Fee Framing and Intertemporal Choice: An Experimental Test of Description Invariance

Framed laboratory experiment with two between-subjects arms, run in supervised in-person sessions at Bangor University. Participants complete the experiment in oTree on their own phones, reached by QR code.

Sequence, identical in both arms until the choice task:
1. Cognitive Reflection Test: three items, three minutes each. If time expires, the page advances automatically and the timeout is recorded.
2. Real-effort task: participants count the zeros in three grids of 150 randomly generated 0s and 1s. The correct count must be entered for each grid to proceed; attempts are unlimited. Completing the task earns a ticket for a lottery with a prize of up to £50.
3. Choice task: a ten-row multiple price list (MPL), where the treatment is applied (see below).
4. A certainty question about the choices just made.
5. A short questionnaire: demographics, financial literacy and perceived financial constraint.
The lottery result is then shown.

Choice task. In each row the participant chooses between Option A, an amount paid tonight, and Option B, £50.00 paid in four weeks. Both options are paid by bank transfer: Option A on the evening of the session, Option B four weeks later. All ten rows must be answered, and choices may switch at most once, from Option A to Option B; the software rejects any other pattern. The amount paid tonight falls from row 1 to row 10: £49.95, £49.75, £49.50, £49.00, £47.50, £45.45, £41.65, £33.35, £16.65, £0.00.

Treatment. The arms differ only in how Option A and its cost are described. All amounts, the page layout and the payment rules are otherwise identical, so payoffs are the same row by row.
- T1 (control), opportunity-cost frame. Option A is shown as the amount itself, e.g. "Receive £49.00". The instructions read: "You may choose to receive a smaller amount tonight, or the full amount in 4 weeks."
- T2 (treatment), early-access-fee frame. Option A is shown as £50.00 minus a fee equal to the difference, e.g. "Receive £50.00 (minus £1.00 Fee)", with fees rising from £0.05 in row 1 to £50.00 in row 10. The instructions read: "You can access these funds tonight by paying an early access fee. Alternatively, you can receive the funds in 4 weeks."
Option B reads "Receive £50.00" in both arms.

Payment. Every participant receives a £2 show-up fee in cash. Each lottery ticket independently wins with probability 1 in 15. For a winner, the software draws one of the ten rows at random and pays the option chosen in that row.

2026-09-28

2027-04-30

Switch row: the first of the ten rows of the multiple price list at which the participant chooses £50.00 in four weeks (Option B) over the amount paid tonight (Option A). An integer from 1 to 10; a lower value means the participant chooses to wait at a smaller cost of receiving money tonight.

Construction. Each participant makes ten choices, row 1 to row 10, between Option A (an amount paid tonight) and Option B (£50.00 in four weeks). The switch row is the first row in which Option B is chosen. All ten rows must be answered, and the software accepts only patterns of zero or more Option A choices followed by zero or more Option B choices. The switch row is therefore unique and exactly observed for every participant who chooses Option B at least once.

Exclusion. A participant who chooses Option A in all ten rows has no switch row. This pattern includes preferring £0.00 tonight to £50.00 in four weeks in row 10, a dominated choice, and is treated as a failure to understand the task. These participants are excluded, and their number is reported by arm.

Discount rate (descriptive only; not an outcome and not used in any test). For the amount A paid tonight in a row, the four-week rate is (50 - A)/A, annualised by simple multiplication by 13, without compounding. Annualised rates by row: 1.30%, 6.53%, 13.13%, 26.53%, 68.42%, 130.14%, 260.62%, 649.03%, 2,603.90%, and no finite value in row 10 (A = £0.00). A participant who switches at row k has a rate between the rates of rows k - 1 and k. Rates are assumed non-negative, so a row-1 switcher's rate lies between 0% and 1.30%. A row-10 switcher's rate has no upper bound; any summary based on interval midpoints excludes row-10 switchers and reports how many were excluded.

Certainty: self-reported certainty, from 0 to 100, about the ten choices made in the multiple price list, measured immediately afterwards (a measure of cognitive uncertainty).
Perceived financial constraint: a single seven-point item, from 1 (Not at all) to 7 (Very much), measured in the final questionnaire.

Both secondary outcomes are measured after the choice task. They are analysed as outcomes of the treatment and are never used as control variables: the description participants saw may have changed them, and adjusting for them would compare groups that are no longer comparable by random assignment.

Reported certainty. On the screen immediately after the choice task, participants see a one-sentence summary of what their choices imply about how they value £50.00 in four weeks, and answer: "How certain are you that these are the choices you would want, when one of your rows is selected as the binding decision?" They respond on a slider from 0% (Uncertain) to 100% (Certain), in steps of 1. The slider shows no starting value, and the page cannot be advanced until it has been moved; any response recorded without the slider having been moved is treated as missing, and such cases are counted by arm. The measure is adapted from Enke and Graeber (2023). It shows whether the fee description changes how certain participants are about their choices.

Reported financial constraint. The last item of the closing questionnaire asks: "To what extent do you feel financially constrained?", answered on a scale from 1 (Not at all) to 7 (Very much). The item is based on Tully, Hershfield and Meyvis (2015). It shows whether the fee description changes how financially constrained participants report feeling. The same item is used, descriptively only, in the exploratory analysis described in the Experimental Design Details.

Design. A framed laboratory experiment with two between-subjects arms, run in supervised in-person sessions at Bangor University and completed on participants' own phones. Each participant completes, in order: a three-item Cognitive Reflection Test (CRT); a real-effort task that earns a lottery ticket; a ten-row choice list between an amount paid tonight and £50.00 paid in four weeks, where the treatment is applied; a certainty question; and a short questionnaire. The arms differ only in how the cost of receiving money tonight is described: in T1 as a smaller amount, in T2 as £50.00 minus an early access fee. Payoffs are identical row by row. Full details are under Intervention.

Assignment. Participants are randomly assigned as individuals, after the CRT and before any treatment material is shown. Assignment is stratified by CRT score (high: 2 or 3 correct; low: 0 or 1): within each stratum in each session, participants are assigned in randomly ordered blocks of four, two to each arm. The software shows each participant the description for their assigned arm, so assignment and treatment coincide.

Amendment of 22 September 2026. This registration was amended before collection of the data used in the confirmatory analysis. Changes and reasons:
- The predicted direction of the main effect is reversed to correct an error. The original registration predicted later switching and higher discount rates. The prediction registered here, that participants shown the fee choose to wait earlier and so show lower implied discount rates, is the one stated in the study protocol approved by the College of Arts, Humanities and Social Sciences AREC, Bangor University, on 2 March 2026 (reference 1397), before any data were collected. A two-sided 90% confidence interval is reported whatever the sign of the estimate, so an effect in the originally registered direction would remain visible.
- The primary outcome changes from the discount rate to the switch row. This changes the unit of measurement, not what is measured; the rate is kept as a descriptive figure.
- Sessions are held in person, supervised, on participants' own phones, instead of online.
- A three-item CRT is added at the start and used to stratify assignment, which was previously unstratified.
- The planned sample falls from 400 (200 per arm) to 240 (120 per arm) to fit the available funding. The minimum detectable effect at this sample size is given in the power calculation.
- The stake falls from £60 to £50; each lottery ticket wins with probability 1 in 15, and one row is paid; both options are paid by bank transfer, as stated to participants; the "(Free)" label is removed from the delayed option.
- The Holt and Laury (2002) risk task is dropped, and with it the joint estimation of risk and time preferences (Andersen et al. 2006) and the risk-corrected discount factor.
- Cognitive uncertainty changes from a control variable to a secondary outcome, because it is measured after the choices. Its question is reworded (quoted under Secondary Outcomes), and the slider must now be moved before the participant can continue. Reported financial constraint is added as a secondary outcome.
- H2 and H3 are registered as exploratory. An analysis plan, set out in the Experimental Design Details, and a power calculation are added.
- Data from earlier pilot sessions are excluded. They were collected on a previous version of the instrument, which lacked several of the changes above and also did not block assignment, record CRT timeouts, or show a certainty-page summary to participants who switch in row 1 or never switch.
- Claims that the design isolates surcharge aversion or measures demand for credit are withdrawn, and the title is changed accordingly. The original title was "Rational Arbitrage or Behavioural Friction? Isolating the Microfoundations of Demand for Buy Now, Pay Later", under which the ethics approval (reference 1397) was granted.

Not available

Randomisation by computer, performed automatically by the experiment software (oTree) at the individual level, stratified and blocked. When a participant completes the third Cognitive Reflection Test (CRT) item, they are placed in a stratum by CRT score (high: 2 or 3 correct; low: 0 or 1) and given the next arm in that stratum's queue for their session. Each queue is built from blocks of four, two T1 and two T2, in an order drawn at random by the software; a new block is drawn when the previous one is used up. Allocation is therefore 1:1 within every completed block. Assignment takes place before the real-effort task and before any treatment material is shown, and no researcher chooses a participant's arm.

Individual participant. There is a single level of randomisation. Assignment is stratified by Cognitive Reflection Test score and blocked within each experimental session, but sessions are not units of randomisation: participants in the same session can be assigned to either arm.

No

240 individuals

240 individuals

T1 (control, opportunity-cost frame): 120 individuals
T2 (treatment, early-access-fee frame): 120 individuals

Outcome and unit: the switch row, the first of ten rows at which the participant chooses to wait (an integer from 1 to 10). Calculated for 240 analysed participants, 120 per arm, at 5% significance and 80% power, as a comparison of two means: MDE = (z_(1-α) + z_(0.80)) × SD × √(1/120 + 1/120). - Main effect, one-sided test (main hypothesis): 0.32 standard deviations of the switch row. - Main effect, two-sided: 0.36 standard deviations. - Difference in the effect between the two Cognitive Reflection Test strata (exploratory): 0.72 standard deviations. The standard deviation of the switch row is not known before data collection. Because the switch row lies between 1 and 10, its standard deviation cannot exceed 4.5 rows. The one-sided MDE is therefore at most 1.44 rows (16% of the nine-row range) and the two-sided MDE at most 1.63 rows (18%). Treatment is not clustered, so no design effect applies. The calculation ignores the precision gained from stratified assignment, which cannot increase the variance of the estimate. Excluding participants who fail to understand the task would reduce the analysed sample and raise the MDE slightly.