Risk, Uncertainty, and Sensitivity Analysis
Transcript Risk, Uncertainty, and Sensitivity Analysis
Risk, Uncertainty, and
How economics can help understand,
analyze, and cope with limited
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
We want to develop a way to describe
risk quantitatively by evaluating the
probability of all possible outcomes.
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 isn’t, 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.
Costello’s options & the “states
Costello can either ride his bike or take
Bus: He loses $0 (breaks even).
Bike: Depends on the “state of nature”
Rain: $2 - $6 = -$4.
No rain: $2 + $2 = $4.
Probabilities & risk attitude
Costello’s expected payoffs are equal:
Bike: .5*(-4) + .5*(4) = $0.
Always bikes: he’s a risk lover
Always buses: he’s risk averse
Flips a coin: he’s risk neutral
His behavior reveals his risk preference.
Risk attitudes in general
Generally speaking, most people risk averse.
Diversification can reduce risk.
Since gov’t can pool risk across all taxpayers,
there is an argument that society is
essentially risk neutral.
Most economic analyses assume risk
Note: may get unequal distribution of costs
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: V1p1+V2p2+…
Example: Air quality regulations
New air quality regulations in Santa
Barbara County will reduce ground level
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.
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?
Control vs. no control (r=2%)
Control now: high cost, no future loss
Cost = $1011
Don’t control now: no cost, maybe high
If high damage = 1013[1/(1.02100) +
1/(1.02101) + 1.(1.02102) + … ]
= (1013/(.02))/(1.02100) = $7 x 1013
If no damage = $0.
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
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
We can calculate that value…this is
“Value of information”
A method for determining how
“sensitive” your model results are to
Sensitivity of NPV, sensitivity of policy
Simplest version: change a parameter,
re-do analysis (“Partial Sensitivity
Climate change: sensitivity to r
Loss from no control
Discount rate (r)
More sophisticated sensitivity
The more nonlinear your model, the
more interesting your sensitivity
Should examine different combinations.
Monte Carlo Sensitivity Analysis:
Choose distributions for parameters.
Let computer “draw” values from distn’s