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.

Participants complete an online, incentivized experiment in which they make four repeated consumption decisions under a fixed price that incorporates a carbon-related charge. In each round, participants choose an integer number of units n={0, 1, 2, 3, 4} of a fictitious product. Each unit provides a declining private value: the first unit yields a value of $15, the second unit a value of $14.5, the third unit a value of $14 and the fourth unit a value of $13.5. The price per unit is fixed at $13 in all rounds and treatments. Monetary payoffs in each round are determined by the sum of the private values of the units purchased minus total expenditures.

Consumption choices are linked to real environmental consequences. For each unit not consumed, the experimenters commit to retire carbon emission allowances equivalent to 50 pounds of CO2. Thus, if a participant foregoes all four units, 200 pounds of CO2 are retired; if three units are foregone, 150 pounds of CO2 are retired; if two units are foregone, 100 pounds are retired; if one unit is foregone, 50 pounds are retired; and if all four units are purchased, no allowances are retired. These offsets are implemented by the research team upon completion of the study.

Participants are randomly assigned to one of several treatment conditions that differ in the presence and structure of a cash rebate. In the no-rebate control condition, participants receive no rebate regardless of their consumption choices. In the sure rebate condition, participants receive a guaranteed rebate of $2 for each unit not consumed. In probabilistic rebate conditions, the per-unit rebate amount remains $2, but it is awarded only with a specified probability. Specifically, participants in the 50% treatment receive the rebate with 50% probability, participants in the 25% treatment receive it with 25% probability, and participants in the 10% treatment receive it with 10% probability. In probabilistic treatments, the rebate lottery is resolved independently at the end of the experiment for the payoff-relevant round.

The decision task is repeated for four rounds. To preserve incentive compatibility while limiting total payments, one of the four rounds is randomly selected at the end of the experiment to determine the participant's final payoff. Participants receive feedback after each round about their monetary payoff and the associated carbon offset. All payments are made in real money.

In addition to the main decision task, participants complete a short incentivized task to elicit individual risk preferences, as well as a demographic questionnaire. The experimental design allows for a comparison of consumption behavior under guaranteed versus probabilistic rebate schemes and for an assessment of how responses vary systematically with the probability of receiving a rebate, while holding prices and private values constant.

In a later amendment to the preregistered design, we added a sixth treatment arm: the Neutral Pricing Benchmark. In this treatment, participants complete an otherwise identical decision task with the same prices, values, feasible choice set, number of rounds, and payoff rule, but there is no mention of carbon emissions, emissions retirement, or rebates. Participants are simply told the unit price and the monetary consequences of their choices. This arm was added to provide a benchmark for whether participants choose the privately optimal quantity when environmental content and rebate-related considerations are removed.

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.

The experiment uses a between-subjects design with random assignment to one of five incentive conditions: no rebate, sure rebate (100 percent probability), or a probabilistic rebate paid with 50 percent, 25 percent, or 10 percent probability. Each participant completes four decision rounds. In each round, participants choose an integer number of units n = {0, 1, 2, 3, 4} of a fictitious consumption good.

The price of the good is fixed at P = $13 per unit. Each unit provides a privately induced monetary value, with values equal to v1 = $15, v2 = $14.5, v3 = $14 and v4 = $13.5 for the first, second, third and fourth unit, respectively. Monetary payoffs in each round are equal to the sum of the values of the purchased units minus total expenditure, plus any rebate realized in that round. In the no-rebate condition, no rebate is available.

In rebate conditions, participants are eligible to receive a monetary rebate of $2 for each unit not consumed. In the sure rebate treatment, the rebate is paid with certainty. In the probabilistic rebate treatments, the rebate is paid with the treatment-specific probability (50 percent, 25 percent, or 10 percent), independently for each participant and round. Participants are informed of the rebate probability associated with their assigned treatment before making decisions.

Each unit of consumption is associated with carbon emissions. For each unit not consumed, the experimenters commit to offset 50 pounds of carbon dioxide. As a result, carbon offsets per round equal 200 pounds if zero units are purchased, 150 pounds if one unit is purchased, 100 pounds if two units are purchased, 50 pounds if one unit is purchased and zero pounds if four units are purchased.

At the end of the experiment, one of the four rounds is randomly selected to determine monetary payoffs. Carbon offsets associated with each round are implemented as described in the instructions. Randomization is conducted at the individual level, and aside from the rebate probability, all participants face identical prices, values, payoff rules, and information.

In a later amendment, a sixth condition was added: the Neutral Pricing Benchmark. The Neutral Pricing Benchmark arm was added after the initial preregistration of the five carbon-pricing conditions. The purpose of this amendment is to introduce a diagnostic benchmark that removes both rebate language and CO2-retirement language while preserving the underlying payoff structure of the task.

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: 1,036 individual participants * 4 rounds = 4,144. 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