5.Risk Uncertainty

7/31/2019 5.Risk Uncertainty

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Risk, Uncertainty,and Sensitivity

AnalysisHow economics can helpunderstand, analyze, and cope with

limited information


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What is risk?

Can be loosely defined as the possibility ofloss or injury. Should be accounted for in social projects

(and regulations) and private decisions. Think of there being different states of

nature that can emerge, and we areuncertain about which we will end up with.

We want to develop a way to describe riskquantitatively by evaluating the probabilityof all possible outcomes.


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Attitude toward risk

Problem: Dean Haston likes to ride herbike to school. If it is raining when shegets up, she can take the bus. If it isnt,she can ride, but runs the risk of itraining on the way home.

Value of riding bike (no rain) = $4 each

way Value of riding bike in rain = -$4 (each

way)

Value of taking bus = $1 (each way)


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Dean Hastons options & thestates of nature

The Asst. Dean can either ride her bike or

take the bus. Bus: She gains $1 each way: $2

Bike: Depends on the state of nature

Rain (on way home): $4 - $4 = 0. No rain: $4 + $4 = $8.


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Which does she prefer?

If the Asst. Dean takes the bus, she knowsshell gain $2 (no uncertainty).

If the Dean rides her bike: If it rains, she gains 0.

If it doesnt rain, she gains $8.

Whether she is better taking the bike or busdepends on 2 things:

The probability of rain

Her attitude toward risk


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The probability of rain

Suppose Pr(rain) = .5Pr(no rain) = .5

Bus: $2 (certain)

Bike: .5(8) - .5(0) = $4 (risky) If she is risk neutral, she takes her bike ($4 > $2)

If she is a risk lover, she takes her bike

If she is sufficiently risk averse, she may bus

Suppose Pr(rain) = .8.Pr(no rain) = .2 Bus: $2

Bike: .2(8) + .8(0) = $1.60 (risky)

If she is risk neutral, she rides the bus ($2 > 1.60)


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Risk more generallyCoin toss pays $10 or $20

Utility

Some good (or $)10 2015

Q: Would this

person rather

get 15 for sure or

play coin toss?

U(15)

.5*U(10)

+ .5*U(20)

This person is

RISK AVERSE


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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 isan argument that society is essentially risk neutral.

Most economic analyses assume risk neutrality.

Note: may get unequal distribution of costs andbenefits.


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Expected payoff moregenerally

Suppose n states of nature.

Vi = payoff under state of nature i.

Pi = probability of state of nature i. Expected payoff is: V1p1+V2p2+

Or S ViPi


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Example: Air qualityregulations

New air quality regulations in SantaBarbara County will reduce ground levelozone.

Reduce probability of lung cancer by.001%; affected population: 100,000.

How many fewer cases of lung cancer

can we expect?about 1 .00001*100,000 = 1.

We dont know who will get sick but thisis our expectation of the number of

cases


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Example: Climate changepolicy

2 states of nature

High damage (probability = 1%)

Cost = $1013/year forever, starting in 100yrs.

Low damage (probability = 99%)

Cost = $0

Cost of control = $1011

Should we engage in control now?


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Control vs. no control (r=2%)

Control now: high cost, no future loss

Cost = $1011

Dont control now: no cost, maybehigh future loss:

If high damage = 1013[1/(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 eventhough high loss is low probabilityevent.


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Value of Information

The real question is not: Should we engagein control or not?

The question is: Should we act now orpostpone the decision until later?

So there is a value to knowing whether thehigh damage state of nature will occur.

We can calculate that valuethis is Valueof information


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Sensitivity Analysis

A method for determining howsensitive your model results are to

parameter values. Sensitivity of NPV, sensitivity of policy

choice.

Simplest version: change aparameter, re-do analysis (PartialSensitivity Analysis)


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Climate change: sensitivity to r

0

1E+11

2E+11

3E+11

4E+11

5E+11

6E+11

7E+11

8E+11

0 0.01 0.02 0.03 0.04 0.05 0.06

Discount rate (r)

Lo

ssfromn

ocontrol


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Sensitivity to Uncertainty on theprobability of high damage

0.00E+00

2.00E+11

4.00E+11

6.00E+11

8.00E+11

1.00E+12

1.20E+12

0 0.005 0.01 0.015 0.02

p

Benefitsand

Costs

Cost

E[Damage]


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More sophisticatedsensitivity

The more nonlinear your model, themore interesting your sensitivityanalysis.

Should examine differentcombinations.

Monte Carlo Sensitivity Analysis:

Choose distributions for parameters. Let computer draw values from

distns

Plot results


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Managing Risk

Risk is a problem of its own

Several tools available to reduce risk

Insurance

Liability


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Insurancefire insuranceexample

Probability of loss: 0.001; Loss=$100,000

Expected annual loss: $100

No insurance

Most years: no loss; some years $100,000 loss

1000 houses pool $100 each/yr ($100,000/yr)

Most yearsone loss

Sometimes no losses, sometimes 2-3 losses

Much less variability in annual losses Fire is amenable to risk pooling

Risks uncorrelated

Earthquake insurance in Cal NOT amenable to risk pooling Most years no loss; some years enormous loss


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Conditions for insurability ofrisks

Loss must be amenable to risk pooling

There must be a clear loss

Loss must be in well-defined period of time Frequency of loss must allow a premium calculation

Moral hazardmust not be severe (eg, hazardouswaste insurance causes folks to be sloppy)

Adverse selectionmust not be severe (eg, only highrisk folks take out insurance)


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Liability a way of regulating risk

For firms/individuals engaged in riskyactivities

Rather than regulate risk, hold partiesresponsbible for negative outcomes

Eg, Oil Tanker Regs

Some regs apply to nature of tankers

Other protection achieved throughliability

Threat of liability reduces riskyactivities

Bankru tc can be a roblem

5.Risk Uncertainty

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