Thomas Douenne
email: thomas.douenne@psemail.eu

Adrien Fabre
email: adrien.fabre@psemail.eu

Stefano Carattini

Linus Mattauch

Joseph Stiglitz

Thierry Verdier

Yellow Vests, Carbon Tax Aversion, and Biased Beliefs

Keywords: Climate Policy, Carbon tax, Bias, Beliefs, Preferences, Tax aversion JEL classification: D72, D91, H23, H31, Q58 Climate Policy, Carbon tax, Bias, Beliefs, Preferences, Tax aversion

This paper helps to understand how beliefs form and determine attitudes towards policies. Using a new survey and official households' survey data, we investigate the case of carbon taxation in France in the context of the Yellow Vests movement that started against it. We find that French people would largely reject a Tax & Dividend policy, i.e. a carbon tax whose revenues are redistributed uniformly to each adult. However, they also overestimate the negative impact of the scheme on their purchasing power, wrongly think it is regressive, and do not perceive it as environmentally effective. Using information about the scheme as instruments to robustly identify causal effects, our econometric analysis shows that if we could rectify these three biased beliefs, it would suffice to generate majority approval. Yet, only a small minority can be convinced by new information and revisions are biased towards pessimism. Finally, if overly pessimistic beliefs cause tax rejection, they also result from it through motivated reasoning, which manifests what we define as "tax aversion".

Introduction

The French government had initially committed to an ambitious trajectory for the price of carbon. 1Initiated in 2014 at 7e/tCO 2 , the French carbon tax reached 44.6e/tCO 2 in 2018 and was supposed to continue growing to hit 86.2e/tCO 2 by 2022. Yet, at the end of 2018, the same government that had accelerated the price trajectory decided to abandon it and froze the tax at its current level for an undetermined period. This turnaround in French climate policy is the direct consequence of the popular protest of the "Yellow Vests", which started against the carbon tax.2 Among several factors, the negative impact of the tax on households' purchasing power has certainly been a key driver of public's discontent. The increasing revenues from the carbon tax were mostly used to fund the budget rather than redistributed to households, raising concerns over the distributive effects of the policy. In order to tackle the negative impact of carbon taxation on households' purchasing power, economists have proposed a mechanism known as "Tax & Dividend", i.e. a carbon tax whose revenue is redistributed uniformly to each adult. This strategy has recently been supported by 3,354 American economists in The Wall Street Journal, "To maximize the fairness and political viability of a rising carbon tax". Implicitly, it is therefore assumed that with a design that ensures that the properties of the tax are aligned with people's preferences one should be able to generate support for it. But is it really sufficient? In this paper, we argue that to understand the link between the properties of a policy and its support, one has to account for a critical ingredient: beliefs.

The objective of this paper is to understand how beliefs about a policy form and then determine attitudes towards it. The recent events undoubtedly make the French carbon tax an interesting case study. In order to explain French attitudes towards carbon taxation, we conducted a survey on a representative sample of 3,002 French households. We focus on a "Tax & Dividend" carbon tax with uniform lump sum compensation, which allows one to specify clearly the distributive effects of the policy, in contrast to the policy abandoned by the government. The reform is approved by only 10% of respondents and disapproved by 70% (the rest do not know or do not want to answer). We analyze the perceptions of three well-known determinants of acceptance of the carbon tax: the impact on one's purchasing power, the progressivity of the scheme, and its environmental effectiveness. We compare subjective beliefs elicited from our new survey to objective impacts on people's purchasing power computed using official households' survey data. This comparison shows that people largely overestimate the negative impact of carbon taxation on their purchasing power. For instance, while 70% of households are expected to win from this policy, only 14% think they would. Similarly, while the scheme proposed in our survey is progressive, a large majority of individuals perceive it as regressive. In addition, a majority of respondents do not believe that such a policy would reduce pollution and fight climate change. Using information reported over their energy equipment and usage, we are able to compute a respondent-specific estimation of the tax incidence. This estimation enables us to look at the heterogeneity in biases. We find that the people most opposed to the policy, and in particular those supportive of the Yellow Vests, are the most biased, i.e. the most inclined to over-estimate their losses. Thus, one may wonder whether biased beliefs lead to policy rejection or if the causality goes in the other direction.

To disentangle the effect of initial biases on attitudes towards the policy from the reversed effect of attitudes on perceptions, we investigate the effect of providing new information to respondents through random treatments. Respondents randomly receive (or not) a piece of information about the progressivity and/or about the effectiveness of the policy, as well as the customized informationderived from our respondent-specific estimation -that their household is expected to win or lose from the policy. We also specify that this latter information is correct in five cases out of six, a probability that we carefully estimated out-of-sample. A first observation is that our treatments fail to rectify pessimistic beliefs. For example, among those advantaged by the reform who wrongly believe they would lose, only 12% are convinced that they would gain when we disclose our estimation to them.

Worse, respondents revise their beliefs in a biased way, giving more weight to new information when it shows they would lose from the reform, i.e. when it provides them with arguments against the tax. We also find robust evidence of motivated reasoning in the formation of beliefs, as those who already approved of the reform are less prone to biases in the revision, while those most opposed to it such as supporters of the Yellow Vests tend to discard new information unless it goes against the tax. Moreover, we find that motivated reasoning is accentuated among highly educated people, suggesting that it stems from an adaptive advantage rather than a cognitive deficiency. The information displayed being random we can then use it as instruments to measure the causal effect of holding certain beliefs on acceptance. In the case of self-interest (taken as one's beliefs about winning or losing purchasing power from the policy), we supplement these treatments by testing the approval for a different Tax & Dividend whose compensation is targeted to people with incomes below a threshold that varies between respondents to create exogenous variations in eligibility. The method we use in this case is noteworthy, as it embeds a regression discontinuity design inside an instrumental variables regression in order to estimate the causal effect of eligibility at different levels of income. Overall, we find that beliefs in self-interest, environmental effectiveness, and progressivity all have a large effect on acceptance: about 40 percentage points (p.p.) for the first two and 27 p.p. for the latter, all else equal. These motives also appear more as complements than substitutes: in a hypothetical scenario where all biased beliefs could be corrected, we estimate an approval rate as high as 90%. This result suggests that rejection of carbon taxation does not commonly result from clashing principles, such as a disinterest in climate or a dislike of price instruments, but rather from biased beliefs about the properties of the reform. Since beliefs are formed endogenously in a motivated way, people's biases gain inertia, so that new information might only push their attitude in one direction. 3The contribution of this paper is two-fold. First, it contributes to a recent literature that has emerged to understand the political economy of climate policies, as this issue is becoming critical in the public debate. For a thorough review of this literature, we refer the reader to [START_REF] Carattini | Overcoming public resistance to carbon taxes[END_REF], and also suggest the more synthetic [START_REF] Klenert | Making carbon pricing work for citizens[END_REF], as well as [START_REF] Millner | Beliefs, Politics, and Environmental Policy[END_REF] for a review of the political obstacles to environmental policies. [START_REF] Stern | Value Orientations, Gender, and Environmental Concern[END_REF] is an early work proposing and testing a model of attitudes for environmental quality aimed at disentangling egoistic from altruistic motives on the one hand, and beliefs from values on the other hand. Among all possible attitudes, they show that beliefs about consequences on self-interest are the only predictor of the willingness to pay Pigouvian taxes. Using a post-electoral survey in Switzerland, Thalmann (2004) also finds a correlation between carbon tax acceptance and self-interest, proxied by the number of cars owned. In surveys on British and Swedish respondents respectively, [START_REF] Bristow | Public acceptability of personal carbon trading and carbon tax[END_REF] and [START_REF] Brannlund | To tax, or not to tax: preferences for climate policy attributes[END_REF] document a higher approval rate when the reform addresses distributional issues. [START_REF] Baranzini | Effectiveness, earmarking and labeling: testing the acceptability of carbon taxes with survey data[END_REF] report that a majority of the people they interviewed in Geneva do not believe the tax would be effective, which confirms what Dresner et al. (2006b) find with focus groups in the UK. Surveying Norwegian people, Kallbekken & Saelen (2011) show that self-interest matters for acceptance, but less than concerns for environmental effectiveness or distributional effects.

On US data, [START_REF] Anderson | Can Pigou at the Polls Stop US Melting the Poles? Working Paper 26146[END_REF] argue that ideology explains most of the support for carbon taxation, and suggest that this effect would dominate that of self-interest.

In the present paper, we also study how acceptance depends on these three motives (i.e. selfinterest, perceived environmental effectiveness and progressivity). We contribute to the literature by providing robust evidence for causal effects where past studies essentially show correlations, often relying on proxies such as fuel consumption to proxy self-interest (e.g. [START_REF] Thalmann | The Public Acceptance of Green Taxes: 2 Million Voters Express Their Opinion[END_REF]Kallbekken & Saelen, 2011;[START_REF] Anderson | Can Pigou at the Polls Stop US Melting the Poles? Working Paper 26146[END_REF]. In contrast to such shortcuts, we do not assume that people are fully rational nor have perfect information. Thus, our methodology offers a novel look at the political economy of climate policies, as it allows one to disentangle erroneous beliefs from pure effects of preferences. 4 The paper also quantifies biases regarding the costs of the carbon tax. To our knowledge, it is the first study that compares subjective beliefs and objective data about the private costs that arise from carbon taxation. Given the intense public debate over the incidence of such a policy, identifying and measuring the discrepancy between actual impacts and their subjective perception is critical.

Beyond the case of carbon pricing, our paper contributes to the literature on biased beliefs and how they relate to attitudes over policies. Recent research has shown how biased beliefs on inequality and social mobility affect people's attitudes regarding distributive policies (e.g. [START_REF] Cruces | Biased perceptions of income distribution and preferences for redistribution: Evidence from a survey experiment[END_REF][START_REF] Kuziemko | How elastic are preferences for redistribution? evidence from randomized survey experiments[END_REF][START_REF] Alesina | Intergenerational Mobility and Preferences for Redistribution[END_REF]. Our paper adds to this literature by investigating the relationship between beliefs and attitudes on climate policies. It also goes further than previous studies by identifying a bi-directional relationship as we show that not only do beliefs determine attitudes, but attitudes over policies in turn shape beliefs. Indeed, using a representative survey, our paper brings evidence consistent with theories of motivated reasoning [START_REF] Kunda | The Case for Motivated Reasoning[END_REF], see [START_REF] Bénabou | Mindful Economics: The Production, Consumption, and Value of Beliefs[END_REF] for a recent review) that have so far been mostly tested in the lab (e.g. [START_REF] Redlawsk | Hot Cognition or Cool Consideration? Testing the Effects of Motivated Reasoning on Political Decision Making[END_REF][START_REF] Thaler | The "Fake News" Effect: An Experiment on Motivated Reasoning and Trust in News[END_REF]. In particular, our results support the recent theory of Little (2019) who formalizes motivated reasoning as a way to reconcile an auxiliary belief (one's self-interest in the reform) to a core belief (here, the policy rejection). We believe our results apply beyond the case of carbon taxation, and illustrate more generally the determinants and consequences of tax aversion. Indeed, the few previous definitions of tax aversion [START_REF] Sussman | Axe the Tax: Taxes are Disliked More than Equivalent Costs[END_REF] are hardly exploitable empirically, as they do not relate the concept to an observable phenomenon. This may contribute to the limited number of papers on this topic (Kallbekken et al., 2011;[START_REF] Kessler | Tax aversion in labor supply[END_REF]. Building upon our results, we can define tax aversion as a gut rejection of a tax (or taxation in general) that influences beliefs about the tax properties such as its effectiveness, fairness, or sameness with an equivalent measure labeled differently. Our work then shows that tax aversion can be identified through motivated reasoning, by observing that the initial tax rejection impacts how one integrates new information into one's beliefs.

The rest of the paper is organized as follows. In section 2, we describe our survey and other data sources. In section 3, we compare subjective perceptions to objective data, and measure the bias regarding the impacts of carbon taxation. In section 4, we highlight new biases in the way individuals revise these beliefs. In section 5, we estimate the effects on acceptance of rectifying biased beliefs. Section 6 concludes. Further results and methodological complements are reported in the Appendix, such as an estimation of the willingness to pay for the carbon tax in Appendix G.

Survey and data

2.1 Our survey, "Beliefs & climate policies"

Survey data collection

The 3,002 responses were collected in February and March 2019 through the survey company Bilendi. This company maintains a panel of French respondents whom they can email with survey links.

Respondents are paid 3e if they fully complete the survey. The respondents who choose to respond are first channeled through some screening questions that ensure that the final sample is representative along six socio-demographic characteristics: gender, age (5 brackets), education (4), socio-professional category [START_REF]Baccalaureate; Bac +2 (BTS, DUT, DEUG, schools of health and social training[END_REF], size of town (5) and region (9). The quotas are relaxed by 5% to 10% relative to actual proportions. Table A.1 in Appendix A shows that our sample is still extremely representative.

Nonetheless, observations are weighted to correct for small differences between sample and population proportions. The median time for completion of the survey was 19 minutes. We made sure that all questions requiring some concentration were in the first half of the survey.

The survey

The full survey in French can be seen online, and the translated questionnaire is detailed in Appendix B. 5 It contains several random branches and treatments that are independent from one another: Particulates information consists of the estimated impact on French mortality (48,000 deaths per year), life expectancy (9 months less), and the assertion that reducing fuel consumption would improve health. The time spent on each block is saved, and links to scientific references are provided to support the information.

Household characteristics

In addition to the quotas strata, socio-demographic characteristics include zip code, household structure, income of the respondent and of their household. A block on energy usage contains questions that allow us to estimate the impact of a carbon tax increase on housing expenditures: size of accommodation, heating type (collective or individual) and energy source; as well as on transport expenditures: number of vehicles, type(s) of fuel, distance travelled last year, and average fuel economy. The distributions of answers are much in-line with official statistics, as shown in Table A.2 in Appendix A.

Partial tax reform One partial tax reform is randomly allocated to the respondent: it consists of an increase in the carbon tax by 50e/tCO 2 specific either to heating fuel and gas, or to gasoline and diesel. Partial reforms on housing and transport feature the same string of questions. We first ask whether the respondent thinks their household would lose more or less than average in case of an unspecified increase in indirect taxation, both for the VAT tax and for the energy considered (housing or transport). Then, we specify in a new block that the revenues of the tax increase would be distributed equally to each adult, entailing a yearly transfer of 50e (resp. 60e) for the partial tax on housing (resp. transport). 6 We also provide the price increases implied by the tax: +13% (resp. +15%) for gas (resp. domestic fuel) on the one hand, and +0.11e (resp. +0.13e) for a liter of gasoline (resp. diesel) on the other. We make clear at the beginning that this survey is conducted by two researchers in social sciences, but we present the policy starting with "The government studies..." to capture the effect of distrust in government that could arise in the actual political process. Then, we ask the respondent whether their household would win, lose, or be unaffected by the reform.

Depending on their answer, we further ask them to estimate their expected gain (or loss) among 5 (or 6) intervals. The interval thresholds are tailored to each respondent, as they are computed in proportion of the number of consumption units of their household (as defined by Eurostat). The questions were not incentivized. Indeed, [START_REF] Sapienza | Economic experts versus average americans[END_REF] show that people think that economic experts are too optimistic regarding the carbon tax, so incentivizing the answers could have led respondents to misreport their true beliefs and shift them towards what they think the researchers expect. Finally, respondents are asked to estimate their own elasticity as well as that of French people. To this end, we borrow the phrasing of [START_REF] Baranzini | Effectiveness, earmarking and labeling: testing the acceptability of carbon taxes with survey data[END_REF], and ask for the expected decrease in consumption that would follow a 30% increase in the price of heating (or equivalently, an increase of 0.50e/L in fuel prices), among 5 brackets.

Tax & Dividend 6 We chose to redistribute per adult instead of per consumption unit to make the scheme more understandable. We limited the number of beneficiaries to two per household to better align with current welfare benefits that depend on the number of consumption units.

Initial perceptions

Our main reform of interest is an increase by 50e/tCO 2 of the French carbon tax, that concerns both housing and transport. 7 The revenues generated are redistributed equally, so that each adult receives a yearly lump sum compensation of 110e (this figure was obtained using typical elasticities, see 2.2.1). After describing the reform, a first block of questions elicits the respondent's perceptions. Their subjective gain is asked in the same manner as for the partial tax.

The priming that "scientists agree that a carbon tax would be effective in reducing pollution" is randomly displayed or not before asking whether the reform would be effective in reducing pollution and fighting climate change. Then, respondents are asked to pick the categories of losers and winners with the reform. Finally, we ask: "Would you approve this reform?" and let the respondent choose between "Yes", "No" and "PNR (I don't know, I don't want to answer)". In the following, we say that a respondent approves a reform if they respond "Yes", and that they accept the reform if they do not respond "No". Given the low rates of approval, we study primarily the acceptance to get tighter confidence intervals. We also provide results for approval, and obtain similar findings.

Opinion after knowledge To assess how beliefs are formed and measure the importance of self-interest and fairness motives in the acceptance of the reform, we provide some information on the effect of the reform. To a random half of the sample, we explain that "this reform would increase the purchasing power of the poorest households and decrease that of the richest, who consume more energy". To two-thirds of the respondents (the remaining half plus one-third of the respondents with that priming on progressivity), we provide customized information explaining that: "In five cases out of six, a household with your characteristics would [win/lose] through the reform. (The characteristics taken into account are: heating using [energy source] for an accommodation of [surface] m 2 ; [distance] km travelled with an average consumption of [fuel economy] L for 100 km.)". Indeed, section 2.2.2 shows that we estimate correctly if a household wins or lose in 83% of cases.

As most respondents do not believe the claim that the reform is progressive, we ask the second half of the sample whether they think so, to analyze the effects of priming on compliant respondents.

We also ask again for the winning category (i.e. if the respondent's household would win, lose or be unaffected by the reform) and for the approval to the reform. Finally, we let the respondent choose the reasons why this reform seems beneficial, and undesirable. We report these results in a companion paper, [START_REF] Douenne | French attitudes on climate change, carbon taxation and other climate policies[END_REF], where we also study the socio-demographic determinants of approval.

Tax & Targeted Dividend In this block, we ask for the winning category and for the approval of four alternative reforms. Each respondent is given just one of them, which differs from the main reform only in the way revenues are recycled. Here, the payments, still equal among recipients, are targeted to adults whose income is below some threshold. The four thresholds correspond to the bottom 20%, 30%, 40%, and 50% of the income distribution. They are computed using inflated deciles of individual income from the Enquête sur les Revenus Socio-Fiscaux (ERFS 2014) produced by Insee (the French national statistics bureau). 8 Respondents whose income lies between two thresholds are allocated randomly to a reform with one of them. When the income is close to only one threshold (i.e. when its percentile in the distribution is below 20 or within [50; 70]), the allocated reform corresponds to that one. When the respondent's income is above 2220e/month (which is the 70th. percentile), the reform they face is determined by the income of the household's second adult. Finally, when both (or the only one) adults in the household earn more than 2220e/month, their reform is allocated randomly between the four variants. Table 2.1 describes the targeted reforms and the proportion of respondents allocated to each of them, along with the proportion one would expect from the ERFS.

The two sets of figures match almost perfectly, indicating that our sample is representative along the income dimension. [START_REF] Douenne | French attitudes on climate change, carbon taxation and other climate policies[END_REF]. In that paper, we examine opinions on environmental policies, including other ways to recycle the revenues of a carbon tax. We measure the knowledge and perceptions of climate change; ask some specific questions on shale gas, the influence of climate change on the choice to give birth, and one's willingness to change their lifestyle. We study the use, availability, and satisfaction with public transportation and active mobility. We also ask for political preferences, including position in relation to the Yellow Vests. Finally, we let the respondent express any comment in a text box.

Ensuring data quality

We took several steps to ensure the best possible data quality. We excluded the 4% of respondents who spent less than 7 minutes on the full survey. We confirm that response time is not significantly correlated with our variables of interest (such as approval or subjective gain). In order to screen out inattentive respondents, a test of quality of the responses was inserted, which asked to select "A little" on a Likert scale. The 9% of respondents who failed the test were also excluded, which yields a final sample of 3002 respondents. Also, when the questions about a reform were spread over different pages, we recalled the details of the reform on each new page. We checked for careless or strange answers on numerical questions, such as income or the size of the household. We flagged 10 respondents with aberrant answers to the size of the household (and capped it to 12) and up to 273 respondents with inconsistent answers, such as a household income smaller than individual income, or a fuel economy higher than 90 liters per 100 km. An examination of these answers shows no significant correlation with our variables of interest, and suggests that these respondents have simply mistaken the question. Among these inconsistent answers, 58 respondents have answered more than 10,000e as their monthly income (despite the word "monthly" being in bold and underlined), with answers in the typical range of French annual incomes. We have divided these figures by 12.

Notations

To improve the understanding of our specifications in the regression Tables, we adopt consistent notations throughout the paper. For questions where possible answers are "Yes"/"No"/"PNR", we define two kinds of dummy variables: the default ones correspond to not "No" answers, while we put a dot on dummy variables for "Yes". For example, acceptance is denoted A while approval is denoted Ȧ. Furthermore, for questions that are asked several times, namely acceptance and winning category, an exponent is added to specify the step at which the question is asked. Table 2.2 describes these exponents as well as the notations corresponding to the different notions of gain that we use.

Uppercase is used for binary and lowercase for continuous variables, Greek letters denote objective notions, with a hat for our estimation of gains and without for the true (unknown) ones. To give another example, the broad notion of self-interest at the initial step, i.e. the belief that one does not lose, is denoted G I , and the strict belief that one wins at Tax & Targeted dividend is denoted ĠT .

Exponent I P F T Gain Subjective True Estimated Numeric g γ γ Binary Ġ (g > 0), G (g ≥ 0) Γ Γ

Official households surveys

Eliciting objective aggregates and distributions

One of the goals of the paper is to compare respondents' perceptions with the actual impact of a carbon tax on households' purchasing power. For this purpose, we use the database constructed by Douenne their vehicle fleet and use over the past week, but most importantly it gives information on annual distances travelled with these vehicles. This last information enables us to recover the distribution of transport fuel expenditures without over-estimating its spread. Such matching is not necessary for housing energies as these already represent consumption over long periods in BdF. Finally, data from National Accounts is used to make the data representative of the year 2017.

Computing tax incidence and revenues From this dataset, we are able to compute the distribution of households' objective net gains in purchasing power after the policies proposed, i.e. the dividend received minus the increase in fossil fuels expenditures. We also use it to determine the total tax revenue to be redistributed lump sum. The formulas used for these computations are given in Appendix C.1. Our computations use typical elasticities found in the literature on French households:

-0.4 for transport and -0.2 for housing, as well as an incidence borne at 80% by consumers.9

Computing households' expected net gains

Simulating expected gains for the feedback Households are asked about yearly distance travelled and average fuel consumption of their private vehicles. From this information, it is then possible to compute the expected cost of a carbon tax on transport fuels. For housing energies, the collected information does not enable such simple calculations. Instead, we use the housing survey Enquête Logement (EL 2013) that provides information on household expenditures in housing energies as well as many demographic and energy characteristics. The survey was conducted between June 2013 and June 2014 over a sample of 27,137 households in metropolitan France. This enables us to compute the expected cost from the carbon tax on housing energies, and regress it on household characteristics.

The results are provided in Appendix C.2, where they are shown to be as least as accurate as the ones obtained from alternative prediction methods and specifications. The distribution of housing energy expenditures is highly comparable to that of BdF. Adding this estimated cost to the one simulated for transportation energies, subtracting the amount received in lump sum transfers, and dividing by the number of consumption units, we estimate the impact of the policy on the purchasing power of each household.

Assessing feedback's accuracy

The previous estimation could have also been conducted with BdF data. Still, running this estimation on the housing survey enables us to test the accuracy of our prediction out-of-sample: for each household in BdF, we compute the impact of the policy on their purchasing power and compare it to the prediction from our simulations. Figure D.1 in Appendix D.2 shows how the probability that our prediction is correct depends on objective gains. For five households out of six, we correctly predict whether their purchasing power would increase or decrease through the policy. We make this ratio symmetrical: among households in BdF predicted to win, 83.4% were actual winners, while among those predicted to lose, 83.4% were actual losers. Since the simulation and its test are done on different households, there is no concern for over-fitting:

the probability that our feedback is correct is not overestimated. Assuming that the characteristics reported by our respondents are correct, there is no reason to believe that the probability of error is higher or lower when simulations are applied to our survey respondents.

3 Biased beliefs

Self-interest

Over-estimation of policy costs Figure 3.1 plots the kernel density of expected net gains for objective data from BdF, and subjective beliefs from our survey. Figure 3.2 compares the CDF of objective vs. subjective net gains. 10 It is evident from these figures that on average, respondents overestimate the cost of the policy, even in the extreme case of perfectly inelastic expenditures. This result holds both for the carbon tax and for partial carbon taxes on transport and housing energies.

The average net gains from the carbon tax on transport, housing, and both, are respectively 18e per consumption unit (c.u.), 6e per c.u., and 24e per c.u. from BdF data. Extrapolating from our survey, we instead find average subjective net gains of respectively -61e, -43e, and -89e. The median gap of 116e between objective and subjective gains indicates a substantial bias towards loss from typical respondents. This bias is widespread, as we find that 89% of respondents underestimate their gain of purchasing power using our household-specific estimation. This proportion remains as high as 77 % when assuming inelastic expenditures, which provides a lower bound on the share who underestimate their net gain in utility. In other words, while 70% of households should benefit (in monetary terms) from the compensated carbon tax, only 14% think they would (and 22% see themselves unaffected).11 Heterogeneity in bias In order to characterize profiles of individuals more likely to mis-perceive their gains, we regress mis-perception over many respondents' characteristics. Mis-perception is defined as a gap between objectively estimated and subjective net gains beyond 110e per c.u., because our estimation differs from true objective gain by more than 110e in only 5% of cases. This definition ensures that the 55% of respondents with a mis-perception have in fact a large bias. Other definitions for the bias yield very similar results. The results given in Table 3.1 show that mis-perception is largely idiosyncratic: controlling for a large set of variables 12 (column 1), the R 2 remains small (0.06). Still, we identify several variables having a significant effect on mis-perception. In particular, females appear to mis-perceive their gain 4 percentage points (p.p.) more on average, all else equal.

Ecologists on the other hand are about 6 p.p. less likely to display a large bias. Interestingly, while the standard left/right political leaning has no significant effect, the position towards the Yellow Vests appears to be the most critical determinant in mis-perception. Relative to respondents who declared to be opposed to the movement, those who declared to "understand", "support", or "be part" of it are 12 The control variables used throughout the paper are described in Appendix H.

more likely to mis-perceive their gains. This effect is increasing with the degree of adhesion, up to 20 p.p. for individuals who declared to be part of the movement. Column (3) additionally includes one's position towards the policy as a covariate: we see that people who approve the policy are 28 p.p. less likely to mis-perceive their gains relative to those who do not accept it, and 10 p.p. less likely relative to those who do not know. We can think that the degree of support of the policy is what determines most of the bias (explaining e.g. why ecologist loses its explanatory power when we control for the support), and that the Yellow Vests variables remain significant only because they capture different degrees of rejection of the tax (which our Yes/No question cannot do).

Overall, typical biases are large and closely related to one's convictions. However, the direction(s) of causality between beliefs and rejection is not resolved at this stage. Section 4 provides robust evidence that some people think they lose because they oppose the tax, while section 5 shows that perceived outcomes causally influence approval. Our findings confirm this result: among our survey respondents, only 17% answered "Yes" when asked whether our Tax & Dividend would be effective in reducing pollution and fighting climate change, 66% answered "No", 18% that they did not know.

Environmental effectiveness

An explanation sometimes encountered to explain perceptions of ineffectiveness is that most people believe that energy consumption is quite inelastic (Kallbekken & Saelen, 2011;[START_REF] Carattini | Overcoming public resistance to carbon taxes[END_REF]. To test this hypothesis, we regress a binary variable E equal to 0 if the respondent does not perceive the policy as environmentally effective and 1 otherwise, on their subjective price elasticity for French people. As respondents were randomly assigned to transport or housing, we run a separate regression for both types of energies. Table D.1 in Appendix D.3 reports results with and without control variables. They all consistently indicate that a respondent anticipating an elasticity of -1 is (on average) 6 p.p. more likely to perceive the policy as effective than one anticipating no elasticity. Although significant, the magnitude of the effect is modest, showing that the perceived ineffectiveness of tax instruments should not be reduced to small subjective elasticities. Indeed, among respondents who perceive the policy as environmentally ineffective, almost half anticipate responses to price changes larger than the literature. 13 A more plausible explanation for perceived ineffectiveness is that people do not believe that the policy would be sufficient to substantially affect pollution and climate change. Taking respondents' average anticipated elasticities for transport and housing energies (that are fairly accurate 13 ), the tax should reduce French greenhouse gas (GhG) emissions by 5.7 Mt of CO 2 equivalent (CO 2 e) each year, according to the simulation from BdF data. This reduction corresponds to 0.8% of French annual emissions, 0.01% of global ones, and does not suffice to reach the official objective of carbon neutrality in 2050. 14 Thus, although respondents do anticipate responses to price incentives, our results suggest that they do not perceive a 50e/tCO 2 national carbon tax as a proportionate reaction to climate change.

Progressivity

It is often argued that a critical barrier to accept carbon taxation is its perceived distributional impact, in particular the higher burden imposed on lower income households (Bristow et to 60% who declare it would not, and 21% who do not know. These results show that beliefs about the distributive effects of carbon taxation are biased, which has not been shown in previous studies. 13 Overall, average subjective elasticities are close to these estimates for transport (at -0.45) and somewhat overestimated for housing (-0.43). Among those who declared that the policy was not effective, 45% (resp. 43%) anticipated an aggregate elasticity at or below -0.5 for housing (resp. for transport), while elasticities obtained from the literature are around -0.2 for housing and -0.4 for transport. 14 The computations are based on households' carbon emissions. In 2014, French GhG consumption based emissions were equal to 712 MtCO2e (CGDD, 2019). 2017 global emissions were 53.5 GtCO2e (UNEP, 2018).

How attitudes shape beliefs

The previous section has shown that people's low acceptance of our Tax & Dividend coincides with biased beliefs about the properties of the scheme. As knowledge about these properties has been shown to be decisive for acceptance [START_REF] Carattini | Overcoming public resistance to carbon taxes[END_REF], it is important to assess how beliefs are formed.

In the following, we test respondents' reactions to information about their gains, environmental effectiveness, and progressivity. If their biased views simply reflect a lack of knowledge, we should expect them to revise their beliefs after new information is provided, what we refer to as "update".

Self-interest

Conservatism and pessimism After telling respondents that given their characteristics, they have 5 chances over 6 to "win" or "lose" from the policy, we observe that only 39% of them agree with our feedback (G F = Γ), far from the 83% expected for a correct update. This result is consistent with findings of the literature that people tend to update like "conservative" Bayesians [START_REF] Edwards | Conservatism in human information processing[END_REF]).

The full transition matrices of people's beliefs are given in Tables D.2 and D.3 in Appendix D.2. More concisely, Table 4.1 reports the share of respondents whose beliefs after being informed are aligned with our feedback, with the corresponding 95% binomial confidence intervals. It shows that, for the 24% of individuals who receive a "lose" feedback ( Γ = 0), the ex post belief is on average consistent with Bayesian updating. If anything, these people would rather tend to agree too much with our noisy signal, especially when excluding people who initially consider themselves as unaffected (i.e. focusing on g I = 0), for whom 83% does not lie in the 95% confidence interval. 15 The observed conservatism on the whole sample therefore comes from respondents who receive a "win" feedback ( Γ = 1). Among the 60% of respondents who initially thought they would lose in this group, only 12% endorse the "win" feedback. This is in sharp contrast with the respondents who initially thought they would win and receive a "lose" feedback, since 82% of them endorse our prediction. Thus, pessimistic beliefs are persistent to our treatment, but optimistic ones are not. Note: The 95% confidence intervals for binomial probabilities are given in brackets.

alignments for different prediction accuracy rules out the possibility that some respondents do not update because their private information would be truly more accurate than our prediction.

There are several ways to rationalize the conservatism and pessimism we observe. The simplest is that respondents perceive our information as biased. They may think we wrongly estimate their likelihood to win and that we are too optimistic. As a result, they may assign relatively more weight to pessimistic information coming from us. This is in line with widespread disagreement between economic experts and the general public about carbon taxation (Sapienza & Zingales, 2013), for which 51% of Americans do not trust that the government would actually pay the promised dividends. A second interpretation is that they give too much value to their private information relative to the base rate one, a phenomenon known as base rate neglect [START_REF] Grether | Bayes Rule as a Descriptive Model: The Representativeness Heuristic[END_REF]. That is to say, pessimistic winners might be over-confident in seeing themselves as specific so that they partly discard the new information, e.g. by thinking they are part of the one-sixth for whom our prediction is erroneous.

Another explanation is that uncertainty makes people see their possible gains as a distribution (see [START_REF] Stiglitz | Addressing Climate Change through Price and Non-Price Interventions[END_REF]. Then, instead of reporting the average of this distribution, people subject to loss-aversion would reason with conservative estimates for their gains, even more so if they believe that this survey can influence policy makers. In the end, these interpretations are of course not mutually exclusive and empirically not distinguishable, as they all lead to too much pessimism in the revision of their beliefs. if the respondent adopts a feedback that invalidates their initial belief, -1 if they update against the feedback that confirms it, or 0 if they do not update. Over the sub-sample of invalidated respondents who should have updated because their initial winning category is not aligned with our feedback, we regress the correct updating, U , over the initial belief not to lose, G I , and a vector of characteristics, C:

Determinants of correct updating

U i = δ 0 + β U G I i + β C C + i for i : sgn (g i ) = sgn (γ i ) , (1)
where sgn is the sign function. The high value for β U reported in column (1) of Table 4.2 again proves that, among those who should have updated, those who initially think they would win (the optimistic losers) update significantly more correctly than those who do not think so (the pessimistic winners).

Many other specifications have been tested, depending on how the unaffected are treated and whether controls are included or not, or with the winning category after the feedback as covariate, and they all confirm a win/lose asymmetry in updating.

Beyond this asymmetry, column (2) shows that some respondents' characteristics are correlated with correct updating. Relative to unemployed and inactive people, retired, active, and students update more correctly, the latter being 25 p.p. more likely to correctly revise their beliefs when invalidated than unemployed and inactive. Similarly to perceptions of net gains, position towards the Yellow Vests is significantly correlated with correct updating. The magnitude of this effect is large, as people who are part of the movement are 17 p.p. less likely to correctly update than people who oppose it. This can be linked to the Yellow Vests' higher distrust of the government, documented in [START_REF] Algan | Qui sont les gilets jaunes et leurs soutiens ? Technical report[END_REF], that could apply to information provided by researchers regarding policies.

Column (3) includes disapproval as a covariate: it indicates that, as for the initial bias in subjective gains, disapproving the reform is associated with a less correct update by 16 p.p. and partly explains the effect of the Yellow Vests. Appendix E confirms that the result holds true when initial subjective gains are accounted for, ruling out the explanation that this less correct updating is entirely due to specific priors of those who disapprove the reform.

Motivated reasoning

The previous result suggests that conservatism in belief revision does not simply follow from people's cognitive difficulties when dealing with Bayes' rule. The higher likelihood to update correctly of those who approve the reform is robust evidence that ideology and political identity shape belief formation. Such directional motivated reasoning has been proposed

by [START_REF] Druckman | The evidence for motivated reasoning in climate change preference formation[END_REF] to explain polarization around beliefs on climate change. Kahan

(2013) provides empirical evidence that political motivated reasoning about climate change is not a reasoning deficiency but rather a reasoning adaptation following the interest that individuals have in conveying "their membership in and loyalty to affinity groups central to their personal well-being".

In our case, the position relative to the Yellow Vests proxies the groups that respondents identify with, and the differentiated updating along this spectrum can be interpreted as motivated reasoning.

Besides, the hypothesis that motivated reasoning follows from a rational adaptation purpose implies that better educated people are more prone to motivated reasoning, as they are more able to formulate specious reasonings and reconcile antagonistic information and ideas. Column (4) supports this hypothesis, as the interaction term between diploma and initial tax approval is positive and significant, even capturing all the effect of initial tax approval. To our knowledge, this result is the first robust evidence of directional and rational motivated reasoning in the context of climate policies, and it provides empirical support for various models of endogenous belief formation. For example, Little (2019) formalizes the idea that directional motives may override accuracy motives and update auxiliary beliefs (in our case, the winning category) in order to preserve their consistency with core beliefs (here, rejection of the tax). Building upon the cognitive and social mechanisms described by [START_REF] Kraft | Why People "Don't Trust the Evidence": Motivated Reasoning and Scientific Beliefs[END_REF] and documented by e.g. [START_REF] Redlawsk | Hot Cognition or Cool Consideration? Testing the Effects of Motivated Reasoning on Political Decision Making[END_REF], we hypothesize the following narrative as one of the possible channels through which aversion for the carbon tax became entrenched. The Yellow Vests first gathered to defend their interest (above all their purchasing power), and a side effect of the daily interactions on roundabouts was to bring material and emotional support to the protesters [START_REF] Challier | Rencontres aux ronds-points[END_REF]. A group identity soon developed, which crystallized shared beliefs and affects such as a rejection of carbon taxation. This group identity gained support from a large majority of the population, notably through social networks. Now, due to the loyalty to the group as well as the affects that have entered their subconscious, Yellow Vests supporters oppose instinctively any carbon tax, and are prone to find excuses to cope with contradictory messages, e.g. by denying the reliability of these messages [START_REF] Golman | The Preference for Belief Consonance[END_REF]. Admittedly, such a narrative falls short of explaining the majority rejection among those who oppose the Yellow Vests (which may originate from biased perceptions more than tax aversion), but it illustrates how biased beliefs can be so persistent among Yellow Vests supporters.

Environmental effectiveness

Progressivity

Table D.6 in Appendix D. 4 shows the absence of effect of explaining that our Tax & Dividend is progressive on perceived progressivity: the correlation between the two is close to 0 (at -0.006) and even has an unexpected negative sign. Column (2) of the same table clarifies why our treatment does not change the overall share of people who think the policy is regressive: those who have a large bias in their perception of gains are in fact more prone to perceive regressivity once provided the information, by 13 p.p. This result may be a manifestation of the boomerang effect with people inclined to motivated reasoning, which has already been documented for Republican attitudes over climate change in the US [START_REF] Zhou | Boomerangs versus Javelins: How Polarization Constrains Communication on Climate Change[END_REF]. Indeed, Hovland et al. (1953) showed that when someone is pressured to make a certain choice, psychological reactance (theorized by [START_REF] Brehm | A theory of psychological reactance[END_REF]) can cause them to resist this pressure by adopting an opposite alternative. Although the effect on those without a large bias is not significant, providing them with information is associated with a lower perceived regressivity by 5 p.p. A possible explanation for the strong belief in regressivity is that people view the tax as regressive (relative to income) and the transfer as neutral (in absolute values), and mistakenly conclude that their combination is regressive. In any case, without a deep explanation of the underlying mechanisms, the progressivity of the policy remains unintuitive for most people, and we cannot convince them easily.

How beliefs determine attitudes

Our results clearly indicate that, as of today, a carbon tax is unlikely to be accepted in France.

However, we have also shown that people largely display incorrect perceptions about the true effects of the policy. Most of them overestimate the negative impact on their purchasing power, think that the policy is regressive, and do not see it as environmentally effective. In this section, we examine to what extent the low acceptance rate reflects intrinsic preferences or wrong perceptions. The question we address is whether correcting biased beliefs would be sufficient for a carbon tax to be accepted.

Self-interest

Identification challenge Among the three-quarters of the respondents expected to win from our

Tax & Dividend, 62% both consider that they would not win and disapprove of the policy. We want to estimate to what extent knowing they would win would lead them to approve of the reform. Because respondents thinking they would win might differ in many respects from those thinking they would not, we cannot simply regress approval on perception of winning.

Main identification strategy In order to identify the effect ceteris paribus of self-interest on acceptance, we exploit exogenous variations in gains and losses. To do so, we consider a Tax & Targeted Dividend, where respondents are randomly assigned to a compensation scheme to which they are eligible or not (see section 2.1.2). Our methodology mixes a random discontinuity design (RDD) and an instrumental variable (IV) strategy. We denote by I 1,i respondent's i income, and by I 2,i the income of the second adult of their household if there is one, which we control for with a dummy variable S i equal to 1 when there is a single adult. Let T 1,i and T 2,i be two binary variables indicating whether these individuals would be eligible for the transfer. 16 We also denote by G T i a dummy variable equal to 0 if respondent i thinks they would lose from the Tax & Targeted Dividend, and 1 otherwise. Similarly, A T i is a dummy variable equal to 0 if respondent i disapproves of this policy and 1 otherwise. We can then write a two-stage least square model, with the following first stage equation:

G T i = α 0 + α 1 T 1,i + α 2 T 2,i + α c c i + α S S i + 2 j=1 α 1,j I j 1,i + α 2,j I j 2,i + η i (2)
where second order terms for income bring more flexibility. We precise that eligibility is defined using income thresholds c i that are randomly allocated to households (see section 2.1.2) and introduced as fixed effects to control for threshold-specific preferences. Formally, we define eligibility of adult k ∈ {1; 2} as:

T k,i =      0, if I k,i > c i 1, otherwise (3)
Finally, the second stage writes:

A T i = β 0 + β 1 G T i + β c c i + β S S i + 2 j=1 β 1,j I j 1,i + β 2,j I j 2,i + i ( 4
)
where G i T denotes the fitted value of G T i from the first stage regression. As can be seen from first stage results in Appendix F.1, eligibility of both respondents and households' second adults are positively correlated with beliefs of winning, so both instruments are relevant. The exclusion restriction states that conditional on income, being eligible affects approval solely through beliefs of winning. The RDD procedure employed in the first stage ensures that this is the case: conditional on income, eligibility is random, and controlling for the target, it should affect acceptance only through self-interest.

Alternative specifications for robustness To further ensure the robustness of the results, we estimate several alternative specifications. First, we run the same RDD + IV design adding control variables (specification 2). In particular, we control for initial acceptance of our Tax & Dividend as this should explain most of the variation in the dependent variable. Second, we compare our results with a simple OLS where we control for relevant variables (3). Third, we use a logit model (4) to 16 As explained in section 2.1.2, we explicitly limit the number of beneficiaries to two per household.

ensure that imposing linearity does not bias the results. Finally, we exploit a methodology similar to the main specification but applied to the customized feedback, without (5) and with (6) control variables. Indeed, as our estimation of gains for this feedback is a continuous variable γ, but the feedback itself is a binary variable Γ, we run an RDD to predict the belief of winning after feedback G F . We then exploit variations around the threshold of zero net gain (which are random conditional on net gain) to explain acceptance A F . This alternative two-stage least square writes:

G F i = α 0 + α 1 Γ i + 2 j=1 α 1,j ( γ i ) j + η i (5)
A F i = β 0 + β 1 G F i + 2 j=1 β 1,j ( γ i ) j + i ( 6
)
where G F i denotes the fitted value of G F i from the first stage regression. The identification assumption of this second IV states that conditional on estimated net gains ( γ), receiving a win feedback ( Γ = 1) affects approval solely through self-interest. Finally, we also investigate alternative versions of the previous models where we estimate the effect to "win" instead of "not to lose", and on "approval" instead of "acceptance".

Results

First stage regression results are given in Appendix F.1. The effective F-Statistics [START_REF] Olea | A robust test for weak instruments[END_REF]) range from 37 to 57, indicating that both targeted transfers and feedback are strong instruments. Table 5.1 provides the second stage results for the six main specifications, and additional specifications can be found in Appendix F.2. Overall, the estimated effects of self-interest indicate that believing not to lose increases acceptance by about 50 p.p. The results obtained for the local average treatment effect (LATE) on compliers in IV regressions -i.e. on people who recognize they would not lose because of the treatment -are significantly higher than for the average treatment effect (ATE) estimated with OLS (57 vs. 44 p.p. for Tax & Targeted Dividend). Given the wide set of control variables used, and in particular our powerful control A I , one can be rather confident that the OLS estimate is unbiased, and that the difference is due to the specificity of compliers in the LATE. This explanation holds for both the targeted scheme and acceptance after feedback and is supported by the findings of section 4.1 for the latter. Indeed, as respondents most likely to revise their beliefs after a "win" feedback are also more in favor of the tax, the IV coefficient for compliers is logically higher than the point estimate found with OLS. The comparisons of columns 1 with 2, and 5 with 6, show that adding control variables does not significantly affect the coefficient for Tax

Environmental effectiveness

Main identification strategy One of the strongest barriers to carbon tax implementation is a widespread perception of its environmental ineffectiveness. Our objective is therefore to assess to what extent learning about the environmental benefits of the tax could increase acceptance. To identify this effect, we estimate a two-stage least squares (2SLS) where the first stage uses random information to explain beliefs about environmental effectiveness, while the second stage regresses acceptance on the fitted exogenous variations in these beliefs. Because information on particulate matter (Z P M ) is poorly correlated with beliefs of effectiveness, we restrict the set of instruments to our primings on the scientific consensus (Z E ) and climate change (Z CC ). As discussed in section 4.2, these instruments are significantly related to our endogenous variable, yet are potentially weak, as our primings do not have a large effect on people's beliefs. If we denote by E a dummy variable equal to 0 if the respondents think the policy is not environmentally effective and 1 otherwise, we can write a 2SLS model as follows:

E i = α 0 + α 1 Z E,i + α 2 Z CC,i + α C C i + η i (7)
A I i = β 0 + β 1 E i + β C C i + i (8)
where E i denotes the fitted value of E i from the first stage regression, and C a vector of characteristics.

Alternative specifications for robustness checks To ensure the robustness of our results, we estimate the previous 2SLS with control variables (1). Acknowledging that our primings could affect acceptation motives other than effectiveness alone, this potential bias should disappear when controlling for many variables including other motives. In addition, we estimate an OLS (2) model to compare the LATE of the first specifications with an ATE, and a logit model (3) to check the robustness of assumptions underlying the linear probability model. Finally, we also estimate two modified versions of our main specifications, where we switch from broad to strict definitions for environmental effectiveness (4) and for tax approval (5).

Results

The first stage regressions results can be found in Appendix F.1. Because of the relatively modest responses to our primings, the instruments are rather weak (effective F-statistic of 6 in column 1), a problem that is alleviated in the case of strict definitions (11 in columns 4 and 5). Given the exogeneity of our instruments, the only concern is a potential bias towards OLS, which would entail estimates that are too conservative in our case. Table 5.2 reports the results of the second stages and alternative specifications. They all consistently indicate a strong positive effect of beliefs about environmental effectiveness on tax acceptance. Overall, the effects are statistically significant, and their size is comparable to that of self-interest, at 48 p.p. for our main IV regression (column 1).

IV OLS logit IV IV (1) (2) (3) (4) (5)
The LATE is again somewhat higher than the ATE estimated with OLS (2) -48 vs. 39 p.p.which is likely due to differences between compliers and other respondents: people who are most likely to change their mind following our information might also be more willing to accept the policy.

Still, the coefficients obtained for the ATE remain large and indicate that beliefs over the policy's environmental effectiveness are critical for acceptance. Results of the logit model close to the ones of OLS confirm that the LPM does not induce a bias in the estimation (3). Lastly, the effect is relatively close with the strict definition of the dependent variable -42 p.p. in (5), showing that the coefficient is not driven by a correlation between "PNR" responses to tax effectiveness and approval.

The critical role found for beliefs about environmental effectiveness is in line with findings of the literature (Saelen & Kallbekken, 2011; Kallbekken & Saelen, 2011; [START_REF] Baranzini | Effectiveness, earmarking and labeling: testing the acceptability of carbon taxes with survey data[END_REF], although previous studies do not properly identify a causal effect. Our results thus confirm that convincing people about the environmental effectiveness of a carbon tax would largely increase acceptance of this instrument.

Progressivity

Identification challenge and strategies As informing respondents does not convince them that our Tax & Dividend is progressive (see section 4.3), we cannot identify the causal effect of understanding the progressivity on acceptance using an IV estimation. Thus, we estimate how one's belief in progressivity correlates with acceptance using simple OLS and logit regressions. Controlling for many respondents' characteristics and other acceptance motives, one can be confident that the effect of progressivity is properly isolated. We focus on the acceptance question after knowledge, i.e.

after asking whether the reform is progressive or not. 18 Table 5.3 presents the results of different regressions, depending on the set of controls and on the choice of variables. Columns (1)-( 4) report regressions of acceptance on the broad definition of motives of acceptance: answers not "No" to progressivity, effectiveness and not "lose" to winning category. On the contrary, columns ( 5)-( 6) use strict definitions for both approval and the covariates, where only "Yes" (or "win") answers activate the dummy variables.

Results On average, believing that the reform is not regressive is associated with a higher acceptance rate by 56 p.p. (column 3), while believing it is progressive is associated with a higher approval rate by 48 p.p. [START_REF] Klenert | Making carbon pricing work for citizens[END_REF]. However, when one introduces other motives of acceptance and their interactions as covariates, with households characteristics as controls, one observes that the effect of progressivity ceteris paribus is lower. The marginal effect of progressivity at the sample mean -i.e. accounting for the average marginal effect of interaction terms -is 27 p.p., slightly lower than the marginal effect obtained for self-interest (40 p.p.) and environmental effectiveness (31 p.p.). The effect obtained for the latter motive is lower than the OLS estimate found in section 5.2, because here acceptance is taken at a later step in the survey and not right after asking about environmental effectiveness, making it less salient. Besides, one might worry that perceived progressivity would be hard to disentangle from beliefs over net gains, as the latter is influenced by the former for a given income. To address or strict (5-6) definitions of the beliefs, where strict dummies do not cover "PNR" or "Unaffected' answers.

Acceptance (A P ) on not "No" Approval ( ȦP ) on "Yes" this dependency, we include the interaction between progressivity and income as a covariate (2, 5). Although the coefficient is negative, in accordance with intuition, the effect is small and not significant. Finally, using the strict definitions of beliefs and approval yields a smaller correlation [START_REF] Klenert | Making carbon pricing work for citizens[END_REF] but similar results when accounting for relevant controls (5), showing that the effects are not driven by a correlation between "PNR" answers.

OLS logit OLS (1) (2) (3) (4) (5) (6)
These results show that progressivity is a motive for acceptance almost as determinant as selfinterest and effectiveness. This concern for distributional effects is consistent with the findings of Kallbekken & Saelen (2011), [START_REF] Brannlund | To tax, or not to tax: preferences for climate policy attributes[END_REF], and Gevrek & Uyduranoglu (2015), but contrasts with the results of [START_REF] Baranzini | Effectiveness, earmarking and labeling: testing the acceptability of carbon taxes with survey data[END_REF], who found that among Genevan, the concern exists but does not affect acceptance of environmental policies.

Complementarity between motives

Table 5.3 (column 1) shows that the combined effect of the three motives together -i.e. adding up their coefficients and the ones of their interactions -is as high as 90 p.p., confirming that these motives are the beliefs critically needed to accept the policy, and that they complement (rather than substitute) one another. Considering approval when respondents do believe that the policy is effective, progressive, and satisfies their self-interest (5), the results are quite similar, although it appears that the two altruistic motives are more complementary: their interaction term is high, and taken together they increase approval by 74 p.p. (marginal effect at the sample mean), against 64 p.p.

for the combination of progressivity and self-interest, and 69 p.p. for self-interest and effectiveness.

The combined effect on approval of the three motives with their strict definition reaches 97 p.p. Thus, in a scenario where everyone would believe in the effectiveness and progressivity of the policy, and the 70% of households who win would know it, our estimation indicates that the approval rate would be as high as 90%. These results suggest that the carbon tax rejection that appears at first glance is mainly due to biases in beliefs (fostered by tax aversion), and that if theses biases could be corrected for, carbon pricing could become close to consensual.

Conclusion

In this paper, we study how beliefs about a policy form and then determine attitudes towards it.

We investigate this question through the study of carbon taxation in France during the Yellow Vests movement, that started against fuel price increases. Our analysis is based on a new survey and consumer survey data, enabling one to compare subjective beliefs with objective impacts on French households. We find that 70% disapprove of a carbon Tax & Dividend policy, which can be explained by biased beliefs about its properties. 89% of our survey respondents overestimate its negative impact on their purchasing power, and most of them do not perceive it as environmentally effective, nor progressive. Biased beliefs appear correlated with people's support for the scheme: the more they oppose the mechanism, the more biased they are. We show that causality between beliefs and attitude towards the policy goes in both directions. People more opposed to the tax are more (pessimistically) biased in their treatment of new information with respect to it, indicating that beliefs about tax impacts are partly shaped by motivated reasoning. At the same time, we find that acceptance is causally determined by beliefs and that if all biased beliefs could be corrected, the approval rate would reach 90%.

However, our treatments that provide accurate arguments in favor of the scheme never convince more than 12% of people. We can relate this conservatism to a strong distrust of the government,

Appendices

A Raw data Please read carefully the information below on climate change.

• Climate change is already responsible for 150,000 deaths annually.

• If greenhouse gas emissions continue on their current trend, the average global warming will be +5°C in 2100 and +8°C in 2250.

• A rapid transition to renewable energies is technically possible and would contain global warming at +2°C.

According to scientists, in the absence of ambitious measures:

• a large proportion of species face an increased risk of extinction;

• natural disasters will intensify (hurricanes, heat waves, droughts, floods, forest fires, etc.); 29. The government is studying a fuel tax increase, whose revenues would be redistributed to all households, regardless of their income. This would imply:

• [an increase in the price of gasoline by 11 cents per liter and diesel by 13 cents per liter / a 13% increase in the price of gas, and a 15% increase in the price of heating oil];

• an annual payment of [60 / 50]

C Estimation for feedback

C.1 Formulas to compute monetary effects of carbon tax policy

In order to compute the monetary impact of a carbon tax increase, we decompose current energy expenditures E(τ ) as a product of current price P (τ ) and current quantities consumed Q(τ ), each being a function of the excise tax τ within which the carbon tax is comprised:19

E (τ ) = P (τ ) Q (τ )
All variations in expenditures can then be expressed as:

dE E (τ ) = dP P (τ ) + dQ Q (τ )
from which we can write the effect of a price change on quantities consumed:

Q τ = Q (τ ) 1 + e dP P (τ )
where e = dQ dP • P Q is the price elasticity of the energetic good considered, that is here assumed constant. For all energies, the final price can itself be decomposed as:

P (τ ) = (p + iτ ) (1 + t)
where t is the value added tax (VAT) rate that applies after excise taxes, i the incidence of excise taxes on consumers assumed constant, and p + (i -1) τ the producer price as a function of τ and for a given value of t. 20 When the carbon price changes so that the excise taxes varies from τ to some level τ , we therefore have:

dP (τ ) P = P (τ ) -P (τ ) P (τ ) = (p + iτ ) (1 + t) -(p + iτ ) (1 + t) (p + iτ ) (1 + t) = i (τ -τ )
p + iτ Thus, following a carbon price increase, one can express the associated increase in expenditures for each energy as:

E τ -E (τ ) = E (τ ) (1 + e) dP P = E (τ ) (1 + e) i (τ -τ ) p + iτ
We can replicate similar calculations to obtain the expected variations in tax revenue T . Starting from its expression -which is the sum of excise taxes and the VAT over this tax -we have:

T (τ ) = Q (τ ) ((1 + t) τ + t (p + (i -1) τ ))
from which we obtain:

T τ -T (τ ) = Q (τ ) 1 + e i (τ -τ ) p + iτ t p + (i -1) τ + (1 + t) τ -Q (τ ) [t (p + (i -1) τ ) + (1 + t) τ ]
Following the literature, we assume price elasticities of -0.4 for transport fuels and -0.2 for housing energies. For the tax incidence on consumers, we assume a value of 0.8. These values were used to compute aggregate variations in tax revenue and determine the level of lump sum transfer per adult that a budget neutral policy would finance. When asked to estimate the impact of the policy on their own purchasing power, respondents simply had to make an estimation over:

E τ -E (τ ) = E (τ ) (1 + e) dP P
where for simplicity dP was given for transport fuels, and dP P for housing energies. Thus, they were not required to make any specific assumption about existing taxes or tax incidence, but simply to estimate their consumption and price elasticity. 20 Hence p is the producer price for a given value of t, when τ = 0.

C.2 Predicting gains and losses

We regress the increase in housing energy expenditures on households' characteristic using EL 2013 survey. Table C.1 presents several specifications for such regression, and its last row shows the out-of-sample error rate, computed with BdF data. All specifications yield a similar error rate of 15-17%. Fearing that respondents could make mistakes when filling the accommodation size in the entry field, we used the first specification in our survey, as it does not rely as heavily as the others on the accommodation size. In order to balance the error rate for losing households that are mistakenly estimated winners, and winners who are mistakenly estimated losers, we add a constant of 16.1 in our estimation of yearly net gain, which is thus the sum of 16.1 plus 110 times one or two (depending on the number of adults) minus increases in transport and housing energy expenditures. We selected OLS as our prediction method for the estimation of net gain because it compared well with respect to alternative methods. We also classified winners and losers using a decision tree, and obtained an very close error rate: [START_REF] Dresner | History and social responses to environmental tax reform in the United Kingdom[END_REF]

H Control variables

Socio-demographics: respondent's income, household's income, sex, age (5 categories), employment status (9 categories), socio-professional category (8 categories), region of France (10 categories), size of town (5 categories), diploma 4 categories, household size, number of people above 14, number of adults, number of c.u., income per c.u., smokes, favored media for news (5 categories).

Politics: extreme left, left, center, right, extreme right, interest in politics (3 categories), conservative, liberal, humanist, patriot, ecologist, apolitical.

Political leaning: extreme left, left, center, right, extreme right, indeterminate.

Energy: heating mode (collective vs. indivual), heating energy (7 categories), annual distance travelled, fuel economy, diesel (binary), gasoline (binary), number of vehicles.

Incomes: income of respondent, income of the second adult, income of respondent squared, income of the second adult squared, dummy for absence of second adult.

Estimated gains: simulated net gain, squared simulated gain.

Figure 2 .

 2 Figure 2.1 presents in a diagram the sequence of treatments (represented by ellipses) and questions (boxes).

Figure 2 . 1 :

 21 Figure 2.1: Diagram of the sequence of treatments (ellipses) and questions (boxes).

( 2020 )

 2020 whose objective was to estimate the distributive effects of a carbon tax for French households. This database matches two households surveys produced by Insee: the consumer survey Budget de Famille (BdF 2011) and the transport survey Enquête Nationale Transports et Déplacements (ENTD 2008). Consumer survey "Budget de Famille" The consumer survey Budget de Famille (BdF 2011) is a household survey providing information over all households' revenues and expenditures, together with many socio-demographic characteristics. It was conducted in several waves from October 2010 to September 2011, over a representative sample of 10,342 French households. The main advantage of BdF when studying the incidence of carbon taxation is that expenditures in both housing and transportation energies are reported. Consumption of housing energies is taken from households' bills, and for most other goods respondents report their expenditures over the past week. As explained in Douenne (2020), this data collection is problematic when looking at the incidence of a tax on transportation energies, as short-run fluctuations in consumption lead to overestimate the variation in expenditures. Transport survey "Enquête Nationale Transports et Déplacements" To overcome this limitation, BdF is matched with the transport survey Enquête Nationale Transports et Déplacements (ENTD 2008). ENTD was conducted in several waves from April 2007 to April 2008, over a representative sample of 20,178 French households. It provides information on households characteristics,

Figure 3

 3 Figure 3.1: Distribution of objective (dark blue) vs. subjective (orange) net gains from our Tax & Dividend.

Figure 3

 3 Figure 3.2: CDF of objective (dark blue) vs. subjective (orange) net gains from our Tax & Dividend.

A

  well established result in the literature on the acceptability of climate policies is the perceived ineffectiveness of Pigouvian instruments (e.g. Dresner et al., 2006a; Kallbekken et al., 2011; Baranzini & Carattini, 2017). In particular, people do not see carbon taxes as effective to fight climate change.

  The observed asymmetry in beliefs' revision echoes a recent literature that has emphasized how people selectively process information regarding themselves or specific events, generally in a way that satisfies their ego[START_REF] Eil | The Good News-Bad News Effect: Asymmetric Processing of Objective Information about Yourself[END_REF][START_REF] Mobius | Managing self-confidence: Theory and experimental evidence[END_REF][START_REF] Sharot | How unrealistic optimism is maintained in the face of reality[END_REF]. Our results show that in the case of a policy considered as undesirable, people give more weight to negative news. Thus, both results are consistent with individuals forming their beliefs in a motivated way. To assess the extent of motivated reasoning, we analyze the heterogeneity in people's updating. To handle the notion of correct updating, we define a variable U which equals +1

  documented e.g. in[START_REF] Alesina | Intergenerational Mobility and Preferences for Redistribution[END_REF] and[START_REF] Algan | Qui sont les gilets jaunes et leurs soutiens ? Technical report[END_REF], echoing recent findings that the ambition of climate policies increases with the level of trust[START_REF] Rafaty | Perceptions of Corruption, Political Distrust, and the Weakening of Climate Policy[END_REF]. These results leave us with three main challenges. First, as it is unlikely that the issue of trust can be resolved in the short run, it seems necessary to find climate policies that would be accepted by a majority. We address this question in a companion paper[START_REF] Douenne | French attitudes on climate change, carbon taxation and other climate policies[END_REF], in which we assess both knowledge and beliefs about climate change, and the preferred policies of French people. Second, as trust in government needs to be restored in the longer run, it is crucial to analyze what causes the distrust and how it can be overcome. Third, it is important to assess to what extent the mechanisms of belief formation and their effects on political attitudes we document can be generalized to other policies and other contexts. Although rejection of the tax may be lower in a different country, biases in perceptions and political polarization are likely common everywhere. Thus, a lesson must be learned for policy design and implementation, to avoid another carbon tax debacle à la Française.

Figure C. 1 :

 1 Figure C.1: Decision tree that classifies households between winners and losers.

Table 2 .

 2 1: Characteristic of the targeted reform by target of the payment.

	Targeted percentiles	≤ 20 ≤ 30 ≤ 40 ≤ 50
	Income threshold (e/month)	780 1140 1430 1670
	Payment to recipients (e/year)	550	360	270	220
	Proportion of respondents	.356 .152 .163 .329
	Expected proportion of respondents .349 .156 .156 .339
	Other questions We do not detail the other questions of the survey, because we analyze them in
	a companion paper,

Table 2 .

 2 2: Notations for the different reforms and for gain notions.

	Step	Initial	After knowledge	with Targeting
	Variants	-	Progressivity Feedback	-

Table 3

 3

	.1: Determinants of bias in subjective gains
		Large bias (| γ -g| > 110)
		OLS	logit	OLS
	Initial tax: PNR (I don't know)			-0.179 * * *
				(0.023)
	Initial tax: Approves			-0.284 * * *
				(0.031)
	Sex: Female	0.036 *	0.030	0.042 * *
		(0.020)	(0.020)	(0.019)
	Ecologist	-0.064 * *	-0.061 * *	-0.025
		(0.026)	(0.026)	(0.026)
	Yellow Vests: PNR	0.039	0.035	0.024
		(0.036)	(0.035)	(0.036)
	Yellow Vests: understands	0.081 * * *	0.062 * * *	0.041 *
		(0.025)	(0.024)	(0.025)
	Yellow Vests: supports	0.108 * * *	0.103 * * *	0.051 *
		(0.026)	(0.025)	(0.026)
	Yellow Vests: is part of	0.202 * * *	0.193 * * *	0.147 * * *
		(0.048)	(0.040)	(0.047)
	Controls: Socio-demo, political leaning
	Observations	3,002	3,002	3,002
	R 2	0.061		0.098

* p<0.1; * * p<0.05; * * * p<0.01

Note: Standard errors are reported in parentheses. For logit, average marginal effects are reported and not coefficients. The list of controls can be found in Appendix H.

Table D .

 D 4 in Appendix D.2 conducts the same analysis for the 28% of respondents whose gain is largely positive or largely negative, i.e. above 110e per c.u. in absolute terms. For such respondents, our out-of-sample prediction of the winning category is correct in 99% of cases, as can be seen in the Figure D.1 in Appendix D.2. The alignments with our feedback are similar for the whole sample and for these respondents for whom we are sure to make a correct prediction. The similarity of Table 4.1: Share of respondents with new beliefs aligned with feedback.

		Aligned with feedback: G F = Γ
		Γ = 1	Γ = 0
		(75.8%)	(24.2%)
	Initial belief winner (g I > 0)	78.8%	81.5%
	(14.0%)	[73.2%; 83.4%]	[65.0%; 91.3%]
	Initial belief unaffected (g I = 0)	21.6%	44.9%
	(21.7%)	[17.6%; 26.2%]	[33.5%; 56.8%]
	Initial belief loser (g I < 0)	12.2%	93.9%
	(64.3%)	[10.3%; 14.5%]	[90.9%; 96.0%]
	Initial belief affected (g I = 0)	26.1%	92.9%
	(78.3%)	[23.7%; 28.7%]	[89.8%; 95.1%]
	All	25.1%	85.7%
	(100%)	[23.0%; 27.3%]	[82.2%; 88.7%]

Table 4

 4

	.2: Asymmetric updating of winning category
			Correct updating (U )
		(1)	(2)	(3)	(4)
	Constant	0.120 * * *	-0.035	-0.146	-0.116
		(0.012)	(0.179)	(0.178)	(0.179)
	Winner, before feedback ( Ġ)	0.695 * * *	0.685 * * *	0.646 * * *	0.659 * * *
		(0.078)	(0.080)	(0.080)	(0.080)
	Initial tax: PNR (I don't know)			0.163 * * *	0.165 * *
				(0.031)	(0.067)
	Initial tax: Approves			0.158 * * *	-0.056
				(0.046)	(0.115)
	Diploma (1 to 4)		0.015	0.016	0.011
			(0.013)	(0.013)	(0.014)
	Diploma × Initial tax: PNR				-0.001
					(0.025)
	Diploma × Initial tax: Approves				0.074 * *
					(0.037)
	Retired		0.143 *	0.146 *	0.142 *
			(0.080)	(0.079)	(0.079)
	Active		0.165 * * *	0.175 * * *	0.175 * * *
			(0.055)	(0.054)	(0.054)
	Student		0.249 * * *	0.234 * * *	0.239 * * *
			(0.076)	(0.075)	(0.075)
	Yellow Vests: PNR		-0.048	-0.043	-0.044
			(0.047)	(0.047)	(0.047)
	Yellow Vests: understands		-0.090 * * *	-0.063 *	-0.064 *
			(0.034)	(0.034)	(0.034)
	Yellow Vests: supports		-0.101 * * *	-0.059 *	-0.060 *
			(0.035)	(0.036)	(0.036)
	Yellow Vests: is part		-0.172 * * *	-0.137 * *	-0.138 * *
			(0.062)	(0.062)	(0.062)
	Among invalidated
	Includes controls
	Observations	1,365	1,365	1,365	1,365
	R 2	0.055	0.111	0.133	0.136

* p<0.1; * * p<0.05; * * * p<0.01 Note: Omitted variables are Unemployed/Inactive and Yellow Vests: opposes. The list of controls can be found in Appendix H.

Table D

 D

.5 in Appendix D.3 reports the effect of displaying relevant information on the belief that our Tax & Dividend is environmentally effective. The effect of reporting a scientific consensus on environmental effectiveness (E) is positive and statistically significant, but its magnitude -around 5 p.p. -seems modest given that the question immediately follows the priming. The effects of information on climate change (CC) or particulates (P M ) are smaller, and only CC is significant, which is understandable as they were displayed at the very beginning of the survey and do not mention any environmental policy. As suggested by

[START_REF] Millner | Beliefs, Politics, and Environmental Policy[END_REF]

, given the complexity of the mechanisms at play, drawing a causal link between causes and consequences of environmental problems requires considerable cognitive effort, making it difficult to convince one about the effectiveness of policies that decentralize efforts to tackle pollution. Finally, we observe that our primings have no significant effect on beliefs over causes and consequences of climate change. Overall, these primings appear insufficient to change most people's mind about climate change and carbon tax effectiveness.

Table 5 .

 5 1: Effect of self-interest on acceptance. This result confirms previous findings of the literature[START_REF] Stern | Value Orientations, Gender, and Environmental Concern[END_REF][START_REF] Thalmann | The Public Acceptance of Green Taxes: 2 Million Voters Express Their Opinion[END_REF][START_REF] Baranzini | Effectiveness, earmarking and labeling: testing the acceptability of carbon taxes with survey data[END_REF]), but contrasts with the results of Kallbekken & Saelen (2011) who found that self-interest plays a limited role in Norway. Their different result could come from their methodological approach that relies on proxies to capture self-interest in regressions, or on differences between preferences of French and Norwegian people. Our results also qualify the findings of[START_REF] Anderson | Can Pigou at the Polls Stop US Melting the Poles? Working Paper 26146[END_REF] who suggest that ideology better predicts carbon tax acceptance than self-interest. By distinguishing beliefs from preferences, we find that ideology plays an indirect role by shaping beliefs about one's self-interest, and that beliefs directly affect acceptance.

		Targeted Acceptance (A T )		Feedback Acceptance (A F )
		IV		OLS	logit	IV
		(1)	(2)	(3)	(4)	(5)	(6)
	Believes does not lose	0.571 * * *	0.567 * * *	0.443 * * *	0.431 * * *	0.517 * * *	0.434 * * *
		(0.092)	(0.092)	(0.014)	(0.018)	(0.170)	(0.135)
	Initial tax Acceptance (A I )		0.339 * * *	0.360 * * *	0.342 * * *		0.428 * * *
			(0.033)	(0.026)	(0.034)		(0.055)
	Controls: Incomes
	Controls: Estimated gain
	Controls: Target of the tax
	Controls: Socio-demo, other motives
	Observations	3,002	3,002	3,002	3,002	1,968	1,968
	R 2	0.033	0.302	0.470		0.044	0.526

* p<0.1; * * p<0.05; * * * p<0.01

Note: Standard errors are reported in parentheses. For logit, average marginal effects are reported and not coefficients. The list of controls can be found in Appendix H.

& Targeted Dividend, but does for acceptance after feedback, where the controls seem to capture part of the specificity of compliers. Overall, both methods yield similar effects: 57 p.p. with targeted transfers and 52 p.p. with the feedback. Finally, results from the logit regression (4) confirm that the assumptions of the linear probability model (LPM) do not bias the results.

17

By isolating beliefs about self-interest ceteris paribus, we showed that this motive has a large effect on carbon tax acceptance.

Table 5 .

 5 2: Effect of believing in environmental effectiveness on acceptance

	Tax Acceptance (A I )	Tax Approval ( ȦI )

Table 5 .

 5 3: Effect of beliefs over progressivity on acceptance. Covariates refer either to broad (1-4)

  Table A.1: Sample characteristics: quotas stratas.

	B Questionnaire
	Priming
	1. [No priming] Welcome to this survey.
	Table A.2: Households' characteristics. It was conceived by two researchers in social science. It lasts about 15-20 minutes.
	Population Sample 2. [Info PM] Welcome to this survey.		Population Sample
	gender It was conceived by two researchers in social science. It lasts about 15-20 minutes. Household composition (mean)
	woman man age Before starting, please read carefully the information below on particulate matter pollution: 0.52 0.53 0.48 Household size 2.36 2.38 0.47 Number of adults 2.03 1.93 c.u. 1.60 1.61
	18-24	0.12	0.11	Energy source (share)
	25-34 35-49 • particulate matter are responsible for 48,000 deaths in France each year; 0.15 0.11 0.24 Gas 0.24 50-64 0.24 Fuel 0.26 >65 0.25 0.27 Accomodation surface (m 2 ) 0.42 0.12 • particulate matter reduce the life expectancy of French people by 9 months;	0.36 0.09
	mean p25 p50 • reducing fuel consumption would reduce the health problems associated with particulate matter. 97 96 profession farmer 0.01 0.01 independent 0.03 69 66 90 90 0.04 executive 0.09 p75 120 115 0.09 intermediate 0.14 0.14 Distance travelled by car (km/year) Source: France Public Health Report (2016)
	employee	0.15	0.16	mean	13,735	15,328
	worker retired 3. [Info CC] Welcome to this survey. 0.12 0.33	0.13 0.33	p25 p50	4,000 10,899	4,000 10,000
	inactive It was conceived by two researchers in social science. It lasts about 15-20 minutes. 0.12 0.11 p75 20,000	20,000
	education			Fuel economy (L/100 km)
	No diploma or Brevet	0.30	0.24	mean	6.39	7.25
	CAP or BEP	0.25	0.26	p25	6	5
	Bac	0.17	0.18	p50	6.5	6
	Higher	0.29	0.31	p75	7.5	7
	size of town
	rural	0.22	0.24	Sources: Matched BdF; except for number of adults
	<20k	0.17	0.18	(ERFS) and domestic fuel (CEREN).
	20-99k	0.14	0.13
	>100k	0.31	0.29
	Paris area	0.16	0.15
	region
	IDF	0.19	0.17
	Nord	0.09	0.10
	Est	0.13	0.12
	SO	0.09	0.09
	Centre	0.10	0.12
	Ouest	0.10	0.10
	Occ	0.09	0.09
	ARA	0.12	0.13
	PACA	0.09	0.09

  Partial reforms [transport / housing] 27. Do you think that an increase in VAT would result in a loss of more purchasing power for your household than for the average French household?

	Yes, much more; Yes, a little more; As much as the average; No, a little less; No, a lot less; PNR
	(Don't know, don't say)
	28. Do you think that an increase in [fuel taxes / taxes on gas and heating oil] would cause your
	household to lose more purchasing power than an average French household?
	Yes, much more; Yes, a little more; As much as the average; No, a little less; No, a lot less; PNR
	(Don't know, don't say)

  According to you, the purchasing power of your household would de-Why do you think this measure is beneficial? (Maximum three responses) Contributes to the fight climate change; Reduces the harmful effects of pollution on health; Reduces traffic congestion; Increases my purchasing power; Increases the purchasing power of the poorest; Please select "A little" (test to check that you are attentive).

	Not at all; A little; A lot; Completely; PNR (Don't know, don't say)
	49. Do you smoke regularly? Yes; No
	Fosters France's independence from fossil energy imports; Prepares the economy for tomorrow's
	challenges; For none of these reasons; Other (specify): 50. How much are you interested in politics?
	Almost not; A little; A lot
	45. Why do you think this measure is unwanted? (Maximum three answers)
	Is ineffective in reducing pollution; Alternatives are insufficient or too expensive; Penalizes rural 51. How would you define yourself? (Several answers possible)
	areas; Decreases my purchasing power; Decreases the purchasing power of some modest households; Extreme left; Left; Center; Right; Extreme right; Liberal; Conservative; Liberal; Humanist; Patriot;
	Harms the economy and employment; Is a pretext for raising taxes; For none of these reasons; Apolitical; Ecologist
	Other (specify): 52. How do you keep yourself informed of current events? Mainly through...
	Tax & targeted dividend
	• an increase of 13% in the price of gas, and 15% in the price of heating oil;
	• an annual payment of [550 / 360 / 270 / 220]e for each adult earning less than [780 / 1140 /
	1430 / 1670]e per month (welfare benefits included, before withholding tax);
	• no compensation for the others.
	We estimate that in your household, [number of recipients] persons would receive this payment.
	In terms of purchasing power, would your household win or lose with such a measure?
	crease: Win; Be unaffected; Lose
	From 0 to [15•uc] e per year; From [15•uc] to [40•uc] e per year; From [40•uc] to [70•uc] e per year; From [70•uc] to [110•uc] e per year; From [110•uc] to [160•uc] e per year; From more than 47. Would you approve such a measure?
	[160•uc] e per year Yes; No; PNR (Don't know, don't say)

e to each adult, or [120 / 100]e per year for a couple. In terms of purchasing power, would your household be a winner or a loser with such a measure? Winner; Unaffected; Loser 30. [Winner selected] According to you, your household's purchasing power would increase: From 0 to [10•uc] e per year; From [10•uc] to [20•uc] e per year; From [20•uc] to [30•uc] e per year; From [30•uc] to [40•uc] e per year; More than [40•uc] e per year 31. [Loser selected] 32. If fuel prices increased by 50 cents per liter, by how much would your household reduce its fuel consumption? 0% -[I already consume almost none / I am already not consuming]; 0% -[I am constrained on all 44. 46. The government is studying an increase in the carbon tax, whose revenues would be redistributed to the [20 / 30 / 40 / 50]% of the poorest French people only. This would imply: • an increase in the price of gasoline by 11 cents per liter and diesel by 13 cents per liter; Other questions The survey is completed by other attitudinal questions, treated in our companion paper, Douenne & Fabre (2020). Hereafter, we only describe questions that are used in the present paper. 48. Television; Press (written or online); Social networks; Radio; Other 53. What do you think of the Yellow Vests? (Several answers possible) I am part of them; I support them; I understand them; I oppose them; PNR (Don't know, don't say) 54. The survey is nearing completion. You can now enter any comments, comments or suggestions in the field below.

  .4% (see Figure C.1). Finally, statistical matching provided an error rate of 17.7%. Table C.1: Determinants of housing energy expenditures.

		Increase in housing energy expenditures (e/year)
		(1)	(2)	(3)
	Constant	-55.51 * * *		-0.634
		(1.237)		(1.489)
	Housing energy: Gas	124.6 * * *		1.173
		(1.037)		(2.323)
	Housing energy: Fuel oil	221.1 * * *	129.8 * * *	130.4 * * *
		(1.719)	(3.752)	(4.002)
	Accommodation size (m 2 )	0.652 * * *		0.024
		(0.012)		(0.015)
	Accommodation size × Gas		1.425 * * *	1.397 * * *
			(0.007)	(0.024)
	Accommodation size × Fuel oil		0.945 * * *	0.922 * * *
			(0.029)	(0.032)
	Observations	26,729	26,729	26,729
	R 2	0.545	0.716	0.599
	Error rate	0.166	0.155	0.155

* p<0.1; * * p<0.05; * * * p<0.01 51

Table D .

 D Table D.1: Effect of subjective elasticities on perceived environmental effectiveness. Table D.2: Transition matrix after telling respondents they are expected to win (75.8%). 3: Transition matrix after telling respondents they are expected to lose (24.2%). Probability that our estimation of net gains correctly predicts the winning category. Table D.5: Effect of primings on beliefs about environmental effectiveness * p<0.05; * * * p<0.01 Table E.1: Asymmetric updating of winning category (complementary results). .1 Two-stage least squares: first stage results Table F.1: First stage regressions results for self-interest p<0.1; * * p<0.05; * * * p<0.01 F.2 Additional specifications Table F.3: Effect of self-interest on acceptance: second stages of alternative specifications.

	D.3 Environmental effectiveness Table F.2: First stage regressions results for environmental effectiveness
	Environmental effectiveness: not 'No' (1) (2) (3) (4) -0.062 * -0.055 * (0.032) (0.032) -0.056 * -0.060 * * (0.030) (0.030) 1,501 1,501 1,501 1,501 0.003 0.002 0.089 0.090 Before \ After Price elasticity: Housing Price elasticity: Transports Controls: Socio-demo, energy incomes, estimated gains Observations R 2 Winner (25%) Unaffected (28%) Loser (47%) Winner (16%) 79% 13% 8% Unaffected (24%) 22% 63% 15% Loser (60%) 12% 18% 70% Before \ After Winner (3%) Unaffected (12%) Loser (86%) Winner (7%) 16% 3% 81% Unaffected (15%) 5% 50% 46% Loser (78%) 1% 5% 94% Figure D.1: Aligned with feedback: G F = Γ Γ = 1 Γ = 0 (81.6%) (18.4%) Initial belief winner (g > 0) 77.6% 78.4% (19.4%) Environmental effectiveness not "No" "Yes" OLS logit OLS (1) (2) (3) (4) Info on Environmental Effectiveness (Z E ) 0.043 * * 0.063 * * * 0.052 * * * 0.059 * * * (0.017) (0.018) (0.018) (0.014) Info on Climate Change (Z CC ) 0.044 * 0.041 * 0.043 * 0.029 (0.024) (0.024) (0.024) (0.018) Info on Particulate Matter (Z P M ) 0.039 0.029 0.037 0.017 (0.024) (0.024) (0.024) (0.019) Z CC × Z P M -0.040 -0.033 -0.042 -0.005 (0.035) (0.034) (0.033) (0.027) Controls: Socio-demographics Observations 3,002 3,002 3,002 3,002 R 2 0.003 0.047 0.075 Table D.6: Effect of information on perceived progressivity Progressivity: not No (P ) (1) (2) (3) Constant 0.419 * * * 0.435 * * * 0.052 (0.022) (0.033) (0.319) Information on progressivity (Z P ) -0.021 0.050 0.051 (0.027) (0.040) (0.041) Large bias (| γ -g| > 110) -0.028 -0.040 (0.045) (0.045) Interaction Z P × (| γ -g| > 110) -0.130 * * -0.117 * * (0.055) (0.055) Controls: Socio-demo, politics Observations 1,444 1,444 1,444 R 2 0.0004 0.018 0.094 (1) (2) (3) (4) Environmental effectiveness not "No" "Yes" (1) (4,5) Correct updating (U ) Constant -0.146 -0.039 -0.110 -0.258 (0.178) (0.179) (0.181) (0.890) Winner, before feedback ( Ġ) 0.646 * * * 0.551 * * * (0.080) (0.083) Initial tax: PNR (I don't know) 0.163 * * * 0.179 * * * 0.199 * * * 0.113 (0.031) (0.032) (0.033) (0.155) Initial tax: Approves 0.158 * * * 0.176 * * * 0.216 * * * -0.162 (0.046) (0.046) (0.049) (0.185) Subjective gain (g) 0.0004 * * 0.001 * * * -0.001 (0.0002) (0.0003) (0.004) Subjective gain: unaffected (g = 0) -0.127 * * * -0.208 * * * -0.331 (0.033) (0.033) (0.219) Bias about gain (g -γ) -0.00005 -0.001 * -0.0003 (0.0001) (0.0003) (0.0002) Diploma (1 to 4) 0.016 0.014 -0.001 0.148 * (0.013) (0.013) (0.013) (0.078) Retired 0.146 * 0.130 * 0.108 0.124 (0.079) (0.079) (0.080) (0.435) Active 0.175 * * * 0.166 * * * 0.160 * * * 0.113 (0.054) (0.054) (0.054) (0.365) Student 0.234 * * * 0.224 * * * 0.183 * * 0.402 (0.075) (0.075) (0.074) (0.526) Yellow Vests: PNR -0.043 -0.045 -0.031 0.013 (0.047) (0.047) (0.048) (0.246) Yellow Vests: understands -0.063 * -0.065 * -0.059 * 0.141 (0.034) (0.034) (0.034) (0.170) Yellow Vests: supports -0.059 * -0.063 * -0.050 -0.156 (0.036) (0.036) (0.036) (0.206) Yellow Vests: is part -0.137 * * -0.141 * * -0.106 * -0.985 * * (0.062) (0.061) (0.063) (0.367) Includes "pessimistic winners" Includes "optimistic losers" Includes controls Observations 1,365 1,365 1,265 100 R 2 0.133 0.144 0.115 0.696 Targeted tax (G T ) After feedback (G F ) (1) (2) (5) (6) Transfer to respondent (T 1 ) 0.268 * * * 0.227 * * * (0.028) (0.027) Transfer to spouse (T 2 ) 0.180 * * * 0.174 * * * (0.031) (0.030) T 1 × T 2 -0.190 * * * -0.161 * * * (0.038) (0.037) Initial tax Acceptance (A I ) 0.163 * * * 0.333 * * * (0.033) (0.038) Simulated winner ( Γ) 0.217 * * * 0.210 * * * (0.036) (0.035) Controls: Incomes Controls: Estimated gain Controls: Target of the tax Controls: Socio-demo, other motives Effective F-Statistic 44.093 40.834 37.966 57.866 Observations 3,002 3,002 1,968 1,968 R 2 0.082 0.177 0.131 0.319 Info on Environmental Effectiveness (Z E ) 0.062 * * * 0.059 * * * (0.017) (0.014) Info on Climate Change (Z CC ) 0.030 * 0.028 * * (0.017) (0.013) Controls: Socio-demo, other motives, incomes, estimated gains Effective F-Statistic 5.886 11.145 Observations 3,002 3,002 R 2 0.121 0.123 Targeted Tax After Feedback Acceptance Approval Acceptance Approval (1) (2) (3) (4) (5) (6) Believes wins 0.636 * * * 0.382 * * * 0.764 * * * 0.612 * * * (0.100) (0.080) (0.251) (0.197) Believes does not lose 0.351 * * * 0.414 * * * (0.073) (0.133) Controls: Incomes Controls: Estimated gain Controls: Target of the tax Observations 3,002 3,002 3,002 1,968 1,968 1,968 R 2 0.033 0.018 0.018 0.044 0.017 0.017 Believes does not lose * p<0.1; * * p<0.05;

* p<0.1; * * p<0.05; * * * p<0.01 D.2 Self-interest Table D.4: Share with new beliefs aligned with feedback, among those with large gain or loss (| γ| > 110). * p<0.1; * * p<0.05; * * * p<0.01 D.4 Progressivity * p<0.1; * * p<0.1; * * p<0.05; * * * p<0.01 Note: Omitted variables are Unemployed/Inactive; Yellow Vests: opposes. Cf. Appendix H for the list of controls. F Estimation of acceptation motives F* * * * p<0.01 Figure G.1: Acceptance rate by subjective gain, which informs one on the willingness to pay for climate mitigation.

More precisely, the "Contribution Climat-Énergie" is a sectoral carbon tax specific to fossil fuels.

Following a massive petition against rising gasoline prices in November 2018, hundreds of thousands of people started protesting. They would wear their recognizable fluorescent clothing and gather on roundabouts and tolls every day, and demonstrate in Paris each Saturday. The Yellow Vests express a general concern for their purchasing power as well as discontent for French elites and institutions.

The "campaign effect" documented by[START_REF] Anderson | Can Pigou at the Polls Stop US Melting the Poles? Working Paper 26146[END_REF] (in the case of referenda in the US state of Washington) is an example of how support for a carbon tax can decrease substantially after it enters the public debate. It may explain why acceptance of an increase in the carbon tax plummeted with the Yellow Vests movement, down from a level

of 48%(ADEME, 2018) in the middle range of other countries'[START_REF] Brechin | Public opinion: a cross-national view[END_REF]. This effect confirms that the French carbon tax may be an insightful case study to understand what could happen in other countries when a controversial policy is publicly debated.

We take preferences over policies as the mapping from beliefs (on facts) to attitudes (on policies), i.e. how attitudes are determined as a function of beliefs. Conversely, motivated reasoning represents the feedback loop from attitudes to beliefs.

preferences-pol.fr/doc_q.php#_e

Electricity is exempt from the French carbon tax "Contribution Climat Energie" (CCE) as it is already taxed by the EU-ETS, and has a low carbon content due to the large share of nuclear power.

Incomes entitled to the household rather to its members, such as certain welfare benefits, are divided equally among the two oldest adults of the household.

These values correspond to the short run uncompensated price elasticities estimated by Douenne (2020), and are in line with previous findings on French households (e.g.[START_REF] Clerc | Elasticité-prix des consommations énergétiques des ménages[END_REF][START_REF] Bureau | Distributional effects of a carbon tax on car fuels in France[END_REF].

The subjective intervals are translated into numerical values, assuming that the distribution within each interval is the same as that of BdF data. Within each bin, we draw values that match the actual distribution for the PDF, while we simply take the actual average for the CDF. Among the several methods that we tried to assign numerical values, all realistic ones yield identical results, and we find an overestimation of policy costs even in the most conservative one (taking the maximal bounds of intervals).

For transport and housing energy taxes, the objective proportions of winners are very similar at respectively 74% and 67%, while the subjective shares are 16% and 17% (with 22% and 30% of unaffected).

We observe that respondents revise their beliefs less when they feel "unaffected", indicating that some of them may have misunderstood this category for "I don't know".

Separation occurs in logistic regressions for self-interest and effectiveness. We made sure this does not lead to biased coefficients by conducting likelihood ratio tests and by running penalized regressions[START_REF] Firth | Bias reduction of maximum likelihood estimates[END_REF][START_REF] Heinze | Fixing the nonconvergence bug in logistic regression with SPLUS and SAS[END_REF].

As self-interest and effectiveness were made salient from the initial questions, treating progressivity after knowledge is the only way to make results comparable across motives.

The French carbon tax "Contribution Climat Energie" is a component of existing taxes on energetic products: TICPE for transport and domestic fuels, TICGN for natural gas.

Christina Hobbs for the proof-reading. We acknowledge financial support from the Cepremap, EUR PGSE (ANR-17-EURE-0001

my trips / I will not reduce it]; From 0% to 10%; From 10% to 20%; From 20% to 30%; More than 30% -[I would change my travel habits significantly / I would change my consumption significantly] 33. In your opinion, if [fuel prices increased by 50 cents per liter / gas and heating oil prices increased by 30%], by how much would French people reduce their consumption on average? From 0% to 3%; From 3% to 10%; From 3% to 10%; From 10% to 20%; From 20% to 30%; More than 30%

Tax & dividend: initial 34. The government is studying an increase in the carbon tax, whose revenues would be redistributed to all households, regardless of their income. This would imply:

• an increase in the price of gasoline by 11 cents per liter and diesel by 13 cents per liter;

• an increase of 13% in the price of gas, and 15% in the price of heating oil;

• an annual payment of 110e to each adult, or 220e per year for a couple.

E Robustness of motivated reasoning

There could be a reason why motivated reasoning would come from an accuracy motive (i.e. the willingness to form a correct representation of reality) rather than a directional motive (i.e. the desire to preserve one's prejudices). The opponents to the reform could process new information in the same Bayesian way as the supporters, but have different (possibly well justified) priors. As argued by [START_REF] Cantoni | Protests as Strategic Games: Experimental Evidence from Hong Kong's Antiauthoritarian Movement*[END_REF], accounting for the heterogeneity in priors is essential to correctly measure the effect of a treatment on beliefs. In our case, the only prior that matters is arguably the subjective gain. Indeed, it could be the case that informing a respondent that they would win makes them revise their subjective gain by, say, 100e upwards, leading most supporters of the reform to discover that they would win, while opponents would keep thinking they would lose.

Column (2) in Table E.1 somehow validates this hypothesis, as even controlling for the bias, a higher subjective gain is significantly associated with a higher propensity to update correctly (while those who feel unaffected update less correctly all else being equal). However, the coefficients relative to the approval are left practically unchanged (compared to column 1) when subjective gain is included. 21 This analysis provides robust evidence in favor of directional motivated reasoning.

Finally, it is worth noticing that these results on motivated reasoning are entirely driven by the "pessimistic winners": we find no effect of motivated reasoning on the "optimistic losers" (columns 3-4). In other terms, the updating of people who wrongly think they win does not depend on their approval, another indication that motivated reasoning is driven by tax aversion. 21 Logically, the coefficient affected by the new specification is the binary version of subjective gain: Winner.

G Willingness to pay

For respondents who believe in effectiveness of our Tax & Dividend, we are able to infer their willingness to pay (WTP) for climate mitigation by studying the acceptance rate in function of subjective gain. We adopt a common practice in the literature and define the WTP as the monetary loss that the median agent is willing to incur [START_REF] Hanemann | Welfare Evaluations in Contingent Valuation Experiments with Discrete Responses[END_REF]. Figure G.1 indicates that this WTP is about 60e/year per c.u., as this corresponds to the subjective loss below which a majority accepts the policy. This WTP is computed only among people who believe that the tax is not ineffective, as it would make little sense to assume that some people are willing to pay for an instrument that does not achieve its expected goal. Indeed, Figure G.1 shows that the "WTP" of the whole sample is zero, meaning that the median person accepts the policy only when they personally gain from it. Our method has several advantages. First, it can be interpreted as a willingness to accept as much as a willingness to pay, because our instrument is neither framed as a good to buy nor as a damage to be compensated for, and net gains do not distinguish cost increases from payments received. Second, our method is more akin to revealed preferences -and hence probably less biased [START_REF] Murphy | A Meta-analysis of Hypothetical Bias in Stated Preference Valuation[END_REF]) -than previous ones, because most studies directly ask respondents to select their preferred option for climate mitigation, be it in a in a contingent valuation method [START_REF] Berrens | Information and effort in contingent valuation surveys: application to global climate change using national internet samples[END_REF][START_REF] Cameron | Individual option prices for climate change mitigation[END_REF][START_REF] Kotchen | Willingness-to-pay and policy-instrument choice for climate-change policy in the United States[END_REF] or in a discrete choice experiment [START_REF] Longo | The internalization of externalities in the production of electricity: Willingness to pay for the attributes of a policy for renewable energy[END_REF][START_REF] Alberini | Preferences for Energy Efficiency vs. Renewables: What Is the Willingness to Pay to Reduce CO2 Emissions? Ecological Economics[END_REF]. Still, our estimation has two notable limitations relative to the literature: it relies on a non-representative sub-sample, and subjective gains are endogenous with acceptance.

To compare our estimation with those of the literature, expressed per household, we have to multiply our WTP by the average number of consumption units by households: 1.6. The WTP per household we get, 96e, lies in the typical range of the literature [START_REF] Jenkins | Political economy constraints on carbon pricing policies: What are the implications for economic efficiency, environmental efficacy, and climate policy design? Energy Policy[END_REF][START_REF] Streimikiene | A Review of Willingness to Pay Studies for Climate Change Mitigation in the Energy Sector[END_REF], suggesting that the protests against carbon taxation encountered in France do not reflect specific preferences for environmental policies.