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…

Reed, Lowenstein & Kalyanaraman (1999) Mixing virtue and vice: Combining the immediacy effect and the diversification heuristic. Journal of Behavioral Decision Making, 12, 257-273.

Low Brow; 56%

High Brow; 44%

Low Brow; 37%

High Brow; 63%

Low Brow; 29%

High Brow; 71%

Choosing for tonight Choosing for next Thursday Choosing for second Thursday

When choosing between a healthy and unhealthy snack for delivery in one week, do people systematically misproject future desires?

Does the future me want different things?

← 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.

Are people a) More likely to choose the unhealthy snack for next weekb) More likely to choose the unhealthy snack for right nowc) About as likely either way

Does the future me want different things?

← 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.

26% chose the unhealthy snack for delivery in one week right after lunch.

Does the future me want different things?

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.

26%74% ← Next Week→Predicted preference

One week later, when allowed to change their choice at the delivery, 70% chose the unhealthy snack for immediate consumption

Does the future me want different things?

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.

26%74%30% 70%

← Next Week→Predicted preference

← Right Now→Actual preference

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

[hyperbolic discounting]

In the future, I expect to prefer the long-term, rational choice. When the future

becomes “right now,” I prefer the

pleasurable choice!

Later v. Now

Hyperbolic discounting with smoking?

In the future, I expect to prefer the long-term, rational choice and quit smoking. When the future

becomes “right now,” I keep 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.

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.

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%

15% predicted

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.

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.

5 years later, 43% were still smoking.

15% predicted

43% actual

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 snackb) Yes, hungry people choose the healthy snackc) 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

Projection bias

I’m not hungry right now, so next week I will prefer the healthy snack just like I do right now.

I’m hungry, so next week I will prefer the unhealthy choice just like I do right now.

Cold state projects to future cold state

Hot state projects to future hot state

Cold v. Hot

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 cold-weather 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.

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.

Projection bias predicts that heroin addicts…

When in a HOT state, I act as if I will always

be in a HOT state.

Before regular dose After regular dose$0

$10

$20

$30

$40

$50

$60

$70

Amount of fu-ture money

willing to give up for double-dose in 5 days

When in a COLD state, I act as if I will always be

in a COLD state.

Before regular dose

After regular dose$0

$10

$20

$30

$40

$50

$60

$70

Amount of future

money will-ing to give up for dou-ble-dose in

5 days

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.