uncertainty: Climate change Unknown Known Outcome/States 2 Choice under risk: The Basics 1 Gamble with income outcome with probability and with probability 1. Expected value = + 1 Expected utility: =

3 Choice under risk: St. Petersburg paradox I will flip the coin, if it is tail I pay you $1 and the gamble is over. If it is head. I will flip again. It it s tail then, I pay you $2, if not I will flip again. With every round, I double the amount I will pay to you if it s tail. How much are you willing to pay to take this gamble? The expected payoff is 2 = = Assume diminishing marginal utility, then expected utility is: 2 < 4 Choice under risk: Expected Utility Theory Von Neumann-Morgenstern expected utility theory: Four axioms: 1. Completeness (well-defined preferences) Real life choices under risk often violate the third axiom. Is this a problem? 2. Transitivity (decide consistently) 3. Independence (irrelevant alternatives do not affect decisions) 4. Continuity 1-2 need to hold to build a utility function that represents preferences. If 1-4 hold there exist a utility function that we can use to present preferences over gambles. Many known violations of these axioms (see i.e. Allais Paradox, Ellsberg paradox) 5 3

4 Choice under risk: Certainty equivalent Certainty equivalent: The certain level of income that yields the same utility as the expected utility of the gamble (what you are WTP to accept the gamble) = = ( ) We can find the certainty equivalent analytically by solving = ( ) for or as in Figure Choice under risk: Risk preferences If < ( ): Risk-averse If = ( ): Risk neutral (we can work with expected values) If > ( ): Risk lover vnm utility functions are concave: Risk-averse > 0 and > 0 (diminishing marginal utility) Cost of risk bearing (CORB) = = = ( ) 7 4

5 Implications for environmental cost-benefit analysis If individuals are risk-averse then just looking at expected values does not tell the full story. E(Y)<CE There is a cost associated with risk bearing Thus, E(NPV) will overstate true net present values. We should account for this (i.e. by using option price or by incorporating CORB) 8 Choice under risk: Riskiness Not often discussed in economics, but essential in finance. The role of riskiness. Essentially, we should not only care about the expected value or expected utility, but also the number of possible outcomes and how much they differ (variance). Strategies: Second order stochastic dominance Return to risk ratio s 9 5

6 Choice under irreversibility (future known) : Flow of amenity services (function of size of wilderness area) Two time periods = 1 (now) and = 2 (future). Optimal policy (reversible): = 0 and = 0 which yields and. Problem with irreversibility <. Then <. Optimal policy (irreversible): = (gray) which gives > and <. Incur cost in = 1 to secure gains in = 2. Cost of irreversibility: Gray area. Unavoidable. Net cost to ignoring irreversibility: Loss incurred in = 2 (green) is larger than gain in = 1 (gray). Avoidable 10 Irreversibility (future unknown) Once lost, lost forever. Same story in risky world as long as > Cost of irreversibility: Gray Net cost of ignoring irreversibility: Again, loss in = 2 (green) larger than gain in = 1 (gray) Irreversibility and future unknown, where some of the uncertainty will be resolved at one point. - Quasi-option value - Value of the information gained by waiting to resolve uncertainty - Oh yes, this also has policy implications

7 Choice under uncertainty Subjective probabilities Assign subjective probabilities to outcomes and treat it as risk Explains how it is possible to make rational choices under uncertainty Is not very helpful when it comes to policy making Maximin, maximax and minimax regret Do not require knowledge of probabilities Adopting a SMS or precautionary approach Do not require knowledge of probabilities or outcomes 12 Choice under uncertainty Maximin Select strategy with leastbad worst outcome Worst outcome: A: 10 (E) B: 5 (C) Since 10>5, choose A over B Maximax Select strategy with best of best outcome Best of best outcome: A: 120 (C) B: 140 (E) Since 140>120, choose B Two strategies: A: Preserve, B: Develop Three possible outcomes: C, D and E Pay-off matrix: C D E A B

8 Choice under uncertainty Minimax regret Select strategy with lowest of the largest regrets Largest regret: A: 130 (E) B: 115 (C) Since 130>115, pick B Two strategies: A: Preserve, B: Develop Three possible outcomes: C, D and E Regret matrix: A 0 (because 120>5) B 115 (120-5) C D E 0 (because 50>30) 20 (50-30) 130 (140-10) 0 (because 140>10) 14 Choice under uncertainty Different results. Maximin and maximax ignores most information in the pay-off matrix (may go against common sense) Minimax: Avoid the most costly mistake Two strategies: A: Preserve, B: Develop Three possible outcomes: C, D and E Pay-off matrix: Optimal strategy? C D E Maximin A Maximax, Minimax regret B

9 Safe minimum standard and precautionary principle SMS: Do not make choices that have possible large and costly irreversible damages (species extinction) Precautionary principle: If there are threats of possible large and costly irreversible damages, do not postpone action due to lack of certainty (climate change) Argument for: Possible large and irreversible damages Irreversibility, uncertainty and sustainability: Do not know future preferences, needs and technology. Do we have the right to constrain future choices? 16 Take home message Incorporating risk, uncertainty and/or irreversibility may change policy recommendations Sub-optimal policies Welfare cost The assumptions and method you choose matter 17 9

10 In class case Dumping of mining waste in the Førde Fjord

11 Case description: Dumping of mining waste in the Førde Fjord In 2008 the company Nordic Mining ASA applied for permission to extract the minerale rutile in Engebø mountain. The plan is to deposit surplus mass from mining drift in a fjord depot (seall) in the Førde Fjord. This will result in that about 4 km of the fjord bottom will be laid desolate for a period of 50 years. The following information is avaiable to you: The Institute of Marine Research discurages mining in the area. They argue this is not sustainble fjord management. The seall will lead to the loss of aquatic organisms and deepsea sh in the area. The Førde Fjord an important spawning area for coastal cod, and the seall will interfere with the spawning. The Førde Fjord is the only known coastal spawning area for the endangered species of bluen. Currents may bring particles from the seall beyond the fjord and into the ocean, but research show that the probability of this happening is small. Mining scientist argue that in this spesic case a seall is a better solution than a landll. This is also the conclusion from the Norwegian Environmnetal Agency. The Engebø mountain has one of the worlds largest deposits of rutile. Rutile is composed of titanium and oxygen. Titanium is used in the aerospace industry, to make dental implants and to create articial hip pads, knees and other parts of the body that must be replaced by wear and tear or accidents. Demand for rutile is very high and in many of the applications you will struggle to nd good replacements. The mining project in Engebøfjellet in Naustdal and Askvoll will contribute to important value creation in the local communities. The mine may provide an extra 500 jobs on a national basis. The estimated benet is 500 million NOK each year and the mining project is argued to strengthen the Norwegian economy. You have been hired to consult the Norwegian goverment in making the decision in wether or not Nordic Mining should get the permission. 1. Given what has been discussed today and earlier in ECN275, how would you approach making a decision in this case? Thinking about the following questions may help: What are the cost and benets of the project? Who are the primery stakeholders? Do you think all primery and secondary stakeholders are accounted for? Identify sources of risk, uncertainty and irreversibility. Do you need anymore information, if yes, what? How does this aect the decision making process? 2. In January 2017 the Norwegian government gave Nordic Mining permission. As an economist, do you agree? Explain your position. 1