11. Intertemporal Decision Making

Question 1

What is an intertemporal choice?

Answer 1

Decisions often have a temporal dimension:
Trade-off between outcomes (costs and benefits) that will have their effect at different times.

Eg. Saving for retirement.

Saving today means less consumption today so a current cost. But more consumption in the future = future benefit.

Eg. Whether to have another glass of wine or not, when to clean the cellar or loft room, when to prepare for a presentation or lecture

Decisions involving time taken on the basis of our intertemporal preferences = our relative evaluation of the present and future.

These preferences also affect policy debates concerning global warming, regulating unhealthy behaviour.

Question 2

What is discounted utility?

Answer 2

Traditional approach in economics: discounted utility (DU)

Developed in the 30s and presumes that we discount future benefits and costs.

Suppose: you are offered to either get 1000 kr today, or 1000 in one year: what is the minimal price I would have to offer you to make you wait = discount rate.

We have to get the present value from today’s perspective.

Discounted utility assumes that we discount at a rate theta < 1.

Question 3

What are discount factors?

Answer 3

Discount factors reflect the value/weight we attach to earlier rather than later consumption.

The lower the discount factor, the more important the present (relative to the future) and the more impatient the person is.

Discount factor = constant and positive:

1) Positive discounting: value present more than future
2) Constant discounting = time consistent: if we say today we prefer 1 glass tomorrow to 2 glasses day after, then we should stick with this if asked again tomorrow.

Question 4

What are the assumptions of discounted utility and why is it so widely accepted in economics?

Answer 4

Idea is based on introspection and personal observation.

It has been so quickly accepted as the dominant tool in economics because of its simplicity, but not as a result of empirical research demonstrating its validity.

Early scholars working on intertemporal decisions mentioned different underlying psychological forces influencing our intertemporal choices. Eg. Uncertainty of human life.

DU model compresses all these psychological concerns into a single parameter = the discount factor.

Question 5

What is the traditional economic theory about discounted utility

Answer 5

Discounted utility = max U = sum of the utilities discounted.

Basic idea: for an impatient agent, utility of consuming a good today, is worth more than consuming it tomorrow; Delaying consumption has to pay off.

Assumptions:
Period utility u(xt/st) is time separable
Future utility is discounted with discount factor delta.
Delta is assumed to be constant over time

Exponential discounting D(1) = 1, delta, delta^2, delta^3,…

Question 6

What are the assumptions of the traditional economic theory of discounted utility?

Answer 6

Consumption independence: utility of an outcome today does not depend on future or past outcomes (pizza vs Thai food).

Discount function is the same for all forms of consumption delta is assumed to be constant over time. This implies that people are time consistent.

If at a time t, I prefer x at date tau > t over y at date r + a, then I prefer x over y for all values of t < tau.

People do not override their consumption plans in the future (if no new information and all else equal)

Time preference can be captured in a unique preference parameter delta.

Question 7

How do we measure time preferences?

Answer 7

Time preferences are often measured in simple choice experiments: decide between sooner and smaller vs. Later and larger rewards.

Eg. Dohmen (2010): representative sample, n>1000, participants make 20 choices in a choice table.

Choice always between a payment available today and a larger amount available in one year.
Early payment: 100 euros
Delayed payment: 100+X euros, where X increases across 20 choices.

Result: people’s choices imply an overall high level of impatience.
Strong heterogeneity among participants.

Question 8

What is the difference between discounting in the short vs the long term?

Answer 8

Thaler: “What makes you indifferent between $15 today and $X in 1 month”. Average reply is X=$20.
Implied yearly discount factor of delta = (15/20)^12 = 0.032

What makes you indifferent between $15 today and $X in 10 years. Average reply: X=100
Implied yearly discount factor delta = (15/100)^1/10 = 0.83

Short-run discount rates seem to be higher than long-run discount rates, i.e. discount factor delta lower for short run than for long run decisions.

Question 9

What is the Marshmellow test?

Answer 9

Often difficult to wait for a delayed reward when immediately gratifying alternative is available.

Marshmellow test is one marshmellow now right in front of you and 2 if you wait.

Question 10

What is the link between self control and declining discount rates.

Answer 10

Often difficult to wait for a delayed rewards when an immediately gratifying alternative is available.

It might be difficult to stop smoking when cigarettes are easily available at every corner. Studies suggest that the relapse rate exceeds 50% during the year after quitting smoking.

Situations like this might lead to preference reversals: initially we take a far-sighted decision, eg to stop smking but subsequentely succumb to temptation.

Possible explanation: preference reversals caused by decreasing, rather than constant discount rates.

Question 11

What did Richard Thaler say about self control and declining discount rates?

Answer 11

Richard Thaler asked subjects to specify the amount of money they would require in one month/one year/ten years to make them indifferent to receiving 15 now.

Median responses: 20,50,100.

Implication: average annual discount rate of 345% over a one-month horizon, 120% over a one year horizon and 19% over a ten-year horizon.

Subjective discount rates decrease. We seem to discount heavier over shorter horizons relative to longer horizons. We seem to get more patient the further away certain consequence lies.

Question 12

What is quasi-hyperbolic discounting?

Answer 12

Preferences for immediate gratification can be modeled with a simple, quasi-hyperbolic discount function (Phelps and Pollak 1968, Laibson 1997)

Idea: introduce one additional parameter beta to account for the additional weight that people seem to attach to today’s consumption.

This is not the correc tmodel of intertemporal choice, but often a useful workhorse.

Telative to today’s consumption, all future periods are discounted with an extra factor beta = present-biased preferences

Between any 2 future periods: exponential discounting with factor delta, from today’s perspective.

Main assumption: beta is between 0 and 1.
The lower the B, the stronger desire for instant grafitication/present-bias
Standard model with exponential discounting is captured in beta=1

Question 13

What are naive and sophisticated agents?

Answer 13

Crucial question: are agents aware of their self-control problem? How do they perceive their future time preferences? In particular: do they anticipate that tomorrow will be today from tomorrow’s perspective?

2 cases:
1) Naive agents: present biased but not aware of the self-control problem. They mistakenly assume that they will stick to today’s plans in the future.

Formally: they believe that beta = 1 in future periods.
Partial naiveté: beta’ > beta

2) Sophisticated agents: present-biased, but take into account that future selves will have the same bias. Correctly predict how they would behave if they wait.

Formally: believe that beta’ = beta in future periods. Look for the subgame perfect equilibrium in teh game played by successive selves.

Question 14

How can you overcome self-control problems?

Answer 14

Commitment devices:
Golden eggs = illiquid assets:
Retirement plans which future selves can only opt out at a considerable cost = early withdrawal penalty.
Buying a house might constrain future selves due to transaction costs when selling it.
Buying yearly membership in a fitness club rather than paying per visit = changes incentives for future selves
Marriage
Market for commitment devices

Question 15

What are the market solutions for overcoming self-control problems?

Answer 15

Market solutions can be ineffective and controversial: inefficent outcomes for naive and partially naive people:
Naive people might not demand commitment goods.
Partially naicve people are aware of self control problems, but underestimate their severity: might buy commitment devices at too high prices.

Question 16

What about public interventions for overcoming self-control problems?

Answer 16

Public interventions: sin taxes make the consumption of harmful products even more expensive: fat and sugar taxes.

Public pension schemes force peole to save, educational campaigns make people aware.

Question 17

What did Beshears et al analyze in 2010?

Answer 17

Many household financial decisions: eg. Choosing a savings rate or asset allocation, determining the optimal amount of life insurance, deciding when and how to refinance a mortgage = complex & difficult.

Potential consequence of complexity is: individuals put off confronting these decisions: current psychological costs cs. Future benefits.

Beshears et al analyze 2 low cost interventions: simplified retirement savings plan decision
Low cost interventions: quick enrollment and easy escalation.

Question 18

What is quick enrollment?

Answer 18

Company with 40.000 employees: virtually all employees were eligible for employer sponsored savings plan. Prior to july 2003: a standard opt-in enrollment process.

Employees were not enrolled in the savings plan unless affirmative election = when they chose to enroll.

They also had to select a before-tax and an after-tax contribution rate and specify how to allocate their contributions across eleven investment options offered.

In July 2003: Quick enrollment: a card distributed to new employees attending some orientation meeting.
Employees who checked abox on card were enrolled in the savings plan at a before-tax contribution of 2% of salary and after tax of 0%. Contributions were invested in a preselcted asset allocation

Returning the Quick Enrollment card was not mandatory and people could still use the standard way.

March 2006: company changed the quick Enrollment pre-selects to a before tax contribution rate of 4% of salary inveested in 100% in an age-appropriate target date retirmeent fund and an after-tax contribution rate of 0%.

Question 19

What did company B do with the quick enrollment?

Answer 19

Company B: 20000 employees, almost all eligible to savings plan and could contribute any combination of before and after tax up to 25% of pay. First 6% of pay contributed was matched by company.

Prior to 2004: employees could invest their own contributions in 9 investment options, including employer stock.

Menu grew to encompass twelve options in 2004, standard optin until 2003, quick enrollment after.

Quick enrollment introduced via mailings to employees not yet enrolled.

In 2004 and 2005, company also sent easy escalation forms to employees enrolled but with a before tax plus after tax contribution below 6%.

Easy esclaation form: employees could check a box to increase their contribution to 6% match while keeping the asset allocation they already had.

Finding: quick enrollment increased savings plan enrollment by 15% points at 2 companies relative to standard enrollment mechanism.

Participation gains generated by Quick enrollment did not subsequently reverse. Similar with easy escalation. 15% of low contributors increased their contribution to the match threshold.

Question 20

What conclusion can we draw fraw from simplication and saving?

Answer 20

Complexity of savings decision discourages employees from timely enrollment in employer-sponsored savings plans, even when individuals would prefer participation to non-participation.

Complexity increases current psychological costs relative to future benefits.

Quick enrollment: reduces complexity by allowing employees to enroll at a contribution rate and asset allocation pre-selected by the employer.

Many other decision domains where simplificaiton could be fruitfully employed to help overcome individuals’ tendency to procrastinate.

Question 21

What is Save More Tomorrow?

Answer 21

Four main features:
1) People only have to save later

2) Increases in pension contribuiton joining a SMarT plan happen when they get their nex pay-raise. No loss in current pay, but a decrease in future gains. By avoiding an immediate feeling of loss, it becomes easier for people to accept increases in pension contributions.
3) The SMarT person’s contribution will gradually increase in percentage points with each pay raise, until it reaches a pre-set maximum.
4) People can opt out at any time. They always have the option of opting out. Freedom of choice is maintained.

Question 22

What are the 3 main take aways from helping people overcome their self-control problems?

Answer 22

1) Reduce complexity –> reduce immediate psychological costs
2) Let peole commit now to changes in the future –> peole are more patient when changes happen in the future; more willing to take the long term perspective. Gives them time to plan and adjust.
3) Changes structured in a way that they do not only entail a real cost/loss: eg. Change in future increases.