Predictably Misbehaving

Lecture 5: Choice Over Time (Again)

Joshua Foster at UW-Oshkosh

Multiple Selves Approach

Moe: Oh, boy! The deep fryer's here. Heheh, I got it used from the navy. You can flash-fry a buffalo in forty seconds.

Homer: Forty seconds?!? But I want it now!

Extreme assumptions of behavior over time

How could we tell whether someone is naive or sophisticated?

• The use of commitment devices indicates sophistication.
• Ulysses is (at least partly) sophisticated.
• Misprediction of future behavior indicates naivete.
• Teenage smokers who predict that they will not be smoking in five years have a slightly higher probability of smoking (74%) than those who predict they will be smoking (72%).

(BTW, non-issue under dynamic consistency.)

Naivete Vs. Sophistication

Ex: When to quit smoking

Naive decision-makers:

1. Start at the beginning (i.e. first time step).
2. Solve for the optimal plan at that time step.
• (Assuming future selves will follow the plan.)
3. The person takes the first step in that plan.
4. Go to the next period and repeat.

Ex: When to quit smoking

Sophisticated decision-makers:

1. Start at the end (i.e. last time step).
2. Solve for optimal action.
• (Assuming the person made it that far.)
3. Go back to the previous period.
4. Solve for the optimal action, taking into account what happens in the future.
5. Go back to the previous period, and repeat.

Applications of Hyperbolic Discounting

Default Effects

Madrian and Shea (2001) QJE 401(k) Participation

• These plans are offered by many employers.
• Primary way to privately save for retirement.
• Employees often decide themselves:
• How much of their pay to allocate to the 401(k)
• How to invest their funds.
• This company offered a match (up to 6% of income):
• For every $1 an employee put in their 401(k)
• The company added 50 cents.

On April 1, 1998, the company changed their policy.

Before:

• Employees could participate after one year.
• Were not automatically enrolled.
• (Could enroll easily at any time.)

After:

• All employees were immediately eligible.
• And they were automatically enrolled.
• (Could unenroll easily at any time.)

The authors compare the choices of these groups:

1. "Window" cohort: those hired in 1998 before April 1
• (Not automatically enrolled.)
2. "New" cohort: those hired in 1998 after April 1
• (Automatically enrolled.)

Results: Participation and Contribution Rates

Participation rates 3-15 months after being hired:

• 37% for the Window cohort
• 86% for the New cohort

The contribution rates were as follows:

The finding that defaults matter is one of the most important discoveries in applied microeconomics.

Getting a Grip on the Default Effect

This appears to be a big mistake by not participating.

• Offered a 50% return on up to 6% of your income.

Example: for an employee making $40,000.

• That's giving up a $1,200 gift from the company.

Even if it is not a mistake, why does the default matter so much?

• It only takes a phone call to change enrollment.

Would people not bother making a phone call for $1,200?

• If they are naive hyperbolic discounters, they might not.
• And as a result, defaults can be extremely important.

Making the Call:

"I'll do it tomorrow"

Costs and Benefits of Making the Call:

• Benefit: will get 5 per day (1,825 per year) extra for the next 30 years starting tomorrow.
• Cost: pain of the phone call today costs 30

Assume a naive hyperbolic discounter discounts the future at 80%.

When to make the call:

• Today: $-30+0.8\cdot[5\cdot 365\cdot 30] = 43770$
• Tomorrow: $0+0.8\cdot[-30+5\cdot 365\cdot 30 - 5] = 43772$

Hence, they put off making the phone call.

• If nothing changes they put off the phone call forever.

"I'll do it this week"

(Really, I will)

This prediction is extreme - and it's because the model is extreme.

• More reasonable prediction might be they delay for a long time.

Let's change the model:

• What would a sophisticate do?
• It's easy to argue they'd do it within a week.
• Waiting 8 days costs 40, valued at $0.8\cdot 40=32$
• Would rather pay the 30 cost today to avoid this outcome.

When exactly they make the call is a more difficult question.

Other Studies on Procrastination

Choi, et al. (2004) in NBER

• 401(k) contribution patterns generalize.
• Remarkably similar results across three industries.

Other Studies on Procrastination

Cronqvist and Thaler (2004) in AER:

• Looks at privatized retirement funds in Sweden.
• Heavily advertised by the government - 456 plans.
• Initially, 43% of participants chose the default.
• After 3 years, 92% of participants chose the default.

Other Studies on Procrastination

DellaVigna and Malmendier (2006) in AER:

• Study gym-goers' behavior at three US health clubs.
• Customers had two options for how to pay:
1. Monthly fee of ~80 for unlimited use.
2. Pay-per-visit fee of 10.

Most choose the monthly contract (89%)

• Those who do exercise 4.8 times/month (average)
• That's about 17 per visit.

Default Effect: go 2.31 months (average) without using membership before canceling.

It can be argued these findings are consistent with both extreme assumptions of hyperbolic discounting.

Naive hyperbolic discounters:

• Gym-goers prefer they exercise a lot in the future.
• Being naive, that's what they think they'll do.
• To save money on gym they buy the monthly membership.
• Short-run impatience kicks in, and they don't use the membership much.

Sophisticated hyperbolic discounters:

• Also prefer to exercise a lot in the future, but realize they won't.
• Use the monthly membership as a commitment tool.
• Willing to pay more (per-visit) if it helps get them to the gym.

Credit Card Teasers

Ausubel (1991) in AER

• Large experiment run by a credit card company.
• Mailed randomized credit card offers of three types:
1. Standard: 6.9% rate for six months and then 16%.
2. Teaser deal: 4.9% followed by 16%.
3. Post-teaser deal: 6.9% followed by 14%.
• 21 months of data on take-ups and borrowing debt.
• Results:
• Teaser is 2.5 more successful than Post-teaser
• Given behavior, Post-teaser is a much better deal.

Credit Card Teasers

Explanations

Possible explanations from hyperbolic discounting:

1. Naive borrowers believe they'll repay quickly.
• Hence the teaser interest rate is most important.
2. Sophisticated borrowers don't want to use their credit cards much in the future.
• Hence choose a high interest rate to restrain future borrowing.