Questions: Intertemporal Choice in Behavioral Economics

Question 1

A person prefers $100 today over $110 tomorrow, but also prefers $110 in 31 days over $100 in 30 days. This preference pattern is best explained by...

• A. Standard exponential discounting with a high discount rate
• B. Hyperbolic or quasi-hyperbolic discounting, which produces present bias and preference reversals
• C. Risk aversion — the person is uncertain about future payments
• D. Loss aversion — the person views delay as a loss

Answer: (B)

Exponential discounting cannot produce this reversal — if you prefer $100 today over $110 tomorrow, exponential discounting requires that you also prefer $100 in 30 days over $110 in 31 days, because the ratio of discount factors between consecutive days is constant. Hyperbolic and quasi-hyperbolic discounting produce steeper discounting for near-future delays than distant-future delays, so the one-day delay looms much larger when it is imminent (today vs. tomorrow) than when it is remote (day 30 vs. day 31). This preference reversal is the hallmark of present bias.

Question 2

In the quasi-hyperbolic (beta-delta) model, a sophisticated agent who knows they have present bias will behave identically to a naive agent who is unaware of their bias.

• T. True
• F. False

Answer: False

Sophisticates and naifs behave differently because sophisticates anticipate their future self-control problems. A sophisticated present-biased agent knows that their future self will over-discount, so they may seek commitment devices (automatic savings enrollment, gym contracts with penalties, deadlines) to constrain future behavior. A naive agent falsely believes they will follow through on plans, so they do not seek commitment and are repeatedly surprised by their own procrastination or impulsive behavior. The distinction between sophistication and naivete has major implications for policy design — commitment devices help sophisticates but may be ignored or avoided by naifs.

Question 3

What is a commitment device, and why does the existence of demand for commitment devices provide evidence against exponential discounting?

Model answer: A commitment device is a mechanism that restricts a person's future choices — such as automatic payroll deductions into a savings account, a gym contract with cancellation penalties, or Odysseus binding himself to the mast. Under exponential discounting, preferences are time-consistent, so there is no reason to constrain your future self — your future self will want exactly what your current self plans. Demand for commitment devices implies that people anticipate their preferences will change in ways they currently consider suboptimal, which is precisely what present bias and time inconsistency predict.

The revealed preference for commitment is among the strongest evidence for time inconsistency. Products like Save More Tomorrow (Thaler and Benartzi), where employees pre-commit to allocating future raises to savings, exploit the fact that people can plan wisely for the distant future but cannot execute those plans when the future becomes the present. The demand for such products is economically irrational under exponential discounting but perfectly rational under quasi-hyperbolic discounting with sophistication.

Question 4

How does the beta parameter in the quasi-hyperbolic model relate to present bias?

Model answer: The beta parameter (0 < beta <= 1) captures the degree of present bias. When beta = 1, the model reduces to standard exponential discounting with no present bias. As beta decreases below 1, the agent places increasingly disproportionate weight on immediate payoffs relative to all future payoffs. Empirical estimates typically place beta between 0.6 and 0.9, meaning people treat the present as 10-40% more valuable than even the very near future, over and above the normal time preference captured by delta.

The beta-delta model (Laibson, 1997) elegantly separates two distinct aspects of time preference: delta captures the standard long-run patience (how much you discount one period against the next in the future), while beta captures the additional pull of the present moment. This two-parameter structure is both tractable and empirically powerful — it generates time-inconsistent behavior with a minimal departure from the standard exponential model, which is why it has become the workhorse model in behavioral economics applications to savings, procrastination, and addiction.