Keywords: Redistribution, fairness, majority rule, social norms, endogenous preferences. JEL H53, D63, D72, D03

When studying attitudes towards redistribution, surveys show that individuals do care about fairness. They also show that the cultural environment in which people grow up affects their preferences about redistribution. In this article we include these two components of the demand for redistribution in order to develop a mechanism for the cultural transmission of the concern for fairness. The preferences of the young are partially shaped through the observation and imitation of others' choices. More specifically, observing during childhood how adults have collectively failed to implement fair redistributive policies lowers the concern during adulthood for fairness or the moral cost of not supporting fair taxation. Based on this mechanism, the model exhibits a multiplicity of history-dependent stationary states that may account for the huge and persistent differences in redistribution observed between Europe and the United States. It also explains why immigrants from countries with a preference for greater redistribution continue to support higher redistribution in their destination country.

Introduction

When studying redistributive attitudes, in a departure from traditional economics, surveys show that individuals do care about fairness [START_REF] Fong | Social preferences, self-interest, and the demand for redistribution[END_REF][START_REF] Corneo | Individual preferences for political redistribution[END_REF][START_REF] Alesina | Preferences for redistribution in the land of opportunities[END_REF][START_REF] Corneo | What's the monetary value of distributive justice ?[END_REF][START_REF] Alesina | Preferences for redistribution[END_REF]. More speci…cally, they underline that people tend to support greater redistribution if they believe that poverty is caused by factors beyond an individual's control, such as luck. The …nding that social concerns matter in explaining redistributive attitudes is also supported by a growing number of lab experiments [START_REF] Tyran | A little fairness may induce a lot of redistribution in democracy[END_REF][START_REF] Ackert | Social preferences and tax policy design : some experimental evidence[END_REF][START_REF] Schildberg-Hörisch | Is the veil of ignorance only a concept about risk ? An experiment[END_REF]Durante et al., 2014). Putting this …nding into an international context, [START_REF] Corneo | Inequality and the State : Comparing US and German preferences[END_REF] shows that individuals in high-redistributive countries such as former West Germany exhibit a greater concern for fairness than individuals in low-redistributive countries such as the United States 1 . Furthermore, [START_REF] Luttmer | Culture, context, and the taste for redistribution[END_REF] and [START_REF] Alesina | Preferences for redistribution[END_REF] show that, after controlling for individual characteristics, immigrants from countries with a preference for greater redistribution continue to give signi…cant support to higher redistribution in their destination country.

Accordingly, the intensity of the concern for others appears to some degree to be culturally shaped at young ages and to stop changing after reaching adulthood 2 . Understanding the development of an agent's preferences when young and the role of the cultural context are then of great importance in explaining individual demands for redistribution, and hence the diversity 1 Twenge et al. (2007) explain for example that social exclusion elicits strong negative feelings that impair the capacity for empathic understanding of others, and as a result, decreases pro-social behaviour (see Gunther Moore et al., 2012, and[START_REF] Alesina | Family values and the regulation of labor[END_REF], for neuroimaging evidence). To that extent, it is to be expected, as found in [START_REF] Corneo | Inequality and the State : Comparing US and German preferences[END_REF], that fairness considerations are undermined in societies with high social exclusion (the poverty rate in 2013 was more than 17% in the United States compared with less than 10% in all the major euro area countries, except Italy ; OECD, 2017), and in turn that these countries do not promote redistributive policies …ghting social exclusion. Note that the poverty rate is the ratio of the number of people whose income falls below the poverty line taken as half the median household income of the total population. 2 Supporting this view, psychologists [START_REF] Mccrae | The stability of personality : observation and evaluations[END_REF] have shown that personality traits stop changing after age 30. See [START_REF] Roberts | The rank-order consistency of personality traits from childhood to old age : a quantitative review of longitudinal studies[END_REF] for a discussion.

in redistributive policies in democratic countries.

Following robust empirical evidence that fairness and culture are two important components of redistributive attitudes, in this article we propose a mechanism for the cultural transmission of the strength of the moral norm or concern for distributive justice. Through oblique socialization, taste is shaped by the observation, imitation 3 and internalization of cultural practices. More speci…cally, we argue that the observation during childhood of redistributive policies that are far from what would be perceived as fair results in a weakened concern for distributive justice.

To characterize the socialization process and the persistence of preferences over generations, deviating from the norm a¤ects preferences with a delay of one generation. The moral cost of not supporting fair taxation is reduced when observing how the previous generation has collectively failed to implement a fair institution. Said di¤erently, our mechanism states that being exposed to unfairness during youth reduces individual responsibility regarding moral duty.

As a …rst result of our mechanism for intergenerational and cultural transmission, assuming that the level of redistribution perceived as fair is higher than the level sel…shly preferred, we explain that immigrants from countries with a preference for greater redistribution continue to support higher redistribution in their destination country because they have a stronger concern for distributive justice. This result is also consistent with the …ndings of [START_REF] Corneo | Inequality and the State : Comparing US and German preferences[END_REF]. As a second result, the persistent di¤erences in redistribution between the United States and Europe are explained through multiple stable stationary states. Indeed, we show that if people are socialized in an environment where practices and institutions are close to (but lower than)

what is perceived as fair, the redistributive institution and the concern for fairness co-evolve and are self-reinforcing such that the cultural transmission process ends with the implementation of the high redistribution level. By contrast, if people are socialized in an environment that is too far from what is perceived as fair, then observation that the moral norm does not prevail in the society reduces individual responsibility regarding moral duty. In that case, the cultural transmission process ends with the implementation of the low redistribution level. At steady state, our model satisfyingly reproduces the fact that redistribution is higher in (continental)

Europe than in the United States while market income inequality appears lower in the former.

This paper belongs to several strands of literature. At the micro level, it is related …rst to the literature on the interaction between social norms and individual behavior, which stresses that the incentive to behave in a certain manner depends on the degree to which we see others acting in this way. For example, in the literature on crime (see [START_REF] Funk | Governemental action, social norms and criminal behavior[END_REF], the strength of the social crime norm is measured by the moral costs that arise from committing a crime. Therefore, as is well established in this literature, if it is observed that many others are committing crimes, the remorse or guilt felt from breaking the social norm is weakened. In the same vein, in Lindbeck (1999), in our setting the choice is not binary. Therefore, to identify the deviation from the moral norm we replace the fraction of deviators by the distance of the collective choice from the norm. This makes it possible to apprehend the intensity of the deviation from the norm more properly. In this …rst strand of literature, the social in ‡uence is generally associated with contemporaneous peer e¤ects. It is thus distinguished from the growing literature on cultural transmission launched by [START_REF] Bisin | The economics of cultural transmission and the dynamics of preferences[END_REF], where culture refers to social norms that persist over long periods and across generations. On the relationship between culture and institutions investigated in this second strand of literature 4 , our paper is most closely related to the work of [START_REF] Tabellini | The scope of cooperation : values and incentives[END_REF]. Here individuals respond to incentives but are also in ‡uenced by norms of good conduct inherited from earlier generations. This leads to multiple historydependent steady states. If a norm of generalized morality initially prevails, then the economy converges to a steady state with high cooperation, and vice versa. [START_REF] Tabellini | The scope of cooperation : values and incentives[END_REF] focuses on the transmission of values within the family (vertical socialization). In our paper, by assuming highly homogenous values at the regional level, parents have few incentives to transmit their values. We therefore speci…cally investigate the e¤ect of the social environment in transmitting values (oblique socialization), taking into account that this cultural transmission channel cannot account for any behavioral persistence beyond the …rst generation of immigrants.

Finally, at the macro level, our paper also builds on the literature and extends the canonical model of Meltzer and Richard 5 (1981) to improve its main prediction that greater income inequality results in greater redistribution -a prediction that has only weak support in the data 6 .

By stressing the importance of the concern for fairness, our approach is most closely related to the seminal paper of [START_REF] Alesina | Fairness and redistribution : US versus Europe[END_REF]. However, the mechanism we propose is structurally di¤erent. In [START_REF] Alesina | Fairness and redistribution : US versus Europe[END_REF], Americans are supposed to support only weak redistribution because they believe that market outcomes are fair, i.e. determined by hard work rather than luck 7 . Indeed, in their framework, as the after-tax return to e¤ort is expected to be high, they work hard and the market outcomes are e¤ectively fair 8 . In other words, in fairness are self-ful…lled. In contrast, in our approach, the di¤erences are sustained because the concern for fairness is endogenous and culturally shaped. The mechanism we propose provides then a new explanation for the huge and persistent di¤erence in redistribution observed between Europe and the United States based on the intergenerational and cultural transmission of the strength of the concern for fairnesss.

The rest of the paper is organized as follows. We present in section 2 an endogenous mechanism for the formation of preferences based on oblique socialization. In section 3, based on this mechanism and assuming that the perception of the fair level of taxation is exogenous and unanimously shared in the population, we show that our model exhibits multiple stable stationary states consistent with the negative correlation between income inequality and redistribution encountered in the data. We also explain why immigrants from countries with a preference for greater redistribution continue to support higher redistribution in their destination country. In section 4, we extend and verify the robustness of our results by considering endogenous and heterogenous views of what is fair. We conclude brie ‡y in the last section.

The social determinants of preferences

To characterize the socialization process, we consider an overlapping generations model in which each individual lives two periods : childhood and adulthood. People are educated and socialized during childhood, and through this process they internalize the cultural practices that will in ‡uence their behavior when they become adults. As adults, they work and consume in order to maximize their utility. Adult individuals also vote on income redistribution in the beginning of the period. In this way, they take into account the distortive e¤ect of redistribution on work e¤ort, as in the seminal paper of [START_REF] Meltzer | A rational theory of the size of government[END_REF].

Inequity aversion

As underlined in the introduction, an abundant literature shows that people's demand for redistribution re ‡ects that they do indeed care about the equity of market income distribution, where factors beyond one's control such as luck characterize the level of unfairness. Accordingly, following [START_REF] Piketty | Social mobility and redistributive politics[END_REF], [START_REF] Alesina | Fairness and redistribution : US versus Europe[END_REF] and [START_REF] Bénabou | Belief in a just world and redistributive politics[END_REF], we assume that the income of an adult at date t is determined conjointly by luck and by e¤ort such that :

y it = A i e it + i (1)
where e it denotes the person's chosen e¤ort, A i 0 his talent or ability and i his luck (or bad luck). It is assumed that fA i ; e it g are private information to agent i. i is assumed unknown before the income distribution and such that E 0 [ i ] = 0, A i and i being independent and identically distributed (i.i.d) across agents. In other words, when deciding his work e¤ort, an individual knows its return but can not know if he will be lucky or not. After the income distribution, i is assumed to be private information to agent i. We then associate any market income distribution at date t with a distribution perceived as fair by the population and with an optimal linear redistributive tax rate f 2 [0; 1] that would allow implementing the fair income distribution. In [START_REF] Alesina | Fairness and redistribution : US versus Europe[END_REF], this level of redistribution is obtained endogenously and is at the basis of the multiplicity of equilibria. In contrast, for the clarity of our purposes, we will consider …rst that the level of redistribution perceived as fair is exogenous and unanimously shared in the population. We will investigate the limits of these assumptions in section 4. We then consider an extended version of the Bolton-Ockenfels model (2000) of distributive preferences in specifying the utility function as follows :

U it = u it ' t f t 2 (2)
where u it denotes the private utility from personal consumption and the work e¤ort, and ' t 0 the strength of the concern for fairness or inequity aversion that we assume was shaped during childhood.

Assuming as in [START_REF] Boldrin | The intergenerational State education and pensions[END_REF] and Docquier et al. ( 2007) that children's consumption is part of their parents'consumption, we then specify the private utility as follows :

u it = c it e 2 it 2 (3)
where c it denotes household consumption (one adult -one child) at date t. The quadratic disutility of e¤ort is for analytical simplicity. At each period t, the government redistributes the income according to a simple …scal scheme characterized by a ‡at-rate tax t and a lumpsum bene…t provided to all adults. Assuming a balanced budget, each adult faces the following budget constraint :

c it = y it (1 t ) + t y t (4)
where y t denotes the mean income at date t.

Oblique socialization

To incorporate social forces into individual behavior, one privileged way is by considering the formation of agents' preferences 9 . Preferences are to some degree socially determined, so that agents internalize preferences that re ‡ect the cultural practices of the society that they inhabit. Through oblique socialization, young individuals internalize, by imitation and learning, preferences that will in ‡uence their behavior when they become adults, which will explain the persistence of the cultural practices.

Assume then that the distributive preferences of an individual youth at date t 1 are in ‡uenced by the observation of the social environment and its degree of fairness. Denoting by t 1 the e¤ective level of taxation at date t 1 while f is the level perceived as fair, we can characterize the social environment by the social distance to distributive justice

S t 1 = f t 1 2 (5)
The higher S t 1 , the more unfair the redistributive system perceived by the population. As the e¤ective level of taxation t 1 results from a collective choice of the adults at date t 1 through voting, a signi…cant S t 1 reveals a low weight attached to the moral norm adherence and a failure in implementing fair taxation. This low weight is therefore transmitted to the young generation through observation and imitation. Having been exposed to unfairness during youth reduces the concern for fairness. Denoting ' t = (S t 1 ), we will then assume in the following that 0 0. Our mechanism is closely related to that of [START_REF] Lindbeck | Social norms and economic incentives in the welfare state[END_REF] and [START_REF] Funk | Governemental action, social norms and criminal behavior[END_REF],

where the disutility of deviating from the norm is non-increasing in the fraction of deviators.

However, in our setting the choice is not a binary choice between working full-time or living o¤ bene…ts, as in [START_REF] Lindbeck | Social norms and economic incentives in the welfare state[END_REF], or following the law or committing a crime, as in Funk In light of these preferences, in the following section we study the resulting individual demands for redistribution and the policy that will be implemented in a democracy.

Redistributive policies in democracies

The economy is populated by a continuum of mass 1 of individuals at each generation endowed with utilities (2) and characterized by their speci…c e¤ort e it , their speci…c talent A i and their speci…c luck i . As already mentioned, A i and i are i.i.d across agents. The optimal e¤ort resulting from the maximization of the expected utility E 0t [U it ] is as follows :

e it = A i (1 t ) (6)
As redistribution lowers the market return to e¤ort, it reduces the e¤ort. In addition, as the return to e¤ort grows with ability, more talented individuals work harder. Considering eq. ( 6), the pre-tax income (1) of an adult at date t can be rewritten as :

y it = a i (1 t ) + i (7)
where

a i = A 2 i .
As the level of e¤ort is reduced by redistribution, obviously the pre-tax income is also reduced.

The individual demands for redistribution

Consistently with our behavioral assumptions, an adult at date t will support the level of redistribution that maximizes his utility. Assuming that the vote occurs at the beginning of the period allows the person to take into account the distortive e¤ect of redistribution on work e¤ort and then on income. Accordingly, considering that he can fully anticipate his future e¤ort choice as a function of the tax rate, the expected utility (before knowing his particular luck) de…ned by eqs. ( 2) and (3) can be written, using eqs. ( 4), ( 6) and ( 7), as :

E 0t [U it j e it ( t )] = a i (1 t ) 2 2 + t a (1 t ) ' t f t 2 (8)
where a denotes the mean a i . De…ning the demand for redistribution of an individual as the level of taxation that maximizes his utility (8) leads then to the following …rst order condition

a i (1 t ) + a (1 t ) t a + 2' t f t
= 0. Therefore, as long as the second order condition a i 2 a 2' t 0 is satis…ed, knowing that ' t = (S t 1 ), individual demands for redistribution at date t can be expressed as :

it = 8 > < > : a a i +2 (S t 1 ) f 2 a a i +2 (S t 1 ) 0 if a i a 2 (S t 1 ) f t otherwise (9)
Considering the second order condition, assuming max i fa i g 2 a is then a su¢ cient condition so that preferences are single-peaked in t .

Individual demands for redistribution as speci…ed in eq. ( 9) decrease with personal income, @ it @a i 0, and increase with the level of redistribution perceived as fair, @ it @ f 0. By exhibiting both sel…sh and fair motives, eq. ( 9) is consistent with empirical surveys [START_REF] Fong | Social preferences, self-interest, and the demand for redistribution[END_REF] Eq. ( 9) also re ‡ects the fact that adults'demands for redistribution at date t are a¤ected by the cultural environment in which they have grown up. More speci…cally, if the level of redistribution perceived as fair by an individual of type i is higher than the level of redistribution he would have chosen under the sel…sh motive, then the degree of unfairness in the environment when young will lower his demand for redistribution :

f a a i 2 a a i max i fa i g 2 a , @ it @S t 1 0.
Denote by a;t the demand for redistribution of an individual of talent a at date t, and s a inf = a a inf 2 a a inf the level of redistribution chosen under the sel…sh motive by the least talented individuals as a inf 0, s a inf 1 2 . It then follows from eq. ( 9) that :

Proposition 1 f s a inf and t 1 f yields @ a;t @ t 1 0 8a ( 2 a).
Following would mean that less able immigrants, those whose levels of redistribution sel…shly preferred are above the fair level, from countries with a preference for greater redistribution would tend to support fewer redistribution compared to native individuals with the same talent. Indeed, as they have been exposed to less unfairness during their youth, their concern for fairness is stronger and they promote the fair level of redistribution that is less than the one sel…shly preferred. Assuming f s a inf and t 1 f is also consistent with the …ndings of [START_REF] Corneo | Inequality and the State : Comparing US and German preferences[END_REF]. Individuals in high-redistributive countries such as former West Germany exhibit a greater concern for fairness than individuals in low-redistributive countries such as the United States.

Two assumptions that have been made to obtain these results deserve attention. First, we assume that adult individuals vote on income redistribution in the beginning of the period, before deciding on their e¤ort. Otherwise, i.e. if individuals do not take into account the distortive e¤ect of redistribution on their work, it is well known that the sel…sh poorer-than-average individual (y it y t ) supports a full income redistribution because he anticipates earning more from redistribution ( t y t ) than he contributes ( t y it ). If the same poorer-than-average individual is purely fair (' t ! +1), he supports the taxation rate f . In that case, it is easy to show that, still assuming t 1 f (< 1), the result turns out to be in contradiction with empirical evidence for a signi…cant part of the population : @ y it y t ;t @ t 1 0. Second, unlike in our assumption, if individuals could have known from the beginning whether they will be lucky or not, a lucky individual, by being wealthier, would have supported less redistribution. From this perspective, our assumption does not alter the qualitative result at the individual level while making the analysis at the collective level easier.

The majority rule

We now assume that, in a democracy, any policy to be implemented must be supported by a majority 10 . In our model, under the su¢ cient condition max i fa i g 2 a, preferences are single-peaked in t . Thus the median-voter theorem applies. It follows from eq. ( 9) that the tax rate selected under majority rule can be expressed as 11 t = a am+2 (S t 1 ) f 2 a am+2 (S t 1 ) , where a m denotes the median a i . Denote by = a a m an aggregate index of income inequality 12 , and normalize a m = 2 (without loss of generality). Assuming that the distribution of (squared) talents a i is skewed to the right yields 0 (so that the median income is lower than the average income as observed). Denote by s = 2(1+ ) the tax rate selected under majority rule if individuals were driven only by their self-interest, i.e. if ' t = 0. This sel…sh tax rate exhibits the standard Meltzer-Richard e¤ect : as income inequality rises, the median voter is poorer compared with the average, and then supports greater redistribution : d s d 0. However, as noted in the introduction, income inequality is a poor predictor of redistributive policies. Di¤erently, with fair motives, the dynamics of redistribution under majority rule can be expressed as a convex combination of the purely interested and the purely intuitively fair tax rates such that :

t+1 = t s + (1 t ) f ( 10
)
where t = 1+ 1+ + (St) 2 [0; 1), 0 0 and 0 = 1+ 1+ + [ f 0] 2
given. t provides a measure of the proximity of the redistributive tax to the purely interested level (relatively to the purely fair level). From that perspective, it is worth noting that the proximity of the redistributive tax 10 As put forward by [START_REF] Corneo | Democratic redistribution and rule of the majority[END_REF], democracies implement to a large degree the level of redistribution demanded by the median voter. 11 We implicitly assume that an immigrant of the …rst generation cannot vote in his new country.

to the purely interested level increases as income inequality increases, @ t @ > 0, and decreases as the concern for fairness increases, @ t @ < 0. Assuming s < f then yields :

Proposition 2 If ' = (S) is su¢ ciently high when approaches f and su¢ ciently low when approaches s , there exist multiple stable stationary states SS 2 s ; f .

To explain this result, note that using eq. ( 5) we can rede…ne eq. ( 10) as t+1 = ( t ), where ( t )

1+ 1+ + [ f t ] 2 s + 1 1+ 1+ + [ f t ] 2 f 2 s ; f , 0 = 0 0 given,
and 0 0 as long as t f . Stationary states, de…ned by = ( ), then lie necessarily between the sel…sh and fair tax rates : 2 s ; f . In addition, stable stationary states are the ones where the graph of cuts the main diagonal from above, and unstable ones are those where it cuts it from below. Knowing that s ( s ) and f > f yields that there exits at least one stable stationary state SS 2 s ; f . As exhibited in eq. ( 10), such a stable stationary state is as close to the fair tax rate as the concern for fairness ' is high. Reciprocally, by assuming that being exposed to unfairness during youth reduces the concern for fairness, the mechanism we are exploring states also that the concern for fairness increases as the tax rate becomes fairer :

' = f 2
where 0 0. Therefore, if lim

! f ; < f f 2
is su¢ ciently high, there exists a stable stationary state close to the fair taxation. At the limit lim

! f ; < f f 2 = +1, it can be shown that SS ! f SS < f . Reasoning
similarly, it is obvious that a stable stationary state is as close to the sel…sh tax rate as the concern for fairness ' is low. If ' = 0, the unique stable stationary state is characterized by

SS = s . Therefore, if lim ! s+ f 2
is su¢ ciently low, there exists a stable stationary state close to the sel…sh taxation. Accordingly, if both lim

! f ; < f f 2
and lim ! s+ f 2 are respectively su¢ ciently high and low, there exist at least two stable stationary states. Indeed, as the graph of crosses the diagonal an odd number of times which may be greater than 3, the number of stable stationary states may be greater than 2 (we do not consider here the non-generic case of uncountable many crossings).

τ t τ t+1 ¿ f ¿ f ¿ s ¿ U S ¿ EU ¿ s ¿ τ t+1 ¿ f ¿ f ¿ s ¿ U S ¿ EU ¿ s ¿ ¿ EU 0 ¿ U S 0 ® > ® ¯> ® > ® ¯> ^® < ® and 0 < ¯<

-Multiplicity and history dependence of redistribution

If we want to restrict our attention to the case with only two stable stationary states, we need to assume, in addition, if is of class C 2 , that the equation 0 ( ) = 1 has two roots in s ; f . Take for example the following function (S) = +S , where and are two strictly positive parameters. As is obvious, the concern for fairness ' =

+[ f ] 2 is high
= ~ 13 ,
where ~ is the unstable stationary state, we can then verify that the dynamics of redistribution is history-dependent if both ^ and ^ (Fig. 1).

As illustrated in Figure 1, if at date t = 0 people are socialized in an environment where practices and institutions are close to but su¢ ciently lower than what is perceived as fair, 0 = EU 0 2 ~ ; EU , then the level of taxation increases at date t = 1, 1 > 0 , such that the perceived unfairness of the institutions decreases, f

1 2 < f 0 2
. The generation that is young at date t = 1 is socialized in an environment that is closer to the fair institution than was the previous generation. Hence, by being exposed to less unfairness, their concern for fairness increases and they will support an institution that will be closer to fairness at date t = 2.

This cultural transmission process ends with the implementation of the high redistribution level characterized by the tax rate EU . The redistributive institution and the concern for fairness coevolve and are self-reinforcing such that lim t!+1 t = EU and lim t!+1

' t 1 = '. On the other hand, if the initial taxation is too far from what is perceived as fair such that 0 = U S 0 2 U S ; ~ , the process is reversed and the concern for fairness as well as the level of redistribution decrease with time to stabilize towards their low levels lim

t!+1 t = U S < f and lim t!+1 ' t 1 = ' < '.
If the conditions for the existence of multiple stationary states are satis…ed, persistent differences in redistribution can exist over long periods, as they are linked to di¤erent preferences for redistribution that are sustained by a process of cultural transmission. As underlined in Proposition 1, if the level of redistribution chosen under the sel…sh motive by the least talented individuals is lower than the level perceived as fair, f s a inf , this may explain why immigrants from countries with a preference for greater redistribution continue to support higher redistribution in their destination country. In addition, as a high level of redistribution lowers the level of e¤ort in the economy, a high-redistribution country is characterized by a lower level of income inequality. Our model then also provides a rationale for the negative correlation between income inequality and redistribution that is encountered in the data.

Note importantly that all our results have been obtained while assuming exogenous, contextindependent and unanimously shared levels of redistribution that are perceived as fair. However, as the level of e¤ort decreases with redistribution, as shown by [START_REF] Alesina | Fairness and redistribution : US versus Europe[END_REF], the importance of luck in the income determination increases, and we should observe a level of redistribution perceived as fair that is lower in the low-redistribution stationary state than in the high-redistribution state. This suggests that the the fair level of redistribution depends on the perception of the economic environment that is in ‡uenced by the level of taxation. In addition, due in particular to di¤erent concepts of distributive justice, it is likely that individuals with similar information about the market outcomes will have di¤erent perceptions of the just level of redistribution in the country. In the next section, we investigate whether incorporating endogenous and heterogenous perceptions at the country level (ex post) and at the individual level (ex ante) …ts with our mechanism of cultural transmission so as to explain the di¤erences in redistribution observed between Europe and the United States.

Extensions

Endogenous perceptions

To characterize the level of redistribution that would be perceived as socially optimal, studies show that individual merit is an important principle at both the individual and aggregate levels.

As shown by Alesina, Glaeser and Sacerdote (2001) for example, the belief that luck rather than e¤ort determines income is a strong predictor of the national level of redistribution. Accordingly, by reducing the relative importance of luck in the income determination, more e¤ort should lead to the perception of an income distribution whose unfairness requires a lower level of redistribution. From that perspective, as redistribution lowers the market return to e¤ort and reduces e¤ort as speci…ed in eq. 6, one would then expect that the level of redistribution perceived as fair under the merit principle increases with the redistributive tax to be such that

f t T f ( t ), where dT f d 0, T f (0) > 0 and T f (1) 1.
However, having endogenous rather than exogenous perceptions does not call into question the capacity of our mechanism to generate multiple stable stationary states. On the one hand, following Proposition 2, if the concern for fairness ' = T f ( ) 2 is su¢ ciently low when the redistributive institution approaches the sel…sh level s , there still exists a stable Having endogenous rather than exogenous perceptions implies that the higher the level of redistribution, the higher the level of redistribution perceived as fair. If the model exhibits two stable stationary states U S < EU , it then yields T f U S < T f EU . As a consequence, if the level of redistribution sel…shly preferred by the least talented individuals is lower than the level of redistribution perceived as fair in the low-redistribution country T f U S s a inf so that Proposition 1 holds, endogenous perceptions also yield that, compared with the previous section with identical and exogenous perceptions of the fair level of redistribution, an individual socialized when young in a high-redistribution country will support less redistribution if he moves as an adult to a low-redistribution country (because the perceived inequity in the income distribution appears lower), while still supporting a higher redistribution in his destination country than do the natives.

a) T f (¿ ) linear τ t τ t+1 ¿ f T f (¿ t ) ¿ s ¿ U S ¿ EU ¿ s ¿ b) T f (¿ ) nonlinear τ t τ t+1 ¿ s ¿ U S ¿ G ¿ s • ¿ T f (¿ t ) ¿ f inf τ t+1 ¿ f sup ¿ F
Note that nonlinearities in the relationship between the level of redistribution perceived as fair and the tax rate may increase the numbers of stable stationary states. This is most obvious (but not necessary) if the equation = T f ( ) exhibits multiple roots ^ f j . Indeed, if the concern for fairness ' = T f ( )

2
is su¢ ciently high when the level of unfairness associated with the redistributive institution measured by T f ( ) 2 approaches zero, there exists a stationary state close to each root ^ f j . As illustrated in Figure 2b in which the level of redistribution perceived as fair under the individual merit principle is de…ned as of GDP at the same date), this nonlinear case does not challenge our mechanism explaining why individuals in high-redistribution countries exhibit a greater concern for fairness than individuals in low-redistribution countries. Indeed, we can see in Figure 2b that the countries characterized by the high levels of redistribution G and F have a quite similar small distance between their e¤ective taxation and the fair one,

T f ( ) = 8 > < > : ^ f inf ^ f sup if otherwise , where s < ^ f inf < < ^ f
T f G G 2 T f F F 2 ,
where the distance T f ( ) 2 re ‡ects the observed unfairness of the redistributive institution. To that extent, the redistributive institution characterized by the low level U S appears less fair,

T f U S U S 2 > T f G G 2 .
In terms of our mechanism based on oblique socialization that states that being exposed to unfairness during youth reduces the concern for fairness, it means that the concern for fairness is lower in the low-redistribution country than in the high-redistribution countries :

' U S < ' 2f G ; F g .
Note also that nonlinearities in the relationship between the level of redistribution perceived as fair and the tax rate can generate multiple stationary states without our oblique socialization e¤ect. For example, following eq. ( 10), there may exist two stationary states U S = s +

(1 ) ^ f inf and EU = s + (1 ) ^ f sup , where = 1+ 1+ +' , if U S < EU . However, in such a speci…cation, it is the endogeneity of the fair tax perception that leads to multiplicity, which is not the case of our mechanism as underlined by the exogenous or linear cases. In addition, without our oblique socialization e¤ect, individuals in high-redistributive countries do not exhibit a greater concern for fairness than do individuals in low-redistributive countries.

From these perspectives, our mechanism appears clearly di¤erent from the one proposed by [START_REF] Alesina | Fairness and redistribution : US versus Europe[END_REF] based on the endogeneity of the fair tax 14 .

Heterogenous perceptions

If individual merit appears to be an important principle to characterize the level of redistribution that would be perceived as socially optimal, its content may give rise to interpretation and then be perceived di¤erently from one individual to another. Certainly, e¤ort and hard work are associated with individual merit. Certainly, luck is seen as a unfair component of income. However, as noted by [START_REF] Schokkaert | Preferences for redistribution and social structure[END_REF], income di¤erences caused by ability or talent may be seen more or less fair according to whether talent is perceived as re ‡ecting former investments in human capital or as innate and then beyond an individual's control. This ambiguity is revealed by several studies whose …ndings are contradictory. For example, Fong 14 Abstracting from expectations, the tax level perceived socially as fair in Alesina and Angeletos (2005) is de…ned as

T f ( ) = arg min 0 2[0;1] R i u d i u f i 2 di , where u f i = A i e i ( ) ei( ) 2 2
denotes the level of utility perceived as fair for an adult of type i, and

u d i = [A i e i ( ) + i ] (1 0 ) + 0 A i e ( ) ei( ) 2 2
the e¤ective level of utility after redistribution. This then yields T f ( ) =

2 2 +(1 ) 2 2 a
, where2 and 2 a denote respectively the variance of and a. If asuming (2001) and [START_REF] Corneo | Individual preferences for political redistribution[END_REF] show on American data that individuals who think that income is determined by luck rather than individual e¤ort and ability are more favorable to redistribution. In the same line, [START_REF] Rustichini | Merit and Justice : An expirimental analysis of attitude to inequality[END_REF] show in the lab that merit is attributed only if e¤ort or ability a¤ect the outcome. By contrast, Isaksson and Lindskog (2009) show that in Denmark individuals who believe that people get rewarded for their ability and talent are more favorable to redistribution. These contradictory …ndings may suggest that the deservingness of income related to talent or ability can be perceived di¤erently across individuals and across societies.

In addition, individual merit cannot sum up all the principles of distributive justice (see [START_REF] Konow | Which is the fairest one of all ? A positive analysis of justice theories[END_REF], for an overview). [START_REF] Forsé | Justice distributive : la hiérachie des principes selon les européens[END_REF] show for example that European countries share an identical hierarchy of moral principles : …rst, the guarantee of basic needs ; second, merit ; and less important, equality of income. Besides, Durante et al. (2014) show that social concerns with respect to redistribution include both the concern for fairness and a dislike of ine¢ ciency that can be associated with the "greatest aggregate happiness", i.e. the utilitarian concept of social justice most closely associated with Bentham (see [START_REF] Konow | Which is the fairest one of all ? A positive analysis of justice theories[END_REF].

These …ndings suggest that the principle characterized by "everyone should get what they deserve" can con ‡ict with other moral concepts in de…ning a socially just redistribution 15 .

To the extent that the content of merit may be perceived di¤erently from one individual to another and that di¤erent concepts of distributive justice may lead to the de…nition of di¤erent socially just levels of redistribution, it is likely that individuals with similar information about the market outcomes will have di¤erent perceptions of the just level of redistribution in the country. Accordingly, escaping from the assumption that the perception of the fair redistributive tax is unanimously shared in the population, assume that di¤erent perceptions may exist across individuals 16 . More speci…cally, abstracting from the endogeneity of perceptions (see section 4.1), assume that f i is i.i.d across individuals, i.e. that each individual is associated with a perception f i irrespective of his own income 17 . The social distance between the perceived social optimal tax rate and the chosen one at date t,

S t = R i h f i t i 2
di, can then be expressed as :

S t = 2 f + f t 2 (11)
where f and 2 f denote respectively the mean and the variance of f i . 2 f provides a measure of the degree of collective agreement to de…ne f as the norm of fair redistribution. If 2 f = 0, the perception of f as the fair redistribution is unanimously shared in the society. This is the case studied in section 3. By contrast, if 2 f is high, f is of low signi…cance in the population for de…ning a shared norm of fair level of redistribution. Therefore, everything else being equal, the social distance between the perceived social optimal tax rate grows with the variance of f i .

How does it impact our results ? If the distributions of a i and f i are both symmetrical, the pivotal voter is the individual with the mean talent a and the mean perception f (see Di Tella and Dubra, 2013). The dynamics of redistribution is then written exactly as in eq. ( 10), except that s = 0 18 and that the fair level of redistribution previously shared unanimously is replaced by its mean f . Following Proposition 2, the guarantee to obtain multiple stable stationary states requires then that the concern for fairness be su¢ ciently high when the redistributive institution approaches the level re ‡ecting the collective norm of fairness f . Therefore, as the diversity of perceptions measured by 2 f increases the social distance to distributive justice and then lowers the concern for fairness, a too high 2 f may prevent the existence of multiple stable stationary states 19 . The existence of multiple stationary states driven by our mechanism does 16 In our setting all voters are equally concerned for others. Therefore, the heterogeneity we examine is di¤erent from the one in Dhami and al-Nowaihi (2010) in which a mixture of fair and sel…sh voters is considered. 17 Supporting this assumption, [START_REF] Piketty | Attitudes vis-à-vis des inégalités en France : existerait-il un consensus ?[END_REF] has shown on French data that on average low-income and high-income individuals have similar socially-optimal levels of income inequality. 18 In that case, s = 0 and the model can no longer exhibit the Meltzer-Richard e¤ect.

not rely on the assumption that the perception of the fair redistributive tax is unanimously shared in the population, i.e. 2 f = 0, even if the degree of collective agreement to de…ne f as the norm of fairness must be high enough.

Note that if f i 2 [0; 1], we can no longer assert that coming from a high-redistribution country is a su¢ cient condition to support a higher redistribution. In particular, if we consider an individual of type a i ; f i = 0 , the more intense the person's concern for distributive justice, the lower the support for redistribution. However, after controlling for observable individual characteristics, only types a i ; f are considered. Therefore, we only need to assume that, on average, the level of redistribution perceived as fair is greater than the level of redistribution sel-…shly preferred by the least talented individuals, f s a inf , to be consistent with the empirical literature.

Conclusion

If it is accepted that humans are driven solely by self-interest, [START_REF] Meltzer | A rational theory of the size of government[END_REF] show that the level of redistribution in a democratic society is increased by inequality in the income distribution. However, this result has only weak support in the data. In this paper, we argue that the failure of the canonical model is due in part to its behavioral assumptions.

Departing from traditional economics, empirical studies and individual surveys show that individuals do care about fairness in their demand for redistribution. These studies also show that the cultural environment in which individuals grow up a¤ects their preferences about redistribution. We include these two components of the demand for redistribution in order to propose a mechanism for the cultural transmission of the concern for fairness. The preferences of the young are partially shaped through observation and imitation of others'choices in a way that is consistent with oblique socialization. More speci…cally, observing during childhood how adults the model exhibits two stable stationary states U S and EU such that s (= 0) < U S < EU < f only if

2 f ^ .
have collectively failed to implement fair redistributive policies lowers the concern for fairness when adult or the moral cost of not supporting a fair taxation. Based on this mechanism, and assuming that the perception of the fair level of taxation is exogenous and unanimously shared in the population, the model exhibits a multiplicity of history-dependent stationary states that may account for the huge and persistent di¤erences in redistribution observed between Europe and the United States. It also explains why immigrants from countries with a high preference for redistribution continue to support higher redistribution in their destination country. These results have been shown to be robust for extended speci…cations of the perception of the fair level of taxation, in particular if they are heterogenous across individuals.

In the speci…cations that we have used, we have …rst considered childhood only as a passive period during which individuals are socialized and internalize cultural practices. However, childhood is also a crucial period during which individuals can actively invest in their human capital through e¤ort at school. Knowing that e¤ort at school depends on the expected return, which is negatively impacted by the future level of redistribution, introducing education explicitly in our model would result in a dynamic of redistribution that is driven not only by history but also by expectations. Second, we have considered socialization only through passive observation and imitation of the society at large (oblique socialization), and not through active e¤orts of the parents to transmit their values (vertical socialization). As mentioned in the introduction, by assuming highly homogenous values at the regional level in most of the article, oblique socialization is highly e¢ cient so that parents have few incentives to transmit their values. However, in the last subsection 4.

Proposition 2

In the text.

Appendix B. The case with (S) = +S Let us de…ne (S) = +S and t = f t the di¤erence between the mean fair and the e¤ective level of taxation. Assuming …rst that = 0, the dynamics of redistribution expressed by eq. ( 10) can be rewritten as :

t+1 = 1 + 1 + + 2 t f s ( 12
)
and stationarity is then de…ned by :

3 f s 2 + 1 + = 0 (13) If ( f s ) 2 1+
4 , eq. ( 13) exhibits three real roots 1 = 0, 2 = f s + q ( f s ) 2 .

In addition, as ,

H > L .
Besides, the dynamic process exhibits only one stationary state L if is large enough such that lim

!+1 = 1 , lim !+1 L = s .
As @ @ > 0 and lim

! f = 0, it follows that if ( f s ) 2 1+ 4
there exists ^ > 0 such that if 0 < ^ the model exhibits two stable stationary states U S and EU , where s < U S < EU < f . De…ning the dynamics as t+1 = ( t ), ^ can be characterized by lim was an exogenous fair level of redistribution unanimously shared in the population. Therefore, it goes straightforwardly that the dynamics of redistribution can be expressed according to eq. ( 10) as t+1 = t s + 1 t ^ f , where t = 1+ 1+ + (St) 2 [0; 1), 0 = 0 0 given,

(S t ) = f ^ f 2 (S t ).
Knowing that S t = T f ( t )

t 2 = f ^ f 2 ^ f t 2
, if (S) = +S , it follows that

(S t ) = +S , where = ^ f f 2
. Accordingly, we deduce from Appendix B that if 0 < ^ then there exists ^ > 0 such that if 0 < ^ the model exhibits two stable stationary states U S and EU , where s < U S < EU < ^ f , as illustrated in Fig. 2a.

The nonlinear case

De…ne (S) = +S and assume that f = ^ f j . It follows (see Appendix B) that if 0 < ^ j , where ^ j = 1+ Consider now that perceptions are de…ned as T f ( ) = 8 > < > :

^ f inf ^ f sup if otherwise , where s < ^ f inf < < ^ f sup 1.
Therefore, if is low enough and low enough (such that is high enough), there are four potential stable stationary states that are U S inf , U S sup , EU inf and EU sup .

However, we deduce from

@ lim !0; >0 U S j @^ f j = 1 2 1 ^ f j s q (^ f j s ) 2 4 1+
< 0 ^ f j > s that, if is low enough, then U S sup < U S inf < ^ f inf < : U S sup cannot be a stationary states associated with the fair level of redistribution ^ f sup . Therefore, as illustrated in Figure 2b, if is low enough and low enough (such that is high enough), the model exhibits three stable stationary states U S = U S inf , G = EU inf and F = EU sup where s < U S < G < ^ f inf < F < ^ f sup . Note that the observed levels of unfairness in the two high-redistribution countries are as follows :

lim !0; >0 ^ f inf G 2 = lim !0; >0 ^ f sup F 2 = 0.

  et al. (1999) the individual guilt and social stigma linked to living on bene…ts decreases with the number of bene…ciaries in the society. In contrast with Funk (2005) and Lindbeck et al.

(

  2005). Therefore, to determine the deviation from the moral norm we replace the fraction of deviators by the distance between the collective choice and the norm. In addition, in our model, to characterize the socialization process, the impact on preferences of deviating from the norm applies with a delay of one generation. The moral cost of not supporting fair taxation is reduced when observing how the previous generation has collectively failed to implement a fair institution. Note that, contrary to Bisin and Verdier (2001) and[START_REF] Bénabou | Belief in a just world and redistributive politics[END_REF], the intergenerational cultural transmision mechanism that we underline occurs through passive observation and imitation of society at large, not through active e¤orts of the parents to transmit values. As highlighted by the empirical …ndings of[START_REF] Dohmen | The intergenerational transmission of risk and trust attitudes[END_REF], those two aspects of the cultural transmission process are relevant in in ‡uencing child attitudes.

Fig.

  Fig.

Fig. 2 - 2 .

 22 Fig. 2 -Multiplicity and endogenous perceptions

sup 1 ,

 1 and (S) = +S , if is low enough and high enough the model now exhibits three stable stationary states U S < G < F (see Appendix C). However, if one considers that G and F characterize the high levels of redistribution observed in Western Europe (for example public social spending amounts to 31:5% and 25:3% of GDP respectively in France and Germany in 2016 ; OECD 2017) and U S the low level observed in the United states (public social spending amounts to 19.3%

2 '

 2 t allows us to rewrite utility asU it = u it ' t ^ f t 2 , i.e. as if ^ f

4 ^ f j s 2 ,

 42 then there exists ^ > 0 such that if 0 < ^ the model exhibits two stable stationary states U

  Indeed, consider two representative individuals of talent a who have grown up at date t 1 in two di¤erent countries D and F characterized by D , everything else being equal. In that case, according to Proposition 1 we will observe

				t 1
	F t 1 f F;D a;t	D;D a;t , where x;z a;t is the demand for redistribution of an adult of talent a at date t
	living in country z and having grown up in country x. From this perspective, if assuming
	f	s a inf and t 1	f , the demands for redistribution as expressed in eq. (9) are consistent
	with the empirical …ndings of Guiso et al. (2006), Alesina and Giuliano (2011) and Luttmer
	and Singhal (2011). Di¤erently, assuming f < s a inf	while t 1	f t 1

Proposition 1

, if the fair level of redistribution is higher than the level sel…shly preferred for all individuals f s a inf and if the level of redistribution observed when young is lower than the fair level t 1 f , the speci…c e¤ect of being an immigrant coming from a high redistribution country is then to support greater redistribution compared to native individuals with the same talent a.

  2, we have stressed that individuals could use di¤erent concepts of distributive justice to de…ne their fair level of redistribution. From these perspectives, incorporating both investment in human capital and vertical socialization in the present analysis appears to be a promising avenue for further research.

								if a a 2 (S t 1 ) f
							0		otherwise
	Accordingly, as S t 1 = f	t 1	2 (eq. 5), it yields :
	@ a;t @ t 1	=	8 > < > :	4 0 (2 a a)	f (2 a a+2 (S t 1 )) 2 a a 2 a a 0	f	t 1	if a a 2 (S t 1 ) f otherwise
	As f	s a inf yields f	a a 2 a a 8 (a

inf ) a 2 a, it follows that if f s a inf and t 1 f , @ a;t @ t 1 0 8 (a inf ) a 2 a.

  which are = 1 and = 2 , where s = 2(1+ ) and = a a m . In addition, if 0 6 = 3 , as long as j 0 j <

						"	#
	"	1+ 1+ + 2 t	f	#	s is continuous and monotonous in 2 t , as	@	1+ 1+ + 2 t @ 2 ( f s ) t
	0, and as lim 2 t !0 characterized by d t+1 @ 1+ 1+ + 2 t @ 2 ( f s ) t d t 1 f = 0, if ( f s ) 2 s q ( f s ) 1+ 4 , there exist two stable stationary states 2 4 1+ 2 , lim t!1 t = 1 , otherwise lim t!1 t = 2 .
	Equivalently, as t = f 0 2 f 3 ; f + 3 then H = lim t , we can assert that assuming ( f s ) 2 t!1 t = f , otherwise L = lim t!1 t = 1 1+ 4 , 0 6 = ^ = f 2 f + s q ( f	3 , if s ) 2	4 1+

In the evolutionary literature, learning from others by imitation is a cheap and e¢ cient way to acquire locally relevant information for adaptation. Accordingly, the propensities to learn and to imitate are part of an evolved psychology shaped by natural selection[START_REF] Boyd | Culture and the evolutionary process[END_REF][START_REF] Boyd | The cultural niche : Why social learning is essential for human adaptation[END_REF].

[START_REF] Algan | Civic virtue and labor market institutions[END_REF] and[START_REF] Alesina | Family values and the regulation of labor[END_REF] investigate the relationship between the labor market institutions and respectively the civic virtue and the family values.

See Postlewaite (2011) for an overview of the di¤erent approaches in the economic literature linking individual behaviors and social environment.

In the empirical literature investigating the link between redistribution and income inequality, the Gini coe¢ cient or the interdecile ratios are often favored to measure income inequality.

If considering that 0 is continuously distributed over [0; 1] or 0; f , the event 0 = ~ has a probability of zero.

a 1 4 , equation = T f ( ) exhibits two or three roots and their model can have two stable stationary states if ' is large enough.

In recent years, a great deal of literature has showed experimentally for example that con ‡icts between deontological principles (considering that the right to get what one deserves is a principle that should be applied to everyone belongs to a deontological conception of justice) and utilitarianism are a general feature of moral thinking (see[START_REF] Greene | The secret joke of Kant's soul[END_REF][START_REF] Sinnott-Armstrong | Abstract+concrete=paradox[END_REF][START_REF] Cushman | The psychology of dilemmas and the philosophy of morality[END_REF].

For example, if (S) = +S , it yields straightforwardly from the proof in Appendix B that, if 0 < ^ ,

Proposition 1

From eq. ( 9) it follows that the preferred tax rate of an individual of talent a is as follows :

a a+2 (S t 1 ) f 2 a a+2 (S t 1 )

Appendix C. Endogenous perceptions

The linear case

In that case, utility [START_REF] Ackert | Social preferences and tax policy design : some experimental evidence[END_REF] becomes

ABOUT OFCE

The Paris-based Observatoire français des conjonctures économiques (OFCE), or French Economic Observatory is an independent and publicly-funded centre whose activities focus on economic research, forecasting and the evaluation of public policy.

Its 1981 founding charter established it as part of the French Fondation nationale des sciences politiques (Sciences Po), and gave it the mission is to "ensure that the fruits of scientific rigour and academic independence serve the public debate about the economy". The OFCE fulfils this mission by conducting theoretical and empirical studies, taking part in international scientific networks, and assuring a regular presence in the media through close cooperation with the French and European public authorities. The work of the OFCE covers most fields of economic analysis, from macroeconomics, growth, social welfare programmes, taxation and employment policy to sustainable development, competition, innovation and regulatory affairs..

ABOUT SCIENCES PO

Sciences Po is an institution of higher education and research in the humanities and social sciences. Its work in law, economics, history, political science and sociology is pursued through ten research units and several crosscutting programmes. Its research community includes over two hundred twenty members and three hundred fifty PhD candidates. Recognized internationally, their work covers a wide range of topics including education, democracies, urban development, globalization and public health. One of Sciences Po's key objectives is to make a significant contribution to methodological, epistemological and theoretical advances in the humanities and social sciences. Sciences Po's mission is also to share the results of its research with the international research community, students, and more broadly, society as a whole.

PARTNERSHIP