Rational Arbitrage or Behavioural Friction? Isolating the Microfoundations of Demand for Buy Now, Pay Later

The experiment utilizes an incentivized Multiple Price List (MPL) design to elicit individual discount rates (IDR) under two distinct framing conditions. Participants face a series of intertemporal choices between a smaller, immediate reward (t = 0) and a larger, delayed reward (t = 4 weeks). The principal value is fixed at £60.

1. Treatment 1 (T1): Time discounting (control): Standard intertemporal choice task where the cost of liquidity is presented as an opportunity cost.
1.1 Option A (Now): Receive £X.
1.2 Option B (Later): Receive £60.

2. Treatment 2 (T2): Loss (surcharge) aversion (fee frame): Mathematically isomorphic to the control, but the cost of liquidity is framed as an explicit “transaction fee” or surcharge.
2.1 Option A (Now): Receive £60 minus £Y Fee.
2.2 Option B (Later): Receive £60 (Free).

The net present value (NPV) of Option A in T2, is identical to the Control condition for every row. This isolates the behavioural effect of “surcharge aversion” from standard time preferences.

To Ensure incentive compatibility, the study employs a Random Incentive System (RIS). One row from one MPL is randomly selected for payment implementation.

2026-02-02

2026-02-27

Individual Discount Rate (IDR)

The primary outcome variable for this study is the Individual Discount Rate (IDR), derived from the subject’s switching point in the time preference Multiple Price Lists (MPLs). This variable is defined as the specific row number (1–10) at which a subject switches their preference from Option A (immediate reward) to Option B (delayed reward). For analysis, this switch point will be converted into an interval-censored Implied Annual Interest Rate (APR), utilising the midpoint of the interval implied by the switch to assign a specific numeric value. We test the null hypothesis (H0) that the distribution of these switch points is identical across the treatments, against the alternative hypothesis (H1) that the “Fee Frame” induces later switching, and thus higher IDRs, due to the behavioural friction of surcharge aversion.

Risk-Corrected Discount Factor and Cognitive Uncertainty

As a secondary structural outcome, we will report the Risk-Corrected Discount Factor (Δ), a parameter estimated via Joint Maximum Likelihood Estimation (MLE). This variable represents the underlying time preference parameter after statistically controlling for the curvature of the utility function (r), which is solved jointly drawing from the Holt & Laury (2002) Risk MPL and the treatments. The purpose of this structural endpoint is to isolate “true” time preference from risk aversion, allowing us to test whether the observed treatment effect persists after controlling for utility curvature as per Andersen et al. (2006).

Additionally, we will measure Cognitive Uncertainty to serve as a control variable for decision noise. This endpoint is defined as the subject's self-reported posterior probability (0–100%) that their choice in the MPL aligns with their true utility, elicited immediately after the main task following the protocol of Enke & Graeber (2023). This measure allows us to test whether the “Fee Framing” treatment introduces significant decision noise or confusion compared to the standard intertemporal frame, ensuring that any observed differences in discount rates are driven by preference shifts rather than computational complexity.

This study is a 2x1 between-subjects Randomized Controlled Trial (RCT) designed to elicit individual discount rates (IDRs) under varying descriptive frames. The experiment is conducted online and consists of four distinct phases:

Phase 1: Endowment Induction (Real Effort Task). To mitigate “house money effects” and ensure engagement, all participants must first complete a Real Effort Task (counting zeros in matrices) to earn their study endowment. Only successful completion grants access to the main decision stage.

Phase 2: The Main Intervention (Time Preference Elicitation). Participants are randomly assigned to one of two experimental groups. In both groups, participants face a Multiple Price List (MPL) consisting of 10 binary choices between a smaller immediate reward (“Tonight”) and a larger delayed reward (“In 4 Weeks”). The Net Present Value (NPV) of the choices are mathematically identical across groups; only the framing of the immediate deduction varies:

- Group 1 (Standard Frame): The immediate option is presented as a reduced principal amount (e.g. “Receive £59.40”).
- Group 2 (Surcharge Frame): The immediate option is presented as the full principal minus a transaction fee (e.g. “Receive £60.00 minus a £0.60 fee”).

Phase 3: Structural Parameter Elicitation. Following the main intervention, all participants complete a secondary incentivized task to elicit risk preferences, utilising the Holt & Laury (2002) Multiple Price List. This allows for the joint estimation of utility curvature and time preference. Subsequently, participants report their “Cognitive Uncertainty” regarding their previous choices (Enke & Graeber, 2023).

Phase 4: Demographics & Financial Literacy. The study concludes with a survey collecting demographic data, a validated Financial Literacy score (Lusardi & Mitchell, 2011), and self-reported credit usage metrics.

Not available

Computerised Simple Randomisation (Bernoulli Trial) is performed algorithmically by the experimental software engine (oTree) at the individual participant level. Upon completing the endowment phase (Phase 1), a pseudo-random number generator (PRNG) assigns subjects to one of the two treatment arms (standard frame vs. fee frame) with a 1:1 allocation ratio (probability, p = 0.5). The assignment is automated, concealed from the participant until the moment of treatment, and independent of any pre-treatment covariates.

Individual

No

Zero

400 Individuals

- Arm 1 (Standard Frame / Control): 200 Individuals
- Arm 2 (Fee Frame / Treatment): 200 Individuals