People’s attitudes toward risk seem more complex than this, e.g.,
Is risk aversion only about decreasing marginal utility of money?
Is status quo bias only about quadratic loss (and what if utility loss is not quadratic?
The same people are sometimes risk-seeking and sometimes risk-averse
e.g., buy insurance and play the lottery
Other empirical puzzles
Disease problem
Imagine the U.S. is preparing for the outbreak of an unusual disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed.
Assume that the exact scientific estimate of the consequences of the programs are as follows:
If Program A is adopted, 200 people will be saved. (72%)
If program B is adopted, there is a 1/3 probability that 600 people will be saved, and 2/3 probability that no people will be saved. (28%)
Disease problem
Imagine the U.S. is preparing for the outbreak of an unusual disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed.
Assume that the exact scientific estimate of the consequences of the programs are as follows:
If Program C is adopted, 400 people will die. (22%)
If program D is adopted, there is a 1/3 probability that no one will die, and 2/3 probability that 600 people will die. (78%)
Loss frames (risk-taking) vs gain frames (risk-aversion)
Challenger vs incumbent candidate campaigns
Pushes for big changes to status quo vs stability
Pushes for or against risky endeavors (e.g., war)
BREAK
Time preference
We say people discount the future if they are willing to pay a premium to have something sooner rather than later (holding all else equal)
Would you prefer to have $100 now or $110 one year from now?
We can think about different functions that determine the “present value” of some future sum
Exponential discounting
Standard rational choice approaches allow for time preference, but under an important constraint: preferences should be consistent across time
If I prefer $110 two years from now to $100 one year from now, I should make the same choice one year from now
This is true of exponential discounting:
The discounted value of some future reward is the value multiplied by a discount factor raised to the power of the time gap (D = delay) between now and then
\[
\text{U}(x_t) = \delta^{D} \text{U}(x)
\]
Example
Exponential discounting
Exponential discounting has a very important property:
The ratio of the discount factor for any two equally spaced time points is equal
Your preferences are consistent across time - you don’t disagree with your future self
Agreeing with yourself
$75 now or $100 one period from now?
$75 10 periods from now or $100 11 periods from now?
$75 100 periods from now or $100 101 periods from now?
# discount factor ratio D = 1 vs D = 0(0.9^1*100) / (0.9^0*75)
[1] 1.2
# discount factor ratio D = 11 vs D = 10(0.9^11*100) / (0.9^10*75)
[1] 1.2
# discount factor ratio D = 101 vs D = 100(0.9^101*100) / (0.9^100*75)
[1] 1.2
People do disagree with themselves across time!!!
Hyberbolic discounting
Hyperbolic discounting is an alternative theory for representing time preferences
People have a strong bias toward the present
This bias is such that there is conflict between present and future selves
People care much more about an immediate delay than they care about future delays of equal length
In each question, you will be able to indicate which combination of temporary jobs created this year and five years from now you think represents the best economy. Some people might think the best economy would create all temporary jobs now even though that would mean higher unemployment five years from now. Other people may think the best economy would create all temporary jobs five years from now even though that would mean higher unemployment now. Still others may think the best economy would divide the number of jobs created between the two periods in some way.
