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Risk and Uncertainty

Econ 373 Environmental Economics February 8, 2012

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What is risk?• "… Uncertainty must be taken in a sense radically

distinct from the familiar notion of Risk, from which it has never been properly separated… The essential fact is that "risk" means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating… It will appear that a measurable uncertainty, or "risk" proper, as we shall use the term, is so far different from an un-measurable one that it is not in effect an uncertainty at all.“ (Frank Knight, 1921)

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What is Risk?•Risk versus Probability•Risk versus Threat•All outcomes versus Negative outcomes:

ex. Risk = Probability of an accident * Consequence in lost money/deaths

orRisk= variability of actual returns on an

investment around an expected return

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The Problem of Risk and Uncertainty

• Scientific and economic uncertainty complicates decisions on environmental policies▫Abatement costs (today and in future periods)▫Sensitivity of the climate system▫Assessment of costs/damages/benefits of a changing climate▫Future technology options▫Population changes ; preferences of future generations▫Economic growth

Problem of irreversibility▫Today’s emissions stay in the atmosphere▫ Investments to reduce emissions will be impossible to recoup if

warming is less damaging

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Risk and Uncertainty

There are known knowns.

There are things we know that we know.

We also know

There are known unknowns.

That is to say

We now know there are some things

We do not know.

But there are also unknown unknowns,

The ones we do not know

We don't know.

D.H.Rumsfeld—Feb. 12, 2002, Department of Defense news briefing

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Definition of Risk and Uncertainty

• Certainty▫We have perfect information about future outcomes

• Risk▫ If probabilities of occurrence of random events are (objectively)

known▫Based on past experience▫E.g. roulette wheels, rolling dices

• Uncertainty▫No objective probability assessment▫Might know the possible outcome but maybe not▫E.g. betting on who will win the next Super bowl

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Probability Concepts

•Ingredients for probability models:▫Specifying the sample space

Ω: sample space- the set of all possible outcomes

ω: outcomes▫Defining events: subset of Ω▫Assignment probabilities

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Example

•Consider a single coin toss.▫Sample space:▫Events: {H}, {T}, {H,T}, ▫Probability: Assume fair coin

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Making Risky Choices

• Expected payoff = sum over all possible outcomes times the probability of each outcome occurring

• EX.OPTION 1 OPTION 2

Probability Profit Probability Profit

70% 5,000 20% -1000

30% 7,000 40% 4,000

20% 7,000

20% 10,000

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Making Risky Choices

• Expected payoff = sum over all possible outcomes times the probability of each outcome occurring.

• EX.OPTION 1 OPTION 2

Probability Profit Probability Profit

70% 5,000 20% -1000

30% 7,000 40% 4,000

20% 7,000

20% 10,000

OPTION 1 OPTION 2Probabilit

y Profit E.V. Probability Profit E.V.

70% 5,000 3,500 20% -1000 -200

30% 7,000 2,100 40% 4,000 1600

20% 7,000 1400

20% 10,000 2000

Expeted Vaue 5,600 Expected Value 4,800

Choose Option 1!

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Limitation of Expected Payoff

• Will you accept a 50/50 bet for $5?

▫ Probably yes

• Will you accept a 50/50 bet for $5m?

• Probably not

• But both have an expected value of 0!• In some way you ‘care’ more about losing $5m than

winning $5m.• Taking expectation in the extreme situation doesn’t

work well.

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Making Risky Choices• Monte Carlo Simulation: Uses repeated sampling to determine

the property of some phenomenon.

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Decision Making under Uncertainty with Known Outcomes but unknown probabilities

• Sensitivity Analysis: Study how the outcome varies depending

on the inputs of the model.• Examples: What is the net present value of a 4kW solar panel

system? (Capital cost: $28,000, 20 yr revenue from avoided electricity cost)

Scenario 1: With 8% discount rate

NPV= -235

Scenario 2: With 3% discount rate

NPV= 1,172

Scenario 3 With 1% discount rate

NPV= 1,799

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Decision Making under Uncertainty with Known Outcomes but unknown probabilities

• MaxMin criterion

▫A ‘pessimistic’ criterion to maximize payoff in the

worst outcome.

▫Identify the worst outcome for each action

▫Select the action where the worst outcome is the

least bad

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Decision Making under Uncertainty with Known Outcomes but unknown probabilities

• MaxMin criterion: choose action 3

Actions States of Nature

A B C

1 20 40 180

2 -40 100 220

3 60 70 90

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Decision Making under Uncertainty with Known Outcomes but unknown probabilities

• MaxMin criterion: choose action 1

Actions States of Nature

A B C

1 40 60 40

2 100 0 0

3 0 30 130

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Decision Making under Uncertainty with Unknown Outcomes

• Ask experts?▫ “Heavier-than-air flying machines are impossible.”

- Lord Kelvin, 1895.▫ “I think there is a world market for maybe five computers.”

- Tom Watson, IBM chair, 1943.

▫ “There is no need for any individual to have a computer in their home.” - Ken Olson, President, Digital Equipment, 1977.

▫There is not the slightest indication that [nuclear energy] will ever be obtainable. It would mean that the atom would have to be shattered at will.” - Albert Einstein, 1932.

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Decision Making under Uncertainty with Unknown Outcomes

• Wait and see policy• Act now, but adjust policy according to new information

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Risk Management

• ”Identification and prioritization of environmental and health risks (actual or potential threat of adverse effects on living organisms and our environment by effluents, emissions, wastes, resource depletion, etc., arising out of activities), followed by coordinated and economical application of resources to sustainably minimize, monitor, and control the adverse impact events or to maximize the realization of opportunities.” (EPA)

• http://www.epa.gov/nrmrl/

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Insurance

•The loss must be amenable to risk pooling•There must be a clear loss•The loss must be in a well-defined period

of time•The frequency of loss must allow a

premium calculation•Moral hazard must not be too severe•Adverse selection must not be significant