Intertemporal Choices

Question 1

Standard Discounted Utility Model Assumptions

Answer 1

Frederick et al (2002):
1. Utility independence= rules out any preference for utility over time
2. Consumption independence= a person’s preference between Italian and Thai restaurant should not be dependent on whether they consumed Italian the night before, or planning to consume the day after.
3. Stationary instantaneous utility= well-being is the same in all periods.
4. Constant discounting and Time consistency = constant discount factor = implies that people’s preferences are time consistent, but people have a preference for immediate rewards and try to delay losses as much as possible
=> LITTLE EMPIRICAL SUPPORT

Question 2

Hyperbolic Discounting

Answer 2

A person has a declining rate of time preference - increasing discount factor, declining discount rate. meaning that they heavily discount the future in relation to the present.

e.g. Preference Reversal:
A: 110 in 31 days or B: 100 in 30 days
=> people choose A
C: 100 today or D: 110 tomorrow
=> people choose C
Violates the assumption of constant discounting, discount factor is increasing over time, discount the future heavily = we are impatient!

Question 3

The Beta-Delta Model of Hyperbolic discounting

Answer 3

D(k)= 1. k=0
βδ^k k>0
see notes, for full

Question 4

Implication of Hyperbolic Discounting

Answer 4

Procrastination - can explain empirical observations in the consumption-saving literature. we tend to procrastinate when it comes to losses and preoperative for gains.
Also: addiction- over-consume harmful products because we do fail to project their addictiveness into the future

Question 5

O’Donoghue and Rabin (1999)

Answer 5

Doing it now or later: Scenario where individuals have to do a report over the span of 4 weeks, in each week there is a movie to watch and therefore have to choose which movie to miss to do the report. Last Week - best movie (Johnny Depp)

Distinguish between 3 groups of individuals:

1. Time consistents - will do the report
2. Naifs: repeatedly put off tasks, because of their self-control problems - incorrectly predict
3. Sophisticates: sophisticates are aware of their time-inconsistency and self-control problems. they can mitigate self-control problems, by foreseeing how much they will procrastinate and will not procrastinate when doing so is too costly.

1 - do the report in Week 1
2 - do the report in Week 4
3 - do the report in Week 2 - solved by backward induction

Question 6

Ashraf et al (2006)

Answer 6

Commitment savings device: SEED - Save, Earn and Enjoy Deposits in Philippines
Three Treatments:
1. Control Group
2. Commitment savings device group - only around 28% took up the savings device
3. Marketing, no commitment

Results:
Significant and positive results of up to 80% increase in savings
Policy implications:
Workers, who are sophisticates - aware of their self-control problems are willing to take the device to mitigate issues. The bank will find it optimal to only provide the commitment device where there are enough sophisticates, otherwise will not take up on the device if time consistent or naif (where they are unaware of their procrastination and self-control problems)
Marketing had no effect

Question 7

Royer et al (2015)

Answer 7

Effect of a commitment device for exercise of workers in a Fortune 500 company. 
Three treatments:
1. Control
2. Incentive only
3. Incentive and commitment

= invested in a commitment device with stakes that they had to go to the gym, otherwise money would go to charity
Results:
1. Incentive-only increased gym attendance by 25% in the first months, then 20% - not long lasting, difference disappeared
2. incentive and commitment - increased by 30%, long-lasting effect

Implications:

1. workers who are sophisticates - aware of self-control issues
2. gender differential: women are more willing - more risk averse (testosterone levels)

Question 8

Kaur et al (2015)

Answer 8

Self-Control at work

Two objectives:

1. test the effect of timing of pay on worker’s effort
2. test whether sophisticates are more willing to choose a contract that penalises them for not achieving a self-chosen threshold

Design:
Two groups:
1. control
2. treatment: offered a contract which penalises them, effort is seen as an investment good

Results:
1. confirms hypothesis 2 about sophisticates

Question 9

Habit Formation Models

Answer 9

The utility from current consumption (“tastes”) can be affected by the level of past consumption - element of habit e.g. smoking cigarettes

assume that all effect of past consumption for current utility enter through a state variable

BM model - addiction = rational, forward looking and time-consistent
Gruber and Kruszegi = forward looking but time-inconsistent.

Question 10

Reference Point Models

Answer 10

According to prospect theory, outcomes are evaluated based on reference points.
Hence, shifting consumption between periods is made less desirable by loss aversion as one will end up losing consumption in one period to make up for the increase in the next period.

Question 11

Loewenstein (1987)

Answer 11

Utility from Anticipation = people are looking forward to experiencing something/watching something and derive utility from that anticipation
Anticipatory utility provides a reason to prefer improvement and for getting unpleasant outcomes over quickly instead of delaying => creates a downward bias on discount rates

e.g. Students rank favourite days, Sunday was ranked below Friday, even though classes where held. Friday was marked by anticipation of the weekend.

Question 12

Loewenstein et al (2000)

Answer 12

Projection Bias = people project their current state and preferences into the future

e.g. workers asked to choose between the healthy and unhealthy snack either when they are hungry or satiated. when hungry, they incorrectly project current hunger into the future and opt for the unhealthy snack in anticipation that it will be more filling.

Question 13

Multiple Self Models

Answer 13

Assumption: there are two agents, one myopic and one far-sighted - alternately take control (good theory, but does not tell us when one dominates the other)

“Planner-doer” model, draws upon the principal-agent theory - myopic doers, care only about immediate gratification and planners who care about the future.

Conclusion: multiple selves - draws connection between inter-temporal choice

Question 14

Guiso et al (2013)

Answer 14

Time Varying Risk aversion - after the Great Depression, risk aversion increases even among those who did not experience any loss - fear drives uncertainty, changing risk preferences.