Hyperbolic discounting : Some old results; some recent results;

some interpretationDaniel Read (WBS)

Yael Grushka-Cockayne (Darden)

Lisheng He (WBS)Umar Taj (WBS)

Intertemporal choices

NOW SOME YEARS HENCE

• Choices between outcomes that occur at different times.

• Usually a trade off between smaller-sooner (SS) and larger-later (LL) outcomes.

Diversity of intertemporal choices

• Employment now or Education now and work later• Misery now or Purgatory later• Submit research now or wait for definitive findings• Children now or Children later• Carbon reduction now or mitigation later• Smoke now or Live longer• Dessert now or Slender Later

• £100 now or £150 in one year

Typical intertemporal choice question

€200 Today €____ in 2 years

What would you demand in 2 years in exchange for giving up € 200 today?

Write down your answer

Measuring your annual “discount rate”% (Up to) € N

2% 2084% 2168% 233

16% 26924% 30748% 438

> 48% >438

£ 200 versus £ ______ in two years

Write down your discount rate.

What are your reasons?

What are your reasons?

• “I am impulsive, and 2 years is a long time to wait.”

• “I could use it to buy my wife/husband/SO/child a gift.”

• “I need the money now;” “I don’t need the money now.”

• “I can earn more by investing the money.”

Normative theory: Intertemporal choices for money and market goods

• Determine the opportunity cost of money?

• The interest rate currently being earned (for savers) or paid (by borrowers)

• If offered a return more than you are earning in your savings account, you should take the later outcome. Otherwise take the earlier one.

I had a reduction schedule carefully worked out. It was supposed to take twelve days. I had the junk [heroin] in solution, and in another bottle distilled water. Every time I took a dropper of solution out to use it, I put the same amount of distilled water in the junk solution bottle. Eventually I would be shooting plain water.

Four days later in Cincinnati, I was out of junk and immobilized. I have never known one of these self-administered reduction cures to work. You find reasons to make each shot an exception that calls for a little extra junk. Finally, the junk is all gone and you still have your habit.

Inconsistent preferences due to time

From Junky

10

A “classic” study

• Office workers chose between junk food or a piece of fruit.

• One week before, and then immediately before, consumption.

530 kCal per 100 g

95 kCal per 100 g

11

The results

Male Female Male FemaleOne week early Now

0%

25%

50%

75%

100%

Read & Van Leeuwen, 1998; See also Kirby and Herrnstein, 1995.

Distribution of choice patterns

Healthy now, Healthy Later

Healthy now, Junk Later

Junk Now, Healthy Later

Junk Now Junk Later0

0.2

0.4

0.6

P(H|Switch) = 93%

P(A|Switch) = 7%

Vice (SS)

Virtue (LL)

Decision utility

Good intentions

Vicious Impulse

Preference reversal

Earlier Time Later

Hyperbolic discounting

But does that study provide evidence for hyperbolic discounting?

• Both kinds of food available at the same time.• We must assume a difference in reward

distribution for the Junk and Healthy food.

Assumption underlying the hyperbolic discounting interpretation

• The utility distribution from junk food is more ‘front loaded’ and adds up to less than the distribution from fruit.

Instantaneous utility / value

Time

Thaler’s (1981) example

A thought experiment: Often replicated … in thought

Our study

Results: When the blue bar is higher we have the “apple” effect.

Now-One year One year-Now Now-One year One year-NowApple questions first Apple questions second

60%

65%

70%

75%

80%

85%

90%

NowOne year

Choice pattern groups

One One (

Impati

ent)

Two O

ne (Anti-hyp

er)

One Two (H

yperb

olic)

Two Tw

o (Pati

ent)

0

50

100

150

200

250

300

350

400

Apple Choices

p(A|Switch) = .47

p(H|Switch) = .53

Two Conclusions

• Average apple choice: 78% now, 80% in one year. Very weak evidence of hyperbolic discounting.

• Many people want one apple in a year.

• Thought experiments are not always the best way to learn about the world

Studies using Google Consumer Surveys

EVERY study in first wave showed anti-hyperbolic discounting

Not the presence of an “indifference” option

Not simply unusually large magnitudes or delays

What do people do when they are “indifferent”?

They disproportionately choose SS.

Amount or Delay within subjects?

This made no difference!

Replicated with UK sample provided by marketing firm.

Percent choosing LL – “anti-hyperbolic” effect is very large.

Effect of Cognitive ability (CRT score)

Effect of age?

More on age

Now-1 year

1 year – 2 year

Pakistan panel:N=2028, National representative sample

• Suppose that you were to receive some money. If you receive the money today you will get Rs. 500, but if you wait one month you will receive Rs. 750.

• If you receive the money in six months you will get Rs. 500, but if you wait seven months you will receive Rs. 750.

Pakistan Wave 1

Pakistan Wave 2

Conclusion

• Impulsivity is observed when trading off “virtues” and “vices”

• Hyperbolic discounting explains this effect, but only occasionally choices for money.– Anti-hyperbolic discounting common– No effect of delay to outcome common– Common experience of temptation or impulsivity requires

explanation• Also, discounting varies among outcomes. We are

patient about library books, less patient about heroin. (If we want both heroin and library books)

What produces “hyperbolic” discounting?

1. Emotions/”visceral” factors 2. Psychophysics3. Multi-criteria discounting

1. Visceral arousal/emotions Triggering stimulus present

or effective? No Yes Act available now?

No No Desire No Action

Desire No Action

Yes No Desire No Action

Desire Action

2. Psychophysics• Psychophysics: Intervals seem smaller when

delayed, and can become “peanuts”.

0 5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

time perception

Psychophysics for other outcomes is uncontroversial

• Diminishing marginal utility/marginal value for money

0.00 € 5.00 € 10.00 € 15.00 € 20.00 € 25.00 € 30.00 € 35.00 € 40.00 € 45.00 € 50.00 €0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

amount perception (value)

3. Multi-dimensional discounting

• Outcomes are typically multi-dimensional.

• The value of each dimension changes as a function of delay at different rates.

• Implication: Time inconsistency

• If the value change is negative (discounting)• Implication: Hyperbolic discounting

p

q

Taste

Health

𝜹𝒕𝒑

𝜸 𝒕𝒒

(Mixed)

p

q

Money

Money

𝜹𝒕𝒑

𝜹𝒕𝒒

(Uniform)

Preference reversals caused by dimension-dependent discounting

Any questions?

• I still don’t know what causes “anti” hyperbolic discounting.

How do students compare to the rest of the UK?