Guilt aversion and redistributive politics: A moral intuitionist approach

Le Garrec, Gilles Working Paper Guilt aversion and redistributive politics: A moral intuitionist approach Economics Discussion Papers, No. 2013-53 Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Le Garrec, Gilles (2013) : Guilt aversion and redistributive politics: A moral intuitionist approach, Economics Discussion Papers, No. 2013-53, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: https://hdl.handle.net/10419/83640 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Licensed under the Creative Commons License - Attribution 3.0 Discussion Paper No. 2013-53 | October 07, 2013 | http://www.economics-ejournal.org/economics/discussionpapers/2013-53 Guilt Aversion and Redistributive Politics: A Moral Intuitionist Approach Gilles Le Garrec Abstract In mainstream economics individuals are supposed to be driven only by their self-interest. By contrast, surveys clearly show that people do care about fairness in their demand for redistribution. In this article, in the spirit of the "new synthesis" in moral psychology (Haidt, 2007: The new synthesis in moral psychology) the author proposes to modelize the voting behavior over redistribution as the interaction between (a) an automatic cognitive process which quickly generates intuitions on the fair level of redistribution, (b) a rational self-oriented reasoning which controls the feeling of guilt associated with fair intuitions. In addition, considering that guilt aversion depends on the cultural context, the author shows that the model exhibits a multiplicity of history-dependent steady states which may account for the huge difference of redistribution observed between Europe and the United States. Published in Special Issue Economics, Psychology and Choice Theory JEL D03 D64 D72 H53 Keywords Redistribution; voting behavior; fairness; behavioral economics Authors Gilles Le Garrec, OFCE, Center for Economic Research – Sciences Po, 69 quai d Orsay, 75340 Paris, [email protected] Citation Gilles Le Garrec (2013). Guilt Aversion and Redistributive Politics: A Moral Intuitionist Approach. Economics Discussion Papers, No 2013-53, Kiel Institute for the World Economy. http://www.economics-ejournal.org/ economics/discussionpapers/2013-53 1 Introduction In mainstream economics individuals are supposed to be driven only by their self interest. As a consequence, when studying the redistributive phenomenon in democracy, the …rst challenge for most economists is to explain why there is so little redistribution in democracy. Indeed, considering that the idea of democracy is captured by the majority rule, as the median citizen is characterized by an income lower than the average, a majority should support a complete income redistribution to satisfy their self interest. As a canonical answer to this issue, Meltzer and Richard (1981) have shown that sel…sh people have no interest to support a overly high redistribution, even if they are poorer than average, because of a tax disincentive e¤ect that lowers productivity. Their model also implies that we should observe a positive correlation between redistribution and income inequality. However, such a correlation is weakly supported by data. While redistribution is sig- ni…cantly higher and more progressive in (continental) Europe than in the United States, their pre-tax income inequality appear similar (see Table 1). By contrast, Perotti (1996), Moene and Wallerstein (2001), de Mello and Tiongson (2006) and Iversen and Soskice (2006) support that the empirical relationship between income inequality and redistribution is the opposite of the predicted one or is insigni…cant. 2 Countries Pre-tax income inequality (GINI) Public Social Spendings (% GDP) Progressivity Index Sweden 0.37 19.8 1.77 France 0.41 18.3 1.73 Germany 0.43 15.5 1.95 UK 0.41 15.2 1.12 US 0.43 10.6 1.31 Table 1. Income inequality (working age population) and social spending (except Old Age) in 2005 (source: OECD and author’s calculation; the progressivity index gives the decrease in percent of income inequality allowed by a social spending of 1% of GDP). In order to improve the canonical model’s predictions, di¤erent dimensions have been investigated1. From a behavioral perspective, the postulate that individuals are driven only by their self interest has been challenged when studying redistribution (Piketty, 1995, Alesina and Angeletos, 2005, Lind, 2007). It has been challenged …rstly because an impressive number of experimental studies have pointed out that individuals do not behave selfishly in the way supposed in mainstream economics (see Batson, 1991, Fehr and Schmidt, 2006). It has also been challenged because analysis of survey data clearly show that people do care about fairness in their demand for redistribution (Fong, 2001, Corneo and Grüner, 2002, Alesina and La Ferrara, 2005, Corneo and Fong, 2008, Alesina and Giuliano, 2010). In line with such …ndings, Alesina, Glaeser and Sacerdote (2001) therefore show that beliefs according to which luck rather than e¤ort determines income2are strong 1Economic (Bénabou, 2000), political (Roemer 1998, Rodriguez, 2004, Iversen and Soskice, 2006, Petrova, 2008, Campante, 2010) and behavioral (Bénabou and Ok, 2001, Bénabou and Tirole, 2006); see Alesina and Angeletos (2004), Lind (2005) and Campante (2010) for overviews. 2From World Values Survey data, they highlight that 54% of Europeans versus 30% of 3 predictors, unlike income inequality, on the national level of redistribution. As a matter of fact, fairness has a major in‡uence in shaping redistributive politics. If voters care only about the welfare of the population when considering redistribution, Piketty (1995) has shown that international di¤erences in the level of redistribution (when countries share identical economic fundamentals) can be explained by di¤erent beliefs about social mobility sustained by an imperfect learning process. Close to the concept of reciprocal altruism, Lind (2007) considers that voters care about their self interest, and the welfare of the members of their own group, more than the rest of the population. In such a context, he shows that both fractionalization and group antagonism reduce redistribution. In the spirit of Gilens (1999), he then supports that the di¤erence of redistribution between Europe and the United States is sustained by a di¤erence in ethnic fractionalization. In Alesina and Angeletos (2005), voters also care about both their self interest and fairness. In their model, fairness is not de…ned according to a utilitarian social welfare as in Piketty (1995) and Lind (2007), but according to a deontological principle (everyone should receive what he deserves) whose relevance is empirically supported in psychology and sociology when considering income distribution (see Schokkaert, 1998, Forsé and Parodi, 2006). With income depending on both e¤ort and luck, they show that cultural variability of the level of redistribution arises as a multiplicity of equilibria resulting from di¤erent self-ful…lled beliefs. By expecting low redistribution, Americans invest in their human capital and generate conditions for low redistribution by reducing the importance of luck in the income determination. Conversely, by expecting a high redistribution, Europeans invest less in their human capital and will support a high redistribution later. In this article, we consider that voters do care both about fairness (in Americans believe that luck rather than e¤ort determines income. 4 the way of Alesina and Angeletos, 2005) and their self interest. In addition, connected to recent …ndings in neurosciences and cognitive psychology, we also explicitly consider that fair and sel…sh motives are generated by two distinct cognitive processes, named following Kahneman (2003) system 1 and system 2 (see also Camerer et al., 2005, Evans, 2008), whose di¤erent features (see Table 2) are of interest in explaining cultural variability of redistributive politics. First, as argued by Haidt (2001, 2007, 2008; see also Nado et al., 2006), an automatic and domain-speci…c cognitive process3 quickly generates and relates moral intuitions (shaped according to Hauser, 2006, and Mikhail, 2007, by a Universal Moral Grammar - UMG) then emotions such as guilt4. Emotions are then integrated into a self-oriented rational cognitive process (system 2 ; see Table 2) such as human behavior is equally driven by emotions and by the standard economic reasoning (Gray, 2004, Bechara, 2004, Cohen, 2005, Pessoa, 2008). Thereafter, considering in the cultural trend of psychology that guilt aversion is context dependent, we show that the huge di¤erence of redistribution observed between Europe and the United States can be sustained by a multiplicity of steady states. 3As explained by Fehr and Schmidt (2006), "the term automatic in this case refers to a process that does not require conscious and e¤ortfull processing but which can nevertheless be inhibited or controlled." 4Supporting this thesis, a large number of both neuroimaging and neuropsychological studies (Greene et al., 2001, 2004, Berthoz et al., 2002, 2006, Moll et al., 2002, 2005, Decety and Chaminade, 2003, Hsu et al., 2008; Damasio, 1994, Anderson et al., 1999, Blair, 2001, Koenigs and Tranel, 2007; see Greene, 2005, Young and Koenigs, 2007 for reviews) show that fair behaviors are associated with brain areas involved in emotional processing (amygdala, insula, ...). 5 system 1 system 2 A¤ective Analytic Automatic Controlled Fast Slow Domain speci…c Domain general Contextualized Abstract Evolutionary rationality Individual rationality Table 2. Main attributes associated with dual-process decision-making. The rest of the paper is organized as follows. In section 2, we present basic decisions such as e¤ort, and the system 1 as an automatic and domainspeci…c cognitive process which quickly generates moral intuitions over the fair level of redistribution. In section 3, in connection with the dual-process theory of decision-making and the "new synthesis" in moral psychology (Haidt, 2007), we specify as described in Figure 1 how the feeling of guilt associated with the moral intuition is integrated into the rational reasoning when voting over redistribution. We then present conditions for the existence of a multiplicity of steady states in order to explain the huge di¤erence of redistribution observed between Europe and the United States. In section 4, we generalize the multiplicity of steady states found in the previous section by considering family background and the intergenerational transmission of inequality. We conclude brie‡y in the last section. 2 Moral intuition and the fair level of redistribution In social sciences, following Kant in philosophy and Kohlberg in psychology, morality is usually associated with a controlled, emotionless and logical reasoning. By contrast, according to Haidt (2007) moral intuition refers 6 Figure 1: Dual-process decision-making and voting over redistribution to "fast, automatic and (usually) a¤ect-laden processes in which an evaluative feeling of good-bad or like-dislike appears in consciousness without any awareness of having gone through steps of search, weighing evidence, or infering a conclusion". In the "new synthesis" in moral psychology he describes, moral reasoning is then mostly a "post-hoc process in which we search for evidence to support our initial intuitive reaction". 2.1 An insight into the lab As an illustration of moral intuition and the emotional processing associated with it when considering redistribution, let us consider the Ultimatum Game (Güth et al, 1982). In this game, two anonymous subjects must agree in the split of a given amount of money ($10). One participant, the proposer, can make one proposal on how to split the money. The other one, the recipient, can either accept or reject the proposal. If he accepts, the proposal is carried out, if not both players get nothing. In theory, in such a one-shot game the proposer should o¤er to the recipient an amount of money as low as possible, and the recipient should accept any proposal superior to 0. By contrast, robust …ndings in the lab show an average proposal of $4 with a large number of 50/50 splits. Besides, if all proposed 50/50 splits are 7 accepted, any proposal below $2.50 has a high probability to be rejected. The Ultimatum Game (with other games such as the Dictator Game and the Trust Game) stresses behaviors which are characterized by fairness and inequity aversion5(Fehr and Schmidt, 1999, Bolton and Ockenfels, 2000). In addition, Sanfey et al. (2003) have shown that the rejection of an unfair proposal (assimilated to a fair punishment) was related to the activation of the anterior insula. The rejection of an unfair proposal has also been associated with an increased skin conductance (van ’t Wout et al., 2006). These …ndings elicit the emotional side of this recipient’s choice. According to the "new synthesis" in moral psychology, an equal share of the money in the Ultimatum Game appears then as a moral intuition. However, the initial distribution of the money in the game can not account for the market income determination in real life. Indeed, in the game the proposer is initially rich only by luck. By contrast, in real life, an individual can have a high income because he works hard. Therefore, as long as personal e¤ort changes the perception of the fair income, it follows that e¤ort as well as luck have to be considered to characterize the income determination. 2.2 E¤ort, motivation and the income determination: basic assumptions The economy is populated by a continuum of individuals whose actions take place according to the timeline on Figure 2. Each individual lives for two periods: childhood and adulthood. When adults, they work in order to maximize their welfare and the consumption of their household. They also vote over income redistribution. When children, they are educated and socialized, and by this process they internalize the cultural practices which will in‡uence their behavior when they become adults. Indeed, as noted 5According to Andreoni and Bernheim (2009), the 50/50 norm may also re‡ect that people like to be perceived as fair. 8 established as a norm. In other words, guilt is context-dependent because it is based on a comparison process with others’behaviors and with cultural practices. As noted by Elster (1998), guilt is a self-evaluative emotion. Supporting such a view, Harlé and Sanfey (2007) and Twenge et al. (2007) have shown that manipulating the environment in prosocial behavior experiments (Ultimatum Game in Harlé and Sanfey, 2007) can change signi…cantly their output. In addition, prosocial behavior experiments (among which UG) undertaken in small-scale societies suggest that "culturally transmitted behavioral variation may substantially a¤ect decision-making" (Henrich, 2000; see also Henrich et al., 2001, 2005). To take into account this cultural side of human behavior, let us then assume that, even if the moral intuition is universal, the self-evaluative expression of guilt is shaped by internalization of cultural practices during childhood through the process of socialization8. More precisely, let us assume that unfairness of the institution observed by a person during his childhood reduces his feeling of guilt when he becomes adult. We can in this case represent the self-evaluative experience of guilt Gtof adults in t by: Gt=f tt2 t1 (11) where t1=hf t1 t1i2represents the unfairness of the institution chosen by the previous adult generation in t1. 3.2 Redistribution, self-control and cultural practices Assume that guilt is integrated into the rational reasoning such as individual demands for redistribution can be characterized by the maximization of the following social utility: 8As stated by Bisin and Verdier (2001), internalization of cultural practices can occur through socialization inside the family and in the society via imitation and learning. 15 Uit =uit  2Gt(12) where is a positive parameter which represents the individual weight of guilt aversion when choosing the level of redistribution. As explained in the introduction, such a speci…cation is in the spirit of modern cognitive neurosciences (Gray, 2004, Bechara, 2004, Cohen, 2005, Pessoa, 2008). It is also consistent with Charness and Dufwenberg (2006) who have experimentally shown in the trust game that guilt aversion was shaping signi…cantly individual behaviors. Considering (6), (4) and (11), maximizing (12) results in the following individual demands for redistribution in t: it =8 > < > : 2(aai)+  t1f 2aai+ t1 0 if aia+f 2t1 otherwise (13) Individual demands for redistribution as speci…ed in (13) decrease with personal income and increase with the degree of unfairness of the income distribution. Eq. (13) is then consistent with empirical surveys (Fong, 2001, Corneo and Grüner, 2002, Alesina and La Ferrara, 2005, Corneo and Fong, 2008, Alesina and Giuliano, 2010). In addition, eq. (13) is consistent with …ndings from Luttmer and Singhal (2011) and Alesina and Giuliano (2010) which stress that culture and socialization when young determine the demand for redistribution. They indeed show that immigrants from highpreference redistribution countries continue to support higher redistribution in their destination country. In eq. (13),  t1can be interpreted as a culturally inherited degree of collective guilt aversion. If it becomes large, individual demands for redistribution get close to the fair level. Under the su¢ cient condition maxifaig  2a, preferences are singlepeaked in and thus the median-voter theorem applies. Knowing in addition that it as de…ned by eq. (13) is a decreasing function of ai, assuming that the distribution of ais skewed to the right, i.e. amed a, yields that the 16 tax rate chosen under the majority rule is speci…ed as:  t=2 (aamed) +  t1f 2aamed + t1 (14) Let s=2(aamed) 2aamed be the taxation rate chosen under the majority rule if individuals were driven only by their self interest, i.e. if =0, we can rewrite (14) as:  t=ts+ (1 t)f(15) where t=2aamed 2aamed + hf t1 t1i2 (16) Any taxation rate chosen under the majority rule is then expressed as a convex combination of the purely interested and the purely fair taxation rates. Proposition 1 Consider the tax sequence ftgt=1 t=0 and assume that f s2q 2aamed , if 02f;f+then lim t!1t=f, otherwise lim t!1t=1 2f+sq(fs)22s where =fsq(fs)22s  2, f= 1 qinf 1L 2;1,L=2 " 2 a,s=2(aamed) 2aamed and  = aamed. The dynamics of redistribution is then history dependent. If the initial level of taxation corresponds to an institution lower but su¢ ciently close to the fair level, the collective degree of guilt aversion transmitted to the young generation increases. When they become adult the next period, the latter will then support a redistribution level closer to the fair level. This emotional contagion process ends with the implementation of the fair institution when the cultural degree of collective guilt aversion becomes signi…cantly large. By contrast, starting su¢ ciently far from the fair level leads to a too strong 17 τt-1 τt δ δ τf τs τEU τUS Figure 3: Multiplicity and history dependancy of redistribution when f s>q2s  signal you should behave according to your own interest which reduces concerns about morality and then the associated collective guilt aversion. It prevents then an emotional contagion to the bene…t of a rational sel…sh control. The process will end with a redistribution level lower than the fair level but higher than the sel…sh one. The multiplicity of steady states results from the interaction between the two distinct processes. First, guilt that people can feel related to their moral duty shapes the voting behavior: the stronger this feeling, the closer to the fair intuition their choice. Second, if people are socialized in an environment whose practices and institutions do not re‡ect the intuitive fairness, internalization of the observed norm you should behave according to your own interest will reduce individual responsability. It will then reduce the self-evaluative feeling of guilt regarding moral duty. By contrast, if people are socialized in an environment whose practices and institutions re‡ect 18 intuitive fairness, the observed norm unfairness is intolerable reinforce the individual feeling of guilt when choices deviate from the moral reference point. If fs2q 2aamed , the convergence towards the two di¤erent steady states depends therefore only on the initial level of taxation as stated in proposition 1. According to our analysis, the high redistribution European style welfare state is then characterized by an emotional contagion whereas the low redistribution American style welfare system is characterized by a rational control: s< US < EU =f. As a consequence, in the European style system, as EU =f, any increase of the di¤erence between mean and median incomes can be associated with a decrease of the relative importance of luck in the wage determination Lwhich tends to reduce the level of redistribution: dEU d<0. By contrast, in the American style system, as an increase of is also associated with a higher sel…sh level of redistribution, ds d>0, the outcome is not straightforward. Proposition 2 If fs2q 2aamed and L < 2,dEU d<0while dUS d> 0under the su¢ cient condition " sfs f+s. Under an unrestrictive condition, the American style system exhibits then a size increased with the di¤erence between mean and median income as in the Meltzer-Richard model (1981). Such a result suggests that Europe and the United States should be dissociated when testing the empirical relationship between redistribution and income inequality. For example, while most cross-country studies (e.g. Perotti, 1996, Moene and Wallerstein, 2001, de Mello and Tiongson, 2006, Iversen and Soskice, 2006) found a negative or insigni…cant relation between redistribution and income inequality, Meltzer and Richard (1983) found a positive relation when considering only the United States from a time-series perspective. 19 4 Family background and the inheritance of inequality So far, we have pointed out, following empirical studies, that if luck is important in the income determination, individual demands for redistribution are stronger. More generally, what is stressed in the surveys to characterize the perceived unfairness of the income distribution and then the individual demands for redistribution are factors beyond one’s control (e.g. Fong, 2001, Alesina and La Ferrara, 2005, Fong et al., 2006, Corneo and Fong, 2008). Along with luck, there is then also family background. Thereafter, one can argue that luck as modelized in eq. (1) is an oversimpli…cation of all the factors beyond one’s control. Indeed, as pointed out by Bowles and Gintis (2002) and d’Addio (2007), earnings are very signi…cantly tied to the parents’earnings9. When considering the income determination characterized by eq. (1), such a correlation can be obtained by assuming that psychological and cognitive skills are genetic inherited traits. However, by showing that the inherited genetic component of IQ is very weak, Bowles and Gintis (2002; see also Bisin and Topa, 2003) weaken the basis of such an assumption. By contrast, it strengthens the idea that family background is an important factor in the income determination which can not be captured by idiosyncratic shocks. In this line, Bourdieu (1984) asserts in particular that cultural consumption is of crucial importance when explaining the capacity of high-income earners to ensure the reproduction of income inequality. On 9As noted in Bowles and Gintis (2002), a widely held consensus among American economists used to be that "Low earnings as well as high earnings are not strongly transmitted from father to sons" (Becker, 1988). However, following Solon (1992) the low correlations between fathers’ and sons’ incomes previously estimated in America were due to measurement errors. With improved methodology and data, Björklund and Jäntti (1997) even show that the intergenerational income mobility in Sweden is higher (however not signi…cantly) than in the United States. 20 one hand, by consuming cultural goods, high-income earners shape wealthier class cultural norms which exclude others. On the other hand, by their cultural practices, they also develop networking activities. Income, cultural capital and social capital are closely related. On a family cultural basis of factors beyond one’s control, in contrast with eq. (1), let us consider that income of an adult in tis characterized by: yij;t =cj;t1+eit (17) where cj;t1represents her parents’cultural consumption in t1, and ei;t her e¤ort. Considering the di¤erent types of consumption goods, we rede…ne the private utility function as: uij;t =1 (1  )1 c i;td1 i;t eem i;t 2 2ai (18) where di;t is the standard …nal consumption and 2[0;1] represents the importance of cultural goods in the consumption. Assuming for simplicity a transformation technology from one standard good to one cultural good, it yields that both forms of consumption which maximize (18) are characterized by: ci;t = [(1 t)yij;t +tyt](19) di;t = (1  ) [(1 t)yij;t +tyt](20) When introducing the optimal behaviors (19) and (20) into the private utility function (18), the latter becomes: uij;t =yij;t (1 t)+ tyt(eem i;t )2 2ai. In this con…guration, the utility maximization considering (17) leads to an unchanged level of extrinsically motivated e¤ort compared to previous sections, i.e. ei;t =ai(2 t). Consider now that the concept of fair income is associated with the 21 principle of equal opportunities between individuals. In this case we can rede…ne the fair level of income as: ^yij;t = ct1+ei;t (21) where ct1is the average cultural consumption. In line with Bowles and Gintis (2002), let us assume that personal cognitive skills characterized by aiare not heritable genetic traits. It yields in particular that the parental cultural consumption cj;t1of an individual ij is not correlated with her cognitive skills ai. The moral intuition resulting from the minimization of (8) stays then similar to (10), i.e. f t= 1q1Lt 2 if Lt2(= 1 otherwise), except that: Lt=2 ct1 2 a (22) where 2 ct1is the variance of parents’cultural consumption in t1. Individual demands for redistribution, still characterized by the maximization of the rational utility minus guilt aversion yij;t (1 t) + tyt (eem i;t )2 2ai 2hf t1 t1i2f tt2, are then as follows: ij;t =ts ij;t + (1 t)f t(23) where s ij;t =2(aai)+(t1j;t1) 2aamed , and t=2aamed 2aamed+ [f t1 t1]2 . Compared with eq. (13), eq. (23) still stresses that individual demands for redistribution depend on the income inequality, the perceived unfairness of the income distribution and the speci…c history of the society. In addition, it stresses the importance of the family background: everything else being equal, an individual raised in a family with high cultural standards tends to support less redistribution. Following eq. (23), the tax rate chosen under the majority rule is then: 22  t=ts t+ (1 t)f t(24) where s t=2(aamed)+(t1med;t1) 2aamed . Consider an institutional stationary history such as k=1;8kt1. In this case we have (see Appendix D): s t= s(1)(25) f t= f(1)(26) where s(1) = 2+ (11)(21) 1 (11)(aamed) 2aamed and f(1) = 1r1 2(11)2(21)2 2[1 2(11)2]. From (25) and (26) we can de…ne a purely fair and a purely self-interested tax rates corresponding respectively to f= ffand s= s(s). It results two continuous and monotonic functions f( )and s( ; ) such as df d 0, where f(0) = 0 and f(1) = p210:41,@s @ 0and @s @0, where s(0;) = s(1) = 2(aamed) 2aamed and s( ; 0) = 0. Proposition 3 Considering a stationnary tax history fk=1gk=t1 k=1,8  ~ (0:55),f( )s( ; ) 2q 2aamed is a su¢ cient condition such as the model exhibits two local steady states characterized by s( ; ) < US < EU =f( ), where f( )f= ffand s( ; ) s= s(s). We can again assert that the possibility of a multiplicity of steady states results from the interaction of the two distinct cognitive processes. Considering family background still allows us to interpret the di¤erence of redistribution between Europe and the United States as a distinction in the nature of the leading cognitive process when voting: a¤ective (system 1) in Europe, rational (system 2 ) in the United States. 23 00.05 0.1 0.15 0.25 0 0.05 0.1 0.15 0.2 0.25 τ-1 τt Γf(τ-1) Γs(τ-1) τEU=τf τUS τs Figure 4: Multiple steady states and family background (ln (a) N(0;0:217), = 0:5,=0:005) 24 [40] Ekman P. (1992), An argument for basic emotions, Cognition and Emotion, 6, pp. 169-200. [41] Elster J. 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(6), Ft=Zif[(1 t) (ai(2 t) + "i) + ta(2 t)] ai(2 t)g2di =Zif(1 t)"it(2 t) (aia)g2di: As aand "are independently distributed over the population, Ft= (1 t)2Zi "2 idi+2 t(2 t)2Zi (aia)2di = (1 t)22 "+2 t(2 t)22 a: It follows that Ft 2 a = (1 t)2L+2(2 t)2 where L=2 " 2 . It follows that @Ft 2 a @t= 4 (1 t)2 t+ 2tL 2and @2Ft 2 a @2 t=42 t+ 2tL 2+ 8 (1 t)2. If L > 2,2 t+ 2tL 2<08t1. It follows that @Ft 2 a @t(1) = 0, @2Ft 2 a @2 t(1) >0and then arg min t1;L>2 Ft= 1. If L2,2 t+ 2tL 2=1q1L 2t1 + q1L 2t. It follows that @Ft 2 a @t(1) = 0,@2Ft 2 a @2 t(1) 0while @Ft 2 a @t1q1L 2= 0, @2Ft 2 a @2 t1q1L 20and then arg min t1;L2 Ft= 1 q1L 2. Appendix B. Proof of proposition 1 Let us de…ne t=f tthe di¤erence between the fair and the e¤ective level of taxation, eq. (15) can be rewritten as: 38 t=2aamed 2aamed + 2 t1fs(27) and the stationnarity is then de…ned by: 3fs2+ 2aamed = 0 (28) If fs2q 2aamed , eq. (28) exhibits three roots = 0,= fs+q(fs)22s  2and =fsq(fs)22s  2. In addition, as lim 2!0 @"2aamed 2aamed+ 2# @2= 0, if f> s, there exists two steady states characterized by = 0 and =fs+q(fs)22s  2, i.e. respectively by =fand =1 2f+sq(fs)22s , where f= 8 < : 1q1L 2 1 if L2 otherwise ,L=2 " 2 a,s=2(aamed) 2aamed and  = aamed. Appendix C. Proof of proposition 2 As far as fs2q 2aamed , the American style system is characterized by the following payroll tax: US =1 2 f+sr(fs)22s ! We have then: @US @=1 20 @@f @+@s @ 2fs@f @@s @2  @s @+ 2   s  2q(fs)22s  1 A(29) =1 20 @1fs q(fs)22s  1 A@f @+1 2 @s @+fs@s @+  @s @  s  q(fs)22s  where @f @0and @s @0. 39 From (29), we deduce that a su¢ cient condition such that @US @0is: fs@s @+  s @s @  s10(30) Obviously, if " s=@s @  s1condition (30) always holds and then @US @0. If "s <1, we can deduce from fs2q 2aamed , (fs)2 2s that fs@s @+(fs)2 2ss "s 10)fs@s @+  s "s 1 0. We can therefore show that condition (30) is satis…ed when 2 + fs s"s  fs s,"s fs f+s: Appendix D. Family background with stationary history From (17), (20) and (2) we have: ci;t = f(1 t) [cj;t1+ (2 t)ai] + t[ct1+ (2 t) a]g(31) Assuming that o¤springs’cognitive skills are randomly determined, independently of their parents’cognitive skills, entails also they are not correlated with their parents’cultural consumption. In such a case, when considering an institutional stationary history such as s=1;8st1, it follows from (31) that 2 ct1=2 c(1) = 2(1 1)2h2 c(1) + (2 t1)22 ai, or equivalently: 2 c(1) = 2(1 1)2(2 1)2 1 2(1 1)22 a and then following (8) and (22) that: f t= f(1) = 1 v u u t1 2(1 1)2(2 1)2 2h1 2(1 1)2i It follows that: 40