Probabilistic Cash Rebates and Consumption Choices under Carbon Pricing

Participants take part in an online decision task in which they choose how many units of a product to purchase at a fixed price that reflects a carbon-related charge. Purchasing fewer units is associated with greater environmental benefits. Depending on the treatment group, participants may receive no cash rebate, a guaranteed cash rebate, or a cash rebate that is awarded with a specified probability. The size of the rebate is fixed, but the likelihood of receiving it varies across groups. Participants make decisions in four rounds and receive feedback about outcomes after each decision round, with one round randomly selected to determine their final payoff.

In a later amendment to the original five-arm design, we added a sixth treatment arm, the Neutral Pricing Benchmark, in which participants complete an otherwise identical purchase task with the same prices, values, feasible choice set, number of rounds, and payoff structure, but with no mention of carbon emissions, emissions retirement, or rebates.

2026-04-01

2026-05-05

The primary outcome is the number of units purchased in Round 1, Yi1 = {0,1,2,3,4}, treated as continuous. This measure also provides the participants desired level for the experimenters commitment to retire carbon emission allowances equivalent to 50 pounds of CO2 per unit not purchased.

Secondary outcomes include the average number of units purchased across all four rounds, Ybar_i = (1/4) * sum_{r=1}^4 Yir, the round-by-round choices Yir, and measures of dynamics such as Yi4 − Yi1.

The study uses a between-subjects experimental design with random assignment to one of five incentive conditions: no rebate, sure rebate, or a probabilistic rebate with a 50%, 25%, or 10% probability. Participants complete a sequence of four decision rounds. In each round, they choose how many units (0–4) of a fictitious consumption good to purchase at a fixed price. Each unit provides a privately induced monetary value to the participant, while consumption is associated with carbon emissions that can be offset by the researchers depending on participants' choices.

In rebate conditions, participants are informed that they may receive a monetary rebate linked to the number of units they choose not to consume. The structure of the rebate varies by treatment in terms of the probability with which it is paid. Participants receive feedback after each round about their own choices and the corresponding carbon offset. At the end of the experiment, one round is randomly selected to determine monetary payoffs.

Randomization is conducted at the individual level, and all participants face the same price, values, and decision environment aside from the rebate probability. The design allows comparison of choices across incentive conditions and across rounds within individuals.

In a later amendment, a sixth condition was added: the Neutral Pricing Benchmark.

Not available

Randomization is implemented by the experimental software (Qualtrics or oTree). Participants are randomly assigned to one of the treatment conditions upon entering the study by the experimental software.

Randomization is conducted at the individual participant level. Each participant is independently assigned to a treatment condition. There is no cluster-level or group-level randomization.

No

Not applicable. Randomization is conducted at the individual participant level, and there are no clusters.

Planned Number of Observations: 1,140 individual participants * 4 rounds = 4,560. N = 1,012 is chosen to achieve 80% power at alpha=0.05 for the primary Sure vs 10% contrast with MDE=0.20 under the prespecified unequal allocation.

Neutral Pricing Benchmark (added in amendment): 104 participants
No rebate (control): 104 participants
Sure rebate (100%): 362 participants
50% rebate: 104 participants
25% rebate: 104 participants
10% rebate: 362 participants
Total: 1,140 participants

See uploaded file in the Analysis Plan section.

carbon_pricing_and_lottery_incentives.pdf