Using Equivalent Offsets to Test Gain–Loss-Based Reference Dependence

The intervention is the decision screen. The Framed arm displays the current value as its difference from the situation benchmark, with the benchmark itself available behind a question-mark button. The Plain arm displays the current value alone. The instructions describe to each arm the screen it sees. The value process, the die and the payment rule are identical across arms.

2026-09-28

2026-10-28

The choice to sell or keep the stock in each of the sixty rounds. For each candidate reference point, the offset statistic S and the offset ratio Q defined in the pre-analysis plan.

For a candidate reference point, reference dependence means that the probability of selling depends on the current value and the candidate only through their difference. Equivalent Offsets follows: raising both by the same amount leaves the probability unchanged. S is the weighted average change in the probability of selling when the current value and the candidate rise together by one point, with weights fixed in advance from the experimental design. Q rescales S so that Q equals 1 under Equivalent Offsets and Q equals 0 when the candidate has no effect on the choice. For each candidate the hypothesis tested is S = 0, equivalently Q = 1. For the single reference points and functional rules, the same hypothesis is also tested jointly across the three levels, 80, 100 and 120, around which the situations’ benchmarks are drawn. Both tests are computed for every candidate.

Predictions. H1: the hypothesis S = 0 is not rejected for the benchmark in the Framed arm, where the benchmark is displayed. H2: the hypothesis S = 0 is rejected for the benchmark in the Plain arm, where the benchmark exists in the design but never appears on screen. It is an open question which candidates built from the stock’s earlier values satisfy the hypothesis in the Plain arm.

The pre-analysis plan defines twenty-three candidates per arm in four groups: twelve single reference points, six functional rules, one six-referent mixture and four lagged distributions. It also specifies reduced-form evidence on path dependence, a linear probability model with participant-clustered inference and a joint test of the five lagged shocks, and a held-out predictive comparison of the eighteen single and functional-rule candidates.

Participants recruited online make sixty binary choices under risk, one per round. In each round a stock has a displayed current value in points. The participant either sells the stock, receiving the current value, or keeps it, receiving the current value plus one of six equally likely movements, −15, −10, −5, +5, +10 or +15 points, determined by a die roll.

The sixty rounds form two stocks of thirty rounds. Each stock has two situations of fifteen rounds, and each situation has its own benchmark value. In every round the current value equals the situation’s benchmark plus a shock drawn uniformly from the integers −15 to +15, independently across rounds. The value sequence does not depend on the participant’s choices.

The two arms differ only in the decision screen. The Framed arm displays the current value as its difference from the situation benchmark, with the benchmark itself available behind a question-mark button. The Plain arm displays the current value alone.

One of the sixty rounds is selected at random for payment, at ten points per dollar, with a floor of USD 3.50 and a cap of USD 17.00. The pre-analysis plan states the value process in full.

Not available

Randomization by computer (oTree software). Participants are recruited on Prolific and enter through a single link. Participant slots are numbered in order of arrival and grouped into non-overlapping pairs: slots 1 and 2, slots 3 and 4, and so on. Within each pair one slot is Plain and one is Framed, and a random draw made before recruitment starts decides which comes first. This keeps the two arms equal in size throughout recruitment. Within the experiment, each participant's sequence of stock values is an independent random draw.

Individual Level

No

600 individuals

36,000 decisions

300 Plain, 300 Framed

Pre-analysis plan