ECON30019 Chap.15 Intertemporal Choice: Discounting and Present Bias
Intertemporal Choice: Discounting and Present Bias
Every earlier chapter compared outcomes arriving at the same moment. Intertemporal choice compares outcomes arriving at different moments, which needs one new object: a rule converting future value into present value. Under exponential discounting a single factor is applied once per period, so patience is one number.
The examinable consequence is stationarity, that the ranking between two dated options depends only on the gap between them and not on how far away both are, and stationarity is what licenses the word plan. The observed pattern breaks it: offered a smaller reward now against a larger one soon, many people take the smaller, while the same people offered the same gap far in the future take the larger.
The repair adds one parameter that discounts everything except the present, and the chapter closes on whether an agent anticipates its own inconsistency.
What this chapter covers
- 01
Why this chapter is here, and what it is built from
- 02
Discounted utility, and patience as a single number
- 03
Stationarity, and why it makes plans meaningful
- 04
Testing stationarity by shifting both dates rather than one
- 05
Preference reversal over time, stated as an observation
- 06
Two discount curves, and the extra step at the origin
- 07
The quasi-hyperbolic form, and the two parameters it separates
- 08
Where the extra parameter cancels and where it does not
- 09
Naive and sophisticated agents, and what each does about the reversal
- 10
Commitment devices, and paying for a smaller choice set
Find the present bias that produces the reversal
- 1Test the distant pair under pure exponential discounting: 120 times 0.95 to the sixth against 100 times 0.95 to the fifth, which reduces to 120 times 0.95 against 100.
- 1Evaluate it: 114 exceeds 100, so the patient choice is predicted, matching the observation.
- 1Test the immediate pair under the same model: it requires 100 to exceed 114, which is false, so no discount factor delivers both choices.
- 1Add present bias and re-test the distant pair: the extra factor multiplies both sides, cancels, and still gives the patient choice for any value.
- 1Re-test the immediate pair: it becomes 100 greater than the parameter times 114.
- 1Solve: the parameter must be below 100 over 114, approximately 0.877, and any value below that reproduces both choices.
Key terms
- Discount factor
- The number between zero and one by which a period's delay multiplies value. Two periods multiply by its square, and so on, so patience is captured by a single parameter.
- Stationarity
- The property that the ranking between two dated options depends only on the gap between them, not on how far away both are. It is what makes a plan stable.
- Preference reversal
- A change in the ranking of two dated rewards as both are brought closer, even though the gap between them is unchanged, which stationarity forbids.
- Present bias
- An extra discount applied to everything that is not immediate, captured by a second parameter that is separate from long-run patience.
- Naive agent
- A present-biased agent that believes its future self will not be present biased, so it plans to start tomorrow and is surprised every time it does not.
- Commitment device
- An action taken now that removes or penalises an option later. Willingness to pay for one is the standard behavioural diagnostic for sophistication.
Intertemporal Choice: Discounting and Present Bias FAQ
What exactly does a present-biased person get wrong?
Nothing about long-run patience, and that is the point. A present-biased person ranks two future rewards exactly as an exponential discounter with the same long-run factor would. The failure is located entirely at one point on the timeline, the present, which is why it can only be demonstrated by comparing a decision made in advance with the same decision made on the day.
How do I tell impatience from present bias?
Impatience is a low long-run factor and produces no reversal: a very impatient person prefers sooner rewards at every horizon and stays consistent. Present bias is a claim about inconsistency across horizons, so it needs two comparisons sharing the same gap. If a question gives you only one comparison, it cannot be evidence of present bias, and saying so is the right answer.
Why would anyone pay for fewer options?
Because a sophisticated agent expects its future self to break the plan. Under any standard model more options are weakly better, so a positive price for having options removed is direct evidence that the person anticipates their own inconsistency. That is what makes willingness to pay for a commitment device the cleanest observable test of sophistication.
Exam move
Solve every question here by finding where the extra parameter cancels. Set up both comparisons algebraically before substituting numbers, and check whether the parameter appears on one side or on both, since that determines which comparison it can affect.
Practise calibration questions, where you are given the observed choices and asked for the range of the parameter consistent with them, because that is the shape assessed work uses. For the naive and sophisticated distinction, answer from an observable behaviour rather than from a description of what the agent believes.
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