Risk, Uncertainty, and Sensitivity Analysis

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Risk, Uncertainty, and Sensitivity Analysis

• How economics can help understand, analyze, and
  cope with limited information

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What is risk?

• Can be loosely defined as the possibility of
  loss or injury.
• Should be accounted for in social projects (and
  regulations) and private decisions.
• We want to develop a way to describe risk
  quantitatively by evaluating the probability of
  all possible outcomes.

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Attitude toward risk

• Problem Costello likes to ride his bike to
  school. If it is raining when he gets up, he can
  take the bus. If it isnt, he can ride, but runs
  the risk of it raining on the way home.
• Value of riding bike 2, value of taking bus
  -1.
• Value of riding in rain -6.

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Costellos options the states of nature

• Costello can either ride his bike or take the
  bus.
• Bus He loses 0 (breaks even).
• Bike Depends on the state of nature
• Rain 2 - 6 -4.
• No rain 2 2 4.

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Probabilities risk attitude

• Pr(rain)0.5.
• Costellos expected payoffs are equal
• Bus 0.
• Bike .5(-4) .5(4) 0.
• If he
• Always bikes hes a risk lover
• Always buses hes risk averse
• Flips a coin hes risk neutral
• His behavior reveals his risk preference.

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Risk attitudes in general

• Generally speaking, most people risk averse.
• Diversification can reduce risk.
• Since govt can pool risk across all taxpayers,
  there is an argument that society is essentially
  risk neutral.
• Most economic analyses assume risk neutrality.
• Note may get unequal distribution of costs and
  benefits.

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Expected payoff more generally

• Suppose n states of nature.
• Vi payoff under state of nature i.
• Pi probability of state of nature i.
• Expected payoff is V1p1V2p2
• Or S ViPi

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Example Air quality regulations

• New air quality regulations in Santa Barbara
  County will reduce ground level ozone.
• Reduce probability of lung cancer by .001,
  affected population 100,000.
• How many fewer cases of lung cancer can we
  expect?about 1
• .00001100,000 1.

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Example Climate change policy

• 2 states of nature
• High damage (probability 1)
• Cost 1013/year forever, starting in 100 yrs.
• Low damage (probability 99)
• Cost 0
• Cost of control 1011
• Should we engage in control now?

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Control vs. no control (r2)

• Control now high cost, no future loss
• Cost 1011
• Dont control now no cost, maybe high future
  loss
• If high damage 10131/(1.02100) 1/(1.02101)
  1.(1.02102)
• (1013/(.02))/(1.02100) 7 x 1013
• If no damage 0.

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Overall evaluation

• Expected cost if control 1011
• Expected cost if no control
• (.01)(7 x 1013) (.99)(0) 7 x 1011
• By this analysis, should control even though high
  loss is low probability event.

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Value of Information

• The real question is not Should we engage in
  control or not?
• The question is Should we act now or postpone
  the decision until later?
• So there is a value to knowing whether the high
  damage state of nature will occur.
• We can calculate that valuethis is Value of
  information

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Sensitivity Analysis

• A method for determining how sensitive your
  model results are to parameter values.
• Sensitivity of NPV, sensitivity of policy choice.
• Simplest version change a parameter, re-do
  analysis (Partial Sensitivity Analysis)

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Climate change sensitivity to r
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More sophisticated sensitivity

• The more nonlinear your model, the more
  interesting your sensitivity analysis.
• Should examine different combinations.
• Monte Carlo Sensitivity Analysis
• Choose distributions for parameters.
• Let computer draw values from distns
• Plot results