Anil Alpman
email: anil.alpman@univ-paris1.fr

François Gardes

The Relevance of Social Norms for Economic Efficiency: Theory and its Empirical Test

Keywords: Social Norms, Social Interactions, Consumer Behavior, Household Production, Economic Development, Social Pressure Indicator JEL Classification: D11, D12, O43, Z13

This paper proposes a new theory of social norms that explores the relation between individuals' income, time allocation decisions, and consumption choices on the one hand, and the determinants of individuals' decision to conform or not to social norms on the other. It is shown that rational consumers may obey inefficient social norms, which in turn would slow economic development. An empirical test of the model is performed for different categories of countries using the World Values Survey, a voluminous cross-country micro dataset. The results yield the gain and the cost of disobeying inefficient social norms, the latter of which can be used as an indicator of social pressure regarding conformity.

Introduction

As an informal institution, social norms determine "the rules of the game" as much, if not more, as formal institutions [START_REF] North | Institutions, Institutional Change and Economic Performance[END_REF](North, , 2005, p. 48-52), p. 48-52), especially in developing countries where formal institutions are often inoperative. Socially accepted and expected behaviors are the rules defined by social norms which can shape, together with formal institutions, various aspects of everyday life such as consumption decisions, property-rights regimes, species of crops grown by farmers, and whether making profits is acceptable (Ray, 1998, p. 155).

Yet, social norms "can become retrogressive" [START_REF] Arrow | Political and Economic Evaluation of Social Effects of Externalities[END_REF], they can be "inimical to development" (Ray, 1998, p. 155), and many social norms "do not benefit anyone" [START_REF] Elster | Social Norms and Economic Theory[END_REF]. In addition, social norms often "go against narrow self-interest" and many "are not socially beneficial" (Bicchieri, 2006, p. 2 and 7). This paper refers to such social norms as inefficient, in the sense that disobeying them could lead to a higher income (see [START_REF] Akerlof | A Theory of Social Custom, of Which Unemployment May be One Consequence[END_REF].

The economic approach rationalizes the persistence of inefficient social norms by arguing that there is a tradeoff between the material well-being of the consumer and its desire to avoid social disapproval (see for example [START_REF] Burke | Social Norms[END_REF][START_REF] Akerlof | A Theory of Social Custom, of Which Unemployment May be One Consequence[END_REF]. However, the challenging and debated points consist in specifying how the mechanisms through which social norms operate affect the consumer's utility, and what are the gain and the cost of disobeying inefficient social norms that ultimately determine the consumer's disobedience level to social norms. 2Following the definition of social norms given by [START_REF] Bicchieri | The Grammar of Society: The Nature and Dynamics of Social Norms[END_REF] and [START_REF] Elster | Rationality and the Emotions[END_REF], social norms, unlike moral norms, have not to be internalized: moral norms are followed because disobeying them triggers the emotion of guilt that leads to a negative sense of self regardless of whether the disobedience is observed [START_REF] Elster | Rationality and the Emotions[END_REF]. Indeed, "moral norms demand . . . an unconditional commitment" (Bicchieri, 2006, p. 20).

"The operation of social norms", on the other hand, "depends crucially on the agent being observed by others" (Elster, 2009, p. 196). [START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF], and [START_REF] Haley | Nobody's watching? Subtle Cues Affect Generosity in an Anonymous Economic Game[END_REF] provide some evidence that the obedience of individuals to social norms is conditional on whether they are observed: when individuals are unobserved, they tend to disobey the social norms that they would have obeyed otherwise. As [START_REF] Elster | Explaining Social Behavior: More Nuts and Bolts for the Social Sciences[END_REF] says, "the shame that sustains social norms is triggered by the perceived contempt of others". Therefore, disobedience per se does not induce a poor sense of self. 3Nevertheless, "the action tendency of contempt is avoidance" (Elster, 2009, p. 199): if an individual is observed disobeying social norms, the society would have a negative opinion about that individual who would be excluded by the society as a response. To avoid exclusion, individuals can conform their behaviors to the expectations of the society without changing, however, their internal values. For instance, if the social norm of wearing black at funerals [START_REF] Elster | Rationality and the Emotions[END_REF] were to change to, say, wear white, would I have a poor sense of myself by complying to this new norm? Probably not. Most likely, people would even provide the necessary effort to conform to the new norm in order to avoid negative judgements and, eventually, to avoid social exclusion.

Ultimately, the origin of the disutility caused by disobedience to social norms is to be found in the deterioration of social interactions (as opposed to social isolation) rather than in an "identity loss" (i.e., a negative sense of self) as in [START_REF] Akerlof | Economics and Identity[END_REF], or "a loss of reputation" as in [START_REF] Akerlof | A Theory of Social Custom, of Which Unemployment May be One Consequence[END_REF]. A good reputation is a mean for fruitful social interactions and thus reputation in itself does not affect directly utility: isolate a man, and his reputation would have no effect on his utility while the absence of social interactions would torment his soul. Unlike the reputation, social interactions are a direct source of utility.

Therefore, this paper considers social interactions as a commodity produced by the consumer that generates utility. It is assumed moreover that disobeying inefficient social norms affects negatively the production of social interactions while it increases the consumer's income. The theoretical model, which is developed in Section 2, shows that, under these assumptions, there is a unique level of disobedience that maximizes utility. This approach enables partial levels of disobedience and incremental evolution of social norms.

The model predicts that the optimal disobedience level depends on individual-specific parameters (the market wage rate, the output elasticities of inputs, and the individual's preferences) and on country-specific parameters (the quality of the economic environment and the tolerance of the society). Within a population, country-specific parameters induce similar disobedience levels while individual-specific parameters allow for some variances. On the other hand, the values of the parameters determine whether inefficient social norms are more likely to persist or to vanish: as long as the cost of disobedience is high compared to its gain, that is, the incentives to disobey inefficient social norms are weak, the average disobedience level in a country would be low and thus inefficient social norms would persist for longer periods, impeding thereby economic development. Hence, social norms are an additional factor that can account for income differences across countries. Moreover, the theoretical results indicate that the optimal level of disobedience affects the level of income, the time allocation, and the consumption choices of the consumer.

The empirical framework is presented in Section 3. That section begins by describing the variables of the World Values Survey which are used in the empirical test, followed by the empirical specification. This paper's approach enables the analysis of the incentives that determine an individual's behavior regarding social norms without necessarily defining any specific norms. The empirical test yields the estimates of the gain and the cost of disobedience to inefficient social norms for rich, emerging, developing, and Arab Spring countries. The estimates of the cost of disobedience provide a valuable indicator: the social pressure put on an individual to not disobey the society's social norms.

The results are presented in Section 4. The level of disobedience as well as the gain and the cost of disobedience for each category of countries are compared and discussed in length in Section 5.

The Model

Assumptions

Utility and Household Production Functions

In addition to the arguments mentioned above, studies in psychology and in behavioral medicine provide further evidence about the importance of social interactions for physical and mental health. 4 Therefore, let the utility be a function of the level of social interactions, denoted Z s , and of the consumption quantity of a composite commodity, denoted Z c . Human nature is assumed to be such that, for a given level of utility, it can exchange social interactions for non-social commodities only to some extend, implying that Z s and Z c are imperfect substitutes. Moreover, it is assumed that each additional unit of Z s satisfies a lower psychical and socioeconomical need. Hence, the utility could be represented by a Cobb-Douglas function:

U = Z θ s Z 1-θ c (1)
Z i , with i = {c, s}, is a final good produced by the consumer who combines market goods, C i , with his time, t i .5 Assuming that inputs are imperfect substitutes with decreasing marginal productivity, the production functions of Z c and Z s can take the Cobb-Douglas form:6

Z c = C β c t 1-β c (2)
and

Z s = µ(x, δ) C α s t 1-α s ( 3
)
where µ is the total factor productivity of C s and t s as a function of the disobedience level to norms, x (the higher is x, the greater is the disobedience level, with x ≥ 0), and the intolerance of the society to disobedience, δ (the higher is δ, the more severely the society punishes disobedience, with δ > 0).

The properties of the total factor productivity are defined by the following assumptions: first, increasing disobedience to norms deteriorates the reputation [START_REF] Akerlof | A Theory of Social Custom, of Which Unemployment May be One Consequence[END_REF] that in turn decreases the production level of social interactions for a given level of inputs. Thus, increasing disobedience to norms decreases µ: ∂µ/∂x < 0 and µ(0, δ) = q > 0 where q is the highest value of µ . Then, it is assumed that people ignore low levels of disobedience and punish each additional level of disobedience more than proportionally. Indeed, ignoring disobedience, avoiding, gossiping, and openly ostracizing are more than proportional punishments. As a consequence, lim x→0 ∂µ/∂x = 0 and µ decreases more than proportionally with increasing x: ∂ 2 µ/∂x 2 < 0.

Thirdly, an increase in the intolerance of the society decreases µ for each level of disobedience (except if the individual does not disobey norms): ∂µ/∂δ < 0 and ∂ 2 µ/(∂x∂δ) < 0. For δ = δ, let x excl denote the level of disobedience for which µ(x excl , δ) = 0. It is assumed that ∀x > x excl , µ(x, δ) = 0, which implies that the individual is socially excluded (i.e., Z s = 0). 7

The Income

Disobeying inefficient social norms may nevertheless be "of pecuniary advantage to the person who disobeys" [START_REF] Akerlof | A Theory of Social Custom, of Which Unemployment May be One Consequence[END_REF]. Consider the following examples: obeying social gender norms may lower the wage rate by inducing inefficient allocation of labor (see [START_REF] Udry | Gender, Agricultural Production, and the Theory of the Household[END_REF][START_REF] Zwarteveen | A Plot of One's Own: Gender Relations and Irrigated Land Allocation Policies in Burkina Faso[END_REF]. Social norms of working places, which forbid pulling strings or rate-busting, may also lower the wage rate for someone who obeys them. Agricultural social norms may prescribe the cropping of a traditional plant even if farmers are not competitive in its production (Ray, 1998, p. 155-156). The social norm of anti-achievement (Elster, 2009, p. 196) or the social norm proscribing profits (Ray, 1998, p. 155) "can discourage the gifted from using his talents" [START_REF] Elster | Social Norms and Economic Theory[END_REF], resulting potentially on a lower wage rate as well.

Therefore, let the wage rate of the consumer be given by the function w:

w(x, W, E, δ) = W + γ(x, E, δ) (5)
where W is the market wage rate prevailing in the profession of the consumer regardless of his behavior vis-à-vis social norms; γ is the monetary gain of disobedience as a function of x, E and δ; and E ≥ 0 is the quality of the economic environment (e.g., the efficiency of formal institutions).

The relation between γ and x is the outcome of an efficiency effect and a punishment effect. The former concerns the increase of the wage rate induced by the efficiency gain that arises from disobeying inefficient social norms. The efficiency effect is assumed to define a decreasing and always positive relation between the marginal gain of disobedience and the level of disobedience; more specifically, let the marginal gain of disobedience tend to infinity around complete obedience and to zero around complete disobedience. The intuition behind this assumption is that each additional level of disobedience reduces the scope of further efficiency gain.

The punishment effect, on the other hand, affects negatively the gain of disobedience (γ) because of sanctions imposed by the society against individuals who disobey social norms. Besides direct material sanctions, emotional sanctions such as avoidance and gossip can also generate material loss for non-conformists by deteriorating their reputation and their desirability on the labor market. As it has been assumed in Section 2.1.1, the society ignores low levels of disobedience, and each additional level of disobedience is punished more than proportionally.

7 An example of a functional form satisfying the expected properties of µ is (in equation [4], q = 1) Therefore, when both effects are combined, the marginal gain of disobedience is decreasing and it becomes negative above a level of disobedience denoted x max because the punishment effect outweighs the efficiency effect. Utility maximizing behavior suggests however that the disobedience level will not be higher than

   µ(x, δ) = 1 -δx 2 if x ≤ 1 δ 1 2 µ(x, δ) = 0 if x > 1 δ 1 2 (
x max , which restricts the possible range of disobedience to x ∈ [0, x max ].8 As a consequence, in-between this range, ∂γ/∂x > 0; ∂ 2 γ/∂x 2 < 0; γ(0, E, δ) = 0 and lim x→0 ∂γ/∂x = +∞ (see Figure 1).

Furthermore, the gain of disobedience (γ) depends on the economic (E) and the social (δ) environment because these are assumed to determine the magnitude of the efficiency and punishment effects. For instance, if the labor market is missing or private property is not properly enforced, that is, if E is low, disobeying social norms mentioned above is likely to have only a minor impact on the wage rate: ∂γ/∂E > 0 and ∂ 2 γ/(∂x∂E) > 0. On the other hand, if the society becomes less tolerant, it will punish each level of disobedience more severely, reducing thereby the gain of disobedience: ∂γ/∂δ < 0 and ∂ 2 γ/(∂x∂δ) < 0.9

Finally, a person would be excluded from the labor market when his behavior becomes socially unacceptable, which would also imply social exclusion. It is therefore assumed that w and µ tend to zero in similar values of x as in Figure 1.

Summary

In this paper, the consumer produces a composite commodity (Z c ) and social interactions (Z s ) by combining his time (t i ) with market goods (C i ). Social interactions is a particular final good: as disobedience to social norms increases, the total factor productivity (µ) associated with social interactions decreases more than proportionally. On the other hand, disobeying social norms increases the wage rate (w) at a decreasing rate. It follows that the disobedience level of a rational individual would never be higher than x max as mentioned above. Hence, in the remainder of this paper, x ∈ [0, x max ]. Note that if all social norms were efficient, individuals would have no incentives to disobey them. This model is therefore concerned with inefficient social norms. The choice variables are Z i , C i , t i and x, and, until Section 2.3, W , E, and δ are omitted in the functions notation for easier readability.

The Consumer's Choices

The consumer's income constraint is

p c C c + p s C s = w(x)t w (7)
and his time constraint is given by

t w + t c + t s = T (8)
where t w is the time spent working on the market, p i is the price of C i , and T is the total available time.

Combine equations ( 7) and ( 8) to obtain the full income constraint:

p c C c + w(x)t c + p s C s + w(x)t s = w(x)T (9)
The optimal levels of t i , C i and Z i are such that they maximize the consumer's utility (1) subject to the production constraints ( 2) and (3), and to the full income constraint (9). The first order condition giving the optimal combination of the factors used in the production of Z i is (see [START_REF] Michael | On the New Theory of Consumer Behavior[END_REF])

∂U ∂Z i ∂Z i ∂C i ∂U ∂Z i ∂Z i ∂t i = ∂Z i /∂C i ∂Z i /∂t i = p i w(x) (10)
Combining the first order condition ( 10) with ( 2) and ( 3) yields the optimal level of inputs:

t * s = t s (Z s , x) = Z s µ(x) p s (1 -α) w(x)α α (11) C * s = C s (Z s , x) = Z s µ(x) w(x)α p s (1 -α) 1-α (12) 7 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée) t * c = t c (Z c , x) = Z c p c (1 -β) w(x)β β (13) C * c = C c (Z c , x) = Z c w(x)β p c (1 -β) 1-β (14)
The optimal consumption levels of Z c and Z s are obtained by equalizing the ratio of their marginal utility to the ratio of their marginal cost:

∂U/∂Z s ∂U/∂Z c = w(x)(∂t s /∂Z s ) + p s (∂C s /∂Z s ) w(x)(∂t c /∂Z c ) + p c (∂C c /∂Z c ) = p α s w(x) 1-α a /µ(x) p β c w(x) 1-β b ≡ π s π c ( 15
)
where b ≡ [β/(1 -β)] (1-β) + [(1 -β)/β] β ; a ≡ [α/(1 -α)] (1-α) + [(1 -α)/α] α ; and π i is the shadow price of Z i .
The full income constraint can be written in terms of final goods:

Z c π c + Z s π s = w(x)T (16)
Combine the first order condition (15) with equation ( 16) to obtain the optimal consumption level of Z s and Z c :

Z * s = Z s (x) = θT a w(x) p s α µ(x) (17)
Z * c = Z c (x) = (1 -θ)T b w(x) p c β (18)
Equations ( 11) to ( 14) suggest that the level of disobedience to inefficient norms affects the optimal level and combination of inputs: for example, an increase in the level of disobedience, by increasing the opportunity cost of time (w), leads time input to be substituted by market goods. Furthermore, Z * c is strictly increasing with the level of disobedience whereas the optimal level of social interactions initially increases with x, and, as disobedience increases further, Z * s starts to decrease because the income effect (i.e., an increase of Z s resulting from an increase of w) is outweighed by the reputation effect, that is, a decrease of Z s resulting from a decrease of µ (see Appendix A).

Optimal Disobedience Level to Inefficient Social Norms

Let V denote the indirect utility as a function of x: The optimal disobedience level is the one that maximizes the indirect utility. This methodology is possible because the choice of the disobedience level to norms is unconstrained, and it does not affect the definition of the first order conditions ( 10) and ( 15). Therefore, maximize V with respect to x (see Appendix B for the second order condition):

V (x) = T θ p α s a θ 1 -θ p β c b 1-θ w(x) αθ+β(1-θ) µ(x) θ (
∂V (x) ∂x = T θ a p α s θ 1 -θ b p β c 1-θ w(x) αθ+β(1-θ) µ(x) θ ∂w(x) ∂x αθ+β(1-θ) w(x) -1 +θ ∂µ(x) ∂x µ(x) -1 = 0 (20)
Using equation ( 5) and including W , E, and δ in the notation of functions, equation ( 20) holds if

- ∂γ(x, E, δ)/∂x ∂µ(x, δ)/∂x = W + γ(x, E, δ) µ(x, δ) α + β(1 -θ)/θ (21)
Given the properties of γ and µ, there is a unique value of x (as a function of the exogenous variables), denoted x * , that verifies equation ( 21) (see Appendix C):

x * = x(θ, α, β, δ, E, W ) (22)
x * is the optimal disobedience level to social norms or, said differently, the optimal social behavior. The optimal social behavior, which shapes economic decisions, is itself determined by economic and social factors.

The relation of x * with respect to θ, α, β, δ, E, and W discussed here below is found by comparative statics analysis (see Appendix D for mathematical details).

An increase in individuals' preferences for social interactions will lead them to obey more inefficient social norms: ∂x * /∂θ < 0. It is also straightforward to understand why the optimal disobedience level will decrease as the society gets more intolerant to disobedience: ∂x * /∂δ < 0.

The relation between the economic environment and the optimal social behavior is also quite intuitive:

as the economic environment improves, the gain of disobeying inefficient norms increases. As mentioned in Section 2.1.2, better institutions-or technological innovations-create an environment where the increase of the wage rate induced by disobedience is likely to be higher than in an environment with inoperative institutions: ∂x * /∂E > 0. This relation is consistent with the economic literature: better institutions and greater tolerance are expected to have a positive impact for economic development.

As the output elasticities of market goods (i.e., α and β) increases, the shadow prices of Z s and Z c become less sensitive to an increase of the wage rate (see equation [15]). As a consequence, the optimal level of disobedience increases: ∂x * /∂β > 0 and ∂x * /∂α > 0.

Lastly, equation ( 19) suggests that the marginal indirect utility of the wage rate is decreasing because In other words, when the market wage rate increases, obeying more to norms generates greater utility by increasing Z s (through an increase in µ) than it generates disutility by decreasing both commodities (through a decrease in γ): ∂x * /∂W < 0.

αθ+β(1-θ) < 1.
Substitute x with x * in equations ( 5), ( 11) to ( 14), ( 17), and ( 18) to find the effective wage rate, the effective level of inputs, the effective level of social interactions, and the effective consumption quantity of the composite commodity. Unless the gain of disobedience is much higher than its cost, or that there is a significant exogenous shock on parameters affecting the optimal disobedience level, individuals will rather obey inefficient social norms, and, as a consequence, inefficient social norms will last for a longer period of time, impeding thereby economic development. 11 This is especially true when the society is more intolerant to disobedience (high δ); the output elasticities of time inputs are important (low α and β); the preference for social interactions is high (high θ); the quality of the economic environment is low (low E); and the market wage rate is high (high W ).

The model accounts for the four characteristic features of social norms pointed out by [START_REF] Burke | Social Norms[END_REF]: first, the existence of one commodity that is positively associated with obedience to inefficient social norms is enough to induce choices that individuals would not have made if they had not to conform. This is the conformity warp effect. The traditional household production model-and the mainstream consumer theory generally speaking-is a special case where social issues arising from non-conformity are supposed to not affect individuals. Then, when the society attaches a high importance to a social norm, its disobedience would be severely punished, that is, δ would be high, and people would not disobey this particular norm.

This captures the long-run stability effect. Thirdly, the social behaviors will converge within a population but not necessarily between populations since the differences in the exogenous variables will lead societies to diverge. This corresponds to the local conformity/global diversity effect. Finally, the existence of a subsistence level of income under which the utility is zero would yield the punctuated equilibrium effect.

This effect suggests that the accumulation of small changes may eventually reach a tipping point where a social norm would suddenly shift. The model predicts that the consumer adjusts its disobedience level at the margin when the market wage rate (W ) decreases marginally. In this context, social norms evolve at a constant pace. However, the tipping point would be reached when the marginal decrease in the market wage rate would induce an income below the subsistence level. In this case, the consumer's disobedience level would have to shift (rather than increasing marginally) to restore the subsistence level of income (provided that the consumer can achieve this income level before the marginal gain of disobedience becomes negative).

10 The value of x that verifies equation ( 21) implies necessarily that the marginal indirect utility of disobedience induced by the increase of w is equal to its marginal disutility induced by the decrease of µ so that the marginal indirect utility of disobedience is zero (∂V /∂x = 0).

11 Since there is a wide range of social behavior between complete obedience to inefficient social norms (i.e. x = 0) and complete disobedience to them (i.e., the disobedience level associated with the most efficient social behavior), it is considered that an individual "rather obeys social norms" if his behavior is closer to complete obedience. Only this wave contains the relevant variables for the empirical investigation conducted in this paper.

The disobedience variable is the answer to the following question: "would you please indicate whether the person for whom it is important to always behave properly and to avoid doing anything people would say is wrong is very much like you, like you, somewhat like you, a little like you, not like you, or not at all like you?"

A social norm concerning the same matter in two different societies may induce, prescribe, or proscribe opposite behaviors. The disobedience variable takes into account such differences. Moreover, this variable encompasses what different societies consider as disobedience.

The Social interactions variable is the "mean" membership level to the following five categories of social activities: membership of church; membership of sport or recreation; membership of art, music, educational; membership of labour unions; and membership of professional organization. For each activity, the interviewee says whether he is not a member (in which case the value of the variable is zero), an inactive member (the value of the variable is one), or an active member (the value of the variable is two). These variables have been summed and divided by five to get the mean membership level. Social interactions is therefore on a scale of eleven: 0, 0.2, 0.4, . . . , 1.8, 2.

The wage rate is proxied by the income variable that is on a scale of ten with one being the lowest and ten being the highest income decile specific to the country. Income encompasses all wages, salaries, pensions, and other incomes that come in.

The market wage rate is proxied by the profession of individuals, and it is on a scale of eleven with the following order: agricultural worker; farmer with own farm; unskilled worker; semi skilled worker; skilled worker; foreman and supervisor; non-manual -office worker (non-supervisory); office worker (supervises others); professional worker such as lawyer, accountant, or teacher; employer/manager of establishment with less than ten employees; employer/manager of establishment with more than ten employees. As the profession requires more skills and responsibilities, the market wage rate is expected to increase.

The control variables are age (restricted to individuals between twenty and seventy-five 13 ); whether the person is unemployed; sex; the highest educational level attained; the number of child; the marital status; the size of town; and the religiosity degree. Table E.3 in the Appendix E gives the descriptive statistics of all the variables. The empirical analysis includes forty-eight countries that were classified by whether they are rich, emerging, developing (according to Word Economic Outlook Update, July 16, 2012), or if they have experienced the Arab Spring (see Table E.4 in the Appendix E).

Empirical Specifications

In order to estimate the gain and the cost of disobedience, the empirical test is performed on the effective wage rate and the effective level of social interactions. Since the proxies for these variables are both ordered outcomes, I use an ordered logit procedure: the income decile to which individual k belongs, which is observed, is assumed to be determined by his effective wage rate. Similarly, the mean membership level to various activities of individual k is assumed to be determined by his effective level of social interactions. As the effective wage rate (the effective level of social interactions) crosses higher thresholds, the income decile (the mean membership level to various activities) to which individual k belongs increases.

Recall that the wage rate is given by w(x, E, δ) = W + γ(x, E, δ). Replacing x by x * gives the effective wage rate denoted w * * :

w * * W, x * = W + γ(x * ) (23)
In equation ( 23), the optimal disobedience level accounts for variations in the economic and social environment. Thus, the empirical specification of w * * is given by

w * * k = η 0 + η 1 W k + 6 j=2 η j D j,k + η 6 H k + k (24)
where D j is a dummy that takes the value 1 if individual k's disobedience level is j (D 1 has been dropped to avoid perfect multicollinearity); η 0 , η 1 , and η j are coefficients to be estimated; η 6 is a vector of coefficients to be estimated; H is a vector of control variables and ∼ Logistic(0, π 2 /3) is the error term.

Let Z * * s denote the effective level of social interactions which is given by

Z * * s = θT a w * * (W, x * ) p s α µ(x * ) (25)
As previously, in equation ( 25), the level of x * accounts for variations in the economic and social environment.

The data do not contain information about the prices of market goods entering the production of social interactions. Therefore, it has to be assumed that all individuals from different countries face the same prices. Hence, let the empirical specification of the effective level of social interactions be:

Z * * s, k = φ 0 + φ 1 w k + 6 j=2 φ j D j,k + φ 7 M k + u k ( 26
)
where φ 0 , φ 1 , and φ j are coefficients to be estimated; φ 7 is a vector of coefficients to be estimated; M is a vector of control variables and u ∼ Logistic(0, π 2 /3) is the error term.

Results

Table 1 shows that each additional level of disobedience is positively related to a higher income up to disobedience levels 5, 4, and 3 in rich, emerging, and developing countries, respectively (since Arab Spring countries went through exceptional events, their results are discussed at the end of this section).

As the disobedience level increases further, its coefficients decreases. For example, in emerging countries, disobedience level 6 has a negative and significant coefficient.

High levels of disobedience having statistically insignificant coefficients indicate that these levels are not significantly associated with a different income level than the highest level of obedience. Therefore, disobedience initially increases income and, as disobedience increases further, the income level decreases to its initial level. These results confirm that above a level of disobedience the punishment effect outweighs the efficiency effect. However, since the different levels of disobedience do not have equal intervals, it cannot be deduced from Table 1 whether the marginal gain of disobeying inefficient social norms is decreasing between two levels of disobedience. In Figure 2, the different disobedience levels are arbitrarily considered as equally distant.

Using the results of Table 1, the figure plots the centered probability ratios, that is, the probabilities of belonging to higher income deciles as disobedience increases from 1 to 2, 1 to 3, 1 to 4, 1 to 5, and 1 to 6

(the reference disobedience level is 1), everything else held constant. 14 For example, in emerging countries, an individual whose disobedience level is 4 is 1.32 times more likely to belong to a higher income decile than an individual whose disobedience level is 1, everything else equal. Moreover, a second order polynomial curve is fitted for the different groups of countries by using the nonlinear least square method. The higher is the curve, the greater is the probability to belong to a higher income decile. Thus, the curve approximates the expected gain of disobedience (which will be simply referred to as the gain of disobedience). Figure 2: The expected gain of disobedience derived from Table 1. The interval between the disobedience levels are arbitrarily considered as equally spaced. The circles, triangles, and squares represents the probability of belonging to a higher income decile for each disobedience level over the probability of that of disobedience level 1. Note that the significancy of these points are as in Table 1. A second order polynomial curve is fitted for the different groups of countries by using the nonlinear least square method.

14 The centered probability ratios are obtained by exponentiating the log odds ratios in Table 1, and then by taking their square roots. The probability ratio (i.e., the risk ratio or the relative risk) has a more intuitive interpretation than the odds ratio, and interpreting odds ratios as probability ratios inflates effect sizes in probability terms [START_REF] Liberman | How Much More Likely? The Implications of Odds Ratios for Probabilities[END_REF]. Liberman shows that the square root of an odds ratio yields the centered probability ratio (because it centers the probability pair around 0.5), which "provides a sort of average of all possible probability ratios for a given odds ratio". According to Liberman, the centered probability ratio is useful for making "general statement across the probability range" and "when one lacks a strong basis for choosing representative probabilities to explore". Although the marginal gain of disobedience may locally increase between two levels of disobedience in Figure 2, overall, the marginal gain of disobedience appears to be decreasing: the fitted curve, which has a strictly decreasing marginal gain, explains 89%, 75%, and 55% of the variance for developing, emerging and rich countries, respectively. Furthermore, the distance between different disobedience levels can be adjusted to obtain a strictly decreasing marginal gain. Therefore, the assumption of decreasing marginal gain of disobedience made in Section 2.1.2 seems plausible.

The Figure 2 shows in addition that the average disobedience levels are below x max as predicted by the model. Overall, the gain of disobedience is the highest in emerging countries followed by developing countries. However, for high levels of disobedience, the gain is the greatest in rich countries.

Table 1 shows furthermore that professions requiring higher qualifications and responsibilities increase income, suggesting that the market wage rate (W ) is positively related to the effective wage rate (w * * ).

However, since professions are classified into broad groups, significant differences appear especially between very distinct groups. For instance, a professional worker (e.g., a lawyer) has a higher income than manual workers in each group of countries whereas the income difference between a professional worker and an employer/manager of an establishment with less than 10 employees depends on the country group.

The relation between the level of disobedience and the level of social interactions is given by the Table 2.

In developing countries, each additional level of disobedience (except level 4) deteriorates increasingly social interactions. In emerging countries disobedience is negatively related to social interactions until disobedience level 4. Disobedience levels 5 and 6 are associated with more social interactions than levels 3 and 4, but less than level 1. This result may arise because the proxy for the effective level of social interactions is not sufficiently precise. Another explanation could be that people belonging to disobedience levels 4 or 5 form a group within themselves and thus their level of social interactions remains relatively high. Concerning rich countries, each additional level of disobedience increases social interactions until level 5, suggesting that the income effect is greater than the reputation effect. Nevertheless, the highest level of disobedience is associated with less social interactions than level 5.

Moreover, Table 2 indicates that the level of social interactions decreases with unemployment (as it is often highlighted in social sciences) and increases with the effective wage rate in rich and developing countries. These results are similar for emerging countries but the negative coefficient of unemployment is not statistically significant and the positive relation between the effective wage rate and the level of social interactions does not hold above income decile 7.

For individuals living in countries that experienced the Arab Spring five years after the WVS 2005 wave, empirical results show that disobedience increases social interactions without affecting the income. Becker and Murphy (2000, p. 144) argue that inefficient social norms, which impoverish the population eventually below the subsistence level, may be conveyed by the elite to protect its privileged position. The model predicts that a decreasing market wage rate (W ) leads to disobedience that in turn slows or offsets the decrease of the wage rate (w). The empirical results of the Arab Spring countries can therefore be interpreted as a rejection of social norms (and as an example of the punctuated equilibrium): the people disobey social norms to maintain their income, and, because the values underlying the struggle are shared by the society, disobedience leads to a higher level of social interactions rather than social exclusion.

Discussion and Concluding Remarks

People "want to be 'rich and famous' " [START_REF] Akerlof | A Theory of Social Custom, of Which Unemployment May be One Consequence[END_REF]. The desire to be rich pushes individuals to disobey social norms whereas the will of being famous, that is, to have plenty of social interactions, may keep inefficient social norms in place. Increasing disobedience leads the consumer to a point where the increase of the wage rate (induced by disobedience) does not compensate, in utility terms, the increase of the social interactions' shadow price (also induced by disobedience). That point corresponds to the optimal disobedience level. It is therefore rational that individuals obey inefficient social norms.

The theoretical model predicts that individuals disobey inefficient social norms as (1) their preference for social interactions decreases;

(2) the society gets more tolerant toward individuals who do not comply to its social norms;

(3) the output elasticities of market goods increases; (4) the market wage rate, that is, the wage rate prevailing in a given profession regardless of the consumer's behavior vis-à-vis social norms, decreases; and (5) the quality of the economic environment, notably the efficiency of formal institutions (e.g., property rights), improves.

The consequences of disobedience to inefficient norms are (a) a higher income level; (b) more consumption of the composite commodity; (c) a lower level of social interactions as long as the reputation effect is greater than the income effect, otherwise the level of social interactions increases; and (d) a substitution of time input by market goods.

When individuals have no incentives to disobey inefficient social norms, these will persist longer. As a consequence, social norms, which form an informal institution, can induce income differences across countries.

Empirical results are consistent with the theory especially for emerging and developing countries, which is not surprising insofar the weight of informal institutions are likely to be more important in these countries.

As predicted by the model, statistics show that the higher is the average disobedience level in a group of countries, the richer is this group (see Figure 2). The comparative analysis here below shows the connection between the theoretical model and the empirical results.

It is widely argued that rich countries have relatively the most efficient formal institutions (E is high).

Moreover, the empirical results have shown that the cost of disobedience in these countries is very low, suggesting that they are relatively more tolerant toward individuals who disobey their social norms (δ is low). It is therefore observed that the average disobedience level is the highest in rich countries and, as a consequence, less inefficient social norms should persist. When social norms are rather efficient, disobedience should induce only a small increase of the wage rate because the scope of the efficiency gain arising from disobedience is limited. As expected, the estimated gain of disobedience is low in rich countries

Emerging countries are characterized by recent improvements in their formal institutions. These improvements have increased the gain of disobedience that in turn has led to a higher disobedience level.

However, since the disobedience level has increased recently and that it is not as high as that of rich countries, more inefficient social norms are likely to persist in emerging countries. As a consequence, the gain of disobedience is higher in emerging countries than in rich countries because the scope of the efficiency gain is wider.

Moreover, the evolution of inefficient social norms in emerging countries seems to be induced mainly by improvements in formal institutions rather than greater tolerance because the intolerance of the society to disobedience is high. Possibly, some groups within the society have less incentives to disobey and therefore the new norms are not accepted by the whole society yet. Such broad range of social behaviors within a society reflects a social evolution which is to be linked with social tensions and inequalities; indeed, the behavioral gap between rich and poor, urban and rural, or educated and non-educated is likely to be rather wide in emerging countries.

The gain of disobedience is lower in developing countries than in emerging countries because the former do not have the economic environment which would allow individuals to fully take advantage of their disobedience to inefficient social norms. Additionally, the level of intolerance to disobedience in developing countries is similar to that of emerging countries. As a result, the incentives to disobey the society's social norms in developing countries are relatively low and thus most people obey them.

The model could be applied to specific norms or to broader issues. For instance, the model suggests that a higher wage rate, induced by disobeying inefficient social norms, results in social interactions to be market

* s ∂x = θT p α s a α ∂w(x) ∂x µ(x) w(x) 1-α + ∂µ(x) ∂x w(x) α (A.1) Given that ∂f (x)/∂x /f (x) = ∂ log f (x) /∂x, ∂Z * s /∂x > 0 if α ∂ log w(x) ∂x > - ∂ log µ(x) ∂x (A.2)
Given the properties of w and µ, deduce that lim x→0 ∂ log w /∂x = +∞ and lim x→0 ∂ log µ /∂x = 0.

As a result, when x → 0, inequality (A.2) holds. On the other hand, lim x→xmax ∂ log w /∂x = 0 and lim x→xmax ∂ log µ /∂x = y with y < 0. Thus, when x → x max , inequality (A.2) does not hold.

Recall that x ∈ [0, x max ]. In between this range, ∂ log w /∂x is decreasing and -∂ log µ /∂x is increasing with x. Let x denote the highest value of x for which inequality (A.2) holds. As long as x < x , Z * s increases with x (income effect), otherwise Z * s decreases with increasing x (reputation effect). Derive equation ( 18

4) 5 Figure 1 :

 51 Figure 1: The total factor productivity and the wage rate functions

10

  Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée) 3. Empirical Framework 3.1. The Database The 2005 wave of the World Values Survey (WVS) provides a voluminous micro database for many countries on issues such as people's values, beliefs, representations, work motivations, and social capital.12

15

  Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

•

  side (RHS hereafter) of equation (A.3) is always positive: Z * c is strictly increasing with x. Appendix B. Maximization of V : second order condition Let du Centre d'Economie de la Sorbonne -2013.38 (Version révisée) and Ψ ≡ αθ + β(1 -θ) (B.2)Hence, ∂V (x)/∂x (equation[20]) can be written as∂V (x) ∂x = ζ w(x) Ψ µ(x) θ ∂ log w(x) ∂x Ψ + ζ w(x) Ψ µ(x) θ θ ∂ log µ(x) ∂x (B.3) ∂V (x)/∂x = 0 corresponds to a maximum if ∂ 2 V (x)/∂x 2 < 0, which implies ζΨ Ψ ∂w(x) ∂x w(x) Ψ-1 µ(x) θ ∂ log w(x) ∂x + w(x) Ψ θ ∂µ(x) ∂x µ(x) θ-1 ∂ log w(x) ∂x + w(x) Ψ µ(x) θ ∂ 2 log w(x) ∂x 2 + ζθ Ψ ∂w(x) ∂x w(x) Ψ-1 µ(x) θ ∂ log µ(x) ∂x + w(x) Ψ θ ∂µ(x) ∂x µ(x) θ-1 ∂ log µ(x) ∂x + w(x) Ψ µ(x) θ ∂ 2 log µ(x) ∂x 2 < 0 (B.4) Divide both side of this inequation by ζ, w(x) Ψ and µ(x) θ , and, after rearranging it, inequation (B∂ log w(x)/∂x ∂ log µ(x)/∂x < 0 and Ψ ∂ 2 log w(x)/∂x 2 + θ ∂ 2 log µ(x)/∂x 2 < 0. Moreover, the first order condition for maximizing V (x) requires that (see equation [20]): of equation (B.7) by θ and then square it. Using equation (B.2), equation (B.7(B.5) is true and ∂ 2 V (x)/∂x 2 < 0 for x * . 21 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée) Appendix C. Uniqueness of the optimal disobedience level ∂V (x)/∂x = 0 if (see equation[20]) : w(x, E, δ) = W + γ(x, E, δ), hence ∂w/∂x = ∂γ/∂x . Thus, dividing both sides of equation (C.1) by θ and rearranging it yields-∂γ(x, E, δ)/∂x ∂µ(x, δ)/∂x = W + γ(x, E, δ) µ(x, δ) α + β(1 -θ)/θ (C.2)Equation (C.1) can be also written as∂ log w(x, E, δ) ∂x α + β(1 -θ) θ = -∂ log µ(x, δ) ∂x (C.3)When x → 0, the left hand side (LHS hereafter) is greater than the RHS. Moreover, ∂ log w /∂x is strictly decreasing and -∂ log µ /∂x is strictly increasing. Thus, there is a unique value of x as a function of the exogenous variables, denoted x * , that verifies (C.3): x * = x(θ, α, β, δ, E, W ) Appendix D. Comparative statics: optimal level of disobedience Let the function F be given by F (x, E, δ, α, β, θ, W ) = α + βSuppose dδ = dα = dβ = dθ = dW = 0. The total derivative of F becomes dF (x, E, δ) du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)Given the properties of w and µ, deduce that ∂F /∂x < 0 and ∂F /∂E > 0, hence when E increases, x * must increase.• Suppose that dE = dα = dβ = dθ = dW = 0. Repeat the same steps, and given the properties of w and .6) indicates that when δ increases, x * will decrease.• dE = dδ = dβ = dθ = dW = 0. Deduce that indicates that when α increases, x * will increase.• dE = dδ = dα = dθ = dW = 0. Deduce that increases, x * must increase.• dE = dδ = dα = dβ = dW = 0. Deduce that .12) indicates that when θ increases, x * will decrease. 23 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

  Therefore, as the market wage rate increases, the marginal utility of the wage rate that was

9 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée) induced by disobedience becomes lower than the marginal disutility of disobedience (see equation [21]). 10

Table 1

 1

	: Income

13 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

Table 1

 1

	: (continued)

Notes:

The coefficients reported in this table are the log odds ratios. Robust standard errors are in brackets. *, **, *** indicate significance different than zero respectively at 90%, 95% and 99% confidence. 14 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

Table 2 :

 2 Social Interactions

	Variables

16 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

Table 2

 2 The coefficients reported in this table are the log odds ratios. Robust standard errors are in brackets. *, **, *** indicate significance different than zero respectively at 90%, 95% and 99% confidence.

	: (continued)

17 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

  goods intensive. This implies that individuals in rich countries maintain their level of social interactions by relying more on, say, trendy cloths, gifts, items reflecting membership to various groups, rather than the time spent for social interactions. As a result, disobedience to social norms affects consumption decisions by increasing the share of the budget allocated to the market goods mentioned above. Furthermore, I have briefly discussed in Section 4 how the model's predictions may offer a complementary explanation about an individual's decision to uprise against the existing institutions.The theory developed in this paper raises new questions. The long term dynamics of the model and the way the society's tolerance is determined appear to be particularly important. The specificity of the long term is that the disobedience level to social norms of an individual can affect the disobedience level of others.

	Appendix A. The variation of Z * s and Z * c induced by a change in x
	Derive equation (17) with respect to (w.r.t. hereafter) x:
	∂Z

19 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

Because integrating social norms into economic models is challenging, models concerned with social norms "have little or no predictive power" according to[START_REF] Postlewaite | Social Norms and Preferences[END_REF].

"What makes something a social or a moral norm is our attitude toward it"[START_REF] Bicchieri | The Grammar of Society: The Nature and Dynamics of Social Norms[END_REF]. Therefore, if disobeying a norm leads a person to have a poor sense of himself, it is because this person considers that specific norm as a moral norm rather than a social norm. 2 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

See Cacioppo et al. (2010),Hawkley and Cacioppo (2010), and Hawkley et al. (2010). 3 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

It is assumed that there is no joint production: an input used in the production of Zs cannot be simultaneously used in the production of Zc.

For example, for housecleaning, an individual can substitute time input by hiring someone through the market to do it for him (note that the hiring process still requires, even though very little, some time). Similarly, an individual who spends little time with his friends may maintain his level of social interactions by offering them many gifts. 4 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

If x > xmax, disobedience would decrease both, w and µ. Thus, a rational individual will never disobey social norms more than xmax.

A possible functional form of the gain of disobedience is γ = Ex τ -δx 2 with 0 < τ < 1 (6) 6 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

Data source: World Values Survey 2005 Official Data File v.20090901, 2009. World Values Survey Association (www.worldvaluessurvey.org)

Such a restriction is made because it is considered that an important fraction of teenagers go to school and have different social norms than adults on the one hand, and that some time is required for the efficiency effect to become noticeable on the other hand. 11 Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

Documents de Travail du Centre d'Economie de la Sorbonne -2013.38 (Version révisée)

Elisabeth Cudeville, the participants at the Annual Congress of the "