Hyperbolic
Discounting
How we
misread
the future
Reading
• Predictably Irrational, Chapter 6, The Influence
of Arousal
• Predictably Irrational, Chapter 7, The Problem
of Procrastination and Self-Control
• Nudge, Chapter 2, Resisting Temptation
Discounting
• Being happy now (today, this week, this year)
is typically more desirable than the prospect
of being happy in the future (tomorrow, next
week, next year)
• Suppose happiness during a time period (day,
week, year) can be measured
• The discount rate is the additional future
happiness that can compensate for the loss of
one unit of happiness in the present
Discounting
• Example:
– For Alice, suppose the loss of one unit of present
happiness can be compensated by the gain of 1.07
units of future happiness
– In this case, Alice’s discount rate is 0.07
– For Bob, suppose the loss of one unit of present
happiness can be compensated by the gain of 1.02
units of future happiness
– Bob’s discount rate is 0.02
• Who is more patient, Alice or Bob?
Discounting
• Example:
– For Alice, suppose the loss of one unit of present
happiness can be compensated by the gain of 1.07
units of future happiness
– In this case, Alice’s discount rate is 0.07
– For Bob, suppose the loss of one unit of present
happiness can be compensated by the gain of 1.02
units of future happiness
– Bob’s discount rate is 0.02
• Who is more patient, Alice or Bob?
Discounting
• The higher your discount rate, the more
important the present is to you (relative to the
future)
• The higher your discount rate, the more
impatient you are
Dynamic Inconsistency
• Typically, when we are making plans about
what we’d do in the future, we are patient
– our discount rates are low
• But when the future finally arrives, we
become impatient and succumb to temptation
– our discount rates spike
• This phenomenon is called hyperbolic
discounting or dynamic inconsistency
Dynamic Inconsistency
• When we think about what we’d do in the
future, we tend to make well thought out
plans
• But when the future finally arrives, we give in
to temptation and abandon the plans we had
made
Does the future me want different things?
Choose among 24 movie videos
• Some are “low brow”
• Some are “high brow”
Does my choice depend on
whether I am picking for
tonight, next Thursday, or the
following Thursday?
Reed, Lowenstein & Kalyanaraman (1999) Mixing virtue and vice: Combining the immediacy effect and the diversification
heuristic. Journal of Behavioral Decision Making, 12, 257-273.
Does the future me want different things?
Did people choose…
a) More “low brow” movies
now, more “high brow”
movies for later
b) More “high brow” movies
now, more “low brow”
movies for later
c) About the same regardless
of whether picking for now
or later
Reed, Lowenstein & Kalyanaraman (1999) Mixing virtue and vice: Combining the immediacy effect and the diversification
heuristic. Journal of Behavioral Decision Making, 12, 257-273.
Next week I will want things that are good for me…
High
Brow,
44%
Lo
Bro
29
Low
Brow,
37%
Low
Brow,
56%
Choosing for tonight
High
Brow,
63%
Choosing for next Thursday
High
Brow,
71%
Choosing for second Thursday
Reed, Lowenstein & Kalyanaraman (1999) Mixing virtue and vice: Combining the immediacy effect and the diversification
heuristic. Journal of Behavioral Decision Making, 12, 257-273.
Does the future me want different things?
When choosing between a healthy and unhealthy
snack for delivery in one week, do people
systematically misproject future desires?
← Next Week→
Predicted preference
← Right Now→
Actual preference
D. Read (Leeds U.) & B. van Leeuwen (Leeds U.), 1998, Predicting hunger: The effects of appetite
and delay on choice. Organizational behavior and human decision processes, 76, 189-205.
Does the future me want different things?
Are people
a) More likely to choose the unhealthy snack for next week
b) More likely to choose the unhealthy snack for right now
c) About as likely either way
← Next Week→
Predicted preference
← Right Now→
Actual preference
D. Read (Leeds U.) & B. van Leeuwen (Leeds U.), 1998, Predicting hunger: The effects of appetite
and delay on choice. Organizational behavior and human decision processes, 76, 189-205.
Does the future me want different things?
26% chose the unhealthy snack for delivery in
one week right after lunch.
74%
← Next Week→
Predicted preference
26%
D. Read (Leeds U.) & B. van Leeuwen (Leeds U.), 1998, Predicting hunger: The effects of appetite
and delay on choice. Organizational behavior and human decision processes, 76, 189-205.
Does the future me want different things?
One week later, when allowed to change their
choice at the delivery, 70% chose the
unhealthy snack for immediate consumption
74%
← Next Week→
26%
30%
← Right Now→
70%
Predicted preference
Actual preference
D. Read (Leeds U.) & B. van Leeuwen (Leeds U.), 1998, Predicting hunger: The effects of appetite
and delay on choice. Organizational behavior and human decision processes, 76, 189-205.
Hyperbolic discounting
This is an example of under-rating the intensity
of future desires
Hyperbolic Discounting, Measured
• Evidence suggests that discounting is steeper
in the immediate future than in the further
future.
• In one study, the median subject is indifferent
between
– $15 now and $20 in one month (for an annual
discount rate of 345 percent) and between
– $15 now and $100 in ten years (for an annual
discount rate of 19 percent).
Hyperbolic Discounting
• When evaluating outcomes in the distant future,
individuals are patient and make plans to
exercise, stop smoking, and look for a better job.
• As the future gets near, the discounting gets
steep, and the individuals engage in binge eating,
light another (last) cigarette, and stay put on their
job.
• Preferences with these features therefore induce
dynamic inconsistency.
Gym Memberships
• In one study, three U.S. health clubs offered a
choice between
– a monthly contract with lump sum fee of
approximately $80 per month and no payment per
visit, and
– a pay-per-visit contract with fee of $10.
• Health club users that choose the monthly
contract attend only 4.4 times per month.
• These users pay $17 per visit even though they
could pay $10 per visit
Homework and Deadlines
• The subjects are fifty-one professionals
enrolled in a section of a semester-long
executive education class at Sloan (MIT), with
three homeworks as a requirement.
• At the beginning of the semester, they set
binding deadlines (with a cost of lower grades
for delay) for each of the homeworks.
Homework and Deadlines
• According to the standard model, they should
set deadlines for the last day of the semester:
– There is no benefit to setting early deadlines,
since they do not receive feedback on the
homeworks, and there is a cost of lower flexibility.
– A maximization without constraints is always
preferable to one with constraints.
Homework and Deadlines
• According to a model of self-control, instead, the
deadlines provide a useful commitment device.
• Since homework completion is an investment
good, individuals spend less time on it than they
wish to ex ante.
• A deadline forces the future self to spend more
time on the assignment.
• The results support the self-control model: 68
percent of the deadlines are set for weeks prior
to the last week, indicating a demand for
commitment.
Homework and Deadlines
• This result leaves open two issues.
– First, do the self-set deadlines improve
performance relative to a setting with no
deadlines?
– Second, is the deadline setting optimal?
• If the individuals are partially naive about the
self-control, they will underestimate the
demand for commitment.
Homework and Deadlines
• In a second (laboratory) experiment, sixty
students complete three proofreading
assignments within twenty-one days.
• The control group can turn in each assignment at
any time within the twenty-one days
• A first treatment group can choose three
deadlines (as in the class-room setting described
above), and
• A second treatment group faces equal-spaced
deadlines.
Homework and Deadlines
• The first result is that self-set deadlines indeed
improve performance:
– The first treatment group does significantly better
than the control group, detecting 50 percent more
errors (on average, 105 versus 70) and earning
substantially more as a result (on average, $13
versus $5).
Homework and Deadlines
• The second result is that the deadline setting
is not optimal:
– the group with equal-spaced deadlines does
significantly better than the other groups, on
average detecting 130 errors and earning $20.
• This provides evidence of partial naiveté
about the self-control problems.
Credit Card Offers
• Borrowers were offered two types of credit
card contracts:
– Low teaser interest rate for first six months,
followed by high post-teaser interest rate after the
first six months
– Higher teaser rate, followed by lower post-teaser
rate
• Borrowers went for the first contract even
though, given their borrowing behavior, they
would have been better off with the second
In the future, I expect to
prefer the long-term, rational
choice.
Later v. Now
When the future
becomes “right
now,” I prefer the
pleasurable choice!
[hyperbolic discounting]
In the future, I expect to
prefer the long-term, rational
choice and quit smoking.
When the future
becomes “right now,”
I keep smoking.
Hyperbolic discounting with smoking?
Self-predicted future behavior in
teenage smoking
15% of light smokers (less than one
cigarette per day) in high school predicted
they “might” be smoking in 5 years.
15%
predicted
5 years later, what percentage
were still smoking?
a) Less than 5%
b) 5% to 15%
c) About 15%
d) 15% to 30%
e) Greater than 30%
L. Johnston (U. Michigan), P. O’Malley (U. Michigan), J. Bachman (U. Michigan), 1993, Illicit drug use, smoking, and drinking by America’s high
school students, college students, and young adults, 1975-1987. National Institute on Drug Abuse: Rockville, Maryland.
Self-predicted future behavior in
teenage smoking
15% of light smokers (less than one
cigarette per day) in high school predicted
they “might” be smoking in 5 years.
15%
predicted
43%
actual
5 years later,
43% were still
smoking.
L. Johnston (U. Michigan), P. O’Malley (U. Michigan), J. Bachman (U. Michigan), 1993, Illicit drug use, smoking, and drinking by America’s high
school students, college students, and young adults, 1975-1987. National Institute on Drug Abuse: Rockville, Maryland.
Emotions
• Hyperbolic discounting may be more likely
when people find themselves in an
emotionally aroused state
Economic Consequences of Hyperbolic
Discounting
• Excessive spending, inadequate saving
(especially for retirement), bankruptcy, and
debt default
• Inadequate personal investment in education
• National neglect of investment on
infrastructure, public education, scientific
research
• Excessive national spending on wars and other
trivial issues that have immediate appeal
PROJECTION BIAS
Projection Bias
• Hyperbolic discounting is not the only kind of
systematically incorrect prediction that we are
prone to
• There’s also projection bias
Projection Bias: our current state (hot v. cold) influences
projections of our future desires.
Cold v. Hot
Does the current state of hunger change which snack people
will order for delivery next week?
a) Yes, hungry people choose the unhealthy snack
b) Yes, hungry people choose the healthy snack
c) No
Projection of future preferences
depends on our current state
People asked right after
lunch (not hungry), chose
the unhealthy snack for
delivery in one week right
after lunch
42% of the time.
People asked four hours
after lunch (hungry), chose
the unhealthy snack for
delivery in one week right
after lunch
78% of the time
I’m not hungry right
now, so next week I
will prefer the
healthy snack.
I’m hungry, so next
week I will prefer
the candy bar.
Cold v. Hot
Cold v. Hot
Projection bias
Cold state projects to future cold state
I’m not hungry right
now, so next week I
will prefer the
healthy snack just like
I do right now.
Hot state projects to future hot state
I’m hungry, so next
week I will prefer
the unhealthy
choice just like I do
right now.
Return rates of cold weather items
• Conlin, O’Donoghue, and Vogelsang (2007)
find that a reduction in the order date
temperature of 30°F—corresponding to a
decrease, for example, from 40°F to 10°F—
increases the average return rate of a coldweather item by 3.96 percent, consistent with
projection bias.
An experiment with
heroin addicts
Heroin addicts in treatment
receive a replacement drug.
It produces a mild high
designed to ward off heroin
cravings.
A double-dose produces a
longer, more intense high.
Choice between money or a
double-dose, either to be
received in five days.
G. Badger (U. Vermont), W. Bickel (U. Arkansas), L . Giordano (Duke), E. Jacobs (S. Illinois U.), G. Loewenstein
(Carnegie Mellon), L. Marsch (St. Luke’s Hospital, NY), 2007, Altered states: The impact of immediate craving
on the valuation of current and future opiods. The Journal of Health Economics, 26, 865-876.
Projection bias predicts that heroin addicts…
a) Would forego more money for the promise of
an extra dose in 5 days if they were currently
craving.
b) Would forego less money for the promise of
an extra dose in 5 days if they were currently
craving.
c) Would forego more money for an immediate
extra dose than for one in 5 days.
d) The state of craving would make no impact
because they don’t get the extra dose for 5
more days.
$70
$60
$50
Amount of
future money $40
willing to give
up for double- $30
dose in 5 days
$20
$10
$0
Before regular dose
When in a HOT state, I
act as if I will always
be in a HOT state.
After regular dose
When in a COLD state,
I act as if I will always
be in a COLD state.
I need a hit now, so
next week I will prefer
an extra dose to $50.
I don’t need
drugs now, so
next week I
will prefer
$50 to an
extra dose.
$70
Amount of $60
future $50
money
willing to $40
give up for $30
doubledose in 5 $20
days
$10
$0
Before regular dose
After regular dose