Hyperbolic discounting Some old results some recent results

Hyperbolic discounting : Some old results; some recent results; some interpretation Daniel Read (WBS) Yael Grushka-Cockayne (Darden) Lisheng He (WBS) Umar Taj (WBS)

Intertemporal choices • Choices between outcomes that occur at different times. • Usually a trade off between smaller-sooner (SS) and larger-later (LL) outcomes. NOW SOME YEARS HENCE

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) 2% 4% 8% 16% 24% 48% > 48% € 208 216 233 269 307 438 >438 N £ 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.

Inconsistent preferences due to time 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. From Junky Four days later in Cincinnati, I was out of junk and immobilized. I have never known one of these selfadministered 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.

A “classic” study • Office workers chose between junk food or a piece of fruit. • One week before, and then immediately before, consumption. 530 k. Cal per 100 g 95 k. Cal per 100 g 10

The results 100% 75% 50% 25% 0% Male Female One week early Read & Van Leeuwen, 1998; See also Kirby and Herrnstein, 1995. Male Female Now 11

Distribution of choice patterns 0, 6 P(H|Switch) = 93% 0, 4 0, 2 P(A|Switch) = 7% 0 Healthy now, Junk Later Junk Now, Healthy Junk Now Junk Later

Hyperbolic discounting Virtue (LL) Vicious Impulse Decision utility Good intentions Vice (SS) Preference reversal Earlier Time Later

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. 89% 84% 79% Now One year 74% 69% 64% Now-One year-Now Apple questions first Now-One year-Now Apple questions second

Choice pattern groups 400 Apple Choices 350 300 250 200 150 p(A|Switch) =. 47 100 p(H|Switch) =. 53 50 0 One (Impatient) Two One (Antihyper) One Two (Hyperbolic) Two (Patient)

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 antihyperbolic 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.

Replicated with UK sample provided by marketing firm. Amount or Delay within subjects? This made no difference!

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

Effect of Cognitive ability (CRT score)

Effect of age?

More on age Now-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. Psychophysics 3. Multi-criteria discounting

1. Visceral arousal/emotions

2. Psychophysics • Psychophysics: Intervals seem smaller when delayed, and can become “peanuts”. time perception 1, 8 1, 6 1, 4 1, 2 1 0, 8 0, 6 0, 4 0, 2 0 0 5 10 15 20 25 30 35 40 45 50

Psychophysics for other outcomes is uncontroversial • Diminishing marginal utility/marginal value for money amount perception (value) 1, 8 1, 6 1, 4 1, 2 1 0, 8 0, 6 0, 4 0, 2 0 0, 00 € 5, 00 € 10, 00 € 15, 00 € 20, 00 € 25, 00 € 30, 00 € 35, 00 € 40, 00 € 45, 00 € 50, 00 €

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