ISSN (Print) 0473-453X

Discussion Paper No. 1227

ISSN (Online) 2435-0982

UNCERTAINTY ABOUT CARBON IMPACT
AND THE WILLINGNESS TO AVOID
CO2 EMISSIONSDavide D. Pace
Taisuke ImaiPeter SchwardmannJoël J. van der Weele

December 2023

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Uncertainty about Carbon Impact and theWillingness to Avoid CO2 Emissions ∗Davide D. Pace1,5

Taisuke Imai2,5Peter Schwardmann3,5Joël J. van der Weele4

1 Ludwig-Maximilians-Universität München
2 Institute of Social and Economic Research, Osaka University
3 Carnegie Mellon University
4 Amsterdam School of Economics, Tinbergen Institute
5 CESifo

December 1, 2023
Abstract
With a large representative survey (N = 1, 128), we document that consumers arevery uncertain about the emissions associated with various actions, which may
affect their willingness to reduce their carbon footprint. We experimentally test
two channels for the behavioural impact of such uncertainty, namely risk aversion
about the impact of mitigating actions and the formation of motivated beliefs
about this impact. In two large online experiments (N = 2, 219), participants
make incentivized trade-offs between personal gain and (uncertain) carbon impact.
We find no evidence that uncertainty affects individual climate change mitigation
efforts through risk aversion or motivated belief channels. The results suggest that
reducing consumer uncertainty through information campaigns is not a policy
panacea and that communicating scientific uncertainty around climate impact
need not backfire.
∗This paper supersedes a previous version circulated with the title “Curbing Carbon: An Experiment on Uncertainty and Information about CO2 Emissions” by a subset of the authors. Financial
support from Deutsche Forschungsgemeinschaft through CRC TRR 190 (Imai, Pace), the Bavarian
Academy of Sciences and Humanities (Schwardmann), the NWO in the context of VIDI grant 452-17004 (van der Weele), the Amsterdam Center for Behavioral Change of the University of Amsterdam,and the initiative, “A Sustainable Future,” at the University of Amsterdam (van der Weele), aregratefully acknowledged. The data collection was approved by the Ethics Committee Economics andBusiness (EBEC) of the University of Amsterdam, with request numbers EC 20191018121005, EC
20200810100845, and EC 20210713120725.

1

Climate action takes place against a backdrop of considerable uncertainty. Scientists
face fundamental uncertainty about the exact contribution of different human activities to aggregate CO2 emissions and about how emissions contribute to climate change
and resulting extreme weather events 1,2 . On top of that, non-experts may be uncertain
about the best estimates of how a given behaviour maps onto CO2 emissions. Understanding how uncertainty about CO2 emissions affects climate action is therefore central
to debates around the costs and benefits of communicating scientific uncertainty aboutclimate change 3–5 and around the effectiveness of carbon labels or other information
campaigns 6,7 .
This paper consists of three studies. Our first study investigates the degree of consumer uncertainty about emissions impact. We survey a large representative sampleof the US population on their beliefs about the CO2 emissions associated with several
common consumer products. We elicit participants’ entire belief distributions for eachproduct using incentivized elicitation methods. The survey shows that people have ahigh degree of subjective uncertainty about the impact of all of these products, with
only 6 per cent expressing high confidence in their guesses.
We then investigate two plausible mechanisms by which such uncertainty may causallyaffect emission mitigation behaviour. The first of these mechanisms is risk aversion.
Uncertainty about the impact of emissions may reduce climate action if people do notplace much value on avoiding high amounts of (potential) emissions. Theoretically,
this requires that the marginal willingness to forgo personal benefits to avoid emissions
declines with each additional unit of emissions. To test this mechanism, our second
study uses large-scale online experiments in which participants’ choices to buy an online convenience product affect real CO2 emissions. We find that participants indeed
have an increasing but concave willingness to mitigate (WTM) CO2 emissions. However, contrary to the predictions of standard decision theory, we do not find an effect of
uncertainty, as consumption of the polluting product is similar in treatments with andwithout uncertainty about emissions.
The second mechanism is the use of “moral wiggle room” that allows consumers
to self-deceive into believing that emissions are small and consumption is harmless, as
happens in other types of ethical decision-making 8–11 . Such self-serving belief formation may also interact with carbon pricing: as CO2 -intensive products become more
expensive, the temptation to form self-serving beliefs decreases 9 . In our third study,
participants may again buy a virtual polluting product. They see a vague signal about
the emissions associated with the product and have to update their beliefs about theemission size. The signal we use provides an opportunity for self-serving belief distortions, but only in a condition where the incentives to hold self-serving beliefs are
known before the signal is seen. We find no evidence that uncertainty is exploited by2

participants to develop self-serving beliefs that the emissions are low, nor do we find aninteraction between prices and belief formation.
We contribute to the literature by documenting the extent of individuals’ uncertainty
about the carbon impact of their actions and by designing novel controlled experiments
to study money-emission trade-offs. Our findings on subjective uncertainty complement
previous evidence that people’s best guesses about the size of CO2 emissions are very
heterogeneous and often too optimistic 6,7 . Moreover, we are the first to study the explicit
and isolated role of uncertainty in affecting climate action. In this way, we complement
earlier studies on information provision, which focus on correcting the bias in consumer
beliefs and have found conflicting evidence on carbon information provision 6,7,12,13 . Weshow that the variance of beliefs has little impact on climate-friendly consumption.
This demonstrates the limits of information campaigns to spur climate action, but
it also suggests that communicating scientific uncertainty does not negatively affectconsumption patterns.
In addition, our findings deliver new insights into the willingness to make sacrifices
to reduce CO2 emissions. Most studies in this literature have relied on hypotheticalchoices, which have been shown to lead to large overstatements in willingness to pay foroffsets 14,15 . A few studies, like ours, use incentivized willingness to pay to retire offsets or
permits but have looked at a single emission quantity 16–18 . We empirically show that thevaluation of such offsets is concave in emission size, in line with concurrent evidence 15 .
This suggests that future welfare measurements can take such nonlinearity into accountwhen scientists estimate the welfare benefits of climate policies, study the demand forcarbon offsets in particular industries like aviation 19 or the optimal pricing of offsets
more generally 20 . Finally, we contribute to the literature on motivated cognition with
our null results on self-serving environmental beliefs and on the interaction between
beliefs and prices 8,9,21,22 .

Results
Study 1: Subjective uncertainty about CO2 emissions. We investigate subjective uncertainty with a representative sample of the US population (N = 1, 128). Our
survey elicited participants’ beliefs regarding the carbon emissions associated with 12
common consumer products and activities. The elicitation process comprises two steps.
First, we asked participants to indicate their best guess about the size of the emissions associated with each product. Then, we elicited the participants’ entire subjective
probability distribution regarding the emissions size of each product. To do so, we partitioned the interval of possible emissions into five bins centred around the participants’
initial guesses. The three central bins have a width equal to 10% of the initial guess;3

Car (1 mile)
Beer (12fl.oz)
Phone call (1h)
Microwave (1kW, 2h)
Milk (1 cup)Shower (avg. use)

Not certain
Less than 50% certain
Extremely uncertain

Egg (6)
Poultry (7oz)
Chocolate (100g)
Coffee (1lb)
Beef (7oz)
Flight (SFO−LAX)
Gas heating (1 month)
0

25

50

75

100

% of participants

Figure 1: The percentage of participants who satisfy three subjective uncertainty criteria. A
participant is Not certain if she puts at least one ball in a bin that does not contain her initial
guess. She is Less than 50% certain if she puts less than 10 balls in the bin which contains
her initial guess. She is Extremely uncertain if she puts four or fewer balls each in the binthat contains her initial guess and in the two adjacent bins. The three criteria are cumulative.
The Extremely uncertain participants are also Less than 50% certain. The participants who
are Less than 50% certain are also Not certain.

the two outer bins contain all the other possible emissions values. We asked the participants to allocate 20 balls across these bins to reflect the probability that the size ofthe emissions belongs to each of them. To incentivize truthful responses, we employedstate-of-the-art techniques from experimental economics 23,24 (see Methods).
We study participants’ uncertainty with three (nonexclusive) nonparametric criteria
based on the ball allocation. A participant is Not certain if she puts at least one ball ina bin that does not contain her initial guess. She is Less than 50% certain if she puts
less than 10 balls in the bin which contains her initial guess. She is Extremely uncertain
if she puts four or fewer balls in each of the three central bins, indicating less than 20%
confidence in being (close to) the correct answer.
Figure 1 depicts the levels of uncertainty for each product. In each case, at least
94% of the participants are Not certain, at least 85% are Less than 50% sure, and at
least 35% are Extremely uncertain. The figure also displays limited variability acrossproducts, indicating that people’s uncertainty is not domain-specific. These results showthat people are aware of having very limited knowledge about the carbon footprint ofcommon products and activities.
Study 2: Does risk aversion towards carbon impact increase polluting activity? This experiment tests whether people are risk-averse towards reducing carbon
emissions. In the experiment, participants had to work on an effortful and tedious en-4

coding task. Before engaging in the task, subjects were offered the option to obtain acomputer code that would do the encoding for them, reducing their burden. However,the code was associated with the release of CO2 emissions into the atmosphere. Acrossconditions, we varied the uncertainty about the size of these emissions. In addition, we
measured willingness to mitigate (WTM) CO2 emissions via an incentive-compatible
multiple price list. We define the WTM as the monetary amount a participant requires
in order to accept the emission of a certain quantity of CO2 . For every subject, weelicit the WTM to avoid 0, 4, 8, 12, 16, or 20 kg of CO2 emissions. The decisions wereincentivized: participants could really accrue private benefits in exchange for increasing
the CO2 emissions in the atmosphere (see Methods).
According to Expected Utility Theory, the classical theory of decisions in economics,
risk aversion is driven by a concave WTM, that is, a declining marginal willingness
to make sacrifices for CO2 reductions. Intuitively, an increase in the variance of theemissions will increase the probability of both very low and very high emissions. A
consumer with a concave WTM will heavily discount the very high emissions, decreasing
the subjective value of offsetting these emissions, even if the expected emissions remain
constant. Consequently, consumers with a concave WTM should be more likely toengage in polluting actions as the (subjective) variance of the emissions grows.
To understand whether WTM is concave, Figure 2a shows the WTM curve aggregated over all subjects. The figure shows that subjects, on average, indeed display adiminishing WTM to reduce carbon emissions. They are willing to sacrifice about £2.7
to avoid 4 kilograms of CO2 emissions, whereas to avoid 20 kilograms of emissions, they
are only willing to forgo only £4. That is, the WTM increases by less than 50% when
the amount of CO2 increases by 500%. The graph shows that this effect is robust if
we exclude subjects who have decreasing valuations (a possible sign of confusion) and
who are top-censored (i.e. they select the maximum WTM of £7 at least once, which
could produce concavity as an artefact). Supplementary Information A.2.2 contains
further details about the variation in concavity across subjects. Supplementary Information A.2.4, instead, discusses how neither cognitive uncertainty 25 nor concave moral
evaluations seem to explain the concavity of the WTM. It also discusses how, given
the framing of the WTM elicitation, the concavity we found is more likely due to amarginally decreasing disutility from CO2 emissions, which are seen as a loss, rather
than decreasing marginal utility from implementing offsets, which are seen as a gain.
We now turn to our main outcome, the purchase of the polluting computer code,
which simplifies the real effort task. Before purchase, participants were randomized
into two treatments. In the Information treatment, the participants knew that theemissions from buying the product were equal to 4kg of CO2 . Instead, in the Uncertainty
treatment, they knew that there was a 40% chance that the emissions were equal to5

aFraction buying the code

6

WTM (£)b

All (1505)
Non−decreasing
and non top−censored (914)

4

2

0

1.00

Information
Uncertainty

0.75

0.50

0.25

0.00
0

4

8
12
CO2 (kg)

16

20

All (1505)

Concave (827)

Subjects

Figure 2: (a) Aggregate WTM. (b) Purchasing decision and uncertainty. Notes: In panel (b),the light-grey bars correspond to the group of subjects whose WTMs exhibit concavity. Bars
indicate 95% CI.

0kg, a 20% chance that the emissions were 4kg, and a 40% chance that they were 8kg.
Thus, the expected emissions are the same in both cases, but the variance is larger in
the Uncertainty treatment.
In line with the reasoning above and our finding that WTM is concave, we hypothesize that uncertainty increases the fraction of subjects who purchase the polluting product. We do not find support for this hypothesis. The left bars in Figure 2b show thatpurchasing decisions are similar in the two treatments (68.5% vs. 69.3%, z = 0.3168,
two-sided p = 0.7514). It is possible, however, that there are offsetting effects for subjects with concave and convex WTM. The right bars in Figure 2b show the treatment
difference only for participants with a concave WTM. Again, we find little evidence forthe hypothesized effect (62.2% vs. 62.7%, z = 0.1494, p = 0.8813).
To provide further statistical backup, we run several regression models, in which
we regress the purchasing decision on the treatment, several concavity scores, and theinteraction of these two (Supplementary Table 4). We also include the average WTM
and several demographic controls. We find little evidence for our hypothesis. Only asingle specification of concavity score produces a significant interaction with the information treatment dummy, yet this effect is not robust to other concavity measures.
However, we do find a statistically significant negative effect of the average WTM onpurchasing decisions, showing that the WTM data is predictive of subjects’ decisions
to get the computer code. We also find some demographic effects, as young people areless likely to buy than old, women less than men, and left-wing less than right-wing(Supplementary Figure 2).

6Study 3: Do participants form self-serving beliefs? We now turn to a second
potential channel through which uncertainty may matter: the formation of motivatedbeliefs. As in study 2, participants made trade-offs between monetary gains and CO2
emissions. These trade-offs were framed as consumer decisions: participants could buy
a virtual product, represented as a nondescript wrapped package on the screen. The
purchase increased their pay-off by the product value of £2, minus the price at which we,the experimenters, offered it. However, purchasing the product resulted in the emissionof CO2 into the atmosphere.
We conducted an online experiment (N = 714) that consisted of a Motivated andan Unmotivated treatment. Both treatments featured uncertainty about the size of theemissions associated with the product. Unlike in the risk aversion experiment discussed
above, we did not state explicit probabilities, as there is evidence that more ambiguous
settings are conducive to the formation of motivated beliefs 26,27 . Participants could
reduce uncertainty by engaging in an attentional task, somewhat akin to reading a
product label, after which we elicited their beliefs about the emission size.
To study motivated beliefs, we vary whether participants complete the attentional
task before or after knowing about the emission-money trade-off. Manipulating thetiming of knowledge of the incentive scheme is a standard design feature in experiments
studying motivated cognition 28–30 . Thus, in the Unmotivated treatment, subjects were
presented with the task before they knew any other details of the experimental design.
In this way, participants have no self-serving motive to distort their attention or beliefs
in the direction of their economic interest. By contrast, in the Motivated treatment, participants engaged in the task after reading the full experimental instructions. Therefore,
they knew that higher numbers corresponded to higher CO2 emissions and indicated amore “inconvenient” trade-off. We hypothesize that the latter treatment will lead tomotivated beliefs, i.e. a lower estimate of the impact of the emissions.
Moreover, we hypothesized that motivated beliefs are more pronounced when the
payoffs from the product are higher 9,22 . To test this last hypothesis, we implemented
three price treatments that varied the price of the product: a low price (£0.25), a
medium price (£1), and a high price (£1.75). The information treatments are orthogonal
to the price treatments, creating a 2 × 3 design (see Methods for details). While thetrade-offs in our experiment are not about concrete, branded products, this simple
design allows us to fully control the price of the products and the uncertainty about
emissions while ensuring that beliefs remain, on average, correct. The average belief inthe Unmotivated treatment is 62.7, not significantly different from 60— the real valueof the emissions (t(303) = 1.31, 95% CI [58.1, 67.3], p = 0.25, two-sided).
We find no evidence of the formation of self-serving beliefs. The left panel of Figure 3
shows the distribution of beliefs in both treatments, where the spikes are driven by the

7

0.6

b

Motivated
Unmotivated

Fraction buying the producta

Fraction

0.4

0.2

0.0

1.00

0.75

0.50

0.25

0.00
0

20

40

60

80

100

120

Motivated

Beliefs

UnmotivatedTreatment

Figure 3: (a) Distributions of beliefs in the Motivated and Unmotivated treatment. (b) Fraction of participants buying the product in the Motivated and Unmotivated treatment. Notes:
In panel (b), bars indicate 95% CI.

nature of the perceptual task (see Methods). We cannot reject the hypothesis that beliefs
about emissions are the same in both treatments (Fisher’s Exact test, p = 0.66, twosided). Moreover, Table 1 provides the results of regressing beliefs from both treatments
on a dummy for the Motivated treatment controlling for individual characteristics. The
coefficient in column (1) is positive, indicating that, if anything, participants in the
Motivated treatment believe that emissions are larger. Hence, the direction of the effectis the opposite of what theories of self-serving beliefs and cognitive dissonance would
predict. However, the coefficient is not significantly different from zero (t(659) = 0.60,
95% CI [−4.36, 8.20], p = 0.548, two-sided). Furthermore, we find no evidence that the
Motivated treatment causes people to spend less time looking at the information as we
discuss in Supplementary Information A.3.2.
This null result obtains despite substantial ambiguity: only 51% of participants
answered the belief question correctly in the Unmotivated treatment, even though theyspent, on average, 50 seconds on the task screen. Moreover, the standard deviationof beliefs is 0.65 times the average, indicating that the degree of uncertainty in theexperiment is sizable. Thus, there was room for motivated subjects to perceive emissions
to be lower than they actually were.
We also test for differences in purchasing behaviour between the two treatments.
The right panel of Figure 3 shows that behaviour is similar in the two treatments. Botha Fisher’s exact test and a t-test based on column (2) of Table 1 fail to reject that
subjects are equally likely to buy the product in the Motivated and in the Unmotivatedtreatment (Fisher’s Exact test: p = 0.483; t-test: t(695) = 1.07, 95% CI [−3.33, 11.34],
p = 0.285; both tests are two-sided). By contrast, a higher product price has a strong
independent impact on purchasing behaviour: Column (4) of Table 1 shows that anincrease in the price of one pound leads to a 13 percentage point decline in purchases.

8

Table 1: Comparison between the Motivated and the Unmotivated treatments.

Beliefs

Motivated

(1)

(2)

(3)

(4)

1.921
(3.199)−4.406(6.226)−4.242(4.127)
6.172(5.215)0.040(0.037)0.051(0.074)−0.128∗∗(0.045)−0.022(0.060)

Yes
695
0.050

Yes
695
0.052

Yes
695
0.092

Yes
695
0.122

Price
Price × MotivatedControls
Observations
R2

Units

Notes: Models include observations from the Motivated and the Unmotivated treatments, where thelatter is the baseline. The regressions exclude 19 participants for which we failed to record the demographic characteristics. Dependent variables are beliefs in columns (1) and (2) and purchasing
decisions (1 if the participant purchased the product) in columns (3) and (4). Control variables: age,gender, student status, education (6 categories), frequency of car usage (5 categories), and nationality(27 categories). Robust standard errors are reported in parentheses. ∗ : p < 0.05; ∗∗ : p < 0.01; ∗∗∗ :p < 0.001.

Discussion
We document that people are uncertain about the CO2 emissions associated with common consumer products. Yet we find no evidence that uncertainty affects climate action
through either risk aversion or the formation of motivated beliefs about the magnitude
of emissions.
Our findings add to a growing literature on the effect of information provision on
climate-related behaviours. While information campaigns are popular among politicians, previous studies have found mixed evidence on the effect of correcting beliefs
about emissions: some labelling studies find small reductions in emissions from informing consumers about the carbon impact of e.g. meat products 6,13,31,32 , whereas otherstudies do not find such an effect 7 . Our findings suggest that while consumer information may reduce uncertainty, this alone may be insufficient to spur voluntary reductions
in emissions. At the same time, our results also suggest that scientists can be upfront
about the uncertainty of their estimates without fear of providing an excuse for polluting
behaviour.
Another set of implications stems from our finding that consumers’ willingness tomitigate the first units of CO2 is much higher than for subsequent units. The first is that
consumers’ behaviour will be sensitive to reference points and to the framing of emission
impact. For instance, framing multiple emission events separately may lead to a higher
willingness to avoid or offset them than framing them as a single event. Future research9could explicitly test this prediction. A second implication concerns the use of people’s
WTM to offset emissions to calculate the benefits of climate policies. The literature
has so far relied on linear extrapolations of the WTM for a single emission amountin order to compute the benefits of reducing one ton of CO2 in the atmosphere 16–18 .
Our results strongly suggest that future studies should measure individual WTM toavoid several emission amounts and should use nonlinear models to produce accurate
estimates of these benefits. It is reasonable to expect that the two implications above
hold, albeit we did not find that the concavity of the WTM curve generates risk aversion
toward emissions. The participants’ WTM is significantly associated with them buying
the polluting product. Hence, the WTM is a meaningful predictor of consumption
behaviour and environmental preferences.
One limitation of our research is that, while we do not find evidence for the formation of motivated beliefs about emission size, it is possible that consumers find otherdimensions for motivated reasoning about climate change 21 . Further research could
investigate these additional dimensions.

Methods
General remarks
The implementation of the CO2 emissions in the experiments. In both of ourexperiments, participants were asked to make decisions that could result in the emission of CO2 . To ensure that these emissions are consequential, we prepared a monetarytransfer to Carbonfund.org, an organization that offsets CO2 emissions. Every time aparticipant made a decision resulting in CO2 emissions, we decreased the amount of ourtransfer. We explicitly communicated this procedure to the participants. We always
framed these decisions as choices between private benefits and emitting CO2 to enhancethe external validity and maximize the salience of the emissions. We took several measures to assure participants of the tangible nature of these CO2 emissions associatedwith the purchase of the product. We emphasized the role of the no-deception policy inobtaining ethical approval for the experiment. Additionally, we promised participants
to send them the invoice for the donation to Carbonfund.org (see Supplementary Information B.5) and actually did so. To ensure that the participants believed that theiractions had environmental consequences, we asked them whether they believed that wewould buy the CO2 offsets as described in the instructions. We find that between 80%
and 84% of the participants expressed trust in our intentions.
Data quality. We took several measures to maximize data quality as described in
Supplementary Information B.4.
10

Study 1: survey about subjective uncertainty
Our survey measures consumers’ prevailing beliefs about the CO2 emissions generated in
the production of common consumer goods. The survey then continues with additionalquestions that we describe and analyze elsewhere 7 .
Our elicitation methods employed incentive-compatible payment schemes developedin the experimental economics literature while maintaining simplicity and participantfriendliness in both instructions and the interface to allow for a representative sample
to participate. Below, we elaborate on each of the elicitation procedures in more detail.
Supplementary Information B.4 presents additional information about the steps we took
to maximize the data quality.
Belief elicitation
In the survey, we elicited participants’ beliefs about the CO2 emissions generated bydriving one mile by car. We then elicited beliefs about 12 common consumer products
and activities listed in Table 2, including food items, household appliance use, andtransportation. To enhance understanding, we provided participants with information
about product specifications and the type of emissions considered by the estimate.a We
retrieved these estimates from top-tier academic journals or from the estimates the UK
government uses for its environmental regulations. We disclosed these scientific sources
only at the end of the experiment. To make the values more meaningful to subjects, we
refrained from eliciting emissions in grams and instead asked about the number of miles
one must drive by car to emit the same amount of CO2 as the product in question, an
approach in line with previous studies 6 .
We divided the belief elicitation into two parts. We first elicited a point estimate forthe modal value of the emissions. Participants indicated how much CO2 each of the 12
products in Table 2 emitted relative to driving one mile by car. Participants answered
all 12 questions on one page, and the order of the products was randomized across participants. A screenshot of the interface is in Supplementary Information B.1. In the restof the experiment, the same order was used every time participants answered additionalquestions about these products. To help participants keep track of their guesses and therankings of the products, we presented an interactive box summarizing their (current)
answers at the bottom of the page, including the ranking of the products by estimatedimpact. We incentivized a correct point estimate with a £4 bonus. We considered an
estimate correct if it was within a 5% interval from the scientific estimate. This incentive scheme truthfully elicits the mode of the subjective probability distribution aboutaParticipants could learn a detailed breakdown of the factors considered in the scientific calculationsof CO2 emissions size. See Supplementary Table 12.

11

Table 2: List of consumer products and activities.

Emission size
Quantity
Beer
Phone call
Microwave
Milk
Egg
Poultry meat
ShowerDark chocolate
Coffee beans
Beef
FlightGas heating

12 fl oz
1 hour
1000W, 2 hour
1 cup
6 eggs
7 oz
Average usage
100g
1 lb
7 oz
SFO to LAX
One month

Estimate

Unit

Source

1.46
1.55
1.76
2.60
4.81
6.78
3.90
16.03
44.41
68.39
304.60606.68

mile
mile
mile
mile
mile
mile
mile
mile
mile
mile
mile
mile

Poore and Nemecek 1
Smith et al. 33
UK BEIS 34
Poore and Nemecek 1
Poore and Nemecek 1
Poore and Nemecek 1
Hackett and Gray 35
Poore and Nemecek 1
Poore and Nemecek 1
Poore and Nemecek 1
UK BEIS 34
Padgett et al. 36

the scientific estimate 23 .b
To understand the participants’ confidence in their answers, we then elicited thesubjective probability distribution of the size of CO2 emissions. For each product, we
presented five “bins” around the point estimate the participant reported in the first partand asked the participant to allocate 20 balls into these five bins. We told participantsthat each bin represents an interval that might contain the scientific estimate and thatthey should allocate the balls to represent their level of confidence that the estimate is,in fact, in that bin. A screenshot of the interface is in Supplementary Information B.1.
We incentivized the elicitation by randomly selecting one of the bins and scoring theanswer according to a randomized quadratic scoring rule. This mechanism encourages
participants to truthfully reveal their belief that the scientific estimate falls in a particular bin 37 . To keep things simple and avoid information overload, we did not provide
participants with the exact details of the scoring rule but made them available with amouse click. We told subjects that they would maximize their expected earnings by
answering truthfully, an approach suggested by Danz et al. 24
Implementation We recruited 1,430 participants on Prolific (https://www.prolific.
co/) between the 3rd and 6th December 2020, and 1,128 completed all the belief elicitation questions described in this paper. We restricted participation to US residents, andwe aimed to collect a sample representative for age, gender, and ethnicity.c Our sampleb

We did not incentivize the questions about the CO2 emissions and the social cost of driving one
mile by a car as we realized that answers to these questions can be straightforwardly obtained on
Google.
c
We compared the demographic characteristics of study participants and information from US
Census Bureau 38 , and confirmed that our sample is representative for gender and ethnicity, but not

12is, on average, 42.6 years old (SD = 15.4), and 48.5% of the participants self-identified
as male. Supplementary Table 1 shows the demographic characteristics of the sample.
In total, participants were asked to answer 21 comprehension questions.
At the end of the survey, we randomly selected one question from the entire study
per participant. There was a 30% probability that one of the belief questions analyzed
above was selected for payment. The average duration of the survey was 51 minutes,
but all the questions described here were in the first half of the study.

Study 2: Risk Aversion experiment
The experiment consists of two parts. In the first part, we measure the participants’valuations of CO2 emissions. In the second part, we ask participants whether theywant to get a valuable but polluting product. The instructions for this experiment are
in Supplementary Information C.2. We preregistered the experimental design and the
hypotheses on AsPredicted.org (see Supplementary Information B.6).
Valuation of CO2 emissions. We measured the participants’ valuation of CO2 emissions by presenting them with trade-offs between money and emissions. Specifically, participants were offered a choice between Option A and Option B. Opting for Option A
meant forgoing any monetary gain but preventing the generation of CO2 emissions. In
contrast, choosing Option B allowed them to earn money but resulted in CO2 emissions. For a given CO2 emission level, the participants had to make 15 choices where
the amount of money they could earn increased from £0 to £7 in 50 pence increments.
These decisions were embedded in a Multiple Price List (see Supplementary Information C.2), which enforced a single switching point between Option A and Option B.
This switching point gives us the participants’ valuation for a given amount of CO2
emissions. To gauge the participants’ certainty regarding their valuations, we employed
the “cognitive uncertainty” elicitation method developed by Enke and Graeber 25 . Thiselicitation was skipped if the participants never switched from Option A to Option B.
In total, the participants saw six Multiple Price Lists, each corresponding to one of
the following emissions levels: 0 kg, 4 kg, 8 kg, 12 kg, 16 kg, and 20 kg. Half of theparticipants saw these lists in ascending order of emission size, while the other half saw
them in descending order.
Consumption decision. In the second part of the experiment, the participants had
the opportunity to receive a valuable yet polluting product, framed as a “computercode”, which significantly speeded up the completion of a time-consuming and laborious
real-effort task. The task involved typing 15 strings, each consisting of 15 characters, infor age (Supplementary Table 2).

13reverse order (Supplementary Figure 6). The participants were required to transcribe
these strings flawlessly to complete the task: any mistakes incurred resulted in an error
message indicating the specific strings that required correction before they could proceedwith the experiment. Those who obtained the computer code were presented with atask in which the code generated all the correct answers, reducing their task to simply
clicking one button to submit them. To ensure task completion without interruption
and to make the task sufficiently “annoying,” we implemented an attention check. The
participants saw a warning sign every 30 seconds, and upon its appearance, they had a
5-second window to click on a button on the screen to confirm their active engagementwith the task. The participants were excluded from the experiment if they failed toclick on the button within the specified time window in more than four instances.
At first, all the participants were required to complete the real-effort task once
without the help of the computer code. In the second round, they had the chance toobtain the code to speed up the completion time. On average, the participants spent 8
minutes and 40 seconds to complete the first task.
Obtaining the code came at the cost of emitting CO2 . There are two treatmentsthat vary the information participants had about the size of the CO2 emissions. In the
Information treatment, participants were informed that purchasing the product would
result in emissions equivalent to 4kg of CO2 . In contrast, in the Uncertainty treatment,
participants were informed of a probability distribution: a 40% probability of emissions
being 0kg, a 20% probability of emissions being 4kg, and a 40% probability of emissions
being 8kg.
Survey. Before the participants complete (or are allowed to skip) the second real effort
task, they complete a questionnaire. A battery of questions elicits people’s moral evaluations of emissions-money trade-offs. Participants indicate the morality acceptabilityof emitting 4, 12, and 20kg of CO2 for either £1 or £5 using a Likert scale, where 1 indicates a decision that is “morally very inappropriate” and 7 a decision that is “morally
very appropriate”. Further questions in the survey ask about attitudes toward climatechange and demographic characteristics.
Sample and data collection. We recruited a total of 1,935 participants throughthe online platform Prolific.co on January 5th , 2023. Following the preregistration,
1,505 participants who successfully completed the final survey were included in theanalysis. Among them, 753 participants were assigned to the Information treatment,
while the remaining 752 were assigned to the Uncertainty treatment. Fifty per centof the participants identified as females, and the average age is 39 years old (min =18, max = 79, SD = 12.51). We restricted participation to individuals based in the
UK. Subjects earned a fixed reward of £3, with the potential for a bonus payment
14

based on their decisions. On average, they earned £3.66, and they took about 34
minutes to complete the tasks. Following the participants’ decisions, we donated $160
to Carbonfund.org to offset CO2 emissions, resulting in a reduction of almost 13 metrictons of CO2 in the atmosphere. The experiment maintained participant anonymity,
as we identified participants only via alphanumerical IDs provided by the platform.
Participants knew that they were taking part in an experiment.

Study 3: Motivated Belief experiment
In this experiment, we offered participants the opportunity to buy a single unit of avirtual product.d If participants decided to purchase the product, they increased their
pay-off by the product value of £2, minus the price at which we, the experimenters,
offered it. Importantly, purchasing the product entailed the emission of CO2 into theatmosphere. We framed the experiment as a market interaction, employing terminology such as “virtual product” and “price,” to make it closer to a real-life purchasing
situation.
We informed participants that purchasing the product would result in CO2 emissions
equivalent to burning 60 litres of gasoline. This emission size had offset costs of £1.07,
commensurate to the other payments in the experiments.e
As we describe next, we orthogonally implemented three price treatments and two
information treatments, resulting in a total of six treatments. Each participant was
assigned to a single treatment. The instructions for this experiment are in Supplementary Information C.3. We preregistered the experimental design and the hypotheses on
AsPredicted.org (see Supplementary Information B.6).
Uncertainty treatments. Our primary focus is on the formation and impact ofbeliefs about the CO2 emissions associated with the product, as well as the role ofemission information. To study this, we employed two treatments, called the Motivatedand Unmotivated treatments, that varied the nature of uncertainty about the size ofthe emissions.
In both treatments, there was uncertainty about the size of the emissions. The
participants had the opportunity to reduce this uncertainty by engaging in an attentional
task designed to mimic real-life consumption scenarios, such as reading product labelsor conducting an online search for information. The task involved examining a matrixdThis product is virtual in the sense that it exists only inside the experiment; it is not a physicalproduct nor a service. Nevertheless, the product is valuable to the participants since their pay-off fromthe experiment increases if they “buy” it.
eUsing a report from the US Environmental Protection Agency 39 , we calculate that burning 60
litres of gasoline produces 140kg of CO2 emissions. At the time of the experiment, Carbonfund.org
offset 1 metric ton of CO2 per every $10 (or £7.9) it receives in donations, so offsetting the products’emissions cost £1.07.

15

of numbers, with the most frequently appearing number representing the emission size,
measured in terms of the CO2 emissions generated by burning a litre of gasoline. We
adapted this task from Sandro Ambuehl’s work 40 , which shows that the informationgathering strategy in this task is influenced by incentives for subsequent decisions.f
Participants had up to one minute to engage with the task, after which we elicited theirbeliefs by asking them which number they believed was the most frequently found in
the table. Providing the correct answer was rewarded with a bonus of £0.10, which
incentivized participants to report the mode of their belief distribution 23 .g
These two treatments differ in the order in which we presented the attentional task
and the information about the emission size. In the Unmotivated treatment, participants
were presented with the task prior to receiving any instruction about the possibility ofemitting CO2 . In this way, we eliminated any self-serving motives that might lead participants to distort their attention or beliefs in the direction of their economic interests.
By contrast, in the Motivated treatment, participants engaged in the task after they
had read the full experimental instructions. Consequently, they were aware that thecorrect answer to the task indicated the magnitude of the CO2 emissions as well as ofthe surplus they could obtain from the product. This treatment enables us to test if thesurplus from buying the product has a causal effect on participants’ belief formation in
the attentional task and, in turn, on the product’s purchase.
At the end of the experiment, we collected demographic information using a survey.
Price treatments. We also investigate the relationship between purchasing decisions
and prices. The effect of prices provides a natural quantitative benchmark for assessing
the effects of beliefs and information, as price incentives are a primary tool used bypolicymakers and are often discussed in the context of reducing carbon emissions.
We implemented three price treatments that varied the price of the product: alow price of £0.25, a medium price of £1, and a high price of £1.75. Participants
were informed that the price was randomly assigned and held no informational content
regarding emission size. We made sure of the participants’ understanding of this aspect
by asking them a comprehension question on the topic.

f

The task can be found in Supplementary Information B.3. The matrix contained a total of 143
numbers drawn from the set {0, 20, 40, 60, 80, 100, 120}. The number 60, the most frequently occurring,appeared 35 times, with 0 and 120 being the next most frequent, each appearing 26 times. All othernumbers appeared 14 times each.
gNote that the experiment had a third treatment which gave people full information about the
carbon impact of the product. This treatment is analyzed and described elsewhere 41 . We do not
analyze it here, as the comparison between the info and the uncertainty treatments is complicated by
the fact that we do not have full information about the belief distributions. Hence, we cannot be surethat the expected value of emissions is constant in the different treatments. Experiment 1 in this study,
therefore, provides higher quality evidence on the effect of precise information on behaviour.

16

Sample and data collection. We recruited 714 participants using Prolific.co, an
online platform, between 9th and 11th May 2019.h Of those, 304 participants were assigned to the Unmotivated treatment (87 faced a £0.25 price, 107 a price of £1.00, and
110 a price of £1.75), and 410 participants were assigned to the Motivated treatment(146 faced a £0.25 price, 125 a price of £1.00, and 139 a price of £1.75). Demographic
information for 19 participants was not successfully recorded (11 and 8 from the Unmotivated and Motivated treatment, respectively). These 30 subjects are included in
the analysis when we run non-parametric tests, but they are excluded in the regression
analysis, which includes the demographic controls.
Fifty per cent of the participants identified as females, 42% are students, and theaverage age is 29 years old. We accepted only EU nationals as participants. The mostrepresented countries in our sample are the UK (34.7%), Poland (14.54%), and Portugal(12.1%). Participants earned a fixed reward of £1.60, with a potential bonus payment
contingent on their decisions. On average, they earned £2.04, and they took less than
13 minutes to complete the tasks. We obtained participants’ demographic information,
including gender, age, student status, and nationality, directly from Prolific.co. Following the participants’ decisions, we donated $911.40 to Carbonfund.org to offset CO2
emissions, resulting in a reduction of over 90 metric tons of CO2 in the atmosphere.
The experiment maintained participant anonymity, as we identified participants only
via alphanumerical IDs provided by the platform. Participants knew that they weretaking part in an experiment.

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21

Supplementary Information

Uncertainty about Carbon Impact and theWillingness to Avoid CO2 Emissions
Davide D. Pace

Taisuke ImaiPeter SchwardmannJoël J. van der Weele

Contents
A Additional Results
A.1 Study 1: Survey about Subjective Uncertainty . . . . . . . . . . . . . . .
A.2 Study 2: Risk Aversion Experiment . . . . . . . . . . . . . . . . . . . . .
A.3 Study 3: Motivated Belief Experiment . . . . . . . . . . . . . . . . . . .
A.4 Robustness Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
3
12
14

B Experimental Materials
B.1 Belief Elicitation in Study 1 . . . . . . . . . . . . . . . . . . . . . . . . .
B.2 Work Task in Study 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3 Attention Task in Study 3 . . . . . . . . . . . . . . . . . . . . . . . . . .
B.4 Measures to Assure Data Quality . . . . . . . . . . . . . . . . . . . . . .
B.5 Invoice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.6 Preregistrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17
17
22
24
25
26
27

References

29

A

Additional Results

A.1

Study 1: Survey about Subjective Uncertainty
Supplementary Table 1: Demographic characteristics.
Education

Age
18-27
28-37
38-47
48-57
58+

223
267
195
186
257

0.198
0.237
0.173
0.165
0.228

Less than high school
8 0.008
High school degree
107 0.104
Some University but no degree 288 0.281
Bachelor Degree
373 0.364
Postgradute degree
249 0.243

GenderHousehold income

FemaleMale
Other

525 0.504
505 0.485
12 0.012- $5,000$5,000 - $15,000$15,000 - $30,000$30,000 - $45,000$45,000 - $60,000$60,000 - $75,000$75,000 - $90,000$90,000 - $105,000$105,000 - $120,000$120,000 - $135,000$135,000 - $150,000$150,000 -Ethnicity
Asian
Black
Mixed
White
Other

70
141
30
776
25

0.067
0.135
0.029
0.745
0.024

Party affiliation
Republican
152 0.148
Republican-leaning independent
68 0.066
Independent
202 0.197
Democratic-leaning independent 147 0.143
Democratic
456 0.445
Political orientation
Conservative
Somewhat conservative
Somewhat liberal
Liberal

100 0.098
225 0.220
324 0.316
376 0.367

Notes: 1,128 participants completed the belief elicitation task.

1

26
68
129
130
136
114
88
83
90
30
37
94

0.025
0.066
0.126
0.127
0.133
0.111
0.086
0.081
0.088
0.029
0.036
0.092

Supplementary Table 2: Representativeness of the sample.

SamplePopulation

Age
18-27
28-37
38-47
48-57
58+

0.198
0.237
0.173
0.165
0.228

0.172
0.176
0.160
0.162 χ2 (4) = 64.658
0.330
p < 0.001

0.510
0.490

0.504 χ2 (1) = 0.1453
0.496
p = 0.7031

0.071
0.143
0.786

0.064
0.142 χ2 (2) = 0.7821
0.794
p = 0.6763

GenderFemaleMale
Ethnicity
Asian
Black
White

Notes: Population-level data is retrieved from US Census Bureau (2022).

2

A.2

Study 2: Risk Aversion Experiment

A.2.1

Demographic characteristics
Supplementary Table 3: Demographic characteristics.

Treatment
All

Information Uncertainty

Age bracket
18-27
28-37
38-47
48-57
58+

277 0.184
482 0.320
354 0.235
235 0.156
157 0.104

0.178
0.331
0.230
0.155
0.106

0.190
0.310
0.241
0.157
0.102

χ2 (4) = 1.06
p = 0.90

GenderMale
FemaleOther

744 0.494
754 0.501
7 0.005

0.490
0.507
0.003

0.499
0.495
0.007

χ2 (2) = 1.47
p = 0.48

Political view
Left
Center-leftCenterCenter-right
Right

295
445
493
214
58

0.196
0.296
0.328
0.142
0.039

0.190
0.303
0.321
0.145
0.041

0.202
0.289
0.334
0.140
0.036

χ2 (4) = 1.06
p = 0.90

EducationLess than high school 27 0.018
High school
330 0.219
Some University
176 0.117
Bachelor
658 0.437
Postgraduate
314 0.209

0.013
0.211
0.120
0.465
0.191

0.023
0.227
0.114
0.410
0.226

χ2 (4) = 7.18
p = 0.127

Income- £5,000£5,000 - £15,000£15,000 - £30,000£30,000 - £45,000£45,000 - £60,000£60,000 - £75,000£75,000 - £90,000£90,000 - £105,000£105,000 -

0.020
0.092
0.220
0.218
0.151
0.139
0.084
0.024
0.052

0.016
0.086
0.217
0.209
0.176
0.104
0.081
0.056
0.056

χ2 (8) = 15.68
p = 0.047

27
134
329
321
246
183
124
60
81

0.018
0.089
0.219
0.213
0.163
0.122
0.082
0.040
0.054

3

A.2.2

Shape of the individual-level WTM curve

We elicited willingness to mitigate (WTM) across six emission levels: 0, 4, 8, 12, 16, and20 kilograms of CO2 emissions. In this analysis, we focus on characterizing the shapeof individual-level WTM curves. Let (ei , wi ) denote the pair of emission size ei and thereported WTM wi ∈ [0, 7], for each i = 1, . . . , 6. It is important to note that in thisanalysis, we consider the entire range of 0-20 kg, as opposed to the more constrained
range of 0-8kg (used in Supplementary Table 4 below) when classifying the shape ofthese curves.
Step 1. For each participant, we construct a piecewise linear WTM curve using linear
interpolation, consisting of five line segments. The WTM curve has five line segments.
The slope of the ith line segment, denoted as si , is given by:si =wi+1 − wi.
ei+1 − eiWe apply the following rule sequentially to classify the shape of the WTM curve.1 We
say that a WTM curve is• constant if si = 0 for all i;• almost constant if max wi − min wi ≤ 0.5, i.e. the step size of the MPL;
• decreasing if si ≤ 0 for all i with at least one strict inequality;• concave if si+1 ≤ si for all i with at least one strict inequality;• convex if si+1 ≥ si for all i with at least one strict inequality;• increasing if si ≥ 0 for all i with at least one strict inequality;• non-monotonic if it does not fall into any of the above categories.
In our dataset, we identified 317 WTM curves as (almost) constant, 38 as decreasing, 299
as concave, 25 as convex, and 522 as increasing. The remaining 303 WTM curves exhibit
a non-monotonic behavior.
Step 2. Let us direct our attention to the subset of 522 participants whose WTM curves
exhibit an increasing trend while not falling into the categories of concave or convex
shapes. Among these participants, 66 individuals have their WTM values censored at a
maximum of £7. Let w̄ represent the largest observed WTM value. If w̄ = 7, we defineē as the smallest emission level ei for which wi = 7. If w̄ < 7, on the other hand, we set
1This means that concave and convex WTM curves in this classification are non-decreasing, andincreasing WTM curves are neither concave nor convex. We classify linear WTM curves as concave.

4

WTM curve(N = 1, 505)
constant(317)

concave(299)

convex(25)

increasing(522)

decreasing(38)

Non-mon
(303)

at 0
(1)

concave†(213)

almost increasing†
(15)

at 7
(12)

convex†(85)

almost decreasing†(1)

increasing(224)

almost constant†(20)

at w ∈ (0, 7)(147)

non-mon(267)

almost constant(157)

Supplementary Figure 1: Classification of individual-level WTM curves.

ē = e6 . Next, we draw a chord connecting two points: (e1 , w1 ) and (ē, w̄). We say that a
WTM curve is concave† (convex† ) if the points (ei , wi ) for which ei ≤ ē lie above (below)
the chord. In our dataset, we identified 213 WTM curves as concave† and 85 as convex† .
Step 3. Finally, we turn to the remaining 303 participants whose WTM curves exhibit
non-monotonic behavior.
First, we say that a WTM curve is almost constant† if the difference between thelargest and smallest WTM values does not exceed £1, which corresponds to two steps in
the MPL. This relaxation captures the shape of an additional 20 WTM curves.
Second, we say that a WTM curve is almost increasing† (almost decreasing† ) if thepiecewise linear WTM curve has only one line segment with a negative (positive) slope,and the relative change of WTM on that segment is “not too large”.2 This relaxation
captures the shape of an additional 16 WTM curves.
Classification summary. Allowing some margin of error, we have established a comprehensive and mutually exclusive classification of individual-level WTM curves as follows: 337 are constant, 512 are concave, 110 are convex, 239 are increasing, 39 aredecreasing, and 267 are non-monotonic.

2

Suppose the sign of the slopes changes on the segment connecting (ej , wj ) and (ej+1 , wj+1 ). We
require the absolute relative change to be less than 10%, i.e., |(wj+1 − wj )/wj | ≤ 0.1.

5

A.2.3Purchasing decisions
Supplementary Table 4: Effect of uncertainty on purchasing decisions.

Information

(1)

(2)

(3)

(4)

(5)

(6)

−0.008(0.024)−0.008(0.034)0.011(0.032)0.014(0.027)−0.032(0.026)−0.069∗(0.035)−0.037∗∗∗(0.009)0.00002(0.034)0.002(0.032)−0.067(0.061)−0.043(0.064)−0.034∗(0.015)

Concavity
Info × Concavity
Average WTM
Concavity alt

Constant

0.571∗∗∗(0.127)0.437∗(0.194)0.644∗∗∗(0.147)0.709∗∗∗(0.118)0.022(0.033)−0.074(0.046)
0.516∗∗(0.170)Controls
Observations
R2

Yes
1,505
0.054

Yes
827
0.058

Yes
678
0.075

Yes
1,162
0.100

Yes
912
0.052

Info × Concavity alt

0.697∗∗∗(0.118)
Yes
1,118
0.102

Notes: Models (1) to (5) are linear regressions. Model (6) is an IV regression. The dependent variable isproduct bought, a dummy equal to 1 if the participant bought the convenience product. Information
is a treatment dummy equal to 1 in the Information treatment. Concavity is given by WTM4 −(WTM0 + WTM8 )/2, Average WTM is given by (WTM0 + WTM4 + WTM8 )/3, and Concavity alt isgiven by dividing Concavity by (WTM8 − WTM0 )/2. Column 1 uses all the observations. Column 2
includes only the participants with a strictly concave WTM in the interval 0-8kg. Column 3 includes
only the participants with a strictly convex or linear WTM in the 0-8kg interval. Column 4 excludes
the participants whose WTM is censored or decreasing in the 0-8kg interval. Column 5 further excludes
the participants for whom WTM0 = WTM8 , since Concavity alt is not defined for them. Column 6
instruments Concavity, Info*Concavity, and Average WTM with their equivalent variables coming fromthe unincentivized WTM elicitation. This column excludes the participants with decreasing or censored
WTM in any of the elicitations. List of control variables common to all regressions: age, gender (male,
female, other), political affiliation (5 categories), education (6 categories), income (7 categories), andtime needed to complete the first real effort task. Robust standard errors are reported in parentheses.
∗: p < 0.05; ∗∗ : p < 0.01; ∗∗∗ : p < 0.001.

6

Coefficient

0.2

0.0

−0.2

l
l
t
r
y
e
n
e
7
7
7
+
tio WTM 8−3 8−4 8−5 : 58 mal choo ersit helo adut entra Righ
a
e
c
e
2
3
4
r
v
s
:
i
C
a
F gh
orm Avg ge: ge: ge:Ag
Un : B ostg n: tion
i
Inf
A
A
A
: H ome ation n: P ntatio ientano : S uc
tio rieorati
uc ation Ed duca al o iticald
E uc
E litic Pol
Po
EdSupplementary Figure 2: Estimated coefficients from a linear regression. Notes: The dependent
variable is product bought, which is a dummy equal to 1 if the participant bought the computercode. The intercept is not shown for a better visual rendering. The baseline categories are:“18-27” for Age, “Male” for Gender, “Less than high school” for Education, and “Left wing”
for Political orientation. Bars indicate 95% CI.

7

A.2.4

Psychological mechanisms behind concavity

We empirically explore two potential psychological mechanisms that may give rise to aconcave WTM curve. The first mechanism relates to individuals’ inability to appreciateincreasingly large (and unfamiliar) amounts of emissions. The second mechanism considers the possibility that the concavity in WTM arises from concave moral judgments about
the acceptability of causing different levels of emissions. Our data does not support eitherof these two mechanisms. However, based on the framing of the elicitation questions, we
propose that the concavity we found is more likely due to a marginally decreasing disutility from CO2 emissions — which are seen as a loss — rather than decreasing marginalutility from implementing offsets — which are seen as a gain.
Increasing cognitive uncertainty. People may perceive the questions involving larger
emission quantities as more challenging due to the inherent complexity of visualizing
the precise scale of higher levels of emissions. This heightened level of complexity canlead participants to experience greater cognitive uncertainty when deciding their WTM,
making them less sensitive to variations in increases in emission sizes. This relation
between cognitive uncertainty and valuation can generate a concave WTM curve within
the framework of an “anchoring and adjustment” model, in which the weight attributed
to the anchor increases with cognitive uncertainty (Enke and Graeber, 2023). The anchor,
in this case, is the default behaviour of not compensating for CO2 emission produced ineveryday life.
The anchoring and adjustment model predicts the concavity of WTM under two conditions: (a) individuals generally do not engage in emissions offsetting, making an anchor
value of £0 a plausible assumption, and (b) cognitive uncertainty increases with emission
size. We find empirical support for both of these underlying assumptions. Specifically,
over 82.7% of our participants reported to “Never” or “Rarely” compensate for theiremissions. Furthermore, in a regression that controls for demographic characteristics, wefind that cognitive uncertainty increases with emission size (t(1231) = 8.132, 95% CI[0.067, 0.109], two-sided p < 0.001).
However, our analysis does not reveal any substantial evidence of a relationship between cognitive uncertainty and the concavity of the WTM curve. In Supplementary
Table 5, we present the results of a regression in which the WTM is regressed on a)
cognitive uncertainty, b) emission levels, c) the square of the emission levels, d) the interaction between cognitive uncertainty and the emission levels, and e) the interaction
between cognitive uncertainty and the square of the emission levels. We include thesquare of the emissions to account for potential nonlinear associations between emissionsand WTM. The interaction between the square of emissions and cognitive uncertainty is
included to explore whether higher levels of uncertainty are linked to more pronounced8Supplementary Table 5: Concavity of WTM and cognitive uncertainty.

Emissions
Emissions2
Cognitive uncertainty
Cognitive uncertainty × Emissions
Cognitive uncertainty × Emissions2
Constant
Controls
Observations
Clusters
R2

(1)

(2)

0.16859∗∗∗(0.01090)−0.00327∗∗∗(0.00043)
0.00776(0.00785)
0.00164(0.00198)−0.00009(0.00009)
0.10094(0.58873)

0.16906∗∗∗(0.01204)−0.00322∗∗∗(0.00048)
0.00940(0.00858)
0.00126(0.00213)−0.00008(0.00009)
0.14302(0.65010)

Yes
7,392
1,232
0.1494

Yes
6,222
1,037
0.1485

Notes: The dependent variable is WTM. The first column includes only the participants that have an
uncensored WTM for all 6 emission amounts. The second column further excludes the participants who
said that offset all their emissions or that they “often” offset their emissions. List of control variables
common to all regressions: age, gender (male, female, other), political affiliation (5 categories), education(6 categories), income (7 categories), and time needed to complete the first real effort task. Standard
errors clustered at the individual level are reported in parentheses. ∗ : p < 0.05; ∗∗ : p < 0.01; ∗∗∗ :p < 0.001.

concavity, which a negative coefficient for the interaction term would indicate. Column (1)of Supplementary Table 5 shows that the coefficient indeed appears negative, but it issmall in magnitude and fails to reach statistical significance (t(1231) = −0.987, 95% CI[−2.6 · 10−4 , 8.5 · 10−5 ], two-sided p = 0.324). Column (2) restricts the sample to subjects
who “Never” or “Rarely” compensate for their emissions and confirms the null result.
Another approach to assess the relationship between an increase in cognitive uncertainty and a concave WTM involves examining whether individuals with greater uncertainty as emissions rise are more likely to exhibit a concave WTM curve. To do this,we define CU j (e) as the cognitive uncertainty of participant j at emission level e. The
increase in cognitive uncertainty can then be quantified as:∆CU = CU j (ē) − CU j (0),where ē denotes the highest emission level for which the participant reported an uncensored WTM. We regress the concave-WTM dummy on ∆CU and find that there is no
statistically significant correlation between the two variables (t(1082) = −0.431, 95% CI

9[−0.004, 0.003], two-sided p = 0.666).3
Based on these two analyses, we conclude that there is insufficient support for theidea that cognitive uncertainty is a driver of concavity in the WTM curve.
Concave moral valuations. Another potential psychological channel that may explain a concave WTM relates to concave moral judgments. Individuals might perceive
emitting 4kg of CO2 as considerably morally worse than emitting 0kg, while the moral
distinction between emitting 4kg and emitting 20kg might seem relatively minor. Such
concave moral evaluations might, in turn, influence and shape the participants’ WTM.
Let µj (e, k) ∈ {1, 2, . . . , 7} denote the moral evaluation assigned by participant j
to emitting ekg of CO2 in exchange for £k, where the range spans from “morally very
appropriate” (1) to “morally very inappropriate” (7). These evaluations are collected foreach e ∈ 4, 12, 20 and k ∈ 1, 5. We aggregate these moral judgments by computing theiraverage over the two values of k, yielding mj (e) = (µj (e, 1) + µj (e, 5))/2. This composite
measure is labelled as “Morality.” Finally, we compute the variable φj as:
φj = mj (12) −mj (4) + mj (20).
2

A positive value of φj indicates that the moral valuation of participant j is concave. The
average φ is 0.107, which is positive and statistically significant (t(1504) = 7.08, 95% CI[0.078, 0.137], two-sided p < 0.001), suggesting that moral judgments are indeed concave.
To investigate whether the presence of concave moral valuations is linked to a concave
WTM, we regress the “concavity” dummy, which is equal to 1 if a participant exhibitsa concave WTM, on the variable φj . The results presented in Supplementary Table 6
indicate that concavity in moral valuations has limited predictive power regarding theconcavity of WTM.
A proposed interpretation based on the questions frame. We propose that the
concavity of the WTM data reflects decreasing marginal disutility from emitting CO2 —emissions perceived as losses— rather than decreasing marginal utility from offsets, which
are viewed as gains. This argument relies on the framing of our WTM questions.
In the WTM elicitation, participants are presented with a choice between “Option
A”, which entails no emissions and no monetary pay-off, and “Option B”, which entails
positive emissions and a monetary bonus. The reference point consists of no emissions.
Participants were informed that emissions would be implemented as follows: 1) we set
3

We follow the classification of individual WTM curve discussed in Section A.2.2. Note that the
concave-WTM is a dummy variable taking a value of 1 when the WTM curve is characterized as either“concave” or “concave† ” in the classification. In this analysis, we excluded participants whose WTM
curves were classified as decreasing or non-monotonic. Additionally, participants with only an uncensoredWTM value at e = 0 were also excluded, as ∆CU is undefined for this subgroup.

10Supplementary Table 6: Concavity of WTM and morality.

Concavity of moral judgment (φ)
Constant
Controls
Observations
R2

(1)

(2)

(3)

(4)

0.022
(0.020)0.212(0.121)0.020(0.020)0.202(0.125)0.016(0.021)
0.233(0.128)0.045(0.026)0.153(0.143)

Yes
1,504
0.040

Yes
1,430
0.040

Yes
1,373
0.042

Yes
1,100
0.040

Notes: The dependent variable is concave, a dummy taking a value of 1 if the WTM curve is either“concave” or “concave† ” based on the classification discussed in Section A.2.2. Samples are increasingly
restrictive, from left to right. Column (1) includes all participants. Column (2) excludes participants who
failed the attention check embedded in the moral judgment elicitation. Column (3) excludes participants
whose mj (e) are decreasing in e. Column (4) excludes participants whose WTM curve is either decreasing
or non-monotonic. List of control variables common to all regressions: age, gender (male, female, other),political affiliation (5 categories), education (6 categories), income (7 categories), and time needed tocomplete the first real effort task. Robust standard errors are reported in parentheses. ∗ : p < 0.05; ∗∗ :p < 0.01; ∗∗∗ : p < 0.001.

aside a portion of the funds to be donated to Carbonfund.org, but 2) we would reduce the
donation if they chose Option B. This procedure establishes the default as the donation togo through, with participants having the option to deviate from this default by choosing
Option B. Moreover, the instructions asked the participants to indicate “the minimum
bonus you require to accept the CO2 emissions”.
The questions are framed similarly to Willingness To Accept (WTA) elicitations,which ask participants to indicate the compensation required to engage in something
they dislike—in our case, allowing the emission of CO2 . Given this framing, the concavity observed in our WTM data suggests that individuals have a marginally decreasing
disutility from emitting CO2 : their aversion to emissions increases less at a rate less thanproportional to the size of emission. This marginally decreasing disutility is surprising
given that most economic models assume convex utility functions in losses.
The preceding discussion raises concerns regarding whether the concavity of WTM
is driven by the way we ask the questions. Recent evidence, however, suggests thisis not the case. Rodemeier (2023) successfully replicates the concavity result using a
Willingness To Pay (WTP) framework, which asks individuals how much they are willingto pay out of their own pocket to offset emissions. In a WTP framework, offsets are
considered as gains. The fact that the WTM exhibits concavity in both the loss andthe gain domains suggests that decisions regarding emissions should be modelled with areference-dependent model characterized by increasing insensitivities as outcomes moveaway from the reference point.

11

A.3

Study 3: Motivated Belief Experiment

A.3.1

Demographic characteristics
Supplementary Table 7: Demographic characteristics.

Treatment
All

Motivated

UnmotivatedAge bracket
18-27
28-37
38-47
48-57
58+

371 0.530
207 0.296
67 0.096
40 0.057
15 0.021

0.536
0.308
0.084
0.055
0.017

0.522
0.279
0.111
0.061
0.027

χ2 (4) = 2.64
p = 0.620

GenderMale
Female

354
359

0.496
0.504

0.493
0.507

0.502
0.498

χ2 (1) = 0.03
p = 0.872

Student
NoYes

417 0.590
290 0.410

0.587
0.413

0.593
0.407

χ2 (1) = 0.01
p = 0.932

EducationLess than high school 17
High school
190
Some University
145
Bachelor
231
Postgraduate
114

0.024
0.273
0.208
0.331
0.164

0.022
0.274
0.204
0.334
0.165

0.027
0.270
0.213
0.328
0.162

χ2 (4) = 0.24
p = 0.993

Income- £5,000£5,000 - £15,000£15,000 - £30,000£30,000 - £45,000£45,000 - £60,000£60,000 - £75,000£75,000 - £90,000£90,000 - £105,000£105,000 -

0.069
0.230
0.289
0.162
0.121
0.076
0.035
0.011
0.006

0.075
0.232
0.290
0.149
0.130
0.066
0.036
0.014
0.008

0.062
0.228
0.287
0.180
0.110
0.088
0.033
0.007
0.004

χ2 (8) = 3.88
p = 0.868

44
146
183
103
77
48
22
7
4

Notes: The table includes observations from the Motivated and the Unmotivated treatment (N = 714).
Missing observations: 14 in age bracket, 1 in gender, 7 in student, 1 in education, 73 in income.

12

A.3.2

Dwell time in the attention task

In this analysis, we investigate whether the Motivated treatment has any impact on
the time subjects spend completing the attention task. This variable is of particularimportance because recent findings in economics and neuroscience suggest that dwell
time on a piece of information causally increases the weight given to that information insubsequent decisions (Pärnamets et al., 2015; Amasino, Pace and van der Weele, 2021;
Engelmann, Hirmas and van der Weele, 2021).
In the context of our study, we observed no substantial differences between the Motivated and Unmotivated treatments. If anything, the participants in the Motivated treatment tended to spend more time on the attention task. As shown in column (1) of
Supplementary Table 8, in which we regress the time the participants spent on the task
(in seconds) on a dummy for the Motivated treatment and on demographic controls,
we observe that in the Motivated treatment spend 1.6 seconds more on the task. However, this difference is not statistically significant (t(655) = 0.53, 95% CI [−4.29, 7.47],
two-sided p = 0.595).
Column (2) confirms this finding, focusing solely on the 91% of participants who completed the task in less than 70 seconds. This subset represents individuals for whom we
can be most confident that they did not take any breaks between receiving the informationand providing their responses (the information was displayed for up to 60 seconds).
Supplementary Table 8: Time spent on the attention task.

(1)

(2)

Motivated treatment

1.593(2.994)0.082(1.508)Controls
Observations
R2

Yes
694
0.067

Yes
632
0.079

Notes: The models are linear regressions with dependent variable the seconds the participants spenton the attention task. The models include the observations from the Motivated and the Unmotivatedtreatment with the Unmotivated as the baseline. The first column includes all the participants for which
we recorded the demographic data, except one for which the program did not record the time spent on
the task. The second column only includes the participants who spent less than 70 seconds to complete
the attention task. Control variables: sex, age, student status, education (6 categories), frequency of car
usage (5 categories), nationality (27 categories). Robust standard errors are reported in parentheses. ∗ :p < 0.05; ∗∗ : p < 0.01; ∗∗∗ : p < 0.001.

13

A.4

Robustness Checks

A.4.1

Subsample by the level of understanding

Supplementary Tables 9 (for the Risk Aversion experiment) and 10 (for the Motivated
Belief experiment) demonstrate the robustness of the null result even when excluding
participants who made mistakes in the comprehension questions.
Supplementary Table 9: Effect of uncertainty on getting the computer code (Risk Aversion
experiment).

Information treatment
Constant# Mistakes
Controls
Observations
R2

(1)

(2)

(3)

(4)

−0.005(0.036)
0.538∗(0.213)0.005(0.027)0.576∗∗∗(0.148)−0.004(0.025)0.587∗∗∗(0.131)−0.004(0.024)0.550∗∗∗(0.130)

0
Yes
668
0.089

≤3
Yes
1,221
0.060

≤6
Yes
1,364
0.054

≤12
Yes
1,460
0.054

Notes: All models are linear regressions with dependent variable product bought: an indicator variableequal to 1 if the participant bought the computer product. Models include the observations from theInformation and the Uncertainty treatments of the Risk Aversion experiment. The Uncertainty treatment is the baseline. Column (1): participants who made no mistakes in the comprehension questions.
Column (2): participants who made 3 or fewer mistakes. Column (3): participants who made 6 or fewer
mistakes. Column (4): participants who made 12 or fewer mistakes. Control variables: gender (male,
female, other), age, education (5 categories), political identification (5 categories), income (9 categories),time needed to complete the real effort task. Robust standard errors are reported in parentheses. ∗ :p < 0.05; ∗∗ : p < 0.01; ∗∗∗ : p < 0.001.

14

Supplementary Table 10: Effect of the Motivated treatment on purchasing and beliefs (Motivated
Belief experiment).

A: Units

(1)

(2)

(3)

(4)

Motivated treatment

0.073(0.060)0.020(0.041)

0.031(0.039)0.034(0.038)# Mistakes
Controls
Observations
R2

0
Yes
324
0.119

≤3
Yes
579
0.108

≤6
Yes
635
0.101

≤12
Yes
670
0.099

B: Beliefs

(1)

(2)

(3)

(4)

Motivated treatment

2.284(4.715)

3.179(3.550)

3.124(3.378)2.727(3.277)# Mistakes
Controls
Observations
R2

0
Yes
324
0.110

≤3
Yes
579
0.049

≤6
Yes
635
0.048

≤12
Yes
670
0.049

Notes: All the models are linear regressions. Dependent variable: (A) a dummy variable equal to 1 if
the participant bought the virtual product, (B) beliefs about the size of the CO2 emissions associatedwith the virtual product. The models include the observations from the Motivated and the Unmotivatedtreatment. The Unmotivated treatment is the baseline. Column (1): participants who made no mistakes
in the comprehension questions. Column (2): participants who made 3 or fewer mistakes. Column (3):participants who made 6 or fewer mistakes. Column (4): participants who made 12 or fewer mistakes.
Control variables: sex, age, student status, education (6 categories), frequency of car usage (5 categories),
nationality (27 categories). Robust standard errors are reported in parentheses. ∗ : p < 0.05; ∗∗ : p < 0.01;∗∗∗: p < 0.001.

15

A.4.2

Subsample by the level of trust

Supplementary Table 11 presents the results after excluding participants who expressed
scepticism about our commitment to actually paying for the CO2 offsets. The null results
remain consistent in this robustness check.
Supplementary Table 11: The effect of trust in researchers.

Risk Aversion(1)
Purchase
Information treatment(2)
Purchase(3)
Belief0.028(0.041)

2.552(3.523)

Yes
579
0.112

Yes
579
0.053

−0.005(0.027)

Motivated treatment
Controls
Observations
R2

Motivated Belief

Yes
1,217
0.056

Notes: All models are linear regressions. Dependent variables: in column (1), an indicator variable equal
to 1 if the participant bought the computer product; in column (2), an indicator variable equal to 1 if
the participant bought the virtual product; in column (3), beliefs about the size of the CO2 emissions
associated with the virtual product. The first column includes the observations from the Information andthe Uncertainty treatments of the Risk Aversion experiment. The second and third columns include theobservations from the Motivated and the Unmotivated treatment from the Motivated Beliefs experiment.
The Unmotivated treatment is the baseline. The Uncertainty treatment is the baseline. In all columns
we exclude the participants who indicated low level of trust towards the CO2 offsets taking place areexcluded from this analysis. In the Risk Aversion experiment, these are the participants that answeredwith a 1, 2, or 3 to the question: “Do you trust that the researchers will indeed buy CO2 offsets
as described in the instructions?”. Where 1 means “not at all” and 5 means “completely”. In the
Motivated Beliefs experiment these are the subjects that answered “No” rather than “Yes” to the samequestion. Control variables in column (1): gender (male, female, other), age, education (5 categories),
political identification (5 categories), income (9 categories), time needed to complete the real effort task.
Control variables in columns (2) and (3): sex, age, student status, education (6 categories), frequency of
car usage (5 categories), nationality (27 categories). Robust standard errors are reported in parentheses.
∗: p < 0.05; ∗∗ : p < 0.01; ∗∗∗ : p < 0.001.

16

B

Experimental Materials

B.1

Belief Elicitation in Study 1

Point estimates of the emission sizes. When asking about the CO2 emissions generated by driving, we allowed the participants to express their guesses either in ounces
or grams so they could use the more familiar unit of measure (Supplementary Figure 3).
For all the other products, we elicited the point estimates on a single interface thatallowed the participants to go back and modify their previous answers easily. The orderof the products on the interface was randomized at the individual level.
The 12 questions were graphically displayed (Supplementary Figure 4). The productin each question was represented by clip art, below which the name of the product andits size appeared. The participants could see which emissions were taken into account by
the scientific estimate by hovering the mouse cursor on an info icon ð shown above eachquestion. The list of products, their amount, and the emissions to be considered were all
described in the instructions as well.
The participants’ answers were summarized in an interactive box displayed at thebottom of the page. The box appeared as soon as a participant filled in the first question
on the screen and it stayed visible until the moment the participant confirmed her answers. The “Confirm” button appeared inside the summary box to draw the participant’s
attention to the box itself.
The summary box graphically showed a participant’s guesses on a line. Crucially, we
designed the line to avoid any anchoring effects. No number appeared on it if the participant had not entered any guesses. Moreover, the scale of the line adjusted dynamicallydepending on the highest guess.
Belief distribution. The elicitation interface showed the name and the quantity of the
product and reminded the participants of their point estimates. The participants could
see which emissions were taken into account by the scientific estimate by hovering themouse cursor on an info icon ð.
The interface displayed five bins for each question (Supplementary Figure 5). The
participant’s point estimate for the product, call it m, was taken as the midpoint of thecentral bin. The central bin covers numbers from 0.95m to 1.05m. The two bins on bothsides of the central bin cover numbers from 0.85m to 0.95m and from 1.05m to 1.15m.
Finally, the farthest two bins cover numbers below 0.85m and above 1.15m, respectively.
The interface showed a box containing the 20 balls the participants had to allocate
among the bins. The participants could move the balls to a bin by (i) moving a slider
below the bin, (ii) directly typing the number of balls they wanted to move in a text field
below the bin, or (iii) clicking on the arrows next to the text field. The participants could
move all the balls back to the box by pressing the button “Reset”.
17Supplementary Table 12: Comments on the calculation of CO2 emissions.

Product

Comment

Beer

It takes into account all the emissions, starting with the productionand ending with the distribution of the products to the consumer.

Phone call

It takes into account the CO2 emissions generated to operate the phone
and the communication network.

Microwave

It takes into account only the emissions generated by the power plantsthat produce the energy used by the microwave.

Milk

It takes into account all the emissions, starting with the productionand ending with the distribution of the products to the consumer.

Egg

It takes into account all the emissions, starting with the productionand ending with the distribution of the products to the consumer.

Poultry meat

It takes into account all the emissions, starting with the productionand ending with the distribution of the products to the consumer.

Shower

It takes into account the emissions generated by warming up the waterand all the emissions connected to the water delivery and cleaning.

Chocolate

It takes into account all the emissions, starting with the productionand ending with the distribution of the products to the consumer.

Coffee

It takes into account all the emissions, starting with the productionand ending with the distribution of the products to the consumer.

Beef

It takes into account all the emissions, starting with the productionand ending with the distribution of the products to the consumer.

Flight

It takes into account only the emissions generated by burning the plane
fuel.

Gas heating

It is the average of the estimates of 10 different carbon footprint calculators.

18

Supplementary Figure 3: Beliefs about CO2 emissions from driving one mile by car.

19

Supplementary Figure 4: Beliefs about CO2 emissions from consumer products and activities.

20

Supplementary Figure 5: Belief distribution.

21

B.2

Work Task in Study 2

The task involved typing 15 strings, each consisting of 15 characters, in reverse order. The
participants were required to transcribe these strings flawlessly to complete the task: any
mistakes incurred resulted in an error message indicating the specific strings that required
correction before they could proceed with the experiment. Participants saw a warning
sign ATTENTION CHECK every 30 seconds, and upon its appearance, they had a 5second window to click the I AM HERE button to confirm their active engagement withthe task (right panel in Supplementary Figure 6). The participants knew that they would
be excluded from the experiment if they failed more than 4 of these attention checks.

22Supplementary Figure 6: Work task.

23

B.3

Attention Task in Study 3

The task involved finding the most frequently appearing number in a matrix of numbers.
The matrix contained a total of 143 numbers, drawn from the set {0, 20, 40, 60, 80, 100, 120}
(Supplementary Figure 7). The number 60, the most frequently occurring, appeared 35
times, with 0 and 120 being the next most frequent, each appearing 26 times. All othernumbers appeared 14 times each. Participants earned £0.10 if they answered 60.

Supplementary Figure 7: The matrix of numbers presented in the attention task.

24

B.4

Measures to Assure Data Quality

Instructions and comprehension questions. To ensure a comprehensive understanding of the essential elements of the instructions by our experimental subjects, wecreated slides that presented the information step by step. Most of the slides were accompanied by explanatory images to facilitate a more intuitive comprehension of the
instructions. Furthermore, we organized the instructions into several sets. Following thecompletion of each set, participants were required to answer a series of comprehension
questions. Importantly, we did not allow subjects to proceed with the experiment until
they had successfully answered all questions in a given set. In total, participants wererequired to answer 7 questions related to the beliefs elicitation in Study 1, 19 questions(5 of which concern the work task and the computer code) in Study 2 and 15 in the
Motivated and Unmotivated treatments in Study 3.
How we made sure that no bot completed the study. Our design incorporates
two elements that mitigate the risk of an automated script (“bot”) completing our experiment. Firstly, our instructions are not machine-readable. As a result, a computer
script would need to provide random answers to the comprehension questions, leading to
an exceptionally high number of answer attempts. This is further exacerbated by several
comprehension questions requiring participants to input precise numerical values. We
kept track of the number of attempts. In the Risk Aversion experiment, none of the participants who reached the end of the experiment needed more than 50 attempts to answer
the comprehension questions, and 95% of them needed less than 22 attempts (the minimum number of attempts was 10). In the Motivated Belief experiment, no participant
needed more than 65 attempts and 95% less than 14 attempts (the minimum number ofattempts was 3).
Secondly, we incorporated three “honey-pots” within our two experiments. Those arequestions hidden from human participants but discernible to a bot that reads the sourcecode of the experimental program and identifies them as questions to be answered. We
considered answering either honey-pot as sufficient evidence that the participant is a bot.
We found no participant who answered these two “hidden” questions.
Combining the evidence from the number of attempts and the honey-pots, we canconfidently conclude that no bot completed our experiment.

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B.5

Invoice

Carbonfund.org - Invoice 10622

https://carbonfund.org/checkout/order-received/38268/?wc_pip_action...

Invoice 10622 for order 38268
Order Date: May 14, 2019

Billing AddressDavide Pace
Roetersstraat 11
1018WB Amsterdam
Netherlands

Shipping
Address

Shipping Method
No shipping

Davide Pace
Roetersstraat 11
1018WB Amsterdam
Netherlands

SKU

Product

generaldonation

General Donation

QuantityPrice1$911.40

Subtotal:$911.40

Payment Method:

Credit Card

Total:$911.40

Name for e-certificate(s): Davide Pace on behalf of
the University of Amsterdam

Customer Details
Email: d.d.pace@uva.nl
This donation is the result of participants decisions in the experiments “Decision Making 6-13”of the University of Amsterdam

1 of 1

5/14/2019, 11:29 AM

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B.6

Preregistrations

CONFIDENTIAL - FOR PEER-REVIEW ONLY
Curbing carbon: Does information about climate impact reduce emissions? (#109190)
Created: 10/11/2022 07:59 AM (PT)This is an anonymized copy (without author names) of the pre-registration. It was created by the author(s) to use during peer-review.
A non-anonymized version (containing author names) should be made available by the authors when the work it supports is made public.

1) Have any data been collected for this study already?
No, no data have been collected for this study yet.
2) What's the main question being asked or hypothesis being tested in this study?
We have two main research questions.
1) Does quantitative information about CO2 emission reduce the acquisition of an emission-intensive product?
2) If so, is the effect of information explained by the declining marginal willingness to pay for mitigating CO2 emissions?
3) Describe the key dependent variable(s) specifying how they will be measured.
Participants can buy a product that results in an uncertain amount of CO2 emissions. The key dependent variable is the consumption of the product (1: if
the participant buys; 0: otherwise). In addition, we elicit willingness to pay to mitigate (WTM) CO2 emissions of various sizes, to explain the reaction to
information (see below). For each emission size, we elicit WTM twice to rule out measurement error (see point 8).
4) How many and which conditions will participants be assigned to?
There are 2 conditions. Each participant will participate in one condition.
Info Treatment: participants know exactly the size of the CO2 emissions of the product (4 kg).
Uncertainty Treatment: participants know CO2 emissions associated with the product are 0 kg with a probability of 0.4, 4 kg with a probability of 0.2, or 8
kg with a probability of 0.4.
5) Specify exactly which analyses you will conduct to examine the main question/hypothesis.
Hypothesis 1: Participants in the Info treatment buy fewer units of the good than participants in the Uncertainty treatment.
We test this hypothesis by means of a Fisher's exact test. We will also perform OLS regressions to control for subject characteristics.
Hypothesis 2: The effect of information increases with higher concavity of WTM (declining marginal willingness to mitigate).
For each individual, we compute a measure of concavity as the WTM 4 kg of CO2 emissions minus the average of the WTM 0 kg and 8 kg. We then regress
the buying decision on the Info treatment dummy, our concavity measure, and the interaction of this concavity measure and the Info treatment dummy. In
the regression, we control for subject characteristics and the average WTM across all three relevant levels. For this analysis, we exclude subjects whose
WTM is top censored for at least one emission amount in the interval [0kg; 8kg] and whose WTM to mitigate is not weakly increasing, i.e., who don't satisfy
the law of demand.
6) Describe exactly how outliers will be defined and handled, and your precise rule(s) for excluding observations.
We exclude observations only if we have evidence that the respondent is not a human (we will run the experiment online). In addition, we will run
robustness checks where we exclude participants who indicate that they don't believe we will actually implement the CO2 emissions.
7) How many observations will be collected or what will determine sample size? No need to justify decision, but be precise about exactly how thenumber will be determined.
We will collect 1500 complete observations on prolific. The sample size in the analysis might be larger because we will include subjects who havecompleted the demographic questionnaire but have not finished the experiment.
8) Anything else you would like to pre-register? (e.g., secondary analyses, variables collected for exploratory purposes, unusual analyses planned?)
We will provide various robustness checks. First, we will do robustness using an alternative specification of the concavity measure, dividing our original
measure by (WTM(8 kg) - WTM(0 kg))/2 to correct for the increase in the WTM. We will also look at the treatment differences for the subsets ofparticipants whose willingness to mitigate is more or less concave than the median.
Second, to combat measurement error in our concavity measure, we will do a second, unincentivized elicitation of WTM. Following the approach in Gillen
et al. (Journal of Political Economy, 2019) we will instrument one measure with the other to eliminate any variation that is not common to both measures.

Version of AsPredicted Questions: 2.00

Available at https://aspredicted.org/LHQ_G98

27

CONFIDENTIAL - FOR PEER-REVIEW ONLY
Taxes, beliefs, and the demand for goods with negative externalities (#23181)
Created: 05/08/2019 05:11 AM (PT)
Shared: 07/10/2019 06:08 AM (PT)This pre-registration is not yet public. This anonymized copy (without author names) was created by the author(s) to use during peer-review. A
non-anonymized version (containing author names) will become publicly available only if an author makes it public. Until that happens the contentsof this pre-registration are confidential.
1) Have any data been collected for this study already?
No, no data have been collected for this study yet.
2) What's the main question being asked or hypothesis being tested in this study?
Policy-makers have two main instruments to change consumer demand for goods that produce a negative externality. They can change the priceusing taxes and subsidies, or they can provide information about the externality. We have three main research questions
1) What is the effect of prices and information on consumption?
2) Do higher prices and information reduce self-serving beliefs about the externality?
3) Does information reduce the effect of price policies by eliminating self-serving beliefs?
3) Describe the key dependent variable(s) specifying how they will be measured.
Participants can buy a good that results in an uncertain externality (CO2 emissions). Thus, the two key dependent variables are:1) Consumption: this is a binary variable (1: if the participant buys the good; 0: otherwise),
2) Beliefs: this is an integer between 0 and 120. It represents participants’ beliefs about the magnitude of the externality they may produce(measured as the equivalent of liters of gasoline).
4) How many and which conditions will participants be assigned to?
Three treatments differ in the way participants are informed about the size of the externality:
Info Treatment: participants know exactly the size of the externality.
Motivated Treatment: The answer to a puzzle gives participants the magnitude of the externality. Participants solve the puzzle after knowing therelation with the externality.
Unmotivated Treatment: The answer to a puzzle indicates to participants the magnitude of the externality. Participants solve the puzzle before
knowing the relation with the externality
In three cross-cutting conditions, we vary the price of the good in the set {0.25, 1, 1.75}, measured in British pounds.
Overall, this leads to 9 conditions, all subjects participate only in one condition.
5) Specify exactly which analyses you will conduct to examine the main question/hypothesis.
Hypothesis 1: Participants in the Info treatment buy fewer units of the good than participants in the Motivated treatment.
We test this hypothesis by means of a Fisher's exact test, pooling all price levels. We will perform regressions to control for subject characteristics.
Hypothesis 2: Participants in the Unmotivated treatment have higher beliefs and buy fewer units of the good than participants in the Motivatedtreatment.
We compare this with a non-parametric rank sum test (beliefs) and Fisther exact test (consumption), pooling all price levels. We will perform
regressions to control for subject characteristics.
Hypothesis 3: In the Motivated treatment, demand is decreasing in prices.
We test this in a linear regression, using a one-sided t-test.
Hypothesis 4: In the Motivated treatment, beliefs are increasing in prices.
We test hypothesis using a linear regression and a one-sided t-test.
Hypothesis 5: Conditional on hypothesis 4 being confirmed, price-sensitivity of demand in the Info treatment is lower than that in the Motivatedtreatment.
We test this in a linear probability model, using a one sided t-test. Note that if the relationship between beliefs and prices is different than in
Verify authenticity:http://aspredicted.org/blind.php?x=i24x2p
Version of AsPredicted Questions: 2.00

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References
Amasino, Dianna, Davide Pace, and Joël J. van der Weele. 2021. “Fair Shares
and Selective Attention.” Tinbergen Institute Discussion Paper 2021-066/I.
Engelmann, Jan, Alejandro Hirmas, and Joël J. van der Weele. 2021. “Top Down
or Bottom Up? Disentangling the Channels of Attention in Risky Choice.” Tinbergen
Institute Discussion Paper 2021-031/I.
Enke, Benjamin, and Thomas Graeber. 2023. “Cognitive uncertainty.” Quarterly
Journal of Economics, 138(4): 2021–2067.
Pärnamets, Philip, Petter Johansson, Lars Hall, Christian Balkenius,
Michael J. Spivey, and Daniel C. Richardson. 2015. “Biasing Moral Decisions
by Exploiting the Dynamics of Eye Gaze.” Proceedings of the National Academy of
Sciences, 112(13): 4170–4175.
Rodemeier, Matthias. 2023. “Willingness to Pay for Carbon Mitigation: Field Evidence from the Market for Carbon Offsets.” IZA Discussion Paper 15939.
US Census Bureau. 2022. “National Population by Characteristics: 2020-2022.” UnitedStates Census Bureau. https://www.census.gov/data/tables/time-series/demo/
popest/2020s-national-detail.html.

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